st: Non-Linear Least Squares with Generalized Method-of-Moments

[<adrien.Amzallag@ecb.int>]

Dear all,

I'm running two separate specifications, one with non-linear least
squares (NLLS) and the other with generalized method-of-moments (GMM)
(I'll leave the theory out of this post but am happy to explain why if
necessary). The NLLS equation takes the following form, where "i" is an
interest rate, "FD" denotes the first-difference operator, "L." is a
one-period lag, and "_t" denotes time subscripts:

NLLS: FD.i_t = (1-{lambda})*(b1*FD.inflation_t + b2*FD.output_gap_t) +
(1-{lambda})*(1-{rho})*(b0 + b1*L.inflation_t + b2*L.output_gap_t -
L.i_t) + {rho}*{lambda}*FD.L.i_t

The GMM model is also run for a separate reason: I need to proxy the
current-period values of inflation and the output gap (i.e. I treat
these variables as endogenous). 

I've been searching the internet and Stata books (incl. the Cameron
'Microeconometrics using Stata') but haven't found a way of combining
the two approaches, for example running the first-stage regressions,
taking the appropriate weighting matrix, and using this into a
non-linear second-stage equation.

I'd very much appreciate some guidance (including on whether I've missed
something econometrically obvious). Many thanks in advance, with
apologies if this message is unclear.

Adrien Amzallag






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