Market Size and Trade in Medical Services*
Jonathan I. Dingel

Joshua D. Gottlieb

Chicago Booth,

University of Chicago

CEPR, and NBER

and NBER

Maya LozinskiPauline Mourot

University of Chicago

Chicago Booth

April 2024

Abstract
We uncover substantial interregional trade in medical services and investigate whether
regional increasing returns explain it. In Medicare data, one-fifth of production involves a doctor treating a patient from another region. Larger regions produce greater
quantity, quality, and variety of medical services, which they “export” to patientsfrom elsewhere, especially smaller regions. We show that these patterns reflect scaleeconomies: greater demand enables larger regions to improve quality, so they attract
patients from elsewhere. Despite concerns about rural access, larger regions have higher
marginal returns to spending. We study counterfactual policies that would lower travel
costs rather than relocating production.
Keywords: healthcare access, market-size effects, Medicare claims data, trade in services
JEL codes: F12, F14, I11, R12* We thank Scott Blatte, Steve Buschbach, Cedric Elkouh, Aaron Haefner, Feng Lin, Luke Motley, Nick

Niers, Noah Sobel-Lewin, Vaidehi Parameswaran, and Xiaoyang Zhang for excellent research assistance. We
are grateful to Rodrigo Adão, Zarek Brot-Goldberg, Don Davis, Rebecca Diamond, Liran Einav, Ed Glaeser,
Tali Han, Tom Holmes, Loukas Karabarbounis, Wojciech Kopczuk, Doug Miller, Sean Nicholson, Bruce
Schakman, Martin Schneider, Bradley Setzler, Jon Skinner, Felix Tintelnot, discussants Jan David Bakker,
Barthelemy Bonadio, Jessie Handbury, Naomi Hausman, Tim Layton, Elena Patel, and many seminar
participants for helpful feedback. We thank the Becker Friedman Institute at the University of Chicago for
funding support and enabling us to access the Medicare claims data. We thank Antoine Levy and Jacob
Moscona for sharing CBSA-level bedrock-depth data and Amitabh Chandra, Maurice Dalton, and Doug
Staiger for hospital quality data and code. Dingel thanks the Cohen and Keenoy Faculty Research Fund at
the University of Chicago Booth School of Business for support. Lozinski thanks the NIH (T32GM007281 and
T32AG051146). jdingel@chicagobooth.edu, jgottlieb@uchicago.edu, mayalozinski@uchicago.edu,
pmourot@chicagobooth.edu.

Rural Americans have worse health outcomes (Finkelstein, Gentzkow, and Williams,
2021), but America’s doctors are disproportionately located in big cities (Rosenblatt andHart, 2000). This contrast might suggest a spatial mismatch between consumers and producers of medical services, and discussions of whether physicians are geographically “maldistributed” go back decades (Newhouse et al., 1982a; Skinner et al., 2019). We consider
an alternative explanation: rather than mismatch, do these patterns reflect the benefits ofspecialization and trade in an industry featuring scale economies?
We find substantial interregional trade in medical services: one-fifth of Medicare production involves a doctor treating a patient from another region. Applying a trade modelto these patient flows, we find that scale economies explain larger regions’ production andexport of higher-quality medical care. After quantifying regional economies of scale andpatients’ willingness to travel, we use the estimated model to explore counterfactual policies
aimed at improving access for patients in smaller regions.
If medical services have increasing returns to scale, there are benefits to geographicallyconcentrating production. Indeed, medicine has long been suggested as an industry in which
the division of labor is limited by the extent of the market (Arrow, 1963; Baumgardner,1988). Absent trade, however, the only way to serve patients in smaller regions would be
to disperse production across space, foregoing the benefits of scale.1 This is likely necessaryfor emergency care. But the vast majority of medical spending is not for emergencies. For
example, if patients with cancer can travel across regions in search of the ideal oncologist—
one specialized in their particular type of cancer, one with a better reputation, or simply abetter personal match—the economic geography of medical care may resemble other tradable
industries. In that case, society would face a proximity-concentration tradeoff : patients who
1

Many economists assume trade costs for medical services are prohibitively high. Hsieh and RossiHansberg (2021): “Producing many cups of coffee, retail services, or health services in the same location
is of no value, since it is impractical to bring them to their final consumers.” Jensen and Kletzer (2005):“Outside of education and healthcare occupations, the typical ‘white-collar’ occupation involves a potentiallytradable activity.” Bartik and Erickcek (2007): “An industry can bring in new dollars by selling its goods
or services to persons or businesses from outside the local economy (‘export-base production’). . . For healthcare institutions, demand for services tends to be more local.”1

consume medical services produced far from home incur trade costs yet benefit from thehigher quality generated by geographically concentrating production.
We investigate these economic forces using Medicare claims data that we introduce inSection 1. Medicare is the federal government’s insurance program for the elderly and disabled and spends four percent of US GDP. Medical service providers submit claims thatreport the specific medical procedure provided, the treatment location, and where the patient lives. Using hundreds of millions of these claims, we find that “imported” medical
procedures—defined as a patient receiving a service provided by a physician in a different
region—constitute about one-fifth of US healthcare consumption. Production is geographically concentrated in larger regions, while consumption is much less so. This contrast means
exported medical services are disproportionately produced in larger regions and imports area larger share of consumption in smaller regions. Although some patients travel thousands ofkilometers for care, patient flows decline rapidly with distance between regions. While thesepatterns establish an important role for regional specialization and trade, they do not reveal
the strength of regional increasing returns or the consequences of healthcare agglomeration.
To guide our investigation of these mechanisms, Section 2 develops a model of trade in
medical services. We adapt standard models to a setting in which the government sets prices,
so quality variation clears markets. The model delivers equations that we use to estimate
regional service quality, the strength of increasing returns, and market-size effects. If there
are regional scale economies, larger markets produce higher-quality care and export it. Wheneconomies of scale are sufficiently strong, the model predicts a strong home-market effect:
greater demand makes larger regions net exporters of medical services. Because market size
matters more at smaller scales, the model predicts less common medical procedures will
respond more to differences in market size. The gravity model of trade flows provides aframework to test this hypothesis, as in Costinot et al. (2019).
In Section 3, we recover revealed-preference estimates of regional service quality by estimating patients’ willingness to travel to each exporting region for medical services. These2

estimates based on trade flows align with conventional measures of quality: they are negatively related to external measures of mortality rates and positively related to other hospitalrankings and safety scores.
We use these revealed-preference estimates to estimate the scale elasticity: how does
serving more patients raise a region’s quality of medical care? This parameter plays a
key role in examining health policy when there are regional increasing returns. We findsubstantial regional increasing returns. We estimate the scale elasticity to be about 0.8: aregion producing 10% more because of greater demand delivers about 8% higher quality.
The same trade flows show that regional increasing returns are large enough to explain thegeographic patterns of production, consumption, and trade documented in Section 1. We finda strong home-market effect in medical services: greater demand induces a greater increasein exports than imports, making larger markets net exporters of medical care. These scaleeffects cannot be attributed to larger markets having lower input costs or medical production
raising population size. This result remains when estimated in the cross-section, a panel, or
instrumented with historical characteristics that predict current production levels.
Section 4 investigates potential sources of regional increasing returns in medical services.
We examine how market-size effects and returns to scale vary with procedure characteristics.
Rare procedures are traded more and over longer distances. For example, half of the patients
having left ventricular assist devices (LVADs) implanted to restore their heart function comefrom outside the surgeon’s region, while only 10% of screening colonoscopies are traded.
Consistent with the model, the home-market effect is substantially stronger for less common
procedures: a larger residential population drives a greater increase in net exports for rare
procedures. Moreover, we estimate that rarer procedures exhibit stronger increasing returns.
A variety of mechanisms could generate these increasing returns to scale: finer specialization among physicians, sharing of lumpy capital equipment, knowledge diffusion, or learningby doing (Marshall, 1890). We show that larger markets have more specialized capital
equipment and physicians. Critically, trade enables patients across regions to share in these3benefits of scale: imports are more likely to be provided by a specialist—an appropriate andmore experienced specialist—and more likely to use rare equipment than locally produced
services.
We use our estimates of scale economies and trade costs to explore the proximityconcentration tradeoff quantitatively in Section 5. Counterfactual policies affect regions
differently depending on their size and trade patterns. We examine the implications of increasing access to care in one region by either increasing reimbursements or reducing travel
costs. Increasing reimbursements has a higher return in more populous regions. Whenraising reimbursements in the largest regions, the aggregate gain in patient market accessper dollar of spending is about 10% higher than when increasing reimbursements in thesmallest regions. Increasing reimbursements in one region reduces output quality in neighboring regions, while improving patients’ market access to the extent they import from thetreated region. Reducing travel costs for one region increases its import demand, which
improves both output quality and market access in neighboring regions. The rich pattern ofconsequences when subsidizing patients in low-output regions highlights the importance oftrade and agglomeration for understanding the incidence of these policies on patients andproducers.
The higher-quality care available in larger markets may not benefit all patients equally.
We find that patients with lower socioeconomic status (SES) are less likely to travel farther
for better care, even when we examine travel patterns within the same billing code. Thus,
the proximity-concentration tradeoff varies by SES; the pattern of aggregate returns masks
important heterogeneity. We also find that the large geographic scope of the United States
explains a meaningful part of the correlation between regional income and health.
This paper builds on research in urban, trade, and health economics. Urban economists
have documented skill-biased agglomeration in production as knowledge workers have become
more numerous and concentrated in skilled cities (Berry and Glaeser, 2005; Moretti, 2011;
Diamond, 2016; Davis and Dingel, 2020; Eckert, Ganapati, and Walsh, 2020). Connecting

4

this to the production and trade of services has been more difficult. Most studies of thegeography of services analyze restaurants and retailers (Davis et al., 2019; Agarwal, Jensen,
and Monte, 2020; Allen et al., 2021; Miyauchi, Nakajima, and Redding, 2021; Burstein, Lein,and Vogel, 2022). We show that—even in a service-based economy—the sizes of both local
and potential export markets influence production and quality. This suggests that healthcare
can serve as an export base for large markets (Bartik and Erickcek, 2007).
The trade literature has examined market-size effects in manufacturing but investigatedservices much less. Davis and Weinstein (2003), Hanson and Xiang (2004), and Bartelme
et al. (2019) link manufactures’ market size to export patterns, in line with the homemarket effect of Krugman (1980) and Helpman and Krugman (1985). Dingel (2017) showsthat market-size effects drive quality specialization across US cities. Market-size effects forpharmaceuticals have been estimated using demographic variation over time (Acemoglu andLinn, 2004) and across countries (Costinot et al., 2019). Services are much less studied, inpart because of the paucity of reliable trade data (Lipsey, 2009; Muñoz, 2022). We advance
this literature using the detailed procedure and location information in medical claims data.
The importance of medical care for health and welfare generates substantial public-policy
interest. Rural locations have worse health outcomes but fewer doctors per capita. Newhouse
et al. (1982a,b,c), Newhouse (1990), and Rosenthal, Zaslavsky, and Newhouse (2005) considered this issue and argued against targeting a uniform geographic distribution of physicians.
Building on this, we measure interregional trade in medical services, estimate the impact ofgeography on patient access, and connect this trade to economies of scale. Modern trade
theory guides our modeling, estimation strategy, and counterfactual policy analysis.

1

Empirical setting and geographic patterns

This section describes the data, documents how production and consumption of medical
services vary with market size, and shows that trade between regions declines with distance.

5

1.1

Empirical setting

Our primary dataset is claims data from Medicare, the largest source of medical spending in
the United States.2 Medicare is the federal government’s insurance program for the elderly
and disabled. It does not directly employ physicians or run its own hospitals. Instead, it pays
bills submitted by independent physicians, physician groups, hospitals, and other medical
service providers. These bills—called “claims” in industry terminology—report the specificservices provided using 5-digit codes from the Healthcare Common Procedure Coding System(HCPCS). There are over 12,000 distinct HCPCS codes, which identify individual procedures
at a granular level.3 In alternative analyses, we use groupings of patient diagnoses to accountfor potential substitution between treatments.
Federal regulation, not pricing decisions by physicians or hospitals, determines the payment for each claim. For physician payments, Medicare sets procedure-specific “reimbursement rates” largely independent of quality, quantity, or region.4 We remove regional pricedifferences from our spending measure as described in Appendix A.2. This produces an expenditure measure purged of spatial variation in reimbursement rates. Patients pay a shareof these reimbursements through copayments and deductibles, but these cost-sharing rules
are constant across regions, and most Medicare patients have a Medigap supplemental or
Medicaid insurance that covers most or all of this cost sharing (Cabral and Mahoney, 2019).
Medicare claims report the ZIP codes of both the place of service and the patient’s residence. Using these, we construct a trade matrix for medical services. We study all medical

2

Appendix A.1 contains more details about our data and processing.
Codes distinguish between, e.g., flu vaccines that protect against three or four strains of flu, whether
administration is intramuscular or intranasal, and patient ages. There are distinct codes for chest X-rays
based on whether the images are of ribs, the breastbone, or the full chest, both sides or one side of the body,and the number of images taken (1, 2, 3, or 4+). By contrast, all of health services are aggregated into oneof the nine service sectors available in Canadian data on interprovincial trade (Anderson, Milot, and Yotov,
2014) and the seventeen service sectors in international trade data (Borchert et al., 2021).
4
While Medicare does have some quality incentive programs, the money at stake is a small share of
Medicare’s overall spending (Gupta, 2021). Medicare has some spatial variation in physician reimbursements,
but it is not very large, and has diminished over time; details on payment rules are in Clemens and Gottlieb(2014). Hospital payments also reflect local wage indices, the hospital’s occupational composition, and otherfactors. Gottlieb et al. (2010) show that price variation does not explain spatial variation in expenditure.
36care provided by physicians, including both professional and facility charges, outside an
emergency room or skilled nursing facility.5 Because Medicare rarely reimbursed telehealthbefore 2020, this trade involves traveling to receive care delivered in-person.6 We aggregate
the ZIP-code-level information up to 306 hospital referral regions (HRRs), which are geographic units defined by the Dartmouth Atlas of Health Care to represent regional markets
for tertiary medical care. HRRs are constructed by aggregating residential areas based onwhere patients were referred for major cardiovascular surgical procedures and for neurosurgery. Each HRR has at least one city where both categories of surgery were performed.
Thus, the construction of these geographic units should tend to minimize trade between
HRRs.7 We construct HRR-to-HRR trade flows by interpreting the patient’s residential
HRR as the importing region and the service location’s HRR as the exporting region.8
Physicians, hospitals, pharmacies, and other healthcare providers submit different typesof claims. We use Traditional Medicare claims data, primarily from 2017, from hospitals,
physicians, and outpatient care providers. One year of data includes around 360 million
services, representing $230 billion in spending.9 These claims are not perfectly representativeof all US healthcare, since Medicare beneficiaries are elderly or disabled.10 But the geographic
distribution of Medicare beneficiaries is quite similar to the overall population, and Medicare
alone finances one-fifth of medical spending. These data likely capture the key features
5

Our results are similar when using only physicians’ professional fees (Appendix Figure D.2 and Appendix
Tables D.8 and D.16).
6
In 2012, Medicare spent only $5 million—less than 0.001% of its expenditures—on telehealth services(Neufeld and Doarn, 2015), lagging other insurers (Dorsey and Topol, 2016).
7
We have also used alternative geographies, including core-based statistical areas (CBSAs), metropolitan
statistical areas (a subset of CBSAs that excludes the smaller micropolitan areas), and commuting zones(CZs). Because these yield consistent findings, we do not report all such estimates.
8
The Medicare claims are US patients receiving care at US service facilities. These data do not report any
international transactions. Throughout this paper, “imports” and “exports” refer to domestic transactions
between regions of the United States.
9
For one portion of spending (physician services), we observe a random 20% sample of these claims; ourspending estimate is scaled up to represent the full Traditional Medicare population.
10
We validate procedure frequencies in the 20% sample of physician services with two alternative data
sources: more comprehensive Medicare data (based on all Traditional Medicare patients, but without information on patients’ locations) and Health Care Cost Institute data for privately insured patients (Appendix A.3). We also study the geographic patterns of production by specialty using the physician registrydata containing the ZIP code and specialty of all physicians registered to practice in the United States.

7

of overall healthcare production and consumption. Appendix Table D.1 reports summary
statistics of HRR production, consumption, and trade volumes.

1.2

Spatial variation in production and consumption

Figure 1 shows maps of healthcare production and consumption across regions, based on theplace of service and patient’s residential address, respectively. The consumption map shows
substantial variation that has been well documented by the Dartmouth Atlas and related literature on geographic variation in healthcare (Fisher et al., 2003a,b; Finkelstein, Gentzkow,
and Williams, 2016). The production map shows even more pronounced variation: more production in large urban agglomerations and less in rural areas. There is substantial variationin production even between immediate neighbors, while consumption varies more smoothly.
The subsequent panels show patterns of trade. Nationally, 19% of production is exported
to a patient in another HRR, and 21% is traded between CBSAs.11 Panel 1(c) shows theratio of production to consumption; a value larger than one means an HRR is a net exporter.
Net-exporting regions tend to be major urban agglomerations, plus places such as Rochester,Minn. and Durham, N.C. that specialize in healthcare. Panel 1(d) shows gross exports as ashare of local production for each HRR. Three-quarters of services produced in the Rochester
metropolitan area, home to the top-rated Mayo Clinic, are provided to patients from otherregions, who travel an average of 545 km to Rochester.12 As a major healthcare exporter
with a population of merely 220,000, Rochester is an outlier: larger regions are responsible
for a disproportionate share of medical services production.
Figure 2 plots the average production and consumption per beneficiary across HRRsof different sizes. Production per beneficiary increases with population, with an elasticity
of 0.05. Consumption per beneficiary is virtually uncorrelated with population; in fact, the11

42% of physician production is exported outside the provider’s Hospital Service Area (HSA), a smaller
Dartmouth Atlas geographic unit. For comparison, 6% of employees work outside their commuting zone ofresidence (Monte, Redding, and Rossi-Hansberg, 2018, Appendix Table B.1). For manufactured goods, we
obtain a 68% export share for metropolitan areas covered by the Commodity Flow Survey.
12
These top hospitals tend to have top physicians; Mourot (2024) documents positive assortative matching.

8

estimated elasticity is slightly negative. The difference between production and consumption
is net trade: larger markets are net exporters and smaller markets are net importers. Gross
trade flows exceed net trade flows, with imports comprising about one-third of consumption
in the smallest regions. Imports per beneficiary decline with an elasticity of -0.35 withrespect to population. Exports per beneficiary are approximately flat, which means totalexports are increasing with local population.

1.3

Bilateral trade and bilateral distance

Despite the clear patterns in Figure 2, geographic variation in trade is far from entirely
explained by market size. The regions with the lowest export shares are Anchorage, Honolulu,
and Yakima, Wash., likely reflecting their remoteness. To account for these geographic
patterns, we examine bilateral trade flows.
Figure 3 depicts how trade varies with the distance between the patient and place ofservice. Panel (a) shows the distribution of distances patients travel for care, distinguishing
between care provided in the patient’s home region and in other regions. Within HRRs, there
is a narrow distribution of distances that peaks around 10 km. When visiting providers in adifferent HRR, patients travel a great variety of distances. There is a local plateau between
approximately 30–100 km, suggesting a fair amount of travel to nearby HRRs, perhaps
indicating regional medical centers. There is substantial long-distance travel for care: many
patients travel hundreds or thousands of kilometers.13
Panel 3(b) shows that trade declines with distance. The blue curve depicts trade volume
against distance (for pairs of HRRs with positive trade flows) after removing fixed effects foreach exporter and each importer.14 This intensive-margin relationship is roughly log-linear.
The red curve shows the extensive margin: the share of pairs with positive trade as a function
13

Patients’ choices to travel these distance underpin our revealed-preference estimates of regional service
quality in Section 3.1. The average patient travels 640 km to Chicago and 740 km to New York City,
compared with less than 146 km to Urbana-Champaign, Ill. or Charlottesville, Va. An older literature cited
in Dranove and Satterthwaite (2000) finds that patients who travel farther incur higher hospital costs.
14
This application of the Frisch-Waugh-Lovell theorem is only feasible for positive trade volumes.

9

of distance. This is 100% for nearby pairs and under 80% for the most distant pairs. These
patterns motivate the inclusion of distance covariates in our gravity-based analysis.
Patients may vary in their ability or willingness to travel, especially by socioeconomic
status. We quantify it here, to the extent feasible in our data, to enrich counterfactual
analysis and interpret welfare implications. Panel 3(c) depicts distance elasticities—how
fast bilateral trade declines with the distance between regions—estimated separately byneighborhood income decile.15 We find a strong, nearly monotonic relationship between
socioeconomic status and the distance elasticity: patients from the highest neighborhoodincome decile exhibit a distance elasticity 25% smaller than those in the lowest decile.16 Thismeans patients from higher-income neighborhoods are more amenable to traveling farther
for medical care. If society faces a proximity-concentration tradeoff, this tradeoff varies bysocioeconomic status. This is especially notable given the empirical setting: Medicare insures
the near-universe of elderly and disabled Americans.

2

Theoretical framework

This section develops a model of regional trade in medical services tailored to our analysis of
US healthcare. We develop a competitive model of a market for one medical procedure thathas a fixed price.17 With fixed prices, quality variation plays a key role in clearing markets.
Patients select quality-differentiated services and face trade costs, so patient flows between
regions follow a gravity equation. Regional increasing returns cause the quality-adjusted
cost of producing a service to decline with scale. The model delivers equations that allow us
to estimate the strength of regional increasing returns and the home-market effect. We use
15

We estimate these distance elasticities using equation (8) as described in Section 2.6.
These estimates are consistent with the interaction that Silver and Zhang (2022) estimate between
income and distance to care. These differences in distance elasticities are not driven by differences in thecomposition of procedures. When we estimate elasticities separately for rare and common services—or evenfor individual procedures (see Appendix Table D.5)—the income gradient of distance elasticities persists.
17
For brevity, we present a competitive model, but the consequences of regional increasing returns for
trade flows in a fixed-price environment do not hinge on this assumption. Appendix B.1 shows that amonopolistic-competition model with one medical provider in each region delivers the same predictions. As
in flexible-price models, many market structures can give rise to a home-market effect (Costinot et al., 2019).
16

10

the estimated model to quantify outcomes in counterfactual policy scenarios.

2.1

DemandWe use a logit model of individuals choosing providers for a given service. Providers andpatients are in regions indexed by i or j, with I denoting the set of regions. All providers ina region are identical. Let Nj denote the number of patients residing in region j who makea choice.18 Patient k in region j choosing a provider in region i obtains utility
Uik = ln δi + ln ρij(k) + ϵik .
The provider-region component δi would usually include a product’s characteristics andprice. With fixed prices, δi is simply the quality of care available in region i. The regionpair component ρij represents bilateral inverse trade costs (proximity). The idiosyncraticcomponent ϵik is independently and identically drawn from a standard Gumbel distribution,
so the probability that patient k selects a provider in region i is
exp ln δi + ln ρij(k).
Pr(Uik > Ui′ k ∀i ̸= i) = P′ + ln ρi′ j(k)
exp
ln
δ
′
i
i ∈0∪I′

There is an outside option denoted by i = 0, which represents individuals choosing to forgocare, and we normalize its common component to zero, ln δ0 = ln ρ0j(k) = 0 ∀k.19
This choice probability implies a gravity equation for the quantity of trade between
any two regions when we aggregate patients’ decisions. Let Qij denote the quantity ofprocedures supplied by providers in i to patients residing in j, and let Q0j denote the numberof patients in j selecting the outside option. Because each patient selects at most one

18

Appendix B.2 extends the model to have multiple patient types.
This formulation of demand is familiar from the hospital competition literature, which has been surveyed
by, e.g., Gaynor and Town (2011) and Gaynor, Ho, and Town (2015). Our competitive model does notdistinguish between hospitals or physicians within a region.
19

11

provider, Nj =Pi∈I∪{0} Qij . The demand by patients in j for procedures performed in i is

Qij = δiwhere Φj ≡

Nj
ρij ,
Φj

(1)

P

i′ ∈0∪I δi′ ρi′ j is the expected value of the choice set for patients in region j. We

call this Φj “patient market access,” as it captures the quality of care available to patientsand their costs of accessing it. Equation (1) is a gravity equation with an origin i component,a destination j component, and an ij pair component. Total demand for care produced in iis
Qi = δi

2.2

X Nj
Φj
j∈I

ρij .

(2)

Production

We assume competitive production of services with free entry and regional increasing returns
that are external to individual providers. That is, each price-taking provider chooses its
output quality and quantity given total regional production, an exogenous factor price,
and an exogenous productivity shifter. A provider in region i that employs L units of thecomposite input to produce service of quality δ produces the following output quantity:

Ai

H(Qi )L.
K(δ)

Improving quality is costly so K(δ) is increasing. Regional increasing returns to scale are a
weakly increasing, concave function H(Qi ) of total regional production, Qi , which competitive producers take as given (Chipman, 1970). The regional productivity shifter Ai captures
any other influences, such as past investments. Provider size L is indeterminate (and unimportant) given the linear production function, external economies of scale, and price-taking
behavior. The composite input is supplied to region i at factor price wi .20 Thus, the unit
20

If the regional factor supply were less than perfectly elastic, we would estimate increasing returns netof the cost of hiring additional inputs. That is, if the factor supply elasticity were β, our estimate of theβscale elasticity α in equation (4) would instead be an estimate of the effective scale elasticity α̃ ≡ α − 1+β.

12cost of producing quality δ in region i is

C(Qi , δi ; wi , Ai ) ≡wi K(δi ).
Ai H(Qi )In our setting, output prices are fixed: the Medicare-determined “reimbursement rate”
R is independent of quality, quantity, and region. Each provider that produces output of thehighest quality produced in region i earns revenue R per unit.
Provider optimization and free entry require the unit cost to equal the reimbursement
rate in each region. Given factor price wi and productivity shifter Ai , the free-entry condition

C(Qi , δi ; wi , Ai ) = R(3)

defines a regional isocost curve: the set of quantity-quality combinations for which theaverage cost of production equals the reimbursement rate. Regional increasing returns makethe isocost curve upward-sloping in (Q, δ) space. With free entry and fixed prices, thebenefits of scale are realized as higher-quality services in higher-output regions.
While our assumptions thus far suffice for qualitative results, we later specify functional
forms for additional predictions and empirical quantification; specifically, K(δi ) = δi andH(Qi ) = Qαi , with a scale elasticity of α ≥ 0.21 In this case, the free-entry condition (3) isR=

2.3

w i δi.
Ai Qαi(4)

Equilibrium

Equilibrium equates supply and demand in each region, Qi =P

j Qij .

Given exogenous

parameters R, {wi , Ai , Ni }i∈I , and {ρij }(i,j)∈(I,I) , an equilibrium is a set of quantities andqualities {Qi , δi }i∈I that simultaneously satisfy equations (2) and (3).
21

There are increasing returns to scale if α > 0. Note that this formulation is compatible with anequilibrium in which region i does not produce the procedure at all: Qi = 0 =⇒ δi = 0.

13

2.4

Scale effects in autarky

In autarky, patients choose whether to receive care, but they cannot travel between regions(ρij = 0 for i ̸∈ {0, j}). In this case, all demand is local and equation (2) simplifies to
Qjj =δj ρjjNj .
1 + δj ρjj(5)

The autarkic equilibrium is at the intersection of the demand curve given by equation (5)and the free-entry isocost curve given by equation (3).22 An increase in population size,∆Nj > 0, affects equilibrium outcomes by shifting the demand curve.
Figure 4 illustrates how greater demand affects quality in autarky. Panel (a) shows therole of returns to scale. The vertical axis shows quality δi and the horizontal axis shows
quantity Qi (on logarithmic scales). Higher quality attracts more patients, so demand is
upward-sloping.23 We show two cases of the free-entry isocost curve defined by equation (4):the horizontal line depicts constant returns (α = 0) and the upward-sloping line depicts
increasing returns (α > 0). With constant returns, a rightward shift in demand (∆Nj >0) causes a proportional increase in quantity produced and no change in output quality.
With increasing returns, higher demand moves producers up the isocost curve. This quality
improvement causes a more-than-proportional increase in quantity produced.
Panel 4(b) shows that an increase in demand raises quality more as the demand curve
is increasingly elastic. The panel depicts two demand curves: the one on the left is moreelastic, as we would expect for a less common procedure.24 Shifting each demand curveto the right raises the equilibrium quality of each procedure because of increasing returns
to scale. This market-size effect is larger for the less common procedure with more elastic

22

For the equilibrium to be Marshallian stable, the demand curve must be steeper than the isocost curveat the intersection. There is a stable equilibrium because equation (5) means Qjj → Nj as δj → ∞.
23
For visual clarity, we draw a log-linear demand curve. The logit demand function (5) is in fact logconvex, which is consistent with all the comparative statics illustrated in Figure 4.
24
The demand function (5) is log-convex, so demand is indeed more elastic at lower quality. This is a
fixed-price counterpart of Marshall’s second law that demand is more elastic at higher prices.

14demand because the demand shift is amplified by a larger increase in quantity demanded.25

2.5

Market-size effects on trade flows

We now consider trade. With multiple regions and finite trade costs (ρij > 0), some patients
will import—i.e., select a provider located in another region. This trade stems from twosources. First, in the logit demand system with finite trade costs, patients have idiosyncratic
preferences that yield a strictly positive probability of choosing every region. Second, when
quality varies, regions producing higher-quality services attract more patients.
Fixing the qualities produced in other regions, an increase in one region’s demand affects
its trade flows through three mechanisms. First, greater total demand for services proportionally increases a region’s demand for imports through the Nj term in equation (1). Second,with increasing returns, an increase in Ni elicits an increase in quality δi , which raises region
i’s gross exports to each region. Costinot et al. (2019) call this the “weak home-market
effect.” Third, if increasing returns are sufficiently strong, quality δi improves so much that
region i’s patient market access Φi rises such that ln δi rises more than ln (Ni /Φi ) does. Thatis, the increase in region i’s gross exports exceeds any increase in its gross imports. This is
the “strong home-market effect”: an increase in local demand raises a region’s net exports.
Figures 4(c) and 4(d) introduce trade and illustrate the distinction between weak andstrong home-market effects.26 Panel (c) depicts the quality and quantity produced in one
region under two scale elasticities. Comparing points B and C, a given increase in demand
elicits a larger quality improvement when increasing returns are stronger. Panel (d) depicts
equilibrium exports and imports as a function of the region’s demand shifter Nj . The import
25

Alternatively, one could obtain this prediction by assuming that demand is log-linear and the isocost
curve is log-concave, so that rare procedures have stronger scale economies. For example, introducing a∂δi Qifixed cost F would yield the isocost curve AwiiQδiα + F Q−1= R̄. In this case, the scale elasticity ∂Q
=
i
i δi
i

αR̄+(1−α)F Qi−1
is decreasing in quantity produced Qi for α ∈ (0, 1). A rightward shift in demand would causeR̄−F Q−1ia larger (log) difference in quality for the low-volume procedure on the steeper part of the isocost curve.
26
These diagrams are fixed-price analogues of Figures II and III in Costinot et al. (2019). See their
discussion of the assumption that one region is large enough to affect its own quality but too small to affect
the quality produced in other regions. This assumption is only made for this figure.

15

curves slope up because an increase in local demand raises demand for imports. The export
curves slope up because of increasing returns: higher local demand increases quality, which
increases gross exports. This is the weak home-market effect. When the scale elasticity α islarger—the free-entry isocost curve in Panel (c) is steeper—greater demand elicits a larger
increase in output quality. This steepens the export curve and flattens the import curvein Panel (d). When the export curve is steeper than the import curve, there is a strong
home-market effect: the increase in demand raises exports more than imports.
As in the autarkic case, we predict larger effects of market size for less common procedures. An increase in demand raises quality more when demand is more elastic, leading
to a stronger home-market effect for rare procedures. If rare procedures also have greater
economies of scale (higher α) that would amplify this contrast. This result motivates a
research design comparing home-market effects for common and rare procedures.
These results also hold when an increase in demand in one region affects equilibriumoutcomes in other regions. To demonstrate this, we examine the home-market effect in theneighborhood of a symmetric equilibrium. If all regions are the same size, Ni = N̄ ∀i, andtrade costs are symmetric, ρii = 1 and ρij = ρ ∈ (0, 1) ∀i ̸∈ {0, j}, there is a symmetricequilibrium with quality δ̄ and patient market access Φ̄ in each region. As detailed inAppendix B.3, we totally differentiate the system of equations in terms of {dδi , dNi }Ii=1 andevaluate a change in one region’s demand N1 at the symmetric equilibrium.
With increasing returns of any magnitude, there is a weak home-market effect; with
sufficiently strong increasing returns, there is a strong home-market effect. When α ∈ (0, 1),
an increase in region 1’s demand elicits an increase its relative service quality:(1 − ρ)δ̄
1 − α (Φ̄ − 1)+d ln δ1 − d ln δj̸=1 =α (1 − ρ)δ̄
Φ̄


−1
d ln N1 > 0.

This higher quality causes region 1 to export more to every other region:16

d ln Q1jd ln N1> 0. Theeffect on the region’s net exports is

1+(I−1)ρ
1 − 1−αα1−ρ d ln N1 .
d ln Q1,j̸=1 − d ln Qj̸=1,1 = (1−ρ)δ̄1−α (1+(I−1)ρ)
+
α
(1−ρ)
1+(1+(I−1)ρ)δ̄(6)α> 1+(|I|−1)ρ
. This occurs if
Net exports increase with population size if and only if 1−α1−ρincreasing returns are sufficiently strong (α is large enough) and trade costs are sufficiently
large (ρ is small enough). Otherwise, there is a weak home-market effect but not a strong
one. Given a strong home-market effect, the effect in equation (6) is diminishing in the
population of patients N̄ , so we predict a stronger home-market effect for rare procedures.

2.6

Estimating quality, scale economies, and home-market effects

The model yields equations for estimating quality δi , the scale elasticity α, and detecting
home-market effects. Equation (1) provides a revealed-preference measure of each region’squality, δi . We assume the region-pair component is ln ρij = γXij + υij , where Xij is avector of observed trade-cost shifters and υij is an orthogonal unobserved component. Taking
expectations and then logs of equation (1) yields gross bilateral trade flows:
ln E [Sij ] = ln δi + ln

Nj
Φj


+ γXij .

(7)

Sij is the value of procedures exported from region i to patients residing in j.27 The right side Ncontains three terms: exporter quality ln δi , importer demand shifter ln Φjj , and observed
trade costs γXij . These trade costs may reflect the opportunity cost of patients’ time, fiscal
costs of travel, and any adverse health consequences of travel. Since our empirical work
excludes emergency care, direct health costs are not likely to be critical.
To estimate each region’s service quality, we replace the first two terms with exporter27

For most of the analysis, we define this as total value across all care, computed as described in Section 1.1.
In some cases, we consider subsets of care or even individual procedures. In the procedure-specific case, thedependent variable is the procedure count Qij rather than spending Sij because no aggregation is required.

17

fixed effects and importer fixed effects, respectively:ln E [Sij ] =

ln δ
|{z}i

+

exporter FE

ln θj
|{z}

+γXij .

(8)

importer FE

The exporter fixed effects are a revealed-preference measure of regional quality, which wevalidate using external quality metrics. The importer fixed effects, combined with an assumption about the number of potential patients (see Appendix C.2), enable us to computeΦj = Nj /θj , a measure of patient market access for those who reside in location j.
The relationship between quality and quantity reveals the scale elasticity of the regional
production function, α. Per the free-entry condition (4), quality is an isoelastic function of
the quantity produced, conditional on price, cost, and productivity shifters. We take thedlog of (4), replace ln δi with its estimate ln
δi from (8), and rearrange terms to obtain theestimating equation:28
ln δi = α ln Qi + ln R − ln wi + ln Ai .

(9)

To learn whether these regional increasing returns explain the pattern of trade describedin Section 1, we estimate a more parsimonious gravity regression that uses each region’s
population as a demand shifter. Following Costinot et al. (2019), we differentiate the system Nof equations (2) and (3) around the symmetric equilibrium and replace ln δi and ln Φjj
in (7) by log population in the producing and consuming regions, respectively, yielding:ln E [Sij ] = λX ln populationi + λM ln populationj + γXij .

(10)

A positive coefficient λX > 0 implies a weak home-market effect as defined in Costinot et al.
(2019): gross exports increase with market size. If λX > λM , the home-market effect isstrong: net exports increase with market size.
28

Appendix A.5 quantifies the potential bias resulting from our observing only the quantity produced for
Traditional Medicare beneficiaries, rather than the total quantity produced for all patients. It shows thatthe bias is small: the estimates in Table 1 should be deflated by about 5%.

18

To estimate these specifications, we must parameterize observed trade costs γXij . We
first use log distance and a same-region dummy, i.e. γXij = γ1 ln distanceij + γ0 1(i = j).
Alternative specifications add (ln distanceij )2 or replace these continuous distance covariateswith indicators for distance deciles. Since observed bilateral trade is zero for many pairsof regions, especially when looking at trade in individual procedures, we use the Poisson
pseudo-maximum-likelihood (PPML) estimator (Santos Silva and Tenreyro, 2006).
In other analyses, we estimate slight variants of these specifications. First, we leverage
population growth over time using a panel regression with a region-pair fixed effect:ln E [Sijt ] = λX ln populationit + λM ln populationjt + ϕij + γt Xij ,(11)

where Sijt denotes the gross bilateral trade flow in year t. In this specification, changes in
population across time periods t identify λX and λM . Second, we contrast common and rare
services by dividing procedures into two groups based on whether their national volume isabove or below that of the median procedure.29 We estimate equation (8) separately forthese two groups to obtain the qualities of rare and common procedures. Let Sijc denote
exports from i to j in category of care c ∈ {common, rare}. The model predicts a stronger
home-market effect for rare procedures, so we estimate the following specification:ln E [Sijc ] = λX ln populationi + λM ln populationj + γXij+ µX ln populationi + µM ln populationj + ψXij · 1(c = rare).

(12)

In the presence of an overall strong home-market effect, theory predicts µX > µM . An
alternate specification introduces ij-pair fixed effects, which absorb all the covariates notinteracted with 1(c = rare). We also estimate similar models with heterogeneity in otherdimensions, such as procedure intensity and frequency of patient engagement, and for specificprocedures.
29

Appendix Figure D.1(b) plots the distribution of import shares across regions for the two groups.

193

Regional increasing returns in medical services

This section tests for increasing returns in healthcare and the implications for trade flows.
Section 3.1 estimates region-level quality of medical care and shows that external quality
indicators line up with revealed-preference measures based on trade flows. Using thesemeasures, Section 3.2 finds substantial regional increasing returns in healthcare production.
Section 3.3 demonstrates a strong home-market effect, implying that scale economies indeed
generate the observed patterns of production and trade.

3.1

Quality estimates

Our revealed-preference measures of regional service quality are the exporter fixed effectsdln
δi from estimating equation (8). Figure 5 relates these fixed effects to external measuresof regional hospital quality. We aggregate estimated hospital mortality from Chandra, Dalton, and Staiger (2023) and the Centers for Medicare and Medicaid Services (CMS) by HRR.
We also count the number of times each region’s hospitals appear on U.S. News Best Hospitals.30 Panels 5(a)–(c) establish that patients travel farther to obtain care from regions withlower hospital mortality rates or better U.S. News rankings. Appendix Table D.2 reports
the corresponding regressions. It also shows a regression relating the exporter fixed effects
simultaneously to a variety of other hospital safety, mortality, accreditation, and other quality measures. This regression has an adjusted R2 of 0.60. While our revealed-preference
estimates capture all attributes that influence patient choices, their relationship to theseother quality measures suggest that our estimates capture many characteristics of clinicalinterest.

30

Compared with the CMS measures, Chandra, Dalton, and Staiger (2023) use empirical Bayes estimationto account for differences in hospital volume and quality drift over time. Appendix A.1 explains how we use
the U.S. News rankings. Appendix Figure D.3 also presents results using Hospital Safety Grades from theLeapfrog Group.

20

3.2

Estimating the scale elasticity

3.2.1

Empirical implementation

We use equation (9) to estimate the strength of regional increasing returns. Regional output
quality depends on the volume of production and exogenous shifters of the isocost curve. One
potential concern with estimating equation (9) by ordinary least squares is reverse causality.
Shifts of the isocost curve would cause movements along the upward-sloping demand curve,
biasing the estimated scale elasticity upwards. We address this by using three instrumentsfor production and differences over time.
Our first instrument is current population. Population is relevant for healthcare output,
since larger populations clearly require more healthcare.31 The instrument is valid if it shifts
only demand and not supply. We show that urban amenities do not make healthcare labor
inputs cheaper in larger markets.
Nevertheless, one potential concern with this instrument is reverse causality. Supposethat success in exporting medical services serves as an employment base that raises current
population size, as epitomized by “anchor institutions.”
We use two further instruments to address this concern. Our second instrument is historical population. In 1940, medicine was a far smaller industry and did not drive local
population in the way it might today. Because local populations persist, population in 1940
predicts current population, so we use the former as an instrument for the latter.
The next instrument goes farther back than 1940 and uses local geology to predict healthcare production. Rosenthal and Strange (2008) and Levy and Moscona (2020) show thatshallower subterranean bedrock makes construction easier, increasing population density.
Bedrock depth also predicts population size, so it is our third instrument for local demand.32
31

The variation in demand predicted by population is overwhelmingly driven by headcount, not income
per capita: the population elasticity of income per capita is below 0.1, and the income elasticity of healthspending is likely below 1.0 (Acemoglu, Finkelstein, and Notowidigdo, 2013).
32
This instrument is currently only available for CBSAs and CZs, not HRRs. Our main results hold whendefining regions as CBSAs and CZs. Levy and Moscona (2020) show that the bedrock instrument has ample
first-stage power for predicting CBSA population density; the same is true for our endogenous variables(population levels).

21

Our final research design uses variation over time. We estimate equation (9) in firstdifferences using changes from 2013 to 2017. This uses the relationship between quality
growth and production growth across regions to estimate the scale elasticity. To similarly
confound both the cross-sectional and first-difference regressions, omitted supply shifters
would have to exhibit similar cross-sectional and temporal variation.

3.2.2

Scale improves qualitydδ i rises substantially with the regional production volume ln Qi .
Estimated service quality ln
Figure 5(d) depicts this relationship, which appears consistent with our isoelastic specification. Table 1 reports regression estimates. The estimated scale elasticity is around 0.8 andstable under various estimation approaches. The first row shows our baseline estimate for the
cross-section, and the second uses variation over time. The third and fourth rows instrumentfor output using contemporaneous or historical population, which exhibit strong first-stage
regressions. The second column omits the diagonal Sii observations when estimating thegravity equation (8), to avoid any bias from having a region’s own local consumption influence both the quality measures and output. The third column controls for (small) spatial
variation in reimbursements, mean two-bedroom property value, and mean annual earnings
for non-healthcare workers. Instrumenting for output tends to reduce the estimated scaleelasticity. Excluding the diagonal of the trade matrix when estimating quality tends to raise
it. Across all 12 estimates, the lowest elasticity is 0.63 and the highest is 1.04.33 The results for CBSAs and CZs, reported in Appendix Tables D.3 and D.4, are also stable acrossspecifications and when using the bedrock instrument.
The rest of this paper demonstrates the economic implications of these scale economies
in three ways. First, Section 3.3 shows that they are large enough to generate the observed
patterns of production and trade in medical services. Second, Section 4 demonstrates mech33

These estimates lie in the middle of other estimated agglomeration elasticities. Kline and Moretti (2013)
estimate an elasticity of 0.4–0.47 from the Tennessee Valley Authority’s investments. In manufacturing,
Greenstone, Hornbeck, and Moretti (2010) report an analogous elasticity above 1 (a 12% increase in totalfactor productivity caused by adding a plant representing 8.6% of the county’s prior output).

22

anisms that contribute to regional increasing returns. Third, Section 5 uses the parameter
estimates to analyze counterfactual scenarios that illustrate how these forces work and provide guidance for healthcare policy in a world with increasing returns.

3.3

A strong home-market effect in medical services

While we have established there are regional increasing returns, we have yet to see if they are
sufficiently strong to explain the fact that larger markets are net exporters. This question
determines whether market size enables larger regions to specialize in healthcare production
and to share the benefits of scale with patients in other regions. We now test for a strong
home-market effect in medical services by estimating equation (10).
Table 2 presents the results. The first column shows significant, positive coefficients on
both provider- and patient-market population.34 The coefficient on provider-market population is substantially greater than that on patient-market population. This demonstrates astrong home-market effect (Costinot et al., 2019). Not only does a larger population increase
gross exports, but it does so more than it increases gross imports by local patients.
The distance elasticity of medical services trade between hospital referral regions is -1.6.
This is substantially larger than the distance elasticity of -0.95 estimated for trade in manufactures between CBSAs (Dingel, 2017).35 This suggests that trade in personal services
incurs greater distance-related costs, relative to the degree of product differentiation acrossregions, than trade in manufactured goods. The most obvious difference is that patientsthemselves must travel to the provider.
The next two columns of Table 2 demonstrate that more flexible distance-covariate specifications do not meaningfully alter the estimated home-market effect. Column 2 introduces
the square of log distance as an additional covariate. Column 3 replaces the parametric distance controls with dummies for deciles of distance. The result is stable across the34

In all estimates using trade matrices, we two-way cluster standard errors by patient and provider market.
We find a distance elasticity of medical services trade between CBSAs of -2.4. The analogous elasticityof health care and social assistance services trade between Canadian provinces is -1.42 (Anderson, Milot, andYotov, 2014). The distance elasticity of international trade is typically near -0.9 (Disdier and Head, 2008).
35

23

columns: both gross and net exports increase with market size.
The fourth column of Table 2 uses the historical population instrument to address concerns about reverse causality. We obtain similar home-market-effect estimates to our baseline
results. Appendix Tables D.6 and D.7 report similar results when using CBSAs or CZs rather
than HRRs as our geographic unit. Appendix Tables D.6 and D.7 also show the results arerobust to instrumenting with historical population and with bedrock depth.
The final column of Table 2 uses changes in population over time to proxy for changes
in demand, per equation (11). The market-pair fixed effects in this specification absorb
all cross-sectional variation. We find a strong home-market effect that is similar to thecross-sectional estimate.

Competing explanations. Our instruments address reverse causality, but all of them
operate through population size. So other channels could generate relationships similar to
the market-size effect we estimate. Most significantly, if doctors prefer to live in big cities(Lee, 2010), as college graduates generally do (Diamond, 2016), they could accept lower
nominal wages and thus reduce healthcare production costs wi in such cities. This would
raise quality in large markets, but through a different mechanism than increasing returns.
Before we address this problem, first note what is not a problem: physicians preferring towork in larger regions for job-related reasons. If a region’s scale enables it to support large
academic medical centers, which attract workers, this is an agglomeration benefit that thescale elasticity α ought to capture.36 More patients enable physicians to specialize, conduct
research, and train medical students. These forces operate through the scale of healthcare
production in the region, and academic medical centers are part of this production function.
The challenge to our interpretation arises if physicians prefer larger markets for non36

The most salient example is Cornell University: after an abortive attempt to have medical training inboth Ithaca and New York City, the Cornell Trustees quickly closed down the Ithaca location and centered
the medical school in New York—where the patients and doctors were more abundant—in the early 20th
century (Flexner, 1910; Gotto and Moon, 2016). As this history illustrates, the potential local demandfor care can drive the location of medical training. In general education, in contrast, university placement
induces economic growth (Moretti, 2004).

24

medical reasons, and this labor supply shift increases quality or reduces costs in larger
markets. We investigate whether this mechanism is strong enough to reduce net costs inlarger markets. Doctors are cheaper in larger markets (Gottlieb et al., 2023), but othercosts rise with population size. Appendix Figure D.4 shows that the population elasticity of
doctors’ earnings is -0.01, but that for non-physicians is 0.043.37 To compute the population
elasticity of overall labor costs, note that non-physician labor’s share of healthcare productionis twice the physician labor’s share (Appendix Table D.9). The population elasticity of laborcosts is thus positive. The higher cost of real estate in larger markets reinforces these higher
labor costs. This spatial variation undermines the idea that amenities make production
cheaper in larger markets. Section 4 further shows that specialty-specific income elasticities
are close to zero on average and unrelated to the number of specialists.
One final concern is measurement error in Medicare’s records of patients’ residences. To
address this, Appendix A.4 first demonstrates our results are robust to excluding states withlarge seasonal populations. Second, we examine how far dialysis patients appear to travel.
We find that residential measurement error is limited and does not drive our results.

4

Mechanisms

This section explores potential sources of scale economies and asks if trade expands the geographic scope of these mechanisms. We focus on professional fees for which payments are
made at the service level.38 Section 4.1 examines how market-size effects vary with procedurecharacteristics, especially the rare-vs-common comparisons suggested by the model. Consistent with our theoretical predictions, rare services exhibit stronger market-size effects. They
also exhibit stronger increasing returns to scale. Section 4.2 shows that division of labor andlumpy capital may be substantial sources of regional increasing returns for medical services.
Section 4.3 directly connects trade to these mechanisms: imported care is more likely to be
37
38

Appendix A.1 discusses subtleties of the income data.
We observe 210 million claim lines representing $89 billion in spending on professional services.

25

performed by specialists, by appropriate specialists, by more experienced physicians, andusing scarce capital equipment, especially for smaller regions’ imports. Trade thus expands
the population benefiting from specialization.

4.1

How market-size effects vary with procedure characteristics

4.1.1

Spatial variation in production and consumption by frequency

Larger regions produce a wider variety of procedures. In Figure 6(a), we count the number of procedures produced in each region and graph these counts within seven procedurecategories against regional population. Larger regions produce a greater variety of care in
all seven categories. Panel (b) shows that this is true for consumption, but to a lesser extent: Aggregating across all seven categories, HRRs in the top decile of population produce
3 times, but consume only 2 times, as many unique procedures as those in the bottom decile.
To better understand the characteristics of the procedures performed in larger markets,
we estimate each procedure’s population elasticity of production per Medicare beneficiary.39
Let Qpi denote the count of procedure p produced in region i. Let Mi denote the numberof Medicare beneficiaries residing in i. For each procedure p, we estimate the following
relationship across regions:Qpi= ζp + βp ln populationi .
ln E
Mi


(13)

The estimated elasticity, β̂p , describes how production varies with market size, and we estimate it using Poisson pseudo-maximum-likelihood.40 If the quantity produced were simply
proportional to population, βp would be zero. Our model suggests that scale effects play alarger role for rare procedures. It predicts less common services will have higher population
39

Davis and Dingel (2020) relate population elasticities to other measures of geographic concentration,such as location quotients, and estimate population elasticities of employment for various skills and sectors.
40
In a robustness check, we have also estimated a zero-inflated Poisson model, to account for the possibility
that fixed costs are especially important for the decision of whether to provide the first instance of a service
in a region. These results (not reported here) are quite similar.

26

elasticities of production.
Production per beneficiary indeed rises with market size, especially for less common
procedures. The blue dots in Figure 6(c) relates the population elasticity of productionP
per beneficiary β̂p to the procedure’s national volume, Qp = i Qpi . Across values of Qp ,procedure output per beneficiary increases with market size. Less common procedures havehigher elasticities, consistent with stronger economies of scale in rare procedures.
This finding raises questions about patients’ access to care. What happens to patients
who live in smaller markets but need rare services? To investigate this, we separately estimate
the population elasticity of consumption per beneficiary for each procedure. Let Gpi denotethe count of procedure p consumed by patients residing in region i. We then estimate ananalogue of equation (13) where we replace the dependent variable with ln E [Gpi /Mi ], anddenote by βpC the resulting coefficient. If βpC ̸= βp , there is size-predicted net trade inprocedure p.
The population elasticity of consumption per beneficiary is smaller for the vast majorityof procedures and less steeply related to a procedure’s national frequency. The red squares in
Figure 6(c) plot the population elasticity of consumption per beneficiary β̂pC of a procedureagainst its national volume ln Qp . While the relationship is negative, the slope for consumption is only one-third that for production. Appendix Table D.10 reports the production,
consumption, and trade patterns for two exemplar procedures: screening colonoscopy and
LVAD implantation. Colonoscopies are common and geographically dispersed, while LVAD
procedures are rare, geographically concentrated, and traded over longer distances.
We have thus far modeled patients as demanding (and providers as producing) specificservice codes. An alternative view is that patients have a particular medical condition that
requires treatment, but the patients may not know what particular care they need; they
simply know they require care. As physicians might use different treatments across regions forthe same condition, our procedure-level results could reflect substitution across procedures.
We address this by conducting a similar analysis across diagnoses.

27

Figure 6(d) shows production and consumption elasticities by diagnosis, rather than byprocedure. The key patterns remain similar: production elasticities are higher, and decline
more rapidly with national patient volume, than consumption elasticities. Both sets ofelasticities have less steep relationships with national volume than for procedures. This
could reflect measurement error within each category: the 482 diagnosis categories we use
are far coarser than the 8,210 procedures in Figure 6(c). Alternatively, it could indicate true
substitution among procedures within a condition that varies with location.
The contrasting population elasticities of production and consumption summarized in
Figure 6 imply trade in medical services between markets of different sizes. Just as theoriesof trade with scale effects would predict, larger markets export rare procedures and smallermarkets import them. For almost all procedures, production increases more than proportionately with market size. Consumption also increases more than proportionately with market
size, but much less so than production. The differences between these elasticities mean net
exports vary with market size. The implied net trade between markets of different sizes isparticularly large for procedures that have small national volumes.

4.1.2

Market-size effects are stronger for rare and resource-intensive procedures

We now use trade flows to explicitly understand where rare medical services are provided
and why. Since Section 3.3 found a strong home-market effect overall, the model predicts
that this should be especially true for rare services. Trade is indeed more prevalent in rare
services (Appendix Figure D.1). We now use the specific pattern of these trade flows to test
the model’s prediction that scale economies drive the production and trade of rare services.
Table 3 reports gravity regressions in which each pair of locations has two observations: one for rare services and one for common. Column 1 repeats our baseline regression
from Table 2 for professional fees and reports similar results. Column 2 limits the sample topairs of location that have positive trade in at least one of the two procedure groups, whichis the estimation sample used in the remainder of the table. We then estimate equation (12),28interacting both provider-market and patient-market population with an indicator for rare
services.
The home-market effect is stronger for rare services. In column 3 of Table 3, the coefficienton provider-market population increases by about 60% relative to common services. The
coefficient on patient-market population shrinks by more than half. Column 4 introduces
location-pair fixed effects. Columns 5 and 6 are analogues of the previous two, but add
a quadratic log-distance term. These results are statistically indistinguishable from theprevious columns. Columns 7 and 8 demonstrate that our result holds when we look acrossdiagnoses rather than procedures. As with the production and consumption elasticities in
Figure 6(d), the magnitude of the difference between rare and common care shrinks. This
could reflect substitution across care within a diagnosis or a less precise classification ofdiagnoses than of procedures. But the qualitative pattern holds and remains significant,consistent with the model’s prediction.
Appendix Table D.11 shows that these results are robust to using our instruments formarket size. Columns 1 and 2 show estimates for common and rare services, respectively,
when instrumenting for population in each region by its 1940 population. Columns 3 and4 repeat the exercise using CBSAs rather than HRRs, and columns 5 and 6 switch to the
bedrock-depth instrument. The results are consistent regardless of geographic unit or instrument.41 This stability suggests that neither the aggregate result nor the variation withprocedure frequency is driven by anchor institutions or similar omitted variables.
The finding that less common procedures exhibit stronger home-market effects is robust
to different ways of defining rare and common care. Appendix Figure D.5 shows that thepattern holds when splitting by deciles of national frequency. Appendix Table D.13 shows
the same pattern among illustrative procedures.
The home-market effect is also stronger for rare procedures when controlling for how often
an individual patient receives the same procedure, which we call a procedure’s “engagement”.
41

Appendix Table D.12 reports analogous results based on commuting zones.

29

If patients are less willing to travel for high-engagement services and these services are morecommon, higher engagement could drive the stronger home-market effect we observe for rare
procedures.42 Appendix Table D.14 shows that patients are indeed more sensitive to distancefor high-engagement procedures, but controlling for this heterogeneity does not meaningfully
alter the estimated differential impacts of population size for rare procedures.
The model predicts larger home-market effects for rare services when they have moreelastic demand or larger scale economies. Fixed costs are one reason the scale elasticity may
be larger for rarer services (see footnote 25). When estimating equation (9) separately byprocedure frequency, we find that scale elasticity is substantially larger for rare services. It
is near 1.0, as shown in the second panel of Appendix Table D.16.
Some procedures require more capital and specialized knowledge, and the consequencesof market size for these resource-intensive procedures may illuminate sources of increasing
returns. Relative value units (RVUs) capture the extent of physician work, expertise, andadditional resources required to perform the procedure and determine the procedure’s Medicare payment. We divide procedures into terciles by intensity as measured by the total
RVUs CMS assigns to a procedure. We find that the home-market effect is increasing inprocedure intensity (Appendix Table D.15). This motivates our investigation of physician
specialization and equipment usage in Section 4.2.
The potential concern about omitted cost shifters from Section 3.3 has an analogue
here: Do the doctors who provide rare services benefit more from urban amenities than those
providing common ones, lowering the cost of producing rare services in larger markets? Thishas facial plausibility if rare services are produced by elite specialists who earn more andmight be more willing to pay for urban amenities through lower compensation.
Examining the population elasticities of physician earnings for each specialty alleviates
this concern. If urban amenities drive specialists’ locations, earnings elasticities should be
42

In fact, the national frequency of a service has a very low correlation with various measures of engagement for that service, so it does not confound this result. The correlation between the share of patients who
had more than one claim for the procedure in a given year and the procedure’s frequency is 0.14.

30negative, especially for rare specialties. But Figure 7(a) shows that the income elasticities areclose to zero on average and uncorrelated with the specialty’s national abundance. However
urban amenities affect physicians’ choices, these choices do not exhibit the compensating
differentials necessary to explain the relationship between market size and specialization.

4.2

Mechanisms for strong regional increasing returns

This section shows that division of labor and lumpy capital are mechanisms behind regional
increasing returns to scale in medical services. This evidence does not preclude other agglomeration mechanisms from also playing a role. Knowledge diffusion (Baicker and Chandra,
2010) and thicker input markets could also be important productivity benefits of scale. We
focus on specialization, physician experience, and equipment use because they can be measured using claims data and are closely related to procedure-level returns to scale.

4.2.1

Scale facilitates the division of labor

One source of increasing returns could be division of labor among physicians. In particular,
the specialized labor required to produce rare services could drive the patterns we foundacross treatments and diagnoses. Specialized services may require physicians with specifictraining, whose presence may require high demand (Dranove, Shanley, and Simon, 1992).
To study this mechanism, we estimate the population elasticity of physicians per capita
for each specialty and relate it to the number of physicians in the specialty. Let Ysi be thenumber of doctors of specialty s in location i.43 We estimate a Poisson model,

Ysi
ln E
= ζsS + βsS ln populationi ,populationi
(14)

for each specialty s by maximum likelihood.
Figure 7(b) shows a clear negative relationship between a specialty’s per capita population
43

Data are from the National Plan and Provider Enumeration System (NPPES); see Appendix A.1.

31

elasticity β̂sS and the national number of physicians in that specialty.44 A natural explanation
for rare procedures and rare specialties both being geographically concentrated in larger
regions is that the size of the market limits the division of labor. To the extent that producing
rare procedures requires specialized physicians, a larger volume of patients makes production
economically viable.

4.2.2

Lumpy capital as a source of regional increasing returns

Another potential source of increasing returns is lumpy capital, namely expensive medical
equipment. For instance, if a piece of medical equipment is rarely used in procedures, small
markets may not use it enough to justify the investment.
We provide evidence consistent with this hypothesis using a CMS dataset that enumerates
the types of equipment used by each medical procedure (HCPCS code).45 We measureequipment use by linking this dataset to procedure-level production data. The frequency
of equipment use Hdi for a piece of equipment d in region i is defined as the sum of theprocedure volume in region i across all procedures that use equipment d. We use a Poissonmodel to estimate the population elasticity of per-capita equipment use:Hdi
= ζdK + βdK ln populationi .
ln E
populationi
(15)

Figure 7(c) plots the population elasticity of per-capita equipment use βdK against log
national use, ln Hd . The strong negative correlation indicates that equipment used less often
tends to concentrate in larger markets. Similar to the patterns for physician specializations,rare capital equipment is disproportionately employed in larger regions.

44

This pattern is not attributable to spatial sorting driven by rare specialties commanding higher earnings.
In fact, a specialty’s number of physicians and mean earnings are uncorrelated. Appendix Table D.17 showsthat controlling for a specialty’s earnings has no effect on the negative relationship between population
elasticity and number of physicians across specialties.
45
See Appendix A.1 for details.

32

4.3

Travel to access specialized services

We next ask whether the distribution of specialist physicians helps explain trade. Figure 8(a)shows the share of imports and of locally produced consumption that are provided by specialists as a function of regional population.46 Imports are significantly more specialist-intensive
than local production. This difference is especially pronounced in the smallest regions, andit remains true throughout the population distribution.
Does trade match patients with the appropriate specialist? Among all specialty care, we
determine the two most common specialties to provide each unique service and label these
the “standard” specialties for that care. We then determine whether each instance of thetreatment was provided by a standard or non-standard specialist.
Figure 8(b) shows the share of imports and of locally produced care provided by nonstandard specialties. Imports are less likely to come from non-standard specialists than local
care, and the distinction is especially pronounced in the smallest regions. The differenceis substantial: Local care in the smallest regions is 40% more likely to be provided by anon-standard specialist than in the largest regions (7% vs. 5%). When importing medical
services, this share falls to 5%—indistinguishable from the largest regions’ locally producedcare.
We conduct a similar analysis based on provider experience. Using the public Medicare
provider data (based on all Traditional Medicare patients), we count the number of times
the physician billed for the specific service in the previous year. We divide this experiencemeasure by the procedure’s national mean and average it across all procedures provided
to patients in an HRR. We then rescale HRR-level experience by the mean across HRRs.
Figure 8(c) shows that, at all population sizes, care imported from other regions is producedby more experienced providers than locally produced care.47 Patients in larger regions see

46

We define “specialist” to mean all physicians except those whose primary specialty is internal medicine,
general practice, or family practice.
47
This comparison restricts attention to the 143 procedures performed in all HRRs. Thus, regionalvariation does not reflect the fact that larger markets produce a greater number of distinct codes (Figure 6(a)).

33more experienced providers for both imported and locally produced care.
Specialists are disproportionately located in larger markets, as are physicians with moreexperience in their procedures. Since imported care is predominantly specialized and provides
patients access to higher experience, we conclude that visiting the appropriate specialist
based on training or experience is part of the value proposition for trade in medical care.
Figure 8(d) shows analogous patterns for rare capital equipment. We measure the shareof care that requires a piece of rare capital equipment and plot these shares separately for
local and imported care against regional population. While locally produced care in larger
markets is more likely to use rare equipment, imported care has a higher rare-equipment
share throughout the population distribution.
This analysis also provides a second validation of our interpretation that trade reflects
quality variation. Patients travel to regions with highly-ranked hospitals, which larger markets tend to have—along with rare equipment and the ability to provide rare services. This
market-size effect strongly predicts gross and net exports. Together, this suggests that
economies of scale play an important role in increasing the quality of care, and trade between regions enables patients from many regions to share the benefits of this agglomeration.

5

Health policy with trade and increasing returns

Given the estimated strength of regional increasing returns, geographically concentrating
healthcare production has substantial benefits. Larger regions support more specialists,
physician experience, specialized equipment, and procedures. But geographic concentration
implies that patients in smaller regions may have limited access to care. We use our estimatesof the scale elasticity α, region-specific qualities δi , and observed trade flows to quantify how
various counterfactual policy scenarios would change each region’s patient market access for
non-emergency care.48 Our results underline the importance of distinguishing between the48

Because our estimation sample excludes emergency services, our estimates and counterfactual scenarios
omit any complementarities between emergency and non-emergency care. Our partial-equilibrium model

34

quality of locally produced services and the quality of services to which local residents haveaccess. They also show how geography may contribute to striking patterns of inequality in
Americans’ health.

5.1

Method to compute counterfactual outcomes

We compute counterfactual equilibrium outcomes relative to the baseline equilibrium. For
Q

Q

the baseline equilibrium, define export shares xij ≡ P ′ ijQ ′ and import shares mij ≡ Nijj . Forjij

every variable or parameter y, denote the ratio of its counterfactual value y ′ to its baseline′

value y by ŷ ≡ yy . Appendix C.1 shows how we solve for the relative counterfactual endogenous qualities (δ̂) using baseline equilibrium shares (xij , mij ), the scale elasticity (α), andrelative counterfactual exogenous parameters (Â, R̂, ŵ, ρ̂, N̂ ). In particular, counterfactual
qualities are given by a system of I equations with unknowns {δ̂i }I=1 :δ̂i = R̂i Âi /ŵi

1
 1−α

xij ρ̂ij N̂jP
i′ ∈I mi′ j δ̂i′ ρ̂i′ jj∈I m0j +

X

α
! 1−α

.

1

 1−α
The first term of this expression, R̂i Âi /ŵi
, shows that the scale elasticity α governs

the effect of exogenous supplier shifters, including reimbursements R̂i , on quality produced
in a region. Reimbursement rates shift the scale of production, and stronger scale economies(higher α) amplify these shifts. The second term shows how changes in other regions influence
local outcomes through trade, combined with scale. Thus, our counterfactual scenarios rely
on both our estimates of the scale elasticity α and observed trade patterns.49,50

assumes elastic factor supplies. Our model and estimates represent long-run elasticities, omitting any adjustment costs or short-run diseconomies of scale due to crowding or queuing.
49
The qualitative results are not sensitive to our exact estimate of α. For instance, cutting α by halfchanges the magnitudes but not the geographic patterns.
50
To compute import shares, we assume that the number of potential patients is proportional to thenumber of Traditional Medicare beneficiaries and infer the share choosing the outside option in each region.
See Appendix C.2. The qualitative and spatial patterns of counterfactual outcomes do not depend on whatshare we assume choose the outside option. Appendices C.3 and C.4 generalize this method of computing
counterfactual outcomes to the model with multiple types of patients introduced in Appendix B.2.

35

5.2

Counterfactual reimbursement rates and travel costs

Local reimbursement increase. Policymakers concerned about a region’s healthcare
access might consider local production subsidies. Figure 9 contrasts the consequences ofraising reimbursements by 30% in Boston and in Paducah, Ky. For the Boston scenario,
Panel (a) depicts the impact on quality of care in each region relative to its baseline value.
Free entry means that higher reimbursements translate to higher-quality care produced in
Boston. Quality declines in the rest of New England as patients substitute away and scaleeconomies translate lower volumes into lower quality (an “agglomeration shadow”, as in
Fujita and Krugman, 1995). These effects diminish with distance to Boston.
Yet regions with larger declines in output quality due to Boston’s expansion experiencelarger improvements in patient market access, Φ̂i (Panel 9(b)). This measure accounts
for changes in the quality of care patients receive and their costs of traveling when theychoose to do so. Patients in Boston benefit the most from the higher reimbursement of
their local production. Outside Boston, regional changes in patient market access are nearly
opposite the changes in local output quality. Nearby regions import enough that the benefitsof improved quality in Boston exceed the declines in the quality of local production, so
their patient market access improves. Regions closer to Boston experience larger declines in
the quality of local production precisely because their residents’ choice sets improve more,
spurring more substitution. In more distant regions, the welfare impacts are virtually zero.
Patients who live in higher-income neighborhoods benefit more. The value of market
access increases by 120% more for third- than for first-tercile patients nationwide (Appendix
Table D.18). This reflects greater consumption of Boston production (column 3).
The consequences of higher reimbursement rates in Paducah, Ky. exhibit very different
spatial patterns than in Boston. Figures 9(c) and 9(d) depict the regional changes in output
quality and patient market access, respectively, caused by a 30% reimbursement increase in
Paducah. Unlike Boston, Paducah is a net importer: its consumption of medical services
exceeds local production by more than one-third. Higher reimbursements that improve out36

put quality in Paducah cause Paducahans to reduce their imports from neighboring regions.
This reduces the quantity produced in neighboring regions, lowering their output quality.
But Panel (d) shows that—unlike the pattern of outcomes in the Boston scenario—thoseregions where output quality declines more are the regions where patient market accessdeclines more.
The contrasting outcomes reflect trade flows in the baseline equilibrium: Boston is a
net exporter of medical services and Paducah is a net importer. Higher reimbursements inBoston cause output quality declines in nearby regions—largely because residents of thoseregions import more when Boston’s quality improves. In contrast, higher reimbursements
in Paducah reduce neighboring regions’ output quality largely because Paducah residents
demand fewer exports from these regions when Paducah’s quality improves. Nearby regions
import little from Paducah, so they benefit little from its improved quality. Appendix
Figure D.6 shows that the lessons from Boston and Paducah generalize: the pattern of
spillovers from increasing reimbursements in one region is driven by that region’s net tradein medical care. To summarize, the spillover consequences of subsidizing production in one
region depend on trade patterns; changes in regional output quality need not align withchanges in regional patient market access.
The distributional consequences of region-specific subsidies depend on which region is
subsidized. We compute the nationwide gains in market access from subsidizing productionin each region, one at a time. Figure 10 shows this gain, scaled by the increase in total
spending, as a function of region size. The aggregate gain in market access per dollar spent ishigher in larger markets: further concentration of production has larger benefits. The graphalso shows the gains per dollar separately by income tercile. Subsidizing production in lesspopulous regions benefits lower-income ZIP codes more. These contrasts reflect geographic
divides in incomes: lower-income patients are more likely to live in and near smaller regions.

37

Reducing travel costs. Rather than subsidizing local production, policies might improve
patient market access in a particular region by facilitating trade. We examine the consequences of a policy that reduces travel costs for Paducahans obtaining care elsewhere.51
Figure 11 shows that, unlike an increase in Paducah reimbursements, this policy has positive
spillovers on neighboring regions. These regions increase their exports to Paducah, and thus
their own scale and quality. This improves their residents’ market access.
Reducing travel costs for Paducahans benefits both Paducah and its neighbors—though
we do not estimate the fiscal costs of subsidizing travel. Paducahans benefit even thoughfacilitating travel reduces the quantity—and thus the quality—produced in Paducah. Analysts looking at the impact of travel subsidies on the quantity or quality of care provided in
Paducah itself would reach very different conclusions than those looking at the impact onpatient market access.
These counterfactual scenarios are subject to significant caveats, and we have not attempted to identify the optimal policy. Even so, this simple model rationalizes important
aspects of the economic geography of US healthcare policy. The counterfactual scenarios highlight our main findings: Healthcare production has substantial local increasing returns, and patient travel plays a meaningful role in enabling access to higher-quality care.
Given these economic mechanisms, regional spillovers are larger when economies of scale
are stronger, depend on the pattern of trade flows, and differ depending on whether policies
subsidize production or travel. This shows the importance of distinguishing between regional
output quality and regional patient access when evaluating healthcare policies.

5.3

Geography and healthcare inequality across countries

Looking at healthcare geography more broadly, a striking fact is that the United States hasa steeper relationship between regional income and mortality than other rich economies.

51

Specifically, ρ̂i,Paducah = 1.3 when i ̸= Paducah. The impact of this change on Paducah residents’market access Φ̂Paducah is similar to a 3% increase in reimbursements in Paducah.

38

Appendix Figure D.8(a) compares the US health-income gradient with Germany’s. We use
our model to explore how much geography can explain this difference in gradients.
To do so, we compute the changes in trade costs that would make the distribution ofmarket potential across US regions comparable to that across German regions.52 This requires broad reductions in travel costs, effectively condensing the United States. It requires
particularly large declines in travel costs for remote US regions.
This transformation reduces the Φi -income elasticity by 21% (Appendix Figure D.8(b)).
This suggests that a substantial part of the inequality in market access can be explainedby the US’s greater geographic area. If the US were Germany’s size, patients from lowerincome areas would see particular benefit: these areas are disproportionately rural, and thus
experience the largest gains in this counterfactual. Viewed from the opposite perspective,
27% of the larger Φi -income elasticity in the United States is because of its geographic scope.

6

Conclusion

Smaller markets have fewer specialized physicians, produce less medical care per capita,
and have worse health outcomes than larger markets. Thanks to trade in medical services,less production does not translate one for one into less consumption of medical services.
Instead, trade affords patients who live in smaller markets access to higher-quality care.
This quality comes in part from consuming services that would otherwise be unavailable,
visiting appropriate specialists, and accessing experienced physicians.
This trade amplifies the scale advantages of large markets and hence the quality of carethey produce. This means the healthcare industry can serve as an export base for large
cities. Substantial scale economies also imply that policies to reallocate care across regions
may impact the quality of care available. The rich and varied patterns of consequences whensubsidizing production or travel in “under-served” markets highlight the importance of trade
and agglomeration for the incidence of these policies on patients and producers.
52

See Appendix C.5 for details. The analysis is similar when we compare the United States to France.

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44

Figure 1: Production, consumption, and trade across regions

45(a) Production per capita(b) Consumption per capita(c) Production divided by consumption(d) Gross exports relative to production

Notes: These maps depict production, consumption, and trade by hospital referral region (HRR). Panel (a) shows dollars of production per capita.
The HRR of production is the location where the service is provided. Panel (b) shows dollars of consumption per capita. The HRR of consumption
is based on the patient’s residential address. Panel (c) shows the ratio of production per capita to consumption per capita. Panel (d) shows grossexports as a share of production. Section 1.1 and Appendices A.1 and A.2 detail how we compute trade flows in physician services (excluding
emergency-room care and skilled nursing facilities) at standardized prices from the Medicare 20% carrier, 100% MedPAR, and 100% outpatient claims
Research Identifiable Files. HRR definitions are from the Dartmouth Atlas Project. The Anchorage and Honolulu HRRs are not depicted.

Figure 2: Production and consumption of medical care across regions

Dollars per resident
Medicare beneficiary

8,000

Production

6,000

Consumption
4,000

Imports

2,000

Exports

0
150k

300k

600k

1.2m

2.4m

4.8m

10m

Population
Population elasticity (log−log regression slope) of transactions per
resident Medicare beneficiary:
Production: 0.05 (0.01), Consumption: −0.02 (0.01)
Exports: −0.02 (0.04), Imports: −0.35 (0.03)

Notes: This figure shows production, consumption, and trade per capita of Medicare services across hospitalreferral regions (HRRs) of different sizes, all smoothed via local averages. The blue series shows production of
medical care per Medicare beneficiary residing in the HRR of production. The red series shows consumptionof medical care per Medicare beneficiary residing in the HRR of consumption. The dashed gray series showsinterregional “exports” of medical care and the dashed black series shows interregional “imports” of medicalcare, again per Medicare beneficiary. Section 1.1 and Appendices A.1 and A.2 detail how we compute tradeflows in physician services (excluding emergency-room care and skilled nursing facilities) at standardized
prices from the Medicare 20% carrier, 100% MedPAR, and 100% outpatient claims Research Identifiable
Files. HRR definitions are from the Dartmouth Atlas Project.

46

Figure 3: Patients travel between regions and trade declines with distance, more so for lower-income patients(b) Trade volume and extensive margin by distance
1

10

.2

.1

0

.8

8

.6

6

4

.4

Frequency

.3

2

.2

Trade (log, residualized).4

Share of pairs with positive trade(a) Distribution of travel distances within and across HRRs

0
1

4

16

64

248

Distance (km)Within HRR

992

−5

3,968

−3

−1

1

Distance (log, residualized)
Log trade, residualized

Across HRR

Share of pairs with positive trade(c) Higher-income patients are less sensitive to distance47
Distance elasticity of trade

−1.5

−2

−2.5
1

2

3

4

5

6

Income decile

7

8

9

10

Notes: Panel (a) shows the distribution of patients’ travel distances when patients obtain care within their home HRR (blue distribution) and when
they travel across HRRs (red distribution). Travel distances measure the distance between home and treatment locations. For travel within a hospitalreferral region, the distance measure reflects the distance between the centroid of the patient’s residential ZIP code and the ZIP code of the service
location. We use ZCTA-to-ZCTA distances downloaded from the National Bureau of Economic Research; those exceeding 160 kilometers are winsorized
at 160 kilometers. For travel across HRRs, we use ZCTA-to-ZCTA distances when they are within 160 kilometers and (for computational ease) use
HRR-to-HRR distances beyond 160 kilometers. In Panel (b), the blue series depicts the volume of trade against distance, after conditioning out the
fixed effects in equation (8), for positive-trade pairs of locations. The red series shows the share of HRR pairs with positive trade as a function of the
distance between them, after conditioning out the importer fixed effects and exporter fixed effects, as in equation (8). Panel (c) depicts the coefficienton log distance obtained by estimating equation (8) separately for each decile of the national ZIP-level median-household-income distribution. The
95% confidence intervals are computed using standard errors two-way clustered by both patient HRR and provider HRR. Patients from higher-income
ZIP codes are less sensitive to distance.

Figure 4: Illustrative model diagrams(a) Autarky: Constant vs. increasing returns
Higher Demand(∆N > 0)DemandLog δ(b) Autarky: Market size and demand elasticity
Log δ

C=R
(α > 0)
δ′
δ

C
A

C=R
(α = 0)B

Less Elastic
DemandMore Elastic
DemandC=R(α > 0)

δ′
δ
δ′
δ

Log Q

Log Q

(c) Quality and quantity depend on scale elasticity
DemandLog δ

C=R(α ≫ 0)
C

δ ′′
δ′
δ

A

C=R
(α > 0)(d) Exports and imports
Log Q

Exports(α ≫ 0)

Imports(α > 0)
Imports(α ≫ 0)
Exports(α > 0)

B

Log Q

Log N

Notes: This figure depicts how increasing demand in one region affects its equilibrium outcomes. In Panels (a)–(c), quantity produced Q is on the horizontal axis and service quality δ is on the vertical axis. The
black lines depict the free-entry isocost curve, C = R, given by equation (3). The blue and cyan lines depict
demand for the region’s service, which we depict as log-linear for visual clarity. (The logit demand functionis actually log-convex, which is consistent with all the depicted comparative statistics.) Equilibrium is theintersection of the demand and isocost curves. An increase in demand is the rightward shift from the solid
to the dashed demand curve. This shift increases equilibrium quality from δ to δ ′ . Panel (a) shows thathigher demand elicits higher quality if there are increasing returns to scale. Panel (b) shows that this quality
improvement is larger when demand is more elastic. Panels (c) and (d) introduce trade and compare theextent of quality improvement under two different magnitudes of increasing returns (α > 0 and α ≫ 0).
These magnitudes govern the patterns of interregional trade, shown in Panel (d) as a function of the numberof potential patients N . Imports from other regions rise with N . With increasing returns to scale (α > 0),exports to other regions also rise with N (a weak home-market effect). When the scale elasticity α is larger(α ≫ 0), the import curve is flatter and the export curve is steeper. With sufficiently strong increasing returns, an increase in local demand causes a greater increase in exports than imports (a strong home-market
effect).

48

Figure 5: Estimated quality is positively correlated with total output and external quality metrics(a) Quality estimates vs. mortality rate (Chandra et al.)(b) Quality estimates vs. mortality rate (CMS)

CA−Los Angeles

2

CA−Los Angeles

2
MN−Rochester

MA−Boston

MA−Boston

NY−New YorkMI−Royal Oak
IL−Evanston
PA−Allentown
NJ−Hackensack

GA−Columbus
TX−El Paso
CA−Stockton
OR−Bend
NC−Hickory WI−Appleton
ID−Idaho Falls

NJ−Ridgewood
OH−Elyria−2MI−Royal Oak

0

CA−Fresno

Exporter FE

0Exporter FE

NY−New YorkWA−Yakima

MN−St Cloud
IL−Blue Island
GA−Columbus
FL−Bradenton
AR−Springdale GA−Albany
IA−Mason City
FL−Ocala
NC−Hickory
WI−Neenah

TX−Mcallen
OH−Elyria−2

ND−Minot

−4

−4

−6

−6
−4

−2

0

2

4

9

Best estimate for overall mortality (Chandra et al., 2023)

49(c) U.S. News vs. estimated quality

11

12

13

14

(d) Quality is higher in regions producing more output

4

2

CA−Los Angeles
TX−Houston
CA−San Diego
MA−Boston
OH−Cleveland
PA−Philadelphia
NY−East Long Island

00NY−New York

Quality lnδi2Exporter FE

10Overall mortality rate across conditions

IL−Chicago

−2

−2

−4
HI− Honolulu−4

AK− Anchorage

−6

−6
0

20

40

USN No. of Features in Top Lists

60

4

5

6

7

8

9

Production lnQi

Notes: The first three panels show the relationship between the exporter fixed effects (our revealed-preference measure of quality) and external quality
measures. The vertical axis shows the exporter fixed effects for each HRR estimated from equation (8). The horizontal axis in Panel (a) is an averageof the hospital mortality rates estimated by Chandra, Dalton, and Staiger (2023) in a region, and in Panel (b) an average of those estimated by
CMS. The negative correlations indicate patients travel farther to obtain care from regions with lower hospital mortality rates. The horizontal axis
in Panel (c) is a count of the number of times each region’s hospitals appear on the U.S. News list of best hospitals. U.S. News produces an overall
ranking as well as rankings for 12 particular specialties. We count the number of times each HRR’s hospitals appear on any of these 13 lists. The
relationship is positive, indicating that patients travel farther to obtain care from regions highly ranked by U.S. News. The horizontal axis in Panel (d)is the volume of production. Section 1.1 and Appendices A.1 and A.2 detail how we compute production and trade of physician services (excluding
emergency-room care and skilled nursing facilities) at standardized prices from the Medicare 20% carrier, 100% MedPAR, and 100% outpatient claims
Research Identifiable Files.

Figure 6: Production and consumption of medical care by market size and service(a) Variety of procedures produced by market size(b) Variety of procedures consumed by market size
4

Distinct procedures
consumed (relative)

Distinct procedures
produced (relative)

4

3

2

1

3

2

1
150k

300k

600k

1.2m

2.4m

4.8m

10m

150k

300k

600k

Population

2.4m

4.8m

10m

Population
Surgery
Anesthesia
Pathology
Other

Evaluation & Management
Radiology
Medical(c) Population elasticities by procedure frequency(d) Population elasticities by diagnosis frequency
Population elasticity of expenditures
per Medicare beneficiary

Evaluation & Management
Radiology
MedicalPopulation elasticity of quantity
per Medicare beneficiary

Surgery
Anesthesia
Pathology
Other

1.2m

.4

.2

0
32

256

2,048

16,384

131,072

1,048,576

National volume of procedure
production

.4

.2

0
32

256

2,048

16,384

131,072

1,048,576

National number of patientsconsumption

production

Production fitted line: y = −0.025 (0.002) * x + 0.380 (0.016)
Consumption fitted line: y = −0.007 (0.002) * x + 0.138 (0.014)
This plot depicts estimated population elasticities per Medicare beneficiary for 8,210 procedures
produced at least 20 times nationally.

consumption

Production fitted line: y = −0.007 (0.003) * x + 0.195 (0.031)
Consumption fitted line: y = −0.001 (0.003) * x + 0.076 (0.028)
This plot depicts estimated population elasticities per Medicare beneficiary for 482 diagnoses
billed for at least 20 patients nationally.

Notes: Panel (a) depicts the number of distinct services produced in an HRR as a function of population.
We use procedure classifications from the American Academy of Professional Coders, which groups codes
into surgeries, anesthesia, radiology, pathology, medical, and evaluation & management services (AAPC,
2021). We combine Category II codes, Category III codes and Multianalyte Assays into “other.” Withineach group, the procedure count is relative to that of the smallest regions. More populous HRRs produce
a greater number of services. Panel (b) depicts the number of distinct services consumed in an HRR as afunction of population. In Panels (c) and (d), the vertical axes are the population elasticities of quantityof medical care produced (blue dots) and consumed (red squares) per local Medicare beneficiary. The
elasticities are computed using the Poisson model in equation (13) based on place of service and patients’
residential location, respectively. Panel (c) estimates these elasticities for each of the procedures provided
at least 20 times nationally in the Medicare data. Panel (d) estimates the elasticities for care provided totreat each of the Clinical Classifications Software Refined (CCSR) diagnoses billed for at least 20 patients
nationally in the Medicare data. Each panel depicts these population elasticities as a function of the national
volume (of procedures and diagnoses, respectively). Section 1.1 and Appendices A.1 and A.2 detail how
we compute production and consumption of physician services (excluding emergency-room care and skilled
nursing facilities) at standardized prices from the Medicare 20% carrier, 100% MedPAR, and 100% outpatient
claims Research Identifiable Files. The contrasting population elasticities of production and consumption
imply trade in medical services between markets of different sizes, with more net trade for rare procedures
and rare diseases.

50

Figure 7: Larger regions produce more specialized care, with more specialized equipment(a) Population elasticities of specialties’ earnings(b) Population elasticities of physician specializations

Maxillofacial Surgery

Geriatric Medicine
Plastic and Reconstructive Surgery
Preventive Medicine
Otolaryngology
Psychiatry
Obstetrics & Gynecology
General Practice
Endocrinology
Allergy/ Immunology
Rheumatology
Anesthesiology
Neuropsychiatry
Infectious Disease
Diagnostic Radiology
Internal
Medicine
Pediatric Medicine
Emergency Medicine
Family Practice
Pathology
Physical Medicine
and Rehabilitation
Medical Oncology
Orthopedic Surgery
Peripheral Vascular Disease
Pulmonary
DiseaseInterventional
Cardiology
Hospitalist
Urology
General Surgery
Interventional
Critical Radiology
CareCardiac(Intensivists)
Neurosurgery
Surgery
Colorectal Surgery (Proctology)
Cardiovascular Disease (Cardiology)
Gastroenterology
Ophthalmology

Neurology
Hospice and Palliative
Care

0

Surgical Oncology
Nuclear Medicine
Sleep Medicine
Genetics

Dermatology
Nephrology
Hematology-Oncology

Radiation Oncology
Interventional Pain Management-.2

Clinical Cardiac Electrophysiology-.4Pain Management

Sports Medicine
Advanced Heart Failure and Transplant Cardiology

Hand Surgery

Population elasticity of MDs in
specialization per capita.2

1.5
Osteopathic Manipulative Medicine
Gynecological Oncology-.6

Population elasticity of earnings

Hematology

1
Transplant Surgery
Pediatric Emergency Medicine
Transplant Hepatology Reproductive Endocrinology.5

Medical Toxicology
Forensic Pathology
Foot and Ankle Surgery
Retina Specialist
Thoracic Surgery

0Internal Medicine

Family Medicine

−.5

400

2,900

22,0004

150,000

32

256

2048

16384

131072

Number of physicians in specialty

Number of physicians in specialty

Slope: −0.052 (0.009)

Slope: 0.005 (0.006)

Population elasticity of equipment use
frequency per capita(c) Population elasticities of equipment use
Augmentative Communication − WhitKit Head Support

2

CO2 Infrared Analyzer (COSMO)

1
Articulator (Model 96H2 − HANAU)

Flow Cytometry Analytic Software

RGP Lens Modification Unit
Mayo Stand0

Table, Exam
CPAP/BiPAP Remote Clinical Unit
Densitometry Unit, Whole Body, DXA−1Whirlpool (Hubbard Tank)

10

100

1k

10k

100k

1m

10m

100m

National equipment use frequency
Slope: −0.056 (0.006)

Notes: Panel (a) shows the population elasticity of income for different medical specialties against the total
number of physicians in those specialties. For each specialty, we estimate the elasticity of income with respect
to population across commuting zones, using data from Gottlieb et al. (2023). The regression line weights
each specialty with the number of physicians in that specialty. The graph shows that these elasticities areunrelated to the total national count of physicians in those specialties. The vertical axis of Panel (b) depicts
the population elasticities of quantity of physicians in an HRR. The population elasticities are computed foreach specialty using the Poisson model in equation (14). The horizontal axis shows the nationwide number ofphysicians in each specialty. The negative relationship indicates that rare specialties are disproportionately
concentrated in high-population regions. Panel (c) plots the population elasticity of equipment use frequency
per capita against the national frequency of equipment use, for each piece of equipment. Pieces of equipmentwith elasticities above the 98th percentile are excluded. The graph shows that rarely-used equipment is used
more intensively in large markets.

51

Figure 8: Imports are specialist-intensive, especially in smaller regions(b) “Non-standard” specialty care

.6

Share performed
by non−standard specialists

Share performed by specialist(a) Specialty care imports

.55

.5

.08

.07

.06

.05

.45
150k

300k

600k

1.2m

2.4m

4.8m

150k

300k

600k

Population
Imports

Locally produced

Imports

Import slope: −0.018 (0.003)
Locally produced slope: −0.002 (0.004)

2.4m

4.8m

Locally produced

Import slope: −0.000 (0.001)
Locally produced slope: −0.004 (0.001)(c) Provider experience(d) Rare capital equipment imports

1.3

.022

Share performed
with rare equipment

Mean normalized experience

1.2m

Population

1.2

1.1

1

.9

.018

.014

.01
150k

300k

600k

1.2m

2.4m

4.8m

150k

300k

600k

Population
Imports

1.2m

2.4m

4.8m

Population

Locally produced

Imports

Imports slope: 0.033 (0.011)
Locally produced slope: 0.035 (0.017)

Locally produced

Import slope: −0.000 (0.000)
Locally produced slope: 0.001 (0.000)

Notes: Panel (a) shows the share of procedures that are performed by a specialist, for imports and locally
produced procedures, by market size. We define generalists as internal-medicine, general-practice, and familypractice physicians and define specialists as all other physicians. Imports are more likely to be performed
by a specialist, and smaller markets’ imports especially so. Panel (b) examines procedures that are typically
performed by specialists, and classifies the “standard” specialists as the top two specialties performing theprocedure nationally. It shows the shares of procedures performed by the “non-standard” specialties inimported specialty care and locally produced specialty care as a function of local population size. Imports
are less likely to be performed by “non-standard” specialties, especially for smaller regions. Panel (c) shows
the mean relative experience of providers for care produced locally and imported by population size of thepatient’s region. This panel describes only procedures that are performed in all hospital referral regions (143procedures). In public-use Medicare data, we define a provider’s experience for a given procedure as thenumber of times they performed the procedure for Traditional Medicare patients in the prior calendar year.
Before aggregating to the regional level, we rescale experience in each procedure so that its mean is one. We
further normalize at the regional level so that the experience of the average HRR is one. On average, patientsin larger markets obtain treatment from more experienced providers. At all population levels, imported careis produced by more experienced providers than local care. Panel (d) shows the share of procedures that use
rare capital equipment in imported and locally produced care by market size. Rare equipment is defined as
those pieces of equipment with below-median use in the Medicare data, defined as in Appendix A.1. We seethat locally produced care in larger markets is more likely to use rare equipment, and imported care has ahigher rare-equipment share throughout the population distribution

52

Figure 9: Counterfactual outcomes for higher reimbursements in one region(a) Change (%) in output quality δi : higher reimbursement in Boston, Mass.

(b) Change (%) in market access Φi : higher reimbursement in Boston, Mass.

(c) Change (%) in output quality δi : higher reimbursement in Paducah, Ky. (d) Change (%) in market access Φi : higher reimbursement in Paducah, Ky.

53
Notes: Panels (a) and (b) show the impacts of increasing reimbursements by 30% in the Boston, Mass. HRR (R̂i = 1.3) based on our estimatedmodel. Panel (a) illustrates the percentage change in quality of care δi provided in each region. Panel (b) illustrates the percentage change in thevalue of market access Φi for patients who live in an region. Panels (c) and (d) are analogous, but for a 30% increase in reimbursements in Paducah,
Ky., a net importer. In all panels, the predicted change for the region whose reimbursement changes (“treated region”) is listed on the map itself. In
both cases, the quality produced in neighboring regions declines (Panels (a) and (c)). Patients in regions near Boston benefit from increased accessto the treated region (Panel (b)), so there is a negative relationship between the percentage changes in δ and Φ across regions. In contrast, patientsin regions near Paducah suffer a decrease in access (Panel (d)). The contrasting outcomes stem from Boston being a net exporter and Paducah being
a net importer in the baseline equilibrium. The exercise is described in detail in Section 5.

Nationwide percentage increasein patient market accessper percentage increase in expenditure

Figure 10: Returns to higher reimbursements in one region by region size

1.5

1

.5

0
150k

300k

600k

1.2m

2.4m

4.8m

10m

Population size of treated region (log scale)
Total
Tercile 2

Tercile 1
Tercile 3

Notes: This figure summarizes the counterfactual outcomes of 30% higher reimbursements in one HRR as
a function
P thatP HRR’s population size. The nationwide return is the percentage
P increase in patient market
accessNΦperpercentage
increaseinnationwide
expenditures
jκ
jκ
κ
j
i Qi Ri . The tercile-specificP
return is the increase in tercile-specific patient market access j Njκ Φjκ . Increasing reimbursements inmore populous HRRs has the highest return when measured as impact on aggregate market access. Subsidies
in less populous regions favor lower-income patients, primarily because there are more low-income patientsliving in and close to smaller regions.

Figure 11: Counterfactual outcomes when changing travel costs for Paducah, Ky. residents(b) Change (%) in patient market access Φi(a) Change (%) in output quality δiNotes: This figure shows the impacts of a counterfactual 30% decrease in travel costs for Paducah residents(ρ̂ij = 1.3 ∀i ̸= Paducah). Panel (a) depicts the percentage change in quality of care δi produced in eachregion. Panel (b) depicts the percentage change in the value of market access Φi for patients who live in aregion. The notes report the changes for Paducah.

54

Table 1: Scale elasticity estimates
All services

Baseline

No Diagonal

Controls

OLS: 2017

0.806(0.031)
0.999(0.079)0.800(0.037)[2141]
0.697(0.063)
[163]

0.961
(0.047)1.045(0.083)0.905(0.057)[2141]
0.924(0.093)
[163]

0.786
(0.041)1.018(0.082)0.777(0.050)[1621]
0.633(0.070)[206]

OLS: 2013–2017 difference
2SLS: population (log)

2SLS: population (1940, log)

Notes: This table reports estimates of α from ordinary least squares (OLS) or two-stage least squares (2SLS)dδ i = α ln Qi + ln Ri + ln wi + ui using Hospital Referral Regions (HRRs) as theregressions of the form lndδ i is estimated in equation (8) using a same-region dummygeographic units. The dependent variable ln
and a quadratic function of log distance. Qi is region i’s total production for Medicare beneficiaries, Ri is
Medicare’s Geographic Adjustment Factor, the wi covariate includes mean two-bedroom property value andmean annual earnings for non-healthcare workers, and ui is an error term. In the “no diagonal” column,dδ i in equation (8). In the third column, the ln Ri and
Sii observations were omitted when estimating ln
ln wi controls are included in the regressions (coefficients not reported). The first-difference specificationdδ i = α∆ ln Qi + ∆ui . In the rows labeled “2SLS,” we instrument for ln Qi using the specified
estimates ∆ln
instruments. The standard errors in parentheses are robust to heteroskedasticity. For 2SLS estimates, firststage effective F -statistics (Montiel Olea and Pflueger, 2013) are reported in square brackets. All estimates
reveal substantial scale economies.

55

Table 2: Aggregate medical services exhibit a strong home-market effect

(1)

(2)

(3)

Cross-sectional PPMLλX Provider-market population (log)λM Patient-market population (log)Distance (log)0.671(0.0543)0.260(0.0547)-1.627(0.0489)

Distance (log, squared)

0.681(0.0505)
0.252(0.0501)
0.344(0.304)-0.199(0.0305)

0.671(0.0366)
0.286(0.0346)(4)
IV: 1940
population(5)
2013–2017
panel

0.757
(0.0547)0.284(0.0467)0.377(0.250)-0.201(0.0247)

0.939(0.151)-0.205(0.148)56

Distance (log) × 2017
p-value for H0 : λX ≤ λM
Observations
Fixed effects
Distance elasticity at mean
Distance deciles-0.00117(0.00667)<0.001
93,636<0.001
93,636<0.001
93,636-1.59<0.001
93,636<0.001
162,678
ij

-1.57
Yes

Notes: This table reports estimates of equations (10) and (11), which evaluate the presence of weak or strong home-market effects. The sample isall HRR pairs (N = 3062 ), multiplied by two for the last column. The dependent variable in all regressions is the value of trade when including
professional and facility (inpatient and outpatient) fees at national average prices. Columns 1 through 4 use 2017 data. In column 1, the independent
variables are patient- and provider-market log population, log distance between HRRs, and an indicator for same-HRR observations (i = j). The
positive coefficient on provider-market log population implies a weak home-market effect, and the fact that this coefficient exceeds that on patientmarket population implies a strong home-market effect. Column 2 makes the distance coefficient more flexible by adding a control for the square oflog distance. Column 3 replaces parametric distance specifications with fixed effects for each decile of the distance distribution. Column 4 uses theprovider-market and patient-market log populations in 1940 as instruments for the contemporaneous log populations when estimating by generalized
method of moments. Column 5 presents estimates of equation (11) including ij fixed effects using data from 2013 and 2017. Section 1.1 andAppendices A.1 and A.2 detail how we compute trade flows in physician services (excluding emergency-room care and skilled nursing facilities) atstandardized prices from the Medicare 20% carrier, 100% MedPAR, and 100% outpatient claims Research Identifiable Files. HRR definitions are fromthe Dartmouth Atlas Project. Standard errors (in parentheses) are two-way clustered by patient market and provider market.

Table 3: The home-market effect is stronger for rare procedures and diagnoses

Procedure(1)(2)
λX Provider-market population (log)λM Patient-market population (log)0.618(0.0516)0.360(0.0519)0.605(0.0493)0.364(0.0492)µX Provider-market population (log) × rareµM Patient-market population (log) × rare57

p-value for H0 : λX ≤ λM
p-value for H0 : µX ≤ µM

0.005

Observations
Distance [linear] controls
Distance [quadratic] controls
Patient-provider-market-pair FEs

187,272
Yes

0.006

110,402
Yes

Procedure(3)(4)

Procedure
(5)
(6)

0.603
0.606
(0.0493)(0.0488)
0.366
0.364
(0.0492)(0.0486)
0.344
0.329
0.362
(0.0447) (0.0405) (0.0452)-0.241-0.239-0.250(0.0606) (0.0587) (0.0612)
0.007<0.001<0.001

110,402
Yes

110,402
Yes
Yes

Diagnosis
(7)
(8)

0.317
(0.0392)-0.220(0.0564)0.601(0.0489)
0.371(0.0486)
0.120
0.110
(0.0232) (0.0206)-0.0986 -0.0915(0.0186) (0.0172)

0.005<0.001<0.0010.008<0.001<0.001

110,402110,402109,658

109,658

Yes

Yes
Yes

Yes

Yes
Yes

Notes: This table reports estimates of equation (12), which introduces interactions with an indicator for whether a procedure or diagnosis is “rare”(provided less often than the median, when adding up all procedures provided nationally). The interactions with patient- and provider-market
population reveal whether the home-market effect is larger for rare procedures/diagnoses. The unit of observation is {rare indicator, exporting HRR,
importing HRR} so the number of observations is 2×3062 in column 1, and the dependent variable in all regressions is the value of trade. Columns 1–6
reflect estimates by procedure and Columns 7 and 8 reflect estimates by diagnosis. Columns 2 onwards drop HRR pairs with zero trade in bothprocedure groups, and column 2 shows that this restriction has a negligible impact on the estimated log population coefficients. Columns 3 onwards
include the rare indicator interacted with patient- and provider-market populations and distance covariates. Columns 1–4 control for distance using
the log of distance between HRRs. Columns 5–8 add a control for the square of log distance. Columns 4, 6, and 8 introduce a fixed effect for eachij pair of patient market and provider market, so these omit all covariates that are not interacted with the rare indicator. The positive coefficienton provider-market population × rare across all columns indicates that the home-market effect is stronger for rare than for common services. The
negative coefficient on patient-market population × rare across all columns indicates that the strong home-market effect has a larger magnitude
for rare services. Valid primary diagnoses observed in 1,000 distinct claims or more nationally in the professional fees 20% sample are included.
Section 1.1 and Appendices A.1 and A.2 detail how we compute these trade flows for physician services (excluding emergency-room care and skilled
nursing facilities) at standardized prices from the Medicare 20% carrier, 100% MedPAR, and 100% outpatient claims Research Identifiable Files. HRR
definitions are from the Dartmouth Atlas Project. Standard errors (in parentheses) are two-way clustered by patient market and provider market.

Appendix – For Online Publication
Market Size and Trade in Medical Services
Jonathan I. Dingel, Joshua D. Gottlieb, Maya Lozinski, and Pauline Mourot
April 2024

A

Data appendix

A.1

Data and processing

Medicare data. For patients enrolled in Traditional (fee-for-service) Medicare, our datacontain a 100% sample of hospital inpatient and outpatient claims. For physician care(provided in the Carrier files), we have all claims from a random 20% sample of patients.
Our main analysis uses data from 2017, but panel analysis uses data from 2013–2017.
One-third of Medicare patients opt out of the traditional version of Medicare, wherecare is paid directly by the government, in favor of a private insurance scheme (“Medicare
Advantage”). In these private schemes, the government pays the insurer a fixed amount per
patient and the insurers are responsible for the patient’s care. Because Medicare does not
pay claim-level bills in these private insurance schemes, the availability and quality of data
for the privately insured patients is lower. We exclude these patients from our analysis.

Geography. We assign ZIP codes to hospital referral regions (HRRs) using a 2016 crosswalk from the Dartmouth Atlas of Healthcare. We assign ZIP codes to core-based statisticalareas (CBSAs) by using the 2010 ZCTA to County Relationship File, updated county definitions, and the September 2018 definitions of CBSAs. For travel within an HRR, wemeasure the distance between the centroids of the patient’s residential ZIP code and the
ZIP code of the service location. We obtain the centroid coordinates from the Census Bureau’s corresponding ZIP code tabulation areas (ZCTAs). For travel across HRRs, we use
ZCTA-to-ZCTA distances when they are within 160 km, and (for computational ease) use
HRR-to-HRR distances beyond 160 km.

Appendix – 1

Socioeconomic status. Our data do not contain patients’ wealth or income. We use median household income in each patient’s residential ZIP code to proxy for their socioeconomic
status and estimate equation (8) separately for each decile of this proxy.

Physician earnings. We use data from Gottlieb et al. (2023) to measure the population
elasticities of doctors’ earnings and the American Community Survey (Ruggles et al., 2022)
to examine other healthcare workers’ earnings and real estate costs.The Gottlieb et al. (2023)
earnings data depicted in Appendix Figure D.4 are only available for 111 commuting zones.
The American Community Survey (ACS) covers far more CBSAs, but this source top-codes
income for a substantial share of doctors. We use these same sources to compute physicians’
share of the labor costs.

Physician specialties. Data come from the National Plan and Provider Enumeration
System (NPPES) data, which cover all physicians, not just those serving Medicare patients.
These data only report the number of doctors/specialists and their location, but contain nofurther information about procedures performed. We restrict attention to the 223 specializations within Allopathic & Osteopathic Physicians. We restrict attention to national provider
identifiers of the “individual” entity type (as opposed to “organization”). We consider eachphysician’s primary specialty, as indicated in the NPPES file. The results shown in Figure 7b look similar (not reported here) when we allow for multiple specialties per physician,a common occurrence in the NPPES data.

Capital equipment. The data on equipment use are obtained from the CMS Physician
Fee Schedule Final Rule documentation for the calculation of practice expense Relative Value
Units. For each HCPCS code, the data report the types of medical equipment that are used
for that procedure. They also report the estimated price, useful life, utilization rate, used
minutes per procedure, etc., of each piece of equipment (used minutes per procedure for thesame piece of equipment can differ by HCPCS code).

Appendix – 2

We combine the CMS equipment requirement data with procedure frequency by geographic area, computed from the public use Medicare data, to obtain the “frequency ofequipment use” for each type of equipment. Specifically, for each HRR, we locate all procedures that use a specific piece of equipment (equipment X), add up the number of billings
for each of those procedures from that HRR, and interpret this total as the number of times
equipment X is being used in that HRR. Similarly, we define the national frequency ofequipment use by adding up the number of billings nationwide across all procedures that use
equipment X. Finally, equipment use frequency per capita is defined as the equipment use
frequency in a geographic unit divided by its population. We then estimate the population
elasticity of equipment use frequency per capita at the HRR level, the same approach as wetake for procedures and specialists. A population elasticity is estimated for each piece ofequipment, for around 580 pieces of equipment (excluding outliers).

Chandra, Dalton, and Staiger (2023) hospital quality measures. Chandra, Dalton,
and Staiger (2023) provide empirical Bayes estimates of hospital mortality across five large
diagnostic cohorts: heart attacks, hip fractures, pneumonia, congestive heart failure, andstrokes. We use the 2014 estimates as this is the closest year to our main analyses. They
also report the number of episodes at the hospital-cohort-year level, which we use as weights
when aggregating across hospitals. We map hospitals to HRRs using the Dartmouth Atlas(https://data.dartmouthatlas.org/supplemental/#hospital).
We aggregate the hospital-cohort level data to the HRR level in two steps. First, we
compute the overall quality measure at the hospital level by regressing the empirical Bayes
estimates on a set of hospital dummies and a set of cohort dummies; hospital-level estimates
are simply the hospital fixed effects from this regression. Next, we aggregate across hospitals
within an HRR by computing the average quality estimate across hospitals in that HRR,
weighted by the number of episodes in each hospital. We standardize the exporter fixed
effects before plotting them against our revealed-preference quality measures.

Appendix – 3

U.S. News and World Report. The publication produces an overall ranking and rankings for 12 particular specialties. We count the number of times each HRR’s hospitals appear
on any of these 13 lists.53 Thus, higher ranking on the horizontal axis indicates a region
has some combination of more top-ranked hospitals, or each of its hospitals performs well inmany specialty areas.
The U.S. News rankings are intended to capture the “Best Hospitals,” a concept associated with providing highly specialized care. So it is natural that there is a stronger
relationship between the U.S. News rankings and exporter fixed effects for rare services; theslope in Figure D.3(b) is twice as large as that for common services in Figure D.3(a). In contrast, safety grades are not differentially relevant for rare services: Figures D.3(c) and D.3(d)show virtually identical slopes.

Depth to bedrock. Following Levy and Moscona (2020), we obtain 250m-cell resolution
absolute depth to bedrock raster data from the International Soil Reference and Information
Centre (ISRIC) SoilGrids 2017 data release. To define boundaries for commuting zones, we
use the 2018-vintage cartographic boundary file for ZCTAs from the Census Bureau andmatch them to commuting zones using definitions from Fowler and Jensen (2020). Median
depth to bedrock is computed over commuting zone boundaries which are based on thecommonly used geodetic coordinate system EPSG:4326.

Clinical Classifications Software Refined (CCSR) diagnoses. We use the ClinicalClassifications Software Refined (CCSR) diagnosis categories produced by the Agency for
Healthcare Research and Quality’s Healthcare Cost and Utilization Project. CCSR aggregates over 70,000 ICD-10-CM diagnosis codes into “clinical categories,” of which 482 haveat least 20 patients each in our data. We split these categories at the median frequency toseparate common from rare diagnoses.

53

Results are similar when we use other methods to aggregate the rankings information, including when
we account for the ordered nature of the lists.

Appendix – 4

A.2

Geographic price adjustments

Professional fees. To adjust for geographic price variation in the professional fees, we
compute a national average price per Healthcare Common Procedure Coding System (HCPCS)
code as the sum of the line allowed amount, which includes the line item’s Medicare-paidand beneficiary-paid amounts (i.e., deductible, copayment, and coinsurance), divided by thesum of the line service count per HCPCS code nationally. We then apply this average priceto all billing for the HCPCS code when computing total spending across services.

Hospital inpatient fees. For 2014–2017, we use the field “final standard payment amount”
in the MedPAR file, which is computed as described in Finkelstein, Gentzkow, and Williams(2016) and Gottlieb et al. (2010). This represents “a standard Medicare payment amount,
without the geographical payment adjustments and some of the other add-on payments that
go to the hospitals” according to the data documentation. To ensure that total national
spending remains identical, we multiply the standardized amount by a constant factor equal
to the ratio of total national spending over the total standardized amount nationally. This
field does not exist for 2013, the first year of our panel. Instead, we use the following process to infer the price adjustment from data available in 2013. We first compute the total
expenditure as the sum of the Medicare payment amount, the primary payer amount, thepass-through amount, the Part A beneficiary co-insurance amount, the beneficiary deductible
amount, and the beneficiary blood deductible amount for 2014 – the last year with the final
standard payment amount field – and 2013. We then compute the ratio of the calculated
total expenditure and the provided standard payment amount for 2014 and scale our total
expenditures in 2013 by that ratio to infer the standardized expenditure amount. To test
this process, we implement an analogous exercise using 2015 data to infer the standardized
price for 2014, and find an R2 ≥ 0.995 between our computed variable and the one provided
in the 2014 data.

Appendix – 5

Hospital outpatient fees. To adjust for geographic price variation in hospital outpatientfees, we compute a national average price per Healthcare Common Procedure Coding System(HCPCS) code, Ambulatory Payment Classifications (APC) code, and revenue center code.
HCPCS codes reflect the procedure performed and APC codes reflect a prospective payment
system applicable to outpatient analogous to Diagnosis Related Groups (DRGs) for inpatient
claims. Revenue center contains information on the place of service, e.g. rehabilitation or
acute care, so we consider two procedures performed in different revenue centers as different
procedures for price adjustment purposes.
The total amount per claim line is calculated as the sum of the claim (Medicare) payment amount, the primary payer amount, the Part B beneficiary co-insurance amount, thebeneficiary Part B deductible amount, and the beneficiary blood deductible amount. Theseamounts are summed nationally for each {HCPCS code, APC code, revenue center code}
triplet, and divided by the frequency of that triplet to obtain a national average price. We
then apply this average price to all instances of that {HCPCS code, APC code, revenue center code} combination when computing total spending across services. To ensure that total
national spending remains identical, we multiply the price-adjusted measures by a constantfactor equal to the ratio of the total national spending over the total price-adjusted spending
nationally.

A.3

Procedure frequency in estimation sample matches other sources

Medicare provides two public-use files based on 100 percent claims data. Neither one issuitable for our main analysis because they do not contain patient location, so cannot be
used to study trade flows. Instead, we use both of the public files to validate aspects of theconfidential (20 percent) sample we must use for our main analysis.
The first public-use file contains the complete count of procedures billed by HCPCS code
but does not have information about providers. We use it to confirm that procedure counts
based on the confidential data do not suffer substantial sampling bias. In Figure D.7(a),Appendix – 6

we split procedure codes into deciles based on their national frequencies, separately in theconfidential and public datasets. This generates a 100-cell matrix by decile pair. We plot theshare of procedures in each cell in this matrix to determine how well the two datasets align.
The vast majority of the codes are on the diagonal, with almost all of the remainder adjacentto the diagonal. This suggests that sampling error is not causing us to mischaracterize
procedure frequency.
Medicare provides a second public file at the level of physician-by-procedure (HCPCScode). This summary does not contain any patient-level information so cannot be used to
study trade flows, but we can use it to replicate analyses based on the location of production
and physician experience. This file is censored such that physician-by-procedure pairs with
10 or fewer observations per year are suppressed, which makes for a more complicated bias
than simple 20 percent random sampling. Nevertheless, all of the results that can be testedon this sample confirm those found in the 20 percent sample.
Since our procedure frequency measures rely on Medicare data, we would mismeasure frequency if the Medicare population uses a substantially different composition of care from thebroader population. For example, childbirth is less common among Medicare beneficiaries.
So our frequency measures may not capture the true national frequency of a procedure.
We address this by comparing procedure frequencies between the Medicare public dataand private data from the Health Care Cost Institute (HCCI). The HCCI data contain claims
for about 55 million privately insured patients (about 35% of individuals with employerbased insurance). We only consider HCPCS codes performed on at least eleven patients in
the HCCI data. Note that frequencies are computed for all providers here, not only MDs
and DOs. The authors acknowledge the assistance of the Health Care Cost Institute (HCCI)
and its data contributors, Aetna, Humana, and Blue Health Intelligence, in providing theclaims data analyzed in this section.
We examine whether procedures classified as above median frequency in one dataset are
above median frequency in the other dataset. Table D.22 shows that 88% of the services

Appendix – 7

above median frequency in Medicare are also as above median frequency in the HCCI data.
Similarly, 82% of the services below median frequency in Medicare are also below medianfrequency in the HCCI data.
We next compare classifications of procedures’ frequency deciles in Figure D.7(b). Analogous to Figure D.7(a), this plot visualizes the share of procedures which fall into each of pairof frequency decile bins in HCCI and Medicare data. The two classifications appear to coincide relatively well, with slightly stronger agreement for very frequent procedures comparedto rare procedures in the Medicare public-use data. Overall, the frequency classifications ofprocedures coincide well between Medicare public-use data and HCCI data.

A.4

Residential measurement error

This appendix uses two methods to investigate potential measurement error in patients’
residential locations. The first source of potential error is “snowbird” patients, who havemultiple residences and therefore may appear to travel farther than they actually do. They
may need medical care while spending months in a warmer HRR that is not the one listed
as their main residence (or vice versa). Our results are robust to two methods of removing potential snowbirds: excluding Arizona, California, and Florida, following Finkelstein,
Gentzkow, and Williams (2016), and excluding the 10% of HRRs with the highest share ofsecond homes in American Community Survey data. These results are in Tables D.19 andD.20. The results are little changed by these sample restrictions.
We test for more general location measurement error by examining how far patients
appear to travel for dialysis. Since Medicare patients requiring dialysis must generally visit
a dialysis center thrice weekly, they are unlikely to go substantial distances for this service.
Table D.21 compares travel distances for dialysis with other care. Dialysis patients appear
to travel less than one-quarter as often as other patients—and even less when excluding
snowbird states—suggesting that our residential location assignment is largely accurate.

Appendix – 8

A.5

Scale elasticity estimation with unobserved market segments

Our data only contain procedure-level production and consumption in Traditional Medicare(TM), not for Medicare Advantage (MA) or non-Medicare (NM) patients. We quantify how
this biases our estimate of the scale elasticity, α, based on geographic variation. Suppose
the production function isln δi = α ln Qi + ui ,where Qi = QTM
+ QMA
+ QNM
is the total quantity produced in region i, of which we onlyiiiTM
observe QTM
as a proxy for Qi , ouri . When we estimate the scale elasticity α using Qi

regression coefficient may be biased:
Cov(α ln Qi , ln QTM
Cov(ui , ln QTM
Cov(ln δi , ln QTM
i )
i )
i )
=
+
= αζ,
TM
TM
TM
Var(ln Qi )Var(ln Qi )Var(ln Qi )+ ui .
where ζ, which governs the bias, is the regression coefficient from ln Qi = ζ ln QTM
i


MA
NM
Q
Q
1 + QiTM + QiTM with respect to
To compute ζ we differentiate the identity Qi = QTM
i
i

i

QTM
i , which we observe:d ln Qi
MANM= 1 + sMA
+ sNM
i ϱi
i ϱi ,
TMd ln Qi
QMAd ln iTM
Q
QMA
MA
i
i
≡
≡
where sMA
is
the
MA
share
of
production
inregioni,ϱii
QTM +QMA +QNM
d ln QTMiiiis thei

TM production elasticity of relative production, and sNM
and ϱNM
are similarly defined foriinon-Medicare (NM) insurance. To make it feasible to estimate these elasticities, we assume
that they are constant across regions. If relative quantities produced are uncorrelated with
the Traditional Medicare quantity produced (ϱMA = ϱNM = 0), then ζ = 1 and αζ is anunbiased estimate of the scale elasticity α.54 Otherwise, we need estimates of the average
production shares s̄MA and s̄NM and the regression coefficients ϱMA and ϱNM to compute ζ.
54

A special case would be if the quantity of care produced outside of TM is perfectly correlated withvolume inside TM, so the shares sMAand sNM
are constant.
iiAppendix – 9

We compute the production shares using data on aggregate expenditures and price deflators from prior research. Medicare, including both TM and MA, paid for $153 billion of
the $525 billion spent nationally on physician services in 2017 (Centers for Medicare andMedicaid Services, 2022). Per capita spending and prices are similar between the two partsof Medicare (Berenson et al., 2015). Given this similarity, we apportion Medicare’s production between TM and MA based on relative enrollment and obtain s̄MA = 0.111. Next we
consider Non-Medicare (NM) production. Private insurance spent $226 billion, which we
deflate by a factor of 1.43 to account for the higher prices private insurance pays to makequantities comparable to Medicare (Lopez and Jacobson, 2020). Medicaid spent roughly$41 billion, which we deflate by its relative price of 0.72 (Zuckerman, Skopec, and Aarons,2021). We incorporate other residual categories of production without price adjustments.55
Combining these, we obtain an average s̄NM = 0.676.
To estimate ϱMA and ϱNM , we assume that relative production is proportionate to relative resident beneficiaries. We obtain the number of TM beneficiaries and number of MA
beneficiaries by HRR from Medicare enrollment data and compute the number of NM patients as total population minus Medicare enrollees.56 Regressing the respective beneficiary
ratios on log TM production yields ϱ̂MA = 0.089 and ϱ̂NM = 0.075. Putting these together
means ζ̂ = 1.060, so our estimated αζ = 0.80 from Table 1 implies a scale elasticity of
0.80= 0.75.
α = 1.060

55

These other categories in the National Health Expenditure data are labeled Other Health Insurance
Programs and Other Third Party Payers, along with out-of-pocket spending. Our simplifying approach hereamounts to assuming Medicare prices for these residual categories.
56
Ideally we would like to use the quantity of production in NM and MA markets, but we do not havethis available at the HRR level. Beneficiaries might seem like a problematic proxy because the compositionof NM beneficiaries varies widely across space, with some regions having a high Medicaid share and others ahigh private share. In aggregate, these two markets turn out to have similar per capita quantities of physician
service spending: while private spending is $1,118 per capita and Medicaid spending is $550 per capita, theprice adjustments mentioned above the quantities are relatively similar at $782 and $764, respectively, whenvalued at Medicare prices.

Appendix – 10

B

Theory appendix

B.1

Monopolistic competition with one firm per region

Suppose that there is a single firm in each region that offers fixed-price services to patients
under monopolistic competition with the firms in other regions. Assume K(δi ) = δi andH(Qi ) = Qαi . The profit-maximizing choice of quality δi by the firm in region i ismax πi =δiw i δiR̄ −Ai Qαi
Qi

where Qi =X

Qij = δi

j

X Nj
j

Φj

ρij

∂πi
R̄
w i δi= 0 =⇒== C(Qi , δi ; wi , Ai )∂δi2−α
Ai QαiThis expression replaces the free-entry condition (4) in the definition of equilibrium. Changing the value of the constant on the left side of this equality does not change any of thesubsequent theoretical predictions. In this respect, the monopolistic-competition model with
one firm per region is isomorphic to the perfect-competition model with external economies
of scale.

B.2

Model with multiple types of patients

This section extends the model to feature multiple types of patients who face different trade
costs. There is a finite set of patient types, which are indexed by κ. A patient type isdefined by the trade costs ρij(k) = ρκij ∀k ∈ κ. Qualities δi , including the outside option δ0 ,are the same for all patient types. The demand by patients of type κ residing in location jfor procedures performed by providers in location i is now given byQκij =

δi Njκ κρ .
Φκj ijAppendix – 11

The aggregate gravity equation is the sum of type-specific gravity equations:

Qij =

X

Qκij = δi

X Njκ
κ

κ

Φκj

ρκij .

(B.1)

The free-entry condition (4) remains unchanged with the introduction of multiple patient
types:
Ri =

wi δi
.
Ai QαiIn equilibrium, market clearing requires that

Qi =

B.3

wi δi
Ai Ri

1/α
= δi

X X Njκ
j

Φκj

κ



ρκij =⇒ δi =

Ai Ri
wi

1/(1−α) X X κ
Nj
j

κ

Φκj

!α/(1−α)ρκij.

Derivations of results in Section 2.5

Abusing notation so that I is both the set and number of regions, equations (2) and (3)together constitute 2I equations with 2I unknowns. For the special case of H(Qi ) = Qαi
and K(δi ) = δi , this reduces to the following I equations with the unknowns {δi }Ii=1 :

δi =

RAi
wi

1
 1−α

P
j∈I

α
! 1−α

ρij

X

i′ ∈0∪I δi′ ρi′ j

Nj

Following Costinot et al. (2019), we examine the home-market effect in the neighborhoodiof a symmetric equilibrium. For brevity, assume RA= 1 ∀i. Note that at the symmetricwi

equilibrium:1−αδ̄ α =

1 + δ̄ +1P

i′ ̸=i δ̄ρ

N̄ +

X
j̸=i

1 + δ̄ +ρPi′ ̸=j δ̄ρN̄ =1 + (I − 1)ρ
Φ̄ − 1 N̄
N̄ =. (B.2)Φ̄Φ̄ δ̄

Given α > 0, totally differentiating the above system of equations in terms of {dδi , dNi }Ii=1

Appendix – 12and evaluating it at the symmetric equilibrium yields the following expression:
"
#
"
#
X
X
X dNj
Φ̄2 1 − α 1−2α
dNi Xδ̄ α dδi = − dδi + ρdδi′ + Φ̄+.
−ρ dδj + ρdδi′ +
ρΦ̄
N̄ α
N̄
N̄
′
′
j̸=i
j̸=i
i ̸=i
i ̸=j
Given dN1 > 0 and dNj = 0 ∀j ̸= 1, we obtain the following expression for d ln δ1 :d ln δ1 =Φ̄d ln N1 − (I − 1)(2ρ + ((I − 2)ρ2 ))d ln δj̸=1δ̄.
Φ2 (1−α) 1−2α
2
α
δ̄
+
1
+
(I
−
1)ρ
α
N̄

(B.3)

Further tedious algebra delivers the following expression for quality changes:(1 − ρ)Φ̄d ln δ1 − d ln δj̸=1 = Φ2 (1−α) 1−2αd ln N1 .
2δ̄ α + (1 − ρ) δ̄
α
N̄
2

1−2α

Equation (B.2) implies that ΦN̄ (1−α)δ̄ α =α1−αα Φ(Φ−1)δ̄(B.4)

and therefore−1
1 − α (Φ̄ − 1)Φ̄
(1 − ρ)δ̄d ln N1 > 0.
d ln N1 =d ln δ1 − d ln δj̸=1 = 1−α  Φ(Φ−1)+α (1 − ρ)δ̄Φ̄
+ (1 − ρ)2 δ̄α(1 − ρ)δ̄The last expression above is reported in Section 2.5.
Prior to deriving the weak and strong home-market effects, we obtain an expression for
1−2α2d ln δjδ̄ α > 0. Combining
for j ̸= 1 around the symmetric equilibrium. Define Q̄ ≡ ΦN̄ (1−α)
d ln N1αthe expressions for d ln δ1 from equation (B.3) and for d ln δ1 − d ln δj̸=1 from equation (B.4)
yields the following:d ln δj̸=1Φ̄Q̄ρ + ρ3 (I − 1) − ρ2 (I − 2) − ρ=d ln N1δ̄ (Q̄ + (1 − ρ)2 )(Q̄ + 1 + ρ2 + 2ρ(I − 1) + Iρ2 (I − 2))Appendix – 13

The weak home-market effect is derived as follows:

ln Q1,j̸=1 = α ln Q1 + ln ρ − ln Φj + ln Nj

!
X
′
dQ
dQ
dQ
1
j
i
ρQα−1
+ Qα−1
+ρ
Qα−1
1
j
i′
d ln N1d ln N1dlnN
1i′ ̸=1,j!
X
d ln δ1
1
d ln δ1d ln δjd ln δi′
=
−
ρδ1
+ δj
+ρ
δi′
d ln N1 Φjd ln N1d ln N1d ln N1i′ ̸=1,jN̄ − Q1j d ln δ1N̄ − Q0j − Q1j d ln δj=−d ln N1d ln N1
N̄
N̄



N̄ − Q1jd ln δ1d ln δjQ0j d ln δj=−+d ln N1 d ln N1N̄N̄ d ln N1
h
Φ
1
Q0j
=
(Qjj + (I − 2)Q1j )(1 − ρ) +2
2
Q̄ + 1 + ρ + 2ρ(I − 1) + Iρ2 (I − 2)δ̄ N̄ Q̄ + (1 − ρ)i× Q̄ + (ρ − 1)2 + 2(I − 1)(ρ − ρ2 ) + (I − 1)(I − 2)[ρ2 − ρ3 ]d ln Q1,j̸=1
d ln Q1α=α−d ln N1d ln N1 Φj> 0.

The condition for the strong home-market effect is derived as follows:
Qαj ρ
Qα1 ρ
P
P
N
−
N1
j
1 + Qα1 ρ + Qαj + i̸=1,j Qαi ρ
1 + Qα1 + Qαj ρ + i̸=1,j Qαi ρQ̄αd ln Q1,j̸=1 − d ln Qj̸=1,1 = d ln Nj − d ln N1 + α 1 + (1 − ρ)(d ln Q1 − d ln Qj )
Φ̄


δ̄
= −d ln N1 + 1 + (1 − ρ)(d ln δ1 − d ln δj )Φ̄
1+(I−1)ρ
1 − 1−αα1−ρ d ln N1 .
=
(1+(I−1)ρ)(1−ρ)δ̄1−α+ 1+(1+(I−1)ρ)δ̄α(1−ρ)
Q1,j̸=1 − Qj̸=1,1 =There is a strong home-market effect in the neighborhood of the symmetric equilibrium
if and only if d ln Q1,j̸=1 − d ln Qj̸=1,1 > 0.


1+(I−1)ρ
1 − 1−αα1−ρ(1−ρ)δ̄1−α (1+(I−1)ρ)+ 1+(1+(I−1)ρ)
α
(1−ρ)
δ̄

 d ln N1 > 0 ⇐⇒Appendix – 14

α
1 + (I − 1)ρ
>
1−α
1−ρ

This is true if α is large enough and ρ is small enough.
Our rare-versus-common prediction concerns how the effect of market size on net exports
varies with the number of potential patients N̄ . Given the scale elasticity α and (inverse)
trade costs ρ, the denominator of the right side of equation (6) is increasing in the symmetricequilibrium quality δ̄. For two procedures that both exhibit a strong home-market effectbecause they have the same scale elasticity and trade costs, the effect of population sizeon net exports will be larger for the procedure with lower service quality. The symmetricequilibrium service quality is increasing in the number of potential patients N̄ because there
are increasing returns (see equation (B.2)). Thus, in the neighborhood of the symmetricequilibrium, the strength of a strong home-market effect is decreasing in the number ofpotential patients.

C

Details of counterfactual calculations

Section C.1 describes how we compute counterfactual equilibrium outcomes relative to baseline equilibrium outcomes in the model. Section C.2 describes the assumptions we make toinfer the number of potential patients Nj and hence import shares mij , which are inputs into
these calculations. Section C.3 describes how to compute counterfactual outcomes in themodel when there are multiple (observed) types of patients who differ in their trade costs.
Section C.4 describes how we infer the number of potential patients of each type.

C.1

Computing equilibrium outcomes in counterfactual scenarios

We compute counterfactual equilibrium outcomes relative to baseline equilibrium outcomesby rewriting the equilibrium system of equations in terms of the initial allocation, constantelasticities, relative exogenous parameters, and relative endogenous equilibrium outcomes, atechnique known as “exact hat algebra” in the trade literature.
If K(δ) = δ and H(Q) = Qα , an equilibrium is a set of quantities and qualities {Qi , δi }i∈I
Appendix – 15

that simultaneously satisfy equations (4) and (1) and Qi =P

j Qij . Consider two equilibria:

the baseline equilibrium and the counterfactual equilibrium. Define export shares xij ≡QijQ

and import shares mij ≡ Nijj in the baseline equilibrium. Denote the counterfactualPparameters and equilibrium outcomes by primes. Plugging Qi = j Qij into equation (4),Pj ′ Qij ′we can write the system of equations for each equilibrium as
δi′ = ′ ′  P

δi =



Ri Ai
wi′

Ri Ai
wi

 P

′
j Qij
j Qij

α

Q′ij = δi′ P ′

ρ′ij

′ ′
i ∈0∪I δi′ ρi′ jαQij = δi P

ρij

i′ ∈0∪I δi′ ρi′ j

Nj′

.

Nj

δ′

′

Define ŷ ≡ yy for every variable y. For example, δ̂i ≡ δii .
We now rewrite the counterfactual equilibrium equations in terms of baseline equilibrium shares xij , mij , the scale elasticity α, (relative) counterfactual exogenous parametersÂ, R̂, ŵ, ρ̂, N̂ , and (relative) counterfactual endogenous qualities δ̂.
First, divide the counterfactual free-entry condition by the baseline free-entry condition
to obtain an expression for relative quality:
R̂i Âi
δi′
=
δi
ŵi

!α
P
′
R̂i Âij∈I Qij
P=ŵij∈I Qij

Q′ij
Qij
Pj∈I Qij Qij
j∈I

!α

X

R̂i Âi
=
ŵi

Q′ij
xij
Qij
j∈I

X

!α
(C.1)

Second, divide the counterfactual gravity equation by the baseline gravity equation to obtainan expression for relative bilateral flows:
ρ′ij



Nj′



Q′ij
δ ′  i′ ∈0∪I δi′′ ρ′i′ j 
= i
= P
ρ
Qij
δi P ′ ij δ ′ ρ ′ NjPi ∈0∪I=Pii jδ̂i ρ̂ij N̂jQi′ ji′ ∈0∪I Nj δ̂i′ ρ̂i′ j=

δi′ ρ′ij Nj′
δi ρij Nj
i′ ∈0∪IP

δi′′ ρ′i′ j
δi′ ρi′ jδρδ
i′ ∈0∪I i′ i′ j i′ ρi′ jδ̂i ρ̂ij N̂jP
m0j + i′ ∈I mi′ j δ̂i′ ρ̂i′ j

Plug this expression for relative bilateral flows into equation (C.1) and rearrange terms toAppendix – 16

obtain the following system of I equations with unknowns {δ̂i }Ii=1 :δ̂i = R̂i Âi /ŵi

C.2

1
 1−α

xij ρ̂ij N̂jP
i′ ∈I mi′ j δ̂i′ ρ̂i′ jj∈I m0j +

X

α
! 1−α

.

(C.2)

Inferring the number of potential patients

A baseline calibration of our model requires α, xij , and mij in order to use equation (C.2) tocompute relative counterfactual outcomes. We have estimated α. The export shares xij ≡
Q
P ij
j Qij

are easily computed using the observed trade matrix.57 The challenge is computingQ

import shares mij ≡ Nijj because we do not observe Nj ; while we observe the number ofMedicare beneficiaries in region j, not all beneficiaries are in the market for all services.
This section describes the assumptions we make in order to infer the values of the relevantmarket size Nj ∀j ∈ I. Specifically, we assume per capita demand is uniform, outside-option
quality is constant across regions, and the average outside-option share is 10%, as described
below.
We have estimated θj = Nj /Φj in equation (8). We observe the number of beneficiaries
δ

enrolled in Traditional Medicare in region j, which we denote SjTM . By definition, m0j = Φ0jj .
We assume δ0j = δ0 ∀j and Nj ∝ SjTM . This implies
m0j =

δ0j
δ0 θj
δ0 θj
=
= TM ,
Φj
Nj
sSj

where s is a constant of proportionality. We set δs0 such that the average outside-option
Pshare is 10%, I1 j m0j = 0.1. This requires δs0 = P 0.1×I. With m0j in hand, we can infer
θj /S TMjjNj :m0j = 1 −Xi∈I

mij = 1 −X
1 X
1Qij =⇒ Nj =Qij .
Nj i∈I
1 − m0j i∈I
Q

With Nj in hand, we can compute all import shares, mij = Nijj ∀i ∈ 0 ∪ I, ∀j ∈ I.
57

Dingel and Tintelnot (2021) document overfitting problems when calibrating gravity models using noisy
observed shares. We obtain similar counterfactual outcomes when calibrating our model using gravitypredicted shares.

Appendix – 17

We exclude the Anchorage, Alaska and Honolulu, Hawaii HRRs from our counterfactual
computations. These geographically isolated and expansive HRRs cover the entire statesof Alaska and Hawaii. The average within-Anchorage-HRR procedure incurs more than 53
kilometers of travel. In the gravity regression, these HRRs have the smallest exporter fixed
effects: very few patients travel to Alaska or Hawaii for care. Alaska’s importer fixed effectis quite large because Alaskans import about 19% of their services and the average importtraverses 3,622 kilometers (6% and 5,496 km for Hawaii). As a result, their implied outsideoption shares would exceed one when we set the nationwide average to 10%. We therefore
exclude the Alaska and Hawaii HRRs from the economy when computing counterfactual
outcomes. Given their considerable geographic isolation, Alaska and Hawaii would havelittle influence on outcomes in other regions.
The qualitative and spatial patterns of counterfactual outcomes are the same if we assume
the average outside-option share is 5% or 20% rather than 10%.

C.3

Counterfactual outcomes with multiple patient types

This section describes how to compute counterfactual equilibrium outcomes relative to baseline equilibrium outcomes when there are multiple patient types who face heterogeneous
trade costs. The derivation is very similar to that of Section C.1. Define import sharesNQ

in the baseline equilibrium. Define patient-type shares njκ ≡ Njκj . We rewrite
mijκ ≡ Nijκjκ
the system of baseline and counterfactual gravity equations (B.1) and free-entry condition (4)as follows:
δi′ = ′ ′  P

δi =



Ri Ai
wi′

Ri Ai
wi

 P

′
j Qij
j Qij

α
α

Q′ij = δi′P

Qij = δi

P

κ

P

ρ′ijκ
′
Njκ
′ ′
i′ ∈0∪I δi′ ρi′ jκ

κ

P

ρijκ
Njκ
i′ ∈0∪I δi′ ρi′ jκ.

As above, dividing the counterfactual free-entry condition by the baseline free-entry condition
yields the expression for relative quality in equation (C.1). Second, divide the counterfactual
gravity equation by the baseline gravity equation to obtain an expression for relative bilateral
Appendix – 18

flows: P ρ′

ρ′ijκ
′
ijκ
′
N
N
′
′
′ ρ′
X njκ ρ̂ijκ
′
jκ
κ
jκ
δ
κ
δ 
i′ ∈0∪I i′ i′ jκ δi  P Φjκ = δˆi= i P
=
N̂jκ

ρijκ
ρijκ
mij
P
Qij
δi
Njκ
δi
κ
κ Φjκ Njκκ mijκ Φ̂jκi′ ∈0∪I δi′ ρi′ jκ
P

Q′ij



P

Plugging this expression for relative bilateral flows into equation (C.1) and then rearranging terms yields the following system of I equations with unknowns {δ̂i }Ii=1 :δ̂i = R̂i Âi /ŵi

1
 1−α

X

xij

X njκ
κ

j∈I

C.4

mijκ ρ̂ijκ
N̂jκ
Pmij m0jκ + i′ ∈I mi′ jκ δ̂i′ ρ̂i′ jκα!! 1−α.

(C.3)

Inferring the number of potential patients of each typeBecause we do not observe patients who select the outside option, we make assumptions
that allow us to infer Njκ and thus njκ and mijκ , which are needed to compute counterfactual outcomes using equation (C.3). We start from a type-specific variant of the gravity
equation (7) with fixed effects, as in the single-type equation (8). The estimating equationisln E [Sijκ ] = ln δi + ln

Njκ
Φjκ



+ γ κ Xij = ln δi + ln θjκ + γ κ Xij .

This yields an estimate of θjκ = Njκ /Φjκ .
As in the single-type case above, we assume per capita demand is uniform and outsideoption quality is constant across regions. We observe the number of beneficiaries of type κTMenrolled in Traditional Medicare in region j, which we denote Sjκ
. We assume δ0j = δ0 ∀j
TM
and Njκ = sSjκ, where s is a constant of proportionality that is common across types. Thisimpliesm0jκ =Let K =

δ0
δ0 θjκ
δ0 θjκ
== TM .
Φjκ
Njκ
sSjκ

δ0
κ 1 denote the number of patient types. We set s such that the average outside-P

Appendix – 19

1
option share, across all types, is 10%, IKPjκ m0jκ = 0.1. This impliesTMθjκ /Sjκ.
m0jκ = 0.1 × 1 PTMj ′ κ′ θj ′ κ′ /Sj ′ κ′
IK

Using the resulting Njκ = 1−m1 0jκ

C.5

Pi∈I Qijκ allows us to compute all import shares.

Comparison of geographic scope between United States andGermany

To summarize differences in geography, we compute a distance-weighted sum of populationPin other regions, regional “market potential” MPi ≡ j̸=i ρij Nj , for regions in each country.
The counterfactual trade costs that make the US distribution of market potential match thatof Germany involve scaling the interregional trade costs ρij by a symmetric matrix ρ̂ij withan average value of 3.6 and a variance of 1.7.

Appendix – 20

D

Additional exhibits
Table D.1: Summary statistics on HRRs and trade between HRR pairs
Panel A: HRRs (N =306)

Mean

Production (millions $)Consumption (millions $)Exports (millions $)Imports (millions $)Exports as a share of production (%)
Imports as a share of consumption (%)
Population (millions)
Traditional Medicare beneficiaries (millions)
Log production ($)
d
Log quality ln
δi

751.1
751.1
140.7
140.7
19.3
24.0
1.06
0.13
20.04
-0.67

Panel B: Trade between HRRs (N =93,330)

Mean

Std. Dev

9.4
314
148
4.9

2.7
3,637
1,707
1.2

Log bilateral trade ($)
Bilateral trade: facility fees (thousands $)Bilateral trade: professional fees (thousands $)Trade-weighted log distance (km)Std. Dev

Min.

Max.

796.2 66.4 5,204.2
725.0 83.0 4,607.3
176.6
6.7 1,570.6
99.1 25.6
688.6
10.9
2.0
70.3
10.7
4.6
59.0
1.21 0.13
10.13
0.12 0.02
0.77
0.87 18.01
22.37
0.89 -5.52
2.18

Notes: Panel A of this table reports summary statistics describing the 306 HRRs. The level of log qualitydln
δi is normalized such that the production-weighted mean is zero. Panel B reports summary statistics
describing trade between the 93, 330 = 306 × 305 HRR pairs. Production, consumption, and trade flows
are computed from the Medicare 20% carrier, 100% MedPar, and 100% outpatient Research Identifiable
Files. All dollar statistics for professional fees are multiplied by 5 to represent the full Traditional Medicare
population. HRR definitions are from the Dartmouth Atlas Project.

Appendix – 21

Table D.2: Revealed-preference quality measure δ̂i is correlated with clinical quality(1)
USN sum of inverse rank
USN number of mentions in top lists
JC share of hospitals with accreditation
JC log number of accredited hospitals
LF average safety grade for HRR
Appendix – 22

CMS overall hospital quality
CMS overall hospital quality (weighted by beds)
CMS overall mortality rate across conditions
CDS log length of stay (empirical Bayes)
CDS log 30-day inpatient (Part A) costs (empirical Bayes)
CDS 30-day mortality rate (empirical Bayes)
CDS 30-day readmissions (empirical Bayes)
Constant
Observations
R-squared
Adj R-squared

(2)

(3)

(4)

0.042
(0.113)0.080
0.028(0.016) (0.015)-0.021(0.147)0.595(0.055)0.140(0.053)-0.043(0.102)0.011(0.104)-0.459-0.165(0.061)(0.070)-1.619(0.809)0.245(0.337)-0.213-0.001(0.047)(0.047)4.091(3.998)-0.6544.539-0.832 -0.570(0.047) (0.703) (0.048) (0.964)
305
306
306
305
0.063
0.138
0.288
0.615
0.060
0.136
0.285
0.599

Notes: This table reports regression estimates of our revealed-preference regional quality measure δ̂i against external quality measures. Acronyms
in each row refer to sources of quality measures. USN: U.S. News; JC: Joint Commission; LF: Leapfrog Group; CMS: Centers for Medicare andMedicaid Services; CDS: Chandra, Dalton, and Staiger (2023).

Table D.3: Scale elasticity estimates for CBSAs
All services

Baseline

No Diagonal

Controls

OLS: 2017

0.929(0.012)0.873(0.039)0.912(0.014)[5671]
0.951(0.021)[912]
0.843(0.067)[39.4]

1.201(0.019)1.176(0.052)
1.189(0.019)[5671]
1.100(0.025)[912]
0.660(0.122)[39.4]

0.934(0.015)0.864(0.033)0.913(0.018)[3522]
0.940(0.026)[784]
0.880(0.077)[27.5]

OLS: 2013–2017 difference
2SLS: population (log)

2SLS: population (1940, log)

2SLS: bedrock depth

Notes: This table reports estimates of α from ordinary least squares (OLS) or two-stage least squares (2SLS)dδ i = α ln Qi + ln Ri + ln wi + ui using core-based statistical areas (CBSAs) as theregressions of the form lndδ i is estimated in equation (8), Qi is region i’s total production
geographic units. The dependent variable ln
for Medicare beneficiaries, Ri is Medicare’s Geographic Adjustment Factor, the wi covariate includes mean
two-bedroom property value and mean annual earnings for non-healthcare workers, and ui is an error term.
In the rows labeled “2SLS” we instrument for ln Qi using the specified instruments. In the second column,dδ i in equation (8). In the thirdlabeled “No Diagonal,” Sii observations were omitted when estimating lncolumn, the ln Ri and ln wi controls are included in the regressions (coefficients not reported). Standard
errors (in parentheses) are robust to heteroskedasticity. For 2SLS estimates, first-stage effective F -statistics(Montiel Olea and Pflueger, 2013) are reported in square brackets.

Appendix – 23

Table D.4: Scale elasticity estimates (commuting zones)
All services

Baseline

No Diagonal

Controls

OLS: 2017

0.936(0.016)0.937(0.036)0.909(0.014)[2203]
0.928(0.018)[984]
0.758(0.040)[76.6]

0.959(0.027)1.043(0.105)0.967(0.019)[2895]
0.899(0.024)[1124]
0.804(0.062)[80.6]

0.953(0.016)0.884(0.032)0.934(0.017)[1675]
0.940(0.020)[838]
0.765(0.056)[35.7]

OLS: 2013–2017 difference
2SLS: population (log)

2SLS: population (1940, log)

2SLS: bedrock depth

Notes: This table reports estimates of α from ordinary least squares (OLS) or two-stage least squares (2SLS)dδ i = α ln Qi + ui using commuting zones (CZs) as the geographic units. They are
regressions of the form lndδ i is estimated in equation (8), Qi is region i’s total
analogous to Table 1. The dependent variable ln
production for Medicare beneficiaries, and ui is an error term. In the “no diagonal” column, Sii observationsdδ i in equation (8). The first-difference specification estimates ∆lndδ i =
were omitted when estimating ln
α∆ ln Qi + ∆ui . In the rows labeled “2SLS,” we instrument for ln Qi using the specified instruments. The
standard errors in parentheses are robust to heteroskedasticity. For 2SLS estimates, first-stage effective F statistics (Montiel Olea and Pflueger, 2013) are reported in square brackets. All estimates reveal substantial
scale economies.

Appendix – 24

Table D.5: Higher-income patients are less sensitive to distance: Procedure-level estimates(1)
25min visit(2)
cataract removal(3)knee joint repair(4)heart artery bypass(5)
gallblader removal

Distance (log) × income tercile 3-1.929(0.0800)
0.118(0.0640)0.208(0.0842)-2.202(0.104)0.152(0.0884)
0.202(0.110)-2.228(0.0837)0.214(0.0713)0.293(0.0855)-2.177(0.0866)
0.185(0.0856)0.455(0.0973)-2.022(0.0819)0.249(0.0723)0.367(0.0931)

Observations
Patient market-income FE & Provider market FE

271,422Yes

268,974
Yes

263,772
Yes

245,632
Yes

252,144
Yes

Distance (log)Distance (log) × income tercile 2

Appendix – 25

Notes: This table reports the coefficient on log distance for each income tercile from gravity regressions estimated separately for five procedures varying
in frequency: 25 min office visit (HCPCS 99214), cataract removal (66984), knee joint repair (27447), heart artery bypass (33533), and gallblader
removal (47562). The dependent variable in all regressions is the number of procedures traded. Each regression includes log distance interacted withan income tercile indicator, an indicator for same-HRR observations (i = j), an exporting HRR fixed effect, and an income-tercile-importing-HRR
fixed effect. The coefficients for higher income terciles are positive, indicating that patients residing in higher-income ZIP codes are less sensitive
to distance. Trade flows are computed from the Medicare 20% carrier Research Identifiable Files. HRR definitions are from the Dartmouth Atlas
Project. Standard errors (in parentheses) are two-way clustered by patient market and provider market.

Table D.6: Estimates of a strong home-market effect by CBSA
(1)

(2)

(3)

Cross-sectional PPMLλX Provider-market population (log)λM Patient-market population (log)Distance (log)0.806(0.0261)
0.242(0.0322)-2.372(0.0509)

Distance (log, squared)
Appendix – 26

0.813
(0.0252)
0.237(0.0316)-3.565(0.338)0.114(0.0341)0.753(0.0237)0.287(0.0299)(4)
IV: 1940
population

(5)
(6)
IV:
2013–2017
Bedrock
panel

0.807
(0.0237)
0.257(0.0295)-3.571(0.296)0.115(0.0290)1.273(0.377)-0.115(0.465)-5.121(1.468)0.240(0.114)

Distance (log) × 2017
p-value for H0 : λX ≤ λM
Observations
Fixed effects
Distance elasticity at mean
Distance deciles

0.864(0.178)0.184(0.148)-0.00255(0.00653)<0.001
857,476<0.001
857,476<0.001
857,476-2.46<0.001
857,476

0.046
781,456

-2.46

-2.79

0.010
472,374ij

Yes

Notes: This table reports estimates of equations (10) and (11), which evaluate the presence of weak or strong home-market effects, using CBSAs as
the geographic units. They are analogous to the HRR results reported in Table 2. The dependent variable in all regressions is the value of tradecomputed by assigning each procedure its national average price. The independent variables are patient- and provider-market log population, log
distance between CBSAs, and an indicator for same-CBSA observations (i = j). The positive coefficient on provider-market log population implies aweak home-market effect, and the fact that this coefficient exceeds that on patient-market population implies a strong home-market effect. Column 2
makes the distance coefficient more flexible by adding a control for the square of log distance. Column 3 replaces parametric distance specifications
with fixed effects for each decile of the distance distribution. Column 4 uses the provider-market and patient-market log populations in 1940 as
instruments for the contemporaneous log populations when estimating by generalized method of moments. Column 5 presents estimates using panel
variation from 2013–2017 and includes ij fixed effects. Trade flows are computed from the Medicare 20% carrier, 100% MedPar, and 100% outpatient
Research Identifiable Files. Standard errors (in parentheses) are two-way clustered by patient market and provider market.

Table D.7: Estimates of a strong home-market effect (commuting zones)
(1)

(2)

(3)

Cross-sectional PPMLλX Provider-market population (log)λM Patient-market population (log)Distance (log)0.857(0.0281)0.118(0.0272)-2.458(0.0752)

Distance (log, squared)
Appendix – 27

0.858
(0.0283)
0.116(0.0270)-3.310(0.514)0.0788(0.0468)

0.790(0.0259)
0.212(0.0270)(4)
IV: 1940
population

(5)
(6)
IV:
2013–2017
Bedrock
panel

0.841
(0.0310)0.144(0.0306)-3.257(0.528)0.0751(0.0472)

1.197(0.316)-0.140(0.206)-3.483(0.566)0.0835(0.0472)

Distance (log) × 2017
p-value for H0 : λX ≤ λM
Observations
Fixed effects
Distance elasticity at mean
Distance deciles

1.048(0.166)-0.0618(0.145)-0.0134(0.00664)<0.001
390,625<0.001
390,625<0.001
390,625-2.51<0.001
390,6250.004
390,625

-2.50

-2.64

<0.001
326,118
ij

Yes

Notes: This table reports estimates of equations (10) and (11), which evaluate the presence of weak and strong home-market effects, using commuting
zones (CZs) as the geographic units. They are analogous to the HRR results reported in Table 2. The dependent variable in all regressions is thevalue of trade computed by assigning each procedure its national average price. The independent variables are patient- and provider-market log
population, log distance between CZs, and an indicator for same-CZ observations (i = j). The positive coefficient on provider-market log population
implies a weak home-market effect, and the fact that this coefficient exceeds that on patient-market population implies a strong home-market effect.
Column 2 makes the distance coefficient more flexible by adding a control for the square of log distance. Column 3 replaces parametric distancespecifications with fixed effects for each decile of the distance distribution. Column 4 uses the provider-market and patient-market log populations in1940 as instruments for the contemporaneous log populations when estimating by generalized method of moments. Trade flows are computed from theMedicare 20% carrier, 100% MedPar, and 100% outpatient Research Identifiable Files. CZ definitions are from Fowler and Jensen (2020). Standard
errors (in parentheses) are two-way clustered by patient market and provider market.

Table D.8: Estimates of a strong home-market effect for professional fees
(1)

(2)

(3)

Cross-sectional PPMLλX Provider-market population (log)λM Patient-market population (log)Distance (log)0.618(0.0516)0.360(0.0519)-1.621(0.0495)

Distance (log, squared)
Appendix – 28

0.622
(0.0506)
0.357(0.0507)-0.721(0.274)-0.0903(0.0269)

0.621(0.0383)
0.380(0.0374)(4)
IV: 1940
population(5)
2013–2017
panel

0.566
(0.0673)
0.369(0.0482)-0.737(0.239)-0.0892(0.0234)

0.951(0.161)-0.119(0.173)Distance (log) × 2017
p-value for H0 : λX ≤ λM
Observations
Fixed effects
Distance elasticity at mean
Distance deciles

0.0144(0.00693)
0.005
93,6360.004
93,636<0.001
93,636

-1.60

0.031
93,636<0.001
129,202
ij

-1.60
Yes

Notes: This table reports estimates of equation (10) and (11), which estimates the presence of weak or strong home-market effects. The sample is all
HRR pairs (N = 3062 ), and the dependent variable in all regressions is the value of trade for professional fees. The independent variables are patientand provider-market log population, log distance between HRRs, and an indicator for same-HRR observations (i = j). The positive coefficient on
provider-market log population implies a weak home-market effect, and the fact that this coefficient exceeds that on patient-market population implies
a strong home-market effect. Column 2 makes the distance coefficient more flexible by adding a control for the square of log distance. Column 3
replaces parametric distance specifications with fixed effects for each decile of the distance distribution. Column 4 uses the provider-market andpatient-market log populations in 1940 as instruments for the contemporaneous log populations when estimating by generalized method of moments(GMM). Column 5 estimates equation (10), which uses panel variation in population by controlling for importer-exporter-pair fixed effects. Tradeflows are computed from the Medicare 20% carrier Research Identifiable Files, using the dollar value of physician services, excluding emergency-roomcare and assigning each procedure its national average price. HRR definitions are from the Dartmouth Atlas Project. Standard errors (in parentheses)
are two-way clustered by patient market and provider market.

Table D.9: Healthcare labor costs by occupation
Category
Other Healthcare workers
Physicians

Number of Workers

Average Earnings ($)

Total Spending ($ Millions)

7,642,379
677,431

51,843
294,560

396,200
199,544

Notes: This table reports the number of physicians and other healthcare workers and their average earnings using American Community Survey(ACS) 2015-2019 5-year estimates for public-use microdata areas that we assign to core-based statistical areas. Total spending is the product ofnumber of workers and average earnings. Note that Gottlieb et al. (2023) report higher physician earnings, averaging $350,000, than shown in thistable due to under-reporting and top-coding in the ACS.

Appendix – 29

Table D.10: Contrasting geographies of colonoscopies and LVAD implantation
Colonoscopy LVAD Implant
CodeN
Physiciansβ̂pproductionβ̂pconsumption
Share traded (HRR)
Share traded (CBSA)Median distance traveled (km)Share > 100km

G0121
58,785
13,469
-0.01
-0.01
0.10
0.11
13.83
0.04

33979
333
177
0.87
0.03
0.48
0.48
65.27
0.37

Notes: This table reports statistics for two HCPCS codes: screening colonoscopy (G0121) and LVAD implantation (33979). We report the number oftimes the procedure is performed in 2017 in our 20% sample of Medicare patients and the number of distinct physicians performing it. The population
elasticities of production and consumption are estimated using the Poisson models in equation (13) based on production HRR and patients’ residential
HRR, respectively. We also report the shares of procedures in which the patient and service location are in different HRRs or CBSAs, the median
distance traveled for all care, and the share in which the patient and service location are more than 100 kilometers apart.

Table D.11: The stronger home-market effect for rare procedures is robust to instrumenting for population

Geography:
Instrument:
Procedure Sample:
Provider-market population (log)Patient-market population (log)Appendix – 30

Distance (log)Distance (log, squared)

Observations
Distance elasticity at mean

(1)
HRR
1940 pop
Common(2)
HRR
1940 pop
Rare

(3)
CBSA
1940 pop
Common

(4)
(5)
(6)
CBSA
CBSA
CBSA
1940 pop Bedrock Bedrock
Rare
CommonRare

0.562(0.0674)
0.372(0.0482)-0.746(0.239)-0.0882(0.0234)

1.127(0.0871)
0.00372(0.107)0.845(0.403)-0.244(0.0457)

0.753(0.0215)0.315(0.0273)-4.734(0.257)0.232(0.0251)

0.915(0.0408)
0.288(0.0372)-1.611(0.930)-0.0515(0.0877)

1.242(0.344)0.0831(0.437)-6.157(1.143)0.345(0.0882)1.790(0.551)-0.617(0.602)-5.017(2.608)0.215(0.203)

93,636-1.60

93,636-1.53

857,476-2.44

857,476-2.12

781,456-2.74

781,456-2.89

Notes: This table reports estimates of equation (10), when separating procedures into those above- and below-median frequency and instrumenting
for log population. The dependent variable in all regressions is the value of trade. Trade flows are computed from the Medicare 20% carrier Research
Identifiable Files, using the dollar value of physician services, excluding emergency-room care and assigning each procedure its national average price.
We report coefficients on provider market population, patient market population, log distance, and log distance squared. Every specification also
includes a same-market (i = j) indicator variable. The odd-numbered columns are trade in above-median-frequency procedures; the even-numberedcolumns are trade in below-median-frequency procedures. In columns 1 and 2, the sample is all HRR pairs (N = 3062 ). In columns 3 and 4, thesample is all CBSA pairs (N = 9262 ). In columns 5 and 6, the sample is all CBSA pairs for which the bedrock-depth instrumental variable is available(N = 8442 ). We use 1940 population counts to produce two instrumental variables: 1940 population in the patient market and 1940 population in theprovider market are instruments for log population in the patient market and log population in the provider market, respectively. Similarly, we use
bedrock depth to produce two instrumental variables for CBSAs. Both the strong home-market effect and its larger magnitude for rare procedures arerobust to instrumenting for population, estimating by GMM. Standard errors (in parentheses) are two-way clustered by patient market and provider
market.

Table D.12: The home-market effect is stronger for rare procedures (commuting zones)

Procedure(1)(2)
λX Provider-market population (log)λM Patient-market population (log)0.813(0.0278)
0.219(0.0264)0.783(0.0279)
0.237(0.0266)µX Provider-market population (log) × rareµM Patient-market population (log) × rare
Appendix – 31

p-value for H0 : λX ≤ λM
p-value for H0 : µX ≤ µM

<0.001

Observations
Distance [linear] controls
Distance [quadratic] controls
Patient-provider-market-pair FEs

781,250
Yes<0.001

157,924
Yes

Procedure(3)(4)

Procedure
(5)
(6)

0.782
0.783
(0.0279)(0.0289)
0.238
0.230
(0.0265)(0.0260)
0.221
0.266
0.219
(0.0351) (0.0343) (0.0355)-0.118-0.127-0.114(0.0377) (0.0276) (0.0378)<0.001<0.001<0.001

157,924
Yes

157,924
Yes
Yes

Diagnosis
(7)
(8)

0.252
(0.0356)-0.107(0.0305)

0.782(0.0291)
0.230(0.0262)
0.05650.0682(0.0137) (0.0152)-0.0224 -0.0263(0.0123) (0.0116)<0.001<0.001<0.001<0.001<0.001<0.001

157,924

157,924

156,206

156,206

Yes

Yes
Yes

Yes

Yes
Yes

Notes: This table reports estimates of equation (12), which introduces interactions with an indicator for whether a procedure is “rare” (provided lessoften than the median procedure, when adding up all procedures provided nationally), using commuting zones (CZs) as the geographic units. Theinteractions with patient- and provider-market population reveal whether the home-market effect is larger for rare procedures. The unit of observationis {rare indicator, exporting CZ, importing CZ} so the number of observations is 2 × 6252 in column 1, and the dependent variable in all regressions
is the value of trade. All columns reflect estimates by procedure. Columns 2 onwards drop CZ pairs with zero trade in both procedure groups, andcolumn 2 shows that this restriction has a negligible impact on the estimated log population coefficients. Columns 3 onwards include the rare indicator
interacted with patient- and provider-market populations and distance covariates. Columns 1–4 control for distance using the log of distance between
CZs. Columns 5–6 add a control for the square of log distance. Columns 4 and 6 introduce a fixed effect for each ij pair of patient market andprovider market, so these omit all covariates that are not interacted with the rare indicator. The positive coefficient on provider-market population ×
rare across all columns indicates that the home-market effect is stronger for rare than for common services. The negative coefficient on patient-market
population × rare across all columns indicates that the strong home-market effect has a larger magnitude for rare services. Trade flows are computedfrom the Medicare 20% carrier Research Identifiable Files, using the dollar value of physician services, excluding emergency-room care and assigningeach procedure its national average price. CZ definitions are from Fowler and Jensen (2020). Standard errors (in parentheses) are two-way clusteredby patient market and provider market.

Table D.13: Gravity regression by procedure: individual procedures exhibit a strong home-market effect

Procedure:
HCPCS code:
Provider-market population (log)Patient-market population (log)Distance (log)Appendix – 32

Distance (log, squared)

p-value for H0 : λX ≤ λM
Observations
Distance elasticity at mean
Total count

(1)
(2)
(3)
Colonoscopy Cataract surgery Brain tumor
G0121
66982
61510

(4)
Brain radiosurgery
61798

(5)
LVAD
33979

(6)
Colon removal
44155

0.454
(0.0600)
0.391(0.0609)-0.497(0.339)-0.116(0.0338)

0.349(0.0819)0.521(0.0711)-0.0800(0.479)-0.170(0.0474)

0.932(0.0936)
0.162(0.0767)
1.033(0.513)-0.266(0.0553)

1.107(0.126)
0.191(0.0943)
1.125(0.608)-0.272(0.0628)

1.332(0.158)0.115(0.136)2.042(0.942)-0.352(0.0940)0.871(0.180)-0.0729(0.159)6.620(2.978)-0.850(0.307)0.280
93,636-1.62
58,7850.891
93,636-1.66
43,547<0.001
93,636-1.56
1,922<0.001
93,636-1.54
754<0.001
93,636
-1.50
333

0.001
93,636-1.58
112

Notes: This table reports estimates of equation (10) for procedure-level trade for six selected HCPCS codes, which vary in how common they are. For
all procedures, the sample is all HRR pairs (N = 3062 ). The dependent variable in all regressions is the value of trade in the procedure (computed
using each procedure’s national average price). The independent variables are patient- and provider-market log population, log distance and square oflog distance between HRRs, and an indicator for same-HRR observations (i = j). The positive coefficient on provider-market log population implies aweak home-market effect, and the fact that this coefficient exceeds that on patient-market population implies a strong home-market effect. Trade flows
are computed from the Medicare 20% carrier Research Identifiable Files. HRR definitions are from the Dartmouth Atlas Project. Standard errors (inparentheses) are two-way clustered by patient market and provider market. The bottom row reports the total national count of the procedure in our
sample. Common procedures include screening colonoscopy (column 1) and cataract surgery (column 2). In a screening colonoscopy, the physician
visualizes the large bowel with a camera to look for cancer. In a cataract surgery, the surgeon removes a cloudy lens from the eye to improve vision.
Relatively rare procedures include brain radiosurgery (column 3), brain tumor removal (column 4), left ventricular assist device (LVAD) implantation(column 5) and colon removal (column 6). In brain radiosurgery, an area of the brain is irradiated, often to kill a tumor. In an LVAD implantation, apump is implanted in the chest to assist a failing heart in pumping blood. Brain tumor and colon removals involve surgical removal of the respective
structures. The rare procedures have larger λ̂X − λ̂M differences.

Table D.14: Home-market effect is stronger for rare services controlling for engagement

Provider-market population (log) × common × high engagement
Provider-market population (log) × rare × low engagement
Provider-market population (log) × rare × high engagement
Patient-market population (log) × common × high engagement
Patient-market population (log) × rare × low engagement
Patient-market population (log) × rare × high engagement
Distance (log) × common × high engagement
Distance (log) × rare × low engagement
Distance (log) × rare × high engagement

(1)

(2)

-0.0370(0.0177)
0.272(0.0454)0.514(0.0777)
0.0381(0.0102)-0.172(0.0338)-0.503(0.0808)-0.0655(0.0141)0.0122(0.0339)-0.155(0.0774)-0.0359(0.0175)0.275(0.0359)
0.389(0.142)0.0369(0.00989)-0.145(0.0221)-0.589(0.242)-0.239(0.0792)
1.049(0.200)2.348(2.519)0.0165(0.00712)-0.0953(0.0177)-0.265(0.293)

220,804
Linear
Yes
-0.07
-0.17

220,804
Quadratic
Yes
-0.00
-1.13

Distance (log, squared) × common × high engagement
Distance (log, squared) × rare × low engagement
Distance (log, squared) × rare × high engagement
Observations
Distance controls
Patient-provider-market-pair FEs
Additional distance elasticity at mean for high engagement: common procedures
Additional distance elasticity at mean for high engagement: rare procedures

Notes: This table reports estimates of a variant of equation (12), which adds interactions with indicators
for whether a procedure is “rare” (provided less often than the median procedure) and for whether a procedure is “high engagement” (median number of distinct claims per patient for the procedure in a given year
is above one) or low engagement. The unit of observation is {rare indicator, high-engagement indicator,
exporting HRR, importing HRR}, and the dependent variable is the value of trade. Each column includes
fixed effects for each ij pair of patient market and provider market, rare versus common procedures, andhigh- versus low-engagement procedures, plus indicators for three categories (common × high-engagement,rare × low-engagement, and rare × high-engagement) interacted with patient- and provider-market populations and distance covariates. Covariates for common × low-engagement procedures are omitted, since theywould lead to collinearity with the ij fixed effects. Column 2 adds a control for the square of log distanceand its interactions. The negative coefficient on provider-market population and the positive coefficienton patient-market population for common and high-engagement procedures indicate that the home-market
effect is slightly less strong compared to common and low-engagement procedures, even though these effects
are not all statistically different from zero. The positive coefficient on provider-market population × rare
and the negative coefficient on patient-market population × rare for both high- and low-engagement procedures indicates that the strong home-market effect is stronger for rare services, whether they are highor low-engagement. The distance elasticity is more negative for high-engagement procedures (both rare
and common). Trade flows are computed from the Medicare 20% carrier Research Identifiable Files. HRR
definitions are from the Dartmouth Atlas Project. Standard errors (in parentheses) are two-way clusteredby patient market and provider market.
Appendix – 33

Table D.15: Home-market effect is stronger for procedures requiring more resources

λX Provider-market population (log)λM Patient-market population (log)

(1)

(2)

(3)

0.623
(0.0512)0.366(0.0512)0.609(0.0487)
0.370(0.0484)

0.596(0.0490)0.391(0.0482)
0.00378(0.0116)-0.0452(0.0100)
0.0848(0.0186)-0.106(0.0172)µX2 Provider-market population (log) × intensity tercile 2µM 2 Patient-market population (log) × intensity tercile 2
Appendix – 34

µX3 Provider-market population (log) × intensity tercile 3µM 3 Patient-market population (log) × intensity tercile 3
p-value for H0 : λX ≤ λM
p-value for H0 : µX2 ≤ µM 2
p-value for H0 : µX3 ≤ µM 3

0.005

Observations
Distance controls
Distance [quadratic] controls
Patient-provider-market-pair FEs

280,908
Yes

0.006

164,670
Yes

(4)

(5)

(6)

0.00325(0.0107)-0.0454(0.0100)
0.0824(0.0160)-0.106(0.0172)

0.598(0.0483)
0.390(0.0476)
0.00613(0.0131)-0.0463(0.0114)0.0929(0.0216)-0.111(0.0188)0.00133(0.0110)-0.0425(0.0101)
0.0777(0.0161)-0.0986(0.0168)

0.015
0.004
<0.001

0.003<0.001

0.013
0.008<0.0010.007<0.001

164,670
Yes

164,670
Yes

164,670

164,670

Yes

Yes
Yes

Yes

Notes: This table reports estimates of a variant of equation (12) using terciles of the intensity of resources needed to produce the procedure rather
than frequency. Procedure intensity is total relative value units (RVUs) in the October 2017 posting of the Medicare physician fee schedule. The unitof observation is {tercile intensity, exporting HRR, importing HRR}, and the dependent variable is the value of trade. Columns 2 onwards drop HRR
pairs with zero trade, and column 2 shows that this restriction has a negligible impact on the estimated log population coefficients. Columns 1–4
control for distance using the log of distance between HRRs. Columns 5 and 6 add a control for the square of log distance. Columns 4 and 6 introduce
a fixed effect for each ij pair of patient market and provider market, so these omit the patient- and provider-market population covariates. Coefficientson provider-market population are statistically significantly larger than coefficients on patient-market population, indicating a strong home-market
effect for all procedures and for procedures in the first tercile of intensity for columns 3 and 5. The positive coefficients on provider-market populationand negative coefficients on patient-market population for intensity terciles 2 and 3 across all columns indicates that the strong home-market effectis stronger for procedures requiring more resources. Trade flows are computed from the Medicare 20% carrier Research Identifiable Files, using thedollar value of physician services, excluding emergency-room care and assigning each procedure its national average price. Procedures associated witha zero total RVU are excluded, excluding 23.4% of spending. HRR definitions are from the Dartmouth Atlas Project. Standard errors (in parentheses)
are two-way clustered by patient market and provider market.

Table D.16: Scale elasticity estimates: all versus rare services
All services

Baseline

No Diagonal

Controls

OLS: 2017

0.751(0.028)0.989(0.086)0.723(0.031)[2073]
0.449(0.072)[90.3]

0.777(0.047)1.030(0.086)0.801(0.053)[2073]
0.671(0.103)[90.3]

0.763(0.040)0.983(0.093)0.727(0.037)[1634]
0.467(0.067)[131]

Rare services

Baseline

No Diagonal

Controls

OLS: 2017

0.972(0.035)1.326(0.264)0.941(0.041)[1581]
0.857(0.065)
[129]

1.119
(0.048)0.859(0.542)1.074(0.053)[1575]
1.078(0.089)
[128]

0.938
(0.041)1.348(0.278)0.897(0.053)[1143]
0.797(0.072)[164]

OLS: 2013–2017 difference
2SLS: population (log)

2SLS: population (1940, log)

OLS: 2013–2017 difference
2SLS: population (log)

2SLS: population (1940, log)

Notes: This table reports estimates of α̂ from ordinary least squares (OLS) or two-stage least squares (2SLS)dδ i = α ln Qi + ln Ri + ln wi + ui , where lndδ i is estimated in equation (8) using
regressions of the form ln
professional fees, Qi is region i’s total production of non-emergency-room physician services for Medicare
beneficiaries, Ri is Medicare’s Geographic Adjustment Factor, the wi covariate includes mean two-bedroom
property value and mean annual earnings for non-healthcare workers, and ui is an error term. In the rows
labeled “2SLS” we instrument for ln Qi using the specified instruments. In the columns labeled “no diag”,dδ i in equation (8). In the third column, the ln Ri and
Qii observations were omitted when estimating ln
ln wi controls are included in the regressions (coefficients not reported). Standard errors (in parenthesis)
are robust to heteroskedasticity. For 2SLS estimates, first-stage effective F -statistics (Montiel Olea andPflueger, 2013) are reported in square brackets. The lower panel reports results for professional fees for rare
procedures. In all specifications, we estimate substantial scale economies. The estimated scale elasticity islarger for rarer services.

Appendix – 35

Table D.17: Specialization earnings and frequency

Dependent variable:
Number of physicians in specialization (log, national)

(1)
(2)
(3)
Per capita population elasticity-0.0716(0.0139)

Mean earnings (log)

Observations
R-squared

209
0.199

-0.245(0.0697)-0.0677(0.0137)-0.174(0.0543)

209
0.050

209
0.223

Appendix – 36

Notes: This table reports estimates of a regression of per capita population elasticity of physician count on the national count of physicians andmean earnings. Each observation is an NPPES taxonomy code. Earnings (wage and business income) data from Gottlieb et al. (2023) are reported
by Medicare specialty groups. We use a crosswalk to map Medicare specialty groups to NPPES taxonomy codes. The estimation sample excludes 11
taxonomy codes that are not mapped to any Medicare specialty. Standard errors (in parentheses) are robust to heteroskedasticity.

Table D.18: Regression of Φ̂jκ on tercile dummies and trade shares

Counterfactual scenario:

Boston Reimbursement Increase
(1)

(2)

(3)

0.0101(0.0173)
0.103(0.0469)

0.0133(0.0175)
0.0979(0.0477)

Constant

0.0856(0.119)0.0860(0.0193)-0.00859(0.00351)-0.0140(0.00470)42.10(0.823)-0.128(0.00633)

Observations
R-squared
HRR fixed effects

874
0.000
No

874
0.971
Yes

874
1.000
Yes

Income tercile = 2
Income tercile = 3
Appendix – 37

mBoston,jκNotes: This table uses linear regressions to summarize how market access changes across HRRs j and income terciles κ in response to a counterfactual
policy: a 30% reimbursement increase in Boston. The dependent variable in all columns is the percentage change in market access, 100 × (Φ̂jκ − 1).
Standard errors (in parentheses) are clustered by market. The constant in the first regression reports the percentage change for the lowest income
terciles, and the coefficients on the other terciles are the additional percentage point gain for those terciles relative to the lowest. When we control
for Boston’s market share mBoston,jκ . the tercile-difference coefficients are much smaller, indicating that differences in baseline trade patterns drive
the distributional impacts.

Table D.19: Estimates of a strong home-market effect excluding AZ, FL, CA

Estimation method:
Provider-market population (log)Patient-market population (log)Distance (log)Appendix – 38

(1)
PPML

(2)
PPML

(3)
PPML

(4)
IV

0.706
(0.0749)0.238(0.0729)-1.715(0.0587)

0.702(0.0652)0.249(0.0624)2.046(0.438)-0.390(0.0445)0.692(0.0431)0.284(0.0389)

0.752(0.0620)0.291(0.0453)
2.094(0.372)-0.394(0.0374)

0.001
67,600<0.001
67,600-1.61<0.001
67,600<0.001
67,600-1.60

Distance (log, squared)

p-value for H0 : λX ≤ λM
Observations
Distance elasticity at mean
Distance deciles

Yes

Notes: This table reports estimates of equation (10), which estimates the presence of weak or strong home-market effects, excluding snowbird states.
The sample is all HRR pairs, excluding those in Arizona, Florida, or California. The dependent variable in all regressions is the value of tradecomputed by assigning each procedure its national average price. The independent variables are patient- and provider-market log population, log
distance between HRRs, and an indicator for same-HRR observations (i = j). The positive coefficient on provider-market log population implies aweak home-market effect, and the fact that this coefficient exceeds that on patient-market population implies a strong home-market effect. Column 2
makes the distance coefficient more flexible by adding a control for the square of log distance. Column 3 replaces parametric distance specifications with
fixed effects for each decile of the distance distribution. Column 4 uses the provider-market and patient-market log populations in 1940 as instruments
for the contemporaneous log populations when estimating by generalized method of moments. Trade flows are computed from the Medicare 20%
carrier, 100% MedPar, and 100% outpatient Research Identifiable Files. HRR definitions are from the Dartmouth Atlas Project. Standard errors (inparentheses) are two-way clustered by patient market and provider market.

Table D.20: Estimates of a strong home-market effect excluding HRRs with high second-home share

Estimation method:
Provider-market population (log)Patient-market population (log)Appendix – 39

Distance (log)

(1)
PPML

(2)
PPML

(3)
PPML

(4)
IV

0.683
(0.0593)0.257(0.0598)-1.639(0.0503)

0.696(0.0555)
0.247(0.0551)
0.643(0.316)-0.233(0.0315)0.684(0.0386)
0.281(0.0365)0.789(0.0567)0.305(0.0513)0.683(0.272)-0.236(0.0269)<0.001
76,176<0.001
76,176-1.57<0.001
76,176<0.001
76,176-1.55

Distance (log, squared)

p-value for H0 : λX ≤ λM
Observations
Distance elasticity at mean
Distance deciles

Yes

Notes: This table reports estimates of equation (10), which estimates the presence of weak or strong home-market effects, excluding HRRs witha high second-home share. The sample is all HRR pairs excluding those in the top 10% based on the share of housing units that are vacant forseasonal/recreational purposes in the 2013–2017 American Community Survey. See Table D.19 notes on the variables, instruments, geographic units,
and standard errors.

Table D.21: Travel for dialysis
Distance (km)[0, 50)[50, 100)[100, .)

Share of output
All (Professional)

All (Facility)

All (Dialysis)

No snowbird states (Dialysis)

Snowbird states (Dialysis)

0.85
0.08
0.07

0.77
0.12
0.11

0.94
0.03
0.03

0.94
0.03
0.02

0.93
0.03
0.04

Appendix – 40

Notes: For the care described in each column and the distance intervals in each row, the entries in this table report the share of patients traveling that
distance from their residential ZIP code to the service location’s ZIP code. The first column shows professional claims (from Medicare’s “carrier” file),
the second column shows facility (hospital) claims, and the third column shows dialysis claims. The remaining columns split dialysis claims between“snowbird” states (AZ, CA, and FL, following Finkelstein, Gentzkow, and Williams 2016) and other states. In non-snowbird states, the table showsthat 94% of patients travel less than 50 km from their home for dialysis, and only 2% more than 100 km. This is less than one-fifth as much as forother facility or professional care, suggesting that residential location is recorded correctly for almost all patients.

Table D.22: Classification of rare and common procedures in Medicare vs. private insurance data
Above median HCCI
Above median CMS

0

1

total

0
1

82
12

18
88

100
100

Notes: This table compares the percentage of procedures classified as rare (above median frequency equals one) or common (above median frequency
equals zero) in the public Medicare data versus the private insurance data from the Health Care Cost Institute (HCCI). Classifying procedures as
rare versus common is consistent when using Medicare or privately insured data.

Figure D.1: Variation in trade shares across procedures and regions(b) Distributions of import shares for common and rare services
25(a) Distribution of import share by procedure

20

5Percent
10
15

3

5

2

1
0

Appendix – 41

Kernel density

4

0

0
0

.2

.4

.6

.8

Imports to consumption ratio
Sample: Procedures performed at least 20 times in 20% sample.

1

.2

.4

.6

.8

1

Imported share of HRR consumption
Above−median frequency

Below−median frequency

Notes: Panel (a) shows the distribution of the imported consumption share across procedures for procedures performed at least 20 times (in our 20%
sample of Medicare claims). Imports are defined as care provided to a patient who lives in one HRR at a service location in a different HRR. Panel (b)splits all services into two groups based on how often they are performed nationally. Those performed less often than the median are shown in red,and those performed more often than the median service are shown in blue. Import shares are substantially higher for the rare services.

Figure D.2: Production and consumption of medical care across regions (professional fees)

Production

Dollars per resident
Medicare beneficiary

3,000
2,500

Consumption

2,000
1,500
1,000

Imports

Exports

500
0
150k

300k

600k

1.2m

2.4m

4.8m

10m

Population
Population elasticity (log−log regression slope) of transactions per
resident Medicare beneficiary:
Production: 0.10 (0.02), Consumption: 0.06 (0.01)
Exports: −0.03 (0.04), Imports: −0.25 (0.03)

Notes: This figure shows production, consumption, and trade per capita of Medicare services across hospitalreferral regions (HRRs) of different sizes, all smoothed via local averages. We use the Medicare 20% carrier
Research Identifiable Files to compute the dollar value of services, excluding emergency-room care, at national
average prices. The blue series shows production of medical care per Medicare beneficiary residing in the
HRR of production. The red series shows consumption of medical care per Medicare beneficiary residingin the HRR of consumption. The dashed gray series shows interregional “exports” of medical care and thedashed black series shows interregional “imports” of medical care, again per Medicare beneficiary. HRR
definitions are from the Dartmouth Atlas Project.

Appendix – 42

Figure D.3: Revealed-preference vs. external quality measures: common and rare(a) U.S. News vs. quality estimated for common services(b) U.S. News vs. quality estimated for rare services
5

Exporter FE (rare procedures)

Exporter FE (common procedures)

4

CA−Los Angeles

2
CA−San Diego
PA−Philadelphia
NY−East Long Island

0

TX−Houston
MA−Boston
OH−Cleveland

NY−New YorkIL−Chicago−2

CA−Los Angeles
CA−San Diego
TX−Houston
OH−Cleveland
MA−Boston
PA−Philadelphia

0NY−East Long Island

NY−New YorkIL−Chicago

−5

−4
20
40
USN No. of Features in Top Lists

060(c) Leapfrog Safety Grade vs. quality for common services

20
40
USN No. of Features in Top Lists

60(d) Leapfrog Safety Grade vs. quality for rare services

2

MN−Rochester
FL−Sarasota

NY−New York0
CA−Salinas
VA−Newport NewsCA−San Luis Obispo

WV−Huntington

NY−Elmira
NY−Bronx−2

MN−Duluth
IA−Mason City

ID−Boise
OR−BendKY−Owensboro
IL−Aurora

WY−Casper

Exporter FE (rare procedures)

2
Exporter FE (common procedures)

Appendix – 43

0

MN−Rochester

NY−New York0
CA−Salinas
FL−Sarasota
ID−Boise

WV−Huntington
NY−Bronx
MN−Duluth−2

VA−Newport NewsOR−BendKY−Owensboro
CA−San Luis Obispo

NY−Elmira
IL−Aurora

IA−Mason City

−4
WY−Casper

−4
−6
2

3
4
Average Leapfrog Safety Grade for HRR

5

2

3
4
Average Leapfrog Safety Grade for HRR

5

Notes: This figure shows the relationships between the exporter fixed effects (our revealed-preference measure of quality), estimated separately forcommon and rare services, and external quality measures. The vertical axis shows the exporter fixed effects for each HRR estimated using tradein common services in Panels (a) and (c), and using trade in rare services in Panels (b) and (d). The horizontal axis in Panels (a) and (b) is acount of the number of times each region’s hospitals appear on the U.S. News list of best hospitals. U.S. News produces an overall ranking as wellas rankings for 12 particular specialties. We count the number of times each HRR’s hospitals appear on any of these 13 lists. Both panels show apositive relationship, indicating that patients travel farther to obtain care from regions highly ranked by U.S. News. The relationship is stronger for
rare services, as the slope is nearly double that for common services. The horizontal axis in Panel (c) and (d) is the average safety grade for hospitals
in an HRR, determined by the Leapfrog Group. The Leapfrog Safety Grades range from A to F, which we scale as integers from 1 (for F) to 5 (forA). We then compute the mean score for all hospitals in the HRR. The Safety Grades are positively associated with the exporter fixed effects for bothrare and common procedures.

Figure D.4: Population elasticities of input costs(b) Physicians’ earnings (CBSAs)
14
13
12
10

11

Log physicians’ earnings

12.6
12.5
12.4
12.3
12.2

Log physicians’ earnings

12.7(a) Physicians’ earnings (commuting zones)

12

14

16

10

12

Log CZ population
Y = 12.57942 − 0.0098 [0.0082] Log CZ population + ε
N = 111; R = 0.0127

16

18

16

18

Y = 12.56702 − 0.0014 [0.0082] Log CBSA population + ε
N = 923; R = 0.0000(d) Median house value

12
11
10

10.4

10.6

10.8

11

Log property value

11.2

13

11.4

(c) Other healthcare workers’ earnings

Log other HC workers’ earnings

14

Log CBSA population

10

12

14

16

18

10

Log CBSA population
Y = 10.35232 + 0.0429 [0.0032] Log CBSA population + ε
N = 926; R = 0.1628

12

14

Log CBSA population
Y = 10.44312 + 0.0616 [0.0110] Log CBSA population + ε
N = 926; R = 0.0331

Notes: This figure depicts relationships between input costs and population sizes. Panel (a) shows physicians’
earnings across 111 commuting zones using data from Gottlieb et al. (2023). Panels (b), (c), and (d) show
variation across CBSAs in physicians’ earnings, other healthcare workers’ earnings, and median house values(a proxy for real estate and other locally priced inputs) using data from the 2015–2019 American Community
Survey.

Appendix – 44

Figure D.5: The home-market effect is stronger for rare procedures

Appendix – 45

Market−size elasticity

1.5

1

.5

0

−.5
0

2

4

6

8

10

Procedure frequency decile
Provider population

Patient population

Notes: This figure groups non-emergency physician-provided services in the Medicare claims data into deciles based on the national frequency of eachprocedure. For each decile, we estimate equation (10) and plot the estimated coefficients on provider- and patient-market log population with their
95% confidence intervals. The blue circles show estimated provider-market population elasticities; the red squares show patient-market population
elasticities. The coefficients on provider-market size always exceed the respective coefficients on patient-market size, indicating a strong home-market
effect. The coefficients on provider-market size monotonically decrease across the deciles. The coefficients on patient-market size monotonicallyincrease across the deciles. Together, these two patterns show that the home-market effect is stronger the less common the procedure.

Figure D.6: Spillovers from higher reimbursements in one region depend on that region’s net imports(a) Correlation of δ̂i and Φ̂i across non-treated regions(b) Change in non-treated regions’ aggregate market access

1.05
MN− ROCHESTER

Nj−weighted change in Φ
for non−treated regions (%)

Appendix – 46

Correlation of δi and Φi changes
across non−treated regions

KY− PADUCAH

.5

0

−.5

MN− ROCHESTER

MA− BOSTON

MA− BOSTON0KY− PADUCAH

−.05

−1

−1.5
−150

−100

−50

Net imports (%, over Nj)

0

50

−1

−.5

0

.5

Net imports (%, over Nj)
Regression line: y = −0.0324 (0.0018) * x + −0.0042 (0.0004)

Notes: This figure characterizes counterfactual outcomes when raising reimbursements by 30 percent in one HRR. We conduct this exercise for eachregion, one at a time, and each observation in each panel represents one such counterfactual scenario. Panel (a) illustrates the contrast in spillovers
as a function of net imports of the treated region. The vertical-axis value for each observation reports the correlation—across all regions other than
the treated one for the exercise in question—between the counterfactual changes δ̂i and Φ̂i . The scatterplot relates these correlations to the treatedregion’s net import share, which is plotted on the horizontal axis. When the treated region is a net exporter, changes in quality δi and in market
access Φi for non-treated regions move in opposite directions: a region whose output quality declines experiences an increase in market access throughimports from the treated region. However, increasing reimbursements in a net-importing region often has the opposite effect: neighboring regionswith quality reductions also experience lower market access, (changes in δi and Φi are positively correlated). For each counterfactual, the vertical-axis
value in Panel (b) shows the aggregate impact on patient market access excluding the treated region. The panel relates this impact to the treatedregion’s net imports, shown on the horizontal axis. When the treated region is a net importer, the aggregate impact on market access for non-treatedregions tends to be smaller or even negative.

Figure D.7: Procedure frequencies are similar across data sources(b) Medicare versus private insurance data

Share ofProcedures
1

0.08

2

0.07

3

0.06

4

0.05

5
6

0.04

7

0.03

8

0.02

9

0.01

10
1 2 3 4 5 6 7 8 9 10
Procedure Frequency Quantile Bin - Public

0.00

The simple correlation between quantile bins is 0.9068

Share ofProcedures
Procedure Frequency Quantile Bin - HCCI

Procedure Frequency Quantile Bin - Confidential(a) Confidential versus public Medicare data

1
2

0.06

3

0.05

4

0.04

5
6

0.03

7

0.02

8
9

0.01

10
1 2 3 4 5 6 7 8 9 10
Procedure Frequency Quantile Bin - Medicare

0.00

The simple correlation between quantile bins is 0.8287

Notes: The first panel shows the share of procedures in each frequency decile in the Medicare public datacompared to the Medicare confidential data. The classification of procedures by frequency deciles appears
largely consistent between the two data sources for Medicare patients. The second panel shows the shareof procedures in each frequency decile in the Medicare versus data on privately insured patients from the
Health Care Cost Institute (HCCI). The classification of procedures by frequency deciles appears largely
consistent when comparing public Medicare data with the privately insured.

Appendix – 47

Figure D.8: Counterfactual health-income gradients if US geography were like Germany
Annual mortality rate per 100,000 inhabitants(a) Mortality-income gradient for the United States and Germany

GER
USA
2000
mortality = 1400 − 0.012 incomemortality = 1700 − 0.019 income

1500

1000

500
$20,000$40,000$60,000
Per capita net disposable income in USD (2017 PPP)(b) Change in US market access gradient for counterfactual with German
trade costs

Market access (log scale)

10,000Baseline
Counterfactual

1,000

100

market access = −11 + 1.7 income
market access = −6.5 + 1.3 income$16,000$22,500$32,000$45,250$64,000
Per capita net disposable income (log scale)Notes: Panel (a) shows the mortality-income gradients across regions in the United States and in Germany.
For the United States, we use county-level data on mortality by age and income (obtained from the Institutefor Health Metrics and Evaluation at the University of Washington). For Germany, we use NUTS3 (“Kreise”)level data on mortality by age (from EuroStat) and income (from the German Federal Statistical Office). We
compute average mortality from age-bracket-specific mortality rates using the 2011–2030 European Standard
Population as the reference distribution. We see a steeper gradient in the United States. Panel (b) considers
to what extend this can be explained by the geography of the United States, in particular the remoteness ofmany regions to big markets. To do this, we conduct a counterfactual analysis, described in Section 5.2 andAppendix C.5. We use our model and estimates to simulate the market access (Φi ) that would emerge if
US geography looked more like Germany, and relate it to areas’ incomes. Panel (b) shows that transformation
reduces the Φi -income elasticity by 21%.

Appendix – 48