Question 1

Asymptotic distribution theory is

Accepted Answer

A) not practically relevant, because we never have an infinite number of observations. 
B) only of theoretical interest. 
C) of interest because it tells you what the distribution approximately looks like in small samples. 
D) the distribution of statistics when the sample size is very large. 
A) not practically relevant, because we never have an infinite number of observations. 
B) only of theoretical interest. 
C) of interest because it tells you what the distribution approximately looks like in small samples. 
D) the distribution of statistics when the sample size is very large. D

Question 2

The OLS estimator is a linear estimator, $\hat { \beta } _ { 1 } = \sum _ { i = 1 } ^ { n } \hat { a } _ { i } Y _ { i }$, where $\hat { a } _ { i } =$
a. $\frac { X _ { i } - \bar { X } } { \sum _ { j = 1 } ^ { n } \left( X _ { j } - \bar { X } \right) ^ { 2 } }$.

b. $\frac { 1 } { n }$.

c. $\frac { X _ { i } - \bar { X } } { \sum _ { j = 1 } ^ { n } \left( X _ { j } - \bar { X } \right) }$.

d. $\frac { X _ { i } } { \sum _ { j = 1 } ^ { n } \left( X _ { j } - \bar { X } \right) ^ { 2 } }$.

Accepted Answer

A

Question 3

The WLS estimator is called infeasible WLS estimator when

Accepted Answer

A) the memory required to compute it on your PC is insufficient. 
B) the conditional variance function is not known. 
C) the numbers used to compute the estimator get too large. 
D) calculating the weights requires you to take a square root of a negative number. 
A) the memory required to compute it on your PC is insufficient. 
B) the conditional variance function is not known. 
C) the numbers used to compute the estimator get too large. 
D) calculating the weights requires you to take a square root of a negative number. B

Question 4

Discuss the properties of the OLS estimator when the regression errors are
homoskedastic and normally distributed.What can you say about the distribution of the
OLS estimator when these features are absent?

Accepted Answer

In the initial discussion of the OLS est

Question 5

The advantage of using heteroskedasticity-robust standard errors is that

Accepted Answer

A) they are easier to compute than the homoskedasticity-only standard errors. 
B) they produce asymptotically valid inferences even if you do not know the form of the conditional variance function. 
C) it makes the OLS estimator BLUE, even in the presence of heteroskedasticity. 
D) they do not unnecessarily complicate matters, since in real-world applications, the functional form of the conditional variance can easily be found. 
A) they are easier to compute than the homoskedasticity-only standard errors. 
B) they produce asymptotically valid inferences even if you do not know the form of the conditional variance function. 
C) it makes the OLS estimator BLUE, even in the presence of heteroskedasticity. 
D) they do not unnecessarily complicate matters, since in real-world applications, the functional form of the conditional variance can easily be found.

Question 6

For this question you may assume that linear combinations of normal variates are
themselves normally distributed.Let a, b, and c be non-zero constants.
(a) $$X \text { and } Y \text { are independently distributed as } N \left( a , \sigma ^ { 2 } \right) \text {. What is the distribution of } ( b X + c Y ) \text { ? }$$

Accepted Answer

The answer of For this question you may assume that...

Question 7

When the errors are heteroskedastic, then

Accepted Answer

A) WLS is efficient in large samples, if the functional form of the heteroskedasticity is known. 
B) OLS is biased. 
C) OLS is still efficient as along as there is no serial correlation in the error terms. 
D) weighted least squares is efficient. 
A) WLS is efficient in large samples, if the functional form of the heteroskedasticity is known. 
B) OLS is biased. 
C) OLS is still efficient as along as there is no serial correlation in the error terms. 
D) weighted least squares is efficient.

Question 8

"I am an applied econometrician and therefore should not have to deal with econometric
theory.There will be others who I leave that to.I am more interested in interpreting the
estimation results." Evaluate.

Accepted Answer

Being presented with regression output a

Question 9

Feasible WLS does not rely on the following condition:

Accepted Answer

A) the conditional variance depends on a variable which does not have to appear in the regression function. 
B) estimating the conditional variance function. 
C) the key assumptions for OLS estimation have to apply when estimating the conditional variance function. 
D) the conditional variance depends on a variable which appears in the regression function. 
A) the conditional variance depends on a variable which does not have to appear in the regression function. 
B) estimating the conditional variance function. 
C) the key assumptions for OLS estimation have to apply when estimating the conditional variance function. 
D) the conditional variance depends on a variable which appears in the regression function.

Question 10

Under the five extended least squares assumptions, the homoskedasticity-only t- distribution in this chapter a. has a Student $t$ distribution with $n$-2 degrees of freedom.
b. has a normal distribution.
c. converges in distribution to a $\chi _ { n - 2 } ^ { 2 }$ distribution.
d. has a Student $t$ distribution with $n$ degrees of freedom.

Accepted Answer

The answer of Under the five extended least squares assumptions,...

Question 11

$E \left( \frac { 1 } { n - 2 } \sum _ { i = 1 } ^ { n } \hat { u } _ { i } ^ { 2 } \right)$

Accepted Answer

A)  is the expected value of the homoskedasticity only standard errors. 
B)  $= \sigma _ { u } ^ { 2 }$ 
C)  exists only asymptotically. 
D)  $= \sigma _ { u } ^ { 2 } / ( \mathrm { n } - 2 )$ 
A)  is the expected value of the homoskedasticity only standard errors. 
B)  $= \sigma _ { u } ^ { 2 }$ 
C)  exists only asymptotically. 
D)  $= \sigma _ { u } ^ { 2 } / ( \mathrm { n } - 2 )$

Question 12

Your textbook states that an implication of the Gauss-Markov theorem is that the sample average, $\bar { Y }$, is the most efficient linear estimator of $E \left( Y _ { i } \right)$ when $Y _ { 1 } , \ldots , Y _ { n }$ are i.i.d. with $E \left( Y _ { i } \right) = \mu _ { Y }$ and $\operatorname { var } \left( Y _ { i } \right) = \sigma _ { Y } ^ { 2 }$. This follows from the regression model with no slope and the fact that the OLS estimator is BLUE.
Provide a proof by assuming a linear estimator in the $Y$ 's, $\tilde { \mu } = \sum _ { i = 1 } ^ { n } a _ { i } Y _ { i }$. (a)State the condition under which this estimator is unbiased.

Accepted Answer

The answer of Your textbook states that an implication of...

Question 13

You need to adjust $S _ { \hat { u } } ^ { 2 }$ by the degrees of freedom to ensure that $s _ { \hat { u } } ^ { 2 }$  is

Accepted Answer

A)  an unbiased estimator of $\sigma _ { u } ^ { 2 }$ 
B)  a consistent estimator of $\sigma _ { u } ^ { 2 }$ 
C)  efficient in small samples. 
D)   F -distributed. 
A)  an unbiased estimator of $\sigma _ { u } ^ { 2 }$ 
B)  a consistent estimator of $\sigma _ { u } ^ { 2 }$ 
C)  efficient in small samples. 
D)   F -distributed.

Question 14

It is possible for an estimator of $\mu _ { Y }$ to be inconsistent while

Accepted Answer

A)  converging in probability to $\mu _ { Y }$ 
B)  $S _ { n } \stackrel { p } { \rightarrow } \mu _ { Y }$ 
C)  unbiased. 
D)  $\operatorname { Pr } \left[ \left| S _ { n } - \mu _ { Y } \right| \geq \delta \right] \rightarrow 0$ 
A)  converging in probability to $\mu _ { Y }$ 
B)  $S _ { n } \stackrel { p } { \rightarrow } \mu _ { Y }$ 
C)  unbiased. 
D)  $\operatorname { Pr } \left[ \left| S _ { n } - \mu _ { Y } \right| \geq \delta \right] \rightarrow 0$

Question 15

The class of linear conditionally unbiased estimators consists of a. all estimators of $\beta _ { 1 }$ that are linear functions of $Y _ { 1 } , \ldots , Y _ { n }$ and that are unbiased, conditional on $X _ { 1 } , \ldots , X _ { n }$.
b. OLS, WLS, and TSLS.
c. those estimators that are asymptotically normally distributed.
d. all estimators of $\beta _ { 1 }$ that are linear functions of $X _ { 1 } , \ldots , X _ { n }$ and that are unbiased, conditional on $X _ { 1 } , \ldots , X _ { n }$.

Accepted Answer

The answer of The class of linear conditionally unbiased estimators...

Question 16

(Requires Appendix material)State and prove the Cauchy-Schwarz Inequality.

Accepted Answer

The answer of (Requires Appendix material)State and prove the Cauchy-Schwarz...

Question 17

"One should never bother with WLS.Using OLS with robust standard errors gives
correct inference, at least asymptotically." True, false, or a bit of both? Explain carefully
what the quote means and evaluate it critically.

Accepted Answer

WLS is a special case of the GLS estimat

Question 18

If, in addition to the least squares assumptions made in the previous chapter on the simple regression model, the errors are homoskedastic, then the OLS estimator is

Accepted Answer

A) identical to the TSLS estimator. 
B) BLUE. 
C) inconsistent. 
D) different from the OLS estimator in the presence of heteroskedasticity. 
A) identical to the TSLS estimator. 
B) BLUE. 
C) inconsistent. 
D) different from the OLS estimator in the presence of heteroskedasticity.

Question 19

Slutsky's theorem combines the Law of Large Numbers

Accepted Answer

A) with continuous functions. 
B) and the normal distribution. 
C) and the Central Limit Theorem. 
D) with conditions for the unbiasedness of an estimator. 
A) with continuous functions. 
B) and the normal distribution. 
C) and the Central Limit Theorem. 
D) with conditions for the unbiasedness of an estimator.

Question 20

Estimation by WLS

Accepted Answer

A) although harder than OLS, will always produce a smaller variance. 
B) does not mean that you should use homoskedasticity-only standard errors on the transformed equation. 
C) requires quite a bit of knowledge about the conditional variance function. 
D) makes it very hard to interpret the coefficients, since the data is now weighted and not any longer in its original form. 
A) although harder than OLS, will always produce a smaller variance. 
B) does not mean that you should use homoskedasticity-only standard errors on the transformed equation. 
C) requires quite a bit of knowledge about the conditional variance function. 
D) makes it very hard to interpret the coefficients, since the data is now weighted and not any longer in its original form.

Asymptotic distribution theory is

The WLS estimator is called infeasible WLS estimator when

Discuss the properties of the OLS estimator when the regression errors are homoskedastic and normally distributed.What can you say about the distribution of the OLS estimator when these features are absent?

The advantage of using heteroskedasticity-robust standard errors is that

When the errors are heteroskedastic, then

"I am an applied econometrician and therefore should not have to deal with econometric theory.There will be others who I leave that to.I am more interested in interpreting the estimation results." Evaluate.

Feasible WLS does not rely on the following condition:

$E \left( \frac { 1 } { n - 2 } \sum _ { i = 1 } ^ { n } \hat { u } _ { i } ^ { 2 } \right)$

You need to adjust $S _ { \hat { u } } ^ { 2 }$ by the degrees of freedom to ensure that $s _ { \hat { u } } ^ { 2 }$ is

It is possible for an estimator of $\mu _ { Y }$ to be inconsistent while

(Requires Appendix material)State and prove the Cauchy-Schwarz Inequality.

"One should never bother with WLS.Using OLS with robust standard errors gives correct inference, at least asymptotically." True, false, or a bit of both? Explain carefully what the quote means and evaluate it critically.

If, in addition to the least squares assumptions made in the previous chapter on the simple regression model, the errors are homoskedastic, then the OLS estimator is

Slutsky's theorem combines the Law of Large Numbers

Estimation by WLS

Economic Questions and Data

Review of Probability

Review of Statistics

Linear Regression With One Regressor

Regression With a Single Regressor: Hypothesis Tests and Confidence Intervals

Linear Regression With Multiple Regressors

Hypothesis Tests and Confidence Intervals in Multiple Regression

Nonlinear Regression Functions

Assessing Studies Based on Multiple Regression

Regression With Panel Data

Regression With a Binary Dependent Variable

Instrumental Variables Regression

Experiments and Quasi-Experiments

Introduction to Time Series Regression and Forecasting

Estimation of Dynamic Causal Effects

Additional Topics in Time Series Regression

The Theory of Multiple Regression

Filters

Exam 17: The Theory of Linear Regression With One Regressor

Asymptotic distribution theory is

The WLS estimator is called infeasible WLS estimator when

Discuss the properties of the OLS estimator when the regression errors are homoskedastic and normally distributed.What can you say about the distribution of the OLS estimator when these features are absent?

The advantage of using heteroskedasticity-robust standard errors is that

When the errors are heteroskedastic, then

"I am an applied econometrician and therefore should not have to deal with econometric theory.There will be others who I leave that to.I am more interested in interpreting the estimation results." Evaluate.

Feasible WLS does not rely on the following condition:

E(1n−2∑i=1nu^i2)E \left( \frac { 1 } { n - 2 } \sum _ { i = 1 } ^ { n } \hat { u } _ { i } ^ { 2 } \right)E(n−21​∑i=1n​u^i2​)

You need to adjust Su^2S _ { \hat { u } } ^ { 2 }Su^2​ by the degrees of freedom to ensure that su^2s _ { \hat { u } } ^ { 2 }su^2​ is

It is possible for an estimator of μY\mu _ { Y }μY​ to be inconsistent while

(Requires Appendix material)State and prove the Cauchy-Schwarz Inequality.

"One should never bother with WLS.Using OLS with robust standard errors gives correct inference, at least asymptotically." True, false, or a bit of both? Explain carefully what the quote means and evaluate it critically.

If, in addition to the least squares assumptions made in the previous chapter on the simple regression model, the errors are homoskedastic, then the OLS estimator is

Slutsky's theorem combines the Law of Large Numbers

Estimation by WLS

Economic Questions and Data

Review of Probability

Review of Statistics

Linear Regression With One Regressor

Regression With a Single Regressor: Hypothesis Tests and Confidence Intervals

Linear Regression With Multiple Regressors

Hypothesis Tests and Confidence Intervals in Multiple Regression

Nonlinear Regression Functions

Assessing Studies Based on Multiple Regression

Regression With Panel Data

Regression With a Binary Dependent Variable

Instrumental Variables Regression

Experiments and Quasi-Experiments

Introduction to Time Series Regression and Forecasting

Estimation of Dynamic Causal Effects

Additional Topics in Time Series Regression

The Theory of Multiple Regression

Filters

$E \left( \frac { 1 } { n - 2 } \sum _ { i = 1 } ^ { n } \hat { u } _ { i } ^ { 2 } \right)$

You need to adjust $S _ { \hat { u } } ^ { 2 }$ by the degrees of freedom to ensure that $s _ { \hat { u } } ^ { 2 }$ is

It is possible for an estimator of $\mu _ { Y }$ to be inconsistent while