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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 Heckman correction ： ウィキペディア英語版 Heckman correction The Heckman correction (the two-stage method, Heckman's lambda or the Heckit method〔Heckit: 'Heck-' from Heckman and '-it' as in probit, tobit, and logit.〕) is any of a number of related statistical methods developed by James Heckman at the University of Chicago in 1976 to 1979 which allow the researcher to correct for selection bias. Selection bias problems are endemic to applied econometric problems, which make Heckman’s original technique, and subsequent refinements by both himself and others, indispensable to applied econometricians. Heckman received the Economics Nobel Prize in 2000 for this achievement. == Method == Statistical analyses based on non-randomly selected samples can lead to erroneous conclusions and poor policy. The Heckman correction, a two-step statistical approach, offers a means of correcting for non-randomly selected samples. Heckman discussed bias from using nonrandom selected samples to estimate behavioral relationships as a specification error. He suggests a two-stage estimation method to correct the bias. The correction is easy to implement and has a firm basis in statistical theory. Heckman’s correction involves a normality assumption, provides a test for sample selection bias and formula for bias corrected model. Suppose that a researcher wants to estimate the determinants of wage offers, but has access to wage observations for only those who work. Since people who work are selected non-randomly from the population, estimating the determinants of wages from the subpopulation who work may introduce bias. The Heckman correction takes place in two stages. In the first stage, the researcher formulates a model, based on economic theory, for the probability of working. The canonical specification for this relationship is a probit regression of the form : $\backslash operatorname(\; D\; =\; 1\; |\; Z\; )\; =\; \backslash Phi(Z\backslash gamma),\backslash ,$ where ''D'' indicates employment (''D'' = 1 if the respondent is employed and ''D'' = 0 otherwise), ''Z'' is a vector of explanatory variables, $\backslash gamma$ is a vector of unknown parameters, and Φ is the cumulative distribution function of the standard normal distribution. Estimation of the model yields results that can be used to predict this employment probability for each individual. In the second stage, the researcher corrects for self-selection by incorporating a transformation of these predicted individual probabilities as an additional explanatory variable. The wage equation may be specified, : $w^$ * = X\beta + u\, where $w^$ * denotes an underlying wage offer, which is not observed if the respondent does not work. The conditional expectation of wages given the person works is then : $E\; (w\; |\; X,\; D=1)\; =\; X\backslash beta\; +\; E\; (u\; |\; X,\; D=1).\backslash ,$ Under the assumption that the error terms are jointly normal, we have : $E\; (w\; |\; X,\; D=1)\; =\; X\backslash beta\; +\; \backslash rho\backslash sigma\_u\; \backslash lambda(Z\backslash gamma),\backslash ,$ where ''ρ'' is the correlation between unobserved determinants of propensity to work $\backslash varepsilon$ and unobserved determinants of wage offers ''u'', ''σ'' ''u'' is the standard deviation of $u$, and $\backslash lambda$ is the inverse Mills ratio evaluated at $Z\backslash gamma$. This equation demonstrates Heckman's insight that sample selection can be viewed as a form of omitted-variables bias, as conditional on both ''X'' and on $\backslash lambda$ it is as if the sample is randomly selected. The wage equation can be estimated by replacing $\backslash gamma$ with Probit estimates from the first stage, constructing the $\backslash lambda$ term, and including it as an additional explanatory variable in linear regression estimation of the wage equation. Since $\backslash sigma\_u\; >\; 0$, the coefficient on $\backslash lambda$ can only be zero if $\backslash rho=0$, so testing the null that the coefficient on $\backslash lambda$ is zero is equivalent to testing for sample selectivity. Heckman's achievements have generated a large number of empirical applications in economics as well as in other social sciences. The original method has subsequently been generalized, by Heckman and by others. 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「Heckman correction」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.