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Article Excerpt
JEL codes: E3, E4, E5
Keywords: monetary aggregates, inflation target, cashless economy.
THERE IS HARDLY any issue of a more fundamental nature, with regard to monetary policy analysis, than whether such analysis can coherently be conducted in models that make no explicit reference whatsoever to any monetary aggregate. Since the use of such models has been common--indeed, standard--in recent years, this issue has been considered by several writers including Alvarez, Lucas, and Weber (2001), McCallum (2001), Nelson (2003), Lucas (2006), and Reynard (2006). Most prominently, Woodford (2008) has devoted a full section of his paper for the Fourth ECB Central Banking Conference (on "The Role of Money") to this particular theoretical topic. (1) Woodford's discussion is meticulously executed and, in most respects, convincing but there are, in my opinion, a few significant points that call for elaboration or modification. The following discussion is intended to provide, in a brief manner, the implied amendments.
1. THE BASIC RESULT
Consider the following representation of the simplified three-equation framework that has been widely used over the past several years in monetary policy analysis:
[y.sub.t] = [b.sub.0] + [b.sub.1]([R.sub.t] - [E.sub.t][DELTA] [p.sub.t+1]) + [E.sub.t][y.sub.t+1] + [v.sub.t], [b.sub.1] (1)
[DELTA][p.sub.t] - [DELTA][p.sup.avg] = [beta]({E.sub.t][DELTA] [p.sub.t+1] - [DELTA][p.sup.avg]) + [kappa]([y.sub.t] - [[bar.y].sub.t]) + [u.sub.t], (2)
[R.sub.1] = [[mu].sub.0 + [DELTA][p.sub.t] + [[mu].sub.1]([DELTA][p.sub.t] - [[pi].sup.*]) + [[mu].sub.2]([y.sub.t] - [[bar.y].sub.t]) + [e.sub.t], [[mu].sub.1] > 0, [[mu].sub.2] > 0. (3)
Here [y.sub.t] and [p.sub.t] are logs of output and the price level in period t, so [DELTA][p.sub.t] = [[pi].sub.t] is inflation while [R.sub.t] is a one-period nominal interest rate. Also, [[bar.y].sub.t] is the flexible-price (or "natural rate") level of [y.sub.t]. Equation (1) represents a forward-looking "expectational IS" function of the type that can be justified by dynamic optimization analysis, as is by now very well known. The stochastic disturbance [v.sub.t] represents the effects of taste shocks and expected changes in the log of government spending; it is assumed to be exogenous, as are the "cost push" and policy shocks [u.sub.t] and [e.sub.t]. (All three are generated by mean-zero covariance-stationary processes.) Strictly speaking, a term involving the expected growth rate of real money balances between t and t + 1 should also appear in equation (1), unless the relevant transaction-cost function is additively separable--which is highly implausible. But my investigation (2001), as well as Woodford's (2003, pp. 111-23), indicates that the effects of this term would be quantitatively unimportant. (2) Equation (2) is a price adjustment relation, based on one of the Calvo type, in which [DELTA][p.sup.avg] is the long-run average inflation rate. Thus, the specification used here, equivalent to that in Woodford (2008) with one exception to be discussed shortly, is one in which prices (of those firms that do not have the option to reoptimize in a period) rise during that period at the rate [DELTA][p.sup.avg]. (3) For present purposes it will suffice to treat St as exogenous, as is usually done in small models, although the present argument would not be altered if investment and therefore St were endogenized. (4)
Finally, equation (3) represents a policy rule of the Taylor (1993) type, which has the effect of adjusting upward the interest rate [R.sub.t] when inflation exceeds its target value [[pi].sup.*] and/or the output gap is positive. For best performance the central bank will choose the parameter [[mu].sub.0] to equal [bar.r], the long-run average real rate of interest, which is implied by (1) to equal - [b.sub.0]/[b.sub.1], presuming that we are abstracting from growth in St and government consumption.
Clearly,...
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