Chapter 5

Which of the following statements is true?

• The standard error of a regression, σ^ , is not an unbiased estimator for σ , the standard deviation of the error, u, in a multiple regression model.

• In time series regressions, OLS estimators are always unbiased.

• Almost all economists agree that unbiasedness is a minimal requirement for an estimator in regression analysis.

• All estimators in a regression model that are consistent are also unbiased.

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

• distribution of ^β j becomes more and more loosely distributed around β j as the sample size grows.

• distribution of ^β j becomes more and more tightly distributed around β j as the sample size grows.

• distribution of ^β j tends toward a standard normal distribution as the sample size grows.

• distribution of ^β j remains unaffected as the sample size grows.

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

• the distribution of ^β j collapses to a single value of zero.

• the distribution of ^β j diverges away from a single value of zero.

• the distribution of ^β j collapses to the single point β j.

• the distribution of ^β j diverges away from β j.

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

• there is no correlation between the dependent variables and the error term.

• there is a perfect correlation between the dependent variables and the error term.

• the sample size is less than the number of parameters in the model.

• there is no correlation between the independent variables and the error term.

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

• biased and consistent.

• unbiased and inconsistent.

• biased and inconsistent.

• unbiased and consistent.

If δ1 = 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 x2 has a positive partial effect on the dependent variable, and δ1 > 0, then the inconsistency in the simple regression slope estimator associated with x1 is negative.

• If x2 has a positive partial effect on the dependent variable, and δ1 > 0, then the inconsistency in the simple regression slope estimator associated with x1 is positive.

• If x1 has a positive partial effect on the dependent variable, and δ1 > 0, then the inconsistency in the simple regression slope estimator associated with x1 is negative.

• If x1 has a positive partial effect on the dependent variable, and δ1 > 0, then the inconsistency in the simple regression slope estimator associated with x1 is positive.

If OLS estimators satisfy asymptotic normality, it implies that:

• they are approximately normally distributed in large enough sample sizes.

• they are approximately normally distributed in samples with less than 10 observations.

• they have a constant mean equal to zero and variance equal to σ2.

• they have a constant mean equal to one and variance equal to σ.

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

• the t statistics are invalid and confidence intervals are valid for small sample sizes

• the t statistics are valid and confidence intervals are invalid for small sample sizes

• the t statistics confidence intervals are valid no matter how large the sample size is

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

If ^β 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 ^β j will refer to the:

• estimated variance of ^β j when the error term is normally distributed.

• estimated variance of a given coefficient when the error term is not normally distributed.

• square root of the estimated variance of ^β j when the error term is normally distributed.

• square root of the estimated variance of ^β j when the error term is not normally distributed.

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

• square root of the sample size.

• product of the sample size and the number of parameters in the model.

• square of the sample size.

• sum of the sample size and the number of parameters in the model.