Efficient Estimation Of Cointegrating Vectors and Testing for Causality in Vector Autoregressions

This paper surveys various methods of estimating cointegrating vectors and testing for causality in cointegrated VARs, and draws some implications for the applied researcher. In a single equation framework a number of estimators can be used, whose asymptotic efficiency depends on the extent to which they correct for possible endogeneity and serial correlation of the regressors. Such estimates are asymptotically equivalent to those obtained using full system methods, even if the cointegration space is multidimensional, provided there are no cross-equation restrictions. Using the triangular representation proposed by Phillips (1988), we show that one can employ in the context of an ECM a least squares estimator if weak exogeneity holds. If not, the alternatives are augmenting it by the leads of the regressors as in Stock and Watson (1993), or using the fully modified (FM) estimator due to Phillips and Hansen (1990). Other possibilities are the nonparametric approach developed by Bierens (1997), or the ARDL formulation due to Pesaran and Shin (1995). As for causality testing, we argue that it should be conducted within an ECM rather than a VAR formulation, as the limit distributions are much more likely to be standard in the former case. Alternatively, one can carry out statistical tests in the context of a VAR in levels estimated either by using the FM-VAR method as in Phillips (1995), or by augmenting the VAR as in Toda and Yamamoto (1995). Other, computationally easier tests have been introduced by Dolado and Lutkepohl (1996) and Saikkonen and Lütkepohl (1996).     

Parameter instability, superexogeneity, and the monetary model of the exchange rate

Parameter Instability, Superexogeneity and the Monetary Model of the Exchange Rate. — This paper argues that failure to test for parameter time invariance yields misleading results. Time heterogeneity other than unit roots will make the parameters of the unrestricted system unstable and statistical inference invalid. However, if the instability stems from a particular subset of variables (superexogenous with respect to the parameters of interest), conditioning on them results in a partial model with stable parameters, and standard inferential procedures can then be used. We apply this methodology to test the monetary model of the exchange rate and find that both system and single-equation estimates support it in the case of yen-dollar exchange rate.     

On Modelling Speculative Prices: The Empirical Literature

Traditionally, financial theory and in particular asset pricing models have assumed (implicitly or explicitly) a certain probabilistic structure for speculative prices. The probabilistic structure is usually defined in terms of specific statistical models and relates to the dependence, heterogeneity and the distribution of such prices. The primary objective of this paper is to trace the development of various statistical models proposed since Bachelier (1900), in an attempt to assess how well these models capture the empirical regularities exhibited by data on speculative prices.     

Decomposing the persistence of real exchange rates

We propose a new methodology for decomposing the persistence of deviations from purchasing power parity (PPP). By directly comparing the impulse response function (IRF) of a vector autoregressive (VAR) model, where the real exchange rate is Granger caused by a set of candidate variables, with the IRF of the equivalent ARMA model for the real exchange rate, we capture the effects of the Granger-causing variables on the half-life of deviations from PPP. Our empirical results for a set of 20 industrial countries suggest that on average around 50% of the persistence of real exchange rates can be attributed to nominal interest rate differentials, inflation differentials and relative business cycle position with the numenaire country. Finally, we provide confidence intervals for the contributions of the aforementioned variables to the persistence of deviations from PPP by means of Monte Carlo simulations.     

Long‐Run PPP under the Presence of Near‐to‐Unit Roots: The Case of the British Pound–US Dollar Rate*

Empirical tests typically provide evidence that the British pound–US dollar exchange rate and the relative wholesale price index contain exact unit roots and exhibit cointegration. However, the cointegrating vector is significantly different from [1, ?1], thus raising doubts on the validity of the purchasing power parity (PPP) hypothesis. Following Elliott (1998 ), we show that if the exchange rate and relative price series contain near‐to‐unit roots in the context of a bivariate system, then any inference on the “cointegrating” vector and consequently on PPP, which is based on standard cointegration estimation methods, will be misleading. We then argue that the existing evidence against the PPP hypothesis in the British pound–US dollar market can be attributed to the finite sample bias of the standard cointegration estimators, arising from an endogenous and “nearly” nonstationary regressor. We also show that when robust procedures are employed the evidence favors the PPP hypothesis.     

The dynamics between stock returns and mutual fund flows: empirical evidence from the Greek market

This paper examines the interaction between mutual fund flows and stock returns in Greece. Specifically, we investigate the possibility of a causality mechanism through which mutual funds flows may affect stock returns and vice versa. The statistical evidence derived from the error correction model indicates that there is a bidirectional causality between mutual fund flows and stock returns. Cointegration results show that mutual funds flows cause stock returns to rise or fall. This may be explained by the fact that, in Greece, equity mutual funds are obliged by law to invest a certain percentage of their cash in stocks. Thus, inflows and outflows of cash in equity funds seem to cause higher and lower stock returns in Greek stock market.     

Unit Root Testing Using Covariates: Some Theory and Evidence

This paper analyzes the conditions under which power gains can be achieved using the Covariate Augmented Dickey-Fuller test (CADF) rather than the conventional Augmented Dickey-Fuller (ADF), and argues that this method has the advantage, relative to univariate unit root tests, of increasing power without suffering from the large size distortions affecting the latter. The inclusion of covariates affects unit root testing by: (a) reducing the standard error of the estimate of the autoregressive parameter without affecting the estimate itself, and/or (b) reducing both the standard error and the absolute value of the estimate itself. Conditions in terms of contemporaneous correlation and Granger causality are derived for case (a) or (b) to arise. As an illustration, it is shown that applying the more powerful CADF (rather than the ADF) test reverses the finding of a unit root for many US macroeconomic series.