Ž . Journal of Health Economics 19 2000 697–718 www.elsevier.nlrlocatereconbase Standard errors for the retransformation problem with heteroscedasticity Chunrong Ai a , Edward C. Norton b, ) a UniÕersity of Florida, Florida, USA b Department of Health Policy and Administration, CBa 7400, McGaÕran-Greenberg Building, UniÕersity of North Carolina at Chapel Hill, Chapel Hill, NC, 27599-7400, USA Received 1 September 1999; received in revised form 1 March 2000; accepted 8 March 2000 Abstract 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. q 2000 Elsevier Science B.V. All rights reserved. JEL classification: C20; I19 Keywords: Retransformation; Heteroscedasticity; Logged dependent variable 1. Introduction Economists often estimate models with a log-transformed dependent variable. Justifications for using the log transformation include to deal with a dependent variable badly skewed to the right, and to interpret a covariate as either an Ž . elasticity or having a multiplicative response Manning, 1998 . The results from ) Corresponding author. Tel.: q 1-919-966-8930; fax: q 1-919-966-6961. Ž . E-mail address: edward norton@unc.edu E.C. Norton . – 0167-6296r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. Ž . PII: S0167-6296 00 00046-1