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Initial conditions and moment restrictions in dynamic panel data model

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  • R Blundell
  • Steven Bond

Abstract

In this paper we consider estimation of the autoregressive error components model. When the autoregressive parameter is moderately large and the number of time series observations is moderately small, the usual Generalised Methods of Moments (GMM) estimator obtained after first differencing has been found to be poorly behaved. Here we consider alternative linear estimators that are designed to improve the properties of the standard first-differenced GMM estimator. We consider two approaches to estimation. The first approach extends the model by adding the observed initial values as an extra regressor. This allows consistent estimates to be obtained by error-components GLS. This estimator is shown to be equivalent to the optimal GMM estimator for the normal homoskedastic error components model. The second approach considers a mild restriction on the initial condition process under which lagged differences in the dependent variable can be used to construct linear moment conditions in the levels equations. The complete set of moment conditions can then be exploited by a linear GMM estimator in a system of first-differenced and levels equations, rendering the non-linear moment conditions redundant for estimation. This estimator is strictly more efficient than non-linear GMM when the additional restriction is valid. Monte Carlo simulations are reported which demonstrate the dramatic improvement in performance of the proposed estimators compared to the usual first-differenced GMM estimator, especially for high values of the autoregressive parameter.

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Paper provided by Economics Group, Nuffield College, University of Oxford in its series Economics Papers with number W14&104..

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Handle: RePEc:nuf:econwp:9614

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  1. Ahn, Seung C. & Schmidt, Peter, 1995. "Efficient estimation of models for dynamic panel data," Journal of Econometrics, Elsevier, vol. 68(1), pages 5-27, July.
  2. Nelson, C. & Startz, R., 1988. "Some Furthere Results On The Exact Small Sample Properties Of The Instrumental Variable Estimator," Working Papers 88-06, University of Washington, Department of Economics.
  3. Prucha, Ingmar R, 1984. "On the Asymptotic Efficiency of Feasible Aitken Estimators for Seemingly Unrelated Regression Models with Error Components," Econometrica, Econometric Society, vol. 52(1), pages 203-07, January.
  4. Arellano, Manuel & Bover, Olympia, 1995. "Another look at the instrumental variable estimation of error-components models," Journal of Econometrics, Elsevier, vol. 68(1), pages 29-51, July.
  5. Crepon, Bruno & Kramarz, Francis & Trognon, Alain, 1997. "Parameters of interest, nuisance parameters and orthogonality conditions An application to autoregressive error component models," Journal of Econometrics, Elsevier, vol. 82(1), pages 135-156.
  6. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
  7. Holtz-Eakin, Douglas & Newey, Whitney & Rosen, Harvey S, 1988. "Estimating Vector Autoregressions with Panel Data," Econometrica, Econometric Society, vol. 56(6), pages 1371-95, November.
  8. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  9. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
  10. Arellano, Manuel & Bond, Stephen, 1991. "Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations," Review of Economic Studies, Wiley Blackwell, vol. 58(2), pages 277-97, April.
  11. Bhargava, Alok & Sargan, J D, 1983. "Estimating Dynamic Random Effects Models from Panel Data Covering Short Time Periods," Econometrica, Econometric Society, vol. 51(6), pages 1635-59, November.
  12. Sevestre, P. & Trognon, A., 1985. "A note on autoregressive error components models," Journal of Econometrics, Elsevier, vol. 28(2), pages 231-245, May.
  13. Nickell, Stephen J, 1981. "Biases in Dynamic Models with Fixed Effects," Econometrica, Econometric Society, vol. 49(6), pages 1417-26, November.
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