Emilio González Coya

We consider GLS and OLS estimation in a linear regression model with serially correlated errors, and we provide the following contributions. First, we clarify when OLS is consistent or not. Second, we give sufficient conditions such that GLS is valid without the assumption of exogenous regressors (uncorrelated with past innovations). Third, we devise a feasible GLS procedure valid whether or not the regressors are exogenous, and which achieves a MSE close to that of the correctly specified infeasible GLS. Fourth, we derive the asymptotic distribution of this feasible GLS estimate: with exogenous regressors, the limit distribution is the same as that of the infeasible GLS estimator. However, with non-exogenous regressors, an additional term is present in the asymptotic variance. We provide a variance estimator, free of tuning parameters, which delivers confidence intervals with asymptotically correct coverage in both cases. We also illustrate how GLS can be more robust than OLS when the regressors are exogenous, even when GLS is based on an incorrect correction. The main assumptions are: a) the regressors are pre-determined (uncorrelated with future innovations); b) the errors are stationary thereby admitting a Wold representation in terms of some unpredictable innovations; c) the moving-average representation of the errors is invertible and implies a short-memory process. We also briefly address issues related to heteroskedastic errors.

Purpose. This paper aims to re-examine the uncovered interest parity (UIP) hypothesis, which posits efficiency in forward foreign exchange and rational expectations. Testing these assumptions involves estimating parameters in a k-step-ahead forecasting model, where forecast errors are expected to be serially correlated up to lags k − 1. When errors are correlated beyond these lags, OLS is no longer consistent unless the regressors are exogenous.

Design/methodology/approach. The authors extend the FGLS procedure developed in Perron and González-Coya (2022) to a setting in which lagged dependent variables are included as regressors. The authors thus provide a consistent and efficient framework to estimate the parameters of a general k-step-ahead linear forecasting equation. Following the work of Perron and Olivari (2023), the authors introduce an instrumental variable (IV)-based approach for this problem that requires pre-determined but not necessarily exogenous IVs for consistency.

Findings. The authors apply the authors’ FGLS procedures to the analysis of the two main specifications to test the UIP. Contrary to most empirical results available in the literature, in particular those based on some OLS regression or GMM, the authors’ robust and efficient procedure cannot reject the null hypothesis that the UIP holds.

Originality/value. Overall, this study’s results can be viewed as overturning the so-called forward discount anomaly. The methods proposed can also be applied to a wide variety of contexts.

We study the Feasible Generalized Least-Squares (FGLS) estimation of the parameters of a linear regression model in the presence of heteroskedasticity of unknown form in the errors. We suggest a Lasso based procedure to estimate the skedastic function of the residuals. The advantage of using Lasso is that it can handle a large number of potential covariates, yet still yields a parsimonious specification. Using extensive simulation experiments, we show that our suggested procedure always provide some improvements in the precision of the parameter of interest (lower Mean-Squared Errors) when heteroskedasticity is present and is equivalent to OLS when there is none. It also performs better than previously suggested procedures. Since the fitted value of the skedastic function falls short of the true specification, we form confidence intervals using a bias-corrected version of the usual heteroskedasticity-robust covariance matrix estimator. These have the correct size and substantially shorter length than when using OLS. Our method is applicable to both cross-section (with a random sample) and time series models, though here we concentrate on the former.