Leeds University Business School

Empirical Investigation of Monetary Models for GBP/USD Exchange Rate in Cointegrating VAR with Exogenous I(1)

Variables and Structural Break

Viet Hoang Nguyen

Leeds University Business SchoolThe University of Leeds

• Monetary Models of Exchange Rate Determination

• Motivations for Our Research

• Econometric Framework

• The Examined Models & Main Considerations

• Data

• Empirical Results

• Conclusions

Introduction

Development in the Literature of Exchange Rate Modelling

• Testing Foreign Exchange Market Efficiency

• Monetary Models of Exchange Rate Determination

• Models of Exchange Rate Volatility

• Nonlinear Models of Exchange Rate

• Foreign Exchange Market Microstructure

(New Micro Exchange Rate Economics)

Monetary Models of Exchange Rate

• Monetary models of exchange rate are often called structural models since they are derived from a system of equations representing equilibrium relationships in monetary markets.

• They emerged as the dominant exchange rate models since the breakdown of the Bretton Woods agreement in the early 1970s.

• These models focus on the ‘relationship between exchange rate and (macro) economic fundamental variables,’ and examine the ‘explanatory power of economic fundamentals in forecasting exchange rate.’

Monetary Models of Exchange Rate

Popular models:

• Meese and Rogoff (1983a) examined three representative models:

– The flexible-price (Frenkel-Bilson) model

– The sticky-price (Dornbusch-Frankel) model

– The sticky-price (Hooper-Morton) model (which also takes into account the current account)

• Mark (1995) initiated:

– The ‘long-horizon’ regression

Monetary Models of Exchange Rate

1. The Flexible-price (Frenkel-Bilson) Model (Model 1):

• Based on Purchasing Power Parity (PPP)

• Monetary equilibria in domestic and foreign economies:

• The derived domestic and foreign price levels:

• The model is based on the assumption of continuous PPP:

Monetary Models of Exchange RateDerivation

tttt rypm ******tttt rypm

tttt rymp ******tttt rymp

*ttt ppe

Monetary Models of Exchange RateDerivation

* ,*

tttttttt urryymmce )()()( ***

)()( *****ttttttt rryymme

• Thus,

• In empirical studies, researchers often imposed two following restrictions:

• And estimated the following model:

Notations: et: Exchange rate; pt: Price level; mt: Money supply; yt: Output;

rt: Interest rate; t: Inflation; TBt: Cumulative trade balances; (*): Foreign variables

2. The Sticky-price (Dornbusch-Frankel) Model (Model 2):

• Allow for deviations from PPP by adding long-run inflation differential

3. The Sticky-price (Hooper-Morton) Model (Model 3):

• Allow for long-run changes in Real Exchange Rate by adding cumulative trade balances of domestic and foreign economies

Monetary Models of Exchange RateDerivation

tttttttttt urryymmce )()()()( ****

tttttttttttt uTBTBrryymmce ****** )()()()(

4. The Long-horizon Regression (Model 4):

• Based on the flexible-price model and further assumes that the UIP (Uncovered Interest rate Parity) holds:

where

are deviations from the fundamental value and the fundamental value, respectively. k = 1, 2 … represents the forecast horizons.

* Employed econometric frameworks:

Linear regression, Unrestricted VAR, Panel Data

Monetary Models of Exchange RateDerivation

kttkkkt ze ,ttt efz )()( **

ttttt yymmf

Mixed results:

• Early gloomy results: Meese and Rogoff (1983a,b), Smith and Wickens (1986), Meese and Rose (1991) suggested the failure of monetary models of exchange rate to beat the random walk in forecasting exchange rate. Suggested causes:

– (1) Instability due to oil price shocks & changes in macroeconomic policy regime; (2) Misspecification of money demand function; (3) Difficulties in modelling expectations of explanatory variables - Meese & Rogoff (1983a).

– The breakdown of PPP - Smith and Wickens (1986)

Monetary Models of Exchange RateMixed Results

Mixed results:

• Recent encouraging results: Groen (2000, 2005), Mark and Sul (2001), Rapach and Wohar (2002), Engle et. al. (2007).

– Improving samples: Groen (2000, 2005), Mark and Sul (2001) used pooled time series in panel data, Rapach and Wohar (2002) used long-span data.

– Examining the cointegration analysis among variables.

– Results suggest that there exists a long-run relationship between exchange rate and monetary fundamentals, and that monetary fundamentals do have predictive power for exchange rate.

– However, researchers still imposed arbitrary restrictions.

Monetary Models of Exchange RateMixed Results

• Is there a long-run relationship between exchange rate and macroeconomic fundamental variables without imposing arbitrary restrictions?

• How does this long-run relationship response to shocks?

• How do variables within the system response to shocks?

• How do macroeconomic fundamentals help to forecast exchange rate in in- and out-of-sample forecast exercises?

Motivations

Cointegrating Vector Auto-Regression (VAR) with

Exogenous I(1) Variables and Structural Break

Initiated by Pesaran et al (2000), Pesaran and Shin (2002)

• Include both endogenous and exogenous variables

• Include unrestricted intercept and restricted trend

• Allow for cointegration between endogenous and exogenous I(1) variables

• Allow for structural break (change in macroeconomic policy regime)

Econometric Framework

Four models under examination:

• The Flexible-price (Frenkel-Bilson) Model (1)

• The Sticky-price (Dornbusch-Frankel) Model (2)

• The Sticky-price (Hooper-Morton) Model (3)

• The Long-run/Long-horizon Regression (4)

Examined Models

Examined Models

Variables in the system Model 1 Model 2 Model 3 Model 4

1. Oil price (po)

2. Foreign Interest Rate (r*)

3. Foreign Output (y*)

4. Foreign Inflation (*)

5. Domestic Interest Rate (r)

6. Exchange Rate (e)

7. Domestic Output (y)

8. Relative Money Supply (m - m*)

9. Domestic Inflation ()

10. Relative CA Balances (ca – ca*)

Break Dummy for Black-Wednesday Event (1992)• We include a trend-shift dummy to account for this event.

• Mervyn King (1997) – ‘In October 1992, following sterling’s departure from the Exchange Rate Mechanism, Britain adopted a new framework for monetary policy.’ One of the two main components is an explicit target for inflation.

• Soderlind (2000), Svensson (1994).

Main Considerations• Long-run relationship between exchange rate and macro-fundamentals

• Impulse response analysis with respect to shocks of interest

• In-sample forecast: Directional change forecast

• Out-of-sample forecast: Central forecast & Event probability forecast

Main Considerations

Theory-suggested Long-run Relationships

(Cointegrating Vectors - CV) in the system:

• Exchange Rate Equation (ExR) - Relationship between exchange rate and macroeconomic/monetary fundamental variables.

• Output Gap (OG) - Relationship between domestic and foreign outputs.

• Interest Rate Parity (UIP) - Relationship between domestic and foreign interest rates.

• Real Interest Rate (Fisher Equation) - Relationship between domestic nominal interest rate and inflation.

Main Considerations

Data

Variables in the system Explanation Source

1. Oil price (po) USD/Barrel IFS

2. Foreign Interest Rate (r*) US 3-Month Treasury Bill Rate IFS

3. Foreign Output (y*) US real GDP IFS

4. Foreign Inflation (*) US CPI Inflation IFS

5. Domestic Interest Rate (r) UK 3-Month Treasury Bill Rate IFS

6. Exchange Rate (e) GBP/USD OECD

7. Domestic Output (y) UK real GDP IFS

8. Relative Money Supply (m - m*) UK’s M4 – US’s M3 OECD

9. Domestic Inflation () UK CPI Inflation IFS

10. Relative CA Balances (ca – ca*) UK’s CA – US’s CA OECD

Examined period: 1980Q1 – 2006Q4

Data

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

1 9 17 25 33 41 49 57 65 73 81 89 97 105

R

3.6

3.8

4

4.2

4.4

4.6

4.8

5

1 9 17 25 33 41 49 57 65 73 81 89 97 105

Y

-1

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

1 9 17 25 33 41 49 57 65 73 81 89 97 105

E

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

1 9 17 25 33 41 49 57 65 73 81 89 97 105

DP

Empirical Results

Model 1 Model 2 Model 3 Model 4

Cointegration Test

Number of Cointegrating Relations 2 3 3 1

Suggested Cointegrating Vectors

Exchange Rate Equation

Interest Rate Parity

Fisher Equation

Output Gap

Restrictions to Identify CVs

Number of Restrictions 10 21 23 3

Empirical Results

Variables in the model ExR UIP Fisher

1. Oil price (po) 0 0 0

2. Foreign Interest Rate (r*) * -1 0

3. Foreign Output (y*) * 0 0

4. Foreign Inflation (*) * 0 0

5. Domestic Interest Rate (r) * 1 1

6. Exchange Rate (e) 1 0 0

7. Domestic Output (y) * 0 0

8. Relative Money Supply (m - m*) -1 0 0

9. Domestic Inflation () * 0 -1

10. Relative CA Balances (ca – ca*) * 0 0

Example: Restrictions on Cointegrating Vectors in Model 3

Conditional Vector-Error Correction Model

wt: vector of endogenous variables.xt: vector of exogenous variables.zt = (xt, wt ) : vector of both exogenous and endogenous variables.bt: break dummy (trend shift).

dt: break dummy (intercept shift).

• Most equations in four models are well-specified with relatively high R2, especially exchange rate equation:

Model 1: R2 = 0.31Model 2: R2 = 0.63Model 3: R2 = 0.61Model 4: R2 = 0.40

Empirical ResultsVector Error Correction Model

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101*1

p

iwttwitwittwtwwt uwzbtzdBAw

Empirical ResultsPersistence Profiles of CVs

Persistence Profiles of Cointegrating Vectors in Exactly-identified Case

0

0.2

0.4

0.6

0.8

1

1.2

1 4 7 10 13 16 19 22 25 28 31 34 37 40

CV1

CV2

0

0.2

0.4

0.6

0.8

1

1.2

1 4 7 10 13 16 19 22 25 28 31 34 37 40

CV1

CV2

CV3

0

0.2

0.4

0.6

0.8

1

1.2

1 4 7 10 13 16 19 22 25 28 31 34 37 40

CV1

CV2

CV3

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1 4 7 10 13 16 19 22 25 28 31 34 37 40

CV1

Model 1 Model 2

Model 3 Model 4

Empirical ResultsPersistence Profiles of CVs

Persistence Profiles of Cointegrating Vectors in Over-identified Case

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1 4 7 10 13 16 19 22 25 28 31 34 37 40

CV1

CV2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1 4 7 10 13 16 19 22 25 28 31 34 37 40

CV1

CV2

CV3

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1 4 7 10 13 16 19 22 25 28 31 34 37 40

CV1

CV2

CV3

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1 4 7 10 13 16 19 22 25 28 31 34 37 40

CV1

Model 1 Model 2

Model 3 Model 4

Empirical ResultsImpulse Response Analysis

Impulse Responses w.r.t Oil Price Shock – Model 3 (Benchmark)

-0.012

-0.01

-0.008

-0.006

-0.004

-0.002

0

0.002

1 4 7 10 13 16 19 22 25 28 31 34 37 40

e

y

dp

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

1 4 7 10 13 16 19 22 25 28 31 34 37 40CV1

CV2

CV3

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1 4 7 10 13 16 19 22 25 28 31 34 37 40

CV1

CV2

CV3

-0.045

-0.04

-0.035

-0.03

-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

1 4 7 10 13 16 19 22 25 28 31 34 37 40

e

y

dcpi

Impulse Responses w.r.t. Domestic Monetary Policy Shock – Model 3

Forecast of Directional Changes:

Estimate models from 1980Q3 - 2004Q4, leave 8 observations from2005Q1 to 2006Q4 for in-sample forecast evaluation.

• Four Events: UD DD DU UU– U: up; D: down.– 1st letter denotes forecast direction; 2nd letter denotes actual

change.– Based on the results of the four events for all variables in the

system, we compute three statistics: Hit ratio, Kuipers Score, and Pesaran-Timmermann statistic

Empirical ResultsIn-sample Forecast Evaluation

• Hit ratio = (DD+UU)/(UD+DD+DU+UU), ratio of correctly-predicted events over the total events.

• Kuipers Score = H-F, where H = UU/(UU+UD) is the proportion of ups that were correctly predicted to occur, and F = DU/(DU+DD) is the proportion of downs that were incorrectly predicted. In the case where the outcome is symmetric, in the sense that we value the ability to forecast ups and downs equally, then the score statistic of zero means no accuracy, whilst high positive and negative values indicate high and low predictive power, respectively.

• Pesaran-Timmermann Statistic is defined as: PT=(P^ - P*)/(V(P^) - V(P*))^(1/2), where P^ is the proportions of correctly predicted movements, P* is the estimate of the probability of correctly predicting the events under the null that forecasts and realizations are independently distributed, and V(P^) and V(P*) are the consistent estimates of the variances. The null hypothesis of independence between forecasts and realizations implies the null hypothesis of the proposed test of predictive failure.

Empirical ResultsIn-sample Forecast Evaluation

Empirical ResultsIn-sample Forecast Evaluation

Variables in the system UD DD DU UU

1. Oil price (po) 2 3 3 0

2. Foreign Interest Rate (r*) 0 0 0 8

3. Foreign Output (y*) 1 4 1 2

4. Foreign Inflation (*) 4 2 1 1

5. Domestic Interest Rate (r) 3 1 0 4

6. Exchange Rate (e) 0 4 1 3

7. Domestic Output (y) 0 2 0 6

8. Relative Money Supply (m - m*) 1 2 2 3

9. Domestic Inflation () 3 1 1 3

10. Relative CA Balances (ca – ca*) 1 5 1 1

Example: In-sample forecast of Model 3

Results in four models:• Hit ratios:

+ 0.768 for Model 1 + 0.639 for Model 2 + 0.688 for Model 3 + 0.675 for Model 4

• Kuipers Score:+ 0.526 for Model 1 + 0.272 for Model 2+ 0.380 for Model 3 + 0.359 for Model 4

• Pesaran-Timmermann test statistics:+ 4.034 for Model 1 + 2.287 for Model 2+ 3.381 for Model 3 + 2.288 for Model 4

All of these Pesaran-Timmermann test statistics (have a standard normal distribution under the null) are statistically significant and the greater value indicates higher accuracy.

Empirical ResultsIn-sample Forecast Evaluation

Empirical ResultsOut-of-sample Forecast Evaluation

Central Forecasts (based on 4-quarter moving average series)

Model 1 Model 2

Model 3 Model 4

0

1

2

3

4

5

6

1 11 21 31 41 51 61 71 81 91 101 111 121 131

fe

L95%

U95%

e

0

1

2

3

4

5

6

1 11 21 31 41 51 61 71 81 91 101 111 121 131

fe

L95%

U95%

e

0

1

2

3

4

5

6

1 11 21 31 41 51 61 71 81 91 101 111 121 131

fe

L95%

U95%

e

3.6

3.8

4

4.2

4.4

4.6

4.8

5

1 11 21 31 41 51 61 71 81 91 101 111 121 131

fe

L95%

U95%

e

Empirical ResultsOut-of-sample Forecast Evaluation

Central Forecasts of Changes (based on 4-quarter MA series)

Model 1 Model 2

Model 3 Model 4

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

fe

L95%

U95%

e

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

fe

L95%

U95%

e

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

fe

L95%

U95%

e

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

fe

L95%

U95%

e

Empirical ResultsPredictive Distribution Function

Absolute changes in Exchange Rate range from 0% - 14%

Model 1 Model 2

Model 3 Model 4

0

0.2

0.4

0.6

0.8

1

1.2

0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

11%

12%

13%

14%

1Q

1Y

4Y

0

0.2

0.4

0.6

0.8

1

1.2

0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

11%

12%

13%

14%

1Q

1Y

4Y

0

0.2

0.4

0.6

0.8

1

1.2

0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

11%

12%

13%

14%

1Q

1Y

4Y

0

0.2

0.4

0.6

0.8

1

1.2

0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

11%

12%

13%

14%

1Q

1Y

4Y

Empirical ResultsExtreme Exchange Rate Changes

Absolute changes in Exchange Rate > 15% - 20%

Model 1 Model 2

Model 3 Model 4

-0.05

0

0.05

0.1

0.15

0.2

0.25

15% 16% 17% 18% 19% 20%

1Q

1Y

4Y

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

15% 16% 17% 18% 19% 20%

1Q

1Y

4Y

-0.05

0

0.05

0.1

0.15

0.2

0.25

15% 16% 17% 18% 19% 20%

1Q

1Y

4Y

-0.05

0

0.05

0.1

0.15

0.2

0.25

15% 16% 17% 18% 19% 20%

1Q

1Y

4Y

• There exists a long-run relationship between exchange rate and macroeconomic fundamentals; The conditional vector error correction equation of exchange rate provides relatively high R2; This suggests that the usual imposition of restrictions on the exchange rate equation, which are not suggested by theory, might have made it misspecified.

• Reasonable impulse responses of key variables with respect to oil price and domestic monetary policy shock; Results also show how sensitive exchange rate and the exchange rate equation are with respect to shocks.

• Promising in-sample forecasts (directional changes), which show the predictive power of macro fundamentals for exchange rate.

• Out-of-sample forecast provide a broad picture of exchange rate forecasting.

• More interesting single events of exchange rate and joint events between exchange rate and other variables (such as current account balances, inflation) will be considered in future research.

Concluding Remarks

• Engle C., Mark N. C. and Kenneth W. (2007) ‘Exchange Rate Models are not as bad as you think’, Working Paper, University of Wisconsin and NBER

• Groen, Jan J. J. (2000) ‘The Monetary Exchange Rate Model as a Long-run Phenomenon,’ Journal of International Economics, vol. 52, 299-319

• Groen, Jan J. J. (2005) ‘Exchange Rate Predictability and Monetary Fundamentals in a Small Multi-Country Panel,’ Journal of Money, Credit, and Banking, vol. 37, no. 3, pp. 495-516

• Lars E. O. Svensson (1994) ‘Fixed Exchange Rates as a Means to Price Stability: What we have learned?,’ European Economic Review, vol. 38, 447-468

• Mark, N. (1995) ‘Exchange Rates and Fundamentals: Evidence on Long-horizon Predictability,’ American Economic Review, vol. 85, 201-218

• Mark, Nelson C. and D. Sul (2001), ‘Nominal Exchange Rates and Monetary Fundamentals: Evidence from a Small Pots-Bretton Woods Panel,’ Journal of International Economics, vol. 53, pp. 29-52

• Meese, R. and Rogoff, K. (1983a) ‘Empirical Exchange Rate Models of the Seventies: Do They Fit Out of Sample?’ Journal of International Economics, vol.14, pp. 3-24

• Meese, R. and Rogoff, K. (1983b) ‘The Out-of-.Sample Failure of Empirical Exchange Rate Models: Sampling Error or Misspecification?’ in J.A. Frenkel (ed.) Exchange Rates and International Macroeconomics, Chicago: Chicago University Press and National Bureau of Economic Research

• Mervyn King (1997) ‘Change in UK Monetary Policy: Rules and Discretion in Practice,’ Journal of Monetary Economics, vol. 39, 81-97

Key References

• Paul Soderlind (2000) ‘Market Expectations in the UK before and after the ERM crisis’, Economica, 67, 1-18

• Pesaran, M. H. and Y. Shin (2002) ‘Long-run Structural Modelling,’ Econometric Review, vol. 21, pp. 49-87

• Pesaran, M. H., Y. Shin and R. J. Smith (2000) ‘Structural Analysis of Vector Error Correction Models with Exogenous I(1) Variables ,’ Journal of Econometrics, vol. 97, pp. 293-343

• Pesaran, M. H. and A. Timmermann (1992) ‘A Simple Nonparametric Test of Predictive Performance,’ Journal of Business & Economic Statistics, vol. 10, no. 4, pp. 461-465

• Rapach, D. and M. Wohar (2002) ‘Testing the Monetary Model of Exchange Rate Determination: New Evidence from a Century of Data,’ Journal of International Economics, vol. 58, pp. 359-385

• Shin, Y. (2007) ‘The Cointegrating VAR Model of the Korean Macro-economy,’ Working Paper, University of Leeds

• Smith, P. N. and M. R. Wikens (1986) ‘An Empirical Investigation into the Causes of Failures if the Monetary Model of the Exchange Rate,’ Journal of Applied Econometrics, vol. 1, no. 2, pp. 143-162

Key References

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