Question

A researcher runs a regression with average hourly earnings AHE as the outcome variable, and two measures (Z and Q) of individual characteristics as explanatory variables. The very large sample is of adults from all over the country. The researcher has i the dataset four dummy variables (N, S, E, W) for each of the four regions of the country. The researcher would like to know whether the location of adults has a big effect on their earnings. What should the regression specification(s) be, and how should the researcher test hypothesis(es) about whether the regions matter for earnings? Make up numerical outcomes for the hypothesis test(s) you propose and determine whether to reject or accept.

Answer 1

The regression specification for the researcher should include the individual characteristics and dummy variables for the regions. Hypothesis tests can be conducted for each region to determine if location has a significant effect on earnings.

Step-by-step explanation:

The regression specification for the researcher should be:

AHE = β₀ + β₁Z + β₂Q + β₃N + β₄S + β₅E + β₆W + ε

To test the hypothesis about whether the regions matter for earnings, the researcher can conduct a t-test for each of the region dummy variables. The null hypothesis for each test would be that the coefficient for the respective region dummy variable is equal to zero, indicating that there is no effect of that region on earnings. If the p-value for any of the tests is less than the chosen significance level (e.g., 0.05), the researcher can reject the null hypothesis and conclude that the location of adults has a significant effect on their earnings.