Intermediate Macroeconomics ECON 3020
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Date Created: 09/21/15
Chapter 6 Economic Growth Empirical facts of economic growth Growth Accounting Identifying the sources of economic growth Malthusian Growth model The Solow exogenous growth model Main Question What affects the level standard of living and rate of growth rate of change in the standard of living of per capita consumption or output We study both aggregate variables eg Y and per capita variables Y N We associate the term standard of living with per capita variables We will study changes in the economic environment that lead to level effects growth effects or both Per Capita Real GDP JAPAN 56 x PERU 075 TAIWAN 56 THALAND 37 1955 1959 1963 0 CD F 1979 1983 1987 Some Facts to be Explained Since the industrial revolution there has been sustained growth in world per capita income PCI Growth experiences are different across countries at any point in time Levels of PCI tend to converge over time among regions within a country and among developed countries but there are persistent differences in PCI levels across countries Natura Log of Per Capita Income Figure 61 Natural Log of Real per Capita Income in the United States 1869 2002 gt5 LII 0 9 uu 75 1860 1880 1900 1920 1940 Year 1960 1980 2000 2020 Income per Worker as a Percentage of the US Figure 62 Output per Worker 150 100 vs Investment Rate o o 039 o a I 39 u o I o I u 0 o 39 g o o u quot I o s quot riffquotP I 39 I I I I I 39 I s 10 15 20 25 30 35 40 45 Investment Rate as a Percentage of Output Income per Worker as a Percentage of US Figure 63 Output per Worker vs the Population Growth Rate 150 100 039 39 I C o o I U 5 C C so i C O C O C I I I q 0 5 o o I 39 Co a 0 I I I 9 45393I 3 I o quotI I I 0 05 1 15 2 25 3 35 4 45 Population Growth Rate in Percent Percentage Growth Rate in Income Per Worker Figure 64 No Convergence Among All Countries 39 n 390 n o 0 o n 0 I o a o a 1 u o o 39 o o n 20 40 60 80 100 Income per Worker as 3 Percentage of the US Percentage Growth Rate in Income Per Worker Figure 65 Convergence Among the Richest Countries 60 7O 80 90 100 110 Income per Worker as a Percentage of the US Percentage Growth Rate in Income per Worker Figure 66 No Convergence Among the Poorest Countries 0 c o o c 39 a a 0 39 a 39a 39 o o l s I o n o 4 6 8 10 12 14 16 18 20 Income per Worker as a Percentage of the US Malthusian Growth Model A formal model of the writings of Thomas Malthus 1798 Main message any increases in technology will be countered by increases in population and hence the standard of liVing cannot keep increasing Production Yt Zt FLtNt Lt Land Population Growth NtlNt g is an increasing function of per capita consumption low consumption poor nutrition g is concave because there are limits to population growth 11 In this model Ct Yt We can then show that Nt1 gZtFLtNt91Nt This equation allows us to solve for steady state population and steady state consumption The steady state is the long run equilibrium of the model Absent any shocks or changes in the economy we will remain at this point What happens when we change technology Does the model match the data Policy Implication need population control Why was Malthus wrong The Solow Growth Model Exogenous Growth Consumers In nite lifetime population grows at a constant rate Nt population Nt1 1bNt Pop grows at rate b b can be negative Each consumer has 1 unit of time no leisure entire population works Consumers receive all output Yt either wage or rm pro ts Saving sYt s is savings rate Constant saving is an assumption Consumption Ct 1sYt Production Firm Yt KtaZtNt1a Zt labor productivity Zt1 1u Zt u is the rate of technology growth and is constant note the textbook does not allow for this type of growth in technology Kt1 1dKt It d depreciation rate Competitive Equilibrium Inelastic labor supply curve determines labor market equilibrium Nt We need to determine the optimal amount of capital Start by substituting in for investment in the capital accumulation equation Km sYt lt1dgtKt Divide both side by ZtNt Dividing a variable by ZtNt is transforming that variable to per capita efficiency units of that variable For example Y t t ZtNt The will be used to refer to per capita efficiency units of a variable This transformation removes growth due to technology and puts the variable in percapita terms Variables that are written in per capita efficiency units have the property that they do not grow once the economy reaches its steady state De nition of a Steady State Output capital consumption and investment in per capita ef ciency units is constant In the steady state the economy has reached the optimal capital labor ratio adjusted for technology growth When an economy reaches its steady state aggregate variables still grow but only at the rate given by the exogenous population and technology growth rates When an economy reaches its steady state percapita variables still grow but only at the rate given by the exogenous technology growth rate 16 continuing by dividing both side by ZtNt Yt KZtNtl OL Kt ZtNt ZtNt ZtNt Which can be written K11lt1ugtlt1bgt W 1 dgtK f Do the same for the production function Iltt1 SYt Kt 1 d ZtNt ZN ZN t t t t Or Ytquotlt Kt0 We call this the concentrated production function Our goal is to nd the optimal amount of capital in per capita ef ciency units K a variable that does not grow in the steady state and then we can add growth back in Given Kquotlt we can nd K1 and then K2 etc Kquotlt is steady state level of capital in per capita ef ciency units of labor 45 degree line is where Kquot t1 Kgtllt t Kt is still growing due to population and technology growth Convergence to steady state Analysis of the Steady State In steady state Kt K K gtKt thtK t t Capital Stock growth rate Since u and b are small ub is close to 0 so capital growth is approximately equal to technology growth plus population growth In per capita terrns capital stock growth is K Ntl 1 Kt Nt t1 Output growth Output grows at the same rate as capital Ct 1sYt and It sYt so C and I grow at the same rate also balanced growth path all aggregates grow at the same rate All growth in percapita terms is due to technological progress Effects of Changes in the Economic Environment Steady State Capital Kt 1 Ktquotlt Kgtllt Increase technology growth 20 All aggregates grow faster but capital per efficiency unit of labor is smaller because with higher technology growth we need more investment which is forgone consumption to keep Kquotlt constant at the optimal Kquotlt Increases in population growth have the same effect on Kquotlt but no effect on per capita growth rates There is a 1 time level decrease What happens after an increase in the savings rate to K consumption output investment Convergence to new level after some change in b takes time 21 Convergence across countries 2 countries that are identical other than initial capital stock will converge to the same level Are countries in the world converging Empirical Evidence on Exogenous Growth Models Solow model helps understand how 3 sources of economic growth capital growth TFP growth and Population growth interact to produce growth in output and consumption Model Predictions 1 In the long run Aggregate Capital Output Consumption and Investment grow at the same rate 22 2 The common growth rate of Per Capita KC 1 Y is equal to the rate of growth in technology 3An increase in saving has no effect on long run growth of aggregate variables or per capita variables 4 Countries with identical technology and population growth rates will converge to the same growth rate in aggregate variables If they also have the same savings rate they will converge to the same level of aggregate variables 23 Do these predictions match the data 1 19501998 Growth Rates output 327 capital 314 very similar 2 Model Growth of Y Growth N Growth A Data The sum of labor growth 163 and TFP growth 169 is close to the 3215 output growth rate 3 High growth countries have had higher savings rates 4 Some evidence of convergence in developed countries but not among poor and rich countries Rich are getting richer Poor are getting Poorer 24 Conditional convergence countries with similar characteristics will converge some evidence Unconditional convergence all countries rich and poor will converge 25 Growth accounting Decompose Output growth into the amount due to changes in capital labor and productivity We can then identify which is the most important source of growth across countries and time periods CobbDouglass production function Yt Zth XNtl39O or 036 Zt is Solow Residual or TFP We use the following equation to decompose output growth 036 064amp t l t l l t l This equation follows from taking the In of the production function in periods t and tl then subtracting the time tl equation from the time t equation 26 Determinants of Output Growth 1990 1998 1990 Y 61363 K 126166 N118795 1998 Y 75519 K149440 N 131458 AinYduetoAinK AinYduetoAinN AinYduetoAinZ PostWar Determinants of Output Growth 1950 Y 16114 K 33882 N 58892 Sources of growth vary by time period and country 27 The Asian Miracle miracle was high output growth rates originally thought to be large increases in TFP Growth Accounting showed the importance of labor growth population growth and participation rates and capital growth high savings rate Is this sustainable Growth Accounting and the Productivity Slowdown in the US TFP growth in 50 s and 60 s was high TFP growth slowed about 1973 and continued to the present 28 Chapter 11 Market Clearing Models of the Business Cycle 7 Wages and prices adjust quickly enough so that marketclearing models of the economy are good approximations to reality 7 Market clearing business cycle models have strong theoretical foundations the microfoundations 7 Real Business Cycle Theory business cycles are the optimal responses of consumers amp rms to TFP shocks 7 Lucas Money Surprise misperception Take the RBC model as a starting point but give the consumer only partial information about economic events 7 Keynesian Coordination Failure Model A marketclearing model with a role for government intervention 1 The Real Business Cycle Model 7 Introduced in the early 1980s Can random TFP shocks we call these real shocks cause business cycles Potential since detrended Solow residuals from the exogenous growth model tracks uctuations in GDP closely 7 TFP changes weather technological innovations government regulations We know that the economy is repeatedly hit with TFP shocks 7 The Solow residual plays a central role in the arguments of both the proponents and opponents of RBC theory 7 The RBC model can be studied with or without money because money has no effect in the model 7 We add money to the model to attempt to explain how the price level changes over the business cycle Proponents of RBC theory calculate Solow residuals TFP or Z in the production function on an annual or quarterly basis They plot these against GDP and point out the close relationship Opponents of RBC theory argue that the Solow residual is mismeasured As we saw earlier there are measurement errors associated with estimating TFP shocks 7 Variable capacity utilization during an expansion capital llly utilized less breaks more overtime in recessions all capital stock is not used 7 The same is true labor rms may keep workers even if using less labor called labor hoarding since training new workers is costly and often rms must pay severance pay rms can encourage workers to work harder in expansions 7 Both of these facts means that labor capital inputs are measured as higher than truth in recessions and lower than truth in expansions hence we measure bigger changes in TFP than in reality 4 7 Example recall that Zt Yt K Nt139 in the CobbDouglass production function 7 Now let YtZtUtK StNt139 so that ZY UK SN139 7 An example 35 2 30 z 25 V 15 20 15 1 10 05 5 o o 1 2 3 7 There is a lot of empirical evidence of procyclical utilization of both labor and capital 7 Care must be taken in interpreting Solow residuals calculated in the standard way 7 Is the fact that we observe variable rates of capacity utilization labor and capital an argument against TFP shocks as the main source of business cycle uctuations 7 We do not incorporate variable utilization directly in our model to keep the analysis tractable The RBC model The complete intertemporal model with a temporary productivity shock a temporary increase in T 7 Which empirical facts of the business cycle does the RBC model match 7 Which empirical facts of the business cycle does the RBC model miss 7 A model with a persistent TFP shock Fiscal Policy in the RBC Model 7 Shocks changes in government spending or taxes may an additional source of uctuations RBC theorists believe that roughly 70 of business cycle uctuations are due to TFP shocks so even the strictest adherents to RBC theory think other shocks are important 7 7 Taxes and government spending do change over time 7 An increase in Government spending in the RBC framework 7 Does the result t empirical facts 7 We would conclude that government spending is procyclical We could argue that this is evidence in favor of scal shocks as another source of business cycles 7 Optimal scal policy in the RBC model What should the government do to counteract a recession caused by a fall in TFP Monetary Policy in the RBC Model 7 In the RBC model prices adjust immediately so eXpansionary monetary policy does not even have a temporary effect on output 7 The fact that money is procyclical is problematic for the classical approach The RBC model predicts that money is acyclical 7 This failure of the RBC model may not be important since money is not a important component of the model 7 An alternative View of money that money is endogenously created by the actions of private individuals and rms not the central bank can eXplain the behavior of the money supply Lucas Misperceptions Model introduces nonneutral money in the short run with markets always in equilibrium Key features of the Misperceptions model 7 Workers have imperfect information about the price level 7 Worker has complete info about hisher own nominal wage 7 Since the worker only buy goods occasionally and not all goods they don t know P 7 Worker doesn t observe aggregate shocks TFP 7 Workers do know the structure of the economy Result An ll in PXW can be perceived as a W ll so worker is induced to work harder An increase in the nominal money supply may increase nominal wages and aggregate prices so real wages are unchanged When PXW increases workers do not know if this is from an increase in MS so they shouldn t work harder or an increase in TTP and hence their real wage so they should work harder Model Assumptions 7 TFP shocks will be assumed to be temporary 7 Money shocks are permanent 7 Consumer does know that both shocks are possible 7 Consumer can deduce which one occurred one period later since they know the structure of the economyr1 Does the Misperception model match empirical business cycle facts Implications for Monetary Policy 7 The Fed can cause Y and N to increase The manner in which this happens is bad people are fooled 7 A better allocation of time and resources occurs when everyone is perfectly informed all markets clear all allocations are optimal the best we can do 7 Market Prices carry important signals about shocks hitting the economy EX Price of Apples rises people buy less apples and producers try to bring more to market both reacting to signal Changes in money make the price signal noisy 7 Optimal monetary policy Make MS as predictable as possible 7 Milton Friedman Federal Reserve should commit to a constant money growth rule Criticisms of Model 7 Money Supply and aggregate price level numbers are published regularly 7 How often can you fool people with the same trick Keynesian Coordination Failure Model 7 There are strategic complementarities between different rms in the economy 7 If one rm or industry increases its output it may be the case that another rm or industry should increase output as well Example Movies in DVD format and DVD players 7 Both industries would bene t by increasing output at the same time and suffer if one industry increased output while the other didn t 7 If both industries are optimistic then we can end up in a high output equilibrium 7 If both industries are pessimistic then we can end up in a low output equilibrium 7 The economy then has multiple equilibria Which equilibrium good or bad we end up at depends on perceptions about the economy that are not directly related to fundamental variables in the economy 7 Statements by government of cials the president the Federal Reserve chairman can impact which equilibrium we are at Media coverage can also affect perceptions of the state of the economy 7 The model assumes that the aggregate production function has increasing returns to scale This does not imply that rm level production functions exhibit increasing returns to scale strategic complementarities give us the aggregate production 1nction with increasing returns to scale 7 The production 1nction is now conveX and hence the labor demand function is now upward sloping 7 The increasing returns to scale needs to be large enough so that the labor demand function is steeper than the labor supply function 7 The output supply curve is now downward sloping Chapter 7 Endogenous Growth Endogenous growth growth in per capita output depends on the economic decisions in the model Government policy and economic growth Endogenous Growth 7 A basic Endogenous growth model Y1 z Kt 7 where z is the constant MPK 7 There is no technology growth and no population growth u b 0 7 S is the savings rate which is constant 7 Investment equals total saving in equilibrium ItSXYtSXZKt 7 The capital stock evolves over time following Km1dSZKt z 7 Which gives the capital stock growth rate of KM l 2 d K t 7 Output Growth is the same 7 C and I grow at the same rate 7 For positive growth the MPK multiplied by the savings rate must be greater than depreciation Exogenous versus Endogenous growth 7 In Endogenous growth model llMPKzorlT SSHin growth rate of all variables 7 Model produces perpetual growth 7 Economic factors have growth effects 7 Key message of Endogenous growth model MPK is not diminishing living standards can rise indefinitely without exogenous changes in technology 7 Key message of Solow model continued increases in standard of living occur only with technological change since we have a diminishing MPK
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