Consider the Following Two Models Involving Binary Variables as Explanatory $\widehat { \text { Wage } }$

question 29

Essay

Consider the following two models involving binary variables as explanatory variables: $\widehat { \text { Wage } }$ = $\widehat { \beta 0 }$ + $\widehat { \beta 1 }$ DFemme and $\widehat { \text { Wage } }$ = $\widehat { \phi _ { 1 } }$ DFemme + $\widehat { \phi _ { 2 } }$ Male
where Wage is the hourly wage rate, DFemme is a binary variable that is equal to 1 if the person is a female, and 0 if the person is a male. Male = 1 - DFemme. Even though you have not learned about regression functions with two explanatory variables (or regressions without an intercept), assume that you had estimated both models, i.e., you obtained the estimates for the regression coefficients.
What is the predicted wage for a male in the two models? What is the predicted wage for a female in the two models? What is the relationship between the ? s and the ?s? Why would you prefer one model over the other?

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Definitions:

Willingness-To-Pay

The maximum amount that a consumer is prepared to pay for a good or service.

Technological Advances

The progress in technology that enhances productivity, efficiency, and quality in various industries.

Trade

The act of buying, selling, or exchanging goods and services between people or entities.

Economic Outcome

The result or consequence of economic activities and policies on an economy's overall condition.