Forthis exercise, we use data file JTRAlN.WF1 to determine the effect ofthe job training grant on hours ofjob training per employee. The basic model forthe three years is
HRSEMPit = [30 + 61D88t + 62D89t + B1GRANTit + [i2GRANTi,t-1 + eit
(i) Estimate the equation using fixed effects. How many firms are used in the FE estimation? How many total observations would be used if each firm had data
on all variables (in particular, HRSEMP) for all three years?
(ii) lnterpret the coefficient on GRANT and comment on its significance.
(iii) Is it surprising that GRANTi,t-1 is insignificant? Explain.
(iv) Do largerfirms provide their employees with more or less training, on average? How big are the differences? (For example, ifa firm has 10% more employees, what is the change in average hours oftraining?)
Consider a family saving function forthe population of all families in the United States:
[31 INC + [i2HHSlZE + [i3EDUC + [i4AGE + e
where HHSIZE is household size, EDUC is years of education ofthe household head, and AGE is age
ofthe household head. Assume that E(e/INC, HHSIZE, EDUC, AGE) = 0.
(i) Suppose that the sample includes only families whose head is over
25 years old. lfwe use OLS on such a sample, do we get unbiased estimators ofthe Bj? Explain.
(ii) Now, suppose our sample includes only
married couples without children. Can we estimate all ofthe parameters in the saving equation? Which ones can we estimate?
we exclude from our sample families that save more than $25,000 per year. Does OLS produce consistent estimators ofthe Bj?
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