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Multiple treatments, like multivalued treatments, generalize the binary treatment effects framework. But rather than focusing on a treatment effect that can take on different values, the focus now is on different types of treatment. One example could be a job training program, where different types of job training are offered to the participants. The case of multiple treatments is relatively difficult to handle, as it can require additional functional form restrictions, especially when addressing the counterfactual or potential outcomes framework.〔 Wooldridge, J. (2005): Econometric Analysis of Cross Section and Panel Data, MIT Press, Cambridge, Mass.〕 Nevertheless, the general instrumental variable framework used to analyze binary treatment effects has been extended to allow for multiple treatments. 〔 Wooldridge, J. (2000): Instrumental Variables Estimation of the Average Treatment Effect in the Correlated Random Coefficient Model. Mimeo, Michigan State University Department of Economics.〕 There are different approaches available to analyze multiple treatment effects. One can think of treatment effects within this framework as the difference in the counterfactual outcomes that would have been observed if the agent faced different general choice sets, with multinomial choices being a natural way to analyze multiple treatments.〔 Heckman, J. J., and E. J. Vytlacil (2007): Econometric Evaluation of Social Programs, Part II: Using the Marginal Treatment Effect to Organize Alternative Econometric Estimators to Evaluate Social Programs, and to Forecast the Effects in New Environments. Handbook of Econometrics, Vol 6, ed. by J. J. Heckman and E. E. Leamer. North Holland.〕 More formally, assume there are ''J'' options available and the value to the agent of choosing option ''j'' is ''Rj (Zj )=vj (Zj ) -ϵj'' where ''εj'' is some unobserved random shock. Then the agent will choose alternative ''j'' such that ''Rj'' ≥ ''Rk'' for all ''k≠j''. There is a potential outcome associated with each possible state, ''Yj'' = ''μj(Xj, Uj)'', where ''X'' is a vector of observered characteristics and ''U'' is a vector of unobserved characteristics. The observed outcome is ''Y= Dj Yj'' where ''Dj'' is an indicator that equals 1 when the treatment equals ''j'' and 0 when it does not equal ''j''. The parameters of interest are the treatment effects ''Yj - Yk'' for pairs ''k'' and ''j''. Other frameworks focus less on the choice dynamics and consider a random coefficient setting for the different treatment options, or use dummy variables for the different possible treatments. For instance, when thinking about two possible treatments that are not mutually exclusive, four indicator variables can fully specify the different treatment options. 〔 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「Multiple treatments」の詳細全文を読む スポンサード リンク
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