We develop two novel methods for establishing coherency conditions in Dynamic Limited Dependent Variables (LDV) Models, which have intuitive interpretations and are easy to implement and generalize. A major advantage of the new approaches is that they indicate how to achieve coherency in models traditionally classified as incoherent through the use of prior sign restrictions on model parameters. This allows us to develop estimation strategies based on Conditional Maximum Likelihood Estimation (CMLE) for simultaneous LDV models without imposing recursivity. We then employ our novel approaches to establish the coherency of several Dynamic LDV models that until now using traditional methods, it was imposible to determine whether they were coherent or incoherent. In the paper, we also develop and summarize the results of a set of extensive Monte-Carlo experiments we used to evaluate the properties of the proposed CMLE and the consequences of employing estimators that make overly restrictive coherency assumptions about the Data Generating Process (DGP). These experiments confirm very substantive Mean-Squared-Error estimation improvements of the CMLE approach developed here. We then apply our framework to analyse the existence and impact of financing constraints as a possibly serious obstacle to innovation by firms. At the same time, innovative firms are more likely to be hampered by financing constraints because of informational asymmetries and a relative inability to offer tangible collateral. Employing direct measures of binding constraints, instead of indirect proxy variables, we use our econometric methods to identify and quantify both direct and reverse interactions between firm innovation and financial constraints. This is achieved for the first time without forcing the econometric models to be recursive, which was required by previous approaches. Our estimates lead us to conclude that binding financing constraints discourage innovation and at the same time innovative firms are more likely to face binding financing constraints. These results are quite striking: ceteris paribus, we estimate that a firm that faces a binding finance constraint is approximately 30% less likely to undertake innovation, while the probability that a firm encounters a binding finance constraint more than doubles if the firm is classified as innovative.Finally, we establish a strong role for state dependence in dynamic versions of our models.
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