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Globalization and Multiproduct Firms

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Globalization and Multiproduct Firms
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  Globalization and Multiproduct Firms  Volker Nocke y University of Mannheim and CEPRStephen Yeaple z Pennsylvania State University and NBERSeptember 16, 2010 Abstract We present an international trade model of multiproduct …rms that focuses on a newsource of …rm heterogeneity: organizational capability. All …rms have a limited span of control, but the resulting trade o¤ between …rm scope and marginal cost is less severe for…rms with greater organizational capability. The model generates a negative relationshipbetween …rm size and market-to-book ratio. Multilateral trade liberalization (globalization)induces a merger wave and results in a reduction of average industry production costs andin a ‡attening of the size distribution of …rms. Keywords : multiproduct …rms, …rm size distribution, trade liberalization, size dis-count, …rm heterogeneity, merger wave, organizational capability JEL Classi…cation : F12, F15  Earlier versions of this paper were circulated and presented under the titles Globalization and Endogenous Firm Scope  and Globalization and the Size Distribution of Multiproduct Firms  . We gratefully acknowledge …-nancial support from the National Science Foundation (grant SES-0422778) and the University of PennsylvaniaResearch Foundation. We thank seminar audiences at: Princeton University, Stanford University, the Pennsyl-vania State University, the London School of Economics, the World Bank, the Universities of Oxford, Toronto,Tübingen, Virginia, Maryland, Calgary, Zurich, Kiel, Essex, Nottingham, the Norwegian School of Manage-ment (Oslo), the Copenhagen Business School, the 2005 NBER ITI Winter Meeting (Stanford), the 2006 NBERITO Working Group Meeting (Cambridge, MA), the 2006 Christmas Meeting of German Economists Abroad(Munich), and the 2009 EIEF Workshop on Structural Approaches to Productivity and Industrial Dynamics(Rome). y Email: volker.nocke@gmail.com. z Email: sry3@psu.edu.  1 Introduction With the increasing availability of huge …rm-level datasets, economists have documented enor-mous variation across …rms along many dimensions, such as productivity, scope (number of products), technology, and managerial practices. Much of this interest, particularly within the…eld of international trade, has been driven by the model of Melitz (2003), which posits that…rms vary in their inherent productivity. The key insight of the Melitz-model is that when…rms vary in their productivity, they sort into serving foreign markets with the implicationthat trade liberalization induces within-industry selection e¤ects: trade liberalization leads toa reallocation of resources from less productive to more productive …rms. More recently, theMelitz-model has been adapted so as to incorporate multiproduct …rms (e.g., Bernard, Reddingand Schott, 2010b; Melitz, Mayer and Ottaviano, 2010). In these models, trade liberalizationcan cause within-…rm selection e¤ects that are akin to the within-industry selection e¤ects thatappear in the srcinal Melitz model.While these selection-driven models have yielded many important insights into the allo-cation of resources across …rms and the productivity e¤ects of trade liberalization, they areremarkably narrow in the sources of …rm heterogeneity that they allow, i.e., random di¤erencesin marginal costs. Given the abundance of research involving models that focus on this oneparticular source of …rm heterogeneity, it seems important to expand the scope of the analysisto other dimensions along which …rms di¤er.In this paper, we present a model of …rm heterogeneity in which …rms di¤er in their abilityto manage many di¤erent products. We explore the implications of …rm heterogeneity in the“span of control,” where the relevant span is not de…ned on …rm size per se but rather on thenumber of products that the …rm produces. Accordingly, the more products a …rm chooses tomanage, the greater is the burden on management, and so the higher are the marginal costs forall products. To focus on …rm heterogeneity in organizational capability relating to the spanof control, we posit that all …rms are equally e¢cient when constrained to produce a singleproduct, but the rate at which the marginal cost of production increases with …rm scope islower for …rms with greater organizational capability.Our focus on the span of control thus de…ned is natural given the huge variation in thenumber of products o¤ered by di¤erent …rms (Bernard, Redding and Schott, 2010b) and theconstant churn in the product lines across …rms (Bernard, Redding and Schott, 2010a). Weargue that the concept of span of control, which has a long tradition in economics (Lucas, 1978),is most naturally interpreted as involving the increased burden to …rm-level organizationalcapabilities posed by a large range of products. Indeed, according to the “resource-basedview of the …rm” in the management literature, greater diversi…cation re‡ects an abundance of 1  organizational capabilities that is optimally directed towards increasing …rm scope (Matsusaka,2001; Collis and Montgomery, 2005).We embed a simple parametric version of our mechanism into a model of monopolisticcompetition à la Asplund and Nocke (2006) and Melitz and Ottaviano (2008), and obtain avariety of insights into the organization of industries, and the e¤ects of trade shocks onto thisorganization. We discuss three implications of the model that provide an interesting contrastwith pure-selection driven models in the spirit of Melitz (2003). First, in our model, …rms withgreater organizational capability choose to manage a larger number of products, so much largerin fact that they end up having higher marginal costs even though they are intrinsically moree¢cient. The model therefore predicts a negative relationship between market-to-book value(Tobin’s Q) and …rm size. Second, in our model, trade liberalization induces a merger wave asit has an asymmetric e¤ect on …rms’ incentives to adjust their scope. Following a reduction intrade costs, some …rms have an incentive to reduce their product range while other …rms have anincentive to expand their scope, thereby a¤ecting the …rm size distribution in a systematic way.Perhaps surprisingly, a multilateral trade liberalization induces a ‡attening of the distributionof domestic sales. Third, our results suggest that some of the e¤ects of the observed productivitye¤ects of trade liberalization may be due to the reallocation of products across …rms. Whileour paper gives rise to some unique empirical predictions, the main contribution of the paperdoes not consist in hitting any particular empirical fact about the structure of production orthe response to trade liberalization, but rather in exploring the e¤ects of a di¤erent dimensionof …rm heterogeneity.Our paper is closely related to two strands in the theoretical trade literature. First, itcontributes to the recent and growing literature that is concerned with the within-industryreallocation e¤ects of trade liberalization (Melitz, 2003; Melitz and Ottaviano, 2008). Second,and more speci…cally, our paper contributes to the nascent literature that is concerned withmultiproduct …rms in international trade (Bernard, Redding and Schott, 2010b; Eckel andNeary, 2010; Mayer, Melitz and Ottaviano, 2010). In all of these papers, …rms essentially drawa distribution of marginal costs for various products of di¤erent degrees of substitutability sothat the marginal cost of any given product is exogenous. Instead, we explore a rather di¤erentmechanism, namely one where a …rm’s marginal cost of production for any given productdepends on the …rm’s choice of scope, and …rms di¤er in the extent of this relationship. In ourmodel, and in contrast to Eckel and Neary (2010), there are no cannibalization e¤ects on thedemand side. Instead, extending a …rm’s range of products induces higher marginal costs forthe …rm’s existing products by diverting managerial attention due to the limited span of control.Another important di¤erence to Eckel and Neary (2010) is that …rms are heterogeneous. Asemphasized above, the model di¤ers from all of the other trade models with heterogeneous2  …rms in that it focuses on a novel dimension of heterogeneity – organizational capability.The plan of the paper is as follows. In the next section, we present our model in a closed-economy setting. There, we analyze how …rms’ choice of scope is a¤ected by …rms’ organi-zational capability, and derive predictions on the relationship between …rm size on the onehand and marginal costs and the market-to-book ratio on the other. In Section 3, we embedthe model in a two-country international trade setting. There, we explore the e¤ects of tradeshocks on the industrial organization of production and the induced size distribution of …rms.We conclude in Section 4. 2 The Closed Economy In this section, we consider a closed economy where monopolistically competitive …rms di¤erexclusively in their organizational capabilities and choose how many products to manage. Tosharpen our focus on …rm heterogeneity in organizational capabilities, we treat products asperfectly symmetric. We then analyze how, in equilibrium, …rms with di¤erent organizationalcapabilities solve the fundamental trade o¤ between …rm scope and marginal costs. 2.1 The Model We consider a closed economy with a mass L of identical consumers with the following linear-quadratic utility function: U  = Z  x ( k ) dk  Z  [ x ( k )] 2 dk  2  Z  x ( k ) dk  2 + H; (1)where x ( k ) is consumption of product k in the di¤erentiated goods industry, H  is consumptionof the outside good, and  > 0 is a parameter that measures the degree of product di¤erentia-tion. Assuming that consumer income is su¢ciently large, each consumer’s inverse demand forproduct k is then given by  p ( k ) = 1  2 x ( k )  4  Z  x ( l ) dl: (2)The outside goods industry is perfectly competitive and uses a constant returns to scaletechnology. In the di¤erentiated goods industry, there is a mass M  of atomless …rms that di¤erin their organizational capabilities. 1 A …rm’s organizational capability is denoted by  2  ;  ,where  >  > 0 , and the distribution of organizational capabilities in the population of …rmsis given by the distribution function G . Each …rm can manage any number n  1 of products. 1 In this section, we remain agnostic about the determinants of  M  . In the next section, we will consider along-run equilibrium in which the mass of …rms is endogenous. 3  Each product is of measure zero and so is each …rm. We assume that …rms have constantmarginal costs at the product level but decreasing returns to the span of control at the …rmlevel: the more products a …rm manages, the higher are its marginal costs for each product.The …rm faces two types of costs. First, there is a …xed cost r per product. This cost canbe thought of as the market price of the property rights over an existing product. Second,there is a constant marginal cost c ( n ;  ) associated with the production of each unit of output,which is the same for all n products. (For simplicity, we will ignore integer constraints on n .)This marginal cost function has the following properties. First, an increase in the number of products increases a …rm’s marginal cost. This induced increase in the …rm’s marginal costmay be due to a reduction in productivity or due to a need to pay higher wages as a resultof diminished managerial attention. The induced higher wage may be due to a variety of reasons, e.g., because of the need to hire better (and therefore more costly) workers or becausethe additional burden on management makes monitoring workers less e¤ective. 2 Second, weassume that the trade o¤ between …rm scope and marginal cost is independent of scope: thereis a constant elasticity of marginal cost with respect to the number of product lines. Third,we abstract from exogenous cost di¤erences amongst single-product …rms and focus insteadon the idea that organizational capability is about how good …rms are at coordinating theproduction of multiple products. We therefore assume that the marginal cost of producing asingle product is independent of organizational capability and that the elasticity of marginalcosts with respect to the number of products is smaller for …rms with greater organizationalcapability. In sum, we impose the following simple functional form: c ( n ;  ) = c 0 n 1 = : (3)Each …rm’s optimization problem consists in choosing the number n of products and thequantity (output) q  k of product k 2 [1 ;n ] so as to maximize its pro…t. (Since …rms aremonopolistically competitive, each …rm could equivalently choose price  p k rather than quantity.) 2.2 Equilibrium Analysis As we show in the Appendix, each …rm in the di¤erentiated goods industry faces – in equilibrium– a linear residual demand curve for each one of its products: D (  p ) = L 2( a   p ) ; 2 Schoar (2002) empirically …nds that those …rms who add new products experience a reduction in total factorproductivity of existing products. She also …nds some evidence that …rms with a greater product range payhigher wages. 4
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