Aug 19, 2012 - For example, data on insurance choices may be used to estimate risk preferences, .... each in brief, alon
Measuring Risk and Time Preferences and Their Connections with Behavior Julian Jamison, Dean Karlan, and Jonathan Zinman* August 19, 2012 CITES AND SUPPORTING MATERIALS INCOMPLETE, BUT READY FOR COMMENTS
*
[email protected], Federal Reserve Bank of Boston, IPA;
[email protected], Yale University, IPA, J-PAL, and NBER;
[email protected], Dartmouth College, IPA, J-PAL, and NBER. Thanks to Lynn Conell-Price, Hannah Trachtman, and Gordon Vermeer for outstanding research assistance, and to the Russell Sage Foundation for funding.
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I.
Introduction
The economics profession builds models based on individual preferences. Estimating values for preference parameters is important for both testing and applying our models. For testing models, preference parameter estimates allow us to assess the predictions models make about relationships between preferences and choices or outcomes. For applying models, preference parameter estimates are inputs for measuring welfare and conducting policy analysis. We examine methods for measuring individual preferences directly not because observing choices is bad, but specifically because we want to understand better the link between preferences and choices. A “revealed preference” approach alone yields inferences that conflate other issues. For example, data on insurance choices may be used to estimate risk preferences, but time preferences, perceptions and unobserved individual heterogeneity in true underlying risk also drive insurance purchase decisions [cite/fn on work that does this by imposing assumptions?]. Similarly, is our tardy production of this paper due to our stable preferences for leisure versus work; to aspects of our choice set that may be mistakenly confounded with our preferences; to procrastination deriving from time-inconsistent preferences (and the absence of a commitment device with a higher cost of failure than the shame of receiving polite but increasingly firm warning emails from the editors); or to a planning problem in which we systematically underestimate the time for the remaining tasks? By eliciting measures of preferences directly, and linking such measures to behavior, we can better validate the underlying model to explain choices. We consider evidence on the direct elicitation of three broad classes of individual preferences. Our coverage of risk preferences includes risk aversion as classically defined, and also ambiguity aversion and loss aversion. Our coverage of time preferences includes the classic issue of how to disentangle preference from other determinants of discount rates, and also time-inconsistency and other sources of costly self-control. Our coverage of process preferences (includes regret and transaction utility) is much shorter, reflecting the lack of similar work on measurement. We thus focus more on identifying key gaps in our knowledge for further research. We do not cover atemporal preferences over different goods in a consumption bundle, or social preferences (see [cites] for reviews). Nor do we cover meta-awareness of one’s (changing) preferences—e.g., projection bias, sophistication/naivete about self-control problems-- about which there has been less work on direct elicitation. For both risk and time preferences we address four types of questions: methods, predictive power of actual behavior, heterogeneity across people, and within-subject stability. On methods, we describe the various commonly used elicitations, and examine how different elicitation and estimation methods affect parameter estimates. Key examples include the roles of monetary incentives versus hypothetical questions; quantitative versus qualitative questions; potential confounds researchers should consider when choosing an elicitation method (e.g., how numeracy may influence lottery choices, and disentangling risk perception from risk preference); and some “quick-and-dirty” methods for researchers facing budget and/or time constraints in the lab or the field.
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Second, we examine how measures predict actual behavior. The primary challenge with posing this question is simple: one needs clean measurement on both sides of the correlation, free of alternative explanations that happen to also correlate with each other. Let’s start with a simple example of the problem. Suppose we want to validate a model of time preferences and investment in new agricultural technology. The policy idea is simple: farmers may not invest in highly profitable investments if they are impatient and thus prefer current consumption to considerably more future consumption. So researchers conduct simple time preference elicitation questions (would you prefer money now or more money later?), and observe if they invest in a higher yield agricultural technology. The researcher finds they are correlated. What can be concluded? Perhaps also the higher yield agricultural technology requires trusting the agricultural extension agent. And so does accepting more money later rather than money immediately. If this were the case, trust, but not necessarily time preferences, would be the underlying mechanism at work. These problems with interpreting correlations between preferences and behavior are likely difficult to overcome perfectly, but must be whittled down as much as possible in order to advance our knowledge on the validity of such measures. Timing is helpful, but not dispositive. If measurement occurs, and then much later the behavior is observed, this may help eliminate reverse causality (although naturally does not remove a myriad of other unobservable correlates). This was the approach taken, e.g., in Karlan (2005) in which trustworthy behavior in a trust game was found to predict repayment of loans a year later, and in Ashraf, Karlan and Yin (2006) in which inconsistent responses to time preference questions predicted later adoption of a commitment savings product. To make this link from preferences to behavior, however, requires a strong methodological emphasis on the details on elicitation methods, and also strong contextual understanding of the decisions people face in the real world, that one is trying to model. Third, we ask how heterogeneous are estimates cross-subjects, and what are the determinants of heterogeneity? This speaks to, among other things, the descriptive power of representative agent models, and to our (limited) ability to “explain”, or at least fit, preferences with observable characteristics. Fourth, we examine how (un)stable parameter estimates are within-subject, across time. This question speaks to meta-questions about what preferences capture (something inviolable and deep, versus something more malleable and highly context-specific). In this context, we also discuss interventions designed to change preferences. We know of only a few cases of the latter, primarily in the context of impatience and self-control. Our approach here errs on the side of breadth, not depth. We hope that each section highlights the challenges involved in the direct elicitation of that set of preferences and their impacts on behavior, in ways that encourage further progress in the development of elicitation methods. We try to be comprehensive about identifying the issues that researchers need to confront, rather than being comprehensive about resolving said issues. Part of this is due to necessity: for most types of preferences, we could find little warranted consensus on best-practice methods. Part of this is due to taste, in that we believe many of the most important research questions here revolve 3
around how to disentangle specific types of preferences from other preferences, from other cognitive inputs into decision making (like expectations, price perceptions, and memory), and from elements of choice sets (like liquidity constraints, and returns to capital).
II.
Uncertainty A.
Overview of Theories and Concepts
Preferences with regard to uncertainty are generally regarded as one of the most fundamental or “primitive” aspects of someone’s utility function. As such, inferences about the nature of these preferences are of vital importance to virtually every discipline and subfield in the social sciences. The experimental study of preferences over risk/uncertainty has breadth and depth commensurate with its importance; a thorough study would be at least book-length (as evidenced by [Cox and Harrison 2008]). As such we provide a primer rather than a manual, and refer the interested reader to Cox and Harrison [2008], and other references below, for further details. We start with the important distinction between attitudes towards and preferences over uncertainty. Attitudes, as typically defined, are a reduced-form combination of both preferences and perceptions about risk likelihood (and/or the cost/benefit of different states of the world conditional on their realization). E.g., someone may exhibit risk averse behavior because of their underlying preferences, conditional on (possibly distorted) expectations, and/or they may exhibit risk averse behavior because of their expectations. So a question that asks: “Do you tend to take risks in choosing when to harvest your crops?” may pick up elements of risk preference (I don’t take the risky action because I have very concave utility and am not willing to expose myself to variance in income), and/or of risk perception (I don’t take the risky action because I perceive bad states of the world, e.g. a heavy rainfall at harvest time, to have a high probability). We avoid the notion of strategic uncertainty, which is due to another agent’s behavior rather than states of nature.1 A brief overview of different theories helps set the stage. Expected utility theory (EUT) reduces preferences over uncertainty to “risk”. Agents face known distributions of probabilities of all states of the world, and perceive these probabilities accurately. Risk preferences can then be categorized in one of three ways: risk aversion (preferring a certain payoff lower than the expected value of a gamble to the gamble itself), risk-seeking (preferring the gamble to a certain payoff equal to the expected value) or risk-neutrality (linear utility). In order to better facilitate this categorization, Arrow [(1965) and Pratt [(1964) formalized two local measures of riskaversion, relative risk aversion (RRA) and absolute risk aversion (ARA,) 2 both of which are positive for risk aversion and negative for risk seeking. Studying risk preference under EUT frequently involves estimating these parameters. It can also involve sketching the utility function more globally, since the study of risk preferences under EUT is equivalent to studying the function’s curvature. However, EUT implies approximate risk neutrality over anything but large 1
For instance, by observing the relative frequency of choices of the risk-dominant action in the stag-hunt game, one could measure the strategic risk-aversion of an individual.
2
RRA is defined as –
and ARA is defined as –
′′ ′
.
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stakes [Rabin 2000], which is a problem for elicitation methods that use small stake questions to calibrate EUT models.3 Other theories posit more complicated structures of preferences over uncertainty. Some complications are due to allowing for added richness or bias in risk perception (e.g., lack of clear or accurate expectations), as in cumulative prospect theory [Tversky and Kahneman 1992], salience theory [Bordalo et al 2012] or ambiguity aversion. Other complications are due to nonlinearities or other discreteness in preferences; e.g., loss aversion in prospect theory, preference for certainty [see, e.g., Andreoni and Sprenger _UCE_ 2012] or rank-dependent utility [Quiggin 1982]; see also Fudenberg and Levine [2012]. Hey [1997] and Starmer [2000] provide a more complete set and description of alternatives to EUT. As with EUT, researchers can use data elicited from choice tasks, in combination with various econometric approaches, to estimate model parameters and/or utility functions under various (often testable) assumptions.
B.
Methods 1.
Methods: Elicitation and Estimation4
There are several general methods to elicit preferences or attitudes over uncertainty. We describe each in brief, along with a summary of key limitations or concerns. Our Appendix contains a concrete example, for each elicitation method, of a choice task or survey question used in that method. We focus on direct elicitation and do not cover papers that infer preferences from field data; see e.g., [Einav et al] for a recent paper using this approach. The Multiple List Price (MPL) method [Miller et al 1969] offers choices between two or more uncertain prospects with fixed payoff amounts and varying probabilities. In the widely-used Holt and Laury [2002] version of MPL, subjects face a single list (visible all at once) of binary decisions between two gambles. The payoffs remain the same in each decision but the probabilities vary, meaning that any respondent with consistent risk preferences should have a “switch” point between preferring gamble A or gamble B (we discuss models that allow for a “trembling hand” or other types of choice-inconsistency in Section []). Tanaka et al [2010] offer a new variant of MPL that elicits utility curvature, curvature of the probability weighting, and the degree of loss aversion (and of time preference) under various assumptions. MPLs have been criticized for assuming linear utility (as discussed in Section III, discount rate estimates from MPLs are biased upward if utility is concave), and for providing interval rather than point identification of preference parameters. The Ordered Lottery Selection method [Binswanger 1980; 1981; Barr 2003] offers choices between two or more uncertain prospects with fixed probabilities and varying payoff amounts. As Harrison and Rutström [2008] discuss, it has been conventional to use 0.5 as the fixed probability, and to offer a certain option along with (several) gambles. These conventions create difficulties for estimating non-EUT models but are not intrinsic features of the design: one could 3
For example: say a person turns down a gamble where he has equal probability of losing $100 or gaining $110. If the only explanation is curved utility, this implies that he will spurn any gambles with equal probability of losing $1000 or gaining any positive amount, no matter how large it is.. 4 Here we borrow especially heavily from the taxonomies and discussions in Harrison et al [2007] and Harrison and Rustrom [2008].
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use a range of probabilities to allow for estimates of probability weighting, and one could eliminate the certain option, and/or vary how the different gambles are arrayed, to test or control for framing/reference point effects [Engle-Warnick et al 2006] A few studies use methods that provide a continuum of choices (in contrast to the discrete choices posed by MPL and OLS), using linear budget constraints. (We discuss the convex time budget method later in this sub-section, and again briefly in the section on time preferences.) Andreoni and Harbaugh [2010] provide choices between gambles with probability of winning an amount x with probability p
