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A strategy to reduce the count of moment conditions in panel data GMM

  • M. E. Bontempi
  • I. Mammi

The problem of instrument proliferation and its consequences (overfitting of endogenous variables, bias of estimates, weakening of Sargan/Hansen test) are well known. The literature provides little guidance on how many instruments is too many. It is common practice to report the instrument count and to test the sensitivity of results to the use of more or fewer instruments. Strategies to alleviate the instrument proliferation problem are the lag-depth truncation and/or the collapse of the instrument set (the latter being an horizontal squeezing of the instrument matrix). However, such strategies involve either a certain degree of arbitrariness (based on the ability and the experience of the researcher) or of trust in the restrictions implicitly imposed (and hence untestable) on the instrument matrix. The aim of the paper is to introduce a new strategy to reduce the instrument count. The technique we propose is statistically founded and purely datadriven and, as such, it can be considered a sort of benchmark solution to the problem of instrument proliferation. We apply the principal component analysis (PCA) on the instrument matrix and exploit the PCA scores as the instrument set for the panel generalized method-of-moments (GMM)estimation. Through extensive Monte Carlo simulations, under alternative characteristics of persistence of the endogenous variables, we compare the performance of the Difference GMM, Level and System GMM estimators when lag truncation, collapsing and our principal component-based IV reduction (PCIVR henceforth) are applied to the instrument set. The same comparison has been carried out with two empirical applications on real data: the first replicates the estimates of Blundell and Bond [1998]; the second exploits a new and large panel data-set in order to assess the role of tangible and intangible capital on productivity. Results show that PCIVR is a promising strategy of instrument reduction.

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Paper provided by Dipartimento Scienze Economiche, Universita' di Bologna in its series Working Papers with number wp843.

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Date of creation: Sep 2012
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Handle: RePEc:bol:bodewp:wp843
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  1. Hall, Bronwyn H. & Mairesse, Jacques, 1995. "Exploring the relationship between R&D and productivity in French manufacturing firms," Journal of Econometrics, Elsevier, vol. 65(1), pages 263-293, January.
  2. Ziliak, James P, 1997. "Efficient Estimation with Panel Data When Instruments Are Predetermined: An Empirical Comparison of Moment-Condition Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(4), pages 419-31, October.
  3. Alastair R. Hall & Fernanda P. M. Peixe, 2003. "A Consistent Method for the Selection of Relevant Instruments," Econometric Reviews, Taylor & Francis Journals, vol. 22(3), pages 269-287, January.
  4. Stock J.H. & Watson M.W., 2002. "Forecasting Using Principal Components From a Large Number of Predictors," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1167-1179, December.
  5. Stock, James H & Watson, Mark W, 2002. "Macroeconomic Forecasting Using Diffusion Indexes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 147-62, April.
  6. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 2002. "The Generalized Dynamic Factor Model: One-Sided Estimation and Forecasting," CEPR Discussion Papers 3432, C.E.P.R. Discussion Papers.
  7. Richard Blundell & Steve Bond, 1995. "Initial conditions and moment restrictions in dynamic panel data models," IFS Working Papers W95/17, Institute for Fiscal Studies.
  8. Hayakawa, Kazuhiko, 2009. "On the effect of mean-nonstationarity in dynamic panel data models," Journal of Econometrics, Elsevier, vol. 153(2), pages 133-135, December.
  9. Jan J. J. Groen & George Kapetanios, 2009. "Parsimonious estimation with many instruments," Staff Reports 386, Federal Reserve Bank of New York.
  10. 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.
  11. Bowsher, Clive G., 2002. "On testing overidentifying restrictions in dynamic panel data models," Economics Letters, Elsevier, vol. 77(2), pages 211-220, October.
  12. Steve Bond & Frank Windmeijer, 2002. "Finite sample inference for GMM estimators in linear panel data models," CeMMAP working papers CWP04/02, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  13. Windmeijer, Frank, 2005. "A finite sample correction for the variance of linear efficient two-step GMM estimators," Journal of Econometrics, Elsevier, vol. 126(1), pages 25-51, May.
  14. Bai, Jushan & Ng, Serena, 2010. "Instrumental Variable Estimation In A Data Rich Environment," Econometric Theory, Cambridge University Press, vol. 26(06), pages 1577-1606, December.
  15. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 2004. "The generalized dynamic factor model consistency and rates," Journal of Econometrics, Elsevier, vol. 119(2), pages 231-255, April.
  16. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 1999. "The Generalized Dynamic Factor Model: Identification and Estimation," CEPR Discussion Papers 2338, C.E.P.R. Discussion Papers.
  17. Chirok Han & Peter C. B. Phillips, 2006. "GMM with Many Moment Conditions," Econometrica, Econometric Society, vol. 74(1), pages 147-192, 01.
  18. Zvi Griliches & Jerry A. Hausman, 1984. "Errors in Variables in Panel Data," NBER Technical Working Papers 0037, National Bureau of Economic Research, Inc.
  19. Maria Elena Bontempi & Jacques Mairesse, 2008. "Intangible Capital and Productivity: An Exploration on a Panel of Italian Manufacturing Firms," NBER Working Papers 14108, National Bureau of Economic Research, Inc.
  20. 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.
  21. van Ark, Bart, 1998. "Productivity," Journal of the Japanese and International Economies, Elsevier, vol. 12(2), pages 171-174, June.
  22. 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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