Complementarity in alliance portfolios and firm innovation

Abstract

This paper assesses the impact on firm innovation of combining alliance-specific and partner-specific attributes within a firm’s alliance portfolio. In a panel data analysis of the innovation performance of 119 firms operating in the pharmaceutical industry during 1985–2007, we test whether firm’s alliance portfolio displays complementarities across four dimensions. The results suggest that specific combinations of attributes may diminish innovation by decreasing the efficiency of diversity management or by generating redundancies. On the other hand, other alliance portfolio practices are mutually reinforcing and thus foster innovation.

Keywords:

• Complementarity
• alliance portfolio, innovation, pharmaceutical industry
• exploration and exploitation

JEL Classifications:

• O31
• O32

1. Introduction

The extant literature has widely acknowledged that the contribution of alliances to fostering firm performance is not achieved through a success of an individual alliance but through the combined effect of the overall portfolio of corporate inter-organisational links (Hoffmann 2007; George et al. 2001). A growing body of literature has therefore focused on the portfolio of multiple simultaneous relationships (e.g. Powell, Koput, and Smith-Doerr 1996; Anand and Khanna 2000; Parise and Casher 2003; Hoffmann 2005, 2007) and scrutinised its role in determining the firm’s growth, innovation and profitability (e.g. Duysters and Lokshin 2011; George et al. 2001; Lavie 2007; de Leeuw, Lokshin, and Duysters 2014; Wuyts, Dutta, and Stremersch 2004).

Alliance portfolios¹ have aggregated properties that are not meaningful (and often not even conceivable) in an individual partnership, but whose impact is critical for firm performance (Ozcan and Eisenhardt 2009). Portfolios, indeed, offer an opportunity to assess the effect of ‘descriptors’ that cannot be observed in an individual relationship (Wuyts, Dutta, and Stremersch 2004, 88). While irreconcilable at the dyadic level, diverse and conflicting characteristics may co-exist at the portfolio level such as repeated and new partners or technologically close and distant partners (Tiwana 2008).

The portfolio configuration may therefore be viewed as a complex architecture that has multiple dimensions (Wassmer 2010). We focus on four main dimensions: functional, relational, structural and attribute. The first two refer to the nature of the alliance ties, and the other two are associated with the partner profiles present in a portfolio. With respect to the tie characteristics, the functional dimension refers to the activity (e.g. marketing, R&D) served by an alliance along the value chain (Lavie and Rosenkopf 2006). The relational dimension refers to the governance form (e.g. equity, and non-equity) of the relationship (Rowley, Behrens, and Krackhardt 2000). With respect to the alliance partner characteristics, we identify the structural dimension that refers to the level of familiarity resulting from previous and repeated ties (Lavie and Rosenkopf 2006) and the attribute dimension that stems from the knowledge heterogeneity of the alliance partners (Rodan and Galunic 2004). Although partners can differ in aspects ranging from their cultural background to their geographical location, we focus on the relative novelty of their reciprocal knowledge bases, which is central for technological innovation (Sampson 2007).

Our contribution to this research stream is to examine whether these specific dimensions within an alliance portfolio enhance or hamper firm’s innovation and whether value-enhancing (complementary) or value-destroying (sub-additive) effects are unleashed when a firm applies certain alliance portfolio practices by engaging in exploration- and exploitation-related alliances spanning the four dimensions.

Previous studies that considered complementarities in innovation, focused on generic strategies such as cooperation, ‘make’ vs. ‘buy’ R&D decisions (e.g. Belderbos, Carree, and Lokshin 2006; Cassiman and Veugelers 2006; Noseleit and de Faria 2013). In this paper, we investigate complementarities at a more aggregate level, namely, among the partner- and tie-related alliance portfolio dimensions.

Our analysis partially builds on the literature that takes a portfolio approach to alliance formation and performance (Gulati and Singh 1998; Hoffmann 2007; Lavie 2007; Ozcan and Eisenhardt 2009; Sarkar, Aulakh, and Madhok 2009; Wassmer 2010). In this paper, we suggest that specific interrelations among dimensions may be sub-additive and weaken innovation by decreasing the efficiency or by generating redundancy effects. On the other hand, other combinations of attributes may be mutually reinforcing (complementarity effects) and thus are value enhancing and fostering innovation.

The rest of the paper is organised as follows. The next section provides conceptual background. We proceed by describing the data, sample, variables and methods. After presenting our empirical results, we discuss the implications and provide concluding remarks.

2. Literature background

There is increasing awareness in the alliance literature that the performance effects of the portfolio go beyond the effects of the individual alliances (Faems, Van Looy, and Debackere 2005; Greve, Rowley, and Shipilov 2013). The investigation of precise portfolio composition that is optimal to foster firm performance has been prominent on the recent alliance research agenda. More specifically, researchers are trying to uncover the mechanisms that make the firm’s set of individual relationships contribute to the performance of an entire portfolio unleashing the potential to create alliance portfolio value (Lavie, Kang, and Rosenkopf 2011). This line of research has put forth that the performance effect of the entire alliance portfolio is higher if there are synergies among its underlying constituencies that guarantee that the full potential of an alliance portfolio is achieved (Lavie and Rosenkopf 2006).

From the recent contributions to this line of research we can distil that the portfolio architecture is essentially a multidimensional construct and is a result of the firm’s choices about which partners to ally with (governance) and what forms these alliances take (Wassmer 2010). Hence, each dimension of an alliance portfolio reflects, at an aggregate level, the underlying elements of individual dyadic ties. To understand whether the collection of individual ties makes an ensemble, it is critical to identify the combinations of dimensions between which complementarities exist, as these will determine how alliance portfolio will affect the overall firm performance. In this paper, we therefore focus on the innovative performance effects of complementarity among portfolio dimensions.

Based on the recent alliance portfolio literature, we identify four main dimensions of an alliance portfolio: functional, relational, structural and attribute. The functional dimension captures the purpose that the alliance ties serve in the portfolio. In the functional dimension, a variety of horizontal and vertical alliance types enhance the development of new products (Rothaermel and Deeds 2006). This distinction is made primarily because R&D alliances and technology grants generate knowledge whereas commercial, marketing and licensing agreements leverage knowledge (Lavie and Rosenkopf 2006).

The relational dimension refers to the governance form of the relationship. In particular, from the transaction cost perspective, alliance structure can be a means to reduce opportunism and transaction costs among partners (Hennart 1988; Oxley 1997). In situations prone to opportunism, equity agreements are generally preferred to more flexible contractual relationships. Companies may choose among various forms of integration, ranging from non-equity to equity agreements, and all forms may favour innovation by contributing to access to specific types of resources (Keil et al. 2008; Sampson 2007).

The structural dimension considers with whom the company is allying. In the existing literature, we find considerable work on the so-called repeated-tie effect (Gulati 1995). In terms of partner selection, firms are often found to select existing partners or partners with whom they have already established a relationship (Goerzen 2007; Gulati and Gargiulo 1999). Allying with the same partners conveys to the firm redundant or repeated knowledge that allows a better understanding of the partners’ resources, enhances trust mechanisms, favours the exchange of complex or tacit knowledge, and ultimately contributes to developing incremental innovations (Saxton 1997; Wuyts, Dutta, and Stremersch 2004). Furthermore, by repeating ties firms avoid the search and switching costs of entering into relationships with new partners (Chung, Singh, and Lee 2000). In the long run, however, choosing existing partners might decrease potential learning effects and lead to collective blindness (Leonard-Barton 1995) and cognitive lock-in effects (Gargiulo and Benassi 2000). New partners, on the other hand, provide new information, nurture new ideas, and favour the exploration of new opportunities (Gilsing and Duysters 2008; Saxton 1997; Wuyts, Dutta, and Stremersch 2004).

The attribute dimension refers to the extent to which the technological bases of the partners differ. Gilsing et al. (2008), for example, argue that large technological distances among partners have a negative effect on ability to understand and capture outside knowledge but increase the potential for novel recombinations. The basic rationale for having partners with similar technology bases is that this similarity is necessary for a fruitful knowledge exchange (Mowery, Oxley, and Silverman 1998). There are valid reasons for having partners with dissimilar knowledge bases. As suggested by Sampson (2007), the potential combinations of similar knowledge are not unlimited and they expire after a certain time. Dissimilarity compensates for this effect and allows the generation of new knowledge. Overall, the portfolio architecture may be represented as the ensemble of the above-mentioned four dimensions as represented in Figure 1.

Figure 1. Portfolio dimensions.

3. Complementarity and sub-additivity among portfolio dimensions

From the above discussion about the characteristics of the portfolio architecture, it emerges that the four portfolio dimensions can be distinguished on the basis of the specific purpose they serve in fostering firm performance.

Although each dimension has the potential to provide a specific contribution, it is the overall portfolio that ultimately affects performance. Thus, it is critical to open the ‘black box’ to understand what drives the value generated by the alliance portfolio. We argue that the value generated by the alliance portfolio, which is a combination of all the dimensions jointly, depends on the interactions among the dimensions. These dimensions can be positively reinforcing each other or can be sub-additive.²

Overall, previous work on alliances appears to suggest that both complementarity and sub-additivity effects may exist among portfolio dimensions and that these effects may contribute in determining firm performance.³ It is worth noticing that we consider specifically, whether complementarities/substitute effects may arise among dimensions. In this sense, we are interested in identifying the ‘extreme’ cases where either synergy is generated or substitution applies.

With respect to complementarities, we first consider the alliance ties. In particular, the relational and the functional dimensions appear to serve complementary goals. As described above, the relational dimension refers to the governance form (e.g. equity and non-equity) of the relationship, whereas the functional dimension refers to the specific activity served by an alliance in the value chain. The former calibrates the level of involvement necessary for an efficient transfer and absorption of the external knowledge. The latter regulates the coverage of business areas where external knowledge may be employed, according to the corporate needs. It may be noted that the optimal level of involvement required for an efficient knowledge transfer cannot be defined in absolute terms but only relative to the specific function this knowledge is intended to serve. For example Mowery, Oxley and Silverman (1996) have demonstrated that equity alliances in particular facilitate more effective knowledge transfer in R&D alliances. The consequence is that the more developed the spectrum of functional areas that the alliance portfolio potentially serves, the more beneficial it is to dispose of various types of relational forms to rely on. Vice versa, the functional corporate areas where knowledge is directed contributes to define the optimum level of commitment needed. Therefore, it may be expected that relational and functional dimensions at the portfolio level complement each other and their contribution to performance is higher jointly than separately. The above considerations that we developed at the portfolio level resonate with the arguments developed by studies at the organisation level: the literature has pointed out that performance may be enhanced if the relational profile and the level of relational involvement is aligned with the function that the alliance serves. For example, Chiesa and Manzini (1998) claim that the scope content of the relationship is supported by the relational form chosen for the cooperation. In fact, choosing the most appropriate organizational form is seen to be crucial for effective cooperation in a specific functional domain. Similarly, Koza and Lewin (1998) argue that the intended innovation objective of the alliances can be favoured when matched with the adequate relational form. They show for example that in exploitation alliances that are equity based (joint ventures), absorptive capacity is less important than in the case of network alliances. Furthermore, Schildt, Maula, and Keil (2005) assessed the performance implications of various relational (governance) modalities (including acquisitions) and argued that a specific innovation scope is achieved differently depending on the level of relational commitment of the relationship. Functional and relational dimensions are considered to reinforce the reciprocal benefits and their potential contribution to the overall innovation performance. Therefore, we expect that complementarities exist between functional and relational dimensions in the portfolio.

H1: Functional and relational dimensions of a firm’s alliance portfolio are complementary.

With respect to sub-additivity, we consider the functional and the structural dimensions. The literature at the organisational level provides a potential rationale for explaining the sub-additivity of functional and structural dimensions. For instance, Lavie and Rosenkopf (2006) consider engaging with new partners to be a form of exploration and with repeated partners to be a form of exploitation. Similarly, they consider that knowledge-generation alliances (e.g. R&D agreements) are oriented towards exploration and knowledge-leveraging alliances (e.g. marketing agreements) are oriented towards exploitation. A similar classification of alliances functions for exploration and exploitation has been adopted by Rothaermel and Deeds (2004). Applying the above consideration to our framework, the functional and structural dimensions may be interpreted as serving, in the context of innovation, the same purpose and therefore they may be conceived as substitutes for one other. We advance the above logic to argue that not only there is no obvious advantage in combining jointly the functional and structural dimensions, but potentially, their combination is detrimental to performance. Organisations need to develop regular patterns of actions to perform specific tasks (Pentland and Rueter 1994). Developing these internal mechanisms required to successfully deal with various alliances functions (as diverse as marketing and R&D) as well as to coordinate dedicated exchange mechanisms with old and new partners may be demanding for organisations. In doing so, organisations are potentially exposed to distorted effect leading to apply to other relationships the experience previously acquired. Partner-specific experience contributes more than generic experience to the creation of value (Gulati, Lavie, and Singh 2009) but it is not agile to transfer the lessons learned from the interaction with one specific partner to another. Applying experience from one partner to another might indeed lead to an inappropriate generalisation of alliance experience (Haleblian and Finkelstein 1999; Reuer, Park, and Zollo 2002), i.e. there is a danger that existing practices will be applied to new situations (new partners) that appear similar but are inherently different. When a portfolio expands in different dimensions but the expansion is redundant (serving the same scope) and requires additional investments, the ability to generate value may be hampered. Otherwise stated, redundancy comes at the price of efficiency.

At the portfolio level, which is the focus of our interest, we argue that the variety of corporate activities that the alliance portfolio may serve does not benefit in itself from the fact that the company has more or less familiarity with its partners. Stated differently, being acquaintances is not, per se, a qualification contributing to the functions alliance serve. The support that the functional dimension (research, development, marketing) may offer to performance is not directly affected by the partners’ familiarity. We may consider that the portfolio is efficient if the partners’ competences are aligned to the function’s goals (rather than to the partners’ familiarity with the company) in an efficient way. Similarly, the alliance function delivers value when there is an alignment with the internal corporate strategy: the fact of disposing of familiar and unfamiliar partners per se does not enhance the alignment to corporate needs. Hence, we propose:

H2: Functional and structural dimensions of a firm’s alliance portfolio are subadditive.

4. Analysis

Prior research has distinguished between objective complementarity (also referred to as ‘production approach’) and behavioural complementarity (also referred to as ‘correlation approach’). The former has been analysed by estimating a full cross-term function under inequality constraints (Mohnen and Röller 2005; Belderbos, Carree, and Lokshin 2006; Percival and Cozzarin 2008). The second approach relies on assessing pairwise correlation coefficients among the adoption equations after controlling for firm-specific effects (e.g. Arora and Gambardella 1990; Belderbos et al. 2004; Cassiman and Veugelers 2006; Catozzella and Vivarelli 2014). As pointed out by Hou (2013), the vast majority of complementarity studies, this study not an exception, have relied on dichotomous variables to measure practices. While it is possible to extend the testing methods to a continuous case when the number of practices exceeds three (cf. Carree, Lokshin, and Belderbos 2011), in practice, such a model is plagued with high correlations among two-, three-, and four-way interaction terms, which often prevents identification.

In what follows, we empirically test such complementarities/sub-additivity effects among portfolio dimensions. Our methodology follows a ‘production function approach’ by which we estimate the impact of (combinations) of alliance portfolio dimensions on firm innovation output. Although we only hypothesise two specific effects, we report complementarity test outcomes among all pair-wise combinations for completeness.

To examine complementarities among portfolio dimensions we apply, as suggested in Hou (2013), a more powerful test that combines methodology discussed in Mohnen and Röller (2005) and in Belderbos, Carree, and Lokshin (2006). The testing procedure requires the estimation of an extended regression with the set of sixteen dummy variables that capture all possible combinations of the four dimensions (functional, relational, structural and attribute). The coefficients on these dummy variables allow us to assess their impact on innovation and to test for complementarity between dimensions. We estimate the following equation:

(1)

where atr = attribute dimension, fun = functional dimension, rel = relational dimension and str = structural dimension of an alliance portfolio. Equation (1) is estimated unconstrained as well as under the (in)equality restrictions (Belderbos, Carree, and Lokshin 2006; Mohnen and Röller 2005). Furthermore, the models control for the R&D of the firms and prior patents (scaled by R&D). The W-vector consists of firm-level control variables, such as size, alliance portfolio size, alliance experience, firm age, cultural distance between home and host countries of alliance partners and time dummies.

The indicator function I captures all exclusive combinations of portfolio dimensions, where the case of a void alliance portfolio is normalised to zero corresponding to Equation (1)⁴ . These 16 binary terms capture the effects of combinations of alliance portfolio dimensions.⁵ The conditions for complementarity/sub-additivity between each pair of dimensions are summarised in the bottom pane of Table A1. For example, the condition for complementarity between functional & relational dimension corresponds to the following ; ; , with at least one inquality holding strictly.

We estimate log-linearised and negative binomial models with fixed firm effects to control for unobserved (time-invariant) firm characteristics. The negative binomial model is attractive as it explicitly accommodates over-dispersion, which is usual in count data (Cameron and Trivedi 2005). Hausman test marginally rejects the random-effects model in favour of the fixed-effects model. The models control for R&D of the firms and the degree to which the firm has been technologically successful in the past.

5. Data and methods

5.1. Sample

To construct our sample, we initially identified 150 publicly traded U.S., European and Japanese manufacturing companies that are among the top global R&D spenders (DTI 2006) and that have their main economic activity in the pharmaceutical (primary SIC code 2834 and code 2836) industry. We limit our sample to this industry because the propensity to patent is high, making patent data appropriate indicators of technological activity (Hall and Bagchi-Sen 2002; Porkolab 2002). The pharma sector provides an interesting sector for our study because it is characterised by a widely dispersed knowledge infrastructure in which both small and large firms play an important role. Because of the dispersed character of the knowledge base, firms are pushed to team up with a wide variety of competent partners in order to keep up with ongoing technological changes in the industry and to reduce the huge costs involved in developing new products. In this sector, new technological opportunities often emerge from small high-tech biotechnology firms, companies tend to engage in a wide array of relationships in order to build a ‘radar-function’ on new technologies. Therefore, given the technological challenges, opportunities and costs of bringing new products to the market, companies in these sectors are extensively involved in strategic alliances with a variety of external partners (Hall and Bagchi-Sen 2002; McKelvey, Alm, and Riccaboni 2003). In particular, large pharmaceutical firms are building a large portfolio of relationships.

We collected patent, accounting (balance sheet) and alliance data at the consolidated corporate level covering a period of 23 years (1985–2007). Because of missing values for R&D and the number of employees our unbalanced estimation sample included 119 firms. The Thomson SDC database was used to gather information about the alliance activities of the selected companies. From this database, we were able to identify some 2372 alliances undertaken by the 119 sample firms from 1985 to 2007. Of these, 1432 are unique-partner alliances. If we remove the focal firms, we are left with about 1900 alliances. We assume that the average duration of an alliance is three years (Gulati 1995; Lavie and Miller 2008), and all ties formed by a focal firm within this time window form its alliance portfolio. We use a three-year window of activities to calculate the alliance portfolios.

We count all the focal firm’s alliances even if some are ties, i.e. alliances between firms in the sample. Firms have on average about seven partners in their alliance portfolios. The largest portfolio in our sample consists of 58 alliances. Data on the R&D expenditure, sales, and number of employees were obtained from the Compustat and Amadeus databases. For information on patenting activity, we used the PATSTAT database. Companies may file patent applications under the names of subsidiaries and therefore for each firm for each year in our sample we searched for patents applied for under the names of the parent firm or their subsidiaries. We considered the patents of an acquired firm to be part of the patent stock of the acquiring company from the acquisition year onwards. In total, we were able to link 77,968 different patent applications to the 119 sample firms over the sample period. We gathered patent information to measure the technological distances between a focal firm and its alliance partners. We then aggregated these distances at a portfolio level.

5.2. Variable construction

The dependent variable in our model is the number of patent applications for each year of each firm. We use patent counts as a proxy for innovation. Although not all patents represent commercialised technologies, patents offer a rich source of information for studies on innovation and have been extensively used as an indicator of invention and innovation (Colombo, Grilli, and Piva 2006; Jaffe and Trajtenberg 2002; Nooteboom, Vanhaverbeke, Duysters, Gilsing, and van den Oord, 2007; Rothaermel and Deeds 2004). The majority of inventions in the pharmaceutical industry are patented (Arundel and Kabla 1998; Campbell 2005) and firm-specific patent application policies are likely to be relatively stable over time. Although patents implicitly indicate the existence of innovation, the interpretation of such data is not uncontroversial. The literature considers patent counts an incomplete indicator of innovation rates because many inventions are protected by secrecy and not all innovations can be patented (Jaffe and Trajtenberg 2002). In line with previous studies (e.g. Schmookler 1966; Sampson 2007), we used the patent application date as the first indication of new capabilities and invention.

5.2.1. Focal independent variables

The functional dimension dummy takes the value one if a firm has a broad spectrum of functional areas (R&D and grant alliances, marketing, licensing, customer, supplier, manufacturing alliances), in its alliance portfolio, and zero otherwise. The relational dimension dummy takes the value one when a firm has both equity and non-equity alliances in its portfolio, and zero otherwise. The structural dimension dummy takes the value one when a firm has links with both repeated and new partners. Finally, the attribute dimension dummy takes the value one if the firm forms alliances with both technologically distant and close partners. To measure this distance, we used patent information (Nooteboom et al. 2007; Sampson 2007). We constructed the distribution of patents of the focal firm i and each of its partners j across patent classes. These distributions are captured by the vectors and where is the number of patents of firm i that are assigned in patent class k in the preceding five years. The uncentred correlation for each pair of alliances of a focal firm i and its partner j is calculated as , where i ≠ j (Jaffe 1986). This measure is bounded between zero and one, with higher values indicating a smaller technological distance. The attribute dimension dummy takes the value one if the standard deviation of this measure computed at a portfolio level is higher than the overall standard deviation for each firm.

5.2.2. Control variables

The empirical model controls for (time-varying) firm-level factors that are likely to impact firm innovation. Performing R&D enhances a firm’s knowledge base and increases its capacity to recognise and assimilate external knowledge from alliance partners (Cohen and Levinthal 1990; Koza and Lewin 1998; Mowery and Oxley 1995; Tsai and Wang 2007; Zahra and George 2002). We include the firm’s R&D stock constructed using the perpetual inventory method with a depreciation rate of 15% (Hall, Mansfield, and Jaffe 1993), and the ratio of the lagged patent stock (also constructed using the perpetual inventory method) to the R&D stock in order to capture differences in the propensity to apply for patents (e.g. Blundell, Griffith, and Van Reenen 1995; Pavitt 1985). We further control for firm size by including in the regressions the logarithm of the number of employees. A larger size brings with it the advantages of a larger resource base, easier access to financial markets and higher alliance-failure tolerance (Cohen and Levin 1989). According to Rothaermel and Alexandre (2009) and Hoang and Rothaermel (2005), repeated routines foster learning effects in managing alliances. We therefore control for alliance experience using the logarithm of the cumulative sum of alliances in which the company engaged. Older companies may be more experienced and have well-established routines in place (Nelson and Winter 1982). Variable age is constructed as the logarithm of the number of years from the date of the company’s foundation to the year of reference. We also control for portfolio size by including the logarithm of the total count of alliances in a portfolio. Since the date of alliance termination is unavailable from the archival sources, such as SDC database, we assumed that alliances have a three-year duration based on the conventions adopted in the alliance literature (see Lavie 2007). A portfolio with a large number of alliances may achieve a higher rate of innovation because of increased ‘exposure to knowledge bases’ (Wuyts, Dutta, and Stremersch 2004, 91).

We also control for differences in the partners’ cultures. To construct this variable, we identified the home country of each partner and subsequently collected Hofstede scores on each of the dimensions, i.e. power distance, individualistic vs collectivistic attitude, masculine vs feminine attitude, and uncertainty avoidance. We then constructed for each focal firm and each of its partners the distribution of the Hofstede scores. These distributions are captured by the vectors and where is the Hofstede score for firm i and dimension k. The uncentred correlation for each pair of alliances of a focal firm i and its partner j is calculated as , where i ≠ j. This measure is bounded between zero and one, with higher values indicating a lower cultural diversity. For a portfolio with L alliances we then compute the average cultural diversity as follows: , where the second term on the right-hand side is the average of the cultural distances between the focal firm and each of its partners. Finally, we include year dummies to account for time-specific factors affecting technological performance.

In our analyses we lagged all the independent variables by one year. In this way, since we use a three-year moving window, we assess complementarities in the four dimensions in up to the four previous years. This is consistent with the literature allowing three to five years for alliances to show their effects on performance (de Man and Duysters 2005).

6. Empirical results

Table 1 shows the descriptive statistics and the correlation matrix for the variables of interest. There is a substantial share of cases in our sample where portfolios have one of the four dimensions only (about 40%, 522 observations). If we look within each dimension, there are about half cases when portfolios have both R&D and non-R&D alliances (57.8%); equity and non-equity alliances (32.5%); high technological distance (52.9%); and both new and repeated partners (29.9%). Further, there is sufficient variation in the portfolios that have two or more dimensions (in addition to being diversified within each dimension); this depends on the particular combination of dimensions. Finally, 3.5% of the portfolios display co-occurrence of exploration- and exploitation-related alliances in each of the four dimensions at the same time (see Table 2).

Table 1. Descriptive statistics and correlations (n = 1300).

Variable	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23
1. Patents	1
2. Functional	−0.05	1
3. Relational	−0.05	−0.05	1
4. Structural	−0.01	−0.03	−0.01	1
5. Attribute	−0.25	−0.21	−0.08	−0.06	1
6. Functional & relational	0.01	−0.10	−0.04	−0.03	−0.17	1
7. Functional & structural	0.04	−0.10	−0.04	−0.03	−0.18	−0.08	1
8. Functional & attribute	0.01	−0.11	−0.04	−0.03	−0.19	−0.09	−0.09	1
9. Relational & structural	−0.00	−0.04	−0.02	−0.01	−0.07	−0.03	−0.03	−0.04	1
10. Structural & attribute	−0.02	−0.05	−0.02	−0.01	−0.08	−0.04	−0.04	−0.05	−0.02	1
11. Relational & attribute	−0.03	−0.05	−0.02	−0.02	−0.09	−0.04	−0.05	−0.05	−0.02	−0.02	1
12. Functional & relational & structural	0.32	−0.12	−0.05	−0.03	−0.21	−0.09	−0.10	−0.11	−0.04	−0.05	−0.05	1
13. Functional & relational & attribute	0.11	−0.08	−0.03	−0.02	−0.14	−0.07	−0.07	−0.08	−0.03	−0.03	−0.04	−0.08	1
14. Relational & structural & attribute	−0.01	−0.03	−0.01	−0.01	−0.05	−0.02	−0.02	−0.03	−0.01	−0.01	−0.01	−0.03	−0.02	1
15. Functional & structural & attribute	0.01	−0.06	−0.02	−0.02	−0.11	−0.05	−0.05	−0.06	−0.02	−0.02	−0.03	−0.06	−0.04	−0.01	1
16. Functional & relational & structural & attribute	0.13	−0.07	−0.03	−0.02	−0.12	−0.05	−0.06	−0.06	−0.02	−0.03	−0.03	−0.07	−0.05	−0.02	−0.03	1
17. Firm size	0.65	−0.06	0.00	−0.01	−0.22	0.04	0.01	0.00	0.05	−0.05	0.02	0.24	0.10	−0.02	−0.03	0.16	1
18. Log (R&D)	0.66	−0.03	−0.10	−0.02	−0.22	0.02	0.10	0.05	−0.01	−0.03	−0.07	0.23	0.08	−0.03	−0.00	0.13	0.83	1
19. Patents/R&D	−0.03	−0.04	0.02	0.01	−0.03	0.03	−0.03	0.05	0.01	−0.01	0.00	0.00	0.02	−0.01	0.13	−0.02	−0.20	−0.34	1
20. Portfolio size	0.60	−0.07	−0.06	−0.02	−0.38	0.04	0.18	−0.05	−0.04	−0.06	−0.09	0.53	0.01	−0.03	0.08	0.20	0.48	0.51	−0.07	1
21. Log (Firm age)	0.46	−0.07	0.04	0.02	−0.09	0.04	0.01	−0.09	0.05	−0.02	0.03	0.12	0.09	−0.01	−0.02	0.14	0.80	0.62	−0.22	0.31	1
22. Experience alliances	0.50	0.02	−0.10	−0.01	−0.43	0.11	0.23	0.04	−0.05	−0.06	−0.15	0.37	0.04	−0.04	0.08	0.18	0.44	0.60	0.12	0.69	0.26	1
23. Cultural distance	0.34	0.08	0.04	0.02	−0.56	0.10	0.18	0.06	−0.02	0.00	−0.05	0.28	0.08	−0.01	0.13	0.16	0.23	0.22	0.04	0.53	−0.04	0.39	1
Mean	58.77	0.11	0.02	0.01	0.27	0.07	0.08	0.09	0.01	0.02	0.02	0.1	0.05	0.01	0.03	0.04	0.45	5.94	0.1	6.65	3.39	2.35	0.65
Std. dev.	93.93	0.31	0.13	0.1	0.44	0.26	0.27	0.29	0.11	0.14	0.15	0.31	0.22	0.08	0.17	0.18	2.15	1.82	0.18	8.56	1.14	1.04	0.3
Min	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	−4.51	0.74	0	0	0	0	0
Max	825	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	4.81	10.65	3.46	58	5.67	4.92	1

Table 2. Contingency of portfolio dimensions (n = 1300).

Dimensions	Number of cases
None	88
Functional	142
Relational	23
Structural	12
Attribute	345
Functional & relational	92
Functional & structural	104
Functional & attribute	122
Relational & structural	16
Structural & attribute	25
Relational & attribute	31
Functional & relational & structural	136
Functional & relational & attribute	69
Relational & structural & attribute only	9
Functional & structural & attribute	40
Functional & relational & structural & attribute	46

Note: The categories are exclusive (combinations of) portfolio dimensions with co-occurrence of exploration- and exploitation-related alliances.

Table 3 lists the estimated coefficients of our models. In the first column of Table 3, we present the results of the base model including the control variables only. In model 1, the variables portfolio size, R&D and patent intensity have the expected positive signs and are statistically significant. In the second column, we introduce the independent variables of interest. According to the likelihood ratio test, model 2 has a significantly higher explanatory power, providing a statistically better fit for the data. The alliance variables represent exclusive (combinations of) types. For instance, the functional variable takes the value 1 (else 0) if the portfolio has only the functional dimension; the functional & relational variable takes the value 1 (else zero) if the portfolio has only the functional and relational dimensions, and so on. By construction, the correlation between these variables is negative and close to zero. For comparison, in model 3 we report results from our model estimated with OLS using a log-transformed dependent variable. Results of these two models are quite consistent.

Table 3. Estimates of Equation (1): firm innovation and alliance portfolio dimensions.

	Model 1	Model 2	Model 3
Intercept	0.208 (0.441)	0.171 (0.451)	0.511 (0.927)
Log(R&D)	0.347*** (0.041)	0.343*** (0.041)	0.664*** (0.032)
Patents/R&D	0.509*** (0.079)	0.503*** (0.079)	2.878*** (0.151)
Firm size	−0.053 (0.039)	−0.034 (0.039)	0.064** (0.030)
Portfolio size	0.010*** (0.003)	0.011*** (0.003)	0.001 (0.005)
Experience alliances	−0.101** (0.048)	−0.140*** (0.051)	0.155*** (0.043)
Log(Firm age)	−0.065 (0.065)	−0.066 (0.066)	−0.056 (0.038)
Cultural distance	0.101 (0.078)	0.027 (0.086)	−0.254** (0.115)
Functional		0.337*** (0.094)	0.222* (0.123)
Relational		0.142 (0.157)	0.275 (0.212)
Structural		0.383** (0.176)	0.198 (0.277)
Attribute		0.186** (0.086)	0.170 (0.109)
Functional & relational		0.189* (0.101)	0.438*** (0.139)
Functional & structural		0.265** (0.103)	0.255* (0.140)
Functional & attribute		0.322*** (0.095)	0.465*** (0.128)
Relational & structural		−0.238 (0.156)	0.333 (0.244)
Structural & attribute		0.504*** (0.145)	0.588*** (0.206)
Relational & attribute		−0.007 (0.136)	0.061 (0.189)
Functional & relational & structural		0.291*** (0.100)	0.511*** (0.147)
Functional & relational & attribute		0.356*** (0.098)	0.574*** (0.148)
Relational & structural & attribute		0.275 (0.204)	0.055 (0.314)
Functional & structural & attribute		0.152 (0.123)	0.223 (0.178)
Functional & relational & structural & attribute		0.321*** (0.108)	0.530*** (0.175)
Log-likelihood	−4333.878	−4310.811	−1656.137

Notes:

n = 1300; year dummies are not shown; numbers in parentheses are standard errors; R²= 0.71 in model 3.

^* p < 0.1

^** p < 0.05

^*** p < 0.01.

In line with the view that alliance portfolio increases innovation, we find that when a firm reports no active dimensions (the reference category is 0 0 0 0, captured by a constant) the propensity to innovate is the lowest (see Table 3, model 2). Of the individual dimensions, those leading to functional (0.34, p < 0.01), structural (0.38, p < 0.05) and attribute (0.19, p < 0.05) are positive and statistically significant. Moreover, several combinations of two dimensions have a significant positive impact. None of the dummy variables have a significant negative impact. Overall, these results clearly confirm the positive impact of alliance portfolios on innovation. A general observation is that we cannot use the magnitude of single point estimates to decide whether or not a joint effect among dimensions increases performance.

Using the estimated beta coefficients on the alliance portfolio dimensions, we now turn to the complementarity and substitutability tests to test the hypotheses. To this end we need to establish whether a pair of dimensions is complementary, implying that firm performance is higher when the dimensions are both present in a portfolio compared to a situation when they are separately used. We follow the inequality-constrained approach (cf. Belderbos, Carree, and Lokshin 2006; Mohnen and Röller 2005) and estimate Equation (1) in both restricted and unrestricted form (see Appendix). We subsequently use the Likelihood-Ratio test to test the validity of the imposed restrictions. Applying a more robust procedure recommended by Hou (2013), we test for complementarity by testing if we can accept the null H ₀: Rβ ≥ 0 vs. H ₁: (Mohnen and Röller 2005) and whether we can reject the null H ₀: Rβ = 0 (Belderbos, Carree, and Lokshin 2006). In testing for sub-additivity the inequality sings above are reversed. Table 4 reports the summary of complementarity tests.

Table 4. Summary of tests for complementarity and sub-additivity between portfolio dimensions.

	Functional & relational	Functional & structural	Functional & attribute	Relational & structural	Relational & attribute	Structural & attribute
Complementarity
TP1: H0: Rβ ≥ 0 vs. H1:	0.06	11.44	4.81	1.27	0.11	2.56
TP2: H0: Rβ = 0 vs. H1: Rβ ≥ 0	13.79	5.66	2.95	4.30	6.31	5.04
Subadditivity
TP1: H0: Rβ ≤ 0 vs. H1:	13.79	5.19	2.79	4.23	6.17	4.92
TP2: H0: Rβ = 0 vs. H1: Rβ ≤ 0	0.06	11.90	4.97	1.33	0.24	2.68

Note:

The reported LR statistics is in TP1 for the test of the null hypothesis of complementarity and in TP2 for the null of the absence of complementarity (sub-additivity) for a given pair of dimensions. The upper bound critical value at a 10% significance level is 7.09 (critical values given in Kodde and Palm, 1986), which implies that the null hypothesis is rejected when the statistic is above 7.09.

Our results indicate that the functional and relational dimensions are complementary in line with Hypothesis 1. The results also reveal that there is significant subadditivity between functional and structural dimensions as predicted by Hypothesis 2. The relational and structural, relational and attribute, and structural and attribute dimension pairs are neither complementary nor sub-additive.

In an attempt to explore this further, we considered several contingencies. For instance, we tested whether large firms are better than small firms at exploiting complementarities. This would be consistent with the notion that in small firms a lack of management time and the increased complexity of the innovation process are likely to result in the underperformance of joint extensive alliance activities. We split the sample into two subsamples: firms with fewer than 1000 employees (n = 585) and firms with more than 1000 employees (n = 714). In general, the results support the increased-complexity expectation. We observe that smaller firms experience the decreasing marginal impact of diverse alliance portfolio sooner, particularly when alliance strategies reflect multiple objectives. The complementarity tests show that in the larger-firm subsample there is clear support for a complementarity effect between the relational & structural dimensions, while in the smaller-firm subsample this effect is absent. In addition, for smaller firms the substitution effect between the functional & structural dimensions is attenuated. Because the samples are smaller, some of the combinations of dimensions are sparsely populated. Therefore, we place a caveat on these results. Finally, as an additional check, we checked and found that the outcomes of the test according to Carree, Lokshin, and Belderbos (2011) testing procedure (not tabulated) are consistent with our reported results.

7. Discussion and conclusion

Despite the growing interest in alliance portfolios in recent years by both scholars and practitioners, there has been limited attention to the effects of portfolio configuration on firm innovation. In this paper, we aim to contribute to the understanding of this phenomenon. In line with the view that performance effects of the portfolio go beyond the effects of individual alliances (Greve, Rowley, and Shipilov 2013) we find that exploiting potential complementary effects among the constituent elements of a portfolio is important to spur performance.

The contribution of this study to the alliance portfolio literature is twofold. First, we contribute to the literature on the performance implications of the portfolio configuration in line with the suggestion of Wassmer (2010). By distinguishing among the partner and tie characteristics, we consider in the portfolio architecture structural, attribute, relational and the functional dimensions (Gulati 1998; Hoffmann 2007; Lavie and Rosenkopf 2006; Rowley, Behrens, and Krackhardt 2000) and how they impact firm innovation individually and jointly.

Second, our study complements previous literature (e.g. Hashai, Kafouros, and Buckley 2015; Van Wijk and Nadolska 2015) by deepening our understanding of the challenges and benefits associated with managing alliance portfolios. Our results suggest that there are both complementarity and sub-additive effects among the portfolio dimensions.

There are important practical implications of our study. Alliance managers need to be aware that the specific combination of practices that a firm is able to deploy represents a key competitive advantage, and complementarities play a critical role in developing this endeavour (Helfat 1997; Teece, Pisano, and Shuen 1997). Complementarities have been found essential also for the development of organisational routines (Becker 2004; George 2005; Teece 1986) and for sustaining performance (Kyriakopoulos and Moorman 2004). Specific combinations among portfolio dimensions have complementarity effects that are ultimately beneficial for performance. Although challenging, monitoring the composition and evolution of the alliance portfolio is therefore critical for innovation. To support managerial endeavours, it is important to identify and exploit complementarities and to avoid the combinations that are detrimental. Managers should therefore pay particular attention to these specific combinations in order to better understand the overall effects of alliances portfolios on the firm’s results. Interestingly, our results indicate that the alliance ties dimension of portfolios is the locus of innovation and it is particularly relevant for enhancing value creation. Thus, managers are encouraged to pay particular attention to this aspect when developing the alliance portfolio architecture. On the other side, an efficient portfolio should avoid to develop both structural and functional dimensions. Innovation may be fostered by focusing on either of the two but not from both jointly. Our findings seem to indicate that a parsimonious and focused approach when developing an alliance portfolio should be preferred.

This study is not without limitations. In our analysis, we only looked at complementarity among practices that are dichotomous. This approach only allows assessing whether there is complementarity in simple ‘adoption’ of practices. Firms may also differ in terms of level of the different dimensions. Taking into account scale would require testing for complementarity among continuous variables, which was not practical due to severe collinearity among the cross-terms.

A number of questions are left for future research. First, in our analysis we addressed the question of complementarity among four dimensions of an alliance portfolio. We abstracted from unpacking complementarity that may be present within each dimension. One such complementarity has recently been investigated by Lavie, Kang, and Rosenkopf (2011) who considered the implication of pursuing both exploration and exploitation in a single dimension for the financial performance of the firm. Further studies may test whether within- or across-dimension features are complementary both innovation and economic performance. We focused on the pharma industry, which is known to have specific alliance dynamics (Stuart, Ozdemir, and Ding 2007). It would be interesting to explore whether our findings apply to other sectors. Finally, the focus of the present study has been at the portfolio level and we have focused in our conceptual elaboration on a limited set of interactions (Functional & Structural and Functional & relational). Future research could consider to expand the above perspective, consider more in detail other pair-wise interactions, foster our understanding of why (or why not) their interaction may generate synergies and asses their effects at the organisational level. Future research could consider the organisational perspective. For example, potentially organisations that are capable of managing both new and old partners as well as technological close and distant partners may be assumed to possess some sort of higher order capabilities which may potentially be positively associated with performance; However, the above situation is prone to creating managerial complexities that may overcome the benefits. For instance, these complexities may derive from the non-transferability (or partial transferability) of the lessons learned from managing old/new partners to managing close/distant partners (and/or vice versa). Companies may thus be tempted to transfer the lessons learned in one dimension across dimensions. Further studies may explore this organisational perspective and dilemmas in more detail. For instance, future research could assess the performance over time of organisations developing different types (with emphasis on different dimensions) of alliance portfolios.

Overall, despite the need for further research and the shortcomings of our contribution, the current analysis does provide a number of interesting new insights in the value drivers in the alliance portfolios.

Disclosure statement

No potential conflict of interest was reported by the authors.

Acknowledgement

We gratefully acknowledge the constructive comments and suggestions made by the editor Grazia Santangelo and two anonymous reviewers. We would also like to thank the participants of the seminars at Maastricht University and Tilburg University for their help and suggestions.

Notes

¹ In this paper, we follow the generally accepted in the literature definition of an alliance portfolio: ‘a focal firm’s past as well as ongoing strategic alliances of all types’ Wassmer (2010, 44).

² We use the following definition of complementarity originally formulated by Milgrom and Roberts (1990, 181) [complementarities among activities occur] ‘if doing (more of) any of them increases the returns to doing (more of) the others’. In contrast, activity x_i and x_j are sub-additive if the implementation of one activity decreases the marginal return from another.

³ Studies of complementarity fall in a rich research tradition, an extensive review of which is beyond the scope of this paper. The examination of complementarity effects has been done with respect to various areas of innovation activities including external and internal R&D (e.g. Belderbos, Lokshin, and Sadowski 2015; Cassiman and Veugelers 2006; Hagedoorn and Wang 2012), partner resources in alliances (e.g. Rothaermel and Boeker 2008), technology-sourcing modalities (e.g. van de Vrande, Vanhaverbeke, and Duysters 2011), the types of external linkages (Belderbos, Carree, and Lokshin 2006; Tiwana 2008), the organizational and technological forms of innovation (Battisti and Stoneman 2010) and the knowledge transfer modes in strategic alliances (e.g. Buckley et al. 2009). In the alliance literature, the relevance of complementarities seems to be well recognized. Attention has been given to various contexts including resource complementarities (Lavie 2007), complementarities of partners’ offering (Parise and Casher 2003), and assets complementarities (Rothaermel 2001).

⁴ Carree, Lokshin, and Belderbos (2011) show equivalence between the exclusive binary variable approach and non-exclusive binary variable approach (see Equation (9), 265.We use exclusive dummy variable approach in our tests.

⁵ The collection of possible combinations defined in binary order is .

Appendix

^{Table A1}

Table A1. Inequality constrained estimates of Equation (1) testing for complementarity or sub-additivity in alliance portfolio.

Independent variables	Model 4	Model 5	Model 6	Model 7	Model 8	Model 9	Model 10	Model 11	Model 12	Model 13	Model 14	Model 15
Intercept	0.150 (0.451)	0.272* (0.156)	0.167 (0.452)	0.390** (0.168)	0.117 (0.450)	0.190 (0.453)	0.190 (0.454)	0.587*** (0.227)	0.089 (0.452)	0.307* (0.170)	0.069 (0.185)	0.136 (0.451)
Log(R&D)	0.352*** (0.041)	0.339*** (0.038)	0.344*** (0.041)	0.336*** (0.038)	0.345*** (0.041)	0.345*** (0.041)	0.344*** (0.041)	0.327*** (0.038)	0.345*** (0.041)	0.338*** (0.038)	0.350*** (0.039)	0.341*** (0.041)
Patents/R&D	0.492*** (0.078)	0.501*** (0.078)	0.496*** (0.079)	0.497*** (0.079)	0.500*** (0.079)	0.501*** (0.079)	0.504*** (0.079)	0.494*** (0.078)	0.495*** (0.078)	0.501*** (0.078)	0.501***(0.078)	0.507*** (0.079)
Firm size	–0.042 (0.039)	–0.030 (0.035)	–0.038 (0.039)	–0.030 (0.035)	–0.039 (0.039)	–0.036 (0.039)	–0.034 (0.039)	–0.017 (0.036)	–0.038 (0.039)	–0.029 (0.035)	–0.043 (0.035)	–0.035 (0.039)
Portfolio size	0.012*** (0.003)	0.011*** (0.003)	0.012*** (0.003)	0.010*** (0.003)	0.011*** (0.003)	0.011*** (0.003)	0.011*** (0.003)	0.012*** (0.003)	0.011*** (0.003)	0.011*** (0.003)	0.011*** (0.003)	0.011*** (0.003)
Experience alliances	–0.140*** (0.051)	–0.138*** (0.050)	–0.135*** (0.051)	–0.131*** (0.050)	–0.139*** (0.050)	–0.143*** (0.051)	–0.144*** (0.051)	–0.129*** (0.050)	–0.150*** (0.050)	–0.137*** (0.050)	–0.138*** (0.050)	–0.146***(0.051)
Log(Firm age)	–0.065 (0.066)	–0.074 (0.059)	–0.067 (0.067)	–0.084 (0.058)	–0.059 (0.066)	–0.072 (0.066)	–0.076 (0.066)	–0.098 (0.059)	–0.054 (0.066)	–0.076 (0.059)	–0.061 (0.060)	–0.059 (0.066)
Cultural distance	0.029 (0.086)	0.022 (0.084)	0.047 (0.086)	0.018 (0.084)	0.043 (0.086)	0.022 (0.087)	0.006 (0.086)	0.011 (0.085)	0.031 (0.086)	0.021 (0.084)	0.044 (0.084)	0.025 (0.086)
Functional	0.319*** (0.094)	0.329*** (0.088)	0.314*** (0.093)	0.306*** (0.088)	0.336*** (0.094)	0.325*** (0.094)	0.299*** (0.093)	0.303*** (0.088)	0.296*** (0.093)	0.328*** (0.090)	0.331*** (0.091)	0.356*** (0.092)
Relational	0.124 (0.157)	0.127 (0.145)	–0.107 (0.127)	0.130 (0.155)	–0.032 (0.128)	0.134 (0.157)	0.152 (0.158)	0.070 (0.146)	0.139 (0.157)	0.123 (0.146)	–0.003 (0.153)	0.145 (0.157)
Structural	–0.027 (0.135)	0.377** (0.175)	0.359** (0.176)	0.334** (0.165)	0.382** (0.176)	0.486*** (0.134)	0.406** (0.176)	0.299* (0.165)	0.273* (0.163)	0.376** (0.175)	0.379** (0.163)	0.391** (0.176)
Attribute	0.154* (0.086)	0.178** (0.079)	0.172** (0.086)	0.183** (0.079)	0.188** (0.086)	0.174** (0.086)	0.188** (0.086)	0.150* (0.078)	0.184** (0.086)	0.175** (0.078)	0.185** (0.080)	0.189** (0.086)
Functional & relational	0.172* (0.100)	0.184* (0.098)	0.197** (0.100)	0.171* (0.097)	0.213** (0.099)	0.180* (0.101)	0.252* (0.094)	0.154 (0.095)	0.238** (0.095)	0.180* (0.097)	0.182* (0.097)	0.229** (0.096)
Functional & structural	0.263** (0.103)	0.259*** (0.100)	0.235** (0.102)	0.250** (0.101)	0.262** (0.103)	0.243** (0.103)	0.318** (0.099)	0.231** (0.098)	0.242** (0.102)	0.257** (0.100)	0.255*** (0.101)	0.248** (0.102)
Functional & attribute	0.340*** (0.091)	0.315*** (0.090)	0.304*** (0.094)	0.254*** (0.089)	0.321*** (0.095)	0.312*** (0.094)	0.312*** (0.093)	0.289*** (0.089)	0.363*** (0.091)	0.313*** (0.090)	0.317*** (0.091)	0.310*** (0.093)
Relational & structural	–0.036 (0.127)	–0.243 (0.155)	–0.057 (0.123)	–0.266* (0.156)	–0.237 (0.156)	–0.116 (0.134)	–0.240 (0.157)	–0.218 (0.151)	–0.159 (0.139)	–0.245 (0.155)	–0.107 (0.135)	–0.244 (0.156)
Structural & attribute	0.389*** (0.134)	0.498*** (0.143)	0.487*** (0.145)	0.171 (0.110)	0.506*** (0.145)	0.416*** (0.130)	0.510*** (0.146)	0.465*** (0.129)	0.558*** (0.138)	0.496*** (0.143)	0.495*** (0.146)	0.509*** (0.146)
Relational & attribute	0.122 (0.101)	–0.015 (0.132)	–0.027 (0.136)	0.031 (0.123)	0.087 (0.120)	–0.022 (0.136)	0.004 (0.136)	–0.051 (0.122)	–0.012 (0.136)	–0.009 (0.135)	0.064 (0.126)	–0.005 (0.136)
Functional & relational & structural	0.254*** (0.099)	0.285*** (0.096)	0.246** (0.098)	0.283*** (0.096)	0.289*** (0.100)	0.270*** (0.099)	0.271*** (0.099)	0.260*** (0.094)	0.307 (0.098)	0.284*** (0.096)	0.281*** (0.097)	0.274*** (0.099)
Functional & relational & attribute	0.309*** (0.097)	0.351*** (0.095)	0.336*** (0.097)	0.333*** (0.096)	0.332*** (0.097)	0.350*** (0.098)	0.392*** (0.094)	0.329*** (0.094)	0.305*** (0.095)	0.350*** (0.095)	0.351*** (0.096)	0.324*** (0.095)
Relational & structural & attribute	0.482*** (0.139)	0.270 (0.203)	0.260 (0.204)	0.028 (0.136)	0.284 (0.204)	–0.050 (0.142)	0.278 (0.205)	0.264* (0.148)	0.126 (0.175)	0.268 (0.203)	–0.040 (0.178)	0.279 (0.204)
Functional & structural & attribute	0.176 (0.118)	0.145 (0.120)	0.119 (0.122)	0.243** (0.112)	0.149 (0.123)	0.173 (0.117)	0.218** (0.109)	0.118 (0.118)	0.218** (0.108)	0.144 (0.120)	0.141 (0.121)	0.202* (0.109)
Functional & relational & structural & attribute	0.269** (0.107)	0.315*** (0.105)	0.291*** (0.107)	0.330*** (0.104)	0.318*** (0.108)	0.336*** (0.107)	0.298*** (0.106)	0.291*** (0.104)	0.282*** (0.105)	0.314*** (0.105)	0.309*** (0.106)	0.369*** (0.102)
Pair of dimensions tested
Imposed constraints	Functional & Relational		Functional & Structural		Functional and Attribute		Relational & Structural		Relational & Attribute		Structural & Attribute
Constraint1	–β fun – β rel + β con + β fun,rel > 0	–β fun – β rel + β con + β fun,rel < 0	–β fun – β str + β con + β fun,str > 0	–β fun – β str + β con + β fun,str < 0	–β fun – β atr + β con + β fun,atr > 0	–β fun – β atr + β con + β fun,atr < 0	–β rel – β str + β con + β rel,str < 0	–β rel – β str + β con + β rel,str > 0	–β rel – β atr + β con + β rel,atr < 0	–β rel – β atr + β con + β rel,atr > 0	–β str – β atr + β con + β str,atr < 0	–β str – β atr + β con + β str,atr > 0
Constraint2	–β fun,atr – β rel,atr + β atr + β fun,rel,atr > 0	–β fun,atr – β rel,atr + β atr + β fun,rel,atr < 0	–β fun,atr – β str,atr + β atr + β fun,str,atr > 0	–β fun,atr – β str,atr + β atr + β fun,str,atr < 0	–β str,atr – β fun,str + β str + β fun,str,atr > 0	–β str,atr – β fun,str + β str + β fun,str,atr < 0	–β fun,rel – β fun,str + β fun + β fun,rel,atr < 0	–β fun,rel – β fun,str + β fun + β fun,rel,atr > 0	–β fun,rel – β fun,atr + β fun + β fun,rel,atr < 0	–β fun,rel – β fun,atr + β fun + β fun,rel,atr > 0	–β fun,str – β fun,atr + β fun + β fun,rel,atr < 0	–β fun,str – β fun,atr + β fun + β fun,rel,atr > 0
Constraint3	–β fun,str – β rel,str + β str + β fun,rel,str > 0	–β fun,str – β– + β str + β fun,rel,str < 0	–β fun,rel – β rel,str + β rel + β fun,rel,str > 0	–β fun,rel – β rel,str + β rel + β fun,rel,str < 0	–β fun,rel – β rel,atr + β rel + β fun,rel,atr > 0	–β fun,rel – β rel,atr + β rel + β fun,rel,atr < 0	–β str,atr – β rel,atr + β atr + β rel,str,atr < 0	–β str,atr – β rel,atr + β atr + β rel,str,atr > 0	–β rel,str – β str,atr + β str + β rel,str,atr < 0	–β rel,str – β str,atr + β str + β rel,str,atr > 0	–β rel,str – β rel,atr + β rel + β rel,str,atr < 0	–β rel,str – β rel,atr + β rel + β rel,str,atr > 0
Constraint4	–β fun,str,atr – β rel,str,atr + β str,atr + β fun,rel,str,atr > 0	–β fun,str,atr – β rel,str,atr + β str,atr + β fun,rel,str,atr < 0	– β fun,rel,atr – β rel,str,atr + β rel,atr + β fun,rel,str,atr > 0	–β fun,rel,atr – β rel,str,atr + β rel,atr + β fun,rel,str,atr < 0	–β fun,rel,str – β rel,str,atr + β rel,str + β fun,rel,st,atr > 0	–β fun,rel,str – β rel,str,atr + β rel,str + β fun,rel,st,atr < 0	–β fun,rel,atr – β fun,str,atr + β fun,atr + β fun,rel,str,atr < 0	–β fun,rel,atr – β fun,str,atr + β fun,atr + β fun,rel,str,atr > 0	–β fun,rel,str – β fun,str,atr + β fun,str + β fun,rel,str,atr < 0	–β fun,rel,str – β fun,str,atr + β fun,str + β fun,rel,str,atr > 0	–β fun,rel,atr – β fun,rel,atr + β fun,rel + β fun,rel,str,atr < 0	–β fun,rel,atr – β fun,rel,atr + β fun,rel + β fun,rel,str,atr > 0
AIC	8711.681	8721.411	8719.058	8716.815	8714.432	8714.409	8710.891	8713.854	8711.731	8713.793	8712.179	8714.543
SBC	8944.337	8943.726	8941.373	8949.470	8941.917	8947.064	8938.376	8941.340	8944.386	8936.108	8939.664	8942.028
Log–Likelihood	–4310.841	–4317.705	–4316.529	–4313.407	–4313.216	–4312.204	–4311.446	–4312.927	–4310.865	–4313.897	–4312.089	–4313.271
Log–Likelihood^‡	–4317.736	–4317.736	–4319.358	–4319.358	–4314.691	–4314.691	–4313.594	–4313.594	–4314.018	–4314.018	–4314.611	–4314.611

Notes:

n = 1300; year dummies are not shown; numbers in parentheses are standard errors;

^* p < 0.1

^** p < 0.05

^*** p < 0.01

^‡ from a model imposing the corresponding constraints as equalities.