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

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: xtabond: Arellano & Bond 1991 |

Date |
Tue, 02 Jul 2002 09:20:25 -0500 |

Gindo Tampubolon <gindo.tampubolon@man.ac.uk> asked how he could replicate columns (c) and (d) of Table 4 in Arellano and Bond (1991). The footnote to the table explains that Arellano and Bond used additional moment conditions based on firm real sales and firm real stocks. Since the firm real stocks variable is not in the dataset, neither of theses columns can be replicated. Gindo also asked how he could obtain the standard errors of the long-run elasticies. This depends on what he means by the long-run elasticities. First, let's dispense with the fact that the coefficients in this model can be interpreted as elasticies and simply refer to the long-run effect of a covariate. Sometimes people refer to the sum of the coefficients on the current and lagged values of a variable as the long-run effect. In this case, since the estimates of the long-run effect are just the sum the of the point estimates on the current and lagged variable, one can use -lincom- to obtain their standard errors. However, the long-run effect of a covariate is usually defined to be the sum of the current and lagged coefficients divided by 1 minus the sum of the lagged coefficients on the dependent variable. In this case, one can use -testnl- for inference on the size the long run effects. Here is an example. First, let's estimate a simple dynamic panel data model. . xtabond n l(0/1).w k , lags(2) Arellano-Bond dynamic panel data Number of obs = 611 Group variable (i): id Number of groups = 140 Wald chi2(5) = 350.58 Time variable (t): year min number of obs = 4 max number of obs = 6 mean number of obs = 4.364286 One-step results ------------------------------------------------------------------------------ n | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- n | LD | .3751428 .1050691 3.57 0.000 .1692112 .5810745 L2D | -.0822723 .0422479 -1.95 0.051 -.1650766 .000532 w | D1 | -.4754038 .0564188 -8.43 0.000 -.5859825 -.364825 LD | .208237 .0832401 2.50 0.012 .0450894 .3713847 k | D1 | .3802498 .0352074 10.80 0.000 .3112446 .449255 _cons | -.0178497 .0041618 -4.29 0.000 -.0260068 -.0096926 ------------------------------------------------------------------------------ Sargan test of over-identifying restrictions: chi2(25) = 97.07 Prob > chi2 = 0.0000 Arellano-Bond test that average autocovariance in residuals of order 1 is 0: H0: no autocorrelation z = -3.02 Pr > z = 0.0026 Arellano-Bond test that average autocovariance in residuals of order 2 is 0: H0: no autocorrelation z = -0.01 Pr > z = 0.9892 Now let's suppose that we are interested in the sum of the coefficients on -w-. Here is an example of how to use -lincom- to obtain the standard error of the estimate of the sum of these coefficients and test the null hypothesis that they sum to zero. . lincom d.w + ld.w ( 1) D.w + LD.w = 0.0 ------------------------------------------------------------------------------ n | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- (1) | -.2671667 .0997334 -2.68 0.007 -.4626405 -.0716929 ------------------------------------------------------------------------------ Now suppose that we are interested in testing the null hypothesis that the sum of the coefficients on w and its lag divided by 1 minus the sum of the coefficients on the lagged -n- is zero. First, let's look at what a point estimate of this quantity would be . di (_b[d.w] + _b[ld.w])/(1-_b[ld.n] - _b[l2d.n]) -.37781866 Now, let's use -testnl- to test the null hypothesis that this expression is zero. . testnl 0 = (_b[d.w] + _b[ld.w])/(1-_b[ld.n] - _b[l2d.n]) (1) 0 = (_b[d.w] + _b[ld.w])/(1-_b[ld.n] - _b[l2d.n]) chi2(1) = 10.03 Prob > chi2 = 0.0015 Finally, you might be interested knowing what the estimated standard error of this expression is. One could use the delta method to compute the standard error. Alternatively, one could use the fact that -testnl- has already computed it, although it is not reported. Note that since our null is that the expression is zero, we have estimate ---------- = sqrt[chi2(1)] std. error which impliles that estimate ------------ = std. error sqrt[chi2(1)] Thus, the estimated standard error of the expression that -testnl- used is . di -.37781866/sqrt(10.03) -.11929794 I hope that this helps. --David ddrukker@stata.com References: Arellano, M. and Bond, S. 1991: Some tests of specification for panel data. Review of Economic Studies, 58 * * 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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