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Hornstein, Andreas; Alexander Wolman,. "Trend inflation, firm-specific capital, and sticky prices." Economic Quarterly. Federal Reserve Bank of Richmond. 2005. HighBeam Research. 25 Apr. 2018 <https://www.highbeam.com>.
Hornstein, Andreas; Alexander Wolman,. "Trend inflation, firm-specific capital, and sticky prices." Economic Quarterly. 2005. HighBeam Research. (April 25, 2018). https://www.highbeam.com/doc/1G1-143065519.html
Hornstein, Andreas; Alexander Wolman,. "Trend inflation, firm-specific capital, and sticky prices." Economic Quarterly. Federal Reserve Bank of Richmond. 2005. Retrieved April 25, 2018 from HighBeam Research: https://www.highbeam.com/doc/1G1-143065519.html
Research on monetary policy, both at academic and monetary policy institutions, has increasingly been performed within an analytical framework that assumes limited nominal price adjustment, "sticky prices" for short. At the heart of much of this analysis is a so-called New Keynesian (NK) "expectational" Phillips curve that relates current inflation, [[pi].sub.t], to expected future inflation and the deviation of marginal cost from trend [^.s.sub.t]:
[[pi].sub.t] = [beta][E.sub.t][[pi].sub.t+1] + [xi][^.s.sub.t], (1)
with [beta], [xi] > 0. Empirical estimates of the coefficient on the marginal cost term, [xi], in this NK Phillips curve tend to be positive but small in absolute value, e.g., Sbordone (2002) and Gali and Gertler (1999). (1) This represents a problem for the sticky-price framework since the coefficient [xi] is directly related to the frequency with which nominal prices are assumed to be adjusted: the coefficient is smaller the less frequently prices are adjusted. Within standard sticky-price models, estimated values of [xi] imply that prices are adjusted less than once per year. This macro estimate of price stickiness is implausibly high from the perspective of the micro estimates surveyed in Wolman (forthcoming).
It has been conjectured widely that nominal rigidities, such as sticky prices, have more persistent real effects if they interact with real rigidities. For example, the basic NK Phillips curve (1) has been derived for an environment with nominal frictions, but essentially no real rigidities: firms rent factors of production--capital and labor--in frictionless markets. Now, suppose that there is a real rigidity in addition to the sticky prices. In particular, assume that capital is specific to individual firms, and it is costly for these firms to adjust their capital stock. Introducing firm-specific capital adjustment costs into sticky-price models substantially complicates the analysis, yet Woodford (2005) manages to derive an almost closed-form solution to this problem. In particular, Woodford (2005) again derives an NK Phillips curve of the form (1), but now the marginal cost coefficient, [xi], depends not only on the extent of price stickiness, but also on the magnitude of capital adjustment costs: the coefficient is smaller the less frequently prices are adjusted and the more costly it is to adjust capital. Thus low estimated values of [xi] do not necessarily imply a high degree of price stickiness.
Woodford's (2005) clean analytical solution of the modified NK Phillips curve does come with a cost. His approach is based on the linear approximation of an economy with Calvo-type nominal price adjustment around an equilibrium with zero average inflation. The assumption of zero average inflation makes the theoretical analysis of the firm aggregation problem possible, yet it is not empirically plausible. Even though in recent years inflation has been remarkably stable in many industrialized countries, average inflation has been positive. Furthermore, most estimates of the NK Phillips curve use data from periods of moderate inflation. Thus, it is important to know whether the behavior of these models is sensitive to the steady-state inflation rate. (2)
In this article we evaluate the relative impact of positive average inflation versus zero inflation in an economy with nominal rigidities and firm-specific capital adjustment costs. Unlike Woodford (2005), we model nominal rigidities as Taylor-type staggered price adjustment, and not as Calvo-type probabilistic price adjustment. This approach is necessary since at this time there are no aggregation results for our economic environment with Calvo-type pricing and nonzero average inflation. We show that for small values of positive average inflation, the Taylor principle, which states that a central bank should increase the nominal interest rate more than one-for-one in response to a deviation of inflation from its target, is no longer sufficient to guarantee that monetary policy does not become a source of unnecessary fluctuations in our economy.
The fundamental difficulty with incorporating firm-specific capital into a model with sticky prices is that firm-specific capital can amplify the heterogeneity associated with price stickiness. With Calvo price setting, firms face a constant exogenous probability of being able to readjust their price. If there are no state variables specific to the firm (other than price), then all firms that adjust in a given period choose the same price. In that case, even though the true distribution of prices is infinite, it is possible to summarize the relevant distribution with just a small number of state variables. (3) If instead capital is firm specific, firms that adjust in the same period generally do not have the same capital stock. Their marginal cost is not the same, and in general they will not choose the same price. Thus, combining Calvo pricing and firm-specific capital appears to lead to an intractable model.
The model is intractable in its exact form, but Sveen and Weinke (2004) and Woodford (2005) have shown how to derive a tractable linear approximation to the model, under the assumption that the average inflation rate is zero. The key to these derivations is the fact that in the zero-inflation steady state there is no heterogeneity: all firms charge the same price.
Given the tractability problem, there is little hope of being able to learn how the Calvo model with firm-specific capital behaves away from a zero-inflation steady state. Fortunately, there is another class of sticky-price models that remains tractable when combined with firm-specific capital. The staggered pricing framework associated with Taylor (1980) assumes that there are J different types of firms; each period a fraction 1/J of firms adjusts their prices, and their prices remain fixed for J periods. Firm-specific capital presents no problems in the Taylor model, because it remains the case that all firms that adjust in a given period enter with the same capital stock and thus will choose the same price.
We solve the linear approximation to the Taylor model numerically and ask whether the model's dynamics are sensitive to the steady-state inflation rate around which we linearize. (4) We find that a small but positive inflation rate can have a big impact on the set of parameters for monetary policy rules and investment adjustment costs for which a rational expectations (RE) equilibrium is unique. (5) If the equilibrium is not unique, that is, there is equilibrium indeterminacy, then possible equilibrium outcomes can depend on shocks that do not constrain the resource feasible allocations in an economy. In these equilibria self-fulfilling expectations that coordinate on such nonfundamental shocks, known as "sunspots," introduce unnecessary fluctuations into the economy.
In standard sticky-price models, monetary policy rules that set the nominal interest rate in response to deviations of inflation from its target value achieve a unique RE equilibrium, if they follow the Taylor principle. The principle states that the nominal interest rates increase more than one-for-one with an increase of the inflation rate. This policy response does not have to be very big, as long as it is greater than one. We show that in the sticky-price model with firm-specific capital, positive steady-state inflation generally increases the region of the parameter space for which there is indeterminacy of equilibrium. In other words, for the same magnitudes of price-stickiness and capital-adjustment costs, monetary policy has to be much more responsive to deviations of inflation from its target in order to maintain a unique RE equilibrium outcome. These results suggest that it may be misleading to interpret history and make policy recommendations based on findings from the zero steady-state inflation case. Our results complement those in Sveen and Weinke (2005), who show that moving from a rental market to firm-specific capital leads to a larger region of the parameter space for which there is indeterminacy of equilibrium when steady-state inflation is zero.
In Section 1 we describe the economy with firm-specific capital adjustment cost and the two types of sticky prices: Calvo-type and Taylor-type nominal price setting. In Section 2 we outline how Woodford (2005) solves the aggregation problem for Calvo-type pricing and derives the modified NK Phillips curve. In Section 3 we characterize the economy with Taylor-type pricing, and in Section 4 we study the impact of capital adjustment costs and nonzero average inflation on the economy with Taylor-type pricing.
1. STICKY-PRICE MODELS WITH FIRM-SPECIFIC CAPITAL
This section presents the common features of Calvo and Taylor sticky-price models. There is an infinitely lived representative household and a continuum of differentiated firms. The firms act as monopolistic competitors in their differentiated output markets, but they are competitive in their differentiated labor markets. The differentiated output goods of the firms are used to produce an aggregate output good in a competitive market. …
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