Notes:

Year Election year

V Democratic share of the two-party presidential vote

I Indicator variable (1 if there is a Democratic incumbent at the time of the election and -1 if there is a Republican incumbent) D Indicator variable (1 if a Democratic incumbent is running for election, -1 if a Republican incumbent is running for election, and 0 otherwise) W Indicator variable (1 for the elections of 1920, 1944, and 1948, and 0 otherwise) G Growth rate of real per capita GDP in the first three quarters of the election year P Absolute value of the growth rate of the GDP deflator in the first 15 quarters of the administration N Number of quarters in the first 15 quarters of the administration in which the growth rate of real per capita GDP is greater than 3.2%

c. Chatterjee et al. suggested considering the following model as a trial model to predict presidential elections:

Estimate this model and comment on the results in relation to the results of the model you have chosen.

9.25. Refer to regression (9.6.4). Test the hypothesis that the rate of increase of average hourly earnings with respect to education differs by gender and race. (Hint: Use multiplicative dummies.)

9.26. Refer to the regression (9.3.1). How would you modify the model to find out if there is any interaction between the gender and the region of residence dummies? Present the results based on this model and compare them with those given in (9.3.1).

9.27. In the model Yi = 01 + 02 Di + u, let Di = 0 for the first 40 observations and Di = 1 for the remaining 60 observations. You are told that ui has zero

CHAPTER NINE: DUMMY VARIABLE REGRESSION MODELS 333

mean and a variance of 100. What are the mean values and variances of the two sets of observations?* 9.28. Refer to the U.S. savings-income regression discussed in the chapter. As an alternative to (9.5.1), consider the following model:

ln Yt = 01 + 02Dt + 03Xt + 04(DtXt) + ut where Y is savings and X is income.

a. Estimate the preceding model and compare the results with those given in (9.5.4). Which is a better model?

b. How would you interpret the dummy coefficient in this model?

c. As we will see in the chapter on heteroscedasticity, very often a log transformation of the dependent variable reduces heteroscedasticity in the data. See if this is the case in the present example by running the regression of log of Y on X for the two periods and see if the estimated error variances in the two periods are statistically the same. If they are, the Chow test can be used to pool the data in the manner indicated in the chapter.

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