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# Consider the mean of wages conditional on education

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Unformatted text preview: ivalently write this model as w = G (ed ) + U = βo + β1 ed + E [abil jed ] + U Melissa Tartari (Yale) Econometrics where U s.t. E [U jed ] = 16 / 93 Identi…cation: an Example - part I Suppose that Y = wages , X = education, and U = ability , and an economic model tells us that: w = g (ed ) + abil = ( βo + β1 ed ) + abil . Consider the mean of wages conditional on education, call it G (ed ): G (ed ) E [w jed ] = βo + β1 ed + E [abil jed ] = g (ed ) + E [abil jed ] We can equivalently write this model as w = G (ed ) + U = βo + β1 ed + E [abil jed ] + U by 2.5 where U s.t. E [U jed ] = The ZCMA says that E [abil jed ] = E [abil ] = 0 which is equivalent to G (ed ) = g (ed ). Unless this assumption holds the co-variation of wages and education will not identify β1 because mean ability will not “stay put” when education changes, rather: ∂E [w jed ]/∂ed = β1 + ∂E [abil jed ]/∂ed . Melissa Tartari (Yale) Econometrics 16 / 93 Identi…cation: an Example - part II Consider the following 3 questions: Melissa Tartari (Yale) Econometrics 17 / 93 Identi…cation: an Example - part II Consider the following 3 questions: Q.1: by how much would the wage of persons i change if her education was increased by one year? Melissa Tartari (Yale) Econometrics 17 / 93 Identi…cation: an Example - part II Consider the following 3 questions: Q.1: by how much would the wage of persons i change if her education was increased by one year? Q.2: by how much would the average wage in the population change if the education of each persons was increased by one year? Melissa Tartari (Yale) Econometrics 17 / 93 Identi…cation: an Example - part II Consider the following 3 questions: Q.1: by how much would the wage of persons i change if her education was increased by one year? Q.2: by how much would the average wage in the population change if the education of each persons was increased by one year? Q.3: suppose that each individual in the current population is replaced with an individual with one more year of education (chosen at random among those w...
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