Mapping a sector's scope transformation and the value of following the evolving core

s Research Summary: A surprisingly neglected facet of sector evolution is the evolutionary analysis of firms', and thus a sector's, scope. Defining a sector as a group of firms that can change their scope over time, we study the transformation of U.S. banking firms. We undertake a sectoral, population-wide study of business-scope transformation, with particular focus on which segments banks expand into. As financial intermediation evolved, a continuously shifting set of activities became associated with “ core banking, ” with scope changing and relatedness itself (measured through coincidence) evolving over the banking sector's history. Banks that expand scope while staying close to this evolving core attain net performance benefits. Identification tests show that the benefits of following the evolving core are robust to endogeneity. Managerial Summary: When does it pay to diversify into new segments? Our study looks at the transformation of U.S. banking firms from 1992 to 2006. Drawing on the full population of banks, we show that, as financial intermediation evolved, a continuously shifting set of activities became associated with “ core banking. ” Bank Holding Companies expanded their scope on aggregate, moving in and out of new segments. We find that while entry into new segments is negatively associated with performance improvement, diversification into this evolving core of activities is positively associated with performance improvement. This redefines “ related diversification ” and its positive value, showing relatedness changes over time, as a function of the evolution of the sector. We find that our results are robust to selection.

study the transformation of U.S. banking firms. We undertake a sectoral, population-wide study of business-scope transformation, with particular focus on which segments banks expand into. As financial intermediation evolved, a continuously shifting set of activities became associated with "core banking," with scope changing and relatedness itself (measured through coincidence) evolving over the banking sector's history.
Banks that expand scope while staying close to this evolving core attain net performance benefits. Identification tests show that the benefits of following the evolving core are robust to endogeneity. Managerial Summary: When does it pay to diversify into new segments? Our study looks at the transformation of U.S. banking firms from 1992 to 2006. Drawing on the full population of banks, we show that, as financial intermediation evolved, a continuously shifting set of activities became associated with "core banking." Bank Holding Companies expanded their scope on aggregate, moving in and out of new segments. We find The views expressed in this document are those of the authors and do not necessarily represent those of the Federal Reserve Bank of New York or the Federal Reserve System. Helfat, & Karim, 2016;Kuppuswamy & Villalonga, 2015;Palich, Cardinal, & Miller, 2000;Villalonga, 2004aVillalonga, , 2004b has stayed at the level of the firm and its evolving portfolio of activities, in isolation from the sectors in which these changes occur. 1 Questions of scope in the context of sectors have figured most prominently in relatedness research, which considers the sector-based similarity of firms on the basis of the portfolio of activities in which they engage. Gort (1962), Wrigley (1970), and Rumelt (1974) originally argued that processes, knowledge bases, or human capital shared across multiple businesses can lead to greater efficiency gains. This was later broadened to encompass the realization of return synergies from joint operations (e.g., Capron & Mitchell, 2013;Montgomery & Hariharan, 1991;Zhou, 2011), or from intertemporal efficiencies (Helfat & Eisenhardt, 2004). Drawing on Teece, Rumelt, Dosi, and Winter (1994), Bryce and Winter (2009) and Lien and Klein (2009) have argued that we can infer the synergies between two segments by observing how many firms have subsidiaries in both, leading to a "bottom-up" indicator, empirically considering a cross section of firms, aggregating them over multiple years. 2 Yet while this approach takes a sector-level focus, it does not consider sectoral dynamics, thus disregarding the fact that relatedness itself may change over time.
What would be the benefits of conducting a sector-level analysis of scope that explicitly focused on a sector's evolutionary dynamics? Narrowing the analysis to all the firms in a single sector would provide a large-scale, quantitative analysis of how sector participants change their scope, while at the same time keeping track of the activities that constitute the sector's "core." We define the core of a sector as that activity, or set of activities, that are most commonly engaged in by firms in that sector. 3 A sector's core is not fixed and may evolve in response to business opportunities, technological options, and regulatory conditions. By tracking such changes, we could see whether or not firms that, in changing their scope, approach or depart from this evolving core are rewarded in terms of performance. In all, taking such an approach would allow us to see whether the Chandlerian thesis applies to large samples, and whether "moving with the times" confers a performance benefit.
To undertake such an analysis, we need a sector-level database that includes all the firms in the sector. Then, by observing the cross-sectional variety of activities that firms engage in, we can reliably establish what is the sector core, and by observing changes in firms' activity portfolios, track the evolution of the core itself. Such comprehensive samples are few and far between, but we are fortunate to have such a setting for the U.S. banking sector.
In U.S. banking, the technology of financial intermediation changed dramatically during the 1990s and 2000s. At the outset, banking firms operated with a very narrow scope, with deposittaking and loan-making representing the core of the sector. Twenty years later, the sector had 1 Population studies that explore aggregate, economy-wide patterns in the prevalence of broad or narrow firms (e.g., Basu, 2010), or consider the effectiveness of different approaches to managing boundaries (Robins & Wiersema, 1995), or explore patterns of entry and exit into more or less related industries (Chang, 1996;Feldman, 2020) have, by and large, ignored industry in their analysis. Empirical research on the merits of becoming broad vs. narrow is occasionally carried out in the context of a particular sector, yet the focus there has been on ensuring comparability (such as Palepu's, 1985 investigation of the entropy measure, applied to a sample of 30 food products firms). By and large, the sectoral context and its evolutionary dynamics are not directly considered. 2 This was in contrast to previous approaches, which had inferred synergies by the distance of a firms' activities in terms of the SIC or NAICS code "tree"-looking, for example, at how many digits they shared. See Caves, Porter, Spence, and Scott (1980), Jacquemin and Berry (1979), or Palepu (1985), for examples; Rumelt (1974) for a critique and alternative; and Weiss (2016) for a review of non-NAICS approaches. 3 Activity is defined following the NAICS, representing the five-digit (i.e., detailed) description of the main business activity undertaken by each subsidiary.
fragmented into a decentralized system in which matching deposit supply and loan demand increasingly took place through much longer credit intermediation chains, with a wide and varying set of other activities emerging as part of core banking (Cetorelli, Mandel, & Mollineaux, 2012). To give a sense of this sector transformation, between 1990 and 2006-the year before the onset of the financial crisis-more than 230 distinct U.S. bank holding companies (BHCs), the main legal vehicle defining the boundaries of a banking firm, incorporated securities-dealer or broker subsidiaries; about 500 took control of insurance agencies; and over 1,000 added special purpose vehicle legal entities to their organizations. While these instances of change in banks' scope are certainly significant, they actually represent just the tip of the iceberg in what has been the largest and deepest process of scope transformation in the history of U.S. banking. Indeed, throughout the 1990s and early 2000s, more than half of the population of BHCs (accounting for about 97% of total sector assets) either created or took control of tens of thousands of subsidiaries, spanning virtually every business segment within the financial services sector and beyond. This created new opportunities for potential synergies across a variety of businesses, and the value of those synergies changed in response to regulatory, technological, and market conditions that evolved over time, across all firms. 4 Rather than focusing, like Chandler, on firms that shaped particular sectors over time, we look at the universe of banking firms in the United States. Our sample illustrates how all such firms changed their scope, combining their deposit and lending activity-the original core of the sector-with other activities within the financial services sector, and even beyond it. Our sample is comprehensive because banking is a regulated segment, so no entity can engage in the activities that it covers without being included in our database. This provides us with information on the entire population of firms in the sector and their ever-evolving scope.
Our comprehensive data clearly show how the core of this shifting field of financial intermediation evolved. It also shows how banks that followed this evolving core performed, compared with those that did not expand or to those that expanded to segments that were more related based on traditional, nonsector specific, or nondynamic measures (such as entropy, or NAICS coherence). We provide a thorough empirical investigation of the marginal impact of expanding, finding that, while expansion overall is detrimental to performance, expansion into the evolving core is, as Chandler would predict, beneficial. We find this result to be robust to potential endogenous selection and to alternative competing explanations. Specifically, we show that moving into vertically integrated segments does not yield any benefit (cf. Williamson, 1975); that the inclusion of (sector-agnostic) entropy measures (Palepu, 1985), constructed as well as our dataset allows, does not affect the results, and we also show that our results are robust to the use of measures of capital-market turbulence, which has recently attracted attention (e.g., Kuppuswamy & Villalonga, 2015;Matvos, Seru, & Silva, 2018). Finally, our results are maintained when we consider BHC performance during and after the 2007-2009 financial crisis.
In addition, we confirm the Chandlerian thesis that sectors change through the way firms change their boundaries. We do so by providing comprehensive and systematic data on an important sector. Our paper extends Teece et al. (1994), who, drawing on the survivor principle originally proposed by Alchian (1950) and reiterated by Stigler (1968), note that the frequent co-occurrence of activities must imply existing synergies among them. This powerful idea, more fully developed by Bryce and Winter (2009), has been used to measure relatedness on the basis of a sample of firms and their NAICS (or SIC) activities. We, too, draw on the survivor principle; however, following 4 For example, the benefits from combining commercial banking with securities dealing and underwriting, following regulatory changes in the late 1980s/early 1990s, appear to have increased firm-level value-add-especially in the runup to the 90s technology boom. Likewise, the surge in asset securitization throughout the 1990s likely created the conditions for banking institutions to add specialty lenders, special purpose vehicles, and servicers, among others.
Chandler, our focus is on how sectors (and the relatedness of the firms within them) evolve. Unlike Bryce and Winter (2009), we do not focus on the inferences that we can draw from what is stable over time, aggregating across time and across sectors. Rather, we focus on the dynamic story of relatedness that emerges bottom-up from our sample, as it changes over time, and track the competitive implications of following this evolving core. In a world of rapidly evolving sectors, from pharmaceuticals and healthcare to media and telecommunications, where businesses' scope is changing constantly over time, such a sector-and time-specific analysis can shed light on what drives sectoral and corporate change, and how such change impacts performance.
2 | THEORETICAL BACKGROUND: RELATEDNESS AND ITS DYNAMICS Alfred Chandler's (1962) groundbreaking analysis of how major firms, from the turn of the 19th century onward, transformed both themselves and their sectors by growing through scale, scope, and managerial innovation, has had a profound influence on our understanding of scope expansions. However, there has been little systematic follow-through on his key insights. While literature on scope and firm relatedness has proliferated, the focus tends to be on contemporaneous relationships. Change over time has been relatively neglected, and the interplay between sectoral-and firm-level scope dynamics has received even less attention. This leaves a surprising gap in the literature, emphasized in Chandler's last two books, on the evolution of electronics (2001) and chemicals companies and pharmaceuticals (2005). The introduction of his last book sums up this neglected issue: The continuing evolution of the enterprises and the industries in which they operate focus on three basic themes: creating barriers to entry, defining the strategic boundaries of the enterprise, and evaluating the limits to growth of an industry and the enterprises within it….
[Firms] define their strategic boundaries through competition with one another. These boundaries reflect the competitive success and failure of the individual enterprises in terms of technical achievements and financial returns. I use the term boundaries because these enterprises are nearly always diversified multi-product producers. (Chandler, 2005, pp. 9-10) Chandler's research aims to shed light on this interplay between firm-level scope change and sector evolution, focusing on evolving patterns at the level of the sector. Using historical methods, he brings considerable subtlety to his analysis, weaving in organizational, institutional, and competitive factors. This inescapably limits breadth (as he unapologetically focuses on the largest firms) and the ability to generalize. While some authors have followed Chandler (such as Silver, 1984, or Langlois & Robertson, 1995, there has been little systematic work on this topic. Much of it has focused more narrowly on the question of vertical integration, motivated by the debates in Transaction Cost Economics (Williamson, 1990), sometimes seen in the context of a deep sectoral study (Stuckey, 1989) but mostly focusing on the analysis of firms and their boundaries (Agarwal & Helfat, 2009). 5 Evolutionary approaches have also centered on the question of vertical scope (Jacobides & Winter, 2005Langlois, 2004). Analyses of sector evolution proper have broadly taken scope and boundaries for granted, or treated them in a limited, coincidental manner (see Malerba, Nelson, Orsenigo, & Winter, 2016). This focus has provided considerable advances in our understanding of capabilities, technology, institutions, and profitability but left scope expansion relatively understudied. Yet, when we consider the transformations under way in sectors from financial services and telecommunications to automobile manufacturing (which is mutating into mobility services), it is clear that we have much to learn from a systematic focus on how firms within sectors change their boundaries.
In a distinct literature stream spanning strategy, finance, and economics, the question of relatedness and its impacts has received much attention (Palich et al., 2000). As a result, a more nuanced understanding of the benefits and shortcomings of diversification has emerged-albeit without an explicit consideration of either the role of scope change or of sector dynamics. 6 In particular, following Gort (1962) and Berry (1971), Rumelt observed that related scope change could yield benefits (Rumelt, 1974, p. 29). Research on this topic advanced considerably in the 1980s and 1990s with the growth of the resource-based view (Markides & Williamson, 1994;Wernerfelt & Montgomery, 1988), which has made significant strides. 7 To assess firm-level scope change, in terms of relatedness, following Jacquemin and Berry (1979), there has been sustained interest in entropy measures (see Palepu, 1985) to assess a firm's portfolio breadth and depth. Robins and Wiersema (1995) provide evidence on the performance impact of scope change and relatedness.
The literature that focuses on change explicitly is much more limited and has only recently started garnering serious focus. Chang (1996) provides an early dynamic approach, mapping the sectors that firms enter into and exit from. The Special Issue in SMJ on the evolution of firm capabilities (Helfat, 2000) considers firm-level scope evolution (Helfat & Raubitschek, 2000;Holbrook, Cohen, Hounshell, & Klepper, 2000), and Lieberman, Lee, and Folta (2017) show the connection between relatedness, exit dynamics, and performance. Feldman (see Feldman, 2020 for a review) focuses on divestitures and the timing of entries and exits as they shape performance, also without a sector focus, whereas in finance, there are economy-wide surveys of the evolution of corporate scope (Basu, 2010). This research has been reinvigorated by burgeoning work on resource reconfiguration (see Folta et al., 2016). Research has focused not only on evidence supporting the value of relatedness but also the underlying mechanisms that make it attractive, beyond resource sharing, and the role of turnover (e.g., Miller & Yang, 2016). 8 6 In finance, the expectation is that, as a result of the costs associated with agency frictions within the organizational hierarchy (e.g., Jensen, 1986;Shleifer & Vishny, 1989), absent capital market imperfections, diversified firms suffer when compared to their narrower peers-as confirmed by findings that diversification dents banks' performance (see, e.g., Stiroh, 2015, for a review). At the same time, questions have been raised in terms of the reasons behind the broadly negative associations between scope and performance. First, research has shown that adverse selection could be the culprit-so that performance declines force diversification, and not the other way around (Campa & Kedia, 2002;Chevalier, 2000;Maksimovic & Phillips, 2002). Second, methodological limitations or measurement error (Villalonga, 2004a, b) have been identified. Numerous contributions have expanded this research, pointing out, among others, the connection between diversification and productivity (Schoar, 2002) and capital market conditions (Almeida, Kim, & Kim, 2015;Matvos et al., 2018) that may make diversification more beneficial. 7 Helfat and Eisenhardt (2004) argue that resource complementarity may not just be intra-temporal (i.e., the contemporaneous use of some common key resources) but may also be inter-temporal (i.e., the ability of firms to shift resources from one market to another over time). Research on resource redeployment (Folta et al., 2016) has provided additional nuance and evidence of the potential benefits of redeploying resources across segments. 8 Lieberman et al. (2017), for instance, argue that related diversification allows firms to reconfigure resources internally.
This makes it easier to redeploy resources (and exit a segment) if a particular expansion doesn't pan out, making expansion ex ante safer and more attractive.
The measurement of relatedness has been a perennial bone of contention in scope-expansion research (Weiss, 2016). Early measures developed by Wrigley (1970) and Rumelt (1974), which highlighted the benefit of relatedness, were based on researcher discretion; they considered different categorical "types" of relatedness, which are still used. The desire to use consistent measurements and the availability of data encouraged the use of the SIC and later NAICS classification schemes, and the distance between sectors in terms of their hierarchical trees, in both strategy (see Chang, 1996;Feldman, 2020;Weiss, 2016) and finance (e.g., Rajan, Servaes, & Zingales, 2000). Jacquemin and Berry (1979) and Caves et al. (1980) proposed the most frequently used measures, 9 which were also relied upon to assess a particular firm's overall portfolio entropy (Palepu, 1985).
NAICS hierarchies, though, do not offer a good assessment of how close segments truly are, as industry classifications are focused on outputs, whereas relatedness often relates to the input side-or to sharing common customers and distribution channels. A number of papers have tried to remedy that. Robins and Wiersema (1995) proposed an alternative measure that draws on the technology and product flows between the segments. Silverman (1999) and Breschi, Lissoni, and Malerba (2003) proposed a patent-based measure. Neffke and Henning (2013) make a convincing case for using labor-market similarity to assess individual business relatedness. However, as Pehrsson (2006) and Weiss (2016) mentioned in their reviews, most studies of relatedness that eschew SIC/NAICS classifications seem to diverge and have failed to establish a single alternative basis for assessing relatedness (see Pil, 2009, for a summary and meta-analysis).
A different analytical strand connects relatedness with an evolutionary analysis of sectors, drawing on the "survivor principle" (Alchian, 1950;Stigler, 1968). This approach illuminates how some combinations of business activities will be more frequent than others, and that these combinations (e.g., in terms of particular NAICS or SIC pairs) imply the existence of relatedness-based synergies (Bryce & Winter, 2009). 10 These views are consistent with the explicitly evolutionary approach taken by Teece et al. (1994) that the scope of a firm at any given time is the result of its past history (and selection environment) and of the current pressures to adjust. Thus, the extent to which certain activities can be more or less related is also a reflection of sector-wide technological factors that should be common to all firms in operation at a given point in time, as well as the intensity of the selection environment. The most thorough empirical investigation of "bottom-up" relatedness is Bryce and Winter (2009), who draw on predominantly manufacturing data to derive their economy-wide relatedness measures between four-digit SIC codes. 11 However, although 9 The widely used Jacquemin and Berry (1979) entropy measure draws on the number of a firms' two-digit SIC sectors (measuring unrelated diversification), and the number of four-digit SIC segments within each two-digit group (measuring related diversification), using a Herfindahl-style concentration measure. The concentric index (e.g., Caves et al., 1980;Montgomery & Hariharan, 1991) also draws on the SIC system hierarchy. It first takes the product of shares of sales for each pair of businesses at the bottom level of the hierarchy and then multiplies that result by a digit representing the relationship between the two businesses in the SIC system. It takes the value 0 when all four-level SIC businesses belong to the same three-digit SIC band, 1 when they belong to the same two-digit group but different threedigit groups, and 2 when they are in different two-digit categories. 10 As Teece (1980) and Bryce and Winter (2009) note the fact that two segments are not found combined in a single firm at a particular time does not imply that there are no synergies or that they are not related, as it may just be the case that the market provides a relatively effective means of combining them instead. They also draw on Richardson (1972) and others, who suggest that combinations within a firm's boundary can also reflect experimentation or the luxury of not needing to be too discriminating when selection pressures are weak. 11 In particular, they draw on the Longitudinal Research Database (LRD) at the Center for Economic Studies (CES) at the U.S. Census Bureau, and consider four-digit SIC codes, so as to create a map of the actual co-occurrence of potential SICs, judged against the potential null of any combination. This operationalizes the ideas in the study by Teece et al. (1994), albeit focusing on manufacturing establishments and creating an economy-wide measure. Bryce and Winter (2009) draw on a panel database, they average out the coincidences they observe in the data-and, as they concede, "the predictive value of our index rests on the premise that the methodology captures fundamental aspects of relatedness among industries… accounted for by relatively durable considerations.".
The issue here is that sectors themselves evolve. New types of relatedness and synergies may emerge, just as old ones wither away, so that focusing on "average" relatedness over time will necessarily exclude an important part of the picture-especially in the context of a sector's unfolding history. Changing technologies of production and organization, as well as regulatory evolution, can shift the comparative advantage, for example, from narrower to broader firmsalong the lines of Chandler (1962); Chandler's (1977Chandler's ( , 2001Chandler's ( , 2005) analysis. This is precisely where we see an opportunity for a contribution to theory and to empirical understanding. Thus, our twofold contribution is to provide a sector-based measure of relatedness that evolves over time, reflecting sector-wide trends, and to use it to assess the value of combinations-as opposed to merely registering their occurrence. 12 Fundamentally, though, our contribution lies in offering a new empirical design that looks at the sector level of analysis as the sector evolves. Our expectation is that the value of particular sector-segment combinations will change over time, as the landscape of opportunities and enabling regulations and technologies evolves. We also expect that firms that move closer to the evolving core of the sector will benefit more from their expansion. Our concern is not to compare the benefits of growth from scale versus scope (Chandler, 1962;1977;1990), or of entry and exit over time (Chang, 1996); rather, it is to determine whether, as a sector's core evolves, moving closer to it yields advantage. We find that it does.

| DATA DESCRIPTION
This study considers how bank holding companies (BHCs), the predominant corporate structures in U.S. banking, changed their scope over time. As regulated entities, all BHCs are required to report any change to their structure, including subsidiaries entering or exiting the organization due to acquisitions of going concerns, de novo formations, sales, changes in ownership status, liquidation, or becoming inactive. For the first time, all this information has been assembled in a consistent panel covering the entire population (Cetorelli & Stern, 2015). Online Appendix A1 contains relevant summary statistics of the database.
By definition, all BHCs control one or more commercial bank subsidiaries-that is, depository institutions that extend credit to households and corporations. Until the late 1980s, the U.S. banking sector had remained highly homogeneous, with such commercial bank subsidiaries being the dominant components of each banking firm, and the related deposit and loan activity representing the core of the sector. This is not surprising, given that U.S. banks had been effectively constrained for decades by the Glass-Steagall Act of 1933, with bank regulators maintaining a very narrow concept of the so-called "business of banking" (Omarova, 2009). This view progressively broadened, however, and by the end of the 1980s an influential Interpretive Letter of the Office of the Comptroller of the Currency set forth a very broad interpretation of activities related to banking, and that were therefore permissible under the laws and regulations of the time (Office 12 We feel that our approach delivers on the concluding exhortation of Bryce and Winter (2009), who note that "[strategies] in a diversified firm, require longitudinal assessments of market entry choices. Yet, perhaps surprisingly, there are a limited number of empirical studies in the literature that take this perspective." of the Comptroller of the Currency, 1989). From that point onward, BHCs could operate in an unrestricted environment for the first time, all subject to the same regulation, launching the significant transformation of scope that characterized the sector for the following two decades.
This change also coincided with the end of a severe, decade-long banking crisis "…of a magnitude not seen since the Great Depression…" (FDIC, 1997). The crisis culminated with the passage of the FDICIA Act in 1991, marking the dawn of modern banking regulation (Spong, 1994). Hence, for the purposes of our study, 1992 marks the start of our panel. When the financial crisis of 2007-2009 struck, the process of scope transformation came to a sudden halt, as the result of changing economic incentives as well as significant regulatory reform introducing new constraints on BHCs' business scope. We therefore use the period between 1992 and 2006 as a laboratory to analyze the process of scope transformation in the sector. 13 Because we focus on firms' performance, we have merged the database with information on BHCs' own consolidated financials (both balance sheet and income statement items). The matched sample consists of a panel of 3,206 unique BHCs for which we have financial data. This set of firms consistently accounts for the virtual totality of banking assets.

| Defining business scope, expansion, and exit
For each subsidiary of a BHC, the database reports its primary and, where applicable, secondary business activity. Only 3% of all subsidiaries in the database ever report a secondary business activity, suggesting that for the vast majority of cases, the subsidiaries are narrow in scope and the database accurately reflects their activities. Also, less than 2% of the subsidiaries ever change their primary or secondary activities-suggesting that, at least in terms of organizational structure, firms change their scope predominantly by creating new subsidiaries or shedding existing ones. Both primary and secondary activities are classified according to the finest (sixdigit) North American Industry Classification System (NAICS) code. Since full six-digit codes are not available for all segments, we aggregated codes at the five-digit level.
We define business scope as the number of different five-digit codes that are under a BHC's organizational umbrella. 14 For example, a BHC that controls (one or more) commercial banks (NAICS 52211), (one or more) securities brokerage firms (NAICS 52312), and (one or more) life insurance carriers (NAICS 52411) would have a scope equal to 3. By extension, we define the expansion of scope as the addition of one or more subsidiaries in a five-digit NAICS that had never been part of the organization before. From here on, we refer to such NAICS as "new" segments, indicating that they are new to the firm (as opposed to new to the sector). We identify an expansion of scope whether it originates from a subsidiary's primary or secondary segment. 15 13 In Online Appendix A7, we have run tests to consider whether expansion into related segments, while beneficial during the growth era of the 1992-2006 expansion, might cause the demise of banks during or after the financial crisis. Our analysis confirms that this is not the case: our findings hold even during one of the sector's most tumultuous periods. 14 For robustness, we also ran all our analyses on four-digit NAICS. This analysis (available upon request) produced consistent results. 15 Restricting the identification to consider only subsidiaries' primary business segment would be a more conservative approach, under the presumption that if a NAICS is observed as a secondary activity, it might not be considered economically important enough to qualify as an expansion of scope. At the same time, including secondary NAICS improves the overall information set on BHCs' activity. We have run the entire analysis excluding secondary NAICS' information, and the results were extremely robust throughout.   Table 1 shows the share of BHCs that hold the top 50 most common five-digit NAICS sorted in descending order based on the 2005 count of BHCs that hold each NAICS. A BHC is defined as holding a NAICS if the NAICS is either the primary or secondary business activity reported by at least one of its subsidiaries. BHC count is the number of BHCs that exist during the year and Sub count is the number of subsidiaries with the NAICS. The underlying source is the database of Cetorelli and Stern (2015).
Conversely, we define exit as the complete elimination of a previously held NAICS (whether through a sale of the entity, spin-off, or liquidation).
3.2 | Commercial banking as common core and evolution of scope Table 1 displays the composition of subsidiaries in the population of BHCs for reference years. The first row shows that the entirety of the population has at least one commercial bank subsidiary (NAICS 52211), thus confirming that commercial banking represents the common core of the sector-that is, the single segment that remains as a perennial fixture of the core throughout its evolution during our study period. That commercial banking represents the sector's common core is also indicated by the importance of commercial bank subsidiaries' assets. Table 2 displays the mean and median ratios of commercial banking assets to total BHC assets, for the entire population and for those subgroups of BHCs that expanded their scope at any point. The figures provide further confirmation that commercial banking represents the common core in the sector-even for BHCs that expand scope.  Table 2 displays both mean and median bank-to-total-BHC-asset ratios, calculated for the entire population in a year and for the subset of scope expanding BHCs. The numerators are the total assets of the commercial bank subsidiaries (NAICS 52211 entities) of each BHC, while the denominators are the consolidated assets of the BHCs, thus including the contribution of non-52211 subsidiaries. Abbreviation: BHCs, bank holding companies.
The finding is unchanged if we construct equivalent ratios using income data instead of asset data. Figure 1a also shows that most BHCs are "simple" organizations when they are first observed in the database, with most entities starting as commercial banks (NAICS 52211) or F I G U R E 1 (a) BHC scope upon entry. It shows a histogram of initial activity scope for all BHCs that file the Y-9C and become bank holding companies (BHCs) during the sample period (1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006). Initial activity scope is the number of unique five-digit NAICS that a BHC holds during its first year as a top-tier BHC, based off the reported primary or secondary NAICS of its controlled subsidiaries. The data underlying the activity scope measure are from the study by Cetorelli and Stern (2015) database of organizational structure. (b). Annual number of BHCs with adoptions or exits. It shows, among Y-9C-filing BHCs, how many BHCs make at least one adoption and/or at least one exit during each year over the sample period (1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)). An adoption occurs for a given year when a BHC controls a subsidiary with a five-digit primary or secondary NAICS code that prior to that year the BHC had never held within its organization. An exit occurs for a given year when it is the final year that a BHC holds a five-digit NAICS that it has held in prior years. The data underlying the adoption and exit statistics are from the study by Cetorelli and Stern (2015) database of organizational structure having subsidiaries in just one or two additional segments. This is a compelling feature of the population, since in most cases, we see a process of business scope transformation driven by a relatively homogeneous base of similar firms-rather than by "legacy" firms that already had a more complex scope before becoming BHCs.
As noted previously, the process of expansion is broadly diffused-not just the practice of a select few. Figure 1b reports, in its upper part, the number of BHCs that pursued some degree of scope expansion in every year. We see a consistent number-about 200 institutions per year in the early 1990s-adding new segments, and then a ramping-up over time, reaching a peak of over 400 per year in the early 2000s. The trend then reverts-but, remarkably, there is still a relatively consistent cross section of institutions entering new segments. Overall, more than half of the observed population engages in at least some degree of scope expansion.
One might object that much of what we see as strategic may simply reflect the passive incorporation of businesses resulting from merger and acquisition (M&A) dynamics. But this is not borne out by the data, which reveals that only 10% of scope expansions were ever the result of M&A activity between BHCs. Nevertheless, in the analysis of performance, we explicitly take into account the M&A dynamics within each BHC. Finally, we document that differences in scope are economically meaningful and not a product of regulatory arbitrage by estimating the relationship between scope and revenue components. We find that ownership of an additional unique five-digit NAICS code is associated with an increase in bank interest and noninterest revenues of about 0.74%. These results are discussed fully in the Online Appendix A2.

| Measuring relatedness and the evolving core
Since our central question is the differential impact of where firms expand to, we need to address the "relatedness" of segments head-on. To do so, we start with traditional, static measures of both NAICS hierarchical distance and NAICS overall coincidence in the BHC sample, and build up to a new, dynamic measure of inferred relatedness. As stated earlier, all BHCs control at least one commercial bank subsidiary (NAICS 52211). Commercial banking was and remains the common core of the sector, even as many BHCs over time embark in significant scope expansion (see Online Appendix A3 for further details). As such, the metrics of relatedness we present below can be constructed from this point of origin.
Following Caves et al. (1980), our first measure is the "distance relatedness" of a given NAICS code relative to code 52211. NAICS codes that share the same first four digits with 52211 are assigned a distance of 1; those that share only the first three digits are assigned 2, and so on. The prediction would be that entering more distant segments should have a relatively worse impact on performance (see a description in the study by, e.g., Markides & Williamson, 1994). A second, albeit simpler metric of relatedness differentiates between scope expansions into financial NAICS (codes beginning with 52) and nonfinancial NAICS (all other codes). This "NAICS 52 relatedness" is particularly relevant in our context, where narrow banks can be contrasted with broader BHCs.
However, as Bryce andWinter (2009), Weiss (2016), and others note, NAICS-distance is a problematic measure of true relatedness, as there may very well be segments that are "further away" from the common core in terms of classification codes, yet close in terms of relatedness. In banking, for example, real estate is a non-NAICS-52 segment that is nevertheless likely to offer direct synergies with commercial banking. Bryce and Winter (2009), following the suggestion of Teece et al. (1994), proposed an alternative approach, where the relatedness of two segments is inferred from the data, by the relative frequency with which those two segments are actually observed in the population under study.
The fact that we have direct and complete observations of the segments for all BHCs in the population allows us to improve on existing measurements of such overall coincidence, as we can observe the relative frequency of co-occurrence of each NAICS in relation to the common core (NAICS 52211). So, for example, in 2005, there were 2,215 BHCs in our observed population (Table 1). All, of course, had at least one 52211 subsidiary. Out of these 2,215 BHCs, 1,088 (or 49%) also reported subsidiaries with NAICS 52599, which includes, for example, mortgage real estate investment trusts, collateralized mortgage obligations, and other special purpose financial vehicles. Also in 2005, 594 BHCs (about 27%) reported control over insurance agency subsidiaries. In the spirit of Bryce and Winter (2009), these two segments are considered more related to commercial banking than, say, credit card issuing, which in the same year was reported by just 20 distinct BHCs (<1%). The expectation here would be that greater coincidence overall would be positively related to the performance impact of expansion into a new area. 16 Following Bryce and Winter (2009), we therefore start by reporting a time-invariant overall inferred relatedness over the entire sample period. This "overall coincidence" measure of a given five-digit NAICS code is defined as the average percent of BHCs holding that NAICS code over the entire sample period.
However, while we draw on Bryce and Winter (2009) to establish the role of overall coincidence, we depart from their analysis since, unlike them, we are not content to look at the timeinvariant aspects of coincidence. 17 For that we consider instead a dynamic measure, which we define as "modal relatedness," by calculating the share of BHCs that own each particular NAICS code at each point in the sample period. This second approach thus yields a time-varying, cross-sectional ranking of the relative importance of each NAICS segment in the U.S. banking sector, which allows to capture the sector's evolution and the shifting patterns in BHCs' structure as they change scope.
We further posit that expanding scope to a commonly owned NAICS code should yield a relatively better performance outcome. This allows us to capture the fact that adopting certain NAICS codes may have very different implications at different points in the banking sector's evolution, as Chandler's pioneering contributions showed. Thus, our proposed metric of modal relatedness 16 That said, there is a scale-specific consideration that might be in play here. If, for instance, some segments (such as having an in-house executive education subsidiary) are only relevant for larger (and, as such, fewer) firms, then this segment is less likely to be commonly held across banks. A finer-grained analysis of a segment's "coincidence conditional on size" might yield a different set of segments but also a different subsample. We fully acknowledge that, beyond "average popularity," a more refined picture might be possible, but we want to assess attributes for the sample as a whole, as further analysis would exceed what can be accomplished in a paper. 17 In addition to focusing on a time-variant measure, we also use a different way to assess relatedness on the basis of observed coincidence. Bryce and Winter (2009) provide an economy-wide measure of coincidence, by looking, within their sample, at all the pair-wise combinations of sectors, and calculating a ratio of actual coincidences divided by theoretically possible coincidences, which yields a score for each pair of sectors. This creates a matrix of links between sectors, and, for the sectors where the coincidences are not observed in the data, they ascribe the shortest path distance between every pair of nodes in the weighted distance matrix. This yields a comprehensive pair-wise measure, which can be used to assess whether an expansion (given the set of sectors of a firm) into a new four-digit SIC is more or less related, drawing on the inferred relatedness the sample has yielded. Our interests are narrower, as we focus on how distant various segments are from the common core (NAICS 52211). This allows us to focus on a more parsimonious, if time-varying measure, explained below.
captures the evolving frequencies of coincidence of each NAICS over time. As Table 1 shows, the relative ranking of segment subsidiaries held by BHCs differs significantly from 1995 and 2000, as technology, competition, and regulation (or perhaps fads) compel banks to change their scope. Figure 2 offers a stark visualization of the changing degree of modal relatedness over the sample period for a representative subset of NAICS codes. For instance, the above mentioned NAICS 52599 was hardly present within the population in the early 1990s but became a staple for BHCs in later years. The reason for its growing popularity was the transformation of the technology of financial intermediation caused by the asset securitization boom, which incited banks to move into it, as new synergies emerged as a result. Conversely, NAICS 53111, which includes entities managing residential dwellings, was popular in the early 1990s-presumably a time when balance-sheet assets such as mortgages and their collateral defined the predominant scope of a commercial bank-but later declined into obscurity, probably mirroring the subsequent evolution toward the originate-anddistribute model of intermediation. NAICS 52312, "Securities brokerage," and 52421, "Insurance agencies and brokerages," start at similar levels of popularity but diverge later on.

| Measuring the correlation of BHC aggregate performance and scope change
Our objective is to assess the performance impact of firms' change of scope, on the basis of where they expand, as sectoral patterns of relatedness evolve. First, to establish a baseline, we look at the impact of any instance of scope expansion-that is, the addition of subsidiaries in new segments by a BHC at a given point in time. Since we run our empirical analysis at an F I G U R E 2 Annual prevalence of selected NAICS. It shows the modal relatedness of four different five-digit NAICS among Y-9C-filing bank holding companies (BHCs) for each year over the sample period (1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006). The right y-axis corresponds to the modal relatedness of NAICS 52599 ("Other Financial Vehicles"), while the left y-axis corresponds to the other three NAICS. Modal relatedness for a NAICS-year equals the number of BHCs that hold that NAICS during any quarter of the year divided by the total number of BHCs in the population (multiplied by 100). A BHC is considered to hold a NAICS if it controls at least one subsidiary whose reported primary or secondary activity is that NAICS. The underlying data are from the Cetorelli and Stern (2015) database of organizational structure annual frequency, we use the sum of new NAICS that appeared in a BHC in a year as a measure of scope expansion. As our interest is in assessing the impact of changing a bank's scope, we also look at exits from NAICS. Our data thus allow us to differentiate the performance impact across banks that build and maintain broader scope, as opposed to those that enter new segments while exiting others at the same time ("turnover"), consistent with the idea of strategic renewal (Capron, Mitchell, & Swaminathan, 2001;Folta et al., 2016). To capture these dynamics, we run the following specification: The benchmark metric of performance is the BHC i accounting return on equity (ROE) measured in year t. The standard objection to using accounting metrics of performance is that they may not properly reflect the overall level of risk-taking. Further, the quality of accounting standards may not be homogeneous in the cross section of firms under study. However, there are good reasons why concerns over the use of accounting metrics are less acute for this particular study. First, net returns reported in BHCs' income statements include a component of "provisioning" for expected losses, which will be naturally correlated with the level of risk each firm is taking. 18 Moreover, in a sector subject to centralized, supervisory monitoring, accounting standards are bound to be more homogeneous and comparable across reporting BHCs than they would be for cross sections of corporations not subject to supervisory authority. Also, the data strongly indicate that scope transformation occurs broadly across the entire population of BHCs and not just among listed companies. For this reason, we run our benchmark analysis on the entire population of BHCs, thus privileging the use of ROE as the default metric of performance. 19 The main regressor of interest is Cum (Cumulative) Adoption, defined as the total number of new NAICS that a BHC has added in the recent past. As we consider potential effects, it is plausible that expanding into a new segment may require a period of adjustment before any beneficial effect pans out. For example, one might expect that a commercial bank expanding into, say, investment banking needs to build a track record before it can generate returns from its new unit. Thus, value-enhancing scope expansions might initially reduce ROE, and only gradually lead to increasing ROEs. 20 To allow for this, we look at scope expansion activity over the previous n years and measure the impact on performance at time t. In our baseline specification, we set j = 3, so that the variables with a t-j subscript are meant to capture a sum over the previous 3 years. 21 18 In fact, one could argue that, for this particular sector, there may be a possible upward bias in the use of market-based metrics: If scope expansion leads to circumstances where a BHC is "too complex to let fail," markets may incorporate a valuation premium associated with this potential regulatory subsidy. 19 We have nevertheless also performed the analysis using a market-based measure of performance, Tobin's Q, as well as metrics of leverage (which also helps assess ROA impact, as ROE = ROA × leverage) and risk, measured by the banks' Z-score. See Online Appendix A8. 20 A similar story can be told for M&A, given the well-known concerns that mergers are costly in the short term because they require firms to integrate their corporate cultures, staff, systems, and so on. 21 We ran alternate specifications from 1 to 5 years, and the effects were most visible with the 3-year lag-which is also, managerially speaking, a sensible period for the fruits of expansion to affect ROE. Tobin's Q impact was, unsurprisingly, over the same period, as the capital markets incorporated these inter-temporal tradeoffs. The consistency between our ROE, cumulative lag results, and the Tobin's Q impact, discussed below, increases our confidence in this specification. Finally, we used different weights, and concluded that under-weighting recent expansions and over-weighting previous ones (i.e., ones 3 years out) helped improve the fit, suggesting that full impact of expansion into new areas does take time, and that 3 years appears to be the most effective predictor.
Financial data for individual subsidiaries are not available, so we cannot measure the intensity of engagement by a BHC in a new segment. 22 However, our focus is on banks that add segments that are new to the banks themselves (i.e., an extensive margin of business scope expansion), and our data are uniquely positioned to inform us about this.
The variable All Exit, meanwhile, measures the total number of NAICS that the BHC completely dropped over the same 3-year period, while the interaction between these first two variables captures the phenomenon of "turnover" as defined above. Controls include the level of scope, that is, the count of unique five-digit NAICS within the BHC, before 3 years of expansions captured by Cum Adoption. We also include basic firm-specific controls that should have a direct and independent impact on the performance of a bank-and for which, at the same time, one could argue that the metric of scope could serve as a proxy. For example, scope per se may not have any particular impact on performance but could simply be a reflection of the size of the bank, with larger banks exhibiting higher returns on average, possibly indicating market power, or easier access to cheaper funding (e.g., Lang & Stulz, 1994). We therefore include the BHC's log assets in all regressions. Likewise, as noted earlier, regulation constrains scope expansion for banking firms with declining performance. Capital adequacy is one of the main factors capturing a bank's quality standing. Hence, we include the BHC's capital-to-asset ratio as a basic control of overall firm quality. Moreover, we control for any M&A activity over the previous 3 ears, as a way to condition on possible scope expansions that might be just the indirect consequence of such activity. In addition, we include the interaction of Cum Adoption with Scope, to allow for nonlinear effects of expanding scope depending on the extent to which scope is broad to begin with. In order to account for latent heterogeneity in the population, we include BHC fixed effects, Φ i , so our analysis informs us on how dynamics of scope transformation affect firms, accounting for their heterogeneity. Also, both expansion decisions and performance could be driven by common unobservable factors changing over time. For example, banks may consider expanding during the upswings of macroeconomic cycles, when their performance may also improve. We address this issue by adding time fixed effects Ψ t to the specification.

| Relatedness and performance
Our goal is to capture the impact of relatedness of different NAICS (which may change as the financial sector evolves), and use this information to assess the performance impact of banks' entry into more or less related new segments. To estimate the possible differential effect on performance of expansions with differing degrees of relatedness, we augment the previous model specification as follows: 22 For many activities, it is also not obvious that total asset size, or total income, would reflect the impact of the new segment. Some have a small organizational footprint but a significant impact (e.g., asset management services, data management, financial technology). Be that as it may, we fully acknowledge that the impact of entry may depend on entry size, and we do not have this information at hand.
where, as before, Cum Adoption measures the total number of new NAICS a BHC added over the previous 3 years, and where Cum Related Adoption measures the degree of relatedness to core banking of the new NAICS included in Cum Adoption. We capture Cum Related Adoption using the four alternative relatedness metrics described above: distance, NAICS 52, overall coincidence, and modal relatedness. This specification allows us to compare the impact of moving into NAICS that are (a) close in terms of their hierarchical tree; (b) financial or nonfinancial by nature; (c) frequently found in BHC portfolios on average; or (d) in NAICS that are popular at a specific time in the sector's evolution, respectively.  Table 3 reports regressions of performance on both unconditional and related adoption of new NAICS based on specification (1) and (2). The dependent variable is a BHC's return on equity. An adoption is defined as the appearance of a new five-digit NAICS within a BHC's organizational structure. Cumulative adoption is the count of a BHC's adoptions over a consecutive 3-year period. Cum. related adoption is a sub-specification of Cumulative adoption based on the adoption relatedness definition specified in each column header. Distance (Column 2) defines related adoption as the average distance (one, two, three, or four digits) from NAICS 52211 of the NAICS adopted by the BHC.

| RESULTS
Column 1 of Table 3 reports the results based on specification (1). This is a benchmark specification where we look for the impact on performance of unconditional scope expansion, as captured by Cum Adoption. As the results in Column 1 indicate, the act of expanding into new NAICS is unconditionally associated with a lower return on equity. 23 Accounting for exiting strategies is also important, suggesting that firms that engage more broadly in scope expansion but also retrench when (presumably) their results are poor, on net display higher ROE. At the same time, the results in Column 1 indicate that overall turnover of segments (as captured by the Cum adoption x exit interaction term) does not improve ROE-if anything, lowers it slightly.
The regression results also indicate that the impact of unconditionally expanding scope seems to have a nonlinear component, with expansion among institutions with large initial scope gradually becoming associated with a positive impact. 24 The importance of unconditional scope expansion is shown even after controlling for BHCs' M&A activity, which we estimate to be associated with lower ROE as well. 25 We continue with the presentation of our main results, where we establish empirical evidence of the differential impact on performance of scope expansion based on the relatedness of the new segments at the time of expansion. Column 2 of Table 3 shows the results of a regression based on specification (2), where Cum Related Adoption measures the average distance (measured from NAICS 52211) of NAICS codes adopted over the previous 3 years. The estimated coefficient for Cum Adoption remains similar to estimates in Column 1, and the coefficient for Cum Related Adoption implies that expansion into NAICS that, on average, share one fewer digit with code 52211 is associated with only slightly lower ROE. Together, the stable effect from overall adoption and the small coefficient for related adoption may result from the fact that code distance is a poor measure of relatedness.
Next, we try the alternative distance-based metric that separates expansion in NAICS 52 segments from any other. In this alternative specification, Cum Related Adoption is the sum of newly adopted segments that are within the 52 range. Column 2 reports that Cum Adoption is associated with lower ROE, and Cum Related Adoption is associated with higher ROE of a similar magnitude. This implies that expansion into nonfinancial (i.e., non-52) NAICS codes is associated with a fall in 23 While expansion might reduce ROE, it might still be beneficial from the vantage point of total value creation, provided that the additional returns produced (ROE-dilutive as they may be) are higher than the cost of capital, leading to a positive NPV. See Jacobides, Winter, and Kassberger (2012) for a broader discussion of total profits versus profitability, and Levinthal and Wu (2010) for a specific illustration of how the pursuit of scale-free resource advantages can reduce profitability and increase profits in diversification. That said, our measure looks at the relative benefits of different types of expansion, so focusing on ROE provides a clean measure. 24 The robustness of this result, however, is challenged in robustness tests (presented in the Online Appendix), which suggest that the nonlinearity is driven by a subset of BHCs that enter the database while already relatively broad in scope to start with (so that we cannot follow their entire evolution). What matters for us, though, is that the main result on unconditional scope expansion remains unchanged, even after the robustness tests. 25 While the baseline control for M&A activity is represented by the cumulative number of subsidiaries acquired through M&A over the previous 3 years, we tried three alternative specifications, for which we ran the full set of analyses reported in the paper (results available upon request). First, we used an indicator variable that was activated if M&A activity occurred; second, we considered all adoptions that were the result of M&A separately; and third, we excluded from the computation of the cumulative adoptions those that were the result of an M&A event at the top-holder level. None of these affected our results. The robustness is also due to the fact that-as remarked earlier-only a small fraction of all scope adoption events come from M&A activity. ROE of about 0.32%, while expansion into financial (i.e., 52) NAICS is associated with a negligible difference in ROE. If we assume that this relatedness measure has less measurement error than the distance-based measure in Column 1, then these results imply that expansion into banking-related NAICS codes has less of an effect on overall ROE than expansion into nonfinancial NAICS codes.
We next turn to the overall coincidence measure of relatedness, computing it, following the implementation of Bryce and Winter (2009), as a time-invariant average for each NAICS over the entire sample. Cum Related Adoption is measured as the sum of overall coincidence relatedness for all of the NAICS that the BHC has adopted over the past 3 years. Is there a significant differential impact on performance associated with scope expansion in NAICS that, on average over the sample period, are more commonly held by BHCs? The estimated coefficient on Cum Related Adoption in Column 3 implies that adopting NAICS codes that are, on average, owned by one percentage point more BHCs over the sample period is associated with 2.13 basis points higher ROE. This estimate is not very precise, which we believe to be understandable given that the banking sector has undergone significant change over the sample period. Indeed, this was the reason we focused on this sector.
Finally, we focus our attention on the evolving metric of modal relatedness, shown in Column 4, which captures the dynamic nature of relatedness. As depicted in Table 1 for 3 representative years, and in Figure 2 for selected NAICS over time, modal relatedness is the timevarying percentage of BHCs in the entire population that hold a given NAICS as part of their portfolio of subsidiaries. 26 Cum Related Adoption is measured as the sum of modal relatedness for all of the NAICS that the BHC has adopted over the past 3 years. Thus, Column 4 reports that adopting NAICS codes that are owned by one percentage point more BHCs in that sample period is associated with 2.15 basis points higher ROE.
Column 4 strongly indicates that expanding into segments that are more popular among BHCs at the time of expansion is associated with higher ROE. Using the estimates in Column 4, we can compare the effects of expanding into a given NAICS code when it is popular or unpopular. We run this exercise focusing on a single NAICS code, reporting the hypothetical impact of its addition to the organizational structure of a BHC for different degrees of prevalence among BHCs at the time of adoption. Take, for instance, NAICS 52421, "Insurance agencies and brokerage." Over the sample period, it had a minimum modal relatedness of 12.2% and a maximum of 37.5%, with fluctuations over time. A BHC that adopted this NAICS at its nadir of modal relatedness is expected to exhibit a lower ROE of approximately 0.15 percentage points (−0.39 + 0.0215*12.2). Adopting this NAICS at its maximum modal relatedness would be associated with a higher net ROE of 0.36 percentage points. Hence, adopting the same NAICS at different points in time can have very different implications for ROE.
The findings, then, suggest that dynamic measures of relatedness are not only theoretically appealing but also have (in the context of a shifting sector) the ability to explain more variance, more consistently than other measures that rely upon NAICS distance or overall coincidence across time (à la Bryce & Winter, 2009). We concur with Weiss (2016) that measures of overall coincidence are superior to those obtained by looking at the NAICS tree and find that looking at the shifting coincidence patterns (i.e., the evolving core of modal NAICS) provides even stronger results, reflecting the changing dynamics of the sector. We find that the average coincidence 26 If modal relatedness is a stock variable, which corresponds to existing research on relatedness inferred by coincidence, we also consider its "flow" counterpart as an additional measure of relatedness. As such, we classify individual NAICS on the basis of how many BHCs expanded in them over the previous year. This yielded a natural ranking, with "hot" NAICS at the top, with the understanding that the fact that many BHCs choose to enter the same segments at the same time may indicate bigger rewards at that time. Using such a flow metric yielded consistent results (available on request). of NAICS is not strongly correlated with success, whereas the evolving coincidence, in the spirit of Chandler (1977Chandler ( , 2001Chandler ( , 2005, appears to be strongly correlated with success.

| Disentangling treatment and selection effects for BHC expansion
Scope transformation is obviously a choice and not a random occurrence, which raises a question over the interpretation of our results. Specifically, banking firms that are improving in terms of ROE may expand in particular ways, or firms with certain characteristics may systematically choose to make strategic scope expansion choices that suit them, so that our main results that rely on modal relatedness could be the result of selection rather than treatment. Our analytical strategy should help to address the impact of selection. First, we draw our inference from model specifications with BHC-level fixed effects, so that any time-invariant, BHC-specific trait that drives expansion dynamics is fully absorbed. Second, our panel regressions include important covariates, such as asset size, level of capitalization, scope before expansion takes place, alternative exiting strategies, and M&A occurrences, which should account for selection through effective use of observables. However, there may still be interpretation challenges. For example, it may still be the case that banks who have been on a better performance path in the past might tend to choose more conservative scope expansion strategies, thus adopting NAICS that are already comparatively popular among BHCs. Such hypothetical systematic difference in expansion choices, solely based on past performance, would represent a violation of the parallel trend assumption: the future ROE of BHCs that adopt NAICS with high modal relatedness is higher not because these NAICS contribute more to overall performance, but simply because their ROE was already on a steeper uptrend than that of BHCs expanding in NAICS with lower modal relatedness. Conditioning on observable covariates and fixed effects may not be sufficient to assuage this concern.
We test the parallel trend assumption using a standard procedure: We identified all BHCs that expanded their scope in a given year and separated them into two groups based on whether they expanded into a NAICS segment with one of the 10 highest modal relatedness scores that year. 27 We then ran regressions of ROE on up to 5 years of lags of this modal relatedness dummy variable. If the ROEs of these two groups of BHCs follow a roughly parallel trend, the point estimates on the lags of the modal dummy should be close to zero. Figure 3 confirms this. F I G U R E 3 Parallel trends. It reports the estimated coefficients of lags (up to 4 years) of an indicator variable that is equal to one for BHCs engaging in a modal expansion at time t = 0, and it is equal to zero for instances in the same year of nonmodal expansions. For each bar, the dot depicts the magnitude of the coefficient and the vertical bars its 95% confidence interval 27 Sensitivity tests setting the modal relatedness "cutoff" as top 5 and top 15 of the rank ordering of segment popularity yielded qualitatively similar results.
On average BHCs that expanded into high modal relatedness NAICS exhibit roughly the same performance in the proximity of the expansion decision as BHCs that did not.
Confirming a nonviolation of the parallel trend assumption provides comfort to a causal interpretation of our results. Yet, the parametric assumptions implicit in our model specification (the vector of observables have a linear impact on the outcome variable) may still generate selection biases. In particular, it is still possible that the outcome variable follows a different dynamic process for treated and untreated units, so that extrapolating the counterfactuals from the simple average treatment effect estimated in the benchmark regressions may still embed some biases. To address this issue, we complement the parametric approach used in our main analysis with three semiparametric treatment effects strategies developed in the field of program evaluation. With the first approach, a regression adjustment method, we allow for the dynamic process for the outcome variable (BHCs' performance) to be different for BHCs that expanded into NAICS segments with high modal relatedness (treated) from those that did not (untreated), and the estimations of the effect of the treatment are adjusted accordingly. The second approach, an inverse-probability weights method, is based on the estimation of the likelihood to be treated, so that in garnering the effect of the treatment, individual observations are weighted differently on the basis of such estimated likelihoods. The third is a combination of the two: a double-robust estimator method, considered to be the preferred approach in the literature (Imbens & Wooldridge, 2009). More details on the implementation of these alternative methods, and the corresponding results are presented in Online Appendix A5. The results, in Table A5, corroborate our main findings, offering strengthened support to the conjecture that expansions in segments with high modal relatedness yield relatively beneficial effects on future BHC performance.

| Vertical integration and changes in scope; change in entropy measures
We ran a battery of tests to confirm the robustness of our choice of relatedness metric. First, we wanted to run a horse race between cumulative-related adoption based on modal relatedness and NAICS 52 relatedness, which was also positive in the results reported in Table 3. Column 1 of Table 4 shows that when including both NAICS 52 and modal relatedness, the latter is more important: The static NAICS 52 coefficient is reduced by 30% when compared to its standalone regression, while the coefficient on modal relatedness decreases by only 13%.
We also want to ensure that our results are not the spurious outcome of some other potential confounding variables. As such, we consider two motivations for changing a firm's scope: a potential desire to bolster vertical integration (VI) given the presence of Williamsonian transaction costs, and the potential desire to overcome external financing frictions during periods of adverse capital market conditions. We construct a metric of how vertically related a BHC's scope expansions are by drawing on Input-Output Accounts Data (IO table) from the Bureau of Economic Analysis (BEA). 28 This is done as follows. Let n be the five-digit NAICS adopted by 28 These tables provide information on how industries in the U.S. economy interact. For a given three-digit NAICS industry i, the BEA constructs the input component of the IO table by calculating the annual U.S. economy-wide dollar value of inputs provided by each three-digit NAICS industry (including industry i itself) for the production of output by industry i. If industry i takes a large proportion of its inputs from industry j, then we can reason that industry j is upstream in the production chain of industry i, and that the two industries are vertically related. Cum. Added VI The sum of Added VI for all NAICS adopted by a BHC in the preceding 3 years

BHC-year
Total Diversification A measure of BHC diversification analogous to entropy from the study by Palepu (1985 where P j is the ratio of subsidiaries in group j to total subsidiaries in the BHC BHC-year the BHC at time t. From the input table at time t-1 we sum across the inputs that n gives to each of the NAICS the BHC already holds. A high value of the sum indicates that the addition of n significantly increases the upstream vertical integration of segments in which the BHC is active. The sum is dynamic in that as a BHC expands its scope, its opportunities for vertical integration also increase: In a BHC with a large scope, there are more NAICS with which the new NAICS n can be vertically related. We then normalize the inputs sum by dividing from it the total amount of inputs (across all segments, regardless of whether they are held by the BHC) used by the NAICS that the BHC already held prior to its expansion. The resulting metric, which we call Added VI, thus captures the extent to which a given scope expansion increases the proportion of upstream production that is housed within the BHC. Column 2 of Table 4 includes Added VI (summed over all NAICS adopted over the past 3 years) and its interaction with modal relatedness, allowing us to assess the extent to which a firm enters into a commonly held VI sector in our BHC population. 29 We find, first, that VI is negative, and second, that the interaction between Cum Modal Adoption and VI is positive: The value of VI increases with a segment's relatedness, positively affecting ROE. More important, adding the variable picking up the relative contribution to VI of the adopted segment in our analysis does not detract from (evolving) relatedness, and thus our key variable of interest, Cum Modal Adoption, remains robust.
Another potential explanatory feature, explored in the diversification literature, is the "entropy measure," introduced by Jacquemin and Berry (1979) and developed further by Palepu (1985). This static measure, used in general population (as opposed to sector study) settings, can be duly modified, to help us see whether the variance in ROE is not caused by firms following the evolving core of the sector, but rather because of the way their diversification pattern (in terms of the evolution of their Palepu score) evolves. Our objective is to see whether the benefits of moving closer to the shifting core of the sector would be robust to a firm-level variable that would consider the BHC's changing entropy profile. So, replicating our model specification, we ran a regression where we included total diversification (in the Palepu sense) at time t-4 and then the change in both total and related diversification (again, following the Palepu-style formulation above) over the following 3 years, as we have to provide a dynamic equivalent of a static measure. Column 3 of Table 4 shows that the new variables do not explain variance in our setting. In Column 4, we included such variables in a horse race with our metrics of scope adoptions. Both Cum Adoption and Cum Modal Adoption preserve their sign and magnitude. Online Appendix 3A contains details about the construction of such measures.
Finally, our results are also robust to the possible confounding factor of coinsurance from diversification (Online Appendix A3), and likewise to running the analysis using market-based metrics of performance (Tobin's Q), and alternative metrics of risk, such as leverage and the BHC's Z-score (see Online Appendix A8).

| CONCLUSION
This article has shed light on the dynamics of sector transformation through the expansion of firms into new segments, focusing on U.S. banking, through the BHC population from 1992 to 2006. As 29 Modal relatedness of some vertically related segments increases over time, and others less so. This reflects BHCs choosing which of their related segments to hold. NAICS 541 ("Professional, Scientific, and Technical Services"), which includes NAICS 54199 (mostly, specialized B2B service providers) and NAICS 54119 ("Legal Services") gains popularity, while NAICS 561 ("Administrative and Support Services") loses popularity over our sample period, even though both maintain similar vertical linkages. Chandler (1962;1977) noted the transformation of corporations is part and parcel of the process of sector evolution. Chandler's last two books, on the evolution of electronics (2001) and pharmaceuticals and chemicals (2005), showed how the biggest firms in these two sectors transformed both themselves and the sector as a whole, by broadening their boundaries. However, the richness and detail of Chandler-like that of other business historians who described such evolution, such as Silver (1984) and Langlois and Robertson (1995)-comes at the cost of an inability to capture the entire sector, or to provide precise estimates of the impact (or indeed appropriateness) of changes in scope. Drawing on a data set of unprecedented depth and detail, we conduct a large-scale study of a significant sector in a time of flux, examining firms' changes in scope and experimentation with new activities as they try to take advantage of their regulatory and institutional environment. Since the rules are identical for all participants, and BHCs all start out as narrow, we can see how such expansion played out. We find that the sector has a clearly defined core that evolves over time, and that following this core pays off.
Our paper complements research in sector evolution with a comprehensive, large-scale sector study of scope transformation, focusing on its drivers and consequences. Within this, the established wisdom is partly confirmed. Expanding into new business segments is found not to be beneficial and has a performance impact that is an order of magnitude greater than creating a new subsidiary in an existing segment. 30 We also consider relatedness. First, we consider its impact as measured by hierarchical NAICS distance and estimate a small and imprecise effect on ROE. We then consider a coarser distinction between financial and nonfinancial expansion and find that nonfinancial expansion is associated with lower ROE than financial expansion. Drawing on Bryce and Winter (2009), we construct a time-invariant measure of relatedness based on the prevalence of certain NAICS codes but estimate imprecise results, which may be caused by the static nature of this measure. Lastly, we consider a dynamic measure of relatedness based on how many BHCs currently hold a given NAICS. We estimate that expansion into popular NAICS is associated with higher overall ROE. This result withstands a battery of endogeneity tests, suggesting that there is a persistent treatment effect of adopting NAICS that are currently popular among other BHCs-"following the times," as it were. This result is robust to the inclusion of measures of vertical integration, changes in the entropy of expanding BHCs, and measures of market risk, and still holds if we exclude BHCs with a minority of assets in commercial banking. Finally, we also show that M&A at the BHC level does not drive our results, suggesting that this expansion is the result of a desire to broaden the scope of the banking firm.
Our paper is the first to offer a systematic account of the dynamics of relatedness, based on coincidence and sectoral evolution and also the first to connect this measure to performance. This extends the thesis of Teece et al. (1994) and shows that there is a net benefit of expanding into the evolving core of a sector, which is not driven by selection. We thus find support for the Chandlerian thesis and also establish why sector studies should be used to understand scope changes, and vice versa. Our approach, consistent with historically based work emphasizing the role of shifting business models in financial services (Cetorelli et al., 2012;Jacobides, Drexler, & Rico, 2014), may thus help us revisit the nature and benefits of relatedness (Rumelt, 1982;Weiss, 2016) and the drivers of resource renewal (Folta et al., 2016).
Our results are robust to using market-based metrics of performance, and are robust to measures relating to vertical integration, capital market volatility, and firm-level entropy changes. As to why BHCs would expand into segments that do not increase ROE, a number of reasons 30 We corroborate this point in the extension analysis reported in Online Appendix A6.
can be put forth, although our paper does not discern them. 31 Our paper is also limited in terms of its normative implications. We have explicitly focused on a benign period of increasingly permissive policy, regulatory flux, and radical technological change that transformed both the process of financial intermediation and the scope of the majority of firms. While we find that related expansion in banking may have helped BHCs in this favorable period and has not adversely affected their fate during the financial crisis, we did not explore the broader social welfare impact that has resulted from the transformation of BHCs. Benefits for BHCs who transform their scope do not imply concomitant benefits for society as a whole; nor do they rule out the possibility of associated negative systemic externalities (Jacobides et al., 2014;Rajan, 2011;Tett, 2009). This in an important issue, and one that deserves dedicated study.
That said, our paper provides the first systematic, large-scale, longitudinal study of scope changes and their performance implications in a sector and raises the need to better combine our understanding of scope and sector evolution-a path we hope will be more widely followed. reviewers provided useful feedback, and Connie Helfat offered valuable Editorial guidance. Jacobides acknowledges financial support from the Institute of Innovation and Entrepreneurship and RAMD at London Business School. Michael Blank has provided invaluable research support. All remaining errors are our own.

DATA AVAILABILITY STATEMENT
Data not available (drawing on proprietary database of the NYFRB, not available for external access) ORCID Michael G. Jacobides https://orcid.org/0000-0002-0615-6191 31 There are three categories of reasons that we think can explain this pattern. The first is economically rational: The most straightforward reason is that, whereas these moves reduce ROE, they still increase total profits and have a positive NPV, inasmuch as the returns are higher than the cost of capital. As Levinthal and Wu (2010) have noted, diversification can cause profitability to decline while total profits continue increasing, so that economically rational expansion dilutes the rates of return. Less plausibly, it may be the case that while unrelated expansions may not contribute to performance year in, year out, they can still contribute to the benefits of scope expansion in particularly adverse states of nature. The second set of reasons for this pattern relates to managerial agency: Different managerial teams have different risk appetites and may "gamble" on new directions-an area we will consider in future research. The third set of reasons relates to fundamental uncertainty: New segments entail uncertainty and experimentation, so there may be little ex ante understanding of what will add value in the first place. Our paper cannot distinguish between these three sets of explanation. Our aim was to document the pattern and leave the exploration of these competing hypotheses for future research.