Deck 11: Random Regressors and Moment Based Estimation

Question 1

If the assumption E(e)= 0 and cov(x,e)= 0 holds,what are the implications of least squares estimators?

A)still BLUE for all sample sizes
B)consistent and normally distributed in very large sample sizes
C)unbiased,but not BLUE for small samples
D)inconsistent and parameter estimates do not converge to true values regardless of sample size.

Answer 1

B

Question 2

When an exogenous instrument is used,IV estimators are

A)consistent and approximately normally distributed in large samples
B)unbiased and BLUE in all sample sizes
C)consistent if z is normally distributed
D)normally distributed in all sample sizes and consistent in large sample sizes

Answer 2

A

Question 3

If you are estimating y = $\beta$ ₁ + $\beta$ ₂x + e
And realize x and y are both random variables,what condition must be true for simple regression estimators to be BLUE?

A)the data have been collected via random sampling
B)the data are time series data
C)e is normally distributed
D)x is normally distributed

Answer 3

the data have been collected via random sampling

Question 4

What does it mean for a variable to be endogenous?

A)it is determined within the system or model
B)it is measured after all other variables are observed
C)it is determined outside the system or model
D)it is measured before all other variables are observed

Question 5

If L is the number of exogenous instruments and B is the number of endogenous regressors in the model,when L = B the model is

A)just identified
B)over identified
C)under identified
D)precisely identified

Question 6

Which of the following is not a desirable characteristic in an instrumental variable,z,to be used in IV/2SLS estimation?

A)cov (z,e)= 0
B)z is unrelated to y
C)high correlation between z & x
D)normally distributed z

Question 7

What should you conclude if you get an F-statistic of 8.3 when testing the strength of an instrument?

A)it depends on the degrees of freedom and critical value of F
B)do not reject H₀;conclude that the instrument is weak and should not be used in 2SLS.
C)reject H₀;conclude the instrument is strong and proceed with 2SLS
D)do not reject H₀;conclude the instrument is strong and use it in 2SLS

Question 8

In 2SLS,how should the strength of an instrument be measured?

A)an F-test on the first stage regression equation
B)the p-value of the instrument's coefficient in the second stage regression
C)the R² in the first stage regression equation
D)an F-test on the second stage regression equation

Question 9

If L is the number of exogenous instruments and B is the number of endogenous regressors in the model,when L > B the model is

A)just identified
B)over identified
C)under identified
D)perfectly identified

Question 10

If,for estimator it is true that p then is

A)efficient
B)consistent
C)accurate
D)independent

Question 11

Which of the following is not a common cause of endogeneity?

A)measurement error
B)simultaneous equations
C)omitted variables
D)continuous variables

Question 12

Which assumption must be true when E(e|x)= 0?

A)E(e)= 0 and var(e)= $\sigma$ ²
B)e = 0
C)E(e)= 0 and cov(x,e)= 0.
D)E(e)= e|x if x≠0

Question 13

If you reject the null hypothesis when performing a Hausman test,what should you conclude?

A)at least one of the explanatory variables is endogenous
B)there are no endogenous variables
C)the 2SLS estimation has corrected the endogeneity in the initial model
D)the 2SLS second stage equation still has endogenous variables

Question 14

If the assumption that cov(x,e)= 0 is not true,what are the implications of least squares estimators?

A)still BLUE for all sample sizes
B)consistent and normally distributed in very large sample sizes
C)unbiased,but not BLUE for small samples
D)inconsistent;parameter estimates do not converge to true values regardless of sample size.

Question 15

What is the 4^th moment of random variable x?

A)E(x)⁴
B) $\Sigma$ x / 4
C)E(x⁴)
D)(E(x⁴)-x⁴)/N

Question 16

What is the null hypothesis for a Hausman test for endogeneity?

A)cov (z,x)> 0
B)cov(x,e)> 0
C)cov(x,e)= 0
D)e is normally distributed

Question 17

If L is the number of exogenous instruments and B is the number of endogenous regressors in the model,when L < B the model is

A)just identified
B)over identified
C)under identified
D)perfectly identified

Question 18

Which of the following statements is true regarding var when estimated by IV using z as an instrument for x?

A)instrumental variable estimation leads to larger variance of estimates compared to OLS
B)instrumental variable estimation leads to smaller variance estimates compared to OLS
C)the variance of the IV estimates can be larger or smaller than OLS,depending on r²_xz
D)there is no way to know which estimator leads to estimates with a larger variance,it depends on the data

Question 19

What is the null hypothesis when performing an F-test to test the strength of an instrument?

A)the instrument is weak,with no $\theta$ different from 0.
B)it is a strong instrument with all $\theta$ significantly different from 0.
C)the instrument is sufficiently strong with at least 1 $\theta$ significantly different from 0.
D)the instrument is weak with all $\theta$ different from 0.