A rational expectatons critque of the Hahn-Solow critique of rational expectations
Solow and Hahn proposed an overlapping generations model in 1995 with which to criticize rational expectations. The agents have perfect foresight, but are subjected to an unanticipated shock in the population. The authors showed that the economy couldn't return to the steady state without monetary intervention. While the model is used to criticize rational expectations, it relies on the straw man of an unanticipated surprise, leaving the agents no possibility of adapting--the critique relies upon a model which lacks the fundamental characteristics of rational expectations. The model is revisited with a Rational Expectations model such that the possibility of a shock in each period is foreseen by agents, and used to form expectations. Rare and small increases and decreases in the population are both possible, with the log of population folowing a random walk, leaving only per capita capi tal as a state variable. While the model cannot be fully solved analytically, it can be solved far enough that complete soliton by high dimensional dynamic programming is possible. After analytic possibilities are exhausted, computation is used to find conditions in which the economy returns to the steady state following a shock, and those in which it diverges or enters a flip cycle--As the Clower constraint does not bind in all possible states of the world, the excess monetary holdings allow return to the steady state in some cases.
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