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From |
"David M. Drukker" <ddrukker@stata.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: xtabond: different results in Stata 10 |

Date |
Tue, 11 Sep 2007 09:42:42 -0500 (CDT) |

Thomas Blake Pepinsky <Thomas.Pepinsky@Colorado.EDU> asked about how the constant term changed in -xtabond- between Stata 9 and Stata 10 Here is the short answer. In Stata 9, -xtabond- reported the estimates of the parameters of the first differenced model, so the reported constant estimate was an estimate of the coefficient on a time trend in the model. In Stata 10, -xtabond- reports estimates of the parameters of the level model, so the reported constant estimate is an estimate of the constant in the level model. In Stata 10, -xtabond- can estimate both a time-trend and a constant. Here is a more detailed answer. I begin with a simple example using the version 9 -xtabond- applied to the familiar Arellano-Bond data. What the variables measure is not important except that this is yearly data so year is a time-trend. . webuse abdata . version 9: xtabond n w k year, noconstant Arellano-Bond dynamic panel-data estimation Number of obs = 751 Group variable: id Number of groups = 140 Wald chi2(.) = . Time variable: year Obs per group: min = 5 avg = 5.364286 max = 7 One-step results ------------------------------------------------------------------------------ D.n | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- n | LD. | .2206198 .0621776 3.55 0.000 .098754 .3424856 w | D1. | -.4588164 .0493884 -9.29 0.000 -.5556158 -.3620169 k | D1. | .3516235 .0277573 12.67 0.000 .2972202 .4060267 year | D1. | -.0239647 .0025211 -9.51 0.000 -.0289059 -.0190234 ------------------------------------------------------------------------------ Sargan test of over-identifying restrictions: chi2(27) = 119.42 Prob > chi2 = 0.0000 Arellano-Bond test that average autocovariance in residuals of order 1 is 0: H0: no autocorrelation z = -1.82 Pr > z = 0.0688 Arellano-Bond test that average autocovariance in residuals of order 2 is 0: H0: no autocorrelation z = -0.86 Pr > z = 0.3922 The variables in the estimates table are in first differences because the estimated parameters are from the first-differenced model. First-differencing causes the year variable to be collinear with the constant, I specified the -noconstant- option. Now, I will issue a similar command in Stata 10, allowing for a constant in the model. . xtabond n w k year Arellano-Bond dynamic panel-data estimation Number of obs = 751 Group variable: id Number of groups = 140 Time variable: year Obs per group: min = 5 avg = 5.364286 max = 7 Number of instruments = 32 Wald chi2(4) = 1974.00 Prob > chi2 = 0.0000 One-step results ------------------------------------------------------------------------------ n | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- n | L1. | .2206198 .0622192 3.55 0.000 .0986724 .3425673 w | -.4588164 .0494215 -9.28 0.000 -.5556807 -.3619521 k | .3516235 .0277759 12.66 0.000 .2971838 .4060632 year | -.0239647 .0025228 -9.50 0.000 -.0289092 -.0190201 _cons | 49.85197 4.982592 10.01 0.000 40.08627 59.61767 ------------------------------------------------------------------------------ Instruments for differenced equation GMM-type: L(2/.).n Standard: D.w D.k D.year Instruments for level equation Standard: _cons The estimates table is in levels. The estimated coefficient on year is an estimate of the coefficient on the time-trend year and the estimated _cons is an estimate of the constant term in the level model. When comparing the two sets of results, I see that the estimated coefficients on D.year and year are the same, as expected. Similarly, we also have equality of the estimates for the coefficients on LD.n and L.n, D.w and w, and D.k and k. There is no constant in the differenced model because it would be collinear with D.year. The estimated constant in the Stata 10 output is for the constant in the level model. The difference in the standard errors is caused the additional parameter that is estimated in the Stata 10 -xtabond. The constant term for the level model is estimated by including a level moment condition. Technically, this moment condition is from an Arellano-Bover/Blundell-Bond estimator, however including only the constant in an Arellano-Bond estimator leaves the other parameters unchanged. The estimated constant for the level model is useful when predicting levels of the dependent variable. The following example illustrates that dropping the constant from the model does not change the remaining estimated parameters. I also point out that the standard errors now match those from the Stata 9 output, because the number of parameters is the same. . xtabond n w k year, noconstant Arellano-Bond dynamic panel-data estimation Number of obs = 751 Group variable: id Number of groups = 140 Time variable: year Obs per group: min = 5 avg = 5.364286 max = 7 Number of instruments = 31 Wald chi2(4) = 1976.65 Prob > chi2 = 0.0000 One-step results ------------------------------------------------------------------------------ n | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- n | L1. | .2206198 .0621776 3.55 0.000 .098754 .3424856 w | -.4588164 .0493884 -9.29 0.000 -.5556158 -.3620169 k | .3516235 .0277573 12.67 0.000 .2972202 .4060267 year | -.0239647 .0025211 -9.51 0.000 -.0289059 -.0190234 ------------------------------------------------------------------------------ Instruments for differenced equation GMM-type: L(2/.).n Standard: D.w D.k D.year Reiterating the main points, 1) in the Stata 9 -xtabond-, the output table was for the parameters in the differenced model; 2) in the Stata 9 -xtabond-, the estimated constant is an estimate of the coefficient on a time trend; 3) in the Stata 10 -xtabond-, the output table is for the parameters of the level model; 4) in the Stata 10 -xtabond-, the estimated constant is an estimate of the constant in the level model; and 5) including a constant in the Stata 10 -xtabond- does not affect any of the other parameter estimates. I hope that this helps. David <ddrukker@stata.com> * * 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/

**References**:**st: xtabond: different results in Stata 10***From:*Thomas Blake Pepinsky <Thomas.Pepinsky@Colorado.EDU>

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