How to improve the substantive interpretation of regression results when the dependent variable is logged

Abstract

Regression models with log-transformed dependent variables are widely used by social scientists to investigate nonlinear relationships between variables. Unfortunately, this transformation complicates the substantive interpretation of estimation results and often leads to incomplete and sometimes even misleading interpretations. We focus on one valuable but underused method, the presentation of quantities of interest such as expected values or first differences on the original scale of the dependent variable. The procedure to derive these quantities differs in seemingly minor but critical aspects from the well-known procedure based on standard linear models. To improve empirical practice, we explain the underlying problem and develop guidelines that help researchers to derive meaningful interpretations from regression results of models with log-transformed dependent variables.