## Ydz

= 0 if the final grade is B or C TUCE = score on an examination given at the beginning of the term to test entering knowledge of macroeconomics PSI = 1 if the new teaching method is used

= 0 otherwise GPA = the entering grade point average Source: L. Spector and M. Mazzeo, "Probit Analysis and Economic Education," Journal of Economic Education, vol. 11, 1980, pp. 37-44.

= 0 if the final grade is B or C TUCE = score on an examination given at the beginning of the term to test entering knowledge of macroeconomics PSI = 1 if the new teaching method is used

= 0 otherwise GPA = the entering grade point average Source: L. Spector and M. Mazzeo, "Probit Analysis and Economic Education," Journal of Economic Education, vol. 11, 1980, pp. 37-44.

CHAPTER FIFTEEN: QUALITATIVE RESPONSE REGRESSION MODELS 605

grade predictors. The logit model here can be written as:

Li = ^ p) = fa1 + fa2GPAi + faTUCEi + faPSIi + ui (15.8.1)

As we noted in Section 15.6, we cannot simply put P, = 1 if a family owns a house, and zero if it does not own a house. Here neither OLS nor weighted least squares (WLS) is helpful. We have to resort to nonlinear estimating procedures using the method of maximum likelihood. The details of this method are given in Appendix 15A, Section 15A.1. Since most modern statistical packages have routines to estimate logit models on the basis of un-grouped data, we will present the results of model (15.8.1) using the data given in Table 15.7 and show how to interpret the results. The results are given in Table 15.8 in tabular form and are obtained by using Eviews 4. Before interpreting these results, some general observations are in order.

1. Since we are using the method of maximum likelihood, which is generally a large-sample method, the estimated standard errors are asymptotic.

2. As a result, instead of using the t statistic to evaluate the statistical significance of a coefficient, we use the (standard normal) Z statistic. So inferences are based on the normal table. Recall that if the sample size is reasonably large, the t distribution converges to the normal distribution.

3. As noted earlier, the conventional measure of goodness of fit, R2, is not particularly meaningful in binary regressand models. Measures similar to R2, called pseudo R2, are available, and there are a variety of them.26 Eviews presents one such measure, the McFadden R2, denoted by RMcF, whose

TABLE 15.8 REGRESSION RESULTS OF (15.8.1)

Dependent Variable: Grade Method: ML-Binary Logit

Convergence achieved after 5 iterations

TABLE 15.8 REGRESSION RESULTS OF (15.8.1)

Dependent Variable: Grade Method: ML-Binary Logit

Convergence achieved after 5 iterations

Variable

Coefficient

Std

. error Z

statistic

Probability