Understanding the Inventory Cycle: A Non-Linear Setting

Abstract

This paper studies the business cycle implications of a nonlinear-production general equilibrium model which allows the existence of inventory investment for the purpose of stockout avoidance. Among the primary contributions is the development of a solution methodology which, by creating a parameterization of the levels of the conditional expectations of the Euler equations, preserves the non-linear nature of the policy functions of the model, and conveniently handles a nonnegativity constraint on inventory holdings. Such a methodology is developed for an economy where inventory investment serves the purpose of stockout-avoidance, as well as for one where inventories intend to smooth production. The production lag present in the stockout-avoidance model is handled in a similar fashion as the way Burnside, Eichenbaum & Rebelo (1993) implements a labor hoarding framework. The parameterized expectations algorithm is implemented following the methodology proposed by Christiano & Fisher (2000), and the approximations of the policy functions are carried out following a procedure similar to the finite elements method found in McGrattan (1996). All the pertaining propositions stated in Wen (2005) also hold in this more general framework. Different calibrations of the model are done to test the robustness of the results.

Keywords: Business cycles, Inventories, Stockout-avoidandace, Production Smoothing

JEL Classification: E13, E22, E32