A Note on the Performance of Simple Specification Tests for the Tobit Model
| Published date | 01 February 1999 |
| DOI | http://doi.org/10.1111/1468-0084.00120 |
| Date | 01 February 1999 |
| Author | Jorgen Hansen,Peter Ericson |
PRACTITIONERS CORNER
A Note on the Performance of Simple Speci®cation Tests for
the Tobit Model
Peter Ericson and Jo
Èrgen Hanseny
I. INTRODUCTION
To explain microeconomic behaviour, complex models have been devel-
oped. It is oftten dif®cult to transform these models to ®t a standard linear
regression framework, and maximum likelihodd (ML) estimation has
become a standard tool. The dif®culty with ML estimation is that the
distributional assumptions may be crucial, and several speci®cation tests
have been proposed to check them. However, to date it has not become a
standard practice to apply these tests, since most of them are burdensome
to implement, and little is known about their performance in small
samples.
The aim in this note is to investigate the small sample properties of a
selection of speci®cation tests for the Tobit model. Emphasis have been put
solely on tests which are computationally tractable. The size of these tests
are presented, as well as their ability to detect certain kinds of heteroscedas-
ticity and non-normality in the error term.
In the next section, the Tobit model is introduced together with the
speci®cation test statistics associated with it. The sampling experiments are
reported in section III, and this note ends with some concluding comments
in section IV.
II. TEST STATISTICS
The censored regression model in its simplest form for an individual i
(i1, ...,n) can be written as
yiâ9xiuiif ui.ÿâ9xi
0otherwise (1)
where âis a (k 31) vector of parameters. Assuming that uiNID(0, ó2),
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 61, 1 (1999)
0305-9049
121
#Blackwell Publishers Ltd, 1999. Published by Blackwell Publishers, 108 Cowley Road, Oxford
OX4 1JF,UK and 350 Main Street, Malden, MA 02148, USA.
yWe are grateful to Christian Belzil, Gordon Fisher, Lennart Flood, and Anders Klevmarken for
many helpful comments on earlier drafts of this paper.
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