Analysis of Hospital Production: An Output Index Approach Martin Gaynor Carnegie Mellon, NBER, CMPO Samuel A. Kleiner Carnegie Mellon William B. Vogt Rand.

Analysis of Hospital Production:An Output Index Approach

Martin GaynorCarnegie Mellon, NBER, CMPO

Samuel A. KleinerCarnegie Mellon

William B. VogtRand and NBER

Conference on Public OrganisationCentre for Market and Public Organisation

University of BristolJune 11-12, 2008

22

Hospital Costs and Policy

• Price regulation– PbR (UK), Medicare, Medicaid (US),…– Want price to reflect marginal costs

• Antitrust– Merging parties normally claim efficiencies defense– That is, economies of scale (possibly scope)– Failing firm defense

• Planning– Want to know scale, scope

• Specialty hospitals– Are scope economies/diseconomies important?– Are scale economies/diseconomies important?

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Hospital Costs and Economics• There are many outputs

– Over 500 DRGs– Thousands of ICD codes

• There is significant individual heterogeneity within outputs– Age, sex, race– Comorbidities, etc

• Hospital have these characteristics in common with other service industries– Outputs difficult to pin down– “Mass-customization”– E.g., education, legal services, haircuts, …– Even “traditional” industries: electric power generation, steel

manufacturing, shoes, brewing,...

4

Output Aggregation

• Too many outputs to estimate econometric cost function with individual outputs– Curse of dimensionality

• Need to aggregate• Economic Theory of Output Index

– Ratios of marginal costs of aggregated outputs are independent of input prices (Hall, 1973)

– Implies that outputs within an aggregation category should be similar with regard to input requirements

55

Previous Hospital Cost Studies • Most hospital studies are conducted using older data (1970s, 80s) • Technology has changed since previous studies• No firm conclusions as to the extent of scale economies and very

limited evidence of scope economies– Scale Economies

• Cowing and Holtman (1983), Vita (1990), Gaynor and Anderson (1995), Carey (1997), Dranove (1998), Hughes and McGuire (2003), Preyra and Pink (2006)

– No Scale Economies• Grannemann et. al. (1986), Keeler and Ying (1996), Conrad and Strauss (1983),

Fournier and Mitchell (1992)

• Output typically defined as discharges or patient days, casemix variable added to function– Ad hoc– Clearly not consistent with requirements for aggregation– Preyra and Pink aggregate inpatient care into primary/secondary, tertiary

6

A Scale Economies Problem

• Outputs captured in a crude way in previous work

• It seems clear that more complex cases typically go to bigger hospitals

• These two facts would seem to argue that scale economies are understated using conventional methods– Big hospitals look more expensive than they are

due to more complex case mix

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Research Objectives

• Develop method for estimating hospital costs which:– takes account of hundreds of outputs– takes account of individual patient heterogeneity– attempts to aggregate in a way that’s consistent with

economic theory

• Use these methods to estimate hospital cost function with CA data

• Use these methods to evaluate scale and scope economies & compare to more typical methods

88

Our Method vs. Previous

• Previous literature uses crude output categories and adds an ad hoc casemix adjustment to take account of heterogeneity

WCasemixOutpatInpatC lnlnlnln 3210

• We construct output indexes which build in output diversity and individual heterogeneity from the start

• We estimate a long run cost function

9

Setup

• Create 76 different hospital outputs– 25 MDC codes

– Each with 3 levels of care (primary, secondary, tertiary)

– Plus outpatient care

• Each individual patient consumes his own individualized quantity of one of these 76 outputs

• Outputs are aggregated upwards via output index

10

Setup, 2

• Normal translog cost function with four aggregate outputs at the top level, primary, secondary, tertiary, outpatient

• Economies of scale, scope for these aggregate outputs estimated in the normal way, roughly• Each top level output is an index of lower level outputs --- corresponding to the 25 MDCs• ρ is a measure of scope economies within top-level outputs

– ρ > 1: economies -- C(Y(Q1,Q2)) < C(Y(Q1, 0))

– ρ < 1: diseconomies -- C(Y(Q1,Q2)) > C(Y(Q1, 0))

10

)),,...,(),,...,(),,...,(( 111 OQQYQQYQQYCCost NT

NS

NP

kkkjkNjk

kj QQY /1

1 )...(

11

Setup, 3

• Each individual consumes a certain quantity of one of the outputs (primary, secondary, tertiary)

• That quantity depends on his characteristics, qik= exp( Xik βk), k = P,S,T

– Individual characteristics include DRG, age, sex, race, number of secondary procedures, number of secondary diagnoses, unscheduled admission

• Accounts for individualized nature of hospital production

12

Setup, 4

• Then, each hospital’s level of each output is calculated by summing over the patients seeking care there:

Iij is an indicator for patient i seeking care at hospital j

In is an indicator for patient i’s diagnosis is in specialty niniji

ikjkn IIqQ

13

Aggregate Output Classes

• Classify inpatient output into four categories based upon input intensiveness– Primary Care: Inpatient illnesses which are least complex to treat– Secondary Care: Complex problems, specialist providers – Tertiary Care: Highly specialized providers, sophisticated equipment– Outpatient Care: Used hospital but not admitted as a registered bed

patient• This classification is based on DRG• Rank DRGS based on: % of hospitals performing DRG, % of

patients traveling for this DRG, % of procedures performed in teaching hospital, DRG weight– Top ranked 10% of discharges: tertiary– Next 40%: secondary– Lowest 50%: primary

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Examples of Tertiary Care

• Nervous System– DRG 3: Craniotomy (brain surgery)– DRG 9: Spinal disorders & injuries

• Circulatory System– DRG 103: Heart transplant– DRG 107: Coronary bypass with cardiac catheter

• Newborn– DRG 386: Extreme immaturity or respiratory distress

syndrome– DRG 387: Prematurity with major problems

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15

Examples of Secondary Care

• Nervous System– DRG 20: Nervous system infection

– DRG 10: Nervous system tumors with complications

• Circulatory System– DRG 130: Peripheral vascular disorders with complications

– DRG 118: Pacemaker replacement

• Newborn– DRG 389: Full-term neonate with major problems

– DRG 388: Premature delivery

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16

Examples of Primary Care

• Nervous System– DRG 23: Nontraumatic stupor & coma

– DRG 524: Transient ischemia (A neurological event with the signs and symptoms of a stroke, but which go away within a short period of time)

• Circulatory System– DRG 131: Peripheral vascular disorders without complications

– DRG 134: Hypertension

• Newborn– DRG 391: Normal newborn

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1717

Estimating q• Motivation: To adjust for patient characteristics which relate to

treatment intensity

• Assume that hospital charges (Hijkn) can be expressed as:

ikn

k

k

jjkijkn q

Q

Y

Y

CH

kjjk eoutput typ, hospitalfor cost marginalover Markup""

k

j

Y

C

n

k

Q

Y

ikqik person by consumed typeoutput ofQuantity

What we observe

Change in cost for output type k at hospital j

Change in output type k for additional unit of specialty n

1818

Output Index• Taking logs and imposing qik= exp( Xik βk), we estimate the equation:

where

α jkn is a hospital-output type-specialty (MDC) specific fixed effect (321×3×25=24,075)

X ik is a vector of observable consumer characteristics (# procedures, # diagnoses, age, etc.)

βk is a vector of coefficients for these characteristics

• Log quantity for individual i based on their observable characteristics:

• Quantity for each hospital for output type k, specialty n is , and the quantity of inpatient output type k at hospital j is

kikik Xq ̂)ln(

ji

ikjknn

qQ

kkkjkNjk

kj QQY /1

1 )...(

iknkikjknijkn XH )ln(

1919

Translog Cost Function

0,11111

M

jij

M

kjk

M

jjk

M

jj

•Second order approximation in logs to an arbitrary functional form with M inputs and K outputs (8 inputs, 4 outputs)

•Shephard’s Lemma implies cost share equations can be written as:

•Estimated using Nonlinear Seemingly Unrelated Regression

K

iiij

M

jjii Ywshare

11

loglog

with restrictions:

K

i

M

jjiij

M

j

M

kkjjk

K

i

K

kkiik

M

jjj

K

iiio

wYww

YYwYwYC

1 11 121

1 121

11

loglogloglog

loglogloglog),(log

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Estimation

• The usual parameters of a translog cost function are estimated

• In addition, ρ for each aggregate output must be estimated– Introduces significant nonlinearities to the

estimation

• In addition, β is estimated for each aggregate output category

2121

Data• Data are from California’s Office of Statewide Health Planning and

Development (OSHPD) for 2003• Discharge Data

– Contains information on patient demographic and diagnosis characteristics– 3.47 million observations out of 3.9 million – Include:

• Individuals with data on total charges• Individuals from hospitals described below

• Financial Data– Contains information on operating expenses, wages, ownership, facility size– 321 Hospitals– Exclude:

• Specialty hospitals (long-term care, psychiatric, chemical dependency, children’s hospitals)

• Hospitals not reporting data on charges (Kaiser & Shriner’s hospitals)

2222

Variables

• Costs: Total Operating Expenses• Inputs

– Hourly wages for Nurses (RNs and LVNs), Technical Labor, Aides & Orderlies, Clerical Labor, Management

– Equipment and Supplies

– Capital price per bed

[sq. ft.]*[construction cost]*[(int. rate) + (depr. rate)]/beds

• Outputs: Primary Care, Secondary Care, Tertiary Care, Outpatient Care

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Data- Individuals

23

24

Data- Hospitals

24

25

Average Quantity Weights-Example

25

• Quantity weights: )ˆexp( kikik Xq

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Diversification Parameter Estimates• Tertiary Care (ρt = 0.44 [0.35, 0.52])

- Implies diversification more expensive

19% savings to providing mean amount of tertiary care (989 discharges) in five MDCs versus ten

• Secondary Care (ρs = 0.48 [0.37, 0.58])

- Implies diversification more expensive8% savings to providing mean amount of secondary care (3,990 discharges) in five MDCs versus ten

• Primary Care (ρp = 1.67 [0.44, 2.89])

- Implies diversification less expensive<1% savings to providing mean amount of primary care (5,129 discharges) in ten MDCs versus five

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2727

Marginal Costs and Input Elasticities

2828

Economies of Scale• For multi-product firms, economies of scale calculated as

where a value greater than 1 indicates economies of scale, less than 1 indicates diseconomies of scale.

nYC

loglog1

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Economies of Scale

29

3030

• Does the output index produce results different than would be produced using previous output definitions?

• How do other studies define & classify output?– Total discharges or total patient days– Inpatient/outpatient– Append a “case mix” index which accounts for the relative

severity of illness for a hospital’s Medicare population

• Re-estimated the cost function – Classify output by inpatient/outpatient – Use discharge count while appending a case mix index

Relative Performance of Output Index

3131

Economies of Scale-Comparison155 beds

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Economies of Scale-Comparison

32

180 beds

33

Economies of Scale-Comparison

33

220 beds

34

Economies of Scale-Comparison

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3535

Economies of Scope

• Is it cheaper to produce N products in N specialized firms or in one firm?– Are there savings from producing tertiary and secondary care

together? How about primary and outpatient care?

• Economies of Scope defined as:

- Implies that the marginal cost of producing product i decreases with increases the amount of product j (weak cost complementarities)

0)(2

ji YY

YC

3636

Economies of Scope•Economies of Scope at the mean hospital ( ≈ 180 beds) between all care types

3737

Summary and Conclusions

• Output index shows diversification across MDCs may be cost increasing for tertiary and secondary care and cost decreasing for primary care

• Output index produces estimates of scale economies higher than those recovered from typical methods

• Economies of scope– Economies of scope between primary care and secondary care, as well as

between primary care and outpatient care

• Suggests potential for efficiencies (and thus possible benefits to consumers) even for large hospitals

• This kind of method may be applicable to other industries.

• Future work: panel data, instrumental variables, quality

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