Limited Dependent Models Probit, Logit, and Tobit Tutorial

Tutorial Outline Limited dependent variables Logit Models Obtaining Marginal Effects Multinomial logits Probit Models Tobit Models Heckman Selection Models

Limited Dependent Variables A limited dependent variable is one in which your dependent variable is constrained within a range. Examples include 0/1 outcomes (major choice, college choice, labor choice) Distance variables (distance cannot be negative)

Logit Probit and Tobit “As between the probit and the logit models, there are no theoretical justifications for favoring one over the other. In practice, researchers often base their choice on convenience.” (Xui, 88) The two yield similar results. It has generally been agreed that this is the case (Cox, 1970, p.28; Maddala, 1983. p23).

Logit Models A logit models the probability that an event occurs or not given a set of independent variables. Command: logit depvar indepvars, options

Practice Open up the labor market participation Run a logit with inlf (in labor force) as your limited dependent variable.

Marginal Effects Margins Using the margins command will require you to explicitly declare factor variables during estimation The default used is that each factor will be considered continuous

Marginal While the t-stats and p-values are accurate for the logit, the coefficients are not the coefficients you want to report. Rather, you want to report the marginal effects. Directly after your logit, find the margins by typing “margins, dydx(*)” The * indicates that you want the marginal effects for all variables in the model

mfx To get the marginal effects after logit type “mfx”

Interpreting coefficients Statistical significance: You can still read statistical significance from the slope dZ/dX. The z-statistic reported for probit or logit is analogous to OLS’s t-statistic. Sign: If dZ/dX is positive, then dProb(Y)/dX is also positive.

Problems in Interpreting Magnitude: The estimated coefficient relates X to Z. We care about the relationship between X and Prob(Y = 1). The effect of X on Prob(Y = 1) varies depending on Z.

Practice Find the marginal effects of you model

Probit Models A probit runs a maximum-likelihood model for a dependent variable that can only take two values (ex: married/not married) It estimates the probability of an event occurring given the regressors. Command: probit depvar indepvars, options

Marginal Effects To find the marginal effects of the probability of an event simply type “margins, dydx(*) Or use the mfx command

Practice Run a probit on the sample and determine the marginal effects.

Tobit Models A tobit fits a model of a dependent variable on independent variables where the censuring values are fixed. Command: tobit depvar indepvar, ll(#) ul(#) ll = lower bound ul = upper bound

Practice Using hours (can’t be less than 0) as your limited dependent variable run a tobit model with this data.

Heckman Selection Models Given this specific data set, it may be useful to use a heckman selection model. Syntax: “heckman depvars indepvars, select (depvar_s=indepvars_s) twostep” “heckman depvars indepvars, select (depvar_s=indepvars_s) vce(robust)”

Practice Run a heckman selection model to determine what factors contribute to the number of hours worked, given the probability of someone choosing to work.

Questions about limited dependent variable models?