1. Scottish Social Survey Network: Master Class 1 Data Analysis with Stata Dr Vernon Gayle and Dr Paul Lambert 23 rd January 2008, University of Stirling The SSSN is funded under Phase II of the ESRC Research Development Initiative

2. Selection Models

3. Pioneering work by Jim Heckman A well known problem in the economics literature Less well know in sociology, social policy, geography etc. Nobel prize winner 2000 Common key references (Heckman 1976;1979)

4. The problem easily stated Example – hourly wage data for 2,000 women 657 don’t work and therefore have no observation Is this ‘non-observation’ completely random? Is there a sample selection bias? What do we do?

5. All Women 0 1 y2 Probit Model Are you in the labour market y 1 Regression Model of Hourly Wage Rate Working Women Only Heckman Model

6. Stata Wage equation Command Yvar X vars heckman wage educ age children, /// select(married children educ age) Selection equation Magic Variable X vars

7. Heckman Approach Whenever we suspect sample selection then this type of approach is hugely attractive Strongly guided by economic theory Consensus regarding what goes into the selection and ‘wage’ equation The drawback….

8. Model Identification Magic Variable – Identification –A variable that affects selection –BUT NOT the outcome –Beware – the model will fit without this! (Identification on functional form) You will be harangued at conference in the US You will not get published in better journals –In our experience it is often hard to clearly identify the underlying social process (e.g. in education) –Panel data can ease the pain a little

9. All Pupils 0 1 0 1 Probit Model Entry To A’Level Route y 1 Probit Model Entry To H.E.y 2 A’Level Route Pupils Bivariate Probit with Sample Selection Example in Gayle, Berridge and Davies (2003)

10. References A good place to start… Winship, C. and Mare, R. (1992) ‘Models for sample selection bias’, Annual Review of Sociology, 18, pp.327-350. More technical Heckman, J.J. (1976) ‘The common structure of statistical models of truncation, sample selection, and limited dependent variables and a simple estimator for such models’, Annals of Economic and Social Measurement, 5, pp. 475–492. Heckman, J. J. (1979) ‘Sample Selection Bias as a Specification Error’, Econometrica, 47, pp.153-161.