The Limits of Mathematics and NP Estimation in ... - Chichilnisky

The Impact of Government-SponsoredTraining Programs on the Labor Market Transitions of Disadvantaged MenThe Impact of Government-Sponsored Training Programs on the Labor Market Transitions of Disadvantaged Men 1359In this three-factor loading model, the correlation between destination states k and k ′ isaρ k,k ′ = k a k ′ + b k b k ′√. (7)a 2 k + b2 k√a 2 k+ ′ bk 2 ′This correlation has the same interpretation as in the two-factor loading model.On the other hand, the correlation between the two origin states j and j ′ is given byρ j,j ′ =a ′ j a ′ j ′ + b′ j b ′ j√√a ′. (8)′ 2j + b ′ 2j a ′ 2j ′ + b ′ 2j ′A positive correlation indicates that those who have short spells in state j are likely to haveshort spell duration in state j ′ as well.Finally, the correlation between origin state j and destination state k is given byb ′ j b kρ k,j =√ , √a ′ 2j + b ′ 2j a 2 k + b2 k(9)where j, j ′ , k, k ′ = 1, . . . , K. This correlation is somewhat trickier to interpret. A positivecoefficient indicates that those who are likely to have short spell duration in state j are alsomore likely to enter state k. Conversely, those who are more likely to have short spell durationin state j are less likely to enter state k.3.4 Specification of conditional hazard functionsAssume an individual is observed in state j during spell l (i.e. x τl−1 = j). Let ψ(j, k) denotethe heterogeneity term for destination k, given the individual is in state j. There are twopossibilities:{ wk , in the two-factor loading model,ψ(j, k) =w j,k , in the three-factor loading model.The conditional hazard function for transition (j, k) is given byh j,k (u | y 1 ,...,y l−1 ; z; ν; θ) =h 0 j,k (u; θ) ϕ(y 1,...,y l−1 ; z; θ) ψ(j, k), (10)where ϕ is a positive function of the exogenous variables and the sequence r, h 0 j,k (u; θ) is thebaseline hazard function for transition (j, k), and ψ(j, k) > 0.We have considered three alternative conditional specifications for the baseline hazardfunctions. For each transition, we have chosen among the following competing specificationson the basis of non-parametric kernel estimations (see Fortin et al. (1999a)):1. Log-logistic DistributionThe baseline hazard function isα j,k , β j,k ∈ IR + .h 0 j,k (u; θ) = β j,k α j,k u α j,k−1(1 + β j,k u α j,k) ,