## Test Bank For Introductory Econometrics A Modern Approach 6th Edition by Jeffrey M. Wooldridge

**CHAPTER NO 5**

1. Which of the following statements is true?

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.

*ANSWER: *a

*RATIONALE: *FEEDBACK: The standard error of a regression is not an unbiased estimator for the standard deviation of the error in a multiple regression model.

*POINTS: *1

*DIFFICULTY: *Moderate

*NATIONAL STANDARDS: *United States – BUSPROG: Analytic

*TOPICS: *Consistency

*KEYWORDS: *Bloom’s: Knowledge

2. If _{j}, an unbiased estimator of _{j}, is consistent, then the:

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.

*ANSWER: *b

*RATIONALE: *FEEDBACK: If _{j}, an unbiased estimator of _{j}, is consistent, then the distribution of _{j} becomes more and more tightly distributed around _{j} as the sample size grows.

*POINTS: *1

*DIFFICULTY: *Moderate

*NATIONAL STANDARDS: *United States – BUSPROG: Analytic

*TOPICS: *Consistency

*KEYWORDS: *Bloom’s: Knowledge

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

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}.

*ANSWER: *c

*RATIONALE: *FEEDBACK: If _{j}, an unbiased estimator of _{j}, is also a consistent estimator of _{j}, then when the sample size tends to infinity the distribution of _{j} collapses to the single point _{j}.

*POINTS: *1

*DIFFICULTY: *Easy

*NATIONAL STANDARDS: *United States – BUSPROG: Analytic

*TOPICS: *Consistency

*KEYWORDS: *Bloom’s: Knowledge

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

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.

*ANSWER: *d

*RATIONALE: *FEEDBACK: In a multiple regression model, the OLS estimator is consistent if there is no correlation between the explanatory variables and the error term.

*POINTS: *1

*DIFFICULTY: *Moderate

*NATIONAL STANDARDS: *United States – BUSPROG: Analytic

*TOPICS: *Consistency

*KEYWORDS: *Bloom’s: Knowledge

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

a. biased and consistent.

b. unbiased and inconsistent.

c. biased and inconsistent.

d. unbiased and consistent.

*ANSWER: *c

*RATIONALE: *FEEDBACK: If the error term is correlated with any of the independent variables, then the OLS estimators are biased and inconsistent.

*POINTS: *1

*DIFFICULTY: *Easy

*NATIONAL STANDARDS: *United States – BUSPROG: Analytic

*TOPICS: *Consistency

*KEYWORDS: *Bloom’s: Knowledge

6. If _{1} = Cov(*x*_{1}*,x*_{2}) / Var(*x*_{1}) where *x*_{1} and *x*_{2} are two independent variables in a regression equation, which of the following statements is true?

a. If *x*_{2} has a positive partial effect on the dependent variable, and _{1} > 0, then the inconsistency in the simple regression slope estimator associated with *x*_{1} is negative.

b. If *x*_{2} has a positive partial effect on the dependent variable, and _{1} > 0, then the inconsistency in the simple regression slope estimator associated with *x*_{1} is positive.

c. If *x*_{1} has a positive partial effect on the dependent variable, and _{1} > 0, then the inconsistency in the simple regression slope estimator associated with *x*_{1} is negative.

d. If *x*_{1} has a positive partial effect on the dependent variable, and _{1} > 0, then the inconsistency in the simple regression slope estimator associated with *x*_{1} is positive.

*ANSWER: *b

*RATIONALE: *FEEDBACK: Given that _{1} = Cov(*x*_{1},*x*_{2})/Var(*x*_{1}) where *x*_{1} and *x*_{2} are two independent variables in a regression equation, if *x*_{2} has a positive partial effect on the dependent variable, and _{1} > 0, then the inconsistency in the simple regression slope estimator associated with *x*_{1} is positive.

*POINTS: *1

*DIFFICULTY: *Moderate

*NATIONAL STANDARDS: *United States – BUSPROG: Analytic

*TOPICS: *Consistency

*KEYWORDS: *Bloom’s: Knowledge

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

a. a zero mean and is correlated with only *x*_{1}.

b. a zero mean and is correlated with *x*_{1} and *x*_{2}.

c. a zero mean and is correlated with only *x*_{2}.

d. a zero mean and is uncorrelated with *x*_{1} and *x*_{2}.

*ANSWER: *d

*RATIONALE: *FEEDBACK: If the model satisfies the first four Gauss-Markov assumptions, then *v* has a zero mean and is uncorrelated with *x*_{1} and *x*_{2}.

*POINTS: *1

*DIFFICULTY: *Moderate

*NATIONAL STANDARDS: *United States – BUSPROG: Analytic

*TOPICS: *Consistency

*KEYWORDS: *Bloom’s: Knowledge

8. If OLS estimators satisfy asymptotic normality, it implies that:

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 .

*ANSWER: *a

*RATIONALE: *Feedback: If OLS estimators satisfy asymptotic normality, it implies that they are approximately normally distributed in large enough sample sizes.

*POINTS: *1

*DIFFICULTY: *Easy

*NATIONAL STANDARDS: *United States – BUSPROG: Analytic

*TOPICS: *Asymptotic Normality and Large Sample Inference

*KEYWORDS: *Bloom’s: Knowledge

9. In a regression model, if variance of the dependent variable, *y*, conditional on an explanatory variable, *x*, or Var(*y*|*x*), is not constant, _____.

a. the *t* statistics are invalid and confidence intervals are valid for small sample sizes

b. the *t* statistics are valid and confidence intervals are invalid for small sample sizes

c. the *t* statistics and the confidence intervals are valid no matter how large the sample size is

d. the *t* statistics and the confidence intervals are both invalid no matter how large the sample size is

*ANSWER: *d

*RATIONALE: *FEEDBACK: If variance of the dependent variable conditional on an explanatory variable is not a constant the usual *t* statistics and the confidence intervals are both invalid no matter how large the sample size is.

*POINTS: *1

*DIFFICULTY: *Moderate

*NATIONAL STANDARDS: *United States – BUSPROG: Analytic

*TOPICS: *Asymptotic Normality and Large Sample Inference

*KEYWORDS: *Bloom’s: Knowledge

10. 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:

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.

*ANSWER: *d

*RATIONALE: *FEEDBACK: Asymptotic standard error refers to the square root of the estimated variance of _{j} when the error term is not normally distributed.

*POINTS: *1

*DIFFICULTY: *Easy

*NATIONAL STANDARDS: *United States – BUSPROG: Analytic

*TOPICS: *Asymptotic Normality and Large Sample Inference

*KEYWORDS: *Bloom’s: Knowledge

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