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Consider the variance of the OLS slope estimator in the following simple regression model, where the sample average of the equals zero (x = 0): Yt = Bo+Birt + Ut The OLS estimator ₁ of 31 can be written as follows, where SST₂ = 2² only if z = 0: B₁ =B₁+ SST₂¹ ££ Itut The variance of B₁ (conditional on 2), accounts for the serial correlation in u, where ² = Var(u) and E(+₁+j) = Cov(uu++j) = ³²: Var(8₁)= 02 +2x SSTXX SST 15-1 Epiztzt-j Suppose the errors in a regression model have AR(1) serial correlation, meaning p³0. Suppose på> 0 for all j. Which of the following can explain the conditions under which OLS standard errors will overstate the true sampling variation? Check all that apply. The independent variables in regression models are often positively correlated over time. The term #tät+j> 0 for most pairs t and t+j. The independent variables in regression models are negatively correlated over time. The term #txt+j<0 for most pairs t and t+j.

Consider the variance of the OLS slope estimator in the following simple regression model, where the sample average of the equals zero (x = 0): Yt = Bo+Birt + Ut The OLS estimator ₁ of 31 can be written as follows, where SST₂ = 2² only if z = 0: B₁ =B₁+ SST₂¹ ££ Itut The variance of B₁ (conditional on 2), accounts for the serial correlation in u, where ² = Var(u) and E(+₁+j) = Cov(uu++j) = ³²: Var(8₁)= 02 +2x SSTXX SST 15-1 Epiztzt-j Suppose the errors in a regression model have AR(1) serial correlation, meaning p³0. Suppose på> 0 for all j. Which of the following can explain the conditions under which OLS standard errors will overstate the true sampling variation? Check all that apply. The independent variables in regression models are often positively correlated over time. The term #tät+j> 0 for most pairs t and t+j. The independent variables in regression models are negatively correlated over time. The term #txt+j<0 for most pairs t and t+j.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Consider the variance of the OLS slope estimator in the following simple regression model, where the sample average of the at equals zero (x = 0): Yt Bo + B1xt + Ut The OLS estimator B₁ of ₁ can be written as follows, where SSTT= B₁ =B₁ + SST₂¹ XtUt The variance of ₁ (conditional on ï), accounts for the serial correlation in u, where ² = Var(u) and E(u+U++j) = Cov(U+U++j) = pio²: Var(B1) SSTX * only if x = 0: 2 n-1 n-t Σp³ætæt-j SST=1j=1 Suppose the errors in a regression model have AR(1) serial correlation, meaning p¹+0. Suppose på> 0 for all j. Which of the following can explain the conditions under which OLS standard errors will overstate the true sampling variation? Check all that apply. O The independent variables in regression models are often positively correlated over time. O The term ætät+j> 0 for most pairs t and t+j. The independent variables in regression models are negatively correlated over time. O The term ætät+j < 0 for most pairs t and t+j.
Transcribed Image Text:Consider the variance of the OLS slope estimator in the following simple regression model, where the sample average of the at equals zero (x = 0): Yt Bo + B1xt + Ut The OLS estimator B₁ of ₁ can be written as follows, where SSTT= B₁ =B₁ + SST₂¹ XtUt The variance of ₁ (conditional on ï), accounts for the serial correlation in u, where ² = Var(u) and E(u+U++j) = Cov(U+U++j) = pio²: Var(B1) SSTX * only if x = 0: 2 n-1 n-t Σp³ætæt-j SST=1j=1 Suppose the errors in a regression model have AR(1) serial correlation, meaning p¹+0. Suppose på> 0 for all j. Which of the following can explain the conditions under which OLS standard errors will overstate the true sampling variation? Check all that apply. O The independent variables in regression models are often positively correlated over time. O The term ætät+j> 0 for most pairs t and t+j. The independent variables in regression models are negatively correlated over time. O The term ætät+j < 0 for most pairs t and t+j.
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