Refer to the Indian wage earners example (Section 9.12) and the data in Table 9.7.

As a reminder, the variables are defined as follows:

WI = weekly wage income in rupees

Age = age in years

D_sex = 1 for male workers and 0 for female workers

DE₂ = a dummy variable taking a value of 1 for workers with up to a primary education

DE₃ = a dummy variable taking a value of 1 for workers with up to a secondary education

DE₄ = a dummy variable taking a value of 1 for workers with higher education

DPT = a dummy variable taking a value of 1 for workers with permanent jobs and a value of 0 for temporary workers

The reference category is male workers with no primary education and temporary jobs.

In Section 9.12, interaction terms were created between the education variables (DE₂, DE₃, and DE₄) and the gender variable (Dsex). What happens if we create interaction terms between the education dummies and the permanent worker dummy variable (DPT)?

a. Estimate the model predicting ln WI containing age, gender, the education dummy variables, and three new interaction terms: DE₂ × DPT, DE₃ × DPT, and DE₄ × DPT. Does there appear to be a significant interaction effect among the new terms?

b. Is there a significant difference between workers with an education level up to primary and those without a primary education? Assess this with respect to both the education dummy variable and the interaction term and explain the results. What about the difference between workers with a secondary level of education and those without a primary level of education? What about the difference between those with an education level beyond secondary, compared to those without a primary level of education?

c. Now assess the results of deleting the education dummies from the model. Do the interaction terms change in significance?