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Testing Identifying Assumptions in Tobit Models

Author

Listed:
  • Acerenza, Santiago

    (Universidad ORT Uruguay)

  • Bartalotti, Otávio

    (Monash University)

  • Veneri, Federico

    (Iowa State University)

Abstract

We develop 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 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. We qualitatively replicate their original findings, but our validity test rejects the IV-Tobit model. Estimating our proposed robust lower bound, we find that an additional \$1,000 in other household income cannot reduce female labor supply by more than 4.2 hours annually, but cannot rule out that the effect is zero.

Suggested Citation

  • Acerenza, Santiago & Bartalotti, Otávio & Veneri, Federico, 2026. "Testing Identifying Assumptions in Tobit Models," IZA Discussion Papers 18594, IZA Network @ LISER.
    • Handle: RePEc:iza:izadps:dp18594
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    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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