Question 1

Let W be the included exogenous variables in a regression function that also has endogenous regressors (X).The W variables can

Accepted Answer

A) be control variables 
B) have the property E(ui|Wi)= 0 
C) make an instrument uncorrelated with u 
D) all of the above 
A) be control variables 
B) have the property E(ui|Wi)= 0 
C) make an instrument uncorrelated with u 
D) all of the above D

Question 2

The logic of control variables in IV regressions

Accepted Answer

A) parallels the logic of control variables in OLS 
B) only applies in the case of homoskedastic errors in the first stage of two stage least squares estimation 
C) is different in a substantial way from the logic of control variables in OLS since there are two stages in estimation 
D) implies that the TSLS is efficient 
A) parallels the logic of control variables in OLS 
B) only applies in the case of homoskedastic errors in the first stage of two stage least squares estimation 
C) is different in a substantial way from the logic of control variables in OLS since there are two stages in estimation 
D) implies that the TSLS is efficient A

Question 3

Estimation of the IV regression model

Accepted Answer

A) requires exact identification. 
B) allows only one endogenous regressor,which is typically correlated with the error term. 
C) requires exact identification or overidentification. 
D) is only possible if the number of instruments is the same as the number of regressors. 
A) requires exact identification. 
B) allows only one endogenous regressor,which is typically correlated with the error term. 
C) requires exact identification or overidentification. 
D) is only possible if the number of instruments is the same as the number of regressors. C

Question 4

For W to be an effective control variable in IV estimation,the following condition must hold

Accepted Answer

A) E(ui)= 0 
B) E(ui|Zi,Wi)= E(ui|Wi) 
C) E(uiuj)≠ 0 
D) there must be an intercept in the regression 
A) E(ui)= 0 
B) E(ui|Zi,Wi)= E(ui|Wi) 
C) E(uiuj)≠ 0 
D) there must be an intercept in the regression

Question 5

Write an essay about where valid instruments come from.Part of your explorations must deal with checking the validity of instruments and what the consequences of weak instruments are.

Accepted Answer

In order for instruments to be valid,the

Question 6

In practice,the most difficult aspect of IV estimation is

Accepted Answer

A) finding instruments that are both relevant and exogenous. 
B) that you have to use two stages in the estimation process. 
C) calculating the J-statistic. 
D) finding instruments that are exogenous.Relevant instruments are easy to find. 
A) finding instruments that are both relevant and exogenous. 
B) that you have to use two stages in the estimation process. 
C) calculating the J-statistic. 
D) finding instruments that are exogenous.Relevant instruments are easy to find.

Question 7

Weak instruments are a problem because

Accepted Answer

A) the TSLS estimator may not be normally distributed,even in large samples. 
B) they result in the instruments not being exogenous. 
C) the TSLS estimator cannot be computed. 
D) you cannot predict the endogenous variables any longer in the first stage. 
A) the TSLS estimator may not be normally distributed,even in large samples. 
B) they result in the instruments not being exogenous. 
C) the TSLS estimator cannot be computed. 
D) you cannot predict the endogenous variables any longer in the first stage.

Question 8

When calculating the TSLS standard errors

Accepted Answer

A) you do not have to worry about heteroskedasticity,since it was eliminated in the first stage 
B) you can use the standard errors reported by OLS estimation of the second stage regression. 
C) the critical values from the standard normal table should be adjusted for the proper degrees of freedom. 
D) you should use heteroskedasticity-robust standard errors. 
A) you do not have to worry about heteroskedasticity,since it was eliminated in the first stage 
B) you can use the standard errors reported by OLS estimation of the second stage regression. 
C) the critical values from the standard normal table should be adjusted for the proper degrees of freedom. 
D) you should use heteroskedasticity-robust standard errors.

Question 9

The distinction between endogenous and exogenous variables is

Accepted Answer

A) that exogenous variables are determined inside the model and endogenous variables are determined outside the model. 
B) dependent on the sample size: for n > 100,endogenous variables become exogenous. 
C) depends on the distribution of the variables: when they are normally distributed,they are exogenous,otherwise they are endogenous. 
D) whether or not the variables are correlated with the error term. 
A) that exogenous variables are determined inside the model and endogenous variables are determined outside the model. 
B) dependent on the sample size: for n > 100,endogenous variables become exogenous. 
C) depends on the distribution of the variables: when they are normally distributed,they are exogenous,otherwise they are endogenous. 
D) whether or not the variables are correlated with the error term.

Question 10

In the case of the simple regression model Yi = β0 + β1Xi + ui,i = 1,…,n,when X and u are correlated,then

Accepted Answer

A) the OLS estimator is biased in small samples only. 
B) OLS and TSLS produce the same estimate. 
C) X is exogenous. 
D) the OLS estimator is inconsistent. 
A) the OLS estimator is biased in small samples only. 
B) OLS and TSLS produce the same estimate. 
C) X is exogenous. 
D) the OLS estimator is inconsistent.

Question 11

The following will not cause correlation between X and u in the simple regression model:

Accepted Answer

A) simultaneous causality. 
B) omitted variables. 
C) irrelevance of the regressor. 
D) errors in variables. 
A) simultaneous causality. 
B) omitted variables. 
C) irrelevance of the regressor. 
D) errors in variables.

Question 12

To study the determinants of growth between the countries of the world,researchers have used panels of countries and observations spanning over long periods of time .Some of these studies have focused on the effect that inflation has on growth and found that although the effect is small for a given time period,it accumulates over time and therefore has an important negative effect.
(a)Explain why the OLS estimator may be biased in this case.
(b)Explain how methods using panel data could potentially alleviate the problem.
(c)Some authors have suggested using an index of central bank independence as an instrumental.Discuss whether or not such an index would be a valid instrument.

Accepted Answer

(a)The presence of simultaneous causalit

Question 13

Endogenous variables

Accepted Answer

A) are correlated with the error term. 
B) always appear on the LHS of regression functions. 
C) cannot be regressors. 
D) are uncorrelated with the error term. 
A) are correlated with the error term. 
B) always appear on the LHS of regression functions. 
C) cannot be regressors. 
D) are uncorrelated with the error term.

Question 14

Here are some examples of the instrumental variables regression model.In each case you are given the number of instruments and the J-statistic.Find the relevant value from the   distribution,using a 1% and 5% significance level,and make a decision whether or not to reject the null hypothesis.
(a)Yi = β0 + β1X1i + ui,i = 1,... ,n;Z1i,Z2i are valid instruments,J = 2.58.
(b)Yi = β0 + β1X1i + β2X2i + β3W1i + ui,i = 1,... ,n;Z1i,Z2i,Z3i,Z4i are valid instruments,J = 9.63.
(c)Yi = β0 + β1X1i + β2W1i + β3W2i + β4W3i + ui,i = 1,... ,n;Z1i,Z2i,Z3i,Z4i are valid instruments,J = 11.86.

Accepted Answer

(a)The test statistic is distributed @#IMG-DLM& an

Question 15

The two conditions for a valid instrument are

Accepted Answer

A) corr(Zi,Xi)= 0 and corr(Zi,ui)≠ 0. 
B) corr(Zi,Xi)= 0 and corr(Zi,ui)= 0. 
C) corr(Zi,Xi)≠ 0 and corr(Zi,ui)= 0. 
D) corr(Zi,Xi)≠ 0 and corr(Zi,ui)≠ 0. 
A) corr(Zi,Xi)= 0 and corr(Zi,ui)≠ 0. 
B) corr(Zi,Xi)= 0 and corr(Zi,ui)= 0. 
C) corr(Zi,Xi)≠ 0 and corr(Zi,ui)= 0. 
D) corr(Zi,Xi)≠ 0 and corr(Zi,ui)≠ 0.

Question 16

When there is a single instrument and single regressor,the TSLS estimator for the slope can be calculated as follows:

Accepted Answer

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

Question 17

Consider the following model of demand and supply of coffee:
Demand:   = β1   + β2   + ui
Supply:   = β3   + β4   + β5Weather + vi
(variables are measure in deviations from means,so that the constant is omitted).
What are the expected signs of the various coefficients this model? Assume that the price of tea and Weather are exogenous variables.Are the coefficients in the supply equation identified? Are the coefficients in the demand equation identified? Are they overidentified? Is this result surprising given that there are more exogenous regressors in the second equation?

Accepted Answer

Changes in Weather will shift the supply

Question 18

The rule-of-thumb for checking for weak instruments is as follows: for the case of a single endogenous regressor,

Accepted Answer

A) a first stage F must be statistically significant to indicate a strong instrument. B) a first stage F > 1.96 indicates that the instruments are weak. C) the t-statistic on each of the instruments must exceed at least 1.64. D) a first stage F < 10 indicates that the instruments are weak. A) a first stage F must be statistically significant to indicate a strong instrument. B) a first stage F > 1.96 indicates that the instruments are weak. C) the t-statistic on each of the instruments must exceed at least 1.64. D) a first stage F < 10 indicates that the instruments are weak.

Question 19

Describe the consequences of estimating an equation by OLS in the presence of an endogenous regressor.How can you overcome these obstacles? Present an alternative estimator and state its properties.

Accepted Answer

In the case of an endogenous regressor,t

Question 20

Consider a competitive market where the demand and the supply depend on the current price of the good.Then fitting a line through the quantity-price outcomes will

Accepted Answer

A) give you an estimate of the demand curve. 
B) estimate neither a demand curve nor a supply curve. 
C) enable you to calculate the price elasticity of supply. 
D) give you the exogenous part of the demand in the first stage of TSLS. 
A) give you an estimate of the demand curve. 
B) estimate neither a demand curve nor a supply curve. 
C) enable you to calculate the price elasticity of supply. 
D) give you the exogenous part of the demand in the first stage of TSLS.

Let W be the included exogenous variables in a regression function that also has endogenous regressors (X).The W variables can

The logic of control variables in IV regressions

Estimation of the IV regression model

For W to be an effective control variable in IV estimation,the following condition must hold

Write an essay about where valid instruments come from.Part of your explorations must deal with checking the validity of instruments and what the consequences of weak instruments are.

In practice,the most difficult aspect of IV estimation is

Weak instruments are a problem because

When calculating the TSLS standard errors

The distinction between endogenous and exogenous variables is

In the case of the simple regression model Yi = β0 + β1Xi + ui,i = 1,…,n,when X and u are correlated,then

The following will not cause correlation between X and u in the simple regression model:

Endogenous variables

The two conditions for a valid instrument are

When there is a single instrument and single regressor,the TSLS estimator for the slope can be calculated as follows:

The rule-of-thumb for checking for weak instruments is as follows: for the case of a single endogenous regressor,

Describe the consequences of estimating an equation by OLS in the presence of an endogenous regressor.How can you overcome these obstacles? Present an alternative estimator and state its properties.

Consider a competitive market where the demand and the supply depend on the current price of the good.Then fitting a line through the quantity-price outcomes will

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

Let W be the included exogenous variables in a regression function that also has endogenous regressors (X).The W variables can

The logic of control variables in IV regressions

Estimation of the IV regression model

For W to be an effective control variable in IV estimation,the following condition must hold

Write an essay about where valid instruments come from.Part of your explorations must deal with checking the validity of instruments and what the consequences of weak instruments are.

In practice,the most difficult aspect of IV estimation is

Weak instruments are a problem because

When calculating the TSLS standard errors

The distinction between endogenous and exogenous variables is

In the case of the simple regression model Yi = β0 + β1Xi + ui,i = 1,…,n,when X and u are correlated,then

The following will not cause correlation between X and u in the simple regression model:

Endogenous variables

The two conditions for a valid instrument are

When there is a single instrument and single regressor,the TSLS estimator for the slope can be calculated as follows:

The rule-of-thumb for checking for weak instruments is as follows: for the case of a single endogenous regressor,

Describe the consequences of estimating an equation by OLS in the presence of an endogenous regressor.How can you overcome these obstacles? Present an alternative estimator and state its properties.

Consider a competitive market where the demand and the supply depend on the current price of the good.Then fitting a line through the quantity-price outcomes will

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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