Efficient Estimation of Learning Models

Résumé En

This paper develops a toolkit of inference and forecasting methods for a large class of nonlinear incomplete-information models. The techniques readily apply to representative-agent economies in which the state of fundamentals is latent and follows a Markov chain. Three main tools are introduced. First, we provide a convenient and efficient estimation method based on indirect inference (Gouriéroux, Monfort and Renault 1993; Smith 1993). Second, we develop a particle filter to recursively estimate the joint distribution of fundamentals and the agent's belief about fundamentals, and provide forecasts. Third, we propose a particle filter-based test of a moment condition involving the hidden state, which holds in a variety of settings; in the context of learning models, this method can be used to assess every period the rationality of agent beliefs about fundamentals. The good empirical performance of these methods is demonstrated on the multifrequency asset pricing model of Calvet and Fisher (2007) applied to a long series of daily aggregate equity excess returns.