Substantial Bias in the Tobit Estimator: Making a Case for Alternatives

Abstract

Censored outcome data are commonly encountered in criminology. Criminologists sometimes use the tobit model to address these censored data. While tobit models make more realistic demands of censored outcome data than ordinary least squares (OLS) regression, they require the researcher to make strong distributional assumptions. When these assumptions are not met, as is often the case in criminological data, tobit models yield biased and inconsistent estimates. We seek to demonstrate this substantial bias in simulation analyses and present easily applied alternative methods. The tobit model and semiparametric alternatives for censored outcome data are applied with simulated data under varying conditions. These simulations are followed with an empirical example using sentencing data. The bias from tobit can be corrected through application of semiparametric alternatives. Criminologists should begin their analyses of censored outcome data with the least restrictive of the available models (CLAD) before progressing to more efficient, but potentially biased, estimators.