A Dissertation Submitted to the Faculty of Arts University of the Witwatersrand, Johannesburg for the Degree of Master of Arts Johannesburg 1972

Diss.--Giessen. / Includes bibliography.

Issued also as Thesis (Ph. D.)--Columbia University. / Textbooks examined: p. 121-123; Bibliography: p. 124-125.

Issued also as Thesis (Ph. D.)--Columbia University. / Textbooks examined: p. 121-123; Bibliography: p. 124-125.

This thesis comprises three principal essays, each of which provides a contribution to the literature on the nonparametric approach to demand analysis. In each essay, I develop novel techniques that follow in the revealed preference tradition, and apply them to tackle a series of questions that concern the mechanisms underlying consumer spending decisions. Each technique developed is tightly linked to a particular nonparametric theory of choice behaviour and is explicitly designed for use with a finite set of observations. My work draws heavily upon results from finite mathematics, into which I integrate insights from information theory and integer programming. The output of this endeavor is a set of methodologies that are largely free of auxiliary assumptions over the form of the unobserved structural functions of interest. Providing greater detail on the work to come, my first essay extends and clarifies the nonparametric approach to forecasting demand behaviour at new budget regimes. Using insights from information theory and integer programming, I construct an operational nonparametric definition of global rationality and develop a methodology that facilitates the recovery of globally rational individual demand predictions. This is the first attempt in the literature to develop a systematic methodology to impose global rationality on nonparametric demand predictions. The resulting forecasts allow for unrestricted preference heterogeneity in the population and I demonstrate how these predictions can be used for coherent welfare analysis. In my second and third essays, I prove new revealed preference testability axioms for models that extend the traditional neoclassical choice framework. Specifically, in my second essay, I address the intertemporal allocation of spending by collectives, whilst my final essay integrates taste variation into the utility maximisation framework. In both of these essays, I develop my testable results into practical algorithms that allow one to recover salient features of individual preferences. In my second essay, a methodology is developed to recover the minimal intrahousehold heterogeneity in theory-consistent discount rates, whilst my final essay develops a quadratic programming procedure that facilitates the recovery of the minimal interpersonal and intertemporal heterogeneity in tastes that is required to rationalise observed choice patterns. Applying these techniques to consumption micro-data yields new empirical insights that are of relevance to the applied literatures on time discounting, family economics and the public policy debate on tobacco control.

This dissertation addresses issues in non-market valuation related to preference uncertainty and to the divergence between willingness to accept (WTA) and willingness to pay (WTP) in contingent valuation method. The contributions are two fold. First, the dissertation contributes to development in non-market valuation by comparing emerging approaches addressing preference uncertainty in the standard contingent valuation framework and by introducing a promising approach, the fuzzy random utility maximization model. Further, the study provides empirical support for the observed divergence between WTA and WTP using a simultaneous equation regression model. Second, the dissertation provides policy implications. The non-market valuation model was calibrated with a survey of western Canadian landowners in 2000 to determine their willingness to accept compensation for planting trees to mitigate climate change. WTA values were then used to analyze the cost effectiveness of sequestering carbon by converting agricultural land to forestry. While estimates of WTA are less than foregone agricultural values, average costs of creating carbon credits still exceed their projected value under a C02-emissions trading scheme. Another results from the survey of Nevada ranchers that asked about WTP for public forage and WTA compensation to part with grazing rights indicate that ranch size, public grazing allotment, financial distress, and long term commitment to ranching are all significant influences on the disparity between WTA and WTP, which gives valuable information to ranch policy.

This thesis is divided into two main parts. The first provides a novel analysis of dynamic optimal taxation under the assumption that individuals in an economy have ‘hidden’ idiosyncratic productivity levels. Specifically, it shows how to derive a complete set of optimality conditions characterising the solution to a problem of this kind. The method relies on constructing perturbations to the consumption-output allocations of agents in a manner that preserves all relevant incentive compatibility restrictions. We are able to use it to generalise the ‘inverse Euler condition’ to cases in which preferences are non-separable between consumption and labour supply, and to prove a number of novel results about optimal income and savings tax wedges. The second main part investigates a more general problem. When policymakers are constrained in their present choices by expectations of future outcomes a well-known time-inconsistency problem hinders optimal decision-making: the preferences of policymakers who exist at different points in time are not in agreement with one another, because of differences in the constraints faced by each. We present a new approach to determining policy in this setting, based on asking: What policy would be chosen by a decisionmaker who did not know the time period in which their choice was to be implemented? This is akin to designing institutions from behind a Rawlsian ‘veil of ignorance’. The theory is used to obtain qualitative policy prescriptions across a number of environments; these policies have several appealing properties that we outline.

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