Simultaneously incomplete and incoherent (SII) dynamic LDV models: with an application to financing constraints and firms’ decision to innovate

We develop novel methods for establishing coherency and completeness conditions in Static and Dynamic Limited Dependent Variables (LDV) Models. We characterize the two distinct problems as “empty-region ”incoherency and “overlap-region” incoherency or incompleteness and show that the two properties can co-exist. We focus on the class of models that can be Simultaneously Incomplete and Incoherent (SII). We propose estimation strategies based on Conditional Maximum Likelihood Estimation (CMLE) for simultaneous dynamic LDV models without imposing recursivity. Point identification is achieved through sign-restrictions on parameters or other prior assumptions that complete the underlying data process. Using as modelling framework the Panel Bivariate Probit model with State Dependence, we analyse the impact of financing constraints on innovation: ceteris paribus, a firm facing binding finance constraints is substantially less likely to undertake innovation, while the probability that a firm encounters a binding finance constraint more than doubles if the firm is innovative. In addition, a strong role for state dependence in dynamic versions of our models is established.