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Three Sources of Increasing Returns to Scale

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Three Sources of Increasing Returns to Scale Three Sources of Increasing Returns to Scale Jinill Kim First draft: March 1996 This draft: April 3, 1997 Abstract This pap er reviews various typ es of increasing returns from a critical p er- sp ective. Increasing returns have b een intro duced b oth at the rm level and at the aggregate level in a monop olistic-comp etition mo del. We show that the degree of the aggregate returns to scale is a linear combination of three return parameters, with the weights determined by the sp eci cation of a zero- pro t condition. Identi cation issues are discussed with an emphasis on recent macro literature. We argue that disaggregate data give information on the market structure rather than the technology. Welfare implications explain why it is imp ortant to identify various increasing returns. Key words : Increasing Returns; Monop olistic Comp etition; Returns to Vari- ety JEL classi cation : E32 Federal Reserve Board, Mail Stop 61, Washington, D.C. 20551. Telephone: (202) 452-2715. E-mail: [email protected]. This is a revised version of a chapter in my dissertation at Yale University. Sp ecial thanks to Christopher Sims for his guidance and supp ort. Thanks also to William Brainard, John Fernald, Rob ert Shiller, Steve Sumner, Michael Wo o dford, and seminar participants at the Universities of Maryland and Virginia, and Federal Reserve Board for their valuable comments. This pap er represents the view of the author and should not b e interpreted as re ecting the views of the Board of Governors of the Federal Reserve System or other memb ers of its sta . 1 Contents 1 Intro duction 2 2 The Mo del 4 2.1 Firms . 5 2.2 Aggregation . 8 2.3 Returns to Scale . 10 2.4 A Dynamic Mo del . 15 3 Implications 19 3.1 Identi cation with Aggregate Data . 19 3.2 Interpretation of Disaggregate Data . 21 3.3 Comparison with a So cial Planner . 24 4 Further research 26 A External Increasing Returns 28 B Input Fixed Cost 29 C Cost Minimization 31 D Fixed Cost Externalities 33 1 Intro duction The hyp othesis of noncomp etitive markets and/or increasing returns to scale has recently b een used in dynamic sto chastic general-equilibrium (DSGE), more often called real-business-cycle, mo dels. Using the Solow residual as a measure of pro duc- tivitychanges is appropriate only under the jointhyp othesis of p erfectly comp etitive markets and constant returns to scale. In a series of pap ers, Hall (1986, 1988, 1990) argues that evidence from the Solow residual is not consistent with this maintained hyp othesis but with the alternativehyp othesis of noncomp etitive markets and/or in- 1 creasing returns to scale. Under this alternativehyp othesis, the Solow residual has 1 Imp erfect comp etition makes equilibrium p ossible in the presence of increasing returns. In- creasing returns are compatible with comp etitive rms if the increasing returns are external to the rms. Internal returns may b e motivated as a representation of external ones, as in Beaudry and Devereux (1995a). The twotyp es are compared using mo dels with b oth typ es of increasing returns in App endix A. 2 endogenous comp onents which cause it to over-represent the contribution of pro duc- tivity sho cks. Furthermore, this alternative hyp othesis helps explain some puzzles in the DSGE literature, e.g. little correlation b etween employment and pro ductivity. Following Dixit and Stiglitz (1977) and Blanchard and Kiyotaki (1987), the monop olistic-comp etition framework has b een widely used in macro economics. The assumption of unrestricted entry and exit implies that pro ts are zero in equilib- 2 rium. In a monop olistically comp etitive market, the technology of constant returns to scale lets rms pro duce p ositive pro ts regardless of their size. Intro ducing in- 3 creasing returns at the rm level leaves ro om for reducing pro ts to zero. The ob jective of this pap er is to discuss three di erent typ es of increasing returns in a monop olistic-comp etition mo del and to derive implications for the related literature. There are two ways of intro ducing increasing returns at the rm level. The more conventional way is including xed costs as part of a rm's technology. This way has b een followed whenever a zero-pro t condition is imp osed. An alternate way is amplifying the constant-returns-to-scale term by a power larger than one, which amounts to diminishing marginal cost. When we incorp orate b oth sources of increasing returns simultaneously, as in Hornstein (1993), their e ect on the ag- gregate returns to scale is di erent from each other. Increasing returns due to the third source o ccurs only at the aggregate level. It involves a technology or a pref- erence for the variety of go o ds. The intro duction of a new go o d might enhance the pro duction eciency and the consumption convenience. Romer (1987) fo cuses on this as an engine of growth and Matsuyama (1995) relates this to complementarities and cumulative pro cesses of macro economics. The mo del in Devereux, Head and Lapham (1996a), even without pro ductivity sho cks, generates business cycle uc- tuations of real variables from government sp ending sho cks since these a ect the varietyofgoods. This pap er shows that, in a static mo del, the resulting degree of aggregate re- turns to scale is the average of the second and the third sources of increasing returns, without any in uence of p ositive xed costs. The derivation of aggregate returns from a rm's technology involves two steps. First, the di erentiated outputs are aggregated to pro duce a measure of aggregate output. Second, a zero-pro t con- 2 See Benassy (1991) for quali cations of zero-pro t conditions. The assumption of zero pro ts matches the observation in Hall (1990) and Rotemb erg and Wo o dford (1995) that there are no signi cant pure pro ts in the United States. 3 Not that all pap ers in DSGE literature imp ose a zero-pro t condition. Hairault and Portier (1993) and Beaudry and Devereux (1995b) do not imp ose a zero-pro t condition and so parameterize b oth xed cost and the numb er of rms. In such mo dels, the rm-level returns to scale are the aggregate returns to scale and the p ermanent presence of p ositive pro ts remain unexplained. For example, the steady-state pro t rate is 17% in the b enchmark mo del of Hairault and Portier (1993). 3 dition is imp osed up on the aggregate version of a rm's technology. Sp eci cation of a zero-pro t condition determines the weights of the averaging. In a dynamic mo del where adjustments to zero pro t are not instantaneous, the market structure of monop olistic comp etition plays a role|the slower the adjustments, the larger the role. Even if market structure do es not directly a ect the technology, this source in uences the resp onse of output in a way indistinguishable from the previous two ways. The aggregate dynamics of a mo del which combines various sources of increasing returns to scale show that there are identi cation problems in the recent macro e- conomics literature using the framework of monop olistic comp etition. We compare various pap ers to see how they sp ecify a zero-pro t condition and what the resulting degree of returns to scale is. We also argue that the literature using disaggregate data provides information di erent from what it intends to provide: on the mar- ket structure rather the technology. Lastly, welfare implications are discussed from the p ersp ective of a so cial planner who do es not need to satisfy zero-pro t condi- tions. While having similar p ositive implications for the aggregate returns, various increasing returns have di erent normative implications. 2 The Mo del To illustrate the p oints in as simple a structure as p ossible, we analyze only the pro duction side of the economy. This analysis is tractable and gives much insight on how di erent returns to scale interact with one another. Most pap ers on monop- olistic comp etition deal with b oth the pro duction and the consumption side of an economy. However, intro ducing a utility function complicates the mo del so that it is dicult to disentangle the pro duction features from consumer b ehavior. Our mo del is a partial-equilibrium mo del, since the pro duction side generates the demand for inputs. The transformation of this mo del into a general-equilibrium framework is straightforward by stacking it with a consumer problem and, if needed, a government problem. The consumer problem would generate the supply function of aggregate inputs through a lab or-leisure choice and capital accumulation. Therefore, through- out this pap er, we may consider the aggregate inputs as exogenous variables. Since a zero-pro t condition is crucial in deriving the economy-wide returns to scale, we will be very careful in discriminating two meanings of `pro duction func- tion.' A structural pro duction function is a purely technological relation without reference to the equilibrium condition of zero pro ts. However, a pro duction func- tion in a reduced form, whether a rm's or an aggregate one, is a combination of the appropriate technology and a zero-pro t condition.
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