Standard errors for the retransformation problem with heteroscedasticity.

Economists often estimate models with a log-transformed dependent variable. The results from the log-transformed model are often retransformed back to the unlogged scale. Other studies have shown how to obtain consistent estimates on the original scale but have not provided variance equations for those estimates. In this paper, we derive the variance for three estimates--the conditional mean of y, the slope of y, and the average slope of y--on the retransformed scale. We then illustrate our proposed procedures with skewed health expenditure data from a sample of Medicaid eligible patients with severe mental illness.