Question

True or False:

( ) Consider the model y=α1+β1x+u, where *x* is an
endogenous covariate and *z* is a valid instrument for
*x.* The model x=α2+β2z+u2 can be said to be a reduced-form
equation for *x*.

( ) Valid instrumental variables are usually very difficult to find.

( ) 2SLS is (under certain assumptions) the most efficient IV estimator.

( ) The normal distribution of the error term is a crucial assumption for making inferences using the 2SLS estimator.

Answer #1

1: It is True because in reduced form equation , corelation between exogenous(independent ) variable and disturbance turm(u2) is zero, that is they are uncorrelated.

2: It is True because you need to show that it is correlated with the endogenous independent variable but not with the residual , which is often not trival.

3: It is true because it is valid in both under exact identification and over identification.

4: it is not true because assumption of normal distribution of error term is valid for testing not for inference. For inference its not necessary to assumptins of normalty of error term.

Model: Y = β0 + β1X + u If E(u|X) 6= 0, then we know the OLS
estimator will be biased and all further inference like Hypothesis
test and Confidence interval will be invalid. In presence of such
violation, we can go to Instrument variable estimation/regression
method to rebuild the valid empirical study. Assume there is a
“good” instrument variable Z for X. (1) How would you argue this is
a valid instrument variable?(Hint: validity condition and relevance
condition) (2)...

Model: Y = β0 + β1X + u If E(u|X) 6= 0, then we know the OLS
estimator will be biased and all further inference like Hypothesis
test and Confidence interval will be invalid. In presence of such
violation, we can go to Instrument variable estimation/regression
method to rebuild the valid empirical study. Assume there is a
“good” instrument variable Z for X. (1) How would you argue this is
a valid instrument variable?(Hint: validity condition and relevance
condition) (2)...

True or False:
1) ____ The treatment effect identified using Regression
Discontinuity Designs (RDD) is typically global, in the sense that
it applies, in principle, to the relevant population as a
whole.
2) ____ Consider the model y=α+βx+u, where x is an endogenous
covariate (i.e., it is correlated with u) and z is a candidate
instrument for x. Even if there is some correlation between z and u
it will be usually better to use IV estimation than OLS estimation...

Suppose y is determined by the true model
y=β0+β1x+β2z+ε, and that
β2 >0 and COV(z,x) < 0. If someone were interested
in estimating β1, and did so by using OLS to estimate y
= β0 + β1x + u, would the OLS estimator of β1
be biased or not? If it is unbiased, explain why. If it is biased,
is the bias positive or negative? Why?

1.Which of the following is true of Chow
test?
a.
It is a type of sign test.
b.
It is only valid under heteroskedasticity.
c.
It is only valid under homoskedasticty.
d.
It is a type of t test.
2.
Consider the following simple regression model
y = β0 +
β1x1 + u. Suppose
Corr(x,u) > 0, Corr(z,x)
> 0, and Corr(z,u) < 0. Then, the IV
estimator has a(n) _____.
a.
substantial bias
b.
downward bias
c.
asymptotic bias...

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