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Learning, Expectations, and Endogenous Business Cycles

Doshchyn, Artur and Giommetti, Nicola (2013): Learning, Expectations, and Endogenous Business Cycles.

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We show that business cycles can emerge and proliferate endogenously in the economy due to the way economic agents learn, form their expectations, and make decisions regarding savings and production for future periods. There are no exogenous shocks of any kind to productivity or any other fundamental parameters of the economy, in contrast to Real Business Cycle models. To our knowledge this thesis is the first attempt to formally introduce adaptive learning and expectation errors as an autonomous source of endogenous business cycles.

We develop a simple, growth-less macroeconomic model, in which agents do not have perfect foresight, learn adaptively to form expec- tations, and solve limited inter-temporal optimization models. The theoretical possibility of cycles largely arises from the nonlinearity of the actual law of motion of price, in particular from the fact that agents always overpredict (underpredict) future prices when they are higher (lower) than equilibrium level. Even though the main version of the model is based on households having a simple logarithmic utility func- tion, we also show that the results hold when a more generic Hyperbolic Absolute Risk Aversion utility function is chosen. Money stock is neutral in the long run in either case.

We conduct simulations in models with agents having both simple logarithmic and HARA utility functions. Following Thomas Sargent (1993), we assume agents to be “rational econometricians” using various econometric adaptive learning tools: Auto ARIMA, VAR and AR(2) models. In all simulations, output and other economic variables indeed display cyclical fluctuations around their equilibrium levels.

Both converging and diverging cycles may be obtained in simulations with Auto ARIMA models, while the VAR learning tool leads to diverging fluctuations in the majority of cases, suggesting that making agents consider several variables increases instability, at least in our setting. It is also observed that higher frequency of model switching is usually accompanied with increasing amplitude of cycles, suggesting the hypothesis that economic crises may happen when agents make drastic revisions of their beliefs about how the economy works. Only converging cycles can be obtained with AR(2), however in this case the economy may get trapped in a so called “false equilibrium”, with output way below or above the true equilibrium level. Even though this is not formally an equilibrium, the convergence towards the true one is so slow that exogenous shocks may be needed to move the economy back on track. This result is in line with the Keynesian view that the economy may remain in a depressed state for quite a long period of time, and active government intervention may be required to speed up the recovery.

Within the developed framework we analyze whether active mone- tary policy (i.e. changes in money stock) can be used for stabilization purposes. It turns out that in the simple case, when agents have loga- rithmic utility function, shifts in money supply can have real effects on the economy only if they are unexpected by agents, or if future price expectations are not adjusted exactly proportionally to the announced monetary interventions. We also show that the second case is not sus- tainable within the adaptive learning environment, so that monetary policy may become ineffective in the long run when, and if, learning is complete.

We prove, however, that monetary interventions always have real effects in the short run in the setting with a more generic HARA utility function. Still, it is highly questionable whether the central bank is able to accurately assess the consequences of its own actions, as that would require it knowing precisely the actual law of motion of the economy, current market’s expectations, and agents’ reaction to news about the upcoming monetary interventions, which, moreover, can change over time.

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