Question 1

Which of the following statements is true?

Accepted Answer

A) The standard error of a regression,   , is not an unbiased estimator for   , the standard deviation of the error, u, in a multiple regression model. 
B) In time series regressions, OLS estimators are always unbiased. 
C) Almost all economists agree that unbiasedness is a minimal requirement for an estimator in regression analysis. 
D) All estimators in a regression model that are consistent are also unbiased. 
A) The standard error of a regression,   , is not an unbiased estimator for   , the standard deviation of the error, u, in a multiple regression model. 
B) In time series regressions, OLS estimators are always unbiased. 
C) Almost all economists agree that unbiasedness is a minimal requirement for an estimator in regression analysis. 
D) All estimators in a regression model that are consistent are also unbiased. A

Question 2

In the multiple regression model   , if x1 is correlated with u but the other independent variables are uncorrelated with u, then all of the OLS estimators are generally consistent.

Accepted Answer

A) True 
 B)False  False

Question 3

If the model   ​ satisfies the first four Gauss-Markov assumptions, then v has:

Accepted Answer

A) ​a zero mean and is correlated with only x1. 
B) ​a zero mean and is correlated with x1 and x2. 
C) ​a zero mean and is correlated with only x2. 
D) a ​zero mean and is uncorrelated with x1 and x2. 
A) ​a zero mean and is correlated with only x1. 
B) ​a zero mean and is correlated with x1 and x2. 
C) ​a zero mean and is correlated with only x2. 
D) a ​zero mean and is uncorrelated with x1 and x2. D

Question 4

If   1 = Cov(x1,x2) / Var(x1) where x1 and x2 are two independent variables in a regression equation, which of the following statements is true?

Accepted Answer

A) If x2 has a positive partial effect on the dependent variable, and   1 > 0, then the inconsistency in the simple regression slope estimator associated with x1 is negative. 
B) If x2 has a positive partial effect on the dependent variable, and   1 > 0, then the inconsistency in the simple regression slope estimator associated with x1 is positive. 
C) If x1 has a positive partial effect on the dependent variable, and   1 > 0, then the inconsistency in the simple regression slope estimator associated with x1 is negative. 
D) If x1 has a positive partial effect on the dependent variable, and   1 > 0, then the inconsistency in the simple regression slope estimator associated with x1 is positive. 
A) If x2 has a positive partial effect on the dependent variable, and   1 > 0, then the inconsistency in the simple regression slope estimator associated with x1 is negative. 
B) If x2 has a positive partial effect on the dependent variable, and   1 > 0, then the inconsistency in the simple regression slope estimator associated with x1 is positive. 
C) If x1 has a positive partial effect on the dependent variable, and   1 > 0, then the inconsistency in the simple regression slope estimator associated with x1 is negative. 
D) If x1 has a positive partial effect on the dependent variable, and   1 > 0, then the inconsistency in the simple regression slope estimator associated with x1 is positive.

Question 5

A useful rule of thumb is that standard errors are expected to shrink at a rate that is the inverse of the:

Accepted Answer

A) square root of the sample size. 
B) product of the sample size and the number of parameters in the model. 
C) square of the sample size. 
D) sum of the sample size and the number of parameters in the model. 
A) square root of the sample size. 
B) product of the sample size and the number of parameters in the model. 
C) square of the sample size. 
D) sum of the sample size and the number of parameters in the model.

Question 6

The F statistic is also referred to as the score statistic.

Accepted Answer

A) True 
 B)False

Question 7

The n-R-squared statistic also refers to the:

Accepted Answer

A) F statistic. 
B) t statistic. 
C) z statistic. 
D) LM statistic. 
A) F statistic. 
B) t statistic. 
C) z statistic. 
D) LM statistic.

Question 8

If   j, an unbiased estimator of   j, is also a consistent estimator of   j, then when the sample size tends to infinity:

Accepted Answer

A) the distribution of   j collapses to a single value of zero. 
B) the distribution of   j diverges away from a single value of zero. 
C) the distribution of   j collapses to the single point   j. 
D) the distribution of   j diverges away from   j. 
A) the distribution of   j collapses to a single value of zero. 
B) the distribution of   j diverges away from a single value of zero. 
C) the distribution of   j collapses to the single point   j. 
D) the distribution of   j diverges away from   j.

Question 9

In a multiple regression model, the OLS estimator is consistent if:

Accepted Answer

A) there is no correlation between the dependent variables and the error term. 
B) there is a perfect correlation between the dependent variables and the error term. 
C) the sample size is less than the number of parameters in the model. 
D) there is no correlation between the independent variables and the error term. 
A) there is no correlation between the dependent variables and the error term. 
B) there is a perfect correlation between the dependent variables and the error term. 
C) the sample size is less than the number of parameters in the model. 
D) there is no correlation between the independent variables and the error term.

Question 10

If   j, an unbiased estimator of   j, is consistent, then the:

Accepted Answer

A) distribution of   j becomes more and more loosely distributed around   j as the sample size grows. 
B) distribution of   j becomes more and more tightly distributed around   j as the sample size grows. 
C) distribution of   j tends toward a standard normal distribution as the sample size grows. 
D) distribution of   j remains unaffected as the sample size grows. 
A) distribution of   j becomes more and more loosely distributed around   j as the sample size grows. 
B) distribution of   j becomes more and more tightly distributed around   j as the sample size grows. 
C) distribution of   j tends toward a standard normal distribution as the sample size grows. 
D) distribution of   j remains unaffected as the sample size grows.

Question 11

If   j is an OLS estimator of a regression coefficient associated with one of the explanatory variables, such that j = 1, 2, …., n, asymptotic standard error of   j will refer to the:

Accepted Answer

A) estimated variance of   j when the error term is normally distributed. 
B) estimated variance of a given coefficient when the error term is not normally distributed. 
C) square root of the estimated variance of   j when the error term is normally distributed. 
D) square root of the estimated variance of   j when the error term is not normally distributed. 
A) estimated variance of   j when the error term is normally distributed. 
B) estimated variance of a given coefficient when the error term is not normally distributed. 
C) square root of the estimated variance of   j when the error term is normally distributed. 
D) square root of the estimated variance of   j when the error term is not normally distributed.

Question 12

If Cov(z,x) ≠ 0, then z and x are correlated.​

Accepted Answer

A) True 
 B)False

Question 13

When the error term is not normally distributed, then   ​ is sometimes called the:

Accepted Answer

A) ​asymptotic standard error. 
B) ​asymptotic t statistic. 
C) ​asymptotic confidence interval. 
D) ​asymptotic normality. 
A) ​asymptotic standard error. 
B) ​asymptotic t statistic. 
C) ​asymptotic confidence interval. 
D) ​asymptotic normality.

Question 14

Even if the error terms in a regression equation, u1, u2, …, un, are not normally distributed, the estimated coefficients can be normally distributed.

Accepted Answer

A) True 
 B)False

Question 15

A normally distributed random variable is symmetrically distributed about its mean, it can take on any positive or negative value (but with zero probability), and more than 95% of the area under the distribution is within two standard deviations.

Accepted Answer

A) True 
 B)False

Question 16

Which of the following statements is true?

Accepted Answer

A) In large samples there are not many discrepancies between the outcomes of the F test and the LM test. 
B) Degrees of freedom of the unrestricted model are necessary for using the LM test. 
C) The LM test can be used to test hypotheses with single restrictions only and provides inefficient results for multiple restrictions. 
D) The LM statistic is derived on the basis of the normality assumption. 
A) In large samples there are not many discrepancies between the outcomes of the F test and the LM test. 
B) Degrees of freedom of the unrestricted model are necessary for using the LM test. 
C) The LM test can be used to test hypotheses with single restrictions only and provides inefficient results for multiple restrictions. 
D) The LM statistic is derived on the basis of the normality assumption.

Question 17

If variance of an independent variable in a regression model, say x1, is greater than 0, or Var(x1) > 0, the inconsistency in   1 (estimator associated with x1) is negative, if x1 and the error term are positively related.

Accepted Answer

A) True 
 B)False

Question 18

The LM statistic follows a:

Accepted Answer

A) t distribution. 
B) f distribution. 
C)    distribution. 
D) binomial distribution. 
A) t distribution. 
B) f distribution. 
C)    distribution. 
D) binomial distribution.

Question 19

If the error term is correlated with any of the independent variables, the OLS estimators are:

Accepted Answer

A) biased and consistent. 
B) unbiased and inconsistent. 
C) biased and inconsistent. 
D) unbiased and consistent. 
A) biased and consistent. 
B) unbiased and inconsistent. 
C) biased and inconsistent. 
D) unbiased and consistent.

Question 20

An auxiliary regression refers to a regression that is used:

Accepted Answer

A) when the dependent variables are qualitative in nature. 
B) when the independent variables are qualitative in nature. 
C) to compute a test statistic but whose coefficients are not of direct interest. 
D) to compute coefficients which are of direct interest in the analysis. 
A) when the dependent variables are qualitative in nature. 
B) when the independent variables are qualitative in nature. 
C) to compute a test statistic but whose coefficients are not of direct interest. 
D) to compute coefficients which are of direct interest in the analysis.

Which of the following statements is true?

In the multiple regression model , if x₁ is correlated with u but the other independent variables are uncorrelated with u, then all of the OLS estimators are generally consistent.

If the model satisfies the first four Gauss-Markov assumptions, then v has:

If ₁ = Cov(x₁,x₂) / Var(x₁) where x₁ and x₂ are two independent variables in a regression equation, which of the following statements is true?

A useful rule of thumb is that standard errors are expected to shrink at a rate that is the inverse of the:

The F statistic is also referred to as the score statistic.

The n-R-squared statistic also refers to the:

If _j, an unbiased estimator of _j, is also a consistent estimator of _j, then when the sample size tends to infinity:

In a multiple regression model, the OLS estimator is consistent if:

If _j, an unbiased estimator of _j, is consistent, then the:

If _j is an OLS estimator of a regression coefficient associated with one of the explanatory variables, such that j = 1, 2, …., n, asymptotic standard error of _j will refer to the:

If Cov(z,x) ≠ 0, then z and x are correlated.

When the error term is not normally distributed, then is sometimes called the:

Even if the error terms in a regression equation, u₁, u₂, …, u_n, are not normally distributed, the estimated coefficients can be normally distributed.

A normally distributed random variable is symmetrically distributed about its mean, it can take on any positive or negative value (but with zero probability), and more than 95% of the area under the distribution is within two standard deviations.

Which of the following statements is true?

If variance of an independent variable in a regression model, say x₁, is greater than 0, or Var(x₁) > 0, the inconsistency in ₁ (estimator associated with x₁) is negative, if x₁ and the error term are positively related.

The LM statistic follows a:

If the error term is correlated with any of the independent variables, the OLS estimators are:

An auxiliary regression refers to a regression that is used:

The Nature of Econometrics and Economic Data

The Simple Regression Model

Multiple Regression Analysis Estimation

Multiple Regression Analysis Inference

Multiple Regression Analysis Further Issues

Multiple Regression Analysis With Qualitative Information

Heteroskedasticity

More on Specification and Data Issues

Basic Regression Analysis With Time Series Data

Further Issues in Using Ols With Time Sries Data

Serial Correlation and Heteroskedasticity in Time Series Regressions

Pooling Cross Sections Across Time Simple Panel Data Methods

Advanced Panel Data Methods

Instrumental Variables Estimation and Two Strage Least Squares

Simultaneous Equations Models

Limited Dependent Variable Models and Sample Selection Correctons

Advanced Time Series Topics

Carrying Out an Empirical Project

Filters

Exam 5: Multiple Regression Analysis Ols Asymptotics

Which of the following statements is true?

In the multiple regression model , if x1 is correlated with u but the other independent variables are uncorrelated with u, then all of the OLS estimators are generally consistent.

If the model ​ satisfies the first four Gauss-Markov assumptions, then v has:

If 1 = Cov(x1,x2) / Var(x1) where x1 and x2 are two independent variables in a regression equation, which of the following statements is true?

A useful rule of thumb is that standard errors are expected to shrink at a rate that is the inverse of the:

The F statistic is also referred to as the score statistic.

The n-R-squared statistic also refers to the:

If j, an unbiased estimator of j, is also a consistent estimator of j, then when the sample size tends to infinity:

In a multiple regression model, the OLS estimator is consistent if:

If j, an unbiased estimator of j, is consistent, then the:

If j is an OLS estimator of a regression coefficient associated with one of the explanatory variables, such that j = 1, 2, …., n, asymptotic standard error of j will refer to the:

If Cov(z,x) ≠ 0, then z and x are correlated.​

When the error term is not normally distributed, then ​ is sometimes called the:

Even if the error terms in a regression equation, u1, u2, …, un, are not normally distributed, the estimated coefficients can be normally distributed.

A normally distributed random variable is symmetrically distributed about its mean, it can take on any positive or negative value (but with zero probability), and more than 95% of the area under the distribution is within two standard deviations.

Which of the following statements is true?

If variance of an independent variable in a regression model, say x1, is greater than 0, or Var(x1) > 0, the inconsistency in 1 (estimator associated with x1) is negative, if x1 and the error term are positively related.

The LM statistic follows a:

If the error term is correlated with any of the independent variables, the OLS estimators are:

An auxiliary regression refers to a regression that is used:

The Nature of Econometrics and Economic Data

The Simple Regression Model

Multiple Regression Analysis Estimation

Multiple Regression Analysis Inference

Multiple Regression Analysis Further Issues

Multiple Regression Analysis With Qualitative Information

Heteroskedasticity

More on Specification and Data Issues

Basic Regression Analysis With Time Series Data

Further Issues in Using Ols With Time Sries Data

Serial Correlation and Heteroskedasticity in Time Series Regressions

Pooling Cross Sections Across Time Simple Panel Data Methods

Advanced Panel Data Methods

Instrumental Variables Estimation and Two Strage Least Squares

Simultaneous Equations Models

Limited Dependent Variable Models and Sample Selection Correctons

Advanced Time Series Topics

Carrying Out an Empirical Project

Filters

In the multiple regression model , if x₁ is correlated with u but the other independent variables are uncorrelated with u, then all of the OLS estimators are generally consistent.

If the model satisfies the first four Gauss-Markov assumptions, then v has:

If ₁ = Cov(x₁,x₂) / Var(x₁) where x₁ and x₂ are two independent variables in a regression equation, which of the following statements is true?

If _j, an unbiased estimator of _j, is also a consistent estimator of _j, then when the sample size tends to infinity:

If _j, an unbiased estimator of _j, is consistent, then the:

If _j is an OLS estimator of a regression coefficient associated with one of the explanatory variables, such that j = 1, 2, …., n, asymptotic standard error of _j will refer to the:

If Cov(z,x) ≠ 0, then z and x are correlated.

When the error term is not normally distributed, then is sometimes called the:

Even if the error terms in a regression equation, u₁, u₂, …, u_n, are not normally distributed, the estimated coefficients can be normally distributed.

If variance of an independent variable in a regression model, say x₁, is greater than 0, or Var(x₁) > 0, the inconsistency in ₁ (estimator associated with x₁) is negative, if x₁ and the error term are positively related.