Question

From univariate to bivariate

Suppose you are interested in studying the effect of education on wages.

You propose the following regression of annual salary on years of education and work experience:

wage=β0 +

β1 educ + β2exper + u

where

	wage = annual salary
	educ = years of formal education
	exper = work experience
	u = error term

In a simple regression analysis with educ as the only explanatory variable, the effects of other factors, such as exper, are . (options on blank are : a. contained in the intercept parameterβ0, B. contained in the error term u, C. contained in the slope parameterβ1, D. not contained in the model)

In the proposed multivariate regression, the effect of exper is . (options on blank are : a. removed from the error term and explicitly included in the regression equation, B. contained in the error term u, C. contained in the intercept parameter β0, D. contained in the slope parameter β1)

PART 2 An important assumption in the regression model with two independent variables is that E(u|x1,x2)=0. Assume for simplicity that the only other relevant factor (contained in the error term) that affects wage is natural ability. That is, natural ability and u are essentially equivalent in your regression.

In the context of your proposed regression, this assumption assumes which of the following?

a. Natural ability is, on average, unrelated to years of education but may be related to work experience.

b. Natural ability is, on average, unrelated to years of education and work experience.

c. Natural ability plays no role in influencing annual salary.

d. Natural ability is, on average, unrelated to work experience but may be related to years of education.

Answer 1

Solution:

1. When an important explanatory variable is omitted from the model, it's effects are incorporated in the error term. Similar to that way, with work experience, not explicitly included in the model, it's effects are contained in the error term. So, correct option is (B).

2. Of course, since without including experience variable, if the effects of it were contained in error term, now with it's inclusion, it's effects from error term will be removed. So, the correct option is (A) removed from error term and explicitly added in the regression equation.

3. To answer this, it's important to note a few things. Firstly, since, natural ability is not included in the model explicitly, we know from above that it's effects are contained in error term. Secondly, we are given that natural ability is indeed a relevant factor, thus, it will influence the annual salary. Lastly, if that assumption has to hold in this case, it means that expectation of error term conditioned on any of the other independent variable, that is expectation of error term conditioned on education and expectation of error term conditioned on work experience should be 0. This further means that, on average (due to expectation), error term and education; and error term and work experience are unrelated to each other. Since, natural ability is similar to the error term here, it means that , on average, natural ability be unrelated to both, education and work experience. Correct option is (B).