Dealing with the Complexity of Economic Calculations

This essay is a response to a growing negative literature that suggests that neoclassical economic theories based on hypotheses of rationality and equilibrium are of limited practical relevance because they require an infeasibly large number of calculations. Many of the negative results are translations of abstract complexity bounds from the computer science literature. I show that these bounds do do not constitute proofs that difficult economic calculations are ``impossible'' and discuss the type of hardware and software that can make it possible to solve very hard problems. I discuss four different ways to break the curse of dimensionality of economic problems: 1) by exploiting special structure, 2) by decomposition, 3) by randomization, and 4) by t aking advantage of ``knowledge capital.'' However these four methods may not be enough. I offer some speculations on the role of decentralization for harnessing the power of massively parallel processors. I conjecture that decentralization is an efficient ``operating system'' for organizing large scale computations on massively parallel systems. Economies, immune systems and brains are all types of massively parallel processors that use decentralization to solve difficult computational problems. However knowledge capital, in the form of effective institutions, is necessary to ensure that decentralization leads to effective cooperation rather than anarchy and chaos. I suggest that onereason why economists have had great difficulty computing approximate solutions to detailed models of individual behavior and large scale models of the economy is that they are not using appropriate hardware and software. Economists should structure their computations to mimic the key operating features of brains and economies, using parallel processing and decentralized `agent-based'' modeling strategies to solve more realistic economic models where solutions arise endogenously as ``emergent computations''.