This paper was presented at the 2009 Babson Conference in Boston, Massachusetts.
- Harold Fried (Union College)
- Loren Tauer (Cornell University)
A measure of entrepreneur success is important to identify current and future successful ventures, in order to further our understanding of the entrepreneurial process and to guide public policies to improve the success rate of start-ups. We propose an index of entrepreneur success that ranges from one to zero that accommodates multiple outputs, that is predicated on multiple inputs, and that mitigates the impact of outliers. The index is calculated for 2,863 firms in 2006 from the Kauffman Foundation Firm Survey. The average value is 0.60 with a standard deviation of 0.32, but with modals around the average, zero, and one. We relate the index to characteristics of the entrepreneur and the venture: age, experience, gender, race, competitive advantage, education, and birthplace. The variables with the most significant statistical impact on the success score are gender and the comparative advantage of the business as assessed by the survey respondent.
Figure 1 illustrates the distinction between average practice and best-practice. A measure of entrepreneur success is on the vertical axis; a possible determinant of entrepreneur success, say start-up experience, is measured on the horizontal axis. The ordinary least squares line though the “middle” of the data estimates average practice. Deviations from the line are assumed to be white noise. The stair case frontier captures best-practice under the assumptions that only observed production points are feasible and input is freely disposable.
Our objective is to generate an index of entrepreneur success based upon a production function approach that accommodates multiple measures of success and incorporates the role of inputs.
There are numerous frontier techniques that can be used to empirically identify best-practice using data from a set of firms. The stochastic frontier approach uses a regression equation but the error term is modified with the addition of a second error (Kumbhakar and Lovell, 2000). This approach has the advantage of permitting statistical inference, but has the disadvantages of strong parametric assumptions and generally is limited to a single left hand side variable. Data envelopment analysis (DEA) is similar to the free disposal hull (FDH) except that it assumes convexity such that production can occur along linear line segments that span frontier observations.
Daraio and Simar (2005) introduced the order-m approach that embeds the free disposal hull (FDH) into a probabilistic framework that mitigates the influence of outlying observations while maintaining the advantages of a non-parametric functional form and allows multiple output variables. We use this approach to construct an index of entrepreneur success. This is useful and essential because some entrepreneurs are extraordinarily successful and that success can mask firms that are simply successful.
The order-m concept is based upon a probabilistic specification of the production process and is specified here as the process of successful entrepreneurship. The entrepreneurship process is described by the joint probability measure (X,Y), where X are inputs and Y are measures of success. This joint probability completely characterizes the probabilistic entrepreneurship process. Under an output orientation, this joint probability can be written as:
FY|X(y|x) = Prob(Y ≤ y |X ≤ x)
The expected order-m frontier for a fixed integer value of m?1 is the expected value of the maximum of m random variables Y1,…..,Ym drawn from the conditional distribution function of Y, given that X? x. Essentially, a firm’s efficiency is computed in reference to a random sample of m other firms drawn with replacement who use the same or fewer inputs than the firm being evaluated. This can be done by Monte-Carlo methods, or more efficiently by numerical integration.