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From |
Evan Markel <markelev@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
st: Failing to reject Arellano-Bond test for AR(1) in first differences imply a random walk? |

Date |
Wed, 24 Apr 2013 17:52:55 -0700 |

Dear listservers, I am estimating an xtabond2 model using a panel where N=434 microfinance institutions (MFI's) and where T=5. After executing xtabond2 system GMM this reduces to N=233 and T=3. My primary concern right now is the implication of failing to reject the null hypothesis of no autocorrelation in the Arellano-Bond test for AR(1). I have read Roodman 2006 and understand that negative first order serial correlation is to be expected in AR(1) because of the mathematical relation between the first difference and the first lag of difference. Specifically (eit)-(eit-1) is related to (eit-1)-(eit-2). But what does this mean when I fail to reject the null. Does it give evidence of a random walk? I have found several examples and discussions stating why first order serial correlation is expected in AR(1), but have not found a discussion on the implications of the contrary. Below is an extract from my xtabond2 output. Instruments for orthogonal deviations equation Standard FOD.(iyear L2.pm) GMM-type (missing=0, separate instruments for each period unless collapsed) L(1/5).(oss lindi lsolid lvillage) Instruments for levels equation Standard iyear L2.pm _cons GMM-type (missing=0, separate instruments for each period unless collapsed) D.(oss lindi lsolid lvillage) ------------------------------------------------------------------------------ Arellano-Bond test for AR(1) in first differences: z = -1.00 Pr > z = 0.315 Arellano-Bond test for AR(2) in first differences: z = 0.10 Pr > z = 0.917 ------------------------------------------------------------------------------ Sargan test of overid. restrictions: chi2(31) = 87.67 Prob > chi2 = 0.000 (Not robust, but not weakened by many instruments.) Hansen test of overid. restrictions: chi2(31) = 19.86 Prob > chi2 = 0.939 (Robust, but weakened by many instruments.) Difference-in-Hansen tests of exogeneity of instrument subsets: GMM instruments for levels Hansen test excluding group: chi2(19) = 12.54 Prob > chi2 = 0.861 Difference (null H = exogenous): chi2(12) = 7.32 Prob > chi2 = 0.836 iv(iyear L2.pm) Hansen test excluding group: chi2(29) = 16.57 Prob > chi2 = 0.968 Difference (null H = exogenous): chi2(2) = 3.29 Prob > chi2 = 0.193 My variable of interest is Operational Self-sufficiency (OSS). Following Roodman 2009 I regress OSS on the lagged level of OSS which yields a low R^2 of .117 possibly signally lag 1.oss is a weak instrument. Maybe this is a source of my failure to reject AR(1)? regress oss l.oss Source | SS df MS Number of obs = 784 -------------+------------------------------ F( 1, 782) = 103.65 Model | 19.0811599 1 19.0811599 Prob > F = 0.0000 Residual | 143.966445 782 .184100313 R-squared = 0.1170 -------------+------------------------------ Adj R-squared = 0.1159 Total | 163.047605 783 .208234489 Root MSE = .42907 ------------------------------------------------------------------------------ oss | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- oss | L1. | .3328396 .0326934 10.18 0.000 .2686624 .3970168 | _cons | .7341655 .0399425 18.38 0.000 .6557582 .8125727 Thank you in advance for your help, Evan M. * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: Failing to reject Arellano-Bond test for AR(1) in first differences imply a random walk?***From:*Evan Markel <markelev@gmail.com>

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