Regressions with asymptotically collinear regressors



Summary  We investigate the asymptotic behaviour of the OLS estimator for regressions with two slowly varying regressors. It is shown that the possibilities include a definite case, when the third-order regular variation is sufficient to determine the asymptotic distribution, and an indefinite case, when higher-order regular variation is required to find the distribution. In the definite case the asymptotic distribution is normal one-dimensional and may belong to one of six types depending on the relative rates of growth of the regressors. The dependence of the asymptotic variance on the parameters of the model is discontinuous. The analysis establishes, in particular, a new link between slow variation and inline image-approximability.