slides_Ch2_W[1]

Consider 29 yi o 1 xi ui and notice that changing

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Unformatted text preview: e unit of measurement of the dVar and eVars change? Melissa Tartari (Yale) Econometrics 42 / 93 Algebraic Properties: Unit of Measurement I How do the OLS estimates change when the unit of measurement of the dVar and eVars change? They do so in an entirely expected way! Melissa Tartari (Yale) Econometrics 42 / 93 Algebraic Properties: Unit of Measurement I How do the OLS estimates change when the unit of measurement of the dVar and eVars change? They do so in an entirely expected way! Consider (2.9) yi = βo + β1 xi + ui , and notice that changing the unit of yi is like multiplying it by some constant number c , call the new dVar yi0 = cyi . Melissa Tartari (Yale) Econometrics 42 / 93 Algebraic Properties: Unit of Measurement I How do the OLS estimates change when the unit of measurement of the dVar and eVars change? They do so in an entirely expected way! Consider (2.9) yi = βo + β1 xi + ui , and notice that changing the unit of yi is like multiplying it by some constant number c , call the new dVar yi0 = cyi . Multiply each side of (2.9) by c cyi = c βo + c β1 xi + cui or equivalently 0 0 yi0 = βo + β1 xi + ui0 Melissa Tartari (Yale) where Econometrics 0 0 βo = c βo & β1 = c β1 42 / 93 Algebraic Properties: Unit of Measurement I How do the OLS estimates change when the unit of measurement of the dVar and eVars change? They do so in an entirely expected way! Consider (2.9) yi = βo + β1 xi + ui , and notice that changing the unit of yi is like multiplying it by some constant number c , call the new dVar yi0 = cyi . Multiply each side of (2.9) by c cyi = c βo + c β1 xi + cui or equivalently 0 0 0 0 yi0 = βo + β1 xi + ui0 where βo = c βo & β1 = c β1 ˆˆ Recall that βo , β1 where the estimates obtained when regressing yi ˆ0 ˆ0 on xi . Thus, if we regress y 0 on xi we obtain estimates β , β s.t. i ˆ0 βo Melissa Tartari (Yale) o ˆ = c βo & Econometrics ˆ0 β1 1 ˆ = c β1 42 / 93 Algebraic Properties: Unit of Measurement II What happe...
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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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