Lecture 1: Traditional Open Macro Models and Monetary Policy

Transcription

1 Lecture 1: Traditional Open Macro Models and Monetary Policy Isabelle Méjean Master Economics and Public Policy, International Macroeconomics October 16 th, 2008

2 Introduction Many important questions in international macroeconomics involve monetary issues The main departure with respect to a closed economy is that several monetary authorities play independently, managing different currencies. Introducing money in a model allows addressing a number of issues: determinants of seignorage, mechanics of exchange-rate systems, long-run effects of money-supply changes on prices and exchange rates

3 Introduction (2) Role of money i) Medium of exchange ii) Store of value iii) Nominal unit of account Nature of money Here, money is meant as currency (abstract from the banking system) Money does not bear interest Simplifying assumption Liquidity premium

4 The Cagan Model

5 Hypotheses Simple empirical model of money and inflation used to study hyperinflations (ie inflation > 50% per month, ex Zimbabwe: % in january 2008) Prices are fully flexible Adjust to clear product, factor and asset markets Long-run analysis Stochastic, discrete-time model Rational expectations

6 Hypotheses (2) Demand for real money balances depends on expected future price-level inflation: m d t p t = ηe t {p t+1 p t } Higher expected inflation lowers the demand for real balances by raising the opportunity cost of holding money Ignore real determinants to focus on hyperinflation period Simplified form of Keynes LM curves: m d t p t = φy t µi t+1, with 1 + i t+1 = (1 + r t+1 ) P t+1 P t Money supply m t exogenously determined

7 Monetary equilibrium In equilibrium: m t = m d t m t p t = ηe t {p t+1 p t } First-order stochastic difference equation explaining price-level dynamics in terms of the money supply

8 Equilibrium price level p t = = p t = η [m t + ηe t {p t+1 }] [ 1 ( ) s t η E t {m s }] 1 + η 1 + η s=t [ 1 ( ) s t η E t {m s }] 1 + η 1 + η s=t no-speculative bubble condition: ( ) T η lim E t {p t+t } = 0 T 1 + η ( ) T η + lim E t {p t+t } t 1 + η The limit is indeed zero unless the absolute value of the log price level grows exponentially at a rate of at least (1 + η)/η

9 Equilibrium price level (2) The price level depends on a weighted average of future expected money supplies, with weights that decline geometrically as the future unfolds Note that: η [ ( ) ] ( ) s t η = η 1 + η 1 η = 1 1+η s=t Money is fully neutral in the absence of nominal rigidities or money illusion

10 Constant money supply m t = m, t Zero expected inflation : E t p t+1 p t = 0, Constant price level: p = m

11 Constant money supply growth m t = m + µt Constant expected inflation : E t p t+1 p t = µ, Constant price level growth: p t = η s=t = m t + µ η(1 + η) 1 + η p t = m t + µη ( ) s t η [m t + µ(s t)] 1 + η

12 Autoregressive money supply m t = ρm t 1 + ε t, 0 ρ 1, E t {ε t+1 } = 0 Price level: p t = m t 1 + η s=t ( ) s t ηρ m t = 1 + η 1 + η ηρ In the limiting case ρ = 1 in which money shocks are expected to be permanent, the solution reduces to p t = m t.

13 Announced rise in money supply m t = m, t < T m t = m, t T Price level: p t = { ( ) T t m + η 1+η ( m m), t < T m, t T The supply shock is integrated in the effective price level as long as it is announced by the government.

14 Announced rise in money supply (2)

15 Seignorage Real revenues a government acquires by using newly issued money to buy goods and nonmoney assets: Seignorage = M t M t 1 P t M t M t 1. M t M t P t If higher money growth raises expected inflation, the demand for real balances may fall, which exerts a negative influence on seignorage revenues Marginal revenue from money growth can be negative Limit to seignorage. Optimal rate of inflation defined by: M Max t M t 1 µ M t ( M s.c. t P t = with. Mt P t E t P t+1 P t µ = Mt Mt 1 M t ) η

16 Optimal Seignorage under Constant Money Growth M t M t 1 = Pt P t 1 = 1 + µ The optimal growth rate of money supply is then: µ = 1 η Inverse function of the semielasticity of real balances with respect to inflation

17 How important is seignorage? Table: Average seignorage revenues in industrialized countries Country % Government spending % GDP Australia Canada France Germany Italy New Zealand Sweden United States Source: Obstfeld & Rogoff from IMF-IFS data

18 Limits Ex 1: The Cagan Model How can we explain periods of hyperinflation, in which governments obviously let money growth exceed the optimal rate? Backward-looking expectations? Credibility issues : On date 0, the government announces that it will stick to the revenue-maximizing rate of money growth If agents believe it, they hold real balances M/P = [(1 + η)/η] η On date 1, the government has an incentive to cheat and choose a higher money growth rate If governments lack credit, agents will anticipate the government s temptation to cheat.

19 Open-economy extension Obstfeld & Rogoff

20 Hypotheses of the model Small open economy Exogenous output Money demand defined by: Flexible prices and PPP: m t p t = ηi t+1 + φy t p t = e t + p t with e t the (log of) nominal exchange rate (home currency per unit of foreign currency) and pt the world foreign-currency price

21 Hypotheses of the model (2) Uncovered interest parity: { } 1 + i t+1 = (1 + it+1)e Et+1 t E t i t+1 = i t+1 + E t e t+1 e t Simple arbitrage argument under perfect foresight and no exchange-rate risk premium Note that the log UIP relation is only an approximation since, by the Jensen s inequality, ln E t {E t+1 } > E t {ln E t+1 }.

22 Exchange-rate dynamics Incorporating the PPP and the IUP conditions into the money demand gives: m t p t e t = ηi t+1 η(e t {e t+1 } e t ) + φy t m t φy t + ηi t+1 p t e t = η(e t {e t+1 } e t ) Solving for e t implies: e t = η s=t ( ) s t η E t {m s φy s + ηi s+1 ps } 1 + η

23 Exchange-rate dynamics (2) Describes the behaviour of nominal exchange rates as a function of expectations of future variables ( asset pricing equations). Nominal exchange-rate depreciation if: the path of the home money supply raises, thus increasing the domestic price level and the exchange rate (through PPP) the real domestic income goes down, thus contracting money demand which exerts a negative pressure on the domestic price level the foreign interest rate increases the foreign price level drops Note that this equation relies on a PPP assumption Long-run Model

24 Autoregressive money growth m t m t 1 = ρ(m t 1 m t 2 ) + ε t where ε iid, E t 1 {ε t } = 0 Expected rate of exchange rate depreciation: E t {e t+1 } e t = η Exchange rate level: s=t ( ) s t η E t {m s+1 m s } 1 + η e t = m t + η ( ) s t η E t {m s+1 m s } 1 + η 1 + η s=t ηρ = m t η ηρ (m t m t 1 ) Impact of an unanticipated shock to m t : direct exchange rate increase ( raises the current nominal money supply) + when ρ > 0, increases expectations of future money growth, thereby pushing the exchange rate even higher.

25 Exchange rate fixing Fixed exchange rate: e t = ē and ηi φy p = 0 Fixed money supply: m t = m = ē Fixed exchange rate: e t = ē and ηi φy p 0 Money supply endogenous, Adjustment to market-driven fluctuations in i Future fixing at some future date T : e t = ē, t T In period T 1: m T 1 φy T 1 + ηi T p T 1 e T 1 = η(e T 1 e T e T 1 ) = 0 i T = i T + E T 1 e T e T 1 = i T i adjusts to satisfy the UIP relation. The monetary equilibrium implies that m also adjusts, whatever the exchange rate level the private sector expects The announcement is not a well-adapted solution for the exchange rate market to converge towards an equilibrium value.