Open Access

This paper-based dissertation deals with the concepts of economic heterogeneity and environmental uncertainty from different perspectives, and at multiple levels of abstraction. At its core sits the observation that heterogeneity and uncertainty are deeply entangled, for there would be no uncertainty without heterogeneity of options to act regarding multiple future states of the world. At the same time, heterogeneity - in the form of diversification - has been suggested as a way to reduce uncertainty in portfolio theory (Markowitz 1952). The dissertation evolves around two research foci: (1) methodological implications of heterogeneity of scientific theories in the face of empirical data (Paper 1), and (2) two different forms of uncertainty are considered, environmental risk (Paper 2) and Knightian uncertainty (Paper 3). Paper 1 develops a new framework for model selection for the special case of fitting size distribution models to empirical data. It combines Bayesian and frequentist statistical approaches with the criterion of model microfoundation, which is to select, all other things considered being equal, the model that comes with a suitable micromodel, that explains, from the perspective of the individual constituent, the genesis of the overall size distribution. The approach is subsequently illustrated with size distribution data on commercial cattle farms in Namibia. We find that the double-Pareto lognormal distribution fits the data best. Our approach might have the potential to reconcile one of the oldest debates in current economics, i.e. the one about the best model to describe and explain the distribution of economic key variables such as income, wealth and city sizes in a country. The second paper revisits the Namibian commercial cattle farm data and uses it to put some theories from the agricultural economics literature regarding farm management under environmental risk to an empirical test. We focus on the relations between inter-annual variability in rainfall (environmental risk), risk preferences, farm size and stocking rate. We demonstrate that the Pareto distribution - which separates the distribution into two parts - is a statistically plausible description of the empirical farm size distribution when ´farm size´ is operationalized by herd size, but not by rangeland area. A statistical group comparison based on the two parts of the Pareto distribution shows that large farms are on average exposed to significantly lower environmental risk. Regarding risk preferences, we do not find any significant differences in mean risk attitude between the two branches. Our analysis confirms the central role of the stocking rate as farm management parameter, and shows that environmental risk and the farmer´s gender are key variables in explaining stocking rates in our data. Paper 3 develops a non-expected-utility approach to decision making under Knightian uncertainty which circumvents some of the conceptual problems of existing approaches. We understand Knightian uncertainty as income lotteries with known payoffs but unknown probabilities in each outcome. Based on seven axioms, we show that there uniquely (up to linear-affine transformations) exists an additive and extensive function from the set of Knightian lotteries to the real numbers that represents uncertainty preferences on the subset of lotteries with fixed positive sum of payoffs over all possible states of the world. We define the concept of uncertainty aversion such that it allows for interpersonal comparison of uncertainty attitudes. Furthermore, we propose Renyi´s (1961) generalized entropy as a one-parameter preference function, where the parameter measures the degree of uncertainty aversion. We illustrate it with a simple decision problem and compare it to other decision rules under uncertainty (maximin, maximax, Laplacian expected utility, minimum regret, Hurwicz).