Simultaneous Inference of Partially Linear Error-in-Covariate Models: an Application to the U.S. Gasoline Demand∗

In this paper, we conduct simultaneous inference of the non-parametric multivariate function of a partially linear model when the covariate terms in both parametric and non-parametric parts are subject to the Berkson measurement errors. Based on semiparametric estimates of the model, we construct a simultaneous confidence region of the multivariate function for simultaneous inference. The developed methodology is applied to perform inference for the U.S. gasoline demand where the income and price variables are measured with errors. The empirical results strongly suggest that the linearity of the U.S. gasoline demand is rejected.