Acknowledgments
The author thanks Duncan Foley, Kenneth Kuttner, David Laidler, and Michael Woodford for helpful discussions.
Notes
1For those who would cling to the economist's language, Woodford includes versions of his basic model in which a demand for money arises from transaction frictions, modeled variously as cash-in-advance or money-in-the-utility-function, but always with the caveat that they add nothing very substantial (either theoretical or empirical). See Section 2.3 “Price-Level Determination with Monetary Frictions” and Section 4.3 “Money and Aggregate Demand.”
2This is how Fischer Black proposed to pin down the price level (Black Citation1987, chapter 11).
3The relevant equations are 1.21 (IS) and 1.28 (LM). Subsequently, Woodford shifts attention from Wicksell-type rules that stabilize the price level to Taylor-type rules that instead stabilize inflation. The Taylor Rule of Equation 2.4 (LM) thus gives rise to the inflation determination Equation 2.9 (pp. 90–91).
4In practice, Woodford works with log-linearized versions of these three equations rewritten as functions of the output gap: (1.12), (1.13), (1.14) on p. 246.
5The equations on pp. 249–50 provide a handy guide for translating the different kinds of shocks into their associated changes in the natural rate of output and real interest.
6If shocks are all aggregate, and central banks have sufficient informational advantage to track changes in the natural rate of interest exactly, then in principle nominal interest rate variation can get back to the first-best. Clearly however this is a special case.
7New capital is just units of the (distorted) composite consumption good purchased and installed irrevocably by the individual firms.
8Nonetheless the fact that implicit rental rates on capital vary across firms is enough to tell us that there is no mechanism for bringing them into line with one another, much less with the market rate of interest, much less the natural rate. The rental rate is implicit because firms are demand constrained so there is no margin along which we can think about increasing output by adding capital. As Woodford says, “the shadow value of additional capital must be computed instead as the reduction in labor costs through substitution of capital inputs for labor, while still supplying the quantity of output that happens to be demanded” (p. 355).
9The essential source document for tracing this element of Woodford's thought is his 2001 paper “Monetary Policy in the Information Economy,” listed in his references as Woodford (2001b) but cited in the text as Woodford (2001c).