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Approximating stochastic processes by finite-state Markov chains is useful for reducing computational complexity when solving dynamic economic models. We provide a new method for accurately discretizing general Markov processes by matching low order moments of the conditional distributions using maximum entropy. In contrast to existing methods, our approach is not limited to linear Gaussian autoregressive processes. We apply our method to numerically solve asset pricing models with various underlying stochastic processes for the fundamentals, including a rare disasters model. Our method outperforms the solution accuracy of existing methods by orders of magnitude, while drastically simplifying the solution algorithm. The performance of our method is robust to parameters such as the number of grid points and the persistence of the process. and seminar participants at Duke, McGill, UCSD, University of Technology Sydney, and the 2016 Computing in Economics and Finance Conference for helpful comments and feedback. We are especially grateful to four anonymous referees for constructive comments and suggestions that significantly improved the paper. Matlab codes are posted in a supplementary file on the journal website,

Forecasts of professional forecasters are anomalous: they are biased, forecast errors are autocorrelated, and predictable by forecast revisions. Sticky or noisy information models seem like unlikely explanations for these anomalies: professional forecasters pay attention constantly and have precise knowledge of the data in question. We propose that these anomalies arise because professional forecasters don't know the model that generates the data. We show that Bayesian agents learning about hard-to-learn features of the data generating process (low frequency behavior) can generate all the prominent aggregate anomalies emphasized in the literature. We show this for two applications: professional forecasts of nominal interest rates for the sample period 1980-2019 and CBO forecasts of GDP growth for the sample period 1976-2019. Our learning model for interest rates also provides an explanation for deviations from the expectations hypothesis of the term structure that does not rely on time-variation in risk premia.

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