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

The Cauchy-Schwartz inequality implies that the asymptotic variance of ​   is:

Accepted Answer

A) ​greater than   . 
B) ​less than or equal to   . 
C)  ​equal to
  . 
D)  ​less than
  . 
A) ​greater than   . 
B) ​less than or equal to   . 
C)  ​equal to
  . 
D)  ​less than
  . B

Question 3

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. A

Question 4

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 5

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

Accepted Answer

A) True 
 B)False

Question 6

The LM statistic requires estimation of the unrestricted model only.

Accepted Answer

A) True 
 B)False

Question 7

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 8

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 9

Which of the following statements is true under the Gauss-Markov assumptions?

Accepted Answer

A) Among a certain class of estimators, OLS estimators are best linear unbiased, but are asymptotically inefficient. 
B) Among a certain class of estimators, OLS estimators are biased but asymptotically efficient. 
C)  Among a certain class of estimators, OLS estimators are best linear unbiased and asymptotically efficient. 
D)  The LM test is independent of the Gauss-Markov assumptions. 
A) Among a certain class of estimators, OLS estimators are best linear unbiased, but are asymptotically inefficient. 
B) Among a certain class of estimators, OLS estimators are biased but asymptotically efficient. 
C)  Among a certain class of estimators, OLS estimators are best linear unbiased and asymptotically efficient. 
D)  The LM test is independent of the Gauss-Markov assumptions.

Question 10

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

Question 11

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 12

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 13

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 14

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

Accepted Answer

A) True 
 B)False

Question 15

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 16

If OLS estimators satisfy asymptotic normality, it implies that:

Accepted Answer

A) they are approximately normally distributed in large enough sample sizes. 
B) they are approximately normally distributed in samples with less than 10 observations. 
C)  they have a constant mean equal to zero and variance equal to
  2. 
D)  they have a constant mean equal to one and variance equal to
  . 
A) they are approximately normally distributed in large enough sample sizes. 
B) they are approximately normally distributed in samples with less than 10 observations. 
C)  they have a constant mean equal to zero and variance equal to
  2. 
D)  they have a constant mean equal to one and variance equal to
  .

Question 17

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 18

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.

Question 19

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 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?

The Cauchy-Schwartz inequality implies that the asymptotic variance of is:

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

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

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

The LM statistic requires estimation of the unrestricted model only.

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

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

Which of the following statements is true under the Gauss-Markov assumptions?

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.

The LM statistic follows a:

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

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:

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

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

If OLS estimators satisfy asymptotic normality, it implies that:

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

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.

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: Binary or Dummy Variables

Heteroskedasticity

More on Specification and Data Problems

Basic Regression Analysis With Time Series Data

Further Issues in Using Ols With Time Series 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 Stage Least Squares

Simultaneous Equations Models

Limited Dependent Variable Models and Sample Selection Corrections

Advanced Time Series Topics

Carrying Out an Empirical Project

Filters

Exam 5: Multiple Regression Analysis: Ols Asymptotics

Which of the following statements is true?

The Cauchy-Schwartz inequality implies that the asymptotic variance of ​ is:

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

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

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

The LM statistic requires estimation of the unrestricted model only.

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

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

Which of the following statements is true under the Gauss-Markov assumptions?

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.

The LM statistic follows a:

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

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:

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

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

If OLS estimators satisfy asymptotic normality, it implies that:

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

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.

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: Binary or Dummy Variables

Heteroskedasticity

More on Specification and Data Problems

Basic Regression Analysis With Time Series Data

Further Issues in Using Ols With Time Series 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 Stage Least Squares

Simultaneous Equations Models

Limited Dependent Variable Models and Sample Selection Corrections

Advanced Time Series Topics

Carrying Out an Empirical Project

Filters

The Cauchy-Schwartz inequality implies that the asymptotic variance of is:

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

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

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

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 _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:

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

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