Columbia University Department of Economics Lecture 18 Economics UN3213 Intermediate Macroeconomics Professor Mart ´ ın Uribe Spring 2019
Announcement Homework 5 due on Monday in class.
Econ UN3213 Interm. Macro Monetary Economics Lecture 18 Topics Today • The End of the German Hyperinflation of 1923 • Cagan’s Nightmare 1
Econ UN3213 Interm. Macro Monetary Economics Lecture 18 A Money-Based Inflation Stabilization Program Consider an economy that starts in period 0 and lasts forever ( t = 0 , 1 , 2 , . . . ). We will study an experiment in which at some date T > 0, the central bank unexpectedly and permanently lowers the growth rate of the money supply from µ > 0 to 0. By unexpectedly, we mean that at any period t < T agents expect that money will grow forever at the rate µ > 0, or M t = (1 + µ ) t M 0 . But then in period T it is announced that the money supply will stop growing and stay constant forever M t = M T for t ≥ T. We wish to characterize the behavior of prices and money demand induced by this stabilization program. 2
Econ UN3213 Interm. Macro Monetary Economics Lecture 18 Let’s recall the building blocks of the Cagan model: (1) Equilibrium in the money market: M t /P t = (1 + i t ) − η Y (2) The Fisher equation : 1 + i t = (1 + r )(1 + E t π t +1 ) (3) Specification of how expectations are formed: Assume that expectations are rational . This means that E t π t +1 = π t +1 (perfect foresight), except in period T in which households are surprised by an unanticipated policy change, so we have that E T − 1 π T will not necessarily be equal to π T . (4) Monetary Policy: The money supply rule states that M t is ex- ogenous and grows at the rate µ > 0 between periods 1 and T , with the initial money supply, M 0 , given. In period T , the government announces, by surprise, that from that period on the money supply will stay constant forever. 3
Econ UN3213 Interm. Macro Monetary Economics Lecture 18 Breaking Down the Equilibrium Dynamics Subperiod 1: The pre-reform period, t ≤ T − 1 . Subperiod 2: The post-reform period, t ≥ T + 1 . Subperiod 3: The reform period, t = T 4
Econ UN3213 Interm. Macro Monetary Economics Lecture 18 (1) The Pre-Reform Period, t ≤ T − 1 Monetary Policy: M t = (1 + µ ) t M 0 for t = 1 , 2 , . . . , T (and this is expected to last forever). Solution: use the guess and verify method. Guess that E t π t +1 = µ for t = 0 , 1 , 2 , . . . , T − 1 . This guess makes sense given the analysis of the previous lecture, because agents expect the money growth rate to be µ forever. This guess and the Fisher equation imply that the nominal interest rate satisfies 1 + i t = (1 + r )(1 + µ ); for t = 0 , 1 , 2 , . . . , T − 1 . 5
Econ UN3213 Interm. Macro Monetary Economics Lecture 18 Then, equilibrium in the money market implies that: M t = [(1 + r )(1 + µ )] − η Y, for t = 0 , 1 , 2 , . . . , T − 1 . (1) P t This means that M t /P t is constant for t = 0 , 1 , 2 , . . . , T − 1. Since M t grows at the rate µ so must P t ., that is, P t /P t − 1 ≡ 1 + π t = 1 + µ, for t = 1 , 2 , . . . , T − 1 . This expression says that inflation is equal to the money growth rate during the pre-stabilization period. This result also corroborates that the inflationary expectations we guessed are actually rational. 6
Econ UN3213 Interm. Macro Monetary Economics Lecture 18 Comments on the Pre-Reform Period • The equilibrium dynamics of inflation, real balances, interest rate, and prices are just like the constant money growth rate regime we analyzed in the last lecture. This makes sense, because agents expect the money growth rate to be equal to µ forever. In particular, they do not anticipate the stabilization program of period T . • The interest rate in t = T − 1 is still high at i T − 1 = (1+ r )(1+ µ ) − 1 even though prices will be stabilized in T . Again, this is because agents expect money growth to continue to be µ indefinitely, so they expect inflation between T − 1 and T to be µ , i.e., E T − 1 π T = µ , and hence the nominal interest rate is still 1 + i T − 1 = (1 + r )(1 + E T − 1 π T ) = (1 + r )(1 + µ ). As we will see shortly, in period T actual inflation will be lower than expected in T − 1. • Real balances are low throughout the pre-reform period. Why? because interest rates are high, so the opportunity cost of holding money is high. 7
Econ UN3213 Interm. Macro Monetary Economics Lecture 18 (2) The Post-Reform Period, t ≥ T + 1 Constant Money Supply: M t = M T , for t = T + 1 , T + 2 , . . . Guess: E t π t +1 = 0, for t = T + 1 , T + 2 , . . . . That is, we guess that people expect prices to be constant over time. This guess makes sense given what we know about this model: since the money growth rate is expected to be nil forever, so is the expected rate of inflation. Then, the nominal interest rate is 1+ i t = (1+ r )(1+ E t π t +1 ) = 1+ r , or i t = r , for t = T + 1 , T + 2 , . . . , the nominal interest rate equals the real interest rate. Real money balances are constant and equal to M t = (1 + r ) − η Y, for t = T + 1 , T + 2 , . . . . (2) P t Because M t /P t and M t are constant, P t must also be constant for t = T +1 , T +2 . . . . That is, inflation is nil, π t = 0 for t = T +2 , T +3 , . . . . Finally, expectations are rational E t π t +1 = π t +1 = 0 for t ≥ T + 1, validating our guess. 8
Econ UN3213 Interm. Macro Monetary Economics Lecture 18 Comments on the Post-Reform Period • With money supply expected to be constant from T onward, there is zero inflation and the nominal interest rate is low, equal to the real rate of interest, r . • Real balances are high in periods T + 1 , T + 2 , T + 3 , . . . because the opportunity cost of money, i.e., the nominal interest rate, is low. 9
Econ UN3213 Interm. Macro Monetary Economics Lecture 18 (3) The Reform Period, t = T Money Supply: M T = (1 + µ ) M T − 1 Guess: E T π T +1 = 0. Nominal Interest rate: (1 + i T ) = (1 + r )(1 + E T π T +1 ) = (1 + r ). Real Money Balances: M T = (1 + r ) − η Y. (3) P T This is the same as in period T + 1. From (2) we have that M T +1 P T +1 = (1+ r ) − η Y. Combining this expressin with (3) we have that M T /P T = M T +1 /P T +1 ; and recalling that M T = M T +1 , we have that P T = P T +1 , or π T +1 = 0. This means that E T π T +1 = π T +1 = 0, which implies that expectations are rational, validating our guess. 10
Econ UN3213 Interm. Macro Monetary Economics Lecture 18 Now combine M T − 1 /P T − 1 = [(1+ r )(1+ µ )] − η Y (equation (1)) with M T /P t = (1 + r ) − η Y (equation (3)) to get M T (1 + r ) η /Y P T M T − 1 [(1 + r )(1 + µ )] η /Y = (1 + µ ) (1 + µ ) η = (1 + µ ) 1 − η < 1 + µ. = P T − 1 That is, π T < µ . This is remarkable, because it says that the inflation rate between periods T − 1 and T falls below µ even though the money supply grows at the rate µ between T − 1 and T . This is the most important prediction of this model for explaining what actually happens at the end of hyperinflations. 11
Econ UN3213 Interm. Macro Monetary Economics Lecture 18 Comments on the Reform Period • Money growth in period T is still high at µ . Nevertheless, real balances are already high, that is M T /P T = Y (1 + r ) − η > Y [(1 + r )(1 + µ )] − η = M T − 1 /P T − 1 . In other words, real balances expand before money growth slows down! • Inflation slows down before money growth slows down! • It is even possible that inflation not only slows down but actually becomes negative. Notice if the interest semi-elasticity of money demand is greater than one in absolute value, η > 1, which is the case of greatest empirical interest, then we would see deflation in the period of reform. 12
Econ UN3213 Interm. Macro Monetary Economics Lecture 18 • The intuition for why inflation slows down even though the money supply is still growing at the rate µ is that in period T everybody expects inflation in the future to be zero. As a result, the interest rate falls in period T , as banks don’t need to compensate depositors for future inflation. In turn, a low interest rate induces people to increase their money holdings. So, the increase in the money supply in period T doesn’t go to prices as before, because people don’t get rid of it, but keep it to rebuild their money holdings • Actual inflation in period T is lower than was expected in period T − 1. Recall that E T − 1 π T = µ and that π T < µ . But this is not a violation of Rational Expectations, since the stabilization program implemented in period T was unpredictable in period T − 1. 13
Econ UN3213 Interm. Macro Monetary Economics Lecture 18 Reliquefication We noted that if the interest semi-elasticity of money demand is greater than unity in absolute value ( η > 1), then prices can actually fall when the reform is implemented. This one-period deflation can be avoided by a one-time increase in the money supply in period T by a rate larger than µ to accommodate the increase in the demand for real moneay balances. Such an increase in nominal balances is called reliquefication . Let ˜ µ T denote the growth rate of the money supply in period T that would prevent the price level from falling. Can you deduce ˜ µ T in terms of µ and η ? 14
Recommend
More recommend
