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re: st: Diffrerence Equation


From   Christopher Baum <kit.baum@bc.edu>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   re: st: Diffrerence Equation
Date   Wed, 26 Oct 2011 11:53:34 -0400

<>

John said

System-GMM estimation comprises a level equation together with a difference equation. The output produced by Stata shows the results of the estimation of the level equation. This is fine when the researcher wants to run a regression of, say, the level of per capita income. However, if the objective is to estimate the growth of per capita income (i.e., a difference in logs), then presumably one would want to see the results of the difference equation instead of those of the level equation. What is the command to tell Stata to show the difference equation in System-GMM estimation?

            In asking this question, I am assuming that if I write simply the standard commands for system-GMM estimation, but use the growth of per capita income as the dependent variable, the results would be wrong because Stata would create a difference equation which would have growth acceleration as the dependent variable. In other words, rather than estimating a system comprising a regression of the level of income and a regression of income growth, Stata would be estimating a system with a regression of income growth and a regression of income acceleration. Is my understanding correct?




This is somewhat of a misconception. The system GMM estimator indeed provides estimates for two _sets_ of equations, one set in differences and one set in levels, subject to the constraint that the respective parameters are equal. In a simple example, consider that we could estimate, using constrained OLS,

y_t = a + b1 y_t-1 + c1 x_t + eps1
delta y_t = b2 delta y_t-1 + c2 delta x_t + eps2

s.t. the constraints b1=b2 and c1=c2. That is essentially what is happening in system GMM.

Kit

Kit Baum   |   Boston College Economics & 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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