Multi-product firms and business cycle dynamics

Abstract

Recent empirical evidence provided by Bernard et al. (2010) and Broda and Weinstein (2010) shows that a significant share of product creation and destruction in U.S. industries occurs within existing firms and accounts for an important share of aggregate output. In the present paper, and consistent with this evidence, we relax the standard assumption of mono-product firms in a dynamic stochastic general equilibrium model. Our analysis is based on a model of firm dynamics with two deviations from the conventional real business cycle framework—imperfect competition with endogenous entry and multi-product firms. The combination of these two features enables our model to successfully generate a mechanism that accounts for the strong procyclicality of product creation. Due to the proliferation effect induced by firm-level adjustments in product scope, we show that our model embodies a quantitatively important magnification mechanism of aggregate shocks.

Introduction

Multi-product enterprises dominate production activity in the U.S. economy. According to Bernard et al. (2010), 39% of firms produce more than one product and generate, on average, 87% of U.S. manufacturing output. ¹ Despite this empirical evidence, multi-product firms have thus far received relatively little attention in macroeconomics. Only recently has a growing body of international trade literature incorporated multi-product firms into models of general equilibrium to address issues related to trade liberalization (see Nocke and Yeaple, 2006, Eckel and Neary, 2010, Mayer et al., 2010, Bernard et al., 2011). ² These contributions show that intra-firm adjustments within multi-product firms are not limited to changes in the scale of production; in fact, the choice of product range adds a new “extensive” margin of firm adjustment that plays an important role in economy-wide shocks such as trade liberalization.

The available empirical evidence has also convincingly documented that the contribution of new products (produced at both existing and new firms) to the overall production is important enough to be a major source of aggregate output fluctuations. In this respect, Bernard et al. (2010) show that 54% of firms change their mix of products within a 5-year census period, with 25% of firms both adding and dropping at least one product. Most importantly, the authors find that over the same period product creation accounts for a significant share of overall production (33%) with the gross contribution of product switching that is as large as the gross contribution of firm entry and exit. The importance of product creation and destruction is also documented by Broda and Weinstein (2010), who show that across product groups, almost one-third of the growth rate of consumption expenditures is reflected in the growth rate of expenditure shares in new product varieties. ³ The authors find that net product creation is strongly procyclical at a quarterly frequency, with the procyclicality driven mainly by creation rather than destruction. ⁴ Given this evidence, two questions naturally arise: (1) what are the main driving forces behind the observed procyclical behavior of product creation?, and (2) what are the aggregate implications of firm-level adjustments along the product scope?

The present paper addresses these questions with a quantitative approach. We embed multi-product firms in a dynamic stochastic general equilibrium model (DSGE) with imperfect competition and endogenous entry. On the one hand, we are interested in building a model that is able to account for the observed cyclical properties of product creation. In particular, we identify a firm-based force, originating from strategic behavior, that explains the strong procyclicality of product creation. On the other hand, we aim to assess the contribution of the intra-firm extensive margin to the response of the economy to productivity and demand-type shocks. Our results show that firm-level adjustments along the product range generate endogenous variations in total factor productivity that magnify the amplitudes of aggregate fluctuations.

In this paper, we depart from the standard Dixit–Stiglitz structure by assuming that, in choosing their product ranges and pricing strategies, companies behave as oligopolists and not as monopolistic competitors. ⁵ As a result, firms co-ordinate their pricing decisions by internalizing demand linkages between the varieties they produce. ⁶ Moreover, because companies are large and produce a non-negligible set of varieties, they also take into account the effects of their pricing decisions on the aggregate price index. In this environment, firms attempt to increase their market shares through product proliferation and we assume that a variety-level fixed production cost bounds their product ranges. Firms pay a fixed period-by-period production cost and earn zero profits in every period. Market structure is then endogenously determined by the entry and exit decisions of individual producers, as well as by their optimal product scope choices.

In this model, the product scope is procyclical. This property stems from the fact that, in a strategic setting, firms use the product range as a tool to relax price competition. The intuition is as follows. In our framework, a company chooses its optimal product scope by accounting for the effects of this choice on both its own and all other firms' pricing decisions. In this respect, we show that increasing the number of varieties produced raises each firm's own price and, as a reaction, induces rivals to cut their products' prices. Consequently, companies try to mitigate price competition by under-expanding their product scopes with respect to a situation of monopolistic competition in which firms behave in a non-strategic manner. Since the strategic effect of the product scope becomes less important as the number of firms increases, the incentive of each company to create new product varieties increases with the number of competitors in the market. Consequently, any shock that induces new firms to enter the market simultaneously prompts incumbents to increase the number of varieties produced. We call this mechanism the proliferation effect. As an implication of such an effect, in our model net product creation is procyclical with product turnover due to the joint contribution of product switching within existing companies and firm entry. By contrast, in a canonical Dixit–Stiglitz framework with monopolistic competition and multi-product firms, the strategic effect of the product scope is not operative, and we show that firms' product ranges are not affected by transitory aggregate shocks.

The proliferation effect has important implications for aggregate dynamics. In fact, product range adjustments at the firm level give rise to endogenous variations in total factor productivity that magnify the amplitudes of economic fluctuations. We show that the combined effect of changes in product scope with firm entry and exit and countercyclical markup variations provides a quantitatively important, endogenous amplification mechanism. By calibrating our model to the U.S. economy, we find that output volatility increases by 50% relative to the canonical real business cycle (RBC) model with perfect competition, and by 17% relative to the mono-product firm model. Interestingly, in our set-up, the proliferation effect is the main channel of shock magnification. We find, in fact, that the contribution of the intra-firm extensive margin to the overall fluctuations of product creation is substantially more important than the contribution of firms' entry. Moreover, we show that, relative to the mono-product firm model, adjustments along the product scope dampen the response of the average markup to exogenous shocks.

This paper is related to an extensive body of literature in macroeconomics that analyzes business cycle fluctuations with imperfect competition. Among the early contributions on this subject, both Chatterjee and Cooper (1993) and Devereux et al. (1996) analyze the effects of entry and exit on business cycle dynamics and show that net business formation is procyclical. The presence of strategic interaction distinguishes our model from these papers, where the market structure is characterized by monopolistic competition. More recent contributions in the field include Comin and Gertler (2006), Bilbiie et al. (2012), Jaimovich and Floetotto (2008) and Etro and Colciago (2010). The first paper attempts to explain medium-term business cycle fluctuations within a model with endogenous productivity dynamics and countercyclical markups. Differently from Comin and Gertler (2006), we consider exogenous shocks and focus on a standard definition of the business cycle. Moreover, due to the presence of strategic interaction, our model generates countercyclical markups, whereas Comin and Gertler (2006) postulate a function for markups that is decreasing in the number of firms. Bilbiie et al. (2012) study the role of product creation in propagating business cycle fluctuations in a model with monopolistic competition and sunk entry costs; the authors analyze the contributions of intensive and extensive margins (i.e., changes in the production of existing goods and the range of available goods) to the economy's responses to changes in aggregate productivity. We differ from this paper in two main respects. First, in Bilbiie et al. (2012), each product unit is interpreted as a product line within a multi-product firm; due to the assumption of a continuum of goods, firm boundaries are left unspecified, without concern for strategic interactions within and across firms. In our paper, we explicitly model multi-product firms by taking strategic firm interactions into account. Second, the source of cyclical movements in markups is different in the two models. In Bilbiie et al. (2012), countercyclical markups are due to demand-side pricing complementarities; in our paper, countercyclical markups are related to variations in the number of competitors and occur due to supply-side considerations. ⁷ Both Jaimovich and Floetotto (2008) and Etro and Colciago (2010) develop an RBC model with mono-product firms and endogenous entry by taking strategic firm interactions into account. Jaimovich and Floetotto (2008) show that oligopolistic behavior generates an important channel of shock magnification that operates through endogenous markup variations. Etro and Colciago (2010) analyze the role of different forms of competition (Bertrand vs Cournot) in the propagation of technology shocks. We differ from these two papers by proposing a DSGE model with multi-product firms. In the context of this market structure, we show that the product range represents an important channel of shock amplification that strengthens the endogenous magnification mechanism embodied in models with mono-product firms. Moreover, our paper provides additional insights into the role of imperfect competition in shaping business cycle fluctuations, showing that cyclical variations in total factor productivity are driven by any shock that boosts aggregate demand, regardless of whether it directly affects technology.

The rest of the paper is organized as follows. Section 2 presents the model, while Section 3 solves it. Section 4 describes the calibration and the main dynamic implications of the model. Finally, Section 5 provides conclusions. The calculation details are provided in the Appendix.