Selection and the age – productivity profile. Evidence from chess players

We use data on professional chess tournaments to study how endogenous selection affectsthe relationship between age and mental productivity in a brain-intensive profession. Weshow that less talented players are more likely to drop out, and that the age-productivitygradient is heterogeneous by ability, making fixed effects estimators inconsistent. Since wedo not observe the players who dropped out of chess before the beginning of our samplingperiod, we cannot exploit the standard Heckman sample selection correction procedure.Therefore, we correct for selection by using an imputation method that repopulates thesample by applying to older cohorts the self-selection patterns observed in younger cohorts.We estimate the age-productivity profile on the repopulated sample using median regres-sions, and find that median productivity increases by close to 5 percent from initial age (15)to peak age (21.6), and declines substantially after the peak. At age 50, it is about 10 percentlower than at age 15. We compare profiles in the unadjusted and in the repopulated sampleand show that failure to adequately address endogenous selection in the former leads tosubstantially over-estimating productivity at any age relative to initial age.