# Replicate Alastair Hall's estimation of the Hansen-Singleton
# Consumption-Based Asset Pricing model.  See Hall's "Generalized
# Method of Moments" (Oxford University Press, 2005, chapter 3).

open hall.gdt
set force_hc on

scalar alpha = 0.5
scalar delta = 0.5
series e = 0

list inst = const consrat(-1) consrat(-2) ewr(-1) ewr(-2)

matrix V0 = 100000*I(nelem(inst))
matrix Z = { inst }
matrix V1 = $nobs*inv(Z'Z)

# one-step estimation, identity matrix for initial weights
gmm e = delta*ewr*consrat^(alpha-1) - 1
  orthog e ; inst
  weights V0
  params alpha delta
end gmm

# one-step estimation, T(Z'Z)^{-1} for initial weights
gmm e = delta*ewr*consrat^(alpha-1) - 1
  orthog e ; inst
  weights V1
  params alpha delta
end gmm

# iterated estimation, identity matrix for initial weights
gmm e = delta*ewr*consrat^(alpha-1) - 1
  orthog e ; inst
  weights V0
  params alpha delta
end gmm --iterate

# iterated estimation, T(Z'Z)^{-1} for initial weights
gmm e = delta*ewr*consrat^(alpha-1) - 1
  orthog e ; inst
  weights V1
  params alpha delta
end gmm --iterate