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Hi it’s just a couple of problems for my Quant class. I need an A
Final Exam
Quantitative Methods/Analytics
Fall 2020
1.In the linear model given in equation (10.8)from Wooldridge Econometrics manual(7thedition), the explanatory variables xt =(xt1, …, xtk)are said to be sequentially exogenous (sometimes called weakly exogenous)ifE(ut|xt,xt-1,…, x1) = 0, t=1, 2, …so that the errors are unpredictable given current and all past values of the explanatoryvariables.
(i) Explain why sequential exogeneity is implied by strict exogeneity.
(ii) Explain why contemporaneous exogeneity is implied by sequential exogeneity.
(iii) Are the OLS estimators generally unbiased under the sequential exogeneity assumption? Explain.
(iv) Consider a model to explain the annual rate of HIV infections (HIVrate) as adistributed lag of per capita condom usage (pccon) for a state, region, or province:
E(HIVratet|pccont,pccontt-1,…) = α0+δ0pccont+δ1pccont-1+δ2pccont-2+δ3pccont-3
Explain why this model satisfies the sequential exogeneity assumption. Does itseem likely that strict exogeneity holds too?
- The following equation represents the effects of tax revenue mix on subsequent employment growth for the population of counties in the United States:
growth =b0 +b1shareP +b2shareI +b3shareS +other factors,where growth is the percentage change in employment from 1980 to 1990, shareP is theshare of property taxes in total tax revenue, shareI is the share of income tax revenues, andshareS is the share of sales tax revenues. All of these variables are measured in 1980. Theomitted share, shareF, includes fees and miscellaneous taxes. By definition, the four sharesadd up to one. Other factors would include expenditures on education, infrastructure, andso on (all measured in 1980).
(i) Why must we omit one of the tax share variables from the equation?
(ii) Give a careful interpretation of b1.
- The following model allows the return to education to depend upon the total amount of both parents’ education, called pareduc:
log (wage) = b0 + b1 educ +b2 educ*pareduc + b3 exper + b4 tenure + u
- i) Show that, in decimal form, the return to another year of education in this model is
Delta log (wage) / Delta educ = b1 +b2 pared, where Delta means change.
What sign do you expect for b2? why?
- ii) The estimated equation is
log (wage) = 5.65 + 0.047 educ + 0.0078 educ*pareduc + 0.019 exper + 0.10 tenure
(0.13) (0.010) (0.00021) (0.004) (0.003)
n= 722, R^2=0.169
Interpret the coefficient in the interaction term.It might help choose two specific values for pareduc- for example, pareduc=32 if both parents have a college education, so pareduc=24 if both parents have a high school education and to compare the estimated return to education
iii) When pareduc is added as a separable variable to the equation, we get:
log(wage) = 4.94 + 0.097 educ + 0.33 pareduc – 0.0016 pareduc + 0.020 exper + 0.010 tenure
(0.38) (0.027) (0.017) (0.0012) (0.004) (0.003)
n=722, R^2=0.174
Does the estimated return to education now depend positively on parent education?
Test the null hypothesis that the return to education does not depend on parent education.
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