Question 1

The linear probability model is

Accepted Answer

A) the application of the multiple regression model with a continuous left-hand side variable and a binary variable as at least one of the regressors. 
B) an example of probit estimation. 
C) another word for logit estimation. 
D) the application of the linear multiple regression model to a binary dependent variable. 
A) the application of the multiple regression model with a continuous left-hand side variable and a binary variable as at least one of the regressors. 
B) an example of probit estimation. 
C) another word for logit estimation. 
D) the application of the linear multiple regression model to a binary dependent variable. D

Question 2

In the binary dependent variable model, a predicted value of 0.6 means that

Accepted Answer

A) the most likely value the dependent variable will take on is 60 percent. 
B) given the values for the explanatory variables, there is a 60 percent probability that the dependent variable will equal one. 
C) the model makes little sense, since the dependent variable can only be 0 or 1. 
D) given the values for the explanatory variables, there is a 40 percent probability that the dependent variable will equal one. 
A) the most likely value the dependent variable will take on is 60 percent. 
B) given the values for the explanatory variables, there is a 60 percent probability that the dependent variable will equal one. 
C) the model makes little sense, since the dependent variable can only be 0 or 1. 
D) given the values for the explanatory variables, there is a 40 percent probability that the dependent variable will equal one. B

Question 3

The probit model

Accepted Answer

A) is the same as the logit model. 
B) always gives the same fit for the predicted values as the linear probability model for values between 0.1 and 0.9. 
C) forces the predicted values to lie between 0 and 1. 
D) should not be used since it is too complicated. 
A) is the same as the logit model. 
B) always gives the same fit for the predicted values as the linear probability model for values between 0.1 and 0.9. 
C) forces the predicted values to lie between 0 and 1. 
D) should not be used since it is too complicated. C

Question 4

In the probit model Pr(Y = 1 | X1, X2,..., Xk)= ?(?0 + ?1X1 + ?xX2 + ... + ?kXk),

Accepted Answer

A) the ?'s do not have a simple interpretation. 
B) the slopes tell you the effect of a unit increase in X on the probability of Y. 
C) ?0 cannot be negative since probabilities have to lie between 0 and 1. 
D) ?0 is the probability of observing Y when all X's are 0 
A) the ?'s do not have a simple interpretation. 
B) the slopes tell you the effect of a unit increase in X on the probability of Y. 
C) ?0 cannot be negative since probabilities have to lie between 0 and 1. 
D) ?0 is the probability of observing Y when all X's are 0

Question 5

(Requires Appendix material)The following are examples of limited dependent variables, with the exception of

Accepted Answer

A) binary dependent variable. 
B) log-log specification. 
C) truncated regression model. 
D) discrete choice model. 
A) binary dependent variable. 
B) log-log specification. 
C) truncated regression model. 
D) discrete choice model.

Question 6

The logit model can be estimated and yields consistent estimates if you are using

Accepted Answer

A) OLS estimation. 
B) maximum likelihood estimation. 
C) differences in means between those individuals with a dependent variable equal to one and those with a dependent variable equal to zero. 
D) the linear probability model. 
A) OLS estimation. 
B) maximum likelihood estimation. 
C) differences in means between those individuals with a dependent variable equal to one and those with a dependent variable equal to zero. 
D) the linear probability model.

Question 7

In the expression Pr(deny = 1 | P/I Ratio, black)= ?(-2.26 + 2.74P/I ratio + 0.71black), the effect of increasing the P/I ratio from 0.3 to 0.4 for a white person

Accepted Answer

A) is 0.274 percentage points. 
B) is 6.1 percentage points. 
C) should not be interpreted without knowledge of the regression R2. 
D) is 2.74 percentage points. 
A) is 0.274 percentage points. 
B) is 6.1 percentage points. 
C) should not be interpreted without knowledge of the regression R2. 
D) is 2.74 percentage points.

Question 8

In the expression Pr(Y = 1 | = ?(?0 + ?1X),

Accepted Answer

A) (?0 + ?1X)plays the role of z in the cumulative standard normal distribution function. 
B) ?1 cannot be negative since probabilities have to lie between 0 and 1. 
C) ?0 cannot be negative since probabilities have to lie between 0 and 1. 
D) min (?0 + ?1X)> 0 since probabilities have to lie between 0 and 1. 
A) (?0 + ?1X)plays the role of z in the cumulative standard normal distribution function. 
B) ?1 cannot be negative since probabilities have to lie between 0 and 1. 
C) ?0 cannot be negative since probabilities have to lie between 0 and 1. 
D) min (?0 + ?1X)> 0 since probabilities have to lie between 0 and 1.

Question 9

(Requires material from Section 11.3 - possibly skipped)For the measure of fit in your regression model with a binary dependent variable, you can meaningfully use the

Accepted Answer

A) regression R2. 
B) size of the regression coefficients. 
C) pseudo R2. 
D) standard error of the regression. 
A) regression R2. 
B) size of the regression coefficients. 
C) pseudo R2. 
D) standard error of the regression.

Question 10

(Requires Advanced material)Only one of the following models can be estimated by OLS:

Accepted Answer

A) Y = AK?L? + u. 
B) Pr(Y = 1 | X)= ?(?0 + ?1X) 
C) Pr(Y = 1 | X)= F(?0 + ?1X)= $\frac { 1 } { 1 + e ^ { - \left( \beta _ { 0 } + \beta _ { 1 } X \right) } }$ 
D) Y = AK? L?u. 
A) Y = AK?L? + u. 
B) Pr(Y = 1 | X)= ?(?0 + ?1X) 
C) Pr(Y = 1 | X)= F(?0 + ?1X)= $\frac { 1 } { 1 + e ^ { - \left( \beta _ { 0 } + \beta _ { 1 } X \right) } }$ 
D) Y = AK? L?u.

Question 11

The binary dependent variable model is an example of a

Accepted Answer

A) regression model, which has as a regressor, among others, a binary variable. 
B) model that cannot be estimated by OLS. 
C) limited dependent variable model. 
D) model where the left-hand variable is measured in base 2. 
A) regression model, which has as a regressor, among others, a binary variable. 
B) model that cannot be estimated by OLS. 
C) limited dependent variable model. 
D) model where the left-hand variable is measured in base 2.

Question 12

The logit model derives its name from

Accepted Answer

A) the logarithmic model. 
B) the probit model. 
C) the logistic function. 
D) the tobit model. 
A) the logarithmic model. 
B) the probit model. 
C) the logistic function. 
D) the tobit model.

Question 13

Nonlinear least squares

Accepted Answer

A) solves the minimization of the sum of squared predictive mistakes through sophisticated mathematical routines, essentially by trial and error methods. 
B) should always be used when you have nonlinear equations. 
C) gives you the same results as maximum likelihood estimation. 
D) is another name for sophisticated least squares. 
A) solves the minimization of the sum of squared predictive mistakes through sophisticated mathematical routines, essentially by trial and error methods. 
B) should always be used when you have nonlinear equations. 
C) gives you the same results as maximum likelihood estimation. 
D) is another name for sophisticated least squares.

Question 14

The maximum likelihood estimation method produces, in general, all of the following desirable properties with the exception of

Accepted Answer

A) efficiency. 
B) consistency. 
C) normally distributed estimators in large samples. 
D) unbiasedness in small samples. 
A) efficiency. 
B) consistency. 
C) normally distributed estimators in large samples. 
D) unbiasedness in small samples.

Question 15

In the probit model Pr(Y = 1 | = ?(?0 + ?1X), ?

Accepted Answer

A) is not defined for ?(0). 
B) is the standard normal cumulative distribution function. 
C) is set to 1.96. 
D) can be computed from the standard normal density function. 
A) is not defined for ?(0). 
B) is the standard normal cumulative distribution function. 
C) is set to 1.96. 
D) can be computed from the standard normal density function.

Question 16

The major flaw of the linear probability model is that

Accepted Answer

A) the actuals can only be 0 and 1, but the predicted are almost always different from that. 
B) the regression R2 cannot be used as a measure of fit. 
C) people do not always make clear-cut decisions. 
D) the predicted values can lie above 1 and below 0. 
A) the actuals can only be 0 and 1, but the predicted are almost always different from that. 
B) the regression R2 cannot be used as a measure of fit. 
C) people do not always make clear-cut decisions. 
D) the predicted values can lie above 1 and below 0.

Question 17

The following tools from multiple regression analysis carry over in a meaningful manner to the linear probability model, with the exception of the

Accepted Answer

A) F-statistic. 
B) significance test using the t-statistic. 
C) 95% confidence interval using ± 1.96 times the standard error. 
D) regression R2. 
A) F-statistic. 
B) significance test using the t-statistic. 
C) 95% confidence interval using ± 1.96 times the standard error. 
D) regression R2.

Question 18

E(Y | X1, ..., Xk)= Pr(Y = 1 | X1,..., Xk)means that

Accepted Answer

A) for a binary variable model, the predicted value from the population regression is the probability that Y=1, given X. 
B) dividing Y by the X's is the same as the probability of Y being the inverse of the sum of the X's. 
C) the exponential of Y is the same as the probability of Y happening. 
D) you are pretty certain that Y takes on a value of 1 given the X's. 
A) for a binary variable model, the predicted value from the population regression is the probability that Y=1, given X. 
B) dividing Y by the X's is the same as the probability of Y being the inverse of the sum of the X's. 
C) the exponential of Y is the same as the probability of Y happening. 
D) you are pretty certain that Y takes on a value of 1 given the X's.

Question 19

In the linear probability model, the interpretation of the slope coefficient is

Accepted Answer

A) the change in odds associated with a unit change in X, holding other regressors constant. 
B) not all that meaningful since the dependent variable is either 0 or 1. 
C) the change in probability that Y=1 associated with a unit change in X, holding others regressors constant. 
D) the response in the dependent variable to a percentage change in the regressor. 
A) the change in odds associated with a unit change in X, holding other regressors constant. 
B) not all that meaningful since the dependent variable is either 0 or 1. 
C) the change in probability that Y=1 associated with a unit change in X, holding others regressors constant. 
D) the response in the dependent variable to a percentage change in the regressor.

Question 20

When having a choice of which estimator to use with a binary dependent variable, use

Accepted Answer

A) probit or logit depending on which method is easiest to use in the software package at hand. 
B) probit for extreme values of X and the linear probability model for values in between. 
C) OLS (linear probability model)since it is easier to interpret. 
D) the estimation method which results in estimates closest to your prior expectations. 
A) probit or logit depending on which method is easiest to use in the software package at hand. 
B) probit for extreme values of X and the linear probability model for values in between. 
C) OLS (linear probability model)since it is easier to interpret. 
D) the estimation method which results in estimates closest to your prior expectations.

The linear probability model is

In the binary dependent variable model, a predicted value of 0.6 means that

The probit model

In the probit model Pr(Y = 1 | X₁, X₂,..., X_k)= ?(?₀ + ?₁X₁ + ?_xX₂ + ... + ?_kX_k),

(Requires Appendix material)The following are examples of limited dependent variables, with the exception of

The logit model can be estimated and yields consistent estimates if you are using

In the expression Pr(deny = 1 | P/I Ratio, black)= ?(-2.26 + 2.74P/I ratio + 0.71black), the effect of increasing the P/I ratio from 0.3 to 0.4 for a white person

In the expression Pr(Y = 1 | = ?(?₀ + ?₁X),

(Requires material from Section 11.3 - possibly skipped)For the measure of fit in your regression model with a binary dependent variable, you can meaningfully use the

(Requires Advanced material)Only one of the following models can be estimated by OLS:

The binary dependent variable model is an example of a

The logit model derives its name from

Nonlinear least squares

The maximum likelihood estimation method produces, in general, all of the following desirable properties with the exception of

In the probit model Pr(Y = 1 | = ?(?₀ + ?₁X), ?

The major flaw of the linear probability model is that

The following tools from multiple regression analysis carry over in a meaningful manner to the linear probability model, with the exception of the

E(Y | X₁, ..., X_k)= Pr(Y = 1 | X₁,..., X_k)means that

In the linear probability model, the interpretation of the slope coefficient is

When having a choice of which estimator to use with a binary dependent variable, use

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

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 Linear Regression With One Regressor

The Theory of Multiple Regression

Filters

Exam 11: Regression With a Binary Dependent Variable

The linear probability model is

In the binary dependent variable model, a predicted value of 0.6 means that

The probit model

In the probit model Pr(Y = 1 | X1, X2,..., Xk)= ?(?0 + ?1X1 + ?xX2 + ... + ?kXk),

(Requires Appendix material)The following are examples of limited dependent variables, with the exception of

The logit model can be estimated and yields consistent estimates if you are using

In the expression Pr(deny = 1 | P/I Ratio, black)= ?(-2.26 + 2.74P/I ratio + 0.71black), the effect of increasing the P/I ratio from 0.3 to 0.4 for a white person

In the expression Pr(Y = 1 | = ?(?0 + ?1X),

(Requires material from Section 11.3 - possibly skipped)For the measure of fit in your regression model with a binary dependent variable, you can meaningfully use the

(Requires Advanced material)Only one of the following models can be estimated by OLS:

The binary dependent variable model is an example of a

The logit model derives its name from

Nonlinear least squares

The maximum likelihood estimation method produces, in general, all of the following desirable properties with the exception of

In the probit model Pr(Y = 1 | = ?(?0 + ?1X), ?

The major flaw of the linear probability model is that

The following tools from multiple regression analysis carry over in a meaningful manner to the linear probability model, with the exception of the

E(Y | X1, ..., Xk)= Pr(Y = 1 | X1,..., Xk)means that

In the linear probability model, the interpretation of the slope coefficient is

When having a choice of which estimator to use with a binary dependent variable, use

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

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 Linear Regression With One Regressor

The Theory of Multiple Regression

Filters

In the probit model Pr(Y = 1 | X₁, X₂,..., X_k)= ?(?₀ + ?₁X₁ + ?_xX₂ + ... + ?_kX_k),

In the expression Pr(Y = 1 | = ?(?₀ + ?₁X),

In the probit model Pr(Y = 1 | = ?(?₀ + ?₁X), ?

E(Y | X₁, ..., X_k)= Pr(Y = 1 | X₁,..., X_k)means that