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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Binary response model with continuous endogenous explanatory variables ： ウィキペディア英語版 Binary response model with continuous endogenous explanatory variables Given a probit model 〔 Greene, W. H. (2003), Econometric Analysis , Prentice Hall , Upper Saddle River, NJ .〕 ''y=1(> 0 )'' where ''y * = x1 β + zδ + u, and u ~ N(0,1)'', without losing generality, ''z'' can be represented as ''z = x1 θ1 + x2 θ2 + v''. When ''u'' is correlated with ''v'', there will be an issue of endogeneity. This can be caused by omitted variables and measurement errors 〔 Fuller, Wayne A. (1987), Measurement error models, John Wiley & Sons, Inc, ISBN 0-471-86187-1〕 . There are also many cases where ''z'' is partially determined by ''y'' and endogeneity issue arises. For instance, in a model evaluating the effect of different patient features on their choice of whether going to hospital, ''y'' is the choice and ''z'' is the amount of the medicine a respondent took, then it is very intuitive that more often the respondent goes to hospital, it is more likely that she took more medicine, hence endogeneity issue arises 〔Bruce A. Rayton. (2006): “Examining the interconnection of job satisfaction and organizational commitment: an application of the bivariate probit model”, The International Journal of Human Resource Management, Vol. 17, Iss. 1.〕. When there are endogenous explanatory variables, the estimator generated by usual estimation procedure will be inconsistent, then the corresponding estimated Average Partial Effect (APE) 〔 Wooldridge, J. (2002): Econometric Analysis of Cross Section and Panel Data, MIT Press, Cambridge, Mass, pp 22.〕 will be inconsistent, too. To address this issue, there are usually two different estimation procedure to generate consistent estimators. Under the normality assumption ''v~N(0,σ2), u = ρv + ε'' must hold, where ''ρ = cov(u , v)/σ2'' and ''ε~N(0,1-ρ2 σ2)''. Then the equation for ''y *'' can be rewritten as ''y * = x1 β + zδ + ρv + ε''. This model can be consistently estimated by 2-Stage Least Square (2SLS): 1) Regress ''z'' on ''(x1, x2)'' and obtain the consistent estimator $\backslash widehat$ and the residual $\backslash hat$ ; 2) Estimate the binary response model on ''(x1, z, $\backslash hat$)'' and get the consistent estimator for the scaled coefficients ''(βρσ, δρσ, ρρσ) ≡ (β, δ, ρ)/√(1 - ρ2 σ2 );'' Then ''(y = 1│x, z)'' = Φ ( x1 $\backslash hat$ρσ + z$\backslash hat$ρσ + $\backslash hat$ρσ$\backslash hat$) . Since the APE of variable $\backslash tilde$ at ($\backslash tilde$,$\backslash tilde$) is given by Ev $(\backslash frac\; +\; z\backslash delta\_\; +\; \backslash rho\_\; v)\}$,$\backslash tilde$) ) By Law of Large Number, a consistent estimator is given as $\backslash frac$$\backslash sum\_^n$$\backslash frac\; \_\; +\; z\backslash hat\_\; +\; \backslash hat\_\; \backslash hat\_i)\}$,$\backslash tilde$) This model can also be consistently estimated by conditional Maximum Likelihood Method〔This issue can also be addressed under the Semiparametric setting, for more details, refere to: Richard W. Blundell; James L. Powell. (2004): ”Endogeneity in Semiparametric Binary Response Models”,Review of Economic Studies 71 (3), pp: 655-679〕 . Because ''P(y, z│x) = P (y│z, x) P (z| x)'' where ''P (y│x, z)'' is given by $(\backslash phi\; (\backslash frac$ and ''P(z│x)'' is given by $\backslash phi\; (\backslash frac\; )$ Then the log-likelihood function for maximization is given by: $\backslash sum\_^n$ $y\_i\; \backslash log\; (\backslash phi\; (\backslash frac\; ))$ Once the consistent estimators are obtained, APE can be calculated following the same procedure given above. All the discussion above is mainly about the probit model. When the distribution assumption is changed, the same logic still applies. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Binary response model with continuous endogenous explanatory variables」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.