The Empirical Reality of Entrepreneurship: How Power Law Distributed Outcomes Call for New Theory and Method

Abstract

Why is it that research findings about entrepreneurship continue to be so disparate? Recent reviews, for example, reveal extreme variances between inputs and outcomes, conflicting empirical findings, inconsistent measures of growth, and weak research designs (Achtenhagen et al., 2010; Leitch et al., 2010). Although some of these challenges are due to the complexity of the phenomenon, the problem may also be due to the inaccuracy of certain unexplored assumptions that permeate the field. In particular, some scholars have argued that Gaussian distributions — the normal curve, which underlies all statistical methods used by the discipline — does not reflect the actual distribution of relevant data (Andriani & McKelvey, 2007; 2009). This one assumption could explain almost all of the disparate findings in the field.

In fact, some scholars propose that entrepreneurship data follow Pareto distributions, also known as power laws (Boisot & McKelvey, 2010; Crawford, 2012). Power law distributions (PLDs) are highly skewed, with “long tails” that identify extreme events, i.e. data which are outside the range of the normal curve. Whereas traditional statistics assumes these are mistakes that need to be removed from the data, in Pareto distributions they are expected, albeit rare; further, these extreme outcomes have a nonlinear influence in the system (Taleb, 2007). PLDs have been found to explain many systems — physical, natural, biological, social, and financial — as cited by Andriani and McKelvey (2009) and McKelvey and Salmador (2011).

When graphed on linear scales, the PLD looks like Figure 1a; graphed on log-log scales, it forms a straight line, as stylized in Figure 1b. Outcomes in the long tail of the distribution, like the largest circle at the bottom right of Figure 1b, are ‘extreme’ compared to the others. In entrepreneurship, nonlinear outcomes might include a new firm that generates 1000 new jobs, $100M in revenue, or a 40,000% increase in growth. As we will identify, these extreme but uncommon events — think Amazon, Google, Facebook — emerge through the same underlying dynamics that produce N=22,000,000 small businesses in America. Unfortunately, linear methods, which underlie all statistical packages, are unable to include these outliers in an analysis, thus making them invisible. Outliers, then, have the potential to skew empirical analyses — and, thus, theory building and testing — across all entrepreneurship research.

We examine two of the most generalizable outcome measures in the domain — number of employees and annual revenue — at three levels of venture emergence: nascent ventures, young firms, and hyper-growth companies. Our goal is to determine whether these outcomes of entrepreneurship are actually PLD rather than conforming to a normal curve. After reporting the results, we draw from extant literature to identify some of the primary causal mechanisms that generate PLDs, and we link seminal entrepreneurship concepts to these mechanisms.

Keywords: Entrepreneurship, Entrepreneurial Startups, Power law distribution, Extreme Outcomes, Skew distribution

JEL Classification: L22, L26