# What’s in a Bill?
A Model of Imperfect Moral Hazard in Healthcare111 The authors are grateful to
participants in the APPAM 2022 Research Conference, as well as seminar
participants at Brigham Young University, Duke University, and the University
of Toronto for useful feedback.

David M. Anderson Duke University, Duke-Margolis Center for Health Policy, 100
Fuqua Drive, Durham, North Carolina, USA. Email<EMAIL_ADDRESS>Alex Hoagland
Corresponding author. University of Toronto, Institute of Health Policy,
Management, and Evaluation, 155 College St, Toronto, Ontario, Canada. Email:
<EMAIL_ADDRESS>Website: alex-hoagland.github.io. Ed Zhu
Boston University, Department of Economics, 270 Bay State Road, Boston, MA
02215. Email<EMAIL_ADDRESS>
###### Abstract

Models of consumer responsiveness to medical care prices are central in the
optimal design of health insurance. However, consumers are rarely given
spending information at the time they consume care, a delay which many models
do not account for and may create distortions in the choice of future care
consumption. We study household responses to scheduled medical services before
and after pricing information arrives, leveraging quasi-experimental variation
in the time it takes for an insurer to process a bill. Immediately after
scheduled services, households increase their spending by roughly 46%;
however, a bill’s arrival causes households to reduce their spending by 7
percentage points (nearly 20% of the initial increase). These corrections are
concentrated among households who are under-informed about their deductible or
whose expenditures fall just short of meeting the deductible, suggesting that
a bill provides useful pricing information. These corrections occur across
many types of health services, including high- and low-value care. We model
household beliefs and learning about expenditures and find that households
overestimate their expenditures by 10% prior to a bill’s arrival. This leads
to an over-consumption of $842.80 ($480.59) for the average (median) affected
household member. There is evidence that households learn from repeated use of
medical services; however, household priors are estimated to be as high as 80%
larger than true prices, leaving low-spending households especially under-
informed. Our results suggest that long deductible periods coupled with price
non-transparency may lead to an over-consumption of medical care.

Keywords: Ex-post moral hazard, price transparency, learning, low-value care
JEL codes: I12, I13, D01, D90

##  1 Introduction

The provision of health insurance plays a vital role in protecting consumers
against the risk of volatile, unpredictable health shocks. However, incomplete
information plagues health insurance markets, ultimately leading both public
institutions (e.g., governments) and private organizations (e.g., insurers) to
provide sub-optimal coverage (Einav and Finkelstein,, 2018; Dave and
Kaestner,, 2009). One of the main sources of this incomplete information is
“ex-post moral hazard,” which captures how an individual’s healthcare
consumption is responsive to changes in the price they face for
care.222Ultimately, ex-post moral hazard captures the extent to which one’s
demand curve for healthcare slopes downward. Note that the use of the term
“moral hazard” to refer to elastic demand responses for medical care
utilization is a slight abuse of notation that is now widely used in this
literature, beginning with Arrow, (1963). Although consistent with the notion
of “hidden action” in the sense that individuals may consumer more care as
they exert less effort in health production, we will refer to moral hazard
more as the extent to which, conditional on health status, individuals adapt
their care consumption decisions to the spot prices of care (Pauly and
Blavin,, 2008; Cutler and Zeckhauser,, 2000)

Consumer price responsiveness ultimately justifies some consumer cost-sharing
out-of-pocket (OOP) (Chandra et al.,, 2010; Goldman and Philipson,, 2007;
Johnson et al.,, 1997). Many studies have found evidence that consumers are
price-responsive in their demand for health care, with health consumption
increasing as individuals move into regions of their insurance contract with
lower marginal costs (Kowalski,, 2016; Duarte,, 2012; Dunn,, 2016).
Subsequently, the rate of consumer exposure to cost-sharing has been
increasing steadily over the last two decades in the United States, nominally
to limit the consumption of excessive or low-value services (Geyman,, 2012).
However, the optimal level of cost-sharing depends in large part on how
consumers respond to changes in the nonlinear pricing scheme of their
insurance plan, including dynamic incentives such as their expectations of
their end-of-year price (Aron-Dine et al.,, 2015; Baicker et al.,, 2015).

However, while increasing exposure to cost-sharing—for example, through
increasing enrollment in high-deductible health plans (HDHPs)—may reduce
overall levels of consumption, individuals report being confused about the
structure of their insurance contract and reducing consumption of even high-
value preventive health services which should be free to them, ultimately
making the plans a blunt instrument (Reed et al.,, 2009; Agarwal et al.,,
2017; Mazurenko et al.,, 2019; Brot-Goldberg et al.,, 2017).333During the
study’s time frame, value-based insurance designs—where certain high-value
services are carved out of cost-sharing obligations for consumers—have become
more prevalent (Chernew et al.,, 2007). This includes certain cost-sharing
exemptions promoted by the Affordable Care Act (ACA). These designs have been
shown to increase quality of care without changing spending decisions (Lee et
al.,, 2013); however, recent work has found that lack of clear guidelines in
these policies may result in confusion about cost-sharing exemptions,
ultimately harming consumers (Hoagland and Shafer,, 2021; Shafer et al.,,
2021). In addition, previous work has failed to find large discontinuities in
consumption around the transition points of a contract, such as the deductible
(Dalton,, 2014). This lack of a sharp response—which would be predicted in a
standard model of moral hazard where only spot prices influence decision-
making—has been previously explained either as evidence of forward-looking
consumers (Aron-Dine et al.,, 2015) or by noting various frictions in the
consumption of health care, including poor understanding of health plan design
(Loewenstein et al.,, 2013). Health insurance literacy is low among many
Americans (Edward et al.,, 2019), and the increasing complexity of insurance
contracts, coupled with price intransparency, may lead to worsening consumer
predictions of incurred but not yet received (IBNR) spending and OOP cost-
sharing.

In this paper, we highlight an overlooked feature of many healthcare systems
with significant implications for models of ex-post moral hazard and cost-
sharing: lack of timely pricing information. Consumers are rarely, if ever,
given information about the total costs of their health services at the point
of service, and are even less likely to be told their expected OOP
contribution then; instead, consumers in our sample wait an average of 4.1
weeks to be given information about the total bill, what the insurer has
elected to pay, and what their realized OOP costs are. In the interim period,
consumers must form expectations about their own realized expenses when making
future care decisions; forming these expectations is a nontrivial task, given
that there is substantial variation in the price of even basic health services
(Gruber,, 2022; Cooper et al.,, 2019).444Appendix Figure A.7 illustrates some
of the variation in prices for common services in our sample. We argue that
this mistimed pricing information limits the effectiveness of cost-sharing in
mitigating over-consumption, particularly in the case of HDHPs.

We study how households with employer-sponsored insurance (ESI) in the US make
medical spending decisions after a significant health expenditure for one of
their household members. Specifically, we assess household responses following
the use of a health service classified as “shoppable” by the Centers for
Medicare & Medicaid Services (CMS), services which are expected to constitute
a nontrivial but unknown amount of OOP spending for the household (CMS,,
2019). We identify the causal effect of a bill’s arrival in changing those
decisions, and further explore the mechanisms generating observed responses.
Before the bill arrives, households must make decisions based on their
expectations of OOP spending, conditional on their underlying health needs and
risk aversion. It may be that risk averse households avoid increasing their
consumption even after meeting a deductible, as they are unsure that they have
actually done so and hesitant to incur additional costs. On the other hand,
households may over-predict OOP spending, leading them to respond in the short
run by over-consuming care. Hence, our work is related to previous work
identifying the strategic delay of services such as dental care (Cabral,,
2017). In particular, we highlight the importance of corerct household beliefs
about spending when making strategic decisions, and show that this type of
behavior applies to a far broader and potentially more expensive set of hard
to predict events across the healthcare system.

We identify the causal parameter of interest—the impact of pricing information
on consumption decisions—based on exogenous variation in the time it takes
insurers to receive and process bills, which affects the length of the
household’s “interim period”. Appendix Figure A.8 illustrates the substantial
variation in how long it takes an insurer to receive and process a claim, both
within and across years. The average household waits 4.1 weeks for a bill from
a shoppable service; however, waiting times tend to be higher at the beginning
of a calendar year and the first month of each quarter, when insurers have
billing changes and new policies to incorporate into their processing
algorithms.555Waiting times are also affected by more general health policies,
such as the national transition to the International Classification of
Diseases, 10th Revision, Clinical Modification (ICD-10-CM), in October 2015.
This transition increased billing complexity by roughly five times and,
subsequently, the rate of administrative frictions in processing billing
information (Caskey et al.,, 2014). Waiting times are also affected by other
time-varying features of the healthcare system that are exogenous to the
household, including the rate at which physicians submit claims to insurers
for reimbursement. As this variation is insurer-specific and unpredictable by
a household, the length of time a household will wait for a bill is exogenous
at the consumer level.

Using a triple-differences regression design, we estimate how scheduled
healthcare consumption generates distinct household consumption spillovers
before and after the bill’s arrival. We find that, in the interim period
between the service and its bill, household members increase their total
health spending by about 46.4% ($55.91 per person per week). However, once the
bill arrives, consumption drops significantly by about one-fifth of that
increase, a reduction of $9.28 per person per week. These results are largest
for households with more limited information before the bill’s arrival,
including households who have consumed none or few services prior to the
shoppable service, as well as those for whom the shoppable service was
expected to be particularly expensive. This suggests that the effects of a
bill are largely the result of eliminating information frictions regarding the
price of care. Finally, we examine heterogeneity in household responses across
a spectrum of services, and find that households are most likely to over-
respond in their use of elastic care, such as preventable hospitalizations and
general practitioner visits or lab services.

These findings are consistent with a model of imperfect moral hazard, in which
households learn to form expectations of their OOP spending as bills arrive
following a delay. We write and estimate a model of consumer learning in the
face of delayed information, where consumers experience a lag between
consuming a good and learning how consumption affected future spot prices. We
use the exogenous variation in our data—now widening the scope of analysis to
include all health services consumed by the household within a year—to
separately identify average beliefs about OOP spending as well as how
households learn from health events over time.

Consistent with the reduced-form regression results, our model predicts that
in the absence of learning, households over-inflate their OOP spending by 11%
without pricing information. As a result, 10.5% of households in our sample
over-consume health services specifically because they believe erroneously
that they have already met their deductible, with the average (median)
affected household spending $842.80 ($480.59) more per household member than
they would have selected under full information. We do find evidence of
consumer learning: at the beginning of the year, households over-inflate their
expectations of OOP spending by an average of 80%, an over-estimate which is
quickly corrected as bills for medical services provide new information.

Taken together, our findings make several important contributions to a
discussion of moral hazard in health care. First, we present the first model
which incorporates price uncertainty into demand for health care and
highlights its implications for discussions of ex-post moral hazard. Our model
is related to literature on learning about prices in microeconomic theory more
broadly, including uncertain prices of financial assets and agricultural goods
(Ngangoue,, 2021; Boyd and Bellemare,, 2020). Our work is also related to a
broader literature on learning models with delays in belief updating (Karlsson
et al.,, 2009; Peng,, 2005). However, in these models delays typically arise
endogenously, either by consumer decisions to delay learning or information
processing limits which slow the usefulness of information. In contrast, our
model exploits exogenous variation in the delayed arrival of information that
lies outside the consumer’s control, but which still affects the marginal
utility and costs associated with choices retroactively. That is, consumers
must commit to expenditures weeks or months before knowing what those
expenditures actually are. Finally, our model allows for household learning
over time across a heterogeneous set of health services.

Second, our findings fit into a larger discussion of the usefulness of price
transparency policies in mitigating large levels of healthcare consumption in
the United States (Muir et al.,, 2012; Zhang et al.,, 2020). In contrast to
previous work—which highlighted how the availability of price information may
change the strategic decisions of patients shopping for a service (Gondi et
al.,, 2021)—we highlight a new mechanism through which price transparency may
affect future care decisions across entire households. Our findings provide
strong evidence that reducing price uncertainty in the weeks or months after a
service may have snowball effects reducing the utilization of unnecessary care
for a greater number of people over a longer duration of time. Policies which
shorten the length of a delay for medical cost estimates would reduce variance
between expected and actual cost-sharing, as would real time claims
adjudication, similar to prescription drug claims adjudication (Hartzema et
al.,, 2011).

Finally, we provide the first policy-relevant estimate of household beliefs
about health expenditures, which also allows us to estimate the effect of
under-information on over-consumption of care. Our model also allows us to
compare alternative plan designs that may limit over-consumption, including
those currently proposed by medical regulators (Korenstein et al.,, 2012;
Elshaug et al.,, 2017).666Although the policy relevance of price uncertainty
in healthcare for developing countries has been noted briefly (Knowles,,
1995), our work is the first to formalize this in a model of learning with
direct policy implications. Our model is useful both in the context of the
United States and other countries where consumers face demand-side cost-
sharing for using health care; this includes a broad range of countries,
including those with universal health care systems that still incorporate some
degree of cost-sharing (e.g., Australia, Germany, and the Netherlands, among
others) (Globerman,, 2016). For a more in-depth discussion of models of
optimal contract design under moral hazard, see Winter, (2013) and Blomqvist,
(1997). Our findings are therefore related to a broader discussion of how
consumers respond to nonlinear health insurance contracts (Brot-Goldberg et
al.,, 2017; Stockley,, 2016) and imperfect belief formation in healthcare
Hoagland, (2022). Similar to these papers, we find that consumers are
responsive to cost-sharing across a broad spectrum of services. However, we
also find that these fluctuations could be smoothed by targeted health
policies, such as plans with shorter time increments for deductibles (Shafer
et al.,, 2022).

We discuss the setting of shoppable services and the data in Section 2. We
then present our methods and identifying assumptions in Section 3, followed by
our empirical results in Section 4. We incorporate these findings into a model
of imperfect moral hazard in Section 5, with estimated results and insights in
Section 6. Finally, Section 7 highlights the relevance of these findings for
optimal design of insurance contracts.

##  2 Setting and Data

###  2.1 Data

Our primary data on household health utilization come from the IBM/Truven
Marketscan Commercial Claims and Encounters Data, spanning from 2006 to 2018.
These data contain detailed inpatient, outpatient, and pharmaceutical claims
for a sample of households enrolled in ESI through large U.S. firms. Each
observation includes diagnostic, procedural, and payment information,
including the date of service and the corresponding date on which the insurer
paid their portion of the claim. In addition, the data includes household,
firm, and insurance plan identifiers.777Note that insurance plan identifiers
are only available through 2013, which will affect the analytical sample used
in the structural exercise.

We limit our analytical sample to enrollees in one of eight large firms with
plan identifiers available. Our final sample includes 386,240 households with
two or more members, full eligibility, and continuous enrollment across their
window of observation. Throughout, spending data has been normalized to 2022
USD using the Consumer Price Index for All Urban Consumers series.

| Full Sample | Plan-Identified Sample
---|---|---
Panel A: Demographics |  |
Age (individual) | 31.67 (0.000) | 31.15 (0.000)
% female (individual) | 0.51 (0.000) | 0.51 (0.000)
Risk Score | 0.29 (0.000) | 0.29 (0.000)
Family Size | 3.08 (0.000) | 3.10 (0.000)
Panel B: Medical Utilization |  |
Total medical spending (indvidiual) | $4,764 [$975] (0.002) | $4,406 [$887] (0.002)
% of individuals with no spending | 0.17 (0.000) | 0.20 (0.000)
OOP medical spending (individual) | $650 [$198] (0.000) | $562 [$167] (0.000)
Household deductible $|$ deductible $>0$ | — | $1,040.24 (0.001)
% Households with zero deductible | — | 0.26 (0.000)
Household coinsurance rate | — | 0.29 (0.000)
% individuals with shoppable services | 0.06 (0.000) | 0.06 (0.000)
Total cost, shoppable service | $5,572 [$3,721] (0.011) | $5,645 [$3,814] (0.015)
OOP, shoppable service | $691 [$388] (0.002) | $574 [$290] (0.002)
Years | 2006–2018 | 2006–2013
$N_{\text{families}}$ | 368,237 | 367,445
$N_{\text{individuals}}$ | 1,357,392 | 1,311,554

  * •

Notes: Enrollees include employees and their covered dependents. Risk scores
are calculated using the CMS-HCC 2014 community model. Household plan
characteristics are calculated as discussed in Section 2. Spending values are
reported in 2022 USD. Standard errors are reported in parentheses; medians
(when reported) are in brackets.

Table 1:  Household Summary Statistics

Table 1 presents summary statistics for the full sample as well as the subset
of the sample with insurance plan identifiers. Households tend to be young and
relatively low-risk, with an average age of 31.7 years and between 3 and 4
household members. Insurance coverage is more generous than average, although
the conditional average deductible is over $1,000, and household members who
select into shoppable services typically spend close to a full year’s OOP
costs on that service alone. Note that the sub-sample with plan identifiers
does not appear substantially different from the full sample, an important
fact given that we use the plan-identified sample in our structural approach
(Section 6). Households in the plan-identified sample incur slightly lower OOP
costs than the full sample; however, this is likely indicative of decreasing
insurance coverage generosity over time, given that the latest 5 years of data
are excluded in this sub-sample.

###  2.2 CMS Shoppable Services

Our goal is to assess how pricing information contained in a medical bill
alters household utilization patterns. In our primary specifications, we
analyzed the impact of medical bills for individual health services that are
expected to generate a significant—but unknown—amount of OOP spending for the
household. We identified the utilization of 30 CMS “shoppable services,” which
correspond to non-urgent services that patients can schedule in advance (CMS,,
2019). We identified these services in the claims data using Current
Procedural Technology (CPT) codes for outpatient and inpatient services and
Diagnostic Related Groups (DRGs) for inpatient hospitalizations; the complete
list of services is available in Appendix Table A.1.888Note that effective
January 1, 2021, hospitals must publish standard charges for these services
online, including negotiated rates. However, this does not affect our
analytical sample which only goes through 2018; instead, we selected these as
services which patients typically schedule or plan for ahead of time, meaning
there is high potential for household strategic response to the service.
Additionally, patients may engage in some form of price shopping for the
procedure ahead of time, although there is little evidence of shopping in
healthcare (Mehrotra et al.,, 2017).

###  2.3 Bill dates & Plan characteristics.

One limitation of our data is that we are not able to view the exact date on
which consumers first received a bill from their provider for the services
rendered. Instead, we observe the date the insurance plan paid the provider
their portion of the pill. As this is the first possible date at which a
patient will receive their Explanation of Benefits (EOB), it is the earliest
date that definitive OOP cost information becomes available to a patient.
Hence, we use this date as a proxy for patient bill information.

Figure 1 presents the distribution of wait times (in weeks) between the date a
shoppable service was received and the date the insurance plan paid their
portion of the service bill. Note that there is substantial variation in this
wait time, with roughly 60% of bills being paid by insurers within the first
four weeks, and the rest taking longer than a month for payment to be settled.
As discussed in Section 1, the variability in the length of this period is
exogenous to the household and allows us to identify the causal impact of
receiving information about OOP expectations on household health utilization.

Figure 1: Variation in Wait Times Between Service Date and Bills’ Arrival

Notes: Figure depicts the distribution of wait times between the date the
service was provided and the date the insurance company paid their portion of
the service bill to the provider, measured in weeks. Only services included as
shoppable health events in our analytical sample are shown here. Vertical
dashed red line indicates the average duration of the waiting period,
approximately 4.5 weeks.

In addition to data on individual health services, we utilize data on
insurance plan characteristics to estimate how households respond during the
period when OOP prices remain unknown to them. In constructing measures for
these characteristics, we follow previous literature (Hoagland,, 2022; Marone
and Sabety,, 2022).999For tractability, our model allows for plans to have a
piecewise-linear cost-sharing contract comprised of: a family deductible, a
simplified non-specialist coinsurance rate, and a family OOP maximum. Measures
are constructed based on the empirical distribution of payments in the claims
data and cost-sharing parameters which minimize the sum of squared residuals
between predicted and observed OOP household spending (Zhang et al.,, 2018;
Marone and Sabety,, 2022). See Hoagland, (2022) Appendix A for a detailed
description of this methodology and an evaluation of the quality of these
inferences.

##  3 Methods

Household consumption of shoppable health services—particularly those with
large expected OOP costs relative to a deductible—may generate strategic
responses in household health spending (Cabral,, 2017). When exact OOP
spending information is not immediately transmitted, responses take place in
two stages: first, households respond to the event itself, based on their
expectations of spending; second, and only after the bill arrives, households
make decisions with full information in hand. Hence, we leverage these two
distinct response periods in a triple-differences regression framework to
estimate spillover responses to scheduled healthcare consumption separately
for the periods before and after a bill’s arrival.

We estimate the causal impact of a bill on spillover spending (e.g., for all
household members excluding the original consumer of the shoppable service).
The estimating equation for total spillover health spending (measured per week
per household-member) in household $i$ at week $t$ of year $y$ is given by
Equation 1:

$\mathbb{E}[\text{spend}_{ity}]=\exp\left\\{\beta_{1}\mathbbm{1}(\text{post\\_service}_{ity})+\beta_{2}\mathbbm{1}(\text{post\\_bill}_{ity})+\alpha_{\mathcal{I}}+\tau_{t}+\gamma_{y}+\xi_{\text{MD}}\right\\},$
(1)

where the two main regressors are dummy variables indicating whether the
shoppable service had already been performed and if the bill for the service
had arrived by week $t$, respectively. In addition, we consider the robustness
of our estimation approach to controlling for various time-invariant fixed
effects, including those for individual households, years, relative week of
the year (to account for within-year seasonality in health spending), and
provider fixed effects (for the providers offering the shoppable service).

We use Poisson regression to estimate multiplicative effects on spending. A
Poisson regression model is advantageous as it allows us to deal with the
skewed nature of our (non-negative) spending data while appropriately
including weeks with zero spending and avoiding a complete specification of
the dependent variable’s distribution (Manning and Mullahy,, 2001). Our
estimator will be consistent as long as the conditional mean of the dependent
variable is correctly specified, as is the case in ordinary least squares
(OLS) regression Gourieroux et al., (1984). Additionally, Poisson regression
allows us to avoid the inconsistency of regression coefficients induced by
heteroskedasticity in a log-linear transformed model (Santos Silva and
Tenreyro,, 2006).101010Poisson regressions were estimated in Stata using the
“ppmlhdfe” command to handle high-dimensional fixed-effects (Correia et al.,,
2020).

A critical assumption for the identification of our parameter of interest
($\beta_{\text{post\\_bill}}$ in Equation 1) is that the arrival of spending
information through the bill is exogenous to the affected households’
strategic spending decisions. Previous work has highlighted the endogeneity
inherent in estimating demand elasticities to major health events, especially
when those events are planned or scheduled in advance (Duarte,, 2012). In our
estimation, as we are not attributing spending responses to changes in price
(e.g., $\beta_{\text{post\\_service}}$ is not a demand elasticity), there are
no potential endogeneity concerns in estimation, as we are including both
strategic and non-strategic responses collectively in
$\beta_{\text{post\\_service}}$. As long as bill arrival times are exogenous
to the household, $\beta_{\text{post\\_bill}}$ will represent a causal
estimate of household “corrections” in response to pricing information.
However, should bills take systematically longer for higher-risk patients (who
might have families who are more likely to respond to health spending in the
first place), our estimates would be inconsistent.

There is strong evidence that variation in the time households wait for a bill
to arrive is exogenous to the household and uncorrelated with underlying
patient risk or procedure severity, as discussed in Section 1. Bill wait times
are highly seasonal within a year for a given payer, depending on both the
total volume of claims they are processing (Appendix Figure A.8) and
administrative frictions of initiating new enrollees and groups to new
benefits. In addition, factors such as new risk-adjustment policies,
transitions in billing systems (such as the 2014-2015 shift to ICD-10-CM), or
even the COVID-19 pandemic can overwhelm payer processing of claims,
occasionally even drastically increasing the wait time before patients learn
with certainty their ultimate OOP costs (Snowbeck,, 2022).

Still, bill wait times may be associated with underlying patient risk,
potentially introducing selection concerns affecting causal inference. If
payers have an incentive to slow down payments for highly-expensive
procedures, or if a higher-complexity patient takes longer to process, bill
times could be systematically longer for the most at-risk patients in our
sample. We test these claims directly in our sample, by comparing differences
in the average total cost of shoppable services based on the length of the
bill wait time in days.

Table LABEL:tab:balance presents the results. For each potential service, the
hypothesis that bills that took longer to arrive ( $d\geq 30$ days) are
associated with more (or less) expensive procedures is tested. We test these
hypotheses for both unadjusted means and averages adjusted for provider-
specific trends. We find that the large volume of procedures in each group
lends itself to statistically significant differences, but not economically
meaningful ones. The average difference across services constitutes only $220,
6.1% of total payments. In addition, the estimated value of the differences
varies widely, with almost a quarter of the included procedures estimated to
have shorter wait times for more expensive instances of the procedure. Taken
together, we find little evidence that bill wait times may be endogenous at
the household level.

##  4 Empirical Results

###  4.1 Effect of Bills on Spending

Table 2 presents the regression results from estimating Equation 1. We find
robust evidence that although spillover household spending increases following
the utilization of a shoppable service, the bills arrival causally affects
these responses Without conditioning on the bill’s arrival, the overall
estimated spending increase is roughly 40.2% of average weekly per-person
household spending (roughly $120). However, this conflates a period prior to
the plan’s payment of the claim where spending is estimated to increase by
46.4%, only to decline by 7.7% once the bill arrives. This decline (roughly
17% of the overall change in spending) is consistently estimated even after
controlling for time-invariant household and year trends as well as for
within-year seasonality and provider fixed-effects. The correction amounts to
$9.28 per person per week for the average household in the sample, or roughly
$482.44 per person annually.

| Main Models | Alternative Specifications
---|---|---
Post Service | 0.402*** | 0.464*** | 0.597*** | 0.472*** | 0.486***
| (0.0022) | (0.0032) | (0.0032) | (0.0032) | (0.0033)
Post Bill |  | -0.077*** | -0.080*** | -0.096*** | -0.076***
|  | (0.0030) | (0.0030) | (0.0030) | (0.0031)
$\overline{\text{spend}_{it}}$ | $120.49 | $120.49 | $120.49 | $120.49 | $120.49
Household FEs | X | X | X | X | X
Year FEs | X | X |  | X | X
Week of Year FEs | X | X |  |  | X
Provider FEs | X | X |  |  |
Observations | 61,860,735 | 61,860,735 | 61,860,735 | 61,860,735 | 61,860,735

  * •

Notes: Table presents results from triple-difference Poisson regressions
highlighting the role of a bill’s arrival on health spending of affected
household members. Each column in this table estimates the impact of a single
household member’s shoppable health service—and accompanying bill—on health
spending for all other household members. Regression coefficients displayed
illustrate the expected change in log household spending (measured per person-
week) associated with the service date and bill arrival (both measured as
dummy variables). Throughout, standard errors were clustered at the household
level.

${}^{*}p<0.05,^{**}p<0.01,^{***}p<0.001$

Table 2:  Estimated Impact of Bill Arrival on Household Health Spending

These findings are consistent with a model in which consumers over-estimate
their actual OOP contributions prior to receiving the definitive pricing
information of a medical bill. Due to this over-estimation, consumers enrolled
in insurance plans with piecewise-linear cost-sharing insurance plan designs
(e.g., a nonzero deductible) may incorrectly assume that the marginal cost
associated with additional services has declined (e.g., by meeting a
deductible). Once the bill arrives correcting any errors in perception,
however, individuals curtail their spending increases in response.

Given that we are using the dates insurance plans pay providers as a proxy for
bill arrival, it is possible that we are artificially splitting the post-
service period into two essentially random periods and attaching significance
to a spurious difference between the two periods. To test this possibility, we
conducted placebo tests, running regressions on artificial data that randomly
assigned consumers new wait times for their bill based on the empirical
distribution of wait times.111111That is, for each individual consuming a
shoppable health service, we kept fixed the service date and artificially
constructed a new bill arrival date as the service date + a random draw of a
bill wait time. Wait times were drawn from the empirical distribution of our
sample (e.g., Figure 1). All regressions were then estimated on the new sample
with an updated $\text{Post\\_Bill}_{it}$ coefficients in each iteration.

Figure 2 presents the results for 250 placebo simulations. The distribution of
all estimated regression coefficients $\beta_{\text{Post\\_Bill}}$ is shown,
compared against the estimated regression coefficient of our preferred
specification ($-0.077$) depicted as the vertical dashed red line. Placebo
coefficients are color-coded by their associated $p$-value. The distribution
of placebo coefficients is centered around zero, with most of the coefficients
statistically indistinguishable from zero. In fact, the only statistically
significant coefficients in the placebo regressions are those that would
indicate a positive correction in spending following the arrival of the bill.
Taken with the results from Table 2, this suggests that it is unlikely that
our results are spurious correlations from a convenient semi-random splitting
of the post-service period.

Figure 2: Distribution of Placebo Regression Coefficients for
$\beta_{\text{post\\_bill}}$

Notes: Figure shows the distribution of placebo regression coefficients for
the dummy variable $\text{Post\\_Bill}_{it}$ in Equation 1 ($n=250$). Each
placebo is constructed by artificially varying wait times for bills based on
the empirical distribution of wait times in the analytical sample. Standard
errors are clustered at the household level. Coefficients are color-coded
based on statistical significance. The vertical dashed red line indicates the
estimated coefficient of the preferred specification (Table 2).

###  4.2 Understanding Mechanisms: Heterogeneity by Deductible Spending

There are several ways households might find bills informative enough to alter
their healthcare utilization patterns. First, households may learn about the
overall prices of the services they received, particularly their own OOP
burden for their care. This may include more detailed information about the
percentage of a household deductible that has now been met as a result of the
service. In particular, a bill that informs consumers that they are still
short of meeting a deductible may generate the corrective action observed in
Section 4.1. Second, households may learn about the extent to which their
insurance does or does not cover certain procedures. In this sense, bills
inform households not about the overall prices of services, but correct a
misunderstanding of the fraction of services they will have to cover OOP.
Finally, a bill may reveal discrepancies between a patient’s understanding of
a service and the provider’s billing, including up-coding practices. This
information may also alter future healthcare spending to the extent that it
erodes household trust in the healthcare system (Webb Hooper et al.,, 2019).

In order to understand the mechanisms driving household responses to bills, we
assessed responses across the distribution of spending patterns prior to the
shoppable service. The intuition for this exercise is that variation in pre-
event spending (specifically, the fraction of a deductible met prior to a
service) is informative of the amount of engagement with the health system in
a particular year. Hence, the extent to which responses to bills vary across
the distribution of pre-event spending indicates the rate at which households
are learning about their own prices of care, rather than learning about other
features of the health care system.

Figure 3: Heterogeneous Bill Effects Across Household Deductible Status at
Time of Service

(a)

(b)

Notes: Panel (a) shows estimated coefficients and 95% confidence intervals for
$\mathbbm{1}\\{\text{Post\\_Service}_{it}\\}$ and
$\mathbbm{1}\\{\text{Post\\_Bill}_{it}\\}$ in Equation 1 by decile of
household deductible spending prior to the event. Standard errors are
clustered at the household level. Deductibles are imputed based on previous
literature (Hoagland,, 2022; Zhang et al.,, 2018). Panel (b) depicts the
estimated post-bill spending increase (e.g., the sum of the coefficients). The
horizontal dashed black line indicates the estimated pooled spending increase
in column 1 of Table 2.

Figure 3 presents results stratified by decile of household deductible
spending prior to the event. The spending responses for both the interim
period between the service and the bill (yellow) and the post-bill correction
(green) are shown in panel (a). Both spending responses and corrections are
largest for households who have spent little towards their deductible before
the event: post-service spending increases are estimated to be as high as 80%
for households with less than 10% of their deductible met, and fall to under
20% for households close to their deductible. Correspondingly, post-bill
corrections are estimated to be as high as 30% (roughly 37.5% of the post-
spending increase) for the low-spending group, and converging to zero for the
high-spending group. In both cases, spending responses for the group closest
to meeting their deductible are statistically indistinguishable from
households who met their deductible prior to the shoppable service. Finally,
households who don’t face changes to their marginal cost of care from the bill
(e.g., those in zero-deductible households and those which have already met
their deductible) exhibit near-zero spending responses to the bill.121212The
coefficient for bill response among the group with zero deductible is
statistically different from zero, but with a coefficient smaller than 5%.
This is likely due to some measurement error in the classification of
individuals as being enrolled in a plan without a deductible, which may still
include some cost-sharing for specific services (e.g., emergency department
use) (Zhang et al.,, 2018).

Panel (b) shows the estimated post-bill spending increase, measured as the sum
of the two estimated regression coefficients. Spending increases following a
bill’s arrival tend to be significantly larger for previously lower-spending
households, including above the average 40.2% spending increase estimated in
Table 2. This may be because households with previously low levels of spending
coordinate their care more, exhibiting a greater tendency for strategic
decision-making (alternatively, this could be due simply to seasonality in
spending patterns). As the level of pre-event deductible spending increases,
however, post-bill responses fall to between 10% and 20%, statistically
indistinguishable from the group of households which have already met their
deductible prior to an event.

Taken together, these results suggest that households respond, at least in
part, to a bill’s information about OOP expenditures. This information appears
to be especially relevant to households who have yet to contribute much to
their deductible, while households without a deductible or who have already
met it exhibit negligible responses to the bill.

Additionally, we can gain further insight as to the mechanisms associated with
bill responses by using additional variation in the relative cost of a
shoppable service. The intuition for this exercise is that high-cost events
are more likely to ultimately alter a household’s marginal cost of services,
while lower-cost events may have similar price uncertainty without any
economically meaningful costs to that uncertainty. Given that price
information is most valuable to households when it communicates whether or not
households have crossed the threshold of their deductible (e.g., marginal
costs are reduced), we can identify the extent to which households learn about
price from their bills—separate from other forms of learning—by comparing
household responses to high- and low-cost events. To do this, we explore two-
way heterogeneity in the effects of household responses considering both pre-
event deductible contributions and the resulting change in deductible spending
after the scheduled health consumption.

Figure 4: Heterogeneous Bill Effects By Household Deductibles and Service Cost

Notes: Figure depicts estimated coefficients for
$\mathbbm{1}\\{\text{Post\\_Bill}_{it}\\}$ in Equation 1 across deciles of
household deductible spending prior to and following an event. Here, sample is
restricted to individuals in a non-zero deductible plan who have not yet met
their deductible at the time of service. Each row indicates a different decile
of deductible spending prior to the event, while each column indicates deciles
following the event. Standard errors are clustered at the household level.
Deductibles are imputed based on previous literature (Hoagland,, 2022; Zhang
et al.,, 2018).

Figure 4 presents the results. We restrict our attention to households
enrolled in plans with a non-zero, unmet deductible at the time of service. We
then separately estimate Equation 1 across cells of households who have
similar deductible spending both before and because of the major health event.
The figure depicts a two-way heatmap of estimated bill responses across cells.
Consistent with Figure 3, we find that households starting at lower levels of
their deductible exhibit greater sensitivity to their bill. In addition, we
find that households appear considerably less responsive to low-cost services;
coefficients are estimated to be much closer to zero when households do not
move across deciles of spending.

Most notably, however, Figure 4 highlights a stark difference in household
responsiveness to events that left households just shy of missing their
deductible, relative to events that pushed households across the threshold.
Across all levels of pre-event spending, estimated coefficients are largest
when a bill arrives for an event that just missed the household deductible. On
the other hand, coefficients are smaller and more likely to be statistically
indistinguishable from zero if the bill reveals that the household has already
met their deductible. This is consistent with a model where households over-
estimate OOP spending—or in other words, the probability of having met a
deductible—thus exhibiting greater spending corrections closer to the
threshold at which marginal costs would change.

Taken together, accounting for heterogeneity in household responsiveness to
bills—including both spending histories and the relative cost of
services—suggests that households are most responsive to bills when the
pricing information they reveal are particularly salient. When households have
little information about their deductible, or when the bill indicates that a
household’s marginal cost of additional care has not changed, the arrival of
pricing information curbs overly large responses in spillover spending
following a shoppable health service.

###  4.3 What Services Are Affected?

Finally, we assess whether household responsiveness to price information
varies across broad categories of medical services, including hospital care,
specific types of outpatient services, and pharmaceutical spending. This
decomposition allows us to examine whether household spending responses—or the
extent to responses are corrected after a bill arrives—varies with any measure
of perceived or real quality of care. Particularly, we examine how bills
affect future utilization of typically high-value health services (e.g.,
preventive screenings, behavioral health services) as well as typically low-
value care (e.g., unnecessary pre-operative screenings, imaging services, or
surgeries).

| Regression Coefficients | Pre-Treatment Averages
---|---|---
| Post Service | Post Bill | % $\geq 0$ | Conditional Mean
Hospital Care |  |  |  |
Emergency Department | 0.108*** | -0.021 | 0.67% | $929.98
| (0.0129) | (0.0133) |  |
Preventable Hospitalizations | 0.371*** | -0.194* | 0.04% | $19,979.89
| (0.0829) | (0.0848) |  |
Outpatient Care |  |  |  |
Behavioral Health | -0.020 | 0.018 | 1.19% | $119.47
| (0.0132) | (0.0134) |  |
Chiropractic Care | -0.005 | 0.027 | 1.86% | $133.39
| (0.0147) | (0.0151) |  |
Evaluation & Management | 1.440*** | -0.518*** | 1.05% | $121.45
| (0.0066) | (0.0062) |  |
Imaging | 0.098*** | -0.037*** | 2.55% | $265.52
| (0.0108) | (0.0111) |  |
Lab Services | 0.198*** | -0.178*** | 3.96% | $62.14
| (0.0113) | (0.0119) |  |
Low-Value Services | 0.084*** | 0.028** | 6.58% | $148.61
| (0.0094) | (0.0097) |  |
Preventive Care | 0.345*** | -0.249*** | 11.68% | $120.47
| (0.0036) | (0.0037) |  |
Specialist Care | 0.550*** | -0.181*** | 0.57% | $114.70
| (0.0192) | (0.0198) |  |
Prescriptions | 0.018*** | -0.006 | 18.30% | $147.14
| (0.0047) | (0.0048) |  |

  * •

Notes: Table shows coefficients from triple-difference regressions capturing
service-specific effects of pricing information ($N=59,177,995$). Columns (1)
and (2) present regression coefficients; column (3) indicates the fraction of
pre-treatment weeks when spending was positive; and column (4) presents pre-
treatment weekly averages, conditional on positive spending. See Appendix
Table XXX for a complete list of the CPT codes for each of the outpatient
categories. ${}^{*}p<0.05,^{**}p<0.01,^{***}p<0.001$

Table 3:  Estimated Impact of Bill Arrival on Service-Specific Spending

Table 3 presents the results. We separately estimated the coefficients for
Equation 1 with each sub-category of spending as its own dependent
variable.131313Appendix Table XXX includes detailed descriptions of the
construction of each of these variables. Overall, we find that households
respond to shoppable services across a spectrum of services, increasing their
consumption in the short-run after a service is performed, and then reducing
that consumption significantly once the bill arrives.

After an individual household member receives a significant health services,
other household members are more likely to seek hospital care, including a
10.8% increase in emergency department visits and a 37.1% increase in visits
for potentially preventable hospitalizations (e.g., admissions to treat
dehydration) (Agency for Healthcare Research and Quality,, 2007). Following
the receipt of the bill, however, use of inpatient care for preventable
hospitalizations falls by roughly 52.3% of the increase (a 19.4% decrease).

Some outpatient services, including those for behavioral health (e.g.,
psychotherapy) and chiropractic care (e.g., physical therapy), are affected
neither by the consumption of a shoppable service nor its accompanying bill;
this is presumably because these services have more inelastic demand and lower
rates of cost-sharing generally. However, we find that when households
increase demand for a type of outpatient service following a major health
event, they tend to over-increase spending. Bill arrivals cause households to
correct spending increases by between 32% and 90%. Households increase their
utilization of general practice visits (e.g., E&M visits, lab work, and
preventive screenings) the most, followed by specialist visits (e.g.,
dermatology). While household demand for prescription drugs increases slightly
following a health event in the home (by 1.8%), we do not observe a
corresponding reduction in demand following the bill’s arrival. This could be
because of the already high levels of pharmaceutical spending relative to
other medical consumption.

Somewhat surprisingly, we do not observe that households reduce their
utilization of low-value care following a bill’s arrival. These services,
which include services such as imaging for lower-back pain, misuse of
prescription medications to manage migraines and bacterial infections, or
unnecessary pre-operative screenings, are determined based on the
recommendations of the Choosing Wisely campaign (Colla et al.,, 2015). We find
that households increase their use of low-value care by 8.4% following a major
service, and then further by another 2.8% once the bill arrives. This may be a
result of a “cascade of care” effect associated with increased consumption of
general medical care, which in turn prompts downstream increases in physician
ordering of low-value services (Ganguli et al.,, 2020). Physicians typically
retain control over when low-value services are performed, in order to reduce
their own uncertainty, liability, or “just to be safe” (Colla and Mainor,,
2017). Our finding of increased consumption of low-value services following
major health events is consistent with prior work, but warrants future
exploration as to whether it is physician- or patient-driven (Hoagland,,
2022).

##  5 Model

Based on the empirical findings from our reduced-form analysis, we propose a
model of imperfect moral hazard, in which consumers make medical care choices
based on beliefs about realized spending. Central to the model is the delayed
nature of pricing information, which may lag behind consumption by weeks or
months while still affecting the spot prices of care in ways that are unknown
to the consumer before the bill arrives. As a result, consumers must form
expectations about realized OOP spending and the implied marginal cost of care
in each period. We first consider a case where consumer beliefs are static
(e.g., where there is no learning) before introducing a learning component to
the model in Section 5.2.

A patient $i$ chooses medical spending in each period $t$, with the choice
variable $m_{it}$ measured in the dollar value of the services.141414To be
consistent with the reduced-form evidence presented above, we model spending
choices at the weekly level and measure spending normalized by household size.
The patient selects $m_{it}$ as a utility-maximizing response to a health
shock $\lambda_{it}$. Following Einav et al., (2013), we calibrate individual
patient utility as a quadratic loss function in the distance between selected
health spending and the unobserved health shock:

$u_{it}=(m_{it}-\lambda_{it})-\frac{1}{2\omega_{i}}(m_{it}-\lambda_{it})^{2}-c_{ijt}(m_{it};M_{\mathcal{I}t}).$
(2)

Here, $\omega_{i}$ is an individual time-invariant “moral hazard” parameter
capturing individual heterogeneity in demand responsiveness to the price of
services.151515For more discussion on this heterogeneity, see Einav et al.,
(2013). In addition, $c_{ijt}(m_{it};M_{\mathcal{I}t})$ denotes the OOP costs
associated with $m_{it}$, which depends on the piecewise-linear cost-sharing
contract of individual $i$’s chosen insurance plan, $j$, as well as the OOP
spending to date at the household level,
$M_{\mathcal{I}t}=\sum_{i\in\mathcal{I}}\sum_{s=1}^{t-1}m_{is}$. Note that an
individual’s OOP costs for services are weakly decreasing in
$M_{\mathcal{I},t}$.

Under full information, patients know both the value of $M_{\mathcal{I}_{t}}$
and how it affects $c_{ij}(\cdot)$. Furthermore, in the case where cost-
sharing is linear at all stages of the contract, a patient’s marginal OOP cost
is given by $c_{ijt}\in[0,1]$, where $c=1$ applies to all services before a
deductible has been met and $c=0$ applies for all services after an OOP-max
has been met. Between the deductible and the OOP-max, $c$ is typically in the
open interval $(0,1)$. With full information about prices, the static choice
of $m_{it}$ in each period is simply the solution to the first order
condition:

$1-\frac{1}{\omega_{i}}(m_{it}-\lambda_{it})-c_{ijt}=0\Rightarrow
m_{it}^{*}=\max\left[0,\lambda_{it}+\omega_{i}(1-c_{ijt})\right].$ (3)

That is, medical expenses in each period are chosen so that the marginal
utility of those services is equal to the marginal (known) OOP cost. In
particular, as $c$ changes from 1 to $c<1$ as households meet their
deductible, household members will have a discontinuous increase in their
medical consumption in future periods.

However, based on the discussion in Section 4, we suppose that
$M_{\mathcal{I},t}$ is not known with certainty at the time a service is
performed. Rather, household spending can be divided into two components:
spending for services whose bills have already arrived (e.g., where prices are
known), and spending for services without pricing information yet available.
For ease of notation, suppose that each bill takes $\tau$ weeks to arrive, so
that a bill for a service procured in week $t$ would arrive in week
$t+\tau$.161616Note that in the empirical estimation of the model, the length
of time between a service and bill’s arrival is allowed to vary across
services; this assumption is only made in this section for ease of exposition.
Based on these components, households respond to a signal of their spending
$\theta$:

$\theta_{it}=\underbrace{\sum_{s=0}^{t-\tau}\sum_{i\in\mathcal{I}}c_{ij}(m_{is})}_{\text{known
spending}}+\underbrace{\sum_{s=t-\tau+1}^{t}\sum_{i\in\mathcal{I}}s_{i}(m_{is}|x_{is}),}_{\tilde{\theta}_{it}=\text{unknown
spending}}$ (4)

where $s_{i}(m_{is}|x_{is})$ represents service-specific signals of spending,
which may depend on individual, household, and service level characteristics.

###  5.1 Simple Case: Constant Under-information

In the simplest case, we suppose that signals do not vary across services, but
rather assume that cost signals are a constant multiple of true costs:

$s_{i}(m_{is}|x_{is})=\beta\cdot c_{ijs}(m_{is}).$ (5)

That is, before a bill arrives, patients inflate (or deflate) their true OOP
spending by a constant parameter $\beta$, which does not vary across services
or individuals.171717Note that allowing $\beta$ to be a random coefficient
varying across individuals is a simple extension of the model; for the present
purposes, however, we focus on an average of $\beta$ across the population of
interest. In the simplest version of the model, we also assume that there is
no learning about $\beta$ over time; we introduce learning in Section 5.2.
Based on these assumptions, a household’s signal of their OOP spending (and
hence, of their marginal cost for additional spending) can be simplified as

$\theta_{it}=\sum_{i\in\mathcal{I}}\sum_{s=0}^{t}(1-D_{is})\beta
c_{ijs}(m_{is})+D_{is}c_{ijs}(m_{is}),$ (6)

where $D_{is}$ is a binary variable indicating if the bill for services
performed in week $s$ has arrived ($D_{is}=1$) or not ($D_{is}=0$). Based on
the household’s value of $\theta_{it}$ in each period, the signal for the
marginal cost of future expenditures in the simple piecewise-linear insurance
contract setting is given by

$\hat{c}_{it}=\begin{cases}1&\theta_{it}<d\\\ c&\theta_{it}\geq d,\end{cases}$
(7)

where $c<1$ in general.181818Note that in practice, we estimate the model on
the sample of individuals enrolled in plans with non-zero deductibles. This is
to cleanly capture the ways in which misperception of OOP spending may affect
discontinuous changes in the marginal cost of spending across thresholds of
the linear insurance contract.

In this simplified case, the central parameter of interest is $\beta$, the
rate at which households systematically over- or under-inflate their true
levels of OOP spending prior to the arrival of the pricing information
contained in a bill. Additional unobservable parameters in the model, which
threaten identification, include heterogeneity in moral hazard $\omega_{i}$
and individual health shocks $\lambda_{it}$. Separate identification of
$\beta$ relies on being able to credibly identify the hyper-parameters
governing the distributions of these characteristics.

When estimating the model, we calibrate these nuisance hyper-parameters to
match moments predicted by (a) previous research and (b) training data not
used in the structural estimation. We use the estimated regression
coefficients predicted by Einav et al., (2013) in order to capture variation
in moral hazard parameters across households.191919Note that these regression
models result in individual-level predictions for $\omega_{i}$; in estimation,
we aggregate these to the household level by taking the mean of
$\log(\omega_{i})$ across all members $i\in\mathcal{I}.$ We model individual-
level health shocks as draws from an individual-specific shifted lognormal
distribution; this distribution captures both the skewed nature of the
observed spending data and the nonzero probability of an individual choosing
zero spending in a period. That is, each individual in each period draws
$\lambda_{it}$ from a distribution $F(\mu_{i},\sigma_{i},\kappa_{i})$ such
that

$\log(\lambda_{it}-\kappa_{i})\sim\mathcal{N}(\mu_{i},\sigma_{i}^{2}).$ (8)

We calibrate the three hyper-parameters $(\mu_{i},\sigma_{i},\kappa_{i})$ to
match the empirical distribution of weekly spending using the individuals in
our analytical sample who are not included in the structural estimation. These
include individuals enrolled in plans with no deductible, as well as patients
enrolled in any type of plan between 2014 to 2018. Individuals in this sample
are grouped into cells based on patient demographics—including age, sex, risk
score quartile, and relationship to the main employee—and the empirical
distribution in each cell is matched to the shifted lognormal
moments.202020This is done using three properties of a shifted lognormal
distribution: $\overline{\lambda}=\exp(\mu+\frac{1}{2}\sigma^{2})+\kappa$,
$\lambda^{M}=\exp(\mu)+\kappa$, and
$\frac{\text{sd}(\lambda)}{\overline{\lambda}}=\sqrt{\exp(\sigma^{2})-1}$,
where $\lambda^{M}$ denotes the median. The solution to this system of
equations given the moments of the empirical distribution of $\lambda$
identifies the three hyperparameters $\mu,\sigma,\kappa$. Once these
parameters are identified, individual-period shocks are drawn for each member
of the model sample and then summed to the household-period level.212121In
order for shocks to be meaningful, we restrict
$\lambda_{\mathcal{I}t}<m_{\mathcal{I}t}$ in each period.

Given these calibrations, identification of the main parameter of interest
$\beta$ comes centrally from exogenous variation (at the household level) in
the length of time required for a bill to arrive after different health
services. This variation may exist across services as well as across
households; importantly, underlying variation in $\tilde{\theta}_{it}$ which
artificially moves households above or below their deductible is central to
identifying how $\beta$ changes household estimates of $\hat{c}$ in ways that
most closely fit the observed choice data.

###  5.2 Learning

Once beliefs about OOP costs can be reasonably calibrated in the model, a
natural question is whether consumers correct their beliefs with repeated
exposure to health information. Households with frequent interactions with the
health system, particularly within a plan year, may have beliefs about their
bills which converge to the truth over time.

To assess this question, we incorporate household learning about the
calibration parameter $\beta$. We model each bill’s arrival as a signal from
which consumers can learn.222222For now, we model each signal as having equal
impact; future extensions of this model could flexibly model heterogeneous
signals based on the total cost of a service or by different service types.
Households are assumed to have prior beliefs about $\beta$ which follow a
normal distribution with a mean $\mu_{\beta,0}$ and variance
$\sigma^{2}_{\beta,0}$:

$\hat{\beta}_{i0}\sim\mathcal{N}(\mu_{\beta,0},\sigma^{2}_{\beta,0}).$ (9)

When a bill arrives for a household conveying information about the prices of
medical services, it in essence communicates that $\beta=1$. Hence, we model
each signal $s_{it}$ as being drawn from a normal distribution centered at 1
and with a signal variance $\sigma^{2}_{s}$:

$s_{it}\sim\mathcal{N}(1,\sigma^{2}_{s}).$ (10)

We assume that households update their prior beliefs in accordance with Bayes’
Rule, conditional on their observed signal. Assuming normal distributions for
both the prior and posterior distributions allows for closed-form solutions
for household beliefs about $\beta$ at each period, and is consistent with
previous learning models (Crawford and Shum,, 2005). This expanded version of
the model therefore has three parameters of interest. First, the average prior
mean $\mu_{\beta,0}$ captures the extent to which households are uninformed
about the relative costs of their medical care at the start of an enrollment
period. The dispersion of this lack of information across households is
captured in the variance of the average prior, $\sigma^{2}_{\beta,0}$.
Finally, the variance of the signal, $\sigma^{2}_{s}$, reflects how precise
the information communicated by each medical bill is, and subsequently how
rapidly household beliefs converge to the true parameter of 1.

Estimating household learning allows deeper insight into the spread of
household beliefs about their expenses both across households in the sample
and over the relative course of an enrollment period. In particular, the speed
with which beliefs converge informs the rate of over-consumption of medical
care relative to fully-informed households. As in the simpler case of the
model, identification of the three learning parameters
$(\mu_{\beta,0},\sigma^{2}_{\beta,0},\sigma^{2}_{s})$ stems from exogenous
variation in bill timing. When the parameter space is expanded, identification
comes from various sources. Within-household variation in expenditures
relative to pending (hence, unknown) OOP expenditures serves to identify both
the starting point of household beliefs (the prior mean) and the rate of
convergence (governed, in this case, by the signal variance). Similarly,
variation in choices across households identifies the spread of beliefs,
summarized in the prior variance; this parameter informs both the spread of
households’ starting beliefs as well as how that spread evolves over time.

##  6 Model Results

###  6.1 The Case of Constant Over-/Under-Estimation

We estimate the model presented in Section 5 for 240,111 households in our
analytical sample enrolled in plans with nonzero deductibles from 2006 to
2013. For each household-week, we simulate household health shocks and draw
idiosyncratic moral hazard parameters; then, for different values of $\beta$,
we estimate household signals of underlying OOP spending and the marginal cost
of incremental spending, $\hat{c}_{it}$. Taken together, these estimates
produce a prediction of spending $m_{it}(\beta)$, which differs as $\beta$
changes. Our primary measure of model fit is the root mean squared error
(RMSE) between observed and predicted levels of weekly spending at the
household level.

Figure 5: Estimating Household Responsiveness $\beta$ to Spending Before
Bills’ Arrival

Notes: Figure depicts the relationship between chosen level of household pre-
bill discounting parameter $\beta$ and the mean squared error (MSE) of the
model presented in Section 5. MSE is measured as the mean squared error
between observed and predicted household spending at the weekly level. For
each value of $\beta$, the median result of 50 simulations with independently
drawn health shocks is shown in the black line; the confidence band
illustrates one standard deviation above and below the median. The blue band
denotes the full range of observed $\min_{\beta}MSE(\beta).$

Figure 5 presents the estimated relationship between $\beta$ and model fit,
based on $35$ simulations with different individual health shocks in each
simulation. The median RMSE for each value of $\beta$, as well as the 5th and
95th percentiles, are shown. Note that in general, RMSE is decreasing in
$\beta$ until the function reaches a minimum at $\beta=1.11$, after which RMSE
increases. The blue band in the figure shows the estimated 95% confidence
region for the minimizing value of $\beta$, $[1.09,1.11]$.

The model estimates, as illustrated, suggest that households over-estimate the
OOP spending of services prior to the arrival of price information by between
9% and 11%. This is consistent with the findings of Section 4, which similarly
illustrated a “correction” in implicit marginal costs following the arrival of
the bill.

We conduct a simple counterfactual analysis to compare how spending
predictions differ given this inflation, against a counterfactual world where
$\beta$ is correctly perceived to be 1 for all household-weeks (see Appendix
Figure A.9 for details on the simulation). We find that over-estimating the
costs of medical services leads to over-spending for 10.5% of households, with
the average (median) affected household spending $842.80 ($480.59) more per
household member in medical services that they would not have selected had
they been correctly informed of their true OOP costs. This corresponds to an
over-spending of 35.2% (33.3%) for the average (median) affected household
(see Section 4 below for more details).232323Note that these percentage
changes are measured relative to the counterfactual predicted spending; that
is, as $(Actual-Counterfactual)/Counterfactual$.

###  6.2 Learning

Finally, we incorporate the possibility of household learning into our
estimates. We estimate that the average household’s prior for $\beta$ is
roughly 1.8, indicating an 80% over-estimate of OOP costs. There is relatively
little variation across households, as captured by the estimated prior
variance parameter $\sigma^{2}_{\beta,0}=0.026.$ Put into context, we estimate
that roughly 95.5% of households (two standard deviations to either side of
the mean) fall in the interval $(1.48,2.12)$, indicating high levels of
misinformation. This further indicates that fewer than 0.15% of households’
initial beliefs about $\beta$ would be expected to be 1 or fewer.

Figure 6: Evolution of Beliefs about $\beta$ Across Plan Year

Notes: Figure depicts average value of $\beta$ across the relative week of a
plan year for the full sample. Gray area indicates one standard deviation of
$\hat{\beta}$ above and one standard deviation below the mean.

Figure 6 shows how beliefs evolve in response to medical spending. We estimate
that bills provide extremely precise information, with the signal variance
term estimated to be 0.001. That is, roughly 95.5% of household signals for
$\beta$ fall in the interval $(0.94,1.06)$. This leads to rapid convergence of
beliefs as the year progresses, as illustrated in the figure in the blue
curve, which indicates the average value of $\hat{\beta}$ across the sample by
week of year. Within the first quarter of the year, average household
inflation for OOP costs has converged to below 25%; by the middle of the plan
year, inflation is within one standard deviation of the truth. However, the
average household does not have sufficiently many medical encounters for their
beliefs to converge completely; by the end of the plan-year, the average
household value of $\beta$ is estimated to be about 1.1, the same value
estimated in the preceding section.

###  6.3 Counterfactual Exercises

The full model with household learning permits the same counterfactual
simulations as above. We estimate predicted spending differences between the
observed data (using the equilibrium model parameters) and three
counterfactual states of the world: one where consumers are fully informed
about their OOP costs at the time of service (e.g., where $\beta=1$ for all
household-weeks); one where priors are re-centered around the truth (e.g.,
where $\mu_{\beta,0}=1$, but the other learning parameters remain unchanged);
and one where deductibles reset more frequently than at the yearly level.
While the first counterfactual exercise assumes full information, the second
exercise allows for idiosyncratic differences across signals, but centered
around the truth. That is, in each household-week, beliefs are centered around
$\beta=1$ but drawn randomly, with decreasing uncertainty over time. Finally,
the exercises in which deductibles reset more frequently capture changes in
both how often household uncertainty affects the estimated marginal costs of
services and the length of time for which uncertainty is allowed to persist.

| Spending/Person |  | Conditional Differences
---|---|---|---
| Average | Median | % Diff $>0$ | Average | Median
Panel A: Non-Learning Model |  |  |  |
Observed Data | $2,007 | $1,126 | – | – | –
Full Information ($\beta$ = 1) | $1,899 | $1,066 | 12.5% | $863 | $487
Deductible Resets Quarterly |  |  |  |  |
Deductible Resets Monthly |  |  |  |  |
Panel B: Learning Model |  |  |  |
Observed Data | $2,135 | $1,189 | – | – | –
Full Information ($\beta$ = 1) | $1,899 | $1,068 | 22.4% | $1,056 | $573
Re-centered Priors ($\mu_{\beta,0}=1$) | $1,895 | $1,064 | 23.4% | $1,023 | $554
Deductible Resets Quarterly |  |  |  |  |
Deductible Resets Monthly |  |  |  |  |

  * •

Notes: Table presents average and median spending per household member
predicted by the models outlined in Section 5 under different assumptions of
the underlying structural parameters. Panel A uses the model described in
Section 5.1 without learning, and Panel B uses the model outlined in Section
5.2. The first row in each panel indicates predicted spending using the
observed choice data and the estimated equilibrium parameters presented in
Section 6. The subsequent rows impose arbitrary assumptions on the parameter
space to capture salient features of counterfactual scenarios, including full
information without learning (row 2), learning with re-centered priors (row 3,
panel B only), and policies shortening the length of a deductible. All
currencies are reported in 2022 USD.

Table 4:  Comparison of Predicted Spending Across Counterfactual States of the
World

Table 4 presents the results.242424See also Appendix Figure A.9 for a
distribution of estimated spending differences. Accounting for greater
heterogeneity in household beliefs about OOP spending results in a greater
fraction of individuals being affected by changes to the learning parameters.
This makes intuitive sense, given that households restricted to no learning in
the simpler model may have been estimated to have reasonably correct beliefs
for the full plan year, when in fact they experienced a period of rapid
learning early in the year. Compared to a state where $\beta$ is fixed at 1,
roughly 22% of households over-consume care, with the average (median)
affected household consuming $1,056 ($573) more per household member. This
corresponds to an over-spending of 45.0% (41.0%) for the average (median)
household relative to the predicted spending under full information. This
over-spending can be nearly entirely attributed to high household priors, as
can be seen in row 3 of Panel B of the table. Re-centering household
priors—without completely eliminating residual uncertainty around prices for
each unique medical event—accounts for more than 95% of the over-spending for
both the average and median household.

Our modeling exercise corroborates the findings of the empirical strategy:
households over-estimate their actual medical expenditures while they wait for
a bill, and these over-estimates are worse in cases where households have
little information with which to form expectations. This results in
significant over-consumption of care, particularly for households on the
margin of meeting their deductible. More frequent signals, shorter waiting
periods for pricing information, and more frequent deductible reset periods
could all help reduce the effects of incorrect beliefs on over-consumption of
care.

##  7 Discussion & Conclusion

This paper assesses how households respond to pricing information in their
strategic decisions for future care consumption. We show that although
households increase their spending following health events which may reduce
the future (spot) marginal cost of care, they do so based on mis-informed
over-estimates of actual spending. When a bill arrives with meaningful and
accurate price information, households curtail their spending increases. This
delayed pricing information meaningfully contributes to over-consumption of
medical care, particularly general medical services which may spark downstream
cascades of care.

We encapsulate our findings into a model of imperfect ex-post moral hazard
with delayed learning from prices. Our model, just as our reduced-form
evidence suggests, indicates that consumers over-inflate expectations of OOP
spending before they receive bills, particularly early on in a plan year. Our
model allows us to consider alternative plan designs—including more frequent
deductible resetting—that might curtail the associated over-expenditures of
such underinformation.

The analysis we present could be extended in several meaningful ways. First,
future work could incorporate observed payment interactions between patients
and physicians, rather than relying on claims data alone. Data on physician
practices—including how quickly physicians submit claims to payers for medical
claims and send bills to patients—may provide insights into both the source of
variation in processing times as well as the potential policy benefits of
reducing the length of provider billing cycles.

In addition, doing so would prevent any measurement error in the exposure
variable arising from our poor proxy. In general, however, the measurement
error associated with our proxy for bill arrival is likely to attenuate our
estimates. This is not because the measurement error is classic, but instead
based on the fact that any measurement error in the actual transmission of
price information would result in contamination bias from the interim period,
when households still do not know their OOP spending. If consumers over-
estimate OOP prices before the bill arrives, any regressions misclassifying
$\mathbbm{1}\\{\text{Post\\_Bill}\\}=1$ when it should be 0 will attenuate the
correction parameter $\beta_{\text{Post\\_Bill}}$ to zero.

More generally, future research could build on the learning model presented
here. This could include a more thorough treatment of heterogeneous learning
across service types, or allowing the learning parameters to be covariate-
dependent in other ways. In particular, exploring the health equity concerns
associated with learning about prices could provide valuable insight in the
persistence of health disparities in accessing even high-value preventive
services (Teutsch et al.,, 2020; McMorrow et al.,, 2014). Finally, future work
could explore the impact of real-times claim adjudication on consumer spending
responses. This could be especially policy-relevant when exploring how
heterogeneity across payers and providers (e.g., integrated care practices)
could be used to leverage improved price transparency.

Increasing understanding of how consumers form expectations about their health
needs and utilization is a vital component of designing optimal insurance
contracts and health policies. Economic modeling and health policy alike are
well-served from incorporating delayed learning as we assess how consumers
make health decisions in real time.

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##  Appendix A Appendix

Figure A.7: Variation in Prices for CPT 59400: Routine Vaginal Delivery

(a)

(b)

Notes: Figures show variation in total and OOP costs associated with CPT code
59400: “Routine obstetric care including antepartum care, vaginal delivery
(with or without episiotomy, and/or forceps) and postpartum care.” Each
vertical bar represents a unique encounter in our analytical data set, with
the height of the bar corresponding to the price (all measured in 2022 USD).

Figure A.8: Variation in Wait Times for Bills

(a)

(b)

Notes: Indicates average wait time (in weeks) between date of service and date
the insurer paid their portion of the claim (the earliest date at which
definitive OOP information is known). Panel (a) illustrates variation in
average wait times across months of the year (pooled across all years) for all
claims in the analytical data; panel (b) limits the sample to only the
shoppable services used as major health events in the text.

Type | Code | Service Description
---|---|---
DRG | 216 | Cardiac valve and other major cardiothoracic procedures w/ cardiac catheterization
DRG | 460 | Spinal fusion, except cervical
DRG | 470 | Major joint replacement or reattachment of lower extremity
DRG | 473 | Cervical spinal fusion
DRG | 743 | Uterine and adnexa procedures for non-malignancy
CPT | 19120 | Removal of 1 or more breast growth, open procedure
CPT | 29826 | Shaving of shoulder bone using an endoscope
CPT | 29881 | Removal of one knee cartilage using an endoscope
CPT | 42820 | Removal of tonsils and adenoid glands (patient younger than age 12)
CPT | 43235 | Diagnostic examination of esophagus, stomach, and/or upper small bowel
CPT | 43239 | Biopsy of the esophagus, stomach, and/or upper small bowel using an endoscope
CPT | 45378 | Diagnostic examination of large bowel using an endoscope
CPT | 45380 | Biopsy of large bowel using an endoscope
CPT | 45385 | Removal of polyps or growths of large bowel using an endoscope
CPT | 45391 | Ultrasound examination of lower large bowel using an endoscope
CPT | 47562 | Removal of gallbladder using an endoscope
CPT | 49505 | Repair of groin hernia (patient age 5 years or older)
CPT | 55700 | Biopsy of prostate gland
CPT | 55866 | Surgical removal of prostate and surrounding lymph nodes using an endoscope
CPT | 59400 | Routine obstetric care for vaginal delivery
CPT | 59510 | Routine obstetric care for cesarean delivery
CPT | 59610 | Routine obstetric care for vaginal delivery after prior cesarean delivery
CPT | 64483 | Injections of anesthetic and/or steroid drug into lower or sacral spine nerve root
CPT | 66821 | Removal of recurring cataract in lens capsule using laser
CPT | 66984 | Removal of cataract with insertion of lens
CPT | 93000 | Electrocardiogram, routine, with interpretation and report
CPT | 93452 | Insertion of catheter into left heart for diagnosis
CPT | 62322 | Injection of substance into spinal canal of lower back or sacrum
CPT | 62323 | Injection of substance into spinal canal of lower back or sacrum

  * •

Notes: Table shows list of procedures used to identify non-urgent “shoppable
services,” which are the exposure of interest in the primary reduced-form
specifications. Services are identified based on lists provided by the Center
for Medicare and Medicaid Services (CMS), using the relevant Diagnostic
Related Groups (DRGs) or Current Procedural Terminology (CPT) codes to
identify procedures.

Table A.1:  Shoppable Services Used in Analytical Sample

Figure A.9: Counterfactual Analysis: Change in Predicted Spending from
Correcting $\beta=1$

(a)

(b)

Notes: Figure shows estimated the differences in predicted (total) per-person
health spending that arise from requiring that $\beta=1$ in Equation 6, rather
than the parameters estimated in the models (see Figure 5). Panel (a) shows
results for the model without learning while panel (b) shows results for the
generalized learning model. Histogram displays distribution of household-year
average differences per person, conditional on a difference greater than 0.
Note that for 87.5% of households in panel (a) and 77.6% of households in
panel (b), no differences in spending are predicted. The dashed line indicates
the average conditional difference in per-person spending while the dot-dashed
line indicates the median in both groups.