Department of Economics
Spring 2006
University of California
Prof. Woroch
Economics 140
:
Problem Set 6 Answer Sheet
I.
For each, decide whether you agree or disagree with part or all of the statement and
explain the reasoning behind your answer in a couple short paragraphs
. Note that you
may agree with part of the statement, but disagree with the rest.
1.
When a linear equation involves a single endogenous explanatory variable, as long as it is
correlated with each of several instruments, TSLS estimation will produce consistent estimates
provided that the predicted values for the endogenous variable and the exogenous variables are
not multicollinear.
Answer
:
Disagree.
The mentioned conditions are necessary for the TSLS estimator to be
consistent, but it is also necessary that all the instruments used in the first stage equation are
uncorrelated with the error term in the structural equation.
Only exogenous instruments will
identify exogenous variation in the endogenous explanatory variable.
If this additional condition
holds as well, then the TSLS estimator is consistent.
2.
The reducedform equation for an endogenous variable expresses an endogenous variable as a
function of all the instruments, while the structural equation may have endogenous variables on
both sides of the equation.
Answer
:
Agree.
In the reduced form equation we are trying to find exogenous variation in an
endogenous variable, so we regress the endogenous variables on the exogenous variables only.
Thus we include both the instrumental variables and the exogenous variables included in the
structural equation as explanatory variables in the reduced form.
A structural equation may include
endogenous explanatory variables, but if it does then we need to use the TSLS estimator as the OLS
estimators of the structural equation will be inconsistent.
3.
One “internal” threat to a controlled experiment is the socalled Hawthorne effect, while one
“external” threat is the occurrence of sample attrition over the course of the experimental period.
Answer
:
Disagree.
Both the Hawthorne effect and sample attrition threaten internal validity as
both can lead to an inconsistent estimator of the treatment effect for the population studied (i.e., the
population from which the sample is drawn).
As the Hawthorne effect implies that subject’s
behavior is influenced by being in an experiment, the estimator may be consistent for the treatment
effect in an experimental setting but it will be an inconsistent estimator for treatment effect on the
population studied in a natural setting.
When there is sample attrition, the sample may no longer be
representative of the population studied causing an estimator based on the select sample to be an
inconsistent estimator of the treatment effect for the population the experimenter intended to study.
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2
PS6 Answers
II. MULTIPART QUESTIONS
: Answer each of the following 3 questions.
The second one
requires the use of the Excel dataset that is posted to the website.
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 Fall '08
 DUNCAN
 Economics, Supply And Demand, TSLS, endogenous variable

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