Re-examining the impact of oil prices on stock returns in the presence of time-varying volatility

Through Monte Carlo simulations, we explore the size, power and probability of making a type II error for a linear model with an exogenous regressor and ARCH or GARCH volatility. We estimate and compare the results for OLS with OLS standard errors, OLS with White's standard errors, and maximum-likelihood estimation (MLE). We find that for small samples, all estimation methods have higher frequencies of type II errors and lower power than the nominal test size suggests. In addition, we find that White's standard errors are an improvement over OLS, but the improvement is much smaller than one might expect, especially when compared to MLE. Increasing the sample size decreases the frequency of type II errors for all methods, but the rate of convergence to the nominal test size is much faster for MLE than the other two methods. Using empirical data from Jan 1986 to November 2021, we show that researchers are more likely to find a statistically significant impact of changes in oil prices on U.S. stock returns if they account for time-varying volatility. Our results have important practical implications and will help in resolving previous inconsistencies in the literature.