- •Preface
- •Contents
- •Chapter 1
- •1.1 International Financial Markets
- •Foreign Exchange
- •Covered Interest Parity
- •Uncovered Interest Parity
- •Futures Contracts
- •1.2 National Accounting Relations
- •National Income Accounting
- •The Balance of Payments
- •1.3 The Central Bank’s Balance Sheet
- •Chapter 2
- •2.1 Unrestricted Vector Autoregressions
- •Lag-Length Determination
- •Granger Causality, Econometric Exogeniety and Causal
- •Priority
- •The Vector Moving-Average Representation
- •Impulse Response Analysis
- •Forecast-Error Variance Decomposition
- •Potential Pitfalls of Unrestricted VARs
- •2.2 Generalized Method of Moments
- •2.3 Simulated Method of Moments
- •2.4 Unit Roots
- •The Levin—Lin Test
- •The Im, Pesaran and Shin Test
- •The Maddala and Wu Test
- •Potential Pitfalls of Panel Unit-Root Tests
- •2.6 Cointegration
- •The Vector Error-Correction Representation
- •2.7 Filtering
- •The Spectral Representation of a Time Series
- •Linear Filters
- •The Hodrick—Prescott Filter
- •Chapter 3
- •The Monetary Model
- •Cassel’s Approach
- •The Commodity-Arbitrage Approach
- •3.5 Testing Monetary Model Predictions
- •MacDonald and Taylor’s Test
- •Problems
- •Chapter 4
- •The Lucas Model
- •4.1 The Barter Economy
- •4.2 The One-Money Monetary Economy
- •4.4 Introduction to the Calibration Method
- •4.5 Calibrating the Lucas Model
- •Appendix—Markov Chains
- •Problems
- •Chapter 5
- •Measurement
- •5.2 Calibrating a Two-Country Model
- •Measurement
- •The Two-Country Model
- •Simulating the Two-Country Model
- •Chapter 6
- •6.1 Deviations From UIP
- •Hansen and Hodrick’s Tests of UIP
- •Fama Decomposition Regressions
- •Estimating pt
- •6.2 Rational Risk Premia
- •6.3 Testing Euler Equations
- •Volatility Bounds
- •6.4 Apparent Violations of Rationality
- •6.5 The ‘Peso Problem’
- •Lewis’s ‘Peso-Problem’ with Bayesian Learning
- •6.6 Noise-Traders
- •Problems
- •Chapter 7
- •The Real Exchange Rate
- •7.1 Some Preliminary Issues
- •7.2 Deviations from the Law-Of-One Price
- •The Balassa—Samuelson Model
- •Size Distortion in Unit-Root Tests
- •Problems
- •Chapter 8
- •The Mundell-Fleming Model
- •Steady-State Equilibrium
- •Exchange rate dynamics
- •8.3 A Stochastic Mundell—Fleming Model
- •8.4 VAR analysis of Mundell—Fleming
- •The Eichenbaum and Evans VAR
- •Clarida-Gali Structural VAR
- •Appendix: Solving the Dornbusch Model
- •Problems
- •Chapter 9
- •9.1 The Redux Model
- •9.2 Pricing to Market
- •Full Pricing-To-Market
- •Problems
- •Chapter 10
- •Target-Zone Models
- •10.1 Fundamentals of Stochastic Calculus
- •Ito’s Lemma
- •10.3 InÞnitesimal Marginal Intervention
- •Estimating and Testing the Krugman Model
- •10.4 Discrete Intervention
- •10.5 Eventual Collapse
- •Chapter 11
- •Balance of Payments Crises
- •Flood—Garber Deterministic Crises
- •11.2 A Second Generation Model
- •Obstfeld’s Multiple Devaluation Threshold Model
- •Bibliography
- •Author Index
- •Subject Index
3.5. TESTING MONETARY MODEL PREDICTIONS |
103 |
Problems
Let the fundamentals have the permanent—transitory components representation
ft = f¯t + zt, |
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(3.27) |
iid |
|
|
where f¯t = f¯t−1 + ²t is the permanent part with ²t N(0, σ²2) and zt = |
||
iid |
|
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ρzt−1+ut is the transitory part with ut N(0, σu2), and 0 < ρ < 1. Note that |
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the time-t expectation of a random walk k periods ahead is E |
(f¯ |
) = f¯, |
t |
t+k |
t |
and the time-t expectation of the AR(1) part k periods ahead is Etzt+k =
ρkz . (3.27) implies the k-step ahead prediction formula E |
(f |
) = f¯ |
+ρkz . |
||
t |
|
t |
t+k |
t |
t |
1. Show that |
1 |
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st = f¯t + |
zt. |
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(3.28) |
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1 + λ(1 − ρ) |
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2.Suppose that the fundamentals are stationary by setting σ² = 0. Then the permanent part f¯t drops out and the fundamentals are governed by a stationary AR(1) process. Show that
Var(st) = µ |
1 |
¶2 |
Var(ft), |
(3.29) |
1 + λ(1 − ρ) |
3.Let’s restore the unit root component in the fundamentals by setting σ²2 > 0 but turn o the transitory part by setting σu2 = 0. Now the fundamentals follow a random walk and the exchange rate is given
exactly by the fundamentals
st = ft. |
(3.30) |
The exchange rate inherits the unit root from ft. Since unit root processes have inÞnite variances, we should take Þrst di erences to induce stationarity. Doing so and taking the variance, (3.30) predicts that the variance of the exchange rate is exactly equal to the variance of the fundamentals.
Now re-introduce the transitory part σu2 > 0. Show that depreciation of the home currency is
∆st = ²t + |
(ρ − 1)zt−1 + ut |
. |
(3.31) |
|
1 + λ(1 − ρ) |
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104 |
CHAPTER 3. THE MONETARY MODEL |
||
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where |
2(1 − ρ) |
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Var(∆st) = σ²2 + |
Var(zt). |
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[1 + λ(1 − ρ)]2 |
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Why does the variance of the depreciation still not exceed the variance of the fundamentals growth?