The Causal problem Let s be a variable denoting time to from eligibility for retirement, negative values indicate that the subject is not yet eligible Let r be the retirement status r=l for the retired and r=o otherwise. Since retirement is an option available only to the eligible workers, the probability to retire is zero if S<0(and it is thus discontinuous at S=0) et(Y,Yo be the two potential household consumption expenditures corresponding to the head being retired or not retired, respectively, and let B=YI-Yo et Y=Yo+rB be observed consumption, where Y=Y, for households whose head is retired and y=Yo otherwiseThe Causal Problem • Let S * be a variable denoting time to/from eligibility for retirement, negative values indicate that the subject is not yet eligible. • Let R be the retirement status, R=1 for the retired and R=0 otherwise. Since retirement is an option available only to the eligible workers, the probability to retire is zero if S*<0 (and it is thus discontinuous at S*=0 ). • Let (Y1 ,Y0 ) be the two potential household consumption expenditures corresponding to the head being retired or not retired, respectively, and let β=Y1 -Y0 . • Let Y = Y0+Rβ be observed consumption, where Y≡Y1 for households whose head is retired and Y≡Y0 otherwise