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st: is it possible to write explicit equation, GMM estimation with constraints ??


From   "Halit Akturk" <halitakturk@gmail.com>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: is it possible to write explicit equation, GMM estimation with constraints ??
Date   Wed, 17 Mar 2010 12:40:46 -0500

Dear all,
I would like to run GMM estimation. I am using Stata10 (SE). I need a little
bit of help. 
Is there any way to write down explicit equation for GMM estimation in
Stata10? The equation I like to estimate has constraints in it so I couldn't
really figure out how to run this using GMM or LIML (limited information
max. likelihood). I specifically wanted to GMM estimate the following
equation (it's a version of IS curve):
x{t}=alpha*E{t}(x{t+1})-delta*[r-E{t}(pi{t+1})]
Where alpha and delta are coefficients, X{t} is output gap measure at time
t, r is nominal interest rate, E{t}(pi{t+1}) is expectation of future
inflation rate in t+1. I am assuming rational expectations so expectational
terms can be dropped and future values can be substituted in with future
error terms which then makes r the only exogenous variable, expectational
variables are endogenous. I want to use 4 lagged output gap and inflation
variables as instruments to consistently estimate the expectational
variables' coefficients. Here is what I have difficulty in doing in Stata10:
---Note that the second expectational term and r has the same coefficient,
how do I tell Stata10 to recognize that?
---Is there any way to tell Stata10 to explicitly write down to equation I
like to estimate?
---can I do summation or subtraction in the instrument list that I specified
in stata10 inside the parenthesis? 
 
I tried running:
ivreg28 x{t} ( x{t+1} r-pi{t+1} = ( L2.x{t+1} L3.x{t+1} L4.x{t+1} L1.pi{t+1}
L2.pi{t+1} L3.pi{t+1} L4.pi{t+1} ), liml (which gives a syntax error)
ivreg28 x{t} r ( x{t+1} pi{t+1} = ( L2.x{t+1} L3.x{t+1} L4.x{t+1} L1.pi{t+1}
L2.pi{t+1} L3.pi{t+1} L4.pi{t+1} ), liml (which runs well but then
coefficients for r and pi{t+1} are different.)
 
Thanks all for your help.
halo.

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