Hello everyone,
I am estimating a panel fixed effect model with AR(1) disturbances using xtregar command. Indeed, the Wooldridge test for autocorrelation using xtserial command rejects the null hypothesis of no autocorrelation in the idiosyncratic error term, and the Hausman test (using xtoverid to account for heteroskedasticity and autocorrelation) rejects the RE model in favor of FE. Besides, my panel is unbalanced, with observations unequally spaced over time. So, xtregar, fe seems to be an appropriate choice.
In order to fully understand what is behind the mechanics, I read carefully the xtregar manual (the one that contains 15 pages). Although I do understand how the Cochrane-Orcutt alike transformation, which is described at the bottom of page 11, removes the AR(1) component (I did the math and found that the transformed disturbances are uncorrelated and homoskedastic), I dont't see how the transformation presented in the next section (see "The within estimator of the fixed-effects model" section, page 12) removes the fixed effect. In fact, the Cochrane-Orcutt transformation mentioned above multiply the fixed effect term by a time varying coefficient, which is equal to sqrt(1-rho^2)*(1-rho^(t_i,j - t_i,j-1))/sqrt(1-rho^(2(t_i,j - t_i,j-1))). But then I don't see how removing the within-panel means and adding back the overall mean does remove the fixed effect. I did the math but could not see how the coefficients in front of the fixed effect cancel out. Besides, what's the point of adding the overall mean since it's constant across individuals and time and that the fixed effect is constant across time within individuals ? Finally, I don't see where the alpha term in the equation written at the end of "the within estimator of the fixed-effects model" section (page 12) comes from, or put in other way, how the alpha coefficients resulting from the transformed data sum to 1.
The Baltagi, Wu (1999) reference only refers to RE estimation, not FE.
I would appreciate any help in order to understand the formulas behind the xtregar, fe command.
Thank you.
I am estimating a panel fixed effect model with AR(1) disturbances using xtregar command. Indeed, the Wooldridge test for autocorrelation using xtserial command rejects the null hypothesis of no autocorrelation in the idiosyncratic error term, and the Hausman test (using xtoverid to account for heteroskedasticity and autocorrelation) rejects the RE model in favor of FE. Besides, my panel is unbalanced, with observations unequally spaced over time. So, xtregar, fe seems to be an appropriate choice.
In order to fully understand what is behind the mechanics, I read carefully the xtregar manual (the one that contains 15 pages). Although I do understand how the Cochrane-Orcutt alike transformation, which is described at the bottom of page 11, removes the AR(1) component (I did the math and found that the transformed disturbances are uncorrelated and homoskedastic), I dont't see how the transformation presented in the next section (see "The within estimator of the fixed-effects model" section, page 12) removes the fixed effect. In fact, the Cochrane-Orcutt transformation mentioned above multiply the fixed effect term by a time varying coefficient, which is equal to sqrt(1-rho^2)*(1-rho^(t_i,j - t_i,j-1))/sqrt(1-rho^(2(t_i,j - t_i,j-1))). But then I don't see how removing the within-panel means and adding back the overall mean does remove the fixed effect. I did the math but could not see how the coefficients in front of the fixed effect cancel out. Besides, what's the point of adding the overall mean since it's constant across individuals and time and that the fixed effect is constant across time within individuals ? Finally, I don't see where the alpha term in the equation written at the end of "the within estimator of the fixed-effects model" section (page 12) comes from, or put in other way, how the alpha coefficients resulting from the transformed data sum to 1.
The Baltagi, Wu (1999) reference only refers to RE estimation, not FE.
I would appreciate any help in order to understand the formulas behind the xtregar, fe command.
Thank you.
