More on testing the normality assumptionin the Tobit Model

Abstract

In a recent volume of this journal, Holden [Testing the normality assumption in the Tobit Model, J. Appl. Stat. 31 (2004) pp. 521–532] presents Monte Carlo evidence comparing several tests for departures from normality in the Tobit Model. This study adds to the work of Holden by considering another test, and several information criteria, for detecting departures from normality in the Tobit Model. The test given here is a modified likelihood ratio statistic based on a partially adaptive estimator of the Censored Regression Model using the approach of Caudill [A partially adaptive estimator for the Censored Regression Model based on a mixture of normal distributions, Working Paper, Department of Economics, Auburn University, 2007]. The information criteria examined include the Akaike’s Information Criterion (AIC), the Consistent AIC (CAIC), the Bayesian information criterion (BIC), and the Akaike’s BIC (ABIC). In terms of fewest ‘rejections’ of a true null, the best performance is exhibited by the CAIC and the BIC, although, like some of the statistics examined by Holden, there are computational difficulties with each.

Keywords:

• Censored Regression Model
• departures from normality

JEL Classification :

• C240

Acknowledgement

The authors thank two anonymous referees and Robert Aykroyd for helpful comments on earlier versions. Any remaining errors are our own.

Notes

We are grateful to an anonymous referee for pointing this out.

Although technically the information criteria are not part of a statistical test, we use the word, rejection, in quotes to make our discussion less cumbersome since the MLR is actually a statistical test.

Most of the samples in the literature using Tobit estimation contain more than 150 observations. Using an EBSCO host search for articles using Tobit analysis from the year 2006 to the present yielded 53 articles. With the smallest and largest samples omitted, the average sample size is over 2300 observations, the median is 456 observations, and the 25th percentile estimate is over 170 observations.