1. Health-related attrition in the BHPS and ECHP Andrew Jones Xander Koolman Nigel Rice Department of Economics and Related Studies, University of York, York, YO10 5DD, United Kingdom Fax: +44-1904-433759 E-mail: amj1@york.ac.uk http://www.york.ac.uk/res/herc/yshe

2. Overview Aim to estimate models of the association between socio-economic status (SES) and self-assessed health (SAH) using current 11 waves of the BHPS (1991-2001) and full 8 waves of the ECHP (1994-2001) The specific objective is to explore the consequences of health- related attrition for these models Panel data introduces risk of survivorship bias Explore the extent and pattern of (health-related) attrition in the data Test and correct for attrition in the empirical models Apply the method of inverse probability weighting to adjust for attrition

8. Multivariate analysis on non-response lTables 5 & 6 present partial effects from probit models for response/non-response at each wave 2,…,11 of BHPS lMain influences on response rates: Education Ethnic group Household composition Evidence of health-related non-response remains (VPOOR, HLLT, HLPRB) Basis for IPW estimators

9. A Brief Introduction to our Model SAH is ordered categorical variable: Please think back over the last 12 months about how your health has been. Compared to people of your own age, would you say that your health has on the whole been excellent/good/fair/poor/very poor? There are repeated measurements (t=1,...., T) for a sample of n individuals (i=1,.....,n). Use latent variable specification, h* it = x it + it (i=1,…,n; t=1,…T i ) y Obtain quasi-ML estimates from pooled ordered probit (POP) with standards errors robust to clustering within individuals y Results presented as average partial effects (e.g. Wooldridge, 2002)

10. Testing for attrition bias Verbeek & Nijman (1992, IER) suggest some simple tests Add NEXT WAVE, ALL WAVES, or NUMBER OF WAVES to ordered probits for SAH Basically testing P(h|x,R) = P(h|x)

11. Selection on observables - inverse probability weights Selection on observables based on ignorability condition (conditional independence assumption), P(R=1|h,x,z) = P(R=1|x,z) z is endogenous to h - see Rotnitzky and Robins, (1997, Stats.in Med.) for similar interpretation - z intermediate variable in causal pathway from x to h Inverse probability weights (Robins, Rotnitzky & Zhao (1995, JASA), Fitzgerald, Gottschalk and Moffitt (1998), Moffitt, Fitzgerald and Gottschalk (1999), Wooldridge (2002)) Testing Do zs significantly affect R? Hausman test of weighted v unweighted estimates Inversion test (Becketti et al. (1988, J.Lab.Ec)) - regress h 0 on x conditioning on R (uses Bayes rule) Note: suggests variant of Nijman and Verbeek tests. By Bayess rule, MAR P(h|x,z,R=1)=P(h|x,z)

12. Implementing inverse probability weighting Follow Wooldridge (2002b) Probits for response/non-response at each wave, 2…T. Use 1/p it to weight contributions to log-likelihoods in pooled probits IWP-1 – use initial period regressors, based on ignorability assumption P(d it =1|h it, h it-1, x it, z i1 ) = P(d it =1|z i1 ), t=2,…,T IWP-2 – use last period regressors, requires monotone attrition and stronger ignorability assumption Gives consistent estimates and conservative inference

13. Verbeek and Nijman (1992) tests for attrition

16. Partial effects of SES on SAH in ECHP lTable 14 shows unweighted and weighted (IPW-1) estimates for unbalanced panel within each country lAll countries show positive association between income/education and SAH lDifferences APEs between weighted and unweighted estimates are very small in all cases

17. Conclusions lDescriptive evidence shows health-related attrition lVariable addition tests: All tests show evidence of attrition bias +ve sign on variables consistent with fact that response rates are positively associated with health lInverse probability weighting: IPW to control for attrition bias has little effect on estimated APEs for income and education in empirical specifications (but age/marital status are affected) lEvidence of socioeconomic gradient in SAH by education and income