Evaluation of the Australian Wage Subsidy Special Youth ...

22
1.3.4 Observables and unobservables
Friedlander et al. (1997) express succinctly the difference between selection on
observables and selection on unobservables. The behaviour of the participants is
expressed in the econometric model:
(21) Y it = c t X i + b t D io + u it t>0 employment
(22) D io = a 0 Z i + e io participation
Again, Y it is the outcome, such as employment, for the ith person in period t , where t=0
is the period where the treatment occurs. The X i and Zi are sets of exogenous
characteristics for the ith individual, that can be overlapping and are measured pre –
program. The importance of measuring pre-program is to avoid endogeneity, where the
characteristics may change after program entry due to the program, these would confound
measurement of the program effect. D io is the program participation binary variable, D io
=1 if participant and D io =0 if not (the comparison group); u it, e io are error terms. The
mean effect of the program in period t after participation is the coefficient b t . If there is
no correlation between the participation and the error in the employment equation
E(D io , u it ) =0, then an unbiased estimate of the coefficient b t is obtained simply from the
employment equation (21).
Correlations between the participation and the employment error E(D io , u it ) ≠ 0, can
arise from selection due to observables or unobservables (Friedlander et al. (1997),
Heckman and Robb (1985), Heckman and Hotz (1989)). The correlation between the
participation and the employment error E(D io , u it ) ≠0 can arise through either Z i or e io, in
the equation (22) representing participation . If the error terms for employment and
participation are uncorrelated E(u it, e io ) = 0 , but there is correlation between the error of
the employment equation and the characteristics affecting participation E( Z i ,u it ) ≠ 0 then
selection is on observables. Conversely, when there is selection on unobservables, the
error terms for employment and participation are correlated E(u it, e io ) ≠ 0 but there is no