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First-order approximation methods are a standard technique for analyzing the local dynamics of dynamic stochastic general equilibrium (DSGE) models. Although linear methods yield quite accurate solutions for abroad class of DSGE models, some important economic issues (e.g., portfolio choice and welfare) cannot be adequately addressed by first-order methods. This paper provides yet another case when first-order methods may be inadequate for capturing the business cycle properties of a DSGE model. In particular, the authors show that increasing returns to scale (due to production externalities) may induce asymmetric business cycles and nonlinear income effects that are not fully captured by linear approximation methods. For example, hump-shaped output dynamics can emerge even when externalities are below the threshold level required for indeterminacy, and output expansion tends to be smoother and longer, whereas contraction tends to be deeper but shorter-lived, as observed in the U.S. economy.
(JEL C63, E0, E32)
Federal Reserve Bank of St. Louis Review, May/June 2011, 93(3), pp. 187-205.
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The standard approach to studying the business cycle implications of dynamic stochastic general equilibrium (DSGE) models is to focus on the models' local dynamics near a steady state through linear (first-order) approximations (such as the loglinearization method of King, Plosser, and Rebelo, 1988). It is well known that for standard real business cycle (RBC) models with constant returns, first-order approximation methods provide quite accurate solutions and higher-order methods give almost identical predictions.
The central twist of this paper is the addition of increasing returns to scale (IRS) caused by production externalities. We show that this simple deviation from standard RBC models generates nontrivial nonlinearities that are not well captured by first-order methods. Importantly, these nonlinearities are increasing in the degree of externalities over parameter ranges that predict a unique bounded rational expectations equilibrium. The model does not rely on local indeterminacy to generate new and interesting dynamics, although one contribution of the paper is the documentation of model properties when the model gives rise to local indeterminacy.1
Specific results of interest are that technology shocks generate asymmetric effects on business cycles. These effects come from second-order components of the model, which are ignored by linear approximation methods. Conditional on a positive technology shock, hump-shaped impulse response functions are predicted for...