Very Preliminary and Incomplete. Comments Welcome.

Export Platforms and Multinational Demand RiskDiversification

Francesco Paolo Conteduca Ekaterina Kazakova∗

This draft: May, 2017

Abstract

This paper analyzes the effects of correlated aggregate demand shocks on multi-national firms’ structure. Accordingly, we build a structural model featuring globalproduction and demand risk in which heterogeneously risk averse managers decide onthe location of production plants, the set of countries to serve from these plants, andthe volume of sales. These decisions hinge on the expected market demand, and thevariance-covariance of the demand shocks in destination markets. The identificationof firm-specific risk aversion coefficients follows from existence and uniqueness of thefirm’s optimal sales portfolio. The empirical analysis uses firm-level data on Germanmultinational companies. Our results support the existence of MNE’s diversificationstrategies when producing and selling abroad.

Keywords: FDI, Multinational Enterprise, Demand Uncertainty, Export Platform,Risk Aversion.JEL Classification: F12, F23, L23.

∗Francesco Paolo Conteduca: Graduate School of Economic and Social Sciences, University of Mannheim, Germany (email:francesco.conteduca@gess.uni-mannheim.de); Ekaterina Kazakova: Graduate School of Economic and Social Sciences, Univer-sity of Mannheim, Germany (email: ekaterina.kazakova@gess.uni-mannheim.de). We are grateful to our supervisors HaraldFadinger, Volker Nocke, and Emanuele Tarantino for their guidance, support and insightful suggestions. We gratefully acknowl-edge the hospitality of the Research Data and Service Centre of the Deutsche Bundesbank and thank them for providing uswith access to the Microdatabase Direct investment (MiDi). We also thank Paola Conconi, Jan De Loecker, Matthias Kehrig,Samuel S. Kortum, Yanping Liu, Glenn Magerman, Marc Melitz, Andreas Moxnes, Kathleen Nosal, Mathieu Parenti, Bee-YanRoberts, André Sapir, Nicolas Schutz, Michelle Sovinsky, Christian Volpe Martincus, and all participants of the GESS ResearchDay, ENTER Jamboree at the UCL 2017, Bonn-Mannheim PhD Workshop 2017, ENTER Seminar at the ECARES, LETCFREIT 2017, and the IO Reading Group at the University of Mannheim for their valuable comments. All remaining errors areour own.

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1 Introduction

The UNCTAD World Investment Report 2015 shows that multinational firms react to de-mand shocks in foreign markets by adjusting foreign investment flows and the internationalorganization of their production. Moreover, they try to anticipate possible changes in themarket demand before entering into foreign markets. In particular, when pondering foreignmarket entry, a multinational firm has regard to the expected demand for its product sinceit cannot observe ex ante the actual demand. Given the ongoing internationalization of mar-kets, the variance and covariance of demand fluctuations can play a crucial role in the choiceof FDI and export destinations. Therefore, a model able to explain the global structure ofmultinational production needs to consider that firms, which face interdependent demand inprospective destination markets, evaluate demand risk.Still, most standard empirical trade models treat foreign markets as independent islands.

Specifically, the traditional factors explaining the structure of trade flows relate to gravityequation variables and exclude any third country effect. Nevertheless, the assumption thatmarkets are isolated among each other is hard to justify, especially referring to multinationalenterprises (MNEs).This paper provides a novel explanation of how multinational firms respond to ex-ante

unobserved country-specific demand risks and sort potential destinations for FDI, basedon the exploitation of the imperfect demand correlations across countries. To analyze theMNE’s behavior when demand is stochastic, we propose a structural model of multinationalproduction with export platforms where weakly risk averse managers decide the locations ofproduction plants, the countries to serve from these plants, and the volume of sales, givenexpected demand in destination markets and correlations among them. A structural modelis key to disentangle the effect of demand diversification incentives on multinational salesstructure from the gravity variables effect. In addition, as we allow for risk averse managers,we are also able to capture the role of correlation between demands in designing multinationalfirms’ global strategy. Our study focuses on multinational firms as these firms typically havemore possibilities of adjusting the intensive margin of sales across markets. Indeed, usingforeign affiliates as export platforms, an MNE not only reduces marginal costs of servingneighboring markets, but also lowers the costs of changing sales structure as a reaction to

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demand fluctuations.1 Therefore, diversification explains a larger share of variation in salesof multinational firms compared with that of pure exporters, as for the latter variable costscan outweigh benefits of diversification. As we allow for the possibility of serving othermarkets from foreign affiliates, we can assess how a change in country’s demand impacts onthe composition of firm’s sales portfolios. Since in reality MNEs serve foreign markets bothfrom home and foreign plants, an alternative model, which prevents foreign affiliates fromexporting, would lead to consider a (potentially) misspecified demand.2

In the proposed framework, because of the assumption of weakly risk averse management,multinational firms are less prone to serve countries in which demand shocks are highlycorrelated, unless the expected returns are large enough. Therefore, an analysis which takesthis aspect into account can evidence the weakness of a pure gravity model by highlightinganother understated determinant of firms’ global activity. The demand risk managementappears particularly relevant because international markets are nowadays more connected.Thus, the main contribution of our paper is to quantify the importance of the diversificationcomponent in affecting the global structure of multinationals.As the 2007 – 2009 crisis showed, MNEs reallocate sales following hedging opportunities.

Specifically, while aggregate trade flows decreased, the shares of FDI inflows in developedto developing regions dramatically changed. FDI flows to developed countries contracted by44% in 2009, while FDI flows to developing and transition economies fell only by 24%. Forthe first time, developing regions accounted for half of global FDI inflows, mainly because oflarge and fast-growing local markets and resilience to the crisis.3 We regard this phenomenonas an evidence of MNEs’ moving toward markets offering diversification opportunities.Demand risk diversification has an impact on the outcomes of trade policies and liberal-

ization. Indeed, when multinational firms exploit correlations among demands, this resultsin spillovers of liberalization and trade policies. In particular, an improvement in the termsof trade in a given country produces larger sales flows toward markets that provide a betterhedge against the risk in the liberalized market.The model also provides a rationale to the imperfect nesting structure of location sets of

MNEs observed in the data. For example, if a less productive multinational firm establishes

1The UNCTAD World Investment Report 2008 highlights the importance of demand factors in shapingthe allocation of multinational production. In particular, multinationals showed more stable sales thanexporters during the crisis. Additionally, the incidence of multinational sales over total sales peaked in thesame period. This supports the idea that multinational firms benefit from diversification more easily.

2According to the UNCTAD World Investment Report 2009, 20% of the gross production by foreignaffiliates is sold outside the country of production.

3For more details see UNCTAD World Investment Report 2010.

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its plants in France and China, a more productive firm does not necessarily establish someplant in these countries, too. It is worth noting that this results hold if either we keepproductivity constant and vary risk aversion or vice versa. Moreover, a higher degree of riskaversion does not necessarily reduce the number of foreign locations a firm decides to bepresent in. As establishing a foreign affiliate changes the incentives to serve the neighboringmarkets, the diversification opportunities can also vary with the characteristics of a locationset chosen by the firm. This can result in a non-monotone entry policy in both productivityand risk aversion. Such feature does not arise in Helpman et al. (2004), as entry in eachcountry is fully determined by a certain country-specific productivity threshold.The empirical analysis uses data on German multinational firms. Among OECD countries,

Germany is one of the largest source of FDI representing the third investor economy in theworld. Consistently with the intuition behind our theoretical model, we show that the levelof correlation across foreign markets directly affects the composition of sales portfolios ofGerman multinationals. Compared to a benchmark postulating risk neutrality, firms tend tosell relatively more to the countries which provide a better hedge. Moreover, the presence ofdiversification opportunities results in higher aggregate sales. Importantly, the risk attitudevaries across managers of German MNEs. This heterogeneity captures the differences of salesportfolio composition and country-specific markups across firms even without introductionof firm-specific shocks in the model.Our paper closely relates to the growing literature on the role of demand risk in inter-

national trade. Di Giovanni and Levchenko (2010) show that countries’ specialization pat-terns depend not only on the comparative advantage, but also on the riskiness of sectors inwhich they have comparative advantage. In Nguyen (2012), given the positive correlationof demands across countries, firms learn by exporting about demand in potential foreigndestinations. Riaño (2011) considers the decision of risk averse managers to irreversiblyinvest in physical capital and to export under the assumption that both productivity anddemand are subject to firm-specific shocks. He shows that the firm’s export decision affectsits investment behavior and that the correlation across time of demand shocks is not relevantfor a risk averse manager provided that the process for productivity is persistent enough.Moreover, exporting increases the volatility of firm’s sales. Kramarz et al. (2016) quantifythe contribution of idiosyncratic demand shocks and the structure of trade to the volatilityof exports, and link the volatility of exporters to the low level of diversification in the clientportfolio held by a firm.The closest contributions to the present work are De Sousa et al. (2016) and Esposito

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(2016), who analyze risk averse exporters in the presence of demand shocks. In particular,using a sample of French firms, De Sousa et al. (2016) show that on average exports isnegatively affected by volatility in the destination markets. Moreover, they provide evidencethat the relative frequency of negative to positive demand shocks is able to affect the exports.Esposito (2016) develops a general equilibrium model featuring exporting firms under firm-specific demand shocks. Using data on Portuguese firms, he shows that firms combines aportfolio of risky export activities to reduce entrepreneurial risk. Since Esposito (2016) andDe Sousa et al. (2016) focus on pure exporters, our work differs from their contributions aswe concentrate our attention on multinational firms conducting their international activityvia export platforms. As MNEs typically face lower marginal costs compared to exporters,the benefits of diversification will more likely outweigh the transportation costs for thisclass of firms. In addition, we distinguish from De Sousa et al. (2016) as we allow forinterdependences of expenditures across destination markets and abstract from possible theskewness of demand shocks; with regard to Esposito (2016), we consider a different type ofshocks. In particular, we focus on the risk affecting the firm both at the industry and atthe macroeconomic level whereas Esposito (2016) focuses on firm-specific demand shocks.In addition, we allow the multinational firms to be heterogeneous in terms of risk aversion.4

One implication of such heterogeneity in risk aversion is that markups are firm-destination-specific. In particular, according to our theory, the markup over cost chosen by a firm in adestination reflects both the degree of firm’s risk aversion and the premium required by thefirm to serve the given destination market. Moreover, heterogeneous risk attitudes interplaywith entry decisions and come as one of the factors breaking down the nesting structure oflocation sets.We also contribute to the literature about FDI location choice under risk. Tintelnot (2016)

highlights non-perfect transferability of technologies and focuses on multinational firms con-ducting vertical FDI. Differently from his contribution, risk in our model comes from thedemand side for horizontal FDI, and the emphasis is on the way multinationals diversifysales exploiting correlations across market demands. Ramondo et al. (2013) analyze theproximity-concentration tradeoff when production costs are stochastic. Their prediction isthat country pairs with a relatively correlated outputs trade more, and that exporting ac-tivity is prevalent in countries with more volatile fluctuations. Chen and Moore (2010) show

4Cucculelli and Ermini (2013) provides evidence that managers differ in risk attitudes in a sample ofItalian manufacturing firms.5 This heterogeneity is also correlated with firm’s characteristics like size, age,and innovativeness. Moreover, different financial conditions can result in differences in hedging opportunitiesby other means than sales.

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theoretically how firm-specific demand shocks change productivity thresholds to enter for-eign locations. However, they do not consider potential interdependencies on the demandside. Rob and Vettas (2003) investigate FDI choices under uncertain growing demand in for-eign markets. Differently from them, we do not restrict the sign of demand change. Campa(1993), Goldberg and Kolstad (1995), and Russ (2007) introduce risk through exchangerate and show that firms take into account exchange rate volatility when making their FDIchoices. Our model also considers shock in prices and exchange rates. Aizenman and Marion(2004) analyze the effects of demand and supply risk on vertical and horizontal FDI, findingthat horizontal FDI is relatively less exposed to foreign market risk. This evidence is in linewith demand diversification of horizontal multinationals. Ramondo and Rappoport (2010)explore the role of FDI flows both as an asset available to consumers for diversification andas a means for transferring technology across countries. In this framework, they show thatthe existence of multinational production affects the amount of goods available in each stateof the world and reduces consumption risk as long as foreign affiliates are located in regionscharacterized by good hedging properties with respect to the world consumption risk.We also contribute to the literature linking firm internationalization, experimentation, and

learning. In particular, Conconi et al. (2016) show that firms learn about their profitabilityin a foreign market by entering there as exporters. Our model considers immediate learningabout demand; upon entering a foreign market all risk about demand realization unravels.Albornoz et al. (2012) consider a model of experimenting exporters who learn about theirown export profitability by entering foreign markets. Under the assumption that profitsexhibit the same positive correlation across different foreign destinations, risk regardingprofits reduces over time not only in the markets the firm is present in, but also in theother unexplored markets. Our contribution allows for a richer correlation structure whichis supported by the data. Moreover, our focus is on multinational enterprises rather thanpure exporters.Finally, our paper bears on recent contributions modeling export platforms and multina-

tional production. In particular, we describe export platforms similarly to Tintelnot (2016).Analogously to Ekholm et al. (2007) and Arkolakis et al. (2013), we are able to describespillover effects of liberalization arising from the complexity of global value chains. In addi-tion to their papers, we introduce demand-side spillovers affecting multinational production.The remainder of the paper is structured as follows. Section 2 provides empirical evidence

on multinational sales diversification. Section 3 introduces the theoretical model and we showhow risk aversion enters firm’s production and FDI decisions. Section 4 discusses the data

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used in the estimation. Section 5 describes the identification strategy and the estimationprocedure. Section 6 presents the main results. Section 7 concludes.

2 Stylized Facts

Fact 1. Firms diversify sales portfolio

The diversification of sales by multinational firms has been widely discussed in the literature.The seminal work of Hirsch and Lev (1971) shows that firms holding a more diversified foreignsales portfolio display also more stable sales. Vannoorenberghe (2012) shows that foreignand domestic sales are negatively correlated at the firm level, which supports the hypothesisthat firms diversify by selling abroad. This finding contradicts the theoretical predictionprovided by models considering only productivity, which imply a positive correlation of salesacross destination markets. Fillat et al. (2015) show that multinational activity is benefitedby geographical diversification of sales.Using data on German multinationals, we find evidence in favor of sales diversification.

In particular, for a firm present in at least two locations (home included), we compute ameasure of sales concentration6 as

C(ω) =

∑J(ω)j=1

(sharej(ω)− 1

J(ω)

)2

J(ω)−1J(ω)

,

where J(ω) is the number of firm ω’s locations and sharej(ω) represents the ratio of firm ω

sales in location j to total firm sales.Figure 1 shows that firms tend to spread their sales across locations rather than concentrate

their activities. We can notice that the mode of the concentration measure in the data isslightly above 0.2.

6Note that C(ω) equals 0 if sales are evenly distributed across different locations (no concentration),and equals 1, if sales are concentrated in only one location (largest possible concentration). Moreover, theproposed measure takes into account the number of foreign locations a MNE is present in.

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Figure 1: Distribution of concentration measure of sales, firm level

Source: Research Data and Service Centre (RDSC) of the Deutsche Bundesbank, Microdatabase Directinvestment (MiDi), 1999-2014, authors’ calculations.

Moreover, as Figure 2 shows, the degree of sales concentration is directly related to firmsize; smaller firms are typically more financially constrained so that holding a portfolio ofwell diversified financial assets is harder for this class of enterprises. As a response to this,they diversify their sales across locations to reduce the degree of riskiness related to theiractivity.

Figure 2: Distribution of concentration measure of sales depending on MNE size, firm level

Note: We define a large firm as a firm with at least 1000 employees.Source: Research Data and Service Centre (RDSC) of the Deutsche Bundesbank, Microdatabase Directinvestment (MiDi), 1999-2014, authors’ calculations.

In addition, diversification patterns cannot be explained by heterogeneity in firm efficiencyas we find no correlation between the proposed measure of sales portfolio diversification and

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firm efficiency.7

Fact 2. Managers of multinational firms are risk averse

There are several papers showing that firms are run by risk averse agents. Cucculelli andErmini (2013) elicit CEOs’ risk attitude in a sample of 178 manufacturing firms of differentsizes. They find that most respondents exhibit an averse attitude toward risk.8 Moreover,their measure of risk aversion varies with different firm characteristics like size and age9.In particular, managers of larger or older firms tend to be less risk averse. Other empiricalpapers like Esposito (2016), De Sousa et al. (2016), Herranz et al. (2015) analyze risk aversionin managerial behavior. In particular, the first two contributions provide empirical evidenceof risk averse attitude of exporters.In addition, several recent surveys show that managers are concerned about the volatility

of demand in international markets and have a negative attitude toward risk. In particular,according to the Capgemini Survey 2011, demand volatility is the most relevant businesschallenge (40% of responses) in the agenda of managers of global companies.10 These resultsare in line with the Capgemini Survey 2012, in which the fraction of responses indicatingdemand volatility as the most relevant concern topped 52%.11 An analogous study conductedby McKinsey in 2010 displays that increasing volatility of customer demand is the mostfrequently mentioned challenge for companies operating in a global environment (37% ofresponses).12 These surveys also point out that firms react to demand risk by adjusting theirproduction and sales plans.The outcomes of these surveys are also relatable to the consideration that managers can

hardly perfectly diversify their endowment of human and physical capital across differentfirms.13 Indeed, in most cases, the relation between a multinational company and a CEOtends to be exclusive. Moreover, Nocke and Thanassoulis (2014) find that risk aversioncan be the outcome of credit constraints and diminishing marginal returns to scale of aninvestment in a pledgeable asset.

7Firm’s productivity estimation is described in the Section 5.1.1.876.4% (93.2%) of respondents are (weakly) risk averse9The average sales, number of employees, and range of supplied products are significantly larger for those

firms run by risk loving managers than for those run by (weakly) risk averse managers.10Based on responses from 300 leading companies managers in Europe, North and Latin America, Asia.

Demand risk result more important than other factors, like increasing material costs, meeting changingcustomer requirements, sustainability, etc.

11Based on responses from 350 leading companies managers in Europe, North and Latin America, Asia.12Survey based on responses from 639 leading companies managers worldwide.13This form of idiosyncratic risk cannot be diversified since markets are incomplete.

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Managers’ risk aversion can be also due to the fact that part of managerial compensationschemes is linked to company performance. In particular, the value of bonuses and com-pany’s shares depends crucially on the market performance realized by the firm. In thisregard, Perrino et al. (2002) highlight that risk-reducing projects attract managers as theybecome more risk averse. Relatedly, Abdel-Khalik (2007) shows that managers want to re-duce volatility of firms they manage to avoid the reduction of company’s market value, asthis would reflect in a decrease of the value of their assets.

Fact 3. Demands are imperfectly correlated across destination mar-kets

Both the World Trade Report 2008 and the World Investment Report 2008 highlight theimportance of imperfectly correlated demands across countries during the 2007 crisis. Whilethe Trade Report claims that exporters did not hedge during the crisis, the Investment Reportstates the opposite for multinational firms. In particular, at the aggregate level multinationalfirms moved their export and production toward those markets considered as more resilientto demand shocks. During the crisis, transition and developing economies worked as a goodhedge for the declining demand in developed regions. In line with this observation, we findthat German multinationals operating both in the OECD and non-OECD countries holdmore diversified portfolios (in terms of sales) than those with production plants only in onetype of the country (see Figure 3).14 Moreover, the extent of sales diversification may beexplained not only by the characteristics of the firms but also by the features of the countries,with particular emphasis on market volatility.

14In the plot, we control for the number of locations the multinationals are present in.

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Figure 3: Distribution of concentration measure of sales depending on country types, firmlevel

Source: Research Data and Service Centre (RDSC) of the Deutsche Bundesbank, Microdatabase Directinvestment (MiDi), 1999-2014, authors’ calculations.

Additionally, we compute the co-variance matrix at 2-digit industry-level consumptionexpenditure15, using production and trade data of the top 45 German export-destinationcountries for the period 2002 – 2006. Figure 4 shows the distribution of bilateral correlationsat the industry level. As it can be noticed, the correlation of demands across countries isimperfect for all industries with the median correlation of demand being below 0.5.

Figure 4: Distribution of demand correlations, product level

0.2

.4.6

.8

Den

sity

−1 −.5 0 .5 1

Bilateral demand correlation

Source: UNIDO INDSTAT2 2016, authors’ calculations.

Therefore, the structure of demand correlations suggests that markets offer hedging oppor-

15For a given industry consumption expenditure is given by the difference between the total productionand net export.

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tunities to multinational firms.

3 Model

We build a partial-equilibrium static trade version of Chaney (2008) withN countries indexedby d ∈ D ≡ 1, . . . , N, and I + 1 industries indexed by i = 0, . . . , I.

3.1 Demand

Each country d admits a representative consumer with level of income equal to Yd. Herpreferences are represented by the following quasi-linear utility function in the homogeneousgood Bd

Ud =I∑i=1

αid lnQid +Bd, (1)

where αid > 0, and Qid denotes a Dixit-Stiglitz aggregate product i

Qid =

[∑ω∈Ωid

qid(ω)σid−1

σid

] σidσid−1

, (2)

with σid > 1 denoting the elasticity of substitution between any two varieties ω and ω′, andΩid denoting the set of varieties of the aggregate product i sold in country d.The inverse demand for the variety ω is given by

pid(ω) = Aidqid(ω)− 1σid , with Aid ≡ αidQ

−σid−1

σidid and Υid ≡ Q

−σid−1

σidid ,

whereas Bd = Yd −∑I

i=1 αid.We assume that each αid is a random exogenous shock to consumer’s preferences relative

to product of industry i in country d. Consumers observe the shocks upon the realizationand take consumption decision accordingly. On the one hand, this shock captures risk at theindustry level. For example, it can represent a change in the quality of the product producedby industry i or an exogenous shift in consumers’ preferences toward the product. On theother hand, this shock also captures risk at the aggregate level, for example, in the form ofa shift of total income or aggregate demand. Demand shocks are correlated across markets.Shocks tend to move in the same (opposite) directions in countries either characterized by

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similar (opposite) tastes for a certain product or having more (less) integrated economies.Assumption 1: αid ∼ Gi(αi,Σi), where Σi has full rank N with

−1 <Σi(d, d

′)√Σi(d, d)Σi(d′, d′)

< 1

for d, d′ = 1, . . . , N , d 6= d′, and Σi(d, d′) <∞.

We restrict each αid and Σi to be finite. The restriction we make on Σi is that the cross-correlations across destination countries are bounded away from −1 and 1. As illustrated inthe previous section, this restriction is not particularly strong.For the following discussion, we let ΣAi = Υ′iΣiΥi denote the variance of Ai.

3.2 Firms

We consider firms producing one single variety ω of some product i. As a consequence ofthis assumption, we drop any industry-related subscript. In addition, we identify a firm bythe index of the variety it produces.Additionally, we assume that firms are weakly risk averse. This assumption reflects the fact

that firms are run by a non-risk-loving management as evidenced in the stylized facts. Inparticular, this assumption entails the fact that managers of firms potentially do not consideronly the (expected) size of a destination market, but also its volatility and its correlationwith the demand in other destination markets.16

Moreover, we assume that a firm can serve a given destination market either by selling theproduct from the home plant or by selling it from a foreign location where it is established.In other words, we allow for the possibility that a firm owns an export platform, from whichit can serve not just local, but also neighboring and other destination markets.Firms are assumed to be heterogeneous in terms of risk preferences. In particular, risk

aversion coefficients are not restricted to be the same across different firms, as this featurecan capture dissimilar attitude toward demand fluctuations and correlation in destinationmarkets. We denote the risk aversion coefficient of the firm producing variety ω by r(ω).

Technology and production costs. Each firm displays a level of productivity that canvary in each location where it operates. On the one hand, this assumption captures possible

16Nocke and Thanassoulis (2014) show that the interaction of credit constraints and diminishing marginalreturns to investment are capable to make the firm to be endogenously risk averse. This can rationalize thecoexistence of risk neutral consumers and risk averse managers.

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losses due to non-perfect transferability of technologies and production skills from parentfirms to foreign affiliates. On the other hand, a parent firm can possibly take advantageof the production infrastructure of its foreign affiliate.17 For each firm ω we denote thelocation-specific productivity vector by ϕ(ω).Firm ω in location l has to bear a variable production cost which we assume to be inversely

proportional to firm’s location-specific productivity ϕl(ω). The variable costs of productionin country l for producing ql(ω) units are given by

C(ql(ω)) =ql(ω)

ϕl(ω).

We assume that firms need to pay a fixed cost of entry fl(ω) to set up a plant in foreignlocation l to serve local and possibly other destination markets. This assumption relates tothe fact that firm incurs in a settlement cost to build or to acquire a foreign plant to servelocal and other destination markets. Moreover, these multinational production costs includefixed costs of production in the location.In addition, firms have to pay an iceberg trade cost τld to serve destination d from location

l with τld > 1. We denote by cld(ω) ≡ τld/ϕl(ω) the constant marginal cost of producingvariety ω in location l and shipping it to country d. It is worth noting that we abstractfrom the presence of export fixed cost.18 This restriction is in line with Tintelnot (2016) andcan be motivated by two considerations. First, MNEs tend to enter sequentially in foreignmarkets,19 and in particular manufacturing firms generally start with exporting rather thansetting up foreign plants. Hence, we implicitly assume that when a firm sets up a foreignaffiliate to export to destination markets, those destination markets were previously reachedby home production. Second, we can think of this fixed cost as embedded into the fixed costof setting up a foreign production plant.The numeraire good is produced with labor and the same technology across all countries,

and is traded at no cost.The risk aversion parameter, the vector of productivities and the multinational production

costs are observable by firms at no cost before making any choice. Given its characteristics,

17More concretely, existing contracts with foreign counterparts, lower input prices, or adoption of advancedtechniques can make a foreign affiliate more productive than its parent. Need for learning, institutionaldifferences between hosting country and home, or technological adjustment cost to bear in the affiliate canlead to productivity losses in foreign markets.

18Fixed costs are omitted for simplicity and tractability of the model given scarcity of data on exportchoices. We believe our main results to be not driven by this assumption.

19See Conconi et al. (2016).

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firm’s profits are determined by three simultaneous decisions. First, a firm takes a locationdecision, i.e. it decides about the set of locations in which to establish its foreign affiliates.We denote this set by L(ω) ∈ L = 2N−1 where we assume that the firm is always presentin its home country. Second, a firm takes a shipment decision, i.e. it decides about optimallocation from which to ship its product to a given destination market. Third, a firm takes aproduction decision, i.e. it selects the output volume to sell in each destination. The threedecisions are taken before observing the actual realizations of demand in the destinationmarkets. Hence, a firm decides under risk and considers the first two moments of demandshocks distribution. In particular, this implies that the quantity produced does not adjustfollowing the realization of production cost and, as a consequence, firm is exposed to pricefluctuations in the destination markets. In the following paragraphs, we describe one decisionat a time.

Shipment decision. This paragraph describes how firms select the optimal location forshipping their varieties to a given destination market. This decision hinges on firm’s pro-ductivity in a location in which it is present, and on iceberg trade costs.Consider the profit realized by firm ω producing in country l and shipping to market d:

πld(ω) = pld(ω)qld(ω)− cld(ω)qld(ω).

A firm chooses the optimal way to serve a destination market given possible locations.As the shipment cost is independent from demand risk, this decision is exclusively based onproduction parameters. Since each firm produces its product variety using a constant returnsto scale technology, a standard cost minimization argument requires that destination d isserved from location l such that the unit cost cld is the lowest possible. In other words,qld(ω) > 0 only if cld = min

l′cl′d(ω) : l′ ∈ L(ω).20

Production decision. Sales across different destination markets can be seen as a portfolioof risky activities held by the firm similarly to the standard setting of consumer’s investmentdecision.21 This implies that sales of an affiliate depend not only on local productivity,

20The optimal location-destination pairs depend on the location choice L(ω). This means that if a firmhas plants in Germany and France, then it could be optimal to serve the Belgian market from France. Atthe same time, if this firm decides to set plant in Netherlands as well, then if it is cheaper to serve Belgiumfrom Netherlands, a firm will do so.

21The crucial difference with the standard setting of consumer’s investment decision is in non-linear shares,meaning that the riskiness of the asset is affected non-linearly by the share of this asset in firm’s portfolio.

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the size of surrounding markets, and the cost of reaching them, but also on the set ofother locations where the firm is present, and the correlation among demands in destinationmarkets. The firm’s manager decides the composition of a production portfolio basing herchoice on the level of productivities of affiliates, the level of trade costs, the expected demandsize in the destination markets, the covariance matrix of industry demand shocks, and herlevel of risk aversion.Firm ω chooses how much to ship to each destination. We assume that firm ω’s manager

has preferences represented by a mean-variance utility function over profits in destinationmarkets. This representation of preferences has been widely used in the literature, and itcan be also considered as a second-order approximation of a twice-differentiable increasingand concave utility function around the expected profits.22

Henceforth, we drop the location index under the assumption that the firm is consideringthe optimal shipment choice. Then, realized profit of the firm selling to the set of destinationcountries d = 1, . . . , N is given by

Π(q(ω)|L(ω),ϕ(ω), r(ω)) =∑d

(pd(ω)qd(ω)− cd(ω)qd(ω))

=∑d

(qd(ω)

σd−1

σd

(Ad − cd(ω)qd(ω)

1σd

)),

where q(ω) denotes the vector of quantities to ship to destination markets given the optimalshipment choice for L. Hence, the expected profit is given by

E[Π(q(ω)|L(ω),ϕ(ω), r(ω))] =∑d

(qd(ω)

σd−1

σd

(E[Ad]− cd(ω)qd(ω)

1σd

)),

whereas the variance of profit is given by

var(Π(q(ω)|L(ω),ϕ(ω), r(ω)) =∑d

∑d′

cov(Ad, Ad′)qd(ω)σd−1

σd qd′(ω)σd′−1

σd′ .

Note that the variance does not depend directly on production costs but it is only relatedto risk in destination markets’ demand.The utility function of the manager is then given by

u(Π(q(ω)|L(ω),ϕ(ω)), r(ω)) = E[Π(q(ω)|L(ω),ϕ(ω), r(ω)]−r(ω)

2var(Π(q(ω)|L(ω),ϕ(ω), r(ω)))

22See Eeckhoudt et al. (2005).

16

where, to recall, r(ω) is manager’s risk aversion. Hence, firm ω’s manager solves the followingutility maximization problem

V (L(ω)) ≡ maxq∈RN+

E [Π(q(ω)|L(ω),ϕ(ω), r(ω))]− r(ω)

2var (Π(q(ω)|L(ω),ϕ(ω), r(ω)) ,

where V (L(ω)) denotes the value function associated to the utility maximization problemas a function of the location set L(ω). We note that Kuhn-Tucker optimality conditions arenecessary given the structure of the constraint set.23 We defer for the moment the discussionabout the concavity of the objective function and we just notice that the constraint functionsare quasi-convex so that first-order conditions are also sufficient.For d ∈ D, the first-order necessary and sufficient condition with respect to qd(ω) is given

by

∂u(Π(q(ω)|L(ω),ϕ(ω), r(ω))

∂qd(ω)=∂E [Π(q(ω)|L(ω),ϕ(ω), r(ω))]

∂qd(ω)

− r(ω)

2

∂var(Π(q(ω)|L(ω),ϕ(ω), r(ω))

∂qd(ω)+ µd(ω) = 0

where∂E[Π(q(ω)|L(ω),ϕ(ω), r(ω))]

∂qd(ω)=σd − 1

σdE[Ad]qd(ω)

− 1σd − cd(ω),

and

∂var(Π(q(ω)|L(ω),ϕ(ω), r(ω)))

∂qd(ω)=

2(σd − 1)

σd

(qd(ω)

− 1σd

∑d′

cov(Ad, Ad′)qd′(ω)σd′−1

σd′

),

and µd(ω) ∈ R+ is the multiplier associated to the non-negativity constraint for qd(ω).Hence, for all qd(ω) it holds

qd(ω)− 1σdσd − 1

σd

(E[Ad]− r(ω)

∑d′

cov(Ad, Ad′)qd′(ω)σd′−1

σd′

)= cd(ω)− µd(ω), d = 1, . . . , N.

(3)In general, the system does not have a closed-form solution. However, for σd = 2, a closed-

form solution24 can be found for all d ∈ D. In particular, the first-order conditions for this23Note that linear constraint qualifications have to hold since the set of the gradient of binding constraints

is a subset of the canonical basis of RN .24We just report the expression for the case in which qd(ω) > 0, so that µd(ω) = 0.

17

case can be rewritten as

qd(ω) =

(E[Ad]

2cd(ω)

)2

︸ ︷︷ ︸under

certainty

·

1− r(ω)∑d′ 6=d cov(Ad,Ad′ )qd′ (ω)

12

EAd

1 + r(ω)var(Ad)2cd(ω)

2

. (4)

The first part of equation represents the quantity a given firm would sell under no riskor no risk aversion. The second part, instead, is the factor by which a firm optimallyrescales the level of production to ship to country d because of risk aversion and demandrisk. In particular, we observe that this factor is decreasing in the specific risk associated todestination d (the variance term var(Ad)), whereas it is increasing with the opportunities ofdiversification offered by market d (the covariance terms cov(Ad, A

′d) in the numerator).

We show in Proposition 1 that a solution to the manager’s utility maximization problemexists and is unique.

Proposition 1. (Existence and Uniqueness). If matrix Σ has cross-correlations boundedaway from −1 and 1, there exists a unique solution to the manager’s utility maximizationproblem. Furthermore, this solution is characterized by the Kuhn-Tucker optimality condi-tions.

Proof. See Appendix A.

Proposition 1 implies that the optimal production portfolio of firm ω exists and is uniquegiven the set of locations of foreign affiliates. Hence, mean and variance of sales are well-defined and unique. As we will show later this guarantees that the measure of manager’srisk aversion implied by our model is well-defined and theoretically identified.The first-order necessary and sufficient conditions can be rearranged to back out the risk

aversion coefficient r(ω).

Proposition 2. (Risk aversion measure). The measure of risk aversion is a function of theoptimal production portfolio, and is equal to

r(ω) =

∑d (Epd(ω)qd(ω)− pd(ω)qd(ω))(q(ω)

σ−1σ

)′ΣAq(ω)

σ−1σ

,

where Epd(ω) is the expected price, pd(ω) is the price under certainty, and q(ω)σ−1σ is a

vector in which each component is the optimal quantity sold in country d to the power of(σd − 1)/σd.

18

Proof. See Appendix B.

In the representation of risk aversion as in Proposition 2, we note that the denominator isgiven by the variance of sales in the destination markets, whereas the numerator measuresthe risk premium a firm asks in terms of revenues. Therefore the risk aversion parametershows what extra markup a firm requires for a given level of riskiness of its sales portfolio.Given heterogeneity in risk aversion, we would expect more risk averse firms to change highermarkups. Moreover, the adjustment of prices after realization of demands would result inchanges of markup related to country. Given that the quantities shipped to each destinationwould be different for same productive, but differently risk averse firms, we can rationalizedifference in adjustment of prices after shock realization.

Location decision. As stated, firm ω has to pay a fixed cost fl(ω) for entering location land setting up a plant there. This cost is observed by the firm before making the locationdecision. In our framework, the sum of fixed costs can be thought as the price of holdinga portfolio of locations from which it is possible to serve local and foreign markets. Fixedcosts are separately subtracted from the value function obtained from the production andshipment decisions. In particular,

maxL(ω)∈2N−1

V (L(ω))−F(L(ω)), where F(L(ω)) =∑l∈L(ω)

fl(ω). (5)

3.3 Comparative Statics

In this section, we demonstrate the effect of risk aversion on MNE’s production and locationchoice on illustrative examples. First, fixing firm’s productivity and plants’ locations, weshow how different demand correlation structures will affect firm’s aggregate and relativesales across countries. Second, we conduct a trade liberalization exercise to show the presenceof spillover effects of bilateral trade liberalization in the presence of risk averse managers anddemand shocks. Finally, we endogenize location choice and look at the location sets of firmswith different risk aversion and productivities.

3.3.1 The Role of Demand Correlations

In this subsection, we will simplify the setup in the following way. We assume that there arethree countries, A, B and C. All over the subsection we keep demand variances, elasticities

19

of substitution, (expected) market sizes and trade costs at the same level across countries.25

We assume for the sake of simplicity that firm ω holds an affiliate exclusively in country Aand decides about its sales portfolio.

Highly correlated economies- Assume that demands in all three countries covary thesame way, but are not perfectly correlated. This could be the case of a German firm (affiliatein country A), producing only domestically and being able to serve additionally France(country B) and Austria (country C). As expected, the absolute volume of sales to marketA will be higher as the firm can avoid additional trade costs. At the same time, the firmwill be selling same amounts to countries B and C. As the firm becomes more risk averse,it decreases the absolute volume of sales to all countries. However, the relative share of eachdestination also changes. A more risk averse firm will diversify more, exploiting non-perfectcomplementaries across markets. In Figure 5 one can see that the relative shares of countriesB and C in aggregate sales increase, while the relative share decreases for market A.

Figure 5: Case 1, Highly correlated economies

Risk aversion

Firm

sales

Sales in country ASales in country BSales in country C

Risk aversion

Share

ofsales

Share of sales in country AShare of sales in country BShare of sales in country C

Risk aversion and firm sales – Only in highly correlated economies

Poorly correlated economies. Now we consider markets such that correlation of de-mands in countries A and B, and A and C is lower than correlation between countries Band C. In this case one can think about a German firm (affiliate in country A) serving theUnited States (country B) and Canada (country C). In this specification the gap betweensales in country A and countries B and C is larger (see Figure 6). Since markets B and C

25In this section, we do not stress attention on safer and more riskier markets, looking at the pure effect ofcorrelations across market demands. Roughly speaking, all countries have the same coefficient of variation.

20

now provide better hedging opportunities for a firm selling in country A, sales in A increase.However, as risk aversion increases, we see a pattern similar to the case featuring highlycorrelated economies.

Figure 6: Case 2, Poorly correlated economies

Risk aversion

Firm

sales

Sales in country ASales in country BSales in country C

Risk aversionShare

ofsales

Share of sales in country AShare of sales in country BShare of sales in country C

Risk aversion and firm sales – Only in poorly correlated economies

Mixed case. In the last case we assume that countries A and B have more correlateddemands than countries A and C, and B and C. As an example, one can think of country Ato be Germany, country B to be Austria, and country C to be China. Given the structure ofdemand correlation, country C now provides the firm with a better hedge to negative fluc-tuations in country A’s demand compared to country B. In this case, depicted on Figure 7,if market sizes are the same, the best-hedging-opportunity country attracts the largest shareof sales in absolute and relative terms so that diversification benefits outweigh the marginalcost benefits of selling in local market. Moreover, as risk aversion increases, shares in B andC increase, while the share of A sales is decreasing.

21

Figure 7: Case 3, Mixed case

Risk aversion

Firm

sales

Sales in country ASales in country BSales in country C

Risk aversion

Shareof

sales

Share of sales in country AShare of sales in country BShare of sales in country C

Risk aversion and firm sales – Both in highly (B) and poorly (C) correlated economies

In all cases one can observe that a more risk averse firm diversifies more and this may distortthe sales distribution compared to risk neutral model. Importantly, managers with differentrisk aversion attribute different importance to each destination market. This will directlytranslate to the choices of location sets firms prefer and reaction to the trade policies. It isinteresting to see under which demand structures a firm sells more (Figure 8). Comparingaggregate sales in the above discussed scenarios, a multinational firm sells more on averagewhen the dispersion of correlations among the available countries is larger, that is, whenthe differences in terms of correlations across demands are more relevant. Thus, keepingeverything else constant, we expect firms to sell more in the industries with a wider spreadof demand correlations.

22

Figure 8: Diversification opportunities and aggregate firm sales

Risk aversion

Totalsales

Risk aversion and firm sales – Different diversification scenarious

Only in highly correlated economiesOnly in poorly correlated economiesBoth in highly (B) and poorly (C) correlated economies

3.3.2 Liberalization Spillovers

The next step is to evaluate the effect of bilateral liberalization in the presence of demandcomplementarities. Similarly to the previous part, we consider a world with three countriesand look at the effect of bilateral liberalization between countries A and B. The effect oftariff reduction depends on the sign of correlation of demands between countries. Whensales in country B increase, the spillover depends on the hedging opportunities in othercountries for this increase in sales.26 In particular, if the demand in a third C countrycomoves with the demand in country B, the sales to destination C will fall. On the contrary,a negative relation between demand fluctuations in a liberalized country and a third countrywill produce positive spillovers in terms of trade flows (see Table 1). Importantly, we expectto see demand-side spillovers for any country-specific changes, for instance, an improvementof investment climate in one particular country would result in reshuffling of trade flows toall relevant foreign markets.

26For the proof see Appendix E.

23

Table 1: Effects of trade liberalization

Reduction of τAB Sales A Sales B Sales Ccorr(A,B) > 0, corr(B,C) > 0 – + –corr(A,B) > 0, corr(B,C) < 0 – + +corr(A,B) < 0, corr(B,C) > 0 + + –corr(A,B) < 0, corr(B,C) < 0 + + +

In this subsection, we restrict the location set to include only country A. In the nextexercise, we drop this restriction and endogenize location choice to take into account theeffect of trade liberalization on the direction and magnitudes of trade flows.

3.3.3 Risk Aversion and Entry

In the trade literature studying the determinants of firm’s entry in a foreign market, firm’sdecision is typically associated with the existence of a country-specific productivity threshold.In particular, one prediction of these models is that only sufficiently productive firms find itprofitable to pay fixed costs of entry in a foreign location. In a multi-country environment,this structural assumption results in a hierarchical order of entry decisions. As a consequence,the locations chosen by firms constitute a sequence of nesting sets. In our model, sincecountries are no longer treated as to be independent, firms can decide on the set of foreignlocations also accounting for the hedging opportunities they are providing. Therefore, we canrationalize the presence of non-hierarchical entry, observed in the data (see Yeaple (2009)).To illustrate this point, we consider a world consisting of six countries, where country A is

the origin country of the multinational firm.27 First, we fix the firm’s productivity level andlook at the entry decisions for different levels of risk aversion. In the numerical example, weobserve that the sets of countries are not nested. Moreover, a higher degree of risk aversiondoes not necessarily reduce the number of foreign locations a firm decides to be present in.

27Costs of entry in the home country are normalized to zero.

24

Table 2: Entry Decision and Risk Aversion

Risk aversion Country A Country B Country C Country D Country E Country FLow risk aversion Yes No No Yes Yes NoMedium risk aversion Yes Yes No No Yes NoHigh risk aversion Yes No Yes Yes No YesVery high risk aversion Yes No No No No YesProductivity Country A Country B Country C Country D Country E Country FLow productivity Yes No No Yes Yes NoMedium productivity Yes No No No Yes NoHigh productivity Yes No No No Yes YesVery high productivity Yes No No No Yes No

Note: “Yes” stands for entry to the market, “No” stands for no entry.

For a moderately risk averse firm it is profitable to enter two locations – country B andcountry C, while a more risk averse firm enters three locations – C, D and F (see Table 2).Analogously, for a given risk aversion, changing the productivity can affect not only thenumber of entered locations, but also the compositions of the set. In particular, a moreproductive firm does not need to enter a larger number of locations. Additionally, a moreproductive firm does not necessarily enter all locations less productive firms are present in.

4 Data

For the empirical analysis, our main data source is the Microdatabase Direct investment28

(MiDi), which contains firm-level information about foreign affiliates of German multina-tional companies.29 More specifically, the data include balance sheet variables of foreigncompanies in which German MNEs have directly (or indirectly) at least 10% (50%) of theshares or voting rights. In addition to the standard balance sheet variables (as capital stock,labor and turnover), we observe the locations of foreign affiliates and the industries30 theyoperate in.The empirical estimation relies on 1,099 German multinational firms operating in 19 differ-

28Deutsche Bundesbank (2016): Microdatabase Direct Investment 1999-2014. Version: 2.0. DeutscheBundesbank. Dataset. http://doi.org/10.12757/Bbk.MiDi.9914.02.03

29The database is maintained by the Deutsche Bundesbank. For other research using the MiDi seeTintelnot (2016), who analyzes cost structure of vertical export platforms, Becker and Muendler (2008), whoestimate responses of MNEs employment at the extensive and intensive margins.

30Industries are classified on 2-digit level NACE Rev. 1.1.

25

ent industries31 and 45 foreign countries32 with 3,232 affiliates33 in 2007. We consider onlythose foreign affiliates in which a German multinational holds the control rights. Table 3shows total the sales and number of firms present in each of the top 10 destinations.34 TheUnited States, Spain and France are the three countries in which German affiliates sell themost. It is worth noting that the number of entrants in the country cannot be perfectlymapped to the productivity level (or size) of the median entrant. This observation givesus room for discussing the importance of demand factors in affecting the choice of foreignlocations. Moreover, the relevance of foreign countries with respect to the aggregate salesdiffers for small-medium and large multinationals (see Appendix C for descriptive statistics).We note that the top countries in generating aggregate sales are Brazil and Japan for largeMNEs, whereas they are Poland, Austria, Italy and Switzerland for small MNEs. Withrespect to the entry pattern, the top locations are China and France for large MNEs, whilethey are the US and Poland for small MNEs.Since our model describes the importance of demand components explaining global pro-

duction structure, we restrict our sample to those MNEs that conduct horizontal FDI. MiDidoes not provide information about the type of FDI conducted by a firm. To control forhorizontal FDI we use a standard proxy which considers an investment relation as horizontalif both parent and affiliate firms operate within the same industry.35

31We aggregate the industries 1500 (manufacture of food products and beverages) and 1600 (manufactureof textiles). This consolidation is in line with NACE Rev. 1.1., which aggregates these two industries atthe upper level DA (manufacture of food products, beverages and tobacco). Moreover, in order to fulfillthe confidentiality requirements for the usage of the dataset, we exclude the industry 2300 (Manufacture ofother non-metallic mineral products).

32The set of countries consists of 26 European countries (Austria, Belgium, Bulgaria, Czech Repub-lic, Denmark, Finland, France, Greece, Hungary, Ireland, Italy, Luxembourg, Malta, Netherlands, Norway,Poland, Portugal, Romania, Russian Federation, Slovakia, Slovenia, Spain, Sweden, Switzerland, Ukraine,United Kingdom), 9 Asian countries (China, Hong Kong, India, Indonesia, Japan, Korea, Malaysia, Singa-pore, Turkey), 5 South American countries (Brazil, Chile, Colombia, Mexico, Peru), two African countries(South Africa, Tunisia), Canada and the United States in North America, and Australia in Oceania. Theseare the countries where at least three different German MNEs operate an affiliate. Given this set of coun-tries, we account for 96% of the total affiliates of MNEs operating in 2007 and performing horizontal FDI.Furthermore, the share of the affiliates we consider generates 99% of the total affiliate sales.

33We aggregate the capital, labor and sales for the affiliates of one MNE operating within the samecountry. As production fragmentation does not provide us with any information about the effect of countrycharacteristics on the incentive to diversify, our main results do not change.

34The ranking is built with respect to the total amount of sales.35This assumption leave us with 86% of the initial sample. This is consistent with the evidence from

Eeckhoudt et al. (2005) that the bulk of FDI is horizontal. Literature proposed also to proxy for horizontalFDI using data on intrafirm trade. Unfortunately, MiDi does not provide this explicit information, butintrafirm trade can be proxied by share of affiliate current assets of which claims on the affiliated enterprises.This measure is less restrictive and includes our subsample. See Overesch and Wamser (2009), who usecurrent assets claim proxy for horizontal FDI for MiDi.

26

Table 3: Descriptive statistics on foreign affiliates and parents by country

Countries Totalsales

Sales affiliate Sales MNE Employment MNE Averageproductivity

NAverage Median Average Median Average Median

United States 47.5 257 26 1758 206 4497 883 3.38 185Spain 22.2 239 27 4201 372 11419 1809 3.38 93France 16.9 105 36 2523 315 6673 1210 3.53 161Brazil 16.6 238 31 4685 809 13290 3255 3.71 70United Kingdom 15.5 135 29 4151 349 10772 1434 4.18 115Czech Republic 13.9 104 21 2279 159 6621 909 3.58 134China 10.8 60 14 2002 307 6290 1453 3.64 181Poland 9.9 75 19 1705 164 4495 778 3.91 132Hungary 9.6 117 20 1838 233 6324 1252 4.09 82Mexico 9.2 196 22 7207 529 18309 2644 3.49 47Germany 577.2 594 109 873 143 2557 676 3.90 971

Note: Total sales are expressed in billion Euro. Sales of affiliate and MNE are expressed in million Euro.Source: Research Data and Service Centre (RDSC) of the Deutsche Bundesbank, Microdatabase Direct invest-ment (MiDi), 1999-2014, authors’ calculations.

We use the AMADEUS database to obtain balance sheet data about the home plants ofGerman multinational firms. In particular, we observe the level of home sales, the numberof employees and the level of capital of the parent companies. In addition, to get unbiasedresults in the analysis of the entry choices, we take into account also those German firmsthat have a plant exclusively in Germany.36

Figure 9 shows the variation in MNE sales and employment. We can conclude that thedata provides us with a large variation in the firm size, implying that the set of firms subjectto the analysis is not solely restricted to the largest German firms.

36We restrict sample of domestic German firms and German exporters to have a balance sheet with atotal above 3 million Euro, since MiDi does not contain information on firms below this threshold.

27

Figure 9: Distribution of German MNEs’ sales and employment in 2007 in manufacturing

(a) Sales (b) Employment

Note: Firms with employment level to the right of the bold vertical line are considered to be large firms(more than 1000 employees). Sales are expressed in the logarithm of million euros. Employment is expressedin the logarithm of the number of employees.Source: Research Data and Service Centre (RDSC) of the Deutsche Bundesbank, Microdatabase Directinvestment (MiDi), 1999-2014, authors’ calculations.

Table 4 shows some descriptive statistics about foreign affiliates operating in each indus-try. First, we can notice that the average and median sales of firms vary across industries,being particularly high in the manufacturing of auto, electrical machinery and basic metals.Moreover, these three industries are characterized by a large range of firm sales and sizes.With regard to foreign entry, producers operating in the chemical and transport sectors holdmore affiliates on average (in the other industries the average MNE is present only in oneforeign country). Industries are quite disperse in terms of share of multinational production.On average foreign affiliate sales generate 27.6% of total sales of a German MNE. In someindustries, the sales produced by the affiliates are larger (auto, minerals, printing) whereasin other sectors most of the production is carried out by the parent firm in Germany (wood,machinery and basic metals). At the same time, the foreign market participation cannotbe perfectly mapped to the concentration of sales across affiliates. The largest level of salesconcentration occurs in basic metals and textile, while this measure is lower in other trans-port and paper manufacturing. One of the hypothesis that can explain this result is thatthe industry characteristics are capable to affect the way a MNE spreads its sales acrossaffiliates.

28

Table 4: Descriptive statistics on affiliates by industries

Industry Sales Employment Numberof affiliates

Concentrationmeasure

Foreignshare (%)

NAverage SD Average SD

Food and tobacco 187 590 356 469 1,6 0,36 29,7 116Textile 38 49 240 287 1,5 0,42 28,8 50Wearing and leather 69 82 440 435 1,5 0,48 26,4 33Wood 69 115 363 321 1,0 0,40 19,8 14Paper 120 182 351 395 1,2 0,35 23,2 40Printing 88 210 342 634 2,4 0,37 32,6 94Chemicals 271 1118 640 1939 3,7 0,43 29,9 433Plastic 69 175 312 529 2,1 0,36 30,5 290Minerals 95 129 488 755 2,2 0,38 33,4 136Basic metals 371 1118 924 2496 1,3 0,49 22,6 79Metal products 73 129 380 575 1,8 0,42 25,4 262Machinery n.e.c. 135 377 516 1321 2,0 0,47 22,2 598Electrical 377 2227 1644 8026 2,1 0,41 26,8 235Communication 359 954 957 1437 1,9 0,39 30,4 90Medical 65 99 308 444 2,0 0,46 27,7 207Auto 1180 5953 2648 11347 3,3 0,38 34,8 319Other transport 226 460 826 1670 2,6 0,46 25,4 65Furniture 45 47 289 274 1,2 0,33 31,3 31

Note: Sales are expressed in million Euro.Source: Research Data and Service Centre (RDSC) of the Deutsche Bundesbank, Microdatabase Directinvestment (MiDi), 1999-2014, authors’ calculations.

To estimate non-firm-specific parameters, such as trade costs, production indexes, and theco-variance matrix of country demands, we use data from UN databases and CEPII.37

5 Estimation

Our estimation consists of two parts. First, given the data on the location set L(ω) inwhich the affiliates of firm ω operate and the aggregate sales

∑d∈L(ω) pd(ω)qd(ω) of the

multinational group, we determine the firm-specific risk aversion parameter r(ω). Our modelyields uniqueness of the risk aversion measure for a given choice of the location set. Theestimation of risk aversion requires additional parametrization and estimation of firm- andcountry-industry-specific parameters (ϕ(ω), τ ,σ, α,Σ,Q).

37Trade flows and home production data are from the COMTRADE, INDSTAT and IDSB. Gravitydummies and distances are from CEPII. COMTRADE concordance tables provide industry-country tradeflows in NACE Rev. 1.1 classification.

29

Second, we estimate firm-country-specific fixed costs of multinational production f(ω).This estimation requires us to evaluate the value of each relevant location set L ∈ L feasiblefor the firm’s entry choice.In this section, we proceed as follows. First, we discuss the estimation of productivities,

trade costs and quantity indexes, and parametrize other country-industry-specific param-eters. Second, we show the procedure to derive the risk aversion coefficients. Third, wediscuss the estimation of entry costs.38

5.1 Productivities and Industry Parameters

5.1.1 Productivities

German companies operating in different countries exhibit different productivity levels acrossaffiliates. This observation can stem from the non-perfect cross-border transferability oftechnologies and different quality of inputs across countries. Hence, we need to control forthe heterogeneity in productivities across affiliates of one firm to control for any confoundingfactor between the supply and demand effects.Since the estimates of productivities enter the risk aversion measure, we discuss the iden-

tification of the latter. Importantly, productivities and risk aversion affect the outcome atdifferent levels. In our framework, productivities are affiliate-specific, while risk aversioncoefficients are group-specific. In particular, for a risk neutral firm higher productivity inone affiliate makes it cheaper to serve all destination markets associated with this location.Therefore, without risk aversion, we expect higher sales to each destination market servedfrom the more productive affiliate proportionately to the trade costs. At the same time, riskaversion shapes sales flows relatively to demand correlations. With a positive risk aversion,an increase in the affiliate productivity results in a reshuffling of the sales portfolio of thegiven affiliate and will change the sales shares in each destination market proportionatelyto the hedging opportunities. Moreover, a risk averse firm adjusts the sales realized in allother affiliates. Since we observe the affiliate sales of firms with different productivities, wecan disentangle the effect of productivity on sales from that of diversification. We use thevariation of sales at the affiliate level to capture the supply parameters, while we use theaggregate sales to determine firm’s risk attitude.In the estimation of productivity, we control for firm- and market-specific demand param-

eters to obtain unbiased productivity estimates with respect to the presence of positive risk

38This estimation will be included in the future version of the present paper.

30

aversion. The equation we estimate at the affiliate level by industry reads as

ln(salesjlω) = β1 + βk ln(capitaljlω) + β` ln(labor jlω) + βa ln(agejlω)

+ concentration measureω + coefficient of variationl + premiuml + ξjlω,

where j denotes the affiliate, l the location of affiliate j, and ξjlω the affiliate-multinational-specific productivity shock. From the previous specification, we obtain the productivityestimate ˆϕjlω according to ϕjlω = exp(ξjlω + β1).We include the concentration measure to capture the diversification incentives of a firm.

Moreover, we include the coefficient of variation of the demand associated to the locationwhere affiliate operates in. We find a significant negative relation between the aggregate salesand volatility of destination market demand. Another problem can potentially arise fromthe fact that we estimate productivity using observed realized sales rather than ex-ante sales(i.e. sales before the realization of the shocks). Indeed, higher sales to a destination can bejust due to a higher realization of the market demand rather than to the level of productivityof the firm in the given market. Therefore, to proxy for the sales premium and the effect ofthe realized market size, we include the difference between the realized and expected marketsize39. We show in Section 6 that the productivity estimates are not correlated with theestimated risk aversion coefficients when controlling for other firm characteristics. Moreover,we find that German MNEs are, on average, more productive at home than in the hostcountries (see Figure 10).

39For the estimation of expected market size, see subsection 5.1.2.

31

Figure 10: Distribution of productivities of foreign affiliates and parents (in logs)

Source: Research Data and Service Centre (RDSC) of the Deutsche Bundesbank, Microdatabase Directinvestment (MiDi), 1999-2014, authors’ calculations.

5.1.2 Industry Parameters

A set of parameters is common to all firms operating within an industry. For the sake of con-venience, we distinguish between supply side parameters, i.e. trade costs, and demand sideparameters, i.e. the elasticity of substitution, quantity indexes, variance-covariance matrixof market sizes, and expected market sizes. Since a closed form solution to the firm’s opti-mization problem does not exist, it is hard to obtain the convergence in a general equilibriummodel. Therefore, we estimate the above parameters outside the model.Estimation of trade costs and quantity indexes is based on the methodology proposed

by Anderson and van Wincoop (2003) for cross-sectional data. In particular, a partialequilibrium model for import flows at the industry level delivers the following equation:

log

(md′d

Md

)= (1− σ) log (τd′d) + (σ − 1) log(Pd) for d, d′ ∈ 1, ..., N,

where md′d is import from d′ to d, and Md is the sum of total import and consumption incountry d. Therefore, share of country d′ in total consumption in country d is described bytrade costs between countries, level of prices in country d and elasticity of substitution.Similar to Anderson and van Wincoop (2003), we can estimate trade costs and price indexes

only conditional to elasticity of substitution σ. As we do not estimate industry-specific

32

elasticity of substitution, we assume σ = 7.40

We model trade costs as a function depending on the distance between the two countries,contiguity, and common language. More precisely, we have

log(τd′d) = β1 log(distd′d) + β2contigd′d + β3langd′d for d, d′ ∈ 1, ..., N.

To estimate industry-specific price indexes, we introduce dummies as in Baldwin andTaglioni (2006). The final equation we are estimating is

log

(md′d

Md

)= β1 log(distd′d) + β2contigd′d + β3langd′d + γd + εd′d,

where βb = (σ − 1)βb for b = 1, 2, 3, γd = (σ − 1) log(Pd), is a country dummy.We assume that trade costs and price indexes are 2-digit industry-specific, and correspond-

ingly use import flows at the 2-digit disaggregation level. Country-industry-specific quantityindexes are obtained from the industry i equilibrium condition in country d: PidQid = αid.Finally, we proxy the total expenditure parameter αid using data on the industry-level

consumption from the IDSB dataset. This dataset contains information about the output,export and import in a country at a 2-digit level. We obtain co-variance matrices fromtime-series data on total expenditure in 46 countries from 2002 to 2006.We assume that αid depends on its lagged value. In particular, we assume that

αid,t = αβid,t−1 expINDi+COUNTRYd+εid,t ,

where εid,t is an innovation term41 with mean 1, and β captures the persistence in theevolution of α. We then estimate the following equation in logs

logαid,t = β logαid,t−1 + INDi + COUNTRYd + εid,t,

where we consider control dummies for industry and country. From this equation we obtainprediction for αid,t given the value of αid,t−1. Hence, we compute the entry (d, d′) of the

40This value is in line with Head and Mayer (2004). Note that this value implies a markup equal to 17%in a risk neutral framework. Importantly, estimates of risk aversion parameters are not sensible to the choiceof the elasticity of substitution.

41We do not restrict this shock term to be uncorrelated across countries and industries.

33

variance-covariance matrix Σi in the following way

Σi(d, d′) =

T∑t=1

(αid,t − αid,t) (αid′,t − αid′,t)T − 1

,

where αid,t and αid′,t denote the expectations of αid,t and αid′,t given the level of αid,t−1 andαid′,t−1, respectively, and T is the number of years we are using for our estimation.

5.2 Risk Aversion

Uniqueness of solution of firm’s problem ensures that aggregate sales across affiliates are awell-defined function of risk aversion. Therefore, we match theoretical sales, predicted byour structural model, with aggregate MNE sales, observed in the data42. We do not restrictrisk aversion to be positive. For each firm, the matching proceeds as follows:

1. Guess risk aversion parameter r(ω).

2. Given the location set L(ω) observed in the data, solve firm’s utility maximizationproblem.

3. Obtain q(ω), and compute implied aggregate theoretical sales∑d∈D

pd(ω)qd(ω).

4. Update r(ω) if distance between theoretical and empirical sales larger than the toler-ance level.43

It is important to note that updating of r(ω) is based on the characteristics of the solution tothe utility maximization problem. Everything else equal, firm’s aggregate sales are strictlydecreasing in risk aversion (see Figure 11). Therefore, we can use a standard bisectionmethod.

Proposition 3. (Risk Aversion and Aggregate Sales). If the solution to the utility maxi-mization problem is interior, then firm’s aggregate sales are decreasing with risk aversion.

Proof. See Appendix D.

42Note that we do not observe expected sales in the data. However, sales to each destination are decreasingwith the level of risk aversion. This together with uniqueness of the solution allows us to match empiricalsales.

43We assume convergence when the absolute difference between empirical and theoretical sales is less than0.01%.

34

Figure 11: Firm Level Dependence of Aggregate Sales from Risk Aversion Parameter

Risk aversion

Firm

sales

Risk Aversion and Firm Sales

Since the risk aversion coefficient enters through the co-variance of demands, we need tohave enough variation in α-parameters as well as in covariances of demands across markets topin down risk aversion. In this regard, Figure 4 shows that the distribution of correlations isdisperse. Moreover, firms’ sales and productivities across affiliates vary a lot, which reflectsthe sensitivity of sales to location-specific parameters (see Figure 9).

5.3 Entry Costs

Equation (4) describes the location decision problem. Each potential set of locations L ∈L generates the corresponding value V (L), for which a multinational needs to pay fixedcosts as sum of all entry costs to countries in set L. Therefore, we face a high-dimensionalcombinatorial problem. To solve it we proceed as follows. First, we estimate the risk aversionparameter from the optimal set of locations a firm selected, which we observe in the data.Using this estimate, we can compute the value of each possible location set the firm did notoptimally select. The choice of location is determined at this stage by the magnitude of fixedcosts of entry.44 Following Tintelnot (2016), we assume that fixed costs follow a log-normaldistribution, N (µf,reg, σf,reg). We define distribution parameters to be region-reg specific,where regions are defined by geographical criteria as in the World Investment Report 2008.For the identification of the relevant parameters, we need to observe for each region entryand non-entry cases. Our data satisfy this requirement. Each firm gets a random draw offixed costs from the corresponding distribution, which is assumed to be independent across

44Observing both location choice and sales allows us to estimate separately risk aversion and fixed costs.

35

regions and countries. We construct the maximum likelihood function L

logL(f) =

∫ω∈Ω

∫1V (L(ω)|f) ≥ V (L′(ω)|f) ∀L′(ω) ∈ LdH(f ;µf,reg, σf,reg).

We assume that a firm can only select a location set with cardinality at most double thecardinality of the largest set observed in the industry. In the absence of nested location sets,we believe that this assumption is reasonable, and good enough at easing the computationalburden.

6 Results

We perform estimation of risk aversion coefficients for 1099 MNEs in the sample in 2007.45

Figure 12 shows the distribution of the estimates of the risk aversion coefficients. Weobserve that estimated risk aversion coefficients are positive for all firms in the sample. Themajority of MNEs display risk aversion coefficients ranging between 0 and 1. In particular,the average risk aversion coefficient in the sample is 0.34 with a standard deviation equal to1.16.

45For data confidentiality, we show results only for 952 firms in the descriptive statistics of risk aversion.Other results are used in the estimation of sales responses to changes in risk aversion.

36

Figure 12: Estimated density of risk aversion

Mean SD p10 p25 p50 p75 p90 N

Risk aversion 0.34 1.16 0.01 0.04 0.11 0.31 0.72 952

Note: Outliers are removed.Source: Research Data and Service Centre (RDSC) of the Deutsche Bundes-bank, Microdatabase Direct investment (MiDi), 1999-2014, authors’ calculations.

Table 5 shows that coefficients of risk aversion greatly differ across industries. The averagerisk aversion ranges from 0.10 in paper manufacturing sector to 1.39 in the manufacturingof basic metals sector.

Table 5: Risk aversion across industries

More risk averseindustries

Risk aversion Less risk averseindustries

Risk aversionAverage SD N Average SD N

Basic metals 1.39 4.98 34 Textile 0.20 0.19 20

Medical 0.79 0.93 68 Printing 0.18 0.30 26

Metal products 0.55 0.66 91 Machinery n.e.c. 0.18 0.92 196

Furniture 0.54 0.71 14 Wearing and leather 0.17 0.16 13

Electrical 0.35 0.49 75 Chemicals 0.14 0.42 90

Food and tobacco 0.34 0.70 44 Other transport 0.14 0.18 18

Plastic 0.31 0.33 93 Wood 0.13 0.14 7

Auto 0.25 0.78 73 Minerals 0.13 0.15 41

Communication 0.24 0.25 31 Paper 0.10 0.09 18

Source: Research Data and Service Centre (RDSC) of the Deutsche Bundesbank, Micro-database Direct investment (MiDi), 1999-2014, authors’ calculations.

37

Heterogeneity in risk aversion can be explained by several factors related to industry char-acteristics. In particular, volatility of demand in the industry seems to play an importantrole. Figure 13 displays the spread of coefficient of variation in each industry given countriesin our sample. On average, larger risk aversion coefficients occur in industries with larger me-dian coefficient of variation (basic metals, medical, electrical). In highly volatile industries,firms are indeed more exposed to demand shocks. Therefore, one expects managers operat-ing in these industries to consider demand risk as a more relevant factor than in low volatileindustries. In terms of our model, this implies a larger level of risk aversion. Interestingly,risk aversion is poorly correlated with average industry size and sales of affiliates. Thus, es-timated risk aversions is mainly connected to industry-specific demand characteristics ratherthan to technological variables.

Figure 13: Distribution of coefficient of variation of demand, product level

0 .2 .4 .6 .8

Coefficient of demand variation

Basic metalsOther Transport

MedicalElectrical

CommunicationOffice

Metal productsMachinery n.e.c.

MineralsFurniture

AutoWood

LeatherPlastic

ChemicalsPrinting

Wearing apparelPaperFood

Textile

Source: UNIDO INDSTAT2 2016, authors’ calculations.

Next, we evaluate the relation between risk aversion and firm-specific characteristics. InTable 6, we present the results of the regression of the estimated risk aversion coefficients ona set of firm’s characteristics. First, we find no significant correlation of risk aversion withproductivity. This observation is important, as we estimate productivities outside the model.Therefore, our measure of firm’s productivity abstracts from the effect of risk aversion effect

38

on sales. Second, we find that risk aversion negatively correlates with firm size. Third, wefind a negative correlation between firm’s age and risk aversion. Our interpretation is thatlarger or more experienced firms are more prone to deal with market risk. Finally, a morerisk averse firm tends to show a more diversified structure of sales. This finding suggeststhat, when they are more concerned about market turmoil, firms take advantage of possiblediversification opportunities more extensively. Moreover, the negative correlation betweenthe concentration measure and risk aversion46 is suggestive that the estimated risk aversioncaptures firm’s attitude toward demand risk.

Table 6: Risk aversion and firm characteristics

I II III

productivity −0.0658

(0.0583)

0.0223

(0.1368)

−0.0829

(0.0589)

size −2.0699∗∗∗

(0.0795)

-1.9597∗∗∗

(0.0801)

−1.9176∗∗∗

(0.0796)

age −0.0819∗∗

(0.0399)

−0.1330∗∗∗

(0.0206)

productivity*age −0.0364

(0.0281)

concentration −0.6905∗∗∗

(0.1429)

constant −1.3460∗∗∗

(0.1922)

0.9009∗∗∗

(0.2697)

−0.5058∗∗

(0.2181)

industry fixed effects Yes Yes YesN 952 952 952

Note: We consider productivity of parent German firm. Risk aversionand productivity are taken in logs. Size is equal to 1 for MNEs withmore than 1000 employees. Concentration is measured according to thecoefficient described in Section 2.Source: Research Data and Service Centre (RDSC) of the Deutsche Bun-desbank, Microdatabase Direct investment (MiDi), 1999-2014, authors’calculations.

We test the theoretical prediction that aggregate MNE sales and risk aversion are negativerelated. Table 11 in Appendix F shows the negative correlation between total group sales

46Note that this result is still valid when we consider other measure of concentration, like the Herfindalindex.

39

and risk aversion, while controlling for firm productivity and number of foreign locations.In addition, we find a positive correlation between share of debt in firms capital and level of

risk aversion.47 The intuition for this finding relates to the fact that financially constrainedfirms are more risk averse when they compose their sales portfolio.To assess the goodness of fit of our model to the real data, we compare the predicted

trade flows with real data across different regions. Table 7 shows that the model predictsaccurately trade flows in most regions. The underprediction of sales in North Americaand overprediction of sales in Asia and Oceania can be partly explained by the fact thattrade costs are estimated outside the model. We believe that estimation procedures of tradecosts, considering more closely multinational trade flows characteristics, would improve theseresults.48

Table 7: Regional trade flows of German multinationals (percentage shares)

Regions Data Model N

Africa 1.1% 1.8% 47

Asia & Oceania 3.4% 10.9% 241

Europe 86.2% 82.2% 896

North America 7.3% 3.1% 205

South America 2.1% 1.9% 69

Source: Research Data and Service Centre(RDSC) of the Deutsche Bundesbank, Mi-crodatabase Direct investment (MiDi), 1999-2014, authors’ calculations.

Next, we estimate a proxy for the elasticity of MNE sales to the level of risk aversion. Wefind that a change of 1% in risk aversion produces a change of sales approximately equal to−0.8%.

47See Table 12 in Appendix F.48One of the possible alternatives is to estimate a gravity equation that takes into account trade flows in

third countries.

40

Table 8: Sales response to exogenous change in risk aversion

Change in risk aversion Mean25th

percentile50th

percentile75th

percentile5% increase −4.13% −4.40% −4.08% −3.79%1% increase −0.85% −0.92% −0.85% −0.78%1% decrease 0.85% 0.79% 0.87% 0.93%

5% decrease 4.46% 4.12% 4.51% 4.82%

Source: Research Data and Service Centre (RDSC) of the Deutsche Bundesbank,Microdatabase Direct investment (MiDi), 1999-2014, authors’ calculations.

We conduct an analogous exercise to measure sensitivity of countries’ trade flows to changesin risk aversion. Figure 14 depicts the increase in sales of German multinationals to countriesin response to a 1% decrease of risk aversion in the sample. Trade flows to all countriesincrease in absolute terms, which is in line with the result obtained in simplified setting inSection 3.3. Moreover, the magnitude of response is negatively correlated with the riskinessof the country. Safer markets gain more from the decrease in risk aversion, while morevolatile economies still remain less attractive and attract relatively lower trade flows. At thesame time, changes in risk aversion affect to a larger extent countries whose economies arestrongly co-moving with German economy. We observe that many developing economies areless sensitive to changes in risk aversion, which is again in line with the intuition providedin the comparative statics exercise: as risk aversion increases, multinationals are less proneto concentrate sales in similar countries and increase relative sales shares in less correlatedcountries.

41

Figure 14: Sales response to exogenous increase in risk aversion, country level

JPN

FRA

CHL

USAMEX

PRT

CHE

GBR

AUS

ITA

DEU

CANMLT

GRC

ZAF

AUT

NLDHUN

HKGMYS

LUX

ESPIRLSVN

DNK

SWE

FIN

BEL

KORPER

SGP

IDN

NORTURCZE

POL

COL

IND

BRA

TUNBGR

CHN

ROU

SVK UKR RUS

0.5

11.

52

Res

pons

e of

cou

ntry

sal

es

.7 .75 .8 .85 .9

Coefficient of variation of demand

Source: Research Data and Service Centre (RDSC) of the Deutsche Bundesbank, Microdatabase Directinvestment (MiDi), 1999-2014, authors’ calculations.

7 Conclusions

In this paper we develop and structurally estimate a model of risk averse multinationalfirms serving foreign markets through export platforms in a framework where the final levelof demand is uncertain. Our analysis based on German multinational companies providesfindings which are consistent with the existence of geographical diversification in the strategyof multinational enterprises. In particular, firms in our sample display a strictly positive valueof risk aversion.Results show that firms are heterogeneous in terms of risk attitudes. This heterogene-

ity can be explained by the firm’s characteristics, as well as industry it operates in. Inparticular,industry-level demand volatility capture part of the variation in risk aversion pa-rameter.We find that sales are sensitive to risk aversion with the elasticity 0.82. Moreover, we

observe that response to the changes in risk aversion varies across countries, being higher forless volatile and more coherent economies.

42

Our framework can be also used to explain implications of liberalization and change ineconomic environment in the presence of demand complementaries. In particular, our modelrationalizes the presence of spillover effects of bilateral liberalization at the regional level.We also find that firms’ location choice does not need to preserve a hierarchical ordering

in neither productivity nor risk aversion.

43

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47

A Existence and Uniqueness

Proposition 1. (Existence and Uniqueness). If matrix Σ has cross-correlations boundedaway from −1 and 1, there exists a unique solution to the manager’s utility maximizationproblem. Furthermore, this solution is characterized by the Kuhn-Tucker optimality condi-tions.

Proof. Before delving into the proof of Proposition 1, we show an auxiliary lemma whichturns out to be useful for the following discussion.

Lemma 1. Let (P1) denote the following problem

maxq∈RN+

u(Π(q(ω)|L(ω),ϕ(ω), r(ω))) =∑d

(qd(ω)

σd−1

σd

(E[Ad]− cd(ω)qd(ω)

1σd

))− r(ω)

2

∑d

∑d′

cov(Ad, A′d)qd(ω)

σd−1

σd qd′(ω)σ′d−1

σ′d

Define sd(ω) = f(qd(ω);σd) := qd(ω)σd−1

σd . Then, the problem (P2) defined as

maxs∈RN+

u(Π(s(ω)|L(ω),ϕ(ω), r(ω))) =∑d

(sd(ω)

(E[Ad]− cd(ω)sd(ω)

1σd−1

))− r(ω)

2

∑d

∑d′

cov(Ad, A′d)sd(ω)sd′(ω).

is equivalent to (P1), i.e. qld(ω) is a solution for (P1) if and only if sld(ω) is a solution for(P2).

Proof. First, note that for qd(ω) ≥ 0 the function f(·) is a bijection. Consider the problems(P1) and (P2). If sd(ω) = qd(ω) = 0, then the statement follows. Assume that qd(ω), sd(ω) >

0. Then, for each d, first order conditions for (P1) and (P2) are given by

∂u(·)∂qd(ω)

=σd − 1

σdE[Ad]qd(ω)

− 1σd−r(ω)

(σd − 1

σdqd(ω)

− 1σd

∑d′

cov(Ad, A′d)qd′(ω)

σd−1

σd

)−cd(ω) = 0,

(6)and

∂u(·)∂sd(ω)

= E[Ad]− r(ω)∑d′

cov(Ad, A′d)sd′(ω)− σd

σd − 1cd(ω)sd(ω)

1σd−1 = 0. (7)

48

respectively. Then, using the definition of sd(ω), we can write (7) as where the last equiva-lence follows from the fact that qd(ω) > 0. So, if qd(ω) solves (6), then sd(ω) solves (7), andvice versa. This shows that problems (P1) and (P2) are equivalent given the definition ofsd(ω), and admit the same solution, provided this solution exists.

Next, we consider the problem (P2). We show that the solution exists and is unique. Then,using Lemma 1, we can extend this result to the original problem (P1).Existence: To show existence, we use the definition of coercive function. A continuous

function f is coercive iflim

‖s(ω)‖→∞f(s(ω)) = +∞.

Note that u(·) can be written as the sum of the expected profits and the variance of profitsmultiplied by a scalar r(ω). These functions, taken with negative sign, are both coercive.49

Moreover, the sum of coercive functions is coercive. We can then apply Proposition 2.1.1 inBertsekas et al. (2003) to conclude the existence of a solution to the utility maximizationproblem.50

Uniqueness: We show that the utility function is strictly concave in sd(ω) = qd(ω)σd−1

σd .Let Hu denote the Hessian matrix associated to the manager’s utility.Note that any element of the main diagonal is given by

Hu(d, d) =∂2u(Π(s(ω)|L(ω), ϕ(ω), r(ω)))

∂sd(ω)2= − σd

(σd − 1)2cd(ω)sd(ω)

2−σdσd−1 − r(ω)var(Ad) < 0.

Moreover, the element outside the main diagonal can be written as

Hu(d, d′) =

∂2u(Π(s(ω)|L(ω), ϕ(ω), r(ω)))

∂sd(ω)2= −r(ω)cov(Ad, Ad′).

LetD ≡ diag

(σd

(σd − 1)2cd(ω)sd(ω)

2−σdσd−1

d

).

49Note that expected profit function is the sum of the profit realized in each destination d, which isa continuous and concave function of sd(ω) admitting a unique global maximizer, (i.e. the solution underno risk aversion/risk). Hence, the expected profit function is coercive when taken with the negative sign.Recall that cross-correlations are bounded away from 1. Hence, the variance of profits is coercive, being acontinuous and convex function of (sd(ω)(ω))d with a minimum.

50Indeed, maximizing a function is equivalent to minimizing its opposite.

49

Thus, the Hessian Hu can be written as

Hu = −(D + r(ω)ΣA).

Then, we note that matrix D is positive definite being a diagonal matrix with all diagonalelements positive. Moreover, r(ω)ΣA is positive definite being the product of a positivescalar with a positive definite matrix. Hence, D + r(ω)ΣA is positive definite being the sumof two positive definite matrices51 implying that Hu is negative definite.Necessity and Sufficient of Kuhn-Tucker Optimality Conditions: We note that

constraint qualification holds at any solution since the set of binding constraints is a subsetof the canonical basis of RN . Sufficiency follows from linearity of the constraint functionsand concavity of objective function.Existence and uniqueness of the solution for P1: A unique solution to P2 ex-

ists. Moreover, Kuhn-Tucker Optimality Conditions are both sufficient and necessary forP2. Then, from Lemma 1, the solution to P1 exists, is unique, and satisfies Kuhn-Tuckeroptimality conditions.

B Risk Aversion Measure

Proposition 2. (Risk aversion measure). The measure of risk aversion is a function ofthe optimal production portfolio, and is equal to

r(ω) =

∑d (Epd(ω)qd(ω)− pd(ω)qd(ω))(q(ω)

σ−1σ

)′ΣAq(ω)

σ−1σ

,

where Epd(ω) is the expected price, pd(ω) is the price under certainty, and q(ω)σ−1σ is a

vector in which each component is the optimal quantity sold in country d to the power of(σd − 1)/σd.

Proof. Let sd(ω) = qd(ω)σid−1

σid .

51See Horn and Johnson (2012).

50

Kuhn-Tucker optimality conditions order with respect to sd(ω) are

∂u(Π(s(ω)|L(ω), ϕ(ω)))

∂sd(ω)=∂E(Π(s(ω)|L(ω), ϕ(ω)))

∂sd(ω)− r(ω)

2

∂var(Π(s(ω)|L(ω), ϕ(ω)))

∂sd(ω)

= EAd −σd

σd − 1cd(ω)sd(ω)

1σd−1 − r(ω)var(Ad)sd(ω)

− r(ω)∑d′∈D

cov(Ad, Ad′)sd′(ω) + µd = 0

EAd −σd

σd − 1cd(ω)sd(ω)

1σd−1 − r(ω)

∑d

cov(Ad, Ad′)sd(ω) + µd = 0 (8)

where µd is the multiplier associated to the non-negativity constraint relative to sd(ω).We note that µd = 0 if sd(ω) > 0. Hence, multiplying both sides of equation (8) by sd(ω),

and summing over d the risk aversion coefficient r can be expressed as follows

r(ω) =

∑d

[EAdsd(ω)− σd

σd−1cd(ω)sd(ω)

σdσd−1

]∑d

∑d′

cov(Ad, Ad′)sd(ω)sd′(ω)=

(Epd(ω)qd(ω)− pd(ω)qd(ω))(q(ω)

σ−1σ

)′Σq(ω)

σ−1σ

≡ SP

SV, (9)

where pd(ω) = σdσd−1

cd(ω) is the price firm ω would set under certainty, SP is the salespremium, and SV is the variance of sales sales variance.

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C Small-Medium and Large Multinationals

Table 9: Descriptive statistics on foreign affiliates and parents of small-medium MNEs bycountry

Countries Totalsales

Sales affiliate Sales MNE Employment NAverage Median Average Median Average Median

United States 2.4 24 14 121 86 428 388 100France 1.6 23 17 116 86 410 372 69Poland 1.3 18 14 111 81 468 474 76Austria 1.3 30 16 124 103 462 411 43Belgium 1.3 84 32 371 148 563 559 15Czech Republic 1.1 16 13 107 83 523 491 70China 1.0 15 9 118 85 538 527 71United Kingdom 1.0 20 13 151 115 501 460 49Italy 0.9 34 20 179 116 420 447 27Switzerland 0.7 19 13 103 84 366 352 37Germany 55.0 90 60 118 83 445 417 612

Note: Total sales are expressed in billion Euro. Sales of affiliate and MNE are expressed in millionEuro. In this table we consider subsample of multinationals with less then 1000 employees.Source: Research Data and Service Centre (RDSC) of the Deutsche Bundesbank, MicrodatabaseDirect investment (MiDi), 1999-2014, authors’ calculations.

Table 10: Descriptive statistics on foreign affiliates and parents of large MNEs by country

Countries Totalsales

Sales affiliate Sales MNE Employment NAverage Median Average Median Average Median

United States 45.1 531 73 3683 716 9286 2905 85Spain 21.7 362 43 6438 848 17396 3117 60Brazil 16.5 275 41 5443 982 15390 4010 60France 15.3 167 63 4328 822 11370 2954 92United Kingdom 14.5 219 48 7120 1310 18397 3840 66Chezh Republic 12.8 199 40 4654 508 13290 2670 64China 9.7 89 23 3218 685 10002 2809 110Hungary 9.0 196 46 3204 718 10861 2755 46Mexico 8.9 255 30 9602 912 24363 4081 35Japan 8.6 346 109 7653 824 17767 3891 25Germany 522.1 1454 344 2161 474 6158 2152 359

Note: Total sales are expressed in billion Euro. Sales of affiliate and MNE are expressed in millionEuro. In this table we consider subsample of multinationals with more then 1000 employees.Source: Research Data and Service Centre (RDSC) of the Deutsche Bundesbank, MicrodatabaseDirect investment (MiDi), 1999-2014, authors’ calculations.

52

D Risk aversion and Aggregate Sales

Proposition 4. (Risk Aversion and Aggregate Sales). If the solution to the utility maxi-mization problem is interior, then firm’s aggregate sales are decreasing with risk aversion.

Proof. Suppose the solution to the utility maximization problem is interior. Then the systemof first-order necessary and sufficient conditions reads as

EAd −σd

σd − 1cd(ω)sd(ω)

1σd−1 − r(ω)

∑d′

cov(Ad, Ad′)sd′(ω) = 0, ∀d ∈ D.

Differentiating both sides with respect to r we obtain

− σd(σd − 1)2

cd(ω)sd(ω)1

σd−1−1sd(ω)−

∑d′

cov(Ad, Ad′)sd′(ω)−r(ω)∑d′

cov(Ad, Ad′)sd′(ω) = 0, ∀d ∈ D.

where sd(ω) ≡ ∂sd(ω)∂r(ω)

for all d ∈ D. Hence, ∀d ∈ D

σdσd − 1

cd(ω)sd(ω)1

σd−1−1sd(ω) = −(σd−1)

(∑d′

cov(Ad, Ad′)sd′(ω) + r(ω)∑d′

cov(Ad, Ad′)sd′(ω)

).

(10)Again, using FOC we observe that

σdσd − 1

cd(ω)sd(ω)1

σd−1 = EAd − r(ω)∑d′

cov(Ad, Ad′)sd′(ω), ∀d ∈ D. (11)

Combining equation (10) and (11) we obtain(EAd − r(ω)

∑d′

cov(Ad, Ad′)sd′(ω)

)sd(ω)

= −(σd − 1)

(∑d′

cov(Ad, Ad′)sd′(ω) + r(ω)∑d′

cov(Ad, Ad′)sd′(ω)

)

for all d, which implies

EAdsd(ω) = −(σd − 1)

(∑d′

cov(Ad, Ad′)sd′(ω) + r(ω)∑d′

cov(Ad, Ad′)sd′(ω)

)+r(ω)

∑d′

cov(Ad, Ad′)sd′(ω)sd(ω).

53

Summing both sides over d we obtain

∑d

EAdsd(ω) = −(σd − 1)

(∑d

∑d′

cov(Ad, Ad′)sd′(ω) + r(ω)∑d

∑d′

cov(Ad, Ad′)sd′(ω)

)+r(ω)

∑d

∑d′

cov(Ad, Ad′)sd′(ω)sd(ω).

(12)

where the left hand side is the derivative of the aggregate sales with respect to r. We wantto show that this derivative is negative.Let’s consider the term in the brackets. Recall that

− σdσd − 1

cd(ω)sd(ω)1

σd−1−1sd(ω) =

∑d′

cov(Ad, Ad′)sd′(ω) + r(ω)∑d′

cov(Ad, Ad′)sd′(ω).

Multiplying both sides by sd(ω), we obtain

− σdσd − 1

cd(ω)sd(ω)1

σd−1−1

(sd(ω))2 =∑d′

cov(Ad, Ad′)sd′(ω)sd(ω)+r(ω)∑d′

cov(Ad, Ad′)sd′(ω)sd(ω).

Summing over d and re-arranging, we obtain∑d

∑d′

cov(Ad, Ad′)sd′(ω)sd(ω) = −r(ω)∑d

∑d′

cov(Ad, Ad′)sd′(ω)sd(ω)

−∑d

σdσd − 1

cd(ω)sd(ω)1

σd−1−1

(sd(ω))2.(13)

We note that the left hand side of the above expression has to be negative since the righthand side is the sum of two negative terms, i.e.∑

d

∑d′

cov(Ad, Ad′)sd′(ω)sd(ω) < 0. (14)

Incidentally we also notice that

r(ω)∑d

∑d′

cov(Ad, Ad′)sd(ω)sd′(ω) +∑d

∑d′

cov(Ad, Ad′)sd′(ω)sd(ω) < 0. (15)

54

Finally, note that var(A′s(ω) + r(ω)A′s(ω)) can be written as∑d

∑d′

cov(Ad, Ad′)sd(ω)sd′(ω) + 2r(ω)∑d

∑d′

cov(Ad, Ad′)sd′(ω)sd(ω)

+r(ω)2∑d

∑d′

cov(Ad, Ad′)sd′(ω)sd(ω) =∑d

∑d′

cov(Ad, Ad′)sd(ω)sd′(ω) + r(ω)∑d

∑d′

cov(Ad, Ad′)sd′(ω)sd(ω)

+r(ω)

(r(ω)

∑d

∑d′

cov(Ad, Ad′)sd′(ω)sd(ω) + r(ω)∑d

∑d′

cov(Ad, Ad′)sd′(ω)sd(ω)

)> 0

(16)

From equation (15) we notice that the term in the brackets is negative. Hence, the sumoutside the brackets has to be positive since the variance is a positive number, i.e.∑

d

∑d′

cov(Ad, Ad′)sd(ω)sd′(ω) + r(ω)∑d

∑d′

cov(Ad, Ad′)sd′(ω)sd(ω) > 0. (17)

Hence, considering equations (12), (13) and (16), we conclude that aggregate sales aredecreasing in r(ω).

E Liberalization

Proposition 5. Unilateral liberalization in destination country increases sales to it.

Proof. Define Yd(ω) ≡∑d′

cov(Ad, Ad′)sd′(ω) and denote with dot derivative w.r.t. τd.

Then,

−σd

(σd−1)2cd(ω)sd(ω)

2−σdσd−1 sd(ω)− r(ω)Yd(ω) = σd

σd−1sd(ω)

1σ−1 cd(ω)

− σd′(σd′−1)2

cd′(ω)sd′(ω)2−σd′σd′−1 sd′(ω)− r(ω)Yd′(ω) = 0 for d′ 6= d.

Sum over d and premultiply by sd(ω)

∑d′

σd′

(σd′ − 1)2cd′(ω)sd′(ω)

2−σd′σd′−1 sd′(ω)2 + r

∑d′

Yd′ sd′(ω) = − σdσd − 1

sd(ω)1

σ−1 sd(ω).

Therefore, sd(ω) = dsd(ω)dτd

< 0.

55

F Firm Characteristics and Risk Aversion

Table 11: Aggregate sales and risk aversion

Dependent variable: total group sales Coefficient SErisk aversion −0.5835∗∗∗ 0.0133

productivity 0.6740∗∗∗ 0.0283

number of affiliates 0.1478∗∗∗ 0.0083

constant 2.7747∗∗∗ 0.0954

industry fixed effects Yes YesN 952

Source: Research Data and Service Centre (RDSC) of the Deutsche Bun-desbank, Microdatabase Direct investment (MiDi), 1999-2014, authors’calculations.

Table 12: Gearing and risk aversion

Dependent variable: gearing Coefficient SErisk aversion 17.5022∗∗ 8.5526

size −21.2136 31.0504

size*risk aversion −13.0365 10.4800

age −4.4616 3.8717

constant 248.1135 37.3606

industry fixed effects Yes YesN 393Source: Research Data and Service Centre (RDSC) ofthe Deutsche Bundesbank, Microdatabase Direct investment(MiDi), 1999-2014, authors’ calculations.

56