AskSia
Plus
1. The assumptions needed for the OLS estimator to be consistent are:
(A)Linear...
Aug 5, 2024
Solution
a
The assumptions needed for the OLS estimator to be consistent are: Linearity, No Perfect Collinearity, and Zero Conditional Mean
b
In small samples, the assumptions needed for the OLS estimator to be BLUE (Best Linear Unbiased Estimator) include: Homoskedasticity, No Serial Correlation, and Normality
c
The false claim regarding the problem of trending regressors is: Both of the approaches in (A) and (B) yield the same R2
d
The false statement regarding random walk processes is: Random walk processes are weakly dependent
e
The test used for the testing of AR(q) serial correlation in the errors is: Breusch-Godfrey test
Answer
(A), (A), (D), (C), (C)
Key Concept
Assumptions for OLS consistency and BLUE, trending regressors, random walk processes, and AR(q) serial correlation tests
Explanation
The assumptions for OLS consistency include Linearity, No Perfect Collinearity, and Zero Conditional Mean. For OLS to be BLUE in small samples, Homoskedasticity, No Serial Correlation, and Normality are required. The false claim about trending regressors is that both approaches yield the same R2. Random walk processes are not weakly dependent. The Breusch-Godfrey test is used for AR(q) serial correlation.
Sure, let's address the questions one by one.
Question 6
Question:
Consider running Feasible-GLS (i.e. Cochrane-Orcutt), where serial correlation in the error term is AR(1) (i.e. ut=ρut−1+et). We have estimated the value of ρ to be -0.23. Which one of the following specifications is correct?
(A) yt−0.77yt−1=β0+β1(xt−0.77xt−1)+et.
(B) yt+0.77yt−1=β0+β1(xt+0.77xt−1)+et.
(C) yt−0.23yt−1=β0+β1(xt−0.23xt−1)+et.
(D) yt+0.23yt−1=β0+β1(xt+0.23xt−1)+et.
Question 7
Question:
Regressing two highly-persistent time series may lead to which of the following:
(A) Misleadingly high t-statistics.
(B) Misleadingly high R-squared.
(C) Serially-correlated residuals.
(D) All of the above.
Solution
a
Cochrane-Orcutt Transformation: The Cochrane-Orcutt method transforms the original regression model to correct for AR(1) serial correlation. The transformation involves subtracting ρ times the lagged values from both sides of the equation
b
Given ρ=−0.23: The correct transformation would be yt−(−0.23)yt−1=β0+β1(xt−(−0.23)xt−1)+et
c
Simplification: Simplifying the equation, we get yt+0.23yt−1=β0+β1(xt+0.23xt−1)+et
Answer
(D) yt+0.23yt−1=β0+β1(xt+0.23xt−1)+et
Key Concept
Cochrane-Orcutt Transformation
Explanation
The Cochrane-Orcutt method corrects for AR(1) serial correlation by transforming the regression model using the estimated ρ. Given ρ=−0.23, the correct transformation adds 0.23 times the lagged values to both sides of the equation.
Solution
a
Spurious Regression: Regressing two highly-persistent (non-stationary) time series can lead to spurious regression results
b
High t-statistics: The t-statistics can be misleadingly high due to the non-stationarity
c
High R-squared: The R-squared value can also be misleadingly high, indicating a strong relationship where none exists
d
Serial Correlation: The residuals from such regressions are often serially correlated
Answer
(D) All of the above
Key Concept
Spurious Regression
Explanation
Regressing two highly-persistent time series can lead to misleadingly high t-statistics and R-squared values, as well as serially-correlated residuals, due to the non-stationary nature of the data.
Sure, let's go through each question one by one.
Question 8
Two time series yt,xt are said to be cointegrated if:
(A) yt,xt are both I(1) and the residual from yt=α+βxt+et is I(0).
(B) yt,xt are both I(0) and the residual from yt=α+βxt+et is I(0).
(C) yt,xt are both I(1) and the residual from yt=α+βxt+et is I(1).
(D) yt,xt are both I(0) and the residual from yt=α+βxt+et is I(1).
Question 9
Which of the following is a correct specification of an error correction model?
(A) Δyt=α0+γ0Δxt+δ(yt−βxt)+ut
(B) Δyt=α0+γ0Δxt+δ(yt−1−βxt−1)+ut
(C) yt=α0+γ0xt+δ(yt−βxt)+ut
(D) yt=α0+γ0xt+δ(yt−1−βxt−1)+ut
Question 10
Which of the following statements is true of spurious regressions?
(A) The OLS estimates of the population parameters are consistent.
(B) Even if the explanatory variables and the dependent variable are independent time series, the R2 can be large.
(C) Spurious regressions are limited to I(0) processes, and are not possible in case of I(1) processes.
(D) Spurious regressions are limited to I(1) processes, and are not possible in case of I(0) processes.
Solution
a
Cointegration Definition: Two time series yt and xt are cointegrated if they are both integrated of order 1, I(1), and their linear combination is integrated of order 0, I(0)
Answer
(A) yt,xt are both I(1) and the residual from yt=α+βxt+et is I(0).
Key Concept
Cointegration
Explanation
Cointegration occurs when two non-stationary time series are combined in such a way that their residual is stationary.
Solution
a
Error Correction Model: An error correction model (ECM) is specified to correct deviations from a long-term equilibrium relationship. The correct form includes the first differences of the variables and the lagged error term
Answer
(B) Δyt=α0+γ0Δxt+δ(yt−1−βxt−1)+ut
Key Concept
Error Correction Model
Explanation
An ECM includes the first differences of the variables and the lagged error term to correct for deviations from equilibrium.
Solution
a
Spurious Regressions: Spurious regressions occur when non-stationary time series are regressed on each other, leading to misleadingly high R2 values and t-statistics
Answer
(B) Even if the explanatory variables and the dependent variable are independent time series, the R2 can be large.
Key Concept
Spurious Regressions
Explanation
Spurious regressions result in high R2 values and significant t-statistics even when there is no true relationship between the variables.
© 2023 AskSia.AI all rights reserved