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IV methods for Tobit models

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  • Chesher, Andrew
  • Kim, Dongwoo
  • Rosen, Adam M.

Abstract

This paper studies models of processes generating censored outcomes with endogenous explanatory variables and instrumental variable restrictions. Tobit-type left censoring at zero is the primary focus in the exposition. Extension to stochastic censoring is sketched. The models do not specify the process determining endogenous explanatory variables and they do not embody restrictions justifying control function approaches. Consequently, they can be partially or point identifying. Identified sets are characterized and it is shown how inference can be performed on scalar functions of partially identified parameters when exogenous variables have rich support. In an application using data on UK household tobacco expenditures inference is conducted on the coefficient of an endogenous total expenditure variable with and without a Gaussian distributional restriction on the unobservable and compared with the results obtained using a point identifying complete triangular model.

Suggested Citation

  • Chesher, Andrew & Kim, Dongwoo & Rosen, Adam M., 2023. "IV methods for Tobit models," Journal of Econometrics, Elsevier, vol. 235(2), pages 1700-1724.
    • Handle: RePEc:eee:econom:v:235:y:2023:i:2:p:1700-1724
    DOI: 10.1016/j.jeconom.2023.01.010
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    More about this item

    Keywords

    Censored outcomes; Endogeneity; Incomplete models; Instrumental variables; Partial identification; Stochastic censoring;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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