Open Economy Macroeconomics, Aalto Universtiy SB, Spring 2016, Solution to Problem Set 4 Jouko Vilmunen Monday, 4 April 2016 Exercise 1 (Poole) The way we normally draw the LM-curve assumes that the central bank uses the money supply as its main policy instrument, ie. the interest rate is free to adjust. Now, assume that instead of fixing the money supply the central bank implements monetary policy by determining (ie. fixing) the nominal interest rate (e.g. in its liquidity operations or by defending an interest rate target via open market operations). Assume that the economy is subject to two types of shocks, one of which originates in the money market (ie. a nominal financial market shock like a money demand shock) and the other in the goods market (ie. a real shock, like changes in "animal spirits" which shows up as a change in investment). The central bank, which cares about output stability, can use either the money supply or the interest rate to manage the economy. Use the IS-LM model to analyze which of the two instruments is better at stabilizing output under a) financial market shock and b) real goods market shock? (Hint: think about the slope of the LM curve) Solution 2 Refer to the follwing figure. a) Assume now that there is a shock in the financial market, like a negative shock to money demand. If the central bank controls the money supply, the initial upward sloping LM-curve is denoted by LM(M0). After the shock LM-curve shifts down and to the right, indicating the the shock induces an excess supply of money. Hence, the economy settle to new equilibrium indicated by the point of intersection of LM(M1) and IS(G0), where output is at the level indicated by label "3". If, on the other hand, the central bank control the interest rate, the LM is horizontal at the level r. (Money stock is endogenous, determined by money demand.) After the shock there is an incipient excess supply of money, which, if the central bank controlled the money supply, would take the economy to the equilibrium at the intersection of LM(M1) and IS(G0). But this cannot be the equilibrium when the central bank controls the interest rate, as it would imply a lower interest rate than r. Hence, given the incipient excess money supply, the central bank start to contract the money supply, which would continue as long the interest rate would stay below r. This implies that the LM-curve would return back to its original position (see figure "rotate back"). Thus, output would stay at the original level ("1"). b) Eg. 1
an expansionary real goods market shock, which takes the IS-curve from IS(G0) to IS(G1). Under money supply policy, the economy settles at the equilibrium indicated by the intersection of LM(M0) and IS(G1) with the output at the level denoted by the label "2". Under an interest rate policy, on the other hand, the interest rate cannot adjust, the output induced increase in money demand has to be accommodated by an increase in the money supply. Hence, under the interest rate rule, the economy settle at the equilibriun in the intersection of LM(Interest) and IS(G1) where the output is at the level indicated by the label "4". Exercise 3 (Balanced budget multiplier) In our IS-LM model the consumption function says that private consumption expenditure depends on the private sector s real disposable income C = c(y T ) where c( ) is the consumption function, y and T denotes, respectively, (real) income and taxes, hence Y T is (real) disposable income.now, government wants to increase public expenditure G and finance this increase by increasing taxes T so that the budget remains in balance (ie. budget deficit G T = 0). How does this combination of policy measures aff ect the macroeconomic equilibrium 2
of the economy? In particular, what can you say about the balanced budget multiplier, ie. the eff ect of balanced budget increase in government spending on aggregate output? Solution 4 Let us do some simple diff erential calculus. demand equation as Write the aggregate y = c(y T ) + I(r) + G + NX Keeping the real exchange rate fixed for now, take the (marginal) change of the aggregate demand equation (denoted generically by the diff erential of a variable x, dx) = c ( dt ) + I dr + dg + NX y where c denotes the derivative of the consumption function withe respect to the real disposable income y T ("marginal prospensity to consume") and NX y signifies partial derivative of the net exort function with respect to the real income ("marginal prosensity to import") and I is the derivative of the investment function with respect to the (real) interest rate. Since dt = dg, we have (1 c NX y ) = (1 c ) dg + I dr From the money market equilibrium with constant real money balances M P = L(y, r) we have L y + dr = 0 dr = L y Substitute this into the goods market equilibrium condition above (1 c NX y ) = (1 c ) dg I L y L ( r 1 c NX y + I L ) y = (1 c ) dg = dg = 1 c 1 c NX y + I Ly Since NX y 0 and I L y 0 the balanced budget multiplier dg 1. If, on the other hand, net exports are independent of domestic income - not so likely an outcome - and investments do not depend on the (real) interest rate (ie. is exogenously determined) the the balanced budget multiplier is one, eg. the closed economy balanced budget multiplier is one! Intuition? Public expenditure aff ects aggregate income directly, taxes only through consumption decisions. Note that this result is conditional on keeping the exchange rate constant. Hence, the full open economy balanced budget multiplier under flexible exchange rates 1 is 1 That is the balanced budget multiplier in the flexible exchange rate version of the Mundell- Fleming model. 3
somewhat different, which can be demonstrated as follows. 2 Given the balance of payment equation B(y, Q) + k(r r f ) = 0 and the fact that in our model B(y, Q) = NX (y, Q), we can eliminate the current account/net export function from the aggregate demand equation by substituting in the capital inflow function y = c(y T ) + I(r) + G k(r r f ) Take the differential and again use the money market equilibrium under a constant money stock to replace dr by Ly ( 1 c + I L y k L ) y = (1 c ) dg = dg = 1 c 1 c NX y + I Ly k Ly Hence, the balanced budget multiplier falls further, once we take into account the exchange rate channel. The fact that the balanced budget multiplier falls from the value of one in a closed economy to less than one in an open economy reflects leakage. Exercise 5 (Consumption and interest rates) The above consumption function is indeed very simple, so let us extend it slightly: assume that in addition to the real disposable income consumption depends also on the real interest rate or, given that inflation expectations are fixed, on the nominal interest rate r, ie. C = c(y T, r), c r < 0 where the notation c r suggests that an increase in the interest rate lowers private consumption expenditure. Think of the central bank tightening monetary policy, ie. contracting the money supply. What happens to the macroeconomic equilibrium of the economy according to our IS-LM model incorporating the above consumption function? Solution 6 Look at the following figure. Contracting the money supply means that the LM-curve shifts up and to the left. But the induced increase in the interest rate will reduce private consumption and, hence, aggregate demand further compared to the more simple consumption function. The economy settles to a new equilibrium dictated by (y1,r1). Note that in the final equilibrium, the interest rate can fall below the initial level. This happens if the aggregate demand effect of the fall in the interest rate is large enough. Note once again that the real exchange rate is kept constant. 2 This part of the solution is just to show you the general case with no intention to require you to deal with it. 4
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Exercise 7 (Crowding out of private expenditure) We know from our IS-LM model that when the government increases public expenditure not only does output increase but also the interest rate increases. So what happens to private investment expenditure? Solution 8 After increasing public expenditure, the interest rate will increase. The intuition is that the increase in public expenditure has to be financed by issuing bonds. This increases supply of government bonds and, hence, reduce their prices, which, in turn, means that the interest rate will increase. Since private investment depends negatively on the interest rate, private investment will fall because of the increase in the interest rate. Conclusion: whereas output increases, the composition of output will change so that the share of investment in GDP falls and that of the combined government and private consumption will increase. 6
Exercise 9 Assume fixed exchange rates. Use the Mundell-Fleming model to trace out what happens to the macroeconomic equilibrium of a small open economy, when the policy maker decides to devalue the domestic currency. Solution 10 Use the above graph. Devaluation improves competitiveness and shifts the goods market equilibrium curve up and to the right, IS0 IS1. This shift puts pressure on the domestic interest rate to increase, which induces an increase in capital inflows. Due to the balance of payment surplus larger capital inflows, in turn, puts pressure on the domestic currency to strenghen, which, after the devaluation, remains fixed again (=assumption). Hence, central bank s forex reserves start to increase, as does the money supply. The combined eff ect of larger capital inflows and increase in money supply is represented by the shift in the BP curve from BP0 to BP1 and the shift of the LM-curve from LM0 to LM1, shifting the macroeconomic equilibrium from (y0,r0) to (y1,r1). 7