Marta Regúlez

Testing the Canonical Model of Exchange Rates with Unobservable Fundamentals

In this paper, the authors test the asset market approach or canonical model of exchange rates. They treat exchange rate fundamentals as unobservable. The empirical results do not reject the canonical model and, therefore, the embedded rational expectations assumption, in sharp contrast with previous empirical evidence. The authors also find evidence of feedback from the exchange rate to fundamentals, which is normally omitted in the theoretical literature. Copyright 1997 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

A factor model of seasonality in stock returns

Published as an article in: The Quarterly Review of Economics and Finance, 2004, vol. 44, issue 2, pages 224-236.

The Monetary Model of Exchange Rates and Cointegration

1. Introduction.- 2. The Monetary Model of Exchange Rate Determination.- I. Introduction.- II. Monetary Models.- III. The Asset Market View.- IV. Empirical Evidence.- V. Treatment of Nonstationary Variables.- 3. Long Run Exchange Rate Determination I.- I. Introduction.- II. Some Preliminary Definitions and Engle and Granger Procedure.- III. Interpretation of Previous Results in terms of Cointegration.- IV. Testing for Cointegration Using Engle and Granger Methodology.- V. Empirical Results.- VI. Conclusions.- Appendix A.- 4. Long Run Exchange Rate Determination II.- I. Introduction.- II. Description of The Time Series Model.- III. The Data And Diagnostic Tests.- III.1. Data Description.- III.2. Diagnostic Tests on the Assumptions of the VAR.- IV. Estimation And Testing For Cointegration.- V. Tests of Several Hypotheses.- V.1. Testing for Known Cointegrating Vectors.- V.1.1 Testing for Trivial Cointegrating Vectors.- V.1.2. Testing for Cointegration between Fundamentals.- V.2. Tests of the same Linear Restrictions on all Cointegrating Vectors.- V.2.1. Testing the Exclusion of a Variable from all Cointegrating Vectors.- V.2.2 Testing for the Restrictions of a Monetary Equation.- VI. Conclusions.- Appendix A.- Appendix B.- 5. Short Run Exchange Rate Determination.- I. Introduction.- II. Weak Exogeneity of the Exchange Rate.- III. Testing for Weak Exogeneity.- IV. The Asset Market View Derived from an Error Correction Model.- V. Conclusions.- Appendix A.- 6. Effect of Non-Normal Disturbances on Likelihood Ratio Tests.- I. Introduction.- II. The Data Generating Process.- III. Hypotheses Tests.- III.1. Tests on the Number of Cointegrating Vectors.- III.2. Tests of Linear Restrictions on the Cointegrating Vector.- III.3. Tests of Restrictions on the Loadings Matrix.- IV. The Simulation Exercise.- IV.1. Empirical Size of the Tests.- IV.2. Power of the Tests.- V. Conclusions.- Appendix A: Size of the Tests.- Appendix B: Power of the Tests.- 7. Estimation of the Time Series Model.- I. Introduction.- II. Two Different Interpretations of the Time Series Model.- III. Estimation of the Model.- III.1. Unrestricted Model.- III.2. Restricted Short Run Dynamics.- III.3. Restricted Long Run Dynamics.- III.4. Restricted Short and Long Run Dynamics.- III.4.1. Gaussian Reduced Rank Maximum Likelihood Estimator.- III.4.2. Two Step Procedure.- 8. Prediction in Cointegrated Systems.- I. Introduction.- II. Properties of the True Forecasts from a Cointegrated System.- III. Estimated Forecasts from a Cointegrated System.- 9. Nominal Exchange Rate Prediction.- I. Introduction.- II. Review of Literature.- III. Forecasting Exercise.- IV. Conclusions.- Appendix A.- 10. A Simulation Exercise.- I. Introduction.- II. The Data Generating Process.- III. Results.- Appendix A.- 11. Conclusions.- Data Appendix.

A note on cointegration and control

Abstract We show that, in the control context analyzed by Granger (1988), the control variable is cointegrated with the dependent variable, as opposed to Grangers result. Moreover, we develop the error correction model relating them.

Long Run Exchange Rate Determination II

The work of Baillie and Selover (1987), Boothe and Glassman (1987) and the previous chapter takes into account the nonstationarity of some of the variables involved in the monetary models. In this context, the equations of exchange rate determination derived from the monetary models are thought of as long-run relationships. From this point of view, deviations of the exchange rate from a linear combination of its fundamentals are stationary, or in other words, they are cointegrated. The methodology used in those studies is that developed by Engle and Granger (1987). The results obtained in all three studies reject the specification of the monetary approach.

Effect of Non-Normal Disturbances on Likelihood Ratio Tests

Since Granger (1981) first introduced the concept of cointegration the field has experienced a great development. There are by now several methods of estimating cointegrating vectors: Ordinary Least Squares (Engle and Granger (1987)), Non-linear Least Squares (Stock (1987)), Principal Components (Stock and Watson (1988)), Canonical Correlations (Bossaerts (1988)) and full information maximum likelihood in a Gaussian system (Johansen (1988b, 1991a)). All these methods of estimation are fairly simple to implement and this is probably why empirical applications grow in number very quickly. Inference, on the other hand, is more difficult to carry out. All known hypotheses tests on the number of cointegrating vectors have non standard asymptotic distributions. In addition, only the ML procedure1 allows the user to carry out inference on the cointegrating vectors and loading matrix based on standard χ2 tests.

Nominal Exchange Rate Prediction

Nominal exchange rate prediction interests many. Economists can use exchange rate prediction exercises as a way of validating structural models of exchange rate determination. Businessmen are interested in forecasting rates to the extent that this will allow them to better hedge against foreign exchange risk. Finally, governments will conduct their domestic economic policy guided by a better knowledge if they have accurate rate forecasts at their disposal.

The Monetary Model of Exchange Rate Determination

Monetary models of exchange rate determination were developed after the collapse of the fixed exchange rate system in the early 70’s. They are descendants of the Mundell-Fleming type of models. Several versions have been put forward giving rise to three main types of models. These are the flexible price monetary model due to Frenkel (1976) and Bilson (1978), the sticky price / real interest rate differential of Dornbusch (1976) and Frankel (1979) and the sticky price-asset monetary model of Hooper and Morton (1982). The modeling strategy is similar in all cases. Ad hoc aggregate macroeconomic relationships are used to obtain a semi-reduced form equation that specifies the level of the exchange rate as a linear function of fundamentals1.

Short Run Exchange Rate Determination

In this chapter we study the short run dynamics of the exchange rate. In particular, we are interested in how the exchange rate reacts to transitory deviations from the long run equilibrium. By inspecting the ECM we can see that the loadings matrix a plays an extremely important role in this matter.

Estimation of The Time Series Model

In this chapter we describe several methods of estimation under different restrictions on the parameters of the model. Johansen’s estimation procedure is just one of the methods analyzed, corresponding to the case when only the long run parameters α and β are restricted. In addition, we also study other types of restrictions, namely, zero restrictions on the short run parameters of the ECM.