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The Monetary Transmission Mechanism ADVANCED MACROECONOMICS Javier Andrés 2009-2010 Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 1 / 51 I. Introduction The standard IS-LM model does not incorporate expectations. However, we can extend the IS-LM in several directions, incorporating agents’expectations, which a¤ect aggregate demand. These expectations di¤er from the ones we have been dealing with so far. Instead of looking at past expectations about current events (i.e. E(xt =It i )) we are going to introduce now current expectations about future events (i.e. E(xt+j =It )). These are crucial in modern macroeconomics and bridge the gap between the real and the …nancial side of the economy. Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 2 / 51 Introduction We are going to analyze two types of transmission mechanisms through which the economy is a¤ected by monetary and …scal policies. In‡ation expectations a¤ect one crucial relative price in the economy: the real interest rate. So far we have take them as given, but they depend of what people expect about future polices and shocks: E( t+1 =It ). s Expectations of interests rates a¤ect people’ decisions about current savings and investment: E(rt+j =It ). Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 3 / 51 II. The hyperin‡ation model Empirical evidence on the four big hyperin‡ation in the 20s (Germany, Austria, Hungary and Poland) Monthly Monthly Country Starts Ends PT/PO Inflation rate (M.) Money growth Austria Oct. 1921 Ag. 1922 70 47 31 Germany Ag. 1922 Nov. 1923 1,0x1010 322 314 6 Greece Nov. 1943 Nov. 1944 4,7x10 365 220 Hungary I Mar. 1923 Feb. 1924 44 46 33 27 Hungary II Ag. 1945 Jul. 1946 2,8x10 19.800 12.200 Poland Jan. 1923 Jan. 1924 699 82 72 5 Russia Dic. 1921 Jan. 1924 1,2x10 57 49 Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 4 / 51 Empirical evidence Main features A period of accelerating in‡ation ( P=P ), increasing money supply (M ) and a continuous fall of M=P . Hyperin‡ation end: prices stopped abruptly and money supply increased slowly to recover the level of M=P . Other features: important …scal de…cits and small real incidence. Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 5 / 51 Empirical evidence 1E+16 (logs) (en logaritm os) 1E+14 1E+12 1E+10 1E+08 1E+06 1E+04 1E+02 | 1921 | 1922 | 1923 | 1924 | Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 6 / 51 Empirical evidence (M 1 = B illetes+ D ep ó sito s v ista )/P recio s 80000 (M1/P) 70000 60000 50000 40000 30000 20000 10000 0 | 1921 | 1922 | 1923 | 1924 Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 7 / 51 Empirical evidence 1 6 0 GDP per capita index In d ic e d e p ro d u c c ió n p e r c a p it a 140 120 100 80 60 1914 1916 1918 1920 1922 1924 1926 1928 1930 1932 1934 1936 1938 Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 8 / 51 Hyperin‡ations Given the small incidence upon real variables it is convenient to analyze hyperin‡ation in a classical model, where money is neutral. In the classical model with exogenous expectations, money demand is determined by the nominal interest rate ( + e ) and the level of output Y : Ld ( + e ; Y ) In this model M=P is constant and changes in M only follow changes in P one-to-one. Thus, we cannot explain the dynamics of real balances during the hyperin‡ation. However, in‡ation expectations are variable. Let us see whether we can set up a model that make consistent the observed movements of in‡ation and real balances during hyperin‡ations. Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 9 / 51 The model The classical model can be represented by recursive blocks: The supply side: the labour market and the production function determine the real wage (W=P ); employment (N ) and output (Y ). Given Y , the IS functions determines the real interest rate ( ) Then given Y , , M and e the LM determines the price level (P ). Mt = Ld ( + e t+1 ; Y ) Pt Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 10 / 51 The model Let us consider the following functional form for the demand for real balances: Ld ( + e t+1 ; Y ) = expf ( + e t+1 )gY Then, the money market equilibrium can be approximated in logs as follows: e Pt+1 Pt e mt pt = ( + t+1 ) + ln Y = + ln Y Pt where mt = ln Mt and pt = ln Pt . Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 11 / 51 The model: solution e Pt+1 Pt We approximate Pt ' (pe t+1 pt ) and assume for simplicity that = ln Y , mt pt = (pe t+1 pt ) A critical assumption is how expectations are formed. We assume rational expectations, so that: pe = E[pt+1 =It ] = pt+1=t t+1 Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 12 / 51 The model: solution Under the rational expectations assumption we obtain a …rst order di¤erence equation: mt pt = (pt+1=t pt ) or: 1 mt + pt = p 1+ 1 + t+1=t This equation admits two possible solutions for pt . Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 13 / 51 Backward-looking solution Backward-looking solution (backward substitution) 1+ 1 pe = t+1 pt mt 1+ 1 pt+1 = pt mt 1+ 1 pt = pt 1 mt 1 where the current price level is a function of money supply in the past and an initial condition p0 : t 1X 1+ i 1 1+ t pt = mt i + p0 i=1 Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 14 / 51 Backward-looking solution This solution is against intuition on many grounds: The current price level is a negative function of money The e¤ect of money on prices increases over time. Thus if there is an increase of M in 2007 its e¤ect increases over time. Current prices depend on lagged money, whereas money demand is forward looking. Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 15 / 51 Forward-looking solution Forward-looking solution (forward substitution) 1 pt+1 = mt+1 + pt+2 1+ 1+ where the current price level is a function of money supply in the future and a transversalitiy condition: 1 X i T 1 pt = mt+i=t + lim pt+T =t 1+ 1+ T !1 1+ i=0 We assume that the following transversality condition holds: T lim pt+T =t = 0 T !1 1+ Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 16 / 51 Forward-looking solution The forward-looking solution has the following properties: The current price level is a positive function of money supply. Money depends on current and expected money supply changes. The e¤ect on current prices is smaller the further in the future are the expected changes in money. Thus p2007 reacts more to changes in M expected in 2008 than those expected in 2009. Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 17 / 51 Dynamic responses to monetary policy changes. The Steady state We de…ne the steady state as a regime in which money is expected to remain constant from now on: mt+i=t = m; 8i; = 0. Thus the solution for the price level (pa ) is, t 1 ! 1 X i 1 1 pa = t m = pt = m=m 1+ 1+ 1+ 1 1+ i=0 Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 18 / 51 Unanticipated permanent increase of the money supply The advantage of including endogenous expectations in the model lies in the possibility of analyzing the dynamic e¤ect of policy changes. Unanticipated change in the money supply: m(t; t; 1). mt+i=t = m + m 8i 1 X i 1 pb = t (m+ m) 1+ 1+ i=0 1 X i 1 = (m+ m) i=0 =m+ m 1+ 1+ Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 19 / 51 Unanticipated permanent increase of the money supply P1 i Thus, since i=0 1+ = 1, the change in pt is given by, pb t pa = t pt = m @p @P M = =1 @m @M P Thus, the long run multiplier is equal to 1 (Food for though: notice that this multiplier coincides with the result we obtain in the basic static model with constant expectations. Why?) Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 20 / 51 Unanticipated permanent increase of the money supply Figure: Unanticipated permanent increase of the money supply Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 21 / 51 Anticipated permanent increase of the money supply Realistic policy changes are never steady state changes. They are rarely permanent and they are often anticipated The framework we have just developed allows us to study these class of policy actions. Anticipated permanent monetary policy change: m(t; t + 2; 1): 1 X i 1 X i 1 1 pc = t m+ (m + m) = 1+ 1+ 1+ 1+ i=0 i=2 X1 i X1 i 1 1 = m+ m= 1+ 1+ 1+ 1+ i=0 i=2 2 = m+ m 1+ In this case the price increase in t is smaller than in the case of a unanticipated change in t and in‡ation is increasing: pc t pa = t pt < m Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 22 / 51 Anticipated permanent increase of the money supply Figure: Anticipated (at t) permanent increase of the money supply from t + 2 onwards) Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 23 / 51 Anticipated permanent increase of the money supply Economic interpretation: The announcement of an increase in the money supply at t + 2 makes that agents expect a price increase in t + 2. Agents try to buy goods before prices increase, that is, there is an increase in aggregate demand. As the supply of goods is given, the higher aggregate demand causes an increase of prices in t. The nominal wage increases but the real wage, the output level and the e real interest rate (rt t ) remain constant. The nominal interest rate increases until the point where the lower money demand is equal to the lower level of real balances in t (m pt ). Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 24 / 51 Anticipated permanent increase of the money supply m(t; t + 10; 1): 9 X i 1 X i 1 1 pd = t m+ (m + m) = 1+ 1+ 1+ 1+ i=0 i=10 1 X i X1 i 1 1 = m+ m= 1+ 1+ 1+ 1+ i=0 i=10 10 = m+ m 1+ The price increase in t is now smaller that in the case where m(t; t + 2; 1): pd < pc t t Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 25 / 51 Anticipated permanent increase of the money supply Figure: Anticipated permanent increase of the money supply in t + 10 Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 26 / 51 Unanticipated transitory increase of the money supply 1 X i 1 1 1 pe t = m+ m=m+ m 1+ 1+ 1+ 1+ i=0 The transitory increase in m induces a price increase in a smaller proportion as compared with the permanent change: 1 pe t pa = t m< m 1+ Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 27 / 51 Anticipated permanent increase of the money supply Agents expect a negative in‡ation in t + 1 since the money supply increase is transitory. The money market is always in equilibrium and the nominal interest rate is now lower: e e rt = + t < since t <0 Figure: Unanticipated transitory increase of the money supply (from2009-2010 Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism t+1 28 / 51 Conclusions The price level changes with announcements of future monetary policy changes. In spite of its simplicity, the model is capable of explaining the main empirical properties of hyperin‡ations. If the regime change of monetary policy is credible, prices will stop with a small cost in terms of real activity. Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 29 / 51 III. The term structure of interest rates In the standard IS-LM there is only one type of bonds, but in the real world there are many types of bonds with di¤erent expiration dates. We distinguish here between short and long-run bonds. The rates of return of these two assets are linked through an arbitrage condition that is usually referred to as the ’ . term structure’ The terms structure of interest rates is represented by the di¤erence between long and short-run interest rates. It is a function of agents’ expectations and thus contains useful information about output growth and in‡ation expectations. Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 30 / 51 Empirical evidence 8 8 Germany Canada 6 6 4 4 2 2 0 0 -2 -2 -4 -4 72 74 76 78 80 82 84 86 88 90 92 94 72 74 76 78 80 82 84 86 88 90 92 94 8 8 United Kingdom United States 6 6 4 4 2 2 0 0 -2 -2 -4 -4 72 74 76 78 80 82 84 86 88 90 92 94 72 74 76 78 80 82 84 86 88 90 92 94 Spread between long and short run interest rates GDP growth int+1 Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 31 / 51 The model Let us consider an otherwise standard IS-LM model with constant prices and two interest rates: mt pt = y t rt yt = Rt + gt pt = p = 0 (all variables except the rates are in logs) Notice that the short-run rate r enters the money demand equation, whereas the long-run rate R enters the investment equation (IS) Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 32 / 51 The model We have two equations and three endogenous variables (y; r; R): We need an additional equation: the arbitrage condition, which is an equilibrium condition in the bonds markets. Equilibrium requires that investors are willing to hold both short-run and long-run bonds. The return of a short-run bond between t and t + 1 is: Ps (1 + r) Ps =r Ps The return of a constant-coupon (CC) bond between t and t + 1 is: L;e CC Pt+1 PtL + PtL PtL Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 33 / 51 The model De…ne Rt CC=PtL : CC CC CC P L;e PtL e Rt+1 Rt rt = + t+1 L = Rt + PtL Pt CC Rt e Rt+1 Rt = Rt e Rt+1 We can write the arbitrage condition as: e e Rt+1 Rt = Rt+1 (Rt rt ) Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 34 / 51 The model We assume that expectations are rational: e Rt+1 = Rt+1 Assuming also that in the steady state Rt = Rt+1 = rt = we can approximate this expression by Rt+1 Rt = (Rt rt ) Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 35 / 51 Solution We solve rt and yt as a function of Rt ; gt and mt : yt = Rt + gt 1 1 1 rt = Rt + gt mt Substituting r in the arbitrage condition by the preceding expression Rt = 1 Rt+1 + 2 gt 3 mt where 3 are 2 positive parameters and 0 < 1 < 1. Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 36 / 51 Forward-looking solution F orward-looking solution T lim 1 Rt+T = 0; T !1 1 X 1 X i i Rt = 2 1 gt+i 3 1 mt+i i=0 i=0 Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 37 / 51 Model Solution: Dynamic responses to changes in monetary and …scal policies. Steady state Assume that: gt = g ; mt = m 8t then a 2 3 Rt = g m = Ra 1 1 1 1 such that R R = (R r) Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 38 / 51 Steady state This implies that in the steady state R and r are equal because no further changes are expected in the economy and hence agents do not expect variations in future short rates. Thus the models behaves in the steady state as in the standard (static) IS-LM model: y= r+g m p= y r Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 39 / 51 Unanticipated permanent change of money supply m(t; t; 1). 1 X 1 X b i i 2 3 Rt = 2 1 gt+i 3 1 mt+i = g (m + m) 1 1 1 1 i=0 i=0 The long-run multiplier is: R 3 = m 1 1 b a 3 Rt Rt = m 1 1 Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 40 / 51 Unanticipated permanent change of money supply The increase in m shifts the LM functions, causing a fall in the short-run interest rates. According to the arbitrage condition, in the new steady state the long-run interest rate also falls, inducing an increase in investment and output, with the resulting shift of the IS. permanent increase of Figure: Unnticipated Monetary Transmission Mechanism the money supply. The Advanced Macroeconomics. J. Andrés () 2009-2010 41 / 51 Anticipated permanent change of money supply m(t; t + 2; 1). 1 X 1 X 1 X c i i i Rt = 2 1g 3 1m 3 1 (m + m) = i=0 i=0 i=2 2 2 3 3 1 = g m m 1 1 1 1 1 1 c a b a j Rt Rt j<j Rt Rt j When m(t; t + j; 1) the e¤ects are greater the smaller the value of j. Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 42 / 51 Anticipated permanent change of money supply Figure: Anticipated (at t) permanent increase of the money supply (from t + 2 onwards). Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 43 / 51 Anticipated permanent change of public spending g(t; t + 2; 1). 1 X 1 X 1 X d i i i Rt = 2 1g + 2 1 (g + g) 3 1m = i=0 i=2 i=0 2 2 2 1 3 = g+ g m 1 1 1 1 1 1 The increase in public spending in t + 2 generates an expected increase in rt+2 . Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 44 / 51 Anticipated permanent change of public spending Thus long-run bond holders want to get rid of some of these to buy short-run bonds. Rational savers will not expect until t + 2 to do so because they want to lead the market in selling their bonds before anyone else does. In a decentralized economy there is no coordination so the attempt by each agent to sell before the others make them to start doing it immediately after the announcement. In doing so, savers try to strike a balance between their current and their desired portfolio. The closer in time is the expected increase in public spending the stronger the movement towards selling long-run bonds today. Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 45 / 51 Anticipated permanent change of public spending Figure: Anticipated (at t) permanent increase of public spending (from t + 2 onwrads). Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 46 / 51 Anticipated permanent change of public spending As people sell long-run bonds at t their price falls and their interest rate increases. A higher Rt reduces investment: there is an anticipated crowding-out. In t + 2 the increase in public spending has expansionary e¤ect on economic activity, but there is a change in the composition of aggregate demand. Notice that the current investment fall leads to a fall in money demand today, so that the current short rate (rt ) falls. This at t the wedge between Rt and rt opens up that is an indication of future increases in short rates due to the expected economic boom. Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 47 / 51 IV. Problem set 1 Consider an economy described by the classical hyperin‡ation model such that: mt pt = (pt+1=t pt ) where m and p are the logs of money supply and prices, and pt+1=t is the rational expectation of pt . 1 Comment the economic interpretation of the preceding equation and explain how we can obtain the forward-looking equation: 1 P1 i pt = 1+ i=0 1+ mt+i=t 2 Assume that the central bank announces in t a permanent increase of its money supply for t + 2: m(t; t + 2; 1). Explain the e¤ects of prices in t, t + 1 and t + 2. What is the economic interpretation? 3 Suppose that instead of a permanent increase, the central bank announces a transitory expansion of money supply until t + 3: m(t; t + 2; t + 3) How is your previous answer a¤ected by this change? Explain. 4 Answer the two preceding questions assuming static expectations. Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 48 / 51 Problem set 1 Consider an economy described by the classical hyperin‡ation model such that: mt pt = (pt+1=t pt ) pt+1=t = pt+1 where m and p are the logs of money supply and prices, and pt+1=t the rational expectation of pt . 1 Obtain the price level in t and t + 1 if mt+i = m; 8i 2 Assume that money supply in t is permanently reduced to M=2 without any announcement by the central bank. Obtain the price level in t and t + 1: 3 Now assume that the central bank announces in t that the reduction of money supply will take e¤ect in t + 3. Is the output level a¤ected in any way? 4 Explain the economic mechanism behind prices changes, and the e¤ects on the nominal and real interest rates. Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 49 / 51 Problem set 1 Consider the following arbitrage condition Rt = 1 Rt+1 + 2 gt 3 mt where 3 are 2 positive parameters and 0 < 1 < 1. 1 Obtain the backward solution. 2 Compare it with the forward solution and justify why the later is the one that makes sense on economic grounds. Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 50 / 51 Problem set 1 Consider the following economy: Rt+1=t Rt yt = R t + gt ; rt = Rt Rt mt pt = yt rt ; Rt+1=t = E [Rr+1 =It ] pt = p = 0 1 where > 0, ; > 0 and y, m, g and p are the logs of output, money supply, public consumption and prices. R and r are the interest rates in the long and short run. 2 Explain these equations. 3 What are the e¤ects of a future permanent increase of money supply ( m(t; t + 3; 1)) on yt , Rt and rt : 4 Answer the preceding question in the following cases: = 0 and = 0 5 Can a future permanent increase of public consumption ( g(t; t + 1; 1)) lead to an output expansion. How is your answer a¤ected if the expectations of long-run interest rates are given by Rt+1=t = rt ? Advanced Macroeconomics. J. Andrés () The Monetary Transmission Mechanism 2009-2010 51 / 51