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:

Aggregate Demand

The total demand for all goods and services in an economy at various price levels, during a specific time period.

Full Employment

An economic situation where all available labor resources are being used in the most efficient way possible, essentially meaning there is no involuntary unemployment.

Keynes

Refers to John Maynard Keynes, an influential British economist whose ideas fundamentally changed the theory and practice of macroeconomics and the economic policies of governments.

Government Spending

Expenditures by the government for goods and services that directly benefit the population, including spending on health, education, defense, and public infrastructure.