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

[Halit Akturk <halitakturk@gmail.com>]

Mr. Baum,
Thanks so much for your very through explanation. Although, I am kind
of new to Statalist and I didn't really write down my problem well,
you explained what I needed exactly.
I have just updated to ivreg2 and run liml estimation similar to the
way you explained to me via the example and the results look great!

Thanks again,
halit.

On Wed, Mar 17, 2010 at 1:12 PM, Christopher Baum <baum@bc.edu> wrote:
>
> <>
> Halit said
>
> 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.)
>
>
> First of all if you are using Stata 10 there is no reason to use ivreg28. Download and use up-to-date ivreg2.  I don't understand what you are doing
> with all those curly braces {t}, as they are not acceptable syntax in Stata. Also, if you want to talk about a future value, use the F. time series operator.
>
> Second, the constraint is merely that the coefficient on r (exog) equal the coeff on future pi (endog). That is a linear restriction which you can just impose in the estimation. You might want to test its validity by estimating them separately and testing for equal and opposite signed values.
>
> I believe the following will do something very similar to what you're thinking of, employing 2-step IV-GMM with HAC standard errors.
>
> --------------------
> use http://fmwww.bc.edu/ec-p/data/wooldridge/phillips, clear
> su
> tsset year
> g r = 5 in 1
> replace r = 5 +0.9 * L.r + rnormal(0,0.01) in 2/l
> // create interest rate net of inflation
> g realr = r - F.inf
> // use unem instead of output gap
> ivreg2 unem (F.unem realr = L(1/4).(unem inf)), noco gmm2s robust bw(4)
> --------------------
>
> And no, you cannot do arithmetic nor apply functions in a varlist. Create the variables first with generate, replace or egen.
>
>
> Kit Baum   |   Boston College Economics and DIW Berlin   |   http://ideas.repec.org/e/pba1.html
> An Introduction to Stata Programming   |   http://www.stata-press.com/books/isp.html
> An Introduction to Modern Econometrics Using Stata   |   http://www.stata-press.com/books/imeus.html
>
>
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