Tobit Analysis

In defining Tobit, James Tobin (1958) quoted a passage about how nothing could not be less than nothing. Tobit permits analyzing dependent variables with zero as their lowest value and that are from CENSORED DATA, and it avoids violating ORDINARY LEAST SQUARES' (OLS) continuity and unboundedness assumptions about DEPENDENT VARIABLES. OLS can produce negative predicted values for such dependent variables and predict something that is less than nothing. Other consequences of using OLS include biased coefficients and incorrectly obtaining statistically insignificant coefficients. Obtaining negative predicted values is the most common problem that Tobit solves, but it can analyze dependent variables with upper, upper and lower, and intermediate limits.

Tobit combines PROBIT ANALYSIS with OLS. Its coefficients allow identifying two effects on a dependent variable: (a) an effect on the probability of exceeding its limiting value(s), and (b) an effect on changing values beyond the limit (McDonald & Moffitt, 1980). For example, neighborhood crime rates cannot be less than zero, but they can have any positive value. For small areas, many will have crime rates of zero. OLS could predict negative crime rates, which are nonsensical (except for burglaries once a year). Manipulating Tobit coefficients permits identifying the effects of INDEPENDENT VARIABLES on the probability of a crime where the crime rate is zero and on changing the crime rate for places with nonzero rates. Tobit adjusts for the inability to measure a dependent variable's values beyond some limit, such as zero, and produces unbiased estimates of the independent variables' effects.

Tobit is a large-sample technique. The case-to-variable ratio should be 10 or more. It can be sensitive to the measurement of independent variables. These should have similar ranges even if transformations are necessary. Its sensitivity to heteroskedasticity can be tested and adjusted for by programs such as LIMDEP. The dependent variable should be continuous beyond its limit value, although Tobit can, at times, model more accurately the distributions of count variables than POISSON REGRESSION. Tobit requires the same signs for the effects it provides. The expected change in probability of having a crime in a no-crime area must be the same as that for the expected change in crime in areas with crimes. Otherwise, different techniques must be used.

The sum of the intercept and products of Tobit coefficients with their independent variables' values can be negative. Tobit coefficients are effects on an unobserved (“latent”) variable. Their decomposition allows interpreting the effects on a dependent variable's observed values. The coefficients' sizes depend on the independent variables' measurement scales. Larger coefficients do not always indicate more important independent variables. Modifying Roncek's (1992) pseudo standardized coefficient by multiplying a Tobit coefficient only by the standard deviation of its independent variables adjusts for its measurement scale. [Page 1135]Dividing each coefficient by the dependent variable's standard deviation or the Tobit model's standard error is irrelevant.