Testing Weak Exogeneity in the Exponential Family : An Application to Financial Marked-Point Processes

A common practice in empirical work is to estimate the conditional mean of a variable y on another variable x, ignoring its marginal density. Weak exogeneity of x for the parameters of interest in the conditional mean ensures valid inference. Available weak exogeneity tests correspond to a Gaussian-linear environment. However, there are some variables, typically related to financial marked-point processes, where non-Gaussian distributions and nonlinear means are much more appropriate assumptions. We propose two tests for weak exogeneity when the density is not necessarily Gaussian but belongs to the the family of exponential densities, and the conditional and marginal means are nonlinear. Both tests exploit dependencies (lack of free variation), under the alternative hypotesis, among parameters in both means. To illustrate this testing procedure, we analyze the relationship between trade size and trade durations for four stocks traded at NYSE. The null hypothesis of weak exogeneity is often rejected, questioning therefore some results in the literature which rely on separate estimation of each density