Quantitative macroeconomics typically disciplines models by matching selected moments. We show how finite-state hidden Markov approximations make likelihood estimation and model selection feasible for nonlinear, non-Gaussian latent processes on short panels, without simulation. We illustrate the method with PSID earnings data. The calibrations that best match moments of earnings dynamics fit complete histories worse than a likelihood-estimated process with a Gaussian persistent component. In a standard saving model, calibrations of one process that fit the targets about equally well imply mean assets that differ by a factor of three. Close agreement with selected moments can leave economic predictions largely undetermined.

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