Granger revisited: t values and the empirical OLS bias with stationary and non-stationary time series using Monte Carlo simulations

Abstract

Granger revisitado: valores t y el sesgo empírico de OLS con series temporales estacionarias y no estacionarias utilizando simulaciones de Monte Carlo

The conduction of a reliable statistical analysis is based on the recognition of the statistical features of the time series at stake and on the underlying probabilistic assumptions of the applied model. Our purpose is to illustrate this kind of analysis using Granger’s groundbreaking ideas. Our Monte Carlo results show that in the presence of stationary and non-stationary time series, the standard ordinary least squares inference could be misleading. We will graphically address the empirical distribution of the estimator’s bias as well as the inconvenience of using standard errors to illustrate how the true variation is underestimated. We recommend following Granger’s suggestions, which we highlight with originality using a “measurement in economics” perspective. Our quantitative exercises are replicable to the extent that we fully shared our codes in addition to using an open-access database of the seminal paper written by Nelson and Plosser (1982). Our main conclusion is simple: empirical researchers should be cautious when drawing qualitative findings based on a standard ordinary least squares inference carried out in the context of a regression analysis.