M.Sc. in Economics Econometrics Module I Topic 7: Censored Regression Model Carol Newman

Censored Regression Model  The Tobit Model  Continuous dependent variable which is constrained or truncated at some value or values  Conventional regression models fail to account for the difference in the DGP for limit vs non-limit observations on the dependent variable  Two components to the DGP:  The probability that an observations will be at the limit  The distribution of the dependent variable for non-limit observations  OLS will yield biased and inconsistent estimates

Censored Regression Model  Derivation of the standard tobit/censored regression model:  Probability of a limit observation assuming  The distribution of the dependent variable conditional on being positive where the inverse mills ratio is defined as:  Model is composed of a discrete and a continuous part

Censored Regression Model  Model is estimated using MLE  Limit observations:  Non-limit observations  Log-likelihood equation: Note: in practice re-parameterised to improve convergence (see Olsen 1978)

Censored Regression Model  Interpretation of the coefficients McDonald and Moffitt Decomposition (1980) Show that (in class):

Censored Regression Model  Properties: Tobit model is inconsistent if assumptions of normality and homoscedasticity of the error term are violated Lagrange multiplier tests can be used to test for violations of these assumptions If errors are found to be non-normal or heteroscedastic likelihood equation must be adjusted