MARKET STRUCTURE AND PRODUCTIVITY: A CONCRETE EXAMPLE. Chad Syverson. Working Paper 10501

Transcription

1 MARKET STRUCTURE AND PRODUCTIVITY: A CONCRETE EXAMPLE Chad Syverson Working Paper 10501

2 NBER WORKING PAPER SERIES MARKET STRUCTURE AND PRODUCTIVITY: A CONCRETE EXAMPLE Chad Syverson Working Paper NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massahusetts Avenue Cambridge, MA May 2004 I thank seminar partiipants at the NBER Summer Institute, the Brookings Institution, the Center for Eonomi Studies, and numerous universities for their omments. I am grateful to Steve Levitt, Ariel Pakes, Mark Roberts, Balazs Szentes, and two anonymous referees for helpful suggestions and Kevin Clisham for answering many tehnial questions about the ready-mixed onrete industry. I am also indebted to John Haltiwanger, Rahel Kranton, Mike Pries, Plutarhos Sakellaris, and John Shea for their instrution and guidane. Funding from a Brookings Researh Fellowship is appreiatively aknowledged. The researh in this paper was onduted while the author was a researh assoiate at the Center for Eonomi Studies, U.S. Bureau of the Census. Researh results and onlusions expressed are those of the author and do not neessarily indiate onurrene by the Bureau of the Census or the Center for Eonomi Studies. This paper has been sreened to ensure that no onfidential information is released. The views expressed herein are those of the author(s) and not neessarily those of the National Bureau of Eonomi Researh by Chad Syverson. All rights reserved. Short setions of text, not to exeed two paragraphs, may be quoted without expliit permission provided that full redit, inluding notie, is given to the soure.

3 Market Struture and Produtivity: A Conrete Example Chad Syverson NBER Working Paper No May 2004 JEL No. L1, L6, D2 ABSTRACT Many studies have doumented large and persistent produtivity differenes aross produers, even within narrowly defined industries. This paper both extends and departs from the past literature, whih foused on tehnologial explanations for these differenes, by proposing that demand-side features also play a role in reating the observed produtivity variation. The speifi mehanism investigated here is the effet of spatial substitutability in the produt market. When produers are densely lustered in a market, it is easier for onsumers to swith between suppliers (making the market in a ertain sense more ompetitive). Relatively ineffiient produers find it more diffiult to operate profitably as a result. Substitutability inreases trunate the produtivity distribution from below, resulting in higher minimum and average produtivity levels as well as less produtivity dispersion. The paper presents a model that makes this proess expliit and empirially tests it using data from U.S. ready-mixed onrete plants, taking advantage of geographi variation in substitutability reated by the industry s high transport osts. The results support the model s preditions and appear robust. Markets with high demand density for ready-mixed onrete and thus high onrete plant densities have higher lower-bound and average produtivity levels and exhibit less produtivity dispersion among their produers. Chad Syverson Department of Eonomis University of Chiago 1126 East 59th Street Chiago, IL and NBER syverson@uhiago.edu

4 I. Introdution Reent empirial work has left little doubt about the magnitude of plant-level produtivity variation: it is enormous. This heterogeneity is also persistent. Perhaps surprisingly, muh of the variation annot be explained by differenes between (even narrowly defined) industries. Studies reviewed in Bartelsman and Doms (2000), for example, have found 85 th -to-15 th total fator produtivity perentile ratios between 2:1 and 4:1 within various fourdigit SIC industries. A theoretial literature has arisen attempting to explain the soures of suh diversity. The great majority of this researh fouses on tehnologial (i.e., supply-side) explanations, suh as management influenes, apital vintage effets, and R & D efforts. 1 While supply-side effets are most ertainly important, this paper fouses instead on the influene of the demand (i.e., output market) side. Speifially, it explores how produt market harateristis an allow suh large produtivity differenes (perhaps arising in part beause of supply-side fators) to persist in long-run equilibrium. Key to the story is the ability of onsumers to substitute the output of one supplier for another. The more diffiult it is for onsumers to swith between ompeting suppliers, the greater the produtivity dispersion that an be sustained. The role of the demand market, and substitutability speifially, in reating the large observed produtivity differenes beomes apparent when one onsiders how suh wide effiieny variations an exist in equilibrium. If onsumers were unenumbered by substitution barriers, prodution would be realloated to a selet few highly produtive plants. Those plants who ould produe output at lower ost than industry rivals would be able to grab additional market share by underutting their opponents pries without sarifiing profitability. Suh output and produtivity patterns are not usually observed in the data, however. Virtually all industries, and indeed even markets within industries, exhibit widely varying produer produtivity levels within them. Barriers to substitution aross produers (i.e., various forms of produt differentiation be they spatial, physial, or brand-driven) an allow less produtive plants to survive and even thrive in long-run equilibrium. Dereases in impediments to substitution, on the other hand, make it more diffiult for low-produtivity plants to profitably operate, trunating the equilibrium produtivity distribution from below. The testable premise of 1 Just a sampling inludes Jovanovi (1982) and Erison and Pakes (1995). See Bartelsman and Doms (2000) for a review of this literature. 1

5 this notion is that in markets where it is easy for industry onsumers to swith suppliers, produtivity distributions should exhibit higher minima, less dispersion, and higher entral tendeny than those in low-substitutability markets. I test this mehanism within a single four-digit SIC industry, ready-mixed onrete (SIC 3273), and fous on a partiular omponent of substitutability, spatial differentiation reated by transport osts. The purpose of the paper, however, is not to give the final word on transport osts and produtivity in a partiular industry. Instead, I hope to show through a detailed ase study how transport osts as well as other substitutability fators might impat produtivity variation and levels throughout the eonomy. The primary advantage of an industry ase study is that it helps ontrol for the influene of tehnology differenes on produtivity heterogeneity, isolating the demand-side impats of interest. Additionally, fousing on an industry with a (relatively) physially homogeneous output that is subjet to substantial transport osts larifies the exerise of formally posing and testing the intuitive hypothesis above. The high transport osts imply the industry is atually a olletion of quasi-independent geographi markets, all potentially subjet to idiosynrati demand movements. I take advantage of this aross-market variation in the empirial tests. Ready-mixed onrete s homogeneity serves to isolate the soure of produt substitutability: sine produers outputs are physially omparable, transport-ost-driven spatial differentiation is what matters. The sharp fous on spatial substitutability is useful beause it is arguably more easily measured than physial or brand-driven produt differentiation. Spatial effets on produtivity are also topis of speifi interest to a onsiderable body of researh. 2 I model and empirially test a spatial ompetitive struture where inreases in demand density (demand per unit area) in loal markets trunate the produer produtivity distribution from below. This implies dense markets will have higher minimum and average produtivity levels and less produtivity dispersion than low-density markets. Further, produers in higher- 2 To see if the results of this ase study hold more broadly, I investigate in Syverson (2004) how aross-industry differenes in measurable output substitutability fators are orrelated with industries plant-level produtivity distribution moments. I find that manufaturing industries with lower transport osts, less physial produt differentiation, and/or lower advertising intensities (all plausibly indiators of greater substitutability) do indeed tend to have less dispersed produtivity distributions with higher averages than industries with more segmented output markets. In exhange for its broader fous, that study gives up some of the ability to ontrol for the produtivity effets of tehnologial differenes that the present empirial approah enjoys. 2

6 density markets will be larger on average and eah serve a greater number of ustomers. 3 Figures 1 and 2 offer preliminary evidene for this mehanism. They show kernel probability density estimates of the total fator produtivity and size distributions for my sample of onrete plants. (The distributions are expressed in terms of deviations from the average aross all plants in a given year.) Two distributions are plotted in eah figure. These orrespond to produers that are loated in markets either above or below the median demand density level in my sample. (The former set of produers numbers roughly 8500, while the latter I preisely desribe how plant produtivity and size are measured and define markets and demand density below.) If the intuition above is orret, we should expet that the produtivity distribution in high-density markets looks like a trunated version of the low-density distribution. This pattern is evident in Figure 1. At low produtivity levels, the distribution of the high-density-market plants onsistently has less weight than the low-density-market distribution. At high produtivity levels, this pattern is reversed. 4 These visual patterns are onfirmed by the omputed means; the average of the high-density distribution is log points greater (s.e. = 0.006) than that of the low-density distribution. While the omparative dispersion of the two distributions is more diffiult to see in the figure, the predition above holds in this regard as well. The standard deviation of the distribution of plants in high-density markets is 0.340, as ompared to for low-density produers (an F-test for equality of variane is easily rejeted). Figure 2 shows that the predited positive orrelation between average plant size and density is also present in my sample, and indeed even more stark. The average-sized high-density-market plant is log points (s.e. = 0.019) larger than the average produer in a low-density market. The impliations of these two figures will be tested in more 3 The mehanism through whih these effets operate will be explained in detail below, but an be summarized as follows. A denser market requires more produers in a given area to serve it. Substitutability is greater in markets where produers are densely paked, beause onrete buyers have aess to more alternative produers. High substitutability orresponds with greater ompetitive pressures, foring low-performing produers out of business. This trunates the long-run equilibrium plant-level produtivity distribution from below and leads to the stated impliations regarding the produer produtivity and size distributions. 4 Of ourse, the high-density distribution will not be an exat trunation of its low-density ounterpart beause of inherent randomness in the data (e.g., measurement error), and beause I am pooling aross markets with different trunation points. Interestingly, still, two features math attributes of a trunated distribution. As an be seen, the modes of the two TFP distributions are very lose to eah other. Furthermore, the quantiles of the high-density markets distribution are outside the 95 perent onfidene interval of quantiles of the low-density distribution, exept at very high TFP levels (above the 95 th perentile). Left-trunated distributions of ourse beome more similar loser to their right tails. 3

7 detail and with greater rigor below, but they are suggestive prima faie evidene in support of the link between substitutability and produer-level produtivity and size distributions. Besides extending the work explaining produtivity (and size) differenes within industries, this paper touhes on other related topis. One is the rih and lengthy literature on the relationship between ompetition and produtivity. 5 Coneptually, produt substitutability and ompetitiveness are quite similar. Markets with greater substitutability are more ompetitive in the sense that their higher ross-prie elastiities more greatly reward (punish) relatively low- (high-) ost produers in terms of market share. Hene the paper s implied positive link between substitutability and average produtivity levels supports the literature s ommon (though not unanimous) notion that ompetition breeds effiieny. 6 A point of ontat with a separate literature arises from the model s ombined impliations for produtivity and size. A urious between-produer form of sale eonomies is implied: produers in denser markets will be both larger and more effiient on average, even if there are no internal sale eonomies in prodution. The observed sale effet is instead the produt of seletive survivorship; less produtive establishments are eliminated when markets beome denser. Observably, this ompetition-driven seletion proess looks very muh like the spatial agglomeration mehanisms disussed in the urban and trade literatures produers in dense markets are more effiient. Interestingly, however, this proess is distint in that it does not rely on tehnologial properties or externalities (suh as internal inreasing returns, Marshallian thik labor market effets, information spillovers, et.) typially appealed to in the literature. The paper is organized as follows. In the next setion, I onstrut a theoretial framework that formalizes the intuitive premise above. The data used to test the theory s impliations is then disussed in Setion III. I test the model in Setion IV and hek the results 5 This literature is muh too large to ite omprehensively. Reent examples inlude Aghion and Howitt (1992), Nikell (1996), Melitz (2003), Raith (2003), and Shmitz (2004). 6 One an remain agnosti about the speifi soure of produtivity gains when ompetition is intensified. One branh of the ompetition-produtivity literature fouses on slak or X-effiieny. That is, ompetition-spurred produtivity growth ours beause produers are fored to take ostly ation to beome more effiient, as in Raith (2003) for example. However, in the mehanism modeled here, produtivity growth is instead ahieved by seletion aross establishments with fixed produtivity levels; less effiient produers are pushed out of the market. Both mehanisms are influened by market ompetitiveness in theory, and both are likely to play a role in reality. Measuring the relative size of the ontribution of eah to determining produtivity differenes is beyond the sope of this paper, however. 4

8 for robustness in the following setion. Setion VI onludes. II. Model To formalize the story linking demand density, output substitutability, and the market produtivity and size distributions, I onstrut a theoretial framework that inorporates onsumers hoosing among spatially differentiated produts sold by heterogeneous-ost suppliers. The model offers testable impliations regarding how the primary exogenous fator of interest, demand density, affets the (endogenously determined) equilibrium produtivity and output distributions. The framework extends the work of Salop (1979) to allow for heterogeneous produer osts. The model also adds asymmetri information among produers regarding their prodution osts, largely as an analytial onveniene in onstruting an equilibrium, but this is not neessary to obtain the tested empirial impliations. Beause I am onerned here with differenes in produtivity distributions aross markets rather than intertemporal flutuations within them, dynamis are not a primary onern. Thus I model a simple two-stage entry/prodution deision meant to apture long-run differenes in outomes aross markets. While simple, the model shows in a straightforward manner how differenes in spatial substitutability (arising from demand density variation) affet the shape of produer produtivity and size distributions in markets. A. Market Struture A ontinuum of onsumers is evenly distributed around a irle of unit irumferene with a density of D onsumers per unit length. Consumers have an inelasti demand for one indivisible unit of ready-mixed onrete, and will purhase if the prie is less than their reservation value. The prie faed by onsumers is equal to the fatory-door prie set by the produer plus a transport ost that inreases linearly in the distane from supplier to onsumer. That is, p = p + tx, where p is the prie paid by the onsumer, x is the length of the ar between the plant and the ustomer, and t parameterizes transport osts. I assume for simpliity that reservation values are high enough to ensure that all onsumers purhase in equilibrium. Thus the total quantity of onrete sold in the market is D. Demand density D is the exogenous variable of fous; I draw testable empirial impliations from its effet on the equilibrium. 5

9 The supply side of the market is determined in a two-stage, simultaneous entry game. In the first stage, a large number of ex-ante idential potential entrants onsider whether to attempt to gain entry aess into the market. To do so, they must pay a sunk setup ost s, whih is idential for all entrants. All produers hoosing to pay s reeive an idiosynrati marginal ost draw i from a ommon distribution g() with support [0, u ], where u is an arbitrary upper bound. The setup ost an be interpreted as resoures spent drawing up a business plan, making initial inquiries into prodution possibilities, and other pre-prodution ativities that would give a produer insight into its osts of prodution. 7 Those paying s learn their own ost draw but do not observe the ost draws of others. In the seond stage, those who have learned their osts deide whether to ommene prodution, given the expeted number and marginal osts of ompetitors. 8 Those hoosing to produe pay a ommon fixed prodution ost f (whih is also assumed to be irretrievable should prodution ommene, say beause of the irreversibility of investment, or beause it aptures the value of forgone alternative uses of the produtive resoures), are then plaed randomly at evenly spaed loations on the irle (hene every loation is idential in expetation), and set their fatory-door prie p. Consumers make their purhases given the resulting set of transportinlusive pries. 7 There is good reason to believe that produers sink resoures into making entry deisions before learning their type. Substantial empirial evidene (e.g., Dunne, Roberts, and Samuelson 1989; Baily, Hulten, and Campbell 1992; and Foster, Haltiwanger, and Krizan 2002) indiates that young plants have higher failure (exit) rates than inumbents. This suggests that entering produers do not typially know very well their own position vis-à-vis their ompetitors with regard to profitability omponents suh as ost types. (The present model abstrats from this earlyprodution period and instead has high-ost firms dropping out of the market before ommening operations.) 8 The assumption that produers deide whether to operate without knowing their ompetitors ost draws allows demand density s impat on the equilibrium produtivity distribution to be obtained analytially. Given the spatial setup of the model, ompetition is loal when produers osts are ommon knowledge; that is, neighbors have a greater impat on optimal strategies than do market produers further away. While one an solve for optimal strategies in the ommon-knowledge onstrut (I show how to do this in the earlier version of this paper; see Syverson 2001), this requires omputational simulations to solve the model, and it is furthermore not obvious what the equilibrium onept neessary to pin down the number of produers should be in suh simulations. An asymmetri information setup transforms the priing game into something similar to those ommonly found in heterogeneous-produer monopolisti ompetition models, where a produer plays against an industry average (in this ase, the other entrants expeted prie). Thus ompetition is no longer loal (at least in the strategi sense obviously, neighbors pries in this model affet realized outomes more so than do the pries of more distant ompetitors), and simulations are no longer neessary to determine the equilibrium distribution of produer ost/produtivity levels. I would further argue that assuming produers have private information about their osts may be realisti; data-gathering empirial eonomists know well how famously possessive firms are about their ost data. Below I ondut omputational robustness heks to see if the obtained results hold up qualitatively to deviations from the present assumptions about ost information. 6

10 While the realized market shares and profits of this entry game are stohasti and depend upon partiular produer ost and loation realizations, one an analytially determine the distribution of the equilibrium set of produers. I show below that the key testable impliation of the model the link between demand density and seletion-driven trunation of the ex-ante produtivity distribution holds regardless of the partiular set of ost and loation realizations. Trunation ours before sales and profits are realized beause high-ost produers have lower expeted profits. I also show, by omputationally simulating a modified version of the model, that the key qualitative results of the benhmark model are robust to hanges in the speified information and timing struture. To solve for the model s equilibrium, onsider first the deision of whether or not to ommene operations for a would-be produer that has already learned its ost draw. The produer will operate in the market if it expets to earn positive profits from doing so. Sine prospetive entrants do not know others ost draws, potential ompetitors are equivalent in expetation. They must therefore deide whether to operate based on the profits resulting from ompeting in a market against an expeted number of n ompetitors harging the same expeted prie. Beause 1) all onsumers purhase in equilibrium, and 2) an assumption on the parameters that will be disussed in detail below, there will be between eah pair of produers a onsumer indifferent to purhasing from either. 9 The partiular loation of this onsumer depends, of ourse, on the pries of the two plants and transport osts. For any two neighboring plants i and j (whih are a distane 1/n apart, where n is the equilibrium number of produers in the market), the indifferent onsumer is loated at a distane x i,j from i, where x i,j solves 1 + txi, j = p j + t xi j n p i,, (1) and p i and p j are the fatory-door pries set by produers i and j, respetively. This equation an be solved to reover x i,j expliitly. The total quantity sold by a produer between rivals j on one side and k on the other is then (x i,j + x i,k )D, where x i,k is similarly defined. 9 Restriting parameter values to ensure an indifferent onsumer between eah pair of produers greatly simplifies analysis of the equilibrium. It eliminates from produers optimal priing deisions the possibility that a realized prie differene between neighboring produers is so large that some produers would apture all of their neighbors ustomers on both sides. (The demand disontinuity inherent to linear transport osts [see Salop 1979] ensures that no produer will ever have zero ustomers on one side and positive sales on the other.) 7

11 However, beause produers do not know their rivals osts or pries when making entry deisions, E(x i,j ) = E(x i,k ): ( ) ( ) ( ) ( ) + = = = n E t p p E x E x E x E i i k i j i ,,. (2) E(p) is the expeted prie harged by other entrants, and E(1/n) is the expeted reiproal of the number of produers, taking equilibrium strategies as given. The expeted profit of a produer setting its fatory-door prie equal to p i is then ( ) ( )( ) ( ) ( ) f D p n E t p p E f D p x E E i i i i i i i + = = 1 2 π. (3) Maximizing this expression with respet to p i yields the produer s optimal prie given its expetations about the equilibrium market outome: ( ) + + = n E t p E p i i (4) Not surprisingly, the optimal prie inreases in the produer s own realized ost, its expetation of its ompetitors pries, and the expetation of n -1. This expression an also be used to ompute rivals expeted pries in terms of the expeted ost draw among equilibrium produers: ( ) ( ) + = n te E p E 1. (5) Substituting (4) and (5) bak into (3) yields markups as well as maximized expeted market share and profits in terms of parameters, the produer s own ost, the expeted ost of its rivals, and the expeted (reiproal of the) number of produers in the market: () i i i n E t E p = (6a) ( ) () i i t n E E t x E = (6b) ( ) () f n te E t D E i i + = π (6). Clearly, prie-ost markups and expeted market shares are delining in i. Thus assuming a large enough u, there will be ost draws that imply negative expeted profits from operations. Therefore a ritial ost draw * exists suh that entrants drawing i > * hoose not to 8

12 produe. 10 This utoff ost draw an be solved for by setting (6) equal to zero: 1 4tf E( π i ) = 0 * = E( ) + 2tE. (7) n D Note that E(), the average ost draw among equilibrium produers, is itself an inreasing funtion of *, sine the latter determines a trunation point of g(). That is, * ( ) ( ) g E () d. (8) G 0 * Substituting (7) bak into (6) yields operating profits (onditional on i *) as a funtion of parameters, the endogenously determined *, and the produer s own ost: D 4tf E( π i i *) = i f t * + 4 D (9) Note that it is possible that some produers with i * deiding to ommene prodution may make negative profits ex-post speifially, those relatively high-ost (but still below *) produers who enter only to find themselves next to ompetitors with lower-thanexpeted osts. However, beause f is sunk, they are willing to remain in the market as long as they are selling positive quantities. Positive sales an be assured by assumptions on the model s parameters that I disuss in the appendix. These same assumptions ensure that there will be an indifferent onsumer between any produer pair in equilibrium. As mentioned previously, this greatly simplifies the analysis. What, then, determines *? To see this, onsider the potential entrant s hoie of whether to pay the sunk ost s in order to reeive a ost draw i. The expeted value of entry, V e, (ommon to all produers sine they are ex-ante idential) is equal to expeted operating profits before knowing one s own ost draw minus the sunk entry ost. I impose a free entry ondition: the (expeted) number of entrants adjusts to set V e to zero. That is, V e 2 * D 4tf = * f g s t D 2 () d = 0. (10) The equilibrium * is the value that solves this expression given parameters D, t, f, s, and the ex- 10 While some osts i > * imply positive expeted profits due to the quadrati form of (6), suh ost levels would also imply (nonsensial) negative markups and expeted quantities sold. 9

13 ante produtivity distribution g(). 11 B. The Comparative Statis of Shifts in Demand Density Cutoff Cost Level *. The omparative stati of primary interest is the sign of d*/dd; in other words, how do differenes in demand density aross markets affet the shape of equilibrium produtivity distributions? Using the impliit funtion theorem, * * V D V dd d e e =, (11) where the numerator, () + + = * * * 4 1 e d g D tf D tf t D tf t D V, (12a) simplifies to ( ) ( ) () 0 4 * 4 1 * 4 1 * 0 2 > + = e d g D tf t t D V. (12b) This expression is positive beause * throughout the region of integration. The demoninator of the impliit funtion theorem is given by ( ) () = * * 2 * 4 * * 4 * e d g D tf t D g f D tf t D V. (13a) Simplifying gives () 0 4 * 2 * * 0 > + = e d g D tf t D V, (13b) beause the first term in (13a) equals zero; allowing in a formerly marginally unprofitable produer by slightly inreasing * has no impat on the value of entry. Therefore d*/dd < 0; the upper bound of the produers ost distribution dereases in 11 The equilibrium * is unique. The logi is as follows. From (6),expeted profits onditional upon i are dereasing in i and stritly inreasing in E(1/n). For any given E(1/n), the expeted value of entry V e for an entry poliy x (that is, where entrants ommit to ommene prodution upon reeiving any marginal ost draw i x) is maximized at x = *, where * is defined as in (7). Sine V e is monotoni in E(1/n), the unique equilibrium * is simply the value of this maximizing entry poliy when E(1/n) is suh that V e = 0. Interested readers an find formal existene and uniqueness proofs of similarly-styled equilibria albeit with different assumptions regarding speifis of the demand and supply strutures in Asplund and Noke (2003) and Melitz (2003). 10

14 demand density. High-ost (low-produtivity) produers aren t profitable in dense markets. This is in aordane with the intuitive story forwarded in the introdution. Two impats of an inrease in demand density (whih is exogenous in the model, and as I will argue, empirially as well) are at work. The diret effet is through the inreased sales and profits for any fixed number of market produers. This inrease in potential profits in isolation would raise the expeted value of entry. To preserve the equilibrium ondition that V e equals zero, E(1/n) must fall in order to lower expeted profits onditional upon i ; see (6). The additional entry dereases the average distane between produers, inreasing substitutability and making it harder for high-ost produers to hold ustomers. Buyers formerly stuk with an ineffiient supplier may now have a lower-ost option. In equilibrium, this raises the bar for suessful entry into the market, yielding the ost/produtivity trunation result. 12 This progressive trunation of the ost distribution from above, oupled with the fat that measured produtivity levels should be inversely related to osts, imply that average and minimum produtivity levels (average and maximum osts) of produers in denser markets should be higher (lower) than in less dense markets. Also, assuming some additional regularities in the distribution, produtivity dispersion should be lower in denser markets. These are the primary empirial impliations I test below. Firm Size. Inreases in demand density indue entry, but do the number of produers grow at a proporational rate to the growth in market demand? In other words, what happens to average firm size as density rises? While the fat that the number of produers enters the model through the expetation of its reiproal (and expetations are not ommutative) preludes an analytial derivation of the elastiity of E(n) with respet to D, the model still offers some guidane along these lines. As is evident in (6a), markups inrease with E(1/n). Thus the average markup falls in D beause of the entry a rise in D indues. But sine the expeted value of entry in equilibrium is always zero, it must be that produers in dense markets who have to over the same sunk entry osts as produers in low-density markets make up for the lower markup by selling more onrete on average. Therefore, we should expet average firm size to rise with 12 One an show that, not surprisingly, a derease in transport osts t implies a shift in * in the same diretion as an inrease in D. Both serve through different mehanisms to inrease substitutability. 11

15 demand density. 13 I test this impliation in the empirial work below. C. Robustness of Comparative Statis As stated above, the advantage of the urrent setup is that it allows analytial derivation of the empirially tested omparative statis. However, to do so it assumes away repriing and further entry after produers sales are realized. It is oneivable that in reality, produers pries would beome ommon knowledge at this point, allowing produers atual osts to be inferred. This would identify market loations ripe for new entry (i.e., those among relatively high-ost produers). There may be other potential produers hoping to take advantage of this identified weakness. And sine these new entrants ould identify the best loation before entering, they ould possibly be less effiient than the marginal entrant above. The urrent model rules out this instane beause the final deision is made before pries (and therefore produer osts whih an be inferred from them) are revealed. To see how allowing ex-post entry affets the omparative statis derived above, I ondut a simple exerise that onsiders a stark ase where, one all pries are realized, a new potential entrant an observe these and then hoose the best loation in whih to enter the market. 14 In Syverson (2001) I show that when all produers osts are known, operating profits for a produer with ost draw i equal D t π i = + si, j j ( 1 si, i ) i f, (14) t n j i where s i,j is the (i,j)-th element of a weighting matrix S. This matrix, whose omputation and properties are disussed in detail in Syverson (2001), aptures the influene of ompetitors osts on a produer s optimal prie as well as the resulting market shares and profits. I an use this expression to ompute the highest ost draw i that an ex-post entrant hoosing to enter at a speifi loation i ould have and still earn nonnegative operating profits. Notie from the seond term in the brakets in (14) that a produer s profits depend on a weighted 2 13 The result that the number of produers grows less than proportionately to the size of the market has been found empirially in other industries by Bresnahan and Reiss (1991) and Campbell and Hopenhayn (2002). 14 Here I assume that inumbents an reset their pries optimally against the entrant and eah other. I also preserve the assumption of equal spaing of produers after the entrant begins operations for tratability. More preisely speaking, then, the new entrant is piking its neighbors rather than a speifi loation on the irle. 12

16 sum of its ompetitors ost levels. Therefore the best loation to enter for any new produer (regardless of its own ost draw) is that loation i where this term is highest i.e., where its losest ompetitors have the highest osts in the market. Setting (14) equal to zero and solving for i at this weakest-ompetitor loation yields the highest ost level an ex-post entrant ould have and still earn nonnegative operating profits. In some sense, this value is a onservative estimate an upper bound of the marginal osts that would be observed empirially, beause it allows the ex-post entrant to loate next to the weakest ompetitors after identifying their loation. It is additionally onservative beause this analysis ignores whether suh ex-post entry would even be profitable in expetation one the sunk entry ost s is figured in. I ompute two versions of this upper-bound ost by simulating the model repeatedly. Details of the simulation proess are in the appendix. For a fixed demand density level and parameter set, 1000 market equilibria are determined as outlined above; potential produers draw osts from a ommon distribution, deide whether to produe, and (if so) set their pries aording to the optimal behavior exposited in the model. Then the ex-post upper bound i is omputed for eah equilibrium using (14). The maximum and average of these upper bounds aross the 1000 trials are then omputed. As a hek on the intuition given above regarding the relative growth of n with respet to D, I also ompute the average produer size in the simulated outomes. This simulation proess is repeated over a range of demand density values. The results of this exerise are shown in Figure 3. It plots for a range of demand density levels the maximum and average upper-bound marginal osts, the average produer size, and for omparison the * implied by the model. As an be seen, the negative relationship between demand density and the highest ost in the market remains. Furthermore, the simulations imply that, as supposed above, higher demand density leads to larger produers on average. While simple, these simulation exerises do suggest that the basi insights of the model should remain in the presene of any (virtually inevitable) deviations between the mehanisms in the model and those existing in reality. III. Data and Measurement Issues A. Produer Produtivity and Size Computing produer-level produtivity and size distribution moments are key to testing the model. I do so using data from U.S. ready-mixed onrete (SIC 3273) plants in the 1982, 13

17 1987, and 1992 Census of Manufatures (CM). 15 The CM mirodata ontain a wealth of information on plants prodution ativities. Importantly here, they also ontain the state and ounty in whih establishments are loated, allowing me to plae produers into defined geographi markets. Eah year of the quinquennial CM ontains information on eah of the roughly 5200 ready-mixed plants operating in the United States. However, very small plants (typially with fewer than five employees) alled Administrative Reord (AR) establishments have imputed data for most prodution variables. These AR plants amount to roughly one third all establishments, though their small size implies they ompose a muh smaller share of employment and output. Beause of their imputed data, I exlude these plants from the main sample. However, I do observe their loation, so I an ount the total number of market produers for use when needed. I augment the standard CM data with the aompanying CM Produt data files. These auxiliary files ontain information on the speifi produts (defined at the seven-digit SIC level) made by eah establishment. This information inludes the total value of shipments by produt for eah plant, and when measurable, produt output in physial units. This physial output measure is available for almost all non-ar ready-mixed onrete plants (indeed, the industry is unusual in that it only ontains a single seven-digit produt). Thus I an measure produers ready-mixed shipments either in dollars or ubi yards. 16 This produt data is valuable from a measurement standpoint. It allows me to use a physial output measure rather than relying on deflated revenue as most plant-level studies must do beause of the dearth of plant-level prie indies. Deflated-revenue output measures pose problems when pries vary aross plants for reasons other than output quality (differenes in 15 In most of the empirial work, I do not distinguish between plants and firms. Most ready-mixed onrete plants in the U.S. during my sample period were single-unit firms (although this fration has been falling over time). For example, 3749 firms ontrolled the 5319 ready-mixed plants operating in In earlier versions, I tested the empirial results for sensitivity to the prevalene of multi-plant firms (along with other tehnologial fators that may vary aross markets), and there were not large differenes see Syverson (2001). Moreover, produtivity still varies aross plants in multi-unit firms, and the seletion mehanism exposited here an also be applied to determine whih plants within a firm survive in equilibrium. 16 In addition to AR plants, I also exlude those few plants who earn less than half of their revenue from ready-mixed onrete. (While plants industry lassifiations are typially based on the produt that omprises the their largest share of revenue, some that were lassified as ready-mixed did not earn the majority of their revenue through readymixed sales.) However, most ready-mixed produers are quite speialized; the average revenue share of readymixed aross all plants in my sample is 95.5 perent. 14

18 demand onditions aross plants, say), beause produtivity measures then embody withinindustry prie variation. That is, plants with higher (lower) than average pries will appear to be more (less) produtive than they really are. As I argue above, the geographi segmentation present in the ready-mixed industry all but ensures that within-industry demand variation exists. 17 I measure produtivity using a standard total fator produtivity index. Plant TFP is omputed as the log of its physial output minus a weighted sum of its logged labor, apital, materials, and energy inputs. That is, TFP it = q α l α k α m α e, (15) it lt it kt it where the weights α j are the input elastiities of input j {l, k, m, e}. While inputs are plantspeifi, I use the industry-level input ost shares as my measure of the orresponding input elastitiies. 18 These ost shares are omputed using reported industry-level labor, materials, and energy expenditures from the CM. Capital expenditures are onstruted as the reported industry equipment and building stoks multiplied by their respetive apital rental rates in ready-mixed onrete s orresponding two-digit industry. 19 Labor inputs are measured as the sum of prodution worker hours (reported diretly in the CM mirodata) and an imputed value for non-prodution worker hours. This imputation uses the method of Davis and Haltiwanger (1991), who multiply the number of non-prodution mt it et it 17 I hek below the robustness of the empirial results to the use of revenue-based output and find that some results do hange from the physial-output-based benhmark, likely due to the nature of intra-industry prie variation. Readers may notie that one an onstrut unit pries using the produt-speifi revenue and physial output data. I do so and explore the onnetion between produt substitutability, osts, and pries in Syverson (2002). 18 Two potentially important assumptions are impliit in this index. First is the assumption of onstant returns to sale. If the sale elastiity were instead different from one, eah of the input elastiities α j should be multiplied by the sale elastiity. Below, I test the results for robustness to this assumption as well as estimate the sale elastiity diretly in an industry prodution funtion (and, in fat, find evidene for onstant returns). The seond assumption is that all industry produers share the same prodution funtion hene the use of industry-level ost shares. While this is a ommon assumption in similar studies, one might be onerned in partiular that many produers mine intermediate materials (gravel and stone aggregate, speifially) on the fatory site. Plants that do so will have quite different fator ost shares than those purhasing these materials from off-site produers. While I do not diretly observe plants soures of intermediate materials, the vast majority of plants have materials revenue shares that are narrowly distributed around the industry average of roughly 65 perent. Given that gravel and stone are major intermediate inputs (aounting for roughly 13 perent of revenues), the narrow distribution suggests on-site mining is the exeption rather than the rule. 19 Capital rental rates are from unpublished data onstruted by the Bureau of Labor Statistis for use in omputing their Multifator Produtivity series. Formulas, related methodology, and data soures are desribed in U.S. Bureau of Labor Statistis (1983) and Harper, Berndt, and Wood (1989). 15

19 workers at the plant by the average annual hours of non-prodution employees in the orresponding two-digit industry (omputed from Current Population Survey data). Equipment and building apital stoks are plants reported book values of eah apital type deflated by the book-to-real value ratio for the orresponding three-digit industry. (These industry-level equipment and strutures stoks are from published Bureau of Eonomi Analysis data.) Any reported mahinery or building rentals by the plant are inflated to stoks by dividing by the typespeifi rental ost from Bureau of Labor Statistis data (see footnote 20). The total produtive apital stok k it is then omputed by summing the equipment and strutures stoks. Materials and energy inputs are simply plants reported expenditures on eah divided by their respetive industry-level deflators from the National Bureau of Eonomi Researh Produtivity Database. 20 B. Loal Markets in the Ready-Mixed Conrete Industry The empirial test of the above model works off variations in demand density aross geographi markets. This of ourse raises the issue of how to suitably define markets within the industry. I use the Bureau of Eonomi Analysis s Component Eonomi Area (CEA) as my market definition. CEAs are olletions of ounties usually but not always entered on Metropolitan Statistial Areas (MSAs). Counties are seleted for inlusion in a given CEA based upon their MSA status, worker ommuting patterns, and newspaper irulation patterns, subjet to the ondition that CEAs must ontain only ontiguous ounties. The seletion riteria ensure that ounties in a given CEA are eonomially intertwined. This lassifiation proess groups the roughly 3200 U.S. ounties into 348 markets that are mutually exlusive and exhaustive of the land mass of the United States The fat that plants an produe multiple produts though most do not, as disussed above poses another produtivity measurement issue. Inputs are reported on an establishment-wide rather than produt-speifi basis. Thus the TFP value for multi-produt onrete plants must impute the share of inputs alloated to ready-mixed prodution. I do so by dividing reported ready-mixed output by its share of total establishment sales. This adjustment method in effet assumes inputs are used proportionately to eah produt s revenue share. For example, a plant produing 1000 ubi yards of ready-mixed onrete aounting for 80 perent of its revenues will have the same TFP as a ompletely speialized plant produing 1250 ubi yards with same measured inputs. Without adjusting the first plant s output, it would appear less produtive beause the inputs it uses to make its other produts would instead be attributed entirely to ready-mixed prodution. Again, the impat of any mismeasurement indued by this approximation is minimized by the fat that industry plants produe ready-mixed onrete almost exlusively. 21 See U. S. Bureau of Eonomi Analysis (1995) for more detailed information about CEA reation. 16

20 The CEA-based market is a ompromise between onfliting requirements. The model assumes that onrete markets are isolated geographi units; plants in one market ompetitively interat only with other plants in the same loal market. Interations with ready-mixed produers in other markets are assumed away. While there are bound to be some ross-cea onrete sales in reality, the high transport osts of the industry make this unlikely. Detailed industry-level shipments data from the 1977 Commodity Transportation Survey support this. Ready-mixed plants shipped 94.4 perent (by weight) of their total output less than 100 miles. Disussions with industry managers also offer anedotal evidene along these lines; stated maximum ideal delivery distanes were between 30- and 45-minute drives from the plant. CEAs are large enough to minimize ross-market shipments. (An additional fator minimizing rossmarket shipments is that most CEA boundaries are in outlying parts of urban areas and are thus less likely to be near areas heavily populated with onrete plants.) CEAs are also not required to adhere to state boundaries, whih would sometimes plae unwarranted market boundaries in eonomially interonneted areas. Of ourse, I do not want to make markets so large that there is very little ompetitive interation between many of the inluded establishments. Plants plaed in too large a market may not all respond to the same market fores either external or the ations of industry ompetitors. CEAs are a suitable ompromise to resolve the tension between isolating markets yet ensuring the produers within them are interonneted. C. Demand Density The key exogenous variable in the model is demand density. To measure this empirially, I use the log of the number of onstrution-setor workers per square mile in the CEA-year market. Constrution setor employment is obtained from County Business Patterns data aggregated at the CEA level. 22 Land areas are from the City and County Data Book. Constrution setor employment is a suitable demand measure beause the setor buys 22 County Business Patterns data oasionally have missing observations due to data dislosure regulations. This is a small matter in the ase of the onstrution setor (SICs 15-17), however. The setor s ubiquity and abundane of small firms allows full dislosure of total employment in nearly all ounties (employment data is withheld in roughly 1.5 perent of the ounty-year observations in my sample). I impute employment when missing by multiplying the number of establishments in eah of nine employment ranges (whih are always reported) by the midpoint of their respetive employment ranges, and summing the result. The impat of using imputes is likely to be even less than their proportion indiates, as the typially small nondislosure ounties are less likely to ontain non-ar readymixed plants. 17

21 most of the ready-mixed onrete industry s output (97.2 perent, aording to the 1987 Benhmark Input-Output tables). I also ontend that this measure is empirially exogenous to the nature of ompetition among loal ready-mixed onrete plants. This is beause onstrution projets require output from a wide array of industries, so the ost share of ready-mixed alone is small. Looking at 1987 again, ready-mixed onrete aounted for only 2.0 perent of the onstrution setor s osts. Therefore a shok to the ompetitiveness of the loal ready-mixed industry (that lowers average onrete pries, say) is unlikely to spur a onstrution boom. Thus ausation travels from onstrution demand to onrete ompetitiveness and not in the reverse diretion. IV. Benhmark Empirial Results To reap the disussion of Setion II, the model implies that higher demand densities should result in the following: Less produtivity dispersion among loal produers. A higher average produtivity level. A higher minimum produtivity level. Larger average plant size in terms of units sold. I ompute six market-level measures to test these impliations. These measures have been seleted to aount for speifi measurement onerns. I measure produtivity dispersion using the interquartile TFP range among produers in eah CEA-year market. I use this ordinal dispersion measure to minimize the influene of spurious outliers. 23 The entral tendeny of the loal produtivity distribution is measured in two ways. One is the median TFP level in the market. Again, an ordinal measure is used to minimize measurement error. The seond is a weighted-average TFP in the market. The weights are produers output market shares (among only those plants in my sample AR plants are exluded sine I observe neither their output nor produtivity level). This measure is more vulnerable to the influene of outliers, of ourse, but it aptures produtivity growth resulting from density-driven market share realloations. As a measure of the market s minimum produtivity level, whih outliers affet above all other 23 It is not unommon for reporting and transription error reate nonsensial observations in produer-level mirodata. Additionally, sine many of my markets have a small number of plants, this inreases the vulnerability of traditionally alulated moments to outlier effets. 18