Regression modelling under general heterogeneity

This paper introduces and analyses a setting with general heterogeneity in regression modelling. It shows that regression models with fixed or time-varying parameters can be estimated by OLS or time-varying OLS methods, respectively, for a very wide class of regressors and noises, not covered by existing modelling theory. The new setting allows the development of asymptotic theory and the estimation of standard errors. The proposed robust confidence interval estimators permit a high degree of heterogeneity in regressors and noise. The estimates of robust standard errors coincide with the well-known estimator of heteroskedasticity-consistent standard errors by White (1980), but are applicable to more general circumstances than just the presence of heteroscedastic noise. They are easy to compute and perform well in Monte Carlo simulations. Their robustness, generality and ease of use make them ideal for applied work. The paper includes a brief empirical illustration.