Sample Selection:Heckman’s Model and
MethodPresenters:
Satya Prakash EnugulaAndrew Wendel
Cagla Yildirim
Selection bias and Sample selection bias Selection bias:• Proper randomization is not in place
Sampling bias:• Systematic error because of the non-random sample
There is no selection problem if: Unmeasured factors uncorrelated Explanatory variables controlled
Reference: http://en.wikipedia.org/wiki/Selection_bias
Heckman’s method for sample selection model
• Also known as “Heckit Model”
• Corrects the issue of the data being nonrandom.
• Heckman’s correction;• Involves normality assumption• Provides a test for sample selection bias• Provides a formula for bias corrected model
Reference: http://en.wikipedia.org/wiki/Heckman_correction
What is the selection problem?
• We want to estimate the determinants of wage offers for woman but…..
• We have access to wage observations for only those who work• People who work are selected non-randomly
Therefore;
• Estimating the determinants of wages from the our sample involves bias• This is where Heckman’s correction takes place.
Reference: http://en.wikipedia.org/wiki/Heckman_correction
Wages, Effects of Education and Utility
Reference: Peter H. Westfall, Horn Professor of Statistics, Texas Tech University
Utility
Education1 2 43 5
Linear relationship between utility and education
60
Reference: Peter H. Westfall, Horn Professor of Statistics, Texas Tech University
Den
sity
Salary
The distribution when education level is 1
Reference: Peter H. Westfall, Horn Professor of Statistics, Texas Tech University
Den
sity
Salary
What if we take out the people who choose not to work?
Reference: Peter H. Westfall, Horn Professor of Statistics, Texas Tech University
Women’s wage
Education1 2 43 5
Linear relationship between women’s wage and education
Reference: Peter H. Westfall, Horn Professor of Statistics, Texas Tech University
The Heckman Model estimation by Maximum Likelihood Estimator :A sample selection model always involves two equations:• The regression equation considering mechanisms determining the outcome
variable.
• The selection equation considering a portion of the sample whose outcome is observed and mechanisms determining the selection process.
iii exy
iii uzw
ix
Reference :http://www.sagepub.com/upm-data/30234_Chapter4.pdf
Assumptions of the model:
1
Reference :http://www.sagepub.com/upm-data/30234_Chapter4.pdf
Cont.
Reference :http://www.sagepub.com/upm-data/30234_Chapter4.pdf
Log Likelihood Function :
Reference :http://www.sagepub.com/upm-data/30234_Chapter4.pdf
Log Likelihood Function (cont.):
Reference :http://grizzly.la.psu.edu/~hbierens/EasyRegTours/HECKMAN_Tourfiles/HECKMAN.PDF