Exploring log-normal distributions in nascent entrepreneurship outcomes:
: Exploring log-normal distributions in nascent entrepreneurship outcomes:

  • Ivan Francisco Rodriguez Hernandez

Student thesis: Doctoral ThesisPhD


Recently, Joo, Aguinis and Bradley (2017), using a novel distribution pitting technique, have found that the exponential tail distributions-- exponential and power law with an exponential cut-off -- and their generative mechanism – namely, incremental differentiation -, are the most frequent distribution in many individual outputs across different organizations, sectors, jobs and activities.However, this may not be totally accurate in nascent entrepreneurship processes: the first section of this research shows that the lognormal distribution in entrepreneurial outcomes seems predominant throughout the different panels – i.e., longitudinal studies - in different countries. We have studied those in which the datasets are in the public domain: Australia, Sweden, US PSED I & II (Reynolds, 2017b). The power law distribution with an exponential cut-off may also be a plausible fit in some particular panel outcomes variables. A definitive conclusion regarding which of these two distributions may be the better fit will require the analysis of the rest of 14 still ongoing longitudinal projects around the world. The pervasiveness of lognormality offers relevant clues to understand nascent entrepreneurial processes, their generative mechanism, and it will offer strategies to allocate resources to foster and promote new entrepreneurial ventures.The second section of this research is the design and implementation of a baseline agent-based model as a research tool, “A nascent entrepreneurial agent-based model”. Inspired by previous simpler entrepreneurial models, our model introduces new layers of complexity, making possible parametrization and calibration. This baseline model, initially with parameters similar to the public available panel datasets --Australia, Sweden, US PSED --, is able to generate the patterns that were found in the empirical results: the heavy-tailed distributions.Although PSED-type of longitudinal panels have been performed in more than a dozen countries, their results and datasets are not publicly available yet. This base model is, therefore, flexible in order to be easily adapted to each of the empirical dataset under study. The model, at this initial stage, has not been fully parametrized and calibrated for any specific country. The baseline model takes the main parameters from the datasets available as examples, in order to show that multiplicative processes --as main generative mechanism-- are able to simulate the empirical patterns. The baseline model is designed as a research tool to experiment and to help entrepreneurship researchers to test their theories, and for exploring in more detail the mechanisms involved in the emergence of new ventures. The baseline model and its background documentation will be openly available to the research community in two major agent-based repositories. Taking this baseline model as a “backbone”, researchers can change parameters, agents, behaviours, schedules or global variables for their own theory building or calibration of their specific country’s simulation.KeywordsHeavy-tailed distributionsPower-law distributionsGenerative processesFitting proceduresNascent venturing processesAgent-based modelling
Date of Award19 Jun 2019
Original languageEnglish
Awarding Institution
  • University of Bath
SupervisorBrian Squire (Supervisor) & Dimo Dimov (Supervisor)

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