102c_lecture9 - Economics 102C - Stanford University Prof....

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Program evaluation 1. Introduction Consider an individual who is faced with the problem of choosing whether to take or not a given "treatment". The type of interventions or treatments one might consider are, among others, training, schooling, military enrolment, occupational choice, labor market capital investment, choice of industrial sector, choice of marital status, investment in risky assets, etc. Assume that d i = 1 if the individual takes the treatment, and 0 otherwise. Associated to each possible alternative there is an outcome, usually an economic return such as earnings. Assume that earnings in each possible state (0,1) are given by: 1 y 0 it = X it & 0 + u 0 it (1.1) y 1 it = X it 1 + u 1 it (1.2) respectively in state 0 (no treatment) and 1(treatment). As is usual in regression analy- sis, the X it are observable and the u j it (j=0,1) are unobservable (at least to the econome- trician) characteristics a/ecting earnings. This model was originally proposed by Roy (1951) based on the principle of comparative advantages. There are two assumptions underlying this model: (a) observable characteristics X it may have a di/erent impact on earnings in di/erent regimes. Hence 1 6 = & 0 . (b) the e/ect of unobservables ( u j it ) also di/ers across regimes, because a certain ability may have a higher return in one city than in others. There are at least two questions one would like to answer in the context of program evaluation: (a) What is the e/ect of training on earnings for a randomly selected member of the population? (this is the average training e/ect, or ATE) (b) Suppose that a trainee i is observed to have post-training earnings of y 1 it . What his earnings would be had he not trained? In other words, what would his earnings have been had he not trained? Let us call these hypothetical earnings y 0 it . How can we calculate y 1 it y 0 it ± , if any? The opposite question is also interesting: suppose that an individual i who has not taken training is observed to have earnings of y 0 it . What did he miss by not training? Put it di/erently, what would his earnings have been had he 1 Note that we have assumed linearity and separability. This can be relaxed in more general settings. Economics 102C - Stanford University Prof. Luigi Pistaferri
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trained? Let us call these hypothetical earnings y 1 it . Here again, how we can calculate, if any, y 1 it y 0 it ± ? (this is the treatment on the treated e/ect, TTE). Question (b) is di¢ cult to answer for one trivial, simple reason: we never observe individual i in both states of the world. Either he trained or he did not. No individual can be contemporaneously in both states. This is the root of all program evaluation problems: a missing variable. If we have y 1 it from data on those who took training, y 0 it somewhere else. In many circumstances we have also to renounce to the idea of constructing
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This note was uploaded on 07/28/2011 for the course ECON 102C taught by Professor Pistaferri,l during the Spring '11 term at Stanford.

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102c_lecture9 - Economics 102C - Stanford University Prof....

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