计量经济学作业

Statistical Approach to Economic issues. (prof. Yunmi Kim)

M2012425 Jin Peng

a)Regress weeksworked on the indicator variable morekids using OLS. On average, do women with more than two children work less than women with two children? How much less?

Yes, Women with more than two children work less than women with two children. The coefficient is -5.386996.

Dependent Variable: WEEKSM1

Method: Least Squares

Date: 05/11/12 Time: 10:34

Sample: 1 254654

Included observations: 254654

Variable Coefficient Std. Error t-Statistic Prob.

C 21.06843 0.054663 385.4245 0.0000

MOREKIDS -5.386996 0.088609 -60.79492 0.0000

R-squared 0.014306 Mean dependent var 19.01833

Adjusted R-squared 0.014302 S.D. dependent var 21.86728

S.E. of regression 21.71034 Akaike info criterion 8.993462

Sum squared resid 1.20E+08 Schwarz criterion 8.993544

Log likelihood -1145109. Hannan-Quinn criter. 8.993486

F-statistic 3696.022 Durbin-Watson stat 1.926530

Prob(F-statistic) 0.000000

b) Explain why the OLS regression estimated in (a) might be inappropriate for estimating the causal effect of fertility (morekids) on labor supply (weeksworked).

The main reason why the OLS regression estimated in (a) might be inappropriate is that one of the assumptions is violated. The independent variable morekids is endogenous, which means independent variable has correlation with error terms. So this OLS is biased.

c) The data set contains the variable samesex, which is equal to 1 if the first two children are of the same sex (boy-boy or girl-girl) and equal to 0 otherwise. Are couples whose first two children are of the same sex more likely to have a third child? Is the effect large? Is it statistically significant?

Yes, The couples whose first two children are of the same sex are more likely to have a third child

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The effect is large and statistically significant. Because the P value is much smaller than the a (0.1% or 0.5%), the null Hypothesis should be rejected. So the we can estimate that the coefficient of variable samesex is not 0.

Dependent Variable: MOREKIDS

Method: Least Squares

Date: 05/11/12 Time: 11:21

Sample: 1 254654

Included observations: 254654

Variable Coefficient Std. Error t-Statistic Prob.

C 0.346425 0.001365 253.7910 0.0000

SAMESEX 0.067525 0.001920 35.17413 0.0000

R-squared 0.004835 Mean dependent var 0.380563

Adjusted R-squared 0.004831 S.D. dependent var 0.485526

S.E. of regression 0.484352 Akaike info criterion 1.387999

Sum squared resid 59740.59 Schwarz criterion 1.388081

Log likelihood -176727.7 Hannan-Quinn criter. 1.388023

F-statistic 1237.219 Durbin-Watson stat 1.949323

Prob(F-statistic) 0.000000

d) Explain why samesex is a valid instrument for the instrumental variable regression of weeksworked on morekids.

The samesex is a valid instrument because according to the outcome of c), the corr(samesex, morekids) is not 0. So the instrument relevance is not 0.

And the first two children’s sex can not be controls , so the the corr( samesex, error term) is 0. So samesex is a good instrument.

e) Is samesex a weak instrument?

No, it is a good instrument, according to the conclusion of c), It has the statistically significance.

f) Estimate the regression of weeksworked on morekids using samesex as an instrument. How large is the fertility effect on labor supply?

The coefficient of fertichanges from -5.386996 to -6.313685, so if one more child increase, the labor supply will decrease 6.313685 hours.

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