spss作业15-17

CHAPTER 15

西北研究院蔡嘉驰131246

15.4 (i) What we choose is part of u t. Then gMIN t and u t are correlated, which causes OLS to be biased and inconsistent.

(ii) I think it is uncorrelate because gGDP t controls for the overall performance of the U.S. economy.

(iii) The change of U.S. minimum may someway change the state minimum and vice versa.

If the state minimum is always the U.S. minimum, then gMIN t is exogenous in this equation and we would just use OLS.

15.7 (i) Because students that would do better anyway are also more likely to attend a choice school.

(ii) Since u1 does not contain income, random assignment of grants within income class means that grant designation is not correlated with unobservables such as student ability, motivation, and family support.

(iii) The reduced form is

choice= π0 + π1faminc + π2grant + v2,

and we need π2≠ 0.

(iv) The reduced form for score is just a linear function of the exogenous variables:

score= α0 + α1faminc + α2grant + v1.

This equation allows us to directly estimate the effect of increasing the grant amount on the test score, holding family income fixed.So it is useful.

C15.1 (i) The regression of log(wage) on sibs gives

log(wage) = 6.861 -0.0279 sibs

(0.022) (0.0059)

n= 935, R2= 0.023.

This is a reduced form simple regression equation. It shows that, controlling for no other factors, one more sibling in the family is associated with monthly salary that is about 2.8% lower.

(ii) It because older children are given priority for higher education, and families may hit budget constraints and may not be able to afford as much education for children born later. The simple regression of educ on brthord gives

educ = 14.15 - 0.283 brthord

(0.13) (0.046)

n= 852, R2= 0.042.

The equation predicts that every one-unit increase in brthord reduces predicted education by about 0.28 years.

(iii) When brthord is used as an IV for educ in the simple wage equation we get

log(wage) = 5.03 + 0.131 educ

(0.42) (0.031)

n= 852.

Because of missing data on brthord, we are using fewer observations than in the previous analyses.

(iv) In the reduced form equation

educ= π0 + π1sibs + π2brthord + v,

we need π2≠ 0 in order for the βj to be identified. We take the null to be H0: π2 = 0, and look to reject H0 at a small significance level.

ˆπ = The regression of educ on sibs and brthord (using 852 observations) yields

2

ˆπ) = 0.057. The p is about 0.000, which rejects H0 fairly strongly. -0.153 and se(

2

Therefore, the identification assumptions appears to hold.

(v) The equation estimated by IV is

log(wage) = 4.94 + 0.137 educ+ 0.0021 sibs

(1.06) (0.075) (0.0174)

n= 852.

βis much larger than we obtained in part (iii). The 95% The standard error on ˆ

educ

βis roughly -.010 to .284, which is very wide and includes the value zero. CI for

educ

βis very large, rendering sibs very insignificant.

The p of ˆ

sibs