Consistent estimation of polychotomous treatment effects with selection-bias and unobserved heterogeneity using panel data correlated random coefficients model

We estimate multiple treatment effects in presence of selection-bias and response heterogeneity, using panel data. A control function was added to a fixed-effects based correlated random coefficients model. Selection model to create the control function was contrasted between multinomial logit and multinomial probit. For the multinomial logit model, parametric and semi-parametric bias correction techniques, as proposed in Lee (Econometrica 51(2):507–512, 1983), Dubin and McFadden (Econometrica 52(2):345–362, 1984) and Dahl (Econometrica 70(6):2367–2420, 2002) respectively, were implemented. We find that controlling time-varying endogeneity, allowing response heterogeneity, the type of bias correction method and the choice of the selection model, each had significant impact on the estimated treatment effects. Using the case of biologic DMARDs, we show that in the presence of heterogeneity and multiple treatments, the specification of the latent index model should be carefully chosen along with selection bias correction techniques appropriate to the choice of the latent index model. These issues have an important impact on policy. Under one set of assumptions, we may accept a formulary expansion policy on biologic DMARDs to be cost-neutral, while rejecting the same policy as not cost-saving under another set of assumptions.