1. 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

2. Outline The main problem Tobit model Heckit model Simulation results
Consclusions

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

4. 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

5. 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.

6. 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

7. Underlying generating process

8. Censored data

9. 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

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

11. Underlying generating process

12. Zero-inflated data

13. 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

14. Measures of efficiency
absolute relative bias
relative root mean square error

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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.

22. Thank you for your attention!