Accelerating emergence: the causal (but contextual) effect of social impact accelerators on nascent for-profit social ventures

Given the legitimacy challenges faced by entrepreneurs, gaining access to the resources necessary to create viable new ventures is often difficult. Accordingly, scholars advocate that entrepreneurs align with high-status partners to convey that they are an accepted part of the sociocultural and organizational landscape. Although startup accelerators have been argued to play this supportive role for high-tech, high-growth ventures, it remains unclear whether they are effective at serving the needs of ventures pursuing social missions alongside business structures, or for-profit social ventures (FPSVs). To explore this issue, we examine whether social impact accelerators (SIAs), accelerators specifically designed to support FPSVs, help such ventures make the transition from mere ideas to viable organizations, a process known as emergence. To determine a causal relationship, we employ a quasi-experimental design and adopt propensity score matching with the nearest neighbor matching algorithm to study 7185 startups that applied to 383 accelerators worldwide from 2013 to 2019. By matching accepted startups to a control group of rejected startups, we find that SIAs, on average, facilitate new venture emergence, with accelerated FPSVs raising more external financing, earning more revenues, and hiring more full-time employees than their unaccelerated counterparts. These results hold when controlling for selection bias, thereby providing robust evidence for a causal relationship between acceleration and startup emergence. However, a subsequent subgroup analysis reveals that this causal effect is contingent across a breadth of “who,” “when,” and “where” contexts, highlighting the idiosyncratic differences that different startups face in the acceleration process. Recent empirical research on the benefits provided by startup accelerators suggests that accelerators help early-stage, commercial, growth-oriented ventures access external financing. While useful in demonstrating the value accelerators provide, we see an opportunity to expand this focus to explore the acceleration effect in a broader context. Given the important role social innovations play in the global economy, we explore how social impact accelerators (SIAs), entities designed to help startups simultaneously scale economic and social impact, help nascent for-profit social ventures (FPSVs) transform into viable, self-sustaining organizations, a process known as emergence. We find that SIAs do indeed facilitate emergence, with accelerated FPSVs raising more external financing, earning more revenues, and hiring more full-time employees than unaccelerated FPSVs. However, the SIA effect varies depending on how old the startup is, the gender composition of the founding team, and where the startup is located. By validating the causal impact of SIAs on FPSV emergence, our findings can inform not only theory and practice, but also public policy focused on bolstering the social innovation ecosystem.


Introduction
The entrepreneurship ecosystem has changed drastically over the last two decades as various types of venture development organizations have evolved to connect startups with the resources they need to emerge into viable organizations (Block et al., 2018). Among them is the startup accelerator. Defined as "learningoriented, fixed-length programs that provide cohorts of ventures with mentoring and education" (Hallen et al., 2020: 380), accelerators are designed to help new ventures define their ideas, build prototypes, identify customer segments, form relationships, scale operations, etc. Amidst the rise of the accelerator phenomenon, both the media and academe have taken notice. Over the past 4 years, Entrepreneur magazine has published more than 1000 articles on startup accelerators, while Inc. magazine has published approximately 400, the overwhelming majority of which tout the positive benefits of acceleration.
A recent review of the scholarly literature on accelerators by Crișan et al. (2021) identifies 98 articles on the topic published between 2004 and August 2019, the vast majority (52%) of which have focused on the positive relationship between acceleration and post-financing outcomes. However, our independent review of the works cited by Crisan et al. (2021) as well as those published since reveals four key characteristics that we believe provide an opportunity to advance our understanding of the role accelerators play in the entrepreneurial ecosystem. First, most extant research focuses on commercial accelerators designed to support growth-oriented, technology-intensive ventures. While important to our understanding of how accelerators can aid nascent ventures, this narrow focus means that we know comparatively little about whether and to what extent the needs of ventures seeking to scale both economic and social outcomes, or for-profit social ventures (FPSVs), are being met by the accelerators designed to help them, or social impact accelerators (SIAs). Given the important role FPSVs play in economic development and delivering social change (e.g., Autio et al., 2014;Bruton et al., 2013;Mair & Marti, 2009), coupled with the calls by leading scholars for more research on the structures and processes that support them (McMullen & Dimov, 2013;Shepherd & Patzelt, 2011), we contend that research on the support SIAs provide to FPSVs is warranted.
Second, despite the wealth of empirical research in the area, there is comparatively little support establishing a causal effect of acceleration. In fact, of the 98 articles cited in Crisan et al. (2021), only one, Gonzalez-Uribe and Leatherbee (2018), employs an analytical technique from which causality can be inferred. Using regression discontinuity design, Gonzalez-Uribe and Leatherbee (2018) find that schooling bundled with basic services, and not basic services by themselves, can significantly increase new venture performance. Since their review, only one additional article (Hallen et al., 2020) claims to have tested for causality. Like Gonzalez-Uribe and Leatherbee (2018), Hallen et al. (2020) find that participation in an accelerator program significantly and positively affects a startup's ability to raise equity financing.
Third, while both studies have provided rich insight into the causal effect of acceleration on financing in single-country samples, we do not yet know whether this effect is generalizable beyond these two countries and/ or whether it holds in other geographic (i.e., "where"), individual/organizational (i.e., "who"), and temporal (i.e., "when") contexts (Newbert et al., 2022). Given the heterogeneity inherent in entrepreneurial ventures (Davidsson, 2003), we believe there is much insight to be gained by exploring how an acceleration effect might differ across a broader range of contextual factors.
Fourth, most extant research has focused on the role accelerator programs play in enabling startups to raise more post-acceleration financing. While such findings help substantiate the widespread belief in the value of accelerators, we do not yet know if acceleration has a causal effect on other outcomes of interest, such as "emergence," or the transition from a startup idea to an operational organization (Tornikoski & Newbert, 2007). While the relationship between acceleration and emergence has been explored in recent research (Newbert et al., 2022), a causal effect has yet to be either theorized or empirically established. Given that emergence is not only one of the most critical milestones in the startup process (Aldrich & Martinez, 2001), but also an outcome targeted by accelerators (GALI, 2016), establishing whether acceleration has a causal effect on this outcome represents an important gap in the literature that needs to be filled.
In response to these four opportunities, we analyze a sample of 7185 FPSVs that applied to a global network of 383 SIAs between 2013 to 2019. We adopt a quasi-experimental design that enables us to compare FPSVs that completed an SIA program with a virtually identical sample of FPSVs that applied to but were rejected by the SIA, while minimizing concerns of selection bias in the process. By analyzing our data with propensity score matching (PSM) with the nearest neighbor matching (NNM) algorithm, we find evidence to suggest that acceleration is indeed a significant causal factor in helping FPSVs emerge. More importantly, subsequent subgroup analysis reveals that this acceleration effect is not uniform across FPSVs; rather, it is dependent on a variety of contextual factors including the gender composition of the FPSV team members (who), the age of the FPSV at the time of application (when), and the country in which the FPSV is operating (where).
We believe our findings contribute to entrepreneurship research and practice in the following ways. First, management scholars have long called on researchers to conduct more causality research (e.g., Aguinis & Jeffrey, 2014). By employing a quasi-experimental design, we add significant empirical rigor to current accelerator findings by providing the first quantitative evidence of a causal "acceleration effect." Second, most of the research on accelerators has sought to predict outcomes related to financing (e.g., Gonzalez-Uribe & Leatherbee, 2018;Hallen et al., 2020;Plummer et al., 2016;Yu, 2020), thereby limiting what we know about the benefits of acceleration. By focusing more holistically on the role accelerators play in facilitating the transformation of a nascent venture into a self-sustaining organization, a process known as "emergence" (Reynolds & Miller, 1992), we expand our understanding of the impact acceleration to a more expansive outcome that is of interest to both nascent ventures and accelerators alike (Cohen & Hochberg, 2014;Tornikoski & Newbert, 2007). Third, as Newbert et al. (2022) point out, although entrepreneurship research tends to identify average effects, there is no "average" entrepreneur. Thus, while generalizations are helpful in understanding the nature of relationships, they can be misleading unless appropriate contextual factors are accounted for. By addressing their call by examining for whom, when, and where acceleration matters, our findings allow for a more fine-grained understanding of the nuances of the acceleration effect. Finally, given the increasing attention governments have given to bolstering the social innovation ecosystem, our findings may also inform SIAs, the entrepreneurs that seek accelerator services, and policy makers who seek to support FPSVs to bring about desired societal change.

Legitimacy challenges facing nascent ventures
New ventures often do not have the financial resources to withstand many missteps (Sørensen & Stuart, 2000) which can lead to higher rates of failure (e.g., Aldrich & Auster, 1986;Levinthal, 1991). As such, Aldrich and Martinez (2001: 45) argue that in the context of early-stage ventures, "the transformation of an idea into an organization requires that entrepreneurs acquire resources." Of course, to acquire resources, the venture must be perceived as being legitimate and be an accepted part of the sociocultural and organizational landscape (i.e., cognitive legitimacy), and behave in ways that are consistent with cultural norms and values as well as government rules and regulations (i.e., sociopolitical legitimacy) (Aldrich, 1999: ch. 9). Being perceived as legitimate has been found to have a direct effect on a new venture's ability to acquire financial, human, and cultural resources (Golant & Sillince, 2007) as legitimacy helps the venture overcome the lack of confidence resource gatekeepers have in its ability to succeed. Resource gatekeeps are concerned with the venture's lack of a proven track record of exchange, proper knowledge of their business environment, established relationships with suppliers, and committed employees (Starr & MacMillan, 1990;Stinchcombe, 1965).
Given these challenges, it is critical for new ventures to gain legitimacy, as it establishes a favorable judgement of worthiness by others that they are an accepted part of the sociocultural and organizational landscape (e.g., Delmar & Shane, 2004;Tornikoski & Newbert, 2007), thereby facilitating the acquisition of the resources they need for survival and growth (Zimmerman & Zeitz, 2002). Because entrepreneurial ventures derive resources from a range of sources (Denis, 2004;Hanlon & Saunders, 2007), legitimacy assessments are audience-dependent (Suchman, 1995) and ultimately exist in the "eyes of the beholder" (Zimmerman & Zeitz, 2002:146). Organizational scholars suggest that one way for new ventures to appear more legitimate to a variety of audiences is to associate themselves with a prominent third party and leverage its well-established reputation (Starr & MacMillan, 1990). Such affiliations are particularly important during the "conception phase," or "the stage in which a new venture's idea or core insight about a product or service opportunity is first conceived and developed" (Fisher et al., 2016: 388). Uncertainty is extremely high during this phase given that market segments are still evolving, and ventures generally do not have tangible metrics or a history of exchange that can help an outside evaluator assess their potential (Stuart et al., 1999). Thus, a symbolic affiliation with a high-status institution (Fisher et al., 2016) can help the nascent ventures decrease uncertainty and, in turn, appear more legitimate to outside evaluators.
In support, Plummer et al. (2016) argue that aligning with a high-status partner is one of the most effective ways that a new venture can convey its legitimacy as it provides additional assurance (beyond that provided by the venture itself) to outsiders that the new venture, which is "shrouded" in uncertainty (Audretsch, 1995) given its lack of history and unobservable nature, is a credible exchange partner. Specifically, associations with prominent third parties have been shown to not only demonstrate the startup's connection to the broader entrepreneurial ecosystem (Busenitz et al., 2005;Starr & MacMillan, 1990;Stuart et al., 1999), but also convey that the startup has been vetted through a formal due diligence process (Stuart et al., 1999), has high-quality products and processes (e.g., Baum & Oliver, 1991;Podolny, 1993;Yli-Renko et al., 2001), and/or has access to the third party's resources (e.g., Plummer et al., 2016;Pollock & Gulati, 2007;Jain & Kini, 2000;Carter & Manaster, 1990;Lee et al., 2011;Certo et al., 2001), all of which can increase a venture's probability of future growth and survival.
2.2 Accelerators as prominent third parties Startup accelerators are defined as "learning-oriented, fixed-length programs that provide cohorts of ventures with mentoring and education" (Hallen et al., 2020: 380). Most traditional accelerator programs (e.g., Y Combinator, Techstars, 500 Startups) seek to help nascent, technology-focused ventures (Hallen et al., 2014) define their ideas, build prototypes, identify customer segments, form relationships, and scale (e.g., Cohen & Hochberg, 2014;Cohen et al., 2019;Yang et al., 2018). In return for providing the resources needed to support these efforts, traditional accelerators generally take a 6-8% equity stake in their cohort ventures (Hallen et al., 2020). These programs are deemed so effective at addressing the needs of early-stage ventures that they are referred to in practitioner circles as "startup factories" (Miller & Bound, 2011: 1). Academic research similarly ascribes many benefits to accelerator participation, finding that ventures backed by accelerators are better at solving business problems (Cohen et al., 2019), survive longer (Del Sarto et al., 2020;Yu, 2020), raise more follow-on investment (Gonzalez-Uribe & Leatherbee, 2018;Hallen et al., 2020), and are viewed as more investable by venture capitalists (Yu, 2020).
Despite the associative role accelerators seem to play in helping high-tech, high-growth ventures transition from mere ideas to viable organizations, a process known as "emergence" (Reynolds & Miller, 1992), it remains unclear whether accelerators are effectively serving the needs of entrepreneurs seeking early-stage support for ventures pursuing alternative missions (Lall et al., 2013) or whether completing an accelerator program can actually enable these ventures to emerge.

The role of social impact accelerators (SIAs)
While virtually all new ventures face the legitimacy challenges described above, those ventures that seek to pursue social missions alongside a business structure, also known as "for-profit social ventures" (FPSVs) (Dees & Anderson, 2003), face additional legitimacy concerns due to the fact that they seek to simultaneously improve societal welfare and generate profit (Battilana & Dorado, 2010;Battilana et al., 2012;Besharov & Smith, 2014). To most resource gatekeepers, this dual mission tends to be viewed as contradictory or paradoxical (Smith et al., 2013) given the "performing tension" they face as they strive to address the competing demands of their multiple, divergent stakeholders (Smith & Lewis, 2011), leading many profit-oriented investors to doubt the long-term viability of FPSVs (Tracey & Jarvis, 2007). Nevertheless, recent research suggests that financial and social objectives are (or at least can be) complementary in nature (Newbert, 2018). Indeed, it is precisely because FPSVs mix for-profit and non-profit approaches in their operations that they have been argued to be actually more enterprising in their goal of becoming financially self-sustainable (Di Domenico et al., 2009) and pursue more innovative business models that can drive revenues and profitability (Austin et al., 2006;Pearce, 2003) than ventures pursuing solely commercial goals.
Notwithstanding these findings, entrepreneurs seeking to create viable FPSVs often have difficulty conveying the legitimacy of their hybrid business models, and their ability to implement them, to resource gatekeepers (Kohl et al., 2013). In light of this "pioneer gap" between early-stage entrepreneurs seeking to launch FPSVs and the resources needed to build them (Kohl et al., 2013) coupled with the increasingly important role social ventures play in economic development and social change (e.g., Autio et al., 2014;Bruton et al., 2013;Mair & Marti, 2009), a new form of accelerator, the social impact accelerator (SIA) (e.g., Echoing Green, Startup Chile), has arisen to help FPSVs bridge the pioneer gap by providing a menu of resources, including but not limited to mentoring, education, networking, access to investors, and connections to the local ecosystem (GALI, 2018). Due to the widespread agreement that the resources provided by accelerators can enable nascent ventures to better cope with a variety of business challenges (Crișan et al., 2021), they are a powerful source of legitimacy for FPSVs that can, in turn, facilitate their access to the additional resources they need in order to emerge into viable, sustainable new organizations (Fisher et al., 2016).

Accelerating emergence
According to Reynolds and Miller (1992), emergence is a multidimensional construct that manifests when the entrepreneur demonstrates intention, receives external financing, generates revenues, and hires employees. Katz and Gartner (1988: 431) in which Reynolds and Millers' (1992) work is grounded, define intention as "an agent seeking information that can be applied toward achieving the goal of creating a new organization." Given that entrepreneurial intention is evident by the actions of any entrepreneur who creates a venture, and specifically applies to an accelerator, we next focus our theorizing on how SIAs should facilitate the emergence of FPSVs with respect to each of the remaining three dimensions.
Resources serve as the "building blocks" of all organizations (Katz & Gartner, 1988: 431). While the needs of startups are varied and often unpredictable, the fungibility that financial capital provides them is paramount as it enables the acquisition of the many other resources necessary to support a venture's business model (Katz & Gartner, 1988;Rawhouser et al., 2017). Accordingly, Mollick (2014) argues that financing is arguably the most critical resource for a nascent venture to acquire. Furthermore, according to a recent report conducted by an SIA consortium, "one of the primary goals of accelerators is to drive incremental funding into promising early-stage ventures" (GALI, 2018). For this reason, Dempwolf et al., (2014: 27) argue that the "immediate goal of an accelerator is to help their startup companies obtain next-stage funding," a claim also advocated by (Cohen et al., 2019).
Despite the need for financial resources by all nascent ventures, investors are only likely to provide capital to those that they perceive to be legitimate (Meyer & Rowan, 1977), thereby increasing the likelihood that it will be capable of generating the financial returns needed to justify the investment. Unfortunately, due to the legitimacy challenges surrounding FPSVs as described above, they are often viewed more skeptically by investors compared to commercially focused ventures (Smith & Lewis, 2011) as FPSVs span dual social and economic logics (Battilana & Lee, 2014;Wry et al., 2014). In such situations of uncertainty, a third-party affiliation can help an investor assess a venture's legitimacy (Sanders & Boivie, 2004), and following this logic, we expect an SIA affiliation will increase the likelihood that investors will provide FPSVs with financial capital.
Hypothesis 1: accelerated FPSVs will raise more external financing than non-accelerated FPSVs.
Receiving financing from external investors does not mean a startup's business model is financially viable. According to Katz and Gartner (1988), nascent ventures also require organic sources of capital to sustain themselves in the long term. Indeed, it is wellaccepted that for a new venture "to survive and prosper, it must have customers for its products" (Hennart, 2014: 119). For nascent ventures, revenues play an important role in their quest to emerge as the cash flow they provide offsets their reliance on external resource providers for their own survival (Gilbert et al., 2006;Lichtenstein et al., 2006). In support, Cohen et al., (2019: 11) note that accelerator directors view revenue growth to be "a particularly important early measure because it indicated whether the company had identified product-market fit." Yet, despite the importance of revenue generation to the emergence of new ventures, most fail to generate self-sustaining streams of income (Baldwin, 1997;Gaskill et al., 1993;Huang & Brown, 1999). One reason for this inability is the perception by potential customers that the venture is not a legitimate market player (Aldrich & Fiol, 1994).
Here again, a third-party affiliation, such as to an SIA, can serve as an important source of legitimization for a FPSV as the SIA's own reputation can convey to potential customers that an otherwise nascent FPSV is actually a credible market player (Soublière & Gehman, 2020). By reducing the uncertainty surrounding a nascent venture and convincing its initial customers that they are not "ill-fated fools" by transacting with it (Aldrich & Fiol, 1994: 650), an SIA affiliation can have a snowball effect. Specifically, research shows that once a new venture establishes itself with early customers, these customers can help the venture cocreate future legitimacy (Bouncken & Tiberius, 2021), bringing even more new business to the firm (Ogden & Watson, 1999). In light of the legitimization benefits of affiliation with an SIA, we expect that completing an SIA program enhance an FPSV's ability to generate revenues.
Hypothesis 2: accelerated FPSVs will earn more revenues than non-accelerated FPSVs.
As nascent startups scale up their business models, subsystems of maintenance must be established to sustain ongoing exchanges with capital providers and customers (Katz & Gartner, 1988). New ventures often struggle staffing the new organizational roles these systems necessitate (Greer et al., 2016;Mayson & Barrett, 2006) as potential employees often have doubts about the longevity of employment opportunities at nascent ventures whose long-term viability is uncertain (Aldrich & Auster, 1986;Navis & Glynn, 2011). This perceived lack of legitimacy is a challenge for new ventures as hiring additional employees is essential to support their ever-expanding operational, strategic, and functional needs (Churchill & Lewis, 1983). In support, empirical research suggests that the hiring of full-time employees is positively related to new venture growth and success (Coad et al., 2017;Katz et al., 2000;Lee, 2014;Leung et al., 2006;Williamson et al., 2002).
One way to resolve the legitimacy challenges inhibiting FPSVs' ability to hire the employees necessary for their survival is by aligning with a credible third party. Such affiliations signal to potential employees that the venture has been vetted as having a promising future by a trustworthy intermediary (Flynn, 1993;Überbacher, 2014;Van Werven et al., 2015;Williamson, 2000). Thus, affiliating with an SIA can make a nascent FPSV, without any indication of long-term viability, appear as an attractive employment opportunity compared to other similar ventures without such an affiliation (De Vos et al., 2003;Lievens et al., 2007). In support of this notion, given that it is widely understood that FPSVs must grow in order to maximize their social impact (Dees, 1998), SIAs have been found to dedicate considerable resources to FPSVs to assist them with the hiring of full-time employees (Cohen et al., 2019;Dempwolf et al., 2014;GALI, 2020). Thus, we expect affiliating with SIAs will facilitate the ability of FPSVs to attract new employees.
Hypothesis 3: accelerated FPSVs will hire more full-time employees than non-accelerated FPSVs.

Data and sample
To test the causality of SIA treatment on FPSV emergence, we adopt a quasi-experimental design. Our sample is drawn from the Global Accelerator Learning Initiative (GALI), a collaborative data collection effort by the Aspen Network of Development Entrepreneurs (ANDE) and Emory University. GALI consists of data from 23,364 social startups that applied to 408 accelerators across the globe between 2013 and 2019. All startups were surveyed at the time of their application, and 1 year later, 9567 of which also completed the follow-up survey (GALI, 2018). Since our focus is on FPSVs, we only include startups that explicitly state their social mission and report their legal structure as for-profit. Our final sample consists of 7185 (31% of the initial sample) startups that applied to 383 accelerators.
This database has several unique features that make it appropriate for testing for the causal effect of acceleration on emergence contingent upon a startup's stage of development. First, the follow-up survey was not only sent to entrepreneurs who completed an accelerator program, but also to those who were rejected at the time of application. The fact that GALI provides pre-and post-acceleration data minimizes concerns over selection bias. Second, because the startups are surveyed within 1 year after their application, we are able to measure the impact of acceleration on emergence within a timeframe that is quite proximal to the treatment effect. Third, both the accelerators and the startups in the database share goals related to emergence namely, helping startups secure funding, scaling operations, and growing the venture (GALI, 2017, 2018); thus, our outcome measure (emergence) is both appropriate and relevant to the treatment (acceleration). Finally, since the database contains information on each startup's stage of development at the time it applied to the accelerator, we are able to control for left-censoring bias (Yang & Aldrich, 2012).

Econometric approach
When testing for the causal impact of accelerator participation on nascent ventures, we would ideally like to randomly assign startups to treatment and control groups to test for causality; however, this is not practical. In reality, not all startups have an equal chance of being "treated" by an accelerator which leads to non-random "treatment assignment." Therefore, to test the causality by using observational data, Rubin and his colleagues suggest utilizing a Potential Outcome (PO) framework and constructing counterfactual models of causation (e.g., Holland, 1986;Little & Rubin, 2000;Rubin, 1974Rubin, , 1978 that determine the effect of an observed treatment and then simulate what would happen if the treatment was not administered. Simply put, a counterfactual outcome determines the difference between what actually happened and what could have happened. Because we can only directly observe and measure what happened but not what could have happened, we implement non-parametric matching methods to evaluate the effect of accelerator treatment on a subpopulation of startups that underwent the treatment (the accelerated, or treated, group) and then compare these outcomes to a sub-population of startups that sought treatment but were not exposed to it (the unaccelerated, or control, group) (see for example Heckman et al., 1998aHeckman et al., , b, 1999. To do so, we employ PSM as it is a preferred way of determining such counterfactual outcomes of interest (Glazerman et al., 2003), especially when dealing with multiple variables on which to match treated and untreated cases (Abadie & Imbens, 2011) as in our study. In matching these cases, we apply the NNM algorithm, a oneto-one matching method (Abadie & Imbens, 2011) that identifies one case from the control group that is similar to each case in the treatment group across all matching variables. The result of this process is a new, balanced control group (Coad et al., 2017;Li, 2013) that is composed of unaccelerated startups that are "almost identical" (Criscuolo et al., 2012) to the accelerated startups in the treatment group so that any differences in outcomes between the two groups can be attributed to the treatment. This counterfactual model then allows us to determine the treatment effect of acceleration.
In order to find suitable matches, we follow Stuart's (2010) recommendation and first compute propensity scores for each startup. Defined as "the probability of study participants receiving a treatment based on observed characteristics" (Li, 2013: 192), a propensity score is calculated for each startup based on a vector of observable characteristics that influence its selection probability into an accelerator. The resulting propensity score for each startup equates to its individual probability of selection into an accelerator, regardless of whether it was actually selected. We then use the NNM algorithm to match each startup in the treatment sample with one startup from the unaccelerated sample that has the closest propensity score (i.e., its "nearest neighbor"). As a result, the reconstructed control sample is composed of unaccelerated startups that are assumed to be virtually identical with accelerated startups in all respects, with the only difference being the "treatment."

Measurement model
Our dependent variable is emergence. Following Tornikoski and Newbert (2007), we operationalize emergence as a set of three continuous variables that reflect [1] the amount of external financing the startup raised, [2] the amount of revenues the startup earned, and [3] the number of full-time employees the startup hired 1 year after applying to the accelerator. We measure each emergence dimension in absolute terms, rather than relative terms (i.e., percent change), given that each accelerated startup is matched with an unaccelerated startup based, in part, on the absolute amount of financing, revenues, and employees it had achieved at the time of application (see discussion of traction variable below). Finally, we log transform each of these variables to normalize the skew.
The treatment variable in our study is acceleration. We operationalize acceleration as a dummy variable, with a value of one if the startup was accepted by and completed the accelerator program and zero if it was rejected by the accelerator.
In order to calculate accurate propensity scores, we must identify variables on which to match accelerated and unaccelerated startups. To do so, we select variables from the dataset that [1] influence the probability of a case receiving the treatment (i.e., being accepted by an accelerator) and [2] relate to the outcome variable (i.e., emergence) (Heckman et al., 1998a, b;Sianesi, 2004;Smith & Todd, 2005). Following Yang et al. (2020), we select the following ventureand team-level matching variables as they have been found to satisfy both of the above requirements in the context of SIAs: the year a startup applied to the accelerator (e.g., Hannan & Carroll, 1992), operating sector (e.g., Wiklund & Shepherd, 2003), venture age, team education (e.g., Van de Ven et al., 1984), intellectual capital (e.g., Baum et al., 2000;Nadeau, 2010), prior accelerator participation (e.g., Cohen et al., 2019), and the broader geographic region each accelerator program is located in (Chan et al., 2020).
Finally, we are also cognizant of the fact that there tends to be significant variance in the progress startups have made toward emergence prior to entering the acceleration process and we cannot treat all ventures as equals. To account for this left-censoring issue (Yang & Aldrich, 2012), we also match startups on the traction they had made toward our outcomes of interest at the time of their application to the accelerator by controlling for (and matching on) the absolute amount of financing, revenues, and employees each startup had achieved at the time of application. Table 1 summarizes the measurement model and  Table 2 shows all relevant correlations.

Validating the matching approach
To run our matching analyses, we use teffects psmatch that incorporates PSM with the NNM algorithm in Stata 16. 1 Figure 1 shows box plots of the propensity scores for the raw data (all treated and all untreated cases) and the matched data (all treated cases and their 1-to-1 matched untreated cases). 2 The y-axis of the box plot shows the mean and quartile distributions of the propensity scores, which equate to accelerator selection probabilities, for both the unaccelerated (control) and accelerated (treated) startups. As we can see from the left half of the graph (raw data), prior to matching, the entire sample of unaccelerated startups has a much lower probability of receiving the treatment than the accelerated startups. This confirms that treatment is not randomly assigned and simply comparing the two groups as they stand would not rule out the possibility that any subsequent differences in outcomes could be the result of a priori difference in the distribution of the matching variables, and not the accelerator intervention, thereby giving us biased results (Rubin, 1974). This evidence justifies our decision to adopt a matching approach (versus a regression approach) as it creates a new control group of startups that has an almost identical distribution of the matching variables to the treated group (Criscuolo et al., 2012) as seen in the right half of Fig. 1. This newly constructed control group has the same probabilistic distribution of receiving the treatment as the treatment group, thereby accounting for the non-random treatment assignment characterizing the observational data used in our study. While the box plots show that the overall mean and quartile distributions of propensity scores for     both the control and treated groups are well matched in aggregate, we also need to verify that the startups in each group match closely with respect to each matching variable from which these propensity scores were derived (Grilli & Rampichini, 2011). Thus, we next plot the probability density function (PDF) for each matching variable for both the raw data and the matched data to determine goodness of fit (Austin, 2011). As we can see from the PDFs in Fig. 2, when all untreated cases are included, vast differences across all matching variables can be seen between accelerated and unaccelerated startups. However, once the control group is reduced by one-to-one matching the treated and untreated cases based on their propensity scores, there is a near-perfect overlap between the distribution of propensity scores for the two groups across each of the individual matching variables. This finding shows that the NNM algorithm successfully matched each treated case with an "almost identical" untreated case, and thus, any treatment effect we find cannot be attributed to the differences in the matching variables but, instead, to the treatment itself. Taken together, the results shown in Figs. 1 and 2 not only confirm that our model is well specified, but also imply that the derived propensity scores in our sample will lead to precise treatment estimates making causal inferences possible (Rubin & Thomas, 1992).

Testing for a causal acceleration effect
Now that we have confirmed that both the treated group and the reconstructed control group have the same likelihood of receiving the treatment, we calculate the ATE for each emergence dimension as follows: where π = proportion in treatment group, T = treatment, Y 0 = control state, and Y 1 = treatment state. As this equation suggests, ATE creates a counterfactual argument to calculate [1] the average potential outcome on the treated group as if it never received treatment and [2] the average potential outcome on the control group as if it did receive treatment, and then determines the differences in these average outcomes. In other words, ATE tells us how much the typical FPSV applying to an accelerator benefitted (or not) as a consequence of receiving (or not) the treatment.
Accounting for all the matching variables, our ATE results presented in Table 3 suggest that, on average, accelerated FPSVs raise significantly more external financing (ß f = 1.563, p = 0.000), have significantly higher revenues (ß r = 0.599, p = 0.000), Because each FPSV in the treatment group is virtually identical to a FPSV in the control group across the entire vector of matching variables at the time of their application to the accelerator, the significant differences in emergence dimensions that we observe can be attributed to the accelerator intervention (Leung et al., 2005). These results support our three hypotheses that establish that SIA intervention leads to FPSV emergence.

Validating the acceleration effect
While our ATE results indicate a causal acceleration effect on FPSV emergence, research also finds that accelerators tend to select the "most promising" startups (Pandey et al., 2017). Thus, it is possible that the accelerated startups would have outperformed unaccelerated startups even in the absence of any accelerator intervention. To rule out this possibility and validate an accelerator treatment effect, we next calculate the average treatment effect on the treated (ATT) as follows: where T = treatment, Y 0 = control state, and Y 1 = treatment state. Unlike ATE analysis, which computes the average difference between the treatment and control groups for each emergence dimension, ATT constructs a different counterfactual argument by comparing the outcomes the treated group actually experienced as a result of the treatment with the hypothetical outcomes the treated group would have experienced in the absence of the treatment (Ho et al., 2007). In other words, the counterfactual argument is only created for the treated group. By comparing actual and simulated emergence outcomes for only the accelerated FPSVs, ATT avoids comparing the outcomes experienced by the "most promising" FPSVs (i.e., those that were accepted) with those of the "least promising" FPSVs (i.e., those that were rejected) at the time of application, thereby accounting for any possible selection effect on the part of the SIA. 3 Our ATT results, presented in the middle row of Table 3, show that after accounting for all the matching variables, an accelerated FPSV will raise significantly more external financing (ß f = 1.104, p = 0.000), earn significantly higher revenues (ß r = 0.535, p = 0.000), and hire significantly more employees (ß e = 0.122, p = 0.000) than it would have, had it not been accelerated. Stated differently, even the "most promising" FPSVs do better with accelerator intervention than they would without it.
To fully conclude the existence of a causal acceleration effect on emergence, we additionally should establish that even FPSVs not selected by an accelerator would benefit from SIA intervention. To do so, we determine the average treatment effect on the untreated (ATU) that simulates what would happen if the supposed "least promising" FPSV was instead accelerated. ATU creates this counterfactual argument and compares it to the actual outcomes experienced by the unaccelerated FPSV to determine the simulated effects of treatment (Abadie & Imbens, 2011). ATU is determined by: where T = treatment, Y 0 = control state, and Y 1 = treatment state.
Our ATU results, presented in the bottom row of Table 3, show that after accounting for all matching variables, an unaccelerated FPSV raises significantly less external financing (ß f = − 1.731, p = 0.000), has significantly lower revenues (ß r = − 0.622, p = 0.000), and hires significantly fewer employees (ß e = − 0.096, p = 0.003) when it is not accelerated, compared to itself were it accelerated. Stated differently, when compared to itself, an unaccelerated FPSV is worse off when it is not accelerated than if it were accelerated.
In sum, both ATT and ATU results show that FPSVs do better with SIA intervention (when compared to their own counterfactual outcomes) than without, thus minimizing concerns of selection bias. By viewing these results in conjunction with the initial ATE results, we can conclude that a causal acceleration effect does exist and that this effect is not confounded by selection bias, confirming our hypotheses. 4

Contextualizing the acceleration effect
Our results above suggest that, on average, an accelerated FPSV will perform better than a similarly matched FPSV that was not accelerated. While this result represents the most comprehensive support of a causal acceleration effect to date, it is at the same time limited by the fact that it reflects only the average effect that the average FPSV will enjoy from acceleration. Yet, as Newbert et al., (2022: 3) argue, because there is no "average" startup, studies that report only samplewide averages "will invariably generate results that are not reflective of the individuals (or groups of individuals) that comprise it, thereby limiting their inferential value." As such, the authors advise empirical researchers to "dig beneath the surface of the samples they analyze" in order to uncover the ways in which the average finding holds (or not) for different types of entrepreneurs, operating in different environments, at different points in time. Newbert et al. (2022) continue by arguing that by exploring these who, where, and when dimensions of context, scholars will be better equipped to [1] identify counterintuitive results that can reveal boundary conditions of current knowledge, or what Davis (1971) has called "interesting" research, and [2] generate advice that can help practicing entrepreneurs meaningfully address real-world problems, or what Tihanyi (2020) has called "important" research. Inspired by this advice, we engage in a subgroup analysis of our main findings to determine whether the average causal acceleration effect we report in Table 3 holds based on the gender composition of the founding team (who), the operating location of the FPSV (where), and/or the age of FPSV at time of acceleration (when).

Who
It is well-established that as entrepreneurs seek resources, a gender bias exists that often favors male entrepreneurs (e.g., Ahl, 2006;Brush et al., 2018;Malmström et al., 2017;Balachandra et al., 2019;Marlow & McAdam, 2012). As a result, women have been found to include men on their founding teams in an effort to gain legitimacy in the eyes of resource gatekeepers (Godwin et al., 2006;Überbacher, 2014: 201). Thus, to better understand "who" the entrepreneurs are that actually benefit from completing an accelerator program, we explore whether and how the gender composition of the FSPV team impacts its ability to emerge. GALI reports the gender of up to three primary founders for each FPSV. Thus, we divide our sample into three subgroups: FPSVs with all-male founding teams, FPSVs with all-female founding teams, and FPSVs with mixed-gender founding teams. We then rerun our PSM analysis with the NNM algorithm and calculate the ATE for each emergence dimension. 5 Our results, presented in the top section of Table 4, suggest that the acceleration effect universally holds for FPSVs with all-male founding across all emergence dimensions; however, when all founders are female, this effect holds only for financing and employment, but not revenues. Finally, FPSVs with mixed-gender teams benefit from the acceleration effect but only in terms of financing and revenues, and not employment.

When
According to Stinchcombe (1965), new firms tend to fail because they lack routines, a proven track record, and social capital. While these challenges remain even into the venture's adolescence (e.g., Bruderl & Schussler, 1990;Fichman & Levinthal, 1991), they tend to subside given that they have had more time to learn-by-doing (Garnsey, 1998). As such, we seek to determine if the acceleration effect varies according to "when" in its lifecycle the FPSV is accelerated by exploring whether and how the FPSV's age impacts its ability to emerge.
GALI reports the founding and application date of each FPSV. Using this data, we divided our sample into three subgroups: FPSVs that applied to an SIA within 1 year of their founding, FPSVs that applied to an SIA between one and 2 years of their founding, and FPSVs that applied to an SIA more than 2 years after their founding. We then rerun our PSM analysis and report our ATE results in the middle section of Table 4. Our results suggest that acceleration only helps firms less than 2 years of age obtain more financing but does not impact the other two emergence dimensions; however, firms that are older than 2 years benefit from acceleration across all three emergence dimensions.

Where
Research in new institutional economics suggests that high-quality institutions provide individuals and firms the support they need to facilitate efficient resource exchanges (North, 1986). In support, empirical research suggests that institutional quality is positively related to entrepreneurial activity in general (Acs & Amorós, 2008) and the growth of new ventures in particular (LiPuma et al., 2013). To investigate if "where" the FPSV is located impacts whether and how it will benefit from acceleration, we explore whether and how the quality of the institutional environment in which it operates impacts its ability to emerge.
To do so, we begin by dividing our full sample into two subgroups: FPSVs operating in OECD countries and FPSVs operating in non-OECD countries. We then rerun our PSM analysis and report our ATE results in the bottom section of Table 4. These subgroup results suggest that FPSVs located in non-OECD countries benefit from the acceleration effect across all emergence dimensions, while those operating in OECD countries benefit only with regard to financing and revenues, but not employment.

Discussion
We believe our findings in support of our hypotheses can inform academics, practitioners, and policymakers in the following ways. First, although evidencebased management scholars have called on researchers to draw causal inferences (e.g., Aguinis & Jeffrey, 2014), most "generally rely on observational datasets and regression models where the independent variables have not been exogenously manipulated" and can, therefore, only provide correlational results (Li, 2013: 1) due to the absence of counterfactuals (Aguinis & Jeffrey, 2014). By using PSM coupled with NNM to match treated and untreated cases on a vector of venture-and team-level characteristics found in prior research to be relevant to the acceleration process (e.g., Yang et al., 2020), our approach combining ATE, ATT, and ATU results affords us the unique opportunity to draw causal inferences about acceleration (Holland, 1986;Little & Rubin, 2000;Rubin, 1974Rubin, , 1978. Li (2013) finds that matching methods are rarely used in management and Anderson et al. (2019) similarly call for innovation and entrepreneurship scholars to adopt such matching methods to improve their ability to detect causal effects in their research. By addressing this call, we hope that our research will encourage more scholars to appreciate the power of quasi-experimental methods and leverage them to test causality in future research.
However, we remind scholars interested in this line of work to consider two factors when conducting causal research on accelerators. To begin, accelerators tend to select the "most promising" startups from their applicant pools (Pandey et al., 2017) and an acceleration effect cannot be established unless selection bias is addressed. Indeed, it is possible that, due to their relatively higher potential at the application stage, startups that are accepted by accelerators may outperform those that are rejected even without any accelerator treatment. In our approach, we account for this possibility by first matching accepted and rejected FPSVs to determine an ATE effect and then controlling for selection bias among the accepted FPSVs by determining the ATT and ATU effects. Thus, we remind scholars to take measures to minimize the possibility that any acceleration effect they identify is confounded by selection bias (Storey, 2000). In addition, it is also important to account for the idiosyncratic histories of nascent ventures at the time they apply to accelerators, which renders virtually all samples of accelerator participants left-censored. We sought to control for left-censoring in our study by avoiding analyzing the FPSVs in our sample as equals (Yang & Aldrich, 2012) and, instead, controlling for the operational, financial, and human capital differences among ventures at the initiation of the data collection process. Thus, we advise future scholars to take similar measures to ensure that they are comparing apples to apples (and not to oranges) to avoid confounding estimates for any causal acceleration effect they may find.
Second, we highlight that the benefits of acceleration extend beyond startup financing as reported in prior studies (e.g., Gonzalez-Uribe & Leatherbee, 2018;Hallen et al., 2020;Plummer et al., 2016;Yu, 2020). While securing additional external capital certainly represents a coveted outcome for nascent ventures, studies predicting its attainment alone necessarily stop short of revealing whether accelerators actually help nascent ventures achieve the higher-level objective of becoming viable, self-sustaining organizations. Our emphasis on emergence is intentional and furthers prior research by revealing that SIAs are indeed instrumental in helping FPSVs achieve this shared goal (Cohen & Hochberg, 2014;GALI, 2020;Tornikoski & Newbert, 2007). The broad generalizability that our study provides, and the fact that we assess emergence within 1 year of acceleration, makes us confident of the central role SIAs play in the emergence process. Perhaps just as importantly, our focus on the process that a startup undergoes in the attainment of resources provides a novel theoretical lens to study new venture development. This is important because few studies seek to understand the process behind the acquisition of such resources (e.g., Brush et al., 2008;Chandler & Hanks, 1993).
Third, as Newbert et al. (2022) highlight, broad generalizations based on sample-wide averages may not tell the whole story. For this reason, they advocate conducting subgroup analyses to delve deeper into the who, when, and where of a set of empirical findings. Consistent with Newbert et al.'s (2022) argument, the results of our subgroup analyses suggest that the acceleration effect is not ubiquitous across all FPSVs; rather, it is dependent upon a host of contextual factors. Specifically, by finding evidence that [1] the presence of female members on an FPSV founding team will make it less likely that the FPSV will fully emerge into viable organizations, [2] the support provided to FPSVs by SIAs may be somewhat redundant (at least with respect to the labor market) in countries with robust institutions, while they may play a more critical role in filling voids in institutionally-weak environments, and [3] SIAs are best able to accelerate those FPSVs that have been in operation long enough to have something to actually accelerate, we add a more nuanced and holistic understanding of for whom, when, and where acceleration is actually beneficial for FPSVs. In so doing, we believe our findings add grist to Newbert et al.'s (2022) advocacy of exploring the critical context in empirical research.
Fourth, in addition to the implications our research has for academics, our results may also inform social entrepreneurs and policymakers. For entrepreneurs, our study sheds light on the expectations SIAs have from their cohort ventures. These innovators should be aware that they may be encouraged to expand rather quickly, pressured to raise external financing, listen to mentors, and immerse themselves in the local ecosystem, even at this relatively early stage in their ventures' lifetimes. Given that our results suggest that SIAs are growth-focused entities where resources, in the form of legitimacy, knowledge, and networks, are provided with an explicit focus on scaling, social entrepreneurs considering applying to an SIA would be wise to evaluate whether their personal ambitions align with those of the SIA.
Finally, our finding that SIAs have a significant impact in helping FPSVs emerge into viable organizations-contingent on the who, when, and where factors explored herein-should be of considerable interest to policymakers that view the SIA as a critical component of the ecosystem that can positively impact the local economy (Audretsch et al., 2020). For example, Hochberg (2016: 40) find that "the arrival of an accelerator is associated with an annual increase of 104% in the number of seed and early-stage VC deals and an increase of 289% in the log total dollar amount of seed and early-stage funding provided in the region." Goswami et al. (2018) similarly find that accelerators can act as a bridge to the entrepreneurial ecosystem and help build local capacity, and this coalescing of resources is especially important for the legitimacy of social impact initiatives (Thompson et al., 2018). By validating SIAs as a vehicle for social and economic change, we believe our findings should encourage governments and foundations that seek to affect societal change to invest in them as a valuable part of the local entrepreneurial ecosystem.

Limitations and further directions for future research
While we believe that our study provides meaningful insights into how SIAs help nascent ventures emerge as viable organizations, we advise readers to interpret our findings with the following limitations in mind.
To begin, a key assumption behind our analysis is that entrepreneurs pursue admittance into accelerator programs in order to actively pursue growth-related outcomes. While we have argued above that emergence is widely believed to be an outcome of importance to both entrepreneurs and accelerators (Aldrich & Martinez, 2001;GALI, 2017), we cannot rule out the possibility that, as autonomous individuals, entrepreneurs may harbor additional motivations for pursuing an accelerator program (e.g., free office space) and/or may choose not to leverage all the resources provided by the accelerator. Thus, to the extent that such tendencies exist to some degree in our sample, we encourage scholars to explore entrepreneur motivation as it relates to the acceleration process in future research. A second limitation that arises from our research is the lack of qualitative measures on SIA acceptance decisions such as presentation effectiveness by the entrepreneur or simply the mental state of the evaluator on a particular day, as an example. While we have near-perfect overlap between the raw and matched data for our treated and control groups, we recognize that considering qualitative measures, in addition to our quantitative measures, could strengthen our findings and further shed light on the impact of SIAs on FPSVs. Thus, we advise scholars interested in this area going forward to collect data on additional factors that help explain how accelerator selection decisions are made to add additional nuance to how ventures emerge as a result of the acceleration process.
Third, our binary measure of gender is admittedly coarse given that it does not capture the full range of gender identities, or one's "self-concept of their gender (regardless of their biological sex)" (Lev, 2004: 397). Thus, while our contextual findings suggest that the acceleration effect is most consistent for allmale teams, it is nevertheless silent on whether and how this effect holds for teams that include transgender, transexual, and/or intersex individuals, or "those who identify outside the female/male binary and those whose gender expression and behavior differs from social expectations" (Moleiro & Pinto, 2015: 2). While data limitations did not allow us to explore non-binary gender identities, given that recent research in entrepreneurship exploring the related concept of sexual orientation hints at the possibility that at least one emergence dimension-namely, external financing-may be influenced by this contextual factor, we encourage scholars to consider it in future studies of emerging ventures.
Finally, while the global nature of our database allows us to generalize our findings, it limits us from exploring country-level attributes in our analysis. To the extent that the manner in which the acceleration process unfolds may be country-specific, we encourage future scholars to delve into these macro-level factors as they investigate the impact of accelerator programs.

Conclusion
Accelerators have become a phenomenon of great interest in the entrepreneurial ecosystem, though their effect on startups so far is equivocal. While ours is one of a small number of studies to find evidence for an acceleration effect, it is the first to suggest a causal effect in the holistic context of emergence, and to account for the who, where, and when factors that impact all accelerators and startups. Our results inform the academic conversation around the effectiveness of SIAs and we believe the insights gained from our findings can and should embolden would-be founders of social ventures of the tangible benefits they may expect from pursuing admission into an SIA program, and scaling their social innovations. Finally, our results also validate the role of SIAs as vehicles for social and economic mobility in the local entrepreneurial ecosystem.

Declarations
Accelerating emergence The causal (but contextual) effect of social impact accelerators on nascent for-profit social ventures.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.