Consider the Following Simple Regression Model Y=β₀+ β₁x₁+ U

question 13

Multiple Choice

Consider the following simple regression model y=β₀+ β₁x₁+ u.Suppose z is an instrument for x. Which of the following statements is true?

• A)The condition Cov(z,u)= 0 can be tested statistically.
• B)The condition Cov(z,x)≠ 0 cannot be tested statistically.
• C)The instrumental variables estimator is always biased if Cov(x,u)≠0.
• D)The ordinary least squares estimator is unbiased if Cov(x,u)≠0.

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Definitions:

Consistent Estimator

A statistical property where an estimator of a parameter tends to converge to the true parameter value as the sample size increases.

Variance

A measure of variability that quantifies the spread of a set of data points around the mean.

Confidence Level

The probability or degree of certainty that a confidence interval would contain the true population parameter if the same procedure were repeated multiple times.

Confidence Interval

A range of values, derived from sample statistics, that is believed to contain the true population parameter with a specified level of confidence.