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Estimation and Testing Using Jackknife IV in Heteroskedastic Regressions With Many Weak Instruments

  • John Chao

    ()

    (University of Maryland)

  • Norman Swanson

    ()

    (Rutgers University)

This paper develops Wald type tests for general possibly nonlinear restrictions, in the context of heteroskedastic IV regression with many weak instruments. In particular, it is ¯rst shown that consistency and asymptotically normality can be obtained when estimating structural parameters using JIVE, even when errors exhibit heteroskedasticity of unkown form. This is not the case, however, with other well known IV estimators, such as LIML, Fuller's modi¯ed LIML, 2SLS, and B2SLS, which are shown to be inconsistent. Second, new covariance matrix estimators (and corresponding Wald test statistics) are proposed for JIVE, which are consistent even when instrument weakness is such that the rate of growth of the concentration parameter, rn is slower than the rate of growth of the the number of instruments, Kn and possibly much slower than the sample size, n, provided that (Kn)^.5 /rn, rn goes to 0 as n goes to infinity. The primary advantage of our tests, relative to those proposed previously in the literature, is that one can test general nonlinear hypotheses, as opposed to simple null hypotheses of the form H0: Beta=Beta star, where beta star is the value of beta under the null. We feel that this feature, taken together with the fact that the tests are robust to unconditional heteroskedasticity, is important from the perspective of empirical application, given that general linear and nonlinear hypotheses are often of interest to empirical researchers, and given that heteroskedasticity is prevalent, particularly in microeconomic datasets.

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File URL: ftp://snde.rutgers.edu/Rutgers/wp/2004-20.pdf
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Paper provided by Rutgers University, Department of Economics in its series Departmental Working Papers with number 200420.

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Length: 20 pages
Date of creation: 16 Sep 2004
Date of revision:
Handle: RePEc:rut:rutres:200420
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  1. Donald, Stephen G. & Whitney Newey, 1999. "Choosing the Number of Instruments," Working papers 99-05, Massachusetts Institute of Technology (MIT), Department of Economics.
  2. H. Kelejian, Harry & Prucha, Ingmar R., 2001. "On the asymptotic distribution of the Moran I test statistic with applications," Journal of Econometrics, Elsevier, vol. 104(2), pages 219-257, September.
  3. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, 07.
  4. John C. Chao & Norman R. Swanson, 2003. "Asymptotic Normality of Single-Equation Estimators for the Case with a Large Number of Weak Instruments," Departmental Working Papers 200312, Rutgers University, Department of Economics.
  5. Hahn, Jinyong, 2002. "Optimal Inference With Many Instruments," Econometric Theory, Cambridge University Press, vol. 18(01), pages 140-168, February.
  6. John C. Chao & Norman Rasmus Swanson, 2004. "Consistent Estimation with a Large Number of Weak Instruments," Yale School of Management Working Papers ysm374, Yale School of Management.
  7. Phillips, Garry D A & Hale, C, 1977. "The Bias of Instrumental Variable Estimators of Simultaneous Equation Systems," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(1), pages 219-28, February.
  8. Morimune, Kimio, 1983. "Approximate Distributions of k-Class Estimators When the Degree of Overidentifiability Is Large Compared with the Sample Size," Econometrica, Econometric Society, vol. 51(3), pages 821-41, May.
  9. Angrist, Joshua D & Krueger, Alan B, 1995. "Split-Sample Instrumental Variables Estimates of the Return to Schooling," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(2), pages 225-35, April.
  10. Whitney Newey & Richard Smith, 2003. "Higher order properties of GMM and generalised empirical likelihood estimators," CeMMAP working papers CWP04/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  11. James H. Stock & Motohiro Yogo, 2002. "Testing for Weak Instruments in Linear IV Regression," NBER Technical Working Papers 0284, National Bureau of Economic Research, Inc.
  12. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
  13. Blomquist, Soren & Dahlberg, Matz, 1999. "Small Sample Properties of LIML and Jackknife IV Estimators: Experiments with Weak Instruments," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(1), pages 69-88, Jan.-Feb..
  14. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May.
  15. Smith, Richard J, 1997. "Alternative Semi-parametric Likelihood Approaches to Generalised Method of Moments Estimation," Economic Journal, Royal Economic Society, vol. 107(441), pages 503-19, March.
  16. Kajal Lahiri & Chuanming Gao, 2001. "A Comparison of Some Recent Bayesian and Classical Procedures for Simultaneous Equation Models with Weak Instruments," Discussion Papers 01-15, University at Albany, SUNY, Department of Economics.
  17. Jiahui Wang & Eric Zivot, 1998. "Inference on Structural Parameters in Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 66(6), pages 1389-1404, November.
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