Variance Estimates in Models with the Box-Cox Transformation: Implications for Estimations and Hypothesis Testing

The variance-covariance matrix of the parameter estimates in a model containing the Box-Cox transformation is analytically examined. Breaking the variance-covariance matrix into components helps in understanding (1) why some estimation algorithms are more efficient than others, (2) why both iterated OLS estimation and first derivative-only gradient estimation methods obtain biased estimates of the variances of the coefficients (with OLS underestimating the variances, and first derivative methods overestimating them), and (3) how the lack of scale invariance in the t-ratios for the linear coefficients makes hypothesis testing very misleading.