Question 1

In the case of exact identification

Accepted Answer

A) you can use the J-statistic in a test of overidentifying restrictions. 
B) you cannot use TSLS for estimation purposes. 
C) you must rely on your personal knowledge of the empirical problem at hand to assess whether the instruments are exogenous. 
D) OLS and TSLS yield the same estimate. 
A) you can use the J-statistic in a test of overidentifying restrictions. 
B) you cannot use TSLS for estimation purposes. 
C) you must rely on your personal knowledge of the empirical problem at hand to assess whether the instruments are exogenous. 
D) OLS and TSLS yield the same estimate.

Question 2

Two Stage Least Squares is calculated as follows;in the first stage:

Accepted Answer

A) Y is regressed on the exogenous variables only.The predicted value of Y is then regressed on the instrumental variables. 
B) the unknown coefficients in the reduced form equation are estimated by OLS,and the predicted values are calculated.In the second stage,Y is regressed on these predicted values and the other exogenous variables. 
C) the exogenous variables are regressed on the instruments.The predicted value of the exogenous variables is then used in the second stage,together with the instruments,to predict the dependent variable. 
D) the unknown coefficients in the reduced form equation are estimated by weighted least squares,and the predicted values are calculated.In the second stage,Y is regressed on these predicted values and the other exogenous variables. 
A) Y is regressed on the exogenous variables only.The predicted value of Y is then regressed on the instrumental variables. 
B) the unknown coefficients in the reduced form equation are estimated by OLS,and the predicted values are calculated.In the second stage,Y is regressed on these predicted values and the other exogenous variables. 
C) the exogenous variables are regressed on the instruments.The predicted value of the exogenous variables is then used in the second stage,together with the instruments,to predict the dependent variable. 
D) the unknown coefficients in the reduced form equation are estimated by weighted least squares,and the predicted values are calculated.In the second stage,Y is regressed on these predicted values and the other exogenous variables.

Question 3

Using some of the examples from your textbook,describe econometric studies which required instrumental variable techniques.In each case emphasize why the need for instrumental variables arises and how authors have approached the problem.Make sure to include a discussion of overidentification,the validity of instruments,and testing procedures in your essay.

Accepted Answer

The textbook mentions several studies wh

Question 4

Your textbook gave an example of attempting to estimate the demand for a good in a market,but being unable to do so because the demand function was not identified.Is this the case for every market? Consider,for example,the demand for sports events.One of your peers estimated the following demand function after collecting data over two years for every one of the 162 home games of the 2000 and 2001 season for the Los Angeles Dodgers.   = 15,005 + 201 × Temperat + 465 × DodgNetWin + 82 × OppNetWin
(8,770)(121)(169)(26)
+ 9647 × DFSaSu + 1328 × Drain + 1609 × D150m + 271 × DDiv - 978 × D2001;
(1505)(3355)(1819)(1,184)(1,143)
R2 = 0.416,SER = 6983
Where Attend is announced stadium attendance,Temperat it the average temperature on game day,DodgNetWin are the net wins of the Dodgers before the game (wins-losses),OppNetWin is the opposing team's net wins at the end of the previous season,and DFSaSu,Drain,D150m,Ddiv,and D2001 are binary variables,taking a value of 1 if the game was played on a weekend,it rained during that day,the opposing team was within a 150 mile radius,plays in the same division as the Dodgers,and during 2001,respectively.Numbers in parenthesis are heteroskedasticity- robust standard errors.
Even if there is no identification problem,is it likely that all regressors are uncorrelated with the error term? If not,what are the consequences?

Accepted Answer

In the case of sports events,often price

Question 5

Consider the a model of the U.S.labor market where the demand for labor depends on the real wage,while the supply of labor is vertical and does not depend on the real wage.You could argue that the supply of labor by households (think of hours supplied by two adults and two children)has not changed much over the last 60 years or so in the U.S.while real wages more than doubled over the same time span.At first that seems strange given the higher participation rate of females over that period,but that increase has been countered by a lower male participation rate (resulting from earlier retirement),an increase in legal holidays,and an increase in vacation days.
a.Write down two equations representing the labor supply and labor demand function,allowing for an error term in each of the demand and supply equation.In addition,assume that the labor market clears.
b.How would you estimate the labor supply equation?
c.Assuming that the error terms are mutually independent i.i.d.random variables,both with mean zero,show that the real wage and the error term of the labor demand equation are correlated.
d.If you find a non-zero correlation,should you estimate the labor demand equation using OLS? If so,what are the consequences?
e.Estimating the labor demand equation by IV estimation,which instrument suggests itself immediately?

Accepted Answer

a.Student may use different symbols,but

Question 6

The IV regression assumptions include all of the following with the exception of

Accepted Answer

A) the error terms must be normally distributed. 
B) E(ui   W1i,…,Wri)= 0. 
C) Large outliers are unlikely: the X's,W's,Z's,and Y's all have nonzero,finite fourth moments. 
D) (X1i,…,Xki,W1i,…,Wri,Z1i,… Zmi,Yi)are i.i.d.draws from their joint distribution. 
A) the error terms must be normally distributed. 
B) E(ui   W1i,…,Wri)= 0. 
C) Large outliers are unlikely: the X's,W's,Z's,and Y's all have nonzero,finite fourth moments. 
D) (X1i,…,Xki,W1i,…,Wri,Z1i,… Zmi,Yi)are i.i.d.draws from their joint distribution.

Question 7

The TSLS estimator is

Accepted Answer

A) consistent and has a normal distribution in large samples. 
B) unbiased. 
C) efficient in small samples. 
D) F-distributed. 
A) consistent and has a normal distribution in large samples. 
B) unbiased. 
C) efficient in small samples. 
D) F-distributed.

Question 8

The conditions for a valid instruments do not include the following:

Accepted Answer

A) each instrument must be uncorrelated with the error term. 
B) each one of the instrumental variables must be normally distributed. 
C) at least one of the instruments must enter the population regression of X on the Zs and the Ws. 
D) perfect multicollinearity between the predicted endogenous variables and the exogenous variables must be ruled out. 
A) each instrument must be uncorrelated with the error term. 
B) each one of the instrumental variables must be normally distributed. 
C) at least one of the instruments must enter the population regression of X on the Zs and the Ws. 
D) perfect multicollinearity between the predicted endogenous variables and the exogenous variables must be ruled out.

Question 9

Write a short essay about the Overidentifying Restrictions Test.What is meant exactly by "overidentification?" State the null hypothesis.Describe how to calculate the J-statistic and what its distribution is.Use an example of two instruments and one endogenous variable to explain under what situation the test will be likely to reject the null hypothesis.What does this example tell you about the exactly identified case? If your variables pass the test,is this sufficient for these variables to be good instruments?

Accepted Answer

The regression coefficients in the regre

Question 10

Consider a model with one endogenous regressor and two instruments.Then the J-statistic will be large

Accepted Answer

A) if the number of observations are very large. 
B) if the coefficients are very different when estimating the coefficients using one instrument at a time. 
C) if the TSLS estimates are very different from the OLS estimates. 
D) when you use homoskedasticity-only standard errors. 
A) if the number of observations are very large. 
B) if the coefficients are very different when estimating the coefficients using one instrument at a time. 
C) if the TSLS estimates are very different from the OLS estimates. 
D) when you use homoskedasticity-only standard errors.

Question 11

Having more relevant instruments

Accepted Answer

A) is a problem because instead of being just identified,the regression now becomes overidentified. 
B) is like having a larger sample size in that the more information is available for use in the IV regressions. 
C) typically results in larger standard errors for the TSLS estimator. 
D) is not as important for inference as having the same number of endogenous variables as instruments. 
A) is a problem because instead of being just identified,the regression now becomes overidentified. 
B) is like having a larger sample size in that the more information is available for use in the IV regressions. 
C) typically results in larger standard errors for the TSLS estimator. 
D) is not as important for inference as having the same number of endogenous variables as instruments.

Question 12

(Requires Chapter 8)When using panel data and in the presence of endogenous regressors

Accepted Answer

A) the TSLS does not exist. 
B) you do not have to worry about the validity of instruments,since there are so many fixed effects. 
C) the OLS estimator is consistent. 
D) application of the TSLS estimator is straightforward if you use two time periods and difference the data. 
A) the TSLS does not exist. 
B) you do not have to worry about the validity of instruments,since there are so many fixed effects. 
C) the OLS estimator is consistent. 
D) application of the TSLS estimator is straightforward if you use two time periods and difference the data.

Question 13

You have been hired as a consultant to estimate the demand for various brands of coffee in the market.You are provided with annual price data for two years by U.S.state and the quantities sold.You want to estimate a demand function for coffee using this data.What problems do you think you will encounter if you estimated the demand equation by OLS?

Accepted Answer

Answers will differ by student.However,t

Question 14

You started your econometrics course by studying the OLS estimator extensively,first for the simple regression case and then for extensions of it.You have now learned about the instrumental variable estimator.Under what situation would you prefer one to the other? Be specific in explaining under which situations one estimation method generates superior results.

Accepted Answer

Under the OLS assumptions,the OLS estima

Question 15

Consider the following two equations to describe labor markets in various sectors of the economy Nd = β0 + β1   + u
Ns = γ0 + γ1   + v
Nd = Ns = N

Accepted Answer

A) W/P is exogenous,n is endogenous 
B) Both n and W/P are endogenous 
C) n is exogenous,W/P is endogenous 
D) the parameters cannot be estimated because it would require two equations to be estimated at the same time (simultaneously) 
A) W/P is exogenous,n is endogenous 
B) Both n and W/P are endogenous 
C) n is exogenous,W/P is endogenous 
D) the parameters cannot be estimated because it would require two equations to be estimated at the same time (simultaneously)

Question 16

Instrumental Variables regression uses instruments to

Accepted Answer

A) establish the Mozart Effect. 
B) increase the regression R2. 
C) eliminate serial correlation. 
D) isolate movements in X that are uncorrelated with u. 
A) establish the Mozart Effect. 
B) increase the regression R2. 
C) eliminate serial correlation. 
D) isolate movements in X that are uncorrelated with u.

Question 17

The reduced form equation for X

Accepted Answer

A) regresses the endogenous variable X on the smallest possible subset of regressors. 
B) relates the endogenous variable X to all the available exogenous variables,both those included in the regression of interest and the instruments. 
C) uses the predicted values of X from the first stage as a regressor in the original equation. 
D) uses smaller standard errors,such as homoskedasticity-only standard errors,for inference. 
A) regresses the endogenous variable X on the smallest possible subset of regressors. 
B) relates the endogenous variable X to all the available exogenous variables,both those included in the regression of interest and the instruments. 
C) uses the predicted values of X from the first stage as a regressor in the original equation. 
D) uses smaller standard errors,such as homoskedasticity-only standard errors,for inference.

Question 18

The J-statistic

Accepted Answer

A) tells you if the instruments are exogenous. 
B) provides you with a test of the hypothesis that the instruments are exogenous for the case of exact identification. 
C) is distributed   where m-k is the degree of overidentification. 
D) is distributed   where m-k is the number of instruments minus the number of regressors. 
A) tells you if the instruments are exogenous. 
B) provides you with a test of the hypothesis that the instruments are exogenous for the case of exact identification. 
C) is distributed   where m-k is the degree of overidentification. 
D) is distributed   where m-k is the number of instruments minus the number of regressors.

Question 19

You have estimated a government reaction function,i.e. ,a multiple regression equation,where a government instrument,say the federal funds rate,depends on past government target variables,such as inflation and unemployment rates.In addition,you added the previous period's popularity deficit of the government,e.g.the (approval rating of the president - 50%),as one of the regressors.Your idea is that the Federal Reserve,although formally independent,will try to expand the economy if the president is unpopular.One of your peers,a political science student,points out that approval ratings depend on the state of the economy and thereby indirectly on government instruments.It is therefore endogenous and should be estimated along with the reaction function.Initially you want to reply by using a phrase that includes the words "money neutrality" but are worried about a lengthy debate.Instead you state that as an economist,you are not concerned about government approval ratings,and that government approval ratings are determined outside your (the economic)model.Does your whim make the regressor exogenous? Why or why not?

Accepted Answer

In general,the question of whether or no

Question 20

(Requires Appendix material)The relationship between the TSLS slope and the corresponding population parameter is:

Accepted Answer

A)    . 
B)    . 
C)    . 
D)    . 
A)    . 
B)    . 
C)    . 
D)    .

In the case of exact identification

Two Stage Least Squares is calculated as follows;in the first stage:

The IV regression assumptions include all of the following with the exception of

The TSLS estimator is

The conditions for a valid instruments do not include the following:

Consider a model with one endogenous regressor and two instruments.Then the J-statistic will be large

Having more relevant instruments

(Requires Chapter 8)When using panel data and in the presence of endogenous regressors

Consider the following two equations to describe labor markets in various sectors of the economy Nd = β0 + β1 + u Ns = γ0 + γ1 + v Nd = Ns = N

Instrumental Variables regression uses instruments to

The reduced form equation for X

The J-statistic

(Requires Appendix material)The relationship between the TSLS slope and the corresponding population parameter is:

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

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 Linear Regression With One Regressor

The Theory of Multiple Regression

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Exam 12: Instrumental Variables Regression

In the case of exact identification

Two Stage Least Squares is calculated as follows;in the first stage:

The IV regression assumptions include all of the following with the exception of

The TSLS estimator is

The conditions for a valid instruments do not include the following:

Consider a model with one endogenous regressor and two instruments.Then the J-statistic will be large

Having more relevant instruments

(Requires Chapter 8)When using panel data and in the presence of endogenous regressors

Consider the following two equations to describe labor markets in various sectors of the economy Nd = β0 + β1 + u Ns = γ0 + γ1 + v Nd = Ns = N

Instrumental Variables regression uses instruments to

The reduced form equation for X

The J-statistic

(Requires Appendix material)The relationship between the TSLS slope and the corresponding population parameter is:

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

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 Linear Regression With One Regressor

The Theory of Multiple Regression

Filters