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Description
We study the macroeconomic effects of nonzero trend inflation in a simple dynamic stochastic general equilibrium model under three common time-dependent pricing schemes: Calvo, truncated-Calvo, and Taylor. We show that, regardless of the pricing mechanism, trend inflation leads to a reduction in the stochastic means of output, consumption and employment, and an increase in the stochastic mean of inflation beyond its deterministic steady-state level. The variability of most aggregates also increases. These effects are quantitatively much stronger with Calvo pricing.
JEL codes: E31, E32, E52
Keywords: sticky prices, monetary policy, inflation targeting.
THE NEW KEYNESIAN PHILLIPS CURVE (henceforth NKPC) is a workhorse of modern macroeconomics. (1) It has been used as a key element of dynamic stochastic general equilibrium (henceforth DSGE) models for theoretical, empirical, and monetary policy analysis. The NKPC holds only under restrictive assumptions. Either trend inflation must be zero or firms must index their prices to past inflation, trend inflation, or target inflation. (2) Solving DSGE models without these assumptions is much more tedious. However, trend inflation rates of zero are exceedingly rare in real-world economies and many prices are observed to remain fixed for long periods of time, suggesting less than full indexation. Moreover, trend levels of inflation tend to change over time. Levin and Piger (2003) and Levin, Natalucci, and Piger (2003) provide evidence on changing trend inflation rates for several developed countries. As well, countries whose central banks have adopted official inflation targets have invariably opted for positive inflation targets. (3)
In the light of this evidence, it is not difficult to motivate the case for studying optimizing pricing behavior without assuming zero trend inflation or complete indexation. In this paper, we study the macroeconomic effects of nonzero trend inflation in a simple DSGE model under Calvo (1983), truncated-Calvo, and Taylor (1979) pricing. We solve the model using a second-order approximation of its equilibrium conditions. In contrast to previous studies, we focus on the effects of trend inflation on the stochastic means of macroeconomic aggregates.
Our main findings can be summarized as follows. Price dispersion across different intermediate inputs increases with trend inflation. The stochastic mean of a summary measure of price dispersion increases by more than its deterministic steady state as trend inflation rises. As a result, the stochastic means of variables such as output, consumption and employment decrease. The stochastic mean of inflation increases by more than trend inflation when the latter is measured by its level in a deterministic steady state. The variability of most aggregates increases with trend inflation, and the persistence of inflation is particularly sensitive to trend inflation. Finally, these results hold qualitatively for all of the pricing schemes that we analyze, but the quantitative effects are much stronger under Calvo pricing than under Taylor or truncated-Calvo pricing.
Our paper is related to previous studies of the effects of trend inflation. Ascari (2004) and Bakhshi et al. (2003) set up dynamic general equilibrium models with Calvo pricing. They showed that because of price dispersion, the level of output declines in the deterministic steady state as trend inflation rises. Ascari analyzed the effects of trend inflation on output persistence by studying impulse response functions of output to a money growth shock with different levels of trend inflation. Bakhshi et al. carefully examined the effects of nonzero trend inflation on the slope of the NKPC. They found that the curve is flatter at higher levels of trend inflation, so that inflation is less responsive to changes in either the output gap or a measure of firms' real marginal cost. Bakhshi et al. used linearized versions of first-order conditions to derive their NKPC whereas Ascari used second-order approximations, but limited his analysis of the model's dynamic properties to impulse response functions. Our paper innovates principally by using second-order approximations to uncover the effects of shocks on the stochastic means of variables as well as their unconditional second moments (volatility and persistence).
The remainder of the paper is organized as follows. In Section 1 we outline our model. In Section 2 we discuss the calibration of the structural parameters and our numerical simulation methodology. We present results in Section 3. Section 4 concludes.
1. THE MODEL
The economy consists of a representative household with an infinite planning horizon, a representative final good firm, a collection of monopolistically competitive firms that produce differentiated intermediate goods, and a monetary authority that sets the short-term nominal interest rate following a Taylor rule. It finances its issuance of cash balances with lump-sum taxation. The demand for money is motivated by real balances in the representative household's utility function.
1.1 Households
The representative household maximizes expected utility given by:
max[E.sub.0][[infinity].summation over (t=0)][[beta].sup.t]U ([C.sub.t], [M.sub.t]/[P.sub.t], [H.sub.t]), (1)
where [C.sub.t] is consumption, [M.sub.t] is nominal balances, [P.sub.t] is the price level, [H.sub.t] is hours worked, and [beta] [member of] (0, 1) is a subjective discount factor. The functional form of period utility is given by:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
where [b.sub.t] is a preference shock which can be interpreted as a money demand shock. The parameter [sigma] > is the elasticity of substitution between consumption and real balances. This functional form leads to a conventional money demand equation with consumption as the scale variable. The preference shock [b.sub.t] follows a stationary AR(1) process in logs:
log([b.sub.t]) = [[rho].sub.b] log([b.sub.t-1]) + (1 - [[rho].sub.b])log(b) + [[epsilon].sub.b,t], (3)
where [[rho].sub.b] [member of] (0, 1), and where the stochastic shock term [[epsilon].sub.b,t] is i.i.d, normal with a zero mean and a standard deviation of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. The representative household's budget constraint in period t is:
[P.sub.t][C.sub.t] + [P.sub.t][I.sub.t] + [P.sub.t]CA[C.sub.t] + [M.sub.t] + [B.sub.t]/[R.sub.t] [less than or equal to] [P.sub.t][w.sub.t][H.sub.t] + [P.sub.t][q.sub.t][K.sub.t] - [T.sub.t] + [D.sub.t] + [M.sub.t-1] + [B.sub.t-1], (4)
where [w.sub.t] is the real wage, [q.sub.t] is the real rental rate of capital, [T.sub.t] is a lump-sum tax, [D.sub.t] denotes nominal dividend payments received from monopolistically competitive firms, [I.sub.t] is real investment, [K.sub.t] is the stock of capital, CA[C.sub.t] is a capital adjustment cost, and [R.sub.t] is the gross nominal interest rate on debt between t and t + 1.
Investment increases the household's stock of capital according to
[K.sub.t+1] = (1 - [delta])[K.sub.t] + [I.sub.t], (5)
where [delta] [member of] (0, 1) is the depreciation rate of capital. Investment is subject to convex adjustment costs of the following form:
CA[C.sub.t] = [sigma]/2 [([I.sub.t]/[K.sub.t] - [delta]).sup.2] [K.sub.t], (6)
where [phi] is a positive parameter. The first-order conditions associated with the optimal choice... |
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