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