This paper proposes a transformed random effects model for analyzing non-normal panel data where both the response and (some of) the covariates are subject to transformations for inducing flexible functional form, normality, homoscedasticity, and simple model structure. We develop a maximum likelihood procedure for model estimation and inference, along with a computational device which makes the estimation procedure feasible in cases of large panels. We provide model specification tests that take into account the fact that parameter values for error components cannot be negative. We illustrate the model and methods with two applications: state production and wage distribution. The empirical results strongly favor the new model to the standard ones where either linear or log-linear functional form is employed. Monte Carlo simulation shows that maximum likelihood inference is quite robust against mild departure from normality. Copyright © 2009 John Wiley & Sons, Ltd.