Firm-Specific Capital and Aggregate Inflation Dynamics in Woodford’s Model,’ manuscript, http://www.faculty.econ.northwestern.edu/faculty/christiano/research/firmspecific/svensson.pdf

This note exposits Woodford’s (2004) strategy for solving the model with capital in Woodford (2003)’s chapter 5. In this model, the capital used by firms is completely firm-specific, and so the standard assumption that there are aggregate rental markets in capital services is ruled out. Similarly, there is no economy-wide market for labor. The assumption that factors are firm-specific only complicates the computation of the parameters in the reduced form equation characterizing aggregate inflation dynamics. All the other equilibrium conditions coincide with the standard ones that occur in the version of Woodford’s model in which capital and labor are homogeneous and are traded in economy-wide factor markets. This is why this note focuses specifically on the equilibrium equation characterizing aggregate inflation dynamics. Woodford’s (2004) strategy for computing the parameters of the reduced form inflation equation as a function of model parameters is based on undetermined coefficients. MATLAB programs for doing these calculations are available on the author’s web site.2 The details of the equation governing aggregate inflation dynamics depend on the details of the model. It turns out that the undetermined coefficient method discussed here is quite flexible. It has been extended to incorporate Kimball (1995)’s specification of demand by Eichenbaum and Fisher (2004). It has been extended to a model with higher-order adjust-ment costs in investment and sticky wages in Altig, Christiano, Eichenbaum, and Linde (2004). For a discussion of the motivation for analyzing models with firm-specific factors of production, see the recent papers by Altig, Christiano, Eichenbaum and Linde (2004)