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
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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,...
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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
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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
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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
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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
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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
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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))
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)),,...,(),,...,(),,...,(( 111 OQQYQQYQQYCCost NT
NS
NP
kkkjkNjk
kj QQY /1
1 )...(
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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
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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
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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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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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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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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
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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
kkkjkNjk
kj QQY /1
1 )...(
iknkikjknijkn XH )ln(
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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
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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
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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)
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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
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Data- Hospitals
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Average Quantity Weights-Example
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• 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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Marginal Costs and Input Elasticities
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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
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• 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
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Economies of Scale-Comparison155 beds
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Economies of Scale-Comparison
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180 beds
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Economies of Scale-Comparison
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220 beds
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Economies of Scale-Comparison
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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
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Economies of Scope•Economies of Scope at the mean hospital ( ≈ 180 beds) between all care types
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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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