- •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
6.6. NOISE-TRADERS |
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Problems
1. (Siegel’s [128] Paradox) Let St be the spot dollar price of the euro and Ft be the 1-period forward rate in dollars per euro. The claim is
if investors are risk-neutral and the forward foreign exchange market (128) is e cient, the forward rate is the rational expectation of the future
spot rate. From the US perspective we write this as
Et(St+1) = Ft.
The risk-neutral, rational-expectations, e cient market statement from an European perspective is
(1/Ft) = Et(1/St+1)
since from the euro-price of the dollar is the reciprocal of the dollareuro rate. Both statements cannot possibly be true. Why not? (Hint: Use Jensen’s inequality).
2.Let the Euler equation for a domestic investor that speculates in forward foreign exchange be
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where u0(c) is marginal utility of real consumption c and P is the domestic price level. From the foreign perspective, the Euler equation
is
1 = Et[u0(ct+1/(St+1Pt+1)]
Ft Et[u0(ct )/Pt+1]
where c is foreign consumption and P is the foreign price level. Suppose further that both domestic and foreign agents are risk neutral. Show that Siegel’s paradox does not pose a problem now that payo s are stated in real terms.16
3.We saw that the slope coe cient in a regression of st −st−1 on ft −st−1 is negative. McCallum [103] shows regressing st − st−2 on ft − st−2 yields a slope coe cient near 1. How can you explain McCallum’s result?
16Engel’s [43] empirical work showed that regression test results on forward exchange rate unbiasedness done with nominal exchange rates were robust to speciÞcations in real terms so evidently Siegel’s paradox is not economically important.
204CHAPTER 6. FOREIGN EXCHANGE MARKET EFFICIENCY
4.(Kaminsky and Peruga [82]). Suppose that the data generating process for observations on consumption growth, inßation, and exchange rates is given by the lognormal distribution, and that the utility function is u(c) = c1−γ. Let lower case letters denote variables in logarithms. We have ∆ct+1 = ln(Ct+1/Ct) be the rate of consumption growth, ∆st+1 = ln(St+1/St) be the depreciation rate, ∆pt+1 = ln(Pt+1/Pt) be the inßation rate, and ft = ln(Ft) be the log one-period forward rate.
If ln(Y ) N(µ, σ2), then Y is said to be log-normally distributed and
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Let Jt consist of lagged values of ct, st, pt and ft be the date t information set available to the econometrician. Conditional on Jt, let yt+1 = (∆st+1, ∆ct+1, ∆pt+1)0 be normally distributed with condi-
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5.Testing the volatility restrictions (Cecchetti et. al. [25]). This exercise develops the volatility bounds analysis so that we can do classical statistical hypothesis tests to compare the implied volatility of the intertemporal marginal rate of substitution and the lower volatility bound. Begin deÞning φ as a vector of parameters that characterize the utility function, and ψ as a vector of parameters associated with the stochastic process governing consumption growth.
Stack the parameters that must be estimated from the data into the
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6.6. NOISE-TRADERS |
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Assume that consistent estimators of both θ0 and Σθ are available.
Now make explicit the fact that the moments of the intertemporal marginal rate of substitution and the volatility bound depend on sample information. The estimated mean and standard deviation of pre-
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How can this result be used to conduct a statistical test of whether a particular model attains the volatility restrictions?
6.(Peso problem). Let the fundamentals, ft = mt −mt −λ(yt −yt ) follow the random walk with drift, ft+1 = δ0 + ft + vt+1, where vt iid with E(vt) = 0 and E(vt2) = σv2. Agents know the fundamentals process with certainty. Forward iteration on (6.33) yields the present value
formula
X∞
st = γ Et(ft+j). j=1
Verify the solution (6.38) by direct substitution of Et(ft+j).
Now let agents believe that the drift may have increased to δ = δ1. Show that Et(ft+j) = ft + j(δ0 − δ1)p0t + jδ1. Use direct substitution of this forecasting formula in the present value formula to verify the solution (6.43) in the text.
206CHAPTER 6. FOREIGN EXCHANGE MARKET EFFICIENCY