Simultaneous dependence between firm-level stock returns

We show that use of ordinary least-squares to explore relationships involving firm-level stock returns as the dependent variable in the face of structured dependence between individual firms leads to an endogeneity problem. This in turn leads to biased and inconsistent least-squares estimates. A maximum likelihood estimation procedure that will produce consistent estimates in these situations is illustrated. This is done using methods that have been developed to deal with spatial dependence between regional data observations, which can be applied to situations involving firm-level observations that exhibit a structure of dependence. In addition, we show how to correctly interpret maximum likelihood parameter estimates from these models in the context of firm-level dependence, and provide a Monte Carlo as well as applied illustration of the magnitude of bias that can arise.