Learning, Monetary Policy Rules, and Real Exchange Rate Dynamics
Nelson C. Mark
University of Notre Dame
Fundamentals given a bad rap Flood and Rose“When it comes to understanding exchange rate volatility,
macroeconomics – “fundamentals” – is irrelevant, except in high inflation countries or in the long run. The large differences in exchange rate volatility across countries and time are simply mysterious from an aggregate perspective.”
Standard Fundamentals
Exchange rate fundamentals of old and many new macro models: m,m*,y,y*,c,c*
PPP fundamentals: a constant Probable long-run connection Tenuous short-run connections
Traditional FundamentalsNominal Exchange Rate and PPP Fundamentals (US-
Germany)
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
1960 1963 1967 1971 1975 1978 1982 1986 1990 1993 1997 2001
Nominal Exchange PPPs
Traditional Fundamentals
Real Exchange Rate
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1960 1964 1968 1972 1976 1980 1984 1988 1992 1996 2000
Monetary FundamentalsReal Levels Regression Monetary Fundamentals
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
73.1 75.1 77.1 79.1 81.1 83.1 85.1 87.1 89.1 91.1 93.1 95.1 97.1
Actual
Fitted
Inflation differentials, real dollar-DM rateInflation Differentials and the Real Exchange Rate
-3
-2
-1
0
1
2
3
4
5
1961 1964 1968 1971 1975 1978 1982 1985 1989 1992 1996 1999 2003
German-USA Inflation
Log real dollar-DM
Inflation differentials, real dollar-DM rate
Inflation Differentials and the Real Exchange Rate
-3
-2
-1
0
1
2
3
4
5
1961 1964 1968 1971 1975 1978 1982 1985 1989 1992 1996 1999 2003
German-USA Inflation
Log real dollar-DM
Inflation differentials, real dollar-DM rateInflation Differentials and the Real Exchange Rate
-5-4-3-2-1012345
1961 1964 1968 1971 1975 1978 1982 1985 1989 1992 1996 1999 2003
Log real dollar-DM
Inflation Differential
Inflation differentials, real $-pound rate
Inflation Differentials and Real Exchange Rate
-4
-2
0
2
4
6
1961 1965 1969 1974 1978 1982 1986 1991 1995 1999 2003
Log real dollar-pound Inf lation dif ferential
Inflation differentials, real dollar-yen rateInflation Differentials and Real Exchange Rate
-3
-2
-1
0
1
2
3
4
5
1961 1965 1969 1973 1977 1981 1985 1989 1993 1997 2001
Log real dollar yenInf lation Dif ferential
Inflation differentials, real dollar-CD rateInflation Differentials and Real Exchange Rate
-5
-4
-3
-2
-1
0
1
2
3
4
1961 1964 1968 1971 1975 1978 1982 1985 1989 1992 1996 1999 2003
Log real exchange rate Inf lation Dif ferential
Alternative macro fundamentals through the lens of Taylor-rules Inflationary expectations
A rate of change Output gap
Deviation from natural level
Real exchange rate and real interest differentials Pricing equation is real interest parity:
Expectations matter Alternative strategies for modeling interest
differential Multivariate setting and monetary policy
reaction functions contribute towards accurately modeling expectations of future interest rates
Model uncertainty and learning Is this a credible framework for understanding
real exchange rate dynamics? Allow model uncertainty
Structural instability Established FACT of life in international finance Source of Meese-Rogoff’s failure to FIT out of sample
Model uncertainty and learning Public attempts to learn “true” values by recursive
least squares Coefficients of process that generates inflation, output gap,
nominal interest rates Ask if long swings could have been explained by
historical fundamentals data Real depreciation of late 70s, the “great appreciation” and
subsequent “great depreciation”
US-GERMANY: Interest rate reaction functions The Fed:
i t T i E t t 1 xxt sst pt pt
The Bundesbank:
i tT i E t t 1 xxti t 1 i tT i t 1 t
i t 1 i t T i t 1 t
US-GERMANY: Interest rate reaction functions
Impose homogeneity
i t 1
i tT
i t 1 t,
i tT
E t
t 1 xx t sqt, i i ,
tiid 0,
2 .
#
#
#
#
US-GERMANY: Interest rate reaction functions GMM estimable differential form
i t 1
t 1 xx t sqt i t 1 t
1 t t 1
t 1 E t t 1
Germany-USA Interest Diffe rential
-8
-6
-4
-2
0
2
4
6
8
1961 1965 1968 1972 1976 1980 1983 1987 1991 1995 1998 2002
DataFitted Values
Forecasting: Companion form
Estimation
The REE path: Inflation, output gap differentials follow VAR(p)
Y t
t, . . . , t p 1, x t, . . . , x t p 1
Y t A
Y t 1 v t
E t t 1 e1 A
Y t
Zvt
1,
Y t
t b
Zvt 1
v 1t,x t bx
Zvt 1
v 2t,
#
#
The REE path: Pricing by real interest parity
st E tst 1 i t
qt E tqt 1 i t E t
t 1
qt E tqt 1 1 1e1
1 xe2 1e1AY t
i t 1 t.
#
Estimated Rational Expectations Real Exchange Rate Path
-600
-400
-200
0
200
400
600
800
1976 1978 1980 1983 1985 1987 1989 1992 1994 1996 1998 2001 2003
DataSource GapHP Gap
Learning Path
r t i t e1 t 1 A t 1Yt
t 1, t 1, ,t 1, x,t 1
i t t 1 1 t 1 ,t 1e1 t 1
1 t 1 x,t 1e2 ,t 1e1A t 1 Y t t 1
i t 1 t
#
Given
Generate
Given
PerceivedLaw of Motion
t 1,A t 1
t 1 0t 1, 1t 1 , 2t 1, 3t 1
qt 0t 1 1t 1 Y t 2t 1
i t 1 3t 1 t
E tqt 1 0t 1 1t 1 t 1 A t 1Y t 2t 1
i t.
Actual Law of Motion
qt 0t 1tY t 2t
i t 1 3t t
0t 0,t 1 1,t 1 e1 ,t 1 2,t 1 1 t 1 1 2,t 1 t 1 1t x,t 1e2 2,t 1 x,t 1e2 ,t 1e1A t 1
,t 1 1e1 1,t 1 A t 1 2t t 1 1 2,t 1 3t 1 2,t 1
Update coefficients
Rv,t Rv,t 1 gtZvt 1
Zvt 1
Rv,t 1
b ,t,bx,t b ,t 1,bx,t 1 gtRvt 1Zvt 1 t, x t
Zvt 1
b ,t 1,bx,t 1
#
#
R i,t R i,t 1 gtZ i,t 1
Z i,t 1
R i,t 1
t t 1 gtR i,t 1 1 Z i,t 1
i t t 1
Z i,t 1
#
#
Rq,t Rq,t 1 gtZq,t
Zq,t
Rq,t 1
t t 1 gtRq,t 1 1 Zq,t qt t 1
Zq,t
#
#
The VAR
InterestDifferential
RealExchangeRate
Gaingt 1/t
Learning Path for Real DM. Gap constructed at source
-250
-200
-150
-100
-50
0
50
100
150
200
250
1976 1978 1980 1983 1985 1987 1989 1992 1994 1996 1998 2001 2003
Data Gain 0Gain 1 Gain 2Gain 3 Gain 4
Rational and Learning Path Comparison
-600
-400
-200
0
200
400
600
800
1976 1978 1980 1983 1985 1987 1989 1992 1994 1996 1998 2001 2003
Data Rational Fixed gain
Rational and Learning Path Comparison (standardized)
-4
-3
-2
-1
0
1
2
3
4
1976 1978 1980 1983 1985 1987 1989 1992 1994 1996 1998 2001 2003
Data Rational Fixed Gain