Alex Maynard

The Forward Premium Anomaly: Statistical Artefact or Economic Puzzle? New Evidence from Robust Tests

Recent literature has questioned statistical inference in predictive regressi on with persistent regressors, suggesting a possible explanation for puzzles suc h as the forward premium anomaly. We therefore revisit this puzzle using three a lternative econometric methods known to provide reliable inference in the presen ce of persistent conditioning variables. While they provide less evidence agains t forward rate unbiasedness than traditional predictive regression tests, we sti ll reject using at least one method for all six currencies. Thus, while the econ ometric problems inherent in predictive regression likely play a role in this an omaly, we are left with an economic puzzle even after accounting for their influence.

Testing for Forward-Rate Unbiasedness: On Regression in Levels and in Returns

Several recent empirical studies have been forced to reject exact 1:1 cointegration between spot and forward exchange rates. Theoretically, this is shown to provide a possible explanation for the puzzling negative estimates reported from spot-return-forward-premium regressions. In particular, the coefficient in this regression has a unit root component in its limit distribution that imparts a bias and skewness to the estimator. Simulations are used to demonstrate how even very small deviations from 1:1 cointegration can result in substantial bias. The empirical evidence suggests that the implied Dickey-Fuller-type terms do exhibit a downward bias, yet are of insufficient magnitude to fully account for the puzzling regression coefficients mentioned above.

COVARIANCE-BASED ORTHOGONALITY TESTS FOR REGRESSORS WITH UNKNOWN PERSISTENCE

This paper develops a new test of orthogonality based on a zero restriction on the covariance between the dependent variable and the predictor. The test provides a useful alternative to regression-based tests when conditioning variables have roots close or equal to unity. In this case standard predictive regression tests can suffer from well-documented size distortion. Moreover, under the alternative hypothesis, they force the dependent variable to share the same order of integration as the predictor, whereas in practice the dependent variable often appears stationary and the predictor may be near-nonstationary. By contrast, the new test does not enforce the same orders of integration and is therefore capable of detecting a rich set of alternatives to orthogonality that are excluded by the standard predictive regression model. Moreover, the test statistic has a standard normal limit distribution for both unit root and local-to-unity conditioning variables, without prior knowledge of the local-to-unity parameter. If the conditioning variable is stationary, the test remains conservative and consistent. Simulations suggest good small-sample performance. As an empirical application, we test for the predictability of stock returns using two persistent predictors, the dividend-price ratio and short-term interest rate.

Sensitivity of Impulse Responses to Small Low-Frequency Comovements: Reconciling the Evidence on the Effects of Technology Shocks

This article clarifies the empirical source of the debate on the effect of technology shocks on hours worked. We find that the contrasting conclusions from levels and differenced vector autoregression specifications, documented in the literature, can be explained by a small low-frequency comovement between hours worked and productivity growth that gives rise to a discontinuity in the solution for the structural coefficients identified by long-run restrictions. Whereas the low-frequency comovement is allowed for in the levels specification, it is implicitly set to 0 in the differenced vector autoregression. Consequently, even when the root of hours is very close to 1 and the low-frequency comovement is quite small, removing it can give rise to biases of sufficient size to account for the empirical difference between the two specifications.

Empirical analysis of corn and soybean basis in Canada

The article examines the factors affecting the basis for corn and soybeans using several time-series techniques to account for potential structural breaks, seasonality, residual serial correlation and structural breaks, as well as potential endogeneity and nonstationarity. The spatio-temporal empirical framework is based on storage and trade theories which assume the relationship between nondelivery location’s spot price and futures price of a storable commodity depends on opportunity cost of capital, warehousing costs, a convenience yield and shipping costs. The interest rate effect is strong for both crops with shipping costs also affecting soybean basis and own inventory levels positively correlated with corn basis. The effect of the wedge between the price of carrying physical grain and the maximum storage rate on basis is positive for both crops. The empirical results, which are robust to multiple estimators, provide stronger evidence of a structural break for the soybean basis than for the corn basis.

Localized level crossing random walk test robust to the presence of structural breaks

A modified version of the nonparametric level crossing random walk test is proposed, in which the crossing level is determined locally. This modification results in a test that is robust to unknown multiple structural breaks in the level and slope of the trend function under both the null and alternative hypotheses. No knowledge regarding the number or timing of the breaks is required. An algorithm is proposed to select the degree of localization in order to maximize bootstrapped power in a proximate model. A computational procedure is then developed to adjust the critical values for the effect of this selection procedure by replicating it under the null hypothesis. The test is applied to Canadian nominal inflation and nominal interest rate series with implications for the Fisher hypothesis.

ECONOMETRIC THEORY, by James Davidson, Blackwell Publishers, 2000

Professor Davidsons Econometric Theory offers a clear, well written, graduate level econometrics textbook, which would be highly appropriate as the principal text for the second and/or third semester of a general Ph.D. econometrics sequence or for a specialized course on time series. It provides good reading material for anyone interested in deepening his or her understanding of econometrics and also a valuable reference source for econometricians. Although the book reviews the basics of multivariate regression, it is written at a level that requires either some degree of mathematical sophistication or prior familiarity with econometrics. As a result, it may be too advanced for a first semester Ph.D. course, except where students have strong preparation.