A data set of 5,000 workers contains the following variables:

• LNEARN: logarithm of annual earnings
• AGE: age in years
• AGE_SQ: square of AGE
• LNAGE: logarithm of AGE

Regression output with HC standard errors is shown below:

	Dependent variable: LNEARN
	(1)	(2)
LNAGE	0.491
	(0.040)
AGE		0.098
		(0.007)
AGE_SQ		-0.001
		(0.0001)
CONSTANT	8.955	8.572
	(0.150)	(0.152)
R2	0.037	0.069

a) Discuss the result in regression (1) by interpreting the coefficient estimate on LNAGE and discussing its statistical significance. Then, based on regression (1), compute the 95% confidence interval for the coefficient on LNAGE.

b) Based on regression (1) and without using a calculator, compute the partial effect of increasing AGE from 20 years to 21 years, and compute the 95% confidence interval for this partial effect. Remember to show your working.

c) Based on regression (2), compute the partial effect of changing AGE as described in Question 15 above. Then, describe how you would conduct a test of whether the partial effect is statistically significant from zero at the 5% significance level. State your null and alternative hypotheses, test statistic, and how you arrive at your decision.

d) continuing from c, suppose the test statistic equals 210. Compute the standard error of the partial effect and the 95% confidence interval of the partial effect.

e) Suppose we construct two new variables:

• AGE18: AGE minus 18
• AGE18_SQ: square of AGE18

Suppose we regress LNEARN on AGE18 and AGE18_SQ. In this regression, what are the coefficient estimates on AGE18 and AGE18_SQ, respectively? Show your working.

f) Suppose some workers in the sample have zero earnings. What is the most serious problem that may occur in the estimation result? Briefly explain why.