help bctobit


bctobit -- Test of the tobit specification


bctobit [, Fixed Nodots bfile(string) reps(integer 499)]


bctobit computes the LM-statistic for testing the tobit specification, against the alternative of a model that is non-linear in the regressors and contains an error term that can be heteroskedastic and non-normally distributed. The test is carried out by taking a Box-Cox transformation of the dependent variable [y^(lambda)-1]/lambda and testing whether the parameter lambda=1. A rejection of the null suggests that the Tobit specification is unsuitable, as an alternative value for lambda would be required to return the linearity, homoskedasticity and normality assumptions that are necessary for consistent estimation. Critical values are obtained via the parametric bootstrap, where the regressors are assumed to be stochastic.


Fixed specifies that the regressors are fixed in the bootstrap null distribution.

Nodots suppresses the bootstrap replication dots.

bfile(string) specifies the name of the saved file which contains the LM-statistics computed from the bootstrap samples.

reps(#) specifies the number of samples to be drawn from the bootstrap DGP in estimating the bootstrap critical values.


bctobit can only be used after tobit estimation and for data that is left-censored at zero. Bootstrap critical values are displayed for 1%, 5% and 10% level tests. Asymptotic critical values are not displayed, as using these can result in large size distortions for small to moderate samples.


. use smoking

. tobit cigarettes income age, ll(0)

Tobit regression Number of obs = 100 LR chi2(2) = 384.59 Prob > chi2 = 0.0000 Log likelihood = -239.60931 Pseudo R2 = 0.4452

------------------------------------------------------------------------------ cigarettes | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- income | .2971682 .0045094 65.90 0.000 .2882194 .306117 age | 1.030025 .0623708 16.51 0.000 .9062523 1.153798 _cons | -130.1278 3.480886 -37.38 0.000 -137.0355 -123.2201 -------------+---------------------------------------------------------------- /sigma | 4.612162 .3614768 3.894823 5.3295 ------------------------------------------------------------------------------ Obs. summary: 20 left-censored observations at cigarettes<=0 80 uncensored observations 0 right-censored observations

. bctobit, nodots

LM test of Tobit specification Bootstrap critical values lm %10 %5 %1 .036358 3.29870 4.6837926 9.4022799


David W. Vincent, Hewlett Packard, UK


Box, G. E. P. and D. R. Cox (1964) “An Analysis of Transformations”, Journal of the Royal Statistical Society, 26, 211-243.

Drukker, D. M. (2002) “Bootstrapping a conditional moments test for normality after tobit estimation”, The Stata Journal, 2, 125-139}.

Moffatt, P. G. (2003) “Hurdle models of loan default”, School of Economic and Social Studies, University of East Anglia, Norwich, UK