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Difference in Difference Meets Generalized Least Squares: Higher Order Properties of Hypotheses Tests

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  • Jerry Hausman

    ()
    (MIT, Department of Economics)

  • Guido Kuersteiner

    ()
    (Department of Economics, Boston University)

Abstract

We investigate 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 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

Paper provided by Boston University - Department of Economics in its series Boston University - Department of Economics - Working Papers Series with number WP2005-010.

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Length: 53 pages
Date of creation: Mar 2005
Date of revision:
Handle: RePEc:bos:wpaper:wp2005-010

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References

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  1. 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.
  2. Jinyong Hahn & Guido Kuersteiner, 2002. "Asymptotically Unbiased Inference for a Dynamic Panel Model with Fixed Effects when Both "n" and "T" Are Large," Econometrica, Econometric Society, vol. 70(4), pages 1639-1657, July.
  3. Rothernberg, Thomas J, 1984. "Hypothesis Testing in Linear Models When the Error Covariance Matrix Is Nonscalar," Econometrica, Econometric Society, vol. 52(4), pages 827-42, July.
  4. 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.
  5. 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.
  6. Arellano, M, 1987. "Computing Robust Standard Errors for Within-Groups Estimators," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 49(4), pages 431-34, November.
  7. Rothenberg, Thomas J, 1988. "Approximate Power Functions for Some Robust Tests of Regression Coefficients," Econometrica, Econometric Society, vol. 56(5), pages 997-1019, September.
  8. Nickell, Stephen J, 1981. "Biases in Dynamic Models with Fixed Effects," Econometrica, Econometric Society, vol. 49(6), pages 1417-26, November.
  9. Mundlak, Yair, 1978. "On the Pooling of Time Series and Cross Section Data," Econometrica, Econometric Society, vol. 46(1), pages 69-85, January.
  10. J. A. Hausman, 1976. "Specification Tests in Econometrics," Working papers 185, Massachusetts Institute of Technology (MIT), Department of Economics.
  11. 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.
  12. Moulton, Brent R., 1986. "Random group effects and the precision of regression estimates," Journal of Econometrics, Elsevier, vol. 32(3), pages 385-397, August.
  13. Gabor Kezdi, 2005. "Robus Standard Error Estimation in Fixed-Effects Panel Models," Econometrics 0508018, EconWPA.
  14. Rothenberg, Thomas J, 1984. "Approximate Normality of Generalized Least Squares Estimates," Econometrica, Econometric Society, vol. 52(4), pages 811-25, July.
  15. 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.
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Citations

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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. 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," Darmstadt Discussion Papers in Economics 57149, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute of Economics (VWL).
  3. Hausman, Jerry & Palmer, Christopher, 2012. "Heteroskedasticity-robust inference in finite samples," Economics Letters, Elsevier, vol. 116(2), pages 232-235.
  4. 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.
  5. 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.

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