Question

Consider the population regression of log earnings [Yᵢ, where Yᵢ= ln(Earningsᵢ)] against two binary variables:

Answer 1

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:

$Y=b_{0}+b_{1}X_{1} +b_{2}X_{2}+b_{3}X_{1}X_{2}$

Here,

Y = dependent variable

$X_{1}$ and $X_{2}$ = independent variables

$X_{1}X_{2}$ = interaction term

$b_{1},\ b_{2}\ and \ b_{3}$ = regression coefficients.

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

The provided regression equation is:

$Y_{i}=\beta _{0}+\beta _{1}D_{1i}+\beta_{2}D_{2i}+\beta _{3}D_{1i}D_{2i}+u_{i}$

$Y_{i}$ = dependent variable

$D_{1i}$ and $D_{2i}$ = 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 $D_{2i}$, i.e. the gender of the $i^{th}$person.

Thus, the correct option is (A).