Deck 5: Multiple Regression Analysis Ols Asymptotics

Question 1

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 1

A

Question 2

An auxiliary regression refers to a regression that is used:

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.

Answer 2

C

Question 3

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 3

D

Question 4

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

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 5

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

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

Which of the following statements is true?

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 7

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.

Question 8

Which of the following statements is true under 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 9

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

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

Question 10

The LM statistic follows a:

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

Question 11

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

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

Question 12

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.

Question 13

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.

Question 14

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

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

Question 15

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.

Question 16

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.

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?

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 _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.

Question 19

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.

Question 20

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.

Question 21

The LM statistic requires estimation of the unrestricted model only.

Question 22

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

Question 23

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

Question 24

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.

Question 25

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