Incremental Cost of Postacute Care in
William D. Spector, Maria Rhona Limcangco, Heather Ladd,
and Dana A. Mukamel
Objectives. To determine whether the case mix index (CMI) based on the 53-
home (NH) costs or whether NHs that have a higher percent of Medicare skilled care
days (%SKILLED) have additional costs.
Data and Sample. Nine hundred and eighty-eight NHs in California in 2005. Data
are from Medicaid cost reports, the Minimum Data Set, and the Economic Census.
Research Design. We estimate hybrid cost functions, which include in addition to
outputs, case mix, ownership, wages, and %SKILLED. Two-stage least-square (2SLS)
analysis was used to deal with the potential endogeneity of %SKILLED and CMI.
Results. On average 11 percent of NHs days were due to skilled care. Based on the
2SLS model, %SKILLED is associated with costs even when controlling for CMI.
The marginal cost of a one percentage point increase in %SKILLED is estimated at
U.S.$70,474 or about 1.2 percent of annual costs for the average cost facility. Sub-
analyses show that the increase in costs is mainly due to additional expenses for non-
therapy ancillaries and rehabilitation.
Conclusion. The 53-RUGs case mix does not account completely for all the variation
in actual costs of care for postacute patients in NHs.
Key Words. Health care costs, Medicare, instrumental variables
Postacute patients are increasingly being treated in nursing homes (NHs).
Spending has risen every year since 2000 (Medicare Payment Advisory Com-
and hip replacements, fractures, strokes, and heart failure (MedPAC 2007).
The percentage of NH care funded by Medicare has increased nationally
from 8.6 percent in 1999 to 13.1 percent in 2005 (Harrington, Swan, and Car-
rillo 2007). Medicaid pays about 43 percent of NH care with the remainder
mostly private pay (Kaiser Commission on Medicaid and the Uninsured 2009).
Medicare and 35 State Medicaid programs use prospective systems
based on case mix for NH reimbursement. This approach provides a fixed
rHealth Research and Educational Trust
Health Services Research
amount, typically set at the average cost for each patient group considered to
be clinically homogenous. State Medicaid programs may also include other
certain types of residents, cost ceilings and floors on specific cost centers, and
incentives for direct care spending (Schlenker 1986; Feng et al. 2006; Rudder,
reimbursement methods, including case mix reimbursement.
The Medicare payment system pays a fixed amount for predefined
patientgroups.With this approach, paymentneeds tobe wellalignedwiththe
cost of caring for patients in these groups. If payment rates for each patient
group are not aligned appropriately with the cost of each group, perverse
incentives arise, leading to both access and quality issues. Some patients may
be less profitable than others and some may represent net losses. These
patients may face difficulty gaining access to NH care because they are finan-
cially less attractive. For those that represent net losses, once admitted, facil-
ities may have difficulty meeting their clinical needs.
Medicare pays only for postacute, skilled care NH patients defined
as those having had at least a 3-day hospital stay for medically necessary
inpatient hospital care, and who require daily skilled care or rehabilitation
services (Centers for Medicare and Medicaid [CMS] 2008). The daily
rate depends on the care needs of the patient as measured by the Resource
Utilization Groups (RUGs), a case mix index (CMI) for NHs, that is expected
to cover operating and capital costs (MedPAC 2009b). A person is classified
into a RUG based on expected minutes of therapy, activities of daily living,
needforspecialservices, and certain clinicalconditions. There were 44 RUGs
during the 1998–2005 period, which were expanded to 53 categories in 2006.
Each RUGs category has a nursing and a rehabilitation weight that
was derived from NH staff time studies performed during the 1990s. There
is an ‘‘other’’ component that covers room and board and capital costs.
The minimum data set (MDS) assessment is used to determine the RUG for
eachpatient.Theincrease inthenumberof groups usedforMedicarefrom44
to 53 was an attempt to better capture the variation in nontherapy ancillary
Address correspondence to William D. Spector, Ph.D., Senior Social Scientist, Agency for
Healthcare Research & Quality, 540 Gaither Rd., Rockville, MD 20850; e-mail: william.spector
@ahrq.hhs.gov. Maria Rhona Limcangco, Ph.D., Analyst, is with the Social & Scientific Systems
Inc., Silver Spring, MD. Heather Ladd, M.S., Research Associate, and Dana A. Mukamel, Ph.D.,
Professor and Senior Fellow, are with the Academy, Health Policy Research, University of
California, Irvine, CA.
106 HSR: Health Services Research 46:1, Part I (February 2011)
(NTA) service costs (such as drugs, laboratory expenses, and respiratory
services) of patients classified into high therapy and extensive services
groups (CMS 2005). A new RUGs, RUG-IV, being proposed for FY2011,
would make adjustments to the groupings based on more recent time
and motion studies and would increase the number of groups to 66 and
expand the number of rehabilitation, special care, and complex care groups
inadequacies. Analyses of the explanatory power of the 44 categories RUGs
shows that it explains about 40–55 percent of staff time costs for all NH res-
idents, with the higher estimate when NTA costs are not included (Fries et al.
1994; White, Pizer, and White 2002). The MedPAC criticizes the RUGs clas-
sification becauseit was developed from staff time studies,and it argues that the
53 category index still does not reflect much of the additional costs of NTAs
because these are not strongly related to staff time. MedPAC suggests ways to
improve diagnostic information using information to classify patients from the
priorhospitalization,to improve reimbursementaccuracy bydevelopinga new
method for reimbursing NTAs and therapies that would use patient and NH
stay characteristics that reflect cost differences, and to implement an outlier
payment system for high NTA and therapy costs (MedPAC 2008).
Analysis of NH cost reports can provide insights into how well the RUGs
classification systemexplainsthevariation inNHcosts.Theannualcostsofcare
of days of care provided, and the wages that the NH pays to provide that care.
NHs that admit a greater percentage of postacute patients will generally have a
higher overall case mix because postacute patients require more complex med-
postacute care, the costs of NHs that provide a higher percentage of postacute
capture the costsforall types of postacutecare,then the percentage of postacute
care provided by the facility will also explain some of the costs.
In this paper, we analyze whether the RUGs CMI sufficiently capture
the cost burden of postacute patients. We estimate cost functions that include
in addition to the RUGs CMI, inpatient days, ownership, and wage index, the
percent of days due to Medicare skilled care days (%SKILLED). If costs
are higher when facilities have a higher %SKILLED, even when controlling
for RUGs (using the 53 RUGS CMI), then this suggests that the currentRUGs
to the impact on total costs, we also estimate the impact on the two cost
Incremental Cost of Postacute Care107
categories that are expected to be affected, as argued by MedPAC——
rehabilitation and NTAs.
Sample and Data
We obtained 2005 Medicaid cost reports from the California Office of State-
wide Health Planning and Development. These are annual financial reports
that are mandated, audited, and used by the state to set Medicaid payment
rates for all skilled NHs in the state. They include information about expen-
ditures, wages, and outputs (e.g., inpatients days and admissions).
The MDS is an individual-level dataset with information about all residents in
the facility, with demographics, physical and mental health status, and infor-
mation about specific treatments. MDS data are collected by NHs upon
admission and at specific time intervals following admission (e.g., every 90
days for long-term care patients and 5, 14, and 30 days for skilled care
patients). Data collection is mandated by the CMS.
used the 2002 Economic Census, Sector 62 to obtain revenue data of reha-
bilitation establishments by zip code. Driving time between NHs and com-
addresses was obtained from the 2005 California Healthcare Cost and Uti-
lization Project State Inpatient Database (HCUP Databases 2005).
There were 1,083 free-standing skilled nursing facilities in California in
2005. We excluded 51 facilities because of missing case mix data and 42
because they were atypical, providing care to special populations such as
subacute pediatrics and residents with developmental and psychiatric disor-
ders. In addition we removed one outlier based on the Cook’s D statistic that
had implausible values. The final sample includes 988 free-standing skilled
The dependent variable was total facility expenditures. Because some NHs
produce other services in addition to inpatient days, such as home care, out-
patient clinics, or day care visits, but the cost reports do not report these costs
separately, inpatient days were adjusted upwards by the ratio of outpatient to
108 HSR: Health Services Research 46:1, Part I (February 2011)
these services. To measure the proportion of postacute care provided by the
NH,weusedskillednursingcare daysfrom thecostreportsandcalculatedthe
percent of days due to skilled care days as the ratio of unadjusted skilled care
days to inpatient days ? 100.
program v5.20 and the Index Maximized grouping option. We included all
assessments that have the required items to calculate RUGs——admission, an-
System (PPS) assessments. In California the quarterly assessment does not
include all items to calculate RUGs and is not used. Each assessment was
assigned a weight using the RUGs total rate from Table 4 of FY2006 SNF PPS
Final Rule (CMS 2009). The total rate is the sum of the nursing, therapy, and
non-case-mix components. These weights were rescaled to make the mean
each resident assessment was weighted by the length of stay associated with
the next assessment date or discharge. For assessments that were not admis-
sions and that occurred after the first of the year, days were counted from
January 1. Thus, the CMI for the facility was calculated as
where days is the number of patient days in RUG group r, and w is case mix
weight for RUG group r.
were calculated as the sum of expenditures reported for physical therapy, oc-
sum of pharmacy, laboratory, respiratory therapy, and other ancillary services.
We used two IVs in the two-stage least-square (2SLS) estimation
approach. A discussion of the IV approach is included in the estimation sec-
tion below. The first IV is the annual revenue of rehabilitation establishments
(defined as offices of physical, occupational, and speech therapists and
audiologists) that provide services to ambulatory patients in the zip code in
which the NH is located, as reported in the Economic Census data. Because
establishments in the Census data are grouped into aggregate revenue strata,
this variable was calculated as IV5SWiNi, where Ni is the number of
rehabilitation establishments in revenue stratum i, and the weights, Wi, is the
Incremental Cost of Postacute Care 109
middle point of the annual revenue range for the revenue stratum (except for
the last category), as follows:
The second IV is the mean driving time between the zip codes of the NH and
15 closest community hospitals. We first estimated the driving time between
each NH and the 305 community hospitals in California using Goggle map
(Zdeb 2010). We then estimated the mean driving time between an NH and
the 15 closest hospitals.
if revenues < U:S:$100;000
if U:S:$100;000 ? revenues ? U:S:$249;999
if U:S:$250;000 ? revenues ? U:S:$499;999
if U:S:$500;000 ? revenues ? U:S:$999;999
if revenues > U:S:$1;000;000
Estimation of Cost Function and Marginal Cost
We estimated a hybrid cost function following Nyman (1988) and Mukamel
and Spector (2000) as follows:
log C ¼ a þ b log W þ gFP þ wCMI þ
diðPDÞiþ k%SKILLED þ m
where C is annual total costs, W is the average staff wages in NHs in the
the percent of skilled care days, and FP is an indicator variable for for-profit
status. We also included squared and cubed terms of the adjusted inpatient
days to allow for both economies and diseconomies of scale depending on the
pattern of signs of the three coefficients (Grannemann, Brown, and Pauly
1986). We used the average wage of nurse aides in the county to account for
staff cost differences across the state. Wages for other nurses are highly cor-
relatedwith thismeasure, and thevast majority ofstaffinNHsarenurse aides.
If the RUGs reimbursement method is capturing the cost of providing
postacute care, then the coefficient of %SKILLED in the cost equation would
be zero. If it is not tracking all costs of postacute care, then the coefficient
would be positive.
Potential Endogeneity of Case Mix and %SKILLED
Costs may be endogenous with both CMI and %SKILLED for the following
reasons. NHs often consider the financial implications of admitting residents
when they develop their admission strategy. If the reimbursement system does
not closely track actual costs of care for all patients, some patients are more
110 HSR: Health Services Research 46:1, Part I (February 2011)
profitable than others. In free-standing NHs, margins have been consistently
higher for postacute than long-stay residents, creating an incentive to prefer
postacute patients in general, and certain types of postacute residents may be
in the mid–1980s, NHs can influence who applies for admission through their
costly postacute care. Through marketing and development of relationships
with other health organizations like hospitals and ambulatory rehabilitation
offices, they may encourage a stream of potential residents who are more fi-
nancially attractive. Furthermore, NHs can influence the RUGs score itself by
determining the amount of services they provide, especially therapy minutes
and therapy disciplines used, which also affects costs. Thus, %SKILLED, RUGs
CMI, and costs are simultaneously determined. If the cost equation is estimated
result in biased estimated coefficients. Consequently we estimated the cost
equation with 2SLS treating both CMI and %SKILLED as endogenous vari-
ables. We perform the Hausman test of endogeneity and present estimates of
boththeOLSand the2SLStodemonstratethebiasintroduced byendogeneity.
At least one instrument is needed per endogenous variable. Good instruments
exclusion criterion, that is, they are not correlated with the cost equation error
the NH and the 15 closest community hospitals (we performed sensitivity an-
alyses using closest 5, 10, and 20 hospitals and as the results were similar, we
present results using 15); (2) the weighted revenue of establishments that pro-
vide rehabilitation to ambulatory patients in the same zip code as the NH.
We expect these IVs to be strong, that is, correlated with both the CMI
less access to postacute residents, and hence will be less likely to be able to
optimize their case mix. This should lead to a negative correlation of CMI and
%SKILLED with this IV. NHs in areas with more demand for rehabilitation
services are likely to have more ambulatory rehabilitation establishments and
more NH rehabilitation. Consequently, we expect a positive relationship of
CMI and %SKILLED with this IV. We use the minimum eigenvalue test pro-
posed by Stocks and Yogo (2005) to test the hypothesis of weak IVs.
Incremental Cost of Postacute Care111
The exclusion criterion is not empirically testable, but the following
arguments suggest that our IVs meet this criterion as well. With respect to the
rehabilitation establishmentinstrument,themost likely threattotheexclusion
criterion is the omission of rehabilitation staff wages from the cost equation. A
high concentration of rehabilitation establishments locally may theoretically
impact therapy wages. However, the IV is defined as the revenues of reha-
the county or MSA level, due to worker mobility. Furthermore, other busi-
nesses besides rehabilitation offices employtherapists, includinghospitalsand
home care agencies. Therefore, it is very unlikely that as defined, our IV is
correlated with therapists’ wages, and hence we believe that it meets the ex-
clusioncriterion.Furthermore,therapistsaccount foro1 percentofNHcosts,
such that the impact on NH costs is likely to be negligible.
For the second IV, the mean driving time to the closest 15 hospitals,
there may be similar concerns that RN wages and rehabilitation wages could
be affected. Differences in the value of the instrument may affect the demand
for RNs and therapists and consequently have impact on the wages faced by
NHs. This in turn may affect hiring decisions and thus impact on costs. The
impact on wages is likely to be small because hospitals are only one source of
demand for these workers. The impact on cost would be negligible because
RNs and therapists represent small shares of NH costs——rehabilitation is o1
percent and RN costs are 5 percent of total NH costs. Minimum NH staffing
regulation also limits the ability of NHs to adjust staffing.
We estimate the marginal cost of an additional percent of skilled days
using 2SLS regression with the IVs as described above. If the coefficient is
significantly different from zero, this suggests that the CMI does not suffi-
ciently account for all difference in costs associated with skilled care.
We calculate the marginal cost of increasing the %SKILLED by one
percentage point. Because we used the log transformation of cost as the
dependentvariable, logscale predictionsmayprovidea biasedestimateofthe
impact of explanatory variables on mean cost. We retransformed the log cost
predictions obtained from the second stage equation using the method
described by Baser (2007). This method appropriately retransforms costs and
accounts for possible bias due to heteroskedasticity in the error term.
To gain insights into what contributes to the costs of postacute patients
in which the dependent variables were the costs of rehabilitation care and
NTAs. We use the same IV regression method as we do for the total cost
analysis and estimate the same models. Following the analyses of MedPAC,
112 HSR: Health Services Research 46:1, Part I (February 2011)
we expect that most of the additional costs will be associated with rehabil-
itation and NTAs.
Table 1 presents descriptive statistics. On average, 11 percent of NH days
were skilled care days, but the variation was large (25th percentile——5.2 per-
cent; 75th percentile——14.8 percent). The average facility had 100 beds,
annual costs of U.S.$5.7 million, and over 32,000 adjusted inpatient days. The
facilities excluded from the analyses were not significantly different from the
study sample in terms of total costs, bed size, wages, or ownership. However,
they had significantly lower percentage of skilled care days (9 percent versus
We did the Hausman endogeneity test and confirmed the endogeneity
of both %SKILLED and CMI (F(2,922)5770, po.00001) and thus proceeded
with the 2SLS analyses. Table 2 shows the first-stage equations. The depen-
dentvariables are %SKILLED and CMI. The incremental F-testswere high——
F(2,922)520.06 for %SKILLED and F(2,980)518.56 for CMI equations,
respectively. The minimum eigenvalue was 10.81, which is above the criti-
cal value of 7.03 for a nominal 5 percent Wald test for a 10 percent rejection
Table1: Descriptive Statistics (N5988)
Total annual cost (U.S.$)
Number of beds
Percent skilled care days
Case mix index
Adjusted inpatient days/10,000z
Log county average CNA wage (U.S.$/hour)
Mean driving time to 15 closest hospital in seconds
nPhysical therapy, occupational therapy, and speech pathology.
wRespiratory therapy, laboratory, pharmacy, and other ancillaries.
zAdjustedinpatientdays ¼ Inpatientdays ? 1 þOutpatientrevenue
Incremental Cost of Postacute Care113
rate, indicating that we can reject the hypothesis of weak instruments (Stocks
and Yogo 2005). We find a negative and significant correlation between CMI
and the mean driving time to the closest 15 hospitals. We also find significant
and positive correlations between CMI and %SKILLED with revenues of
ambulatory rehabilitation establishments in the same zip code as the NH.
Table 3 compares the results of the regression of the log of total cost
comparing the OLS with the 2SLS results. The estimated coefficients are very
similar except for the coefficient for %SKILLED and CMI. Both models show
the expected relationship between adjusted inpatient days and costs. The pos-
itive, negative, and then positive coefficients produce a typical S-shaped curve,
suggesting increasing returns to scale followed by decreasing returns. As ex-
Although both coefficients are significant (po.001) in the OLS, for
%SKILLED the IV estimate in the 2SLS is almost twice the OLS estimate——
compared with 1.245.
Table 4 shows the marginal costs from the 2SLS estimation of total
by one percentage point, for the average facility, was U.S.$70,473, or 1.2
percent of the annual cost. For the subanalysis, the instruments remained
Percent Skilled Care Days and Case Mix Index (p-Values in Parentheses);
Case Mix Indexw
0.016 (o0.001)IV: Revenue of establishments offering
rehabilitation services in the zip code (in millions)
IV: Mean driving time to 15 closest hospital
Adjusted inpatient days
Adjusted inpatient days squared
Adjusted inpatient days cubed
Log county average CNA wage (U.S.$/hour)
For profit status
nIncremental F-test, F(2,980)520.066.
wIncremental F-test, F(2,980)518.561.
5% Wald test.
114HSR: Health Services Research 46:1, Part I (February 2011)
strong in each of these 2SLS procedures. R2s were generally high, ranging
in costs due to a higher %SKILLED was due to higher rehabilitation costs and
32 percent was due to higher NTA costs.
costsoftreatingthevariety ofpatientsthat NHsserve.Case mixreimbursement
(p-Values in Parentheses); N5988
Independent Variables OLS 2SLS
Percent skilled care days
Predicted percent skilled care days
Case mix index
Predicted case mix index
Adjusted inpatient days
Adjusted inpatient days squared
Adjusted inpatient days cubed
Log county average CNA wage (U.S.$/hour)
For profit status
0. 012 (0.043)
OLS, ordinary least square; 2SLS, two-stage least square.
Days Due to Skilled Care (%SKILLED) by Expense Category
Marginal Cost for a One Percentage Point Increase in Percent of
% of Total Marginal
Note. Results based on 2SLS analysis with marginal cost calculated using Baser log retrans-
formation method (Baser 2007).
nAs a percent of U.S.$70,474.
wPhysical therapy, occupational therapy, and speech pathology.
zRespiratory therapy, laboratory, pharmacy, and other ancillaries.
2SLS, two-stage least square.
Incremental Cost of Postacute Care 115
method dominates reimbursement for both skilled and long-term care. It is
important that these case mix reimbursement systems be well aligned with the
to attract specific types of patients and may create barriers to access.
It has been difficult to design NH case mix reimbursement systems to
properly meet the costs of care for all postacute patients. MedPAC suggests that
the complex needs of postacute patients and their associated costs have been
intravenous medications, and respiratory care. MedPAC raised concerns about
the impact on access for these patients (MedPAC 2009a). To the extent that
reimbursement is not paying appropriately for these patients, NHs treating a
higherproportion of thesepatientswill bedisproportionately affected.Thispaper
It specifically examines the issue of whether the discrepancy is greater in facilities
that have a higher proportion of skilled care days. The analyses confirm that this
CMI does not capture all the costs and that additional costs are associated with
percentage point of skilled care days. The extra costs are mainly associated with
rehabilitation and NTAs. These findings are broadly consistent with MedPAC’s
suggestions that with the 53-RUG index there is an underpayment for NTA
expenses and some rehabilitation patients who have very high therapy costs.
Several strengths and limitations of this study should be noted. An im-
portant strength is the ability to account for the endogeneity of the postacute
care percent and case mix. A limitation of the study is that it is based on data
from one state. Although Medicare reimbursement is applied to states uni-
formly, Medicaid rates and reimbursement methodologies vary. Other supply
factors may also differ. This may differentially affect the cost structure of NHs.
Although the California RUGs case mix measure in this study is not based on
quarterlyassessments,calculationsofthecasemixin onestatewith ‘‘RUGable’’
quarterly assessments, with and without the quarterly assessments, showed
little difference in the facility case mix scores. Furthermore, as a cross-sectional
study, the analysis is vulnerable to omitted variable bias. Sensitivity analyses
were carried out to determine whether alternative controls were needed to
minimize missing variable bias. Competition as measured by the Herfindahl–
Hirschman Index and indicators of regional location were included in alternative
specifications. Competition was not statistically significant and region affected the
size of the wage rate variable, suggesting that that variable was picking up
regional differences in labor supply and other cost factors. In both cases the
coefficient of interest, %SKILLED, and the strength of the IV, were not
116 HSR: Health Services Research 46:1, Part I (February 2011)
affected. Therefore, we report the cost equations without competition and
On August 11, 2009, CMS published the skilled nursing facility prospec-
tive payment Final Rule for FY2010 and 2011 (CMS 2009). With this rule it
on time and motion study data collected in 2006–2007. The 53-RUGs were
based on staff-time studies from 1997. With the final rule, CMS expanded the
RUGs classification system from 53 to 66 groups. The RUG-IV expands and
makes technical adjustments to rehabilitation, clinically complex, special care,
extensive care, and rehabilitation groups. The revised index is intended to be
applied using v3.0 of the MDS. Although these changes ought to better reflect
the costs of some of the highest cost rehabilitation patients, the approach to
paying NTAs, however, remains the same and is proportional to nursing staff
costs. MedPAC has criticized this approach because staff time does not suffi-
ciently explain the variation in the cost of NTAs. It appears that CMS is in-
terested in exploring alternative approaches to reimbursing NTAs but did not
the Final Rule are likely to improve the explanatory power of theRUGs, future
research should determinetowhatextentthenewchangesin RUGssufficiently
account for differences in the actual costs of skilled care patients in NHs. The
study wepresenthereshould berepeated in severalyearstime,when datafrom
the new RUGs become available, to determine whether the 66 RUGs system
has corrected the shortcomings and resulting disincentives in the current sys-
tem, or if further refinements, such as an outlier methodology for high reha-
bilitation patients and new approaches to reimbursing NTAs, are needed.
Joint Acknowledgment/Disclosure Statement: The research was partially supported
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Additional supporting information may be found in the online version of this
Appendix SA1: Author Matrix.
Please note: Wiley-Blackwell is not responsible for the content or function-
ality ofany supportingmaterialssupplied by theauthors.Any queries(otherthan
missing material) should be directed to the corresponding author for the article.
Incremental Cost of Postacute Care119