Book Econometric Analysis of Cross Section and Panel Data By Wooldridge - Chapter 1 pot

... limit theory. See, for example, Quah (19 94), Pesaran and Smith (19 95), Kao (19 99), and Phillips and Moon (19 99). 1. 2.2 Asymptotic Analysis Throughout this book we focus on asymptotic properties, ... advanced settings. For example, in Chapters 7, 10 , and 11 we will see that as- suming fixed regressors or fixed instrumental variables in panel data models imposes often unr...

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... two-equation population model y 1 ¼ g 10 þ g 11 x 11 þ g 12 x 12 þ a 1 x 13 þ a 2 x 14 þ u 1 ð7:54Þ y 2 ¼ g 20 þ g 21 x 21 þ a 1 x 22 þ a 2 x 23 þ g 24 x 24 þ u 2 ð7:55Þ where we have imposed cross ... consistency of b à under Assumptions SGLS .1 and SGLS.2 by writing b à ¼ b þ N 1 X N i 1 X 0 i W 1 X i ! 1 N 1 X N i 1 X 0 i W 1 u i ! ð7:30Þ B...

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... T 1 0 B B B B @ 1 C C C C A 11 :16 Þ where x o it is defined in expression (11 .13 ). Note that Z i has T 1 rows to correspond Chapter 11 304 11 More Topics in Linear Unobserved E¤ects Models This chapter ... equation (11 . 21) . Papke estimates equation (11 . 21) by 2SLS, using Dy i; tÀ2 as an instrument for Dy i; t 1 ; because of the lags used, equation (11 . 21) can be estim...

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... mean z 1 d 1 þ a 1 y 2 þ y 1 v 2 ¼ z 1 d 1 þ a 1 y 2 þðh 1 =t 2 2 Þðy 2 À zd 2 Þ and variance t 2 1 ¼ s 2 1 Àðh 2 1 =t 2 2 Þ, where s 2 1 ¼ Varðu 1 Þ, t 2 2 ¼ Varðv 2 Þ, and h 1 ¼ Covðu 1 ; v 2 Þ. ... y 2 þ 1is max½0; z 1 d 1 þ a 1 ðy 2 þ 1 þu 1 Àmax½0; z 1 d 1 þ a 1 y 2 þ u 1  Averaging this expression across the distribution of u 1 gi...

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... Eðy 1 jx; y 2 ¼ 1 depend on the vector of interest, b 1 ? First, under Assumption 17 .1 and equation (17 .19 ), Eðy 1 jx; v 2 Þ¼x 1 b 1 þ Eðu 1 jx; v 2 Þ¼x 1 b 1 þ Eðu 1 jv 2 Þ¼x 1 b 1 þ g 1 v 2 17 : 21 where ... equation, write y 1 ¼ z 1 d 1 þ a 1 y 2 þ g 1 v 3 þ e 1 17 :39Þ where e 1 1 u 1 À Eðu 1 jv 3 Þ. Since ðe 1 ; v 3 Þ is independent...

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... jx 1 ; x 2 Þ¼b 0 þ b 1 x 1 þ b 2 x 2 þ b 3 x 1 x 2 and define z 1 1 x 1 x 2 . Then, from Property CE.3, Eðy jx 1 ; x 2 ; z 1 Þ¼b 0 þ b 1 x 1 þ b 2 x 2 þ b 3 z 1 ð2:46Þ The right-hand side of equation ... parameters. Problems 2 .1. Given random variables y, x 1 , and x 2 , consider the model Eðy jx 1 ; x 2 Þ¼b 0 þ b 1 x 1 þ b 2 x 2 þ b 3 x 2 2 þ b 4 x 1 x 2...

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... derivations, we will write relationships 1 to 4 as o p 1 þo p 1 ¼o p 1 ,O p 1 þ O p 1 ¼O p 1 ,O p 1 ÁO p 1 ¼O p 1 , and o p 1 ÁO p 1 ¼o p 1 , respectively. Be- Chapter 336 consistency certainly ... 3.2: If w N ¼ o p 1 , x N ¼ o p 1 , y N ¼ O p 1 , and z N ¼ O p 1 , then (1) w N þ x N ¼ o p 1 ; (2) y N þ z N ¼ O p 1 ; (3) y N z N ¼ O p 1 ; and (4) x N z N ¼ o p 1...

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... zero and is uncorrelated with each of the regressors: EðuÞ¼0; Covðx j ; uÞ¼0; j ¼ 1; 2; ; K ð4:2Þ Eðy jx 1 ; x 2 Þ¼b 0 þ b 1 x 1 þ b 2 x 2 þ b 3 x 1 x 2 þ b 4 x 2 2 Let m 1 1 Eðx 1 Þ and m 2 1 Eðx 2 Þ ... the dis- tributions of y and y 1 are identical, then ja 1 j < 1. This is the regression-to-the-mean phenomenon in a dynamic setting. {Hint: Show that a 1 ¼...

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... ! N 1 X N i 1 z 0 i z i ! 1 N 1 X N i 1 z 0 i x i ! 2 4 3 5 1 Á N 1 X N i 1 x 0 i z i ! N 1 X N i 1 z 0 i z i ! 1 N 1 X N i 1 z 0 i u i ! and, using Assumptions 2SLS .1 and 2SLS.2, ... indicator of q, written as q 1 ¼ d 1 q þ a 1 , d 1 0 0, where a 1 has zero mean and is uncorrelated with each of x j , q,andv. In addition, z 1 ; z 2 ; ; z M is a...

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... is y 1 ¼ z 1 d 1 þ a 1 y 2 þ u 1 ð6:9Þ where z 1 is 1 Â L 1 (including a constant), d 1 is L 1 Â 1, and u 1 is the unobserved dis- turbance. The set of all exogenous variables is denoted by the 1 ... over time? Chapter 613 8 y 1 ¼ z 1 d 1 þ y 2 a 1 þ u 1 ð6: 21 where z 1 is 1 Â L 1 and y 2 is 1 Â G 1 . The 1 Â L vector of all exogeno...

Ngày tải lên: 06/07/2014, 08:20