Applying gmm Simply mapping a given problem into the very general notation Using price Elm ()xI+1-pI=0 Using returns Elm (bR+1-1=0 It is common to add instruments as well, you multiply both SIdes E,[m21(b)R1]=1 By any variable z. observed at time t, and take unconditional expectation, resulting in E,[m1(b)R121]=E() Or E{m1(b)R1-1}=0(2) (1)And(2)are both important for asset pricing testApplying GMM • Simply mapping a given problem into the very general notation: • Using price • Using returns (1) • It is common to add instruments as well, you multiply both sides of • By any variable observed at time t, and take unconditional expectation, resulting in • Or E[mt+1(b)xt+1 − pt] = 0 E[mt+1(b)Rt+1 −1] = 0 Et[mt+1(b)Rt+1] =1 t z [ ( ) ] ( ) t t 1 t 1 t t E m b R z = E z + + { } [ ( ) 1] 0 (2) Et mt+1 b Rt+1 − zt = (1) And (2) are both important for asset pricing test