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How can we do that first we need a random sample from

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Unformatted text preview: at? First we need a random sample from the population: f(yi , xi ) ji = 1, ..., ng. Observe that we can write yi = βo + β1 xi + ui for each i (2.9) How do we use this data? There exist several estimation procedures: Method of Moments Melissa Tartari (Yale) Econometrics 20 / 93 Three Estimation Methods Having established the key assumption under which ( βo , β1 ) are identi…able - ZCMA - we are now in the business of estimating these unknown parameters. How can we do that? First we need a random sample from the population: f(yi , xi ) ji = 1, ..., ng. Observe that we can write yi = βo + β1 xi + ui for each i (2.9) How do we use this data? There exist several estimation procedures: Method of Moments Least Squares Melissa Tartari (Yale) Econometrics 20 / 93 Three Estimation Methods Having established the key assumption under which ( βo , β1 ) are identi…able - ZCMA - we are now in the business of estimating these unknown parameters. How can we do that? First we need a random sample from the population: f(yi , xi ) ji = 1, ..., ng. Observe that we can write yi = βo + β1 xi + ui for each i (2.9) How do we use this data? There exist several estimation procedures: Method of Moments Least Squares Maximum Likelihood Melissa Tartari (Yale) Econometrics 20 / 93 The MoM: the Basics Observe that because of E [u jx ] = 0 we also have that E [ux ] = E [E [ux jx ]] = E [xE [u jx ]] = E [x 0] = 0. Melissa Tartari (Yale) Econometrics 21 / 93 The MoM: the Basics Observe that because of E [u jx ] = 0 we also have that E [ux ] = E [E [ux jx ]] = E [xE [u jx ]] = E [x 0] = 0. Thus, we have two moment conditions : E [u ] = 0 ) E [xu ] = 0 Melissa Tartari (Yale) E [y βo β1 x ] = 0 E [x (y βo β1 x )] = 0 Econometrics (2.12 & 2.13) 21 / 93 The MoM: the Basics Observe that because of E [u jx ] = 0 we also have that E [ux ] = E [E [ux jx ]] = E [xE [u jx ]] = E [x 0] = 0. Thus, we have two moment conditions : E [u ] = 0 ) E [xu ] = 0 E [y βo β1 x ] = 0 E [x (y βo β1 x )] = 0 (2.1...
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This note was uploaded on 02/13/2014 for the course ECON 350 taught by Professor Donaldbrown during the Fall '10 term at Yale.

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