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# Intermediate Macro Analysis ECON 202

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This 131 page Class Notes was uploaded by Miracle Muller MD on Thursday October 29, 2015. The Class Notes belongs to ECON 202 at Wellesley College taught by Staff in Fall. Since its upload, it has received 11 views. For similar materials see /class/230949/econ-202-wellesley-college in Economcs at Wellesley College.

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Date Created: 10/29/15

Fall Semester 05 06 Akila Weempana Lecture 17 The Aggregate DemandAggregate Supply Model H OVERVIEW 0 By now you should be familiar with the basic lS LM model and be able to use it to analyze real world economic issues As the last lecture indicated the lS LM model despite its sim plicity is very powerful and can be used to understand several interesting types of economic developments 0 However a signi cant weakness still remains namely the inability to think about how changes in the economy affect in ation In other words even though we have the Solow model to think about the economy in the long run and the lS LM model to think about the economy in the short run we have no intermediate run model 0 In the next few lectures we will extend the lS LM model so as to be able to use it for thinking about price adjustment In today s class we will derive the basic components of the model an aggregate demand curve and an aggregate supply curve and then put the model together and use it in the next few classes 11 USING THE IS LM MODEL TO OBTAIN AN AGGREGATE DEMAND CURVE o The aggregate demand curve summarizes the relationship between the price level and the quantity of domestic output demanded by consumers rms the government and foreigners o Graphically we can derive this curve from the lS LM diagrams Consider an increase in the price level P When P goes up money demand increases bringing about an excess demand for money the LM curve shifts inward raising r and lowering Y When P goes down money demand decreases bringing about a an excess supply of money the LM curve shifts outward lowering r and raising Y o By repeating this experiment for different price levels we can map out the negative relationship between P and Y along the AD curve T IS LM Model P AD Model LM P1 LM P0 LM P2 P1 P0 P2 Shifts in vs Movements Along The AD Curve 0 Any shift in the lS LM model that is caused by a change in prices is represented as a movement along the AD curve Any other shift in the IS curve or the LM curve that increases income will be a shift out in the AD curve and any change in the lS LM model that reduces income will be a shift in of the AD curve EXAMPLE 1 An Increase in G P AD Model EXAMPLE 2 A Decrease in the M9 P AD Model Mathematical Derviation 0f the AD curve 0 As an aside let s derive the AD curve mathematically The equations for the IS and the LM curves can be written as follows Y MOIGNXMBT ISCurve 1 d M9 r 7 kY7 P LMCurve 0 Substituting in for r from the LM curve we can get the following Y anmiv xwgl nukwf k 7 Ms YltgtY MCIGNX7M 17 h wk r r r 7 M5 M d YltTgt i MCIGNX77M 7 U39h I I 7 MB Msiid Y I hw kCHIGINXllth kgtP Ml o This equation is an analytical expression for the AD curve it shows the negative non linear relationship between the price level and output This is just for informative purposes we will not appeal to this equation at all in the rest of the semester III Aggregate Supply 0 The aggregate supply curve summarizes the relationship between the price level and the quantity of output supplied in the economy The aggregate supply curve is derived based on a series of simplifying assumptions about the adjustment of prices 0 In the short run we assume that prices are xed Why 7 Firms can t change prices right away menu costs supply contracts 7 Firms can t change wages right away staggered wage contracts so they don t change prices either 0 In addition in the short run rms can produce above potential output the level of output that can be produced using the economy s resources of K L and A c We can rationalize the economy s ability to exceed potential output in the short run by the use of overtime excess capacity unused machinery etc On the other hand the economy will at times produce below potential output because of unutilized resources high unemployment idle machinery etc o The assumption of xed prices and expandable output imply a short run aggregate supply curve SRAS that is horizontal Note that this is de nitely a simplifying assumption prices are not completely xed in the short run and output is not in nitely expandable either so in reality the SRAS may only be at in the vicinity of current output and upward sloping elsewhere We will however use a horizontal SRAS in our analysis 0 In the long run we assume that output is xed at the level of potential output what the economy can produce given KL and technology available We assume that potential output is exogenously given it is endogenous in the Solow model but not in AD AS model Thus the long run aggregate supply curve LRAS is vertical 0 The intersection of SRAS and AD indicates where we are now Y0 the short run equilibrium and the intersection of LRAS and AD indicates the long run equilibrium of the economy Y potential output AD AS Model P LRAS P0 SRAS l l l l AD l l l Y Yo Y Shifts in the SRAS Curve Short Run 0 In the short run the aggregate supply curve is xed ie SRAS does not move The only time it will shift is if there is a SUDDEN increase or decrease in prices in which case the SRAS curve will shift up or down o If there is an unexpected increase in prices eg an oil price increase the SRAS will shift up reducing the current output level from Y0 to Y1 o If there is an unexpected decrease in prices eg an oil price decrease the SRAS will shift down increasing the current output level from Y0 to Y1 P Sudden increase in P P LRAS P1 SRAS7 l P0 l l l SRAS P0 l l l l P1 l l l l l l AD l l l l l l l l l l l l Y Y1 Y0 Y Y0 Y1 Intermediate Run Sudden decrease in P LRAS SRAS l SRAS AD Y Y o In the intermediate run prices will adjust As prices adjust the SRAS curve will shift up or down Whether prices increase or decrease depends on the relative level of current output with respect to potential output There are 3 cases for analysis Case 1 The short run equilibrium is below potential output 7 If the short run equilibrium Y0 ie where the IS and LM curves intersect is below the potential output level Y then over time prices fall because there is insuf cient demand for goods and services 7 We can see this in the AD diagram where as P falls the SRAS moves down along the AD curve until the economy reaches potential output 7 Note that there is a corresponding movement along the lS LM diagram7 as P falls7 the LM curve shifts out until equilibrium is reached at the level of potential output in the long run T lS LM Model P AD AS Model LRAS SRAS l l l l SRAS l l l l Y Y0 3 Case 2 The short run equilibrium is above potential output 7 If the short run equilibrium Y1 ie where the IS and LM curves intersect is above the potential output level Y then over time prices rise because there is excess demand for goods and services 7 We can see this in the AD diagram where we move along the AD curve as P rises until the economy reaches potential output 7 On the lS LM diagram as P rises7 the LM curve shifts in until equilibrium is reached at the level of potential output in the long run T lS LM Model P AD AS Model LRAS P SRAS P0 i SRAS D Y Yo Y Yo Case 3 The short run equilibrium is at potential output 7 If the short run equilibrium Y1 ie where the IS and LM curves intersect is at the potential output level Y then over time prices do not change because there is no mis match between the demand for goods and services and the economy s ability to produce goods and services 7 There is no change in either the AD diagram or the lS LM diagram T IS LM Model P AD Model LRAS P P0 SRAS YY0 Shifts in the LRAS Curve 0 In general the long run aggregate supply curve is xed ie LRAS does not move The only time it will shift is if there is a change in potential output o If there is an increase in potential output eg the economy has more capital labor or technology growth than it would otherwise have had the LRAS will shift to the right raising the current potential output level from Y to Yf o If there is a decrease in potential output eg the economy has more capital labor or tech nology growth than it would otherwise have had the LRAS will shift to the left decreasing the potential output level from Y to Yf P Increase in Potential Output P Decrease in Potential Output JRAS LRAS LRAS LRAS P0 SRAS P0 SRAS AD AD Y Y W W W W Fall Semester 05 06 Akila Weempana Lecture 9 The Solow Model With Technology 1 OVERVIEW H o In the last lecture we examined the behavior of the Solow model away from the steady state We found that the predictions of the Solow model would enable us to have intuitive explanations for differences in growth rates among countries that are away from steady state 0 We also showed that the Solow model is unable to explain differences in steady state growth rates across countries the model predicts that all countries have a per capita output growth rate of zero 0 Furthermore there is no possibility for sustained economic growth since all economies con verge to a long run growth rate of zero Today s lecture extends the Solow model in order to incorporate technology Hopefully adding technology to the model will preserve the sensible predictions of the basic Solow model and improve some of the less sensible predictions of the basic model 0 The structure of the lectures is the same we will rst derive the model with technology algebraically Then we will use a modi ed Solow diagram to perform comparative static analysis and conclude by assessing the predictions of the model THE SOLOW MODEL WITH TECHNOLOGY 0 What is technology Essentially technology is ideas or knowledge In particular technology is knowledge about how to put inputs together to make more output Essentially having better technology means being able to produce more output from a given quantity of inputs 0 What we classify as technology can range from engineering knowledge to business inno vations like assembly line production to service concepts like Wal Mart or multiplex movie theaters The Production Function 0 The production function in the Solow model is modi ed to include technology and can be written as Y K AL1 D o The particular technology described in the above equation is known as laboraugmenting technology basically ideas that help make labor more productive We can also specify technology as being of the capital augmenting type ie ideas that make capital more productive or of the total factor productivity type ideas that make both capital and labor more productive The It turns out that once we work with the model lab r t t clm l gy the other two types are easy to work with AL is known as the number of effective units of labor Technology makes workers more effective each worker counts as A workers in production so there are effectively AL workers in the economy We assume that the growth rate of technology is exogenous g In other words our model doesn t explicitly determine what causes technology to grow instead we assume the growth rate of technology is equal to a constant rate 9 As before we will assume that the growth rate of the labor force is given exogenously from outside the model equal to 71 By taking logs and differentiating the production function we can obtain the following Y K AL1 D lnYalnK17alnLlnA y K L A j axtll allztzl aglt1eagtltnggt From this we can see that in order to understand the growth rate of Y we need to understand the growth rate of K which is determined endogenously within the model This leads us to the second equation in the Solow model the capital accumulation equation which describes how the capital stock evolves over time Capital Accumulation Equation The second equation of the model is exactly the same K3Y76K The major difference from the basic Solow model is the transformation of the model Instead of working with per worker variables we instead work with per effective worker variables We de nek andy I is known as capital per effective worker and y is known as output per effective worker This follows from the concept that since each worker is worth A workers there are effectively AL workers in the economy We chose to normalize this way because we need to take into account both the presence of labor and technology in the model As you will see below rewriting the model as a function of a single variables requires us to move to per effective worker instead of per worker terms Note the relationship between the per worker variables and the per effective worker variables g LL 7 AL A A 7 YiYLiy y ET Z o So7 if the idea of effective workers7 is unintuitive to you7 another way to think of is as capital per worker per unit of technology7 i i i i i y 7 K AL1 o The production function can be written in per effective worker terms as E 7 T 155a which means that 271 0 The capital accumulation equation can be written in per effective worker terms as well K k Eiltm lnK7lnALElnK7lnA7lnL k 7 K A L TE 7 XTZTZ 3Y6K7ginis 7679771 SyAL 813 KAL76971I76971 1 sy76gnl o This equation states that net investment per effective worker the change in the capital stock per effective worker is the difference between gross investment per effective worker 331 and the level of break even investment per worker 71 g 6k o The intuition underlying this equation is not too difficult to follow 1 Gross investment per effective worker is equal to saving per effective worker follows from the national income accounting identity gross investment savings to Some of this new capital per effective worker must be used to replenish depreciated capital per worker In addition for every worker7 there are n 9 new effective workers laborgrowing at n and technology growing at g entering the economy7 each of whom require k units of capital 71 gk to keep capital per effective worker unchanged OJ The basic intuition is that unless you replace worn out capital7 provide each new worker with the same amount of capital7 and invest in capital to keep up with technology then capital per effective worker in the economy will fall So the level of break even investment per effective worker the amount of investment per effective worker necessary to leave capital per effective worker unchanged is equal to n g 6 III THE SOLOW DIAGRAM o The two equations of the Solow Model can be written in per effective worker terms as ga sy7ng6l PT xr Q31 c We combine these 2 equations graphically into a new Solow diagram The new Solow diagram plots savings per effective worker and the break even level of investment per effective worker as functions of the capital stock per effective worker 0 Some features of the diagram 1 n g 6I is a straight line from the origin with slope n g 6 2 y Is is a concave function For those of you who are mathematically inclined you can show that i aka l gt 0 is an increasing function of k and that the slope of 37 falls as I increases aa 71IDquot2 lt 0 because 04 lt 1 3 3y is just a dampened version of the y curve because 3 is a constant fraction between 0 and 1 o The Solow diagram looks as follows Savingslnvestment per effective worker 71 g 6 y E I syEsI The Steady State 0 From this diagram we can show that the economy has a steady state level of capital per effective worker which we denote as If that it gravitates towards over time H When I lt If savings per effective worker gt break even investment per effective worker ie 3y gt n g 6I I increases over time ie Igt 0 When I gt If savings per effective worker lt breakfeven investment per effective worker to ie 3y lt n g 6I I decreases over time ie Ilt 0 At I I savings per effective worker break even investment per effective worker 03 ie 3y n g 6I I is constant over time ie IE 0 Describing the Economy at the Steady State 0 At the steady state we know that I is constant I Therefore O Since y 1 we can rst take logs to get lngj aln1 and then take derivatives of both 2040 Q Sides to get 27 k K k 7 Taking logs and differentiating both sides we get 7 AL A We also know that 1s k A k7 A E Zj inVZ is 7 A 7 Since k is constant at steady state we get that g 7 Z 7 9 We can use the fact that y to show that g g and therefore show that g 9 Finally since k taking logs and differentiating both sides we get E a Since k is growing at a rate 9 in steady state we get that g 71 Similarly we can use the fact that y to show that and therefore show that 9 n We can also graph the paths of 1 37 k y K and Y over time The steady state time paths are in lny quotat E w 3 k 70 y 270 t t lnk lny 59 39 t t 111K gn t lnY gn Fall Semester 05 06 Akila Weerapana Lecture 3 The Solow Growth Model 1 OVERVIEW 0 Economic growth is by far the most important topic in economics 1 can try to describe to you how important it is but my words would pale in comparison to the words of the Nobel Prize winning economist Robert Lucas who stated the following in a 1998 paper Is there some action a gouernment of India could take that would lead the Indian economy to grow like Indonesia s or Egypt sf2 If so what eractlyf2 If not what is it about the nature of Indiaquot that makes it so The consequences for human welfare inuolued in questions like these are simply staggering Once one starts to think about them it is hard to think about anything else 0 Another way to emphasize the importance of this is to use the following fact If an economy grows at g we can show that it doubles roughly every 709 years So if an economy grows at 2 it will double every 35 years and if it grows at 7 it will double every 10 years 0 Using this rule we can illustrate the power of economic growth using an example From 1960 1995 South Korea grew at 6 a year This means that their economy doubled every 115 years on average Over a period of 35 years income would double 3 times an 8 fold increase Had they grown at 5 a year they would have doubled their income every 14 years Over a 35 year period income would double 25 times increase 225 565 fold Had they grown at 4 a year they would have doubled their income every 175 years Over a 35 year period their income would double 2 times increase 4 fold Therefore even a 1 2 change in growth rates can lead to large changes in income If we know what drives growth we can have signi cant positive impacts on the living standards of people all over the world 11 A MODEL OF ECONOMIC GROWTH o What constitutes a good model of economic growth Let s rst use our intuition and identify some important determinants of economic growth Capital Geography Labor Trade Human Capital Corruption Technology lnstitutions Infrastructure 0 Myriad factors can affect economic growth in a country but we can broadly conclude that growth is basically determined by its ability to produce goods and services How does it produce goods and services It uses two important inputs labor and capital and combines them with know how to produce output economists refer to the knowledge about putting inputs together as technology III Labor and capital are called inputs Technology enables us to put inputs together in order to make output Silicon and metal to make computer chips Rubber and chrome to make tires etc So we can write down a production function that describes how labor capital and technology get transformed into output Y FK L T where K is capital L is labor and T is technology If output is produced using these 3 factors then growth in output must come from growth in either K L or T Basically an economy can start producing more output if it has more workers more machines or better ways of putting together machines and workers A good model should enable us to understand the importance of most if not all of these variables for economic growth It should also help us understand less intuitive questions such as whether growth will increase permanently or temporarily in response to changes in the capital stock for example Alternatively it should help us understand whether an economy will invest in more capital when it has better technology or whether it will continue to use the same amount of capital and make better use of it We will use the most famous model of economic growth pioneered by Robert Solow who won a Nobel Prize The model has many simplifying assumptions yet it is a useful start for our analysis of growth In my opinion the Solow model is the best economic model It is simple yet yields powerful intuitive conclusions It has very clear simplifying assumptions that can be relaxed to make the model more complex The Solow Model consists of two equations a production function and a capital accumulation equation The Solow Model The Production Function We make the following assumptions about the production function 1 There are only 2 inputs which we will denote by K capital and L labor and 1 output good which we will denote by Y to The production function exhibits Constant Returns to Scale ie doubling K and L doubles Y The production function exhibits diminishing return to labor and capital increases in one input holding the other constant yield fewer and fewer additional units of output OJ q We will assume that the growth rate of the labor force is given exogenously from outside the model Let the growth rate of the labor force n o A production function that works well is of the CobbDouglas form Y Ku Ll D where 04 which is positive and lt 1 is the share of output produced by capital eg if 04 03 then 30 of output is produced by capital and 70 by labor o By taking logs and differentiating we can obtain the following Y KaLl lnY Lunar 17 a lnL Y K L i y a 17 JOE K a 17 an c From this we can see that in order to understand the growth rate of Y we need to understand the growth rate of K which is determined endogenously within the model This leads us to the second equation in the Solow model the capital accumulation equation which describes how the capital stock evolves over time The Capital Accumulation Equation 0 The second equation of the model is KsY76K In this equation 3 is the saving rate a fraction of every unit of output is saved and 6 is the depreciation rate a fraction of every unit of capital is worn out Both 3 and 6 are exogenous to the model 0 lntuition for this equation lies in the national income accounting identity for a closed economy where X 7 M 0 Y C I G c We can then rearrange to get Y 7 C 7 T T 7 G I where T total tax revenue This identity states that Private Savings Gov t Savings Gross lnvestment or equivalently that Total Savings Gross Investment 0 In a closed economy gross investment new additions to the capital stock is constrained to be equal to the amount of savings in the economy 0 However some of these new additions to the capital stock merely replenish worn out portions of the existing capital stock This amount is known as replacement investmen 7 0 Therefore net investment the change in the capital stock is the difference between gross T T T t and replacement o In the capital accumulation equation sY 7 6K then sY Total Savings Gross lnvestment 6K Replacement lnvestment sY 7 6K Net lnvestment c When 7 total savings exceeds replacement investmentsY gt 6K7 the capital stock increases K gt 0 7 total savings is less than replacement investmentsY lt 6K7 the capital stock decreases K lt 0 7 total savings equals replacement investment sY 6K the capital stock does not change K 0 0 Note 6K is also referred to as the break even level of investment the amount of investment necessary to leave the capital stock unchanged Fall Semester 39013902 Akila Weerapana Lecture 5 Introduction to Economic Growth 1 OVERVIEW p 1 p 1 As we talked about brie y on the first day of class the study of macroeconomics can be broken down into two distinct parts the study of economic growth and the study of economic uctuations Today s class is the first of ve lectures in which we will take a look at economic growth Basically we will try to explain why real GDP in the US has been rising upwards over time In Econ 202 we will take a more indepth look at economic growth where we look at differences in growth across countries and within countries over time For now we will restrict ourselves to sketching a basic theory of economic growth and examining some of the important driving forces indicated by the theory WHAT IS ECONOMIC GROWTH AND WHY IS IT IMPORTANT The first step is to distinguish between economic growth and economic uctuations A graph for output in the US can be separated into two parts the general upward trend and the uctuations around the upward trend The trend portion of GDP is known as Potential Output When we talk about economic growth we are talking about increases in potential output faster economic growth would mean a steeper trend in output Rule of Thumb If an economy grows at g we can show that it doubles roughly every B years So if an g economy grows at 2 it will double every 35 years and if it grows at 7 it will double every 10 years Using this rule we can illustrate the power of economic growth using an example 0 From 19601995 South Korea grew at 6 a year Their economy doubled every 115 years on average so over a period of 35 years income would double 3 times an 8 fold increase 0 Had they grown at 5 a year they would have doubled their income every 14 years Over a 35 year period income would double 25 times increase 225 565 fold 0 Had they grown at 4 a year they would have doubled their income every 175 years Over a 35 year period their income would double 2 times increase 4 fold Therefore even a 1 2 change in the rate of growth can lead to large changes in income If we know what drives growth we can make signi cant improvements in the living standards of people all over the world Lucas Quote 1988 quotIs there some action a government of India could take that would lead the Indian economy to grow like Indonesia39s or Egypt39s If so what exactly If not what is it about the quotnature of Indiaquot that makes it so The consequences for human welfare involved in questions like these are simply staggering Once one starts to think about them it is hard to think about anything else quot Use your intuition and identify some important determinants of economic growth Capital Geography Labor Trade Human Capital Corruption Technology InstitutionsProperty Rights Infrastructure III WHAT ARE THE PRINCIPAL DETERMINANTS OF ECONOMIC GROWTH o The theory of economic growth tells us that the potential output of an economy is its average amount of goods and services produced in the economy Output can be higher than potential for short periods of time we will see why this can happen and it can be lower than potential output for other periods of time 0 Overall though the output of the economy is determined by its ability to produce goods and services How does it produce goods and services It uses two important inputs labor and capital and combines them with knowhow to produce output economists refer to the knowledge about putting inputs together as technology 0 Labor and capital are called inputs Technology enables us to put inputs together in order to make output Silicon and metal to make computer chips Rubber and chrome to make tires etc 0 So we can write down a production function that describes how labor capital and technology get transformed into output Y F K L T where K is capital L is labor and T is technology 0 If output is produced using these 3 factors then grth in output must come from growth in either K L or T Basically an economy can start producing more output if it has more workers more machines or better ways of putting together machines and workers 0 How can a country make its labor capital or technology grow faster That is the secret to unlocking the mysteries of economic growth What we will do over the next 3 lectures is to examine each of these three in detail to gain some insight into what successful grth oriented policies may be Fall Semester 05 06 Akila Weempana Lecture 26 The Open Economy IS LM Model 1 OVERVIEW H In the last two lectures of the class we will develop an open economy version of the lS LM model known as the Mundell Fleming model This model was rst developed by Robert Mundell who won a Nobel Prize in Economics in 1999 partly for this effort 0 In today s lecture we discuss how incorporating open economy features speci cally a freely adjusting exchange rate changes the description of the IS curve and the LM curve We then analyze the equilibrium of the model and discuss how to model the impact of changes in scal and monetary policy EXCHANGE RATE BASICS The rst step is to de ne and understand some important concepts related to exchange rates The nominal exchange rate between two countries is the relative price of the two countries7 currency We will de ne the nominal exchange rate between 2 countries in terms of domestic currency per unit of foreign currency The USJapan exchange rate is given as 000833 39 per Yen instead of as 120 Yen per We use E to denote the nominal exchange rate 0 An increase in E is called a depreciation of the domestic currency ie the 39 has decreased in value it requires more dollars to buy a unit of foreign currency while a decrease in E is known as an appreciation 0 An appreciation of the exchange rate will make foreign goods cheaper to domestic residents imports increase and domestic goods more expensive to foreign residents exports go down Thus NX goes down 0 A depreciation in the exchange rate will make domestic goods cheaper to foreigners raising exports and making foreign goods more expensive to domestic residents lowering imports In other words NX rises c We can roughly categorize countries as falling into 2 main categories of exchange rate regimes exible exchange rate systems also known as oating exchange rate systems and xed exchange rate systems also known as pegged exchange rate systems In a exible exchange rate system the value of the currency is determined by the market ie by the interactions of thousands of banks rms and other institutions seeking to buy and sell currency for trade and investment reasons 0 As we saw above changes in the value of a currency cause imports and exports to uctuate In order to avoid the impact of such volatility on the economy some countries particularly small countries that depend a lot on trade choose to keep their exchange rate xed III THE ISLM MODEL IN AN OPEN ECONOMY WITH FLEXIBLE EXCHANGE RATES In a exible exchange rate system the exchange rate the price of foreign currency is set by supply and demand Excess demand for a currency all else equal would lead to an appreciation of the currency Excess supply of a currency all else equal will lead to a depreciation of that currency We can then examine how the IS LM model will change when we account for exible exchange rates The most important thing to keep in mind is that the closed economy effects still continue to hold in other words an increase in G will shift out the IS curve A decrease in money supply will shift in the LM curve etc The key is that we now have additional changes coming from the open economy dimension which we have to incorporate into our analysis IS Curve under Flexible Exchange Rates We can write down a NX function of the form NX NX nE where n is a parameter that describes how sensitive net exports are to movements in the exchange rate What we require then is a theory about the determination of the exchange rate Models that accurately describe the behavior of nominal exchange rates are very hard to nd but for now we will focus on a short run determinant of the nominal exchange rate namely the interest rate An increase in the domestic interest rate relative to the foreign interest rate will bring an increase in demand for 39 today as foreigners seek to buy US assets The increased demand leads to an appreciation of the This appreciation of the US dollar will make foreign goods cheaper make domestic goods more expensive and reduce net exports So the IS curve will shift in Conversely a decrease in the domestic interest rate relative to the foreign interest rate will reduce the demand for 39 today as foreigners seek to buy foreign assets The decreased demand leads to a depreciation of the This depreciation of the US dollar will lower the price of US goods relative to foreign goods and improve the trade balance ie raise net exports pushing the IS curve out So under exible exchange rates the open economy has an additional effect on the IS curve via the effects on NX LM Curve under Flexible Exchange Rates The analysis of the LM curve in an open economy is not at all different from the closed economy case The demand for money still depends on the interest rate price level and on income We still continue to assume that the supply of money is set by the Federal Reserve or the central bank The Complete MundellFlerning Model under Flexible Exchange Rates 0 In a closed economy case changes in scal policy affected the IS curve while changes in monetary policy affected the LM curve The basic features of these results hold up in the open economy case as well 0 However changes in scal and monetary policy have an additional impact on the economy through changes in the interest rate This occurs because changes in the interest rate cause money to ow from one country to another The impacts of these money ows affect exchange rates and thus NX and Y as well 0 For example consider an increase in government purchases which will shift out the IS curve and result in an increase in the domestic interest rate 0 In a closed economy setting this would be the only impact of the government policy In an open economy setting there is an additional channel that we have to consider namely that the higher interest rate will bring about an in ow of money from other countries The impact of this additional channel namely the in ow or out ow of funds varies according to the type of exchange rate system that the country possesses 0 Under a oating exchange rate system this will cause an appreciation of the nominal exchange rate which lowers our exports to other countries This causes the IS curve to shift in o The impact of these monetary ows depends on the size of the economy and on the type of exchange rate system We will only focus on a small open economy because oftime constraints You can take Econ 213 or Econ 313 if you want to explore these issues further IV FISCAL AND MONETARY POLICY IN A SMALL OPEN ECONOMY UNDER FLEXIBLE EXCHANGE RATES o The rst case is a small open economy with exible exchange rates A small open economy is one that trades with the rest of the world but is too small for changes in its macroeconomic variables to have a signi cant impact on other countries 0 In particular it is an economy where changes in monetary or scal policy affect only its own equilibrium interest rate and equilibrium output Interest rates in the rest of the world are assumed to be unaffected 0 So a small open economy has to take the world interest rate as given its actions don t affect the world interest rate Therefore its own interest rate has to always adjust to equal the world rate c Any deviation from the world interest rate will result in large capital ows either to or from the country these ows will change the exchange rate and affect NX until the interest rate returns to the world interest rate Expansio nary Fiscal Policy 7 Increase in G Shifts IS to IS and causes r to increase above rw and Y to increase to Y1 This brings about an in ow of money into the country causing the currency to appreciate The appreciation reduces net exports and shifts the IS curve back The process will continue until T has returned to the world interest rate So expansionary scal policy has no short run effect in a small open economy under oating exchange rates This case is shown in Figure 1 Y1 T1 is the closed economy short run equilibrium while Y2 r2 is the open economy short run equilibrium Expansio nary Monetary Policy Increase in money supply Shifts LM to LM and reduces r below rw This brings about an out ow of money out of the country causing the currency to depreciate The depreciation increases net exports and shifts the IS curve out The process will continue until T has returned to the world interest rate So expansionary monetary policy has powerful short run effects in a small open economy under oating exchange rates This case is shown in Figure 2 Y1 T1 is the closed economy short run equilibrium while Y2 r2 is the open economy short run equilibrium 7 Increase in M 5 Increase in G o In summary expansionary monetary policy has extremely powerful short run effects in a small open economy under oating exchange rates while expansionary scal policy has no effect at all 0 The general intuition is that expansionary scal policy tends to raise interest rates which results in a currency appreciation that has a negative impact on net exports and therefore on domestic output Similarly expansionary monetary policy tends to lower interest rates resulting in a currency depreciation that stimulates net exports and therefore increases output Fall Semester 05 06 Akila Weempana Lecture 27 Fixed Exchange Rates I OVERVIEW H o In the last lecture we looked at the short run impact of monetary and scal policy in an open economy under exible exchange rates 0 With expansionary scal policy the increase in interest rates would be accompanied by an in ow of money from abroad causing an appreciation of the currency This in turn reduces NX and lowers Y 0 With expansionary monetary policy the decrease in interest rates would be accompanied by an out ow of money to other countries causing a depreciation of the currency This in turn increases NX and raises Y o The impact of policy ows varies depending on the type of exchange rate system In today s class we will examine the impact of scal and monetary policy in a country with a xed exchange rate system FIXED EXCHANGE RATE SYSTEMS 0 Many countries still have an exchange rate system where the central bank announces a xed exchange rate for the currency and then agrees to buy and sell the domestic currency at this value c This can be done by keeping reserves of foreign currency along with domestic currency reserves that any central bank already has If demand for foreign currency exceeds supply the central bank meets the excess demand by running down its reserves If supply exceeds demand the central bank absorbs the excess supply by increasing its foreign currency reserves 0 The basic motivation for keeping exchange rates xed is the belief that a stable exchange rate will help facilitate trade and investment ows between countries by reducing uctuations in relative prices and by reducing uncertainty III THE ISLM MODEL IN AN OPEN ECONOMY WITH FIXED EXCHANGE RATES c As before it is vital to keep in mind that the closed economy effects still continue to hold in other words an increase in G will shift out the IS curve A decrease in money supply will shift in the LM curve etc 0 Once again we now have additional changes coming from the open economy dimension which we have to incorporate into our analysis In the case of xed exchange rates this additional effect will fall on the LM curve through increases and decreases in the money supply because the central bank is handing out or taking in domestic currency for foreign currency IS Curve under Fixed Exchange Rates Under exible exchange rates the open economy has an additional effect on the IS curve through depreciation and appreciation of the currency There is no additional effect under xed exchange rates because E is by de nition xed LM Curve under Fixed Exchange Rates The real demand for money still depends on the interest rate and on income We still continue to assume that the nominal supply of money is set by the Federal Reserve or the central bank In the closed economy case the Fed was assumed to change the money supply principally by buying and selling bonds In the open economy under a xed exchange rate regime the central bank will also change the money supply through the exchange of domestic and foreign currency When the central bank exchanges domestic currency for foreign currency it is increasing the domestic money supply the LM curve shifts out This is illustrated in Figure 1 below When it exchanges foreign currency for domestic currency it decreases the amount of domestic currency in circulation the LM curve shifts in This is illustrated in Figure 2 below So under xed exchange rates the open economy has an additional effect on the LM curve 7 7 Figure 2 Figure l III FISCAL AND MONETARY POLICY IN A SMALL OPEN ECONOMY UNDER FIXED EXCHANGE RATES 0 Consider a small open economy with xed exchange rates As with a exible exchange rate the small open economy still cannot deviate from the world interest rate any such attempt will result in capital ows either to or from the country seeking to obtain higher returns In the exible exchange rate case these in ows caused the value of the currency to change affecting NX shifting the IS curve and restoring interest rate parity with the world In the xed exchange rate case of course the exchange rate by de nition will not change This time the mechanism is through changes in money supply that result from the Central Bank exchange of domestic currency for foreign currency These changes in money supply affect interest rates until the interest rate is driven back to the world interest rate Expansio nary Fiscal Policy Increase in G Shifts Is to 18 and causes r to increase above rw and Y to increase to Y1 This brings about an in ow of money into the country The central bank takes in foreign money and hands out domestic money increasing the domestic money supply The increase in MS shifts the LM curve out lowering interest rates The process will continue until T has returned to the world interest rate So expansionary scal policy has very powerful short run effect in a small open economy under xed exchange rates This case is shown in Figure 3 Y1 T1 is the closed economy short run equilibrium while Y2 r2 is the open economy short run equilibrium Expansio nary Monetary Policy Increase in money supply Shifts LM to LM and reduces r below rw This brings about an out ow of money out of the country The Central bank hands out foreign money in exchange for domestic money reducing its holdings of foreign reserves and reducing the domestic money supply The fall in the money supply shifts the LM curve in raising interest rates The process will continue until T has returned to the world interest rate So expansionary monetary policy is ineffective in a small open economy under xed exchange rates This case is shown in Figure 4 Y1 T1 is the closed economy short run equilibrium while Y2 r2 is the open economy short run equilibrium 7 Increase in G Increase in M5 Y2 YoY2 So expansionary scal policy has powerful short run effects on output in a small open economy under xed exchange rates while expansionary monetary policy has no effect in a small open economy under xed exchange rates The general intuition is that expansionary scal policy tends to raise interest rates7 which results in an in ow of money that results in an increase in the domestic money supply This leads to a further expansionary effect on domestic output Similarly7 expansionary monetary policy tends to lower interest rates7 resulting in a out ow of money that counters the original monetary expansion Fall Semester 05 06 Akila Weempana Lecture 8 The Golden Rule I OVERVIEW H o In a previous class we derived the algebraic solution for the steady state We showed that increases in the saving rate decreases in the rate of depreciation or decreases in the population growth rate will increase steady state per capita income Given that an increase in the saving rate will increase steady state per capita income does that mean that countries should always try to invest more In other words is the optimal rate of savinginvestment equal to 100 Or is there some other rate of investment that is optimal Today s class looks at this critical issue Knowing the optimal rate of saving will help us understand whether or not countries like the United States that save very little should try to be more like countries like Japan or China that save a lot more CONSUMPTION IN THE STEADY STATE You have seen by now that the Solow model can generate a variety of steady states for a country depending on factors such as the saving rate depreciation rate population growth rate etc o The question of how to rank these steady states if at all becomes an interesting question in other words could we say that one steady state is better than another If so what criteria do we use to rank them 0 In economics we typically rank on the basis of utility So in order to rank steady states we should also look at what the model has to say about consumption after all consumer utility is gained from consumption not from production In the Solow model steady state consumption per worker is given by the expression 6 y 8yE18y 0 Therefore steady state consumption varies according to the steady state capital stock which determines output Graphically steady state consumption is the difference between the output per worker curve and the saving per worker curve at steady state the dotted line in the Solow diagram Savinglnvestment per worker III CALCULATING THE GOLDEN RULE LEVEL OF SAVING Since 34 191 in steady state we can rewrite steady state consumption as 0 7 lt17 s 15 This expression gives us the critical intuition to understand why the optimal rate of saving is not equal to one Since 0 2 s g 1 consider the extremes When 3 0 steady state output 34 0 So steady state consumption will also a be zero In other words we are consuming everything we produce saving nothing but alas since output is zero that just means consumption is zero as well 7amp6 17 is as high as it could be for a given 71 and 6 But steady state consumption will still be zero since we are consuming nothing of what we produce saving everything On the other hand when 3 1 steady state output 34 lt So at the extremes steady state consumption will be zero This must mean that there is a saving rate or rates between zero and one that maximizes consumption as you can see from the diagram below That optimal level of saving is called the Golden Rule level of saving denoted as SGOLD in the diagram below Consumption per worker SGOLD o The steady state that maximizes consumption occurs when 0 From the above expres sion7 using the chain rule this point is where 0 1 7 s y 1 n6 7y 1 n n6 71 1 Q n6 0 Using algebra we can show that this is where 0 173 lt1 gt3lt a lt1 als 3 m 7 7 a iltn6gt 7 1 s lt17agts 1 173lta s 1704 71 7a OZ 1 704 1 il if 1 8 304 o In other words7 the optimal rate of saving7 the one that maximizes steady state consumption is equal to a the share of output produced by capital So in an economy where 30 of the output is produced by capital7 the optimal saving rate is also 307 ie 3 out of every 10 units of output should be savedinvested and the rest consumed o If you save more ie 4 out of every 10 units of output OR if you save less ie 2 out of every 10 units of output you end up with a lower steady state level of consumption IV INTUITION FOR THE GOLDEN RULE LEVEL OF SAVING o The result that steady state consumption is maximized when 3 04 is an intriguing result But why does this result make sense intuitively o In order to get a good intuitive understanding7 think about why we would choose to saveinvest instead of consuming output By savinginvesting we forgo consumption today but the addi tional investment gives us more capital7 which can be used to produce more output leading to potentially more consumption in the future In other words7 we are trading off today s consumption for future consumption when we decide to save 0 How much future consumption we get depends on how much output we can produce using the new investment In other words7 our future consumption depends on the marginal product of capital Mathematically MPK 2 0 At steady state dy dk0 MPK 7 dl dl akail 71 7194 at From the above expression we can see the following 304 MPKn6 slta MPKgtn6 sgta MPKltn6 The steady state with the highest level of consumption is where the is equal to n 6 in other words the steady state with the highest level of consumption is where the marginal product of capital MPK is equal to n 6 lntuitively if s lt a the marginal product is more than enough to cover depreciation of the extra unit in the amount of 6 and to provide the 71 new workers with an additional unit of capital then it is better to save can increase k and consume the extra production At some point when 3 lt 04 the marginal product is exactly enough to cover depreciation of the extra unit in the amount of 6 and to provide the 71 new workers with an additional unit of capital That is the optimal level of saving If we continue to save the extra units do not produce enough to pay for depreciation and for equipping new workers so consumption falls it s better to consume rather than save Therefore the optimal amount of consumption is when the marginal product of capital is exactly enough to cover depreciation and the needs of new workers ie where MPKn 6 Saving rates in excess of 04 are deemed inef cient oversaving77 for we are saving more to consume less in the future We would be better off consuming more today which will allow us to continue to consume more in the future as well Saving rates below 04 are deemed undersaving We can increase future consumption by saving more ie consuming less today We don t call these points inef cient for there is a trade off to be made consume less today for more tomorrow or more today for less tomorrow Unlike in the oversaving case there is no free lunch A country that is undersaving is sacri cing future generation s consumption for the current generation s consumption A country that is inefficiently oversaving is unnecessarily reducing consumption of both current and future generations Fall Semester 05 06 Akila Weempana Lecture 5 Comparative Statics Using the Solow Diagram L H I OVERVIEW 0 In the last lecture we looked at how to use the Solow diagram to analyze the dynamics of the economy laid out by the Solow model We showed that the economy moves over time to a per capita capital stock known as the steady state77 of the model We also looked at how we can use the Solow diagram to depict the impact of changes to the economy whether it be changes that shift the investment or the break even lines or changes that move us along the lines In today s class we will build on that analysis by doing a complete analysis of how changes to the capital stock the labor stock the growth rate of population the depreciation rate etc affect the steady state of the economy and in how the economy transitions from the old steady state to the new one We will rst describe the steady state path of the economy ie the path the economy will take in the absence of shocks and show how or whether particular shocks move the economy away from the steady state path DESCRIBING THE ECONOMY AT THE STEADY STATE 0 As we saw in the last class the model predicts that at the steady state k is constant k If Therefore 0 Since 24 047 we can rst take logs to get lny aln k and then take derivatives of both sides to get 23 E 04 0 We also know that k Taking logs and differentiating both sides we get E 7 a K 7 k L F i t t r 0 Since k is constant at steady state we get that 71 Similarly we can use the fact that y to show that and therefore show that 7r We can also graph the paths of k y K and Y over time The graphs given below use a log scale the natural log of the variable is on the y axis and time is on the z axis The slope of this graph therefore is the derivative of the natural log of the variable with respect to time Recall however that the derivative of the natural log of a variable with respect to time gives us the growth rate of that variable eg will 5 Therefore if a variable is growing at a rate 9 then it can be represented as a straight line with slope g on a log scale graph k o The time paths of k y K and Y at steady state are lnk lny Ink 0 my g0 t an lnY III COMPARATIVE STATICS EXERCISES 0 Now that we have an idea of what the steady state of the economy looks like we can do a complete analysis of how certain types of shocks affect the economy 0 We will rst draw a Solow diagram and depict how the shock causes the curves to shift if at all or causes a movement along the curves if at all 0 Then using the Solow diagram we will infer the time paths for k and y Finally we will use these time paths along with the exogenous time path of L to gure out the time paths of K and Y An Increase in the Saving Rate 0 Suppose the economy is at the steady state when the saving rate increases from s to s For simplicity assume that this is the only change in the economy 0 We can use the Solow diagram to illustrate the effects of the change in the diagram the saving per worker line shifts upwards from 3y to 33 At the old steady state k3 saving per worker exceed the level of break even investment per worker s yg gt n 6k3 therefore k increases o This process continues until the new steady state kf is reached At this new steady state7 the saving per worker line is once more equal to break even investment per worker s yf n therefore k does not change 0 This is illustrated in the diagram below Savinglnvestment per worker 0 Let to be the point at which the saving rate increased and 251 be the time at which the economy returned to steady state We can draw the following graphs to show the path of k and y lnk lny ln k1 1n yi I ln k I ln m I I I I 0 Note in the graph for k 1 Before to the economy is at steady state k is constant at kg 2 Between to and 251 k is increasing over time see Solow diagram 3 After 251 the economy is back at steady state k is constant at 0 NOTE The dotted line shows the path of the variable in the absence of an increase in the saving rate 0 Since y k and 04 is constant7 the graph for y looks exactly the same as the graph for k 0 Since nothing happened to the labor force it continued to grow exogenously at rate a the graph for L can be drawn easily lnL 0 Finally we can use these three graphs to deduce the behavior of K and Y using the fact that k and y You can do this mathematically or somewhat intuitively I will try and show you both ways Intuitive Method 0 Before to k is constant A ratio will only stay constant if the numerator and the denominator both grow at a rate it Therefore if L is increasing at a rate a then K must also be increasing at a rate a in order to keep the ratio constant 0 Between t0 and t1 k is increasing over time A ratio will only increase when the numerator grows faster than the denominator Given that L is increasing at a rate a then K must be increasing at a rate gt n in order to make the ratio grow 0 After t1 the economy is back at steady state k is constant Once again the numerator and denominator must grow at the same rate Given that L is growing at a rate a then K must also be growing at a rate a as in the case before to Mathematical Method o If you want to do this more mathematically remember that 7 Given that the growth rate of the population is constant over this period this implies that g g 7 a You can now use what you derived earlier about how k evolves over time to nd out the evolution ofK o For instance before to k is constant at the old steady state Therefore 0 7 n a n 0 Between to and t1 k is increasing over time Therefore n a gt it since gt 0 0 After t1 k is constant at the new steady state Therefore 0 7 n a n 0 You can use similar analysis on the graphs of y and L to derive the graph for the path of Y In this case the graph for Y looks similar to the graph for K An Increase in the Population Growth Rate 0 Consider an increase in the growth rate of population 71 in an economy that is at steady state Once again we assume that this is the only change in the economy 0 In the Solow diagram we see that this increase causes the break even line to become steeper at every level of k the break even level of investment is higher because of more new workers entering the economy 0 When the break even line becomes steeper we see that at the original steady state k3 saving is no longer sufficient to cover break even investment syg lt n 6 3 therefore k falls over time until the new lower steady state is reached at At that point saving is just sufficient to cover break even investment 5y n 6kf so k does not change over time any further 0 The Solow diagram would look as follows Savingslnvestment per worker o The dynamics of the endogenous variables k and y can be determined using the Solow diagram o The graphs for k should then be constant at k3 until to7 at which point k begins to decline until 251 when it reaches its new steady state k where k becomes constant again 0 Since y k and 04 has not changed7 the graph for y lnk ln 1 ln 71 looks identical to the graph for k lny ln k1 ln yf o The evolution of the labor force is more interesting h ere There is an increase in the growth rate of population at to causing the slope of the curve to change from n to n gt n c As before7 we can use either math or intuition to determine the time paths of the variables K and Y from the time paths of k y and L 0 Consider the behavior of K where we once again use the fact that k 5 L Before to k is constant Therefore the numerator and denominator must be growing at the same rate Since L is increasing at a rate 71 then K must also be increasing at a rate 71 0 Between to and 251 k is decreasing This must imply than the numerator Given that L is increasing at a increasing at a rate lt n that the denominator is growing faster rate at a rate 71 gt n then K must be 0 Note that we can only deduce that the the growth rate of K must be lt n we can t using this technique show that the growth rate is n lt lt n This condition is however true7 and you can assume it when drawing the graph 0 After the economy is back at steady state k is constant Once again7 the numerator and denominator are growing at the same rate However7 given that L is now growing at a rate 71 then K must also be growing at a rate n is K is growing faster than it did before 0 The analysis for Y will be identical since we can use the fact that y to deduce the time path for Y from the time paths for y and L an lnY o The basic intuition for why an increase in the growth rate of population lowers steady state output per person comes from diminishing returns Having more workers enables us to produce more output but without a corresponding increase in capital7 diminishing returns to labor will imply that the increase in output is insufficient to provide for the new entrants Fall Semester 05 06 Akila Weempana Lecture 24 Government Purchases I OVERVIEW 0 In today s lecture7 we will look in more detail at all government spending7 not just government purchases Recall that only government spending on goods and services is counted as G in the IS LM model However7 many of the interesting issues involving scal policy involve discussion of the entire government budget and not just the spending on goods and services c We will also discuss the interplay between taxing and spending decisions In particular we will talk about budget de cits and the distinctions between de cits and the debt II COMPOSITION OF THE FEDERAL BUDGET 0 Before we talk about the consequences of de cits and the impact of government spending7 it is important to realize what the government spends its money on o In 2004 the budgetary allocations were as follows 1 Social Security 21 2 National Defense 20 3 Medicare 13 4 Income Security 8 5 Medicaid 8 6 Interest on Debt 7 7 Retirement 6 8 Education 3 9 Transportation 3 10 Housing 2 11 Justice 2 12 Health 2 13 Veterans A airs 1 14 Environment 1 15 International A airs 1 16 Agriculture 1 17 Research 1 o The breakdown of government revenue was as follows 1 Personal Taxes 43 2 Social Security and Medicare Taxes 39 3 Corporate Taxes 10 4 Ebrcise Taxes 4 5 Estate Taxes 1 6 Customs 1 III 7 Federal Reserve 1 8 Miscellaneous 1 The budget balance in 1998 was 69 billion in 1999 124 billion in 2000 236 billion in 2001 1271 billion in 2002 157 billion in 2003 3753 billion in 2004 412 billion In 2005 the budget de cit is forecast to be 365 billion We are back to a world of de cits again If we exclude social security the budget balance in 2003 also called the on budget balance was 567 billion ie a de cit Of 567 billion The balance on social security social security tax receipts payments sometimes referred to as the off budget surplus is 155 billion We can see that a large part of government spending is on entitlement programs and social programs and not on the purchase of goods and services which is what we count as part of GDP An increase in spending on social security payments or food stamps for example does not increase G and shift out the lS curve Government purchases are not a major part of government spending in fact there is evidence that government purchases are not actively used to stabilize the business cycle However there are automatic stabilizers like unemployment insurance income taxes AFDC and other welfare programs that are useful in stabilizing the economy DEFICITS AND DEBT The difference between de cits and debt is important to keep in mind De cits are a ow variable the excess of expenditure over revenue in any given year Debt is a stock variable the total outstanding amount of money owed by the government Basically if D is the debt at time t then Dt1 1 itDt y 7 7 where it is the interest rate on the debt Note that y is ALL government spending not just government purchases G 739 is ALL tax revenue y 7 7 is what is known as the primary de cit the excess of government expenditure over receipts ignoring interest payments Accumulated debt in the Us is about 36 of GDP which is actually small in percentage terms compared to a lot of countries De cits are nanced in 3 ways by using marketable securities treasury bills notes and bonds distinguished by duration and by non marketable securities such as savings bonds Surpluses in various trust funds like social security are also used occasionally In some countries de cits are nanced by printing money Why Do We Care About De cits 1 to An increase in government purchases or a cut in taxes can shift out the IS curve and increase Y in the short run Even though this is helpful in a recession in an economy that is already at potential this expansionary policy will also raise r crowd out I and may have adverse long run consequences for the economy Going beyond our traditional lSLM analysis as the government issues more bonds the price of bonds will fall increasing the yield Higher expected yields raise long term interest rates today and can sti e growth 3 Furthermore as the debtGDP ratio rises the risk of default will become high This in turn will require that the government run budget surpluses in the future to repay the debt could lead to higher future taxes lower Consumption today 4 Unfair to future generations Transferring the burden to your children and grandchildren and leaving them with the responsibility of paying off the debt IVPROJECTHNVSCW BUDGETSURPLUSESOVERIHHENEXT DECADE o The Congressional Budget Office CBO provides projections of budget surpluses for the next decade These numbers can be found on the web at wwwcbogov 2000 Projec ons 05 06 07 08 09 10 11 12 OnBud Surp 539 487 477 473 463 461 370 229 O iBud Surp 175 189 209 227 244 260 275 286 TotSurp 365 298 268 246 219 201 95 57 Debt 4656 4965 5246 5506 5737 5949 6054 6004 BalanceGDP 3 23 2 17 15 13 06 03 DebtGDP 381 385 386 385 382 378 367 348 15 183 305 122 5726 06 291 o The CEO is mandated to produce budget forecasts using certain assumptions These assump tions are important to understand in evaluating the accuracy of the forecasts o The assumptions used by the CBO are DH The CEO assumes real GDP growth of 30 a year for the next 10 years According to the CBO the projections start with the Congress s most recent budgetary decisions and show what would happen to the federal budget if no policy changes were made over the projection period7 OJ According to the CBO For revenues and entitlement programs such as Social Security or Medicare the baseline projections generally assume that current laws will continue without change 0 For discretionary spending CBO as directed by the De cit Control Act assumes that budget authority for discretionary programs grows at the rate of in ation each year after 2001 0 So in using these projections one has to be careful about the potential for substantial changes given the current combination of economic woes proposals for tax reform and proposals for social security reform Politicians often manipulate these numbers for the purposes of making policy changes but these numbers are often very misleading In the very long run the real issue is the cost of entitlement programs like Social Security and Medicare Even though Social Security receipts will exceed expenditures in the next 10 years this will change over the next 30 years as the demographics of the US population changes o For example the number of 65 year olds will increase from 13 to 20 while the working age population will fall from 60 to 56 So current primary surpluses are a little misleading avoiding entitlement cutbacks for political gain can not go on for ever Current predictions of Medicare Medicaid and Social Security growth show that these programs will grow from 8 of GDP to 16 in the next 30 years c Attempts to address the issue of spiraling growth in entitlements include 7 Means testing Restrict bene ts to low income elderly 7 Control medical costs How The billion dollar question 7 Increase retirement age Currently popular citing the improvements in health and longevity Fall Semester 05 06 Akila Weempana Lecture 4 The Solow Diagram L H OVERVIEW 0 In the last lecture we discussed the importance of economic growth and the importance of models We then derived a model of economic growth the Solow growth model which basi cally consisted of two equations a production function and a capital accumulation equation 0 In today s lecture we will rst transform these equations into per capita terms in other words write the equations in terms of output and capital per capita This will make the model more tractable We will then use these two equations to draw a diagram known as the Solow diagram We will then use this diagram to do various comparative statics77 exercises where we analyze the impact of changes in saving rates population growth rates the capital stock etc on economic growth in the short run and in the long run THE PERCAPITA VERSION OF THE SOLOW MODEL 0 In order to make working with the model a little easier we transform the model into per capita terms De ne the following per capita variables y output per worker and k capital per worker I will use per capita and per worker Note that every person is a worker in this model interchangeably o The production function can be written in per capita terms as W E g which means that y k c The capital accumulation equation can be written in per capita terms as well K gig L kfE k Z k SE76 791 6 E 77717 in lti gt7lt6ngt27lt6ngt sy76nk This equation states that net investment per worker the change in the capital stock per worker is the difference between gross investment per worker 3y and the level of break even investment per worker 71 6k o The intuition underlying this equation is not too difficult to follow 1 Gross investment per worker is equal to savings per worker From gross investment savings Some of this new capital per worker must be used to replenish depreciated capital per worker In addition for every worker7 there are 71 new workers entering the economy7 each of whom require k units of capital to keep capital per worker unchanged to The basic intuition is that unless you replace worn out capital and provide each new worker with the same amount of capital7 then capital per worker in the economy will fall So the level of break even investment per worker the amount of investment per worker necessary to leave capital per worker unchanged is equal to n 6k OJ III THE SOLOW DIAGRAM o The two equations of the Solow Model can be written in per capita terms as y k is sy7n6k c We combine these 2 equations graphically into a diagram7 known as a Solow diagram The Solow diagram plots savings per worker and the break even level of investment per worker as functions of the capital stock per worker 0 Some features of the diagram 1 n 6k is a straight line from the origin with slope n 6 2 y k is a concave function For those of you who are mathematically inclined you can show that ii aka l gt 0 is an increasing function of k and that the slope of y falls as k increases 2 aa 71k0quot2 lt 0 because 04 lt 1 3 3y is just a dampened version of the y curve because 3 is a constant fraction between 0 and 1 o The Solow diagram looks as follows Investment per worker n6k y E k 3y E 3k kt III THE STEADY STATE 0 From this diagram we can show that the economy has a steady state level of capital per worker which we denote as 1 that it gravitates towards over time 1 When k lt If savings per worker gt break even investment per worker ie 3y gt n6k k increases over time ie k gt O 2 When k gt If savings per worker lt break even investment per worker ie 3y lt n6k k decreases over time ie k lt O 3 At k 1 savings per worker break even investment per worker ie 3y n 6k k is constant over time ie k 0 0 Once the economy reaches If the steady state it stays there The intuition is that the amount of savinginvesting the economy does at that point is exactly enough to cover the break even needs so the number of machines per worker stays unchanged By the way there is another not quite as interesting steady state in the model Can you nd it Changes in the Steady State 0 Now that we have identi ed the steady state of the economy and gured out how to draw the Solow diagram we are ready to analyze the impact of particular changes to the economy 0 These changes fall into two categories 1 Changes in the economy that cause the savings line or the break even line to shift 2 Changes in the economy that cause a move along the savings line or the break even line 0 The rst category consists of changes that change the shape of the savings line or the break even line Given that the savings line is 3k and the break even line is n 6k we can see that changes in san or 6 will cause shifts in the curves the rst two moving the savings line and the last two moving the break even line 0 The second category consists of things that suddenly change the level of k capital per worker in the economy Since k is on the horizontal axis of the Solow diagram a sudden change in k will mean a sudden movement along both the savings line and the break even line Sudden changes in k can be driven by sudden changes in K or sudden changes in L EXAMPLE 1 An increase in the savings rate An increase in s will shift the savings line up At the initial steady state7 we will be investing more than we need to break even so the level of capital per worker will rise This will continue until the new steady state at kf is reached lnvestment per worker EXAMPLE 2 An increase in the growth rate of population An increase in n will shift the break even investment line up At the initial steady state7 we will be investing less than we need to break even so the level of capital per worker will fall This will continue until the new steady state at k is reached lnvestment per worker EXAMPLE 3 A sudden increase in the capital stock If K rises suddenly then k will rise as well7 say to k1 on the Solow diagram At k1 we will be investing less than we need to break even so the level of capital per worker will fall This will continue until the economy returns to the old steady state Savingslnvestment per worker Fall Semester 05 06 Akila Weempana Lecture 16 The ISLM Model I OVERVIEW 0 In the last two lectures we derived the IS LM model which is a short run model of the determination of output The model has two main parts an IS curve that summarizes all the combinations of Y and r consistent with goods market equilibrium and an LM curve that summarizes all the combinations of Y and r that are consistent with money market equilibrium 0 We also discussed why the IS curve slopes downward while the LM curve slopes upward We also discussed circumstances under which the IS curve or the LM curve would shift Today s lecture puts the two sides of the model together and shows how to nd equilibrium output and the equilibrium interest rate for an economy Furthermore it will also examine what happens to the equilibrium output and interest rate when there is a change in monetary or scal policy II THE SHORT RUN EQUILIBRIUM IN A CLOSED ECONOMY 0 Since the IS curve summarizes all combinations of income and interest rates that clear the market for goods and services while the LM curve summarizes all combinations of income and interest rates that clear the money market equilibrium income and the equilibrium interest rate are at the intersection of the two curves 7 o Anywhere other than the intersection which we label To and Y0 we would expect there to be changes in Y or r that restore either goods market or money market equilibrium Generally we believe that the money market adjusts very quickly so the economy will rarely be off the LM curve However it will not stay off the IS curve for very long either as rms can adjust production to bring it in line with demand 0 Consider a point like A Even though the money market is in equilibrium the goods market is not we are off the IS curve At that low interest rate Y is too low to clear the goods market so rms increase production and Y rises As Y rises T has to rise as well in order to maintain money market equilibrium so the economy moves towards the intersection point 0 Now consider a point like B Once again the money market is in equilibrium but the goods market is not we are off the IS curve At that high interest rate Y is too high to clear the goods market so rms decrease production and Y falls As Y falls T has to fall as well in order to maintain money market equilibrium so the economy moves towards the intersection point 111 USING THE IS LM MODEL TO ANALYZE POLICY Fiscal Policy Government Spending o Expansionary scal policy in the form of government spending shifts the IS curve out by the full Keynesian multiplier effect ie an increase in exogenous government purchases shifts the IS curve out by 171317 AG However the presence of an upward sloping LM curve means that the increase in the equilibrium level of Y is less than in the Keynesian case In other words the spending multiplier in the IS LM model is smaller than the spending multiplier in the Keynesian model o Graphically we can see that the increase in Y from Y0 to Y1 the IS LM multiplier effect is less than the shift out of the IS curve from Y0 to Y the Keynesian multiplier effect T Decrease in G Increase in G c We can get intuition for why the multiplier effects are smaller by looking at what happens to the various components of the IS curve and the LM curve when G increases you should be able to gure out what happens when G decreases 7 C C b17tY T since Y is higher 7 I T7 Br T since r increased 7 G T G increased according to the question 7 NX lt gt NX is exogenous and unchanged 7 MS lt gt Exogenous and unchanged 7 Md lt gt T since r increased and T since Y increased We know that they must offset because MS Md and MS lt gt 0 Notice that the increase in exogenous government purchases increases r which in turn reduces l and reduces the overall positive impact of the increased government spending 0 The opposite would be true for contractionary scal policy in the form of lower government purchases This shifts the IS curve in by the full multiplier effect ie a decrease in exogenous government purchases shifts the IS curve in by AG However the presence of an upward sloping LM curve means that the decrease in the equilibrium level of Y is less than the multiplier effect c Graphically we can seethat the decrease in Y is less than the shift in of the IS curve from Y0 to Y1 instead of to Y Fiscal Policy Taxes 0 Expansionary scal policy can also take the form of tax cuts Given an lS curve of the form Y 171117 C T T G NX 7 Br we can see that changes in the tax rate affects the slope of the IS curve 1 14717 0 Therefore lower income taxes will lead to a atter slope of the IS curve resulting in a higher GDP because people have more money to spend on goods and services Lower Taxes Higher Taxes LM LM Y0 Y1 Y1 Y0 0 Conversely contractionary scal policy in the form oftax increases will make the slope steeper The result is lower GDP in the economy because the higher taxes reduces consumer income and therefore causes consumption to fall as well 0 Once again we can better understand the economic impact of tax cuts by looking at what happens to the various components ofthe lS curve and the LM curve You should test yourself by guring out what happens when there is a tax increase 7 C O b1 7 tY T since Y is higher AND because t is lower 7 I f7 Br l since r increased 7 G lt gt G is exogenous and unchanged 7 NX lt gt NX is exogenous and unchanged 7 MS lt gt Exogenous and unchanged 7 Md lt gt l since r increased and T since Y increased We know that they must offset because MS Md and MS lt gt Monetary Policy c We can also use the lS LM model to think about monetary policy decisions When the Fed pursues an expansionary monetary policy ie it increases the money supply we showed that this would cause the LM curve to shift to the right From the graph below we see that this causes GDP to rise and interest rates to fall in the economy 7 7 Contractionary Monetary Policy Expansionary Monetary Policy o lntuitively expansionary monetary policy has a positive impact on Y because the increase in real money supply over real money demand causes interest rates to fall in order to restore money market equilibrium On the goods market side the lower interest rates result in increased investment spending which in turn increases Y o The opposite would be true for contractionary monetary policy The decrease in real money supply over real money demand causes interest rates to rise in order to restore money market equilibrium On the goods market side the higher interest rates result in decreased investment spending which in turn lowers Y 0 Once again we can better understand the economic impact of expansionary monetary policy by looking at what happens to the various components of the IS curve and the LM curve You should try and gure out the corresponding impact of a contractionary monetary policy 7 C O b17tY T since Y is higher 7 I I7 Br T since r decreased 7 G lt gt G is exogenous and unchanged 7 NX lt gt NX is exogenous and unchanged 7 M9 T Increase in M9 7 Md T Since r decreased and Y increased IV POLICY INTERACTIONS o The interaction between scal and monetary policy is very important Suppose that there is a negative shock ot the economy say in the form of a fall in consumer con dence This will shift the IS curve back 0 We can show using the IS LM model that the appropriate policy response to this shock is to use expansionary policy scal monetary or both How much of expansionary scal policy in the gures below this is assumed to be in the form of higher G for example depends greatly on what the Fed does with monetary policy and how much expansionary monetary policy is needed depends on what the government does with scal policy OPTION 1 The Fed does nothing The response is entirely from expansionary scal policy OPTION 2 The government does nothing The response is entirely from expansionary monetary policy OPTION 3 The Fed and the government both use expansionary scal policy to move us back to the original leve of output Less expansionary scal and less expansionary monetary policy is needed than in the absence of the other o A potential aw in the lS LM model seems to be the prediction that accommodation by the Fed is always better the Fed should increase MS all the time because it only leads to higher output and lower prices This is not true in the real world where we think of the Fed as being very cautious about expanding the money supply during booms In order to inject realism into the model we may need to expand it to endogenize the determination of prices Fall Semester 05 06 Akila Weempana Lecture 11 Assessing the Solow Model with Technology 1 OVERVIEW 0 In the last lecture we looked at the results of some comparative static exercises using the Solow model with technology We showed that the impact of an increase in the savings rate is identical to the impact in the basic Solow model there is a short term increase in the growth rate of per capita output but in the long run growth is unchanged In other words7 the increase in savings has a level effect7 not a growth effect c We also looked at the impact of an increase in the growth rate of technology The impact of an increase in the growth rate of technology has a growth effect the steady state growth rate of output and capital per capita is increased In today s class7 we will take a closer look at the steady state of the Solow model with technology We then assess the predictions of the Solow model with technology and think about what avenues remain to be explored II COMPARING STEADY STATES c We can also do some comparative statics exercises using a little algebra instead of graphs We know that at the steady state O Therefore7 using the capital accumulation equation 1sgjing6lwecanshow 0 sy7ng6l ng6l 837 04 skgtk ng6l S 7 l1704 n g 6 m 1 78 gtlia ng6 0 Using the fact that y 1 we can then show that S amp ltng6gt 0 Using the fact that I g and y we can show that S k At Q31 4 1 a 179 d A 3 17a 111 Note that in steady state k and y are not constant they are growing over time hence the subscript t because technology is growing Finally using the fact that k and y we can show that i 179 1 m K AtLt lt gt and Y AtLt lt S S ng6 ng6 As is the case with k and y K and Y are not constant in steady state either they are growing over time both because technology is growing but also because the population is growing WHAT CAN THE SOLOW MODEL WITH TECHNOLOGY EXPLAIN Now that we have an idea about the properties of the model let s assess the intuitiveness of the predictions of the Solow model with technology 1 Why are some countries rich and others poor The Solow model with technology like the basic Solow model predicts that countries with high investment savings rates low population growth rates and low rates of capital depre ciation are likely to have more capital and output per worker In addition countries that have a high level of technology A or a high growth rate of technology 9 are also likely to be have more capital and output per worker in the steady s ate The model also predicts that all else being equal countries with a larger population are likely to be have more aggregate output which is the same conclusion reached by the basic model 2 Why do some countries grow faster than others The Solow model with technology provides an explanation for differences in per capita eco nomic growth across countries in the long run all countries have a steady state output per capita growth rate that is equivalent to the growth rate of technology So countries with a high rate of technological progress are likely to grow faster Even though the rate of population growth still has a positive impact upon the growth rate of the overall economy the rate of technological progress also matters the growth rate of Y is n g 3 How can economies exhibit sustained economic growth In per capita terms the Solow model with technology recti es a major aw of the basic model it provides an explanation for why countries can grow in a sustained systematic manner for long periods of time technological progress Technology is the engine of economic growth As in the basic model a country that increases its savings rate or lowers its population growth rate to increase the steady state level of output it can reach will see a positive spurt of growth in the short run o In addition a country that can increase its rate of technological progress will be able to move from a slow rate of growth to a high rate of economic growth even in the long run Conclusion 0 The Solow model with technology preserves the basic framework of the simple Solow model but also provides a good intuitive framework for thinking about potential explanations for growth differentials and sustained economic growth 0 Even though the answers make good intuitive sense we need to verify if the model does a good job empirically can it explain growth and level differentials across countries IV EMPIRICAL TESTS OF THE SOLOW MODEL WITH TECHNOLOGY 0 Even though the predictions of the model make some intuitive sense7 we would also like the model to be a good empirical model as well 0 A seminal paper by Gregory Mankiw7 David Romer and Philippe Weil showed that the Solow model with technology can explain about 60 of the differences in economic growth across a sample of 98 countries much of the explanation comes from differences in population growth rates and savings rates 0 They modify the model to include human capital educational attainment and show that the performance of the model is further enhanced This modi ed model can explain about 78 of the differences in economic growth across countries 0 They model human capital as an input very similar to physical capital a portion of savings is invested to accumulate human capital7 some of which merely replaces depreciated human capital 0 However7 we will limit our discussion of the speci cs of their empirical ndings because of econometric limitations and think of a different approach to test the empirical validity of the Solow model 0 For each country i in the sample7 recall that given data on savings rates7 population growth rates etc we can write down an expression for steady state output per worker as 179 EA y lm6igi o The level of technology in each country can be backed out from a Cobb Douglas production function Yz39 K AiLiV D Y Aim Kng y m KaIllia Ai i i o The expression for 34 may fail to pin down the scale of the economy ie we may not be able to calculate the exact 39 value of per capita GDP 0 Therefore we need to express steady state output per worker of the economy relative to a base country the Us for example Let be the relative steady state output per worker of country i i 9i 1 Mr 7 Al m5igil i 179 9US AUS nUs5Us9Usl c We can also calculate the actual relative income level for country i as well For example the actual relative income in 1998 is given by 3398 where we use the dollar value of real GDP per capita for each of the countries and for the US ie A98 y 9139 38 yUS If the model s predictions are valid a graph of on 3398 should show the observations clustered around a 45 degree line See graphs shown in class and in the Jones textbook Observations clustered around a 45 degree line con rm the validity of the Solow model only if all the economies are close to steady state 0 Economies that are away from steady state need not lie close to the 45 degree line because we are using the predicted steady state value of relative GDP ln drawing conclusions about the empirical validity of the Solow model from these charts we should be aware that they depend on the following assumptions 1 69 are assumed to be the same across countries technology transfers equalize 9 across countries to An adjustment has been made for differences in human capital differences across coun tries so that the actual methodology is a little more complicated than outlined above OJ We rst assume A is the same across countries See Class Graph 1 the t is not very goodYou can nd this graph in Jones Page 52 We then allow for differences in A across countries and nd see Class Graph 2 the t is much betterYou can nd this graph in Jones Page 54 OTHER TYPES OF TECHNOLOGY 0 In addition to labor augmenting technology we can think of two other types of technology capital augmenting technology and total factor productivity 0 Capital Augmenting Technology Technology that works well with capital Can be captured in a Cobb Douglas production function as Y CK D Ll c Total Factor Productivity Technology that works with all inputs factors to produce output Can be captured in a Cobb Douglas production function as Y BKu L 0 If we know how to work with the Solow model with labor augmenting technology7 we can easily handle the other types of technology as well For example7 we can rewrite the production function for capital augmenting technology so that it resembles a production function with labor augmenting technology as Y 0K L1 D i 1 K CH L Therefore we can see that this economy can be considered to be identical to a labor augmenting technology economy if C A In other words7 if we are given an economy where capital augmenting technology is growing at a rate 97 then we can treat it as being equivalent to an economy where labor augmenting technology is increasing at a rate This is true because CE A implies that A i a c 7 a A 17 a C 17 a 9 In the steady state of an economy where capital augmenting technology is growing at a rate 97 capital per worker and output per worker are increasing at a rate 170439 We can also rewrite a production function with TFP in terms oflabor augmenting technology as BKoleiuz 1 L 170 K BE L Y Therefore we can see that this economy can be considered to be identical to a labor augmenting technology economy if B A In other words7 if we are given an economy where TFP is growing at a rate 97 then we can treat it as being equivalent to an economy where labor augmenting technology is increasing 1 at a rate This is true because B A implies that i 1 7 1 7 1 7 Oz 7 1 7 04 9 Therefore in the steady state of an economy7 where capital augmenting technology is growing at a rate 97 capital per worker and output per worker are increasing at a rate 5 B A A 170 Fall Semester 05 06 Akila Weempana Lecture 19 Monetary and Fiscal Policy H H OVERVIEW 0 In the last class we looked at the total impact of monetary policy and scal policy on output and prices in the short run and the long run 0 In today s class we will take a closer look at monetary and scal policy We will rst de ne what good77 monetary and scal policy is then take a look at the delicate task the Fed has to follow in coordinating monetary policy with the scal policy choice of the government 0 We will also examine some limitations of the IS LMAD AS model These limitations are important to keep in mind and come mostly from lack of information about Y coordination failures and timing discrepancies GOOD FISCAL POLICY 0 In the last class we took a signi cant step towards identifying what a good 7 scal policy would like If the economy is in recession the government should act decisively to pursue an expansionary scal policy that will move Y back to Y That policy should get good bang for the buck ie have as large a multiplier effect as possible who should get the tax cuts 0 Furthermore expansionary policy that is pursued after the economy reaches Y is de nitely NOT good policy it will crowd out investment in the long run 0 There is however one possible reason to pursue an expansionary scal policy if the economy is at Y That is if the expansionary policy is one that is likely to improve Y o Spending increases that could increases the potential output level of the economy include things like more research spending into new technology development building an electricity grid a new highway system improving scienti c education in schools etc 0 Some economists known as supply siders believe that tax cuts can encourage people and rms to work harder and thus increase Y The evidence on supply side tax cuts is weak likely only to hold at very high tax rates 0 The evidence on bene cial spending by the government is also mixed because it is dif cult to judge whether or not the research money is being spent productively 0 So even though good77 scal policy can have an effect on Y you should always be skeptical unless you had good reason to believe that Y has improved 0 We can show the impact of a good scal policy consider an increase in government purchases in the form of higher research and development spending that shifts the IS curve and the AD curve out It will also shift the level of potential output out to Yf This will increase output to Y1 interest rates to T1 and leave prices unchanged in the short run 0 Over time since output is greater than potential prices begin to rise Since potential output is also higher at Yf however prices do not rise by as much as in Case 2 because they only increase as long as Y exceeds the new potential output As a result the LM curve does not shift in as much The end result is a higher level of output at Yf higher interest rates at r2 but not as high as in case 1 and higher prices Pf but again not as high as in case 1 LRAs P LR AS A 1 SRAS P0 l bKAS 4 7 AD N AD l l Y Y Yf Y1 III GOOD MONETARY POLICY In the last class we also identi ed what a good 7 monetary policy would like If the economy is in recession the Federal Reserve should act decisively to pursue an expansionary monetary policy that will move Y back to Y c When the economy is back at Y the Fed should NOT pursue an expansionary policy at all Finally if Y gt Y the Fed may want to pursue a contractionary monetary policy in order to stop prices from rising o In order to identify what a good monetary policy is one should know a few details about the goals and procedures of the Fed 0 First the Fed has a longer term horizon than the government Governments facing elections every 2 6 years are often tempted to implement policy changes that bene t the economy in the short run but have little or no impact on output in the long run In other words expansionary policies that push Y above Y in the short run but only crowd out investment and cause in ation in the long run are considered to be desirable by the government In contrast the Board of Governors of the Federal Reserve are appointed to 14 year terms in office Thus their horizons are much longer and they pursue policies that are good for the long term health of the economy 0 Economists also attach great importance to the degree of independence granted to the central bank in a country by the government The degree of freedom given to the central bank varies widely across countries but the Us and Germany are recognized to have very independent central banks o In the US7 the governor of the Federal Reserve is appointed to terms that span multiple presidents to preserve independence In general7 the likelihood that a president would replace the current chairman of the Federal Reserve is remote Some call Alan Greenspan the most powerful man in the world 0 Economists believe that greater central bank independence leads to better economic perfor mance by allowing the Central Bank to focus on the long run and by disassociating the central bank from having to continually worry about the short term bene ts to the economy IV POLICY COORDINATION 0 Now that we have established the long term perspective and the independence of the Central Bank to a certain degree the next task is to see how the Fed should react to various changes in the economy 0 For illustration purposes7 we will focus on three scal policy cases a tax cut7 a spending increase that does not affect Yquot and a spending increase that raises Yquot Case 1 A Tax Cut 0 We saw that a tax cut in an economy that is at potenital output will result in much higher interest rates7 and higher in ation with no positive effect on output in the long run 0 The Fed may not like this change in the economy given its long term outlook in which case it can immediately pursue a contractionary monetary policy that will shift the LM curve in immediately and move the economy back to Y Since the AD curve shifts back in to Y Y is not above Yquot and there is no change in P over time See Figure below 0 In comparison to the long term effects of the taX cut7 pursuing this contractionary policy enables the Fed to keep P unchanged instead of having it increase while achieving the same long term levels of Y7 and r that would have resulted if it did not act 7 P LRAS P0 SRAS 4 AD i AD Y Y Case 2 An Increase in Government Spending Y is unaffected 0 Now consider the case of an increase in government purchases that leaves Yquot unaffected We saw that this increase in government purchases increases interest rates and prices and leaves output unchanged in the long run 0 As before7 we can see that the Fed does not like this change in the economy so it reduces the money supply shifting the LM curve back This will shift the AD curve in and move the economy back to Yquot o By acting immediately to cut off in ation the Fed leaves the economy with the same long term level of output and interest rates that it would have had as a result of the higher government purchases in the absence of the contractionary policy7 but is able to prevent P from rising p LRAS P0 SRAS 4 AD i AD Y Y Case 3 An Increase in Government Spending Y is affected 0 Finally consider the case of an increase in government purchases that also raises Yquot We saw that this increase in government purchases mildly increases interest rates and prices and also increases output in the long run 0 The Fed clearly prefers this type of government spending since it causes less in ation and also raises output in the long run It will respond less drastically7 and with a less contractionary policy will move the economy to the new level of potential output P LRAS LRAS P0 N iAS III PROBLEMS WITH POLICY COORDINATION Inside and Outside Lags 0 Even though the above analysis provides a very nice framework for thinking about policy coordination issues in real life policymaking is much more challenging 0 One reason for the additional real life complexity is that policy takes times to implement and time to impact the economy 0 For example scal policy takes a long time to enact but a relatively short time to take effect This is known as an inside lag or an implementation lag Why Consider the scal policymaking process in the United States a bill has to introduced in committee in the House or the Senate be approved in committee be approved in the full House or the full Senate any amendments debated upon and voted on then sent to the other body for approval whereby some more committee meetings may be needed to reconcile differences in the two bills and then sent to the president for approval The entire process can take from 6 months to a year hardly the speedy response that our IS LM model indicates 0 However during this time the economy is not standing still many changes are taking place so that at the time that the bill is nally approved the economic conditions may have changed so much that the original intent of the bill may be moot o In contrast monetary policy is relatively quick to implement since it only requires the approval of the Federal Open Market Committee a group of policymakers within the Federal Reserve System This makes monetary policy more nimble than scal policy in responding to changes in the economy 0 However monetary policy is by no means perfect either Monetary policy has a relatively short implementation lag but is said to have a long outside lag or impact lag which is simply the time it takes for the enacted policy to have an economic impact Why It is because monetary policy makers change only a single short term interest rate the Federal Funds rate through their actions Changes in the FF rate affect shorter and longer term interest rates and hence eventually affect investment spending but it may take a long time for those effects to be felt since consumers and rms don t embark on new housing or investment projects at the drop of a hat In contrast scal policy once enacted should have an immediate impact at the moment of spending the impact in the case of a tax cut will also not be long because consumers can spend even before they actually le their tax returns knowing their tax bill will be lower Uncertainty about Y o In the initial analysis we did we showed that the Fed will in general prefer to move the economy to Y Some economists refer to this as the Fed being like Goldilocks liking the economy to not be too hot or be too cold but instead wanting it to be just righ 7 0 However unlike Goldilocks it is not clear what just righ 7 means in the context ofthe Federal Reserve because Y is not observable So the Fed often has to use their best judgment to decide whether the economy is too hot or too cold This si why monetary policy is said to be as much art as science o The Fed will often act incrementally making small changes to interest rates over a period of months so that they can observe whether the economy is growing too slow or too fast by what is happening to prices and output 0 In recent times uncertainty about Y has been particularly acute both during the new economy77 speculations that accompanied the asset bubble in 1999 and also in the recent increases in measured productivity which has led the Fed to keep interest rates low for a longer period of time than they would otherwise have Fall Semester 05 06 Akila Weempana Lecture 25 Ricardian Equivalence 1 OVERVIEW H o In today s lecture we will examine a sophisticated theory about the interplay between scal policy and the decisions of consumers in the economy 0 This theory known as Ricardian equivalence implies that the impact of taxing and spending decisions on the economy may be counter intuitive to what we would expect from our basic lS LM analysis 0 Therefore the standard lS LM analysis has to be modi ed somewhat if we take into account the ideas of the proponents of the theory of Ricardian equivalence RICARDIAN EQUIVALENCE The theory of Ricardian equivalence was re introduced into economics by Robert Barro The essence of the theory is that scal policies that worsen the long run budget position and require government s to issue more bonds don t stimulate the economy very much Proponents of Ricardian equivalence build their case on two assumptions The rst is that the government faced an inter temporal budget constraint similar to that faced by a consumer In other words recall that the consumer faced a lifetime budget constraint ignoring interest rates that was of the form We can derive a similar budget constraint for the government of the form 00 v ZR t0 Here P is government expenditures at time t I did not use G because that only refers to purchases of goods and services and 739 is government revenues I did not use T because that only refers to tax revenues M8 t H o 0 According to this budget constraint the government can t run a de cit forever therefore an increase in expenditure or a tax cut today that raises spending above revenues will have to be nanced through a future tax increase or a future decrease in spending that raises revenue above spending 0 The second key assumption is that consumers being rational forward looking creatures will not increase consumption in response to a debt nanced tax cut and will cut back consumption in response to a debt nanced increase in government spending in anticipation of future tax hikes 0 These two assumptions have powerful macroeconomic implications In particular they imply collectively that tax cuts and spending increases nanced by increasing government debt will not have an impact on the economy 0 Why Consider a decision by the government to issue a tax cut In the regular IS LM analysis this tax cut will increase consumer spending and thus raise GDP In the Ricardian world consumers will only increase their spending IF the tax cut does not worsen the government s long run budget position forcing it to issue more debt Otherwise consumers seeing the increase in the current de cit will anticipate that the government will have to raise their taxes in the future to run the surpluses they need to pay off the increased debt Since this is simply a trade off of lower taxes today for higher taxes tomorrow consumers will not be richer in terms of lifetime income and thus will not increase consumption 0 Similarly consider a decision by the government to increase G In the regular IS LM analysis this increase in G will raise GDP In the Ricardian world however consumers will keep a close eye on whether the government can afford this increase in G If the government can t afford it ie they will increase G by running a de cit and increasing the debt consumers know that the government will have to raise their taxes in the future to run the surpluses they need to pay off the increased debt Facing higher taxes tomorrow consumers will be poorer in terms of lifetime income and thus will decrease consumption this fall in C will counter the increase in G o Ricardian equivalence also means that future budget situations can have macroeconomic impacts today For example the announcement of future cuts in government spending will increase current consumption because the government will not have to collect as much taxes in the future So even without increasing G in fact by announcing that G will in fact DECREASE the government can stimulate the economy today 0 Economists have presented several counter arguments to this Ricardian analysis including 1 Consumer myopia 2 Borrowing constraints 3 The timing of the expected future tax increase may be on a future generation 0 Barro countered the last of these arguments by pointing out that people care about their kids and may not wish to burden them with tax increases individuals may have in nite horizons Even if you don t agree with the hyper rationality of the true Ricardian you should consider this to be a good balance to the hyper irrationality of the IS LM model where consumers were completely indifferent to the scal situation of the government Fall Semester 05 06 Akila Weempana Lecture 15 The LM Curve I OVERVIEW H o In the last lecture we derived the IS curve the rst part of the model of economic uctuations known as the IS LM model The IS Curve summarized all the combinations of interest rates and GDP that clear the market for goods and services in the economy 0 However keep in mind that ANY point along the IS curve is consistent with equilibrium in the market for goods and services the IS curve by itself cannot gives us the value of output in the economy because it does not have anything to say about the level of interest rates in the economy In today s class completed our development of the IS LM model by looking at the LM curve a relationship that describes the behavior of the money market which determines interest rates in the economy THE LM Liquidity Preference Money Demand CURVE o What is referred to as money in this section is currency coins and dollar bills issued by the Federal Reserve and checking account balances held in banks by the public and by rms 0 To simplify things we assume that money does not pay interest and that all other non monetary nancial assets savings accounts certi cates of deposits bonds money market accounts pay an interest rate of r o The LM curve consists of the combinations of income and interest rates that clear the market for money balances ie equate money demand and money supply In order to identify the combinations of Y and r that make up the LM curve we rst look at the demand for money 0 We can express the demand for money as a function of the interest rate on nancial assets r prices P and income Y Y r M f lt 7 o The intuition for this function is as follows 1 When r is high the demand for money is low because money pays no interest the opportunity cost of holding money instead of other nancial assets rises 2 When Y is high the demand for money is high richer people who buy more goods are likely to hold more money 3 When prices P are high the demand for money is high since people need more money to complete their transactions 0 NOTE The appropriate interest rate here is the nominal interest rate the actual interest rate paid to the holders of nancial assets If we use i to denote the nominal interest rate the relationship between the real and nominal interest rates can be expressed asi r Expected rate of in ation Since the lS LM model is a short run model that works with an exogenous xed price level 15 so expected in ation can be thought of as being insigni cant in which case 2 z r A simple algebraic form would be Md 15led kYi hr where k and h are parameters that denote how sensitive money demand is to GDP income and to the interest rate respectively We also acknowledge that money demand can be affected by other factors the introduction of ATM s for example the term Md represents exogenous changes to money demand perhaps driven by these other factors Price enters multiplicatively into the above money demand function because all else equal a doubling of the price level will require us to hold twice as much money to buy the same amount of goods and services We assume that the supply of money is exogenously set by the Federal Reserve Let the exogenous money supply be denoted by M9 In equilibrium money supply money demand The LM curve can therefore be written as MS Md which is equivalent to MSPMdkY7wl We can rewrite this as an upward sloping positive relationship between T and Y as k 7 Y lntuitively we can explain the upward sloping LM curve as follows If income is high then the demand for money will be high relative to the xed supply In order to equilibrate money demand and money supply interest rates have to also be high to reduce money demand 1W rg P Similarly if income is low then the demand for money will be low relative to the xed supply In order to equilibrate money demand and money supply interest rates have to be low to increase money demand Graphically we can draw the LM curve as 7 LM Curve III THE SLOPE AND INTERCEPT OF THE LM CURVE The Slope o The slope of the LM Curve is 37 k W E o The LM curve is steep when the absolute value of the slope is large This occurs when 1 The parameter k is large 2 The parameter h is small 0 What is the intuition for these results Well a steep LM curve means that a given increase in Y requires a large increase in interest rates to equilibrate the money market A high value of k means that money demand increases dramatically when Y increases by a given amount This requires a large increase in interest rates to restore equilibrium 0 Similarly a low value of h means that money demand does not respond very much to interest rates This implies that for any increase in money demand driven by an increase in Y interest rates have to increase dramatically to restore equilibrium The Intercepts o The intercept of the LM curve can be found by setting Y 0 as 7 s r 7 l W 7 M h P o The horizontal intercept ofthe LM curve can be found by setting r 0 This can be calculated as 1 M9 7 d y 7 g l P 7 M l 0 However keep in mind that neither the interest rate nor the output level can be negative so the LM curve will only be de ned in the northwest quadrant 0 These are not particularly intuitive and for the most part we will almost never use the exact values in our analysis once we gure out what causes the intercepts to change IV SHIFTS IN VS MOVEMENTS ALONG THE LM CURVE o The other important thing to note is that changes in money demand brought about by changes in Y or by changes in r are re ected as movements along the LM curve When income decreases money demand falls and as a result interest rates must decrease to restore money market equilibrium When income increases money demand rises and as a result interest rates must increase to restore money market equilibrium 1 7 P 7 E P 7 So there are three factors money supply M9 exogenous money demand Md and price P that shift the LM curve 0 What causes the LM curve to shift The intercepts are r Md 7 MS and Y MS 7 Md H If the Fed increases the money supply expansionary monetary policy then from the equation we can see that the vertical r intercept will be lower and the horizontal Y intercept will be larger ie the LM curve shifts out to the right to Conversely if the Fed decreases the money supply contractionary monetary policy then we can see that the vertical r intercept term will be higher and the horizontal Y intercept will be smaller the LM curve shifts in to the left Since P appears in the denominator of the Rigs term above you can see that an increase in the price level has the same effect as a decrease in the money supply it shifts the LM curve in to the left Conversely a decrease in the price level has the same effect as an increase in the money supply it shifts the LM curve out to the right OJ q Exogenous increases in the demand for money have the opposite impact from increases in the supply of money From the above equation we can see that an increase in exogenous money demand raises the vertical intercept and makes the horizontal intercept smaller the LM curve shifts in to the left Conversely exogenous decreases in the demand for money lowers the vertical intercept and makes the horizontal intercept larger the LM curve shifts out to the right Once again keeping track of the math can be tedious so its best to seek intuitive explanations The basic intuition is that the movement of interest rates depends on the relationship between money demand and money supply Exogenous changes that bring about excess money demand ie drive money demand above money supply cause interest rates to rise in order to lower money demand and equi librate money demand and supply The LM curve will shift in These changes include a fall in money supply a rise in prices or an increase in exogenous money demand Exogenous changes that bring about excess money supply ie drive money supply above money demand cause interest rates to fall in order to raise money demand and equilibrate money demand and supply The LM curve will shift out These changes include an increase in money supply a fall in prices or a decrease in exogenous money demand Another way of intuitively understanding the LM curve is as follows When there is an excess supply of money people are more likely to put the extra money into non monetary nancial assets so issuers of those assets can offer lower rates of interest yet still attract buyers Conversely when there is an excess demand for money people are less likely to put money into non monetary nancial assets so issuers of those assets must offer higher rates of interest to attract buyers A couple of graphical examples are provided below EXAMPLE 1 An increase in the supply of money by the Fed M9 T will result in an excess supply of money This will cause the LM curve to shift outwards in order to restore equilibrium Old M CurV eW LM Curve Y EXAMPLE 2 o A decrease in the supply of money by the Fed M9 l will result in an excess demand for money This will cause the LM curve to shift inwards in order to restore equilibrium 7 New LM CurV Old LM Curve Y EXAMPLE 3 0 An increase in the price level will raise money demand and result in an excess demand for money This will cause the LM curve to shift inwards to restore equilibrium New LM CurV Old LM Curve Y EXAMPLE 4 o A decrease in the price level will lower money demand and result in an excess supply of money This will push interest rates down for any level of Y This will cause the LM curve to shift outwards 7 Old M CurV eW LM Curve Y Fall Semester 05 06 Akila Weempana Lecture 22 Consumption I OVERVIEW 0 In the last 20 of the class we explore the microeconomics underlying each of the component parts of the IS Curve in a thorough manner rst consumption then investment government spending and net exports and the open economy in order This will enable us to look at more sophisticated economic concepts beyond the scope of the IS LM model 0 We initially focus on the consumption decision which is the largest component of GDP about 65 of GDP It is also the most important from an individual s perspective In the IS LM analysis we worked with a very simple Keynesian consumption function where consumption today depended only on current disposable income While this is analytically convenient it does not in anyway capture the complications of the consumption decision that people undertake everyday II FORWARD LOOKING THEORIES OF CONSUMPTION o In the IS LM model we used the Keynesian consumption function C C b1 7 tY Any changes to Consumption that are unrelated to current income are captured by the exoge nous consumption term C However we would like to incorporate some of these additional determinants more directly into our consumption function 0 The Keynesian consumption function seemed to hold up empirically when researchers used data over a long period of time The MPC b seemed to be about 093 However when they surveyed the consumption patterns of households over shorter periods of time they found that the MPC was much lower about 072 Since the Keynesian Consumption function did not allow for the pattern of consumption to differ between the short run and the long run a better theory was required 0 There were two such theories proposed in the 1960 s Milton Friedman s Permanent In come Hypothesis and Franco Modigliani s Life Cycle Hypothesis These 2 theories collectively are often referred to as the Forward Looking Theories of Consumption and share a common economic intuition This intuition is built on the assumption that consumers are forward looking individuals who calculate a plan for their future consumption and then attempt to smooth consumption as much as possible The Life Cycle Theory of Consumption o Modigliani s life cycle model describes individuals as going through several phases in life youth when typically little or no income is earned middle aged working years when most of their income is earned and the retired years when they have to live off savings and social security 0 Consumers then are likely to dissave when young and old and save when they are middle aged so as to consume most of their resources over their lifetime 0 This can help explain the discrepancies in the short and long run link between C and Y In the long run C and Y will be closely related as individuals will consume most of their income so the MP0 will be high But in the short run many groups such as the young the old and the working will not consume in proportion to their incomes because they will be either saving or dissaving depending on the stage of the life cycle that they are in KC The Permanent Income Hypothesis Friedman s Permanent lncome Hypothesis is similar to the Life Cycle Theory Instead of fo cusing on the age of the consumer Friedman focused on the type of income that the consumer received He categorized income into 2 types permanent income and transitory income Permanent income is income that people expected to last into the future while transitory income consists of temporary deviations from permanent income He then observed that the MP0 out of permanent income should be close to 1 while the MP0 from temporary income should be considerably less than 1 because individuals would tend to smooth consumption over time The intuitive reasonableness of this argument can be illustrated by thinking about a Powerball lottery winner who has a choice of receiving a single lumpsum payment of 150 million or something like 30 annual payments of 10 million a year The single lump sum would be counted as transitory income while the 10 million payment would count as permanent income lntuition would tell us that they would increase annual consumption by about 10 million a year in the 2nd case a MP0 close to 1 while they would save most of the 150 million in the rst case a MP0 close to 0 o This too can explain the short and long run differences in consumption When we use long term data permanent income dominates income so we would expect MPG to be close to 1 However when looking at short term data income consists of both permanent and transitory income so the MP0 would be much lower The next question that arises is how much C goes up in response to an increase in transitory income The answer to this depends on the horizon over which I plan my consumption A simple example Consider an individual who lives for T periods and earns an income of Y in period t where t 1 2 T Since we only want to focus on the distinction between permanent and temporary income we will make certain assumptions for simplicity s sake In particular we will assume that the interest rate is zero and that the individual does not discount future utility This implies I ll be happy to show to anyone who cares that the individual prefers to keep consumption completely smooth ie consume the same amount every period The budget constraint faced by the individual is We can use the fact that all the consumption levels are identical to write this as lt Ttl In other words consumption will always be equal to average income Now suppose the individual got a raise so that their salary increased by a constant dollar amount Z every period ie their new income in a given period is Y Z Since the FCC conditions are unchanged we know that 01 Cg CT C will still hold Using the new budget constraint the solution will be a 1 C i T t mz 1 1 T f 20 Z t1 So consumption will increase by Z every period ie by the amount of the permanent income Suppose instead that the individual had received a raise of Z dollars in the rst period and no raises thereafter Using the new budget constraint the solution will be 71 1 1 07 Y 72 T T T ma T 04 Z t1 In other words consumption will increase by ZT every period Based on this we can conclude that the MP0 out of permanent income is 1 MP0 out of temporary income is As the horizon gets longer the tendency to consume out of temporary income goes to zero III IMPLICATIONS FOR ISLM ANALYSIS Both the Friedman and the Modigliani approaches to modeling consumption have powerful implications for IS LM analysis The length of tax cuts matter because we have to distinguish between permanent and tem porary income If individuals are forward looking then a temporary tax cut will affect them less than an equivalent tax cut that is permanent will So we would have to incorporate the permanency of tax cuts into our IS LM analysis Example A permanent tax cut announced in 1964 stimulated the economy because consumption increased In contrast was the 1968 Vietnam War tax surcharge which lasted 1 year7 this did not reduce aggregate demand at all because people smoothed out the tax increase over their lifetimes Expectations matter So announcements of future tax cuts will affect consumption today because forward looking consumers are likely to take the future into account While the permanent income hypothesis can explain some puzzles it still is not empirically foolproof In particular7 consumption seems to depend much more on current income than on future income Potential explanations for this are H Irrationality Consumers are likely to believe that good times will always stay and bad times will go away to Short sightedness Consumers are not forward looking to the degree predicted by Fried man and Modigliani OJ Uncertainty about future income so they save money for a rainy day q Liquidity constrained consumers even though people like to smooth consumption they are unable to spend more than they earn so they will use temporary income increases to nance consumption Fall Semester 05 06 Akila Weerapana Lecture 13 The Keynesian Multiplier 1 OVERVIEW H c We have now completed our discussion of economic growth and will move on to the next portion of our class which focuses on the short run in particular on economic uctuations Rather than trying to motivate the topic myself let me use the words of Keynes In the long run we are all dead Economists set themselves too easy too useless a task if in tempestuous seasons they can only tell us that when the storm is long past the ocean will be flat again John Maynard Keynes o In this section of the course we will begin to develop a theory that explains how uctuations in the demand for goods and services in the whole economy can cause uctuations in output in the short run 0 Why do these uctuations in spending occur What role can scal and monetary policy play in preventing such uctuations from occurring These are the questions we will try to tackle in this section WHAT IS THE LONG RUN This is the question that vexes macroeconomists You will rarely nd a macroeconomist who is willing to offer a speci c opinion about the length of elapsed time that constitutes the long run Instead they are very evasive Keynes himself avoided the question in a most articulate fashion by saying In the long run we are all dead 0 So rather than offer up a time based de nition of the difference between the long run and the short run I will offer the following alternate de nitions of what distinguishes long run economic analysis from short run economic analysis The Long Run 7 Discussions about the Solow Model and the growth path of the economy 7 In the long run output potential output Potential output full employment output is the output produced by the economy making full use of the capital labor and technology available to it 7 The Solow model describes how K L A evolve over time ie describes potential output 7 Prices are completely exible output is determined completely by production in other words prices adjust to equate demand and supply but demand can t in uence output it only affects price 7 Fiscal and monetary policy can only work if they affect the economy s ability to supply goods and services ie produce output III The Short Run Discussions about uctuations around the growth path of the economy In the short run output 7 potential output ie we can deviate from the growth path of the economy Prices are sticky slow to change as a result demand can determine output because prices do not adjust to equate supply and demand 7 Fiscal policy the government s decisions about expenditure and taxation and monetary policy central banks decisions regarding money supply in uence demand and therefore in uence output So the basic distinction is that the economy s ability to produce in the long run is constrained by the capital labor and technology it has available In the short run output does not have to always equal this level of potential output It can either be higher booms or lower recessions During certain periods of time there is a lot of spending on goods and services thus leading producers to produce more goods This temporary boost in production can be accomplished by working machines extra hard by cutting back on maintenance by asking workers to work overtime by hiring part time workers etc During other periods of time there is a cutback in spending on goods and services thus leading producers to produce fewer goods This temporary cutback in production can be accomplished by idling machines reorganizing workplaces laying off workers etc The goal is to come up with a model that explains what types of changes cause spending to rise or fall suddenly how those changes are transmitted through the economy and what role monetary and scal policy has to play in stabilizing these positive and negative spurts in output THE KEYNESIAN CROSS MODEL In this section we will begin to develop a theory that explains how uctuations in aggregate demand demand for goods and services in the whole economy can cause uctuations in output in the short run The intellectual history of the model dates back to the Great Depression an extremely severe economic downturn that could not be easily explained by uctuations of aggregate supply changes in the quantity of goods and services produced in the economy caused by changes in the factors of production capital and labor or by changes in technology Keynes argued that a fall in aggregate demand caused the sudden economic downturn that led to the Great Depression and that there was a signi cant role for the government to play in controlling such downturns in economic activity The basic model the lS LM model is a short run model that explains the determination of national income for a given price level We can use this model to derive an aggregate demand curve for the economy and determine how prices adjust over time A preliminary step is to derive a simpler model of the demand for goods and services known as the Keynesian Cross which we can then generalize to obtain the lS LM model The Keynesian Cross is the simplest model of the demand for goods and services considered in this class We can express the expenditure of households rms foreigners and the government on domestic goods and services as E C I G NX We specify the following consumption function that relates consumption C to disposable income after tax income CCMYi In the consumption function I is the marginal propensity of consumption MPG the fraction of an additional 39 of disposable income that is used for consumption and C is exogenous consumption consumption unrelated to current income We assume that investment T government purchases 1 lump sum taxes T and net exports N X are exogenous In equilibrium Expenditure Output E Y We can now express the model as Y Y CIGNX OMyi fGNX Solving for Y from the above the equilibrium level of output in this model can be algebraically expressed as 7 7 7 7 7 7 CIGNX7bT Y 171 The Multiplier We can use the Keynesian Cross to examine the impact of a change in any of the exogenous variables 539 T G or NX on the value of Y From the above expression we see that a 1 unit increase in any of these variables increases Y by units This increase is gt 1 because the marginal propensity to consume 1 is lt 1 The translation of a 1 unit change in any of the exogenous variables into a more than 1 unit increase in Y is known as the multiplier effect with being called the spending multiplier The mechanism by which this happens can be explained fairly easily Suppose government purchases goes up by 1 unit Because Y C I G NX this will bring about a 1 unit increase in income known as a direct effect When income has gone up by 1 unit because of the direct effect consumption will increase by 1 units since the consumer spends b of every dollar that heshe receives This is called a feedback effect This feedback effect does not end here the increase in consumption causes income to go up by 1 units which in turn causes consumption to rise by 2 units and so on ad in nitum If we denote the change in government purchases by AG and the corresponding impact on output by AY then we can express the net impact of an increase in G on Y as AYAG1bb2AGlt gt So an increase in government purchases causes a larger increase in output and a fall in government purchases causes a larger fall in output For intuition think about an example such as the shutdown of a defense base in CA a reduction in G Since most military bases employ a large number of people 10000 workers a shut down of a base has huge economic consequences For example many people in the surrounding area have jobs at the base cooking cleaning and clerical work These people will lose their jobs their incomes would fall and their spending on food clothing and education will go down The owners of services near the base will lose income because the soldiers will no longer be getting hair cuts drinking beer or buying CDs Finally farmers and other local suppliers of fresh produce will lose a huge market for their supplies and will cut back on the scale of production of food products All in all a 10 million reduction in G will lead to a larger decline in output in the economy The Keynesian Cross Model With Income Taxes The basic Keynesian cross model dealt with an economy that had lump sum taxes The resulting multiplier was m which implies a multiplier of 10 for a reasonable MP0 of 09 This is an extremely unrealistically large multiplier It means that a government can increase GDP by 10 merely by spending 1 We can reduce the size of the multiplier by considering an economy with income taxes instead of lump sum taxes However to keep the analysis simple we will focus on a at tax system rather than a graduated tax system We specify the following consumption function that relates consumption C to disposable income after tax income 0 3 b1 7 tY In the above equation 25 is the at tax rate As before we assume that investment government purchases and net exports are exogenous We can now express the model as Y CIGNX Y C b17tYTGNX Solving for the equilibrium level of output in this model gives us 7 3 f G N X Y 17121725 o A 1 unit increase in any of the exogenous variables increases Y by 171617 units Note that 1 1 7171704 lt E The multiplier is smaller under an income tax system than under a lump sum tax system Why Consider a 1 unit increase in G This will have a direct effect of raising Y by 1 unit However C will only increase by b1 7 25 units because 25 units are taxed away by the government In other words at each stage of the feedback process the government takes away a fraction in taxes which reduces the overall impact on the economy If we think of a tax rate of 02 20 the size of the multiplier will be This is considerably less than 10 but still high 1 7 1 170908 E i 3395739 o In particular the government can increase spending or cut taxes and obtain a multiplied pos itive effect on output This would seem to imply that government spending has only positive effects which seems rather unintuitive We need to build on this model by incorporating the impact of government spending on other variables such as investment through changes in the interest rate and in in ation into our model Fall Semester 05 06 Akila Weempana Lecture 12 Growth Accounting and Productivity 1 OVERVIEW H Last week we discussed the Solow model with technology and showed that technology is the key to economic growth technology is said to be the engine of economic growth In this lecture we will discuss how to measure technology We will rst de ne two measures of technology labor productivity and total factor productivity and discuss potential strengths and weaknesses of these measures We will then look at the empirical evidence on the importance of increases in technology using the recent boom in productivity in the US and the East Asian Currency Crisis of 1997 as illustrative examples LABOR PRODUCTIVITY Labor productivity is the most commonly used measure of technology In the popular media you will often see labor productivity simply referred to as productivity Labor productivity is easy to de ne it is output per hour of work You should see from the de nition immediately that labor productivity is not a perfect mea sure of the overall level of technology in the economy For example increases in capital will raise output per hour of work and hence increase labor productivity but we are in fact using more inputs rather than making better use of inputs Labor productivity is however a very good indicator of ef ciency gains in labor intensive industries It also gives us information about the path of wage movements for example high labor productivity implies the potential for higher wages because workers are producing more per hour of work One of the most striking features of the current economic recovery has been the increase in productivity and how it may be related to the boom in computer hardware software as well as the development and widespread use of the internet Higher labor productivity growth is good for the economy because it is strongly correlated with high GDP growth We can see this by looking at a simple de nition GDP GDP Hours WorkedHours Worked Labor Productivity Hours Worked Therefore Growth Rate of GDP Growth Rate of Labor Productivity Growth Rate of Hours Worked One unusual feature of the recent recovery is that the rapid increase in productivity has resulted in an unusual situation a surprising high growth rate of GDP coupled with a slow recovery in employment As you can see from the above equation higher labor productivity growth can lead to higher GDP growth even when there is little or no growth in hours worked So higher productivity can sometimes lead to high unemployment as rms are able to produce more with their existing workers and not resort to hiring new workers As a result you are likely to come across articles that almost seem to be blaming productivity as something bad for the economy This is not what one would consider good economics It is VITAL that you do NOT consider labor productivity to be a bad thing In fact an economy that has labor productivity growth of 2 a year and an increase in hours worked of 15 a year will see GDP growth of 35 a year An increase in labor productivity to 3 a year should in fact make 45 GDP growth more likely rather than reduce the growth rate of hours worked to 05 The following tables summarize some of the relevant data on productivity growth in the United States in the post war period United States 19542004 from same These graphs and the charts we looked at in class illustrate the following important features 7 Productivity growth slowed down in the United States in the 1970s and 1980s 7 It picked up again in the late 1990s and early 2000s Recent labor productivity numbers have been remarkably high 7 GDP growth labor productivity and TFP growth move together 111 TOTAL FACTOR PRODUCTIVITY The second measure of productivity used more by economists but lately also by consulting rms etc is Total Factor Productivity also known as TFP Sometimes this measure is also called Multi Factor Productivity We measure the growth rate of TE using what is known as the Growth Accounting formula a simple formula derived by taking logs and differentiating the production function L 1 7 7 lt agtL B Y K E v a Essentially TFP growth is a residual the portion of output growth that can not be explained by growth in inputs We have to be careful about measuring the inputs for example try to control for improvements in the quality of capital goods and also control for differences in hours worked and the quality of labor Because of measurement and other problems TFP is also known as the Solow Residual what Solow humbly called a measure of our ignorance Recall that the Solow model predicts that the steady state growth of output per capita should be equal to the growth rate of labor augmenting technology Since the growth rate of labor augmenting technology is proportional to TFP we should see a close link between movements in TE and movements in output per worker One of the most important applications of growth accounting was performed by the economist Alwyn Young His papers The Tyranny of Numbers and A Tale of Two Cities studied the driving forces behind economic growth in East Asia by decomposing growth in these East Asian countries into growth from capital growth from labor and growth from technology We will focus our attention on 7 East Asian countries which made remarkable progress in up grading their living standards alleviating poverty equalizing income distribution educating their people etc The 7 countries we focus on are Hong Kong Indonesia Malaysia Singapore South Korea Taiwan and Thailand The dramatic improvements these countries made were re ected in extremely high growth rates of real GDP and real GDP per capita from the early 1960 s to the late 1990 s The 1997 economic crisis hit most of these countries hard some like lndonesia are still in deep trouble The crisis was a hodgepodge of falling currencies spiraling de cits collapsing stock markets high in ation and nancial bankruptcies We will discuss the details of the crisis in a subse quent lecture for now we will concentrate on taking a careful look at the successes that these countries achieved over a 30 year period Decomposing growth is essentially a growth accounting exercise Alwyn Youn separated the growth in these countries into growth from capital accumulation growth from labor accumulation and growth from TFP Young showed that these East Asian countries made remarkable progress in 1 Labor force participation 2 Educational attainment 3 Investment in physical capital SELECTED EAST ASIAN COUNTRIES 19661 However TFP growth was relatively small for all of these countries So Young speculated that despite the stellar record of performance that these countries had displayed over the last 30 years that they would not be able to continue to grow very fast in the future His ideas were essentially grounded on the Solow model long run growth rate could not be higher than the growth rate of technology after all technology was the engine of growth While the above improvements could bring short run improvements in growth rates it seems unlikely that the improvements could be long term Lots of controversy surrounding the analysis in the paper when it rst came out With hindsight Young has been vindicated The lesson for these East Asian countries and for those who lent money to them seems to be that they should not have borrowed thinking that their economies would continue to boom as they had in the past Or at the very least the countries should have made sure that they invested wisely and productively However there are many positive lessons to be learned from the East Asian countries Many countries need to gure out how to accumulate factors like investment and improve educational attainment Fall Semester 05 06 Akila Weempana Lecture 7 Growth Away From Steady State 1 OVERVIEW 0 In the last lecture we examined some properties of the steady state In the lecture before that we drew the graphs for the time paths of k y K and Y in various comparative statics exercises One of the issues left unresolved was the shape of the graph during the transition period Essentially we need to have a better explanation of the growth rates of these variables away from steady state Today s lecture takes a closer look at the behavior of economies away from steady state 0 This is important because many of the interesting growth stories in the world are countries in transition Consider China whose economy grows at 10 a year China couldn t be in steady state because at a 10 growth rate their income would double every 7 years and be 16384 times larger than today in a hundred years time So to understand the behavior of economic growth in China we need to dig deeper into the Solow model 11 GROWTH RATES AWAY FROM STEADY STATE 0 Let s take another look at what the Solow model has to say about growth rates of y and Y away from steady state In order to do this we look at a modi ed Solow diagram obtained from the capital accumulation equation is sy7n6k7n6 is 3k T7n6 k s g 7n6 o The graph for Mia is downward sloping since an increase in k raises the value of the denom inator To put it in terms of derivatives we can show that 5271 3a 7 1WDquot2 lt 0 2 9471 0 Furthermore we can calculate the 2nd derivative as positive because 3a 7 1a 7 2k0quot3 gt 0 In other words the shape of this curve is convex 0 You can also show that limkno Mia 00 and limknoo Mia 0 o n 6 is of course just a horizontal line that doesn t change with I o The picture below graphs these two lines The difference between the k1 and the n 6 lines indicated by the dotted lines in the gure below shows the growth rate of k ie gives us the value of In this diagram for any level of capital per worker k the gap betweenthe downward sloping curve and the horizontal line is the growth rate of capital per worker c We can conclude the following 1 At the steady state the point at which the two lines cross 5 0 k 2 As the economy approaches steady state from below gt 0 but getting closer to O is 3 As the economy approaches steady state from above E lt 0 but getting closer to 0 This is what gives us the concave and convex shapes in drawing the time paths of variables When moving from a lower constant steady state to a higher constant steady state we should see a positive growth rate that is gradually approaching zero ie a concave shape 0 Conversely when moving from a higher constant steady state to a lower constant steady state we should see a negative growth rate that is gradually approaching zero ie a convex shape 0 Using the fact that y k we can also derive the following results for the growth rate of y 1 At the steady state the point at which the two lines cross 0 2 As the economy approaches steady state from below gt 0 but getting closer to O 3 As the economy approaches steady state from above lt 0 but getting closer to 0 0 Basically the Solow model predicts that the further below steady state an economy is the faster output per worker will grow and the further above steady state an economy is the slower output per worker will grow 0 Finally using the fact that Z n we can also derive the following prediction the further below steady state an economy is the faster total output will grow and the further above steady state an economy is the slower total output will grow III MORE SUBTLETIES REGARDING GROWTH RATES AWAY FROM STEADY STATE THIS IS OPTIONAL ONLY FOR THE REALLY CURIOUS c When we discussed comparative static exercises using the Solow model one of the interesting cases occurred when the population growth rate increased from n to n c We showed that in the initial steady state total output was growing at a rate 71 and in the new steady state total output was growing at a rate 71 In the interim our calculations indicated that the growth rate would be lt 71 but we could not say whether or not it would be gt n c We can use the diagram above to show that the transition growth rate is always between the initial steady state growth rate and the new steady state growth rate 0 The picture below graphs the two lines 71 6 the old break even line and n 6 the new break even line 0 At the old steady state where growth was previously zero now growth will be lt 0 Since the difference between the k1 and the n 6 lines indicated by the dotted lines in the gure below shows the growth rate of k we can calculate the exact value of growth as being 9 7n6 E n67n6n7n 179 k0 c We can summarize the growth rates of the key variables in the following table Time 0gt gt717 1 At the old steady state now n 7 n lt 0 Since n we have that at the old steady state n7 n n n lt n 2 As the economy approaches the new steady state from above 71 7 n lt lt 0 but increasing and getting closer to 0 Since g n we have that as we approach the new steady state 71 lt lt 71 but increasing and approaching 71 o In other words the interim growth rate of the K variable is initially 71 but then gradually approaching 71 giving us the shape below It never drops below 71 an IV CONVERGENCE 0 Even though we said that the Solow model did not do a good job explaining differences in steady state growth rates it does better at explaining differences in growth rates across countries that are away from steady state 0 One early explanation for differences in growth rates across countries was the theory of con vergence namely the idea that poor countries would grow faster than rich ones The underlying economic intuition was that because of diminishing returns countries with a low level of k would have a higher marginal product of capital and hence attract more investment and grow faster 0 However the empirical evidence convergence seems to show that convergence only seems to hold within industrialized economies such as the OECD countries If you look at a larger sample of countries then poor countries do not seem to grow faster than rich ones Refer to graphs shown in class 0 Those graphs suggest a modi cation of the theory of convergence among countries with the same steady state level of capital per worker poorer countries will grow faster than rich ones More rigorous analysis can be used to show that the model also predicts that among countries that don t have the same steady state countries that are further below their own steady state grow faster This modi ed theory of convergence is also known as Conditional Convergence Consider the sample of countries in which we failed to nd a link between the level of y and the growth rate of y we now nd a stronger link between the deviation of y from steady state and the growth rate of y Refer to class graphs The difference between convergence and conditional convergence can be shown in the following example Consider the United States and Mali The theory of convergence says that if lt it must be the case that 3 yMALI yUS y MALI y Us Conditional convergence says that this is not necessarily true instead the idea is that if lt then gt 3 regardless of whether Mali was poorer than t UMSALI 9 US 9 MALI 9 US e In other words the theory of Convergence says that a poorer a country is the faster it will grow That theory does not seem to be supported in reality The theory of Conditional Convergence states that the poorer an economy is relative to its steady state the faster output per worker will grow In other words it is not whether a country is poor or whether a country is rich7 but whether it is poor or rich relative to its steady state The Solow model predicts conditional convergence instead of convergence Therefore it does a decent job of explaining differences in growth rates across countries Fall Semester 05 06 Akila Weempana Lecture 6 Assessing the Basic Solow Model I OVERVIEW H o In the last class we looked at a couple of comparative statics exercises The rst was the impact of a change in the saving rate on capital and output in the economy We showed that the change in the saving rate did not have a long run impact on the growth rate of output 0 However there was a short run increase in the growth rate and as a result the economy reached a higher level of steady state output A change in the saving rate is therefore said to have a level effect on output but NOT have a growth effect ie it affects the steady state level of output but not the long run growth rate of output 0 The second was the impact of a change in the population growth rate on capital and output in the economy We showed that the change in the population growth rate while raising both the level and the growth rate of total output in the economy left the level of per capita output lower than it would have been in the absence of the increased population growth 0 Today s class looks at some of the mathematical properties of the steady state to understand how economic changes affect the endogenous variables of the model COMPARING STEADY STATES USING ALGEBRA o In economics we typically use calculus to do comparative statics exercises Given an economic model we would solve for the endogenous variables as functions of the exogenous variables and the parameters then take derivatives or partial derivatives to show how the endogenous variable will change when an exogenous variable or a parameter changes However thus far with the Solow model we have used diagrams instead of calculus to perform the various comparative statics exercises The reason for doing so is that the Solow model is a dynamic model whose behavior is governed by a differential equation the now familiar 1 3y 771 6k equation Since differential equations is not a pre requisite for this course we won t solve this equation for the value of k at a given point in time We can however avoid the complications of the differential equation and use calculus if we restrict our focus to the steady state Why Because at the steady state 0 thus eliminating the troublesome left hand side of the above equation 0 The capital accumulation equation can now be written as using to denote steady state values 0 334 7 n 6k This simpli es to 334 E 3kW n6 fail s 5 170 If n6 i 3 179 k 7 n6 Using the fact that y k we can then show that 7 8 y ltn6gt From these expressions we can see that the Solow model predicts that increases in the saving rate will raise steady state income per capita since digs gt 0 The model also predicts that increases in the depreciation rate and the population growth rate will reduce steady state income per capita ie 23 lt 0 and 33 lt 0 In addition using the fact that k g and y we can show that s a s a KtLt n6 andYtLt n6 From these expressions we can see that the Solow model predicts that increases in the saving i i i i dw rate Will ra1se steady state aggregate 1ncome since is gt 0 Similarly increases in the depreciation rate will reduce steady state aggregate income since dYquot lt 0 Third increases in the size of the population labor force will increase aggregate income dYquot dL Finally an increase in the growth rate of the population will actually increase aggregate income 13 gt O This may seem inconsistent with the above expression given that 71 appears in the denominator but don t forget that n is also part of Lt ie Lt Loam Since exponential functions grow faster than linear functions the Lt term increases faster than the 16gt E dY in gt 0 term decreases implying that We can also take a look at what the algebraic solutions say about steady state growth Since 5 1 91 s n6 n6 we can see that per capita output and capital is constant in steady state the right hand sides of the expressions If 7 and 3f gt m are all parameters Similarly we can see that in steady state K and Y are not constant they are growing over time hence the subscript t because the population is growing In other words steady state aggregate output and capital will grow at the same rate as the population III ASSESSING THE PREDICTIONS OF THE SOLOW MODEL 0 Now that we have an idea about the properties of the Solow model7 let s assess the intuitiveness of the predictions of the Solow model 1 Why are some countries rich and others poor 0 The Solow model predicts that countries with high investment saving rates7 low population growth rates and low rates of depreciation are likely to have more output per worker o The model also predicts that all else being equal7 ie if the investment rates7 population growth rates and depreciation rates are the same7 countries with a larger population are likely to be have larger economies o The predictions of the model are therefore quite sensible in answering this question 2 Why do some countries grow faster than others 0 The Solow model has very little to say about difference in per capita economic growth across countries in the long run all countries have a steady state output per capita growth rate of zero this is an unsatisfying answer and a weakness of the model 0 The Solow model has a little bit more to say about the growth rate of total output it is equal to the rate of population growth This seems to say that countries with high population growth rates should grow faster 0 This is not a very intuitive answer it is more palatable if you think of n as the growth rate of the labor force But the model does not provide us the ability to distinguish the labor force from the population 3 How can economies exhibit sustained economic growth 0 ln per capita terms7 the Solow model does not allow for sustained growth so it may not be helpful for describing the behavior of the Us economy for example We therefore need to expand the Solow model7 by adding technology7 in order to improve its predictions 0 In addition to being intuitive7 predictions of a model should also be consistent with reality7 ie be empirically sound ls it true that a countries with high investment saving rates7 low population growth rates and low rates of depreciation are likely to be richer in per capita terms b among countries with similar population growth rates7 saving rates and depreciation rates7 countries with larger populations have larger economies c all countries have the same steady state growth rate of output per worker and capital per worker namely7 zero d countries with higher rates of population growth will be the ones whose economies will grow faster in the aggregate o In class7 we will also examine the viability of these claims using data for the last few decades for a range of countries Fall Semester 05 06 Akila Weempana Lecture 14 The IS Curve 1 OVERVIEW H In the last lecture we derived the most basic model of economic uctuations using the Keyne sian Cross Model Starting with this class we put together a more advanced macroeconomic model known as the lS LM model 0 We can use this model to examine the impact of scal and monetary policy as well as to study the impact of changes in investment consumption and net exports in the economy An important feature of the lS LM model to keep in mind is that it is a short run model of the economy as you will see the model works with an exogenously given price level 0 Once we have completed our development of the lS LM model we will then extend it to do the Aggregate Demand model which allows us to do intermediate term analysis developing the ability to think intelligently about the impact of policy changes on in ation THE IS Investment Savings CURVE o The lS curve derives a relationship between interest rates and income in the short run It modi es the Keynesian Cross by disposing of the unrealistic assumption that investment is exogeneously determined and instead speci es a simple negative relationship between invest ment and the interest rate 0 The linear investment function is of the form I I 7 Br where r is the real interest rate We can interpret I as what Keynes termed animal spirits changes in investment that are unrelated to the interest rate but come about because of investor con dence for example 0 The parameter 3 measures how much investment responds to the real interest rate 0 The real interest rate nominal interest rate rate of in ation ie r i 7 7139 We use r to refer to an average real interest rate in the economy rather than the rate of return on any particular type of asset 0 An increase in the interest rate reduces investment by making it more expensive for rms to borrow money to make investment purchases and also by increasing the opportunity cost for those who plan to nance investment projects using their own funds By reducing investment high real interest rates will correspondingly reduce GDP Having made these modi cations we can now summarize the goods market in the economy as follows Y CIGNX C C b1itY I I737 G G NX NX c We combine these equations to derive the IS curve all the combinations of Y and r that cause the market for goods and services to clear YC b17tYfi rGNX o This can be simpli ed as 1 Y 17121725 mm WIEEHN Xh Br 0 Since we showed that the multiplier is u 1717317 this can be re written as YMCTGNX7MBT This is the equation for the IS curve7 the relationship between Y and r that ensure that the goods market is in equilibrium spendingproduction 0 Note that when interest rates are high7 investment falls and therefore Y must fall as well the IS curve should show a negative relationship between T and Y This can be shown graphically as follows 7 S Curve III THE SLOPE AND INTERCEPT OF THE IS CURVE 0 One of the quirks of economists is our habit of writing equations of the form M fN and drawing graphs of the inverse N gM Examples include demand and supply curves7 which we write as Q fP but then graph with P on the vertical axis and now the IS curve which we write as Y fr but then draw with r on the vertical axis 0 The lS Curve7 rewritten in a graph friendly but not intuition friendly manner is 17 7 7 7 1 70 I G NX77Y r B lBLH The Slope o The slope of the IS Curve is 37 1 W 67 o The IS curve is steep when the absolute value of the slope is large This occurs when 1 The parameter 3 is small 2 The multiplier u is small What is the intuition for these results Well a steep IS curve means that Y does not respond very much to r In other words a change in the real interest rate does not have a signi cant impact on GDP 0 According to the above math this happens when 3 is small ie when investment does not respond very much to the real interest rate It could also happen when the multiplier u is small because a given change in investment has fewer feedback effects when the multiplier is small The Intercepts o The intercept of the IS curve can be found by setting Y 0 as C I G NX o This can be thought of as the highest possible real interest rate in the economy but for the most part we will have limited use for it in our analysis Of slightly more interest is the horizontal intercept of the IS curve which can be found by setting r 0 to be MC G I NX or limit C I G NX This you may recall is the Keynesian Cross solution of the problem w ere we ignored real interest rates IV SHIFTS SLOPE CHANGES AND MOVEMENTS ALONG THE IS CURVE Movements Along the Curve 0 Since we are graphing the relationship between T and Y the key thing to note is that changes in Y caused by changes in r are re ected as movements along the IS curve 0 When interest rates decrease spending rises and as a result output increases as well This is re ected in a movement to a lower point on the IS curve where interest rates are lower and output is higher 0 Conversely when interest rates increase spending falls and as a result output decreases as well This is re ected in a movement to a higher point on the IS curve where interest rates are higher and output is lower Parallel Shifts of the IS Curve 0 On the other hand changes in Y that are brought about by factors other than interest rates will cause Y to change regardless of the level of interest rates in the economy o The IS Curve7 rewritten in a graph friendly manner is 1 7 7 7 7 1 767 CIGNX 77W B BM 0 We can see that changes in exogenous spending consumer con dence7 investor con dence etc will not change the slope but will change the intercept in other words7 they will cause the IS curve to shift What direction will the IS curve shift in response to changes in these variables We can summarize the changes as follows 1 Increases in consumer con dence C7 investor con dence I7 government purchases or net exports N X will raise expenditure7 and therefore production of goods and services7 shifting the IS curve out Reductions in consumer or investor con dence or government purchases or net exports will reduce expenditure and shift the IS curve in A reduction in lump sum taxes T if they happen to be in the model7 they are not in the model above will increase expenditure on goods and services and therefore increase output as well This will cause the IS curve will shift out Conversely7 an increase in lump sum taxes T if they happen to be in the model will shift the IS curve in to EXAMPLE 1 0 An increase in G will raise spending7 and therefore production7 of domestic goods and ser vices This will cause the IS curve to shift outwards From the equation for the IS curve7 Y MC G I NX 7 u r we can see that u E 1717317 In other words7 an increase in government purchases of AG will cause the IS curve to shift out by 1717314 AG 7 Old IS Curve ew IS Curve V EXAMPLE 2 o A fall in investor con dence will reduce investment spending on goods and services and therefore cause the IS curve to shift in From the equation for the IS curve7 Y MC G I NX 7 u r we can see that u E W ie a decrease in exogenous investment of AI will cause the IS curve to shift in by 1717314 AI ew IS Curve Old IS Curve V Slope Shifts of the IS Curve 0 Remember that the IS Curve rewritten in a graph friendly manner is 1 7 7 7 7 1 T CIGNX 77W B l l W 0 Changes in the multiplier u will not change the intercept but will change the slope of the IS curve As we discussed before if the multiplier becomes larger the IS curve becomes atter and if it becomes smaller the IS curve becomes steeper 0 Given the expression for the spending multiplier of u W we need to think about how changes in b and changes in t affect the multiplier o The intuition is fairly simple the multiplier increases the slope becomes atter if tax rates fall or if the marginal propensity to consume rises H Increases in the marginal propensity to consume 1 will increase the multiplier and make the IS curve atter Conversely decreases in b will make the IS curve steeper to Decreases in income tax rates 25 will increase the multiplier and make the IS curve atter Conversely increases in 25 will make the IS curve steeper EXAMPLE 1 0 An increase in the marginal propensity to consume7 bwhich raises the multiplier u 1717614 and will cause the IS curve to have a atter slope 7 ew IS Curve Old IS Curve EXAMPLE 2 o A higher income tax rate will lower the multiplier u Palliaand will cause the IS curve to have a steeper slope 7 Old IS Curve ew IS Curve V DO I REALLY HAVE TO MEMORIZE ALL OF THIS 0 N07 you do not have to memorize each of these changes The goal is to have an intuitive understanding of the IS curve 0 Keep in mind that the IS curve is summarizing the inverse relationship between interest rates and GDP in the economy If you are in doubt as to how a particular change should be re ected in the IS curve7 you need to only ask two questions First is the change in Y or in r If so then it should be simply a matter of moving to a different spot on the IS curve Second does the change increase or decrease expenditure on domestic goods and services If it is an increase then it should cause Y to rise ie be a rightward movement of the IS curve if the answer is a decrease then it should cause Y to fall it should be a leftward movement of the IS curve That s 95 of the battle All that remains is whether the rightward or leftward movement is a parallel shift or a slope change If the driving force is a change in exogenous spending there will be a parallel shift If the driving force is a change in the multiplier there will be a slope change Fall Semester 05 06 Akila Weempana Lecture 21 Disin ation and the Phillips Curve I OVERVIEW H o In the last lecture we looked at the Phillips Curve and examined the run tradeoff between in ation and unemployment alternatively in ation and output using Okun s law We showed that the tradeoff would only be available in the very short run unless expectations were xed With changing expectations be they rational or adaptive the tradeoff would quickly become unfavorable to the policymaker With rational expectations it is perhaps safe to say that there is no long run tradeoff between in ation and output 0 We can also turn the problem around and think about what the government has to do in order to reduce in ation Let s consider an economy that has been at the natural rate of unemployment with high in ation of say 6 a year for the last few years Suppose the task of the policy maker is to eventually reduce in ation to 3 a year c We consider disin ation under xed expectations and changing expectations both adaptive and rational The analysis is essentially similar to what we covered in the last lecture Now instead of trying to reduce unemployment and thinking of the in ation cost she must pay the policy maker is trying to reduce in ation and thinking of the unemployment cost she must pay DISINFLATION WITH FIXED EXPECTATIONS 0 Let s return to the Phillips Curve we considered in the last lecture 7139 we 7 u 7 5 Supposing under the conditions described above that in ation has been 6 for the last few years and that expected in ation is therefore xed at 6 o For convenience we assume the economy is at the natural rate so that we can represent our starting position at point A on the gure below with we 6 and therefore 7139 6 as well 0 The policy maker is asked to permanently reduce in ation to 3 As you can see this would require that the unemployment rate be raised by 3 percentage points from 5 to 8 Point B on the graph 0 Furthermore since expectations do not change the only way to reduce in ation permanently is to raise unemployment permanently as well The policymaker has a thankless job in this case 7r III DISINFLATION WHEN EXPECTATIONS CHANGE Case 1 Adaptive Expectations Now let s consider the same task reducing in ation from 6 to 3 a year with adaptive expectations Once again to keep things simple we will assume that 713e 731 and that we start off at the natural rate of unemployment Since the slope of the Phillips Curve is 1 in order to reduce in ation by 3 percentage points unemployment has to be raised by 3 percentage points as well Interestingly the monetary policy maker can choose to raise unemployment by 3 percentage points in different ways as we shall see below Example A short severe recession Let s do the same exercise as in the xed expectations case to see how haVing expectations that change impacts the policy maker s actions We represent our starting position at point A on the gure below with we 6 and therefore 7139 6 as well The policy maker is asked to permanently reduce in ation to 3 As you can see this would require that the unemployment rate be raised by 3 percentage points from 5 to 8 Point B on the graph In the next period since in ation today was only 3 expected in ation will now be 3 as well the Phillips Curve shifts down As a result we no longer need to stay at an unemployment rate of 8 and we move back to the natural rate Point C 0 At Point C in ation and expected in ation are both now at 3 unemployment is at the natural rate and we haev permanently reduced in ation after a severe yet short recession 0 This is a much better outcome than the case of xed expectations where the increase in unemployment was permanent 7139 6397 A 3397 C B u u 71395 6 7r Example A long mild recession o It turns out we can accomplish the same task without putting as many people out of work Suppose that instead of raising the unemployment rate by 3 percentage points we instead raised it by 1 percentage point from 5 to 6 This would lower in ation by 1 percentage point given the slope of 1 on the Phillips Curve from 6 to 5 This would move us to Point B in the Figure below Since actual in ation is only 5 instead of 6 expected in ation for next year recall that we assumed 713e 7131 will also be 5 The Phillips Curve will shift down Now if the policy maker keeps unemployment at 6 then in ation will fall to 4 Point C on the graph Furthermore in the next period expected in ation will now be 4 This causes the Phillips curve to shift down again 0 ln period 3 the policymaker can reduce in ation to 3 by continuing to keep unemployment at 6 Point D on the graph As before expected in ation falls this time to 3 and the Phillips Curve shifts down again 0 ln period 4 we no longer need to keep unemployment at 6 to reduce in ation to 3 Since expected in ation has come down to 3 we can move the economy back to the natural rate Point E on the graph at which point the economy will remain at 3 in ation since expected in ation and actual in ation now coincide again resulting in no further shifting of the Phillips Curve 7r we6 we5 we3 14 0 So by increasing unemployment by 1 percentage point above the natural rate and keeping it there for 3 periods we managed to reduce in ation by 3 percentage points Compare that to the previous case where we raised unemployment by 3 percentage points a sharper recession but only kept it there fore 1 period a shorter recession 0 When we have this simplest form of adaptive expectations we can easily come up with many different plans Since reducing in ation by 3 percentage points required a total of 3 percentage points of unemployment we could choose any combination ofm extra points of unemployment and n periods where m x n 3 o In other words raising unemployment by 3 percentage points for 1 period raising unemploy ment by 1 percentage points for 3 periods raising unemployment by 05 percentage points for 6 periods by 15 percentage points for 2 periods all would be possible paths of disin ation o The policymaker gets to choose what she thinks is best for the economy Case 2 Rational Expectations 0 Some economists believe that disin ation can be done painlessly and quickly under rational expectations The pre requisite for this is the policy maker s ability to convince the agents in the economy that she represents a clean break with the past 0 For example under adaptive expectations agents would always expect last period s in ation However someone who inherits the economy described in the previous section can reduce in ation immediately WITHOUT a recession if she can credibly convince people to reduce their in ation expectations to 3 0 Then as can be seen in the graph below we can immediately move from 6 in ation to 3 in ation as the Phillips Curve shifts down go from Point A to Point B in the graph below 7r 6 7 A 3 7 B I M u 71395 6 7139s 3 IV SUMMARY OF PHILLIPS CURVE AND ISLMAD MODEL SECTIONS OF THE CLASS 0 Over the last few lectures we have developed a simple model of the economy and examined the monetary policy maker s response to various economic developments We also took a closer look at the apparent tradeoff that the monetary policy maker faced between the two key macroeconomic variables in ation and unemployment c There are some lessons that we can take away from this analysis 1 to DJ The output gap is not the only variable that affects in ation changes in expected in a tion can have an impact on current in ation So a policymaker with a good reputation for ghting in ation can bene t from the fact that people s expectations of low in ation actually help bring about low in ation The tradeoff that apparently exists between in ation and unemployment is only short run7 at best A monetary policy maker who systematically tries to lower unemployment below the natural rate will only succeed in causing higher and higher rates of in ation to appear in the economy So you may as well try to keep Y at I Expectations work against a monetary policy maker who is trying to systematically push u below the natural rate7 however7 expectations can be very helpful when a policymaker is trying to reduce in ation in the economy Some economists argue that disin ation can be painless if agents are fully rational and the monetary policy maker is completely credible Fall Semester 05 06 Akila Weempana Lecture 18 The Complete Model I OVERVIEW 0 In the last class7 we looked at the complete model involving both IS LM analysis and aggregate demand analysis We showed that the relationship between the level of potential output and the short run equilibrium output from the IS LM model determine whether prices increase or decrease in the intermediate run 0 Today we will take a close look at how we can use the complete model to analyze monetary policy decisions as well as scal policy decisions Adding in ation to the IS LM model greatly enhances its usefulness as a tool for evaluating monetary policy decisions in particular 0 In the next class7 we will return to some of the applications we examined using the IS LM model and take a fresh look at them using the aggregate demandaggregate supply model 11 FISCAL POLICY IN THE LONG RUN Case 1 An Increase in G 0 Suppose the economy was initially at potential output If the government increases the purchases of goods and services then the IS curve will shift out and the AD curve will shift out as well In the short run interest rates will rise from To to 71 output will rise from Y to Y1 and prices will not change 0 From the AD curve we see that the short run equilibrium level of output will exceed potential output Then over time prices will increase 0 As P increases the LM curve will start shifting back7 this process will continue until the economy returns to the original level of potential output In the long run interest rates are much higher at r2 Output has returned back to potential output Y Prices7 however are higher at P Notice that the long run multiplier effects of an increase in G is zero Output is unchanged in the long run c We can get intuition for why the multiplier effects are smaller by looking at what happens to the various components of the IS curve and the LM curve when G increases you should be able to gure out what happens when G decreases 7 C C b17tY lt gt since Y is unchanged 7 I T7 Br l since r increased 7 G T G increased7 according to the question 7 NX lt gt NX is exogenous and unchanged 7 MS lt gt Exogenous and unchanged 7 Md lt gt l since r increased and T since P increased We know that they must offset because MS Md and MS lt gt Case 2 A Tax Cut 0 Let s assume the economy starts out at YThe rst task is to look at what would happen to the economy as a result of the tax cut The tax cut will swing the IS curve out ie shift it out and make it atter and also shift the AD curve out as well 0 In the short run7 output rises to Y1 interest rates rise to T1 and prices remain unchanged Since output is above potential prices will rise over time shifting the LM curve back gradually to LM The long term impact is to raise prices to P leave output unchanged at Y1 and leave interest rates higher at 72 See below 0 Again7 notice that the long run effects of a tax cut is zero Output is unchanged in the long run 72 Tl LM LM ya x p LRAS We can look at what happens to the various components of the IS curve and the LM curve when t decreases you should be able to gure out what happens when t increases C O b1 7 tY T since Y is unchanged but t is lower I f 7 Br l since r increased G lt gt G is exogenous and unchanged NX lt gt NX is exogenous and unchanged M 9 lt gt Exogenous and unchanged Md lt gt l since r increased and T since P increased We know that they must offset because MS Md and MS lt gt III MONETARY POLICY IN THE LONG RUN We can use this model to examine the impact of monetary policy in the long run Suppose the economy was initially at potential output If the Fed increases the supply of money then the LM curve will shift out and the AD curve will shift out as well In the short run interest rates will fall from To to 71 output will rise from Y to Y1 and prices will not change since SRAS is horizontal From the new AD curve we see that the short run equilibrium level of output exceeds potential output Over time prices will increase as the economy moves back to the level of potential output As P increases the LM curve will start shifting back7 this process will continue until the LM curve returns back to the original location In the long run interest rates have returned to the original level of To Output has also returned back to potential output Y Prices7 however are higher at P While the short run effects of expansionary monetary policy in an economy that was at potential was to raise Y7 in the long run7 all the policy manages to accomplish is to raise prices7 ie cause in ation o This is one of the most important ideas in macroeconomics that monetary policy can only in uence the real economy ie output in the short run when prices are xed or sticky but not in the long run when prices are exible Y3 Y1 Y3 Y1 7 C C b17tY lt gt since Y is unchanged 7 I f7 Br lt gt since r is unchanged 7 G lt gt G is exogenous and unchanged 7 NX lt gt NX is exogenous and unchanged 7 M9 T lncreased 7 Md T Since P increased Fall Semester 05 06 Akila Weempana Lecture 23 Investment I OVERVIEW H o In the last class we explored the microeconomics underlying consumption in more detail We moved beyond the simple Keynesian consumption function and explored two forward looking theories of consumption the life cycle hypothesis and the permanent income hypothesis If consumption is the largest component of GDP then investment is the most volatile com ponent of GDP and perhaps also the most important from a long term perspective of the economy Today s lecture takes a closer look at investment 0 We divide investment into 3 parts H Business xed investment structures and equipment 104 of GDP to Residential investment housing newly built as residences or for rental purposes 42 of GDP OJ Inventory investment goods produced but unsold and kept in storage 08 of GDP 0 Most of our attention will be focused on the business xed investment and residential invest ment decisions INTRODUCTION TO THE TERM STRUCTURE OF INTEREST RATES o The monetary policy maker typically in uences short term interest rates by hisher actions in the United States the Federal Funds rate is the rate most directly in uenced by the Fed 0 However the Fed Funds rate is an interest rate at which banks lend and borrow money overnight However most investor decisions deal with much longer term interest rates mort gage loans are for 30 years business loans can be for 1 10 years etc The relationship between short and long term interest rates also known as the term structure of interest rates is one of the most important and relevant for day to day life economic relationships Therefore to understand the impact of monetary policy on investment we need to better understand the relationship between short term interest rates and long term interest rates in the economy Most interest rates student loans car loans mortgages etc are based off the interest rate on government bonds issued by the Federal government which are considered to be safe assets Thus a bank looking to make a 30 year mortgage loan to a home buyer will charge an interest rate that is somewhat higher than the interest rate she could earn on a 30 year government bond After all if she can earn a riskless return by buying a 30 year government bond she would need a higher return to make a risky mortgage loan o This is also why it pays for you as individuals to have good credit The better your credit is the lower the interest rate you will have to pay on a loan since the lender will charge you a lower premium over the safe return Bonds 0 You should have learned about the basics of the bond market in 102 the following is a brief refresher course 0 A bond is a nancial instrument that promises the holder a xed sum of money at a pre speci ed date in the future which is also known as the maturity date Some bonds also promise the holder a stream of xed interest payments known as coupon payments in the meantime c There are three different types of bonds bonds issued by the Us government bonds issued by various state and local governments and bonds issued by private and public corporations 0 Bonds issued by the Us government fall into three categories Treasury Bills Treasury Notes and Treasury Bonds Treasury Bills or T Bills as they are popularly known have durations of 13 weeks 26 weeks and 52 weeks Treasury Notes come in durations of 2 years 5 years and 10 years Treasury bonds have a 30 year term 0 Most bonds have a face value or par value which is the amount that the holder of the bond is entitled to at the end of the period The bond also has a coupon rate which is the amount of money a person will receive in a year divided by the face value of the bond o If you buy a 30 year Treasury bond with a face value of 1000 and a coupon rate of 5 then you will be holding an instrument that pays you 1000 after 30 years and also pays you 50 per year in the interim period c All these bonds are traded on a bond market You can buy bonds directly from the issuer the Us government for example holds auctions in which they sell bonds or on a secondary bond market What Affects the Price of Bonds 0 The worst enemy of bond investors is in ation Higher in ation reduces the face value and the value of the stream of interest payments of the bond So the price of bonds will start falling The fall in the price of bonds is linked to the general rise in interest rates that take place in the presence of rising in ation 0 So rising interest rates in the rest of the economy tend to reduce demand for and the price of bonds Reductions in interest rates tend to raise demand for and the price of bonds 0 The continuously changing price of the bond makes it important to calculate the yield of the bond which can differ from the coupon rate of the bond 7 If for example we purchased the 1000 bond with a coupon rate of 5 for 975 then the actual interest rate the yield earned by the owner of the bond is in fact higher than 5 Since the owner is making 50 a year on a 975 investment she is actually earning 513 7 Similarly if the price of the bond was 1050 then the yield of the bond is only 465 o The price of the bond and the yield of the bond move in opposite directions 0 As we pointed out earlier interest rates in the overall economy and bond yields tend to move together How Reliable are Bonds 0 Since buying a bond means exchanging money today in exchange for nothing more than a written promise for future payments one has to always worry about the reliability of the issuer 0 Government bonds issued by the Federal Government are assumed to be safe while bonds issued by state and local governments vary dramatically in quality Similarly bonds issued by GM are very different from bonds issued by Mushy Peas R Us in terms of how reliable the issuer is c There are several services that rate the reliability of bonds much like your credit report assesses your creditworthiness The most well known of these ratings services are Moody s and Standard and Poor s Standard and Poor s rates its bonds AAA AA A BBB BB B 000 CC with and for extra differentiation Moody s uses a ratings system Aaa Aa A Baa Ba B Caa and C The AAA category generally consists of the super safe blue chip companies 0 Typically the lower your bond rating the higher the interest rate you have to offer in order to compensate people for holding a more risky bond So companies with a AAA rating are able to borrow money a lot cheaper than a company with a CCC rating can 0 Since US government bonds carry virtually no default risk they become useful as bench marks for other interest rates in the economy So 30 year mortgage rate uctuations are closely related to uctuations in the yield on government bonds If we understand the rela tionship between the yields on government bonds of differing maturities we will have a good understanding of how other interest rates behave in the economy The Expectations Hypothesis 0 A simple theory of the relationship between long term bonds and short term bonds can be built using the idea that a perfectly valid alternative to buying a 10000 ten year bond would be to buy two 5 year bonds one today and one ve years from now which will guarantee a 10000 payment at the end of 10 years 0 Using rm to denote the annual yield at time t on a bond of duration m we can express this simple equivalency as 10710 5T5 5T5t5 This simpli es to the following intuitive relationship 1 710 5 mt Tst5l c We could have just as well have calculated the cost of buying 10 successive 1 year bonds to guarantee us 10000 at the end of 10 years In that case we would get the following relationship 1 710 E 71 Tit1 T1t2 Tit9l o In other words the yield on the 10 year bond would be the average ofthe yields on 10 successive 1 year bonds This relationship is known as the Expectations Hypothesis it basically gives us a way of understanding the term structure of interest rates by stating that long term interest rates are equal to the average of expected short term interest rates 0 To put it another way the expectations hypothesis states that if short bond yields are expected to rise over time then current long bond yields which are an average of today s and rising future short bond yields would exceed current short bond yields 0 In contrast if short bond yields are expected to fall over time then we would expect to nd that current long bond yields are lower than current short bond yields Yield Curve 0 The relationship between short term interest rates and long term interest rates in the economy can be summarized by a yield curve which is a graph of bond yields against bond durations The shape of this yield curve has important implications for the path of monetary policy Yield 3 mo 6 mo 12 mo o If the yield curve is upward sloping as shown above long term yields exceed short term yields the expectations hypothesis states that short term yields are expected to rise over time Yield Conversely if the yield curve slopes down as shown above then short term yields exceed long term yields according to the expectations hypothesis short term yields are supposed to decrease over time Finally if the yield curve were at then long term yields are equal to short term yields the expectations hypothesis states that short rates are supposed to be constant Monetary Policy and the Yield Curve How does this all relate to monetary policy Suppose the Fed announces that they are lowering short term interest rates today with more interest rate cuts to follow in the near future If short rates are expected to decline over time then we would expect that long term interest rates today will fall as well Lower long rates will mean that all the interest rates that are relevant to consumers will fall and as a result the economy will bene t from extra spending by rms and consumers So the Fed is able to transmit its policy actions which affect very short term rates to the real economy which depends on long term interest rates by creating expectations about the path of interest rate movements Understanding the expectations hypothesis and the term structure of interest rates is therefore an important component of understanding how monetary policy decisions are transmitted to the real economy Fall Semester 05 06 Akila Weempana Lecture 10 Comparative Static Analysis I OVERVIEW In the last lecture we derived the Solow model with technology We drew a modi ed version of a Solow diagram in terms of capital per effective worker and then looked at the properties of the steady state In the steady state capital per worker and output per worker grow at the rate of technology while capital and output grow at the rate of population the growth rate of technology Today s lecture looks at the results of some comparative static exercises using the Solow model with technology As with the basic Solow model we can look at the economic impact of changes in the rate of population growth the saving rate the rate of depreciation or the level of capital or labor in the economy In addition to these changes we can also look at changes in the growth rate of technology as well as the impact of changes in the level of technology As I mentioned earlier hopefully adding technology to the model will preserve the sensible predictions of the basic Solow model and improve some of the less sensible predictions of the basic model II SAMPLE COMPARATIVE STATICS EXERCISE An Increase in the Saving Rate Suppose the economy is at the steady state when the saving rate increases from s to s For simplicity assume that this is the only change in the economy We can use the Solow diagram to illustrate the effects of the change in the diagram the saving per worker line shifts upwards from 3y to 33 At the old steady state 93 saving per worker exceed the level of break even investment per worker 5373 gt g n 3153 therefore I increases This process continues until the new steady state is reached At this new steady state the saving per worker line is once more equal to break even investment per worker 5 37 9 n therefore k does not change This is illustrated in the diagram below Savinglnvestment per effective worker 0 Let to be the point at which the saving rate increased and 251 be the time at which the economy returned to steady state We can draw the following graphs to show the path of k and y lnI lny ln I51 1n Iii I I I I ln If I ln 7 I I I I 0 Note in the graph for I 1 Before to the economy is at steady state I is constant at 2 Between to and t1 7 I is increasing over time see Solow diagram 3 After 251 the economy is back at steady state I is constant at 0 NOTE The dotted line shows the path of the variable in the absence of an increase in the saving rate 0 Since y IE and 04 is constant7 the graph for y looks exactly the same as the graph for 0 Since nothing happened to technology or labor they continued to grow exogenously at rate 9 and 71 respectively the graphs for A and L can be drawn easily c We can use these the graphs for I and y along with the graph for A to deduce the behavior of k and y using the fact that k g and y 0 Before to7 I is constant Therefore if A is increasing at a rate 9 then k must also be increasing at a rate 9 in order to keep the ratio constant 0 Between to and 2517 I is increasing over time Given that A is increasing at a rate 9 then k must be increasing at a rate gt g in order to make the ratio grow 0 After 251 the economy is back at steady state I is constant Given that A is growing at a rate 9 then k must also be growing at a rate 97 as in the case before to o The graph for y can be derived in the same way and in this case will look identical to the graph for k lnk lny 0 Finally we can use the graphs for k and y along with the graph for L to deduce the behavior of K and Y7 using the fact that k and y o I will leave it up to you to check that the graphs look like the following An Increase in the Growth Rate of Technology 0 Suppose the economy is at the steady state when the growth rate of technology increases from g to 9 For simplicity7 assume that this is the only change in the economy 0 Then the break even investment per effective worker line becomes steeper At the old steady state7 saving per e ective worker lies below the level of break even investment per effective worker therefore k decreases 0 Why does this happen Well7 at the old steady state7 the break even requirements are higher with better technology more investment needs to be used to keep capital per effective worker constant Essentially7 more investment is needed to make use of the faster growing technology 0 This process continues until the new steady state is reached At this new steady state7 saving per effective worker is once more equal to break even investment per effective worker o The Solow diagram would look as follows Savinglnvestment per effective worker 9 n5 9n615 31 o The dynamics ofthe endogenous variables I and y can be determined using the Solow diagram 0 The graphs for I should then be constant at until to at which point I begins to decline until 251 when it reaches its new steady state kf where k becomes constant again 0 Since y Igu 7and 04 has not changed7 the graph for 37 looks identical to the graph for k in lny o The evolution of technology is more interesting here There is an increase in the growth rate of technology at to causing the slope of the curve to change from g to g gt g The growth of the labor supply is constant at a rate 71 lnA lnL o Xs before7 we can determine the time paths of the variables k and y from the time paths of Is y and A 0 Consider the behavior of k where that I Before to7 I is constant Therefore since A is increasing at a rate 9 then k must also be increasing at a rate 9 0 Between to and 2517 I is decreasing Given that A is increasing at a rate at a rate 9 gt 9 then k must be increasing at a rate lt 9 0 Recall once again that we can only deduce that the the growth rate of k must be lt 9 using this technique but as we showed in an earlier class the growth rate is g lt lt 9 0 After the economy is back at steady state I is constant Given that A is now growing at a rate 9 then k must also be growing at a rate 9 ie k is growing faster than it did before 0 The analysis for y will be identical since we can use the fact that y to deduce the time path for y from the time paths for y and A lnk lny o The basic intuition for why an increase in the growth rate of technology lowers steady state output per effective worker comes from the fact that at the old steady state the break even requirements are higher with better technology more investment needs to be used to keep capital per effective worker constant Essentially more investment is needed to make use of the faster growing technology 0 We can see however that capital per worker and output per worker are both on higher growth trajectories even though it takes time for the economy to reach the higher growth part of g c As before we can use either math or intuition to determine the time paths of the variables K and Y from the time paths of k y and L Once again I leave it up to you to show the following time paths for K and Y Fall Semester 04 05 Akila Weempana Lecture 5 The Phillips Curve I OVERVIEW H 0 Over the last few lectures we rst developed then worked with a simple model of the macroe conomy the AD IA model One component of the AD IA model that we did not really spend much time on was the process by which the IA curve shifts both in the short run and over time o In today s class we will go over the Phillips Curve a topic which you learned about in Economics 202 The Phillips curve describes the dynamics of in ation ie tells a more detailed story about how the IA curve shifts over time We will rst review key concepts of the Phillips Curve that should be familiar with and then think about two different scenarios faced by a monetary policy maker i trying to bring unemployment down and calculating the cost in terms of higher in ation and ii trying to bring in ation down and calculating the cost in terms of higher unemployment THE PHILLIPS CURVE 0 First let s digress a little to look at another important macroeconomic variable that we have not discussed very much in the class namely unemployment In order to be counted as unemployed a worker has to be in the labor force looking for a job but unable to nd one The unemployment rate can be written as u where L is the size of the labor force and U is the number of unemployed workers The labor force is essentially the number of people 16 years of age or over who are either working or looking for work When Y Y unemployment is said to be at its natural rate u u In general the natural rate of unemployment is not zero bc people will always be losing jobs for some reason technology trade etc The natural rate is high when the job losing rate is high and when the job nding rate is low Countries can have different natural rates of unemployment For example European coun tries which have low job nding rates will have high natural rates while Japan which has low job losing rates has a low natural rate of unemployment In the ADIA model if Y gt Y then in ation would rise If Y lt Y then in ation would fall We can transform this into a relationship between in ation and unemployment by using what is known as Okun s law Okun s law essentially says that the deviation of Y from Y is negatively related to deviations of u from u So if u lt u then in ation would rise If u gt u then in ation would fall In the long run in ation would neither rise nor fall but remain study at a level that is determined by expected in ation and by in ation shocks The following mathematical relationship captures the Phillips Curve 7ft1 7r51 Nut U Et1 In the above77rt1 is the percent change in price from time t to time 25 17549 7 sometimes written as Et7rt1 is the expected in ation rate7 ie what we think at time t the percent change in price from time t to time t1 will be Et1 captures supply shocks to in ation such as oil price shocks that take place between time t and time 25 1 and ut 774 is the difference between the current unemployment rate and the natural rate In the above relationship is a parameter that measures the sensitivity of in ation to movements in unemployment This version of the Phillips Curve7 developed by Milton Friedman and Edmund Phelps in the 1960 s is what is referred to as the modern Phillips Curve Expectations Augmented Phillips Curve lt essentially relates in ation from this period to the next to three things the state of the economy this period7 this period s expectations of in ation between now and the next period and supply shocks that could hit the economy between now and the next period These 3 components of in ation have more formal names 1 The we term is called expected in ation This is the rate of in ation that can exist even when the economy is at full employment to The 7u 7 u term is called demand pull in ation This is the more traditional in ation that results from the strength or weakness ofthe economy When unemployment dips below the natural rate output is above potential then there is in ation in the economy because demand is greater than what the economy can produce over the long run OJ The 6 term is known as cost push in ation this term captures all other shocks to in ation unrelated to expectations and to labor markets A fall in the price of oil can be interpreted as a negative 6 while a rise in the price of oil can be interpreted as a positive 6 We can also lag the equation back one period and write it in a more familiar form as 7rt 713957 ut1 7 u 6t This simply states that the change in prices from last period to this period7 depends on what we expected in ation to be this period7 unexpected supply shocks that hit the economy this period and what the state of the economy was last period How are expectations formed We can think of three different types of expectations 1 Fixed expectations agents in the economy form expectations about what in ation will be and they don t deviate from these expectations While this helps us obtain a useful benchmark7 this type of xed expectations is clearly unrealistic to Adaptive expectations depend only on the past history of the economy eg 713e 7131 In this case7 once in ation enters the economy it becomes hard to get rid of As Solow put it When we expect in ation7 we have in ation and when we have in ation we expect in ation 3 Rational expectations people form expectations based on all available information in cluding the past history of the economy III THE INFLATIONARY COST OF LOWER UNEMPLOYMENT c We will rst examine the cost in terms of higher in ation that a policy maker trying to reduce unemployment below the natural rate would have to bear Case 1 Fixed Expectations 0 In the short run7 provided that expected in ation stays constant7 a policy maker who controls aggregate demand can trade off in ation for unemployment c We can illustrate this best by thinking of a simple example Consider a Phillips Curve of the form 7rt1 7r1 7 ut 7 u Et1 and let s suppose that 17 the natural rate of unemployment is 5 and that expected in ation will ALWAYS stay constant at 2 Then the Phillips Curve can be written as 71341 71ut 7 o A graph of this Phillips Curve is given below Suppose also that the economy is currently at potential output so unemployment is at the natural rate 713 the rate of in ation between the current period and next period can then be found at point A on the graph we can also calculate it mathematically as being m1 002 7 005 7 005 002 E 2 0 Now suppose that the policymaker wants to reduce unemployment below the natural rate of unemployment to say 4 Because expectations do not change she can do so by increasing in ation to 7rt1 002 7 004 7 005 003 E 3 This is represented as point B in the diagram below Similarly7 if she wants to reduce unemployment to 3 This can be found either graphically or by looking at the Phillips Curve to see that 7rt1 002 7 0037 005 a 004 E 4 This is represented as point C in the diagram below 7rt1 4397 C 3397 B 2397 A I I I I ut 376 476 u Case 2 Adaptive Expectations 0 When expectations are changing it becomes very di icult for a policy maker who controls aggregate demand to trade off in ation for unemployment in the long run 0 We can illustrate this best by thinking of a simple example like before Suppose that expec tations are adaptive To keep things even more simple we further assume that the adaptive expectations are of the form 7r1 7139 Let s also suppose that 1 and the natural rate of unemployment is 5 o The Phillips Curve for this economy is given by 7rt1 mi 7 ut 7 005 0 Suppose that the in ation rate from last period to this period 7139 was 2 and that unemploy ment is currently at the natural rate7 at 5 We can then calculate that the actual rate of in ation to be 7rt1 002 7 005 7 005 002 E 2 o The Phillips Curve can be graphically displayed in the gure below7with the initial point represented as point A 7r 57 47 C 37 B 8 27 I 7ft3 4 A 7rf2 3 7rf1 2 4 76 u Ut 0 Now suppose as before that the policymaker wants to reduce unemployment at time t to 4 She can do so if she s willing to tolerate an increase in in ation to 7rt1 3 Point B on the graph lf expectations are adaptive however the expected value of in ation won t be constant In the next period since actual in ation turned out to be 7rt1 3 people will revise their expectations 7rf2 3 This causes the Phillips Curve to shift upwards Why When unemployment is at its natural rate in ation is equal to expected in ation However expected in ation has now increased to 3 so the curve must have shift up 0 ln period 25 1 the policy maker will have to be willing to tolerate an in ation rate of 7rt2 4 just to keep unemployment at ut1 4 Point C on the graph The tradeoff has become more unfavorable 4 in ation for 4 unemployment instead of 3 in ation for 4 unemployment The tradeoff will continue to become more unfavorable because in period t 2 expected in ation will now be 7r3 4 This causes the Phillips curve to shift upwards again The policymaker has to be willing to tolerate an in ation rate of 7rt3 5 in order to keep unemployment at ut2 4 Point D on the graph This shift up of the Phillips Curve will continue and make the long run tradeoff seem very unattractive since very high in ation rates are needed to keep unemployment below the natural rate Case 3 Rational Expectations o If expectations were rational in the country described in the previous example we will be formed on all the information available to the agents in the economy not just the history of in ation c We can show that under rational expectations the tradeoff between in ation and unemploy ment will be even worse than in the previous case Suppose that in ation had been constant at 2 for a while so that we start at point like A with 7rf1 2 and therefore n1 2 c As in the previous case we move to point B when the government reduces unemployment to at 4 resulting in an in ation rate of 7rt1 3 0 ln period t people expected 2 in ation but the government gave them 3 in ation as a byproduct of their quest to reduce unemployment Therefore agents may revise their expectations upwards to 7rf2 3 in the next period If the government wants to keep the economy at 4 unemployment Ut1 4 then in ation will rise to 4 n2 4 Point O So far the analysis is similar to the adaptive expectations case Period 25 2 is where things may start to diverge In the adaptive expectations case people automatically revised their expectations upwards to 7r3 4 since actual in ation in period t 2 was 4 However agents who are rational may not behave in the same manner For example they may think in the following way hmm when I expected 2 in ation the government gave me 3 and when I expected 3 in ation they gave me 4 So ifl expect 4 they will most likely give me 5 so I should just make all my decisions with an expected in ation rate of 5 In other words they may set 7r3 5 o This causes the Phillips Curve to shift upwards by more as expected in ation increases to 5 instead of 4 Then the government needs to tolerate 7rt3 6 to keep the economy at the current level of unemployment Point D on the graph In the next period expected in ation may climb even higher and the tradeoff becomes untenable much more rapidly One could even argue there is no tradeoff beyond more than a couple of periods under rational Wag 5 7rf2 3 2 u IV THE UNEMPLOYMENT COST OF LOWER INFLATION c We can also turn the problem around and think about what the government has to do in order to reduce in ation Let s consider an economy that has been at the natural rate of unemployment with high in ation of say 6 a year for the last few years Suppose the task of the policy maker is to eventually reduce in ation to 3 a year c We consider disin ation under xed expectations and changing expectations both adaptive and rational The analysis is essentially similar except that now7 instead of trying to reduce unemployment and thinking of the in ation cost she must pay7 the policy maker is trying to reduce in ation and thinking of the unemployment cost she must pay Case 1 Fixed Expectations 0 Let s return to the Phillips Curve we considered in the last set of examples 7rt1 7r1 7 ut 7 5 Suppose that in ation has been 6 for the last few years and that expected in ation is therefore xed at 6 o For convenience we assume the economy is at the natural rate7 so that we can represent our starting position at point A on the gure below with 7rf1 6 and therefore n1 6 as well The policy maker is asked to permanently reduce in ation to 7rt1 3 As you can see this would require that the unemployment rate be raised by 3 percentage points7 from 5 to 8 Point B on the graph 0 Furthermore7 since expectations do not change7 the only way to reduce in ation permanently is to raise unemployment permanently as well The policymaker has a thankless job in this case 7Tt1 lt 7rte1 6 6 7 A 3 7 B 39 M Case 2 Adaptive Expectations Now let s consider the same task reducing in ation from 6 to 3 a year with adaptive expectations Once again to keep things simple we will assume that 7r1 7139 and that we start off at the natural rate of unemployment Since the slope of the Phillips Curve is 1 in order to reduce in ation by 3 percentage points unemployment has to be raised by 3 percentage points as well Interestingly the monetary policy maker can choose to raise unemployment by 3 percentage points in different ways as we shall see below Example A short severe recession Let s do the same exercise as in the xed expectations case to see how haVing expectations that change impacts the policy maker s actions We represent our starting position at point A on the gure below with 7rf1 6 and therefore 7rt1 6 as well The policy maker is asked to permanently reduce in ation to 3 As you can see this would require that the unemployment rate be raised by 3 percentage points from 5 to 8 Point B on the graph ln period 25 1 since in ation was only 7rt1 3 expected in ation will now be 7rf2 3 as well the Phillips Curve shifts down As a result we no longer need to stay at an unemployment rate of ut1 8 and we move back to the natural rate Point C At Point C in ation and expected in ation are both now at 3 unemployment is at the natural rate and we haeV permanently reduced in ation after a severe yet short recession This is a much better outcome than the case of xed expectations where the increase in unemployment was permanent 7ft1 6 7 A 3 7 C B u u 7139 1 7 6 Example A long mild recession o It turns out we can accomplish the same task without putting as many people out of work Suppose that instead of raising the unemployment rate by 3 percentage points we instead raised it by 1 percentage point from at 5 to at 6 This would lower in ation by 1 percentage point given the slope of 1 on the Phillips Curve from n1 6 to 7rt1 5 This would move us to Point B in the Figure below 0 Since actual in ation is only 5 instead of 6 expected in ation for next year will also be 7rf2 5 The Phillips Curve will shift down Now if the policy maker keeps unemployment at ut1 6 then in ation will fall to 7rt2 4 Point C on the graph Furthermore in the next period expected in ation will now be 7r3 4 the Phillips curve to shift down again 0 ln period t2 the policymaker can reduce in ation to n3 3 by continuing to keep unemployment at ut2 6 Point D on the graph As before expected in ation falls this time to 7r4 3 and the Phillips Curve shifts down again 0 ln period t3 we no longer need to keep unemployment at ut3 6 to reduce in ation to n4 3 Since expected in ation has come down to 3 we can move the economy back to the natural rate Point E on the graph at which point the economy will remain at 3 in ation since expected in ation and actual in ation now coincide again resulting in no further shifting of the Phillips Curve 7rt1 71f 6 7rf2 5 14 7134 3 0 So by increasing unemployment by 1 percentage point above the natural rate and keeping it there for 3 periods we managed to reduce in ation by 3 percentage points Compare that to the previous case where we raised unemployment by 3 percentage points a sharper recession but only kept it there fore 1 period a shorter recession 0 When we have this simplest form of adaptive expectations we can easily come up with many different plans Since reducing in ation by 3 percentage points required a total of 3 percentage points of unemployment we could choose any combination ofm extra points of unemployment and n periods where m x n 3 o In other words raising unemployment by 3 percentage points for 1 period raising unemploy ment by 1 percentage points for 3 periods raising unemployment by 05 percentage points for 6 periods by 15 percentage points for 2 periods all would be possible paths of disin ation o The policymaker gets to choose what she thinks is best for the economy Case 3 Rational Expectations 0 Some economists believe that disin ation can be done painlessly and quickly under rational expectations The pre requisite for this is the policy maker s ability to conVince the agents in the economy that she represents a clean break with the past 0 For example under adaptive expectations agents would always expect last period s in ation However someone who inherits the economy described in the preVious section can reduce in ation immediately WITHOUT a recession if she can credibly conVince people to reduce their in ation expectations to 7r1 3 0 Then as can be seen in the graph below we can immediately move from 6 in ation to 3 in ation as the Phillips Curve shifts down go from Point A to Point B in the graph below 7ft1 6397 A 3397 B I M u wt 6 7135 3

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