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# 162 Class Note for ECON 434 with Professor Ickes at PSU

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The Current Account Balance Part One Barry W lckes Econ 434 Fall 2008 1 Introduction The current account balance is a measure of a country s transactions with the rest of the world It includes all current transactions hence the name lts counterpoint is the capital account which measures transactions involving lOU s We will look at the capital account when we turn to the balance of payments which includes both the current and capital accounts Now our attention is on the determinants of the current account 1 00 000 HHI39I n H n nn 71 00 72 00 V3 00 V4 00 75 00 76 00 Figure 1 Current Account Balance of the US as a Share of GDP One thing we know is that the current account balance of the US is negative and that this de cit keeps growing see gure 1 We want to understand why a country would run a current account de cit and what are the implications This will enable us to later study how a country can adjust to restore balance to the current account If a country runs a current account de cit it must be borrowing from the rest of the world Hence if the US has been running current account de cits for some time it must mean that Current Account Part one Fall 2008 zo 13 lllllllllllllllllllllllllll me im um m2 mu use as 1090 me 1994 ms was ma 2902 20m Suurce BEA lntemahunal lnveslrmnt Posiliun Figure 2 US Net International Investment Position share of GDP our debt has increased or our net international investment position has decreased1 This is evident in gure 2 One can see that until the mid71980 s the US net position was positive 7 the US was a net international creditor Since then however the US has become the world s largest debtor So the question about sustainability of the current account de cit can be framed another way for how long will the rest of the world allow the US to keep going further into debt There is a limit to how long a private agent can do this What about a country What about a reserveecurrency country One way to think about the net international investment position or net foreign assets of a country is just the cumulative sum of the current account ie NFA 210AM where N FA are net foreign assets at time t and GA is the current account balance of the country at time t This would be good intuition a person s debt is the cumulative total of past borrowing and lending But there is an additional consideration changes in the value of assets Valuation effects can occur because the returns on assets we own abroad may differ from those foreigners own here and also from capital gains and losses due to movements in the dollar Normally one would think that these factors would balance out 7 why should a 1You might be tempted to think that the net International investment position is Just the cumulative sum of the current account This would be good intuition A person s debt is the cumulative total of past hoiiowing and lending But there is an additional consideiation changes in the value of assets Valuation effects can occur because the returns on assets we own abroad may di ei from those foreigners own heie and also from capital gains and losses due to movements in the dollar lt tums out that these valuation effects aie quite impoitant so we shall discuss them in more detail later Current Account Part one Fall 2008 country enjoy such an advantage But the US is a bit different after all the dollar is the world s reserve currency The US borrows in its own currency something other countries cannot do2 And other countries may forsake returns to invest in a safe haven like the US It turns out that these valuation effects are quite large so it is worth some mention It is interesting to compare the naive measure with one that corrects for differences in returns and capital gains and losses In gure 3 we have the naive and two estimates that include these valuation adjustments Several things are apparent from the gure First the US in the mid750 s was a huge net creditor with a stock of NFA equal to almost 15 of GDP while now the US is a big debtor the stock of NFA almost 726 of GDP Second notice that on the naive measure the US becomes a net debtor sooner than actual 7 in other words the exorbitant privilege has helped our true status Third when the US was a creditor the naive measure overstated the true position 7 it made the US net foreign position seem more positive and now the opposite This last point means that the valuation effects have been stabilizing l l l l l l l l l l 55 ED 65 7o 75 so 85 90 95 0o 7 7 Cumulaled Currem Account 7 NFA 777 HP markelvalue Figure 3 US NFA Relative to GDP To see this de ne the valuation effect as simply the difference between our quottruequot net foreign assets NFA and the naive measure VE NFA 7 21 GAE The valuation effects 2De Gaulle was reputed to have called thls an exhorbltant prlvelege but apparently ll was hls nance mlmaler Glseard d Estalng who really sad ll Current Account Part one Fall 2008 10 08 us 04 02 00 702 l l 706 5395 6390 6395 7390 7395 8390 235 9390 9395 no Figure 4 Valuation e ects are displayed in gure 4 and we can see that during the Bretton Woods period they were in fact negative while since the breakdown of Bretton Woods they are positive Essentially valuation e ects were negative when the US was a net creditor and are positive now that the US is a net debtor The interesting question is to explain the source of the privilege but we leave that for a bit later Now we turn to the determination of the current account balance The current account balance is comprised of the trade balance and other current types of transactions such a ows of investment income tourism and foreign aid one important determinant therefore is the real exchange rate which is the relative price of foreign goods relative to domestic goods But that puts the cart before the horse It is most useful to start by considering an intertemporal framework that is by thinking about choices over time We can ignore for the moment the relative price of goods produced in dj erent countries and focus on goods produced at dj erent points of time We can learn a surprising amount with such a simple approach 11 The Cumnt Account in an Inte39rtempoml Framework Typically we think about trade in goods and services when we speak about the current account but this is not the simplest way to begin More basic in fact is trade across periods intertemporal trade This gives us an alternative way to think about the current account Current Account Part one Fall 2008 from the conventional focus on imports and exports It shows us a different causal factor with regard to the current account And it is very useful for thinking about capital ows Consider a small economy with identical consumers They choose consumption to maxi mize utility UMQM MQ D where is the discount factor Agents desire to smooth consumption and this behavior extends to the economy as a whole3 lncome in each of the two periods is given by Y1 and Y2 We can think of these at rst as endowments 7 manna from heaven If the economy were closed then the problem would be trivial C1 Y1 etc But if borrowing and lending are allowed then consumption possibilities are subject to the intertemporal budget constraint 02 Y2 C Y 11T 11T Consumption does not have to be at the endowment point but can be at a preferred point as in gure 5 Welfare is clearly higher due to access to world capital markets We maximize equation 1 subject to the constraint The rst order conditions imply 01 1 7 u02 3 01 ucz i 1 us1 71 Q where us1 is the marginal utility of consumption in period one Expression 4 is just the familiar condition that the marginal rate of substitution between the present and future con sumption and the right hand side is the price of future consumption in terms of present consumption Expression 3 is called an Euler equation Notice what it implies At an optimum the agent must be indifferent between consuming today or tomorrow Otherwise it could not be 3We abstract from differences among households in the economy to focus on differences across economies Current Account Part one Fall 2008 an optimum Now suppose an agent reduce consumption by one unit this period Utility would fall this period by the marginal utility of consumption ucl the left hand side of But consumption would be higher next period By how much A unit saved today raises consumption by 1 7 next period And so utility rises by 1 7 ch But we have to discount this back to the current period so we multiply by and this gives the right hand side of Now suppose that 1 41 then it follows that consumption would still equal income in each period We can call this interest rate the autarchy rate of interest 7 94 Notice that is the rate at which future consumption can be transformed into present consumption and is the rate at which we discount future over present consumption When these two are equal we do not want to alter our consumption pro le Everybody has an autarky rate of interest though it will be different for different individuals or economies It is a benchmark interest rate that we can use to assess whether the economy will borrow or lend in the current period Whether this economy will engage in international borrowing or lending depends on the actual terms of trade in our case the world interest rate Suppose that the world interest rate is less than the autarchy interest rate 7 lt Ta This means that the premium required to induce people to smooth consumption is greater than what can be had with international lending Hence current consumption will rise relative to autarchy while second period consumption will decrease Thus we will have borrowing in period one equal to B1 C1 7 Y1 In the next period the borrowing must be repaid Hence C2 Y2 7 1 7 Bl Now the current account balance in an economy is the change in the value of its net claims on the rest of the world In our simple model with only consumption the current account balance is equal to national savings which is negative in our example In a model with investment the current account would equal the difference between savings and investment In general if At is the economy s net foreign assets at the end of period t then the current 4Notethatif then1raandthusra717116716 W5 Current Account Part one Fall 2008 A CZ CYe1rcrm 1rYYZ Y z C C 2 Y z 1r P Y Yl AzC1 C1 CAI Figure 5 Consumption over Time and the Current Account account can be de ned as CA AH1 7 A 5 Y m 7 C 6 NX Hit 7 Where NX is the net exports exports less imports also called the trade balance Remark 1 It is useful to recall national income accounting In this model without inuestment 07 gouernment we have only two uses for output consumption and net ewports Hence YECNX The economy Will run a current account de cit today the rest of the world acquires claims on the economy s future income Next period the economy s current account Will be in surplus this must occur in a two period model That is the current account in period two Will be equal to the negative of the current account in period one plus interest CA2527 A202Y27 Y2C2C2 8 Current Account Part one Fall 2008 But in a two period model A2 must be zero so CA2NX2Y2702 in period two the current account is equal to net exports as there is no further lending But we know from 2 that C2 Y2 7 1 rC1 7 Hence NX2 52702 323271r017Y1 71rY170171rNX1 9 NX2 NX110 10 the present value of the country s borrowing must be zero This is just an intertemporal budget constraint5 Remark 2 Strictly 10 is true because we started the rst period with zero assets More generally we should assume that we enter the initial period with some leuel of assets that could be positiue or negatiue Suppose we entered period one with net foreign assets equal to A0 Our intertemporal budget constraint would thus be C2 Y2 C Y 11r 11r 140 Thus our lifetime resources are augmented by whateuer assets we are born with or debt burdened with if A0 lt 0 Second7period consumption is now 02 Y2 7 1 r01 7 Y1 7 A0 Then the last line in empression 9 aboue is now NX2 17 Y1 Cl17 140 17 NX1 1rAo 5It may be easier to see this by noticing that if a country runs a current account de cit today it will have to repay the debt next period plus interest There will be a debt equal to CA1 and in period two the debt will equal CA11 r So CA2 71 rCA1 or CA1 0 which is just expression 10 8 Current Account Part one Fall 2008 and thus equation 10 is now NXg NX1 1 7 17 A0 11gt which says that the present ualue offuture net emports the left hand side is equal to principal and interest payments on initial net foreign assets Thus if we start initially with a debt born with debt A0 lt 0 the present ualue of future net emportss must be positiue If we are born with positiue net foreign assets A0 gt 0 then the present ualue of future net emports can be negatiue Erpression 1 will be useful for thinking about the US Currently we have an initial leuel of debt Hence the present ualue of future net emports must be positiue So euen if currently we have a negatiue net emports soluency implies that somewhere in the future it will turn positiue We will return to this later 12 Longere Time Horizon ln a model with a longer time horizon we would modify the constraints which would allow periods of surplus and de cit to persist for several periods This is straightforward lt is useful to begin with the de nition of the current account balance CAt AHl 7 At Yt rAt 7 Ct 12 This can be rewritten as 1 JV TlAt Yt Ct At1 13 NX 7 AH1 14 This is true for any period so we can now move this forward one period 1 7 At1 NXt1 At2 Current Account Part one Fall 2008 OI Am 7 15 Now use expression 16 in 13 to eliminate At 71 7 At NXt 7 AHl 17 NX 7 18 lt19 and if you do this again you will get 17 17 2 17 27 71TAt NXt NXt1 Jr NXt2 At3 keep doing this and we have NXt1 NXt2 NXt3 Atn 17 1r2 1r3 Hm 71rAt NXt Notice that each time we keep moving the net foreign debt term farther to the future Suppose we kept doing this all the way to some T far in the future We would have tT 1 set 1 T 1 7 At 2 1 7 NXS 7 1 H AM 20 5t Expression 20 is interesting The rst term is just the present value of net inquotpo7 ts6 The second term is the present value of net foreign debt sometime far in the future Let s examine this term rst How should we think about this quotterminalquot value of net foreign assets 1n a nite horizon model we know this would have to be zero we cannot have negative net assets in the last 6Or the present value of the negative of net exports Or the present value of the negative of the trade balance 10 Current Account Part one Fall 2008 period of life since there is no future in which to pay it back But it could not be optimal to have positive net foreign assets in the last period because we would never get to consume So in a nite horizon model we would have something like 1 T TAtT1 0 Of course this can be true only if AHTH 0 Now in the in nite horizon we just let T gt 00 As T gt 00 we require the present value of future net foreign assets to go to zero lianoo AHTH 0 7Why These considerations imply that our intertemporal budget constraint can be simpli ed It now can be written as tT 1 set 1 Mt 2 1 NXS 5t so the present value of future trade surpluses is equal to the initial debt we start with The key principle is that periods of de cit can only be sustained if lenders expect offsetting future surpluses We shall see in fact that for a country to be able to borrow lenders must believe that the intertemporal constraint expression 10 or its equivalent will be satis ed It is when lenders no longer believe that it can be satis ed that they stop lending If they stop lending current account de cits fall immediately so the constraint is satis ed but in a rather painful way 7Why There are two cases to consider 0 If lianoo T TAtT1 lt 0 we would be running a Ponzi scheme8038ltp typequottexparaquot tagquotBody Textquot gtCharles Ponzi duped investors by offerring incredible returns7 which he at rst paid from the deposits of new investors He originally planned to use the resources to arbitrage inter national postage stamp prices But he never did Once the source of new deposits slowed7 his scheme unravelled But his name is now attached to the Ponzi game If you examine 20 it is apparent that T with lianoo AtT1 lt 0 that the present value of what we spend is forever greater than what we produce Foreigners would be lending to us continuously without end Obviously our debt T would have to grow faster than the rate of interest for lianoo AtT1 to be strictly negative But they would not do so7 since they could consume resources themselves No economy will provide T resources to another for free forever Hence7 we cannot have lianoo AtT1 lt 0 o What about the opposite what if lianoo T TAtT1 gt 0 This would mean that the present value of all the resources the home country uses never converges up to the present value of output We would be making an unrequited gift to foreigners This cannot be optimal We would never consume all we produce Since we have shown that the present value of net foreign assets cannot become strictly negative or strictly T positive as T goes to in nity7 it follows that we have to have the condition that lianoo AtT1 0 11 Current Account Part one Fall 2008 As we shall see determination of exchange rates and interest rates in the global econ omy are determined by these key factors the time pattern of income the desire to smooth consumption and expectations about future consumption and income possibilities9 15 Investment So far the only way to provide for future consumption was to hoard or to lend to another country at the world interest rate 7 Now suppose that economies can also invest 7 that is accumulate capital goods Capital goods may be purchased because they yield a return 7 output is higher if more capital is used lnvestment is the process of increasing the stock of capital The decision to invest involves a comparison of the rate of return from investing with that of lending We have production function that relates output to capital FK We note that the marginal product of capital is positive notationally F K gt 0 but that there are diminishing marginal returns that is F K declines as K increases How does a country raise K By investing in other words by using some of the endowment to raise tomorrow s capital stock Consider gure 6 with initial endowment point A By using some of Y1 for investment we can achieve the production point 13 The difference Y1 7 Q1 is equal to rst period investment The point P is the pro t maximizing production point given the interest rate You can see that by noting that any other point on the curve AB with the same slope has an intercept that is to the left of point E Point E is the present value of production at point 13 and point D is the present value of the endowment point A Hence you can think of the difference E 7 D as the present value of the pro ts from investing until point P 9The rst discussion of consumption7smoothing behavior is probably the biblical story of Joseph in Egypt Recall his forecast dream about 7 good years followed by 7 bad years He proposed storing a fth of grain production each year of plenty was appointed Prime Minister by Pharoh and helped Egypt avoid famine Notice that he engaged in domestic investment at a zero rate of return prior to depreciation Why not invest abroad Interest rates in Babylonia at the time were 2033 At such rates consumption could have been higher in all periods That is why didn t Joseph advocate international consumption smoothing Presumably it is because of the insecurity of such contracts at the time Similarly in the fall of 2002 Brazil had trouble borrowing even though interest rates are very high compared with world rates When the central bank of Brazil tried to roll over its debt the auction opped after election7wary investors demanded interest rates as high as 50 percent for the paper maturing after the Oct 6 vote It is not just the interest rate that counts but that returns related to risk 12 Current Account Part one Fall 2008 Figure 6 Production Possibilities Notice that we have said nothing about consumption yet The reason is that consumption choices depend on whether or not we can borrow or lend internationally If the economy is closed then we are stuck to consume somewhere along AB In gure 6 consumption in each period is also at 13 there is noway to obtain more resources Notice that consuming along the budget line between point P and E is impossible in a closed economy So in the closed economy case you can see that Y C I which follows since we already noted that Y1 7 Q1 I and we noted that Q1 C Now suppose that we can borrow or lend at the rate of interest 7 then our position is greatly augmented Now investment and consumption decisions in a given period can be separated We can invest more than the difference between current income and consumption We can borrow from abroad We now have gure 7 which has the same production possibilities as in gure 6 but we have added borrowing and lending Given the interest rate and the preferences the consumption choice 6 is separated from the production choice Notice that point C would not be feasible in a closed economy 1 lays outside the production frontier So international borrowing and lending in this case borrowing in period one improves welfare 13 Current Account Part one Fall 2008 Figure 7 Production Possibilities in a Small Open Economy We can see that in period one there is a current account de cit equal to C1 7 Q1 ln period two this is repaid as C2 lt Q210 ln period two we are repaying principal plus interest but we are better off for it given the preferences as represented here What if there was initial debt We would still separate decisions but our consumption possibilities would be reduced by the level of initial debt Suppose initial debt is A0 We know that the present value of consumption is now reduced by 1 7 A0 So given our endowment at point A and the world interest rate production is still maximized at point 13 This leads to a present value of E But we subtract from this the initial debt level and we have point W in gure 8 The optimal consumption C Allowing investment means that we now have two ways in which wealth can be held foreign assets A and capital K Total domestic wealth at the end of period t is now AHl Kt 10lncleecl7 we can see more Since the slope of a right triangle is the rise over the run7 you can see that glzgi 1 7 Now it is obvious that iccAAzl so 33 71 7 which we can arrange as CA1 7 or CA1 f f 0 as in expression 10 above 14 Current Account Part one Fall 2008 Figure 8 Production and consumption with initial debt 1gnoring depreciation11 the capital stock evolves according to Kt Kt It 21 We can write the change in domestic wealth or national saving as Am Km 7 A K K M 7 C 7 G 22 where 1 have added government spending G for completeness The key point of 22 is that domestic wealth increases sometimes called accumulation only if earnings exceed spending on consumption government included Now we can rearrange 22 using 21 to obtain the current account CA AH1 7 A K TAt 7 C 7 Gt 7 It 23 Notice that the rst equality says that the current account surplus is equal to net accumulation of foreign assets12 And if we de ne savings St E Yt 7 At 7 Ct 7 Gt then the current account 11Let 5 be the rate of depreciation Then expression 21 stands for the case of 5 0 If 0 lt 5 lt 1 then we would re7write expression 21 as Kt1 1 75Kt It If there is 100 depreciation 5 1 then Kt1 It 12It is important to recognize that this is the negative of net capital in ow Capital ows into a country as it accumulates liabilities The lender acquires foreign assets 15 Current Account Part one Fall 2008 can also be written as CAt St 7 It 24 In words national saving in excess of domestic capital formation ows into net foreign asset accumulation This points to the important point that the current account is fundamentally an tntertemporal phenomenon How is investment related to the rate of interest Notice that a higher interest rate means that the present value of future pro ts is lower 1n the two period model the net return to investment can be written as 7T5 7 t1 25 P t 1 7n where 7Tf1 is expected future pro ts13 A higher interest rate means that p is lower hence the demand for investment should decrease with the rate of interest and rise with higher expected future pro taloility14 This gives us the negatively sloped investment function in gure 12 It is interesting to look at the experience of Norway in this regard In the mid 70 s the Norwegian current account went into large de cit as investment increased to exploit energy resources Savings also dropped for permanent income reasons The increased value of energy resources caused Norway to borrow against higher future income This is evident in the time path of the current account as in gure 9 Separation Theorem and the Small Economy In a small open economy the invest ment decision is separate from the consumption decision Given the world interest rate 7 investment takes place where the marginal rate of transformation is equal to l 5 Suppose that i lt TA Then the country would invest to take advantage of productive opportunities 13Notice that if there were more periods I could sell the capital good But in the twoiperiod case the world ends so the value of the capital good at the end of that period is zero7 and pro ts are the only return 1 fActually what we have actually shown is that the demand for capital goods depends negatively on the rate of interest Investment is the change in the demand for capital goods It is not immediately clear why this also depends on the rate of interest Economists usually assume there are some adjustment costs that explain this We will just assume it 16 Current Account Part one Fall 2008 Fraction of GDP 0 4 Investment 03 0 2 Saving 01 01 Current account 1973 1976 1979 1982 1985 1983 1991 1994 Figure 12 Norway s savinginvestmem balance 197394 Source OECD Figure 9 Savings Investment and the Current Account in Norway Consumption need not be reduced however Indeed a current account de cit can allow for greater consumption and investment than would be the case in autarchy In gure 10 the optimal production point is at B 6 and the optimal consumption point is at 0 Notice that utility is higher at C than at the autarchy point The economy runs a current account de cit in period I equal to C1 7 Y1 while in period two there is a current account surplus Two important implications follow from gure 10 0 production is more valuable at point 3 than at the original endowment point 0 welfare is higher at point C So access to the world capital market is bene cial for the small open economy 7 production and consumption opportunities are enhanced 14 A TwoiCountry World Economy Dealing with small open economies we could take the world interest rate as given Let us brie y see how our analysis must change in a two country model Abstract from investment 17 Current Account Part one Fall 2008 02 B C V Y1 01 01 Figure 10 Investment and the Current Account and let their be two economies home and foreign with exogenously given endowments Notice that equilibrium in the global market requires YtYfCtCf 26 at each date t This is equivalent to the statement that world savings must be zero St 5 0 27 Notice that this is also equivalent because of the absence of investment to the statement that the world current account must sum to zero CAt CA 0 How is the world interest rate determined in this model We make use of expression 27 Notice that savings in each country is an increasing function of 7 Moreover savings is negative when 7 lt TA and savings is positive when 7 gt TA Suppose that 7quot gt TA the foreign country has a higher autarchy rate of interest than the home country Equilibrium in the goods market thus requires that the world interest rate satisfy TA lt 7 lt 7quot This is evident in gure 11 Notice that at the equilibrium rate of interest SH 75F What happens if home output in period 2 increases exogenously This raises the home country s borrowing at every interest rate This amounts to a shift to the left of SS The world interest rate must increase Although the increase in Y2 makes people better off due to increased total output the home country must pay a higher rate of interest this period for its borrowing 18 Current Account Part one Fall 2008 sra sH Home 3 sF Foreign s Figure 11 Interest Rate Determination in the Two Country Model One can interpret this as shift in the terms of trade The home country imports current consumption from the foreign country The increase in the world interest rate causes the terms of trade to move to the foreign country s advantage The commodity that it exports is now more valuable than it used to be It should be clear that world welfare is enhanced when intertemporal trade is opened between these economies You should be able to show that starting at the autarky points in both countries intertemporal trade raises welfare in each Thinking about gure 11 one might characterize emerging economies as those where Ta is very high and the more mature economies as those where it is lower This ts with the earning consumption pro les of economies as well as individuals The ability to transfer savings from the mature to the young enhances the opportunities of both 14 Investment in the TwoiCountry Model Now let us add investment once again lnvestment in each country is a negative function of the rate of interest This follows from the principles of pro t maximization more below We can plot savings and investment for each economy but note that in an open economy savings and investment need not be equal in each country only in sum We have gure 12 Notice that the excess of savings over investment in the home country is equal to the excess of investment over savings in the foreign country This is what determines global equilibrium 19 Current Account Part one Fall 2008 L IH SH s home sF IF s foreign L Figure 12 Global Equilibrium with lnvestment Another way to express this is that world savings equals world investment StSf It 1 28 which is equivalent to C14 CA 0 We can examine the impact of a change in foreign savings in the same way now Consider gure 13 Initially the world interest rate is equal to 7 84 When foreign savings falls to Sf there is an excess demand for world savings at rgv Hence the world interest rate must rise to 7 14 which causes both home savings to rise and reduces the demand from the foreign country Notice that we could equally well describe this in terms of current accounts At 7 84 the home country has a current account surplus and the foreign country a current account de cit When foreign savings falls the current account de cit in the foreign country increases At the old rate the current account de cit in the foreign county is larger than the current account surplus in the home country This causes world interest rates to rise to 7 14 At this new equilibrium world interest rate the current account balance in the home country SH 7 H 751 7 IF the current account balance of the foreign country 15 Global Savings Glut We can use the two country model to investigate some questions about global imbalances The basic feature of the global environment is the large US current account de cit and large 20 Current Account Part one Fall 2008 71 LW D 70 1 SH 81 home 8 1 81 fomgn 3H IH F F Figure 13 A Decrease in Foreign Savings I 5 1 In I0 51 home 51 foreign Figure 14 US Fiscal Expansion current account surpluses in the rest of the world This raises the question of what is the cause of the imbalance Notice that the same pattern of imbalances could arise if the US is the quotcausequot say by excessive scal expansion or if the rest of the world is the cause by saving quottoo muchquot In either case there will be a current account de cit in the US and a current account surplus in ROW There is one major difference with these two scenarios however and this relates to the world interest rate Suppose we start with zero current account balances in both countries at interest rate 7 34 as in gure 14 Now suppose that the US has a scal expansion shifting the investment function to the right Io At the old world interest rate there is an excess demand for funds at 7 84 the US has a current account de cit and ROW does not The world interest 21 Current Account Part one Fall 2008 r 5 5 W 70 W C 7t b 71 Io I ID 81 home 81 foreign Figure 15 A Global Savings Glut rate has to rise to 7 14 to satisfy the global market clearing condition CAt CA 0 1n the new equilibrium CAt lt 0 and CA gt 0 But the key point is that 7 14 gt Tgv Now consider what happens if the primary mechanism is a glut of foreign savings This could occur either if foreign savings increases or foreign investment falls In gure 15we again start at 7 84 with zero current account balances in both countries Now shift 1 to the left This creates a current account surplus in ROW and to satisfy the global market clearing condition the world interest rate must fall to 7 14 in gure 15 Notice that we have the same pattern of current account balances in the two cases But there is one key difference in the glut case world interest rates are low in the US party case world interest rates are high Current global imbalances are a mixture of both cases The US has experienced a large scal expansion And ROW seems to have an excess of savings over investment The latter seems important because currently world real interest rates are low not high The fact that ROW is willing to buy US iou s at a rapid rate keeps interest rates low and fuels spending in the US do homebuyers thank the Chinese for low interest rates It is rather easy to understand the causes of scal expansion But why a global savings glut One point that will be important to consider is that countries elsewhere are building up reserves to use as insurance against future currency crises Countries that experienced large output losses as the result of the Asian crisis or countries that just observed this want to have reserves they can use in case another crisis is likely Thus they save and hold dollars rather than invest in productive capacity If this is true then the lack of alternative means to cope with currency 22 Current Account Part one Fall 2008 crises is leading to expensive self insurance schemes The cost to each country is the difference between the return to investment and the meager return on US Treasury bills Of course the US gains as we are the quotsellersquot of this insurance 16 The Missing Surplus The world economy as a whole is closed so one would expect that world savings would equal world investment While individual countries can run current account surpluses and de cits overall these must balance out This seems obvious but if we look at the sum of the current accounts from all countries we observe a persistent world current account de cit This is evident in the following table Table 1 Measured World Current Account Balance 1980 1993 Billions of US year World Current Account Balance 1980 385 1981 683 1982 1002 1983 612 1984 734 1985 808 1986 767 1987 623 1988 789 1989 1081 1990 1438 1991 1224 1992 1224 1993 888 1t is also evident in gure 16 which shows that the statistical discrepancy has grown in 23 Current Account Part one Fall 2008 3400 3200 W4 2001 2002 2003 2005 73200 Billions of Dollars 73400 73600 73800 Advanced omex Emerging us o Statistical Economies Market and Developing Economies Discrepancy Figure 16 Current Account Balances by Major Grouping more recent times as well Notice that the discrepancies in the table or in the gure are quite large larger in fact than the current accounts of many countries One would expect errors to cancel out if they are random Yet the discrepancies here are systematic the world runs a persistent current account de cit What might account for this One factor could be statistical errors but a little re ection suggests that this cannot account for the systematic bias A second factor might re ect timing Goods that are exported in late December of a given year might not reach their destination until January of the next year Hence the exports and imports may show up in different years If we think about oil exports this could explain why this is so large but it still does not exactly explain the persistent de cit indeed it seems to predict a surplus A more convincing explanation concerns misreporting of interest income lnterest pay ments earned abroad are often not reported to government authorities in the recipient coun try This happens if the recipient wishes to evade taxes But the payor of the interest will report the transfer So there will be a debit in the current account of the payor but not corresponding credit for the recipient who evades This could cause a persistent negative balance Consistent with this explanation is the fact that world interest payments have risen greatly since the early 1980 s As world interest rates declined in the mid 1980 s so did the world 24 Current Account Part one Fall 2008 current account de cit and as world interest rates rebounded in the late 1980 s the world de cit increased again So the pattern seems correct This also is evident in gure 16 since world interest rates have been lower in the recent period than in the 1980 s A recent lMF study shows that in addition to this factor it appears that most of the world s shipping eets are registered in countries that do not report maritime freight earnings to the IMF This accounts for another good part of the de cit 2 Some Dynamics Same Theory An alternative way to see this is looking at the dynamic analysis of the transition to the steady state We continue with a two period model but focus on lifecycle aspects Suppose output is given by Yt AthLiiB This is a Cobb Douglas production function It is convenient has constant returns to scale and diminishing marginal productivity It is useful to write this in per capita terms 7 simply divide through by labor Then we have imwwi mgr 29 or y AM 30 We can represent this graphically in gure 17 Y AH V Figure 17 A Nicely Behaved Production Function 25 Current Account Part one Fall 2008 Agents work consume and save when they are young and spend when they are old Assume they leave no bequests to make life simple What do agents earn We suppose that the wage is equal to the marginal product of labor15 wt 1 5V1ka 31 and the rate of interest is equal to the marginal product of capital 73 Atk l These derive from pro t maximization and are standard assumptions What do these expressions mean Because lt 1 the wage rises with increases in k but less than proportionally This makes sense 7 if you add capital workers are more productive but how many computers can one person use With regard to the rate of return notice that 7 1 lt 0 so increases in k lead to a fall in 7 This also makes sense This is the most important thing to think about these expressions16 Now we further assume that agents consume a of their incomes when young17 So savings is equal to 1 7 001 Capital wears out each period so the capital stock per worker in period t 1 is equal to savings of the young ie kt1 st 1 7 04wt Now substitute from 15To see this note that the marginal product of labor is the derivative of the production function with respect to labor 2 1 7 AK BL B and since k g by de nition it follows that 1 7 AK BL Q 1 7 3 AM 16Notice that 73kt kt Atkfbl Atkf is capital s share of income the rate of return times the capital stock Now add to this the expression for the wage and we get Atkf 1 7 MAM Atkf 9 17This is obviously makes life simpler It follows if utility is given by u c fc a with the budget constraint cl 621 7 1 w The FOO for this utility maximization problem are 171 17a 7 0461 62 7A 1 7 16306 A1 7 1 so 1 7 1611 0461171621 7 1 which implies that 2 7 1 Now using the budget constraint substitute for 62 and obtain c1 in WW1 mm 7 cm 1 7 a a 01 lm i 011 which can be simpli ed to cl am 26 Current Account Part one Fall 2008 expression 31 for wt We obtain kt1 1 7 Oowt 1 7 500 7 yltkf 32 GUM 33 which we refer to as the transition equation Why is the transition equation expression 32 interesting Notice that it tells us how the capital stock evolves over time More speci cally notice that a higher capital stock today means more next period because it leads to more income and savings but that there are diminishing returns since lt 1 This expression is useful for understanding capital accumulation It also tells us when the process stops that is when we are in the steady state This is the equilibrium where all variables grow at the same rate so the capital labor ratio is constant To nd this value we set kt kt1 in the transition equation 3 k 17 1X17 Atk SO i 17 am 7 MW 34 where g is the steady state value of the capital labor ratio the value where the transition equation intersects the 45 degree line in gure 18 Notice that if the capital labor ratio is initially below its steady state value kt lt then savings leads to increases in the capital labor ratio Similarly if we start off with too high a capital stock we decumulate until we reach Notice that at E however savings is just su icient to keep the capital labor ratio constant There is no net savings or net investment at this value of the capital labor ratio 27 Current Account Part one Fall 2008 45 km G06 P 7 I V P 7 I Figure 18 The Transition Equation We can see some interesting comparative statics from gure 18 Suppose that the level of productivity At increases This shifts up the transition curve and we have a higher steady state value of k Similarly for a rise in the savings rate We could think of economies having different steady states because of different values for these parameters Now consider the two country world with the US and Japan In gure 19 we show the autarkic equilibrium We suppose that E gt gus which could arise due to a higher savings rate in Japan Notice that without trade in capital Japan would have higher output consumption and savings per person that in the US As long as Japan had a higher savings rate this would persist Now suppose that capital markets are liberalized Now Japanese savers can invest in the US Why would they want to Because the rate of return on capital is lower in Japan with its higher value of k Recall that the interest rate is given by n Atk l so given that E gt US W Atkfff lt Atkfff W5 35 It follows that the Japanese would earn a higher return investing in the US But this would raise capital accumulation in the US and lower it in Japan With open capital markets this process continues until the rates of return are equal in the two countries But from expression 35 it is clear that this occurs when the E gus Notice that this also means that wages are 28 Current Account Part one Fall 2008 km A 45El P L m 1 m I V kt I k Figure 19 Autarkic Equilibrium equalized in the two countries Economists refer to this as factor price equalization We can see this in gure 20 where we converge to the world steady state capital labor ratio gm How is w determined It is as if there is one country since factor prices are equalized So just sum total savings in each country and divide by total population Letting N be the population in Japan and let at1 be the assets accumulated Then kt1 39Na a1 36 where this is now the world capital labor ratio How about the world transition equation Notice that factor price equalization implies that wages are equalized in the two countries So asset accumulation differs only by the different savings rates But world capital accumulation will depend on the world savings rate which is the weighted average of those in each country N04N04 Q W 37 and the transition equation for the world is given by kt1 1 7 a MAM 38 29 Current Account Part one Fall 2008 k Japan World V kt Figure 20 Equilibirium in the Two Country Model and which gives the world steady state in the same way as before This de nes the world transition path in gure 20 and we can obtain the steady state capital stock in a similar fashion as before Note however that in the new steady state the capital labor ratio for each country will be equal to gm If this were not the case then the return to capital would differ in the two countries Since the US saves less than Japan this means that some of the savings required to have a capital labor ratio equal to w will have to come from Japan Thus Japan will have positive net foreign assets and the US will have negative net foreign assets How about the transition to the new steady state Suppose that the world capital labor ratio is greater than its steady state value k1 gt gm To be speci c suppose that initially the US and Japan had equal savings rates so initially the transition curve was the one labelled Japan in gure 21 Notice that at k1 we can see that asset accumulation is higher in Japan than in the US using gure 21 Now let the US savings rate fall The new world steady state is at gm but the transition involves a decrease from E to gm We want to understand this transition To see this start at k1 and read upwards Using the transition curve for the US we can see that assets in the next period will be ags a2J for Japan while the world capital labor ratio will be k2 It is apparent that the US saving is too low agS lt k2 lt aZJ The difference is made up by Japanese investment in the US So the US has a negative net foreign asset 30 Current Account Part one Fall 2008 km 45 a k Japan 2 g E 1 x a I World 5 E I US I r 2 I st k I I I x I l I kt k kW k1 kJ Figure 21 Adjustment to the Steady State Fall in US Savings Rate position while for Japan this is positive Notice that this will still be true in the steady state given the position of the transition curves in gure 21 2 Bene ts of Capital Mobility When we move from autarky to capital mobility both countries are better off The simplest way to see this is to suppose that Japan and the US are equal in size N N which makes the pictures simpler And continue to suppose that under autarky E gt hug We know that if capital ows are allowed that we move to a new steady state kw where E gt kw gt EUs 1n the new steady state capital ows from Japan to the US The US is better off because it attracts capital and Japan is better off because it earns a higher rate of return This is evident if we look at the production function as in gure 22 In the new steady state both countries have the common capital labor ratio kw so both produce the same output level QW Clearly 3W gt 115 so the US is better off But so is Japan To see this notice that it transfers E 7 kw AB ED to the US It earn a rate of return that is higher than it could domestically This is clear because the rate of return to capital the tangent at point A in the open steady state is greater than that at the autarky level for 31 Current Account Part one Fall 2008 45 y Ak B yW F D yUS E Bk kUS kW kJ Figure 22 Autarky versus Capital Mobility Japan the tangent at point G Japan s new level of income is thus W Ag gt y because of the transfer of income from the US But notice that the US is also better off net of the transfer because its per capita income rises by DA but it only has to transfer FD BC to Japan Thus Japan gains CG and the US gains FA from capital mobility in the new steady state Capital mobility improves incomes in both countries because it expands opportunities We shall have moment to discuss some caveats to this below What about a small country It is easy to think about a small country in the model The only change in the analysis is that capital accumulation in the small country does not impact the world capital labor ratio So the transition curve for the world is given and changes in the small country effect only its capital labor ratio For example suppose that a small country Benin was closed from the rest of the world and was in steady state with E gt w as in gure 23 Now suppose that Benin opens up to the world capital market Since Benin is small its behavior cannot effect world interest 32 Current Account Part one Fall 2008 rates and since initially its capital labor ratio was higher than gm this means that interest rates in Benin were below world rates So savers in Benin will want to hold less capital and more foreign assets Hence after opening to the world capital will ow out until k1 gm and Benin savers will hold net foreign assets 61 In fact this will happen right away in the model because capital wears out each period Notice that though the capital labor ratio falls in Benin its citizens are better off They are getting a higher return on their savings so they can afford higher lifetime consumption The only odd part of the story is that usually we think of emerging economies as having lower 18 capital labor ratios But then opening tells this story in reverse km 45 Benin orld w k Figure 23 A small country case 21 Caveat Notice that the transition to the new steady state gm requires capital to ow from Japan to the US This leads to factor price equalization Assuming that capital can move freely between the US and Japan is not a bad assumption But this may not be true generally How mobile is capital internationally is an important questions Not only may countries impose barriers to capital mobility but there may be institutional barriers as well Bad policy may 18But see the caveat below 33 Current Account Part one Fall 2008 lead to large risk premia which must be paid to attract capital to emerging economies One reason for this may be currency risk something we will discuss at length Another point to keep in mind is that we have assumed that productivity A is equal in both countries This is unlikely to be true especially for developing countries We consider this below in section 23 22 Net Foreign Assets We can say something else about net foreign assets and the trade balance First note that net foreign investment the current account balance in any period is equal to the change in US net foreign assets Kf between periods If Kf t1 39 Now if we started in autarky in period 0 then Kg 0 With open markets we know that for the US Klf lt 0 as the US will import capital from abroad That means net foreign investment will also be negative given expression 39 Eventually we will reach a steady state however and then th 1 th by de nition So eventually net foreign investment will be zero To recap then if starts negative and is zero in the steady state Now look to the de nition of the current account If X 7 M nth 40 It follows that in period 0 we must be running a trade de cit Xi 7 Mt lt 0 Why Well we know that of lt 0 and Kg 0 so from expression 40 there must be a trade de cit Can this continue forever Clearly the answer is no In the steady state we have seem that if 0 But we have also seen that in the steady state th lt 019 Then from expression 40 it follows that Xi 7 Mt gt 0 We can see this graphically in gure 24 We are in autarky until to With opening we have negative net foreign assets 7K1 and negative current account 7X0 7 M0 Eventually 19The important point is that K is the stock of net foreign assets and I is the change in the stock of net foreign assets In the new steady state the stock is constant and it is negative 34 Current Account Part one Fall 2008 net foreign assets reach the steady state level if at time E In the new steady state clearly AK I 0 But with F lt 0 7 lt 0 So clearly we must have Xi 7 Mt 77 gt 0 ime i NI Figure 24 Adjustment to the Steady State The intuition is clear Initially the US runs a trade de cit to import capital But the US must pay interest on the capital Since net foreign assets are negative in the steady state the US will have to pay interest each period Hence in steady state the US must earn a trade surplus to pay Japan the interest on the capital they invested If you have followed the argument to this point you may wonder about the path of the current account Itf It starts at zero then becomes negative then rises back to zero and stays there forever This may seem to violate the intertemporal budget constraint Shouldn t the current account be positive in the future to offset the de cit in the initial periods This is certainly true in any model with a nite time horizon In a nite horizon model there is a last period and nobody is ever going to plan to hold positive debt after death since you cannot get paid back after you are dead If we know that next period is the last period we will arrange our affairs so that accounts are balanced when time is up But in an in nite timehorizon model the intertemporal budget constraint is a bit different There is an in nity of future periods You can always borrow this period and pay it back next period That is you roll over the debt as long as people will lend to you When will they lend to you As 35 Current Account Part one Fall 2008 long as you can service the debt The constraint is now that the debt not rise so fast that it cannot be serviced If the debt grew faster than the economy for example then eventually the debt would be so large that interest payments would exceed production 7 an impossible situation20 But if the debt is constant and the economy is growing the burden is falling each period making repayment easier In the case we consider net foreign assets are constant in the steady state Since it is constant the present value of this amount is going to zero 23 A Rise in Productivity What about an increase in productivity in the US To make life simple suppose that initially Japan and the US have the same savings rate productivity level and technologies and that we are initially in steady state equilibrium Then we know that E U5 and HUS mfg AtkEf 73 41 Now suppose that Aim gt A2 This will cause the transition curve to shift up for the US At the initial capital stock the rate of return is now higher in the US than in Japan Japanese savers will want to invest in the US rather than in Japan which will increase the rate of capital accumulation in the US and speed the adjustment of the capital stock Japanese savers still save their income at the same rate 04 as before But they hold more foreign assets and less domestic capital Notice that immediately after the productivity change we must have TtUS Agskf gt Agki Ti because Aim gt A2 and nothing else has changed The only way returns can become equalized is if 121 rises21 This raises the return to investing in Japan and reduces it in the US So Japan will spend less domestically and acquire more foreign assets In other words its current account balance will improve 20This would be a Ponzi game 7 a process that is only feasible if one can nd an increasing number of gullible people each period But the number required would be exponential That is why a Ponzi game always collapses Economists thus refer to the intertemporal budget constraint as a noiPonzi game condition For more on Ponzi see httpenwikipediaorgwikiPonziischeme 21 Notice that this means that an improvement in technology in a country leads to more capital accumulation After the fact we would observe that y increased and that k increased We might like to know how much of the growth in income was due to technology and how much to capital accumulation But our measurement could be distorted by the induced investment that was the result of the improvement in A Why is this important Because in practice economists measure A as a residual after measuring the effect of the growth in k on y 36 Current Account Part one Fall 2008 Since we started with 41 net capital ows were zero in the initial equilibrium The increase in productivity will cause a net capital in ow so thH gt th for Japan and thH lt th for the US That is Ifquot gt 0 and IZUS lt 0 This follows because Japanese savers are acquiring more US assets than they are selling and vice versa From 39 and 40 it follows that the current account in Japan must become positive and in the US it must become negative The deterioration of the US current account is of course just another way of noting the in ow of foreign capital 7 the net capital in ow The current account de cit is enabling the US to adjust to the productivity improvement Japanese savers whose preferences recall are identical to American savers preferences will hold more US assets to improve the average return on their savings To do so requires them to accumulate foreign assets and this can only be done through current account surpluses 1n the steady state E and F115 will be constant so no further net foreign accumulation is necessary The adjustment of the current account and net foreign assets looks the same as in gure 24 Future US current account surpluses are needed to repay the current account de cit This response of the current account to a rise in productivity may be a good explanation of why the US had a current account de cit in the 1990 s Capital owed to the US in response to a rise in productivity This seems less likely to explain the situation in the last several years as is evident in gure 25 You can clearly see that investment was increasing in the 1990 s but that it has declined as a share of GDP since 2000 Meanwhile there has been a big decline in net public savings In the new steady state output is higher in the US than before This new higher level of output allows the US to service the debt or transfer the income on foreign owned capital to Japan This transfer allows Japan to have higher consumption than would be possible in autarky since in that case Japan would not be able to share in the productivity gains in the US Is the US also better off in the open case Certainly 1n the autarchic case there would be less savings available so it would take longer to get to the new steady state E The present value of consumption would thus be lower With open capital markets we get to the new steady state value sooner so total consumption possibilities are increased The Japanese 37 Current Account Part one Fall 2008 MO 29 00 53 4quot 23 on 23 43 an 1270 972 137A 975 975 195 32 1954 i685 IBM 3930 I987 IRE B 2000 12 ElletsteholdSavmgS N Covpolale Sawngs N Net Forelgn Savtngs Source BEA US International Transactions Figure 25 US Savings and Investment 19702003 obtain some of these gains but not all 7 will decrease Thus the interest differential will fall until Notice that as 1 4ka increases we reach the new steady state In the new steady state we must have E lt Egg It is the capital stock that adjusts to the difference in productivity levels If these differences remain so will capitalelabor ratios That helps explain why capital ows do not equalize capital labor ratios in the US and India If you ignored the differences in productivity then you would expect the return to capital to be higher in the poorer country as it has less capital Then you might expect capital to ow from rich to poor countries This does not seem to happen One reason is risk of course and we shall have lots of reasons to discuss this But another is productivity and it is worth a mention here A little arithmetic will go a long way right now 22How much larger the US capital stock w111 be than Japan s clearly depends on p which determines the rate at which the interest rate changes as k does ngotice that now we have different steadyrstate capitalrlabor ratios in the two countries This was not the case when we looked at different savings rates The reason 1e that differences in productivity affect the marginal product of capital So for factor pnee equalization It s w111 have to d er 38 Current Account Part one Fall 2008 First let us suppose that there were not differences in productivity India s per capita income is about that of the US If AIndZa AUS it follows that Now a good estimate of capital s share of national income would be 04 a rough average of the two countries This would imply that the capital labor ratio in the US is 1525 m 871 times greater than it is in India This is obviously way too high It would imply that we save at a rate per worker that is 800 times higher than that of India Moreover if the capital labor ratio were really this much higher in the US than in India the return to capital in India would be about 58 times higher24 But this should mean that capital should ow from the US to India at quite a rapid rate Some does but not that much25 Why One reason could be TFP differences Aluma lt AUS would alter the rate of return calculation26 Explaining these differences is one of the most important issues in development economics But we will ignore them here for the most part 24 War and the Current Account War provides an interesting way to test some of the predictions of the model During a war expenditure rises above its long run level while savings typically decreases Future income is borrowed against to ght the war It is a period of temporarily high spending so we would expect the current account to deteriorate 1n non belligerent countries on the other hand the terms for lending improve In terms of gure 11 the SS curve shifts to the left for the belligerents The world interest rate must rise This increases the return to the neutral countries from lending We should expect the current 24To see this note that if we ignore A the marginal product of capital per worker is 7 le8 1 From expression 30 it follows that k ylB Now using this in the expression for 7 we obtain 7 Since yUS 15 yIndia we have Tfndia 717515 Now 151395 is about 58 so the rate of return would have to be 58 times higher in India than the US 25This is sometimes referred to as the Lucas Paradox Robert Lucas rst pointed out that capital ows to developing countries were too small compared with predictions of standard economic models 26You can see this by taking the opposite assumption TUS rma and letting differences in A explain the higher US output 39 Current Account Part one Fall 2008 Fracliun 0 our 015 01 ms Sweuen c uu5 70 Japan us WWW 39 39 39 lam 1m ms was 1397 mm ms 92 was r912 Flgur 16 Curran ascunnu u Japan and swcdcu Imam Figure 26 Current Account Balances in Japan and Sweden accounts of the neutral countries to improve This feature is indeed evident in the experience of Japan and Sweden in WW1 as in gure 26 Lending by neutrals to belligerents is an old feature of history But there is one limitation A sovereign borrower may repudiate his debts27 There is no enforcement mechanism you can use against a sovereign borrower short of war28 This is what Edward Ill did after his invasion of Rance yielded poor results As a consequence international lending is constrained by fear of repudiation as well Success in war increases borrowing ability This means that the observed effect of war on the current account is attenuated somewhat by the fear of repudiation 27Accordrng to Adam Snorth HWhen natrona1 debts have once been accumulated to a certarn degree there rs scarce Ibeheve a srng1e rnstance of therr havrng been fairly and corup1ete1y pard The 1rberatron of pubhc revenue 1f rt has ever been brought about at am has a1ways been brought about by a bankruptcy soroetrnres by an avowed one but a1ways by a rea1 one though frequently by a pretended paynrent rn a deprecrated currency When rt beconres necessary for a state to dec1are itself bankrupt rn the same manner as when rt beconres necessary for an rndrvrdua1 to do so a fair open and avowed bankruptcy rs a1ways the measure whrch rs both 1east drshonourab1e to the debtor and 1east fruitful to the credrtor Wea1th of Natrons Book v Chapter III 882 28You may wonder then why people lend to soverergns that rs why don t they always repudrate debts What rs the sanctron that prevents repudratronv Thrs rs an rnterestrng questron rs access to caprta1nrarkets the answer7 That rs do countrres fear the 1oss of future borrowrng opportunrtres so much that they pay back 1oans that they otherwrse would repudratev Thrs rs an rnterestrng theory but what about countrres that default on therr debts but str11 are ab1e to borrow rn rnternatrona1 ruarketsv We wrh return to thrsrssue1ater 25When the RussorJapanese war broke out Japan borrowed at an annua1 rate of 7 5 but by 1905 once rt was c1ear that Japan was gorng to wrn the war rts cost of borrowrng fell to 5 5 40

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