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Testing identifying assumptions in Tobit Models

Author

Listed:
  • Santiago Acerenza
  • Ot'avio Bartalotti
  • Federico Veneri

Abstract

We develop sharp, testable implications for the identifying assumptions of Tobit and IV-Tobit models: linear index, (joint) normality of errors, treatment (instrument) exogeneity, and relevance. The new sharp testable equalities can detect all possible observable violations of the identifying conditions. The proposed test procedure for the model's validity uses existing inference methods for intersection bounds. Simulations suggest adequate test size and power in detecting exogeneity and error structure violations. We review and propose alternatives to partially identify the parameters of interest under less restrictive assumptions. We revisit a study of married women's labor supply in Lee (1995) to demonstrate the test's practical implementation.

Suggested Citation

  • Santiago Acerenza & Ot'avio Bartalotti & Federico Veneri, 2024. "Testing identifying assumptions in Tobit Models," Papers 2408.02573, arXiv.org, revised Dec 2025.
    • Handle: RePEc:arx:papers:2408.02573
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    References listed on IDEAS

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    1. David M. Drukker, 2002. "Bootstrapping a conditional moments test for normality after tobit estimation," Stata Journal, StataCorp LLC, vol. 2(2), pages 125-139, May.
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    3. Smith, Richard J & Blundell, Richard W, 1986. "An Exogeneity Test for a Simultaneous Equation Tobit Model with an Application to Labor Supply," Econometrica, Econometric Society, vol. 54(3), pages 679-685, May.
    4. Cragg, John G, 1971. "Some Statistical Models for Limited Dependent Variables with Application to the Demand for Durable Goods," Econometrica, Econometric Society, vol. 39(5), pages 829-844, September.
    5. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-1070, September.
    6. Yoichi Arai & Yu‐Chin Hsu & Toru Kitagawa & Ismael Mourifié & Yuanyuan Wan, 2022. "Testing identifying assumptions in fuzzy regression discontinuity designs," Quantitative Economics, Econometric Society, vol. 13(1), pages 1-28, January.
    7. Tsunao Okumura & Emiko Usui, 2014. "Concave‐monotone treatment response and monotone treatment selection: With an application to the returns to schooling," Quantitative Economics, Econometric Society, vol. 5, pages 175-194, March.
    8. Han, Sukjin & Vytlacil, Edward J., 2017. "Identification in a generalization of bivariate probit models with dummy endogenous regressors," Journal of Econometrics, Elsevier, vol. 199(1), pages 63-73.
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    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: 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
    • C34 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Truncated and Censored Models; Switching Regression Models

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