Hi all. Is anyone have the STATA result for William Greene – Econometric Analysis 8th. Chapter 6, Application for 1 and 3.
Example.
In application 1 in chapter 3 and application 1 in chapter 5, we examined Koop and tobias’s data on wages, education, ability, and so on. We continue the analysis here. (the source, location and configuration of the data are given in the earlier application.) We consider the model
ln Wage = b1 + b2 Educ + b3 Ability + b4 Experience
+ b5 Mother’s education + b6 Father’s education + b7 Broken home + b8 Siblings + e.
- compute the full regression by least squares and report your results. Based on your results, what is the estimate of the marginal value, in $/hour, of an additional year of education, for someone who has 12 years of education when all other variables are at their means and Broken home = 0?
- WeareinterestedinpossiblenonlinearitiesintheeffectofeducationonlnWage. (Koop and tobias focused on experience. as before, we are not attempting to replicate their results.) a histogram of the education variable shows values from 9 to 20, a spike at 12 years (high school graduation), and a second at 15. consider aggregating the education variable into a set of dummy variables:
HS = 1 if Educ … 12,0 otherwise
Col = 1 if Educ 7 12 and Educ … 16, 0 otherwise
Grad = 1 if Educ 7 16, 0 otherwise.
replace Educ in the model with (Col, Grad), making high school (HS) the base category, and recompute the model. report all results. how do the results change? Based on your results, what is the marginal value of a college degree? What is the marginal impact on ln Wage of a graduate degree?
c. the aggregation in part b actually loses quite a bit of information. another way to introduce nonlinearity in education is through the function itself. add Educ2 to the equation in part a and recompute the model. again, report all results. What changes are suggested? test the hypothesis that the quadratic term in the equation is not needed—that is, that its coefficient is zero. Based on your results, sketch a profile of log wages as a function of education.
d. onemightsuspectthatthevalueofeducationisenhancedbygreaterability.We could examine this effect by introducing an interaction of the two variables in the equation. add the variable
Educ_Ability = Educ * Ability
to the base model in part a. now, what is the marginal value of an additional year of education? the sample mean value of ability is 0.052374. compute a confidence interval for the marginal impact on ln Wage of an additional year of education for a person of average ability.
e. combine the models in c and d. add both Educ2 and Educ_Ability to the base model in part a and reestimate. as before, report all results and describe your findings. if we define low ability as less than the mean and high ability as greater than the mean, the sample averages are -0.798563 for the 7,864 low-ability individuals in the sample and + 0.717891 for the 10,055 high-ability individuals in the sample. using the formulation in part c, with this new functional form, sketch, describe, and compare the log wage profiles for low- and high-ability individuals.
in solow’s classic (1957) study of technical change in the u.s. economy, he suggests the following aggregate production function: q(t) = A(t) f [k(t)], where q(t) is aggregate output per work hour, k(t) is the aggregate capital labor ratio, and A(t) is the technology index. solow considered four static models,
q/A = a + b ln k, q/A = a – b/k, ln(q/A) = a + b ln k,andln(q/A) = a + b/k. solow’s data for the years 1909 to 1949 are listed in appendix table F6.4.
- use these data to estimate the a and b of the four functions listed above. (Note: Your results will not quite match solow’s. see the next exercise for resolution of the discrepancy.)
- in the aforementioned study, solow states:
a scatter of q / A against k is shown in chart 4. considering the amount of a priori doctoring which the raw figures have undergone, the fit is remarkably tight. except, that is, for the layer of points which are obviously too high. these maverick observations relate to the seven last years of the period, 1943–1949. From the way they lie almost exactly parallel to the main scatter, one is tempted to conclude that in 1943 the aggregate production function simply shifted.
compute a scatter diagram of q / A against k and verify the result he notes above. - estimate the four models you estimated in the previous problem including a dummy variable for the years 1943 to 1949. how do your results change? (Note: these results match those reported by solow, although he did not report the
coefficient on the dummy variable.) - solow went on to surmise that, in fact, the data were fundamentally different
in the years before 1943 than during and after. use a chow test to examine the difference in the two subperiods using your four functional forms. note that with the dummy variable, you can do the test by introducing an interaction term between the dummy and whichever function of k appears in the regression. use an F test to test the hypothesis.