Sunday, September 3, 2017

Emodiversity: Robust Predictor of Outcomes or Statistical Artifact?

Brown, N. J. L., & Coyne, J. C. (2017). Emodiversity: Robust Predictor of Outcomes or Statistical Artifact? Journal of Experimental Psychology. General. DOI: 10.1037/xge0000330

Abstract: This article examines the concept of emodiversity, put forward by Quoidbach et al. (2014) as a novel source of information about “the health of the human emotional ecosystem” (p. 2057). Quoidbach et al. drew an analogy between emodiversity as a desirable property of a person’s emotional make-up and biological diversity as a desirable property of an ecosystem. They claimed that emodiversity was an independent predictor of better mental and physical health outcomes in two large-scale studies. Here, we show that Quoidbach et al.’s construct of emodiversity suffers from several theoretical and practical deficiencies, which make these authors’ use of Shannon’s (1948) entropy formula to measure emodiversity highly questionable. Our reanalysis of Quoidbach et al.’s two studies shows that the apparently substantial effects that these authors reported are likely due to a failure to conduct appropriate hierarchical regression in one case, and to suppression effects in the other. It appears that Quoidbach et al.’s claims about emodiversity may reduce to little more than a set of computational and statistical artifacts.

Big Data Surveillance: The Case of Policing

Big Data Surveillance: The Case of Policing. Sarah Brayne. American Sociological Review. https://doi.org/10.1177/0003122417725865

Abstract: This article examines the intersection of two structural developments: the growth of surveillance and the rise of “big data.” Drawing on observations and interviews conducted within the Los Angeles Police Department, I offer an empirical account of how the adoption of big data analytics does—and does not—transform police surveillance practices. I argue that the adoption of big data analytics facilitates amplifications of prior surveillance practices and fundamental transformations in surveillance activities. First, discretionary assessments of risk are supplemented and quantified using risk scores. Second, data are used for predictive, rather than reactive or explanatory, purposes. Third, the proliferation of automatic alert systems makes it possible to systematically surveil an unprecedentedly large number of people. Fourth, the threshold for inclusion in law enforcement databases is lower, now including individuals who have not had direct police contact. Fifth, previously separate data systems are merged, facilitating the spread of surveillance into a wide range of institutions. Based on these findings, I develop a theoretical model of big data surveillance that can be applied to institutional domains beyond the criminal justice system. Finally, I highlight the social consequences of big data surveillance for law and social inequality.

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For example, after a series of copper wire thefts in the city, the police found the car involved by drawing a radius in Palantir around the three places the wire was stolen from, setting up time bounds around the time they knew the thefts occurred at each site, and querying the system for any license plates captured by ALPRs in all three locations during those time periods.

[...]

I encountered several other examples of law enforcement using external data originally collected for non–criminal justice purposes, including data from repossession and collections agencies; social media, foreclosure, and electronic toll pass data; and address and usage information from utility bills. Respondents also indicated they were working on integrating hospital, pay parking lot, and university camera feeds; rebate data such as address information from contact lens rebates; and call data from pizza chains, including names, addresses, and phone numbers from Papa Johns and Pizza Hut. In some instances, it is simply easier for law enforcement to purchase privately collected data than to rely on in-house data because there are fewer constitutional protections, reporting requirements, and appellate checks on private sector surveillance and data collection (Pasquale 2014).  Moreover, respondents explained, privately collected data is sometimes more up-to-date.

How quickly can we adapt to change? An assessment of hurricane damage mitigation efforts using forecast uncertainty.

How quickly can we adapt to change? An assessment of hurricane damage mitigation efforts using forecast uncertainty. By Andrew Martinez


Abstract: Our ability to adapt to extreme weather is increasingly relevant as the frequency and intensity of these events alters due to climate change. It is important to understand the effectiveness of adaptation given the uncertainty associated with future climate events. However, there has been little analysis of short-term adaptation efforts. We propose a novel approach of using errors from hurricane forecasts to evaluate short-term hurricane damage mitigation efforts. We construct a statistical model of damages for all hurricanes to strike the continental United States since 1955. While we allow for many possible drivers of damages, using model selection methods we find that a small subset explains most of the variation. We also find evidence supporting short-term adaptation effects prior to a hurricane landfall. Our results show that the 67 percent improvement in hurricane forecasts over the past 60 years is associated with damages being 16-63 percent lower than they otherwise would have been. Accounting for outlying observations narrows this range to 16-24 percent.

Keywords: Adaptation, Natural Disasters, Uncertainty


JEL Reference: C51, C52, Q51, Q54

Sex differences in jealousy: the (Lack of) influence of researcher theoretical perspective

Sex differences in jealousy: the (Lack of) influence of researcher theoretical perspective. John Edlund et al. The Journal of Social Psycholog, http://dx.doi.org/10.1080/00224545.2017.1365686

According to the theory of evolved sex differences in jealousy (Buss, Larsen, Westen, & Semmelroth, 1992), ancestral women’s challenge of ensuring paternal investment exerted selective pressures that increased women’s jealousy in response to emotional infidelity, whereas ancestral men’s challenge of paternal uncertainty exerted selective pressures that increased men’s jealousy in response to sexual infidelity. Observing that women experience greater jealousy in response to emotional infidelity (relative to men) and that men experience greater jealousy in response to sexual infidelity (relative to women) is known as the sex differences in jealousy effect. This effect has been explored in several ways (see Edlund & Sagarin, 2017 for a comprehensive review). Most relevant to the goals of this paper are the approaches taken by Sheets and Wolfe (2001), in which participants were asked to imagine an infidelity and respond to forced-choice questions , and the approach taken by Edlund, Heider, Scherer, Farc, and Sagarin (2006), in which participants were asked to respond on continuous items .

However, this sex difference in jealousy effect has not been without significant controversy in the literature. For instance, DeSteno and colleagues (DeSteno, Bartlett, Bravermann, & Salovey, 2002) have suggested that men and women had differential interpretations of the forced-choice questions (called the “double-shot” hypothesis); however, Buss and colleagues (Buss et al., 1999) later demonstrated that the double-shot hypothesis cannot explain the relationship between participant sex and jealousy. Harris (2002) questioned whether sex differences in cognitive focus (not emotional jealousy) in response to actual experiences with infidelity mirrored hypothetical reactions and whether the effect in the hypothetical reaction literature was an artifact of the forced-choice measure. Edlund and colleagues (Edlund et al., 2006) later demonstrated that sex differences in jealousy in response to actual experiences with infidelity mirrored hypothetical reactions in both forced-choice and continuous measures. Importantly, meta-analyses have confirmed that this effect reliably emerges with both forced-choice (Harris, 2002) and continuous measures of jealousy (Sagarin et al., 2012).  One significant point of contention in the literature, and the one addressed in the current study, is whether successfully observing a sex difference in jealousy effect is driven by the theoretical perspective of the researchers. Many of the studies attempting to refute the theory of evolved sex differences in jealousy have been published in general psychological journals (e.g., Psychological Science) and in social psychology journals (e.g., Personality and Social Psychology Bulletin). Conversely, many of the studies supporting the sex difference in jealousy have been published in journals oriented toward evolutionary psychology (e.g., Evolutionary Psychology). This discrepancy is highlighted by Edlund and Sagarin (2017), who demonstrate the differences in the publication outlets, but they do not offer evidence as to whether the theoretical perspective of the researchers is the driving factor in the eventual publication outlets.

Given the disparate nature of the researchers on both sides of the debate and the resultant diversity in the outlets in which their findings have been published, one of the goals of the present research was to bring diverse researchers together (many of whom have never published with one another) to investigate whether theoretical perspective impacted the sex difference in jealousy. We also sought to provide another replication of the sex difference in jealousy effect while examining both continuous and forced-choice measures. Finally, we sought to extend the sex difference in jealousy literature by incorporating an individual difference measure – a self-perceived measure of how high quality a mate one is (i.e., mate value) – as a potential moderator of the sex difference in jealousy effect. For instance, research has shown that mate value moderates one’s preferences in a mate (e.g., Edlund & Sagarin, 2010; Reeve, Kelly, & Welling, 2017), as well as one’s intention to commit an infidelity (Starratt, Weekes-Shackelford, & Shackelford, 2017). As such, given mate value’s impact on intentions towards infidelity, we wanted to explore if it would similarly impact the reactions to an infidelity.

[...]

In summary, we have demonstrated that the sex difference in jealousy occurs in both forcedchoice and continuous response scale formats. We also demonstrated that the theoretical perspective of the researchers has no bearing on the results obtained when using identical tools. Finally, we have demonstrated that mate value moderates the sex difference in jealousy.

Kevin Bryan on “The Development Effects of the Extractive Colonial Economy,” M. Dell & B. Olken

Kevin Bryan's comments on “The Development Effects of the Extractive Colonial Economy,” M. Dell & B. Olken (2017).

Find the full text, links to other info, etc., in A Fine Theorem blog, Jun 22 2017, https://afinetheorem.wordpress.com/2017/06/22/the-development-effects-of-the-extractive-colonial-economy-m-dell-b-olken-2017/

A good rule of thumb is that you will want to read any working paper Melissa Dell puts out. Her main interest is the long-run path-dependent effect of historical institutions, with rigorous quantitative investigation of the subtle conditionality of the past. For instance, in her earlier work on Peru (Econometrica, 2010), mine slavery in the colonial era led to fewer hacienda style plantations at the end of the era, which led to less political power without those large landholders in the early democratic era, which led to fewer public goods throughout the 20th century, which led to less education and income today in eras that used to have mine slavery. One way to read this is that local inequality is the past may, through political institutions, be a good thing today! History is not as simple as “inequality is the past causes bad outcomes today” or “extractive institutions in the past cause bad outcomes today” or “colonial economic distortions cause bad outcomes today”. [...]

Dell’s new paper looks at the cultuurstelsel, a policy the Dutch imposed on Java in the mid-19th century. Essentially, the Netherlands was broke and Java was suitable for sugar, so the Dutch required villages in certain regions to use huge portions of their arable land, and labor effort, to produce sugar for export. They built roads and some rail, as well as sugar factories (now generally long gone), as part of this effort, and the land used for sugar production generally became public village land controlled at the behest of local leaders. This was back in the mid-1800s, so surely it shouldn’t affect anything of substance today?

But it did! Take a look at villages near the old sugar plantations, or that were forced to plant sugar, and you’ll find higher incomes, higher education levels, high school attendance rates even back in the late colonial era, higher population densities, and more workers today in retail and manufacturing. Dell and Olken did some wild data matching using a great database of geographic names collected by the US government to match the historic villages where these sugar plants, and these labor requirements, were located with modern village and town locations. They then constructed “placebo” factories – locations along coastal rivers in sugar growing regions with appropriate topography where a plant could have been located but wasn’t. In particular, as in the famous Salop circle, you won’t locate a factory too close to an existing one, but there are many counterfactual equilibria where we just shift all the factories one way or the other. By comparing the predicted effect of distance from the real factory on outcomes today with the predicted effect of distance from the huge number of hypothetical factories, you can isolate the historic local influence of the real factory from other local features which can’t be controlled for.

Consumption right next to old, long-destroyed factories is 14% higher than even five kilometers away, education is 1.25 years longer on average, electrification, road, and rail density are all substantially higher, and industrial production upstream and downstream from sugar (e.g., farm machinery upstream, and processed foods downstream) are also much more likely to be located in villages with historic factories even if there is no sugar production anymore in that region!

It’s not just the factory and Dutch investments that matter, however. Consider the villages, up to 10 kilometers away, which were forced to grow the raw cane. Their elites took private land for this purpose, and land inequality remains higher in villages that were forced to grow cane compared to villages right next door that were outside the Dutch-imposed boundary. But this public land permitted surplus extraction in an agricultural society which could be used for public goods, like schooling, which would later become important! These villages were much more likely to have schools especially before the 1970s, when public schooling in Indonesia was limited, and today are higher density, richer, more educated, and less agricultural than villages nearby which weren’t forced to grow cane. This all has shades of the long debate on “forward linkages” in agricultural societies, where it is hypothesized that agricultural surplus benefits industrialization by providing the surplus necessary for education and capital to be purchased; [...].

Are you surprised by these results? [me: NO!] They fascinate me, honestly. Think through the logic: forced labor (in the surrounding villages) and extractive capital (rail and factories built solely to export a crop in little use domestically) both have positive long-run local effects! They do so by affecting institutions – whether villages have the ability to produce public goods like education – and by affecting incentives – the production of capital used up- and downstream. One can easily imagine cases where forced labor and extractive capital have negative long-run effects, and we have great papers by Daron Acemoglu, Nathan Nunn, Sara Lowes and others on precisely this point. But it is also very easy for societies to get trapped in bad path dependent equilibria, for which outside intervention, even ethically shameful ones, can (perhaps inadvertently) cause useful shifts in incentives and institutions! I recall a visit to Babeldaob, the main island in Palau. During the Japanese colonial period, the island was heavily industrialized as part of Japan’s war machine. These factories were destroyed by the Allies in World War 2. Yet despite their extractive history, a local told me many on the island believe that the industrial development of the region was permanently harmed when those factories were damaged. [...]

2017 Working Paper is here [https://scholar.harvard.edu/files/dell/files/170414draft.pdf] (no RePEc IDEAS version). For more on sugar and institutions, I highly recommend Christian Dippel, Avner Greif and Dan Trefler’s recent paper on Caribbean sugar. The price of sugar fell enormously in the late 19th century, yet wages on islands which lost the ability to productively export sugar rose. Why? Planters in places like Barbados had so much money from their sugar exports that they could manipulate local governance and the police, while planters in places like the Virgin Islands became too poor to do the same. This decreased labor coercion, permitting workers on sugar plantations to work small plots or move to other industries, raising wages in the end. [...].

Saturday, September 2, 2017

Much ado about grit: A meta-analytic synthesis of the grit literature

Credé, M., Tynan, M. C., & Harms, P. D. (2017). Much ado about grit: A meta-analytic synthesis of the grit literature. Journal of Personality and Social Psychology, 113(3), 492-511.
http://dx.doi.org/10.1037/pspp0000102

Abstract: Grit has been presented as a higher order personality trait that is highly predictive of both success and performance and distinct from other traits such as conscientiousness. This paper provides a meta-analytic review of the grit literature with a particular focus on the structure of grit and the relation between grit and performance, retention, conscientiousness, cognitive ability, and demographic variables. Our results based on 584 effect sizes from 88 independent samples representing 66,807 individuals indicate that the higher order structure of grit is not confirmed, that grit is only moderately correlated with performance and retention, and that grit is very strongly correlated with conscientiousness. We also find that the perseverance of effort facet has significantly stronger criterion validities than the consistency of interest facet and that perseverance of effort explains variance in academic performance even after controlling for conscientiousness. In aggregate our results suggest that interventions designed to enhance grit may only have weak effects on performance and success, that the construct validity of grit is in question, and that the primary utility of the grit construct may lie in the perseverance facet.

We cannot be impartial most of the time... Our judgement gets clouded by our political preferences --- again

Kahan, Dan M. and Peters, Ellen, Rumors of the 'Nonreplication' of the 'Motivated Numeracy Effect' are Greatly Exaggerated (August 26, 2017). Available at SSRN: https://ssrn.com/abstract=3026941

Abstract: This paper does three things. First, it describes the design defects (principally, the lack of statistical power) that make it misleading for Ballarini & Sloman (2017) to claim that they “failed to replicate” the results of Kahan, Peters et al. (2017). Second, it presents the positive results of our own replication study. Finally, we conclude with a brief discussion of why confining assertions of non-replication to studies that satisfy emerging replication protocols—in particular the imperative of “faithful recreation of a study with high statistical power” (Brandt, Ijzerman et al 2014, p. 217)—is essential to the contribution such studies can make as building blocks of a cumulative science.

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The authors ask a neutral problem (if a skin cream works well or not for some rash), and a politicized question (is a change in gun laws associated to more or to less crime?) in a form called covariance detection task (they present fictional studies with fictional results and ask the subjects whether the study supports one answer or the other). They do not ask subjects what they think of the real world, just if the study supports or not an answer or the other... But the subjects cannot be neutral. The authors add:

This “covariance detection” task is hard. Consistent with existing literature, ***only 30%*** of the MN sample overall supplied the correct answer in the “skin rash” group. Skin-rash group participants who scored in the 95th percentile of numeracy, in contrast, tended to get the correct answer in the “skin rash” treatment group ***around 75%*** of the time.

The high-numeracy participants in that group also tended to identify the correct solution—but only when that solution affirmed the position associated with their political identity (crime increases for “Liberal Democrat” vs. crime decreases for “Conservative Republican”). When the correct answer disconfirmed (or “threatened”) the position associated with their political identity (crime increased for Liberal Democrat and crime decreased for Conservative Republican), the high-numeracy participants performed no better than the low- and moderately-numerate participants who shared their identity (Kahan, Peters, et al., 2017).

This result is not consistent with the widespread assumption that political and cultural conflict over scientific data is rooted in the prevalence of System-1 thinking in the general population. It is more consistent with an alternative view that sees numeracy and other forms of System-2 reasoning as re-sources that can be used in the service of identity-protective cognition, a form of motivated information processing that aims to maintain correspondence between an individual’s factual beliefs and the factual beliefs known to be markers of membership in, and loyalty to, one’s cultural group (Bolsen et al. 2014; Kahan 2013, 2009; Sherman & Cohen 2006).

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Check also: Biased Policy Professionals. Sheheryar Banuri, Stefan Dercon, and Varun Gauri. World Bank Policy Research Working Paper 8113. https://www.bipartisanalliance.com/2017/08/biased-policy-professionals-world-bank.html

And: Dispelling the Myth: Training in Education or Neuroscience Decreases but Does Not Eliminate Beliefs in Neuromyths. Kelly Macdonald et al. Frontiers in Psychology, Aug 10 2017. https://www.bipartisanalliance.com/2017/08/training-in-education-or-neuroscience.html

And: Wisdom and how to cultivate it: Review of emerging evidence for a constructivist model of wise thinking. Igor Grossmann. European Psychologist, in press. Pre-print: https://www.bipartisanalliance.com/2017/08/wisdom-and-how-to-cultivate-it-review.html

Facial Width-to-height Ratio Does Not Predict Self-reported Behavioral Tendencies

Kosinski, Michal. 2017. “Facial Width-to-height Ratio Does Not Predict Self-reported Behavioral Tendencies”. PsyArXiv. September 2. doi:10.1177/0956797617716929.

Abstract: A growing number of studies have linked facial width-to-height ratio (fWHR) with various antisocial or violent behavioral tendencies. However, those studies have predominantly been laboratory based and low powered. This work reexamined the links between fWHR and behavioral tendencies in a large sample of 137,163 participants. Behavioral tendencies were measured using 55 well-established psychometric scales, including self-report scales measuring intelligence, domains and facets of the five-factor model of personality, impulsiveness, sense of fairness, sensational interests, self-monitoring, impression management, and satisfaction with life. The findings revealed that fWHR is not substantially linked with any of these self-reported measures of behavioral tendencies, calling into question whether the links between fWHR and behavior generalize beyond the small samples and specific experimental settings that have been used in past fWHR research.

Contrary to the hypothesis, predicted pleasure eating sweets was significantly lower than observed pleasure

Fallon, Matthew D., "The Role of Affective Forecasting and the Impact Bias in Nutritional Health Behaviors" (2017). Grand Valley State University, Masters Theses. 854. http://scholarworks.gvsu.edu/theses/854

Abstract: Previous literature on affective forecasting has studied its role in health decisions, but there is little research investigating affective forecasting in diet choices and eating behaviors. The present study collected affective forecasts from 43 college participants before eating an indulgent snack and then observed emotions immediately after eating the snack. We predicted that emotion predictions would be significantly stronger than observed emotions, in support of previous literature on the impact bias. We also predicted that optimism would predict a stronger impact bias and that extraversion and neuroticism would have a role in forecasts and observed emotions. Contrary to our hypothesis, predicted pleasure (M=2.12) was significantly lower than observed pleasure (M=2.34), F(1,42)=5.44, p=.025. Likewise, for participants who ate M&Ms rather than cookies or chips, participants had significantly higher observed positive emotion (M=1.95) than they had predicted (1.73), F(1,14)=5.78, p=.031. Trait optimism had significant interaction effects for positive affect, for each food chosen, such that as optimism increases, predicted affect increased more rapidly than observed affect. Neuroticism and extraversion were found to significantly influence predicted and observed positive affect, but had no effect on the accuracy of the affective forecasts. The present findings did not indicate the presence of an impact bias, but support previous affective forecasting literature in other aspects. These findings indicate that many of the phenomena in affective forecasting influence food forecasts. This holds implications for future research on affective forecasting in food choice and interventions targeting forecasting errors to improve diet.

Friday, September 1, 2017

The estimated 79% heritability of schizophrenia is congruent with previous reports and indicates a substantial genetic risk

Heritability of schizophrenia and schizophrenia spectrum based on the nationwide Danish Twin Register. Rikke Hilker, MD, PhD. Biological Psychiatry. https://doi.org/10.1016/j.biopsych.2017.08.017

Abstract

Background: Twin studies have provided evidence that both genetic and environmental factors contribute to schizophrenia risk. Heritability estimates of schizophrenia in twin samples have varied methodologically. This study provides updated heritability estimates based on nationwide twin data and an improved statistical methodology.

Method: Combining two nationwide registers, the Danish Twin Register and the Danish Psychiatric Research Register, we identified a sample of twins born 1951-2000 (N=31,524 twin pairs). Twins were followed up until June 1st 2011. Liability threshold models adjusting for censoring with inverse probability weighting were used to estimate probandwise concordance rates and heritability of the diagnoses of schizophrenia and schizophrenia spectrum disorders.

Results: The probandwise concordance rate of schizophrenia is 33% in monozygotic (MZ) twins and 7% in dizygotic (DZ) twins. We estimated the heritability of schizophrenia to be 79%. When expanding illness outcome to include schizophrenia spectrum disorders, the heritability estimate was almost similar, 73%.

Conclusion: The key strength of this study is the application of a novel statistical method accounting for censoring in the follow-up period to a nationwide twin sample. The estimated 79% heritability of schizophrenia is congruent with previous reports and indicates a substantial genetic risk. The high genetic risk also applies to a broader phenotype of schizophrenia spectrum disorders. The low concordance rate of 33% in MZ twins demonstrates that illness vulnerability is not solely indicated by genetic factors.

Key words: Heritability schizophrenia twin study censoring concordance register

Superior Pattern Detectors Efficiently Learn, Activate, Apply, and Update Social Stereotypes

Superior Pattern Detectors Efficiently Learn, Activate, Apply, and Update Social Stereotypes. David Lick, Adam Alter and Jonathan Freeman. Journal of Experimental Psychology: General, https://doi.org/10.1037/xge0000349

Abstract: Superior cognitive abilities are generally associated with positive outcomes such as academic achievement and social mobility. Here, we explore the darker side of cognitive ability, highlighting robust links between pattern detection and stereotyping. Across 6 studies, we find that superior pattern detectors efficiently learn and use stereotypes about social groups. This pattern holds across explicit (Studies 1 and 2), implicit (Studies 2 and 4), and behavioral measures of stereotyping (Study 3). We also find that superior pattern detectors readily update their stereotypes when confronted with new information (Study 5), making them particularly susceptible to counterstereotype training (Study 6). Pattern detection skills therefore equip people to act as naïve empiricists who calibrate their stereotypes to match incoming information. These findings highlight novel effects of individual aptitudes on social–cognitive processes.

Group identity as a source of threat and means of compensation: Establishing personal control through group identification and ideology

Goode, C., Keefer, L. A., Branscombe, N. R., and Molina, L. E. (2017) Group identity as a source of threat and means of compensation: Establishing personal control through group identification and ideology. Eur. J. Soc. Psychol., 47: 259–272. doi: 10.1002/ejsp.2259.

Abstract: Compensatory control theory proposes that individuals can assuage threatened personal control by endorsing external systems or agents that provide a sense that the world is meaningfully ordered. Recent research drawing on this perspective finds that one means by which individuals can compensate for a loss of control is adherence to ideological beliefs about the social world. This prior work, however, has largely neglected the role of social groups in defining either the nature of control threat or the means by which individuals compensate for these threats. In four experiments (N = 466), we test the possibility that group-based threats to personal control can be effectively managed by defensively identifying with the threatened group and its values. We provide evidence for the specificity of these effects by demonstrating that defensive identification and ideology endorsement are specific to the content of the group-based threat.

Hispanics choose vehicles that are about 5-8% more expensive

Visible Consumption and Race: Evidence from Auto-Loans. Konstantinos Tzioumis. U.S. Department of the Treasury Working Paper, July 2017.

Abstract: This paper uses auto-loan applications to assess differences in consumption preferences across races. After controlling for income and age, Whites and Blacks are found to have similar choices in terms of vehicle value, while Hispanics choose vehicles that are about 5-8% more expensive. These results add to the literature by drawing on documented choices rather than realized purchases.