Effect of using Tobit and Heckit models in regression estimation for data with many zeros Tetiana Ianevych and Veronika Serhiienko Taras Shevchenko National University of Kyiv, Ukraine Jelgava, Latvia 2018

Outline The main problem Tobit model Heckit model Simulation results Consclusions

The main problem Data contain number of zero observations Estimators have undesirable or unacceptable precision

Why the zeros are present in the data? a result of censoring Tobit model a decision that the researcher has no control over for some reason Heckit model or some other models

Tobit model & Censoring Data are censored when we have partial information about the value of a variable— we know it is beyond some boundary, but not how far above or below it. For example, censoring occurs when a value occurs outside the range of a measuring instrument. For example, a bathroom scale might only measure up to 140 kg. If a 160 kg individual is weighed using the scale, the observer would only know that the individual's weight is at least 140 kg.

Formally, it can be written as The most common choice is τ = τy =0 and where This mathematical model was introduced by Tobin in 1958 and is known as Tobit model or a censored regression model

Underlying generating process

Censored data

Heckit model This type of model is appropriate when yi = 0 because of the non-observable response. It means that knowledge yi = 0 is uninformative in estimating the determinants of the level of yi . The Heckit model was introduced by Heckman in 1979

Heckit model can be formulated using : “participation” equation and “consumption” equation

Underlying generating process

Zero-inflated data

Simulation study Our objective is to investigate the effect of using Tobit and Heckit models in regression estimation for data containing different percent of zero values within SRS sampling design

Measures of efficiency absolute relative bias relative root mean square error

Tobit - 26% Our first simulated population U consists of N=1000 elements for which we produce 26% of zero values using censoring. Sampling size is 100. Horvitz-Thompson estimator (%) GREG estimator LM assisted (%) Tobit assisted (%) ARB 0.139 2.764 0.185 RRMSE 9.287 7.200 7.073

Tobit - 51% The second simulated population U consists of N=1000 elements for which we produce 51% of zero values using censoring. Sampling size is 100. Horvitz-Thompson estimator (%) GREG estimator LM assisted (%) Tobit assisted (%) ARB 0.380 10.203 0.690 RRMSE 13.986 13.972 13.782

Tobit - 72% The third simulated population U consists of N=1000 elements for which we produce 72% of zero values using censoring. Sampling size is 100. Horvitz-Thompson estimator (%) GREG estimator LM assisted (%) Tobit assisted (%) ARB 0.109 0.522 1.170 RRMSE 21.039 20.150 28.089

Heckit - 30% Simulated population U consists of N=1000 elements for which we produce 30% of zero values using Heckit model. Sampling size is 100. Horvitz-Thompson estimator (%) GREG estimator LM assisted (%) Heckit assisted (%) ARB 8.497 14.869 13.334 RRMSE 27.845 23.302 22.537

Heckit - 51% The simulated population U consists of N=1000 elements for which we produce 51% of zero values using Heckit model. Sampling size is 100. Horvitz-Thompson estimator (%) GREG estimator LM assisted (%) Heckit assisted (%) ARB 0.181 0.941 0.988 RRMSE 21.528 16.331 16.317

Heckit - 73% The simulated population U consists of N=1000 elements for which we produce 73% of zero values using Heckit model. Sampling size is 100. Horvitz-Thompson estimator (%) GREG estimator LM assisted (%) Heckit assisted (%) ARB 0.269 1.429 1.362 RRMSE 25.007 19.627 19.603

Conclusions usage of GREG estimators leads to biased but better results with regards to the accuracy. usage of the Tobit and Heckit-based estimators improve the quality of GREG estimator with regard to both bias and mean square error if the number of zero-values is not large. If it is large - the improvement can be lost. if the underlying process of zero-values appearing does not correspond well with estimator the improvement can be lost for both Tobit and Heckit models.

Thank you for your attention!