Monetary policy responses and strategic price setting

Monetary policy responses and strategic price setting

Economics Letters 95 (2007) 327 – 333 www.elsevier.com/locate/econbase Monetary policy responses and strategic price setting George J. Bratsiotis ⁎ S...

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Economics Letters 95 (2007) 327 – 333 www.elsevier.com/locate/econbase

Monetary policy responses and strategic price setting George J. Bratsiotis ⁎ School of Social Sciences, The University of Manchester, Dover Street, Manchester M13 9PL, UK Centre of Growth and Business Cycle Research (CGBCR), UK Department of Economics, University of Athens, 8 Pesmazoglou Street, 10559, Athens, Greece Received 11 January 2006; received in revised form 21 September 2006; accepted 11 October 2006 Available online 21 March 2007

Abstract This paper shows that the systematic component of monetary policy is a potential determinant of the degree of strategic complementarity. Among its wider implications this result also points to an important interaction between the systematic and irregular components of monetary policy. © 2006 Elsevier B.V. All rights reserved. Keywords: Monetary policy rules; Price setting; Strategic complementarity; Real rigidities JEL classification: E31; E32; E52

1. Introduction As it has been stressed throughout the literature, in economies with nominal rigidities the degree of strategic complementarity in price setting is a crucial parameter in determining the slope of the New Keynesian Phillips Curve and the dynamic behavior of macroeconomic variables in the business cycle, (see Woodford, 2003). By strategic price setting, at the macroeconomic level, we refer to the effect that a change in the average price of other products, Pt, has on the optimal price of a firm's own product, p⁎t ( j), hence ∂log p⁎t ( j) / ∂log Pt. Strategic price setting is determined by two opposing effects: a relative price and an aggregate ⁎ School of Social Sciences, The University of Manchester, Dover Street, Manchester M13 9PL, UK. Tel.: +44 161 275 3910. E-mail address: [email protected] 0165-1765/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2006.10.014

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demand effect. In general, if the positive relative price effect dominates the negative aggregate demand effect then, ∂log p⁎t ( j) / ∂log Pt N 0 and pricing decisions are said to be strategic complements, whereas if the opposite is true then, ∂log p⁎t ( j) / ∂log Pt b 0 and prices are said to be strategic substitutes. 1 Sources of strategic complementarity have been sought in imperfections in goods, labor and financial markets. Imperfections or asymmetries in the inputs of factors of production, (i.e. due to labor or capital heterogeneity), increasing returns to scale and asymmetric product revenue conditions are some of the most common sources of strategic complementarity, (see Ball and Romer, 1990; Kimball, 1995; Kiley, 1997; Woodford, 2003). Conversely, assuming economy-wide factors and relaxing the assumptions of increasing returns and other asymmetries, eliminates real rigidities and encourages strategic substitutability. This paper shows that monetary policy itself may be an important determinant of the degree of strategic complementarity. When monetary policy responds asymmetrically to the contemporaneous levels of output and the aggregate price it affects the trade-off between the relative price and the aggregate demand effects that is crucial in strategic price setting. A higher relative response to output dampens the aggregate demand effect in relation to the relative price effect and encourages strategic complementarity. Conversely, a higher relative response to the aggregate price increases the aggregate demand effect in relation to the relative price effect; this reduces strategic complementarity and encourages strategic substitutability. The above result supports the conventional wisdom among many macroeconomists recently, that the systematic part of monetary policy may play a more important role for the dynamic behavior of macro variables in the business cycle than irregular exogenous monetary shocks.2 It also points to an interaction between the systematic and irregular components of monetary policy rules, as the parameters of policy rules affect, through the endogenous response of the degree of strategic complementarity, the response of the economy to exogenous departures from these rules. 2. The model Consider a standard general equilibrium macroeconomic model where each firm produces a differentiated intermediate good j, j ∈ [0,1], used in the production of a composite final good. The household's expected utility is additively separable and increasing in consumption (C) and real money balances (M / P), while decreasing in the labor supplied, (N). !   1−cc 1−cm l 1þd X M C ðM =P Þ N t t t ; ð1Þ bt þ xm −xN t U C; ; Nj ¼ E0 P 1−c 1−c 1þd c m t¼0 where 0 b β b 1, is the discount factor; 0 b γc,γm b 1; δ = 1 / η N 0; η is the labor supply elasticity. Assuming Dixit–Stiglitz preferences the demand for product j is, 

pt ð jÞ ct ð jÞ ¼ Ct Pt 1 2

−r

;

rN1;

See Blanchard and Fischer (1988) and Woodford (2003). For a recent discussion see Woodford (2003) and Walsh (2006).

ð2Þ

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R r=ðr−1Þ R 1=ð1−rÞ 1 1 where, Ct ¼ 0 ct ð jÞðr−1Þ=r dj and Pt ¼ 0 pt ð jÞ1−r dj are the CES consumption index and aggregate price index respectively. Each household chooses consumption, real money balances and labor supply given the competitive wage, Wt, and subject to their budget constraint, Pt Ct þ Mt −Mt−1 þ Bt ¼ Wt Nt þ ð1 þ it−1 ÞBt−1 þ Vt ;

ð3Þ

where M, i, B, V, denote respectively the nominal values of, money, interest rate, bonds and profits. The household's maximization problem results in the familiar first order conditions,  1 ¼ Et bRtþ1

Ctþ1 Ct

−cc

;

where Rtþ1 ¼ ð1 þ it ÞPt =Ptþ1 :

ð4Þ

 −cm it c c Mt ¼ xm Ct ; 1 þ it Pt

ð5Þ

Wt c 1=g ¼ xN Ct c Nt : Pt

ð6Þ

Production in each firm relies on homogenous labor, yt( j) = AtNt( j), where At is productivity. Having assumed economy-wide factors all firms share identical real marginal costs, st ð jÞ ¼ st ¼

Wt =Pt : At

ð7Þ

3. Strategic price setting Using the above information the log-linearized optimal price of firm j is, 3 pt̂ ð jÞ ¼ Pt̂ þ fY t̂ −At;̂ ⁎

ð8Þ

where Xˆ t = Xt − X is the percent deviation of Xt from its steady state X and ζ = 1 / η + γc is the output ˆ t be nominal aggregate demand, so that elasticity of the general equilibrium real marginal cost. Letting D ˆ ˆ Ŷt = Dt − Pt in Eq. (8), we obtain, Ap⁎t ð jÞ Ap⁎ ð jÞ AY ̂ ¼1þ t ¼ 1−f; APt̂ AY ̂ AP t̂ 3

ð9Þ

As with the rest of the literature, in discussing strategic price behavior this paper implicitly assumes less than fully flexible prices. If, p⁎t ( j) = Pˆt, then given our assumption of economy-wide factors there would be no role for strategic pricing.

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where with the unit income elasticity of demand, implied by the Dixit–Stiglitz preferences, we obtain ∂Ŷt / ∂Pˆt = −1 and ∂p⁎t ( j) / ∂Ŷt = ζ. Thus values of, ζ b 1 result in strategic complementarity, whereas ζ N 1 result in strategic substitutability. In general, the lower is ζ (below one) the higher is strategic complementarity or real rigidity (Ball and Romer, 1990). Intuitively, an increase in the aggregate price level (i.e. due to an exogenous shock) has a twofold effect on the optimal price of each firm. First, it reduces its real price and so keeping aggregate demand constant, each producer must match the aggregate price increase in an effort to keep their real price constant; this is a relative price effect and is positive and equal to one, ∂pt( j) / ∂Pt = 1. Second, for any given nominal aggregate demand, a higher aggregate price reduces real aggregate demand (hence product demand) and this results in a desired decrease in product prices; this is an aggregate demand effect and is negative, @p⁎t @ Y^ ¼ b 0; the total effect is ∂pˆ ⁎t ( j) / ∂Pˆt = 1 − ζ. The stronger is the strategic complementarity among @ Y^ @ P^t firms, the smaller is the aggregate demand effect (i.e. ζ) in relation to the relative price effect and the less sensitive is the real marginal cost to changes in output; hence the lower is the cost of any producer from not adjusting prices to changes in aggregate demand following a change in the aggregate price level. This results in small upward changes in real prices. The opposite is true if prices are strategic substitutes. In this case, ζ N 1 and as the aggregate demand effect dominates the relative price effect real prices are moderated as a response to a higher aggregate price. Next we show that monetary policy can affect the aggregate demand effect in price setting. This is true for any systematic monetary policy that reacts endogenously but asymmetrically to the contemporaneous level output and the aggregate price. The simplest way to demonstrate this is by the use of two popular monetary rules that act as policy reaction functions in these two variables. 3.1. Strategic pricing under a simple monetary policy rule First consider a static money demand where consumption equals real balances, so that at equilibrium, Y ̂t ¼ M̂ t −Pt̂ :

ð10Þ

Let Eq. (10) interact with the following simple monetary policy rule, 4 ex M̂ t ¼ M̂ t −/k Pt̂ ;

ð11Þ

ˆ tex is the exogenous component of the money stock. An active policy rule of this form implies where M the following aggregate demand, ex Y ̂t ¼ M̂ t −/k Pt̂ −Pt̂ :

ð12Þ

From Eqs. (8) and (12) the strategic price setting effect is, Ap⁎t ð jÞ Ap⁎ ð jÞ AY ̂ ¼1þ t ¼ 1−fð1 þ /k Þ: AP ̂ t AY ̂ AP t̂ 4

ð13Þ

Similar monetary policy rules have been used widely. Taylor (1980), for example, considers an accommodating monetary ˆ t = ϕπPˆt. policy rule where, M

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For any given ζ, the aggregate demand effect is shown to be affected by the relative monetary response to the aggregate price, ϕπ. As monetary policy responds only to aggregate prices, and not to output, the elasticity of the aggregate demand to a change in the aggregate price is no longer ∂Ŷ / ∂Pˆt = − 1, but ∂Ŷ / ∂Pˆt = − 1, but ∂Ŷ / ∂Pˆt = − (1 + ϕπ). A higher ϕπ is shown to increase the responsiveness of aggregate demand to a change in the aggregate price level and increase the aggregate demand effect in relation to the relative price effect. Such policy reduces strategic price complementarity and encourages strategic price substitutability among firms. 3.2. Strategic pricing under a simple interest rate rule We now consider a dynamic aggregate demand driven by an interest rate rule, as adopted in the most recent literature. Log-linearising Eq. (4) obtains, ̂ þ Pt̂ Þ; Y ̂t ¼ Et Y ̂tþ1 −ð1=cc Þðit ̂−Et Ptþ1

ð14Þ

where, ˆit is set according to a Taylor-type interest rate rule, ex ̂ Þ þ / Y ̂t ; it ̂ ¼ it ̂ þ /k ðPt̂ −Pt−1 y

ð15Þ

where ˆi tex is an exogenous component, Pˆt − Pˆt−1 = πt is inflation and Ŷt is the output gap. An active policy rule of this form implies the following aggregate demand, Y ̂t ¼

 1  ̂ Þ þ ðEt Ptþ1 ̂ ̂ −PtÞ cc Et Y ̂tþ1 −itex −/k ðPt̂ −Pt−1 c c þ /y

ð16Þ

From Eqs. (8) and (16) the strategic price effect is, ! Ap⁎t ð jÞ Ap⁎t ð jÞ AY ̂ 1 þ /k : ¼1þ ¼ 1−f cc þ /y APt̂ AY ̂ AP t̂

ð17Þ

By setting γc = 1, Eq. (17) becomes identical to Eq. (13), but with a similar response for the output gap here. 5 As with Eq. (13), monetary policy, in the form of an interest rate rule here, affects strategic price setting through the aggregate demand effect. Both Eqs. (13) and (17) indicate that it is the relative policy weights (i.e. the ratio (1 + ϕπ) / (1 + ϕy)) that matters for the latter effect. If monetary policy responses to the contemporaneous levels of output and the aggregate price are symmetric, (ϕy = ϕπ), then with γc = 1, ∂Ŷt / ∂Pˆt = −1 and ∂pˆ t⁎( j) / ∂Pˆt = 1 − ζ. In this case, systematic monetary policy resembles exogenous monetary policy (i.e. ϕy = ϕπ = 0), as it no longer affects the aggregate demand effect or the degree of strategic complementarity. In general, a higher relative weight on price stability increases the aggregate demand effect in relation to the relative price effect and encourages strategic substitutability. Conversely, Note that Eq. (10) implies γc = 1 in Eq. (4). Hence, if the money supply in Eq. (11) responded to output as well as the aggregate price, then the effects in Eqs. (13) and (17) would be identical. 5

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Table 1 Monetary policy and strategic price effects ∂pj⁎ / ∂P

Policy weights ϕy

ϕπ

ζ = 0.1

ζ = 0.5

ζ=1

ζ=2

ζ = 10

0.5 1.5 2.5 3.5 0.5 0.5 0.5 0.5

1.5 1.5 1.5 1.5 1.7 2.5 3.5 5.0

0.833 0.900 0.929 0.944 0.820 0.767 0.700 0.600

0.167 0.500 0.643 0.722 0.100 − 0.167 − 0.500 − 1.000

−0.667 0.000 0.286 0.444 −0.800 −1.333 −2.000 −3.000

−2.333 −1.000 −0.429 −0.111 −2.600 −3.667 −5.000 −7.000

−15.667 −9.000 −6.143 −4.556 −17.000 −22.333 −29.000 −39.000

a higher relative weight on output stability dampens the aggregate demand effect in relation to the relative price effect and encourages real price rigidity. As Table 1 shows, the final effect is, ∂log pˆt⁎( j) / ∂log Pˆt ⋛ 0 and depends on both the relative size of monetary policy responses, (ϕy,ϕπ), and the supply side factors affecting strategic price decisions (i.e. ζ). 6 The above results imply an interaction between the systematic and irregular parts of monetary policy rules, since the former (through the parameters ϕy,ϕπ), can affect the way the economy responds to ˆ tex and ˆitex here). irregular shocks in the exogenous components of policy rules, (i.e. M 4. Concluding remarks This paper shows that the systematic component of monetary policy may be a potential determinant of the degree of strategic complementarity. The intuition of this result is based on the way that systematic monetary policy affects the trade-off between the relative price and the aggregate demand effect in price setting. Monetary policy that aims at price stability implies that the monetary authority is prepared to change aggregate demand by any amount necessary to eliminate inflation; this increases the aggregate demand effect, lowers real rigidity and encourages strategic price substitutability. This, for example, may explain why in times of strong anti-inflation policy prices may be adjusting downwards faster. Conversely, when monetary policy is more sensitive to the output gap, then it aims mainly to dampen output fluctuations and this reduces the aggregate demand effect in relation to the relative price effect. The rationale here is that by ironing out booms and recessions, monetary policy also reduces the firms' incentives to adjust prices, thus encouraging conditions of strategic price complementarity or real rigidity. The main finding in this paper points to an important interaction between the irregular and systematic components of monetary rules: irregular monetary shocks initiate exogenous departures from the rule, yet how the economy responds to the latter is determined, among other factors, by the systematic policy weights in the rule which affect endogenously the degree of strategic complementarity, a parameter that is widely believed to be a crucial determinant of the dynamic behavior of the economy within the business cycle.

6

Table 1, considers for clarity the case of gc = 1 and the same value range for ζ as in Woodford (2003).

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Acknowledgment I am grateful to an anonymous referee for the helpful comments and suggestions. References Ball, L., Romer, D., 1990. Real rigidities and the non-neutrality of money. Review of Economic Studies 57, 128–203. Blanchard, O., Fischer, S., 1988. Lectures in Macroeconomics. MIT Press, Cambridge, Mass. Kiley, M.T., 1997. Staggered price setting and real rigidities. Federal Reserve Board FEDS. Working Paper, vol. 1997-46. Kimball, M., 1995. The quantitative analytics of the basic neomonetarist model. Journal of Money, Credit, and Banking 27, 1241–1277. Taylor, J.B., 1980. Aggregate dynamics and staggered contracts. Journal of Political Economy 88, 1–23. Walsh, Carl E., 2006. The contribution of theory to practice in monetary policy: recent developments. Working Paper. http://econ. ucsc.edu/~walshc/. Woodford, M., 2003. Interest and Prices: Foundations of a Theory of Monetary Policy. Princeton University Press.