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Source: Douglas C. Montgomery and Elizabeth A. Peck, Introduction to Linear Regression Analysis, John Wiley & Sons, New York, 1982, p. 243 (notation changed).

Source: Douglas C. Montgomery and Elizabeth A. Peck, Introduction to Linear Regression Analysis, John Wiley & Sons, New York, 1982, p. 243 (notation changed).

15.17. To find out who has a bank account (checking, savings, etc.) and who doesn't, John Caskey and Andrew Peterson estimated a probit model for the years 1977 and 1989, using data on U.S. households. The results are given in Table 15.23. The values of the slope coefficients given in the table measure the implied effect of a unit change in a regressor on the probability that a household has a bank account, these marginal effects being calculated at the mean values of the regressors included in the model.

a. For 1977, what is the effect of marital status on ownership of a bank account? And for 1989? Do these results make economic sense?

b. Why is the coefficient for the minority variable negative for both 1977 and 1989?

c. How can you rationalize the negative sign for the number of children variable?

d. What does the chi-square statistic given in the table suggest? (Hint: exercise 15.13.)

15.18. Monte Carlo study: As an aid to understanding the probit model, William Becker and Donald Waldman assumed the following*:

Then, letting Yi = —1 + 3X + Si, where Si is assumed standard normal (i.e., zero mean and unit variance), they generated a sample of 35 observations as shown in Table 15.24.

a. From the data on Y and X given in this table, can you estimate an LPM? Remember that the true E(Y | X) =-1 + 3X.

b. Given X = 0.48, estimate E(Y | X = 0.48) and compare it with the true E(Y| X = 0.48). Note X = 0.48.

William E. Becker and Donald M. Waldman, "A Graphical Interpretation of Probit Coefficients," Journal of Economic Education, vol. 20, no. 4, Fall 1989, pp. 371-378.

632 PART THREE: TOPICS IN ECONOMETRICS

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