This paper investigates how people perceive two important implications of compounding random growth. First, as has been established in the literature, decision makers have a tendency to neglect nonlinear growth. Our experiments add to the evidence of this effect by measuring it in a context with random growth rates. Second, people underestimate the level of asymmetry in growth processes—skewness is “hidden.” This is a novel effect in the academic literature (modulo the independent description inStutzer and Grant(2013)) and may be especially relevant in the context of preferences that consider quantiles of the outcome distribution, like value-at-risk or expected utility with convex utility functions. However, it is important to note that this paper is about misperception, not preferences, and that we measure the effects irrespective of risk attitudes. Questions about compound interest are, by now, standard procedure in surveys about financial literacy, see e.g., the relevant module in the Health and Retirement Survey documented inLusardi and Mitchell(2011). The typical evidence is that calculations of multiplicative growth effects show a strong downward bias, often to the extent that all compounding is ignored. One may speculate that if decision makers were trained in the use of log returns, the bias could be reduced. At least some of our experiments give the respondents a very good shot at detecting the nonlinear effects of growth, since we use highly selected and quantitatively skilled students and partially provide them with calculators. It is perhaps all the more notable that we, too, find a strong bias towards linear perceptions.
In Study 3 we also indicate that the effect of skewness is relevant beyond abstract settings. We chose a setting where leveraged ETFs are on offer, as these assets were primarily bought and held by household investors who do not usually have sophisticated risk management tools available. Just as many of these household investors were surprised by the losses they incurred, our participants show a misperception of the effects of leverage, in line with exponential growth bias.
The results may well extend to other contexts of household finance. As we describe in the Introduction, compounding of stochastic growth is often required in contexts of retirement savings. It will be difficult to quantify the effects of the many established anomalies in savings behavior. But progress is made step by step. Our stylized experiments, with full control over information flow and incentives, can at least establish that the expectation of compound distributions deviates
1.6. Conclusion 19
predictably from the rational benchmark. Our experiments also show that long investment horizons increase the strength of the misperception.
2
Investment Behavior in
Peer-to-Peer Lending
Measuring Applicant Quality to Detect Discrimina-
tion
This chapter is based on joint work with Georg Weizsäcker.
22 2. Investment Behavior in Peer-to-Peer Lending
2.1
Introduction
Many interesting aspects of gender discrimination concern the interaction of an applicant’s gender and quality. Are women’s success chances more or less correlated with quality than men’s? The answer to this question may well differ from what the unconditional success rates of men and women suggest. Employers, sponsors or other potential discriminators may, for example, favor women over men overall but reward the quality of women’s applications less than for men; or they may show the opposite pattern. Allocations and incentives can be severely influenced by such “slope-discriminating” behavior that may appear on top of potential “level-effect” discrimination. Analogous statements are true for analyses that include controls for the quality of applications: the inclusion of interaction terms may bigly change the interpretation of results.
A major difficulty for the analyst is to measure the quality of an application. In most empirical applications, only proxies for applicant quality are available and their interpretation is often all too flexible. The statistical connection between a given proxy and quality may be nonlinear (more generally, difficult to correctly specify) and it may be different for men and women. Both of these effects may also be subject to differential measurement error and to selection effects. A substantial portion of these measurement problems arises simply because the objective of the employer or sponsor is not self-evident. For example, job applicants promise a high-dimensional array of outcomes to the potential employer. It is usually beyond the analyst’s power to assess the employers’ aggregate valuations of these outcomes.
In this paper, we focus on a narrow financial context, peer-to-peer lending between German households on the online platform smava.de. Here, the applicant is a borrower who describes a project and makes a take-it-or-leave-it offer to all potential lenders. The outcome of such a credit application can be reasonably reduced to a single number: its expected internal rate of return. We observe all characteristics of the offered contract and of the applicant that are available to the potential lender, allowing us to assess this measure of predictable quality in detail and with high precision. The nature of the interaction between lender and borrower precludes any other relation between them. Risk considerations are also minimal, due to the platform’s specific insurance mechanism, implying that the expected rate of return is a natural candidate for the lender’s objective.
Using our inferred measure of quality, we analyze the applicant’s chances of success, with a particular focus on the interaction between gender and quality. We address measurement error by modeling the applicant’s quality with a detailed structure and by including a statistical correction method (the SIMEX procedure ofStefanski and Cook(1995) adapted to our context). We find significant effects of both slope discrimination and level discrimination. Women have higher success rates than men, conditional on quality, but this gender difference is driven by a larger increase of men’s success rate in quality: women appear to get the benefit of the doubt, such that low-quality applications of women are almost equally successful as high-quality applications of women and men. The low-quality applications of men, in contrast, are much less likely to be successful. In terms of chances of a project being fully funded, the success of a below-median-quality application by a man is about half of that of an analogous application by a woman, whereas both genders’ above-median-quality applications are equally successful.
Within the larger literature on discrimination, the result is noteworthy in that it confirms a particular feature of (some kinds of) statistical discrimination: if the potential discriminators—here, the predominantly male lenders—find it harder to judge a woman than to judge a man, then weak male applicants should have lower success. This feature is usually not found in discrimination studies, largely because a male-favoring level effect outweighs it. We also show that simpler proxies of quality yield different conclusions. One natural candidate proxy for quality is the applicant’s credit rating. Its correlation with success, like that of our own quality measure, suggests that women enjoy positive level discrimination in our context, but not a slope effect. An alternative proxy, the