slides_Ch2_W[1]

6 entail in the wage example if u is ability and

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Unformatted text preview: the randomness of the assignment), those individuals with high education are on average as able as those with low education; that is, in the “perfect” experiment E [U jX ] = 0 holds by construction and needs not be assumed; Melissa Tartari (Yale) Econometrics 10 / 93 Identi…cation: the ZCMA II What does (2.6) entail in the wage example if U is ability and drive and X is education? It means that if we could observe ability and drive we would see that more educated individuals have on average the same ability and drive that those individuals that are less educated. The ZCMA reproduces what we may term the “perfect” experiment : imagine being able to assign education randomly to individuals; in particular, the assignment is independent of ability and drive; then, by construction (that is, by the randomness of the assignment), those individuals with high education are on average as able as those with low education; that is, in the “perfect” experiment E [U jX ] = 0 holds by construction and needs not be assumed; outside of the “perfect” experiment E [U jX ] = 0 does not necessarily hold and, if stated, it is an assumption. Melissa Tartari (Yale) Econometrics 10 / 93 Identi…cation: the Regression Function In the SLRM we call E [y jx ] the regression function. Melissa Tartari (Yale) Econometrics 11 / 93 Identi…cation: the Regression Function In the SLRM we call E [y jx ] the regression function. Assumption 2.6. implies the regression function is: E [Y jX ] = βo + β1 E [X jX ] + E [U jX ] = βo + β1 X Melissa Tartari (Yale) Econometrics (2.8) (1) 11 / 93 Identi…cation: the Regression Function In the SLRM we call E [y jx ] the regression function. Assumption 2.6. implies the regression function is: E [Y jX ] = βo + β1 E [X jX ] + E [U jX ] = βo + β1 X (2.8) (1) For any given value x of X , the distribution of Y is centered about E [Y jX = x ] (see …gure 2.1): we can write Y as made up of two components, Y = E [Y jX ] + U Melissa Tartari (Yale) Econometrics 11 / 93 Identi…cation: Food for Thought I Recall the end of Chapter 1 slides, we claimed that:...
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