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Set identification with Tobin regressors

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Author Info
Victor Chernozhukov () (Institute for Fiscal Studies and Massachusetts Institute of Technology)
Roberto Rigobon
Thomas Stoker () (Institute for Fiscal Studies and Massachusetts Institute of Technology)

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Abstract

We give semiparametric identification and estimation results for econometric models with a regressor that is endogenous, bound censored and selected,called a Tobin regressor. First, we show that true parameter value is set identified and characterize the identification sets. Second, we propose novel estimation and inference methods for this true value. These estimation and inference methods are of independent interest and apply to any problem where the true parameter value is point identified conditional on some nuisance parameter values that are set-identified. By fixing the nuisance parameter value in some suitable region, we can proceed with regular point and interval estimation. Then, we take the union over nuisance parameter values of the point and interval estimates to form the final set estimates and confidence set estimates. The initial point or interval estimates can be frequentist or Bayesian. The final set estimates are set-consistent for the true parameter value, and confidence set estimates have frequentist validity in the sense of covering this value with at least a prespecified probability in large samples. We apply our identification, estimation, and inference procedures to study the effects of changes in housing wealth on household consumption. Our set estimates fall in plausible ranges, significantly above low OLS estimates and below high IV estimates that do not account for the Tobin regressor structure.

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Publisher Info
Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP12/09.

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Date of creation: May 2009
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Handle: RePEc:ifs:cemmap:12/09

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  1. Andrew Chesher, 2003. "Identification in Nonseparable Models," Econometrica, Econometric Society, vol. 71(5), pages 1405-1441, 09. [Downloadable!] (restricted)
  2. Joanne Cutler, 2004. "The Relationship between Consumption, Income and Wealth in Hong Kong," Macroeconomics 0403013, EconWPA. [Downloadable!]
  3. Liang H. & Wang S. & Robins J.M. & Carroll R.J., 2004. "Estimation in Partially Linear Models With Missing Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 357-367, January. [Downloadable!] (restricted)
  4. Joanne Cutler, 2004. "The Relationship between Consumption, Income and Wealth in Hong Kong," Working Papers 012004, Hong Kong Institute for Monetary Research. [Downloadable!]
  5. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, 01. [Downloadable!] (restricted)
  6. Lee, Sokbae, 2007. "Endogeneity in quantile regression models: A control function approach," Journal of Econometrics, Elsevier, vol. 141(2), pages 1131-1158, December. [Downloadable!] (restricted)
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  7. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, 09. [Downloadable!] (restricted)
  8. Charles F. Manski & Elie Tamer, 2002. "Inference on Regressions with Interval Data on a Regressor or Outcome," Econometrica, Econometric Society, vol. 70(2), pages 519-546, March. [Downloadable!] (restricted)
  9. Xiaohong Chen & Han Hong & Elie Tamer, 2005. "Measurement Error Models with Auxiliary Data," Review of Economic Studies, Blackwell Publishing, vol. 72(2), pages 343-366, 04. [Downloadable!] (restricted)
  10. Christopher D. Carroll & Misuzu Otsuka & Jirka Slacalek, 2006. "How Large Is the Housing Wealth Effect? A New Approach," NBER Working Papers 12746, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  11. John D. Benjamin & Peter Chinloy & G. Donald Jud, 2004. "Why do Households Concentrate Their Wealth in Housing?," Journal of Real Estate Research, American Real Estate Society, vol. 26(4), pages 329-344. [Downloadable!]
  12. He, Xuming & Shao, Qi-Man, 2000. "On Parameters of Increasing Dimensions," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 120-135, April. [Downloadable!] (restricted)
  13. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July. [Downloadable!] (restricted)
  14. Hong H. & Chernozhukov V., 2002. "Three-Step Censored Quantile Regression and Extramarital Affairs," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 872-882, September. [Downloadable!] (restricted)
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