Question

Data from 200 Dependent Variable AHE In(AHE) In(AHE) In(AHE) In(AHE) In(AHE) In(AHE) In(AHE) 0.147* 0.146 0.1900.1170.160 0.042 0.042 (0.056 0056 (0.064) 0.439 0.024 0.030 (0.002) 0.00210.0021-0.00270.0017 -0.0023 0.0007 (0.0007) (0.0009) 0.0009) (0.0011) 0.725 (0.052) In(Age) -0.123 (0.084) Female x Age 0.097 (0.084) 0.0019 (0.0014) 0.0015 Female x Age (0.0014) 0.064 0.091 Bachelor x Age 0.083)(0.084) Bachelor xAge -0.0009 -0.0013 0.0014 (0.0014) Female .158-0.180*0.180** -0.180-0.210 3580.2101.764 (0.0100.010 (0.010) (0014) 230 (0.014) (1.239) (0.176) Bachelor 6.865 0.405 0405 0.405* 0.3780.378-0.769 1.186 (0.185 (0.010)(0010 (0.010) (0.014) (0.014) 228) 239) Female × Bachelor 0.064 0.063 0066 0.066 0.02 002 (0.021) (0.021) 0.078 8 0.633 (0.177 (0.613 0.612 (0819) 0819) (0.945) 0.059 1.884 856 0.897) (0.053) 0.128 633 0.604 -0.095 Intercept F-statistic and p-values on joint hypotheses 53.04 36.72 (a) F-statistic on terms involving Age 98.54 100.30 (0.00) 51.42 0.00 0.0 (0.00) (0.00) (b) Interaction terms 7.15 (0.00 (0.00) 6.43 with Age and Age (0.02) 7.884 0.457 0.457 0.456 0456 0456 SER 0.457 0.457 0.1897 0.1921 0.1924 0.1929 0.19370.1943 0.1950 01959 R2 Significant at the *5% and ** 1% significance level. For the regressions above, notice that the dependent variable is written in bold at the top of the column. It is usually ln(Average Hourly Earnings) but is simply Average Hourly Earnings for regression 1. The term "Bachelor" is an indicator variable which is 1 if the person has a college degree. In your answers below, try to comment on statistics that relate to the regression overall and statistics that relate to particular variables.

Using symbols, write the homoskedasticity-only formula for the joint hypothesis test statistic.

Answer 1

The formula for the homoskedasticity-only for the joint hypothesis test is:

(R2 restricted 7 (I-Rrizedn esriczed-1) restricted ln-

R²_unrestricted is the R-square for the unrestricted regression

R²_restricted is the R-square for the restricted regression

q = Number of restrictions

k = Number of terms in the unrestricted regression equation