Systematically Misclassified Binary Dependant Variables

SYSTEMATICALLY MISCLASSIFIED BINARY DEPENDANT VARIABLES
approximately equal to our desired values for α0
and α
1
(0.02, 0.05, 0.1 or 0.2), by
numerically integrating (16) and (17) using Gauss-Legendre quadrature. We also ran two
more sets of Monte Carlo runs with asymmetric misclassification for ( α0, α
1)
=(0.02, 0.2)
and (0.2, 0.02). These results are shown in Tables 1-3. Finally, we ran three sets of Monte
Carlo runs with symmetric but constant misclassification probabilities, reported in tables
4-6. The observed dependant variable,
according to equation (12).
o
y , was generated by adding misclassification
For each set of parameters, we generated a random sample, and used that sample
to estimate the model parameters using, (i) the standard probit model (Probit); (ii) HAS1;
and (iii) GHAS. The results are based on 200 Monte Carlo runs, each with a random
sample of 5000 observations, for each of the sets of parameter values described in the
preceding paragraph. The standard errors reported are the standard deviations of each
set of 200 estimates.
Our findings, though based on a different data generating process, are broadly in
line with the findings of Hausman et al., (section 4): (i) Even in the case of a small amount
of misclassification, ordinary probit produces estimates that are biased by 15-25%; (ii) The
problem worsens as the amount of misclassification grows; (iii) Not only does probit yield
inconsistent estimates, but it can also overstate the precision of the estimates. Our results
show that the three observations are valid, not only for the case with random
misclassification, but also for the more general case with covariate-dependant
misclassification. The problems with the ordinary probit model in the presence of a
15