The Complexity of Economic Policy: I. Restricted Local Optima in Tax Policy Design

Economists traditionally tackle normative problems by computing optimal policy, ie the one that maximizes a social welfare function. In practice, however, a succession of marginal changes to a limited number of policy instruments are implemented, until no further improvement is feasible. I call such an outcome a ‘restricted local optimum’. I consider the outcome of such a tatonment process for a government that wants to optimally set taxes given a tax code with a fixed number of brackets. I show that there is history dependence, in that several local optima may be reached, and which one is reached depends on initial conditions. History dependence is stronger (ie there are more local optima), the more complex the design of economic policy, ie the greater the number of tax brackets. It is also typically stronger, the greater the interaction of policy instruments with one another – which in my model is equivalent to agents having a more elastic labour supply behaviour. Finally, for a given economy and a given tax code, I define the latter’s average performance as the average value of the social welfare function across all the local optima. One finds that it eventually sharply falls with the number of brackets, so that the best performing tax code typically involves no more than three brackets.