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Consider the population regression of log earnings [Yᵢ, where Yᵢ= ln(Earningsᵢ)] against two binary variables:
whether a worker is married (D₁ᵢ, where D₁ᵢ =1 if the person is married) and the worker’s gender (D₂ᵢ, where D₂ᵢ =1 if the ith person is female), and the product of the two binary variables:
Yᵢ = β₀ + β₁D₁ᵢ + β₂D₂ᵢ + β₃(D₁ᵢ×D₂ᵢ) + uᵢ.
The interaction term:

A) allows the population effect on log earnings of being married to depend on gender
B) does not make sense since it could be zero for married males
C) indicates the effect of being married on log earnings
D) cannot be estimated without the presence of a continuous variable

Respuesta :

Answer:

A) allows the population effect on log earnings of being married to depend on gender

Step-by-step explanation:

The regression equation of a dependent variable based on two or more independent variables is of the form:

[tex]Y=b_{0}+b_{1}X_{1} +b_{2}X_{2}+b_{3}X_{1}X_{2}[/tex]

Here,

Y = dependent variable

[tex]X_{1}[/tex] and [tex]X_{2}[/tex] = independent variables

[tex]X_{1}X_{2}[/tex] = interaction term

[tex]b_{1},\ b_{2}\ and \ b_{3}[/tex] = regression coefficients.

If there is a significant interaction effect present then this implies that the effect of one independent variable ([tex]X_{1}[/tex] or[tex]X_{2}[/tex] ) on the dependent variable (Y) differs every time with different value of the other independent variable  ([tex]X_{1}[/tex] or[tex]X_{2}[/tex] ) .

The provided regression equation is:

[tex]Y_{i}=\beta _{0}+\beta _{1}D_{1i}+\beta_{2}D_{2i}+\beta _{3}D_{1i}D_{2i}+u_{i}[/tex]

[tex]Y_{i}[/tex] = dependent variable

[tex]D_{1i}[/tex] and [tex]D_{2i}[/tex] = independent variables

In this case the interaction term is defined as follows:

The effect of being married on log earnings is dependent on different values of the variables [tex]D_{2i}[/tex], i.e. the gender of the [tex]i^{th}[/tex]person.

Thus, the correct option is (A).

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