GMM and asset pricing model continued USing b,, form an estimate s of S=∑Eu(6)x-( Second-stage estimate b2=arg min gr(b)sg,(b) 6 is a consistent, asymptotically normal, and asymptotically efficient estimate of the parameter vector b The variance-covariance matrix of b. is var(b)=-(dsd) · Where abGMM and asset pricing model--- continued • Using , form an estimate of • • Second-stage estimate • is a consistent, asymptotically normal, and asymptotically efficient estimate of the parameter vector b. • The variance-covariance matrix of is • • Where 1 ˆ b S ˆ { } ) ˆ ( ˆ )' ˆ argmin ( ˆ 1 b 2 ˆ g T b S g T b b − = ∑ ∞ =−∞ = − j t t j S E[u ( b ) u ( b)'] 2 ˆ b 2 ˆ b 1 1 2 ( ' ) 1 ) ˆ var( − − = d S d T b b g b d T ∂ ∂ = ( )