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From |
Christopher Baum <baum@bc.edu> |

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Wed, 17 Mar 2010 14:12:03 -0400 |

<> 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 * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: is it possible to write explicit equation, GMM estimation with constraints ??***From:*Halit Akturk <halitakturk@gmail.com>

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