Econometrics I ab exercises-Chapter 5 Exercises on endogeneity ...

<strong>Econometrics</strong> I
<strong>ab</strong> <strong>exercises</strong>-<strong>Chapter</strong> 5
<strong>Exercises</strong> on endogeneity
5.1) (Ex. 15.12 Wooldridge). Use the data in WAGE2.RAW for this exercise:
(i) We want to explain log(wage) based on educ, but educ is an endogenous vari<strong>ab</strong>le. Use IV to
estimate this model, using sibs as an instrumental vari<strong>ab</strong>le. Moreover, run the regression of
educ on sibs to test the correlation between educ and sibs.
(ii) The vari<strong>ab</strong>le brthord is birth order (brthord is one for a first-born child, two for a second-born
child, and so on). Explain why educ and brthord might be negatively correlated. Regress educ
on brthord to determine whether there is a statistically significant negative correlation.
(iii) Now, suppose that we include number of siblings as an explanatory vari<strong>ab</strong>le in the wage
equation; this controls for family background, to some extent
log(wage) = β 0 + β 1 educ + β 2 sibs + u.
Suppose that we want to use brthord as an IV for educ, assuming that sibs is exogenous. The
reduced form for educ is:
State and test the identification assumption.
educ = π 0 + π 1 sibs + π 2 brthord + v.
(iv) Estimate the equation from part (iii) using brthord as an IV for educ (and sibs as its own
IV). Comment on the standard errors for β 1 y de β 2 .
(v) Using the fitted values from part (iii), educ, ˆ compute the correlation between
Use this result to explain your findings from part (iv).
ˆ educ and sibs.
5.2) (Ex. 15.13 Wooldridge) The data in FERTIL2.RAW includes, for women in Botswana during
1988, information on number of children, years of education, age, and religious and economic status
vari<strong>ab</strong>les.
(i) Estimate this model by OLS
children = β 0 + β 1 educ + β 2 age + β 3 age 2 + u
and interpret the estimates. In particular, holding age fixed, what is the estimated effect of
another year of education on fertility If 100 women receive another year of education, how
many fewer children are they expected to have
(ii) frsthalf is a dummy vari<strong>ab</strong>le equal to one if the woman was born during the first six months
of the year. Assuming that frsthalf is uncorrelated with the error term from part (i), show
that frsthalf is a reason<strong>ab</strong>le IV candidate for educ. (Hint: You need to do a regression.)
(iii) Estimate the model from part (i) by using frsthalf as an IV for educ. Compare the estimated
effect of education with the OLS estimate from part (i).
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(iv) Add the binary vari<strong>ab</strong>les electric, tv, and bicycle to the model and assume these are exogenous.
Estimate the equation by OLS and 2SLS and compare the estimated coefficients
on educ. Interpret the coefficient on tv and explain why television ownership has a negative
effect on fertility.
5.3). The aim of this exercise is to compare the estimations obtained with 2SLS with others obtained
by incorrect methods. The data is WAGE2.
(i) Use 2SLS to estimate:
log(wage) = β 0 + β 1 educ + β 2 exper + β 3 tenure + β 4 black + u,
using sibs as instrumental vari<strong>ab</strong>le for educ.
(ii) Estimate now the reression of educ on sibs, exper, tenure and black. Then plug in educ ˆ in
the equation of part (i) and estimate it by OLS. Compare these ˆβ j with the ones obtained in
part (i) and their standard errors. Comment these standard errors.
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