# Papers

## Published Papers

Risk, Ambiguity, and Giffen Assets.

Journal of Economic Theory, Paper

Volume 186, March 2020

It is natural to believe that a consumer will respond to a price rise by lowering the amount purchased. When this does not occur we say that the consumer displays Giffen behaviour. While counterintuitive, Giffen behaviour is not precluded by the usual assumptions made in economic theory. I investigate conditions on preferences for financial assets which precludes Giffen behaviour. When the consumer has expected utility preferences I identify a condition on the consumer's coefficient of relative risk aversion which is necessary and sufficient to preclude Giffen behavior. I show that this condition remains the same when the consumer displays ambiguity aversion as characterized by the Choquet Expected Utility model yet when the consumer displays ambiguity aversion in the closely related Maxmin Expected Utility model then Giffen behavior will almost certainly occur.

Intertemporal Consumption with Risk: A Revealed Preference Analysis.

Review of Economics and Statistics, Paper

Forthcoming

Joint with Bin Miao, John Quah, Songfa Zhong.

We run an experiment designed to elicit preferences over time and state contingent payouts. We analyze the data using new non-parametric revealed preference tests (building on Nishimura, OK, and Quah (2017)) that allow for structural restrictions on the utility function. Our analysis provides evidence in favor of preferences satisfying several reasonable and commonly made assumptions. However, participants systematically violate a major consequence of the popular discounted expected utility model known as correlation neutrality.

Are Consumers (Approximately) Rational?: Shifting the Burden of Proof

Review of Economics and Statistics, Paper

Forthcoming

Joint with Laurens Cherchye, Bram De Rock, Thomas Demuynck.

We propose a novel technique for testing whether observed consumption behavior is approximately consistent with the hypothesis of utility maximization. Our test is conservative in that it concludes that a consumer is approximately rational if their behavior (consumption decisions) can be distinguished from random draws from an unknown distribution. This method can be seen as an application of the classical statistical technique known as a permutation test to the context of revealed preferences.

## Working Papers

Estimating Very Large Demand Systems

INET Oxford Working Paper No. 2023-01, Paper

Joint with Jeremy Large and John K.-H. Quah.

We present a discrete choice, random utility model and a new estimation technique for analyzing consumer demand for large numbers of products. We allow the consumer to purchase multiple units of any product and to purchase multiple products at once (think of a consumer selecting a bundle of goods in a supermarket). In our model each product has an associated unobservable vector of attributes from which the consumer derives utility. Our model allows for heterogeneous utility functions across consumers, complex patterns of substitution and complementarity across products, and nonlinear price effects. The dimension of the attribute space is, by assumption, much smaller than the number of products, which effectively reduces the size of the consumption space and simplifies estimation. Nonetheless, because the number of bundles available is massive, a new estimation technique, which is based on the practice of negative sampling in machine learning, is needed to sidestep an intractable likelihood function. We prove consistency of our estimator, validate the consistency result through simulation exercises, and estimate our model using supermarket scanner data.

Money Pumps and Bounded Rationality

ArXiv Working Paper 2404.04843, Paper

Joint with Matt Polisson and John K.-H. Quah.

The standard criterion of rationality in economics is the maximization of a utility function that is stable across multiple observations of an agent's choice behavior. In this paper, we discuss two notions of the money pump that characterize two corresponding notions of utility-maximization. We explain the senses in which the amount of money that can be pumped from a consumer is a useful measure of the consumer's departure from utility-maximization.

Goodness-of-fit and utility estimation: what's possible and what's not

ArXiv Working Paper 2405.08464, Paper

Joint with John K.-H. Quah.

A goodness-of-fit index measures the consistency of consumption data with a given model of utility-maximization. We show that for the class of well-behaved (i.e., continuous and increasing) utility functions there is no goodness-of-fit index that is continuous and accurate, where the latter means that a perfect score is obtained if and only if a dataset can be rationalized by a well-behaved utility function. However, standard goodness-of-fit indices are (in a sense we make precise) essentially accurate. Goodness-of-fit indices are typically generated by loss functions and here we find that standard loss functions typically do not yield a best-fitting utility function when they are minimized. Nonetheless, welfare comparisons can be made by working out a robust preference relation from the data.

Revealed preference and revealed preference cycles: a survey

Invited submission for a special issue of the Journal of Mathematical Economics

ArXiv Working Paper 2405.08459, Paper

Joint with Pawel Dziewulski and John K.-H. Quah.

We survey the revealed preference literature with an emphasis on acyclicity conditions such as the generalized axiom of revealed preferences (GARP). We cover Afriat's Theorem which shows that GARP is the only testable implication of well-behaved utility maximization, Matzkin and Richter (1991) and Lee and Wong (2005) who show that the strong axiom of revealed preferences (SARP) is the only testable implication of utility maximization with single-valued demand, Forges and Minelli (2009) who show that a simple modification of GARP characterizes utility maximization with non-linear budget sets, Reny (2015) who shows that GARP continues to be the only testable implication of utility maximization even when rationalizing infinitely many observations, and Nishimura, Ok, and Quah (2017) who show that a simple modification of GARP can be used to test for utility maximization which are increasing in a given order of interest. We also cover, among other things, discrete consumption, rationalizing choice with differentiable utility, measuring departures from GARP, revealed price preferences, and other related topics.

Theory Consistent Non-Parametric Demand Estimation, Paper

I develop a non-parametric technique for estimating demand functions which is (i) statistically consistent (converges to any true demand function as the sample size increases) and (ii) theory consistent (there is a utility function which generates the estimated function). I argue that both properties (i) and (ii) should be considered indispensable. Yet, previous estimators have not been able to simultaneously satisfy both properties. Property (i) prevents the estimator from incorporating ad-hoc functional form restrictions which unjustifiably constrain what the data is allowed to tell the researcher. Property (ii) is the key ingredient required to comment on the preferences of consumers. Without (ii) it is challenging to discuss even the most basic issues concerning consumer well-being.

The estimation technique I develop simultaneously estimates the demand function and the indirect utility function of the consumer, from which is it easy to obtain the corresponding estimates of the consumer's expenditure function and Hicksian demand. This gives immediate access to familiar welfare measures like the equivalent variation and compensating variation for a price change.

Stochastic choice and rationality with linear budgets, Paper

I introduce a model of a consumer choosing consumption bundles stochastically from linear budget sets. The model ascribes a single utility function and an ``irrationality'' parameter to the consumer where the irrationality parameter represents the extent to which choice deviates from perfectly rational deterministic behavior. The model can be characterized by a version of Luce's independence of irrelevant alternatives. I show how the irrationality parameter can be estimated from choice data via a linear programming problem which can be understood as a relaxation of the Afriat inequalities. The method is brought to household expenditure data to investigate whether, within a specific demographic group, everyone has the same preferences which are imperfectly maximized. Some evidence in favor of this hypothesis is found in Canadian households while UK households are often seen to act, as a group, less rationally than even random behavior would imply.

## Works in Progress

Rationalizing Choices with Best Behaved Utility Functions: Behavior and Welfare

Joint with Gavin Kader.

We present a natural definition of what it means for one utility function to be better-behaved than a second. We show that to every instance of purchasing behavior there is at least one "best-behaved" rationalizing utility function. That is, there is a utility function which (i) explains the data and (ii) is (weakly) better behaved than any other rationalizing utility function. We show how to make welfare statements, demand predictions, and measure a consumer's level of rationality using these best-behaved rationalizing utility functions.

Testing Quasilinear Random Utility

Joint with Gregory Cox and John K.-H. Quah.

We develop a test of the random quasilinear utility model in the same context as Kitamura and Stoye (Econometrica, 2018). That is, given finitely many distributions of demand (i.e. distributions over consumption bundles) at different price levels we provide a method for discerning if these distributions of demand were generated through maximizing a random quasilinear utility function.