Panel conditional and multinomial logit with time-varying parameters

Panel conditional logit estimators (PCLE) in the literature use mostly time-constant parameters. If the panel periods are volatile or long, however, the model parameters can change much. Hence this paper generalizes PCLE with time-constant parameters to PCLE with time-varying parameters; both static and dynamic PCLE are considered for this. The main finding is that time-varying parameters are fully allowed for static PCLE and the dynamic "pseudo" PCLE of [Bartolucci, F. and V. Nigro. 2010. "A Dynamic Model for Binary Panel Data with Unobserved Heterogeneity Admitting a n $ n$-Consistent Conditional Estimator." Econometrica 78: 719-733] that are thus recommended to practitioners. As a further generalization, static "panel conditional multinomial logit estimator (PML)" with time-varying parameters is also examined. As it turns out, time-varying parameters are also fully allowed for PML. With no error term serial correlation allowed in PCLE and dynamic PCLE's being restrictive in their assumptions, time-varying parameters provide an alternative avenue to inject dynamics and flexibility into PCLE and PML. Since PCLE and PML converge straightforwardly in computation, allowing time-varying parameters in PCLE and PML is "computationally free." A simulation study is also provided.