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SOLUTIONS TO PROBLEMS
There is functional form misspecification if
0, where these are the population
Therefore, we test the joint significance of
these variables using the
-squared form of the
With 2 and
, the 10% critical value is 2.30 awhile the 5% critical value is 3.00.
-value is slightly above .05, which is reasonable evidence of functional form
(Of course, whether this has a practical impact on the estimated partial effects
for various levels of the explanatory variables is a different matter.)
(i) Eligibility for the federally funded school lunch program is very tightly linked to being
economically disadvantaged. Therefore, the percentage of students eligible for the lunch program
is very similar to the percentage of students living in poverty.
(ii) We can use our usual reasoning on omitting important variables from a regression
The variables log(
are negatively correlated:
school districts with
poorer children spend, on average, less on schools.
From Table 3.2, omitting
(the proxy for
) from the regression produces an upward biased estimator of
[ignoring the presence of log(
) in the model].
So when we control for the poverty rate, the
effect of spending falls.
(iii) Once we control for
, the coefficient on log(
) becomes negative and has a
of about –2.17, which is significant at the 5% level against a two-sided alternative.
coefficient implies that
10% increase in enrollment leads to a drop in
of .126 percentage points.
Therefore, a ten percentage point increase in
leads to about a 3.23 percentage point fall in
, a sizeable effect.
(v) In column (1) we are explaining very little of the variation in pass rates on the MEAP
less than 3%.
In column (2), we are explaining almost 19% (which still leaves much
Clearly most of the variation in
is explained by variation in
This is a common finding in studies of school performance: family income (or related
factors, such as living in poverty) are much more important in explaining student performance
than are spending per student or other school characteristics.
The sample selection in this case is arguably endogenous.
Because prospective students may
look at campus crime as one factor in deciding where to attend college, colleges with high crime
rates have an incentive not to report crime statistics. If this is the case, then the chance of