Finance, Organization, and the Product Mix of Exporters

Transcription

1 Finance, Organization, and the Product Mix of Exporters Dalia Marin Davide Suverato Thierry Verdier Monday 15 th May, 2017 Abstract Multi-product firms, though more efficient, have a dark side, they trade at a conglomerate discount. Exporters suffer a smaller conglomerate discount compared to domestic firms. We introduce an internal capital market into a two factor model of multi-product firms to explain these facts. We find that in the competition for funds inside the firm, the managers of the best divisions are empire builders and strategically over-report their costs receiving excessive financing possibly crowding out funding of less good divisions. This pattern of capital allocation is consistent with the observed capital expenditures across divisions of publicly listed US companies and explains the lower market to book value of conglomerates. We find further that a tougher trade environment leaves less room for the mis-reporting of costs improving the efficiency of the internal capital market. Finally, we find that firms face a trade-off between introducing a new product or exporting an existing one which tends to make exporters less diversified than domestic firms. The latter two mechanisms explain why the conglomerate discount is lower for exporters. University of Munich University of Munich Paris School of Economics We would like to thank Philipp Herkenhoff for excellent research assistance.

2 1 Introduction In the last 15 years the theory of international trade has made major progress in bringing trade models closer to the real word. Firms are heterogeneous in productivity so that only a minor fractions of firms engage in trade, a feature observed in the data Melitz (2003). More recently, models of trade have incorporated firms with multi-products (also called conglomerates) accounting for the fact that 91 percent of US manufacturing sales are produced by firms with more than one good Bernard, Redding, and Schott (2010). Moreover, firms face credit constraints so that only the most productive and largest firms are able to overcome this constraint to finance their exports (Chaney (2016), Manova (2008)). In these novel developments in international trade the major source of heterogeneity in firm size and productivity remains exogenous. The firms productivity is a sufficient statistics to determine entry, production and export decisions as well as external funding. Funding of projects will always go to the most productive firms with the most productive projects and all projects with positive profits will be financed. However, an internal capital market in which funds are distributed inside the firm organization may not always allocate resources in the same way as an external capital market and it may not fund all projects with positive returns. As we show in this paper, multiproduct firms and exporters finance their products predominantly via an internal capital market. 1 Examining how firms allocate funds to projects inside firms is vital to understanding which products firms finance, produce, and export. Therefore, we need to micro found the theory of multi-product firms in a theory of organization. As a matter of fact, the firms decision of how many business segments to put under the same roof is fundamentally an organizational question. Several features of the data on conglomerates may only be understood from an organizational perspective of multi-product firms. Multi-product firms are more productive Schoar (2002) than single product firms. But they have a dark side, they have lower Tobin s q compared to single product firms, multi -product firms trade at a conglomerate discount (Lang and Stulz (1994), Ozbas and Scharfstein (2009)). Moreover, we establish for the 1 see also Marin and Schnitzer (2011). 2

3 first time that exporters as well as firms more exposed to import competition trade at a lower conglomerate discount compared to domestic firms. This suggest that there is something special about firms exposed to international trade. Opening the black box of multi-product firms will allow us to address these features of the data. In this paper we introduce an internal capital market into a model of multi-product firms to explain the number of products a firm finances and exports. This allows us to bring together in a unified framework two separate strands of the literature in international trade - trade and finance on the one hand and multi-product firms on the other. More specifically, we model the internal capital market along the ideas of Stein (1997) and Scharfstein and Stein (2000) and we incorporate these ideas into a two factor version of Mayer, Melitz, and Ottaviano (2014) model of multi-product firms with monopolistic competition (henceforth MMO). 2 Firms produce from one to many competing products and they are heterogeneous in terms of productivity. The main novelty of our framework is that we introduce two agents in the firm: the owner/headquarters and divisional managers. 3 There is an informational asymmetry between the headquarters and divisional managers in firms. The headquarters knows all firm s projects but not as good as each division manager on his own project. The headquarters is responsible for two actions: she collects the overall amount of funding the firm depends on and, after fund raising, she allocates funds across firms projects. Divisional managers compete for the funds available to the firms. The headquarters ranks the projects relative to the other projects of the firm. The headquarters creates value by engaging in winner picking by actively reallocating funds across projects. Divisional managers try to influence the capital allocation of the headquarters by not reporting truthfully their costs. Divisional managers of the firm like to invest. The larger the empire they run, the more private benefits they get. As a result, the best divisions will over-report the funds they need (they pretend to be less efficient than they really are to secure more funds) and they do not run the risk of not being financed because they know the distribution of costs of the other competing divisions. The best divisions end up 2 For other models of multi-product firms, see Eckel and Neary (2010), Bernard, Redding, and Schott (2011), and Nocke and Yeaple (2014). 3 To simplify matters we do not distinguish between the owner and the headquarters. In our framework the owner is also the headquarters. For the distinct role of a headquarters, see Gertner, Scharfstein, and Stein (1994). 3

4 receiving more capital than is optimal. This explains why conglomerates have a lower Tobin s q compared to single-product firms. We gain several additional insights from introducing an internal capital market into the theory of multi-product firms. First, a tougher competitive environment makes the working of the internal capital market more efficient. Trade reduces the distortions generated by the internal capital market. Tougher competition lowers the cost level at which firms can survive in the market. Divisional managers use this cut-off cost level as a benchmark when they decide how much to deviate from their true costs when they ask for funds from the headquarters. This way, trade liberalization leaves less room for the mis-reporting of costs in the competition for funds. Hence, firms exposed to trade will run their internal capital market more efficiently which explains why the conglomerate discount is lower in exporters. Furthermore, our model yields a novel trade-off between introducing a new product or exporting an existing one. Exporting may face a profitability constraint of domestic sales rather than a financial constraint. Firms may not want to devote financial resources to exporting because allocating funds to a new product may be more profitable. 4 The model predicts that exporters tend to be less diversified than domestic firms which is an additional reason why exporters suffer a lower conglomerate discount compared to domestic firms. The paper contributes in several ways to the literature on corporate finance and trade. First, in Stein (1997) the internal capital market is efficient. Headquarters has always the incentive to allocate capital to the most productive projects. In our model, managers of the best divisions are empire builders and they try to influence the capital allocation decisions of the headquarters by over reporting their costs. Thus, in our model the internal capital market creates distortions that benefit in particular the best divisions of the firm. Second, in Scharfstein and Stein (2000) the weak divisions receive more capital at the expense of the good divisions. Because the marginal product of the managers of weak divisions is relatively 4 This is a major departure from the current approach investigating the relationship between finance and trade, see Foley and Manova (2015). 4

5 low, they are willing to spend more time trying to convince headquarters to get a larger capital budget. In our model the weak divisions do not have an incentive to try to secure funds by underreporting their costs (by pretending they are more efficient than they really are to secure funds), because they have to commit to a level of profits which they have to deliver after receiving the capital allocation. Therefore, it does not make sense for them to ask for funds in the first place. Thus, in contrast to Scharfstein and Stein (2000), in our model the distortion in the internal capital market arises in the best divisions rather than in the weak divisions. In the empirical section of the paper we examine the actual capital expenditures across divisions of publicly listed US firms and we indeed find that the mis allocation of capital arises in the strongest divisions rather than the weakest divisions of the firms. Third, in contrast to MMO who abstract from financial issues, in our model with capital as a second factor of production not all projects with positive profits will be financed as projects have to be at least as profitable as the external capital market. We add three novel contributions to MMO. First, the pool of financed projects changes, both in the extensive and in the intensive margin depending on the extend of over-reporting and on the return of investment on the external capital market. Second, tougher competition has two opposing effects on the efficiency of firms: trade allocates more resources to the best products which are managed with excessive high costs. But at the same time, trade reduces the over-reporting of costs leading to a more efficient firm allocation. Third, in MMO tougher competition leads to a narrower product scope. This mechanism is also at work in our model. But there is an additional mechanism which tends to increase the number of products per firm. Tougher competition increases the return on investment (by reducing overreporting across all products) and, hence, may increase the number of products which are financed. The paper is also related to the literature that introduces organizations into trade models. Marin and Verdier (2008, 2012, 2014) introduce the authority-based hierarchy model of the firm of Aghion and Tirole (1997) model of the firm, and Caliendo and Rossi-Hansberg (2012) bring knowledge-based hierarchies into international trade and all these papers show that in a more competitive trade environment firms reorganize to a more decentralized organization. McLaren (2002), 5

6 Grossman and Helpman (2002) and Conconi, Legros, and Newman (2012) show that international trade may lead to more outsourcing of activity outside the firm. 5 Marin and Schnitzer (2011), and Antràs and Foley (2015) explore the financial behavior of firms engaged in trade and foreign direct investment, and Marin and Schnitzer (1995) Marin and Schnitzer (2005) analyze how financial problems can lead to the emergence of new institutions in international trade and in emerging markets. 6 The paper is organized in the following sections. In section 2 we report some stylized features of the data on multi-product firms that our theory tries to explain. Section 3 presents the model of multi-product firms under monopolistic competition. Section 4 describes the competition for funds in an internal capital market and shows that funding will be distorted towards the best divisions of the firm. Section 5 shows how the mis allocations in the internal capital market may reduce Tobin s q of multi-product firms relative to single-product firms. The section also examines the actual pattern of capital expenditures across divisions of publicly listed US firms. Section 6 solves for the industry equilibrium and section 7 opens the economy to international trade and presents the new trade-off between exporting and domestic sales and explores the new channels through which trade influences the product-mix of firms. Section 8 concludes. In the Appendix A we calibrate the model for reasonable parameter values and we show that the predicted values of capital allocation across divisions and of Tobin s q nearly overlap with the actual values of publicly listed US firms. Appendix B offers a generalization of the behavior of managers. 2 Stylized Facts In this section we establish some facts about multi-product firms engaged in international trade to motivate the theory we develop in the paper. We use firm-level data of publicly listed US firms in the manufacturing sector covering the period from Worldscope. In addition to standard balance sheet information, the data include basic accounting information on SIC 4- digit level business segments, such as sales, assets, capital expenditure, operating profits, and 5 For a survey of the literature on trade and organization, see Antràs and Rossi-Hansberg (2009) and Marin (2016). 6 For a survey of the literature on finance and trade, see Foley and Manova (2015). 6

7 depreciation. For the purposes of this section we use firm-level data and exploit the fact that we know whether a firm is a multi-product firm in a given year. To clean the data, we drop firms with anomalous accounting data (capital expenditures smaller than sales or assets, zero depreciation, negative capital spending). The cleaned sample consists of publicly listed US firms and contains 586 distinct domestic firms (without exports and without foreign affiliates) and 1089 exporters (see Table 1). The share of exporters among all firms of 32.6% is a lower bound, since the total number of firms of 3341 include firms with missing export information, while those are excluded from the exporter count. The exporter share in our sample is unusually large. Bernard, Jensen, Redding, and Schott (2007) show based on US census data on manufacturing firms that exporting is a rare activity as only 18 percent of firms are exporters. However, our sample consists of the largest and publicly traded US companies which may explain why exporting firms are so frequently observed in our data. Among the domestic firms 163 are conglomerates with more than one business segment and 516 are singleproduct firms, while among exporters 551 are multi-product firms and 802 are single-segment firms. Thus, the share of conglomerates in percent of firms is much larger among exporters compared to domestic firms (50.6 % vs 27.8 %) and is roughly in line with what Bernard et al. (2010) report based on Census data (39%). The numbers do not add up to the total number of exporters and domestic firms, respectively, because of double counting when firms switch their exporting and/or conglomerate status over time. Firms count as exporter conglomerate when they are a conglomerate at least once while they are an exporter and as a single segment exporter when they are a singleproduct firm at least once while they are an exporter. Firms count as a domestic conglomerate when they are a conglomerate at least once while they are a domestic firm and they count as a single segment domestic firm when they are a single segment firm at least once while they are a domestic firm. In Table 2 we compare firms with a single-segment to multi-segment firms for exporters and domestic firms. Conglomerate firms are larger than single-product firms on the basis of sales and assets and have larger capital expenditures. Multi-product firms are also more profitable as measured by the cash flow to sales ratio. We measure cash flow as operating profits plus depreciation. 7

8 Table 1 The Data exporters 1089 exporter conglomerates 551 exporter single segment 802 conglomerate share of exporters 50.60% domestic firms 586 domestic conglomerates 163 domestic single segment 516 conglomerate share of domestic firms 27.82% exporter share 32.60% firms 3341 observations (firm-years) Note: The table counts distinct firms. Sub-categories do not sum to the totals because some firms switch their exporting and/or conglomerate status over time. Among the 3341 firms 1126 switch their conglomerate status, which is 33.7% of firms. The table reads as follows: There are 1089 firms that are an exporter at least once over the sample period. Of these 1089 firms, 551 are a conglomerate at least once while they are an exporter and 802 firms are a single-segment firm at least once while they are an exporter. Exporters and domestic firms do not add up to 3341 because we exclude pure multinational firms and firms with missing export information. The exporter share of 32.60% is a lower bound since the total number of firms of 3341 includes firms with missing export information, while those are excluded from the exporter count. If firms with missing export values and positive FDI sales are also counted as exporters, then the export share rises to 62.4%. The data cover the period Nonetheless, multi-product firms have lower Tobin s q compared to single-product firms. 7 This is the well known conglomerate discount which has been established by the corporate finance literature in the 1990s. Multi-product firms trade at a discount compared to single product firms (see Berger and Ofek (1995), Shin and Stulz (1998). In Table 3 we look at the financing behavior of these US companies to find out how important the internal capital market is as a source of financing for these firms. Interestingly, the internal cash flow is the most important source of funding of conglomerates and exporters. Multi-product firms rely in 40% of funding on internal cash flow as a source of finance of their investments compared to single segment firms (17.8%). Moreover, exporters also use internal cash flow more frequently to fund their activity compared to domestic firms (31% vs -3.5%). Debt and equity finance are more important for domestic firms than for exporters (50.7% vs 33%). The high share of funding 7 Tobin s q is calculated as the market value of assets over the book value of assets, where the market value of assets is calculated as the book value of assets plus market capitalization minus the sum of the value of common equity and balance sheet deferred taxes. 8

9 Table 2 Summary Statistics Domestic Firms Exporters single segment conglomerate single segment conglomerate median values sales (mio US$) assets (mio US$) capital expenditure (mio US$) cash flow (mio US$) capital expenditure / sales cash flow / sales Tobin's Q Note: All numbers are median values. Domestic firms are with zero FDI sales and zero export sales. Exporters may also include positive FDI sales. The numbers are calculated from a pooled unbalanced panel of publicly listed US firms in manufacturing (SIC ) in the period Firms reporting capital expenditure larger than sales or assets, negative sales, non-positive depreciation, or negative capital expenditure were removed from the sample. Domestic single segment firms with negative cash flow at the median apparently finance their activity out of equity and debt as can be seen by Table 3. of multi-product firms and exporters via an internal capital market justifies the focus of our paper on this type of finance. Table 3 The Financing of Firms in percent of total funds mean values source of funds all firms single segment conglomerates domestic exporter cashflow long term debt equity fixed asset sales investment decrease other sources total amount available (m US$) observations In Figure 1 we revisit the data on the conglomerate discount to establish its validity for the more recent years. We plot the ratio of Tobin s q of multi-product firms to single-product firms for US manufacturing firms in the period We report the discount separately for domestic and exporting firms. Several points are noteworthy. We start with domestic firms. Tobin s q of multi-product firms are 60 to 80 percent of those of single-product firms. The discount appears to have become larger over the last 17 years. This is not only due to the recent financial crisis in 2008, 9

10 since the trend increase in the discount started already in the late 1990s. Interestingly, exporting firms have a strikingly smaller conglomerate discount compared to domestic firms. Multi-product exporters trade at about 90 percent of the market value compared to single-product exporters. Moreover, the discount in exporting firms has remained the same over the last 15 years or may have even disappeard for exporters since The corporate finance literature has argued that the conglomerate discount is due to misallocations in the internal capital market of conglomerates. A number of papers have presented evidence of inefficient internal capital markets (see Lamont (1997), Shin and Stulz (1998), Rajan, Servaes, and Zingales (2000), Ozbas and Scharfstein (2009)). The smaller discount in exporting firms may indicate that the exposure to international trade may in some way act as a disciplining device in the internal capital allocation process of multi-product firms, an issue we will adress in the model presented in the next section. Figure 1: Tobin's q ratio of multi-segment firms to single-segment firms mean values ratio of mean qs year of observation exporting firms domestic firms To see whether the pattern in Figure 1 is robust, we run regressions with and without industry and year fixed effects controlling for a list of firm characteristics (shown in Table 4). The dependent variable is the log of Tobin s q. Conglomerate is a dummy with value 1 when the firm has more 10

11 than one product, exporter is a dummy with value 1 when the firm is an exporter. To control for firm characteristics we include firm size (firm sales) and firm s cash flow. The purpose of including industry-fixed effects is to address the possibility that differences in Tobin s q among industries may explain the results. We include year-fixed effects to account for a changing state of the business cycle during the sample period. We compute robust standard errors that allow for correlated error terms at the firm level. Being a conglomerate reduces Tobin s q by 17 to 21 percent depending on specification. The interaction with the variable exporter decreases the discount by about 12 and 13 percentage points supporting the results of Figure 1 that firms engaged in international trade appear to almost escape the conglomerate discount that domestic firms are suffering. In column 2, 3, and 4 of Table 3 the conglomerate discount is larger (between 19% and 20% rather than 17 %) when we do not control for industry fixed effects (at the 4-digit level) and/or firm characteristics suggesting that the discount in Figure 1 appears to be too large. Table 4: dependent variable The Conglomerate Discount (1) (2) (3) (4) (5) log Tobin's q conglomerate *** *** *** *** *** [0.062] [0.063] [0.058] [0.059] [0.060] exporter * ** * [0.054] [0.047] [0.053] [0.054] [0.053] conglomerate x exporter 0.118* 0.124* 0.131** 0.113* 0.120* [0.067] [0.068] [0.065] [0.066] [0.066] log cash flow 0.125*** 0.150*** 0.044*** 0.125*** [0.015] [0.015] [0.008] [0.015] log sales *** *** 0.032*** *** [0.019] [0.017] [0.010] [0.018] industry FE YES NO YES YES YES year FE NO YES YES YES YES cluster level firm firm firm firm firm number of clusters sample manuf manuf manuf manuf manuf Adj. R-Squared observations 4,766 4,766 4,766 4,766 4,766 OLS regressions with standard errors clustered at the firm level in brackets. Industry fixed effects at the SIC 4-digit level. Conglomerate firms are those that are active in more than one SIC 4-digit industry. Exporters are firms with positive export sales and may or may not have positive FDI sales in addition. Cash flow is defined as the sum of operating income and depreciation. *** p<0.01, ** p<0.05, * p<

12 The previous analysis shows that trading firms have a lower conglomerate discount. In addition to this firm level evidence we show next that this pattern can also be seen at the sectoral level (in industry equilibrium). Figure 2 provides a glimpse of the relevant pattern by depicting the raw correlation between the conglomerate discount (median level of Tobin s q of multi-product firms relative to single-product firms) between 1997 and 2014 and the import penetration ratio (imports relative to domestic consumption) at the 2-digit SIC code level. The import penetration ratio is based on Comtrade data. There is clear evidence of a positive relationship between the ratio of Tobin s q (a larger Tobin s q of conglomerates relative to single product firms means a smaller conglomerate discount) in sectors more exposed to import competition. The relationship is highly significant at the 1 percent level when we add time and industry fixed effects to control for the business cycle and industry variations in Tobin s q. Figure 2: Conglomerate discount and import competition year FE and industry FE purged ratio of median qs import penetration ratio Note: The graph shows the ratio of median Tobin's q of multi-segment to single-segment firms by 2-digit SIC industry-year and the import penetration ratio calculated as imports over domestic consumption (=production-exports+imports). For the line we regress the q ratio and import penetration ratio separately on year fixed effects and industry fixed effects and then regress the residuals on one another. Significance is based on robust standard errors. Regression equation: y = ***x + Year FE + Industry FE + u. The standard error is.46 In the next section, we proceed to develop a theory which explicitly models the capital allocation process in multi-product firms. We will show that the internal capital market generates misallocations in funding which are reduced when firms are exposed to more international competition. 12

13 3 Model In this section we develop a model of multi product firms in a general equilibrium framework of monopolistic competition among heterogeneous firms, endogenous firm entry and endogenous product scope, along the lines of Mayer et al. (2014), (MMO hereafter). We introduce two new elements: (i) capital is a second factor of production in addition to labor, and idle capital can always be reallocated to the market; (ii) the cost structure is not entirely known to the owner of the firm. As in MMO, firm entry and the introduction of a new product respond to the toughness of competition in the output market. In addition, our setup shows how an internal capital market develops and drives the allocation of resources across divisions. Given that capital can be reallocated on the external market, the distortion introduced by the internal capital market makes entry more difficult, tends to reduce the number of products, and determines a mis allocation of capital across financed divisions. 3.1 Endowments and ownership A country is a production economy populated by a measure L of identical consumers and a large number of firms. Out of the pool of consumers, many are workers who supply inelastically one unit of labor at a given wage and hold a uniform share of the total capital in the economy K. In addition to workers, there are two types of agents. The owners, who made a specific investment to develop a technology and raised the capital to establish a firm based on a core competence. The managers, who have private knowledge on know how to customize an existing technology to obtain a new product. 3.2 Preferences and demand Preferences are defined over a continuum of measure V of horizontally differentiated varieties and two homogeneous goods, which are different in terms of their factor content. The utility function is given by: U = q c l + θqc k + α V 0 q c vdv + γ 2 V 0 (q c v) 2 dv + η 2 ( V 0 q c vdi) 2 (1) 13

14 where q c l and q c k represent the individual consumption of a labor-based and a capital-based good respectively, while q c v represents the individual consumption of a variety v of differentiated good. The parameter θ > 0 indexes the relative taste for the capital-based goods with respect to the laborbased goods, while α > 0 and η > 0 parametrize the substitution pattern between the bundle of homogeneous goods and the variates of differentiated goods. The degree of product differentiation across varieties is fixed by means of the parameter γ 0 such that for γ = 0 varieties are perfect substitutes and consumers care for aggregate consumption only. We assume that the homogeneous goods are always consumed ql c, qc k > 0. The marginal utilities for all varieties are bounded, such that there exits a chock price at which the demand is zero. For each consumed variety the inverse demand is p v = α γq c v ηq c. The uncompensated demand is linear qv c = 1 γ (α p v ηq c ). Integrating over V consumed varieties yields Q c = 1 γ (α ηqc ) V V γ p where p = 1 V V 0 p vdv is the average price across consumed varieties. The individual consumption of differentiated good is: Q c = (α p) yields: q c v = is p max = 1 γ+ηv α γ+ηv 1 γ p v + ηm γ+ηv V γ+ηv. Substituting back in the demand for a given variety 1 γ p. The chock price that shuts down the demand of a given variety (γα + ηv p). The individual demand for a given variety can be written in terms of the chock price: q c v = 1 γ (pmax p v ). For every consumed variety 0 < p v < p max, which implies p max α. Aggregating over L consumers yields the aggregate demand for a consumed variety: q v = L γ (pmax p v ) (2) Income which is not allocated to the consumption of differentiated goods equals the expenditure on homogeneous goods. Let the variance of prices across varieties be σp 2 = 1 V V 0 (p v p) 2 dv then the income each consumer allocates to differentiated goods is I c d = pqc V γ σ2 p. Let I c be the consumer s total income, then I c o = I c I c d > 0 is the individual expenditure on homogeneous goods. Goods q c l and q c k are perfect substitutes, they will be both consumed at the relative price p k pl that I c o = p l q c l + p kq c k. = θ and such 14

15 3.3 Technology and production The production of one unit of the labor-based homogeneous good y l requires one unit of labor, whereas producing one unit of capital-based homogeneous good y k requires to rent one unit of capital. The market for homogeneous goods and the factor markets are perfectly competitive. As a consequence, the prices of the two homogeneous goods p l and p k are respectively equal to wage w and rental rate r. Both homogeneous goods are consumed in equilibrium when r w = θ. The labor-based homogeneous good is chosen as the numeraire, which yields p l = w = 1 and p k = r = θ. The production of a variety i of differentiated good employs both labor and capital according to a Coob-Douglas technology with constant returns to scale. Labor and capital are combined with a labor share λ (0, 1), such that one unit of composite factor is given by l (i) λ k (i) 1 λ. In every incumbent firm production is established around the core competence of the owner. Looking for profit maximization, the owner might introduce a discrete number of additional varieties but for each new product the owner must delegate the control on production to a manager who has knowledge on how to customize the realization of a specific product starting from the core competence. In order to capture this idea, we assume that hiring a manager to produce a product that is i = 0, 1, 2,... units of distance from the core-competence increases the marginal cost geometrically, with power j and step factor 1/ω where the parameter ω (0, 1) indexes the flexibility of a technology as the easiness of introducing new varieties. Let c > 0 be the marginal cost of the core competence in a given firm, then the production of a given variety that is i = 0, 1, 2,... units of distance from the core competence in a firm with flexibility ω is given by: y (i; c, ω) = ϕ l (i)λ k (i) 1 λ cω i (3) where ϕ = ( ) 1 λ (1 λ)+θ ( λθ λ. λθ 1 λ) The conditional factor demands are linear in output: l (i; y) = ( 1 λ ) (1 λ) ( λ λθ cω i y/ϕ for labor and k (i; y) = λθ 1 λ) cω i y/ϕ for capital. The optimal capital labor ratio does not depend on idiosyncratic firm characteristics 1 λ λθ. The cost function C (i; y) = cω i y is linear in output. structure of marginal costs at the firm. Thus the values of core marginal cost and flexibility determine the 15

16 3.4 Firm entry Perspective firm owners invest f i units of labor and rent f e units of capital to develop a technology. The core competence cost becomes known to the perspective firm owner only after the specific investment is made, at this point the decision whether to enter the market or not is made. In both cases, the financiers have to be paid while the invested labor is sunk and it does not have a value afterward. The realization of core competence cost is understood as an idiosyncratic random draw c G(c) from an exogenous cumulative density function G(c) defined on the support c (0, 1). The flexibility of a technology is not known. The owner has a prior on what might be the realization of flexibility, as an idiosyncratic random draw ω F (ω) from an exogenous cumulative density function F (ω) defined on the support ω (0, 1). The uncertainty embedded in the entry decision is a key feature of the industry equilibrium and it will be described in a dedicated Section. 3.5 Firm equilibrium allocation Firms are heterogeneous with respect to core marginal cost and flexibility. Consider a firm with core competence cost c and flexibility ω which is endowed with f e units of capital raised by the owner at the time of firm entry. For every given variety with distance i = 0, 1, 2,... from the core competence, the demand function (2) yields a marginal revenue 2p i p max, while technology (3) implies a marginal cost cω i. Quantity and price that maximize profit are: q (x i, c) = L 2γ (c D x i c) (4) p (x i, c) = 1 2 (c D + x i c) where c D = p max is the maximum cost c below which a firm has positive demand on the core product and we replaced the customization cost ω i = x i for convenience in the following exposition. Market 16

17 clearing determines the equilibrium factor demands: l (x i, c) = 1 L ϕ l 2γ (c D x i c) x i c (5) k (x i, c) = 1 L ϕ k 2γ (c D x i c) x i c where 1/ϕ l = ( ) 1 λ (1 λ) ( λ 1 λθ ϕ and 1/ϕ k = λθ 1 1 λ) ϕ. Revenue, cost, profit and return on investment in equilibrium are given by: r (x i, c) = L 4γ ζ (x i, c) = L 2γ (c D x i c) x i c π (x i, c) = L 4γ (c D x i c) 2 roi (x i, c) = ϕ k 2θ ( c 2 D (x i c) 2) (6) ( ) cd x i c 1 Equations (4)-(6) characterize the equilibrium allocation for a given product with customization cost x i 1 supplied by a firm with marginal cost c for the core competence. 8 Every incumbent firm produces at least the core competence. Thus, a necessary condition for the firm to be in the market is that c c D. The capital available to finance the first nocore product is equal to the funds raised at entry f e minus the optimal allocation of capital to the core competence: f m (c, 1) = f e 1 L ϕ k 2γ (c D c) c 0. Let x 1 be the customization cost of the first no-core product then the capital available to finance the second no-core product is f m (c, 2) = f m (c, 1) 1 L ϕ k 2γ (c D x 1 c) x 1 c 0. Let products be ordered in a numerable sequence indexed by i = 0, 1, 2,.... Call x i the customization cost of the product that comes i-th in the sequence and for convenience let the sequence start with the core competence and be weakly monotone in the customization cost: 1 = x 0 < x 1 x 2... x i... x m. The rule that determines the stock of capital available to finance the i-th product in a firm with core competence c c D can 8 Notice that the allocation of capital across products is a non monotonic function of the customization cost. It can be seen that for relatively bad products in terms of efficiency, such that x ic > c D/2, the higher the customization cost x i the lower is the optimal capital allocation. However, for good products, such that x ic < c D/2 the optimal amount of capital is increasing with the customization cost x i. 17

18 be written recursively: f m (c, 0) = f e (7) f m (c, i) = f m (c, i 1) k (x i 1, c) The number of products for an incumbent firm with core marginal cost c c D are constrained by profitability and capital availability: M (c) 1 + max {i : x i c c D f m (c, i) > 0} (8) Firms endowed with a core marginal cost c c D such that f m (c, 1) < 0 become mono-product firms. Only firms endowed with a core marginal cost c < c D such that f m (c, m) > 0 might eventually become multi-product firms with M (c) = 1 + m products. Fulfilling both the constraints of profitability and capital availability is a necessary but not sufficient condition for a product to be financed. An if and only if statement can only be made after taking a stand on whether the firm finances a product also with a sub optimal level of capital or not. Since the owner does not know the true customization cost, we assume that either a product i is financed with the optimal level of capital requested by the manager k(x i, c) or it is not financed at all. 9 This assumption rules out the possibility that the owner strategically deviates from the optimal capital allocation across divisions, given the available information. Thus, any inefficiency of the internal capital market predicted by the model is due to the behavior of division managers. Under this scenario, a profit maximizing firm allocates capital across divisions following the ranking of products by return on investment. Sorting products for increasing customization costs yields the same ranking one would obtain by sorting products for decreasing profit or return on investment. Thus, each of the first i-th products in terms of profit should be financed before the product in position i+1 does. The total profit of a firm endowed with core competence cost c and 9 As we will discuss later, this assumption can be weakened. In equilibrium, it will be sufficient that financing a division with a different level of capital than the one requested by the manager yields a return on investment which is lower than the rental price for capital on the external market. 18

19 a sequence of customization costs {x i } m i=0 is given by: M(c) Π ({x i } m i=0, c) = i=0 π (x i, c) (9) Although the owner raised f e units of capital, the total asset used in production by a given firm is B ({x i } m i=0, c) = M(c) i=0 k(x i, c). The capital which is not used in production f e B ({x i } m i=0, c) is idle and can be traded in the external market at the rental price θ. As a consequence, the yield of capital in the external market sets a lower bound for the return on investment of divisions at the firm. Only products with a return on investment roi(x i, c) θ are financed, thus every product in the market has a marginal cost x i c c D /(1 + 2θ 2 /ϕ k ). It is now clear that capital plays a special role, other than being introduced as a second factor of production. Capital has a market value outside the firm. Since idle capital can be reallocated on the external market the selection of products at the firm level is driven by the comparison with the external rental price for capital and not only based on making a positive profit. Thus, the less flexible the technology and the more likely firms are constrained by the profitability of their products rather than by an external financial constraint. To see this, assume that the external financial constraint is binding B ({x i } m i=0, c) > f e while the profitability constraint is not roi(x m, c) θ. Then the owner might be willing to finance the m th product even providing less than the optimal capital allocation. We ruled this out by assumption, but notice that this comes without loss of generality as long as under financing a division yields a return on investment lower than θ. For the financial constraint to be binding, it has to be the case that although the most peripheral division is financed with an under provision of capital, nevertheless it yields a return on investment which is higher than what can be gained on the external market. Apart from this (fairly extreme) situation, the profitability constraint is binding while the financial constraint is not Note that the profitability constraint is also binding for the export decision, as we discuss in Section 6. External financial constraints do not play any role on the decision to export. This is a major departure from the current approach investigating the relationship between finance and trade, see Foley and Manova (2015). 19

20 3.6 Tobin s Q Following the motivation in the previous paragraph, we restrict the scenario to the case in which in equilibrium the profitability requirement roi(x i, c) θ is binding while the external financial constraint is still inactive B ({x i } m i=0, c) f e. As a consequence, firms are neither over nor under capitalized. The stock of capital B ({x i } m i=0, c) is the minimum level of asset required by a firm with core competence cost c and vector of customization costs {x i } m i=0. Therefore, θb ({x i} m i=0, c) shall be interpreted as the book value of the firm; which will be different in general from the amount of capital f e that all firms start endowed with. 11 The information on the core competence cost c and on the customization cost structure {x i } m i=0 are not observable in the market, thus the book value does not coincide with the market value of the firm. Total profit is the value generated by the firm, hence the Tobin s Q which measures the ratio of the market value over the book value of the firm is given by: T ({x i } m i=0, c) = Π ({x i} m i=0, c) θb ({x i } m i=0, c) = ϕ ( ) k cd E[x]c c D 2θ E[x]c D E[x 2 ]c c 1 (10) where E[x] = 1 M(c) M(c) i=0 x i and E[x 2 ] = 1 M(c) M(c) i=0 x2 i are the first and the second moments of the vector of customization costs. Conditional on the market cutoff c D and on the core competence cost c, the Tobin s Q of a multi product firm is decreasing with the mean E[x] and increasing with the variance E[x 2 ] E[x] 2 of the customization costs across divisions. Intuitively, Tobin s Q increases with the variance because firms can optimally reallocate capital across products seeking for efficiency. 12 The empirical observation that the ratio between the Tobin s Q of a multi product firm, or conglomerate, and the Tobin s Q of a mono product firm is lower than 1 motivated the terminology conglomerate discount. In this framework firms with lower core competence cost are more likely to become multi product and make a higher return on investment, for a given level of flexibility. Nevertheless, (10) shows that the Tobin s Q of a multi product firm depends on the ratio between 11 Notice that our analysis accommodates the empirically relevant scenario in which firms are heterogeneous in their book value. 12 This argument is equivalent to a channel of love for variety but at the production level. 20

21 average profit and average capital allocation across divisions. Thus, the Tobin s Q can be lower for firms with many divisions than for mono product firms due to two channels. First, although a multi product firm makes higher profits in its core product than a mono product firm, this is not necessarily true for the no core products. Hence, the average profit across divisions is closer to the profit of a mono product firm and it might actually be lower. Second, if a multi product firm tends to allocate more capital per division than a mono product firm, then even a slightly higher average profit across divisions would not compensate for the heavier book value Conglomerate discount The Tobin s Q of a multi product firm (10) can be easily compared with the return on investment of a mono product firm (6) with the same core competence cost. The Tobin s Q of the multi product c firm is lower if and only if c D < E[x] 1. Notice that the restriction on the minimum profitability E[x 2 ] E[x] of a division roi(x i, c) θ implies c c D ω i 1+2θ 2 /ϕ k. Therefore the sufficient condition θ(1 λ) E[x] 1 E[x 2 ] E[x] 1 ω (11) implies that the Tobin s Q of a multi product firm is lower than the market over book value of a single product firm endowed with the same core competence cost. Substituting for the development of the geometric series E[x] = 1 1 ω (m+1) m+1 and E[x 2 ] = 1 1 ω 2(m+1) 1 ω 1 m+1 1 ω 2 yields the right hand side of (11) as a function of the flexibility parameter ω and the number of non core products m; a numerical inspection shows that its is increasing in ω and decreasing in m. The left hand side of (11) is decreasing in the rental price of capital θ and in the capital share of the production process (1 λ). Thus for a sufficiently high relative price of capital and capital share in the production process it is always possible to find a value ω (0, 1) such that for every flexibility level ω [ω, 1) a multi product firm with m = 1, 2,..., m divisions exhibits a lower Tobin s Q than a mono product firm endowed with the same core competence cost. To the end of understanding how the model can reproduce analytically the implications of a 13 In section 4 we show that multi-product firms will allocate more capital per division compared to single-product firms. 21

22 conglomerate discount, two remarks are appropriate. First, it can be argued that the measurement of a conglomerate discount as discussed in (11) is local, in the sense that it compares multi and mono product firms around the same level of core competence cost. Instead, the empirical observation of a conglomerate discount refers to the average (or the median) Tobin s Q of multi versus single product firms. This concern can be addressed by looking at the exogenous distribution of flexibility levels F (ω). Independently on the exogenous distribution of core competence costs, if it is very likely that a firm has a technology with very low level of flexibility then the model would predict that conglomerates are rare. This is consistent with the evidence, and moreover it delivers a framework in which in expectation there are more single product firms than multi product firms in a neighborhood of every given level of core competence cost. Therefore, the model also predicts a conglomerate discount when considering the average (or the median) Tobin s Q. Second, while the flexibility parameter ω is exogenous, the number of non core products is endogenous as it depends on the core competence cost. However, notice that for a given level of core competence cost the number of divisions is ultimately determined by a comparison with the market cutoff c D. This variable is determined in general equilibrium and it is not a function of firm idiosyncratic variables. Therefore, for a given exogenous distribution G(c) with increasing density G (c) > 0 it is always possible to close the model for a sufficiently low value of the endogenous market cutoff c D such that the equilibrium number of products for the firm endowed with the median core competence cost is bounded above. Under this circumstance, the model predicts a conglomerate discount based on the median as observed in the empirical studies, although for super star conglomerates the discount can be lower or even disappear. The present Section has shown how the introduction of capital in an otherwise standard model of multi product firms changes the perception of a multi product firm as synonymous of an efficient allocation of resources. A distinctive feature of our framework, with respect to existing ones such as Eckel and Neary (2010), is the interplay between the flexibility of the technology and the value of capital on the external market. The latter dimension has an impact on the overall capitalization of the firm. Under plausible assumptions on the technology, this framework can predict both the selection of most productive firms into multi production and the conglomerate discount. However, 22

23 this does not offer a role to the organization in explaining the dark side of conglomerates. The next Section shows how asymmetric information arising within the firm organization distorts both the selection of products and the allocation of capital across divisions. Thus, the model implies that the inefficiencies which characterize the internal capital market of a conglomerate are endogenous to the firm organization and respond to firm characteristics and market competition. 4 Internal capital market Consider a firm which enters the market with a core competence cost c < c D, such that the owner has the chance to decide whether to finance additional products other than the core. The owner knows the marginal cost of the core product. But, for every additional product i = 1, 2,..., m only the manager of that particular product knows the true customization cost x i. This know-how is the manager s private information and whenever a manager has an incentive to report a different customization cost z i x i than the true one an asymmetric information problem arises. After a firm enters the market, the core competence cost of the firm c, the market cutoff c D, and the external market price for capital θ are common knowledge for both managers and the owner. Given this scenario, owner and managers commit to a contract with the following characteristics: (a) managers simultaneously report a customization cost for their own division z i, which corresponds to a request of being financed with k (z i, c) units of capital according with the optimal factor demand (5); (b) if the owner finances the product line i with capital k (z i, c) then the manager commits to run the division optimally according with (4) (6) and deliver a profit π (z i, c); (c) the owner prefers to keep some capital idle rather than financing a division with an arbitrary amount of capital that does not match what the manager asks for. The contract (a) (c) is known to both parties. No bargaining, recall or coordination occur. A number of incentive compatibility constraints applies: (d) managers do not report a customization cost that is lower than 1 as it would imply that their product is actually an intermediate stage of the core competence, z i 1 i; (e) the owner can always sell idle capital on the external market at a rental price θ. Therefore, the 23