Econometric Analysis of Cross Section and Panel Data - Free

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Chapter 9
When estimating a simultaneous equations system, it is important to remember the
pros and cons of full system estimation. If all equations are correctly specified, system
procedures are asymptotically more e‰cient than a single-equation procedure such as
2SLS. But single-equation methods are more robust. If interest lies, say, in the first
equation of a system, 2SLS is consistent and asymptotically normal provided the
first equation is correctly specified and the instruments are exogenous. However, if
one equation in a system is misspecified, the 3SLS or GMM estimates of all the parameters
are generally inconsistent.
Example 9.5 (Labor Supply for Married, Working Women): Using the data in
MROZ.RAW, we estimate a labor supply function for working, married women.
Rather than specify a demand function, we specify the second equation as a wage
o¤er function and impose the equilibrium condition:
hours ¼ g 12 logðwageÞþd 10 þ d 11 educ þ d 12 age þ d 13 kidslt6
þ d 14 kidsge6 þ d 15 nwifeinc þ u 1
logðwageÞ ¼g 21 hours þ d 20 þ d 21 educ þ d 22 exper þ d 23 exper 2 þ u 2
ð9:28Þ
ð9:29Þ
where kidslt6 is number of children less than 6, kidsge6 is number of children between
6 and 18, and nwifeinc is income other than the woman’s labor income. We assume
that u 1 and u 2 have zero mean conditional on educ, age, kidslt6, kidsge6, nwifeinc,
and exper.
The key restriction on the labor supply function is that exper (and exper 2 ) have no
direct e¤ect on current annual hours. This identifies the labor supply function with
one overidentifying restriction, as used by Mroz (1987). We estimate the labor supply
function first by OLS [to see what ignoring the endogeneity of logðwageÞ does] and
then by 2SLS, using as instruments all exogenous variables in equations (9.28) and
(9.29).
There are 428 women who worked at some time during the survey year, 1975. The
average annual hours are about 1,303 with a minimum of 12 and a maximum of
4,950.
We first estimate the labor supply function by OLS:
ho^urs ¼ 2;114:7
ð340:1Þ
17:41 logðwageÞ 14:44 educ 7:73 age
ð54:22Þ
ð17:97Þ ð5:53Þ
342:50 kidslt6 115:02 kidsge6 4:35 nwifeinc
ð100:01Þ ð30:83Þ ð3:66Þ