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 School The University of Leeds
Introduction • Monetary Models of Exchange Rate Determination • Motivations for Our Research • Econometric Framework • The Examined Models & Main Considerations • Data • Empirical Results • Conclusions
Monetary Models of Exchange Rate 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 Derivation 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:
= - - b - b + q - q * * * * * e m m ( y y ) ( r r ) t t t t t t t Monetary Models of Exchange Rate Derivation • 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
Monetary Models of Exchange Rate Derivation 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 Rate Derivation 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 Rate Mixed Results 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 Rate Mixed 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.
Motivations • 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?
Econometric Framework 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)
Examined Models 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)
Main Considerations 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.
Data Examined period: 1980Q1 – 2006Q4
Empirical Results Example: Restrictions on Cointegrating Vectors in Model 3
Empirical Results Vector Error Correction Model 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 = 0.31 Model 2: R2 = 0.63 Model 3: R2 = 0.61 Model 4: R2 = 0.40
Model 1 Model 2 Model 3 Model 4 Empirical Results Persistence Profiles of CVs Persistence Profiles of Cointegrating Vectors in Exactly-identified Case
Model 1 Model 2 Model 3 Model 4 Empirical Results Persistence Profiles of CVs Persistence Profiles of Cointegrating Vectors in Over-identified Case
Empirical Results Impulse Response Analysis Impulse Responses w.r.t Oil Price Shock – Model 3 (Benchmark) Impulse Responses w.r.t. Domestic Monetary Policy Shock – Model 3
Empirical Results In-sample Forecast Evaluation Forecast of Directional Changes: Estimate models from 1980Q3 - 2004Q4, leave 8 observations from 2005Q1 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 Results In-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 Results In-sample Forecast Evaluation Example: In-sample forecast of Model 3
Empirical Results In-sample Forecast Evaluation 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.
Model 1 Model 2 Model 3 Model 4 Empirical Results Out-of-sample Forecast Evaluation Central Forecasts (based on 4-quarter moving average series)
Model 1 Model 2 Model 3 Model 4 Empirical Results Out-of-sample Forecast Evaluation Central Forecasts of Changes (based on 4-quarter MA series)
Model 1 Model 2 Model 3 Model 4 Empirical Results Predictive Distribution Function Absolute changes in Exchange Rate range from 0% - 14%
Model 1 Model 2 Model 3 Model 4 Empirical Results Extreme Exchange Rate Changes Absolute changes in Exchange Rate > 15% - 20%
Concluding Remarks • 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.
Key References • 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