数字启发法与P2P借贷信用风险：一项实证研究

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"1 Numerological Heuristics and Credit Risk in P2P Lending 摘要：启发式方法，作为决策过程中的心理捷径，对决策行为有着广泛的影响。尽管已经有许多关于各种启发式方法的研究，但对于选择何种启发式方法能反映出决策者的特性这一问题，相关研究却相对匮乏。本研究利用来自中国领先P2P借贷平台人人贷的详尽数据，包括超过750万个投标记录和74.2万笔贷款申请，深入研究了两个关键的数字启发式：整数启发法和幸运数字法。这两个启发式方法在提交的贷款金额中占据了超过80%的比例。我们发现，这两种方法对贷款的筹资结果和还款表现产生了不同的影响。具体来说，我们观察到整数贷款在被资金支持后通常较难获得资金，且在获得资金后更可能出现违约情况，而含有幸运数字的贷款则表现出相反的效应，它们更容易获得资金并且违约率较低。通过双变量Probit模型，我们同时估算了借款人在两种启发式方法间的抉择，并揭示出这种选择体现了借款人的信用和认知特征。我们的研究表明，对于采用四舍五入（幸运数字）的借款，其选择的启发式方法可以作为评估借款人信用质量的一个指标，整数贷款可能暗示了较差的借款人素质，而幸运数字贷款可能预示着优质借款人。此外，我们的研究还关注了信息不对称在P2P借贷中的作用，尤其是在数字启发式选择的过程中。信息不对称可能导致投资者无法完全了解借款人的风险状况，而启发式选择提供了一种潜在的方式来弥补这种信息差距，帮助投资者间接评估信用风险。通过识别并理解这些数字模式，投资者和平台可以改进风险评估策略，降低违约风险，并优化投资组合。本论文提供了一个分析框架，通过借款人选择的数字启发式来提取信用风险信息，从而有助于改善P2P借贷市场的风险管理和效率。这些发现不仅对学术界理解启发式决策和信贷市场动态具有重要意义，也为实践者提供了有价值的风险评估工具和策略。"

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shortcuts.

When setting loan amounts, for instance, borrowers commonly resort to such numerological

heuristics. As will be shown in the data description section, we find an overrepresentation of round

numbers and lucky numbers in loan amounts.

The definition of round numbers varies slightly in different studies. Bhattacharya et al. (2012) and

Kuo et al. (2014) identify round numbers by focusing on the last two digits, and Lin and Pursiainen (2021)

define round numbers as divisible by 1,000 or 500. For the platform we study, the loan amount and bid

amount must be multiples of RMB 50, such as 1,050, 2,000, etc., and 87.33% of the loan amounts applied

for are divisible by 1,000. It is also noteworthy that defining roundness by focusing on the last several

digits of a number is affected by the order of magnitude. For instance, it is beyond question that a 4-digit

number divisible by 1,000 (such as 5,000) is round, however, this may not hold for other numbers with

more nonzero digits, such as a 6-digit number 321,000. Although 321,000 is a multiple of 1,000, it is

questionable whether it should be classified as round. Given this concern, we adopt a stricter criterion in

our main analysis and recognize an amount with only one nonzero number in the leftmost digit, and zero

in all other digits as round. As an illustration, 30,000 is round according to our measure but 31,000 is not.

For robustness, we also construct two alternative proxies of loan roundness. In the first measure, we

relax the previous roundness measure and define a loan amount as round if it (1) has one nonzero figure

at the leftmost digit or (2) has two nonzero figures at the leftmost two digits with the second digit being 5

(i.e., semi-round). For instance, 35,000 is not a round number following the strict criterion, but it is

classified as a round number under the relaxed definition. The second roundness measure is a continuous

variable in the range of (0, 1), defined as the number of zeros from the rightmost digit divided by total

number of digits.

Next, we turn to the definition of lucky numbers. The luckiness of numbers is culture specific. In

most of Western countries, the number 13 is considered unlucky (Dyl and Maberly, 1988), whereas in

China number 8 is considered lucky (the pronunciation sounds like “getting rich”) and number 4 is unlucky

(the pronunciation is similar to “death”). The number 6 is also liked, because people believe it means that

everything will go smoothly (possibly from the I-Ching

). Simmons and Schindler (2003) document a

disproportionately higher frequency of the number 8 in Chinese advertisements than the number 4. Block

and Kramer (2009) show an illogical result whereby Chinese consumers in Taiwan are willing to pay more

The use of heuristics is also common in the financial market, Gao et al. (2019) provide evidence that even sophisticated

institutional investors are subject to heuristics as well.

I-Ching, also known as Yi Jing or Book of Changes, is an ancient Chinese divination text, which relates the combination of

numbers to luckiness.

Electronic copy available at: https://ssrn.com/abstract=3575390

for a package of 8 tennis balls than one with 10. Following the literature, we designate lucky numbers as

those having 8 and not 4 in the loan amount (Bhattacharya et al., 2018).

Similar to roundness measures, we also develop a relaxed measure of lucky number as those having

8 or 6 but not 4 (Shum et al., 2014; Hirshleifer et al., 2018), as well as a continuous measure defined as

the frequency count of 8 divided by the total number of digits. These alternative measures of loan amount

roundness and luckiness are used in Section 6.1 to demonstrate that our main findings are robust to

alternative definitions of round and lucky numbers.

3. Literature Review and Hypothesis Development

Heuristics are a concept stemmed from cognitive psychology, known as tools to reduce complex tasks of

assessing probabilities and predicting values to simpler judgmental operations (Tversky and Kahneman,

1974). One of the most popular definitions is: a plausible form of “rule of thumb” or “mental shortcut” in

problem solving (see Perkins, 1981; Gregory and Muntermann, 2014; Kuo et al., 2014, among others).

Although the use of heuristics reduces mental burden in decision making, it could lead to biased decision-

making (Tversky and Kahneman, 1974). This definition highlights the role of heuristics as a tradeoff

between accuracy and effort (Payne et al., 1993; Shah and Oppenheimer, 2008). Thus, a direct implication

is that the use of heuristics may lead to suboptimal outcomes.

Another strand of literature, following Simon (1955), defines heuristics as methods for “finding

satisfactory solutions” (see Rowe, 1987; Papi, 2012, among others). It is important to note that if

satisficing decisions are achieved through improved performance, the adoption of heuristics could also

generate better outcomes and higher utilities. Psychologists are adopting a more comprehensive view of

heuristics. Gigerenzer and Gaissmaier (2011) define heuristics as “a strategy that ignores part of the

information, with the goal of making decisions more quickly, frugally, and/or accurately than more

complex methods”. In this definition, the keywords “quickly” and “frugally” underline heuristics as

mental shortcuts, and the keyword “accurately” emphasizes the possibility that heuristics are performance

enhancing.

In our context of setting loan amounts on a P2P lending platform, if a borrower’s heuristic usage is

related to effort saving, then it should be associated with inferior performance, and reveals the borrower’s

cognitive limitations. However, if the heuristic is used to improve the performance (e.g., increasing

funding success rate) to a satisfactory level, then heuristic usage should predict superior outcomes.

Electronic copy available at: https://ssrn.com/abstract=3575390

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