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.

#

REE Solution

2 1 ,

3 11 ,

1 xe2 e1A e1AI A 1,

0 1 2e1 I A 1.

#

#

#

#

qt 0 1 Y t 2i t 1 3 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

Alternative gain specifications

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

Conclusions

Macro fundamentals approach not yet dead Taylor rule fundamentals first cut. Probably need to add a model of the risk premium