Finance, Organization, and the Product Mix of Exporters

Dalia Marin∗ Davide Suverato† Thierry Verdier‡

Monday 15th May, 2017

Abstract

Multi-product firms, though more efficient, have a dark side, they trade at a conglomeratediscount. Exporters suffer a smaller conglomerate discount compared to domestic firms. Weintroduce an internal capital market into a two factor model of multi-product firms to explainthese facts. We find that in the competition for funds inside the firm, the managers of the best di-visions are empire builders and strategically over-report their costs receiving excessive financingpossibly crowding out funding of less good divisions. This pattern of capital allocation is con-sistent with the observed capital expenditures across divisions of publicly listed US companiesand explains the lower market to book value of conglomerates. We find further that a toughertrade environment leaves less room for the mis-reporting of costs improving the efficiency ofthe internal capital market. Finally, we find that firms face a trade-off between introducing anew product or exporting an existing one which tends to make exporters less diversified thandomestic firms. The latter two mechanisms explain why the conglomerate discount is lower forexporters.

∗University of Munich†University of Munich‡Paris School of EconomicsWe would like to thank Philipp Herkenhoff for excellent research assistance.

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, multi-

product 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

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), andNocke and Yeaple (2014).

3 To simplify matters we do not distinguish between the owner and the headquarters. In our framework the owner isalso the headquarters. For the distinct role of a headquarters, see Gertner, Scharfstein, and Stein (1994).

3

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 export-

ing 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 allo-

cating 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, seeFoley and Manova (2015).

4

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 under-

reporting 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 over-

reporting 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 com-

petitive trade environment firms reorganize to a more decentralized organization. McLaren (2002),

5

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 Antras 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 finan-

cial 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 1997-2014 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 Antras and Rossi-Hansberg (2009) and Marin (2016).6 For a survey of the literature on finance and trade, see Foley and Manova (2015).

6

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 in-

clude 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 single-

product 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 single-

product 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 seg-

ment 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 mea-

sured by the cash flow to sales ratio. We measure cash flow as operating profits plus depreciation.

7

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) 31689Note: 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 1997-2014.

Table 1 The Data

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 litera-

ture 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 iscalculated as the book value of assets plus market capitalization minus the sum of the value of common equity andbalance sheet deferred taxes.

8

single segment conglomerate single segment conglomerate

sales (mio US$) 8.291 35.923 43.537 262.732assets (mio US$) 16.102 39.562 45.473 255.634capital expenditure (mio US$) 0.251 1.236 1.192 8.930cash flow (mio US$) -1.002 1.273 3.762 36.155capital expenditure / sales 0.028 0.033 0.027 0.029cash flow / sales -0.355 0.047 0.105 0.135Tobin's Q 2.345 1.446 1.488 1.339

Table 2 Summary StatisticsDomestic Firms Exporters

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 2000-3999) in the period 1997-2014. 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.

median values

of multi-product firms and exporters via an internal capital market justifies the focus of our paper

on this type of finance.

mean values

source of funds all firms single segment conglomerates domestic exporter

cashflow 25.61 17.84 40.01 -3.50 31.23

long term debt 23.49 21.50 27.18 24.23 22.23

equity 14.44 17.79 8.24 26.48 10.89

fixed asset sales 2.86 2.14 4.19 1.70 3.25

investment decrease 15.92 18.28 11.56 18.83 15.16

other sources 15.73 19.35 9.01 24.24 15.06

total amount available (m US$) 543.40 269.10 1051.50 68.40 352.23

observations 31364 20368 10996 2532 5933

Table 3 The Financing of Firmsin percent of total funds

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 1997-2012. 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

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 2010. 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.

.5.6

.7.8

.91

ratio

of m

ean

qs

1995 2000 2005 2010 2015year of observation

exporting firms domestic firms

mean valuesratio of multi-segment firms to single-segment firms

Figure 1: Tobin's q

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

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.

(1) (2) (3) (4) (5)

dependent variable

conglomerate -0.175*** -0.207*** -0.194*** -0.189*** -0.167***[0.062] [0.063] [0.058] [0.059] [0.060]

exporter -0.079 -0.040 -0.094* -0.106** -0.094*[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 -0.109*** -0.155*** 0.032*** -0.109***[0.019] [0.017] [0.010] [0.018]

industry FE YES NO YES YES YESyear FE NO YES YES YES YEScluster level firm firm firm firm firmnumber of clusters 1009 1009 1009 1009 1009sample manuf manuf manuf manuf manufAdj. R-Squared 0.234 0.126 0.244 0.262 0.280observations 4,766 4,766 4,766 4,766 4,766

Table 4: The Conglomerate Discount

log Tobin's q

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<0.1.

11

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.

-1-.5

0.5

1ra

tio o

f med

ian

qs

-.15 -.1 -.05 0 .05 .1import penetration ratio

Note: The graph shows the ratio of median Tobin's q of multi-segment to single-segmentfirms by 2-digit SIC industry-year and the import penetration ratio calculated as imports overdomestic consumption (=production-exports+imports). For the line we regress the q ratio and importpenetration ratio separately on year fixed effects and industry fixed effects and then regressthe residuals on one another. Significance is based on robust standard errors.Regression equation: y = 0.91 + 1.48***x + Year FE + Industry FE + u.The standard error is .46

year FE and industry FE purgedFigure 2: Conglomerate discount and import competition

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 misalloca-

tions in funding which are reduced when firms are exposed to more international competition.

12

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 = qcl + θqck + α

∫ V

0qcvdv +

γ

2

∫ V

0(qcv)

2 dv +η

2

(∫ V

0qcvdi

)2

(1)

13

where qcl and qck represent the individual consumption of a labor-based and a capital-based good

respectively, while qcv 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 labor-

based 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 qcl , qck > 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 pv = α− γqcv − ηQc. The uncompensated demand is

linear qcv = 1γ (α− pv − ηQc). Integrating over V consumed varieties yieldsQc = 1

γ (α− ηQc)V−Vγ p

where p = 1V

∫ V0 pvdv is the average price across consumed varieties. The individual consumption

of differentiated good is: Qc = (α− p) Vγ+ηV . Substituting back in the demand for a given variety

yields: qcv = αγ+ηV −

1γ pv + ηM

γ+ηV1γ p. The chock price that shuts down the demand of a given variety

is pmax = 1γ+ηV (γα+ ηV p). The individual demand for a given variety can be written in terms

of the chock price: qcv = 1γ (pmax − pv). For every consumed variety 0 < pv < pmax, which implies

pmax ≤ α. Aggregating over L consumers yields the aggregate demand for a consumed variety:

qv =L

γ(pmax − pv) (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 σ2p = 1

V

∫ V0 (pv − p)2 dv then the

income each consumer allocates to differentiated goods is Icd = pQc− Vγ σ

2p. Let Ic be the consumer’s

total income, then Ico = Ic − Icd > 0 is the individual expenditure on homogeneous goods. Goods

qcl and qck are perfect substitutes, they will be both consumed at the relative price pkpl

= θ and such

that Ico = plqcl + pkq

ck.

14

3.3 Technology and production

The production of one unit of the labor-based homogeneous good yl requires one unit of labor,

whereas producing one unit of capital-based homogeneous good yk 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 pl and pk are respectively equal to

wage w and rental rate r. Both homogeneous goods are consumed in equilibrium when rw = θ. The

labor-based homogeneous good is chosen as the numeraire, which yields pl = w = 1 and pk = 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 vari-

eties 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 geo-

metrically, 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) = ϕl (i)λ k (i)1−λ

cω−i(3)

where ϕ =(

1−λλθ

)−(1−λ)+θ(λθ

1−λ

)−λ. The conditional factor demands are linear in output: l (i; y) =(

1−λλθ

)−(1−λ)cω−iy/ϕ for labor and k (i; y) =

(λθ

1−λ

)−λcω−iy/ϕ for capital. The optimal capital

labor ratio does not depend on idiosyncratic firm characteristics 1−λλθ . The cost function C (i; y) =

cω−iy is linear in output. Thus the values of core marginal cost and flexibility determine the

structure of marginal costs at the firm.

15

3.4 Firm entry

Perspective firm owners invest fi units of labor and rent fe 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 fe 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 2pi − pmax, while technology (3)

implies a marginal cost cω−i. Quantity and price that maximize profit are:

q (xi, c) =L

2γ(cD − xic) (4)

p (xi, c) =1

2(cD + xic)

where cD = pmax is the maximum cost c below which a firm has positive demand on the core product

and we replaced the customization cost ω−i = xi for convenience in the following exposition. Market

16

clearing determines the equilibrium factor demands:

l (xi, c) =1

ϕl

L

2γ(cD − xic)xic (5)

k (xi, c) =1

ϕk

L

2γ(cD − xic)xic

where 1/ϕl =(

1−λλθ

)−(1−λ) 1ϕ and 1/ϕk =

(λθ

1−λ

)−λ1ϕ . Revenue, cost, profit and return on invest-

ment in equilibrium are given by:

r (xi, c) =L

4γ

(c2D − (xic)

2)

(6)

ζ (xi, c) =L

2γ(cD − xic)xic

π (xi, c) =L

4γ(cD − xic)2

roi (xi, c) =ϕk2θ

(cDxic− 1

)

Equations (4)-(6) characterize the equilibrium allocation for a given product with customization

cost xi ≥ 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 ≤ cD. The capital available to finance the first no-

core product is equal to the funds raised at entry fe minus the optimal allocation of capital to

the core competence: fm (c, 1) = fe − 1ϕk

L2γ (cD − c) c ≥ 0. Let x1 be the customization cost

of the first no-core product then the capital available to finance the second no-core product is

fm (c, 2) = fm (c, 1) − 1ϕk

L2γ (cD − x1c)x1c ≥ 0. Let products be ordered in a numerable sequence

indexed by i = 0, 1, 2, ... . Call xi 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 = x0 < x1 ≤ x2 ≤ ... xi ... ≤ xm. The rule that determines

the stock of capital available to finance the i-th product in a firm with core competence c ≤ cD can

8 Notice that the allocation of capital across products is a non monotonic function of the customization cost. It can beseen that for relatively bad products in terms of efficiency, such that xic > cD/2, the higher the customization costxi the lower is the optimal capital allocation. However, for good products, such that xic < cD/2 the optimal amountof capital is increasing with the customization cost xi.

17

be written recursively:

fm (c, 0) = fe (7)

fm (c, i) = fm (c, i− 1)− k (xi−1, c)

The number of products for an incumbent firm with core marginal cost c ≤ cD are constrained by

profitability and capital availability:

M (c) ≤ 1 + max i : xic ≤ cD ∧ fm (c, i) > 0 (8)

Firms endowed with a core marginal cost c ≤ cD such that fm (c, 1) < 0 become mono-product

firms. Only firms endowed with a core marginal cost c < cD such that fm (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(xi, 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 divisionwith a different level of capital than the one requested by the manager yields a return on investment which is lowerthan the rental price for capital on the external market.

18

a sequence of customization costs ximi=0 is given by:

Π (ximi=0 , c) =

M(c)∑i=0

π (xi, c) (9)

Although the owner raised fe units of capital, the total asset used in production by a given firm is

B (ximi=0 , c) =∑M(c)

i=0 k(xi, c). The capital which is not used in production fe −B (ximi=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(xi, c) ≥ θ are financed, thus every product in

the market has a marginal cost xic ≤ cD/(1 + 2θ2/ϕk).

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 (ximi=0 , c) > fe while the profitability constraint is not roi(xm, 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.10

10 Note that the profitability constraint is also binding for the export decision, as we discuss in Section 6. Externalfinancial constraints do not play any role on the decision to export. This is a major departure from the currentapproach investigating the relationship between finance and trade, see Foley and Manova (2015).

19

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(xi, c) ≥ θ is binding while the external financial

constraint is still inactive B (ximi=0 , c) ≤ fe. As a consequence, firms are neither over– nor under–

capitalized. The stock of capital B (ximi=0 , c) is the minimum level of asset required by a firm

with core competence cost c and vector of customization costs ximi=0. Therefore, θB (ximi=0 , c)

shall be interpreted as the book value of the firm; which will be different in general from the amount

of capital fe that all firms start endowed with.11

The information on the core competence cost c and on the customization cost structure ximi=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 (ximi=0 , c) =Π (ximi=0 , c)

θB (ximi=0 , c)=ϕk2θ

(cD − E[x]c

E[x]cD − E[x2]c

cDc− 1

)(10)

where E[x] = 1M(c)

∑M(c)i=0 xi and E[x2] = 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 cD 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[x2] − 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 “con-

glomerate”, 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 theirbook value.

12 This argument is equivalent to a channel of ’love for variety’ but at the production level.

20

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.13

3.7 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

firm is lower if and only if ccD

< E[x]−1E[x2]−E[x]

. Notice that the restriction on the minimum profitability

of a division roi(xi, c) ≥ θ implies ccD≤ ωi

1+2θ2/ϕk. Therefore the sufficient condition

1

1 + 2θ(1− λ)≤ E[x]− 1

E[x2]− 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] = 1m+1

1−ω−(m+1)

1−ω−1 and E[x2] = 1m+1

1−ω−2(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-productfirms.

21

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 cD. 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 cD 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

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 dis-

torts 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 < cD, 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 xi. This know-how is

the manager’s private information and whenever a manager has an incentive to report a different

customization cost zi 6= xi 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 cD, 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 zi, which corre-

sponds to a request of being financed with k (zi, c) units of capital according with the optimal

factor demand (5);

(b) if the owner finances the product line i with capital k (zi, c) then the manager commits to run

the division optimally according with (4)–(6) and deliver a profit π (zi, 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, zi ≥ 1 ∀i;

(e) the owner can always sell idle capital on the external market at a rental price θ. Therefore, the

23

return on investment (6) on every given financed product must look at least as good as the return

on the external market, zi ≤ cD/c1+2θ2/ϕk

≡ z(c, cD);

(f ) managers cannot sell capital on the market. As a consequence, they will operate with all the

capital they received if they received any;

(g) the number of possible products is large and applying for funding is costless. Therefore, any

owner who finances m ≥ 1 products made the decision not to finance at least one product.

Under the contract environment (a)–(g), managers choose how much to report as customization

cost zi before production starts and, if they are financed, they run their own division making use of

the true customization cost xi. The owner takes the reported costs as given and chooses the number

of products to finance and the allocation of capital for each product. After production starts the

owner observes the transactions of every division of the firm with output and factor markets and

the rights of control are such that managers do not strategically deviate from what they committed

to. We are now in the position to discuss the optimal behavior of the managers.

4.1 Managers

Managers anticipate that the owner will observe the quantity that has been sold q (zi, c), price

p (zi, c), factor employment, k (zi, c) and l (zi, c), revenue r (zi, c), production cost ζ (zi, c) and profit

π (zi, c). These performances must be in line with the optimal behavior (4)–(6) given the reported

cost zi. Nevertheless, the actual production is not verifiable by the owner, only the amount of

output sold in the market is observable. Whenever a manager is capable to make his/her division

produce more than what the manager commits to y (i, c) > q (zi, c) the excess of production is not

under the control of the owner and the manager can make use of it to obtain a private benefit.

In this context, managers have an incentive to mis–report the true customization cost; but,

at the same time, the competition for funding forces managers to face a trade off. In fact, by

reporting a higher customization cost than the true one managers build a wedge between the true

performances of the division and the results they are accountable for. On the other side, managers

are aware that the probability of being financed is lower the higher is the reported cost. Rational

managers choose to report the customization cost zi that maximizes their own expected private

24

benefit.

Private benefit. Managers employ the total amount of capital they are endowed with. Therefore,

technology (3) yields the output of a division with true customization cost xi that has been financed

with k (zi, c) units of capital y (i, c) = ϕl(zi,c)λk(zi,c)

1−λ

cxi≤ q (xi, c); where the employment of labor

is implied by the optimal capital labor ratio l (zi, c) = λθ1−λk (zi, c) such that the reported marginal

cost is actually czi. Because of market clearing, a total amount of q (zi, c) = ϕl(zi,c)λk(zi,c)

1−λ

cziunits

of output are sold in the market. The manager’s private benefit originates from the excess of

production y (i, c)− q (zi, c):

b (µ, xi, c) =LcD2γ

(µ− 1)

(1− xic

cDµ

)(12)

where b (µ, xi, c) is the private benefit of a manager employed in a firm with core competence cost

c reporting a customization cost zi = µxi for an arbitrary real value µ > 0. The private benefit

(12) is a quadratic function in the mis–reporting factor µ. Managers of a good product, such that

xic < cD, make a positive private benefit when they over–report µ ∈(

1, cDxic

). Managers of a bad

product xic > cD, one it would not be financed under perfect information, make a positive private

benefit when they under–report µ ∈(cDxic, 1)

. The private benefit has one maximum, which is

reached when the factor of mis–reporting is µi = 12

(1 + cD

xic

). As a consequence, for µ < µi the

private benefit is increasing in the factor of mis–reporting b′µ (µ, xi, c) > 0.

Competition for funding. Each manager which applies to run a division in a given firm knows the

core competence cost c and the customization cost of her own product but not the one of others.

A manager makes a decision on the reported customization cost zi by choosing a factor of mis–

reporting µi0 over the true cost, such that zi = µixi. All managers report their customization cost

simultaneously, without coordination and taking as given what other managers do. Thus, when

making the decision managers must guess whether they will be successful and their product will be

financed. We capture this scenario assuming that managers have a prior on the distribution of the

true customization cost among those products which will be financed. Let j = 1, 2, ...,m indicate

25

the ranking of non–core products which are financed in a firm with core competence cost c, then

managers understand the vector of coefficients xji=1,2,...,m as a sequence of independent random

draws x > 1 from an inverse Pareto distribution with shape parameter ν = 1/m > 0 and upper

bound cD/c > 1. The probability of the event xj ≤ x is given by(xccD

)νfor every x ∈ (1, cDc ].14

Since zj = µjxj , for a given vector of mis–reporting factors µjj=1,2,...,m the probability that a firm

with core competence cost c finances m products with a reported customization cost zj ≤ z is given

by∏mj=1

(ccD

zµj

)ν. Therefore, a manager with true customization cost xi applying to a firm with

core competence cost c and reporting a customization cost z = µxi faces a probability Pi (µ) =(xiccD

)mν∏mj=1

(µµj

)λthat there are m = 1, 2, ... managers reporting a lower customization cost.

The choice of µ is bounded below by µi

= 1/xi such that zi ≥ 1; and it is bounded above by µi =

cDxic

11+2θ2/ϕk

such that zi ≤ z(c, cD). Since the potential number of products is large and applying for

funding is costless, a manager who reports the maximum of the support has probability Pi (µi) = 1

that m other managers applied with a better proposal. This condition allows us to account for

the strategic interaction among m ≥ 1 managers∏mj=1 µ

−νj =

(1 + 2θ2/ϕk

)mν. Thus, conditional

on a market cutoff cD and a core competence cost c ≤ cD, the probability that m products are

financed, all with reported customization cost lower or equal to µxi is given by Pi (µ) =(µµi

)mν.

Profit and return on investment are monotonic decreasing function of the reported customization

cost. Therefore, Pi (µ) is also the probability that a product with reported customization cost µxi

does not enter the first m positions in the firm ranking by return on investment. As a consequence

ψi (µ) = 1− Pi (µ), hence

ψi (µ) = 1−[(

1 + 2θ2/ϕk)(µxic

cD

)]mν(13)

is the probability that a product with reported customization cost µxi is financed by a firm with

14 In the following it will be instructive to keep the notation with the parameter ν and then substitute for ν = 1/monly in the proofs. In fact, for ν = 1/m the policy for managers will not depend on the number of product lines theowner will actually finance. This is not necessary for the existence of an equilibrium but it is a desirable propertybecause it guarantees the uniqueness of the manager’s policy without the requirement that managers have a prior onthe number of products. Notice that this choice is consistent with the idea that the technology of a range of productscannot be understood. In fact, under the restriction ν = 1/m, the prior density function of productivity becomesflatter the higher is the number of product lines, such that the expected average productivity is undetermined form ≥ 1 products.

26

core competence cost c that allocates capital to m ≥ 1 products other than the core competence.

The probability that a product with true customization cost xi is financed decreases with the yield

of capital in the external market θ and with the cost of its technology with respect to the market

xiccD

. Managers cannot affect these patterns. But a further strategic channel is also present: the

higher is the level of mis–reporting, indeed the reported cost of a product with respect to the true

one, and the higher is the probability that the division is not financed ψ′µ (µ) < 0.

We are now in the position to characterize the manager’s problem. The manager of a given product

that is i = 1, 2, ... units of distance from the core competence chooses µi in the interior of the

compact set[µi, µi

]such that the expected benefit is maximized:

µ?i = arg maxµ∈[µ

i,µi]

ψi (µ) b (µ, xi, c) (14)

The problem (14) is a well–defined concave problem that admits a unique solution.15

Proposition 1. A solution µ?i (xi, c, cD, θ) to the manager’s problem (14) does exist and it is

unique. Only managers with products that are good enough xi <cD/c

1+2θ2/ϕkapply for funds and

they over–report the customization cost µ?i (xi, c, cD, θ) > 1. The general equilibrium properties of

managers’ decision are such that:

(1.1) µ?i is decreasing in xi

(1.2) µ?i is decreasing in c

(1.3) µ?i is increasing in cD

(1.4) µ?i is decreasing in θ

Proof. The proof of Proposition 1 is in the appendix.

15 In the modeling of the competition across managers we made two assumptions which are not innocuous, althoughthey shall be considered reasonable. First, each manager thinks that she is playing against the ”field” of othermanagers with customization costs distributed according to a distribution that ultimately does not depend on thenumber of products. Second, each manager thinks that if she plays her maximal possible misreporting, she is loosingfor sure the possibility to be financed. These assumptions are made for tractability. The cost is to restrict the solutionof an otherwise fully rational bayesian approach to a free entry auction under imperfect information. Given this,we get some interesting implications in terms of mis–reporting behavior and their connections to the competitiveenvironment of the firm.

27

The intuition behind the result of Proposition 1 is that managers can only gain a positive private

benefit if they make their division look worse than what it actually is, by over–reporting the true

cost. In fact, once they are financed, they are committed to a less performing target than what their

division will achieve and they benefit from the difference between the actual performance (which is

unobservable) and the true performance that can be observed in the market. Only managers with

relatively good products have the room to over–report and still face a positive probability of being

financed. Managers with bad products either do not have the chance to be financed or they would

make a negative value by committing to a reported cost that is compatible with being financed.

The comparative statics have clear economic interpretations. A lower cost xic leaves room for

more over–reporting; which implies that: within the same firm, managers of better products over–

report relatively more; across firms, over–reporting is larger for the relatively more efficient firms.

A tougher market (lower cD) or a higher value for capital in the external market θ both decrease

the room for reporting higher costs than the true one. This shall be desirable, not only for the

owner but also for the economy. In fact, over–reporting reduces the output that is actually sold

in the market. This is true at the intensive margin, since output per product decreases in zi. But

it is also true at the extensive margin, since the number of products at each firm M(c) tends to

decrease if the divisions closer to the core are excessively financed.

4.2 Generalization of managers’ behavior

In the previous paragraphs we have assumed that managers enjoy a private benefit which is ex-

plained by an excess of production. As a result, we have seen that managers have the incentive to

over–report production costs. In this section we extend the previous result in two directions. First,

we show that when managers are rewarded also in terms of the observable amount of output then

managers with the worse products have the incentive to under–report. Second, we show that the

predictions of the model apply to the case in which a much broader definition of private benefit is

considered.

28

Compensation for managers provides the incentive to under–report. In the finance

literature it has been argued that managers who spend more effort in “getting along” with the

owner instead of managing their division might be successful in obtaining too much funds at the

expenses of divisions that are better managed. We are not interested in taking a stand on this

conjecture, but to the aim of accounting for the conglomerate discount it seems appropriate to

show that our framework can reproduce the same implication, without calling for more ad–hoc

arguments. Consider relatively bad products which are far from the core, hence in the region in

which capital allocation is decreasing in reported customization cost. The model predicts that these

divisions will receive excess funding if their managers under–report the true cost. The following

analysis extends the result of Proposition 1 to build the incentive to under–report for the worse

products only.

Assume that the owner pays a compensation to the managers, in terms of a share (1− ε) ∈

[0, 1) of the output of her own division. The expected benefit of a manager of a product with

customization cost xi who applies for funds in a firm with core competence cost c is:

µ?i = arg maxµ∈[µ

i,µi]

ψi (µ) [b (µ, xi, c) + (1− ε) q (µxi, c)] (15)

The problem (15) is a well–defined concave problem that admits a unique solution.

Proposition 2. A solution µ?i (xi, c, cD, θ) to the manager’s problem (15) does exist, it is unique

and it prescribes a lower reported cost than in the absence of compensation µ?i (xi, c, cD, θ) <

µ?i (xi, c, cD, θ) .

Proof. The proof of Proposition 2 is in the appendix.

The intuition behind the results of Proposition 2 can be understood in comparison with the scenario

without managers’ compensation η = 1. Introducing a positive contribution of observable output

η ∈ (0, 1) in the manager’s private benefit (15) yields a second channel through which the manager

gains. The higher is the true cost and more the manager tries to just get financed so that she can

29

share the output afterward. This channel pushes in the direction of under–reporting whereas the

incentive for over–reporting is still present, as managers gain by committing to a lower performance

than the one that is achievable. For managers with relatively worse products the new channel

dominates: they will apply for funds (which did not happen before) and they will under–report.

For managers of better products, the possibility to share production is an incentive to decrease the

amount of over–reporting and by doing so increasing the output they will share after production.

In conclusion, Proposition 1 shows that the asymmetric information between owner and managers

causes an inefficient internal market for capital. Moreover, it also sheds light on the effect of

market conditions cD, θ and idiosyncratic technological characteristics c, ω on the internal

capital market. Proposition 2 shows that the introduction of compensation for managers induces

a reduction of over–reporting in relatively good divisions and introduces the possibility of under–

reporting for relatively bad divisions.16 We are now in the position to determine the equilibrium

of the industry.

5 Inefficient internal capital allocation

In the baseline framework of Section 3 we have shown that the model delivers a prediction for the

Tobin’s Q which can lead to a conglomerate discount; see the discussion on (10). However, this

channel would remain fairly mechanical if it was only due to the interplay between the core marginal

cost and the flexibility, since both dimensions of the technology are exogenous. In contrast, in the

previous Section we have shown that the strategic behavior of managers, distorts the allocation

of capital across divisions. This channel is not due to the technology, but to the asymmetric

information within the organization. And Proposition 1 shows that this channel of inefficiency

responds to firm and product characteristics as well as to the toughness of the competition.

Inefficiencies in the internal capital market amplify the conglomerate discount. To see this,

notice that over–reporting zi = µixi for µi > 1 increases the mean of customization cost E[z] > E[x],

compared to fair reporting. Moreover, the relative larger over–reporting at the best divisions

16 Moreover, Lemma 1 in the appendix shows that the results of our framework apply to a much more general specificationof the private benefit.

30

tends to decrease the variance of customization cost. Both channels decrease the Tobin’s Q of a

conglomerate firm

T (zimi=0 , c) =ϕk2θ

(cD − E[z]c

E[z]cD − E[z2]c

cDc− 1

)≤ T (ximi=0 , c) (16)

whereas the Tobin’s Q of a single product firm is of course not affected by this channel. The

two mechanisms previously described reinforce each other: over–reporting decreases the return on

investment; and the larger over–reporting at the relatively better products tends to dispropor-

tionately increase the allocation of capital at divisions with lower return on investment than the

core.

The model has three implications for the capital allocation across divisions. First, the ineffi-

ciency of the internal capital market is mainly due to excessive financing. Second, in particular the

best divisions are relatively more over–financed than the worst divisions. Third, the relationship

between capital allocated to a division and its position in the ranking by return on investment

should have an inverted–U shape. Either the best division has the largest capital allocation, or

divisions which are closer to the best one have larger but comparable amount of capital; while, for

products which are further away from the best one, the allocation of capital is decreasing the lower

the return on investment. We examine this in the next section.

5.1 Capital allocation in publicly listed US firms

In this section we want to examine whether we can find evidence for the model’s prediction that the

distortions in the internal capital market arise in particular in the strongest divisions of firms. 17.

In Proposition 1 the model predicts that there will be more over-reporting in the more productive

firms and within firms in the most productive divisions. As the divisions of the firm become less

productive, the over-reporting of costs are expected to decline as division managers will have to take

into account that by over-reporting too much they run the risk of not being financed. The over-

17 The empirical finance literature on the internal capital market does not examine the actual capital allocation acrossdivisions as we do in this section. The finance literature focuses on the comparison of multi-segment firms withsingle-segment firms in their capital expenditures and/or their responses to profit opportunities (see Oszbas andScharfstein (2010) and to the sensitivity of investment to their cash flow (see Shin and Stulz (1998))

31

reporting of costs are expected to decline when we rank divisions in the firm by their productivity

level until we reach the marginal division which does not over-report as its high cost level enables

the division to get funding only without over-reporting its costs.

To find evidence for these predictions we want to compare the actual capital allocation across

divisions in US firms (in which the distortions described in the paper are assumed to be present if the

model is correct) with a hypothetical capital allocation across divisions in which these distortions

are absent. To find a benchmark capital allocation without distortions we focus on those firms in

which managers are incentivized by owning part of the company. The incentives of managers who

own part of the company are expected to be more aligned with those of the owner of the firm.

Therefore, we expect managers of good divisions in these companies to engage in less strategic

over-reporting of costs or they may not over-report at all.18

To get information on the ownership share of managers in our publicly listed US firms we merged

the Worldscope data with data on executive pay by BoardEx. BoardEx provides information about

the board members of a company. The data include information on the remuneration packages of

board members for 90 countries with 22,500 firms. We use the information on managers of US

firms. Besides a fixed wage, managers are compensated for their service by stocks, options, and

long-term incentive plans. Stocks, options and long-term incentive plans sum up to the total

wealth of a manager which is our measure for the stake a particular manager has in the company.

We then aggregate these values at the firm-year level. This tells us how large the stake of the

board as whole is in a given year. We match these data with the US publicly listed firms from

Worldscope. Our matching is based on International Securities Identification Numbers (ISINs),

a 12-character alpha-numeric code that uniquely identifies securities including bonds, warrants,

and stocks in particular. Then, conditional on the right country, we use the user-written Stata

command reclink2 (Wasi and Flaaen (2015)) to match companies from the two datasets based on

names. The command was specifically designed to facilitate the merging of two datasets with

no common identifier. We then checked the links by hand and discarded wrong matches. To

compute the ownership share, we divide the stake of a board in a given year by the year-end

18 In the Appendix B we show how the incentives for over-reporting decline when managers own part of the company.

32

market capitalization of the respective firm in the same year. This information is included in the

Worldscope data. After the matching we are left with 7472 firm-year observations.

In Figure 3 we examine possible distortions in the internal capital market in publicly listed US

firms with 2 or more segments. In addition, we show the capital allocation of firms with different

numbers of segments separately to see whether the distortion in the internal capital market changes

when firms produce more goods.19 On the horizontal axis we rank the business segments of the

firms by their return on assets (cash flow/assets) as a measure of their productivity. Segment 1 has

the largest return and segment 8 the lowest. The vertical axis reports the median level of capital

expenditures in US$1000 relative to the firms’ employment (to control for the size of the firm).

To identify possible distortions in the allocation of funds we plot the capital allocation in firms in

which managers own only a small share of the company and compare it with the capital allocation

in which managers own a large share of the company. Managers with a low stake have an ownership

share below the median share of 1.4%. They own on average 0.7 % of the company. The solid line

in Figure 3 reports the capital allocation in firms with an ownership share below the median. It

is supposed to capture the capital allocation with over-reporting of costs as managers without a

stake in the company will maximize their private benefit rather than the profits of the firm.

We also plot the capital allocation in firms in which managers own a large share of the company.

Managers with a large stake have an ownership share above the median. They own on average 7%

of the company. This is the dashed line in Figure 3 and it is supposed to capture the capital

allocation without over-reporting of costs as the incentives of managers in this group are expected

to be aligned with the company they work for. The solid line (capital allocation with distortions)

is expected to lie above the dashed line (capital allocation without distortions) as managers will

ask for more funding in the capital market with distortions as their private benefit rises with the

amount of capital they get. Moreover, if the model is correct we expect the distance between

the two curves to be largest in the best performing segments and to eventually disappear as the

divisions become less productive. In the marginal segment with the highest costs that still will

be financed the capital expenditures with distortions is expected to equal the capital expenditures

19 We include only independent segments in the analysis which do not stand in an input-output relationship to othersegments. For the procedure, see Herkenhoff, Marin, and Suverato (2017).

33

without distortions.

0

2

4

6

$1

00

0 / E

mp

loye

e

0 2 4 6 8 Return on Assets

Firms with 2 segments

0

2

4

6

0 2 4 6 8 Return on Assets

Firms with 3 segments

0

2

4

6

0 2 4 6 8 Return on Assets

Firms with 4 segments

0

2

4

6

$1

00

0 / E

mp

loye

e

0 2 4 6 8 Return on Assets

Firms with 5 segments

0

2

4

6

0 2 4 6 8 Return on Assets

Firms with 6plus segments

Note: The red/dashed line shows firms with an ownership share of the board larger than the median, the blue/solid line shows those with an ownership share of the board below the median. Ownership share is measured as total wealth owned by managers relative to market capitalization. Total wealth is the value of cumulative holdings over time of stock, options and long term incentive plans of a firm's board. Significance of the difference is based on Pearson Chi-squared test for the equality of medians. ***: p<0.01, **: p<0.05, *: p<0.1

(per employee) by ownership share of the board: above/below median

median values

Figure 3: Capital Expenditures across Business Segments

*** **

*** ***

*** *** *** *** **

We indeed find this pattern in Figure 3. The distance between the two curves, our measure

of the distortion, is largest in segment 1 and 2 and disappears in segment 5. Note also, that the

capital allocation in Figure 3 reaches its maximum in segment 2 when the firm moves from its

core product to the next best product. This pattern arises for two reasons.20 First, segment

2 will require more funding than segment 1, because its costs are larger. Second, the distortion

between the reported costs and the true costs will be largest in segment 2 as the headquarters has

incomplete information about how large the customization costs are from moving from the core to

the next best product. After segment 2 further products down the line are allocated less capital,

because managers of the less efficient segments will ask for less funding to increase their chances

of getting financed. Segment 5 is the marginal division in which there is no over-reporting and

the two curves coincide. Note also that in firms with more than 5 segments the two curves almost

coincide. Firms with more than 5 segments have no over-reporting of costs at the strong divisions.

This might suggest that over-reporting constraints the number of products that can be financed.

20 For a formal derivation, see the appendix.

34

Excessive funding of the best divisions may crowd out funding of products which are worthwhile

to undertake.

020

4060

$100

0 / E

mpl

oyee

-.2 0 .2 .4Return on Assets

Note: The red/triangular markers show manufacturing firms with an ownership share larger than the median, theblue/round markers show those with an ownership share below the median. Ownership share is measured as totalwealth owned by managers relative to market capitalization. Total wealth is the value of cumulative holdings overtime of stock, options and long term incentive plans of a firm's board.Regression lines: low ownership: y = 8.60 + 117.33***x + u. High ownership: y = 18.41 + 6.25x + uStandard errors are 24.04 (low ownership) and 4.35 (high ownership).

(per employee)by ownership share of the board: above/below median

Figure 4: Capital Expenditures across Firms

Next, we want to examine whether the over-reporting of costs is on average larger in more

productive firms as is predicted by Proposition 1. We do this with the help of Figure 4 which

is a binned scatter plot that allows us to visualize large datasets. We employ the user-written

binscatter command (Stepner (2017)) in Stata which groups the observations into equally sized

bins and plots the means of the those bins. On the horizontal axis we rank the firms by their

return on assets (cash flow/total assets) as a measure of their productivity. On the vertical axis we

report the amount of capital these firms spend in US$1000 per employee. The blue line (with round

markers) reports the capital allocation in firms with an ownership share of the board below the

median (capital allocation with distortion), while the red line (with triangular markers) shows the

same for firms with an ownership share of the board above the median (capital allocation without

distortion). The data allow us to identify the marginal firm for which both capital expenditures

coincide with a return on assets of 8.8 percent and capital expenditures below US$19,000 per

employee. More productive firms receive on average more capital in an internal capital market

35

with distortions compared to one without distortions. The most productive firms in our data (with

a rate of return of almost 40%) receive on average almost US$40,000 more capital per employee in

the internal capital market with distortions compared to firms with the same rate of return in an

internal capital market without distortions. As predicted by our theory the distortion (the distance

between the two curves) is largest in the most profitable firms and steadily becomes smaller as

the profitability of the firms declines. Interestingly, Figure 4 shows that there is almost no under-

reporting of costs as there is only one pair of bins for firms with negative returns on assets for

which the pattern is reversed (with triangular markers above round markers). Managers may have

an incentive to under-report their costs in order to get funding when they expect to share some of

the profits afterwards (see Appendix B).

6 Industry equilibrium in autarky

An entrepreneur does not know the core competence cost neither the customization costs before

raising the fe units of capital which will be needed to eventually finance a firm, hence become a

firm owner. This information requires a specific investment in knowledge of fi units of labor that

do not have a market value afterward. The core competence cost c > 0 is revealed as a random

draw from a distribution with cumulative density function G(c). The vector of customization

costs is consistent with the structure of production zi = ω−i but ω ∈ (0, 1) is understood as a

random variable with a cumulative density F (ω), instead of the true flexibility parameter ω. This

information is sufficient to determine whether there are financiers willing to invest in the developed

technology: with probability [1−G(cD)] it will be better to allocate capital on the external market;

with probability G(cD) the entrepreneur is able to raise fe units of capital and finance a new firm

which then enters the market. In the second case the entrepreneur becomes the owner of a firm

endowed with fe units of capital which has been described in the previous sections.

In equilibrium firms are not financially constraint, in the sense that the endowment of capital

raised at entry is sufficient to finance all the products with a return on investment larger than

the rental price for capital on the external market. This allows the expected profit of a firm

36

unconditional on entry,

Πe(cD) =

∫ 1

0

∞∑i=0

∫ ωicD

0

L

4γ

[c2D − 2cD ω−ic+ (ω−ic)2

]dG(c)

dF (ω) ,

to be determined in closed form, as follows. A parametrization of the technology G(c) = ( ccM

)ρ

for ρ > 1 yields∫ ωicD

0 dG(c) =cρDcρM

(ωρi),∫ ωicD

0 cdG(c) = ρρ+1

c1+ρD

cρM

(ωi+ρi

)and

∫ ωicD0 c2dG(c) =

ρρ+2

c2+ρD

cρM

(ω2i+ρi

)which simplifies the expression for the expected value,

Πe(cD) =

∫ 1

0

∞∑i=0

c2+ρD

cρM

[1

(1 + 2θ2/ϕK)ρ− 2

(1 + 2θ2/ϕk)1+ρ

ρ

ρ+ 1+

1

(1 + 2θ2/ϕk)2+ρ

ρ

ρ+ 2

](ωρ)i

4

L

γ

dF (ω)

=

∫ 1

0

[c2+ρD

L

φπγ

∞∑i=0

(ωρ)i]dF (ω)

=

∫ 1

0c2+ρD

L

φπγ

1

1− ωρdF (ω) ,

where φπ = 4cρM

[1

(1+2θ2/ϕk)ρ− 2

(1+2θ2/ϕk)1+ρρρ+1 + 1

(1+2θ2/ϕk)2+ρρρ+2

]−1and the series converges∑∞

i=0 (ωρ)i = 11−ωρ . Thus a closed form expression for the expected value is obtained for every

given continuous distribution F (ω) defined on the unit interval. Without loss of generality the

constant Ω =∫ 1

01

1−ωρdF (ω) > 1 completes the characterization of the expected profit of a firm

unconditional on entry:

Πe(cD) =

[ΩL

φπγ

]c2+ρD (17)

The expected asset of a firm unconditional on entry is:

Ke(cD) =

[ΩL

φkγ

]c2+ρD (18)

where φk = 2ϕkcρM

[1

(1+2θ2/ϕk)1+ρρρ+1 −

1(1+2θ2/ϕk)2+ρ

ρρ+2

]−1. The expected value generated by a

firm unconditional on entry should at least compensate for the sunk cost of the investment in

knowledge plus the opportunity cost of the financiers. In an equilibrium with free entry of firms

37

the two values coincide:

Πe(cD) + θ [fe −Ke(cD)] ≡ fi + θfe (19)

Notice that the initial amount of capital raised by the owner does not play any role in the endogenous

firm entry. This is the case because of footloose capital: the specific investment which is taken

upfront is in terms of the owner’s labor, while idle capital can always be reallocated to the external

market. The free entry condition (19) determines the cutoff core competence cost below which

firms face a positive demand on the domestic economy:21

cD =

[(1

φπ− θ

φk

)−1 γfiΩL

] 12+ρ

(20)

The market cutoff cD (20) and the solution to the manager problem (14), or its extension (15),

characterize the equilibrium allocation at the firm.

Let the economy be populated by many firms, each characterized by idiosyncratic levels of

core competence cost and flexibility. Then, by the law of large numbers the average profit among

incumbent firms attains the expected value of a firm Π ≡ Πe(cD)/G(cD). The definitions of

the average price across varieties p = (cD + v)/2 and of the chock price pmax yield the mass of

varieties V , given pmax ≡ cD, where v = 1H(cD)

∫ cD0 vdH(v) is the average cost across varieties

and H(v) =∫ 1

0

∑∞i=0G

(ωiv)dF (ω) attains the measure of varieties which can be produced at a

marginal cost lower or equal to v. The parametrization of the technology for the core competence

cost G(c) =(

ccM

)ρyields the cumulative density function H(v) = ΩG(v) and allows the average

cost, the average price across varieties, and the mass of varieties to be determined:

v =ρ

1 + ρ

cD1 + 2θ2/ϕk

(21)

p =

(1 +

1

1 + 2θ2/ϕk

ρ

1 + ρ

)cD2

V =2γ(ρ+ 1)

η

1 + 2θ2/ϕk1 + 2θ2/ϕk + ρ2θ2/ϕk

α− cDcD

21 Notice that since ϕk = θ1−λ and φk is proportional to ϕk then in the limit in which capital is not used in production

λ→ 1 then the market cutoff coincides with the analogous level in Mayer et al. (2014).

38

Clearly the derivation of the aggregate results follows Mayer et al. (2014), with the distinction of

idiosyncratic heterogeneity regarding the customization costs and the presence of an external market

for capital. However, firm level differences in customization costs across products are averaged out,

regardless whether these differences come from heterogeneity in production flexibility ω or they

are caused by managers’ mis–reporting µ?i (xi, c, cD, θ) 6= 1. Instead, the presence of a market for

capital affects the aggregate equilibrium. A higher rental price for capital causes lower average cost,

lower average price and less varieties.22 The reason is that a higher rental price for capital induces

a further selection on varieties, since only those products with a return on investment higher than

θ will be financed.

7 Industry equilibrium in open economy

In this section we analyze an open economy equilibrium, with the purpose to assess how the

functioning of the internal capital market can explain the lower conglomerate discount for exporter

firms which we have observed in the data. The focus of our analysis is not on market size or

geography, therefore we restrict the discussion to a scenario in which firms have access to a portion

of the worldwide foreign market which is symmetric to the domestic one. Markets are segmented

and any produced variety can be exported subject to the payment of an iceberg trade cost τ > 1.

7.1 Equilibrium with exporters

Following Melitz and Ottaviano (2008) and Mayer et al. (2014), the segmentation between domestic

and foreign markets implies that a domestic producer with core competence cost c would serve the

foreign market as a local producer with core competence cost τc. With this substitution, the firm

level variables (2)–(6) can be rewritten for an exported product, and out of those profit, capital

22 Notice that in the limit for capital not used in production λ→ 1 the aggregate variables (21) attains the same valuesas in Mayer et al. (2014).

39

and return on investment are of particular interest for the following analysis:

πx (zi, c) =τ2L

4γ(cxD − zic)

2

kx (zi, c) =1

ϕk

τ2L

2γ(cxD − zic) zic

roix (zi, c) =ϕk2θ

(cxDzic− 1

)

where cxD = cDτ < cD is the minimum core competence cost for which a firm makes profit when

exporting to the foreign market. Those products with a marginal cost zic < cxD/(1 + 2θ2/ϕk) ≡ cxD

can eventually be financed and in that case they are produced, sold in the domestic market and

also exported. The decision to export a product or not is made by the owner given the reported

customization costs and we assume that managers do not internalize this possibility when deciding

the factor of mis–reporting.23 Hence, the analysis of the industry equilibrium of the previous section

can be conducted including the eventual profit and capital allocation due to exported products. The

open economy level of expected profit and capital usage unconditional on entry are equivalent to

their counterparts in closed economy Πope (cD) = (1 + τ−ρ) Πe(cD) and Kop

e (cD) = (1 + τ−ρ)Ke(cD)

but for the market size, which is (1 + τ−ρ) times larger. The cost cutoff which satisfies free entry

in open economy is given by:

copD =

[(1

φπ− θ

φk

)−1 γfiΩ (1 + τ−ρ)L

] 12+ρ

(22)

thus it is lower than in the closed economy case.

7.2 Exporting versus adding a product

For a given product the return on investment due to export is lower than the one the firm realizes on

domestic sales. However, when a firm allocates capital to the production of the exported quantity

of a given product i the return on that capital can be higher than the return on investment the

23 There is large evidence suggesting a pattern in which products are developed for the domestic market first and thenthey are eventually introduced in a foreign market. In our static framework it would be odd to assume that thepossibility of export plays a role when managers are proposing a product for the first time.

40

next product i + 1. Given the structure of the customization cost zi = µiω−i, the model predicts

that a firm finances the export of the i–th product before financing the production of the j > i

division if and only if:

µjµi

> ωj−iτ (23)

Since the factor of mis–reporting is decreasing in the true customization cost µj < µi then τ <

1/ωj−i is a necessary condition for an equilibrium in which the product i is exported by a firm

which is producing at least j > i products. Thus for a given transport cost, more flexibility – higher

ω ∈ (0, 1) – makes the introduction of a new product more attractive than exporting.

This is a novel linkage between trade and product mix with respect to what the literature on

multi–product firm has already developed. The presence of an external market for capital not only

implies that products with too low return on investment are not financed, but also that the export

of some subset of products is not financed in favor of more products sold in the domestic market.

Since firms do not export as long as allocating capital to do so is more profitable than introducing

a new product, then the profit per unit of capital shall not be lower in exporter multi–product

firms compared to non–exporters multi–product firms. Rigidities in the production process (due to

the geometric discrete increase in the customization cost) does not allow to rule out the possibility

that for a peculiar random idiosyncratic draw (c, ω) this patter is unattended. However, for a

large number of firms, the model predicts that the average (or median) Tobin’s Q of conglomerate

exporters is higher than the one of conglomerate not exporters.24 Thus, the model captures the

observed empirical pattern: the conglomerate discount is lower for exporters than for non–exporters.

7.3 The internal capital market and the propagation of trade

Trade induces tougher competition, which takes the form of a lower market cutoff cost copD < cD.

This triggers welfare gains from trade which are due to the selection of best producers and products

into the export market and, within multi–product firms, they are also due to the reallocation of

production toward the relatively best divisions. These implications belong to the MMO framework

24 This is true under the same assumptions on the exogenous distributions of core competence cost G′(c) and flexibilityF (ω) that guarantee the existence of a conglomerate discount; as we discussed in Section 3.

41

that our approach nests. However, a novel set of predictions arises from studying the effect of trade–

induced tougher competition on the inefficient internal capital market of multi–product firms.

The role played by an internal capital market in which asymmetric information leads to mis–

reporting can be understood looking at two products within the same firm. Consider a given firm

with core competence c < cD and flexibility ω ∈ (0, 1) such that at least two products i and i′ are

produced. Let i < i′ and call i the main product and i′ the peripheral product, according with the

distance from the core competence. The relative output of the two products is given by:

q(c, zi)

q(c, z′i)=cD − ziccD − zi′c

=cD − µ?iω−iccD − µ?i′ω−i

′c(24)

where zi < zi′ because the true sorting is preserved xi < xi′ . The response to a tougher competition

(hence cD decreases) is proportional to the wedge zi′ − zi and it is magnified the larger the costs c

and zi′ . Thus a tougher competition skews production toward the main product; and the greater

are the core competence cost and the marginal cost of the peripheral product the stronger is the

reallocation of output toward the core product. These predictions are consistent with existing

frameworks, such as Eckel and Neary (2010) and Mayer et al. (2014). The distinctive contribution

of our framework is to shed light on how a tougher competition propagates through an inefficient

internal capital market. The model predicts three novel insights.

(i) Proposition 1 shows that the factor of mis–reporting is larger in the main product than in the

peripheral product µ?(xi) > µ?(xi′). Therefore, when more production is shifted toward the core

products the internal capital market allocates more resources toward the range of products in which

managers tend to over–report the true customization costs.

(ii) Proposition 1 shows that a lower market cutoff cost reduces the factor of mis–reporting across all

productsdµ?idcD

> 0. Therefore, an increase in the toughness of the competition makes the production

of those divisions which are closer to the core more efficient.

(iii) The return on investment for a given product is decreasing in the reported customization

cost. This implies that an increase in the toughness of the competition, by reducing the factor of

mis–reporting, increases the return on investment of all products. Through this channel, products

42

which where not financed before might now be produced, because they become profitable enough.

The first and second effects have an opposite impact on the efficiency of the firm: more resources

are allocated to products which are managed with excessively high costs with respect to the first

best allocation under fair reporting; but at the same time, the toughness of competition reduces the

over–reporting, such that the firm allocation becomes more similar to the one under fair reporting.

The third effect has an impact on the scope of the firm. Under fair reporting a tougher competition

leads to a narrower scope. This channel is also present here, but another and counteracting force is

at work. As competition reduces the inefficiency of the internal capital market more products will

be financed because they are more likely to have a return on investment which is higher then the

rental price of capital in the external market. This rich set of results shows that the inefficiency of

the internal capital market due to the strategic behavior of managers plays a role in the propagation

of external shocks to market competition.

8 Conclusion

[To be written.]

43

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46

9 Appendix

9.1 Proof of Proposition 1

Proof. Substituting for (12) and (13) in (14) yields:

µ?i = arg maxµ∈[µ

i,µi]

(1− (αiµ)mν

) (µ− 1) (1− βiµ)

where βi = xiccD

and αi =(1 + 2θ2/ϕk

)βi ≡ 1/µi. Every project requires a customization cost xi > 1.

Reporting a customization cost that is lower than one is not admissible as it will signal the project outcome

as an intermediate step of the core competence zi > 1. Therefore µ > 1/xi = µi∈ (0, 1). The probability

that a product i is financed is greater than zero for µ < 1/αi, therefore rational managers who apply for

funding must choose µ < 1/αi = µi. These two arguments yield the compact set of feasible solutions

[1/xi, 1/αi], which is not empty as long as c < cD/[1 + 2θ2/ϕk

]= cD. Therefore, owners with a higher cost

than cD will not find a manager who is willing to apply for funding and commit to the contract (a)–(g). In

what follows we will focus on c ≤ cD.

Consider managers of bad products, βi ≥ 1. Conditional on being financed, they make a positive private

benefit only if µ ∈ (1/βi, 1). Since αi > βi then 1/αi < 1/βi ≤ 1. It follows that a manager with βi ≥ 1

will never apply for funding. The same conclusion applies to managers endowed with better products such

that βi ∈[

11+2θ2/ϕk

, 1)

, which still implies αi ≥ 1 and indeed a negative expected private benefit in the

support µ < 1/αi. Only the managers endowed with βi <1

1+2θ2/ϕkcan expect a positive private benefit in

the support µ < 1/αi and they apply for funding. They have an incentive to over–report, since they make a

positive expected private benefit when µ ∈ (1, 1/αi). In what follows we will focus on the optimal decision

of managers who have an incentive to apply for funding βi <1

1+2θ2/ϕkand αi ≤ 1.

Substituting for ν = 1/m, and computing the first and second order conditions yields:

f.o.c. : µ2i − 2γiµ+ δi = 0

s.o.c. : µi − γi < 0

where γi = αi+βi+αiβi

3αiβi≡ 1

3 (1/βi + 1/αi + 1) > 1 and δi = αi+βi+13αiβi

≡ γi+ 1−αiβi

3αiβi> γi. The roots of the f.o.c.

are µ(−) = γi−√γ2i − δi and µ(+) = γi+

√γ2i − δi. The solutions are real if and only if γ2

i −γi− 13

1−αiβi

αiβi> 0,

47

which is always the case for γi >12

(1 +

√1− 4

31−αiβi

αiβi

). Since αiβi < 1, then γi ≥ 1 is a sufficient condition,

and γi ≥ 1 for every αiβi < 1. It follows that both roots are real, positive and they sort on the positive

real segment as 0 < µ(−) < γi < µ(+). The expected private benefit increases for µ < µ(−) then falls in the

interval(µ(−), µ(+)

)and it increases afterward µ > µ(+). The unique interior solution that solves the f.o.c.

and satisfies the s.o.c. is µ?i = µ(−) which identifies the maximum expected private benefit as a positive value

in the support [1, 1/αi]; notice that the expected private benefit is zero at the extremes of the support.

Let χ =(1 + 2θ2/ϕk

)> 1, then notice that δi =

(γi − 1

3

)+ 3χ

(1+χ)2

(γi − 1

3

)2where the ratio χ

(1+χ)2is

decreasing in χ. The difference γ2i − δi =

(1− 3χ

(1+χ)2

)γ2i +

(1− 2χ

(1+χ)2

)γi− 1

3

(1− χ

(1+χ)2

)is positive and

increasing in γi. For every γi > 1 such a difference is increasing in χ, therefore the maximum is achieved in

the limit χ→∞ at γ2i + γi − 1

3 > 1 and the minimum is achieved in the limit χ→ 1 at 14γ

2i + 1

2γi −16 >

12 .

It follows that 12/√γ2i − δi < 1 ∀ γi > 1. The comparative statics on the solution following a change in γi

yields:

dµ?idγi

= 1− 1

2

2(

1− 3χ(1+χ)2

)γi +

(1− 2χ

(1+χ)2

)[(

1− 3χ(1+χ)2

)γ2i +

(1− 2χ

(1+χ)2

)γi − 1

3

(1− χ

(1+χ)2

)]1/2 > 0 , ∀ γi > 1

where the sign is implied by the fact that(

1− 3χ(1+χ)2

)< 1. Now notice that γi is a decreasing function of

βi = xiccD

and αi =(1 + 2θ2/ϕk

)βi. Therefore,

dµ?i

dxi< 0,

dµ?i

dc < 0,dµ?

i

dcD> 0 and

dµ?i

dθ < 0.

9.2 Proof of Proposition 2

Proof. Substituting for (4), (12) and (13) in (15) yields:

µ?i = arg maxµ∈[µ

i,µi]

(1− αiµ) (µ− ε) (1− βiµ)

where we have set λ = 1/m and we discussed αi > βi > 0, µ > 1/xi and µ < 1/αi < 1/βi. The expected

profit is positive if and only if µ ∈ (η, 1/αi). This is the same result one finds in Proposition 1, with the

simple but crucial difference that the firm takes a share ε ∈ (0, 1] of total output. The fact that managers

can gain from output sold in the market implies two major differences. First, managers of bad products,

such that αi > 1, can expect a positive benefit when the share of output that goes to the firm’s owner is not

the unity η < 1/αi < 1 by under–reporting their true cost of a factor µ ∈ (ε, 1/αi) < 1. Second, managers of

good products, such that αi ≤ 1, also gain a positive benefit when they under–report by a factor µ ∈ (η, 1).

48

In general a solution to the problem (15) yields a positive expected benefit for µ ∈ (ε, 1/αi) which when a

compensation is taken into account implies that also under–reporting µ < 1 and a fair reporting µ = 1 are

possible optimal choices.

The first and second order conditions of (15) are:

f.o.c. : µ2i − 2γiµ+ δi = 0

s.o.c. : µi − γi < 0

where γi = αi+βi+αiβi

3αiβi≡ 1

3 (1/βi + 1/αi + 1) and δi = (αi+βi)ε+13αiβi

≡ δi − (1− ε) αi+βi

3αiβi. The roots of the

f.o.c. are µ(−) = γi−√γ2i − δi + (1− η) αi+βi

3αiβiand µ(+) = γi +

√γ2i − δi + (1− η) αi+βi

3αiβi. If µ(−) is real and

positive then the same holds for µ(+) and they sort on the positive real segment as 0 < µ(−) < γi < µ(+).

The expected private benefit increases for µ < µ(−) then falls in the interval(µ(−), µ(+)

)and it increases

afterward µ > µ(+). The unique interior solution that solves the f.o.c. and satisfies the s.o.c. is µ?i = µ(−).

Notice that η ∈ (0, 1] =⇒ µ?i ≤ µ?i with equality that holds at ε = 1.

9.3 A general characterization of the manager’s private benefit

The assumption that manager’s private benefit is increasing with the output of the division is

in line with what has been done and motivated by the finance literature (see Stein (1997) and

Scharfstein and Stein (2000) as an example). Nevertheless, a legitimate concern arises: How general

are the results we derived? Since managers have an incentive to under–report the true cost of their

division to increase the probability of being financed, we must assume that the private benefit is

increasing with the reported cost as a necessary condition for the existence of optimal strategies.

However, it can be argued that the rational behind managers’ private benefit is not the excess

of production. In the following we show how the implications of the model hold whenever the

unobservable private benefit of managers is positively correlated with revenue, cost, profit and

input allocation of a division.

Lemma 1. The qualitative implications of Propositions 1 and 2 are robust to the case in which

the private benefit is modeled as an excess of revenue r(xi, c) − r(zi, c), profit π(xi, c) − π(zi, c),

return on investment roi(xi, c) − roi(zi, c) and any positive convex combination of these measures

49

with output of a division.

Proof. Consider the performances of a division (6). Revenue, profit and return on investment are decreasing

functions of the marginal cost and increasing functions of the cutoff cost. The same monotonic patterns hold

for the output of a division. Therefore, modeling the private benefit as any convex combination of revenue,

profit, return on investment and output of a division, where each component has a positive weight, yields

the same qualitative predictions of Propositions 1 and 2.

9.4 The implications of the model for capital allocation across divisions

This model is flexible enough to predict the observed patterns for the distribution of capital across divisions.

Looking at managers who can be financed zic < cD/[1 + 2θ2/ϕk

]≡ cD, the model predicts a pattern that

matches the one described under the necessary condition ϕk > 2θ2, which since ϕk = θ1−λ it only requires a

very mild condition on the labor share of the production process given the rental price for capital λ > 1− 12θ .

It can be argued that when the scarcer factor is labor, such that θ < 1/2, the condition is always satisfied

and the left arm of the inverted–U shape relationship is present. If capital is as scarce as labor θ = 1 then a

larger labor share λ > 1/2 is necessary to maintain the possibility of an increasing capital allocation moving

away from the core. When capital is the scarcer factor θ ≥ 1 and the technology is less labor intensive

λ ≤ 1/2 then the allocation of capital across financed products is decreasing in their return on investment,

with the highest capital allocation to the core competence.

The predictions of the model based on Proposition 1 become particularly interesting when looking at

the allocation of capital across products. Through the lent of the model, the inefficiency due to the internal

capital market takes the form of over–financing the better divisions (eventually also at the expenses of

under–financing relatively worse divisions). In this framework over–reporting leads to more capital than

under fair reporting for good divisions, such that zic ≤ cD/2 which is the maximum of the bell shape

relationship between capital and customization cost, from (5). For divisions which are above this threshold

of customization cost zic > cD/2 over–reporting leads to under–financing the division with respect to what

it would be optimal under fair reporting.

50

10 Simulation

[Preliminary and incomplete.]

For a given gross rental price of capital θ and labor share in the production process λ, the predictions

of the model regarding the conglomerate discount depend on the exogenous c.d.f. core competence

costs G(c) and flexibility F (ω), while the level of Tobin’s Q is shifted by the extent of the initial

investment fi.

The parameters of the aggregate demand play a minor role, so I normalize them to: α = 1, γ = 1, L = 1.

I set the gross rental price for capital to θ = 1, indeed a unit of capital is worthy as much as a unit of labor;

and I look at a production process with labor share λ = 0.65. The core competence cost follows a Pareto. I set

the location parameter cM = 1 and the shape parameter to ρ = 2. Only the latter has a meaningful impact

on the results, in particular a more uniform distribution (as ρ → 1) increases the predicted conglomerate

discount. As discussed in Section 3, the c.d.f. F (ω) should allocate a large probability mass on prohibitive

values of flexibility ω ∈ (0, 1). I capture this pattern by modeling the flexibility as a binary random variable,

which takes the high value 0.8 with low probability pω = 0.2 and the low value 0.1 otherwise. A lower

probability to have a flexible technology (as pω → 0) increases the predicted conglomerate discount.

Given this calibration I extract 20 thousand random draws of core competence cost and flexibility levels

c, ω and I feed the model. I set the initial investment cost to fi = 0.1. Larger values of the initial investment

would increase the market cutoff cD leading to lower Tobin’s Q, but the effect on the conglomerate discount

is negligible. Finally, I set the iceberg trade cost τ = 1.3, where 1 corresponds to free trade and an infinitely

large trade cost yields the equilibrium in autarky. Simulating the model yields a median Tobin’s Q of

TQmono = 1.955 for mono–product firms and TQmulti = 1.514 for multi–product firms, which implies a

conglomerate discount of CD = 1− 0.770. Splitting the sample for export status, the conglomerate discount

of non–exporters is CDdom = 1 − 0.648 and the conglomerate discount of exporters is CDexp = 1 − 0.849.

Thus, the conglomerate discount of exporter is lower. Figure (1) yields the allocation of capital across

divisions by group of firms from firms with 2 products up to 6 products. The blue line is the actual

allocation, based on over–reporting, the red line is the counter factual under a fair reporting. The general

pattern is that both lines have an inverted–U shape with the blue line above the red line for earlier divisions,

then the two schedules cross on the decreasing arm of the blue line. However on the horizontal axis there are

51

1 1.5 27.5

8

8.5

9

9.5x 10-3 2 products

capi

tal p

er d

ivis

ions

division1 1.5 2 2.5 3

9.2

9.25

9.3

9.35

9.4

9.45

9.5x 10-3 3 products

capi

tal p

er d

ivis

ions

division1 2 3 4

9.1

9.15

9.2

9.25

9.3

9.35

9.4

9.45

9.5x 10-3 4 products

capi

tal p

er d

ivis

ions

division

1 2 3 4 5

8.8

8.9

9

9.1

9.2

9.3

9.4

9.5

9.6x 10-3 5 products

capi

tal p

er d

ivis

ions

division0 2 4 6

8.2

8.4

8.6

8.8

9

9.2

9.4

9.6

9.8x 10-3 6 products

capi

tal p

er d

ivis

ions

division0 2 4 6 8

7.5

8

8.5

9

9.5

10x 10-3 7 products

capi

tal p

er d

ivis

ions

division

Figure 1: Allocation of capital across divisions.

the divisions, therefore although the line is continuous it has a meaning only when it corresponds to a natural

number on the horizontal axis. This creates a confusion when looking at firms with 3 products. The general

pattern is not violated, simply for this set of values the peak of the blue line cannot be seen, (it would be

to the left of the peak of the red line) which simply means that the second product is already “bad enough”

to exhibit under–financing. Figure (2) shows the value of Tobin’s Q in relation with the number of products

0 10 20 30 400

2

4

6

8

10

12

14

16

18

20

M(c)

Tobi

n Q

Tobin Q by group of firms

0 10 20 30 40

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

3.2

M(c)

Tobi

n Q

, ave

rage

Tobin Q by group of firms

0 10 20 30 40

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

M(c)

Tobi

n Q

, med

ian

Tobin Q by group of firms

Figure 2: Tobin’s Q

of the firm. The left panel shows the raw values, the other two panels show the average and the median

Tobin’s Q among the firms with a given number of products. The green bar is the (average and median)

Tobin’s Q for mono–product firm and the red bar sets the (average and median) Tobin’s Q of multi–product

52

firms. Clearly firms which are more productive finance more products and tend to have a higher Tobin’s

Q. However, the rigidity of the technology and the inefficiency of the internal capital market deteriorates

the market–to–book value of conglomerates. Only super–star conglomerates show a median Tobin’s Q value

which is higher than the one of mono–product firm.

Figures (3) and (4) complete the argument showing the kernel density and cumulate density of Tobin’s Q

across mono–product firms (ble line) and multi–product firms (red–line). Clearly the distribution of Tobin’s

0 5 10 15 20 25 300

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8Kernel pdf of the TQ, (blue mono and red multi)

Figure 3: P.D.F. of the Tobin’s Q by multi–product status

0 2 4 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Kernel cdf of the TQ, (blue mono and red multi)

Figure 4: C.D.F. of the Tobin’s Q by multi–product status

Q across mono–product firm has a much longer right tail and a higher mode. Both features show how the

median Tobin’s Q of a multi–product firm is lower than the one of a mono–product firm. Finally, Figure (5)

53

0 2 4 6 8 10 120

1

2

3

4

5

6

7

8Kernel pdf of the TQ, (blue domestic conglomerates and red exporter conglomerates)

Figure 5: P.D.F. of the Tobin’s Q for conglomerates by export status.

shows the p.d.f. of the Tobin’s Q for conglomerates by export status. Clearly domestic conglomerates are

extremely concentrated at low Tobin’s Q values, while a larger mode and a much larger right tail characterize

the distribution of Tobin’s Q for conglomerate exporters.

54