The open-economy LM curve is no different from the closed-economy LM curve.

Transcription

1 5. MONEY MARKET EQUILIBRIUM: DERIVING THE LM CURVE 5 Money Market Equilibrium: Deriving the LM Curve In this section, we derive a set of combinations of Y and i that ensures equilibrium in the money market, which can be represented graphically as the LM curve. The open-economy LM curve is no different from the closed-economy LM curve. 5.1 Deriving the LM Curve Let s first recap the money market: In the short run, the price level is assumed to be sticky at a level P, and the money market is in equilibrium when the demand for real money balances L (i) Y equals the real money supply M/P : to a rise in the interest rate from i 1 to i 2. Thus, the LM curve is downwardsloping, indicating that there is a negative relationship between i and Y for which the money market is in equilibrium. M P = L (i) Y Note that the nominal interest rate adjusts to bring the money market into equilibrium. We now derive the LM curve by asking a question: What happens in the money market when an economy s output changes? Initially, the level of output is Y 1 and the money market is in equilibrium at point 1, where real money demand is on MD 1 at M/P = L (i 1 ) Y 1. Then, an increase in output from Y 1 to Y 2 leads Page: 27

2 5. MONEY MARKET EQUILIBRIUM: DERIVING THE LM CURVE 5.2 Factors That Shift the LM Curve We consider the factors that shift the LM curve. An important reason for a shift in the LM curve is a change in the real money supply M/P. The LM curve tells us the interest rate i that equilibrates the money market at any given level of output Y. Given Y, we know that the equilibrium interest rate i depends on real money supply M/P, and so the position of the LM curve depends on M/P. As in the figure, an increase in the nominal money supply M with sticky prices raises real money supply from M 1 /P to M 2 /P and shifts the real money supply curve to the right from MS 1 to MS 2, thereby lowering the equilibrium interest rate from i 1 to i 2. This decrease in the interest rate when the level of output is unchanged at Y means a downward shift of the LM curve from LM 1 to LM 2. LM = LM ( M/P ) In this short-run model of the economy, prices are sticky and treated as given, so any change in the real money supply in the short run is caused by changes in the nominal money supply M, which for now we take as given (or exogenous). Thus, the position of the LM curve is a function of real money supply: In addition to changes in the money supply, exogenous changes in real money demand will also cause the LM curve to shift. For example, for a given money supply, a decrease in the demand for real money balances at a given level output Y will tend to lower the interest rate, all else equal, which would be depicted as a shift down in the LM curve. Page: 28

3 5. MONEY MARKET EQUILIBRIUM: DERIVING THE LM CURVE 5.3 Summing Up the LM Curve When prices are sticky, the LM curve summarize the relationship between output Y and the interest rate i necessary to keep the money market in short-run equilibrium. 1. The LM curve is upward-sloping. In the money market, if output rises, real money demand rises and to maintain equilibrium, real money demand must contract. This contraction in real money demand is accomplished by a rise in the interest rate. Thus, when output Y rises, the interest rate i also increases. 2. As for shifts in the LM curve, the following factors shift the LM curve shifts: M (rise in nominal money supply) Any shift left in the money demand function IS curve shifts down/right }{{} Decrease in equilibrium interest rate i at a given level of output Y Page: 29

4 6. THE SHORT-RUN IS-LM-FX MODEL OF AN OPEN ECONOMY 6 The Short-Run IS-LM-FX Model of an Open Economy We are now in a position to fully characterize an open economy that is in equilibrium in goods, money, and forex market, as shown in the IS-LM-FX figure that combines the goods market (the IS curve), the money market (the LM curve), and the forex (FX) market diagrams. 1. In panel (a), the IS and LM curves are both drawn. The goods and forex markets are in equilibrium when the economy is on the IS curve. The money market is in equilibrium when the economy is on the LM curve. Thus, all three markets are in equilibrium if and only if the economy is at point 1, the unique point of intersection of IS and LM. 2. In panel (b), the forex (FX) market is shown. The domestic return DR in the forex market equals the money market interest rate i. Equilibrium is at point 1 where the foreign return F R equals the domestic return DR equal to i. In the remainder of this chapter, we will use this IS-LM-FX model to analyze the short-run response of an open economy to various types shocks. In particular, we look at how government policies affect the economy in the short run and the extent to which they can be employed to enhance macroeconomic performance and stability. Page: 30

5 6. THE SHORT-RUN IS-LM-FX MODEL OF AN OPEN ECONOMY 6.1 Macroeconomic Policies in the Short Run We focus on the two main policy actions: 1. Changes in monetary policy, implemented through changes in the money supply M. 2. Changes in fiscal policy, involving changes in government spending G or taxes T. That is, we use the IS-LM-FX model to look at how a nation s key macro variables (output, exchange rates, trade balance) are affected in the short run by changes in these government macroeconomic policies. More importantly, we will examine only "temporary" changes in these policies. Long-run expectations about the future state of the economy are unaffected by the policy changes (in particular, the expected future exchange rate E e is held fixed.) This is because we are primarily interested in how governments use monetary and fiscal policies to handle temporary shocks and business cycles in the short run, and our model is applicable only in the short run. The key lesson of this section is that policies matter and can have significant macroeconomic effects in the short run. Moreover, their impacts depend in a big way on the type of exchange rate regime in place. So, we will examine temporary policy changes under (1) floating exchange rates and (2) fixed exchange rates separately. The key assumptions of this section are as follows: (1) The economy begins in a state of long-run equilibrium; (2) We then consider policy changes in the home economy, assuming that conditions in the foreign economy (i.e., the rest of the world) are unchanged; (3) The home economy is subject to the usual short-run assumption of a sticky price level at home and abroad; (4) Furthermore, we assume that the forex market operates freely and unrestricted by capital controls and that the exchange rate is determined by market forces. Page: 31

6 6. THE SHORT-RUN IS-LM-FX MODEL OF AN OPEN ECONOMY Monetary Policy under Floating Exchange Rates In this policy experiment, we consider a temporary monetary expansion in the home country when the exchange rate is allowed to float. The results are shown in the figure below. M/P LM shifts right (MS shifts right i for any given Y ), causing i and thus, DR shifts down, causing E Y A temporary monetary expansion under floating exchange rates is effective in combating economic downturns by boosting output it raises output at home, lowers the interest rate, causes a depreciation of the exchange rate, and is usually predicted to increase the trade balance. That is, monetary expansion tends to lower the home interest rate, all else equal. A lower interest rate stimulates demand in two ways: 1. i I directly in the goods market D 2. i E in the forex market T B (via expenditure switching) D Theoretically, what happens to T B cannot be predicted with certainty: (1) Y IM T B ; (2) E EP /P T B. In practice, economists tend to assume that the latter outweights the former. Page: 32

7 6. THE SHORT-RUN IS-LM-FX MODEL OF AN OPEN ECONOMY Monetary Policy under Fixed Exchange Rates Now let s look at what happens when a temporary monetary expansion occurs in a home country that pegs its exchange rate with respect to the foreign country at E. The key to understanding this experiment is to recall the UIP: the home interest rate must equal the foreign interest rate under a fixed exchange rate. The figure shows the results: A temporary monetary expansion that increases the money supply from M 1 to M 2 would shift the LM curve down in panel (a). In panel (b), the lower interest rate would imply that the exchange rate must depreciate, rising from E to E 2. This depreciation is inconsistent with the pegged exchange rate. So the policy makers cannot move LM in this way. They must leave the money supply equal to M 1 and the economy cannot deviate from its initial equilibrium. shift in the LM curve would violate this restriction and break the fixed exchange rate. Monetary policy under fixed exchange rates is impossible to undertake. Fixing the exchange rate means giving up monetary policy autonomy. In an earlier chapter, we learned about the trilemma: countries cannot simultaneously allow capital mobility, maintain fixed exchange rates, and pursue an autonomous monetary policy, which work in the IS-LM-FX framework. Under a fixed exchange rate, autonomous monetary policy is not an option. Remember that under a fixed exchange rate, the home interest rate must exactly equal the foreign interest rate, i = i, according to the UIP condition, so any Page: 33

8 6. THE SHORT-RUN IS-LM-FX MODEL OF AN OPEN ECONOMY Fiscal Policy under Floating Exchange Rates We consider a temporary increase in government spending from G 1 to G 2 in the home country that adopts a floating exchange rate regime. The results are shown the figure. G IS shifts right, causing i and DR shifts up, causing E. 1. Direct effect: G D An expansion of fiscal policy under floating exchange rates might be temporary effective. It raises output at home, raises the interest rate, causes an appreciation of the exchange rate, and decreases the trade balance. It indirectly leads to a crowding out of investment and net exports, and thus limits the rise in output to less than an increase in government spending. 2. Indirect effect: (1) i I D ; (2) i E T B D As the interest rate rises (decreasing investment) and the exchange rate appreciates (decreasing the trade balance), demand falls. This limits the rise in demand to less than the increase in government spending. Note that this impact of fiscal expansion on investment is often referred to as crowding out. Thus, in an open economy, fiscal expansion not only crowds out investment (by raising the interest rate) but also crowds out net exports (by causing the exchange rate to appreciate). Over time, it limits the rise in output to less than the increase in government spending. Page: 34

9 6. THE SHORT-RUN IS-LM-FX MODEL OF AN OPEN ECONOMY Fiscal Policy under Fixed Exchange Rates We consider a temporary increase in government spending when the home country pegs its exchange rate with respect to the foreign country at E. The key to understanding this experiment is that any fiscal policy action will be paired with a change in the money supply that shifts the LM curve: under a fixed exchange rate regime, the real money supply must be adjusted to ensure the nominal exchange rate remains fixed. The results are shown in the figure below. A temporary fiscal expansion would shift the IS curve to the right in panel (a), leading to an increase in the interest rate, which would then cause the domestic return to rise. In panel (b), the higher interest rate would imply that the exchange rate must appreciate, falling from E to E 2. Thus, when a country is operating under a fixed exchange, fiscal policy is supereffective because any fiscal expansion by the government forces an immediate monetary expansion by the central bank to keep the exchange rate steady the double and simultaneous expansion of demand by the fiscal and monetary authorities imposes a huge stimulus on the economy. A temporary expansion of fiscal policy under fixed exchange rates raises output at home by a considerable amount. To maintain the peg, however, the monetary authority must now intervene, shifting the LM curve down, from LM 1 to LM 2. The fiscal expansion thus prompts a monetary expansion. In the end, the interest rate and exchange rate are left unchanged, and output expands dramatically from Y 1 to Y 2. Page: 35

10 6. THE SHORT-RUN IS-LM-FX MODEL OF AN OPEN ECONOMY 6.2 Summary of the Impacts of Monetary and Fiscal Policies We have examined the operation of fiscal and monetary policies under both floating and fixed exchange rates and have seen how the impacts of these policies differ dramatically depending on the exchange rate regime. The outcomes can be summarized as follows (the effects would be reversed for contractionary policies): 1. In a floating exchange rate regime, autonomous monetary and fiscal polices are feasible. (a) The power of monetary policy to expand demand comes from two forces in the short run: (1) lower interest rates boost investment and (2) a depreciated exchange rate (caused by lower interest rates) boosts the trade balance, all else equal. In the end, though, the trade balance will experience downward pressure from an import rise due to the increase in home output/income. The net effect on output and investment is positive, and the net effect on the trade balance is unclear but in practice, it is likely to be positive too. Note that the row of zeros for monetary expansion under fixed exchange rates reflects the fact that this infeasible policy cannot be undertaken. (b) Expansionary fiscal policy is also effective, even though the impact of extra spending is offset by crowding out in two areas: (1) investment is crowed out by higher interest rates and (2) the trade balance is crowed out by an appreciated exchange rate. Thus, on net, investment falls and the trade balance also falls, the latter effect is unambiguously amplified by additional import demand due to increased home output. Page: 36

11 6. THE SHORT-RUN IS-LM-FX MODEL OF AN OPEN ECONOMY 2. In a fixed exchange rate regime, only fiscal policy is feasible. (a) Monetary policy loses its power for two reasons: (1) interest parity implies that the domestic interest rate cannot move independently of the foreign interest rate, so investment demand cannot be manipulated; (2) the peg means that there can be no movement in the exchange rate, so the trade balance cannot be manipulated by expenditure switching. (b) Fiscal expansion requires a monetary expansion to keep interest rates steady and maintain the peg. Fiscal policy becomes ultra-power in a fixed exchange rate setting the reason for this is that if interest rates and exchange rates are held steady by the central bank, investment and the trade balance are never crowed out by fiscal policy. Monetary policy follows fiscal policy and amplifies it. Page: 37

12 7. STABILIZATION POLICY 7 Stabilization Policy We have seen that macroeconomic policies can affect economic activity in the short run These effects open up the possibility that the authorities can use changes in policies to try to keep the economy at or near its full-employment level of output this is the essence of stabilization policy. If the economy is hit by a temporary adverse shock, policy makers could use expansionary monetary and fiscal policies to prevent a deep recession. For example, suppose a temporary adverse shock such as a sudden decline in investment, consumption, or export demand shifts the IS curve to the left. Or suppose an adverse shock such as a sudden increase in money demand suddenly moves the LM curve up. Either shock would cause home output to fall. In principle, the home policy makers could offset these shocks by using fiscal/monetary policy to shift either the IS curve or LM curve (or both) to cause an offsetting increase in output. Conversely, if the economy is pushed by a shock above its full employment level of output, contractionary policies could tame the boom. When used judiciously, monetary and fiscal policies can thus be used to stabilize the economy and absorb shocks. In practice, however, stabilization policy is challenging. If the economy is stable and growing, an additional temporary monetary or fiscal stimulus may cause an unsustainable boom that will, when the stimulus is withdrawn, turn into an undesirable bust mistakes in both fiscal and monetary policy have been made in the past and will undoubtedly be made in the future. In their efforts to do good, policy makers must be careful not to destabilize the economy through the ill-timed, inappropriate, or excessive use of monetary and fiscal policies. Page: 38

13 7. STABILIZATION POLICY 7.1 Application: Australia, New Zealand, and the Asian Crisis of 1997 Australia and New Zealand are open economies that rely on export demand from East Asian economies. In 1997, the East Asian economic crisis led to a recession in these countries, reducing demand for exports of Australia and New Zealand. Australia and New Zealand represent the home country and East Asian economies do the foreign country. A decrease in foreign output, Y, leads to a decrease in the home country s trade balance (through decreasing exports). From the model, the net effect of the decrease in export demand and the monetary expansion is as follows: 1. No change in output. 2. Decrease in nominal interest rate investment increases. 3. Increase in the exchange rate ambiguous effect on the trade balance because decrease in foreign income reduces exports whereas depreciation increases exports. This is illustrated as a leftward shift in the IS on Figure As a result, this would lead to an economic contraction in the home country (i.e., Australia and New Zealand). What is the appropriate stabilization policy? In this case, either fiscal or monetary expansion is the answer. Both countries chose to use monetary policy. The central banks in both countries expanded the real money supply, shifting the LM curve to the right and reducing interest rates. Page: 39

14 7. STABILIZATION POLICY The figure shows data for the Australia and New Zealand economies in this period. Australian and New Zealand exports were likely to be badly hit after the 1997 Asian crisis as the incomes of their key trading partners contracted. 1. Both countries were operating on a floating exchange rate. To bolster demand, the central banks in both countries pursued an expansionary monetary policy, lowering interest rates, as shown in panel (a), and allowing the domestic currency to depreciate about 30% in nominal terms, as shown in panel (b). 2. This contributed to a real depreciation of about 20% to 30% in the short run, as shown in panel (c). As a result, the trade balance of both countries moved strongly toward surplus, illustrated in panel (d), and thus demand was higher than it would otherwise have been. In each country, a recession was avoided. Page: 40

15 7. STABILIZATION POLICY 7.2 Problems in Policy Design and Implementation We have looked at open-economy macroeconomics in the short run and at the roles that monetary and fiscal policies can play in determining economic outcomes. Our simple models have clear consequences. If policy makers were really operating in such an uncomplicated environment, they would have the ability to exert substantial control and could always keep output steady with no unemployed resources and no inflation pressures. However, in practice, their ability to implement such policies is limited by several factors. 1. Policy constraints Policy makers may not always have the freedom to implement desirable stabilization policies. For example, a fixed exchange rate rules out any use of monetary policy. In the case of fiscal policy, countries with weak tax systems or poor creditworthiness problems that affl ict developing countries may find themselves unable to tax or borrow to finance an expansion of spending even if they wished to do so. 2. Incomplete information and the inside lag Our models assume that the policy makers have full knowledge of the state of the economy before they take corrective action: they observe the economy s IS and LM curves and what shocks have hit. In reality, macroeconomic data are compiled slowly and it may take weeks/months for policy makers to fully understand the state of the economy today. Even then, it will take time to formulate a policy response (the lag between the timing of the shock and the policy action is known as an inside lag). On the monetary side, there may be a delay between policy meetings. On the fiscal side, it may take time to pass a bill through the legislature and then enable a real change Page: 41

16 7. STABILIZATION POLICY in spending or taxing activity by the public sector. 3. Policy response and the outside lag Even with perfect information on the economy, policy makers then have to formulate the right response given by the model. In particular, they must not be distracted by other policies or agendas, nor subject to influence by interest groups that might wish to see different policies enacted. It may also take time for an implemented policy to have real economic effects, through the spending decisions of the public and private sectors (the lag between policy actions and effects is called an outside lag). The outside lag is a particular problem for monetary policy. While the central bank can control shortterm nominal interest rates, what matters for investment spending is long-term real interest rates. It usually takes more than a year for a change in monetary policy to seriously impact the real economy. 4. Long-horizon plans If households and businesses making decisions about consumption and investment plan over long horizons, they may be less responsive to temporary policy changes. For example, if a business borrows to finance capital expansion, it will likely borrow over a long period of time. Slightly higher interest rates today may be unsuccessful in deterring this investment decision because the business knows the higher interest rates are temporary. 5. Weak links from the nominal exchange rate to the real exchange rate Our models assume that changes in nominal exchange rates translate into changes in the real exchange rate, the rate that matters for export/import decisions. But, the reality can be somewhat different for some goods and services. For example, the dollar depreciated 42% against the euro from 2002 to 2004, but the U.S. prices of Page: 42

17 7. STABILIZATION POLICY German cars like BMWs barely changed. Why? There are a number of reasons for this weak pass-through phenomenon, including the dollarization of trade and large distribution margins that create a wedge between port prices and retail prices. The forces of arbitrage may also be weak as a result of noncompetitive market structures. For example, BMW sells through exclusive dealers and government regulation requires that cars meet different standards in Europe versus the U.S.. These obstacles allow a firm like BMW to price to market: to charge a steady U.S. price even as the exchange rate moves temporarily. If a firm can bear the exchange rate risk, it might do this to avoid the volatile sales and alienated customers that might result from repeatedly changing its U.S. retail price list. 6. Weak links from the real exchange rate to the trade balance Our models assume that real exchange rate changes lead to changes in the trade balance. However, there may be several reasons why these linkages are weak in reality. transaction costs. One major reason is Suppose the exchange rate is $1 per euro and an American is consuming a domestic good that costs $100 as opposed to a European good costing 100 = $100. If the dollar appreciates to $0.95 per euro, then the European good looks cheaper on paper, only $95. Should the American switch to the import? (a) Yes, if the good can be moved without cost but there are few such goods. (b) If shipping costs $10, it still makes sense to consume the domestic good until the exchange rate falls below $0.90 per euro. Practically, this means that expenditure switching may be a nonlinear phenomenon: it will be weak at first and then much stronger as the real exchange rate change grows larger. This phenomenon, coupled with the J curve effects discussed earlier, may cause the response of the trade balance in the short run to be small or even in the wrong direction. Page: 43

18 7. STABILIZATION POLICY 7. Pegged currency blocs Our model predictions are also affected by the fact that for some major countries in the real world, their exchange rate arrangements are characterized often not as a result of their own choice by a mix of floating and fixed exchange rate system with different trading partners. From 2002 to 2004, the U.S. dollar depreciated markedly against the euro, pound, and several other floating currencies, but in the "Dollar Bloc" (Japan, China, India, and others), the monetary authorities have ensured that the variation in the value of their currencies against the dollar is small or zero. When a large bloc of other currencies pegs to the U.S. dollar, this limits the ability of the U.S. to engineer a real effective depreciation. Page: 44

19 7. STABILIZATION POLICY 7.3 Application: Macroeconomic Policies in the Liquidity Trap One of the most controversial experiments in macroeconomic policy making began in as monetary and fiscal authorities around the world tried to respond to the major recession that followed the global financial crisis. The unusual aspect of this crisis was the very rapid realization that monetary policy "alone" could not fully offset the magnitude of the shock to demand. Here is the situation after a severe negative shock to demand. In the context of our IS-LM-FX model, as consumption and investment fell for exogenous reasons, the shock moved the IS curve very far leftward. One major source of the demand shock was that banks were very afraid of taking on risk and sharply reduced their lending to firms and households and even when they did lend, they were still charging very high interest rates. Thus, even with very expansionary monetary policy, that is, a large rightward shift of the LM curve, low policy rates did not translate into cheap borrowing for the private sector. Once the U.S. Fed had brought its policy rate to zero in December 2008, there was little more it could do to simulate demand using conventional monetary policies. Page: 45

20 7. STABILIZATION POLICY This particular situation is depicted by the blue lines in the figure. After the demand shock and the Fed s response to it, the IS curve has moved so far in to IS 1 and the LM curve has moved so far out to LM 1, so that the IS and LM curves now intersect at a very low interest rate: so low that it is equal to zero. The situation is unusual because monetary policy is powerless in this situation: it cannot be used to lower interest rates because interest rates can t go any lower. In the diagram, moving the LM curve out to LM 2 does not dislodge the economy from the horizontal portion of the LM curve: we are still stuck on the IS 1 curve at a point 1 and a 0% percent interest rate. This unfortunate state of affairs is known as the zero lower bound (ZLB). It is also known as a liquidity trap because liquid money and interest-bearing assets have the same interest rate of zero, so there is no opportunity cost to holding money, and thus changes in the supply of central bank money have no effect on the incentive to switch between money and interest-bearing assets. Page: 46

21 7. STABILIZATION POLICY Can anything be done? YES. The bad news is that fiscal policy is the only tool now available to increase demand. The good news is that fiscal policy has the potential to be super powerful in this situation, because as long as interest rates are stuck at zero and the monetary authorities keep them there, government spending will not crowd out investment or net exports, in contrast to the typical situation we studied earlier. In 2009 because the Fed and the private sector anticipated more than a year or two of very high unemployment and falling inflation, everyone had expectations of zero interest rates for a long period. The U.S. used fiscal policy to try to counteract the recession, but it did not work as well as one might have hoped. The U.S. government s fiscal response took two forms. 1. First were the automatic stabilizer built into existing fiscal policies, changes in government spending and taxes that automatically move in countercyclical directions. In our models, we have assumed that taxes and government spending are fixed. In reality, however, they are not fixed, but vary systematically with income. When income Y falls in a recession, receipts from income taxes, sales taxes, and so on, all tend to fall as well. 2. The second was the American Recovery and Reinvestment Act (ARRA), better known as the "stimulus" bill. This policy was signed into law on Feb. 17, 2009; Originally hoped for a $1.4 trillion package, mostly for extra government consumption and investment spending, and also for aid to states; Spread over 2 to 3 years from However, the final compromise deal with Congress was only half as big, $787 billion over three years, and was tilted toward temporary tax cuts; Most of the stimulus was scheduled to take effect in 2010, not 2009, reflecting the policy lags. Page: 47

22 7. STABILIZATION POLICY Some key outcomes are shown in the figure. 1. In the U.S. economic slump of , actual GDP had fallen 6% below the estimate potential (full-employment) level of GDP by the first quarter of 2009, as seen in panel (a) this was the worst U.S. recession since the 1930s. This output gap of 6% of GDP or over $1 trillion at an annual rate left a huge hole to be filled by fiscal policy. Even if the entire stimulus was spent, the fiscal package could at best have filled only about 1.5% of GDP. Thus, Policy makers in the government and many observers knew the package was too small, but politics stood in the way of a larger package. 3. Thus, government spending G was left to do a great deal of the stimulation, but problems arose because of the contrary effects of state and local government policies: on the government spending side there was no stimulus at all in the aggregate. Increases in federal government expenditure were fully offset by cuts in state and local government expenditure, as seen in panel (b) 2. One intention of ARRA was to support private spending through tax cuts, but this tax part of the stimulus appeared to do very little: Significant reductions in federal taxes seen in panel (b) were insuffi cient to prop up consumption expenditure, as seen in panel (a), because consumers used whatever "extra" money they got from tax cuts to pay down their debts or save, being unsure about the economic recovery and worried about the risks of unemployment. Page: 48

23 7. STABILIZATION POLICY To sum up, the aggregate U.S. fiscal stimulus had four major weakness: 1. It was rolled out too slowly, due to policy lags. 2. The overall package was too small, given the magnitude of the decline in aggregate demand. 3. The government spending portion of the stimulus, for which positive expenditure effects were certain, ended up being close to zero, due to state and local cuts. 4. This left almost all the work to tax cuts (automatic and discretionary) that recipients, for good reasons, were more likely to save rather than spend. With monetary policy impotent and fiscal policy weak and ill designed, the economy remained mired in its worst slump since the 1930s Great Depression. Page: 49

24 8. THE APPENDIX 8 The Appendix 8.1 The Marshall-Lerner Condition Our model assumes that a depreciation of a country s currency (a rise in q) will cause the trade balance T B to move toward surplus (a rise in T B). q T B Is this assumption justified? For simplicity, assume T B = 0 or EX = IM. Let s consider a small percentage change in the real exchange rate, say, q/q = +1% (a home real depreciation of 1%), indicating that this is approximately a foreign real appreciation of 1% since the foreign real exchange rate q = 1/q, and thus, q /q = 1%: q q = +1%; q q = 1% As we have argued, when home exports look cheaper to foreigners (foreign exports look cheaper to home entities), the real value of home (foreign) exports expressed in home (foreign) units of output, that is, real exports, will "unambiguously" rise in other words, when the real exchange rate increases, real exports must rise. This effect is described by the elasticity of home (foreign) exports with respect to the home (foreign) real exchange rate denoted by η (η ): EX (q) EX (q) = η q q = η%; EX (q ) EX (q ) Note that these elasticity can be rewritten as: = η q q = η % / EX (q) q EX (q) q d log (EX (q)) = d log (q) = η; / EX (q ) q = d log (EX (q )) EX (q ) q d log (q ) = η (8.1) Page: 50

25 8. THE APPENDIX We now consider the trade link between the two countries: Foreign exports must equal home imports, measured in any consistent units. In home real output units, Home imports in units of home ouput = IM (q) }{{} Home imports (real) and Foreign exports in units of home ouput = (1/P ) }{{} Divided by home price level to convert to home output units E }{{} Exchange rate converts foreign to domestic currency P }{{} Price of foreign basket in foreign currency EX (q ) }{{} Foreign imports (real) } {{ } } Value of foreign exports in foreign currency {{ } Value of foreign exports in home currency Equating these two terms, we find that: IM (q) = EP P EX (q ) or IM (q) = q EX (q ) (8.2) Intuitively, the quantity of home imports (measured in home output) IM must equal the quantity of foreign exports EX (measured in foreign output units) multiplied by a factor q that converts units of foreign goods to units of home goods (since q is the price of foreign goods relative to home goods, that is, home goods per unit of foreign goods). Page: 51

26 8. THE APPENDIX From equation (8.2), we have: d log (IM (q)) d log (q) = 1 + d log (EX (q )) d log (q) Since q = 1/q and d log (EX (q )) /d log (q ) = η, this elasticity of home imports with respect to the home real exchange rate (the left hand side) can be expressed as: IM(q) IM(q) / q q = d log(im(q)) d log(q) = 1 η (8.3) What is going on here? On the home import side, two effects come into play: Foreigners export a lower volume of their more expensive goods measured in foreign output units (a volume effect of η %), but those goods will cost more for home importers in terms of home output (a price effect of +1%) the price effect follows because the real exchange rate (the relative price of foreign goods in terms of domestic goods) has increased (by 1%), and this makes every unit of imports cost more in home real terms. Finally, we examine the effect of the real depreciation on the trade balance, based on the elasticities of exports and imports with respect to the real exchange rate (i.e., equations (8.1) and (8.3)). Starting from balanced trade with EX = IM, a 1% home real depreciation will cause EX to change by η% and IM to change by 1 η %. Thus, the trade balance (initially zero) will increase (to become positive) if and only if the former impact on EX exceeds the latter impact on IM (η > 1 η ) or, equivalently: η + η > 1 (8.4) It is known as the Marshall-Lerner condition: it says that the trade balance will increase only after a real depreciation if the responsiveness of trade volumes to real exchange rate changes is suffi ciently large (or suffi ciently elastic) to ensure that the volume effect ( η + η ) exceed the price effects ( 1). Page: 52