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Difference in difference meets generalized least squares: Higher order properties of hypotheses tests

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  • Hausman, Jerry
  • Kuersteiner, Guido

Abstract

We investigate the estimation and inference in difference in difference econometric models used in the analysis of treatment effects. When the innovations in such models display serial correlation, commonly used ordinary least squares (OLS) procedures are inefficient and may lead to tests with incorrect size. Implementation of feasible generalized least squares (FGLS) procedures is often hindered by too few observations in the cross-section to allow for unrestricted estimation of the weight matrix without leading to tests with similar size distortions as conventional OLS based procedures. We analyze the small sample properties of FGLS based tests with a formal higher order Edgeworth expansion that allows us to construct a size corrected version of the test. We also address the question of optimal temporal aggregation as a method to reduce the dimension of the weight matrix. We apply our procedure to data on regulation of mobile telephone service prices. We find that a size corrected FGLS based test outperforms tests based on OLS.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 144 (2008)
Issue (Month): 2 (June)
Pages: 371-391

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Handle: RePEc:eee:econom:v:144:y:2008:i:2:p:371-391

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Web page: http://www.elsevier.com/locate/jeconom

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References

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  1. Hausman, Jerry A, 1978. "Specification Tests in Econometrics," Econometrica, Econometric Society, vol. 46(6), pages 1251-71, November.
  2. Hansen, Christian B., 2007. "Generalized least squares inference in panel and multilevel models with serial correlation and fixed effects," Journal of Econometrics, Elsevier, vol. 140(2), pages 670-694, October.
  3. Mundlak, Yair, 1978. "On the Pooling of Time Series and Cross Section Data," Econometrica, Econometric Society, vol. 46(1), pages 69-85, January.
  4. Kiefer, Nicholas M., 1980. "Estimation of fixed effect models for time series of cross-sections with arbitrary intertemporal covariance," Journal of Econometrics, Elsevier, vol. 14(2), pages 195-202, October.
  5. Nickell, Stephen J, 1981. "Biases in Dynamic Models with Fixed Effects," Econometrica, Econometric Society, vol. 49(6), pages 1417-26, November.
  6. Moulton, Brent R., 1986. "Random group effects and the precision of regression estimates," Journal of Econometrics, Elsevier, vol. 32(3), pages 385-397, August.
  7. Jinyong Hahn & Jerry Hausman & Guido Kuersteiner, 2005. "Bias Corrected Instrumental Variables Estimation for Dynamic Panel Models with Fixed E¤ects," Boston University - Department of Economics - Working Papers Series WP2005-024, Boston University - Department of Economics.
  8. Rothenberg, Thomas J, 1988. "Approximate Power Functions for Some Robust Tests of Regression Coefficients," Econometrica, Econometric Society, vol. 56(5), pages 997-1019, September.
  9. Gabor Kezdi, 2005. "Robus Standard Error Estimation in Fixed-Effects Panel Models," Econometrics 0508018, EconWPA.
  10. Magnus, J.R. & Neudecker, H., 1979. "The commutation matrix: Some properties and applications," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153207, Tilburg University.
  11. Marianne Bertrand & Esther Duflo & Sendhil Mullainathan, 2002. "How Much Should We Trust Differences-in-Differences Estimates?," NBER Working Papers 8841, National Bureau of Economic Research, Inc.
  12. Rothenberg, Thomas J, 1984. "Approximate Normality of Generalized Least Squares Estimates," Econometrica, Econometric Society, vol. 52(4), pages 811-25, July.
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Cited by:
  1. A. Colin Cameron & Douglas L. Miller, 2010. "Robust Inference with Clustered Data," Working Papers 106, University of California, Davis, Department of Economics.
  2. Ben Vollaard, 2005. "Police numbers up, crime rates down. The effect of police on crime in the Netherlands, 1996-2003," Law and Economics 0501006, EconWPA.
  3. Jerry A. Hausman & Christopher J. Palmer, 2011. "Heteroskedasticity-Robust Inference in Finite Samples," NBER Working Papers 17698, National Bureau of Economic Research, Inc.
  4. Sudip Ranjan Basu, 2008. "Does WTO accession affect domestic economic policies and institutions?," IHEID Working Papers 03-2008, Economics Section, The Graduate Institute of International Studies, revised Feb 2008.
  5. Karlsson, Martin & Nilsson, Therese & Pichler, Stefan, 2012. "What Doesn't Kill You Makes You Stronger? The Impact of the 1918 Spanish Flu Epidemic on Economic Performance in Sweden," Working Paper Series 911, Research Institute of Industrial Economics.

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