GMM and asset pricing model Any asset pricing model implies E(p)=E[m, (6) t+1 Equivalently E[p, -m, (6)x 1=0 or E(m. (6)R4 1-1]=0 Where x and p are typically vectors; we typically check whether a model for m can price a number of assets simultaneously So the equation is often called moment conditions Define errors as u, (6)=m,.(6)*+, The sample mean is 8(6)=2u,(b)=ErJu,(L The first stage estimate of b minimizes a quadratic form of the sample mean of the errors b,=arg min6 87(6)Wg(b) For some arbitrary matrix w(often W=l)GMM and asset pricing model • Any asset pricing model implies • Equivalently or • Where x and p are typically vectors; we typically check whether a model for m can price a number of assets simultaneously. So the equation is often called moment conditions. • Define errors as • The sample mean is • The first stage estimate of b minimizes a quadratic form of the sample mean of the errors, • • For some arbitrary matrix W (often W=I) ( ) [ ( ) ] t = t+1 t+1 E p E m b x E [ pt − mt+1( b ) xt+1] = 0 t t t t u b = m b x − p +1 +1 ( ) ( ) ∑= = = T t T ut b ET ut b T g b 1 ( ) [ ( )] 1 ( ) { } ) ˆ )' ( ˆ argmin ( ˆ b1 ˆ g T b Wg T b b = E [ mt+1( b ) Rt+1 − 1 ] = 0