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From |
ddrukker@stata.com (David M. Drukker, Stata Corp.) |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: xtabond |

Date |
Fri, 01 Aug 2003 11:34:54 -0500 |

Ki Young Park <kpark3@uchicago.edu> asked about why his attempt to estimate a model with -xtabond- failed. The short answer is that his call to -xtabond- specified too many instruments. Now for some details. Ki noted that > I am currently working on panel data estimation with predetermined > variables. My panel data has i=50 and t=123. If Ki's data is balanced with no missing observations and Ki was interested in a model with only one lag of the endogenous variable then a full -xtabond- specification would include (123-2)*(123-1)/2 = 7381 instruments. Since Ki specifies predetermined variables, Ki is actually asking for many more instruments. It is worth while to review the properties of some of the different estimators in dynamic panel data models with predetermined variables when the number of panels, n, goes to infinity and the number of time periods, T, is fixed. 1) Standard Random- and Fixed-effects estimators are inconsistent 2) There are simple instrumental variables estimators derived by Anderson and Hsiao that provide consistent but inefficient estimates. One of these estimators cannot identify an autoregressive lag coefficient of .5, the other can. (See Arellano and Bond (1991) for details.) 3) The Arellano-Bond estimator provides consistent estimates that are more efficient than the Anderson-Hsiao estimators. In addition, since the Arellano-Bond estimator is explicitly derived as a GMM estimator, the Arellano-Bond estimator has many nice generalizations that handle heteroskedasticity, specification testing, et cetera. 4) The GMM literature, and its more recent counterpart in Generalized Empirical Likelihood, has shown that using too many instruments for a given sample size in a GMM estimator can produce significant finite sample bias. The properties of the above estimators are derived under the assumptions that n -> infinity and that T is fixed. Since Ki's data has n = 50 and T = 123, it is not clear that Ki would want to choose an estimator based on n -> infinity and T fixed asymptotics. While -xtabond- should exit more quickly, when asked to estimate models with too many instruments, it is not clear that Ki actually wants to use -xtabond-. Ki can restrict the number of lags of the dependent variable that -xtabond- uses to create instruments by specifying the -maxlags()- option and similarly for the number of lags of the predetermined variables in the -pre( varlist, lagstruct(prelags, premaxlags)- option. However, even setting maxlag(1) will specify more instruments than is likely desirable. The reason is that you can still create a lot of instruments from that first lag of the dependent variable. Ki may want to use a simpler Anderson-Hsiao estimator estimator using -xtivreg-. With T so large, Ki is probably better off carefully specifying the instruments by hand than letting any Arellano-Bond estimator pick them up automatically. -- David ddrukker@stata.com References Arellano, M. and Bond, S. 1991. ``Some Tests for Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations". The Review of Economic Studies, 58(2), pages 277-297. * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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