Question

I am confuse about question 1 and two of problem 10, chapter 7 of introductory econometric (Wooldridge). May you assist?

Answer 1

This is the problem 10, chapter 7 of Introductory Econometric (Wooldridge):

For a child i living in a particular school district, let voucher_i be a dummy variable equal to one if a child is selected to participate in a school voucher program, and let score_i be that child’s score on a subsequent standardized exam. Suppose that the participation variable, voucher_i, is completely randomized in the sense that it is independent of both observed and unobserved factors that can affect the test score.

i) If you run a simple regression score_i on voucher_i using a random sample of size n, does the OLS estimator provide an unbiased estimator of the effect of the voucher program?

ii) Suppose you can collect additional background information, such as family income family structure(e.g., whether the child lives with both parents), and parents’ education levels. Do you need to control for these factors to obtain an unbiased estimator of the effects of the voucher program? Explain.

iii )Why should you include the family background variables in the regression? Is there a situation in which you would not include the background variables?

Ans:

(i)

Merely randomness of data does not ensure unbiasedness of OLS estimator. The OLS estimator would provide an unbiased estimator of the effect of the voucher program provided following conditions are satisfied: a) linearity of parameter b) no autocorrelation c) homogeneity of error variance d) no relationship between explanatory variable and random variable e) expectation of error equals zero f) no specification error.

(ii)

If we are running simple regression model then control for these factors while obtaining unbiased estimator of the effect of voucher program is necessary but if we are running a multiple regression model involving all of these factors then there is no need of controlling any of the variables while estimating unbiased estimator of any independent variable such as voucher in this case.

(iii)

Family background is an important factor determining scores of child. If the child belongs to a family where everyone is well educated, then he/she is likely to a better score as compare to a child who belongs to a illiterate family. Also the income level of family plays an important role here. A boy from a rich family is likely to have good health and hence might score more than a child from a poor family.

If we assume that all the child belongs to a homogeneous society [homogeneous in all respect], then there is no need of including background variables in the regression model.