Expectations with No Regrets (Job Talk)

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Abstract: I develop a general learning framework in order to answer the question ``how do expectations evolve?" I consider a recursive general-equilibrium framework that nests a large class of macroeconomic models due to the agents’ uncertainty of the economy's law of motion. I impose a learning framework based on the idea that agents try to minimise losses in their future expected payoff occurring due to such uncertainties. Unlike the vast majority of the learning literature in macroeconomics, the entire learning process is phrased in terms of the structural model and a reduced form, thus I offer a solution to the critique of Williams (2003). I give conditions under which the cumulative payoff loss, or `regret', is small compared to the total payoff that the agent might have had had she adhered to the model supplying the optimal payoff in hindsight. An immediate outcome of the theory is that an agent's expectations are fundamentally both forward-looking and backward looking, which is consistent with a very large body of empirical evidence from recent years. I examine some of the economic implications in a simple permanent income model with linear marginal utility. No-regret learning results in generic violation of the ``random walk hypothesis" studied ever since Hall’s (1978) classical paper. Namely – contrary to rational expectations prediction, under no-regret learning consumption would typically not follow a random walk nor would it be a martingale. Nevertheless, under some conditions on the convergence of the learning process and its rate of convergence, consumption has a central limit theorem.

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