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Introduction to Econometrics 3rd Edition by James Stock, James Stock
النسخة 3الرقم المعياري الدولي: 978-9352863501Introduction to Econometrics 3rd Edition by James Stock, James Stock
النسخة 3الرقم المعياري الدولي: 978-9352863501 تمرين 13
Consider the regression model in matrix form, Y = X + W + U , where X is an n × k 1 matrix of regressors and W is an n × k 2 matrix of regressors. Then, as shown in Exercise 18.17, the OLS estimator ß can be expressed ![Consider the regression model in matrix form, Y = X + W + U , where X is an n × k 1 matrix of regressors and W is an n × k 2 matrix of regressors. Then, as shown in Exercise 18.17, the OLS estimator ß can be expressed Now let be the binary variable fixed effects estimator computed by estimating Equation (10.11) by OLS and let be the de-meaning fixed effects estimator computed by estimating Equation (10.14) by OLS, in which the entity-specific sample means have been subtracted from X and Y. Use the expression for given above to prove that . [ Hint : Write Equation (10.11) using a full set of fixed effects, D 1 i , D 2 i , …, Dn i and no constant term. Include all of the fixed effects in W. Write out the matrix M W X.]](https://d2lvgg3v3hfg70.cloudfront.net/SM2686/11eb9b5b_3f62_a30f_bf3e_27afa5a28a59_SM2686_11.jpg)
Now let![Consider the regression model in matrix form, Y = X + W + U , where X is an n × k 1 matrix of regressors and W is an n × k 2 matrix of regressors. Then, as shown in Exercise 18.17, the OLS estimator ß can be expressed Now let be the binary variable fixed effects estimator computed by estimating Equation (10.11) by OLS and let be the de-meaning fixed effects estimator computed by estimating Equation (10.14) by OLS, in which the entity-specific sample means have been subtracted from X and Y. Use the expression for given above to prove that . [ Hint : Write Equation (10.11) using a full set of fixed effects, D 1 i , D 2 i , …, Dn i and no constant term. Include all of the fixed effects in W. Write out the matrix M W X.]](https://d2lvgg3v3hfg70.cloudfront.net/SM2686/11eb9b5b_3f62_ca20_bf3e_a16d2ff18b18_SM2686_11.jpg)
be the "binary variable" fixed effects estimator computed by estimating Equation (10.11) by OLS and let ![Consider the regression model in matrix form, Y = X + W + U , where X is an n × k 1 matrix of regressors and W is an n × k 2 matrix of regressors. Then, as shown in Exercise 18.17, the OLS estimator ß can be expressed Now let be the binary variable fixed effects estimator computed by estimating Equation (10.11) by OLS and let be the de-meaning fixed effects estimator computed by estimating Equation (10.14) by OLS, in which the entity-specific sample means have been subtracted from X and Y. Use the expression for given above to prove that . [ Hint : Write Equation (10.11) using a full set of fixed effects, D 1 i , D 2 i , …, Dn i and no constant term. Include all of the fixed effects in W. Write out the matrix M W X.]](https://d2lvgg3v3hfg70.cloudfront.net/SM2686/11eb9b5b_3f62_ca21_bf3e_1bcae5ba72fa_SM2686_11.jpg)
be the "de-meaning" fixed effects estimator computed by estimating Equation (10.14) by OLS, in which the entity-specific sample means have been subtracted from X and Y. Use the expression for ![Consider the regression model in matrix form, Y = X + W + U , where X is an n × k 1 matrix of regressors and W is an n × k 2 matrix of regressors. Then, as shown in Exercise 18.17, the OLS estimator ß can be expressed Now let be the binary variable fixed effects estimator computed by estimating Equation (10.11) by OLS and let be the de-meaning fixed effects estimator computed by estimating Equation (10.14) by OLS, in which the entity-specific sample means have been subtracted from X and Y. Use the expression for given above to prove that . [ Hint : Write Equation (10.11) using a full set of fixed effects, D 1 i , D 2 i , …, Dn i and no constant term. Include all of the fixed effects in W. Write out the matrix M W X.]](https://d2lvgg3v3hfg70.cloudfront.net/SM2686/11eb9b5b_3f62_ca22_bf3e_f132bd65f2b4_SM2686_11.jpg)
given above to prove that ![Consider the regression model in matrix form, Y = X + W + U , where X is an n × k 1 matrix of regressors and W is an n × k 2 matrix of regressors. Then, as shown in Exercise 18.17, the OLS estimator ß can be expressed Now let be the binary variable fixed effects estimator computed by estimating Equation (10.11) by OLS and let be the de-meaning fixed effects estimator computed by estimating Equation (10.14) by OLS, in which the entity-specific sample means have been subtracted from X and Y. Use the expression for given above to prove that . [ Hint : Write Equation (10.11) using a full set of fixed effects, D 1 i , D 2 i , …, Dn i and no constant term. Include all of the fixed effects in W. Write out the matrix M W X.]](https://d2lvgg3v3hfg70.cloudfront.net/SM2686/11eb9b5b_3f62_f133_bf3e_9fad5287946a_SM2686_11.jpg)
. [ Hint : Write Equation (10.11) using a full set of fixed effects, D 1 i , D 2 i , …, Dn i and no constant term. Include all of the fixed effects in W. Write out the matrix M W X.]
Now let
be the "binary variable" fixed effects estimator computed by estimating Equation (10.11) by OLS and let be the "de-meaning" fixed effects estimator computed by estimating Equation (10.14) by OLS, in which the entity-specific sample means have been subtracted from X and Y. Use the expression for given above to prove that . [ Hint : Write Equation (10.11) using a full set of fixed effects, D 1 i , D 2 i , …, Dn i and no constant term. Include all of the fixed effects in W. Write out the matrix M W X.]التوضيح
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موثّق
The given regression equation is 
For a ...
Introduction to Econometrics 3rd Edition by James Stock, James Stock
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