CATASTROPHE THEORY AND PUBLIC POLICY
The Dynamics of Provider Behavior
In The Nursing Home Industry
William Ammentorp
University of Minnesota
Paul Gunderson
Minnesota Center For Health Statistics
ABSTRACT
Major changes in the demographics of aging in the United States
have created demands for geriatric care which cannot be met by
existing services. Most states have elected to address this
policy issue by offering incentives to providers to promote
investment in long term care facilities. These offerings have
been only marginally successful due to the relative
attractiveness of competing investment options. This paper
explores provider reaction to policy incentives using a System
Dynamics model derived from Catastrophe Theory. Provider
behavior is seen as unstable under competing investment options;
a behavioral condition which conforms to the typical "Cusp
Catastrophe". .
HUMAN SERVICE POLICY:
The fundamental purpose of public policy for the human services
is to match service delivery capacity with the objective needs
of citizens. (Levin. and Roberts, 1978) Laying aside political
concerns, the policy process serves to translate aggregate
demands into programs and service delivery systems. From this
perspective, the efficacy of a particular policy can be
determined by the degree to which resulting services conform to
public demand. (Hirsch and Bergan, 1976) This approach is
essentially one where the policy maker(s) attempt to respond to
a demand 'signal' by implementing appropriate programs.
The key events in this process are pictured in Figure 1. We
would expect a well-conceived policy to provide services to
match changing demands. The match should be as shown; a smooth,
controlled response which 'tracks' the pattern of demand in a
timely, proportional manner. (Ammentorp, Gunderson and
Broderick, 1977) In effect, the policy system acts as a
"control' on service demand so that there is neither an excess
nor a shortage of service capacity.
POLICY RESPONSE
TO SERVICE DEMAND
Units of
Service
New
Demand
Level
Old
Demand
Level
~ ‘Time
q T I
Demand _ Policy Clients
Perceived Enacted Enrolled
The key words in the previous paragraph are '‘'timely' and
"proportional'. As Figure 1 shows, there is a finite delay
between the initiation of policy and the availability of
service. There is a second delay which relates to the duration
of the service episode. In combination, these two delays result
in unfilled demand and continued policy pressure. Proportional
response insures that excess service capacity will not be
provided and that public resources will be efficiently allocated
across several policy areas. The policy system will, in effect,
be ‘in control'.
Controlled policy responses are due to several interrelated
factors. Figure 2 shows how exogenously generated Service
Demands result in a Discrepancy between Demand and current
levels of Service Supply. This, in turn, leads to Policy
Actions and the provision of Policy Incentives to motivate
Provider Responses. However, these reactions are Delayed in
time and subject to competitive Investment Alternatives. Thus,
Service Supply does not immediately adjust to new levels of
Demand and, when Incentives are insufficient, may not respond at
all.
=
INCENTIVES IN
POLICY SYSTEMS
RESPONSE
DELAYS.
-(- ALTERNATIVE
INVESTMENT
+ i
PROVIDER
” RESPONSE
SERVICE
‘SUPPLY
t
POLICY ~
INCENTIVES.
SERVICE
DEMAND
DISCREPANCY =
POLICY -
ACTION :
Many of the human services follow the above incentive model.
Medicare prospective payments set a price on specific hospital
services so that incentives exist for efficient operation and
specialized services can be offered profitably. (Grimaldi and
Micheletti, 1983) Long term care services for the elderly and
handicapped are similarly priced to offer returns to investments
made by providers. (Baldwin, 1980; Deane, 1983) In each policy
arena, provider behavior and the resulting supply of services is
controlled more or less effectively by the balance between
policy incentives and alternative investments.
The events sketched in Figure 2 show that the delivery of human
services is at least a three-part problem. First, accurate
assessment of needs must occur if services are to be relevant.
Second, the policy process must recognize need and translate it
into viable programs and services. Finally, service providers
must be induced to make appropriate programmatic and
institutional arrangements for client services.
In the past, most policy research has concentrated on the link
between client needs and public programs. While these studies
have helped to refine estimation and program management
practices, they have largely neglected the behavior of
providers. As a result, policy analysts are often surprised by
provider behavior. Witness the 'trafficing' in nursing home
facilities brought about by capital funding practices (Scanlon
and Feder, 1981), variance in hospital use under Medicare
(Gornick, 1982), and manager reactions to attempts to control
facility expenditures (Ammentorp, 1985).
LONG TERM CARE POLICY: :
The long term care delivery system is one where all three
elements of the policy problem are present. There are
uncertainties in estimating the need for nursing home care
within the elderly population and significant differences in the
workings of state policy making systems. But, most importartly,
long term care is a service which is, for the most part,
provided by for-profit vendors. Thus, the responsiveness of
providers to policy incentives becomes the central issue in long
term care delivery.
Long term care is a critical policy issue at present. Americans
are not only living longer, their survival rates are based on
ever-larger age cohorts. The Minnesota data shown in Table 1
illustrate this point.
TABLE 1
MINNESOTA POPULATION
PROJECTIONS 1985-2005
AGE 1985 1990 1995 2000 2005
65-69 154242 160250 158394 150769 162107
70-74 129842 135719 142602 141643 135566
75-79 99110 108843 116729 123955 124656
80-84 69048 75579 85464 92811 99871
85+ 60215 68542 78602 90781 102579
A key observation to be made from the data in Table 1 is that
the State will experience substantial growth in the numbers of
the very old. Thus, the balance of long term care needs will
shift toward institutional systems and the State will need to
provide for a greatly increased delivery of nursing home
services. As Krebs points out, policy makers must either
allocate significantly larger resources to long term care or
provide some means of rationing access to services. (Krebs,
1983)
-5-
POLICY SYSTEMS DYNAMICS:
Policy issues raised by the above demographic trends can be
addressed by constructing models of service delivery and policy
systems. (Ammentorp and Gunderson, 1984) Figure 3 shows how the
stock of long term care beds is influenced by several key policy
decisions.
NURSING HOME
SERVICE SYSTEM
DEPRECIATION
FROM POLICY -~ --~~_
Ps NY
5
Ns
. SERVICE \
a DELIVERY aakeeaiaes 53
ADD CAPACITY SUB
A —
t ‘
, ‘
/
- CONSTRUCTION ' UTILIZATION
FROM POLICY $ PARAMETER
'
I, a
AVAILABLE Beps~
ACTUAL |
SERVICE |\. NEED
ICOVERAGE| ~*~ ~..- FROM DEMAND
The level variable in Figure 3 (Service Delivery Capacity) is
the number of approved long term care beds available. It is
added to by construction and/or licensure decisions made in the
policy system and reduced by depreciation of facilities. This
is suggested by the ‘From Policy' arrows which impact the ADD
and SUB rates above.
The objective number of beds in long term care facilities is
adjusted by a Utilization Parameter to arrive at current
estimates of Available Beds. This number is compared to the
Need estimate to determine ‘the degree of Actual Service
Coverage. In this computation, it is important to note that
policy makers may adjust both Utilization and Need by setting
elgibility and compensation criteria.
The structure of the policy system which controls service
delivery is shown in Figure 4.
NURSING HOME
POLICY SYSTEMS
FUNDED CONSTRUCTION
DEPRECIATION TO SERVICE
TO SERVICE
ma SS DELAY.
q
'
Y
INVESTMENT
DECISION
’ 7 .
a N 7 .
* SHRUCTURE oe ALTERNATIVE
ROI
POLICY
ACTION
a Benvice
at “7
RESOURCE ---~ \ oa COVERAGE
SUPPLY \ F
cy
DISCREPANCY
,
DESIRED
SERVICE
COVERAGE
Here, the driving force for Policy Action is the Discrepancy
between Actual Service Coverage and Desired Service Coverage.
This takes the form of comparison between the numpers of elgible
clients estimated by demographic studies and the current count
of Available Beds. When a Discrepancy indicates a need for
additional service capacity, policy makers weigh the cost of
meeting need against alternative denands on public resources.
This results in some form of Incentive Structure which is
communicated to care providers.
Incentives take two basic forms in this model; Funded
Depreciation allows providers to recover capital investment over
time, and effective interest rates offered for new investment.
It is this latter inducement that is the key to developing long
term care facilities in the magnitude necessary. (McCaffree,
1979)
As providers consider potential earnings on capital, they
necessarily consider alternative investments. ROI (return on
investment) from these alternatives shapes the Investment
Decision of the provider. Then, after a construction delay, new
capacity can come on line to reduce the need for service
coverage.
These assumptions have been programmed as a DYNAMO model and
initialized for current Minnesota data and policies. (Ammentorp
and Gunderson, 1984) When these assumptions are tested, the
model exhibits two distinct modes of behavior.
INCENTIVE MODE DECLINE MODE
BO.000T, .ereseeeseesereeae deers: B0.000T, ,..seseseerereneees
60.000T 60.0007}
‘
1
40.0007}
5
40.000T| B
20.0007}... 20.000T|
|
i
!
0.0007] i
1985.0 1995.0 2005.0
0.000T|
1985.0
In the ‘Decline Mode', the model shows the effect of current
State limits on nursing home construction; over time, the gap
between need and capacity widens as the elderly population
continues to increase while facilities decline through
depreciation. The ‘Incentive Mode' shows relatively good
adjustment of service capacity to need and, in fact, if the
incentive assumptions of the model are correct, it should be
possible to attain any desired balance between need and
capacity.
However, the model is overly simplistic in its treatment of the
role of incentives. Due to this limited perspective, the model
cannot be used as a reliable guide to policy making. Instead,
the model must be enriched to better represent the impact of
incentives on an environment where there are varying investment
alternatives.
-8-
A THEORY OF PROVIDER BEHAVIOR:
We can begin to address the shortcomings of the above policy
model by considering the impact of relative rates of return on
the investment decisions of providers. If provider behavior is
represented as the probability of investment in long term care
facilities, we can create a function in three dimensional space.
Probability of
Investment in
Nursing Home
Facilities
Behavioral
Surface
Yield on
Alternative
Investments
i
Yield on
Nursing Home
Investments.
The surface shown in Figure 6 represents the determination of
provider investment probabilities by the relative rates of
return .on- nursing home and competitive investments. As these
rates vary, we would expect providers to adjust their long term
care investments to improve yield on capital. These variations
result in probabilities which range from plus or iwinus one -
corresponding to high long term care facility investment and
facility sell-off respectively.
In this model, investment behavior is seen as the dependent
variable to be predicted by the relative yields on long term
care and alternative investments(the contol variables). If
investment (I) and control (C) variables are related by some
function, £(1,C), the condition for equilibrium behavior
becomes:
(1.0) MIN(I,C)=£(I,C)
From a dynamic perspective, this becomes:
(1.1) I =~ 0£/ 1 = - GRAD £
and MIN £ corresponds to:
(1.2) GRAD £ = 0
As the control factors (C) vary, the solutions to (1.2) form the
surface shown in Figure 6. (Wilson, 1981) Any changes in the
control factors (investment yields) will result in a new
solution to (1.2) and a new equilibrium for investment behavior.
Thus, the surface of Figure 6 is one which ‘suggests smooth
transitions aimong investment probabilities throughout the range
of alternative yields.
This is, however, a somewhat unrealistic view of provider
decision making. Provider decisions are more likely to be
bimodal in that investors are more or less committed to one
alternative or the other and choices are not so easily adjusted.
The bimodality of provider behavior suggests that catastrophe
theory may better account for investment decision
making. (Zeeman, 1976)
Catastrophe theory refers to those behavioral surfaces where
there are multiple solutions to equation (1.2). In Figure 7, we
show a folded surface in the (I1,C) space corresponding to this-
condition. This surface has been called the ‘cusp catastrophe'
since the projection of the fold unto the control (C) plane is a
cusp-like figure. (Thom, 1975)
INVESTMENT DECISION:
CUSP MODEL
Facility
Investment
Me .
y o
Behavior
Surface
Market
T
1
!
1
I
1
Investment. 4 y
—<! 1
1
{
1
u
Behavior
Controt Facility yS
Incentive .
Surface
Market
Incentive
Uncertainty:
-10-
Catastrophe theory is well-suited to problems in bimodal choice
oa following conditions are fulfilled (Poston and Stewart,
19 : .
a) Abrupt Changes In Behavior:
Long term care investment or sell-off is an abrupt
change which represents the shift of capital from
one investment alternative to the other. Since
long term care facilities are not generally stock
companies, changes in investment involve
significant capital movements and are,
necessarily, abrupt.
b) Hysteresis:
This means that an abrupt transition in behavior
cannot be directly retraced. For exanple,
considerable changes in alternative yields may be
needed before a recent long term care investment
would be withdrawn.
¢) Inaccessibility:
Catastrophic changes in behavior are possible when
the behavior surface is folded as shown in Figure
7. j%XIn effect, there are multiple solutions to the
gradient equation (1.2) for some combination of
the control variables. Solutions represented by
the intermediate (shaded) layer in Figure 7 are
unstable and, hence, inaccessible. (Wright, 1981)
d) Divergence:
As behavior approaches the point of the fold in
Figure 7, small differences in the relative
magnitude of the control variables can lead the
system to either the upper or lower equilibrium
surface. In effect, small changes in relative
interest rates can 'commit' investors to either
long term care or alternative investments.
APPLYING THE THEORY:
Incorporating the behavioral surface in a System Dynamics model
is obviously a formidable task. The equation f£(I,C) is unknown,
except in the very general way it has been described, and
estimation of equilibrium points for the system is statistically
impossible, given current data bases. Consequently, we must
rely on certain typical cases where the theory might contribute
to our understanding of provider investment behavior.
To proceed, we distinguish between our two control factors. The
yield on long term care investments is called a 'norinal' factor
and the yield on alternative investments a ‘splitting' factor.
(Scapens, 1981) The role of these factors in determining
investinent behavior can best be understood by cutting Figure 7
at two points on the alternative investment yield axis. At low
-ll-
values of alternative yields, we obtain a section which shows
investment probability as a function of long term care yields
(Figure 8a).
PROVIDER INVESTMENT BEHAVIOR
WITH ALTERNATIVE YIELD
AS A SPLITTING FACTOR
a) Low Alternative Yield b) High Alternative Yield
Facility Investment Probability
Facility Investment Probability
Facitity Incentive Facility Incentive
However, as the 'splitting' factor increases, the section of
Figure 7 will cut the behavior surface in the cusp region with a
resulting section like that shown in Figure 8b. The increase in
alternative yields has effectively 'split' the behavioral
options into two modes. The implication of this split is the
potential for catastrophic changes in behavior as represented by
the overlapping curves in Figure 8b.
Transition marked (A) in Figure 8b represents a catastrophic
sell-off of long term care facilities. Similarly, the (B)
transition is one which marks an abrupt shift of investment into
long term care facilities. It is important to note that these
are delayed phenomena. (Wright, 1981, p.8) That is, movement
along the upper behavior surface in (8b) will not result in a
catastrophic jump to the lower surface until the left-hand edge
is. reached. This is consistent with the concept of the
splitting variable as one which has a delayed impact on
behavior.
The two behavioral modes illustrated in Figure 8 were used to
modify the long term care model. In effect, the model was
enriched to incorporate different provider investment behaviors
at several levels of market investment yield. Historical data
-12-
on nursing home investment, yield on nursing home capital, and
market interest rates in Minnesota were used to set the
parameters of the model. Where possible, comparisons to
National data were used to increase confidence in these
estimates.
LONG TERM CARE
MODEL OUTPUT
CATASTROPHE MODE
Long Term
Care Beds
80,000,
Buy tn’
‘Need
60,000)
40,000)
Sell Off
20,000)
Time
1985 1995 2005
Figure 9 shows how the model responds to two scenerios. With
competitive investment yields held constant, a gradual decline
in long term care investment yields leads to gradual reductions
in capacity until that point where a catastrophic 'Sell Off'
occurs.
For Minnesota, the second scenerio is more important. Given
constant alternative investment yields, gradual increases in
incentives for long term care investment result in steady, but
small, increases in capacity. However, at some point in this
process, massive shifts of investment are made and the model
exhibits a 'Buy In‘ catastrophe.
If the underlying assumptions are correct, the provision of
investment incentives to long term care providers is a matter of
the fine tuning of offerings. Policy makers must provide
adequate incentives to move needed capital out of alternative
investments but not make such attractive offers as to encourage
catastrophic responses. Clearly, control over investment must
-13-
be a balance of incentives and limits imposed by license to
prevent construction of excess capacity.
IMPLICATIONS:
At this writing, the catastrophe theory approach to policy
incentives appears to hold considerable promise as a general
guide to policy makers. However, several elements in the model
are in. need of additional research. The hysteresis effect
postulated by the theory must be emperically grounded. This is
a matter of studying bimodal investment choice of providers.
(Blase, 1979; Goodwin, 1977) Further, the supply of capital
available for long term care investment must be accurately
estimated as must the liquidity of these and competing
investments.
The model also exhibits a weakness in the way it captures policy
maker behavior. It is probably unreasonable to assume that
decisions will follow directly from citizens demands. Instead,
some complex functions which weighs alternative demands for
resources must be included in the model.
Despite these limitations, the catastrophe theory model extends
our understanding of the policy process in the human services.
It adds a significant dimension to the general theory of Levin
and Roberts (1978) and serves to highlight needed research into
provider investment decision making.
REFERENCES:
Ammentorp, W. "Implementing Human Service Policy: Financial
Models for Coordination and Control", Computers in Human
Services, in press.
Ammentorp, W. and P. Gunderson. "Public Policy and Service
Capacity", Proceedings of the Data Use Conference on Small Area
Statistics, National Center For Health Statistics, Washington,
D.C., 1984.
Ammentorp, W., Gunderson, P. and M. Broderick. “Design
Parameters For Human Service Systems", Paper presented at
Regional Science Association Conference, Minneapolis, Minn.,
1977.
Baldwin, C. "Nursing Home Finance: Capital Incentives Under
Medicaid", Waltham, Mass., Brandeis University, 1980.
Blase, J. “Hysteresis and Catastrophe Theory: Emperical
Identification in Transport Modelling, Environment and Planning,
V. 11, pp. 675-688.
Cuthbert, R. "Modelling the Catastrophic Effects of Expenditure
Cuts", Further Education Staff College, Coombe Lodge, England,
1981.
~14-
Deane, R. "New Concepts in Nursing Home Reimbursement", Mimeo,
Available from author (1983)
Goodwin, P. “Habit and Hysteresis in Modal Choice", Urban
Studies, V. 14, pp. 95-98.
Gornick, M. "Trends and Regional Variations Use Under Medicare",
Health Care Financing Review, Vol. 3, No. 3, pp. 41-73, 1982.
Grimaldi, P. and J. Micheletti. Medicare's Prospective Payment
Plan, Chicago, I1l., Pluribus, 1983~
Hirsch, G. and P. Bergan. “Simulating Ambulatory Care Systems",
Proceedings —- Sumner Computer Simulation Conference, 1976, pp.
877-884.
Krebs, H. Natural and Political Observations Made Upon the Bills
of Mortality, Madison, Wis.; Office of the State Demographer,
1982.
Levin, G. and E. Roberts, Dynamics of Human Service Delivery,
Boston, Mass., Ballinger, 1977. y
McCaffree,K., et.al. "Capital and the Reimbursement of the Costs
of Nursing Home Services", in V. Laporte and J. Rubin (eds),
Reform and Regulation in Long Term Care, New York, Praeger,
1979.
Postle, D. Catastrophe Theory, Fontana, 1980.
Poston, T. and I. Stewart. Catastrophe Theory and Its
Applications, London, Pitman, 1978.
Scanlon, W. and J. Feder. The Impact of Public Policies on the
Nursing Home Market, Report to the National Center for Health
Services Research, April, 1981, Report No. PB 82 - 115254.
Scapens, R., R. Ryan and L. Fletcher, “Explaining Corporate
Failure: A Catastrophe Theory Approach",J. of Business Finance
and Accounting, V. 8, No.1 (1981) pp. 1-26.
Smith, W. "Using Catastrophe Theory to Gain Insight Into
Consumer Purchase Decisions",Management Review, V.73, No.4
(1984), pp. 48-53.
Thom, R. Structural Stability and Morphogenesis, Reading, Mass.,
W. Benjamin, 1975.
Wilson, A. G. Catastrophe Theory and Bifurcation, Berkeley,
Calif., Univ. of Calif. Press, 1981.
Zeeman, E.C. “Catastrophe Theory", Scientific American, V.234,
No.4 (1976), pp. 65-83.
