Model Choice and Size Distribution: A Bayequentist Approach

We propose a new three step model selection framework for size distributions in empirical data. It generalizes a recent frequentist plausibility-of-fit analysis (Step 1) and combines it with the Bayesian Akaike Information Criterion (Step 2). We enhance these statistical criteria with the additional criterion of stochastic microfoundation (Step 3) which is to select the model that comes with a stochastic description of size dynamics. A numerical performance test of Step 1 shows that the method is able to correctly identify the distribution that a sample was drawn from. We then illustrate use and usefulness of our approach by investigating the size distribution of 399 commercial cattle farms in Namibia's semi-arid rangelands. With help of our framework, we infer that Gibrat's `law of proportionate effect' holds for our sample, albeit with two modifying assumptions: (1) farm ages are exponentially distributed and (2) the initial farm size distribution was lognormal. We conclude that the framework proposed here has the potential to reconcile the ongoing debate about size distribution models in empirical data, the two most prominent of which are the Pareto and the lognormal distribution. It might therefore provide a basis for the unification of these two major literature strands.