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Set identification with Tobin regressors

Author

Listed:
  • Victor Chernozhukov

    () (Institute for Fiscal Studies and MIT)

  • Roberto Rigobon

    (Institute for Fiscal Studies)

  • Thomas M. Stoker

    () (Institute for Fiscal Studies and MIT)

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.

Suggested Citation

  • Victor Chernozhukov & Roberto Rigobon & Thomas M. Stoker, 2009. "Set identification with Tobin regressors," CeMMAP working papers CWP12/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:12/09
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    File URL: http://cemmap.ifs.org.uk/wps/cwp1209.pdf
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    References listed on IDEAS

    as
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