Chapter 4 Theories of Business Cycle

Transcription

1 Chapter 4 Theories of Business Cycle In this chapter we introduce theories that explain short-term business cycles. The word short-term is tricky. Three years may be short-term for some people (e.g., macroeconomist), but long-term for others (e.g., stock market speculators). Here we avoid giving precise definition and loosely define short-term as the time frame within which prices are inflexible. In the previous chapter, for the purpose of discussing long-run equilibrium, we assume that prices (including wage) are flexible. This implies that output is determined only by technology and inputs, which must be fully employed, thanks to the flexible prices. In other words, output and income are determined by the supply side of the economy, in the long run. We will make the same assumption (flexible price) in the next chapter when we talk about economic growth, which must also be understood in long time span. While some economists may argue that short-run fluctuations are also due to real shocks to the supply side, this text does not take such extreme stand. Instead, we shall relax the assumption of flexible prices and discuss the implications of sticky price on the economy. As we shall see, the stick-price assumption makes the demand side important, at least in the short run. The demand side can be influenced by many factors including, among others, consumer and investor confidence, monetary and fiscal policies of the government, and so on. The bad thing about a sticky-price economy is that the economic performance may be quite volatile. The good (or relieving) thing is that government policies may be useful in taming violent up-and-downs. In the rest of the chapter, we first give a brief overview of business cycles in China and the US. We then introduce the crucial assumption of sticky price. Under this assumption, we introduce the celebrated IS-LM model, which is the leading interpretation of the Keynesian theory. Next we derive the Aggregate Demand (AD) model from the IS-LM model, which makes the sticky-price assumption explicit. Then we introduce the Mundell-Fleming model, which is an open-economy Keynesian model. After finishing the discussions on the demand side, we introduce a theory of aggregate supply, which in a sense completes the model. Finally, we introduce a dynamic AD-AS model. 4.1 Business Cycles The business cycle is the upward and downward movement of output around the longterm trend. The business cycle is most often measured in terms of the growth rate of real GDP. A stylized business cycle starts from a peak, where the growth rate is the highest and the economic activity is the most vibrant. Then the growth rate starts to decline. If the growth rate declines to the negative territory, we say the economy falls

2 in a recession. The growth rate continues to decline, till reaching a trough. Then the growth picks up. When the growth rate rises above zero, we say that the economy is in expansion. The economy continues to expand and eventually reaches another peak, finishing a business cycle. (See Figure 1) Figure 1: A Stylized Business Cycle The actual business cycle is much more complicated. See Figure 2 for a graph of the quarterly real GDP growth of the United States from the end of World War II to Figure 2: Growth Rate of Real GDP in the US Source: FRED, U.S. Bureau of Economic Analysis. We can see from the figure that the growth rate is persistent, meaning that high growth often follows high growth. In addition, expansion is often long and recession (grey area) is often short-lived.

3 Figure 3 shows the growth rate of real GDP in China from 1953 to We can see that the growth rate before the 1978 was highly volatile, often due to political instability. The reform of 1978 ushered in more than 30 years of high growth. Since 1990s, the business cycles of China became more and more synchronized with those in other economies. The slowdown in late 1990s and the boom-and-bust around are accompanied with the Asian Financial Crisis and the Global Financial Crisis, respectively. Figure 3: Macroeconomic Fluctuations in China 4.2 The Keynesian Cross Before we introduce the IS-LM model, we first study a simple model called The Keynesian Cross. We assume that the planned expenditure is the sum of planned consumption, planned investment and planned government purchase, PE = C(Y T) + I + G, where the tax (T), investment (I), and the government purchase (G) are exogenously fixed. In equilibrium, the planned expenditure has to be equal to the actual expenditure (Y), Y = PE = C(Y T) + I + G. (1) If the actual expenditure exceeds the planned expenditure, the inventory would be lower. This would induce firms to produce more. If the actual expenditure is lower than the planned, the inventory accumulation would induce firms to produce less. If the consumption function is linear, e.g., C(Y T) = C 0 + C 1 (Y T), then the righthand-side is a straight line with slope C 1 < 1, while the left-hand-side is a 45 degree

4 line. In this case, the solution of (1) can be graphically represented as the cross of the two lines (Figure 4), hence the name The Keynesian Cross. Figure 4: The Keynesian Cross The Keynesian Cross may be employed to study the effect of fiscal policy on output (income). Mathematically, the equilibrium condition (Y = C(Y T) + I + G) defines an implicit function Y(G, T, I). Y G Y and T measures, respectively, the effects of government purchase and tax on total income (or output). Using the implicit function theorem, we obtain Y G = 1 1 C (Y T). Note that C (Y T) is the marginal propensity to consume (MPC). Rewriting the above equation, we have Y = 1, which is often called the government purchase G 1 MPC multiplier. Similarly, we have Y C (Y T) 1 C (Y T) = MPC 1 MPC, T = which is called the tax multiplier. The above analysis is simplified if we assume that the consumption function is linear, C(Y T) = C 0 + C 1 (Y T), where the constant C 1 is exactly the marginal propensity consume (MPC). It is clear that the magnitude of Y G Y is always bigger than. This can be understood by noting that tax cuts affect the disposable income, which in turn induces individuals to consume, raising aggregate demand. That is to say, the immediate effect of tax cuts on the aggregate demand is moderated by MPC, which is always smaller than 1. The T

5 government spending (e.g., on public works), however, directly raises the aggregate demand. The multiplier effect is often used to justify fiscal stimulus. A multiplier greater than 1, in particular, is considered a necessary condition for government expenditures on public works. This is not the case, at least when the economy is in a deep recession and many resources (including the labor force) are idle. The government spending on public works would employ idle resources to build something useful, which is better than doing nothing. In other words, if the opportunity costs of the resources for building public works are low (e.g., employed people in a deep recession), then building public works always raises aggregate welfare. A big multiplier effect is thus a plus, not a necessary condition. We can easily extend the above analysis to an open economy, where part of the planned consumption, investment, and government spending are expended on imported goods. In this case, the increase in G (even when all of it are spent on domestic goods) would bring less increase in total income, since not all income generated from transactions (i.e., G) goes to domestic households, who are further induced to consume. This effect is often called leakage of fiscal stimulus. The leakage effect may lead to coordination failure in the world stage to combat global recession: every country is reluctant to implement stimulus package that benefits other countries as well. 4.3 The IS-LM Model In the Keynesian Cross model, investment is considered exogenous and there is no role for interest rate. In fact, an increase in investment would lead to the same multiplier effect as the government purchase. More realistically, however, investment should be considered endogenous, depending on, among other factors, financing cost measured by interest rate. We now present the IS-LM model that endogenizes interest rate, which determines investment. IS stands for investment and saving. LM stands for liquidity and money. The IS-LM model consists two equations that describe the financial market (IS, or equivalently the market for goods and services) and the money market (LM). The IS- LM model is the leading interpretation of John Maynard Keynes s theory, which was developed in the depth of the Great Depression. The IS Equation Assume that investment is a function of the interest rate, I = I(r). We assume that I(r) is differentiable and I < 0. That is, higher interest rate increases the borrowing cost, hence lowers the level of investment in the economy.

6 The IS equation is given by Y = C(Y T) + I(r) + G. The IS equation characterizes the equilibrium of the market for loanable funds (or goods market equilibrium). Treating T and G as exogenous, the IS equation defines an implicit function of Y(r) or r(y). That is, the IS curve. Since I(r) is a decreasing function, a decline in r results in higher investment, which leads further to higher Y. Hence r(y) is downward sloping. Using the implicit function theorem, we obtain the slope of the IS curve, dr dy = 1 C I = 1 C I, which is obviously negative. Figure 5 illustrates an IS curve. Every point on the IS curve is an equilibrium. As T or G changes, the curve would shift, leftward or rightward. Figure 5: The IS Curve For example, if there is an increase in government spending, say ΔG, then the IS curve would shift to the right. To see this, let s fix r. This makes the IS equation look like the Keynesian Cross equilibrium. A ΔG increase in government spending would result in an increase of ΔG 1 MPC in Y. This is true for every r. Hence a ΔG -increase in government spending would shift the IS curve to the right by illustration of the above argument is in Figure 6. ΔG 1 MPC. A graphical

7 Figure 6: The Effect of An Increase in Government Spending The LM Equation The LM equation characterizes the money market equilibrium (Liquidity demand = Money supply), M = L(r, Y). P M is the money supply, which is assumed to be exogenously given. (Imagine that the monetary authority controls M.) P is the price level, which is assumed to be fixed in the short term. L(r, Y) is decreasing in r and increasing in Y. L 1 < 0, L 2 > 0. Like the IS equation, the LM equation also defines an implicit function of Y(r) or r(y), the LM curve. The LM equation theorizes Keynes view of how interest rate is determined. It was called the theory of liquidity preference. Given M and P, for the LM equation to hold, a decline in r must be accompanied by a decline in Y. Hence the LM curve is an upward-sloping curve. To see this, suppose that there is a decline in income. This would reduce demand for money. Given the fixed money supply, the interest rate must decline.

8 Figure 7: The LM Curve Points on an LM curve are all consistent with equilibria in the money market, given a money supply M and a price level P. Fixing M and P, a change in Y or r would result in movement along the LM. Using the implicit function theorem, we obtain the slope of the LM curve, dr dy = L 2 L 1 δl(r, Y) δy δl(r, Y) δr There are two interesting extreme cases: if L 1 =, the LM curve is horizontal. On the other hand, if L 1 = 0, the LM curve is vertical. An change in M or P, however, would shift the LM curve, leftward or rightward. For example, if the monetary authority increases M, then the LM curve would shift rightward. See Figure 8 for an illustration..

9 Figure 8: The Effect of Monetary Expansion on the LM Curve The IS-LM Model The IS-LM model is composed of two equations characterizing goods and money markets, respectively, Y = C(Y T) + I(r) + G (2) M P = L(r, Y). (3) The equilibrium of the economy is the solution to the above two equations, i.e., the point at which the IS curve and the LM curve cross. See Figure 9 for an illustration.

10 Figure 9: The IS-LM Model Using the IS-LM model, we may explain a typical business cycle. Start with the peak of the previous cycle, when the economy overheats, optimistic investors over-leverage, and asset prices deviates substantially from what fundamentals can support. The stock market crashes, due to some bad news (failure of a major bank, credit tightening, etc.). This leads to less wealth for households and higher financing costs for businesses. Perhaps more importantly, the stock crash dents investor and consumer confidence almost immediately, resulting in less demand for consumption and investment goods. These would shift the IS curve to the left, resulting in less output and higher unemployment, which further depresses consumption demand. The nominal interest rate is usually determined by the monetary authority. If the monetary authority does not act quick enough, the real interest rate may increase, since inflation rate often decreases after financial crisis. The rise in real interest rate would make mortgage payment more expansive and depress housing prices, leading to less wealth for households and more bad loans for banks because of home foreclosures. As banks worry about their balance sheets, they reduce lending and further depress corporate and households investment. The government would eventually intervene. First, the monetary authority may cut interest rate and expand money supply, shifting the LM curve to the right. Second, the fiscal authority may reduce tax rate and increase government spending, shifting the IS curve to the right. As the consumer and investor sentiment gradually improve, households and companies start to spend money on consumption and investment goods again. These spending create more income for other households and companies, starting a virtuous cycle. The economy continues to expand and people use higher and higher leverage, paving way for the next round of boom-and-bust.

11 Policy Analysis with IS-LM We may analyze the effect of monetary and fiscal policy on the economy using the IS- LM model. Holding P fixed, we take total differentiation of the IS-LM equations and obtain (1 C )dy I dr = dg C dt PL 2 dy + PL 1 dr = dm, where I = I (r), L 1 = L(r,Y) r, L 2 = L(r,Y), and Y C = C (Y T) is the marginal propensity to consume (MPC). Expressing in matrix form, we have 1 C I [ ] [ dy ] = [dg C dt PL 2 PL 1 dr dm ] Using the Cramer s, we can obtain: The effect of increasing government purchases on income and interest rate: dy dg and dr dg The effect of tax reduction on income and interest rate: dy dt and dr dt The effect of expansionary monetary policy on income and interest rate: dr dm. dy dm and To analyze the effect of fiscal policies, we hold M fixed (that is,dm = 0). Using the Cramer s Rule, we obtain dy = L 1(dG C dt) L 1 (1 C ) + I. L 2 dr = L 2(dG C dt) L 1 (1 C ) + I L 2. The effect of fiscal policies can be summarized as follows, The effect of government purchase on output: dy dg = L 1 L 1 (1 C )+I L 2 > 0 The effect of government purchase on interest rate: dr dg = L 2 L 1 (1 C )+I L 2 > 0 The effect of tax on output: dy dt = L 1 C L 1 (1 C )+I L 2 < 0 The effect of tax on interest rate: dr dt = L 2 C L 1 (1 C )+I L 2 < 0 We can see that fiscal stimulus (increasing G or cutting T) leads to higher output (income) and higher interest rate. To analyze the effect of monetary policy, we hold G and T fixed, we obtain

12 dy dm = I P(L 1 (1 C ) + I L 2 ) > 0 dr dm = (1 C ) P(L 1 (1 C ) + I L 2 ) < 0 Expansionary monetary policy (e.g., QE) would result in lower interest rate and higher output (income). Figure 10 graphically illustrates the effect of expansionary fiscal and monetary policies. We can see that when the economy is in a recession, the government can use fiscal or/and monetary policies to stimulate output, at least temporarily. Many economists believe that the increases in output/income/employment would start a virtuous cycle that would ultimately lead to sustainable recovery. Figure 10: The Effect of Expansionary Fiscal and Monetary Policies There are two interesting extreme cases. First, when L 1 δl(r,y) =, monetary policy has no effect on output. Graphically, this case corresponds to the case where the LM curve is horizontal. This case is also called liquidity trap, a situation where increases in money supply fails to lower interest rate. For example, when nominal δr

13 interest rate is already zero and monetary expansion fails to produce inflation, we say we are in a liquidity trap. In the liquidity trap, fiscal policy is effective and exhibits the multiplier effects in the Keynesian Cross model: dy = 1 and dy = C dg 1 C dt 1 C. The reason why fiscal policy is so effective in the liquidity trap is that interest rate fails to increase, so that there is no crowding-out effect at all. In the second extreme case, when L 1 δl(r,y) δr = 0, fiscal policy has no effect on output. Graphically, this case corresponds to the case where the LM curve is vertical. In this case, only monetary policy matters. This was the position that the Monetarists took (e.g., Milton Friedman) during the stagflation in the 1970s. Note that in this case, money demand is not dependent on interest rate. This is exactly what the quantity money of money ( M P = ky) implies. Figure 11 illustrates the IS-LM models for liquidity trap, quantity theory of money, and the normal case. Figure 11: Liquidity Trap, Quantity Theory of Money, and the Normal Case 4.4 The Aggregate Demand Model

14 The IS-LM model characterizes the demand side of the economy: consumption, investment, and government expenditure. Given a price level P, we can solve for an equilibrium output (income) Y. In other words, the IS-LM equations define an implicit function P(Y), which we call the aggregate demand (AD) curve. The word aggregate here emphasizes the fact that we are dealing with total demand in the whole economy. To determine the shape of the AD curve, we fix T, G, and M, and take total differentiation of both IS and LM equations, dy = C (Y T)dY + I (r)dr 0 = L(r, Y)dP + P(L 1 (r, Y)dr + L 2 (r, Y)dY) From the above equation, we obtain dy dp = LI P(L 1 (1 C ) + I L 2 ). Since I < 0, L 1 < 0, I < 0, 0 < C < 1, we have dy < 0, indicating a downwardsloping AD curve. Figure 12 illustrates the graphical derivation of the AD curve. A decline in price increases the real balance of money supply, shifting the LM curve to the right. Hence the decline in price corresponds to higher output (income). In other words, the aggregate demand curve is downward-sloping. dp

15 Figure 12: The Graphical Derivation of the AD Curve The Effects of Fiscal and Monetary Policies The fiscal and monetary policies would shift the AD curve. To see how the AD curve shifts, we need to fix P and examine the effects of the changes in exogenous variables (G, T, M) on Y. This is exactly the policy analyses based on the IS-LM model. We know from the previous analysis that in the IS-LM model, dy dg dy dy > 0, < 0, and > 0. dt dm This says that increasing government expenditure, tax cut, and monetary expansion would all shift the AD curve to the right. Figure 13 illustrates this point graphically.

16 Figure 13: The Effect of Expansionary Fiscal and Monetary Policies Using the AD curve, we can analyze the effect of policies on the price level, that is, inflation. In the short run, we can assume that the aggregate supply curve is horizontal. This assumption is equivalent to the sticky-price assumption, saying that the increase (decrease) in aggregate demand fails to raise (lower) the price level. In this case, fiscal or monetary stimulus is effective in increasing output, at least in the short run. (Figure 14)

17 Figure 14: Short-Run Effect of Stimulus Measure In the long run, however, price is flexible and the classical theory applies. The economy would produce the natural level, Y, regardless of price. In this case, the aggregate supply curve would be vertical (See Figure 15), and a shift of AD curve to the right would only raise price level (inflation) and fail to raise output. Figure 15: The Effect of Stimulus Measure in the Long Run

18 If we believe that both narratives are correct, we can combine the two together. Suppose the economy is in its long-run equilibrium, producing the natural level of output, Y, and the policy makers want to stimulate the economy. In the short run, the stimulus measures would raise the output above the natural without producing much inflation, thanks to the sticky price. As time goes by, however, factor prices (labor, material, energy, etc.) would rise in the over-heated economy. Eventually the economy would move from the short-run equilibrium to the long-run equilibrium at Y, but with a higher price level. See Figure 16 for an illustration. Figure 16: From Short-Run to Long-Run Equilibrium The above narrative is a typical classical argument against government stimulus. If we start from an output level BELOW the natural level, we can have an argument that is much friendlier to stimulus measures. An output level below the natural level is almost always associated with high unemployment rate and low inflation (or even deflation). At this point, a fiscal or monetary stimulus would raise the output to or above Y, reducing unemployment rate and starting a virtuous cycle toward recovery. As time goes by, the price level increases and the danger of deflation recedes. Inflation is not necessarily harmful. In fact, most economists would agree that moderate inflation is good for economic growth. So knowing the state of the economy is important for making a policy judgement. Indeed, a sensible policy maker can be compared with a physician treating a sick man. He should make all efforts to know about the physiological condition of the sick. He should also try his best to know what has shocked the sick away from the healthy

19 equilibrium. A fever caused by a virus should be treated differently from one caused by infection. For the policy maker, he should make all efforts not only to know how the economy is performing, but also what kind of shock is affecting the economy. For example, inflation that is caused by demand shocks (e.g., asset bubble, investment boom) should be treated very differently from inflation that is caused by supply shocks (e.g., severe drought, formation of an international oil cartel, etc.). Suppose there is a positive shock to the aggregate demand, thanks to a surge in investment, and the inflation rises to dangerous level (say, above 5%). The sensible policy would be raising interest rate, so that money and credit can be tightened. This would shift the LM curve and the AD curve to the left and cool down the economy. Suppose, however, there is an adverse supply shock. For example, OPEC restricted oil supply in 1970s and the oil price soared as a result, raising cost of production all over the world. The rise of production cost would push up the price level. Given the aggregate demand, equilibrium output would drop and the unemployment rate would rise. The combination of inflation and economic stagnation is famously termed stagflation. See Figure 17 for a graphical illustration of the stagflation. Figure 17: Stagflation Is it sensible to use monetary tightening to bring down the inflation caused by the supply shock? The monetary tightening would shift the LM curve and the AD curve to the left, aggravating the recession and unemployment problem. This policy is obviously not favorable, compared to doing nothing and waiting for inflation to come down. Another policy option is to conduct fiscal stimulation, raising aggregate demand and reducing

20 unemployment. This would shift the AD curve to the right and hopefully restore the output to the natural level, at the cost of permanently higher price level. There is no clear winner between this accommodative approach and doing nothing. If the unemployment problem is severe, then the accommodative approach would be arguably better. See Figure 18 for an illustration of accommodating the adverse supply shock. Figure 18: Accommodate An Adverse Supply Shock 4.5 The Open Economy In this section we consider open economy that trades with other countries. We first introduce a model of small open economy with floating exchange rate. We discuss how exchange rate may be determined in the foreign exchange market and how exchange rate behaves as the channel for macro-policies to take effect on the economy. We then introduce a model of small open economy with fixed exchange rate. We discuss what the fixed exchange rate implies for the economy and how policies may affect the output and money supply. In the end we introduce a model of large open economy with floating exchange rate. Note that in this section we assume perfect mobility of capital, which says that money can go in and out of the economy freely. In the simplified world our model describes, the perfect capital mobility implies that there is a common interest rate for the world. Otherwise people can borrow money from low-interest-rate countries and lend to highinterest-rate countries and make risk-free profit. Finally, as in the previous chapter, the small economy means that its saving and investment does not affect the world interest

21 rate. The large economy, in contrast, can influence the world interest rate. In a floating exchange rate regime, the exchange rate is allowed to fluctuate according to the foreign exchange market. The monetary authority may or may not intervene with the foreign exchange market. If the monetary authority does not intervene with the foreign exchange market, we call it a clean float. There are different forms of fixed exchange rate in history, including gold standard, monetary union (e.g., Euro area), currency boards, and so on. In a typical fixed exchange rate regime, the monetary authority stands ready to buy or sell the domestic currency at pre-determined price (exchange rate with a foreign currency). If the domestic currency tends to appreciate, the monetary authority has to sell domestic currency and buy the foreign currency in the foreign exchange market. For the monetary authority, selling domestic currency is injecting money into the economy, expanding the money supply. If the domestic currency faces depreciation pressure, the monetary authority has to do the opposite, buy domestic currency and sell the foreign currency. This is to withdraw liquidity from the market and decrease the money supply. The advantage of having a floating exchange rate is that the country can make monetary policies independently from other central banks in the world. As we see above, if exchange rate is fixed, money supply has to change with the occurrences of appreciation/depreciation pressure. The monetary authority is thus unable to pursue objectives other than the defending of the fixed exchange rate. The disadvantage of floating exchange rate is that the country has to live with an exchange rate that is often excessively volatile. The advantage of having a fixed exchange rate (often with a major trading partner) is often the stability of exchange rate, which facilitates international trade and investment. For countries with a poor record of responsible monetary policy, fixing exchange rate with a major foreign currency is a way of importing responsible monetary policy from abroad. Often times, defending the exchange rate can rally more political support than conducting responsible monetary policy. The disadvantage of the fixed exchange rate is, first, the loss of the independence of monetary policy. Second, to defend fixed exchange rate against speculative attacks, the country has to accumulate a substantial amount of foreign exchange reserve. The foreign reserve must have liquidity and safety, which necessarily implies low return. If a country has high growth and high domestic interest rate, maintaining a massive foreign exchange reserve results in a loss of welfare for the country. Small Open Economy with Floating Exchange Rate We now introduce the celebrated Mundell-Fleming Model of small open economy with floating exchange rate. The model is a close relative to IS-LM, consisting of two equations characterizing goods and money markets, respectively,

22 Y = C(Y T) + I(r ) + G + X(e) (4) M P = (5) L(r, Y), where r is the world interest rate and X(e) is the net export, which is assumed to be a decreasing function of exchange rate e. The IS equation in (4) can be rewritten as S(Y, T, G) Y C(Y T) G = I(r ) + X(e). We may understand the solution to the IS equation as an equilibrium in the foreign exchange market. The supply side of the foreign currency is X(e), which is earned from net export. The demand side is the excess saving S(Y, T, G) I(r ), which has to go somewhere abroad. The two endogenous variables in the model are Y and e. The IS equation obviously defines an implicit function Y(e). A lower e obviously corresponds to a higher Y (using the Keynesian Cross or, mathematically, the implicit function theorem). Hence the IS curve is downward-sloping. There is only one endogenous variable Y in the LM equation, which uniquely determines Y, hence a vertical LM curve. Figure 19 illustrates the joint equilibrium in the foreign exchange market and the money market. Figure 19: IS-LM Curves of The Small Open Economy with Floating Exchange Rate Policy Analysis using the Mundell-Fleming Model Exercises: What are the effects of the following events?

23 Fiscal stimulus (raising G or lower T) Monetary stimulus We can see from the above exercise that the exchange rate e plays a similar role in the standard IS-LM model. Fiscal stimulus leads to appreciation of the domestic currency, which crowds out the net export, leaving the output unchanged. Monetary stimulus leads to depreciation of the domestic currency, stimulating net export and the total output (income). Small Open Economy with Fixed Exchange Rate To study a small open economy with a fixed exchange rate, we may assume that there are only two economies in the world. The large economy is much bigger than the small one, so that the world real interest rate is solely determined by the saving and investment behavior of the large one. Because capital flow is free, the small economy shares the same real interest rate. To maintain the fixed exchange rate, the monetary authority of the small economy stands ready to buy the domestic currency using foreign reserve when there is depreciation pressure, or buy the foreign currency by issuing domestic currency when there is appreciation pressure, at the fixed exchange rate. Since both operations would change money supply, money supply in the small open economy with fixed exchange rate is necessarily endogenous. The IS-LM model of the small open economy with fixed exchange rate is given by, Y = C(Y T) + I(r ) + G + X(e ) (6) M P = (7) L(r, Y), where r is the world interest rate and e is the fixed exchange rate. The endogenous variables are output (Y) and money supply (M), and the exogenous variables include r, e, T, G and P (if we restrict the analysis to the short term). It is clear that the IS equation in (6) determines the level of output or income, Y, regardless of money supply (M). In the LM equation (7), higher M would correspond to higher Y. Figure 20 illustrates the graphical solution to the model. Since M is drawn on the Y-axis, the IS curve is vertical and the LM curve is upward-sloping.

24 Figure 20: IS-LM Curves of The Small Open Economy with Fixed Exchange Rate It can be easily checked that fiscal stimulus would shift the IS curve to the right, raising both output (income) and money supply. To understand why money supply would expand, recall that in the small open economy with floating exchange rate, fiscal stimulus would tend to strengthen domestic currency. To keep the currency from appreciating, the monetary authority has to issue more domestic currency and buy the foreign currency, hence the monetary expansion. In another thought experiment, suppose that the world real interest rate rises. This would shift the IS curve to the left and the LM curve to the right (think about why), resulting in lower output and a tightened money supply. To understand why money supply has to decrease, note that the rise in the world interest rate puts depreciation pressure on the domestic currency. To defend the fixed exchange rate, the monetary authority has to buy the domestic currency (withdraw money from the economy). This thought experiment rhythms with many episodes in the history of international finance. Whenever the dollar index rises substantially, many small countries with rigid exchange rate would experience economic slowdown, monetary tightening, and eventually currency crises. The Asian Financial Crisis in the late 1990s was a vivid example. A Model of Large Open Economy with Flexible Exchange Rate The large open economy differs from the small one in that the capital outflow of the

25 large open economy would have an impact on the world interest rate. We consider the following model, Y C(Y T) G = I(r) + F(r), (8) M P = L(r, Y), (9) F(r) = X(e). (10) F(r) denotes the net capital outflow, which is assumed to be a function of the real interest rate. Since more capital outflow depresses the world interest rate, F(r) is assumed to be a decreasing function, i.e., F (r) < 0. X(e) denotes the net export, which is as usual assumed to be a decreasing function of the exchange rate. The equation in (8) is obviously the IS equation, describing the equilibrium in the market for loanable funds (or equivalently, market for goods and services). The equation in (9) is the familiar LM equation, characterizing the equilibrium in the money market. The equation in (10) is new, characterizing the equilibrium in the foreign exchange market, where the exporters are the supply side and the capital outflow is the demand side. In this model of three equilibrium conditions, there are of course three endogenous variables: Y, r, and e. All other variables, including the sticky price P, are exogenously given. The model looks complicated, but it is in fact easy to solve. Note that the exchange rate e does not appear in the first two equations in (8) and (9). So Y and r can be determined as in the usual IS-LM model. With r determined, e is also determined by solving the equation in (10). Graphically, Figure 21 shows how the model can be solved. The analysis based on the model is straightforward.

26 Figure 21: The Model of Large Open Economy Exercises: What would be the effects of the following changes? Fiscal stimulus Monetary stimulus A protectionist policy shock (e.g., an import tax) A Summary of Policy Analyses Based on IS-LM Models The closed economy considered in Section 4.3 can be regarded, conceptually, an extremely large economy. Indeed, the economy of the earth must be closed, since there is not interstellar trade so far. In the extremely large economy, share of trade in the economy is negligible and the exchange rate is not important. Based on the closedeconomy model, we learn that fiscal stimulus would raise output and real interest rate, and that monetary stimulus would also raise output but lower real interest rate. On the other extreme is the small open-economy model, where interest rate is determined outside and the exchange rate is a very important variable. If the exchange rate is fixed, the fiscal stimulus would raise output. Monetary stimulus, however, is ruled out, since monetary policy is no longer independent under the fixed exchange rate. If the small open economy has a floating exchange rate, it has an independent monetary policy. Monetary stimulus would lead to the depreciation of the domestic currency and raise output. Fiscal stimulus, in contrast, is completely ineffective in raising output, since it would lead to appreciation of the exchange rate and lower net export.

27 The large open-economy model is somewhere between the two extremes. The effects of fiscal and monetary policies are also somewhere between those of the two extremes. Figure 22 summarizes the effects of fiscal and monetary stimulus on the three models considered in this chapter. The effects of cooling measures are, of course, the opposite. Figure 22: Summary of Policy Effects 4.6 Theory of Aggregate Supply In the previous section we assume that the aggregate supply curve is either vertical (the classical long-run case), or horizontal (the short-run sticky-price case). These are two extreme cases of a general theory of aggregate supply, a subject we study in this section. We first introduce a linear aggregate supply equation. From this we derive the wellknown Phillips curve. Finally we discuss policy implications. The linear aggregate supply (AS) is given by Y = Y + α(p EP), α > 0, where Y is output, Y is the natural level of output, P is the price level, EP is the expected price level, and α is a parameter that measures the sensitivity of output to deviation of price from the expected level. If the price level is higher than the expected level, the economy overheats (the output exceeds the natural level); If the price is lower than the expected level, then the economy underperforms its potential. The above AS equation can be intuitively understood using the imperfect information argument as follows. Suppose that each firm in the economy produces a single good and there are many goods in the market. If we assume that each firm has imperfect information on the overall price level. Without perfect information, they may mistake an overall price rise as a rise in the relative price of the good they produce. If the overall (11)

28 price level rises, many firms make more efforts to produce more, hence the upwardsloping AS. The linear AS equation can also be derived the sticky-price argument. Assume that there are two types of firms: (1) flexible-price firms, which set price according to P f = P + γ(y Y ). And (2) sticky-price firms, which set the price by P s = EP. Let s be the fraction of sticky-price firms, 0 < s < 1, the overall price level would be P = sp s + (1 s)p f = sep + (1 s)(p + γ(y Y )). Re-arranging the terms, we obtain (1 s)γ P = EP + (Y Y ). s Obviously this is the same equation as in (11) and α = s (1 s)γ. If we draw the price level P on the Y-axis, which is conventional in economics, the AS curve has slope of 1/α (Figure 23). Figure 23: The Aggregate Supply (AS) Curve The slope of the AS curve is obviously an important parameter. If the slope approaches infinity, then the AS curve would become vertical. The classical analysis based on flexible price would apply in this case. The imperfect-information argument for the

29 upward-sloping AS curve tells us that the AS curve would be steeper for those economies with volatile aggregate price level, where people would learn to differentiate relative price changes from overall inflation. The sticky-price argument tells us that the AS curve would be steeper for those economies with higher average level of inflation, where prices are relatively more flexible. Combining the above two, we may safely say that the AS curve would be steeper in economies with high and volatile inflation. It is thus no wonder that classical economics made a comeback in 1970s, an era marked by exactly high and volatile inflation. If the AS curve is not vertical, changes in AD would lead to changes in output and employment in the short run. In the long run, however, the output (employment) would get back to the natural level. Figure 24 shows a typical dynamic response to a demand shock. Suppose the economy is initially at point A, producing the natural level of output. An unexpected increase in AD would raise the price level from EP 1 to P 2 and the output rises above Y (point B). In the long run, the expected price level rises to EP 3, shifting AS 1 to AS 2. The output returns to the natural level. Figure 24: An AD-AS Analysis For policy makers, they obviously have a choice to stimulate the economy when the output is below natural level and unemployment rate is high. The stimulus would temporarily raise output and employment, with the cost of higher inflation in the longer term. The celebrated Phillips Curve quantifies this trade-off between employment and

30 inflation. Phillips Curve The modern Phillips curve is characterized by the following equation, π = Eπ β(u u n ) + v. Where π is inflation rate, Eπ is expected inflation, u is unemployment rate, u n is the natural level of unemployment rate, and v is supply shock. We may call (u u n ) cyclical unemployment, which is deviation of unemployment from the natural level. β is a key parameter that measures the sensitivity of inflation to the cyclical unemployment. The Phillips curve can be derived as follows. Let p t = log(p t ). Note that π t = p t p t 1. Rewrite the short-run AS equation in (11) as, p t = Ep t + 1 α (Y t Y ) + v t where we add a supply shock v. Subtracting p t 1 from the equation, we obtain π t = Eπ t + 1 α (Y t Y ) + v t. Plugging in the Okun s law, 1 α (Y t Y ) = β(u t u n ), we obtain π t = Eπ t β(u t u n ) + v t. The Phillips curve indicates a trade-off between inflation and unemployment: it may take the cost of inflation to reduce unemployment. The trade-off can also be framed between inflation and output. There is a concept called sacrifice ratio, which is defined by the percentage of a year s real GDP growth that must be forgone to reduce inflation by 1 percentage point. In the U.S., a typical estimate of the sacrifice ratio is about 5: for every percentage point that inflation is to fall, 5 percent of one year s GDP growth must be sacrificed. If the policy of monetary tightening is highly credible, the sacrifice ratio can be much smaller. We can infer from the Phillips curve equation that there are four factors that may affect inflation: (1) change in inflation expectation; (2) the cyclical unemployment (u t u n ); (3) supply shock (v t ) ; (4) change in natural rate of unemployment (u n ). Roughly speaking, inflation expectation is the average view of future inflation. That the expectation can move inflation can be understood by noting that when everyone expects prices to go up, prices will indeed go up. The drop in cyclical unemployment leads to demand-pull inflation. Note that when unemployment rate drops, more workers have jobs and they have more income to spend, hence higher demand in the economy. The supply shock (v t ) is related with cost-push inflation. Obviously, a positive v t pushes up inflation. Finally, the natural rate of unemployment (u n ) itself may change

31 overtime, albeit very slowly. One way to make the inflation expectation operational is to assume that the future inflation equals the current inflation, E t 1 π t = π t 1. This assumption is called the adaptive expectation of inflation. If this assumption holds, then inflation is expected to stay at the current level, implying inertia in the movement of inflation. More generally, we may assume that E t 1 π t = β 0 + β 1 π t β d π t d. That is, the expected inflation is a linear combination of the lagged value. If β β d = 1, the inflation also exhibits inertia. Another approach is to assume that the inflation expectation is rational, meaning that the economic agent form expectation using all relevant information and that the expectation is correct in average. Under the rational expectation hypothesis, the tradeoff between inflation and output (employment) can cease to exist, since people can correctly evaluate policies and adjust their expectation of inflation. Note, finally, that it is only a hypothesis that there exists a natural rate of unemployment, which is called natural-rate hypothesis. An alternative hypothesis is hysteresis, which states that the natural rate of unemployment may be time-varying and the level of unemployment rate depends not only on the current state of economy, but also the historical path. For example, a sustained period of unemployment may make the skill set of the unemployed obsolete. 4.7 A Dynamic AD-AS Model A static model specifies a set of simultaneous relations among variables, which is often assumed to hold in an equilibrium or steady state. For example, the Keynesian cross model, Y t = C(Y t T t ) + I t + G t, is a static model. In this model, the subscript t can be omitted. And most models considered in this course are static. A dynamic model specifies a set of time-dependent relations, which necessarily involves lags of endogenous variables. For example, if we assume adaptive expectation, the Phillips curve becomes π t = π t 1 β(u t u n ) + v t, which is a dynamic model. Let s consider a simple linear AD-AS model, Y t = P t + u t, Y t = P t + v t, where u and v denote shocks to the supply and the demand, respectively. Solving the model, we obtain P t = (v t u t ) and Y t = (3u t + 2v t )/5. This is a static model. In this model, a unit negative shock to u would result in a unit instantaneous price increase and a 0.6 decline in Y t. The shock does not affect the future price or output. Now we change the supply equation to

32 Y t = P t 1 + u t. Then the model becomes a dynamic model. In a dynamic model, an exogenous shock leads to a series of changes to endogenous variables. We refer to simple_adas.xlsx for a numerical illustration. We now present a more useful dynamic AD-AS model. We first specify the threeequation model. Then we solve the model, representing each endogenous variable with exogenous and predetermined variables. Finally we apply the model to macroeconomic analysis. The model has three equations: (1) IS equation; (2) Phillips Curve equation; (3) a monetary policy rule (LM equation). We specify the IS equation as y t = y α(r t ρ) + u t, where y t = log(y t ), y = log(y ), r t is real interest rate, u t is the demand-side shock, α is a constant measuring how demand respond to changes in r t, and ρ is a constant called the natural rate of interest. We further specify r t as the ex ante real interest rate, r t = i t E t π t+1, where i t is the nominal interest rate and E t π t+1 is the expected next-period inflation at period t. Then we specify a Phillips-curve-like equation for the dynamics of inflation, π t = E t 1 π t + φ(y t y ) + v t, where(y t y ) is called the output gap, v t is the supply-side shock, and φ is a constant measuring how inflation responds to the output gap. The above equation characterizes the trade-off between inflation and output (unemployment). Hence we call it the Phillips curve equation. We assume that the monetary authority determines the nominal interest rate by the following rule i t = π t + ρ + θ π (π t π ) + θ y (y t y ), where π is inflation target, θ π and θ y are constants measuring how the monetary authority would respond to inflation and output gap, respectively. The famous Taylor rule for the Fed is given by federal fund rate = inflation (inflation 2) + 0.5(GDP gap) The above monetary policy rule implies that the monetary authority has two objectives:

33 (1) keep a moderate inflation; (2) promote a maximum sustainable output and employment. To make the conditional expectation E t 1 π t operational, we assume adaptive expectation (i.e., E t 1 π t = π t 1 ). Putting all above equations together, we have y t = y α(i t π t ρ) + u t, π t = π t 1 + φ(y t y ) + v t, i t = π t + ρ + θ π (π t π ) + θ y (y t y ). In this model, the endogenous variables are y t, π t, and i t. The exogenous variables are y, π, u t, and v t. And there is a predetermined variable: π t 1. It is useful to define a steady state. Here we define the steady state as the state where inflation is constant and there are no shocks, u t = v t = 0. It is easy to see that in the steady state, y t = y, π t = π, i t = π + ρ, and r t = ρ. In the steady state, real variables (y t, r t ) do not depend on monetary policy, and monetary policy only influences the inflation (π t ) and nominal variables (i t ). Hence the steady state satisfies the classical dichotomy and monetary neutrality. There are three equations and three unknowns (endogenous variables). We may solve the system of equations and obtain π t = a 1 (π t 1 + v t ) + a 2 π + a 3 u t, y t = y + a 4 (π π t 1 v t ) + a 5 u t, where a 1 = (1 + φαθ π 1+αθ y ) and a 5 = 1 1+αθ y +φαθ π. 1, a 2 = φαθ π 1+αθ y +φαθ π, a 3 = φ 1+αθ y +φαθ π, a 4 = αθ π 1+αθ y +φαθ π, Similarly we may represent i t as linear functions of exogenous and predetermined variables, simply by plugging π t and y t into the monetary policy rule. These solutions are called the reduced-form model. Calibration is an approach for assigning values to the parameters in the model. Often these values are taken from empirical and experimental studies. We assume α = 1, ρ = 2, ϕ = 0.25, θ π = 0.5, and θ y = 0.5. Furthermore, we assume y = 100 and π = 2. We refer to dynamic_adas.xlsx for a series of experiments on this dynamic AD-AS model.