Bias corrected z-tests for regression models

In regression settings the e ect of a covariate, accounting for all the others, on the dependent variable is typically tested by using a z-statistic. Under regularity conditions on the model and assuming the null hypothesis holds, the associated Wald pivot is asymptotically normally distributed. However, its  nite- sample distribution can be far from Gaussian when the sample size is small or moderate relative to the dimension of the global parameter. In this work, asymptotic bias correction of the Wald z-statistic is proposed as a means to improve the accuracy of  rst-order inference for the regression coe cients.