Model Complexity, Expectations, and Asset Prices

This paper analyses how limits to the complexity of statistical models used by market participants can shape asset prices. We consider an economy in which the stochastic process that governs the evolution of economic variables may not have a simple representation, and yet, agents are only capable of entertaining statistical models with a certain level of complexity. As a result, they may end up with a lower-dimensional approximation that does not fully capture the intertemporal complexity of the true data-generating process. We first characterize the implications of the resulting departure from rational expectations and relate the extent of return and forecast-error predictability at various horizons to the complexity of agents’ models and the statistical properties of the underlying process. We then apply our framework to study violations of uncovered interest rate parity in foreign exchange markets. We find that constraints on the complexity of agents’ models can generate return predictability patterns that are simultaneously consistent with the well-known forward discount and predictability reversal puzzles.