Moderating influence of product diversification on the international diversification-performance relationship: A meta-analysis

Numerous studies have examined the impact of international diversification on firm performance. However, the literature is characterised by inconsistent findings, suggesting the need for a quantitative review and synthesis of the hypothesised relationships. Using a sample of 263 effect sizes from 187 primary studies between 1974 and 2021, we conduct a meta-analysis to test the relationship between international diversification and firm performance, and the moderating effect of product diversification. The results of our meta-analysis indicate that the relationship between international diversification and firm performance is non-linear inverted U-shaped. Furthermore, we find that performance is higher in firms with low/related product diversity and lower in firms with high/unrelated product diversity, suggesting that the dual-diversification strategy is detrimental to firm performance. Although there is no significant difference in the performance of firms from advanced and emerging economies, the results highlight the importance of intangible assets for diversified firms.


Introduction
International diversification represents the extent to which firms undertake value-adding activities in foreign markets (Hennart, 2007). Over the past several decades, a thriving body of literature has attempted to ascertain the nature and shape of the international diversification-performance (ID-P) relationship. Scholars have explored the topic using various theoretical approaches, such as market power theory (Grant, 1987), transaction cost theory (Tallman & Li, 1996), portfolio theory (Denis, Denis, & Yost, 2002), organisational learning theory (Ruigrok & Wagner, 2003), institution-based view (Delios, Xu, & Beamish, 2008), and the Uppsala model of internationalisation (Almodóvar & Rugman, 2014). Despite the large number of studies, the literature remains divided on the nature of the relationship between international diversification and firm performance.
Different arguments on the ID-P relationship have emerged over the years. Early studies focused on the risk reduction aspect of internationalisation, and a central theme within this literature is that investment in uncorrelated economies reduces the risk of market failure. Thus, firms with higher foreign operations among the total operations earn stable earnings compared to firms with lower foreign operations (Kim, Hwang, & Burgers, 1993;Rugman, 1976). Next, international diversification allows firms to spread their fixed costs over a wider scope, standardise production and amortise investment in R&D, thereby achieving economies of scale (Hitt, Hoskisson, & Kim, 1997;Kobrin, 1991). Some studies have argued that firms with a wider geographic scope are able to increase profitability by tapping the arbitrage arising from uneven economic development of nations (Ghemawat, 2001;Porter, 1990), Others have suggested that learning is an increasing function of internationalisation and exposure to diverse environments contributes positively to the development of knowledge and intangible assets of the firm, which aids in scanning for new market opportunities (Contractor, Kundu, & Hsu, 2003). As evident from these arguments, there are different theoretical perspectives on the ID-P relationship. Palich, Cardinal, and Miller (2000) used a three-stage identification process to classify a research field as mature: first, a substantial number of empirical studies have been conducted; second, the results are reasonably consistent and generalisable; and third, the research has led to a general consensus regarding the key relationships. Thus, it is safe to classify the literature on the ID-P relationship as immature because it is characterised by an ongoing debate concerning the nature of the relationship. No less than four different relationships have been suggested: positive (Delios et al., 2008;Grant, 1987;Zahra, Ireland, & Hitt, 2000), negative (Chang & Wang, 2007;Riahi-Belkaoui, 2003), curvilinear (Gaur & Kumar, 2009;Ruigrok & Wagner, 2003), and no direct relationship (2011;Hennart, 2007). The nature of the curvilinear relationship is characterised by further dispute. Therefore, U-shaped (Capar & Kotabe, 2003;Contractor, Kumar, & Kundu, 2007), inverted Ushaped (Borda, Geleilate, Newburry, & Kundu, 2017;Grant, Jammine, & Thomas, 1988), S-shaped (Lu & Beamish, 2004;Ruigrok, Amann, & Wagner, 2007), and, more recently, M− shaped (Almodóvar & Rugman, 2014;Mendoza, Espinosa-Méndez, & Araya-Castillo, 2019) and W-shaped (Zhou, 2018) relationships have been suggested. Evidently, the literature is far from reaching a consensus.
Another issue that persists in the literature is the moderation effect of product diversification on the ID-P relationship. While product diversification has been suggested to have a positive effect on firm performance because it provides opportunities to achieve synergies (Michael Geringer, Beamish, & Dacosta, 1989;Hitt et al., 1997), the literature has been divided on the combined effects of international and product diversification. On the one hand, studies have suggested that an integrated product-international diversification strategy yields stable returns because it reduces variance exposure (Kim et al., 1993). On the other hand, management complexities and costs of governance increase substantially as firms venture into new product segments and geographic domains (Qian, 2002;Tallman & Li, 1996). Thus, the literature again falls short of reaching a consensus.
To address these inconsistencies, our primary goal is to ascertain the nature of the ID-P relationship by conducting a meta-analysis of 187 primary studies. Our second goal is to test the nature of the ID-P relationship under the moderation effect of product diversification. We argue that the inconsistencies in the literature are attributable to the different theoretical approaches, sample locations, and firm-level characteristics, such as size and intangible assets. Our approach is both theoretically and empirically driven. Theoretically, we draw upon the internalisation/transaction cost theory and the knowledge/resourcebased view. This approach provides the scope for exploring and comparing various views posited by the ID-P literature, such as flexibility/risk reduction (Kim et al., 1993;Rugman, 1976), economies of scale (Grant et al., 1988;Hitt et al., 1997;Miller, Lavie, & Delios, 2016), learning effects (Contractor et al., 2003;Lu & Beamish, 2001), and governance costs (Chang & Wang, 2007). In addition, integrating the views from the aforementioned theories allows us to conduct an indepth examination of the interaction between international and product diversification. Specifically, we emphasise that the interrelatedness between knowledge acquired through international and product diversification allows firms to achieve synergies. Thus, firms are able to achieve higher performance through a dual diversification strategy.
Empirically, we use meta-analytical techniques to integrate the distorted findings from existing studies to reveal underlying relationships and hidden moderation effects (Hunter & Schmidt, 1990). Buckley, Devinney, and Tang (2014) argue that this feature of meta-analysis is particularly useful in the field of international business, where samples are based on the availability of data from different countries at different points in time. Our meta-analytical tests include linear relationships as well as all previously proposed curvilinear ID-P relationships (e.g., U-, inverted U-, S-, M-, and W-shaped relationships) more than any other meta-analytical study on the topic (Bausch & Krist, 2007;Yang & Driffield, 2012), thus adding novelty to our work. The remainder of the paper is structured as follows. In the following section, we discuss the theory and frame our hypotheses. Next, we explain the methods employed to conduct the meta-analysis. Subsequently, we discuss the results before providing concluding remarks.

Theory and hypotheses
The ID-P relationship has been explored using several theoretical lenses. In a broader sense, the literature has evolved along two distinct arguments (Hennart, 2007). First, international diversification has been argued to offer operational flexibility and risk reduction incentives. From a portfolio theory perspective, Rugman (1976) argues that firms are able to reduce the variance in their earnings by spreading their operations across various countries as long as the economies of the countries are not perfectly correlated. Thus, the stability of earnings is an increasing function of international diversification. Similarly, the real options theory suggests that geographically dispersed foreign subsidiaries offer the option to switch production when uncertainty occurs in a country (Kogut & Kulatilaka, 1994;Tang & Tikoo, 1999).
Second, international diversification has been argued to increase profitability and firm performance by offering scale economies, and access to wider resources and market opportunities. Firms are able to achieve scale economies by spreading common and centralised expenses over a wider geographic scope (Hitt et al., 1997). Thus, internationally diversified firms should be more profitable than their domestic counterparts. From a resource-based perspective, profitability through international diversification has been linked to access to resources. For example, Contractor et al. (2003) argue that internationally diversified firms are able to access cheap labour, natural resources and advanced technologies. Similarly, Chen and Tan (2012) argue that international diversification allows firms to acquire unique resources and overcome domestic constraints, thus giving them a competitive advantage. The learning theory suggests that firms operating in multiple markets simultaneously are able to absorb new knowledge and seek better opportunities that may otherwise be unavailable to less diversified firms (Hitt et al., 1997). Furthermore, a wider geographic scope also allows firms to switch production and sales from less profitable markets to more profitable ones (Thomas & Eden, 2004).
However, these arguments have been contradicted. The transaction cost theory challenges both the risk reduction and profit maximisation arguments. First, the transaction cost theory suggests that firms choose to invest in countries that are culturally and economically related. Thus, the risk reduction benefits are not fully materialised unless the firm chooses to diversify across different product segments (Hennart, 2007). Second, Hennart (2007) argues that profits can be maximised from investments made in fewer countries provided the firm is capable of tapping a market sufficiently large to achieve scale economies. Some scholars have argued that performance is an inverse function of international diversification because of the liability of foreignness (Denis et al., 2002;Lu & Beamish, 2001). Related to the liability of foreignness argument, others have argued that cross-national differences increase the costs of integration and coordination and decrease firm performance (Patel, Criaco, & Naldi, 2018). From a cultural distance perspective, Ruigrok and Wagner (2003) argue that performance decreases with an increase in international diversification because expansion into culturally unrelated environments creates an imbalance between internal competencies and the external environment.
Over time, the ID-P literature has evolved from simple linear relationships to more complex non-linear relationships by combining the aforementioned arguments and theoretical perspectives. For instance, Grant (1987) and Hitt et al. (1997) use the scale economies and governance costs arguments to posit an inverted U-shaped relationship such that higher performance from international diversification results from efficient resource allocation decisions. However, performance decreases at higher levels of international diversification because of the increase in administrative and coordination costs. Some scholars have argued that the ID-P curve displays a U-shaped relationship rather than an inverted U-shaped relationship. According to this stream of research, performance decreases during the initial stages of international diversification due to the liability of foreignness (Lu & Beamish, 2001), crossnational differences (Ruigrok & Wagner, 2003) and the inability of firms to manage start-up costs (Miller et al., 2016). However, performance gradually increases as the learning effect kicks in and firms are able to obtain scale economies. Building on U-and inverted U-shaped relationships, recent studies have managed to develop more complex sigmoid S-shaped and quartic M-and W-shaped relationships. We summarise the various ID-P relationships and the different theoretical arguments in Table 1.

International diversification and firm performance
As noted above, the relationship between international diversification and firm performance is complex. In this section, we formulate preliminary hypotheses to guide our meta-analysis. The extant literature attributes the positive impact of international diversification on performance to the possibility of internalising ownership advantages over a wider scope, exploiting market imperfections and extracting arbitrage from uneven economic growth, risk diversification, economies of scale, and access to knowledge resources.
First, multinationality is an efficient organisation structure to transfer and exploit various firm-specific advantages (2001; Dunning, 1980;Kirca et al., 2011) andinternalise market imperfections (2009;Buckley & Casson, 1976;Rugman, 1976). Firm-specific advantages, which include intangible assets, patents, technological know-how, brand names, trademarks, and various managerial and organisational skills, have a tendency to extract monopoly rents for their owners. Such assets are usually difficult to sell and are not location-bound (Verbeke, Li, & Goerzen, 2009). It is more advantageous for firms to exploit such resources in external markets by internalising market imperfections (Morck & Yeung, 1991). Kirca, Roth, Hult, and Cavusgil (2012) argue that the value of intangible assets is enhanced in direct proportion to the degree of international diversification. Thus, a firm with a wider geographic scope is able to exploit more market imperfections and attain benefits of internalising the ownership advantages, which indicates that internationally diversified firms are likely to extract higher returns on investment than domestic firms. In addition to exploiting market imperfections, a wider geographic scope increases the potential of extracting arbitrage (Contractor et al., 2003). Firms with their operations spread across different economies are able to reap the benefits of country-specific resources, such as low labour costs, better technology, or unique natural resources (Ghemawat, 2001;Kobrin, 1991;Porter, 1990).
Second, flexibility imparted by international diversification allows the firm to maintain steady performance growth by shifting production to favourable environments when uncertainty occurs in a particular country (Kim et al., 1993;. For instance, operating in one country may be riskier than operating in others, and multicountry investments serve as a buffer should the environment of one country turn unfavourable. Similarly, by investing in countries whose economies are not integrated or correlated, the overall operations of the firm are not affected if the economy of one country goes into decline (Shapiro, 1978). Therefore, international diversification imparts flexibility to the firm to respond to changes in the external environment (Denis et al., 2002). While this flexibility might not have a direct effect on firm profitability, it does leave the firm with an option to reduce its losses or to maintain stable earnings (Belderbos & Zou, 2009;Kogut & Kulatilaka, 1994;Rugman, 1976).
Third, it has been argued that international diversification increases profitability through scale economies. A wider geographic scope permits the firm to standardise products, streamline production, and coordinate R&D activities (Hitt et al., 1997;Kobrin, 1991). Through these activities, the firm is able to achieve scale economies and increase returns on fixed costs. In a similar vein, Contractor et al. (2003) posit that the advantages of international diversification accrue from the possibility of spreading the central costs across nations. Thus, firms with a wider geographic scope are able to achieve scale economies and increase profitability.
Fourth, international diversification allows the firm to increase its knowledge resources. The expansion of firms beyond their national borders after acquiring essential knowledge about foreign markets has been a central theme in the internationalisation literature (Johanson & Vahlne, 1977. International expansion aids this process by enhancing the firm's knowledge base through experiential learning (Autio, Sapienza, & Almeida, 2000;Vermeulen & Barkema, 2001). Moreover, exposure to diverse environments stimulates firms to develop diverse capabilities (Kim et al., 1993). Similarly, a wider geographic scope allows the firm to observe competition trends and identify new market opportunities (Contractor et al., 2003).
While international diversification does accrue benefits, evidence has suggested that performance declines with an increase in geographic scope. The transaction cost theory suggests that high levels of international operation generally increase governance costs (Williamson, 1985). Foreign investments are asset-specific, location-specific, and irreversible (Li & Rugman, 2007;Williamson, 1985). Because irreversible investments represent sunk costs (O'Brien & Folta, 2009), the amounts invested previously are non-recoverable; thus, new investments would require commitment of additional resources.
Internationally diversified firms have to deal with an assortment of institutional and cultural challenges. Institutional theorists argue that cross-border expansion increases the difficulties of establishing organisational legitimacy (Kostova & Zaheer, 1999;Zaheer, 1995). Applying this logic, the more internationally diversified a firm is, the more challenges it will face in establishing legitimacy in different countries. Evidence also suggests that cultural distance between nations has a detrimental effect on firm and subsidiary performance (Beugelsdijk, Kostova, Kunst, Spadafora, & van Essen, 2018;Luo & Peng, 1999). Hennart (2007) argues that the cost of governance increases significantly with cultural distance because with an increase in distance, firms need additional knowledge to direct their actions effectively. Therefore, becoming acquainted with new cultures is an important step towards improving performance in a foreign country (Dhanaraj & Beamish, 2009) and necessitates that firms familiarise themselves with the new cultural environment, a process that consumes additional resources.
International diversification represents the spatial expansion of the firm across its domestic borders into new countries (Hitt et al., 1997), and over-diversification is subject to risks of regional and geographical diversity. Regional differences and the increased costs of coordinating geographically dispersed operations can potentially negate the benefits that arise from multinationality (Michael Geringer et al., 1989). Investing in a geographically distant country adds logistical costs and generally requires additional labour to manage the supply chain. Moreover, excessive international diversification means handling matters with clients and suppliers from different physical domains and cultural and linguistic backgrounds, which in turn impose restrictions and constraints on the strategies of the firm (Feely & Harzing, 2003;Grinblatt & Keloharju, 2001;Siddharthan & Lall, 1982).
As noted, the benefits and costs associated with international diversification accrue at different stages of internationalisation. To guide our research, we formulate the following hypothesis by reconciling the aforementioned theoretical arguments.
Hypothesis 1. The relationship between international diversification and firm performance is non-linear inverted U-shaped.

Moderating influence of product diversification
Product diversification refers to the expansion of firms into related and unrelated product segments (Michael Geringer et al., 1989;Qian, 2002) or into vertical and horizontal segments (Qian, 1997;Tsang & Yip, 2007;Zhao & Luo, 2002). While international and product diversification coexist in an international business context, the interaction between the two is complex and the extant literature has provided competing views on their combined effect on firm performance.
One view argues that firms exploit the synergies arising from international and product diversification to enhance performance (Chang & Wang, 2007;Chao, Kim, Zhao, & Hsu, 2012;Hitt et al., 1997). The synergy from a dual-diversification strategy creates an environment in which firms obtain economies of scale by using common brand names and production facilities to serve different geographies (Pennings, Barkema, & Douma, 1994) or by introducing new products to cater to the demands of diverse customer groups (Hsu, 2006;Tallman & Li, 1996). Some scholars have linked diversification synergies to the learning effect. Since both international and product diversification involve a Cross-national (regional) differences: Risk of failure increases due to complexity arising from regional differences.  (2007) Learning effect & Governance costs: Liability of foreignness and newness faced by firms while entering into new markets outweigh the incremental benefits of international expansion. The learning acquired during the initial stages of expansion helps firms organise internal structures and adapt to external environments. At the point of "international threshold" governance and coordination costs outweigh the benefits of internationalisation.

M Almodóvar and
Rugman (2014) The ID-P relationship displays an S-curve, although at the initial stages of internationalisation, performance increases because of opportunistic sales.

M Markides (2019)
Cross-national (regional) differences, Learning effect, & Governance costs: Performance is high during the initial stages of international diversification because the number of countries and foreign affiliates are low and firms can take advantage of their organisational infrastructure without making additional investments. However, as the number of countries and affiliates increase, the cross-national distance increases and performance decreases. Gradually, firms gain advantage using the knowledge acquired during the initial stages of international diversification. Finally, the costs of internationalisation extend beyond a certain threshold and exceed the benefits of entering new markets. significant investment in R&D, firms build up a reservoir of knowledge that can be implemented across different business activities. The knowledge accrued through this process can be cross-implemented and thus mutually beneficial for furthering the knowledge reservoir for future use (Grant, 1996). Moreover, the costs of sharing, adopting and implementing the skills and capabilities of other business units are lower if they operate in similar product environments (Chang & Wang, 2007). Therefore, firms that implement a related product diversification strategy in an international environment are in a position to adapt and react to external changes by using their interdivisional knowledge resources. Another view posits that the integration of both diversification modes is detrimental to firm performance because of the added costs of governance and coordination. In general, the costs of governance increase as the global portfolio enlarges (Williamson, 1985). Thus, a diversified product portfolio will only add to the governance costs. In line with this, Tallman and Li (1996) argue that governance costs associated with a dual international-product diversification strategy outstrip the returns on investments and deplete firm performance. Hitt et al. (1997) argue that costs of communication and coordination are a positive function of increased foreign transactions. When these firms expand into new product segments, the interdependence between subsidiaries increases, thus leading to a complex organisational structure. The complex organisational structure increases information asymmetry and negatively affects managerial efficiency because of the confusion and inadequate understanding associated with a varied business portfolio (Chang & Wang, 2007).
Efficient management of international diversification based on learning gained during product diversification builds for a weak argument because both diversification modes require separate skills that are non-transferable and non-exchangeable. The added costs of acquiring knowledge about either new products or geographies will reduce the positive returns of diversification. In line with this argument, evidence shows that the costs of acquiring information are different for both diversification modes (Denis et al., 2002;Lu & Beamish, 2004). Therefore, firms that expand along the two dimensions of diversification are at a double cost disadvantage compared to firms that expand along only a single dimension (i.e., either firms that diversify into new geographic locations or firms that diversify into new product segments).
The complexities of managing a dual-diversified portfolio also arise externally. As firms expand into new product segments, they stretch their internal resources to a point where they may struggle to adapt to their new competitive environment (Ruigrok & Wagner, 2003). When product-diversified firms expand into new geographies, the differences in infrastructure and regulations, in particular patent regulations, may create obstacles in selling their products and achieving a competitive position in the new environment (Chang & Wang, 2007). It can also be argued that product-diversified firms, especially those from advanced economies, may find it difficult to sell their 'hi-tech' goods in developing or least developed countries because of the lack of familiarity of local consumers with technological advancements. Such firms will have to further diversify to develop goods particularly suited to local demands. Based on these arguments, we formulate the following hypothesis: Hypothesis 2. Product diversification moderates the ID-P relationship such that performance will be higher among firms with low/related product diversification and lower among firms with high/unrelated product diversification.
Fourth, consistent with Cooper (1998) and Lee and Madhavan (2010), we traced relevant articles using the ancestry approach, which is a technique used to backward trace references using the articles in hand. The ancestry approach (alternatively "snowballing" or "pearl growing") has been emphasised by scholars as essential to meta-analysis studies (Booth, 2008;Ones, Viswesvaran, & Schmidt, 2017;Steel, Beugelsdijk, & Aguinis, 2021). Fifth, we forward-traced articles using the "Cited by" function on Google Scholar. Sixth, we searched for "grey literature" to address issues related to publication bias (Eisend & Tarrahi, 2014), filedrawer problems (Rosenthal, 1995), and the "Matthew Effect" (Steel et al., 2021). After combining the six data collection stages, we were able to accumulate an initial pool of over 900 studies.
We screened the initial pool by including full-length studies that reported usable statistical information on the hypothesised relationships (e.g., sample size N, correlation coefficient r, t-statistic, F-value, z-value, and β coefficient) and by excluding duplicate studies and overlapping samples. In some cases, we transformed the t-statistic, F-value or z-value into r using the methods recommended by Hunter and Schmidt (1990) and Lipsey and Wilson (2001) and the β coefficient into r using the formula provided by Peterson and Brown (2005). After inserting the inclusion and exclusion criteria, we were left with a usable sample of 263 effect sizes from 187 primary studies (178 published in 57 journals and 9 unpublished papers) dated between 1974 and 2021. Fig. 1 summarises our literature search and screening process. The observation period for all 187 studies ranged from 1960 to 2016. The list of studies included in the meta-analysis is available from the authors upon request.

Measurement of variables
We included six different categories of firm performance. The accounting measures include ROA (Berry & Kaul, 2016), ROS (Thomas, 2006), ROE (Pattnaik & Elango, 2009), ROI (Rugman, 1976), OCTS FSTS = Foreign sales to total sales, FRTR = Foreign revenue to total revenue, FSFC = Foreign subsidiaries to foreign countries, FVMV = Firm value to market value, ID = International diversification, OCTS = Operating costs to total sales, ROA = Return on assets, ROE = Return on equity, ROI = Return on investment, ROS = Return on sales. (Ruigrok & Wagner, 2003), and EBIT (Chen & Hsu, 2010). Market-based measures include Tobin's Q (Christophe & Lee, 2005), FVBV or MVBV (Goerzen & Beamish, 2003), and share price or cumulative abnormal returns (Doukas & Lang, 2003). Revenue-based measures include sales growth (Siddharthan & Lall, 1982) and profitability (Riviere & Bass, 2019). Following Delios et al. (2008), we included subsidiary survival as a performance measure. Few studies have included composite or combination performance measures (e.g., Hsu & Pereira, 2008;Pangarkar, 2008). Given the great degree of variation in operationalising composite measures, we include such studies under a single category. The measurement of international diversification was a critical issue that had to be resolved to enable the testing of the relationship between international diversification and firm performance. Palich et al. (2000) used a categorical variable to classify single product firms as least diversified; and multi-product firms as highly diversified. The measurement of international diversification is more complicated than the measurement of product diversification. Internationally diversified firms include those operating in a few countries but having a higher return on sales and those with subsidiaries spread across multiple countries and regions. To resolve this issue, we adopted the 'type of multinationality' classification used in previous studies (Annavarjula & Beldona, 2000;Kirca et al., 2012;Thomas & Eden, 2004). Accordingly, studies that examined the intensity or depth of internationalisation (e.g., FSTS, FRTR, FATA, foreign sales) were coded 0; studies that examined the spread or breadth of a firm's foreign operations (e.g., country count, subsidiary count, FSFC) were coded 1; and studies that included a composite measure for international diversification (i.e., including both the intensity and spread of internationalisation) were coded 2.
Following Palich et al. (2000) and Schommer et al. (2019), we operationalised product diversification as related and unrelated. We sourced this information from the original studies by looking for key terms, including 'related/unrelated', 'vertical/horizontal expansion', 'core/noncore', or 'single/multiple sector'. Testing for the performance implications of international diversification necessitates that we control for firm-specific assets, as suggested by the internalisation theory (2009; Buckley & Casson, 1976). Accordingly, we included firm size, R&D intensity and advertising intensity. Firm size was measured as a categorical variable (0 = SME/INV sample, 1 = MNE sample, 2 = mixed/ unclassified sample). For R&D and advertising intensity, we adopted the approach of Bausch and Krist (2007) and split our sample into studies that reported the average R&D or advertising expenses to total sales above or below 5 percent. Home country development was included as a categorical variable (0 = advanced economy, 1 = emerging economy). We included median sample years reported in individual studies to observe the change in the ID-P relationship over time (Schommer et al., 2019;Tang & Buckley, 2020). Finally, we included a dummy variable to check for endogeneity bias.

Method of meta-analysis
We employed two meta-analytical methods. First, we conducted the Hedges-Olkin type meta-analysis (HOMA), which involves regressing the correlation coefficients onto the hypothesised variables (Hedges & Olkin, 1985). We used both Pearson's correlation coefficients and partial correlation coefficients in the HOMA analysis. Second, consistent with recent meta-analytical studies (Bailey, 2018;Schommer et al., 2019), we conducted a meta-regression analysis (MARA). This method allowed us to test the moderation effects and allowed us to control for methodological artefacts. We used the Biostat Comprehensive Meta Analysis Version 3 software package to conduct our analysis.
Before running the meta-analyses, we corrected for statistical errors following various recommended procedures. First, to maintain consistency with the direction of effects, we reverse-coded variables that used an inverted scale (Schommer et al., 2019). For example, a high value of the Herfindahl index or Rumelt's category indicated low diversification, and in the survival models, 0 indicated survival and 1 indicated exit. After reverse-coding the items, a high value of the Herfindahl index and Rumelt's categories indicated high diversification, and in the survival models, 0 indicated exit and 1 indicated survival. Thus, we were able to obtain consistency with the direction of effects.
Second, to correct for skewness in the sample distribution, r-values were back transformed using Fisher's z-transformation (Silver & Dunlap, 1987). Initially, the r-values were transformed into Fisher's z-values using the following formula: , where r denotes the correlation between variables i and j for study k. The estimated z-values were averaged by assigning the weight of N-3, where N denotes the sample size of each observation, and the results were back transformed into the correlation coefficient r using the following formula: r = e 2z ij − 1 e 2z ij +1 , where z denotes the weighted z-value between variables i and j.

General findings
An overview of the ID-P relationship is presented in Table 2. The results suggest that the ID-P relationship is positive, with an average correlation coefficient of 0.076 (p < 0.001). The mean r for ID is statistically significant, as indicated by the confidence intervals, which do not include zero (Whitener, 1990). However, there is a high degree of variance, as indicated by the high Q and I 2 values. The mean r is 0.079 for Intensity/Depth (p < 0.001), 0.037 for Spread/Breadth (p < 0.01), and 0.119 for Composite (p < 0.001). The positive and statistically significant mean correlations indicate a moderating influence of the measure of international diversification on the overall ID-P relationship (Marano et al., 2016). Another indication of the moderating effect is the nonoverlapping confidence intervals for Intensity/Depth (CI = 0.058 to 0.100) and Spread/Breadth (CI = 0.015 to 0.057).
The results in Table 2 also suggest that the heterogeneity in the ID-P relationship can be partly attributed to the choice of firm performance measure. A general observation suggests a great degree of variation among the choice of performance measures, with ROA, ROS, and ROE being preferred by over 66% of the total effect sizes. For accounting performance measures, the relationship is positive for ROA, ROS, ROE and EBIT, whereas the relationship for OCTS is negative and nonsignificant for ROI. For the market-based performance measures, the relationship is positive for Tobin's Q and FVMV and non-significant for Share price/CAR. For revenue-based measures, the ID-P relationship is positive for Sales growth and non-significant for Profitability. Furthermore, the ID-P relationship is positive for Composite and Self-reported performance measures. Overall, the finding that the ID-P relationship is positive is consistent with prior meta-analyses (Bausch & Krist, 2007;Geleilate et al., 2016;Kirca et al., 2011;Marano et al., 2016).

Curvilinearity diagnostics
We provide the results for curvilinearity diagnostics in Table 3. We separated 97 effect sizes reporting curvilinear relationships from the main sample. Furthermore, we separated studies depending upon the nature of curvilinearity. In the U-shaped models, the linear term is positive (mean r = -0.052, p < 0.5) but the quadratic term is non-significant. In the inverted U-shaped ID-P models, the linear term is  (2008)    positive (mean r = 0.084, p < 0.01), and the quadratic term is negative (mean r = -0.060, p < 0.001). The results for cuboid relationships are non-significant for all three terms (linear, quadratic, and cubic). For the quartic M− shaped models, the linear term is positive (mean r = 0.133, p < 0.01), the quadratic term is negative (mean r = -0.068, p < 0.001), and both cubic and quartic terms are non-significant. The results for Wshaped models are significant only for the linear term (mean r = -0.069, p < 0.001). A consolidation of these results points towards an inverted U-shaped ID-P relationship, and therefore, supports our Hypothesis 1. It is important to note that the number of effect sizes for the quartic M− shaped (K = 5) and W-shaped (K = 2) models is significantly lower than that for the quadratic (K = 50) and cuboid models (K = 40), which makes it difficult to generalise our findings.

Moderator analysis
In Table 4, we present the Hedges-Olkin type meta-analysis results for the moderation analysis of product diversification and contextual factors, such as firm size, firm R&D intensity and level of home country development. As suggested, the mean r for the overall PD is non-significant, the mean r for high/unrelated PD is negative (mean r = -0.089, p < 0.001), whereas the mean r for Low/Related PD is positive (mean r = 0.036, p < 0.05). Supporting Hypothesis 2, the results suggest that High/ Unrelated PD has a negative influence on the ID-P relationship and Low/ Related PD has a positive influence. Moreover, the confidence intervals for High/Unrelated PD and Low/Related PD do not overlap, which suggests a clear and separate moderation effect of both product diversification strategies.
Consistent with the internalisation theory, we tested the influence of contextual factors on the ID-P relationship. First, we tested whether the ID-P relationship is affected by firm size. As shown in Table 4, Firm size has a significant but relatively small impact on the ID-P relationship (mean r = 0.063, p < 0.001). Furthermore, the performance seems to be smaller in MNEs (mean r = 0.046, p < 0.05) compared to a mixed sample of firms (mean r = 0.088, p < 0.001). Second, we tested whether ownership of intangible assets benefited internationally diversified firms. The results in Table 4 suggest that both Firm R&D intensity (mean r = 0.093, p < 0.001) and Firm advertising intensity (mean r = 0.058, p < 0.001) have a positive influence on the ID-P relationship. The mean r is higher among firms with High R&D intensity (mean r = 0.175, p < 0.001) and High advertising intensity (mean r = 0.069, p < 0.05). Finally, we tested the influence of the country of origin effect on the ID-P relationship. Table 4 reveals no difference between the performance of internationally diversified firms from both advanced (mean r = 0.077, p < 0.001) and Emerging economies (mean r = 0.076, p < 0.001). In fact, the near identical mean r for both sub-groups challenges common wisdom that firms from advanced economies tend to outperform their counterparts from emerging economies.
We conducted additional diagnostics to test the nature of curvilinearity based on the level of home country development and firm size. As shown in Table 5, the inverted U-shaped curve appears to be stronger in firms from Advanced economies and in MNEs. While we did not find any significant S-shaped relationship in the home country or firm size analyses, in the M− shaped models, the ID-P relationship is significant only for the quadratic terms among Advanced economies, Emerging economies and MNEs. This corroborates our initial finding that the ID-P relationship has an inverted U-shaped.

Meta-regression analysis
We provide the meta-regression analysis results for the ID-P relationship in Table 6. Model 1 includes control variables. Model 2 includes the linear and squared terms for international diversification and Model 3 tests the moderation effect of overall product diversification. Model 4 and Model 5 test the moderation effect of high product diversification, and Model 6 and Model 7 test the moderation effect of low product diversification. We predicted that product diversification moderates the ID-P relationship such that the performance of firms with low/related product diversity will be higher than in firms with high/unrelated product diversity. In Model 2, the coefficients for ID (β = 0.048, p < 0.001) and ID 2 (β = -0.027, p < 0.1) indicate an inverted U-shaped curve, thus corroborating our findings in section 4.2 and lending support to Hypothesis 1. After inserting PD (β = -0.141, p < 0.1) in Model 3, the coefficient for ID (β = 0.014, p < 0.01) weakens, whereas, the coefficient for ID 2 (β = -0.130, p < 0.05) strengthens, suggesting a clear moderation effect of product diversification. The coefficients for High PD in Model 4 (β = -0.200, p < 0.01) and Model 5 (β = -0.220, p < 0.01) indicate that high product diversification has a negative and significant impact on firm performance. The interaction term ID × High PD (β = -0.130, p < 0.1) in Model 5 supports our hypothesis that performance is lower for international firms with high product diversity. Furthermore, the positive coefficients for Low PD in Model 6 (β = 0.351, p < 0.05) and Model 7  (β = 0.372, p < 0.05) suggest that performance in firms with low/related PD is high. The coefficient associated with the interaction term ID × Low PD is positive and significant (β = 0.157, p < 0.1), which supports the hypothesis that performance in firms with low product diversity in high.
The MARA results reveal that the relationship between international diversification and product diversification is complex in nature. As shown in Table 6, the coefficient for High PD is stronger in Model 5 (β = -0.220, p < 0.01) than in Model 4 (β = -0.200, p < 0.01) and the coefficient for Low PD is stronger in Model 7 (β = 0.372, p < 0.01) than in Model 6 (β = -0.351, p < 0.01). The change in coefficients after entering respective interaction terms points towards a potential two-way interaction between international diversification and product diversification.

Table 5
Results for moderation effects of home country development and firm size in curvilinear models a.

Model
Quadratic ( ⋃ curve) Quadratic (∩curve) Cuboid (S curve) Quartic (M curve)   ID  ID 2  ID  ID 2  ID  ID 2  ID 3  ID  ID 2  ID 3  ID  a. Quartic W-shaped curve not included in the analysis because of the small effect size, K = Effect size, N = Sample size, ID = International diversification ***p < 0.001, **p < 0.01, *p < 0.05 Table 6 Meta-regression analysis results. Unstandardised beta coefficients with robust standard error in parentheses ID = International diversification, PD = Product diversification, ***p < 0.001, **p < 0.01, *p < 0.05, ǂ p < 0.1 While we argued that product diversification increases coordination and governance costs, our findings suggest that firms are able to recover some of the costs by exploiting their knowledge resources in foreign markets.
In addition, the results in Table 6 are not affected by the size of firms, as indicated by the non-significant coefficients for the control variable Firm size. As indicated by Models 6 (β = -0.020, p < 0.05) and 7 (β = -0.013, p < 0.05), the performance among firms with low product diversification is negatively associated with Home country development. The ID-P relationship and the interaction between international diversification and product diversification seem to be unchanged over the 1974-2021 period, as indicated by the non-significant coefficient associated with the Median sample year. However, as indicated in Model 6 (β = -0.002, p < 0.1) and Model 7 (β = -0.001, p < 0.1), the ID-P relationship for firms with low product diversification tends to have become marginally negative over time. Consistent with Marano, Arregle, Hitt, Spadafora, and Essen (2016), the moderating effect of Endogeneity bias is negative (β = -0.035, p < 0.1), thus confirming that studies controlling for endogeneity tend to report weaker results.

Reliability and robustness tests
We were concerned with the reliability of our results, including the sampling error variance, artefact correction, overlapping samples, presence of outliers, and publication bias. It is essential to check for sampling error variance because the study validity varies according to sampling error. We checked for sampling error variance following the procedure recommended by Hunter and Schmidt (1990). Accordingly, the sampling error variance was estimated as follows: S 2 e = (1− r 2 ) 2 N− 1 , where r is the correlation coefficient and N is the average effect size. The estimated sampling error variance in our study was at an acceptable level of 0.087 (8.79%).
Since there is no best method for artefact correction, it is advisable to conduct a meta-analysis using both corrected and uncorrected effects. To test the robustness of our findings, we replaced the z-transformed correlations with raw correlations. Consistent with the results in Table 2, the mean r for ID was 0.076 (p < 0.001, CI = 0.061 to 0.090). Similarly, the results in Table 3 were consistent after replacing the z-transformed values with raw correlations. To determine whether our results were affected by overlapping samples, we conducted separate analyses for single-effect size data (K = 207). The results were similar to those in Table 2, where the mean r for ID was 0.074 (p < 0.001, CI = 0.058 to 0.090). Detailed results for both robustness tests are available from the authors upon request.
Because of the considerably large sample size, it was mandatory to check if the results were distorted due to the presence of outliers (Yuan & Bentler, 2001). Consistent with Hunter and Schmidt (1990), we checked the outliers using the 'data trimming' technique. Two recommended methods of data trimming are as follows: (1) most extreme 10%, i.e., 5% of the highest and 5% of the lowest values (Huber, 1981;Walfish, 2006); and (2) 2% of the top and bottom extremes (Hunter & Schmidt, 1990). There were no significant changes in the results after running the analyses using either trimming method.
Publication bias is a critical issue in meta-analyses. We took the necessary measures to avoid bias at the data collection and coding stage, and statistical tests are available to detect publication bias. The commonly used tests to detect publication bias are Rosenthal (1979) Fail-safe N andDuval andTweedie (2000) trim-and-fill method. As reflected in Table 2, the Fail-safe N suggests that 31,391 studies reporting null results are required to bring the overall results of this meta-analysis to a point of non-significance. The results for Duval and Tweedie (2000) trim-and-fill method indicate that the number of missing studies due to publication bias using estimator R 0 is 23. The funnel plot presented in Fig. 2 shows our sample distribution along with 23 imputed studies.

Summary and discussion
The two main objectives of this paper were to critically evaluate the nature of the ID-P relationship and to test the moderation effect of product diversification. To attain our objectives, we conducted a metaanalytical review of 263 effect sizes from 187 primary studies between 1974 and 2021. The observation period of almost five decades allowed us to include a diverse set of theoretical approaches, empirical models, and hypothesised relationships. Our focus was on the nature of the hypothesised relationships, and we observed that the ID-P relationship gradually developed from a simple positive linear relationship to a more complex sigmoid and M− shaped relationship. We provide a comparative summary between our study and prior reviews and meta-analyses on the ID-P relationship in Table 7.
This study makes two contributions to the literature. First, our results help resolve the debate on the nature of the ID-P relationship. After testing different linear and non-linear models, we conclude that the ID-P relationship has an inverted U shape. We do not find any support for the U curve, S curve, or quartic M and W curves. The meta-analytical results are only significant until the quadratic terms, or until 'Stage 1 and 2 ′ of internationalisation (Contractor, 2007;Contractor et al., 2007). This finding is in contrast to previous meta-analyses, such as by Kirca et al. (2012) and Yang and Driffield (2012), who reported a U-shaped ID-P relationship, or Marano et al. (2016), who did not find support for a curvilinear relationship.
Our second contribution is related to the moderating role of product diversification. Internationally diversified firms with low product diversity outperformed firms with high product diversity. This finding corroborates the findings of Bausch and Krist (2007). Interestingly, our results point towards reverse causality between international diversification and product diversification. By expanding in foreign markets, firms partly recover the costs associated with product diversification. Hence, performance is marginally higher for firms pursuing a dual international-product diversification strategy.

Theoretical implications
Our study contributes to the literature on the ID-P relationship along the internalisation and transaction cost theory. As noted by the internalisation theory Buckley & Casson, 1976), market imperfections are the basis for returns from cross-border activities. Firms are able to exploit market imperfections using their intangible assets, which is the key for higher performance during early stages of internationalisation. The decrease in firm performance at advanced stages of internationalisation can be explained by (1) increased governance and coordination costs; (2) knowledge burden on the management teams; and (3) changes in external markets that make the intangible assets of the firm redundant.
Our argument that related product diversification is beneficial for global firms is consistent with the line of research positing that common knowledge permits effective learning across business units (Chang & Wang, 2007;Grant, 1996;Makri, Hitt, & Lane, 2010;Zappa & Robins, 2016). The findings from our meta-analysis support the view that firms exploit the interdependencies across business and geographic segments to achieve synergistic gains. It is less costly to share knowledge among business units operating in similar segments, which partly explains the positive performance. The existing reservoir of knowledge can then be developed further over time to enter new segments and geographies.
Following the internalisation theory, we controlled for intangible assets to test whether the ID-P relationship remained positive. As evident from our results, performance is higher among firms with higher R&D and advertising intensity. While this result highlights the importance of resources and ownership advantages for successful international growth (Dunning, 1988;2000), it also supports our notion that changes in external market conditions can be approached by higher investment in knowledge acquisition activities.

Methodological implications
The ID-P literature is characterised by measurement and modelling issues. Unlike product diversification, where a subsidiary can be categorised as related or unrelated by comparing the SIC codes, categorising a foreign subsidiary as internationally related or unrelated is more complex. Although there is no established methodology for categorising a foreign subsidiary as internationally related or unrelated, the international diversity of a firm can be classified based on the proportion of the firm's sales in related and unrelated country clusters (Chan Kim, Hwang, & Burgers, 1989;Vachani, 1991). Country clusters can be classified based on socio-economic ties or cultural similarities between countries (Minkov & Hofstede, 2012;Ronen & Shenkar, 1985).
It is also worth considering that the negative relationship between over-diversification and firm performance may not necessarily imply that diversifying firms are not generating enough returns (Markides, 1995). Hence, it is essential for scholars interested in examining the link between diversification and performance to consider the marginal contribution of diversification to overall firm performance. Only after conducting a comparative analysis of the two phenomena will we be able to better understand the intrinsic nature of the diversificationperformance relationship.

Managerial implications
The results of our study have key implications for managers. Our finding that low/related product diversification has a positive moderating effect on the ID-P relationship encourages managers to pursue an integrated international-product diversification strategy with the caveat that the firm expands into related product segments. In support of Hitt et al. (1997), we argue that managerial learning takes place during the process of diversification, which encourages firms to invest in R&D activities to maintain a steady flow of knowledge. However, the learning effect is two-directional. Through international diversification, firms acquire key knowledge about the local demand conditions in the host country, which is useful in designing products or brands to suit the local market. Similarly, knowledge acquired through product diversification helps firms identify new markets.
Our findings suggest that firm performance decreases at higher levels of international diversification and that the relationship is stronger among firms with high/unrelated product diversification. Although a dual diversification strategy offers several alternatives to expand business operations across a broader spectrum of product and geographic segments, it increases the knowledge burden on managers and reduces their efficiency to make timely decisions. In addition, diversification activities may also create a feeling of complacency among managers for having done the job of researching new products and geographic segments. This is likely to have a detrimental effect on managerial decisionmaking capability and subsequently on firm performance.
One factor that remains underexplored is the openness of the host country to imports, inward FDI and new products. An openness to imports and inward FDI means that the host government provides several incentives, including a reduction in tariff and non-tariff barriers, making the environment conducive for foreign investors and traders (Banga, 2003;Sambharya & Rasheed, 2015). Openness to new products means that consumers are generally willing to buy unfamiliar or new products. Thus, the demand for new products can be expected to remain stable, at least in the short run. We expect that the presence of both of these factors will encourage firms to pursue an integrated international-product diversification strategy.

Limitations and future research direction
Common with most meta-analyses, our study is subject to both theoretical and methodological limitations. The first limitation of our study is affiliated with the measurement of product diversification. We examined the moderation effect of product diversification on the ID-P relationship. Although we examined different degrees of international diversification, we were not able to replicate the same method in the case of product diversification, which was mainly due to the assortment of measures that have been used in the extant literature. We identified several measures of product diversification, including the Herfindahltype measure (Lin, Liu, & Cheng, 2011;Lu & Beamish, 2004)  Stone, 2018), Rumelt (1982) categorisation (Bühner, 1987), SIC relatedness (Borda et al., 2017;Doukas & Lang, 2003;Zhao & Luo, 2002) and SIC count (Denis et al., 2002). While the Herfindahl-type measure and entropy measures consider the share of a firm's sales across various industry segments (Tallman & Li, 1996;Wan, 1998), the SIC relatedness or SIC counts, as the name suggests, measures the mere presence of a firm's activities in different industry segments. Evidently, there is no clear guideline to categorise 'depth' or 'breadth' of product diversification. Since we were unable to test the independent effects of various categories of product diversification, our results provide only a rudimentary understanding of the moderation effect of product diversification on the relationship between international diversification and firm performance. Future studies are thus encouraged to test the interaction between various facets of international diversification and product diversification, and their implications for firm performance.
Second, it is difficult to conclude whether product diversification was an intentional decision or a causal effect of international expansion. It can also be true that firms initially invest in developing new products and then enter international markets (Hitt, Hoskisson, & Ireland, 1994). This limitation can be partly levied against sampling bias because several studies included in our sample do not provide detailed information on the host country location. An intriguing question that still requires scholarly attention is: which markets do diversifying firms choose to invest, and why? Thus, future research must address the modelling and sampling issues to provide a robust understanding of the diversification-performance relationship.
Third, our analyses suggest that future empirical studies on the ID-P relationship should consider integrating samples from diverse home countries. As indicated in Table 3, the majority of our sample studies focused on internationalisation by advanced economy firms. This characteristic of the literature is problematic because it gives us a biased perspective of the ID-P relationship and highlights the restrictions of the extant literature (Geleilate et al., 2016). Unlike emerging economy firms, advanced economy firms have access to superior intangible assets (Gubbi, Aulakh, Ray, Sarkar, & Chittoor, 2010). The main source of knowledge for advanced economy firms is their headquarters, whereas the learning for emerging economy firms largely takes place through their foreign subsidiaries (Awate, Larsen, & Mudambi, 2015). This gives an added incentive to emerging economy firms to diversify into new markets and procure knowledge that would otherwise be unavailable in their home countries. Moreover, the home country institutional environment and governance mechanisms determine the internationalisation patterns of firms (Singh & Gaur, 2009). Owing to the similar institutional environments, advanced economy firms tend to internationalise to other advanced economies (Gaur & Lu, 2007), whereas emerging economy firms first enter other emerging economies and gradually enter more advanced economies (Madhok & Keyhani, 2012). Evidently, home country context matters in the internationalisation pattern of firms and it is important that future studies address these theoretical and methodological issues. While having data from more countries would certainly enhance the findings (Geleilate et al., 2016), future studies are encouraged to expand our understanding by integrating new variables and theoretical frameworks.

Conclusions
In this paper, we sought answers to one of the most researched yet unresolved issues in the international business and management literature: How does international diversification affect firm performance? By using meta-analytical techniques, we were able to delve deep into the literature and reveal certain facts that can help us broaden our understanding of the topic but also pose new challenges for future researchers. In particular, we provide statistical evidence that the ID-P relationship is non-linear inverted U-shaped, and is moderated by product diversification with performance being higher in firms with low product diversity, and lower in firms with high product diversity. Moreover, our study highlights the importance of using appropriate measurement scales and adequate controls. To summarise, the ID-P literature is far from being considered a mature research field, and our findings provide key guidelines for future research.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. 1. The ID-P relationship is nonlinear inverted Ushaped.
2. High product diversification has a stronger negative moderation effect on ID-P relationship.
3. The ID-P relationship and moderation effect of product diversification varies across homecountries. Performance is higher among advanced country firms and lower in emerging country firms.
a. Moderating effect of product diversification on international diversification-performance relationship. CA = Content analysis, HOMA = Hedges-Olkin type meta-analysis, MARA = Meta-regression analysis, HiLMMA = Hierarchical linear model meta-analysis, SLR = Systematic literature review, TR = Theoretical review.
analytical methods. This work is supported by Academy of Finland (project #317400).