Table A.4: Summary Statistics (n = 112) Type Mean Std.Err.
Female binary 0.446 0.047 Age numeric 22.625 0.209 Log-Income numeric 6.380 0.067 Experience binary 0.304 0.044 CRT numeric 2.214 0.082
Table A.5: Number of Observations at the Bounds (n = 112) δ2 δ4
≥ 95% 23 14
0% 2 0
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Appendix B
Rational Planners or Myopic Fools?
Liquidity Constraints, Positive Expectations and Anomalies in Intertemporal Choice
This chapter has not yet been published elsewhere.
B.1 Introduction
Many of the most important choices we make involve alternatives with consequences occurring at different points in time. Prominent examples are how much to save for later consumption, when to pay off debts, or in which training to invest. Understanding the drivers of these choices is paramount to predicting individual behavior and market outcomes. In particular, the design of incentive mechanisms, information programs or optimal defaults helping individuals to behave in a more rational way needs to be based on a sound knowledge of where and how to intervene.
This paper contributes to a better understanding of intertemporal choice behavior.
It is motivated by a large number of puzzling findings apparently inconsistent with ex-ponential discounted utility, the canonical model of intertemporal choice. Indeed, most solutions proposed to address these issues still suffer from fundamental shortcomings.
They typically focus on one single “anomaly” only and fail at predicting the vast number of at least equally important stylized facts. Hyperbolic discounting models (Ainslie, 1975;
Herrnstein, 1981; Mazur, 1987; Laibson, 1997; Harris and Laibson, 2008), for example, capture the decline of discount rates in time horizon. They do not, however, provide an explanation for why subject’s behavior differs from standard predictions in many more respects.
Empirical evidence documents the following results. First, aggregate behavior departs in systematic ways from exponential discounting (Loewenstein and Thaler, 1989; Loewen-stein and Prelec, 1992; Frederick et al., 2002). Quite robust “anomalies” are that discount rates lie far beyond market interest rates, decline in time horizon and in outcome magni-tude, and are larger for gains compared to losses. A coherent explanation encompassing all these findings is still lacking.
Second, quantitative result, such as estimated discount rates or the size of these effects, vary tremendously across and within studies (Frederick et al., 2002).1 This seems puzzling as most experiments are based on similar designs and are conducted among similar cohorts, i.e. subjects that are very homogenous with respect to their education, income and age.
Third, recent longitudinal studies show that behavior is not as dynamically stable as current preference models imply (Sayman et al., 2007; Airoldi et al., 2009). The reason for this finding is still underresearched, but suggests that intertemporal behavior may be influenced by other factors than intrinsic preferences.
1In their overview article, Frederick et al. (2002) report discount rates ranging from -6 percent per annum to infinity.
Fourth, many studies find a substantial fraction of subjects exhibiting discount rates increasing in time horizon (Read et al., 2005b; Sayman et al., 2007; Airoldi et al., 2009;
Abdellaoui et al., 2010).2 So far, it is not clear whether this behavior is due to errors, trait or other reasons.
Providing an intuitively appealing and unifying explanation for all these findings is the goal pursued by this article. When individuals want to sustain a smooth consump-tion path, but are prevented from doing so because they are borrowing constrained and only hold few liquid assets, positive income expectations can have a significant effect on their behavior. Opting for new alternatives materializing at dates when consumption is expected to be relatively low allows them to reach consumption paths which better measure up to their preferences. That such considerations can play an important role in time discounting is supported by empirical evidence. In a study conducted among rural households in developing countries, Holden et al. (1998) find that liquidity-constrained households show much higher discount rates than others.
The idea that liquidity constraints provide a powerful approach for explaining empir-ical regularities is not new. Deaton (1991) shows that such restrictions can explain many important findings in consumer behavior not captured by most other models. The novelty of our research is to apply this idea to unravel “anomalies” and other puzzling findings in intertemporal choice behavior. We argue that new alternatives are not evaluated in full isolation, as it is usually (implicitly) assumed in empirical studies, but that there are situations where subjective income expectations are reflected in subject’s behavior.
We present the following insights. First, we show that all allegedly anomalous patterns naturally arise for a liquidity-constrained, relative impatient consumer with positive, but rational expectations. In fact, all the “anomalies” are closely intertwined with each other.
Hyperbolic discounting behavior can even be dynamically consistent. Heterogeneity in the consumers’ constraints and subjective expectations provide an explanation for why fairly homogenous subjects substantially differ in behavior.
Second, our approach is first to provide a rationale for so far unexplained behavioral patterns found in empirical data. As time passes, the consumer may face a different life and job situation or may be confronted with an altered economic environment. Her ac-cess to liquidity and her expectations about future consumption are therefore likely to change over time. As a result, our model gives a justification for the ostensibly dynamic instability of revealed choice behavior. Furthermore, if the consumer expects her income
2Studies reporting similar results are Frederick (1999), Rubinstein (2003), Read et al. (2005a) and Attema et al. (2009).
to substantially decline in the not so distant future, but she is unable to accumulate sufficient liquid assets to smooth away the upcoming low-consumption periods, she ex-hibits increasing discount rates. Consequently, the distribution of exponential, hyperbolic and counter-hyperbolic types in the population may be largely governed by the liquidity constraints subjects face and the expectations they hold.
Third, in the latter part of the paper we provide empirical support for our approach.
We use data from two consumption-savings experiments with monetary incentives, one conducted among junior students (mostly undergraduates) and one among senior students (higher-semester graduates and post-graduates). This data is particularly suitable for testing our conjectures not only because most previous experiments were conducted among students, but also because students are the probably best example for subjects who are limited with respect to their liquidity and who hold significant positive expectations. In accordance with our theoretical model, we find a strong link between income expectations and discounting behavior. A simple binary measure for positive income expectations can explain a large part of the anomalously looking behavior found in our data. Estimation of a structural model further reveals that our approach does well in capturing these systematic patterns. Estimated rates of time preference lie in the vicinity of 10% per annum and are considerably lower than discount rates observed on the descriptive level (larger than 70% per annum). Most interestingly, estimated time preferences are not statistically distinguishable from constant ones. Senior students do not only reveal a more pronounced decline of discount rates in outcome magnitude, but, consistent with their earlier entry into the job market, also seem to expect a larger rise in consumption.
Finally, we discuss the possibility that these behavioral patterns are not necessarily caused by rational planners, i.e. liquidity-constrained consumers with positive, but ratio-nal expectations, but may also be due to myopic fools, overoptimistic consumers who are possibly not liquidity constrained. This alternative explanation for a link between subjec-tive expectations and discounting behavior is motivated by the finding that subjects often hold optimistically biased beliefs when it comes to asses future life events, such as income (Weinstein, 1980, 1987; Dominitz, 1998; Armor and Taylor, 2002). Such consumers will exhibit the typical “anomalies”, but, similar to consumers with hyperbolic preferences, their behavior will not be dynamically consistent. More recent research also indicates that the same mechanism can explain why people suffer from self-control problems. Nordgren et al. (2009) find that people often overestimate their capacity for impulse control, leading them to overexpose themselves to temptations.3
3There may also be rational reasons for self-control problems. Subjects are required to exert willpower
That different motives can result in observationally equivalent behavior has strong implications for the design of proper policy instruments helping economic agents to behave in a more rational way without harming those that already do. This is of particular importance for paternalistic regulations, programs or regulations helping on an individual basis (Camerer et al., 2003). We reason why mechanisms distinguishing rational planners from myopic fools are ultimately needed to make suitable policy recommendations and propose possible starting points to develop such mechanisms.
The remainder of this article is structured as follows. Section B.2 introduces the theoretical model and its predictions. Section B.3 presents the experiments, the econo-metric specification and the empirical results. Section B.4 discusses some implications our findings have, provides directions for future research and concludes.