Estimation by Method of moments Number of moment condition needed Y=βo+βX1+β22+β33+…+阝×k+E k+1 parameters to estimate. Need k+1 moment conditions ■ Assumption#1 ■E(6)=0 implies e(y)-βo-β1E(X)-β2E(X2)-….kE(xX)=0 ■ Assumption#2 (eX)=0 implies E[(y-βo-β11-…-β×1]=0 Since Cova, X, =E(Ex1)-EsE(X,= E(ex,), the assumption really imply s and x are uncorrelated a Assumption #3: E(EX2)=0 Assumption #4: E(Ex3)=0 Assumption #k+1: E(ex)=0 Ka-fu Wong C2007 ECON1003: Analysis of Economic Data Lesson 11-8Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Lesson11-8 Estimation by Method of moments Number of moment condition needed Y = b0 + b1X1 + b2X2 + b3X3 + … + bkXk + e k+1 parameters to estimate. Need k+1 moment conditions. ◼ Assumption #1 ◼ E(e) = 0 implies E(y) – b0 – b1 E(x1 ) – b2 E(x2 ) - … bk E(xk )= 0 ◼ Assumption #2 ◼ E(ex1 ) =0 implies E[(y – b0 – b1x1 - … - bkxk )x1 ]=0 ◼ Since Cov(e, x1 ) = E(ex1 ) – E(e)E(x1 ) = E(ex1 ), the assumption really imply e and x are uncorrelated. ◼ Assumption #3: E(ex2 ) =0 ◼ Assumption #4: E(ex3 ) =0 ◼ … ◼ Assumption #k+1: E(exk ) =0