You Have Collected a Sub-Sample from the Current Population Survey $\widehat{\text { ahe }}$

question 47

Essay

You have collected a sub-sample from the Current Population Survey for the western region of the United States. Running a regression of average hourly earnings (ahe)on an intercept only, you get the following result: $\widehat{\text { ahe }}$ = $\widehat{\beta}$ ₀ = 18.58
a. Interpret the result.
b. You decide to include a single explanatory variable without an intercept. The binary variable DFemme takes on a value of "1" for females but is "0" otherwise. The regression result changes as follows: $\widehat{\text { ahe} }$ = $\widehat{\beta}$ ₁×DFemme = 16.50×DFemme
What is the interpretation now?
c. You generate a new binary variable DMale by subtracting DFemme from 1, and run the new regression: $\widehat{\text { ahe }}$ = $\widehat{\beta}$ ₂×DMale = 20.09×DMale
_{What is the interpretation of the coefficient now?}
d. After thinking about the above results, you recognize that you could have generated the last two results either by running a regression on both binary variables, or on an intercept and one of the binary variables. What would the results have been?

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Definitions:

Race Relations

The interactions and social dynamics between people of different racial backgrounds, often scrutinizing the history, quality, and complexities of these encounters.

Federal Government

The national government of the United States, created by the Constitution, comprising the legislative, executive, and judicial branches.

African-American Population

Individuals in the United States who have African ancestry, focusing on their cultural, social, and demographic aspects.

Immigrants

Individuals who move from one country to another, often for reasons like seeking employment, escaping conflicts, or reuniting with family.