Categorical › Logistic regression

Tobit (censored) regression

Tobit regression estimates a linear model by maximum likelihood when the outcome is censored at a lower and/or upper limit.

What is Tobit (censored) regression?

When the outcome piles up at a boundary — spending that can't go below zero, top-coded income, demand capped by capacity — OLS is biased because the observed values understate the latent variable near the limit. Tobit models the latent linear response and the censoring jointly by maximum likelihood.

Coefficients are effects on the latent variable; the marginal effect on the observed (censored) outcome is smaller and depends on the censoring probability.

When should I use Tobit (censored) regression?

  • A continuous outcome bounded/censored at a known limit with a mass point there.
  • Corner-solution outcomes (many exact zeros).

What data does it need?

Censored dependent variable + numeric regressors + left and/or right censoring limits.

What does it report?

Coefficients (est / SE / z / p), scale σ, log-likelihood, Wald χ², and censored-observation counts.

What does it assume?

  • Normal, homoskedastic latent errors — Tobit is sensitive to both.
  • The censoring limit is known and constant.

How do I interpret the result?

A positive coefficient raises the latent outcome; translate to the observed scale via marginal effects if you need the effect on realized values.

See also

References

  • Tobin (1958). Estimation of relationships for limited dependent variables. Econometrica 26.
  • Kleiber & Zeileis (2008). Applied Econometrics.