A regression on earnings and height result in the following results

Yi = -512.7 + 707.7(Xi)

where Yi is Earnings (average annual earnings in 2012 dollars) and Xi is height in inches for individual i.

One explanation for the statistically significant effect of height on earnings is that there is an omitted variable bias. Cognitive ability which affects worker productivity (and therefore wages) would be correlated with height. The mechanism is that poor nutrition and other harmful environmental factors in utero and in early childhood have negative effects on poor both cognitive ability as well as physical development.

a. Suppose this mechanism is correct. Would this above regression suggest that the coefficient on height has a positive or negative bias? Explain.

b. Since there is no data on cognitive ability, years of education could be a control for cognitive ability since those with higher cognitive ability would be more likely to attend school longer. The regression includes dummy variables that are one if the individual is in a specific education level:

LT_HS: less than 12 years (<12 years of education)

HS: has a high school diploma (12 years of education)

SC: some college (less than a bachelor's degree) (<16 years of education)

C: college degree if the individual has a bachelor's degree. (>=16 years of education)

The regressions are done for men and women separately. The results are below with heteroskedasticity robust standard errors are presented below.

Yi = -512.7 + 707.7(Xi) - 317(LT_HS) - 203(HS) - 125(SC)

• Do the negative signs on the education dummies make sense? Explain why or why not.
• Consider the following test after the regression for women. What is being tested? What is the result/interpretation of the results.

test lt_hs hs SC

(1) lt_hs = 0

(2) hs = 0

(3) SC = 0

F( 3, 9969) = 577.93

Prob>F = 0.0000