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.

Discuss the difference between regressions 4 and 5. What is the evaluation to be made between these two versions? What statistics do we consider to help make that evaluation? What is the economic interpretation (the additional insight into causation) of the difference between the two regressions?

Answer 1

In this case, the model 5 can be considered as original model and model 4 can be considered as a restricted model. Model 4 has one regressor less which is the interaction term: Female x Bachelor

The evaluation we are interested in doing is that whether this interaction term is significant in predicting the dependent variable or not. Hence, the null hypothesis will be:

Ho: The coefficient of interaction term = 0

To test the hypothesis, we will compute the statistic which has the formula:

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

Here, q = 1 which is the number of restrictions

Hence, after computing the statistic, we will take the decision whether this interaction term is significant or not.

The economic interpretation of the difference between the two regressions is that whether the effect of the first causal variable, Being a female or not (Gender) on the outcome ( ln(Average hourly earnings) ) is dependent on the state of the second causal variable which is that having a college degree or not.