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Introductory Econometrics 4th Edition by Jeffrey Wooldridge
Edition 4ISBN: 978-0324660609Introductory Econometrics 4th Edition by Jeffrey Wooldridge
Edition 4ISBN: 978-0324660609 Exercise 7
With a single explanatory variable, the equation used to obtain the between estimator is ![With a single explanatory variable, the equation used to obtain the between estimator is where the overbar represents the average over time. We can assume that E(ai) = 0 because we have included an intercept in the equation. Suppose that i. is uncorrelated with but Cov(xit, ai) = xa for all t (and i because of random sampling in the cross section). (i) Letting be the between estimator, that is, the OLS estimator using the time aver¬ages, show that where the probability limit is defined as N . [Hint: See equations] (ii) Assume further that the xit, for all t = 1, 2,T, are uncorrelated with constant variance a2. Show that plim = 1 + T ( xa 2x). (iii) If the explanatory variables are not very highly correlated across time, what does part (ii) suggest about whether the inconsistency in the between estimator is smaller when there are more time periods Equation](https://d2lvgg3v3hfg70.cloudfront.net/SM2712/11eb9ee2_f16f_b7fd_8edd_e7f259f3da19_SM2712_00.jpg)
where the overbar represents the average over time. We can assume that E(ai) = 0 because we have included an intercept in the equation. Suppose that i. is uncorrelated with![With a single explanatory variable, the equation used to obtain the between estimator is where the overbar represents the average over time. We can assume that E(ai) = 0 because we have included an intercept in the equation. Suppose that i. is uncorrelated with but Cov(xit, ai) = xa for all t (and i because of random sampling in the cross section). (i) Letting be the between estimator, that is, the OLS estimator using the time aver¬ages, show that where the probability limit is defined as N . [Hint: See equations] (ii) Assume further that the xit, for all t = 1, 2,T, are uncorrelated with constant variance a2. Show that plim = 1 + T ( xa 2x). (iii) If the explanatory variables are not very highly correlated across time, what does part (ii) suggest about whether the inconsistency in the between estimator is smaller when there are more time periods Equation](https://d2lvgg3v3hfg70.cloudfront.net/SM2712/11eb9ee2_f16f_b7fe_8edd_19467f1fe86d_SM2712_11.jpg)
but Cov(xit, ai) = xa for all t (and i because of random sampling in the cross section).
(i) Letting![With a single explanatory variable, the equation used to obtain the between estimator is where the overbar represents the average over time. We can assume that E(ai) = 0 because we have included an intercept in the equation. Suppose that i. is uncorrelated with but Cov(xit, ai) = xa for all t (and i because of random sampling in the cross section). (i) Letting be the between estimator, that is, the OLS estimator using the time aver¬ages, show that where the probability limit is defined as N . [Hint: See equations] (ii) Assume further that the xit, for all t = 1, 2,T, are uncorrelated with constant variance a2. Show that plim = 1 + T ( xa 2x). (iii) If the explanatory variables are not very highly correlated across time, what does part (ii) suggest about whether the inconsistency in the between estimator is smaller when there are more time periods Equation](https://d2lvgg3v3hfg70.cloudfront.net/SM2712/11eb9ee2_f16f_b7ff_8edd_a91c40b7fb6e_SM2712_11.jpg)
be the between estimator, that is, the OLS estimator using the time aver¬ages, show that ![With a single explanatory variable, the equation used to obtain the between estimator is where the overbar represents the average over time. We can assume that E(ai) = 0 because we have included an intercept in the equation. Suppose that i. is uncorrelated with but Cov(xit, ai) = xa for all t (and i because of random sampling in the cross section). (i) Letting be the between estimator, that is, the OLS estimator using the time aver¬ages, show that where the probability limit is defined as N . [Hint: See equations] (ii) Assume further that the xit, for all t = 1, 2,T, are uncorrelated with constant variance a2. Show that plim = 1 + T ( xa 2x). (iii) If the explanatory variables are not very highly correlated across time, what does part (ii) suggest about whether the inconsistency in the between estimator is smaller when there are more time periods Equation](https://d2lvgg3v3hfg70.cloudfront.net/SM2712/11eb9ee2_f16f_b800_8edd_ddd6f0f08be8_SM2712_11.jpg)
where the probability limit is defined as N . [Hint: See equations]
(ii) Assume further that the xit, for all t = 1, 2,T, are uncorrelated with constant variance a2. Show that plim![With a single explanatory variable, the equation used to obtain the between estimator is where the overbar represents the average over time. We can assume that E(ai) = 0 because we have included an intercept in the equation. Suppose that i. is uncorrelated with but Cov(xit, ai) = xa for all t (and i because of random sampling in the cross section). (i) Letting be the between estimator, that is, the OLS estimator using the time aver¬ages, show that where the probability limit is defined as N . [Hint: See equations] (ii) Assume further that the xit, for all t = 1, 2,T, are uncorrelated with constant variance a2. Show that plim = 1 + T ( xa 2x). (iii) If the explanatory variables are not very highly correlated across time, what does part (ii) suggest about whether the inconsistency in the between estimator is smaller when there are more time periods Equation](https://d2lvgg3v3hfg70.cloudfront.net/SM2712/11eb9ee2_f16f_de11_8edd_6d0f8e26b53a_SM2712_11.jpg)
= 1 + T ( xa 2x).
(iii) If the explanatory variables are not very highly correlated across time, what does part (ii) suggest about whether the inconsistency in the between estimator is smaller when there are more time periods
Equation![With a single explanatory variable, the equation used to obtain the between estimator is where the overbar represents the average over time. We can assume that E(ai) = 0 because we have included an intercept in the equation. Suppose that i. is uncorrelated with but Cov(xit, ai) = xa for all t (and i because of random sampling in the cross section). (i) Letting be the between estimator, that is, the OLS estimator using the time aver¬ages, show that where the probability limit is defined as N . [Hint: See equations] (ii) Assume further that the xit, for all t = 1, 2,T, are uncorrelated with constant variance a2. Show that plim = 1 + T ( xa 2x). (iii) If the explanatory variables are not very highly correlated across time, what does part (ii) suggest about whether the inconsistency in the between estimator is smaller when there are more time periods Equation](https://d2lvgg3v3hfg70.cloudfront.net/SM2712/11eb9ee2_f16f_de12_8edd_0366fc856370_SM2712_11.jpg)
![With a single explanatory variable, the equation used to obtain the between estimator is where the overbar represents the average over time. We can assume that E(ai) = 0 because we have included an intercept in the equation. Suppose that i. is uncorrelated with but Cov(xit, ai) = xa for all t (and i because of random sampling in the cross section). (i) Letting be the between estimator, that is, the OLS estimator using the time aver¬ages, show that where the probability limit is defined as N . [Hint: See equations] (ii) Assume further that the xit, for all t = 1, 2,T, are uncorrelated with constant variance a2. Show that plim = 1 + T ( xa 2x). (iii) If the explanatory variables are not very highly correlated across time, what does part (ii) suggest about whether the inconsistency in the between estimator is smaller when there are more time periods Equation](https://d2lvgg3v3hfg70.cloudfront.net/SM2712/11eb9ee2_f16f_de13_8edd_9b5226748405_SM2712_11.jpg)
where the overbar represents the average over time. We can assume that E(ai) = 0 because we have included an intercept in the equation. Suppose that i. is uncorrelated with
but Cov(xit, ai) = xa for all t (and i because of random sampling in the cross section).(i) Letting
be the between estimator, that is, the OLS estimator using the time aver¬ages, show that where the probability limit is defined as N . [Hint: See equations]
(ii) Assume further that the xit, for all t = 1, 2,T, are uncorrelated with constant variance a2. Show that plim
= 1 + T ( xa 2x).(iii) If the explanatory variables are not very highly correlated across time, what does part (ii) suggest about whether the inconsistency in the between estimator is smaller when there are more time periods
Equation
Explanation
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Consider the single explanatory variable...
Introductory Econometrics 4th Edition by Jeffrey Wooldridge
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