Book Econometric Analysis of Cross Section and Panel Data By Wooldridge - Chapter 2 pdf

... b 2 x 2 þ b 3 x 2 2 2: 3Þ Eðy jx 1 ; x 2 Þ¼b 0 þ b 1 x 1 þ b 2 x 2 þ b 3 x 1 x 2 2: 4Þ Eðy jx 1 ; x 2 Þ¼exp½b 0 þ b 1 logðx 1 Þþb 2 x 2 ; y b 0; x 1 > 0 2: 5Þ The model in equation (2. 2) is ... 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 a. Fi...

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... z 2 (for example, edu- cation, experience, and amount of job training) and unobserved attributes u 2 ,we write the wage o¤er function as w o ðhÞ¼g 2 h þ z 2 d 2 þ u 2 ð8 :2 Again, for given z 2 and ... u i2 Þ 0 , and write W À1 ¼ s 11 s 12 s 12 s 22  a. Find EðZ 0 i W À1 u i Þ and show that it is not necessarily zero under the orthogonality conditions Eðz 0...

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... variance s and covariances of the elements of v i . Under Assumption RE.1a, Eðc i u it Þ¼0, t ¼ 1; 2; ; T, and so Eðv 2 it Þ¼Eðc 2 i Þþ2Eðc i u it ÞþEðu 2 it Þ¼s 2 c þ s 2 u where s 2 c ¼ Eðc 2 i Þ. ... Eðc 2 i Þ¼s 2 c Therefore, under assumptions RE.1, (10 .28 ), and (10 .29 ), W takes the special form W ¼ Eðv i v 0 i Þ¼ s 2 c þ s 2 u s 2 c ÁÁÁ s 2 c s 2...

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... scalar function of x and y. 13.5. In the context of CMLE, consider a reparameterization of the kind in Section 12. 6 .2: f ¼ gðyÞ, where the Jacobian of g, GðyÞ, is continuous and nonsingular for ... is continuous on Y ÂG and that y o and g o are identified. Asymptotic normality of the two-step MLE follow s directly from the results on two-step M-estimation in Chapter 12....

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... Review of Economic Studies 47, 22 5 23 8. Chamberlain, G. (19 82) , ‘‘Multivariate Regression Models for Panel Data, ’’ Journal of Econometrics 18, 5–46. Chamberlain, G. (1984), ‘ Panel Data, ’’ in Handbook ... Consistency of Maximum Likelihood Estimation Despite Misspecification of Distribution,’’ Econometrica 51, 22 5 22 8. Ruud, P. (1984), ‘‘Tests of Specification in Econome...

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... cross section analysis the asymptotics is as the number of observations, denoted N throughout this book, tends to infinity. Usually what is meant by this statement is obvious. For panel data analysis, ... Pesaran and Smith (1995), Kao (1999), and Phillips and Moon (1999). 1 .2. 2 Asymptotic Analysis Throughout this book we focus on asymptotic properties, as opposed to...

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... square root of the appropriate diagonal ele- ment of ^ VV N =N. The asymptotic standard errors can be loosely thought of as estimating the standard deviations of the elements of ^ yy N , and they ... ¼ ^ yy 1 = ^ yy 2 be an estimator of g ¼ y 1 =y 2 . a. Show that plim ^ gg ¼ g. b. Find Avarð ^ ggÞ in terms of y and Avarð ^ yyÞ using the delta method. c. If, for a sample...

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... zero and is uncorrelated with each of the regressors: EðuÞ¼0; Covðx j ; uÞ¼0; j ¼ 1; 2; ; K ð4 :2 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 ... Linear Model and OLS Estimation 53 II LINEAR MODELS In this part we begin our econometric analysis of linear models for cross section and panel data. In Chapter...

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... ð5 :28 Þ where x 1 is 1 Â K 1 and x 2 is 1 Â K 2 , and interest lies in testing the K 2 restrictions H 0 : b 2 ¼ 0 against H 1 : b 2 0 0 ð5 :29 Þ Both x 1 and x 2 can contain endogenous and exogenous variables. Let ... ! À1 N À1 X N i¼1 z 0 i u i ! and, using Assumptions 2SLS.1 and 2SLS .2, apply the law of large numbers to each term along with Slutsky’s theorem. 5 ....

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... jxÞ¼0 and Eðu 2 jxÞ¼s 2 . b. Show that, under the additional assumption (6 .27 ), E½ðu 2 i À s 2 Þ 2 ðh i À m h Þ 0 ðh i À m h Þ ¼ h 2 E½ðh i À m h Þ 0 ðh i À m h Þ where h 2 ¼ E½ðu 2 À s 2 Þ 2 . c. ... that Avarð ^ aa 1 Þ¼Avarð ~ aa 1 Þþb 2 3 Avarðx 2 Þ¼Avarð ~ aa 1 Þþb 2 3 ðs 2 2 =NÞ where a 1 ¼ b 1 þ b 3 m 2 , ~ aa 1 is the estimator of a 1 if we knew m...

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