Quaderni di Dipartimento, EPMQ, Università degli Studi di Pavia, No. 203

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1 econstor Der Oen-Access-Publikationsserver der ZBW Leibniz-Informationszentrum Wirtschaft The Oen Access Publication Server of the ZBW Leibniz Information Centre for Economics Vaona, Andrea; Snower, Dennis J. Working Paer Increasing returns to scale and the long-run Phillis curve Quaderni di Diartimento, EPMQ, Università degli Studi di Pavia, No. 203 Provided in Cooeration with: University of Pavia, Deartment of Economics and Quantitative Methods (EPMQ) Suggested Citation: Vaona, Andrea; Snower, Dennis J. (2007) : Increasing returns to scale and the long-run Phillis curve, Quaderni di Diartimento, EPMQ, Università degli Studi di Pavia, No. 203 This Version is available at: htt://hdl.handle.net/049/28859 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch geseichert und koiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Oen-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and coied for your ersonal and scholarly uroses. You are not to coy documents for ublic or commercial uroses, to exhibit the documents ublicly, to make them ublicly available on the internet, or to distribute or otherwise use the documents in ublic. If the documents have been made available under an Oen Content Licence (esecially Creative Commons Licences), you may exercise further usage rights as secified in the indicated licence. zbw Leibniz-Informationszentrum Wirtschaft Leibniz Information Centre for Economics

2 Quaderni di Diartimento Increasing Returns to Scale and the Long-Run Phillis Curve Andrea Vaona (Università di Pavia) Dennis Snower (Kiel Institute) # 203 (9-07) Diartimento di economia olitica e metodi quantitativi Università degli studi di Pavia Via San Felice, 5 I-2700 Pavia Settembre 2007

3 Increasing Returns to Scale and the Long-Run Phillis Curve Andrea Vaona and Dennis Snower yz Aril 2, 2007 Abstract A growing body of emirical evidence shows that there exists a longrun ositive tradeo between in ation and real macroeconomic activity. Within a New Keynesian framewok, we examine how increasing returns generate a ositive long-run relation between in ation and outut. Keywords: Phillis curve, In ation, Increasing returns, nominal inertia, monetary olicy. JEL classi cation code: E3, E20, E40, E50. Deartment of Economics and Quantitative Methods of the University of Pavia and Kiel Institute for the World Economy, Via S. Felice 5, 2700, Pavia, Italy. anvaona@libero.it. y Kiel Institute for the World Economy and Christian-Albrechts University, Kiel; Düsternbrooker Weg 20, D2405 Kiel, Germany. Tel.: (+49) dennis.snower@ifw-kiel.de. z The authors would like to thank for helful comments an anonymous referee and the attendants to the seminar held on the 2st February 2006 at the Kiel Institute for the World Economy. The usual disclaimer alies.

4 Introduction There is a growing body of emirical evidence that there exists a ositive longrun relationshi between in ation and real macroeconomic activity. According to the oint estimates of Bernanke and Mihov (998), a % deviation of nonborrowed reserves causes a 0.5% increase in outut in the long run. Mankiw (200), commenting on this result, writes that..if one does not aroach the data with a rior favouring 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. The analysis of Akerlof, Dickens and Perry (996) shows that in the long run the unemloyment rate can increase from 5.9% to 7.6% when reducing the in ation rate from 3% to nil. According to Akerlof, Dickens and Perry (2000), a rate of in ation of 2.6% imlies a long-run equilibrium rate of unemloyment that is.7 ercentage oints lower than either at no in ation or at a rate above 6 ercent. 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) consider Sanish data and nd that, deending on the model seci cation, one ercentage oint of ermanent disin ation imlies a ermanent outut loss between 0.5 and 0.25 ercentage oints. King and Watson (994) nd that, over ve years, the cost of a % ermanent reduction in in ation amounts to a cumulative increase in unemloyment ranging between 3.7% and.5%, deending on the identifying assumtions adoted. Karanassou, Sala and Snower (2003, 2005) nd such a trade-o for the U.S. and the E.U. as well: a 0% increase in money growth leads to a fall of 3.4 ercentage oints in unemloyment. Studies analysing the steady state roerties of the New Keynesian models, as King and Wolman (996), Ascari (998, 2000), Devereux and Yetman (2002) and Graham and Snower (2003), suort long-run money non-suerneutrality. Recent exlanations of this attern focused on 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) 2

5 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 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 with di erent strength in various sectors of the economy, including rms and lants both in the manufacturing and in the retail 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 trade-o, 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: The fact that increasing returns might have an imact on economic uctuations was also ointed out by Leijonhufvud (986). 3

6 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 mt V m t t c t = t () n w t t + t = 0 (2) 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: 4

7 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: t = " N X i=0 i;t i y t (8) # 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 steady state solution 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: money growth has a ositive imact on the level of outut in the long-run 2. 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. Fig. 2 shows that increasing the value of v makes the long-run Phillis curve steeer for v < and atter for v > : An exlanation of this attern is o ered in the next section. 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. A straightforward way to model this concet is to relace (5) with a Skiba (978) roduction function whereby v is greater than one when outut is 2 As in King and Wolman (996) under di erent assumtions. 5

8 smaller than a certain threshold level y and smaller for greater levels of outut. Figure 3 shows how welfare evaluated as in Woodford (998) would change with such a roduction function, setting y = y(j = :5) for illustrative uroses. Welfare increases in the increasing returns ortion of the roduction function and decreases thereafter. This result is not sensitive to di erent values of. 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. 4, 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 : The greater is the elasticity of substitution among roducts, the greater are both roduct cycling and labour cycling. In resence of increasing returns, this generates greater economies leading to greater outut gains after an increase in in ation 3. To understand how the Phillis curve changes for di erent values of v, it is necessary to kee in mind that rms choose their outut and their rice by equating their marginal cost to their marginal revenue. Over the contract eriod, the marginal cost schedule and the marginal revenue one shift in order to kee the rice xed and to let rms outut move. As showed by Figure 5, the absolute value of the elasticity of the marginal cost function is greater the more v is far from one. The greater is the elasticity of the marginal cost function, the smaller are the changes in outut necessary to move the marginal cost schedule over the contract eriod. Small changes in outut imlies small (dis-)economies from cycling for (v < ) v > and so a atter long run Phillis Curve 4. In sum, the long-run Phillis curve deends on the technologies available to the rms: increasing returns imly a ositive relation between macroeco- 3 Conversely, it is ossible to show that, in resence of decreasing returns to scale, the greater is and the greater are the outut losses deriving from higher in ation rates. 4 In a Taylor model it is ossible to kee track of the outut of the various cohorts of rms. It is worth considering that v = :02 imlies a standard deviation of the levels of outut of the cohorts of rms equal to 0.5% of that imlied by v = :0: Instead, v = 0:67 imlies a standard deviation equal to 4% of that roduced by v = 0:95. This further suorts the intuition o ered for the e ect of v on the sloe of the long-run Phillis curve. 6

9 nomic 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( ) ( ) 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( ) 8 ) v v >< = v ( >: ) N N v v 0 N N( ) ( ) 9 >= v v >; (2) 0 y 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 0 y = (4) y 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 mind, it is ossible to set endogenously by using (2) the consumtion rst order condition n t = t w t t 7

10 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] Bernanke, B. S. and Mihov, I., 998, Measuring Monetary Policy, The Quarterly Journal of Economics, 3, [7] Betancourt, R. and M. Malanoski, 999, An estimable model of suermarket behavior: rices, distribution services and some e ects of cometition, Emirica, 26, [8] Devereux, M. P. and J. Yetman, (2002), Menu costs and the long-run outut in ation trade-o, Economics Letters 76, [9] 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 8

11 [0] Graham, L. and D. Snower, 2003, The real e ects of money growth in dynamic general equilibrium, ECB Working Paer 42. [] Karanassou, M., Sala, H. and D. J. Snower, 2003, The Euroean Phillis curve: does the NAIRU exist?, Alied Economics Quarterly, 2, [2] 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. [3] 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, [4] King, R. G. and A. L. Wolman, 996, In ation targeting in a St. Louis model of the 2st century, Proceedings, Federal Reserve Bank of St. Louis, [5] Leijonhufvud, A., 986, Caitalism and the Factory System, in Langlois, R. N., ed., Economics as a rocess, Cambridge University Press, Cambridge, UK, [6] Mankiw, N.G., 200, The inexorable and mysterious tradeo between in- ation and unemloyment, The Economic Journal, May, C45-C6. [7] Ramey, V. A., 99, Nonconvex costs and the behavior of inventories, The Journal of Political Economy, 99, [8] 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 [9] Skiba, A. K., 978, Otimal growth with a convex-concave roduction function, Econometrica, 46, [20] Woodford, M., 998, Doing Without Money: Controlling In ation in a Post-Monetary World, Review of Economic Dynamics,,

12 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 Long-Run Outut-Inflation Relationshi for Different Values of ν and θ =0 3 Outut Level (ercentage deviation from outut under flexible rices) v=0.95 v=.0 v=0.67 v= Money Growth (ercentage rate)

13 Figure 3 Welfare for different values of φ and ercentage money growth rates with a Skiba (978) roduction function Note: ν is equal to.0 u to y*=y(µ µ=.5) and to 0.67 thereafter. Figure 4 The cost function with varying marginal cost. 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

14 Figure 5 The elasticity of the marginal cost function for different values of v v v v