Learning in the Limit:

Income Inference from Credit Extensions

Xiao Yin∗

Jan, 2024

Abstract

Increases in credit limits raise consumption signifcantly, even for consumers who

are not borrowing-constrained. Combining a randomized controlled trial with

administrative and survey data, I show that credit limit extensions signifcantly

increase consumers’ expectations about future income. The increase in income

expectations is due to beliefs about higher future labor productivity instead of

planned increases in labor supply. Controlling for changes in consumer expectations

regarding future income, the response of consumption to credit limit extensions is

weakened by 37%.

Keywords: Consumption, MPC, MPB, Field Experiments, Income Expectations.

JEL codes: D14, D15, D91, E21, E51, G21.

∗Yin: University College London, xiao.yin@ucl.ac.uk. I deeply appreciate the valuable comments

from Ulrike Malmendier, Yuriy Gorodnichenko, David Sraer, and Michael Weber. I also appreciate the

valuable comments from Deniz Aydin, Matteo Benetton, Markus Brunnermeier, Stefano DellaVigna,

Rawley Heimer (discussant), Amir Kermani, Chen Lian, Peter Maxted, Maarten Meeuwis (discussant),

Emi Nakamura, and Annette Vissing-Jørgensen. I am thankful for the valuable comments from various

seminars and conferences.
I Introduction

Credit limit plays a crucial role in household consumption savings decisions, underpinning

the extent to which consumers can borrow to smooth consumption. Empirical evidence

shows a substantial average spending response to credit limit changes. Meanwhile, even

for consumers who are far from being borrowing-constrained, extensions of the credit limit

still induce non-trivial amounts of increases in total consumption1. This is contrary to

predictions by the standard bufer-stock model, which posits that credit limit variations

should not signifcantly impact overall spending for consumers who are not liquidityconstrained. This raises questions about the mechanisms at the micro-level through which

credit limit extensions infuence consumer spending.

Standard estimation of the spending responses to borrowing limit extensions relies

on arguably random variations in credit limits. An implicit assumption in these settings

is that consumers in the feld also treat credit supply events as random. However, banks’

credit extension decisions are rarely random and are usually a function of the economic

conditions and consumer characteristics. An intriguing question is how consumers think

about banks’ credit supply decisions. That is, do consumers always treat credit supply, in

the form of extended credit limits, as random shocks only to their borrowing constraints,

or do they believe credit supply is an endogenous outcome that contains information the

consumers are not fully informed about? Motivated by this question, this paper studies

the efects of credit extensions on consumption by afecting expectations.

Studying how credit supply afects consumer beliefs is challenging, as one needs to

identify belief changes around feld credit supply events. To cope with this difculty,

this study involves a collaboration with a large commercial bank in China, focusing

on how consumers modify their expectations in response to credit expansions. The

methodology combines a randomized controlled trial (RCT) with administrative and

survey data. In this setup, the bank had initially planned to increase the credit card

limits of 17,000 customers, following its usual internal underwriting process. However,

for experimental purposes, the limit increases were delayed by 12 months for a randomly

1See Gross and Souleles (2002), Agarwal et al. (2017), D’Acunto et al. (2020), and Aydin (2022) for

some examples.

1
selected control group. The remaining customers (the treated group) received the planned

credit limit increase. Given that the increases in credit supply are based on the bank’s

usual underwriting process, the setting gives a nice opportunity to identify the efects of

limit extensions in the feld.

To isolate the possible belief channel in credit supply, I use random information

treatment that varies the degree of inferencing from limit extensions. The basic idea is

that, to the extreme, if the consumers know that the credit supply decision is purely

random, then they should not infer anything from it. To accomplish this, I separate those

in the treatment group into two subgroups: T1 and T2. While for both T1 and T2,

participants received a notice about the increase in their credit limit (Figure 1), as the

bank customers would normally receive for such events, for T2, participants were also

shown the following fact about the design of the study at receiving the limit-increase

notice:

The increase in credit limit is based on a limit-increase event. In this event, among a portion

of customers with a good credit score, we randomly selected a group of users, including

yourself, and increased their credit limits.

The information treatment informs that the limit increase is sent to a randomly selected

group of customers, conditional on having a good credit score. It seeks to weaken, if

any, how much consumers infer information from credit supply decisions. If there is no

belief channel in credit supply, consumption responses should be statistically indiferent

between T1 and T2.

I begin the analysis by studying responses of unsecured debt and spending to limit

extensions. I fnd a large consumption response to limit extension. Specifcally, for each

CNY higher credit limit, consumers in T1 increase spending by 0.37 CNY and accumulate

0.15 CNY more unsecured debt over six months. These numbers are respectively close to

the estimated marginal propensity to consume out of limit change (MPCL) and marginal

propensity to borrow out of limit change (MPB) from the previous literature2. Comparing

the consumption responses between T1 and T2 sheds light on the existence of a belief

channel in credit supply. In particular, I fnd that the consumption responses are about

2For example, estimated MPCL is between 0.2 and 0.6 in Agarwal et al. (2017) over 12 months;

estimated MPB is 0.11 at a 12-month horizon in Gross and Souleles (2002), between 0.08 and 0.3 in

Agarwal et al. (2017), and 0.16 over nine months in Aydin (2022).

2
37% smaller for T2 as compared with T1. Therefore, informing about the randomness in

the credit expansion decision has large negative efects on total consumption, indicating

a non-trivial weight of a belief channel in the consumption responses to credit supply.

To study the efects of limit increase on beliefs, I sent a survey to about 70% of the

participants in all groups within ten days after the experiments. The survey aimed to elicit

the beliefs of the participants’ future perspectives. It mainly asked about expectations

about diferent components of consumer budget constraints (e.g., consumption, saving,

income, delinquency probability, etc.). The results on expectations can be summarized as

1. For T1:

(a) limit extensions signifcantly increase expectations of future consumption and

income conditional on having the same job.

(b) there is no signifcant efect on expectations of future default rate and a

marginally positive efect on expected future savings.

(c) there is no signifcant efect on the number of hours planned to work, but

signifcant negative efects on forecasted unemployment possibility.

(d) there is no signifcant efect on the highest attainable credit limit in the shortrun or long-run.

2. For T2, there is no signifcant efect on any elements.

The fndings of this study are notable in several respects. Firstly, results 1.a and

1.b suggest that after receiving an increased credit limit, consumers anticipate higher

future consumption, which they believe will be fnanced by increased income rather than

by drawing down savings. This challenges the bufer stock model, where an extension

in credit limit is expected to boost total consumption by reducing savings, based on the

mechanism that a higher credit limit enables smoother consumption and lessens the need

for precautionary savings.

However, results 1.a and 1.b do not explain why consumers expect their income to

rise following a credit limit increase. Possible explanations might include increased labor

supply due to enhanced entrepreneurship (Herkenhof et al., 2021), better labor mobility

(Doornik et al., 2021), or reduced fnancial distress (Sergeyev et al., 2023). Result 1.c,

however, dismisses these supply-side explanations by indicating that consumers do not

3
expect to work more hours after a credit limit increase. This rules out the idea that a

relaxed fnancial constraint or reduced fnancial distress leads to an increased labor supply.

Moreover, the expectation of higher future income, conditional on retaining the same job,

negates the hypothesis of improved labor mobility. Instead, the anticipation of lower

unemployment risk and higher future earnings suggests that consumers may interpret

credit expansions as signals of higher labor demand or increased marginal productivity.

The results, therefore, posit an income-inference channel through which credit limit

extensions afect consumption.

I rationalize the results with a simple model, focusing on how consumers infer

information from credit supply. In this model, consumers with variable income and

potential borrowing constraints make consumption decisions. Their income is infuenced

by both idiosyncratic and systematic factors, with the latter varying among consumer

types. A key assumption is that consumers are imperfectly informed about the

impact of the systematic components on their income, possibly due to inattention

to the macroeconomic conditions (Mankiw and Reis, 2002; Reis, 2006; Coibion and

Gorodnichenko, 2012) or not fully understand the economic dynamics (Hansen, 2007;

Collin-Dufresne et al., 2016; Andre et al., 2022). Banks, while not informed of the

idiosyncratic income shocks, have partial insights into systematic shocks. In this

framework, credit supply decisions convey the bankˆa€TMs beliefs about the economy and,

thus, future income trends, which consumers then factor into their expectations.

The model suggests that credit limit supply infuences consumption through two

channels: one is the precautionary channel, which eases the inability to smooth

consumption, and the other is the income-inference channel, which alters beliefs about

future income. It predicts that credit limit increases impact consumption even for

individuals unlikely to reach their borrowing limits, a phenomenon that is inconsistent

with the bufer stock model but documented in prior empirical studies (Agarwal et al.,

2017; Aydin, 2022; D’Acunto et al., 2020). For people with no income volatility, the

model implies that the weight of the income inference channel is zero. Consequently, for

such individuals, changes in income expectations should be negligible, and consumption

responses should be close to zero if they also have substantial liquidity. This prediction

aligns with the empirical fnding that belief changes are insignifcant for those with no

4
income variation before the experiment, and the marginal propensity to consume (MPCL)

is signifcantly positive for those with high liquid savings relative to annual income, yet

becomes insignifcant further conditional on low pre-experiment income volatility.

I further investigate the type of information consumers might be inferring from credit

limit increases. An explanation is that consumers are imperfectly informed about the

macroeconomic movements, either due to inattention to current economic states (Mankiw

and Reis, 2002; Reis, 2006; Coibion and Gorodnichenko, 2012) or possessing a diferent

degree of understanding of the structural parameters that govern macroeconomic trends

(Hansen, 2007; Collin-Dufresne et al., 2016; Andre et al., 2022). On the other hand,

credit supply that moves with the business cycles (Bassett et al., 2014; Fishman et al.,

2020; Weitzner and Howes, 2023), informs the consumers about the underlying or near

future macroeconomic conditions. If consumers are inferring information about the

macroeconomic conditions, they should be more likely to update beliefs about the economy

following credit expansions. In addition, those with a more signifcant change in income

expectations should be those who are less certain about assessing the current economic

performance, or those inclined to believe that macroeconomic shocks signifcantly impact

their income. I fnd evidence supporting this channel. Notably, consumers in T1 also

associate limit extensions with higher economic growth and lower unemployment rates.

At the same time, changes in income expectations are minimal among individuals who

are 1. highly confdent in their evaluation of the macroeconomy, and 2. do not perceive

macroeconomic fuctuations as having a signifcant impact on their income. In sum, the

fndings suggest a mechanism where lending standards vary across the business cycle.

Consumers, imperfectly informed about macroeconomic states, deduce information about

productivity from credit supply decisions, leading to altered income expectations and

subsequent changes in consumption.

The extent to which consumers infer income from credit supply depends on the banks’

decision-making processes. More sophisticated banks may have a deeper understanding of

overall economic conditions, while less sophisticated ones might rely primarily on payment

history. An interesting question is whether Chinese banks difer in their lending practices

compared to others. To explore the applicability of the income-inference channel in

diferent settings, the study concludes with survey results from the United States, collected

5
through online platforms. These surveys assessed responses to randomized hypothetical

scenarios of credit limit increases. The fndings indicate that, in hypothetical situations,

larger credit limit increases are associated with expectations of higher future income

and consumption without changes in savings, default rates, or labor supply. However,

when these increases are perceived as purely random, they do not signifcantly impact

expectations. These outcomes align with the main study’s fndings in the Chinese context,

suggesting that US participants also adjust their income expectations following higher

credit limit increases.

Related Literature This paper mainly contributes to two strands of literature.

First, it contributes to the study of borrowing limits and consumption (Zeldes, 1989;

Ludvigson, 1999; Gross and Souleles, 2002; Agarwal et al., 2017; Guerrieri and Lorenzoni,

2017; Chava et al., 2020; D’Acunto et al., 2020; Gross et al., 2020; Aydin, 2022). Recent

major progress is Aydin (2022), which provides a clean empirical estimation of the

marginal propensity to borrow using an RCT in Turkey. Although previous literature

mainly relies on the bufer-stock model to explain how credit limits afect consumption,

the efect of credit expansions on consumer spending through changing beliefs is still an

open question. The lack of evidence lies in the difculties of combining an RCT with both

observational and expectation data. The paper combines feld credit supply events with

survey data to provide a complete picture of how consumers change their beliefs about

credit limit extension. The fndings facilitate direct testing of the efects of credit supply

on consumers’ beliefs. It also helps provide new insights into macroeconomic models

incorporating credit supply shocks.

In addition, this paper contributes to a growing literature that focuses on the role of

beliefs in explaining consumers’ spending-saving decisions3. For example, Ameriks et al.

(2016), Ameriks et al. (2020), and Ameriks et al. (2020) provide recent advances by linking

survey evidence to retirement choices. Manski (2004), Ameriks et al. (2020), and Giglio

et al. (2021) study the relationship between investor beliefs and stock investment. Bucks

and Pence (2008), Bailey et al. (2019), and Kuchler et al. (2022) analyze how beliefs afect

mortgage-leverage choices. A related study is Soman and Cheema (2002), who show that

participants’ reported MPCL is larger when credit-limit assignments accurately refect

3See DellaVigna (2009) and Benjamin (2019) for a review.

6
future earning potential. This paper builds on this literature by exploring a quantitative

survey matched to administrative and transaction-level data to explore consumer spending

and borrowing decisions.

II Conceptual Framework

A. Setup

In this section, I lay out a simple model to illustrate the main channels through which

consumers change their spending after a credit constraint shock. The model spans three

periods and consists of k types of consumers indexed by i. There are Nk consumers in

each type k. Consumer i’s utility in t has the form

b

C2 u(Ci,t) = Ci,t − i,t 2

where Ci,t is consumer i’s consumption in period t. i is endowed with an initial asset Ai,0

and receive income Yi,t at the beginning of each period. The budget constraints in the

three periods are, respectively

Ai,t = Ai,t−1 + Yi,t − Ci,t

where Ai,t is the total savings at the end of t. In this simple model, the discount factor

and interest rate are both set to zero. At the beginning of period 3, Yi,3 is realized. The

game ends afterwards, and consumer i consumes everything and ends the game with zero

saving, i.e. Ai,3 = 0. Besides, consumer i faces a borrowing limit Li such that

Ai,t ≥ −Li.

Income is stochastic and follows

∆Yi,t+1 = αi,t + ρkXt+1,

X e t+1 = ρXXt.

7
αi,t ∼ N (αi, σα

2 ) is the component of income for which the mean is only known to i.

Xt+1 captures the systematic shocks to income (e.g. macroeconomic shocks to growth,

productivity, or infation, etc.). Xet = Xt+εX,t, and εX,t is an innovation to the systematic

factor. Each type k consumers have a diferent level of exposure ρk to the shock. The

income process can be written as

∆Yi,t+1 = αi,t + ρkXXet.

The key information friction is that consumers have noisy perceptions about the

contribution of current systematic shocks on future income growth. That is, the consumers

are imperfectly informed about ρkXXet. There are two possibilities. First, consumers are

imperfectly informed about Xet because of inattention to current information (Mankiw and

Reis, 2002; Reis, 2006; Coibion and Gorodnichenko, 2012). Alternatively, consumers could

be uncertain about ρkX due to lacking the knowledge about the structural parameters

governing the dynamics of the model (Hansen, 2007; Collin-Dufresne et al., 2016). For

simplicity, I do not diferentiate between these two cases. Instead, let

∆Yi,t+1 = αi,t + ρei,t.

where ρei,t = ρkXXet is the contribution of current economic states on consumers’ future

�  income. Consumers have a prior of ρei,t that follows N ρ0

0 e . i,t, σ2

B. Supply of Credit Limits

There is a monopolistic bank that decides on a level of borrowing limit Li at the beginning

of t1, before the consumers’ optimal decisions. For simplicity, let the bank be fully

attentive to Xet. The bank observes ρei,t with a diferent precision. This could be that

the bank is less inattentive to the current economic states or that the bank can estimate

ρkX with the regression

∆Yi,t = α + ρkXXet−1 + εi,t.

In this case, assuming εi,t ∼ N(0, σ2), then the bank’s estimate of ρkX, ρB follows ε kX,

= σ2 2 2 ρ N(ρ B e kX, σρ

2), where σ2 ε /(Nks ) and sX is the sample variance of Xt. Let ei,t = ρ ρ X kX

B Xt

8
be the bank’s estimates of the systematic component in i’s income. Then, from the bank’s

perspective, ρeB ∼ N(ρei,t, σe2), where σe2 = σ2Xt

2. i,t ρ ρ ρ

Note that ρkX = ρkρX. It is also possible that the consumers and the bank only

difer in estimating ρX. A reason is that households and professionals have heterogeneous

reasonings about how macroeconomic shocks would afect the future economy, which is

consistent with recent fndings in Andre et al. (2022).

After estimating ρeB

i,t, the bank sets Li following the rule

ρB Li = f(ei,t, θi), (1)

where θi captures other characteristics that afect the credit supply decisions. I assume

that Li is monotonic in ρeB

i,t.

C. Learning from Credit Limit Changes

After receiving the credit limit Li, consumer i infers the future income change as perceived

by the bank via Bayesian learning. First, the consumers form the subjective beliefs of ρei,t

B

as

ρB Ec[ei,t] = f −1

(Li) ≡ g(Li).

With rational learning, consumers correctly infer the functional form of f, and Ec[ρeB

i,t] =

ρeB That is to say, rational learning indicates that the bank cannot change Li to over- i,t.

signal its beliefs.

With the supplied credit limit Li, the posterior of consumer i’s belief about future

income growth has the expected value of

ρbi,t = ρe0

i,t − κi[g(Li) − ρe0i,t], (2)

where κi = σ0

2/(σ02 + σeρ2) is the Kalman gain of the learning process.

Note that Bayesian learning does not require that the bank has better predictability

of ρei,t. As long as the bank’s signal precision is not 0, and individuals are not perfectly

informed about ρei,t, credit supply that incorporates the bank’s beliefs also changes

consumers’ beliefs.

9
	

In addition, whether g′ is positive or negative is ambiguous and depends on the bank’s

objectives. When g′ > 0, credit limits increase with the bank’s belief about consumer

future income. If the efects of negative shocks to income on default rate is low, then g′

could be negative, as a lower income increases interest income from taking more debt.

For simplicity, the model is loose on how credit limit is afected by bank beliefs about

income growth. Instead, under the assumption of rational learning, consumers are correct

in guessing the function form of g(Li). (3) implies the following proposition:

Proposition 1: Suppose g′ >0, a higher credit limit increases posterior income

expectations, and the change is larger when consumers have a higher signal-to-noise

ratio, κi.

D. Optimality Condition

Given a three-period setup and quadratic utility, the solution of the model is standard.

Consumer i’s optimal decision can be determined using backward induction. In period 3,

consumer i consumes everything available. Optimal consumption in periods 2 and 1 can

be written as

  Ai,1 + Yi,2 + Ei,2[Yi,3] C∗ = min , Ai,1 + Yi,2 + Li , i,2 2

 Ci,

∗

1 = min Ei,1[Ci,

∗

2], Ai,0 + Yi,1 + Li .

Suppose consumer i’s t1 consumption isn’t binding; then the consumption rule in period

1 is the classic Hall (1978)’s martingale. When the borrowing limit is binding, consumer

i consumes all resources available.

E. Marginal Propensity to Consume out of Liquidity

Borrowing the language from Gross and Souleles (2002), I analyze consumer i’s MPCL

as the efects of a one-unit increase in Li on Ci,

∗

1. When borrowing is currently binding

before and after the credit shock, MPCL equals one. Extensive literature documents that

MPCL is large even if the borrowing limit is slack. To analyze the MPCL for fnancially

10
unconstrained consumers, consider the case when

Ci,

∗

1 = Ei,1[Ci,

∗

2]. (3)

For brevity, I assume ρ ̃i,3 is zero. Given that future income is normal. The probability

that consumption in the second period does not bind is

    Ai,1 + Yi,2 + Yi,3 2Li + Ai,1 − αi Pi,2(not binding) = P < Ai,1 + Yi,2 + Li = Φ (4) 2 σα

where Φ(·) is the standard normal CDF. From (5), the probability of a slack borrowing

limit is larger if the saving is higher, the credit limit is larger, the income growth from

period two to three is smaller, or the income volatility is smaller.

Combining (4) and (5) yields

Ci,

∗

1 = Cei,2 − (1 − Φ)(Cei,2 − Cei,2) (5)

where Cei,2 = (Ai,1+E1[Yi,2]+E1[Yi,3])/2 is the optimal level of t2 consumption when there

is no borrowing limit, and Cei,2 = Ai,1 + E1[Yi,2] + Li is the highest level of t2 consumption

when borrowing limit binds in t2.

The MPCL for currently unconstrained consumers is then derived by total

diferentiating Ci,

∗

1 with respect to Li, which yields

  ∂Ci,

∗

1 1  ̃  ̄  2φ 1 = Ci,2 − Ci,2 + (1 − Φ) + Kg′

(Li) , (6) ∂Li ω σα ω | {z } | {z }

income−inference precautionary

where ω =  ̄ 1 + 1/2 + (1 − Φ)/2 + (C ̃i,2 − Ci,2)φ/σα is a number that is larger than one.

As shown from (6), there are two channels through which credit expansion afects current

consumption for unconstrained consumers. The frst bracket captures the conventional

precautionary channel. Through this channel, an increase in credit limit increases current

consumption by both reducing the probability of a binding constraint and increasing the

debt capacity in the future. In addition, an income-inference channel is captured by the

second term on the right-hand side of (6). Suppose g′ > 0; the bank would ofer more

11
credit limits if the bank perceives a higher income in the future. Then, a one-unit increase

in credit limit signals to consumer i that the bank believes that consumer i’s income will

grow by g′ units. The marginal efect of the signal on consumer i’s income expectation is

g′

. (6) suggests the following proposition:

Proposition 2: Suppose credit expansion from the bank signals higher future income

growth to the consumers. The unconditional level of MPCL is smaller than that when

controlling for the efects of credit expansion on income expectations.

III Methodology

A. Data and Institutional Environment

The data for this study is sourced from a large national commercial bank in China and

is one of the country’s top ten banks in terms of total assets. In 2023, the bank reported

assets exceeding $1 trillion, serving over 50 million active customers and managing 80

million active credit cards. This extensive customer base ensures that the sample is

representative of the diverse demographic distribution of consumers in China.

For daily transactions, most people in China use Alipay or Weixin Pay as payment

methods. Using such payment tools requires the users to link their accounts with bank

cards or credit cards, similar to using PayPal and Apple Pay in the US. The credit cards

considered in this study are very similar to those in other countries. In general, each credit

card is assigned a credit limit, and consumers can accumulate balances smaller than this

limit every month and use the card as a payment method. Consumers earn diferent

levels of discounts and cashback for purchasing certain types of goods or services. At the

end of each billing cycle, a minimum repayment is required (usually 10% of the current

outstanding balance). Above this amount, consumers can choose to repay any proportion

of the current outstanding balance. Consumers who repay all accumulated balances do not

incur any interest costs and enjoy the rewards from cashback and transaction discounts.

For the unpaid amounts, the debt is carried over to the next billing cycle with a daily

interest rate of fve basis points.

Credit card use in China has grown signifcantly since 2016. From 2016 to 2022, the

total outstanding balance from credit cards in China has grown from 3.6 trillion CNY

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to 8.7 trillion CNY. During the same time, the total credit limits has increased from 9.1

trillion CNY to 22.3 trillion CNY. Credit cards and other personal credit from commercial

banks in China remain the most used method for consumption-based unsecured debt.

Similar products from FinTech platforms and consumption debt companies, including

Alibaba’s Huabei, have been gaining market share recently. However, the total market

share from these companies is still relatively small, taking around 20% of all consumptionbased credit debt in 2023.4

B. Measuring Income, Debt, and Spending

I follow the steps the bank uses to classify income. Specifcally, individual income is

classifed based on regular infows. The bank classifes income into two main categories:

salary and business cash fows. Salary is defned as the periodical monthly infows of

income, bonuses, and commissions if the consumer declares that they work as an employee.

The bank calculates this number in one of two ways. First, if income is paid through direct

deposit to this bank, then the number is directly labeled as salary. Otherwise, the bank

can identify monthly income if the consumer’s social security insurance is paid through

this bank, which is usually a fxed portion of the consumer’s income5. As for income from

business operations, the measure is the diference between total infow and total outfow

when these transactions are categorized as business operations. This category is usually

the main source of income for self-employed individuals, given the requirements of income

information for the analysis. I restrict the sample to those whose income information is

observed at the bank. This restriction drops the sample by around 35%.

When all the incomes in our sample are aggregated, the split of the two components

comes out to be 70.16% from salary and 29.84% from business operations. To verify

that these fgures are accurately computed at the individual level, I match the income

computed at the consumer-year level from the bank to the individual-level data from the

4See here and here for the sources.

5In China, social security payments have six components: fve types of insurance and a housing

provident fund. The types of insurance are paid with a fxed proportion of workers’ monthly income.

One such insurance is retirement savings insurance, which is like the retirement savings plan in other

countries. The monthly contribution is 8% of income. However, the income base is usually capped at the

two tails of the income distribution. The numbers difer for diferent geographic areas. The uncapped

distribution is wide enough to cover most of the workers in China. In the analysis, I remove the consumers

in the capped region. This only causes an around 7% drop of the sample.

13
administrative government agency6. The results of this comparison are shown in Panel B

of Figure B.1. in the Online Appendix. The results show a very high relationship between

the income from the bank and that from the administrative agency. Fitting a regression

between the two yields an R2 of 0.80.

Debt data is from the Credit Reference Center of the People’s Bank of China (the

ofcial credit registry), based on the credit reports retrieved by the bank. The Credit

Reference Center aggregates personal credit information from all fnancial institutions.

Therefore, studies of debt behavior are expected to capture the overall borrowing outlook

of the consumers.

The main analysis is based on interest-incurring debt due to complete coverage. In

addition, I calculate total spending as the sum of all purchasing transactions in a given

period. There are advantages and drawbacks of this measure. First, since the data is

from a single provider, it has issues covering all spending histories of the participants.

However, testing the bufer-stock model necessitates spending data. In particular, the

bufer-stock model suggests that the consumption response to limit increases for highliquidity consumers is also positive, but debt needs are, in general, close to zero for

these individuals. In this case, testing the mechanisms of how limit extensions afect

consumption requires a focus on the spending patterns of high-liquidity consumers.

To eliminate the sample-coverage problems associated with using data from one

fnancial institution, I leverage the fndings that many consumers only use one bank

for daily transactions7, and focus on consumers who use this bank as their main source

of transactions. I select this sample based on two criteria. The frst criterion depends

on the sample. For Sample I which did not receive the survey, the frst criterion is that

the total credit card purchasing volume from the bank accounts for over 95% of total

credit card purchasing volume from all fnancial institutions both before and after the

experiment. For Sample II which received the survey, participants are asked the following

survey question

How many banks do you usually use for transaction purposes?

6Data from the administrative government agency is only available for 37% of the participants who

agreed to share the data with the bank.

7Nelson (2022) shows that, depending on their FICO scores, at least 80% to over 90% of the consumers

in the US hold only one primary credit card account.

14
The frst flter is that the participants answered one to this question. Following Ganong

and Noel (2019), the second flter is that there are at least 15 spending transactions on

average each month over the 12 months before the surveys. The two flters ensure that

the consumers use only one bank for transaction purposes, and this bank is the one the

participants are referring to.

I verify the efectiveness of the selected samples with two tests. First, I also elicit

total past consumption with the following question

What was the total amount of your spending during the past 12 months (excluding

investment and purchases of durable goods including housing, cars, etc.)?

I then compare this number with the total spending amount based on summing up all

purchasing transactions for the selected sample. Panel C of Figure B.1 in the online

appendix shows the binned scatter plots of the two. A regression between the two yields

an intercept of zero, a slope of 0.98, and an R2 of 0.58. This indicates a very high

correlation between the two measures, especially when the survey measure of consumption

is, in general, very noisy.

The second test is to study the changes in cross-bank transfers before and after the

experiment. If the participants start to use this bank more after the experiment, I should

see a positive change in the net infow transfer for the treatment groups. Table B.4 in the

online appendix shows that the changes in transfer for the treatment groups, focusing on

the selected samples, are insignifcantly from zero, indicating that changes in consumption

are unlikely results of changes in the banks the participants choose to use for transactions.

C. Experimental Design

Figure 1 describes the procedure. There are four steps in the procedure. Specifcally,

1. Sample construction: From Jun 19 to Jun 23, the bank selected a group of

consumers (around 50000 from 57 cities) and decided to increase their credit limits.

The amounts of increase were based on the bank’s credit-scoring rules. Then 17000

individuals were selected as the subjects in this study. The selected individuals were

then grouped into two subsamples. In each subsample, subjects were assigned to

15
Figure 1. Timeline of the Experiments

This fgure gives the timeline of the two experiments. Sub-fgure A is for the pilot study, which spans from

May 2019 to June 2019. Sub-fgure B is for the main study, which spans from March 2020 to October 2020.

either one of a control group, treatment group 1 (T1), and treatment group 2 (T2).

The numbers of subjects in each group are shown in the table in Figure 1.

2. Treatment: On Jul 03, credit limits were changed to the pre-determined level

for participants in the two treatment groups. Treated participants were sent a

text message about such changes. At the same time, participants in T2 were also

informed that the changes were based on a research project. The additional disclosed

information was

16
The increase in credit limit is based on a limit-increase event. In this event, among a

portion of customers with a good credit record, we randomly selected some users, including

yourself, and increased their credit limits.

3. Post-experiment survey: On Jul 03, after the treatment notice, participants in

sample II were invited to fll out a survey8 through text messages. The survey had

to be completed before Jul 12. A reminder text about flling out the surveys was

sent on Jul 10.

4. Limit changes to control: the new credit limits for the control group as

determined in step 1 are expected to be pushed on Jul 03 2024.

Mapped to (6), the treatment efect on T1 estimates the total efects of the credit limit

on consumption. The information treatment to T2 seeks to exogenously vary g′

(Li). T1

and T2, therefore, enable the decomposition of the two channels in (6).

1. demand efects and selective responding

The use of surveys helps study consumer beliefs around credit supply. However, survey

collections could come with potential problems. For example, receiving the survey might

induce the participants to respond or behave diferently based on the anticipation of the

survey senders’ intention (survey demand efects). In addition, since taking the survey is

time-consuming, the response rate is always less than perfect. If the decision to respond

to the survey systematically varies with participants’ characteristics, treatment efects

will sufer from selection biases.

Several features of the survey design aim to eliminate potential confounding efects

from flling out the surveys. For example, since the survey is sent through the bank,

participants might want to use the survey answers to signal better creditworthiness. To

prevent the participants from developing such strategic motives, the survey starts by

showing the participants

8Section A in the online appendix shows the survey in English.

17
This study is in collaboration with [the author], an Assistant Professor in Economics [...].

The data will only be analyzed by [the author] for scientifc research purposes and will not

be evaluated by this bank. We will not disclose participants’ personal information in any

respect. We will not, to any extent, change the types of fnancial products we provide,

including credit scores, credit limits, deposit and borrowing interesting rates, etc., based on

the participants’ personal answers. Please answer the survey based on your true thoughts.

This explicit framing, especially the disclosure that the data would not be analyzed by

the bank, was designed to minimize the possibility that consumers provide answers that

depart from their true beliefs in the hope of obtaining better services from the bank. I

further check this concern by focusing on consumers whose borrowing relationship are with

other banks both before and after the experiments in Section 4.C. Since these consumers

do not borrow from this bank, they are expected to have less incentive to cater to the

bank in the sample.

Another concern is the loss of sample representativeness due to selectively responding

to the survey. To exclude this problem, the survey design tried to minimize the time to

complete with a very large compensation. In total, participants have to take 15 questions.

In addition, there are six questions that are sent to a random 30% of the participants.

The average time to complete the survey was around 6 minutes, and the compensation

was 15 CNY. This is equivalent to an hourly rate of around 150 CNY, which is higher

than the 95th income percentile of all urban residents in China.

In the end, the survey response rate is around 67%. This is a very high number

compared with previous literature. The high response rate is due to the high reward

associated with completing the survey. However, due to imperfect response rates,

samples with and without surveys difer in some dimensions. Section 3.D. compares

the distribution of the surveyed sample and the unsurveyed sample. In general, there are

more males completing the surveys. Those who complete the survey are more likely to

be younger, less educated, earn less, and less wealthy. However, the diferences are not

especially large between the two samples.

2. sanity checks of survey answers

To check the quality of the surveys, I compare the survey answers about past income with

the information from the bank’s database. Panel A of Figure B.1 from the Appendix

18
presents the binned scatter plot of consumers’ average monthly incomes over the 12 months

before the experiment from the survey and that from the bank’s database. The plot shows

a clear linear relationship. A regression between the two measures gives an R2 of 0.74.

This fnding indicates the high quality of the survey.

3. external validity of the experiment

Since the experiment is based on the bank’s usual internal underwriting process, the

selected consumers might be systematically diferent from the average Chinese consumer.

This is because credit supply usually targets those whom the banks perceive as having

more needs for credit. A potentially selective sample casts doubt on the external validity

of the experiment.

To assess the representativeness of the sample, I compare the demographics between

the sample and a 3% random sample for the bank database covering all customers. Since

the bank is one of the largest banks in China, its customer base should be representative of

the overall Chinese urban residents. Table B.1 presents the results, as expected, in general,

the participants in the sample have fewer spending, income, saving, and credit limits, and

more debt. That is, the participants in the experiments seem to have a larger need for

more credit. However, the diferences are not excessively large. For all characteristics, the

diferences are below 15%. Therefore, the sample is broadly representative of the whole

Chinese urban population.

D. Summary Statistics

Table 1 gives the summary statistics based on pre-experiment characteristics. Panel A

summarizes those in Sample I, and Panel B summarizes those in Sample II. Sub-panels

1, 2, and 3 respectively describe the control group, T1, and T2. For the sample without

surveys, the average age of the participants is around 39 years old, and around 50%

are female. Over half of the participants have college degrees. The average outstanding

interest-incurring debt is about 7.5 thousand CNY, and around 17.5 CNY if conditional

on holding a positive amount of debt. A simple calculation indicates around 43% of

the participants hold positive unsecured debt. This proportion is at the lower bound

19
TABLE 1. Summary Statistics

This table gives the summary statistics of the sample. Panel A is based on the sample without surveys

(sample I), and panel B is based on the sample with the surveys (sample II). The units of the variables

excluding Age, Female, and College are in thousands of CNY. The column Dif gives the diferences in

the average values between the given group and the control group. t-stats are the associated t-statistics,

testing the signifcance of the diferences in the means. All variables are winsorized at 1% level.

Mean SD N Mean SD Dif t-stats N Mean SD Dif t-stats N

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)

Panel A: Sample I – Without Survey

Panel A1: Control Panel A2: T1 Panel A3: T2

Age 38.82 9.85 2050 38.71 9.49 -0.11 -0.38 2331 38.81 9.91 -0.01 -0.01 1119

Female 0.50 0.50 2050 0.50 0.50 0.00 0.18 2331 0.50 0.50 -0.01 -0.32 1119

College 0.56 0.50 2050 0.55 0.50 -0.02 -1.20 2331 0.54 0.50 -0.02 -1.01 1119

Income 10.46 8.41 2050 10.18 7.19 -0.04 -1.17 2331 10.66 8.20 0.21 0.70 1119

Saving 168.13 214.53 2050 171.39 184.64 0.53 0.31 2331 172.42 208.51 4.29 0.57 1119

Debt 7.34 13.48 2050 7.25 9.83 -0.01 -0.24 2331 7.91 14.45 0.57 1.24 1119

Debt|Debt>0 17.69 15.95 851 16.86 7.90 -0.13 -1.33 1003 18.03 17.14 0.34 0.44 491

Limit 87.29 99.45 2050 85.99 103.65 -0.20 -0.41 2331 89.39 117.43 2.10 0.54 1119

∆ Limit 11.93 8.75 2050 11.62 7.73 -0.05 -1.25 2331 12.02 9.02 0.09 0.27 1119

Panel B: Sample II – With Survey

Panel B1: Control Panel A2: T1 Panel A3: T2

Age 37.91 10.25 1588 37.62 9.50 -0.29 -0.74 1875 37.83 9.75 -0.08 -0.16 1097

Female 0.43 0.50 1588 0.41 0.49 -0.02 -1.01 1875 0.42 0.49 -0.01 -0.52 1097

College 0.46 0.50 1588 0.47 0.50 0.02 0.92 1875 0.47 0.50 0.01 0.52 1097

Income 9.69 8.74 1588 9.48 6.99 -0.21 -0.65 1875 9.83 8.65 0.15 0.35 1097

Saving 139.05 149.84 1588 139.91 138.71 0.86 0.15 1875 146.14 139.33 7.09 0.97 1097

Debt 7.40 13.37 1588 7.01 10.10 -0.39 -0.79 1875 7.07 13.40 -0.33 -0.54 1097

Debt|Debt>0 16.54 15.76 711 16.99 8.81 0.45 0.54 774 16.39 16.25 -0.15 -0.15 473

Limit 23.25 27.19 1588 22.33 26.53 -0.92 -0.81 1875 24.18 31.89 0.94 0.65 1097

∆ Limit 12.01 9.09 1588 11.73 8.20 -0.29 -0.82 1875 12.40 8.94 0.39 0.87 1097

Survey

Spending 7.77 13.57 1588 7.94 12.92 0.17 0.32 1875 8.09 11.09 0.32 0.48 1097

Income 9.61 9.60 1588 9.54 7.75 -0.07 -0.19 1875 9.95 10.88 0.34 0.73 1097

Liquid Wealth 155.59 266.48 1588 150.71 188.84 -4.88 -0.53 1875 154.00 233.84 -1.59 -0.14 1097

Total Wealth 431.39 900.12 1588 426.85 678.23 -4.54 -0.14 1875 443.92 725.35 12.53 0.31 1097

of the range of 40% to 80% found in the previous literature using US data (Gross and

Souleles, 2002; Zinman, 2009; Fulford, 2015). The average increase in credit limit is

around 11.8 thousand CNY. This magnitude is economically signifcant. It is around

14% of the pre-experiment average total credit limit and around 10% of the average

pre-experiment annual income. Columns (7) and (12) give the t-statistics testing the

diferences between the control and treatment groups. All samples are quite balanced, with

no statistical diferences among any of the dimensions. This indicates the efectiveness of

the randomization.

20
Figure 2. Evolution of Debt and Spending - Unsurveyed Sample

This fgure plots the evolution of total non-durable debt and spending on both sides of the experimental

period for Sample I. In each panel, the x-axis gives the months in 2023. The solid red line shows the

evolution of T1, the blue dashed line shows the evolution of T2, and the gray dotted line shows the

evolution of the control group. The gray vertical line gives the time of the treatment. All lines are

vertically shifted so that the value for the control group at the treatment time is 0.

A: Non-durable Debt B: Spending

IV Results

A. Consumption Responses to Limit Extensions

I frst present results about the consumption dynamics around the experiment. The

analysis only focuses on Sample I, to which surveys are not sent. As guided by Proposition

2, suppose credit limit afects consumption only through the precautionary motive, as

usually suggested in the bufer stock model, then one should expect similar spending

dynamics for both treatment groups because the realized changes in credit limits are

statistically indiferent between the two groups. However, if the supply of credit limits

afects consumer beliefs, then the consumption response for those in treatment group 2,

after informing about the randomness in the supply decisions, should be diferent.

Figure 2 plots the evolution of the changes in unsecured debt and total spending

around the experiment. I scale the changes around the experiment by the pre-determined

limit changes. So, the magnitudes give an interpretation in terms of marginal propensity.

The x-axis is the months in 2023. In both plots, the solid red line and the dashed blue line

represent T1 and T2, and the dotted gray line represents the control group. The shaded

regions are two times the standard errors. Both debt and spending are residualized by

21
TABLE 2. The Efects of Limit Increase on Debt and Spending

This table assesses the efects of credit extension on non-durable debt and spending. Panel A is the

three-month changes and panel B is the six-month changes. T1 and T2 are respectively the two treatment

group identifers. Coefcients are divided by the pre-determined average increase in credit limit to give

an interpretation of marginal propensity. In each column, Diference is the diference in the estimates

between T1 and T2. Controls include gender, province fxed efects, industry fxed efects, a dummy

variable labeling if the participants are younger than 38, and a dummy variable for having at least a

college degree. All variables are winsorized at the 1% level.

Panel A: 3 Months Panel B: 6 Months

∆B ∆B ∆C ∆C ∆B ∆B ∆C ∆C

(1) (2) (3) (4) (5) (6) (7) (8)

T1 0.088*** 0.086*** 0.201*** 0.197*** 0.157*** 0.152*** 0.374*** 0.367***

(0.007) (0.009) (0.028) (0.033) (0.012) (0.015) (0.042) (0.050)

T2 0.059*** 0.055*** 0.126*** 0.124*** 0.104*** 0.100*** 0.240*** 0.232***

(0.007) (0.008) (0.034) (0.034) (0.012) (0.013) (0.044) (0.044)

Diference 0.029*** 0.031*** 0.074** 0.073** 0.054*** 0.052*** 0.135*** 0.134**

(0.007) (0.011) (0.031) (0.035) (0.014) (0.018) (0.051) (0.058)

Controls No Yes No Yes No Yes No Yes

N 5500 5500 2221 2221 5500 5500 2221 2221

Standard errors clustered at city level in parentheses

* p <0.10 ** p <0.05 *** p <0.01

month-fxed efects. As shown, the sharp increase in spending right after the experiment

for the two treatment groups indicates the efectiveness of the experiment. Besides, the

spending response of T2 is signifcantly smaller than that in T1. A divergence in the

evolution of debt and spending between T1 and T2 indicates changes in credit limit afect

factors other than instant borrowing capacity.

I continue to study the average treatment efects (ATE) of credit limits on spending.

Table 2 gives the intent-to-treat (ITT) estimates of the experiment. I scale the estimates

by the average changes in credit limit in the sample. In this case, the numbers in Table

2 have the interpretation of MPB and MPCL. That is, average changes in borrowing

and spending for each CNY higher credit limit. Panels A and B, respectively, give the

3-month and 6-month responses. As shown, each CNY higher credit limit increases the

borrowing of T1 by 8.6 cents over three months and 15.2 cents over six months. At the

same time, each CNY higher credit limit increases the spending of T1 by 19.7 cents over

three months and 36.7 cents over six months. These estimates are close to the documented

MPB out of credit limit and MPCL in the previous literature (Gross and Souleles, 2002;

Agarwal et al., 2017; Aydin, 2022), which is usually in the range of $0.09 to $0.20 for

22
MPB and 0.2 to 0.6 for MPCL (Agarwal et al., 2017). The spending responses are much

larger than the debt responses. This is consistent with both the bufer-stock model and

credit limit changing beliefs. For example, in the bufer-stock model, even for consumers

with high liquidity, a larger credit limit reduces the precautionary motive and increases

consumption by reducing total savings.

For comparison, each CNY higher credit limit increases the borrowing of T2 by 5.5

cents over three months and 10 cents over six months. At the same time, each CNY

higher credit limit increases the spending of T2 by 12.4 cents over three months and 23.2

cents over six months. These diferences are signifcantly diferent from zero, indicating

that there is a belief channel that afects spending responses to limit changes.

B. Expectation Responses to Limit Changes

Informing that the credit supply decision involves randomization reduces consumption

responses to limit extensions by more than one-third. This indicates that credit

supply afects consumption decisions in addition to relaxing the instantaneous borrowing

constraints. In this section, I use the survey data from Sample II to dissect the efects

of credit supply on consumer subjective beliefs about various components of their budget

constraints.

Since the survey response rate is not perfect, I frst study the consumption responses

of the surveyed sample to compare the two samples. The evolution of debt and spending

for the surveyed sample is in Figure 3. Consumption responses are generally slightly

larger for the surveyed sample, as these consumers have relatively less liquidity. However,

the diferences are not signifcantly large, with the 6-month responses only around 13%

larger. In addition, the patterns are very similar across the two samples.

The ITT estimates of limit changes on expectations are in Table 3. Similar to the

estimation of MPB and MPCL, I scale all estimates by the average changes in credit

limits. So, the coefcients are in terms of each CNY increase in credit limit. For changes

in wealth and credit limits, the units are in terms of each thousand CNY increase in

credit limit. The results from T1 show that a higher credit limit signifcantly increases

subjective expectations about future consumption and income, and marginally higher

expected liquid saving and lower expected unemployment rate. However, there are no

23
Figure 3. Evolution of Debt and Spending - Surveyed Sample

This fgure plots the evolution of total non-durable debt and spending on both sides of the experimental

period for Sample II. In each panel, the x-axis gives the months in 2023. The solid red line shows the

evolution of T1, the blue dashed line shows the evolution of T2, and the gray dotted line shows the

evolution of the control group. The gray vertical line gives the time of the treatment. All lines are

vertically shifted so that the value for the control group at the treatment time is 0. The analysis is based

on the sample of participants to whom questions 16 to 21 are not sent.

A: Pilot Study B: Main Study

signifcant changes in subjective labor supply as captured by the number of hours likely

to work. At the same time, future borrowing capacity, as captured by the one-year and

fve-year change in total credit limit or default probability all stays unchanged. As for

T2, when informed about the randomization in credit supply, ex-ante expectations about

consumption, income, saving, and unemployment all become insignifcant.

The results in Table 3 suggest that, in response to a higher credit limit, consumers

believe that they will consume more in the future, consistent with the empirical fndings

in the literature. In addition, the higher consumption is believed to be fnanced by

more income in the future due to either higher marginal productivity of labor or lower

unemployment risk, but not through drawing down savings, increasing default frequency,

or increasing labor supply. Indiferent responses to subjective limit growth suggest

that the information treatment attenuates consumption responses by erasing consumers’

updates about future earnings ability rather than indirectly informing a less persistent

increase in credit supply.

The fndings show that, from the consumer perspective, the reason for more spending

after a higher credit limit is inconsistent with the bufer-stock model. In the bufer24
TABLE 3. The Efects of Limit Increase on Expectation Changes

This table assesses the efects of credit extension on expectations. E[∆C], E[∆Y], and E[∆Hrs] are

respectively the diference between expected total spending, total income, and hours to work every week

over the 12 months after and before the experiment. E[∆L.W] and E[∆T.W] are respectively the diference

between expected liquid wealth and total wealth 12 months after the experiment and right before the

experiment. E[u] and E[p(d)] are the expected unemployment probability and delinquent probability

over the 12 months after the experiment. E[∆L]-1Y and E[∆L]-5Y are the expected growth rate of

one-year and fve-year credit limits. T1 and T2 are respectively the two treatment group identifers.

Coefcients are divided by the pre-determined average increase in credit limit to give an interpretation

of marginal propensity. All variables are winsorized at the 1% level. The analysis is based on the sample

of participants to whom questions 16 to 21 are not sent.

E[∆C]

(1)

E[∆Y]

(2)

E[∆L.W]

(3)

E[∆T.W]

(4)

E[∆Hrs]

(5)

E[u]

(6)

E[p(d)]

(7)

E[∆L]-1Y

(8)

E[∆L]-5Y

(9)

T1 0.277** 0.381*** 0.001* 0.001 0.000 -0.283* -0.064 0.943 0.474

T2

(0.136)

-0.030

(0.080)

0.079

(0.000)

0.000

(0.002)

-0.002

(0.000)

0.000

(0.156)

-0.020

(0.170)

0.133

(9.874)

0.958

(2.042)

0.695

(0.102) (0.100) (0.001) (0.002) (0.000) (0.214) (0.209) (0.707) (3.044)

Controls Yes Yes Yes Yes Yes Yes Yes Yes Yes

N 5125 5125 5125 5125 5125 5125 5125 5125 5125

Standard errors clustered at city level in parentheses

* p <0.10 ** p <0.05 *** p <0.01

stock model, a higher credit limit increases consumption by reducing savings. This is

because a higher credit limit alleviates precautionary motives by increasing the ability to

smooth consumption. However, from Table 3, subjective beliefs about total wealth do

not decrease; rather, they increase marginally. The results, therefore, suggest that the

precautionary motive is unlikely the sole reason for which the supply of credit lines afects

consumption.

In addition, tables 2 and 3 show that increases in credit limits raise consumption

and expectations only about future total income, either through a lower unemployment

rate or higher income conditional on having the same job. Informing the randomness of

the supply decision eliminates the belief changes and reduces consumption responses by

around 37%. Mapped to (5). The results indicate a weight of 37% for the income-inference

channel through which limit extensions afect total consumption.

A concern of sending out surveys through the bank is that consumers might want to

misreport creditworthiness to signal a lower risk type. This is unlikely in this study for two

reasons. First, the disclosure information on the survey explicitly informs the participants

25
Figure 4. Distributions of Belief Changes

This fgures plots the expected changes in consumption (left column) and income (right column) using

the sample receiving the post-experiment surveys (sample II). Panels A and B give the control group;

panels C and D give the treatment group 1; panels E and F give the treatment group 2. The illustration

is based on samples winsorized at 5% level. The analysis is based on the sample of participants to whom

questions 16 to 21 are not sent.

A: E[∆C] - Control B: E[∆Y] - Control

C: E[∆C] - T1 D: E[∆Y] - T1

E: E[∆C] - T2 F: E[∆Y] - T2

26
that the bank will not analyze the data. Second, from Table 3, even though income is

reported to be higher, subjective beliefs about default rates aren’t smaller9. Therefore,

it is improbable that consumers are signaling to have lower risk. An additional test is to

focus on the expectation and debt responses for those whose borrowing relationship is with

other banks. If consumers use the survey to strategically misreport income, then those

who do not use this bank for daily transactions would have less incentive to misreport.

In the online appendix Table B.3, I restrict the sample to consumers who only use credit

cards at other banks both before and after the experiment. Panel A gives the results for

the unsurveyed sample (Sample I), and Panel B focuses on the surveyed sample (Sample

II). The results are close to that using the whole sample. This fnding suggests that

the reported higher income is unlikely a result of strategic misreporting to cater to the

bank. In sum, the results in Table 3 suggest that credit expansions positively change

consumers’ beliefs about labor productivity, increasing consumption through a higher

expected income.

Limit shocks have a large average impact on income expectations. However, behaviors

of inferencing from credit supply should be heterogeneous and largely depend on factors

like ex-ante degrees of income uncertainty. Heterogeneity in belief changes is also

evident from directly exploring the distributions. Figure 4 plots the histograms of

expectation changes separately for the three groups. As shown, for both the control

group and treatment group 2, the changes in beliefs are more symmetric around zero. For

treatment group 1, expectation changes with respect to consumption and income are more

distributed to the positive region. However, the belief changes are not entirely positive,

with around 45% of the participants having a negative or zero change in the belief of future

income after the experiment. At the same time, the impacts are very heterogeneous, with

many people having no belief change. Despite measurement errors from surveys, Figure

4 shows that the large average belief change is due to a large proportion of consumers

having large belief changes, instead of everyone having similar belief changes.

9A possibility is that many consumers who have self-control problems but are sophisticated to be

aware of this problem would conjecture an over-spending behavior, which is followed by a higher default

probability.

27
TABLE 4. The Efects of Limit Increase on Debt and Spending by Income Uncertainties

This table assesses the efects of credit extension on non-durable debt and spending by income

uncertainties. Panels A1 and A2 split the sample by whether pre-experiment income has zero or positive

volatility. Panels B1 and B2 split the sample by whether consumers have the type that has a low or

high cross-sectional income variability. Splits are conditional on deciles of pre-determined limit changes.

Coefcients are divided by the pre-determined average increase in credit limit to give an interpretation

of marginal propensity. All variables are winsorized at the 1% level. The analysis is based on the sample

of participants to whom questions 16 to 21 are not sent.

∆B ∆C E[∆Y] ∆B ∆C E[∆Y]

(1) (2) (3) (4) (5) (6)

Panel A1: SD(Y) = 0 Panel A2: SD(Y) > 0

T1 0.081*** 0.249*** -0.031 0.172*** 0.433*** 0.610***

(0.025) (0.083) (0.030) (0.018) (0.060) (0.118)

T2 0.078** 0.223** -0.007 0.107*** 0.249*** -0.073

(0.035) (0.090) (0.035) (0.014) (0.057) (0.149)

Dif 0.003 0.026 -0.024 0.064*** 0.184** 0.683**

(0.039) (0.122) (0.042) (0.021) (0.079) (0.192)

Controls Yes Yes Yes Yes Yes Yes

N 1165 1152 1141 4326 1068 3984

Panel B1: Low XS Var Panel B2: High XS Var

T1 0.121*** 0.255*** 0.203** 0.197*** 0.517*** 0.594***

(0.018) (0.048) (0.103) (0.024) (0.092) (0.144)

T2 0.091*** 0.203*** 0.087 0.106*** 0.270*** 0.058

(0.017) (0.054) (0.112) (0.017) (0.072) (0.211)

Dif 0.029 0.051 0.116 0.091*** 0.247** 0.536**

(0.021) (0.058) (0.157) (0.026) (0.110) (0.247)

Controls Yes Yes Yes Yes Yes Yes

N 3084 1269 2562 2410 952 2563

Standard errors clustered at city level in parentheses

* p <0.10 ** p <0.05 *** p <0.01

C. Heterogeneity by Income Uncertainty

As suggested by Proposition 1, if consumers infer information about income growth from

credit supply, then the degree of updating is larger when the signal-to-noise ratio is larger.

Directly testing this hypothesis requires observing the signal-to-noise ratio. Since I do

not observe the precisions of bank signals, I instead focus on income uncertainty. In

particular, when consumer income is less uncertain, the diference between the ATEs of

treatments 1 and 2 is supposed to be smaller. In the extreme case, when income has zero

variation, there should be no diference between the ATEs of treatments 1 and 2.

To test this hypothesis, I frst study how the ATEs associated with the two treatments

difer by consumer income volatility. Since, for many participants, income is only

28
observed for a short number of years, measuring individual income volatility is difcult.

Therefore, I use two proxies for income uncertainty. First, to measure income variability

within individuals, I use a coarser measure by splitting individuals based on whether

the variability of monthly income is zero or positive within the 12 months before the

experiment. A caveat is that since at the intensive margin, the amounts of increased credit

limit are not random but based on the bank’s assessment of consumers’ creditworthiness,

unconditionally separating the customers by income volatility may be inducing selection

bias due to diferent amounts of increases in credit limit. In this case, ATEs could be

diferent only because MPCL is not linear. To cope with this concern, I frst separate

consumers into ten groups by the proposed amounts of limit increase and then split the

consumers by income volatility within the ten limit-increase groups. Doing so controls

the bank’s assessment of the consumers’ change in creditworthiness.

The results are in Table 4. Columns (1) to (6) give the ATEs separately for those

whose log monthly income has zero and positive variation. As shown, for those whose

income has zero variation, there is no change in income expectations for either treatment

group. In addition, diferences between the ATEs of the two treatments in spending

responses become insignifcant. Meanwhile, for those with positive income variations,

changes in income expectations become strongly and signifcantly diferent from zero for

T1. At the same time, diferences between the ATEs of the two treatments in spending

responses are also larger than the baseline estimates. The results in columns (1) to

(6) are consistent with Proposition 1, such that when prior uncertainty about future

income growth is likely to be low, information content in credit supply has less efect on

consumption.

As a second measure, I construct a statistic of cross-sectional income variability.

Specifcally, I use a deep neural network to cluster individuals into 20 types using a random

3% sample of the bank’s database over the fve years before the experiment (around 5

million observations with more than 200 variables). Then, I calculate a cross-sectional

variance of income (XS Var ) as the within-type variance of log income growth in 2023.

Given that consumers are usually less advantaged to observe income information about

other consumers of similar type, this measure of cross-sectional income variability also

suggests to what extent the bank is able to observe income patterns for similar individuals.

29
TABLE 5. The Efects of Limit Increase on Debt and Spending by Expectation Changes

This table assesses the efects of credit extension on non-durable debt and spending by expectation

changes. Columns (1) and (2) split the sample by expectations of consumption changes. Columns

(3) and (4) split the sample by expectations of income changes. Coefcients are divided by the predetermined average increase in credit limit to give an interpretation of marginal propensity. All variables

are winsorized at the 1% level. The analysis is based on the sample of participants to whom questions

16 to 21 are not sent.

E[∆C] E[∆Y]

Low

(1)

High

(2)

Low

(3)

High

(4)

Panel A: ∆B - 6M

T1

T2

0.101**

(0.043)

0.063

(0.044)

0.252***

(0.049)

0.163***

(0.047)

0.093**

(0.042)

0.053

(0.043)

0.259***

(0.052)

0.173***

(0.051)

Controls

N

Yes

2872

Yes

2253

Yes

2925

Yes

2200

Panel B: ∆C

T1

T2

Controls

N

0.172*

(0.086)

0.099

(0.093)

Yes

1148

0.562***

(0.091)

0.372***

(0.104)

Yes

911

0.153*

(0.089)

0.073

(0.094)

Yes

1162

0.586***

(0.099)

0.398***

(0.107)

Yes

897

Standard errors clustered at city level in parentheses

* p <0.10 ** p <0.05 *** p <0.01

Columns (7) to (12) of Table 4 give the ATEs separately for those whose XS Var is below

and above the sample median. Consistent with the conjecture, the diference between the

ATEs is larger when the XS Var is larger.

D. Expectation Changes and Spending Responses

In response to a higher credit limit pushed by banks, consumers increase total consumption

substantially. Survey results show that consumers also increase their expectations about

future consumption and labor productivity. A natural question is whether the increases

in consumption are, at least partly, driven by the changes in expectation. The comparison

of the two treatment groups suggests that the diferences in the spending responses are

likely driven by belief diferences after receiving credit extensions. In this section, I

further test the relationship between spending responses and expectation changes. In

30
Table 5, I estimate the ATEs of limit extensions on debt and spending by changes

in expected consumption and income. If spending responses are partially driven by

changes in expectations, then one should expect a larger spending response when changes

in expectations are also large. Columns (1) and (2) split the sample by changes in

consumption expectations by each group, and columns (3) and (4) split the sample by

changes in income expectations by each group. The results show that for those who

have larger changes in expectation, spending responses are also higher. This is consistent

with expectation changes afecting consumption. Furthermore, in Table B.3 in the online

appendix, I show that there is no diference in spending responses if ranked by changes

in expectations with respect to other factors.

E. Subjective Beliefs about Credit Limit Extensions

As a direct test of the income-inference channel, I elicit consumer subjective beliefs about

credit supply as a function of bank-perceived consumer future income growth. I rely on

the following two questions from the survey:

Suppose banks increase your credit card limit by 5000 CNY this month. This would mean

that the banks expect your total income to change by over the next 12 months.

Note: use a negative number for decreases.

Suppose banks increase your credit card limit by 10000 CNY this month. This would mean

that the banks expect your total income to change by over the next 12 months.

Note: use a negative number for decreases.

These questions are sent to a 30% random sample of the participants. Suppose the answers

from the two questions are respectively x1,i and x2,i, I then calculate the consumers’

subjective beliefs about the credit limit sensitivity to bank-perceived income growth, λi,

as

x2,i − x1,i λi = . (7) 5000

Mapped to (2), λi = g′

(Li) is the marginal relationship between credit limit and

bank beliefs about consumers’ future income growth. When λi = 1, consumer i believes

31
Figure 5. Timeline of the Experiments

In this fgure, panel A plots the distribution of consumer subjective beliefs about the sensitivity of income

growth as perceived by the bank to credit extension, λi, which is calculated using (7). The plot is cut at

1% level. The right plot gives the changes in income expectations for each CNY higher pre-determined

increase in credit limit. The estimates are conditional on four λi groups. Splits of λi groups are conditional

on treatment groups and limit-increase deciles.

A: Pilot Study B: Main Study

that the bank’s supply of credit limit moves one-for-one with the bank’s prediction about

consumers’ future income changes.

Figure 5 plots the distribution of λi. It shows that there is a large heterogeneity

in consumers’ subjective beliefs about the sensitivity of credit supply to bank-perceived

income growth. Around 35% of the consumers believe λi ≤ 0. However, most of the

participants believe credit-limit extensions are associated with higher income growth in

the future. The economic signifcance of λi is large. Its average value is 0.81, and the

median is 0.60. Thus, for a 1-CNY increase in the credit limit, consumers, on average,

believe the bank expects their income to increase by 0.81-CNY over the next 12 months.

From a Bayesian-learning perspective, Figure 5 Panel A suggests that consumers, on

average, learn about their future income from credit limit extension as a signal of income

changes, with a signal sensitivity of 0.81. Given that the posterior income expectation is

0.381, the Kalman gain of the learning process is around 0.47.

Proposition 1 states that change in income expectations after receiving limit

extensions should move positively with the signal sensitivity of income growth λi. In

Panel B of Figure 5, I split the sample by λi into four groups and then plot the average

change in income expectations by λi-groups within each treatment group. Consistent

32
with proposition 1, participants in T1 have a larger change in income expectations after

the experiment, and this change increases with λi. Income changes are also close to zero,

especially when λi is close to zero. At the same time, there is no apparent association

between λi and changes in income expectation for the other two groups.

In sum, the results from Figure 5 indicate that consumers believe that limit extensions

are positively associated with banks’ beliefs about future income growth. Consistent with

Bayesian learning, consumers with uncertain income streams adjust income expectations

upwards in response to a positive credit supply shock.

F. What Information is Inferred?

I further investigate the type of information consumers infer from credit limit increases. A

natural explanation is that consumers are imperfectly informed about the macroeconomic

conditions (Mankiw and Reis, 2002; Reis, 2006; Coibion and Gorodnichenko, 2012; Andre

et al., 2022), and update beliefs according to cyclical movements in credit supply (Bassett

et al., 2014; Fishman et al., 2020; Weitzner and Howes, 2023), whereas the latter contains

information about the macro assessment from professionals that works at the fnancial

sector. If consumers infer information about the macroeconomy, then participants in

treatment group 1 should update their beliefs about macroeconomic variables after

receiving the limit shocks. To explore this conjecture, I use the following two questions.

Q14/15: How much will the overall Chinese economy/unemployment rate change (in

percentage relative to the current level) over the next year?

Q14 and Q15 were sent to a random 30% of the participants. I use the growth rate

of the overall Chinese economy to approximate the GDP growth. The results are in

Table 6. After the experiment, participants in T1 increased their expectations about

the GDP growth over the next 12 months by 4.6% and decreased their expectations

about unemployment rates by 20.8%. Note that the latter is the percentage change in

unemployment rates. Therefore, suppose the ex-ante expectation of the unemployment

rate is 5%, then T1’s expectation of the unemployment rate becomes around 4% after the

experiment. In contrast, there are no signifcant changes in the expectations about the

macroeconomy for T1. The results are, therefore, consistent with consumers believing

33
TABLE 6. Limit Increase and Macro Expectations

This table assesses the efects of credit extensions on expectations on macroeconomic variables. ∆ GDP

is the growth rate of the overall Chinese economy. ∆ Unemp Rate is the percentage change in the

unemployment rate.

E[∆ GDP] E[∆ GDP] E[∆ Unemp Rate] E[∆ Unemp Rate]

(1) (2) (3) (4)

T1 0.049*** 0.046*** -0.208*** -0.231***

(0.018) (0.017) (0.065) (0.063)

T2 0.015 0.017 -0.047 -0.054

(0.022) (0.021) (0.070) (0.072)

Controls No Yes No Yes

N 2310 2310 2310 2310

Standard errors clustered at city level in parentheses

* p <0.10 ** p <0.05 *** p <0.01

that credit supply is pro-cyclical, such that positive changes in credit limit are a result

of an expansionary economy. This is consistent with the fndings about the cyclicality

of credit supply (Bassett et al., 2014; Fishman et al., 2020; Weitzner and Howes, 2023).

In addition, as evident from T2, when participants are informed that the limit supply

decisions are random conditional on having a good payment history, expectations stay

constant after receiving changes in credit limit.

When consumers change income expectations after credit supply shocks by making

inferences about the aggregate economy, expectation changes should rely on consumers’

uncertainty about the aggregate economy and the sensitivity to how macroeconomic

movements afect individual income. For the former case, even if credit supply contains

information about aggregate economic states, for consumers that have low uncertainty

about the economic states, inferences from credit supply should be minimal. As for

the latter, inferences should also depend on how much individual income is afected by

macroeconomic shocks. This is to say, for someone whose unemployment probability and

personal income have zero co-variability with aggregate unemployment probability and

GDP growth, then expectation changes should also be small. Testing the heterogeneity

of income expectation changes by macroeconomic uncertainty and income sensitivity to

macroeconomic movements is efective in informing this macroeconomic inference channel.

To construct a measure of macroeconomic uncertainty, I use the following question.

34
TABLE 7. Limit Increase and Income Expectations – Macroeconomic Channel

This table assesses the efects of credit extensions on income expectations by how limit changes afect

personal income through providing information on macroeconomic states. Macro Uncertainty is low if

the participants have high confdence about the current macroeconomic state. Growth Sensitivity is

high if the participants believe aggregate GDP growth has large afects personal income. Unemployment

Sensitivity is high if the participants believe aggregate unemployment rate growth has large efects on

personal income.

Macro Uncertainty Growth Sensitivity Unemployment Sensitivity

Low

(1)

High

(2)

Low

(3)

High

(4)

Low

(5)

High

(6)

T1

T2

0.199

(0.231)

0.077

(0.240)

0.446**

(0.228)

0.089

(0.219)

0.132

(0.243)

0.049

(0.222)

0.500***

(0.201)

0.107

(0.189)

0.099

(0.274)

0.029

(0.208)

0.569***

(0.211)

0.138

(0.180)

Controls

N

Yes

943

Yes

1367

Yes

1255

Yes

1055

Yes

1078

Yes

1232

Standard errors clustered at city level in parentheses

* p <0.10 ** p <0.05 *** p <0.01

Q16: How confdent are you in evaluating whether the overall economy is functioning

efectively at the moment?

I rely on the following two questions to measure income sensitivity to macroeconomic

movements.

Q17: Suppose the overall economy in China grows by 5% relative to the current level over

the next year. How would this afect your total income over the next year?

Q18: Suppose the unemployment rate in China decreases by 10% relative to the current

level over the next year. How would this afect your total income over the next year?

Q16 to Q18 are sent to the same random 30% of the participants. Q16 measures

how confdent the participants are about the current economic state, and Q17 and Q18

give subjective beliefs about how movements in GDP and unemployment afect individual

income. If income inference is due to consumers updating perceptions about the current

macroeconomic state from credit supply, then expectation changes should be larger for

those who are less confdent in evaluating the macroeconomic performance. To test

this conjecture, I defne those who answer very confdent as having low macroeconomic

uncertainty and the rest as having high macroeconomic uncertainty. I then study

35
expectation changes separately for these two groups. The results are in columns (1)

and (2) of Table 7. Consistent with the conjecture, those in T1 who report to have high

macroeconomic uncertainty also have a larger change in income expectations.

In addition, if limit extensions afect income expectations by signaling the

heterogeneous impacts of macroeconomic states on individual income, then one should

see those with more positive answers to Q17 and more negative answers to Q18 having

larger changes in income expectations. In columns (3) through (6) in Table 7, I split

the participants and defne those as having high growth sensitivity if their answers to

Q17 are above the median and having high unemployment sensitivity if their answers

to Q18 are below the median. Consistent with the conjecture, those in T1 who report

having high growth sensitivity or unemployment sensitivity also have a larger change in

income expectations. More importantly, for those with low macroeconomic uncertainty

or income sensitivity to macroeconomic movements, changes in income expectations are

insignifcant. This indicates that information about the macroeconomic state is the only

economically important information consumers are learning about from credit supply.

Other types of information, including individuals’ relative performance to their peers, are

unlikely the reasons that consumers are learning from limit extensions.

Consumers believe that credit supply is associated with an expansionary aggregate

economy. Those who think that a booming period afects their income to a greater

extent have a larger change in income expectations. However, recent literature documents

that expansionary credit conditions are usually associated with deteriorated instead of

improved economic conditions in the future (L ́oepez-Salido et al., 2017; Mian et al.,

2017). Figure B.2 in the online appendix provides further evidence in the US such

that periods with higher growth of credit limits are also times with higher subjective

future income growth but lower realized future GDP growth. The recent literature on

the extrapolative-expectation formation process is a possible explanation for this seeming

inconsistency. Suppose lending standards are looser during booming periods (Bassett

et al., 2014; Fishman et al., 2020; Weitzner and Howes, 2023), then credit supply reacts

positively to current economic shocks. Consumers, equipped with incomplete information

about the current state of the economy, update their beliefs accordingly in response to

credit expansions. With extrapolative expectation formation process (Bordalo et al.,

36
2018), this positive news would be over-extrapolated to the future, amplifying the positive

relationship between current credit supply decisions and expected future income. When

misbeliefs are later resolved, consumption growth decreases, inducing a boom-then-bust

pattern.

G. Implications from US Data

Presumably, the existence of income inference from credit supply depends on the nature

of banks’ decision-making process. For more sophisticated banks, supply reacts more to

lenders’ beliefs about the economy and how economic shocks afect consumers, while for

less sophisticated banks, credit supply could be purely based on individuals’ payment

history. A natural question is if China is special as the banks use more statistical analysis

during its lending practices. To shed light on the likelihood of the existence of the

income-inference channel in other settings, I present some survey results based on US

data collected through Prolifc, an online survey platform10. Recent studies note that

data from online survey platforms can have high quality when compared with traditional,

larger surveys and feld experiments (Haaland et al., 2023; Douglas et al., 2023).

Without an experiment and administrative data, I cannot determine the causal

efects of credit expansion on consumers’ expectations and spending behaviors through the

income-inference channel in the US. However, I use reported decisions under randomized

hypothetical scenarios to show consumers’ expectation changes after credit supply. This

strategy is similar to the reported preference approach in estimating MPC out of one-time

wealth shock (Shapiro and Slemrod, 2003; Jappelli and Pistaferri, 2014; Graziani et al.,

2016; Parker and Souleles, 2019; Fuster et al., 2020; Jappelli and Pistaferri, 2020).

The survey design is similar to the main study. Participants are required to be

credit-card holders that are either part-time or full-time employed. For the recruited

participants, I frst randomly split them into two groups. Then, for group 1, participants

are asked to consider the following scenarios:

For the following questions, please imagine a scenario where your bank has chosen you to

raise your credit card limit by X%.

For group 2, participants are shown the following text:

10The survey design, results, and the collection method are provided in the Online Appendix C.

37
For the following questions, please imagine a scenario where your bank has chosen you at

random to raise your credit card limit by X%. This decision by the bank is entirely random

and not infuenced by any assessment of pertinent factors.

In both texts, X is the hypothetical limit change and is randomly picked from

{10, 15, 20, 25, 30}.

The two scenarios mirror the two treatments in the main study. Specifcally, in

addition to the information shown to group 1, group 2 also receives an additional

assumption that the credit supply is purely random. By informing about the randomness

of the credit supply, the information shown to group 2 aims to isolate any belief channels

in credit supply. To elicit belief changes, I then ask the following fve questions.

Q1-3: How much do you think your Y would change over the next year?

Q4: What’s the probability that you would default on your debt over the next year?

Q5: How many hours would you work on average every week over the next year?

Y is an element of {income, spending, saving}. Comparing how answers to these questions

vary with X between groups 1 and 2 sheds light on the informational efects of credit

supply. The results are shown in Table C.1 in online appendix C. Consistent with the

fndings in the Chinese setting, for group 1, a higher hypothetical increase in credit limit

increases expectations about future consumption and income. Meanwhile, there is no

change in saving, default probability, or labor supply. For the results from group 2,

when credit supply is assumed to be random, there is no signifcant association between

reported future economic activities and limit extensions. The results are similar to those

documented in the main study. That is, credit supply increases beliefs about future

income and consumption but not saving default rate or labor supply. In addition, if

credit supply is purely random, changes in expected future income and consumption

become insignifcant. Therefore, consumers in the US are also likely to change expected

labor productivity after receiving limit extensions.

V Conclusion

This paper represents an initial practice into understanding how changes in credit supply

causally impact subjective beliefs at the micro level and, consequently, how these altered

38
beliefs infuence consumer spending and borrowing behaviors. Traditional studies on

the macroeconomic efects of credit supply often assume that economic agents possess

full-information rational expectations, leaving the analysis of credit supply’s impact on

beliefs largely unexplored. This study documents a notable fnding: extensions in credit

limits boost consumers’ beliefs regarding their future labor productivity. It estimates

that approximately 37% of the increased consumption following higher credit limits can

be attributed to this shift in income expectations.

However, this is just the beginning of a broader investigation. There’s a need for

further research to comprehensively understand the macroeconomic implications when

lenders and borrowers have access to diferent sets of information. Additionally, the

study touches on the nuances of banks’ credit supply decisions, which may vary based on

the statistical precision that can be achieved with diferent borrower characteristics. For

instance, credit supply decisions grounded in statistical analysis might disproportionately

favor individuals for whom the bank can derive more accurate predictions (Fuster et al.,

2022). This aspect raises interesting questions about the potential asymmetric impacts

of monetary policies across various industries, infuenced by banks’ abilities to make

statistical inferences. Future research could benefcially explore the distributional efects

of monetary policy in scenarios where banks depend on statistical analysis to make credit

supply decisions, further illuminating the complex dynamics at play in credit markets.

39
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42
For Online Publication

Appendix to “Learning in the Limit: Income Inference from Credit

Extensions” by Xiao Yin

A. Survey

Please read the following information carefully.

The use of credit cards is one important channel for residents to make daily consumption. To better

understand the impact of credit cards on people’s lives, we selected a certain number of active users to

participate in a survey. The survey is expected to take between 5 to 10 minutes. If you choose to take

the survey, you will be awarded 15 CNY.

This study is in collaboration with Xiao Yin, an assistant professor of economics at UCL in the UK. The

data will only be analyzed by Xiao Yin for scientifc research purposes and will not be evaluated by this

bank. We will not disclose participants’ personal information in any respect. We will not, to any extent,

change the types of fnancial products we provide, including credit scores, credit limits, deposit rates,

etc., based on the participants’ personal answers. Therefore, please answer based on your true thoughts.

• Yes

• No

1
1. How many banks do you usually use for transaction purposes?

(a) 1

(b) 2

(c) 3 or more

2. Your total income over the past 12 months is .

Note: income includes wages, salaries, bonuses, commission, etc., excluding capital gains and

fnancial return from fnancial investments.

3. What was the total amount of your spending during the past 12 months (excluding investment

and purchases of durable goods including housing, cars, etc.)?

4. What is the current value of your total wealth?

Note: total wealth is the value of all assets such as cash, savings, houses, stock market wealth, and

all other liquid and fxed assets minus all debts you owe.

5. How many hours on average do you work every week over the past 12 months?

6. Over the next 12 months, conditional on not switching jobs, what’s the level of total income you

are most likely to get?

7. What’s the most likely level of your total wealth in 12 months?

8. Over the next 12 months, how much would you most likely spend on average every month

(excluding investment and purchases over durable goods including housing, cars, etc.)?

9. How many hours on average will you work every week over the next 12 months?

10. What’s the probability that you will lose your job over the next 12 months?

11. What’s the probability that you will not be able to make a payment to your borrowing over the

next 12 months?

Note: Please answer zero if you do not plan to borrow over the next 12 months.

12. Compared to your current total credit limit across all fnancial institutions or platforms, how much

would your total credit limit be (in percentage) in one year?

(a) Decreases by more than 50%

(b) Decreases by between 25% and 50%

(c) Decreases by between 10% to 25%

(d) Decreases by between 0% to 10%

(e) Stays roughly the same.

(f) Increases by between 0% to 10%

(g) Increases by between 10% to 25%

(h) Increases by between 25% and 50%

(i) Increases by more than 50%

2
13. Compared to your current total credit limit across all fnancial institutions or platforms, how much

would your total credit limit be (in percentage) in fve years?

(a) Decreases by more than 50%

(b) Decreases by between 25% and 50%

(c) Decreases by between 10% to 25%

(d) Decreases by between 0% to 10%

(e) Stays roughly the same.

(f) Increases by between 0% to 10%

(g) Increases by between 10% to 25%

(h) Increases by between 25% and 50%

(i) Increases by between 50% and 100%

(j) Increases by between 100% and 200%

(k) Increases by more than 200%

14. How much will the overall Chinese economy change (in percentage relative to the current level)

over the next year?

(a) Decreases by more than 20%

(b) Decreases by between 15% and 20%

(c) Decreases by between 10% to 15%

(d) Decreases by between 5% to 10%

(e) Decreases by between 2.5% to 5%

(f) Decreases by between 0% to 2.5%

(g) Stays roughly the same.

(h) Increases by between 0% to 2.5%

(i) Increases by between 2.5% to 5%

(j) Increases by between 5% to 10%

(k) Increases by between 10% to 25%

(l) Increases by between 25% and 30%

(m) Increases by more than 20%

15. How much will the unemployment (in percentage relative to the current level) over the next year?

(a) Decreases by more than 20%

(b) Decreases by between 15% and 20%

(c) Decreases by between 10% to 15%

(d) Decreases by between 5% to 10%

(e) Decreases by between 2.5% to 5%

(f) Decreases by between 0% to 2.5%

(g) Stays roughly the same.

3
(h) Increases by between 0% to 2.5%

(i) Increases by between 2.5% to 5%

(j) Increases by between 5% to 10%

(k) Increases by between 10% to 25%

(l) Increases by between 25% and 30%

(m) Increases by more than 20%

16. (Random 30%) How confdent are you in evaluating whether the overall economy is functioning

efectively at the moment? 11

(a) not very confdent

(b) somewhat confdent

(c) very confdent

17. (Random 30%) Suppose the overall economy in China grows by 5% relative to the current level

over the next year, how would this afect your total income over the same period?

(a) Decreases by more than 20%

(b) Decreases by between 15% and 20%

(c) Decreases by between 10% to 15%

(d) Decreases by between 5% to 10%

(e) Decreases by between 2.5% to 5%

(f) Decreases by between 0% to 2.5%

(g) Stays roughly the same.

(h) Increases by between 0% to 2.5%

(i) Increases by between 2.5% to 5%

(j) Increases by between 5% to 10%

(k) Increases by between 10% to 25%

(l) Increases by between 25% and 30%

(m) Increases by more than 20%

18. (Random 30%) Suppose the unemployment rate in China decreases by 10% relative to the current

level over the next year, how would this afect your total income over the same period?

(a) Decreases by more than 20%

(b) Decreases by between 15% and 20%

(c) Decreases by between 10% to 15%

(d) Decreases by between 5% to 10%

(e) Decreases by between 2.5% to 5%

(f) Decreases by between 0% to 2.5%

11Questions 16 to 21 are sent tot the same set of individuals.

4
(g) Stays roughly the same.

(h) Increases by between 0% to 2.5%

(i) Increases by between 2.5% to 5%

(j) Increases by between 5% to 10%

(k) Increases by between 10% to 25%

(l) Increases by between 25% and 30%

(m) Increases by more than 20%

19. (Random 30%) Suppose banks increase your credit card limit by 5000 CNY this month. This

would mean that the banks expect your total income to be changed by in the next 12

months.

Note: use a negative number for decreases.

20. (Random 30%) Suppose banks increase your credit card limit by 10000 CNY this month. This

would mean that the banks expect your total income to be changed by in the next 12

months.

Note: use a negative number for decreases.

21. (Random 30%) Rather than receiving 100 Yuan today, which options would you choose? (select

all that apply)

(a) 100 Yuan in 6 months.

(b) 102.5 Yuan in 6 months.

(c) 105 Yuan in 6 months.

(d) 107.5 Yuan in 6 months.

(e) 110 Yuan in 6 months.

(f) 112.5 Yuan in 6 months.

(g) 115 Yuan and more in 6 months.

5
B: Additional Results

Figure A.1. Sanity Check of Survey Data

This fgure performs the sanity check of the survey data. Panel A is a binned scatter plot of income

calculated from transaction history vs reported income. Panel B is a binned scatter plot of income

calculated from administration and that from transaction history. Panel C is a binned scatter plot of

past consumption calculated from transaction history vs reported past consumption; data is restricted

to those who reported only using this bank for daily transactions. Panel D is a binned scatter plot of

past consumption calculated from transaction history vs that from the credit registry; data is restricted

to those who reported to have liquid savings less than one week of income.

A: Income from Transaction Histories and Surveys B: Income from Administration and Transaction Histories

C: Spending from Transaction Histories and Surveys D: Spending from Transaction Histories and Credit Registry

6
Figure B.2: Limit Growth and Income Growth

This fgure plots the relationship between measures of future income growth on year-on-year quarterly

credit limit growth. On both panels, the x-axis is the log changes in aggregate credit limits from quarter

t - 3 to quarter t. Data is from New York Fed’s Survey of Consumer Expectations. On Panel A, the

y-axis is the average quarter-t one-year-ahead expected income growth from New York Fed’s Survey of

Consumer Expectation. On Panel B, the y-axis is the quarterly GDP growth from a quarter t to quarter

t+3. Data is from Fred. Sample periods are from 1999Q1 to 2023Q3.

A: Future Income Expectations B: GDP Growth

7
Table B.1. Sample Comparison

This table compares the main sample and a 3% of the whole sample in the bank.

(1) (2) (3) (4) (5) 6 7 8 9 10

Panel A: Survey Sample Panel B: Whole Sample

Mean SD p25 Median p75 Mean SD p25 Median p75

Age 39.28 9.00 29 39 48 40.83 10.21 28 39 48

Female 0.52 0.50 0 1 1 0.50 0.50 0 0 1

Spending 7.57 10.30 1.85 4.88 9.40 9.30 13.42 2.12 5.19 11.96

Income 10.57 14.04 4.52 7.70 16.01 12.12 16.81 5.58 9.40 17.83

Saving 169.61 193.04 10.07 27.30 127.62 172.29 236.17 11.82 52.01 160.01

Limit 87.88 110.88 13.39 54.13 155.27 92.77 152.81 18.10 65.86 183.17

Debt 7.67 10.08 0.00 0.00 9.53 7.03 15.78 0.00 0.00 14.21

Debt|Debt> 0 11.96 11.14 4.36 11.81 22.82 14.44 16.77 2.90 12.90 26.34

8
Table B.2: Efects of Limit Increases - Restricted Sample

The table compares the debt and expectation responses, restricted to those who only use credit cards at

other fnancial institutions.

Panel A: Main Sample Panel B: Surveyed Sample

D B - 3M D B - 6M D B - 3M D B - 6M D E[Y]

(1) (2) (3) (4) (6)

T1 0.082*** 0.141*** 0.097*** 0.175*** 0.394***

(0.012) (0.020) (0.021) (0.032) (0.130)

T2 0.049*** 0.087*** 0.062*** 0.113*** 0.013

(0.014) (0.022) (0.023) (0.035) (0.181)

Dif 0.032** 0.054** 0.035 0.062* 0.381**

(0.015) (0.027) (0.024) (0.038) (0.184)

Controls Yes Yes Yes Yes Yes

N 2234 2234 1215 1215 1215

9
Table B.3: Spending Responses by Expectation Changes

This table compares the spending responses by changes in expectations.

E[L.W] E[T.W] E[Hrs] E[u] E[pd] E[L] - 6M E[L] - 5Y

Low High Low High Low High Low High Low High Low High Low High

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (11) (12)

Panel A: B - 6M

T1 0.200*** 0.167*** 0.248*** 0.117*** 0.202*** 0.220*** 0.216*** 0.229*** 0.223*** 0.225*** 0.203*** 0.174*** 0.209*** 0.182***

(0.046) (0.036) (0.041) (0.039) (0.035) (0.066) (0.034) (0.066) (0.035) (0.055) (0.048) (0.043) (0.047) (0.041)

T2 0.120*** 0.109*** 0.122*** 0.107** 0.127*** 0.127*** 0.116*** 0.138*** 0.113*** 0.123** 0.124** 0.110** 0.116*** 0.119**

(0.042) (0.037) (0.040) (0.042) (0.032) (0.051) (0.031) (0.056) (0.031) (0.063) (0.037) (0.045) (0.035) (0.047)

N 2588 2523 2698 2413 4084 1027 4142 969 4408 702 2561 2550 2564 2547

Panel A: C

T1 0.334*** 0.342*** 0.311*** 0.364*** 0.350*** 0.301*** 0.333*** 0.367*** 0.332*** 0.460*** 0.360*** 0.372*** 0.379*** 0.349***

(0.055) (0.069) (0.056) (0.072) (0.049) (0.102) (0.054) (0.093) (0.050) (0.097) (0.030) (0.084) (0.033) (0.081)

T2 0.236*** 0.213*** 0.224*** 0.219*** 0.246*** 0.209** 0.224*** 0.199** 0.217*** 0.198** 0.215*** 0.184** 0.201*** 0.195**

(0.062) (0.070) (0.059) (0.071) (0.058) (0.077) (0.058) (0.082) (0.056) (0.094) (0.036) (0.092) (0.040) (0.087)

N 2588 2522 2698 2412 4083 1027 4141 969 4408 701 2560 2550 2563 2547

10
Table B.4. Transfers

This table studies the efects of the experiment on between-fnancial institutions transfers. Infow is the

transfer from other banks to the bank in the sample plus deposits. Outfow is the transfer from the bank

in the sample to other banks plus withdraws.

Infow Infow Outfow Outfow

(1) (2) (3) (4)

T1 0.032 0.047 0.063 0.069

(0.064) (0.071) (0.082) (0.089)

T2 -0.075 -0.069 -0.052 -0.033

(0.069) (0.088) (0.077) (0.086)

Controls No Yes No Yes

N 5500 5500 5500 5500

11
Table B.5: Expectation Changes by Industries

This table studies expectation changes by XS Var and sector tradability. XS Var is defned in section

IV.C in the main text. Following M ̈uller and Verner (2023), participants are labeled as in a tradable

sector if they work in agriculture, manufacturing, or mining. Non-tradable include other sectors.

E[Y] E[Hrs] E[u]

Non-Tradable Tradable Non-Tradable Tradable Non-Tradable Tradable

(1) (2) (3) (4) (5) (6)

Panel A: Low XS Var

T1 0.204 0.093 -0.000 -0.000 -0.077 0.003

(0.173) (0.176) (0.000) (0.000) (0.153) (0.147)

T2 0.042 0.033 0.000 0.000 -0.031 -0.045

(0.181) (0.251) (0.000) (0.000) (0.166) (0.173)

Controls Yes Yes Yes Yes Yes Yes

N 693 462 693 462 693 462

Panel B: High XS Var

T1 0.554*** 0.434*** -0.000 -0.000 -0.309** -0.242

(0.167) (0.182) (0.000) (0.000) (0.158) (0.171)

T2 0.082 0.063 0.000 0.000 -0.062 -0.032

(0.226) (0.244) (0.000) (0.000) (0.109) (0.150)

Controls Yes Yes Yes Yes Yes Yes

N 693 462 693 462 693 462

12
C. US Survey

1. How many credit cards do you use for daily spending?

(a) 0

(b) 1

(c) 2

(d) 3

(e) 4 or more

2. What’s the total level of your credit limit over all fnancial institutions?

(a) less than 2000

(b) 2000 - 5000

(c) 5000 - 10000

(d) 10000 - 20000

(e) 20000 - 40000

(f) 40000 - 70000

(g) 70000 - 100000

(h) more than 10000

(10%) For the following questions, we would like you to consider the scenario that your bank has

decided to increase your credit card limit by 10%.

(10%) For the following questions, we would like you to consider the scenario that your bank has

decided to increase your credit card limit by 15%.

(10%) For the following questions, we would like you to consider the scenario that your bank has

decided to increase your credit card limit by 20%.

(10%) For the following questions, we would like you to consider the scenario that your bank has

decided to increase your credit card limit by 25%.

(10%) For the following questions, we would like you to consider the scenario that your bank has

decided to increase your credit card limit by 30%.

(10%) For the following questions, please imagine a scenario where your bank has chosen you at

random to raise your credit card limit by 10%. This decision by the bank is entirely random and

not infuenced by any assessment of pertinent factors.

13
(10%) For the following questions, please imagine a scenario where your bank has chosen you at

random to raise your credit card limit by 15%. This decision by the bank is entirely random and

not infuenced by any assessment of pertinent factors.

(10%) For the following questions, please imagine a scenario where your bank has chosen you at

random to raise your credit card limit by 20%. This decision by the bank is entirely random and

not infuenced by any assessment of pertinent factors.

(10%) For the following questions, please imagine a scenario where your bank has chosen you at

random to raise your credit card limit by 25%. This decision by the bank is entirely random and

not infuenced by any assessment of pertinent factors.

(10%) For the following questions, please imagine a scenario where your bank has chosen you at

random to raise your credit card limit by 30%. This decision by the bank is entirely random and

not infuenced by any assessment of pertinent factors.

3. How much do you think your spending would change over the next year?

(a) decreases by more than 20%

(b) decreases by 15% to 20%

(c) decreases by 10% to 15%

(d) decreases by 5% to 10%

(e) decreases by 0% to 5%

(f) stays the same

(g) increases by 0% to 5%

(h) increases by 5% to 10%

(i) increases by 10% to 15%

(j) increases by 15% to 20%

(k) increases by more than 20%

4. How much do you think your income would change over the next year?

(a) decreases by more than 20%

(b) decreases by 15% to 20%

(c) decreases by 10% to 15%

(d) decreases by 5% to 10%

(e) decreases by 0% to 5%

(f) stays the same

(g) increases by 0% to 5%

(h) increases by 5% to 10%

14
(i) increases by 10% to 15%

(j) increases by 15% to 20%

(k) increases by more than 20%

5. How much do you think your savings would change over the next year?

(a) decreases by more than 20%

(b) decreases by 15% to 20%

(c) decreases by 10% to 15%

(d) decreases by 5% to 10%

(e) decreases by 0% to 5%

(f) stays the same

(g) increases by 0% to 5%

(h) increases by 5% to 10%

(i) increases by 10% to 15%

(j) increases by 15% to 20%

(k) increases by more than 20%

6. What’s the probability that you would default on your debt over the next year?

7. How many hours would you work on average every week over the next year?

8. How much do you think your credit limit over all fnancial institutions would change over the next

year?

(a) decreases by more than 20%

(b) decreases by 15% to 20%

(c) decreases by 10% to 15%

(d) decreases by 5% to 10%

(e) decreases by 0% to 5%

(f) stays the same

(g) increases by 0% to 5%

(h) increases by 5% to 10%

(i) increases by 10% to 15%

(j) increases by 15% to 20%

(k) increases by more than 20%

15
Table C.1: US Results

This table presents results about hypothetical limit extensions on expectation. E[∆log C], E[∆log Y],

E[∆log W], E[∆log L] are respectively the expected next-year growth of total consumption, income,

wealth, and credit limits. E[p(d)] and E[Hrs] are respectively the expected default probability and hours

planned to work over the next year. Data is based on part-time and full-time employees with credit cards

from SurveyMonkey. Results are winsorized at 1% level.

E[∆log C]

(1)

E[∆log Y]

(2)

E[∆log W]

(3)

E[p(d)]

(4)

E[Hrs]

(5)

E[∆log L]

(6)

Panel A: No Information

∆log Limit 0.190**

(0.088)

0.234***

(0.078)

0.068

(0.079)

0.101

(0.095)

-0.035

(0.374)

0.163*

(0.081)

Controls

N

Yes

344

Yes

344

Yes

344

Yes

344

Yes

344

Yes

344

Panel B: Random Extensions

∆log Limit 0.021

(0.075)

0.074

(0.063)

-0.016

(0.065)

0.065

(0.062)

0.002

(0.329)

0.153*

(0.082)

Controls

N

Yes

348

Yes

348

Yes

348

Yes

348

Yes

348

Yes

348

16