The Kiel Institute for the World Economy

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1 The Kiel Institute for the World Economy Duesternbrooker Weg Kiel (Germany) Kieler Working Paer No. 277 Increasing Returns to Scale and the Long-Run Phillis Curve by Andrea Vaona and Dennis Snower May 2006 The resonsibility for the contents of the working aers rests with the authors, not the Institute. Since working aers are of a reliminary nature, it may be useful to contact the author of a articular working aer about results or caveats before referring to, or quoting, a aer. Any comments on working aers should be sent directly to the authors.

2 Increasing Returns to Scale and the Long-Run Phillis Curve Andrea Vaonaa and Dennis J. Snowerb May 7, 2006 Abstract: A growing body of emirical evidence shows that there exists a long-run ositive tradeoff between inflation and real macroeconomic activity. Within a New Keynesian framewok, we examine how increasing returns generate a ositive long-run relation between inflation and outut. Keywords: Phillis curve, Inflation, Increasing returns, nominal inertia, monetary olicy. JEL classification: E3, E20, E40, E50. Andrea Vaona The Kiel Institute for the World Economy and University of Verona, Deartment of Economic Sciences Polo Zanotto, Viale dell Università 4, 3729 Verona, Italy Telehone: andrea.vaona@economia.univr.it. Dennis J. Snower The Kiel Institute for the World Economy 2400 Kiel, Germany Telehone: dennis.snower@ifw-kiel.de athe Kiel Institute for the World Economy and University of Verona, Deartment of Economic Sciences, Polo Zanotto, Viale dell Università 4, 3729, Verona, Italy. Tel.: (+39) andrea.vaona@economia.univr.it. b The Kiel Institute for the World Economy and Christian-Albrechts University, Kiel; Düsternbrooker Weg 20, D2405 Kiel, Germany. Tel.: (+49) dennis.snower@ifw-kiel.de.

3 Introduction There is a growing body of emirical evidence that there is a long-run tradeo between in ation and real macroeconomic activity. Mankiw (200) writes that..if one does not aroach the data with a rior favoring long-run neutrality, one would not leave the data with that osterior. The data s best guess is that monetary shocks leave ermanent scars on the economy. Akerlof, Dickens and Perry (996, 2000) nd that the Phillis curve becomes downward-sloing at low in ation rates when there are ermanent downward wage rigidities or deartures from rational exectations. Ball (997) rovides evidence indicating that countries which had comaratively large and long declines in in ation also tended to have comaratively large increases in their NAIRUs. Dolado, Lóez- Salido and Vega (2000) nd some evidence of a long-run in ation-unemloyment tradeo for Sain during Fair (2000), Fisher and Seater (993), King and Watson (994), and Karanassou, Sala and Snower (2003, 2005) nd such a tradeo for the U.S. and the E.U. as well. This body of evidence is somewhat at odds with mainstream theory. The microfounded New Keynesian Phillis Curve (NKPC), often written as t = E t t+ a (u t u n ) + " t (where t is in ation, u t is unemloyment, and is the discount factor), imlies a long-run in ation-unemloyment tradeo, but this tradeo is generally considered too stee to account for evidence such as that above. When the microfoundations of the NKPC are analyzed, as in Ascari (998, 2000), Devereux and Yetman (2002) and Graham and Snower (2003), we nd that the long-run Phillis curve tradeo is due to three factors:. When rices are sticky due to Taylor or Calvo rice staggering, in ation causes relative rices to vary over the contract eriod. The relative rice variations lead consumers to substitute between goods - a henomenon we may call "roduct cycling". If these goods are imerfect substitutes, then roduct cycling is ine cient, so that a rise in in ation leads to a fall in aggregate roduct demand. 2. When the outut is roduced by labor (or other roductive factors), then roduct cycling gives rise to "labor cycling", i.e. substitutions among factors roducing the roducts. In the resence of diminishing returns to labor, such labor cycling is ine cient, so that a rise in in ation leads to a further fall in outut. 3. Under rice staggering, the rice of a roduct deends on the resent and future rice level. The greater the rate of time discount, the more closely the roduct rice deends on the current (rather than the future) rice level - for the simle reason that the future is valued less. Thus, the greater the rate of money growth and in ation, the lower will rices be set relative to the money suly. Consequently real money balances rise, leading to a rise in outut. The rst two e ects imly a negative relation between in ation and outut, whereas the third imlies a ositive e ect. It can be shown that, excet at 2

4 very low in ation rates, the rst two e ects dominate the third (Graham and Snower, 2003). The contribution of this aer is to examine the imlications of increasing returns on this analysis. The emirical evidence indicates that increasing returns are observable in various sectors of the economy, including rms and lants both in the manufacturing and in the retailing sector (see, for examle, Betancourt and Malanoski, 999, Ramey, 99, and Roberts and Suina, 997). We show that in the resence of increasing returns, labor cycling leads to e ciency gains. The greater the in ation rate, the greater the degree of labor cycling and the greater these e ciency gains. Consequently, labor cycling gives rise to a ositive relation between in ation and outut. For reasonable calibrated values, we show that this e ect is su ciently strong as to generate a ositive in ation-outut tradeo, even in the resence of roduct cycling. An increase in money growth (and thus in ation) leads to a su ciently large increase in outut to be roughly consonant with the emirical evidence above. The ushot of our analysis is that returns to scale matter for the shae of the long-run Phillis curve. The aer is organized as follows. Section resents our dynamic general equilibrium model, which is quite standard, excet for the inclusion of increasing returns to scale. We derive the corresonding long-run Phillis curve. Section 2 clari es the underlying intuition for our results. Section 3 concludes. 2 The Model The economy has three markets: a erfectly cometitive labour market, a monoolistically cometitive intermediate goods market with staggered rices, and a erfectly cometitive nal goods market. The money suly grows at rate ( ). All nominal values are detrended in terms of the money suly. Consumers maximize their utility over consumtion (c t ), real money holdings ( mt t ) and working time (n t ) subject to the budget and resource constraints: max fc t;m t;n tg t=0 X "ln t c t + V mt t subject to t y t = t c t + m t m t t y t = w t n t + t t # n+ t + where t is the aggregate rice level, y t is the level of outut, t are ro ts, is the time discount factor, and and are ositive constants. First-order conditions for consumtion, labour and money holdings are c t = t () n t + t w t t = 0 (2) 3

5 mt V m t t t t + t+ t+ = 0 (3) In the intermediate roduct market, each rm is an imerfectly cometitive rice setter, under Taylor rice staggering. Seci cally, the i th rm sets the rice it of the i th good in eriod t for a contract eriod that lasts until eriod t+n. This rice is set so as to maximize its ro t subject to its roduct demand (derived from (7), below) and its roduction function: N max E X t t+i i;t f i;tg i=0 t+i i y w t+i i;t+i n t+i t+i i;t subject to y i;t+i = t+i i y t+i (4) y i;t+i = n v i;t+i (5) where y i;t+i is the i th outut at time t + i, w t+i is the nominal wage, n t+i is emloyment, and y t+i is aggregate outut. The elasticity of substitution among intermediate goods,, is a ositive constant. Since there are increasing returns to scale, v > in the roduction function. The rst-order condition imlies the following rice setting equation: i;t = v ( ) P N i=0 t+i y v w t+i i;t+i t+i PN (6) yi;t+i i=0 t+i t+i i The second-order condition imlies that v < In the nal roduct market, erfectly cometitive rms buy an horizontally di erentiated inut, y i;t, to roduce an homogenous outut, y t. They set outut so as to maximize their ro t subject to their roduction function:. max fy i;tg ty t s:t:y t = NX i=0 NX i=0 y i;t i y i;t (7)! i;t Solving (7), we obtain the demand function for the intermediate good y i;t : y i;t = i;t t i The free entry condition gives the aggregate rice index: y t (8) 4

6 t = " N X i=0 i;t i # The general equilibrium is the solution of the equation system comrising the consumtion condition () ; the leisure condition (2) ; the money balance condition (3) ; the roduction function (5) ; the rice setting equation (6) ; the intermediate good demand (8) ; the rice index (9), as well as the market clearing condition: (9) y t = c t (0) The solution technique is outlined in the aendix. We calibrate the system for standard arameter values showed in Table. The resulting long-run relation between money growth (equal to in ation) and outut (for two di erent values of the elasticity of substitution ) is ictured in Fig.. Observe that a ermanent increase in money growth has a sizable e ect on the level of outut. The classical dichotomy breaks down in a nontrivial way: the real and monetary sides of the economy are not indeendent of one another in the long run. Furthermore, note that a rise in the elasticity of substitution imlies an increase in the outut e ect of monetary olicy, given that substitution ine ciencies decrease. Our analysis does not however imly that the Phillis curve necessarily remains uward-sloing over the entire range of relevant money growth rates. The reason is that roduction functions often dislay increasing returns only as long as factor utilization is not too high. Once outut exceeds some critical level, diminishing returns often set in and then the Phillis curve becomes downwardsloing. Finally, we turn to the intuition underlying our results. 3 Intuition As noted in the introductory section, aggregate rice level in ation under staggered rice setting leads an instability of relative rices that generates "roduct cycling" (households substitutions among di erent roducts) and "labor cycling" ( rms substitutions among di erent labor tyes). Product cycling is ine cient when the roducts are imerfect substitutes; labor cycling is ine - cient under diminishing returns, but e cient under increasing returns. The nature of the latter ine ciency or e ciency is illustrated in Fig. 2, which ictures a total cost function. Under increasing returns, the marginal cost function is declining, and thus when roduction uctuates between A + and A, there is an increase in e ciency due to the concavity of the cost function, as the average total cost is equal to C 2 and not to C. Conversely, under diminishing returns, the marginal cost function is increasing, so that when roduction uctuations between B + and B take lace, there is a dro in e ciency, since the average total cost is equal to C 3 and not to C 4 : 5

7 The greater is the elasticity of substitution among roducts, the smaller is the ine ciency from roduct cycling and thus the greater the ermanent outut gain from an increase in in ation. In sum, the long-run Phillis curve tradeo deends on the technologies available to the rms: increasing returns imly a ositive relation between macroeconomic activity and money growth; and - abstracting from the time discounting e ect that is dominant at very low in ation rates - diminishing returns imly a negative relation. 4 Aendix: Solving the General Equilibrium System For sake of simlicity we normalize the real wage to. Then given that i;t is constant in steady state at the value 0, we used (9) to obtain: 0 = N ( ) N( ) From (6), we nd the level of outut for cohort zero: () y 0 = ( v ( ) 0 Then it is ossible to use P N i=0 i i v P N i=0 i i( ) y 0 = 8 ) v v >< = v ( >: ) 0 N N v v N N( ) ( ) 9 >= >; v v (2) 0 y (3) to derive the steady state level of aggregate outut, y. The steady state values of y i;t+i for i = ; :::; N can be comuted by taking the ratio of (8) for di erent cohorts. For instance for cohort zero and cohort one: y 0 y = 0 y = 0 y i i (4) where variables without subscrits are at their steady state values. From y i, one can derive n i by using (5) : n i = y v i n i is the demand for labour of cohort i, therefore summing n i over all the cohorts of the rms will gives n, the aggregate quantity of labour. Having this in hand, it is ossible to set endogenously by using (2) 6

8 the consumtion rst order condition n t = t w t t c t = t and the aggregate equilibrium condition so that y t = c t = n y where variables without time subscrits are variables at their steady state values. Recalling that mt c = and y = c (3) yields the steady state value of t : m = V m References [] Akerlof, G. A., W. T. Dickens and G. L. Perry, 996, The macroeconomics of low in ation, Brookings Paers on Economics Activity, -76. [2] Akerlof, G. A., W.T Dickens and W.L. Perry, 2000, Near rational wage and rice setting and the long-run Phillis curve, Brookings Paers on Economic Activity, -60. [3] Ascari, G., 998, Suerneutrality of money in staggered wage-setting models, Macroeconomic Dynamics 2, [4] Ascari, G., 2000, Otimising agents, staggered wages and ersistence in the real e ects of monetary shocks, Economic Journal 0, [5] Ball, L., 997, Disin ation and the NAIRU, in: Romer, C.D. and D.H. Romer, eds., Reducing In ation: Motivation and Strategy, University of Chicago Press, Chicago. [6] Betancourt, R. and M. Malanoski, 999, An estimable model of suermarket behavior: rices, distribution services and some e ects of cometition, Emirica, 26, [7] Devereux, M. P. and J. Yetman, (200), Menu costs and the long-run outut in ation trade-o, Economics Letters 76, [8] Dolado, J. J., J. D. Lóez-Salido and J. L. Vega, 2000, Sanish unemloyment and in ation ersistence: are there Phillis trade-o s?, Sanish Economic Review, 2, w 7

9 [9] Fair, R. C., 2000, Testing the NAIRU model for the United States, The Review of Economics and Statistics, 82, [0] Fisher, M. and J. Seater, 993, Long-run neutrality and suerneutrality in an ARIMA framework, American Economic Review, 83, [] Graham, L. and D. Snower, 2003, The real e ects of money growth in dynamic general equilibrium, ECB Working Paer 42. [2] Karanassou, M., Sala, H. and D. J. Snower, 2003, The Euroean Phillis curve: does the NAIRU exist?, Alied Economics Quarterly, 2, [3] Karanassou, M., Sala, H. and D. J. Snower, 2005, A rearaisal of the Long- Run in ation unemloyment trade o, The Euroean Journal of Political Economy, 2, -32. [4] King, R.G. and M.W. Watson, 994, The ost-war U.S. Phillis curve: a revisionist econometric history, Carnegie-Rochester Conference Series on Public Policy 4, [5] Mankiw, N.G., 200, The inexorable and mysterious tradeo between in- ation and unemloyment, The Economic Journal, May, C45-C6. [6] Ramey, V. A. 99, Nonconvex costs and the behavior of inventories, The Journal of Political Economy, 99, [7] Roberts, M. J. and D. Suina 997, Outut rice and marku disersion in micro data: the roles of roducer heterogeneity and noise, NBER Working Paers

10 Table Baseline Calibrated Parameter Values φ θ N β v (/N).0 Figure The Long-Run Outut-Inflation Relationshi for Different Values of θ and ν= Outut Level (ercentage deviation from outut under flexible rices) θ =0 θ = Money Growth (ercentage rate) Figure 2 The Cost Function Total Costs Declining Marginal Cost C C 3 C 4 C C 2 Increasing Marginal Cost A A-ε A+ε B-ε B B+ε Outut Quantity