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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 Neglected Heterogeneity in Tobit Model ： ウィキペディア英語版 Neglected Heterogeneity in Tobit Model In a Tobit model 〔Tobin, James (1958). "Estimation of relationships for limited dependent variables". Econometrica 26 (1): pp24–36.〕 ''y=y *1 (y * > 0 )'' where ''y * = xβ + u'' and ''u| x'' ~ N (0, ''σ''2), if a heterogeneity component ''v'' is neglected, i.e. the true model should be ''y * = xβ + γv + u'' , the neglected heterogeneity issue 〔For the details about testing the heterogeneity issue, refer to Andrew Chesher (1984), “Testing for Neglected Heterogeneity”, Econometrica 4, pp. 865-872〕 will arise. For instance, if ''y=y *'' is the profit of a firm, ''y'' is the observed profit of the firm, and ''x'' only includes the variables about demand side, then the model neglects the variables about the supply side ''v'' , which should be included in the true model. In this example, the neglected heterogeneity issue arises. If the neglected heterogeneity satisfies the independent condition 〔Wooldridge, J. (2002): Econometric Analysis of Cross Section and Panel Data, MIT Press, Cambridge, Mass, pp 529.〕 ''v| x'' ~ N (0, ''s''2) and ''v'' is independent with ''u'' , for instance ''v'' is the price of the raw materials which are unrelated with the demand side features, the true model can be rewritten as: ''y=y *1 (y * > 0 )'' , where ''$y^$ * = x\beta + \tilde , $\backslash tilde$ | x ~ ♦ (0, γ2 s2 + σ2 )'' Then, if run the Tobit model of ''y'' on ''x'' , the estimate for ''β'' will still be consistent but the error variance estimate will be for ''γ2 s2 + σ2'' rather than ''σ2'' . In this simple case, the estimation Average Partial Effect (APE)〔Wooldridge, J. (2002): Econometric Analysis of Cross Section and Panel Data, MIT Press, Cambridge, Mass, pp 22.〕 ''∂E (y'' | ''x ) / ∂xi'' can be computed based on those estimates. If ''v'' is correlated with ''x'',〔Wooldridge, J. (2002): Econometric Analysis of Cross Section and Panel Data, MIT Press, Cambridge, Mass, pp 531-533.〕 for instance, ''v'' denotes the advertisement cost which has strong interactive relationship with the demand side, then estimation through the Tobit model without considering the neglected heterogeneity will cause an endogeneity issue implicitly. Now, rewrite the model as: ''y * = x1β1 + x2β2 + γv + u'' ; ''x2 = x1δ1 + z δ2 + η'' . where η is a normal error and only correlated only with ''v'' . Then ''v'' can be represented as ''v = θη + ε'' where ε is independent with ''u'' . Then, the model can be rewritten as: ''y * = x1β1 + x2β2 + γθη + γε + u '' ; ''x2 = x1δ1 + z δ2 + η'' . or more succinctly ''y * = x1β1 + x2β2 + γθη + ũ ''; ''x2 = x1δ1 + z δ2 + η'' . where $\backslash tilde\; \backslash mid\; x,\; z\; \backslash sim\; (0,\; \backslash tilde\; ^2)$ . Then the coefficients ''β, δ , γθ'' and $\backslash tilde\; ^2$ can be consistently estimated by a 2-stage procedure: (1) 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「Neglected Heterogeneity in Tobit Model」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.