Grossman–Hart–Moore Goes to Italy: Rethinking the Boundaries of the Firm

This paper provides new empirical evidence on the boundaries of the firm, as shaped by the ownership (make-or-buy) and location (domestic-or-foreign) decisions of sourcing. In particular, we draw on the Grossman–Hart–Moore framework to investigate the role of input characteristics, investment spillovers and firm productivity in ownership and location decisions. For the purpose of the empirical analysis, we rely on original survey data of a stratified sample of Italian manufacturing firms, headquartered in Lombardy. Our probit, multinomial probit and conditional mixed process estimations suggest a number of robust regularities. Some of them confirm so far unexplored theoretical predictions from the Grossman–Hart–Moore framework; others provide new insights on specific relationships on which the theory is silent. As for ownership, we find that reliance on specific inputs and intangible inputs fosters integration over non-integration; moreover, firms acknowledging cross spillover effects are more likely to opt for joint-venture than non-integration. As for location, domestic sourcing prevails over foreign sourcing in presence of investment spillovers, whereas input characteristics play no role. Lastly, productivity is a major driver of the boundaries of the firm in that productive firms are more likely to source abroad than domestically. Holding across different econometric models and a number of robustness checks, our results contribute to the property rights theory of the firm and its recent developments.


Introduction
The increasing fragmentation of production across firms and countries' boundaries is unanimously considered the distinctive feature of the world economy over the last four decades (Antras 2020).Trade liberalisation and falling transportation costs, alongside rapid advances in information and communication technologies (ICT), are recognised as the driving forces behind it (Baldwin and Venables 2013;Alfaro et al. 2019;Antras and de Gortari 2020).
Still, recent events and emerging trends in the global economy have started to question the long-term prospects of 'global value chains' (GVCs).In light of the large research and development (R&D) expenditure required to keep pace with innovation, some slowdown in the adoption of ever more performing ICT can be expected (Antras 2020).Furthermore, the COVID-19 pandemic, the invasion of Ukraine by Russia and the technology war between US and China have exposed GVCs' vulnerability to international crises, eventually calling for a medium-run re-engineering of the boundaries of the firm (Javorcik 2020).
In our terminology, studying the boundaries of the firm means discussing which production tasks should be internalised and which should be externalised, either in the domestic or in a foreign country.For the sake of simplicity, consider a stylised framework in which production of a final good requires intermediate inputs.In this context, the final good producer takes two crucial decisions over sourcing.On one hand, it has to decide whether to manufacture the inputs by itself or to buy them from an independent input supplier.On the other hand, it has to decide whether to employ domestic or foreign components.We refer to the final good producer's makeor-buy choice as the ownership decision, and to the domestic-or-foreign choice as the location decision.In this simple framework, studying the boundaries of the firm means addressing sourcing issues, as shaped by ownership and location considerations.
Since GVCs entail fragmentation of production across firms and countries, to fully evaluate their medium and long-term prospects one needs to assess how the boundaries of the firm respond to changes in the global economy.To this aim, we empirically investigate determinants of the ownership and location decisions using original survey data of a representative sample of Italian manufacturing firms headquartered in Lombardy, one of the most industrialised European regions.Taking advantage of our rich database, we provide new evidence on so far unexplored determinants of ownership and location choices.
We rely on the property rights theory of the firm (PRT) as from the seminal contributions of Grossman and Hart (1986), Hart and Moore (1990) and Hart (1995)-henceforth referred to as the Grossman-Hart-Moore (GHM) framework-and its most recent developments,1 to model ownership and location decisions.More specifically, we consider three ownership regimes-integration, nonintegration2 and joint-venture-and two possible locations-domestic and foreign.
Accordingly, our estimates rely on the probit, multinomial probit and conditional mixed process models.
From a theoretical point of view, we expect input characteristics to affect the ownership decision when integration is compared with non-integration (Antras and Helpman 2004).From an empirical point of view, we confirm that reliance on specific inputs and intangible inputs is a major driver of the make-or-buy decision.In our sample, firms employing specific inputs and intangible inputs prefer integration over non-integration; however, input characteristics neither affect the comparison between joint-venture and non-integration nor the location decision of Italian firms.Theoretically unexplored in the GHM framework, these findings are original of the present study.
A distinctive feature of GVCs is the continuous exchange of information about production activities as well as market conditions between the trading partners (Antras and Chor 2022).In an incomplete contract environment, such information flows are likely to translate into investment spillovers. 3Based on recent developments of the PRT (Gattai and Natale 2016), we expect cross spillovers to be positive and statistically significant in explaining the ownership decision, when joint-venture is compared with non-integration.We report consistent evidence with our data.Moreover, we find that cross spillovers favour integration over non-integration-although this effect is much weaker than in the joint-venture/non-integration comparison-and the location choice, with domestic sourcing being favoured against foreign sourcing.These results are a novel contribution of the present analysis since no theoretical clue was available from the GHM framework on these matters.
Finally, we document a role for firm productivity in the domestic-or-foreign decision because productive firms are more likely to source abroad than domestically.This finding, consistent with the theory (Antras and Helpman 2004), confirms previous evidence on related issues (De Ponti and Gattai 2022;Bernasconi et al. 2022).
At this stage, it is worth mentioning that all the above results hold across different econometric models and a number of robustness checks.
To summarise, we believe that our contribution to the literature is twofold.On one hand, detailed survey data on input characteristics and investment spillovers allow us providing new evidence on the predictions of the PRT.Most of these predictions have so far remained unexplored due to the lack of suitable firm-level data.On the other hand, we document robust regularities on which the PRT is silent and thus deserve further investigation and may open new developments in the GHM framework.
The rest of the paper is organised as follows.Section 2 reviews the literature inspiring our conceptual framework.Section 3 describes the data.Section 4 presents our empirical methodology and results.Section 5 concludes and suggests future lines of research.

Literature Review
The boundaries of the firm have been studied quite extensively in the last two decades, from a variety of perspectives (for a survey, see Kano et al. 2020).Our conceptual framework grounds on the Contract Theory approach.In this field, a number of competing paradigms on the ownership decision have been developed to predict the boundaries of the firm (for a survey, see Gibbons 2005).Among these, the PRT has become particularly influential.Developed by Grossman, Hart and Moore in a series of seminal papers (Grossman and Hart 1986;Hart and Moore 1990;Hart 1995), the PRT casts the make-or-buy choice in terms of asset ownership.
In what follows, we describe the GHM framework (Sect.2.1) and comment on recent developments that go beyond GHM either to model the location decision (Sect.2.2) or to elaborate on the ownership decision (Sect.2.3).

The Grossman-Hart-Moore Framework
Following Hart (1995), consider two firms-a final good producer (FP) and an input supplier (IS)-and two physical assets-a 1 and a 2 , the former needed for final good production and the latter for input supply.Before production starts, FP and IS can undertake some investment in human capital that enlarges the surplus the parties generate when trading together more than it increases the value of the parties' outside option.In the PRT jargon, investments are relation-specific, i.e. they pay off more inside than outside the FP-IS relationship.
FP and IS would benefit from writing an enforceable contract over the division of the surplus and the amount of investment in human capital each party should undertake.However, it is a tenet of the legal profession (Schwartz 1992) that trading parties may fail to specify such a 'complete' contract. 4It amounts to say that contracts tend to be 'incomplete'.As such, they turn out to be vague or silent on a number of key features (Tirole 1999) and have gaps, missing provisions or ambiguities (Salaniè 1997).
Still, parties can allocate property rights over assets, giving rise to four possible ownership regimes: non-integration (FP owns a 1 , and IS owns a 2 ), FP-integration (FP owns a 1 and a 2 ), IS-integration (IS owns a 1 and a 2 ) and joint control (both FP and IS have a veto power over the use of a 1 and a 2 ).We can think of FP-integration and IS-integration as backward and forward integration, respectively.In what follows, we drop the distinction between backward and forward and refer to either regime as integration.
If exchanges could be fully regulated by contracts, property rights would be irrelevant.When contracts are instead incomplete, the allocation of property rights matters because it confers residual control rights, i.e. the rights to decide whenever an unforeseen contingency, uncovered by the contract, occurs.Thus, in the GHM framework, the allocation of property rights defines the boundaries of the firm.
In particular, the choice of the ownership regime has efficiency implications because the marginal return of the investment in human capital by party i depends on the number of assets that party has access to.More specifically, it is increasing in the number of assets it controls as the latter affects the value of its outside option.Put another way, relation-specificity applies also in a marginal sense.Suppose parties fail to achieve an agreement on the division of the surplus.The party in control of the assets can exclude the non-controlling party from the usage of the assets and employ them to pursue its outside option.This increases the controlling party's bargaining position in the division of the surplus from trade, in turn depriving the non-controlling party of the return from the investment in human capital and reducing its incentive to invest.In a sense, relation-specific investments bound the parties together, preventing them from easily switching to alternative partners in case of disagreement.The combination of contract incompleteness and relation-specific investments produces underinvestment because parties fear to be held-up.Affecting the parties' incentive to invest, the allocation of property rights determines the total surplus from trade.
As the most notable finding, non-integration is the optimal ownership regime when assets are independent.In this case, each party's investment is equally important in the generation of surplus.On the other hand, integration is optimal when assets are complementary.In this case, one party's investment is more important than the other party's investment in the generation of the surplus. 5In light of the above, joint control cannot do better than integration as it reduces the controlling party's incentive to invest without increasing the non-controlling party's incentive to invest.Likewise, joint control cannot outperform non-integration as it reduces both parties' incentive to invest.Therefore, joint control is never optimal in the GHM framework.

Beyond Grossman-Hart-Moore: from Local to Global Sourcing
A major limitation of the PRT in its original formulation is that it does not consider the international dimension of sourcing.In the 1990s, when sourcing was a local phenomenon, the PRT settled the debate about the boundaries of the firm.
However, globalisation has become an issue nowadays and sourcing can no longer be considered local.As a global phenomenon, it is governed by the interplay between ownership and location decisions.Absent joint control,6 this causes four instances of firms' boundaries, denoted as domestic integration, domestic non-integration, foreign integration and foreign non-integration.
As a global phenomenon, sourcing has been recently investigated at the crossroad between Contract Theory and International Economics (for a survey, see Antras 2014;Gattai 2006;Spencer 2005). 7From a theoretical perspective, the most important contributions are those by McLaren (2000), Grossman and Helpman (2002, 2003, 2005), Antras (2003), Ottaviano and Turrini (2007), and Antras and Helpman (2004).The framework, common to these theoretical models, is that final good production requires relation-specific inputs that the firm procures under contract incompleteness.McLaren (2000) and Grossman and Helpman (2002) focused on the domestic side of the ownership decision.Grossman and Helpman (2003), Antras (2003), and Ottaviano and Turrini (2007) analysed the foreign side of the ownership decision.Grossman and Helpman (2005) studied the location decision.For the purpose of the present work, particular attention should be devoted to Antras and Helpman (2004), addressing ownership and location concerns in a joint theoretical framework.In this model, the ownership decision is sensitive to relation-specificity.As relying on specific inputs is risky under contract incompleteness, firms employing specific inputs prefer integration.The location decision depends on productivity.As operating abroad is costlier than operating domestically, only the most productive firms can undertake foreign sourcing.Assuming firms' heterogeneity, à la Melitz (2003), Antras and Helpman (2004) showed that in low-tech sectors, integration never occurs: lower-productivity firms engage in domestic non-integration, and higher-productivity firms engage in foreign non-integration.However, in high-tech sectors, all sourcing strategies may be undertaken: lower-productivity firms rely on domestic inputs, and higher-productivity firms rely on foreign inputs; among firms that source in the same country, the most productive engage in integration, and the least productive in non-integration. 8 In the last two decades, a burgeoning empirical literature has grown rapidly to test the main predictions of Antras and Helpman (2004).Depending on data availability, Tomiura (2007a), Defever and Toubal (2013), and Corcos et al. (2013) studied the relative attractiveness of foreign non-integration and foreign integration.Tomiura (2005Tomiura ( , 2009) ) and Ito et al. (2011) analysed foreign non-integration and domestic nonintegration.Tomiura (2007b), Federico (2010), Kohler andSmolka (2011, 2021), De Ponti and Gattai (2022) and Bernasconi et al. (2022) considered all sourcing strategies in a joint empirical framework.The available evidence confirms the main theoretical predictions of the Beyond GHM: from local to global sourcing literature: irrespective of the year and country of analysis, firms that commit to foreign sourcing are, on average, more productive than firms that commit to domestic sourcing.Moreover, firms that engage in integration are, on average, more productive than firms that engage in non-integration.

Beyond Grossman-Hart-Moore: a Room for Joint Control
Another limitation of the PRT in its original formulation is that it fails to explain joint control, an allocation of property rights very common in cross-border investments.Even absent limits on foreign ownership, firms investing abroad may opt for jointventures rather than fully-owned subsidiaries (Arora and Fosfuri 2000;Desai et al. 2002;Filatotchev et al. 2007).In this sub-section, we review theoretical contributions that go beyond GHM by elaborating on the ownership decision as to embrace joint control. 9 A number of studies have restored the optimality of joint control by relaxing the assumptions of the original PRT framework (for a survey, see Gattai and Natale 2017).A few contributions consider solutions to ex-post bargaining other than the Nash 8 Antràs and Helpman (2008) allow for different degrees of contract incompleteness. 9Lack of suitable data has so far prevented empirical analysis on these matters.
bargaining solution (Chiu 1998;de Meza and Lockwood 1998;Halonen 2002;Manzini and Mariotti 2004;Schmitz 2013).Other studies introduce inefficiencies in ex-post bargaining (Bai et al. 2004;Matouschek 2004;Schmitz 2008;Hart 2009;Muller and Schmitz 2014) or allow for changes in the rules governing the allocation of property rights (Noldeke and Schmidt 1998;Maskin and Tirole 1999;Von Lilienfeld-Toal 2003;Gans 2005;Bai et al. 2004;Wang and Zhu 2005;Annen 2009).Lastly, a few contributions extend the Grossman-Hart-Moore framework accounting for repeated interaction (Halonen 2002;Rosenkranz and Schmitz 2004) or investigating the effect of the parties' investments on the ranking of ownership regimes (Rajan and Zingales 1998;Bel 2013;Cai 2003;Hart 1995;Rosenkranz andSchmitz 1999, 2003;Gattai and Natale 2016).For the sake of the present work, the latter group of theories is of particular interest, because of the testable predictions it derives.
Recall from Sect.2.1 that, when assets are independent, non-integration is preferred to integration.Rajan and Zingales (1998) and Bel (2013) show that joint control can be optimal when assets are substitute, i.e. the marginal benefit of investment decreases in the number of assets that a party controls.This is because joint control is akin to block a party's access to its own outside option and thus it reduces that party's incentive to invest.Cai (2003) considers two types of investment-specific and general.Specific investment is productive only within the relationship, while general investment is productive within the relationship and outside it.As long as specific and general investments are substitute in the cost function, any regime other than joint control induces too much general and too little specific investment.This establishes the optimality of joint control.
In Grossman and Hart (1986) and Hart and Moore (1990), parties invest in human capital; therefore, party i benefits from party j's investment only if they trade together.This implies the absence of investment spillovers in the PRT original framework, the so-called 'cross spillovers'.When investment is embedded in physical rather than human capital, Hart (1995) shows that joint control might be optimal.Under joint control, no party can use the asset without the consent of the other, which neutralizes the effect of any investment spillovers.Joint control dominates integration as long as the increase in the non-controlling party's investment raises the total surplus more than the decrease in the controlling party's investment reduces it.
Finally, Rosenkranz andSchmitz (1999, 2003) show the optimality of joint control in a set-up with just one asset and knowledge spillovers across parties.Gattai and Natale (2016) generalise this result to the case of two or more assets, accounting for 'asset-embodied' investments and 'footloose' investments as a source of cross spillovers.As the model predicts, joint control may prevail in presence of footloose investments.
To the best of our knowledge, lack of suitable data has so far prevented empirical analysis of the Beyond GHM: a room for joint control literature.

Data
This paper exploits original survey data, collected by the Authors for the purpose of a research project carried on at Università degli Studi di Milano-Bicocca.Data collection took place between April and July 2020, and involved a representative sample of Italian manufacturing firms headquartered in Lombardy.
Located in the North of Italy, Lombardy is one of the most developed and open regions in Europe.Its GDP per capita exceeds the national (EU) average by 34% (28%), and its volume of trade over value-added (73%) is 30% greater than the national average (Eurostat 2023).Lombardy's participation in GVCs is also remarkable with over 50% of its gross exports originating from participation in GVCs.Furthermore, Lombardy's share of value-added from foreign sources is the highest among Italian regions, witness to the importance of the region's international backward linkages (Iammarino et al. 2019).In order to address the boundaries of the firm consistently with the Beyond GHM: from local to global sourcing literature, Lombardy turned out to be the ideal locus for our study, since all sourcing strategies are represented in this region (Assolombarda 2019).
Our target sample of 1000 firms is drawn from the last national firm census and stratified according to geographical location, manufacturing activity, and firm size.Geographical location stratification is based on four macro areas that group neighbouring provinces according to their productive specialisation: northwest, northeast, southwest, and southeast. 10The manufacturing activity stratification follows Pavitt's (1984) taxonomy, which classifies industries into four macro categories according to the source of technology and technical change: supplier-dominated, specialised suppliers, science-based, and scale intensive.Firm size stratification reflects the number of employees and is based on three main classes: firms with fewer than 10 employees, firms with 10-49 employees, and firms with more than 50 employees.
The number of firms in each stratum of the target sample was obtained to ensure proportionality with the total number of firms in the same stratum of the population.
All firms were contacted by phone and a multiple-choice questionnaire, relative to firms' background information and sourcing behaviour in 2019, was emailed to senior managers and CEOs. 11 This study included 718 enterprises with a response rate of 70%.After dropping those firms that miss the relevant variable values, our sample consists of 562 firms, and it is highly representative of the entire population (Table 1).
Regarding the geographical location, the majority of firms are from the southwest area (38.26%), followed by the northeast (29.18%), northwest (25.09%), and southeast (7.47%).This evidence suggests that the manufacturing core of Lombardy is centred in Lodi, Milano, Monza e Brianza, and Pavia, whereas Cremona and Mantova account for a limited share of the local business.
For the manufacturing activity, supplier-dominated operations are the main economic activity, involving 38.79% of the sampled firms.They are followed by the ), with the latter representing the smallest segment.These data confirm that the industrial texture of Lombardy is highly diversified, with multiple specialisations leading to a balanced mixture of traditional and high-tech activities.
Finally, regarding firm size, most of our firms (57.12%) are rather small, with fewer than 10 employees.Medium and large firms account for a limited 28.29% and 14.59% of the total, respectively.Given the importance of Lombardy for the Italian economy (ASR 2021), this suggests that a mass of small and medium enterprises, rather than a handful of huge conglomerates, is responsible for consistent shares of national valueadded, GDP, export, and import.
With the questionnaire, we requested firms to report their core sourcing strategy in 2019.12Following the Beyond GHM: from local to global sourcing literature, we allowed the boundaries of the firm to rise from a combination of ownership and location decisions; following the Beyond GHM: a room for joint control literature, we elaborated on Antras and Helpman's (2004) taxonomy to incorporate the joint-venture into the firm's ownership decision, adding to integration and non-integration.To this aim, we adopted a wide definition of joint-ventures to embrace all partnerships among firms in which the percentage of ownership lays between 10 and 95%, consistent with Raff et al. (2012). 13egarding the location decision, 74.02% of our firms engage in domestic sourcing, employing 'made in Italy' components, whereas 25.98% prefer foreign sourcing, relying on foreign inputs (Table 3).As for the ownership decision, 64.59% of the sampled firms buy their inputs from independent suppliers, engaging in non-integration, against 35.41% that manufacture the components themselves either within their own boundaries (integration) or in joint-venture with an independent firm.Interestingly, only 7.12% of our firms rely on the latter, whereas integration involves 28.29% of the respondents.
When ownership and location decisions are combined, domestic non-integration becomes pervasive, accounting for 46.26% of the respondents; domestic integration and foreign non-integration follow closely, with shares equal to 23.67% and 18.33%, respectively.On the contrary, foreign integration (4.63%), domestic joint-venture (4.09%) and foreign joint-venture (3.02%) involve just a handful of respondents, consistent with Assolombarda (2019). 14or the purpose of the present research, our survey data have been complemented with balance sheet information downloaded from AIDA, a comprehensive database on Italian enterprises administered by Bureau van Dijk.This allows us explaining the boundaries of the firms through firm-level variables, according to the literature reviewed in Sect. 2.

Empirical Analysis
This section provides a detailed overview of our empirical analysis.In Sect.4.1, we introduce the variables used for econometric purposes; in Sect.4.2, we present the empirical methods and discuss our main results and robustness checks.

Dependent Variables
To assess the boundaries of Italian firms, we consider multiple dependent variables, in line with previous studies on global sourcing (Kohler and Smolka 2011;Federico 2010).
As for the location decision, the binary variable Location i is coded to capture firm i's domestic-or-foreign choice.It takes value 0 for firms engaged exclusively in domestic sourcing; and value 1 for firms engaged in foreign sourcing (regardless of their domestic strategies). 15s for the ownership decision, the categorical variable Ownership i is defined to capture firm i's make-or-buy choice: it is assigned value 0 for firms engaged exclusively in non-integration; value 1 for firms engaged in integration (regardless of their non-integration strategies); and value 2 for firms engaged in joint-venture (regardless of their non-integration and/or integration strategies).In the spirit of Antras and Helpman (2004), the three instances of ownership covered by our categorical variable Ownership i are independent alternatives and do not follow an ordering of any kind.
At this stage, it is worth mentioning that our definition of Location i is consistent with previous contributions on global sourcing (Mazzanti et al. 2009(Mazzanti et al. , 2011;;Federico 2010).On the contrary, our categorisation of Ownership i is completely original of the present study in that it widens the make-or-buy choice to consider joint-venture adding to integration and non-integration.This marks a clear departure from previous contributions that rely on a binary rather than a categorical variable of ownership (De Ponti and Gattai 2022;Bernasconi et al. 2022).

Core Independent Variables
Consistent with the literature reviewed in Sect.2, our core independent variables are TFP_lp i , specific inputs i , intangible inputs i and spillovers i .In what follows, we briefly comment on these variables and their expected sign.
TFP_lp i is our measure of productivity.It is the logarithm of total factor productivity, estimated according to the semi-parametric method of Levinsohn and Petrin (2003) to address the simultaneity and selection biases.Accordingly, we assume the production function of firm i at time t to be Cobb-Douglas.In this framework, the logarithm of firm i's output at time t can be expressed as a function of the logarithm of the freely variable input labour, the logarithm of the intermediate input, and the logarithm of the state variable capital.Following Gal (2013), we measure the firm's output in terms of value-added, the input labour as the number of employees, intermediate input as material costs, and capital stock as tangible fixed assets.The entire 2014-2019 time series for value-added, number of employees, material costs, and tangible fixed assets is exploited to implement the 'levpet' routine available in Stata.According to the Beyond GHM: from local to global sourcing literature, productivity is a major driver of firms' location and ownership decisions in that more productive firms are more likely to prefer foreign over domestic sourcing and integration over non-integration.(Antras and Helpman 2004).Therefore, we expect TFP_lp i to be positive and statistically significant in explaining Location i and Ownership i , meaning that the probability of engaging in foreign sourcing and integration increases in firm-level productivity.
Despite its widespread adoption, the Beyond GHM: from local to global sourcing literature neglects joint control; this deprives us of a theoretical underpinning for our investigation of the determinants of the joint-venture/non-integration choice.Nevertheless, we explore econometrically the role of productivity and provide a discussion of possible mechanisms driving our results.
Adding to TFP_lp i , specific inputs i and intangible inputs i are core regressors in our empirical framework.As reviewed in Sect.2, relation-specific investments are at the heart of the Grossman-Hart-Moore framework in that a combination of relationspecific investments and contract incompleteness favours integration to mitigate holdup concerns (Hart 1995).Relation-specific investments are not directly observable in our data.However, they are likely related to the characteristics of the inputs used for production purposes, which we investigated through survey interviews.To account for the multifaceted nature of production processes, we asked our respondents to define the relevance of four types of potential inputs-denoted as tangible, intangible, standardised and specific-according to a 1-5 Likert scale with 1 (5) denoting minimal (maximal) relevance. 16In our terminology, tangible inputs have physical substance, like components and raw materials; intangible inputs lack physical substance, like patens and know-how.Standardised inputs are untailored to a particular final good, so that they can be quickly replaced; specific inputs are tailored to a particular final product and cannot be easily employed in alternative use.Recall from Sect. 2 that GHM accounts only for investments in human capital; this suggests to investigate the relevance of intangible inputs in firm i's production process.Moreover, in the GHM framework investments are relation-specific; this points to assessing the relevance of specific inputs the most.Drawing on our data, specific inputs i (intangible inputs i ) is coded as a binary variable, taking value 1 for firms regarding specific (intangible) inputs as very relevant for their production processes.17From a theoretical point of view, we expect specific inputs i and intangible inputs i to be positive and statistically significant in explaining Ownership i , when integration is compared with non-integration.The Beyond GHM: a room for joint control literature is silent on whether they also affect the choice of joint-venture versus non-integration and the location decision.Absent a theoretical prior on these matters, we explore econometrically the role of input characteristics and discuss potential mechanisms behind our results.
Lastly, spillovers i is an index capturing the magnitude of cross (footloose) spillovers between firm i and its suppliers.From a theoretical point of view, cross spillovers are of particular interest in addressing the ownership decision.According to the Beyond GHM: a room for joint control literature, joint-ventures can be optimal when cross spillovers are accounted for (Gattai and Natale 2016).From an empirical point of view, we consider a wide array of spillovers potentially arising between firm i and its suppliers.They range from human capital to advertising, from R&D to organisational innovation, from industry knowledge to reliability, from visibility to product quality.With the questionnaire, we asked our respondents to define the relevance on a 1-5 Likert scale of each spillover from the firm itself to its suppliers, as well as viceversa (i.e. from the suppliers to the firm itself). 18Such a two-sided perspective is key to define cross spillovers, which are computed with the following procedure.First, for each spillover, we take the average between firm i's and its suppliers' evaluations, the socalled spillover-specific average; second, we take the average across spillover-specific averages to measure the overall importance of cross spillovers in the relationship involving firm i and its suppliers.Drawing on the Beyond GHM: a room for joint control literature, we expect spillovers i to be positive and statistically significant in explaining Ownership i , when joint-venture is compared with non-integration.
The literature envisages no role for cross spillovers in shaping location decisions.Still, we explore this issue econometrically and provide a discussion of possible mechanisms driving our results.
At this stage, it is worth mentioning that our measure of productivity is consistent with previous contributions on the topic (Kohler and Smolka 2011;Giovannetti et al. 2013Giovannetti et al. , 2015)).However, the lack of firm-level data on the nature of inputs and spillovers has so far prevented proper econometric analyses on these matters.Therefore, our definition of specific inputs i , intangible inputs i and spillovers i are to be considered an original contribution of the present study.

Control Independent Variables
Drawing on existing literature, we consider a series of additional controls to account for firm, industry, and geographical heterogeneity.
At the firm level, we control for the firm's age (age i ), group membership (group i ), employment (size i ) and profitability (EBITDA i ), in line with Giovannetti et al. (2013Giovannetti et al. ( , 2015) ) and D 'Angelo et al. (2016).
At the industry level, we control for Pavitt macro industries by means of binary variables for supplier-dominated, science-based, specialised suppliers and scale intensive industries.
At the geographical level, macro areas fixed effects take the form of binary variables for firms headquartered in the northwest, northeast, southwest and southeast of Lombardy. 19or expositional convenience, Table 2 provides a brief description of the variables used for econometric purposes, while summary statistics of categorical and continuous variables are available from panels (a) and (b) of Table 3, respectively.Ownershi p i Categorical variable, capturing firm i's make-or-buy sourcing choice.Taking value 0 for firms engaged exclusively in non-integration; value 1 for firms engaged in integration (regardless of their non-integration strategies); value 2 for firms engaged in joint-venture (regardless of their non-integration and/or integration strategies) Independent variables T F P_lp i Continuous variable.It denotes the log of total factor productivity, estimated using the semiparametric-estimation-based approach by Levinsohn and Petrin (2003)

Descriptive Statistics and Mean Comparison Tests
To explain the boundaries of Italian firms, Table 4 displays comparative descriptive statistics and mean comparison tests by location and ownership decisions of our respondents.For every core independent variable, panel (1) of Table 4 displays the number of observations and the mean in the groups of firms engaged in domestic versus foreign sourcing, thus providing a first insight on the location decision.A preliminary investigation of the data suggests that foreign sourcing is associated with higher productivity compared with domestic sourcing.Consistent with the Beyond GHM: from local to global sourcing literature, firms engaged in the former exhibit higher mean values of TFP_lp i than firms engaged in the latter, and differences in the means (foreign-domestic) are positive and statistically significant.Put another way, firms relying on foreign inputs systematically differ from firms relying on 'made in Italy' components in terms of TFP_lp i .
Panels (2.1) and (2.2) of Table 4 focus on the ownership decision, comparing TFP_lp i , specific inputs i , intangible inputs i and spillovers i across firms engaged in joint-venture versus non-integration, and firms engaged in integration versus non-integration, respectively.Interestingly, joint-venture firms systematically differ from non-integration firms in terms of productivity and cross spillovers.Evidence reveals that differences in the means (joint-venture-non-integration) for TFP_lp i and spillovers i are positive and statistically significant.This suggests that more productive firms prefer manufacturing the inputs themselves in joint-venture with an independent firm, rather than relying on an independent input supplier.At the same time, firms benefitting more from cross spillovers tend to prefer joint-venture over non-integration, in line with theoretical predictions of the Beyond GHM: a room for joint control literature.As for the comparison between integration and non-integration firms, panel (2.2) of Table 4 reveals that the former systematically differ from the latter in terms of TFP_lp i , specific inputs i , intangible inputs i and spillovers i .As the most notable finding, all differences in the means (integration-non-integration) are positive and statistically significant.Put another way, firms that manufacture the inputs themselves within their own boundaries tend to be different from firms that rely on independent input suppliers.In our sample, the integration firms are characterised by higher productivity, deeper reliance on specific inputs and intangible inputs and present cross spillovers compared with non-integration firms, in line with theoretical predictions of the Beyond GHM: from local to global sourcing and the Beyond GHM: a room for joint control literatures.

Econometric Models and Specifications
Our econometric approach is twofold.As a first step, we estimate Eqs. ( 1) and ( 2) separately.Equation (1) captures the sampled firms' location decision, and it is set as follows: (1) with variables defined in Sect.4.1.Given the binary nature of our dependent variable Location i , we rely on a probit model to estimate Eq. ( 1).Our full model probit specification regresses Location i on the core independent variables measuring productivity, reliance on specific inputs, intangible inputs and cross spillovers, together with additional regressors of group membership, age, size, financial performance, industrial and geographical controls.
According to the literature reviewed in Sect.2, Eq. ( 2) captures the sampled firms' ownership decision, and it is set as follows: (2) with variables defined in Sect.4.1.Due to the categorical nature of our dependent variable Ownership i , Eq. ( 2) is estimated in a multinomial probit framework, using the same regressors and specifications as those in Eq. ( 1).Being the most represented sourcing strategy in our sample and in accordance to the theoretical model by Antras and Helpman (2004), non-integration is used as a baseline category.
As a second step in our econometric approach, we acknowledge that ownership and location decisions might be related to some extent.In our data, this is evident from the fact that the intersection between Ownership i and Location i is not empty. 20 To account for the interplay between ownership and location decisions, we estimate Eqs. ( 1) and ( 2) jointly by means of the conditional mixed process (CMP) model (Roodman 2011(Roodman , 2022)).Loosely speaking, the CMP framework resembles that of the Seemingly Unrelated Regressions, with the difference that dependent variables need not be continuous. 21Therefore, it is possible to estimate our probit and multinomial probit models in a system, as shown in (3): All dependent and independent variables are as in Eqs. ( 1) and ( 2).Moreover, we retain the same specifications to facilitate comparisons with our previous results.Coherently with the multinomial probit estimated in (2), we assume errors are independent and identically distributed.
At this stage, it is worth mentioning that our probit, multinomial probit and conditional mixed process models are estimated using survey estimation methods to reduce the potential bias originating from the uneven survey response rate.We weigh each observation by the inverse of the probability of being sampled using, for every stratum, location-and industry-specific information on the total number of firms in the population and the sample (Kohler and Smolka 2011;Gattai and Trovato 2016).
On a general note, the cross-sectional nature of our data limits the empirical methods we could employ, as well as the ability of our estimates to establish causal relationships. 20See Sect. 3. 21 An alternative approach could imply estimating a multinomial probit model in which the dependent variable captures all instances of sourcing in a mutually exclusive way.We prefer sticking to the CMP framework due to data constraints.Indeed, some instances of sourcing account for a very limited number of observations in our data, once we combine the ownership and location dimensions.See Sect. 3 for more details.
Although balance sheet data from AIDA cover the 2014-2019 period, our survey data refer only to 2019.Nevertheless, the different models estimated, the adoption of empirical corrective actions and the various robustness checks allow identifying recurring regularities across results, providing significant insights on the relationship of interest.In that regard, aiming to reduce the simultaneity bias which may affect our estimates, all explanatory variables are 1-year lagged (D'Angelo et al. 2016). 22nother concern with our data is the potentially high degree of multicollinearity among regressors.To check whether this is an issue, we present pairwise correlations between independent variables and compute the Variance Inflation Factor (VIF) coefficients.Table 5 shows that pairwise correlations between independent variables are rather weak.Moreover, Table 6 reveals that the VIF coefficients are below the critical cut-offs.Therefore, we conclude that multicollinearity does not cast doubts on the reliability of our results (Hair et al. 2010).
In our data, the location decision is a matter of firm-level productivity and relevance of cross spillovers.As the most notable finding, the estimated coefficient of TFP_lp i is positive and statistically significant at the 1% level.In line with the Beyond GHM: from local to global sourcing literature, the more productive the firm, the more likely it is to opt for foreign sourcing.This evidence is fully consistent with previous results from Mazzanti et al. (2009Mazzanti et al. ( , 2011) ) and Federico (2010).
The coefficient of spillovers i is also negative and statistically significant at the 5% level.This seems to suggest that relevance of cross spillovers favours domestic over foreign sourcing.
As documented in Sect.2, the effect of cross spillovers is unexplored in the literature on location decisions.Still, we may expect they play a role in orienting the domesticor-foreign choice.Anticipating the beneficial effects of the exposure to each other's activities, final good producers and input suppliers are likely to co-locate, in order to reduce interaction costs.As long as foreign sourcing entails larger interaction costs than domestic sourcing, we expect domestic sourcing to prevail over foreign sourcing in presence of cross spillovers. 23Therefore, our result of a negative and statistically significant coefficient of spillovers i is to be considered a novel contribution of the present study to the understanding of locations decisions.
Concerning the ownership decision, Table 8 reports our multinomial probit estimates of Eq. ( 2).
Consistent with the categorical nature of Ownership i and the choice of nonintegration as our baseline category, Table 8 displays two columns: in (a), we estimate the probability that firm i engages in joint-venture rather than non-integration; in (b), the comparison between integration and non-integration is instead addressed.
In our data, the ownership decision is a matter of relevance of specific inputs, intangible inputs and cross spillovers.Concerning the likelihood of joint-venture versus  non-integration, in panel (a) of Table 8, the estimated coefficient of spillovers i is positive and statistically significant at the 1% level.This means that the more dependent the firm is on cross spillovers, the more likely it is to opt for joint-venture.This result should be regarded as a novel contribution of the present study: to the best of our knowledge, ours is the first attempt at studying the relative attractiveness of jointventures in a global sourcing framework.Theoretical models belonging to the Beyond GHM: a room for joint control literature focus on joint-ventures and show that they are more likely to emerge when cross spillovers are accounted for.However, the absence of suitable firm-level data has so far prevented a proper test of such a theoretical prediction.In a sense, our estimates fill the gap by confirming that cross spillovers are a positive driver of joint-venture against the baseline category of non-integration.Concerning the likelihood of integration versus non-integration, in panel (b) of Table 8, the estimated coefficients of specific inputs i and intangible inputs i are positive and statistically significant at the 1% and 5% levels, respectively, witness to the importance of relation specificity for ownership matters.These results confirm that relation specificity favours integration to mitigate hold-up concerns, consistent with the theoretical predictions of the Beyond GHM: from local to global sourcing literature and previous evidence from De Ponti and Gattai (2022) and Bernasconi et al. (2022).Interestingly, the estimated coefficient of spillovers i is also positive and statistically significant.This suggests that the relevance of cross spillovers affects not only the joint-venture versus non-integration but also the integration versus non-integration choice.While the former prediction was formally derived within the Beyond GHM: a room for joint control literature, to the best of our knowledge, the second has not been explicitly modelled yet.In this regard, a novel contribution of this paper is to show that the relevance of cross spillovers shapes the preference for integration over non-integration.From a qualitative point of view, the effect of spillovers i is consistent throughout panels (a) and (b) of Table 8, in that statistical significance and sign are preserved, regardless of the ownership regime-joint-venture or integration-compared with the baseline category of non-integration.However, from a quantitative point of view, remarkable differences emerge.In particular, the coefficient of spillovers i is much larger in panel (a) than in panel (b), witness to the key role played by cross spillovers in the joint-venture/non-integration more than integration/non-integration trade-off.Notice also that the estimated coefficient of spillovers i is significant at the 1% level in panel (a), and only at the 5% level in panel (b), which seems to confirm that cross spillovers matter more for addressing the joint-venture/non-integration than the integration/non-integration choice.
Regarding additional controls, only group membership is positively related with the probability of integration, as shown in panel (b) of Table 8.
After estimating Eqs. ( 1) and (2) separately with the probit and multinomial probit models described above, we estimate them jointly in a CMP framework.Results are reported in Table 9, in which the left-hand side panel deals with the location decision and the right-hand side panel with the ownership decision.
A comparison among Tables 7, 8 and 9 reveals that our results are completely consistent when switching from independent to joint estimates of Eqs. ( 1) and (2).Regarding location, in the left-hand panel of Table 9, foreign sourcing seems to depend on firm-level productivity and relevance of cross spillovers.From our estimates, the coefficient of TFP_lp i is positive and statistically significant at the 1% level.This means that the probability of foreign sourcing increases in firm-level productivity, which is consistent with our results displayed in Table 7.Moreover, the coefficient of spillovers i is negative and statistically significant at the 5% level, suggesting that the relevance of cross spillovers encourages domestic over foreign sourcing.Being robust to the inclusion of firm-level controls, this result is line with our probit estimates reported in Table 7. Regarding ownership, in the right-hand panel of Table 9, we focus on the joint-venture versus non-integration and integration versus non-integration choices.Notably, the coefficients of specific inputs i and intangible inputs i turn out to be positive and statistically significant drivers in the integration/non-integration trade-off, whereas they play no role in orienting the choice of joint-venture versus non-integration.This result, witness to the importance of relation specificity, is fully consistent with our evidence displayed in Table 8.Lastly, the estimated coefficient of spillovers i is positive and statistically significant no matter the ownership regime compared with the baseline category.Nevertheless, the effect of cross spillovers is more pronounced when dealing with joint-ventures.Indeed, the magnitude of the coefficient is much larger  8 and 9, cross spillovers matter more for choosing joint-venture than integration over non-integration.

Robustness Checks
To verify the consistency of our findings, we introduce several robustness checks.First, we re-run the regressions allowing for a 3-year rather than a 1-year lag in our continuous firm-level variables.This helps addressing the simultaneity bias despite the cross-sectional design of our data (D'Angelo et al. 2016).Results displayed in Tables 10, 11 and 12 are highly consistent with those reported in Tables 7, 8, and 9. Second, we consider an alternative measure of productivity (TFP_w i ) computed according to the estimation-based approach due to Wooldridge (2009).Such method overcomes collinearity issues in the input choice, that might depend on the simultaneous selection of materials and labour, as well as assuming no frictions in the labour market (Gal 2013).Results are robust and fully aligned with those summarised in Sect.4.2.3 (see Tables 13, 14, 15).

Concluding Remarks
With this paper, Grossman-Hart-Moore goes to Italy.Drawing on the GHM framework, we provide new evidence on the boundaries of the firm investigating the role of input characteristics, investment spillovers and productivity in ownership and location decisions.
We believe that robust evidence on the above is essential for our understanding of the medium and long-term responses of GVCs to recent changes and emerging trends in the global economy.
Lack of reliable data has so far prevented similar investigations.To fill this gap, we conducted survey interviews between April and July 2020 of a sample of 718 Italian manufacturing firms headquartered in Lombardy, one of the most industrialised European regions.Stratified by size, manufacturing activity, and geographical location and with a response rate of 70%, our sample provides direct information on many aspects of firms' production processes, including input characteristics and investment spillovers that our study emphasizes as relevant in explaining the boundaries of the firm.
Our probit, multinomial probit and conditional mixed process estimations suggest a number of robust regularities.As for ownership, we go beyond the standard taxonomy of Antras and Helpman (2004) and widen the make-or-buy choice as to consider three ownership regimes-non-integration, integration and joint-venture.Our estimates suggest that reliance on specific inputs and intangible inputs fosters integration over non-integration; moreover, firms acknowledging cross spillover effects are more likely to opt for joint-venture than for non-integration.As for location, we stick to the standard taxonomy of Antras and Helpman (2004) and compare domestic versus foreign sourcing.In our sample, the former prevails over the latter in presence of cross spillovers, whereas input characteristics seem to play no role.Lastly, productivity is a major driver of the boundaries of the firm in that productive firms are more likely to source abroad than domestically.
Holding across different econometric models and a number of robustness checks, our results contribute to the PRT and its recent developments.In particular, our contribution to the literature is twofold.On one hand, our detailed survey data provide new evidence on the predictions of the PRT.Put another way, some results from our econometric analysis confirm so far unexplored theoretical propositions from the GHM framework.On the other hand, taking advantage of our rich database, we unveil regularities on which the PRT is silent.This suggests further investigation and may open new developments in the GHM framework.
Our empirical findings leave room for a few policy-making and corporate practice remarks.In light of the relevant role played by productivity in firms' international engagement decisions, its enhancement might be crucial, should internationalisation be a corporate objective.As far as the ownership decision is concerned, our results illustrate integration is highly positively correlated to firm's reliance on specific and intangible inputs.Hence, firms might benefit from a proper assessment of their production processes to steer their ownership decisions on sourcing.
Nevertheless, we acknowledge limitations to our analysis.First, due to the survey design, our data have a cross-sectional nature.Unfortunately, this prevents a proper causal analysis and poses endogeneity concerns.A second wave of interviews to the same sample could eventually mitigate this issue.Second, external validity can be a concern.Albeit our sample is highly representative of the Lombard population of firms, it provides evidence on a single region within a single country in a single year.To improve on external validity, our survey could be extended as to collect cross-region and/or cross-country firm-level data.Third, there is a measurement issue.Survey interviews provide us with detailed information on the variables of interest, otherwise not available.However, this comes at the cost of relying on firms' selfreported measures of inputs characteristics and investment spillovers.Integrating selfreported with objective firm-level measures, if available, would provide an appropriate robustness check.Lastly, data constraints prevent us from relying on a continuous rather than discrete categorisation of ownership and location decisions.Developing the survey design as to collect granular information on the exact percentage of ownership of the foreign affiliates and the relative share of different sourcing strategies in case of multiple strategies would allow for a better understanding of the boundaries of the firm.
Improving on these limitations is a suggestion for future research.

Table 1
Population and sample of Lombard enterprises, by geographical location, manufacturing activity, and firm size scale intensive (23.49%), specialised suppliers (21.17%) and science-based activities (16.55%

Table 2
Variables description

Table 3
Descriptive statistics of categorical and continuous variables

Table 7
Location decision

Table 9
Location and ownership decisions

Table 12
Location and ownership decisions, robustness check, 3-year lag

Table 15
Location and ownership decisions, robustness check, TFP à la Wooldridge