Pricing To Habits and the Law of One Price: Appendix

This appendix expands the model presented in Ravn, Schmitt-Grohé, and Uribe (2006b) to allow for government purchases. It also contains a detailed derivation of the equilbirium conditions, the deterministic steady state, the calibration, the functional forms, and the simulation results. 1 The Model The model economy consists of two countries, the home country and the foreign country. Each country specializes in the production of a set of differentiated goods. We denote by a the class of goods produced by the home country and by b the class of goods produced by the foreign country. 1.1 Households Consider an economy populated by a large number of households with preferences described by the utility function E0 t=0 βtU(xct, ht). (1) The variable xct is a composite defined as xct = χ(xca,t, xcb,t), (2) where the aggregator function χ is assumed to be increasing and homogenous of degree one in both arguments. The variable xca,t is a habit-adjusted composite consumption good of varieties of goods of type a. Following Ravn, Schmitt-Grohé, and Uribe (2006a), we introduce deep habits. Specifically, we assume that habits form at the level of each individual variety of goods instead of at the level of the aggregate consumption good. We assume that deep habits are external to the individual household (i.e., we model catching up with the Joneses good by good). Formally, xca,t is given by xca,t