On the convergence of Bayesian posterior processes in linear economic models Counting equations and unknowns

I propose a technique, counting ‘equations’ and ‘unknowns’, for determining when the posterior distributions of the parameters of a linear regression process converge to their true values. This is applied to examples and to the infinite-horizon optimal control of this linear regression process with learning, and in particular to the problem of a monopolist seeking to maximize profits with unknown demand curve. Such a monopolist has a tradeoff between choosing an action to maximize the current-period reward and to maximize the information value of that action. I use the above technique to determine the monopolist’s limiting behavior and to determine whether in the limit it learns the true parameter values of the demand curve.