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Title: Financing guaranteed renewable health insurance
Author: Robert D. Lieberthal, PhD
Affiliation: Jefferson School of Population Health, Thomas Jefferson University
Telephone: (215) 503-3852
Fax: (215) 923-7583
E-mail: [email protected]
Disclosure: This research was part of my dissertation. It was funded by an Agency for
Healthcare Research and Quality dissertation grant R36 HS018835-01.
Acknowledgements: I wish to thank my dissertation committee, comprised of Mark Pauly
(advisor and chair), Scott Harrington, Greg Nini, and Jessica Wachter for their feedback
on this work.
Title
Financing guaranteed renewable health insurance
Abstract Guaranteed renewable health insurance gives individuals long-term protection against
reclassification risk through a one-sided commitment. Insurers finance this risk,
managing the associated long-term liability through a contract reserve. The value of the
liability is uncertain because medical trend is highly stochastic. Insurers could manage
uncertainty about the value of the liability by investing contract reserves in correlated
assets to hedge medical spending growth. However, securities markets are probably
unable to fully hedge the risk of medical spending growth, and may not provide any
significant hedge for this important risk. A simple rule for investment of assets, utilizing
a diversified portfolio, is the best strategy for guaranteed renewable health insurance
reserves. New asset classes, whether created by public or private entities, may facilitate
risk management of stochastic medical trend for long-term health insurance contracts.
Keywords Guaranteed renewability; Medical spending growth; Cost curve; Healthcare finance;
Reclassification risk; Contract reserves
Introduction Individual health insurance coverage has long been guaranteed renewable, which
protected individuals against reunderwriting. Guaranteed renewable or ―time consistent‖
health insurance combined protection against current spells of illness and future
reclassification costs into one long-term contract (Pauly et al., 1995, Cochrane, 1995).
Consumers paid initial insurance premiums that are higher than the prevailing spot
premiums to get this extra protection. In return, insurance companies committed to
rerating based only on class experience, and to avoid individual reunderwriting.
Currently, the enactment of the Patient Protection and Affordable Care Act has
brought into question the use of required contract reserves for guaranteed renewability.
For example, insurers in North Carolina have been forced to refund reserves meant to
stabilize premiums that will not be needed after the PPACA comes into full effect
(Young, 2010). Insurers will continue to consider the effect of guaranteed renewable
insurance on their risk profile, as well as more general effects stemming from a risk pool
that ages, and becomes more expensive, over time. This is both because of the existence
of medical loss ratio (MLR) rules that may restrain the use of contract reserves, and
because of continuing demand for, and problems in, the long-term care insurance market
(Jost, 2010, Eldridge, Lynn, 2011). In these and other cases, insurers should charge front
loaded premiums, but the investment policy for those front loaded premiums has not been
well investigated. Determining how well front loaded insurance can be financed, as well
as determining which asset classes should be used to finance such insurance, is the
motivation of this study.
The actuarial mechanism for keeping low risk insureds in an insurance contract is
the contract reserve fund. Greater than spot market premiums flow into the reserve. The
reserve later cross-subsidizes the premiums of those who become high risk, allowing
them to pay actuarially favorable rates relative to the spot market without driving the low
risks out of the guaranteed renewable pool. To make the contract zero profit in
expectation, the reserve is calculated based on the shadow price of purchasing annual
renewal insurance for high types for the remaining term of premium protection specified
in the plan (Herring, Pauly, 2006). There have been also been allegations that high
premium growth for new insureds–duration rating–represents a violation of guaranteed
renewability and general protection against reunderwriting (Bluhm, 1993).
The value of the shadow benefits rises as future insurance becomes more
expensive and as medical trend becomes more unpredictable. The general level of
medical spending, or trend, is a key input assumption in determining the future cost of
medical spending (Bluhm, 2007). Health insurers could limit their exposure to rising
medical spending, for example through a pure indemnity arrangement, but in practice,
they do not because this exposes the insureds to more risk. It can be harder to limit future
benefits in health insurance contracts, since insured individuals want access to new
medical technologies. Retroactively removing previously allowable benefits could violate
the spirit or the letter of a guaranteed renewable or other long-term health insurance
contract. As a result, the value of the benefit in guaranteed renewable insurance is linked
to the rise in medical spending. However, insurers that charge adequately for prefunding
future spending growth could be charging rates that are unaffordable, or seem exorbitant,
when compared to spot rates.
The predictability of spending growth is a key driver of its effect on long-term
health insurance through the trend assumption. Guaranteed renewable premiums are
based on the expected future costs of insurance, which does include trend (Herring,
Pauly, 2006). While the trend is stochastic, the insurer still imputes the average expected
trend into the policy. The insurer may also factor the size of potential fluctuations into the
contract reserve. The economic fair price for the insurance could include a risk premium
for the additional risk the insurer is taking on, but in a competitive market with an
available hedge, this risk premium would not be added to the cost of the insurance.
In a setting with stochastic trend, the insurer also has to be concerned about the
credibility of the data used to predict future trends. The longer the time horizon for the
contract, the more the insurer wants to know about the longer term stochastic properties
of medical spending growth. The specific time series properties of spending growth
determine how to manage it with contract reserves. If each year's growth is a draw from a
distribution with noise, then gains and losses should balance out over time. The point of
reserves would be to cover shortfalls, especially if higher than expected spending
occurred in the early years of the contract.
If spending growth is serially correlated, then it is more likely that several years
of higher than expected growth could cause accumulated losses. In that case, the insurer
would be interested in above average asset returns, and would be willing to sacrifice
below average asset returns in the situation where spending growth was below trend for
several years. This could come from taking a long position in an asset that paid off more
when medical spending growth was unusually high, or a short position in an asset that
pays off less when medical spending growth is unusually high. Whether the correlation
between medical spending growth and returns is positive, negative, or zero, the time
series properties of trend should be factored into the reserve policy. Insurers should set a
policy that maximizes firm value or minimizes the probability of having a negative
reserve, i.e. ruin, rather than maximizing the value of the assets invested through the
contract reserve. The minimum probability of ruin that can be achieved may limit the
term of guaranteed renewable and other long-term forms of protection through health
insurance, making some risks uninsurable (Cutler, 1993).
Methodological background Separating trend from error is the first step in searching for a hedge for medical
spending growth. This means fitting the observed series of insured spending to a model. I
fit the spending growth time series to two models: a linear regression and an adaptive
expectations model. The linear regression model is designed to assess the predictability
of spending growth and the variables that might improve the fit of the regression model.
The adaptive expectations model separates the deterministic portion of trend, which is the
long run average trend assumption, from the stochastic portion of trend, which generates
risk for the insurer. The stochastic portion of the trend is then expressed as a prediction
error.
Prediction errors are used to determine if effective hedges exist. In the example of
commodities, an individual that enters into a futures contract that guarantees a set price
for the delivery of a commodity will not have an additional need to predict or reserve
against changes in the commodity price. Similarly for medical spending, if there were an
asset or group of assets that covary with the unpredicted portion of medical spending,
then they would be a useful hedge. The amount of reserves a health insurer would have to
set aside would be decreased toward the amount needed to prefund predictable increases
in medical spending. The higher the correlation between residual spending growth and
asset returns, the better the hedge. Such contracts have been attempted for insurance and
health insurance specifically, with limited success (Cox, Schwebach, 1992). There is no
similar model for asset returns, which are assumed to include all available information
(Fama, 1970).
The adaptive expectations model is specifically designed to generate prediction
errors and then find the correlation between errors and asset returns. The idea is that, for
medical spending growth, there is a long-term trend line and then errors around that trend
line. The errors arise as a disturbance term that is random and uncorrelated across time.
The size of errors around the trend line is not known, so deviations from the prior long-
term trend are factored into the long-term trend based on an updating factor. The
updating factor θ can range from 0 to 1, and is not known ahead of time. By estimating
the equation and varying the parameter θ, I can test the correlation between assets and
deviations from trend for a range of possible updating factors, giving the correlations
under different possible scenarios for how quickly the long-term trend in spending
growth is updated.
The underlying data generating function for medical spending growth has almost
certainly changed over time. The time since the last trend break is important for health
insurance risk because, aside from any particular model of medical spending growth is
the question of how long any relationship will persist. The problem is determining the
stationarity of the time series data, or whether there is a single consistent trend over time.
Whether the data available can answer these questions is an important part of how long
guaranteed renewable contracts could last. These issues are addressed further in the
Results section as part of the unit root test.
The investment problem The investment problem is to find a hedge that is appropriate for the specific
insurance liability. It is the role of reserves to manage unhedged risk, specifically the
asset investments for the contract reserves set up by the insurer. The size of the forecast
errors informs the size of the contract reserves under guaranteed renewability. It might
also inform the investment policy of the insurer. Medical spending growth is a shock that
is common across all policyholders, so managing stochastic medical trend is also a
service provided to policyholders if the insurer can implement a hedging strategy that is
too complex or costly for individuals. The goal of the insurance company managers is not
to maximize the value of assets, but to maximize the value of the firm. Managers may be
focused specifically on minimizing the probability of ruin, which is the probability that
liabilities exceed assets (Hipp, Plum, 2000). Hedging serves this objective by allowing
assets to serve as a buffer against liabilities.
I search for hedges across a broad set of assets that are based on Fama-French
portfolios. Broad equity and bond asset classes make hedging assets results generalizable.
Popular, broadly available asset classes give data with a long enough history to test
against the spending data series. I also utilize specific return data on healthcare and
healthcare subsectors, which allows me to test the proposition that healthcare assets may
be a hedge for liabilities arising from medical spending growth (Jennings et al., 2009).
Almost no hedge is perfect, so there may be some gap between what predictions
and hedging can do and the size of medical spending growth risk. The size of the gap is
also important, as it would determine how important it is to try new assets, examine
policies that create new assets, or measure the size of risk that cannot be managed with a
hedging investment policy.
There is also a point where the risk becomes uninsurable to an insurer, and
possibly to any entity. One example would be investments with large transaction costs or
large leverage requirements. Contracts where the class average guaranteed extends for a
large number of years, or public insurance programs where a government commits to
keep a health insurance program unchanged for an extended period, are two examples.
The issue of insurability is tied to the availability of hedges, whether directly for the
insurance company or indirectly for the government that cannot bear too large of a risk.
Estimation methods In my model, insurance companies write contracts indexed to the total nominal
level of medical spending. As a result, the medical spending growth that I am explaining
with the regression is nominal medical spending. Insurance companies take trend as a
given, insure the portion that is attributable to guaranteed renewability, and pass the rest
on to insureds to the extent allowed through prospective pricing.
I consider two ways that insurance companies can utilize data from securities
returns to improve the management of risk arising from stochastic medical trend. One is
informational, as an explanatory variable that improves the prediction of trend. Then,
returns could be a hedge, or could simply be a tool to improve setting the deterministic
trend assumption when pricing insurance. I discuss this in the ―Returns as explanatory
variables‖ subsection below. Second, insurance companies could try to model the long
run average rate of trend, and see if securities returns can help explain forecast errors, or
variations from the trend line. In this case, securities are not used to improve the forecast,
but only to provide a hedge. I discuss this in the ―Adaptive expectations‖ subsection
below.
Returns as explanatory variables
I assess the year-on-year predictability of per capita insurer spending growth by
regressing current spending growth on lagged spending growth. My regression equation
with only lagged spending growth as an explanatory variable is:
1-t10t trendmedical trendmedical
Equation 1: Basic regression for medical spending growth
Given this model, insurance companies can then add variables that would improve
the predictability of medical spending growth. For example, general price inflation will
tend to increase nominal medical spending. The returns on securities could be one such
explanatory factor, either due to direct links (e.g. higher drug profits come from higher
spending and raise the price of pharmaceutical stocks) or indirect links (wealth effects
increase medical spending and are reflected in overall market returns). In that case, a
vector of variables v with an associated vector of coefficients Β can represent all of the
other explanatory variables.
v1-t10t trendmedical trendmedical
Equation 2: Forecast of medical spending growth with additional regressors
Adaptive expectations
I use a simple adaptive expectations model to determine the long-term expected
rate of nominal medical spending growth. The long-term rate of growth is equal to the
prior long-term rate of growth plus a linear ―adjustment‖ for the prior difference between
the expected rate of growth and the experienced rate of growth. The updating equation is:
ttD
tD
tDtDtDtD
at timegrowth of rate dexperience theis )(
tat timegrowth of rate termlong theis )(
where
))1()1(()1()(
Equation 3: Adaptive expectations updating equation
originally proposed by Bodie, 1976.
The updating factor θ for the adjustment ranges from 0 to 1. θ is not known a
priori. I calculate estimates of tD , the expected rate of growth, over a range of values for
θ. The choice of updating factor determines the time series of forecast errors in the
model. )()()( tDtDtd are the unanticipated shocks that result, and differ by choice of
θ. Therefore, this model shows the size of shocks for a range of possible updating factors.
The test of the ability of assets to hedge medical spending growth is the effect of
spending shocks on excess return. I use the following specification:
)()(
where
)()( 10
(t)DtRtR
tdtR
e
e
Equation 4: Test of effect of spending shocks on securities returns
originally proposed by Bodie, 1976. In my case, )(tRe is the excess return, that is, the
return to assets in excess of the long-term trend in medical spending.
I use this method as a test of the use of securities to hedge spending growth. If the
coefficient on 1 is significant, then the return index used to calculate )(tRe is a good
hedge. The sign of the coefficient indicates whether the hedging position is long or short.
There may be positive coefficients for some assets, such as healthcare stocks, if there is a
positive correlation between above trend spending growth and returns to healthcare
securities. There may be negative correlations, say to the overall market, if above average
healthcare costs depress profits of most public companies.
Data The National Health Expenditure Survey tabulates data on total and per capita
medical spending. CMS also surveys health plans to tabulate medical spending per
insurance plan enrollee. The data includes per capital spending by private plans and
Medicare, and further splits the data into all benefits and common benefits provided by
both plans (for example, Medicare did not offer drug benefits until 2003 (Centers for
Medicare and Medicaid Services, 2011)). The data for per capita insurer expenditures is
similar, growing at rates of 7-8% over the period 1982-2008 (see Table 1).
Private insurance growth rates are substantial with a high degree of variance.
There is not a single year of negative spending growth in the data. The advantage of the
data is that it focuses on the spending for insured lives, which will allow me to evaluate
hedges for health insurers. Part of the risk I want to measure is the portion of trend due to
with general changes in the type and quantity of medical care delivered, which is
reflected in the insured spending time series. One disadvantage is that it the measure of
average spending is aggregated across many types of private health insurance plans. The
goal is to measure and find a hedge for a common shock that should affect all types of
individual health insurance.
All benefits Common benefits
Insurance type Medicare Private Medicare Private
mean 7.08 7.91 6.08 7.33
sd 3.50 3.56 2.83 3.22
skewness 0.07 0.35 0.59 0.16
kurtosis 3.76 2.22 4.19 2.09
min -1.50 1.87 0.08 2.18
max 15.21 15.33 14.1 13.69
p25 4.90 4.89 4.38 4.84
p75 8.96 10.39 7.37 9.62 Table 1: Per capita nominal insurer expenditures 1982-2008, rate of change (%)
I show initial statistics on bond returns in Table 2. For the risk-free rate, I use one-
month Treasury bills. These are a standard in the literature because they are U.S.
government securities of short duration, which eliminates default risk and inflation risk.
The data comes from the Fama/French factor for risk-free rates (the factors are described
in Fama, French, 1993, and are available from Fama, French, 2010). The return on bonds
that I use as investments to hedge growth comes from ten-year government bonds and
Moody‘s index of AAA rated corporate bonds. Both are total return indices, and so
contain interest and principal payments. The data come from the Global Financial Data
Total Return database (Global Financial Data, 2011).
I use the Fama/French factors to generate returns for the stock market, health care
stocks as a whole, and health care subsectors stock returns (Fama, French, 2010). The
Fama/French returns are value weighted and cover stocks on the major U.S. exchanges.
The negative skews show the fact that shocks in the distributions of stock returns are
often negative (Campbell, Hentschel, 1992). Health sector returns may have a high beta–
they have higher mean returns than the market but also higher variance (see Table 3).
Bond class
Returns 10 Year
Government Bonds
AAA Corporate
Bonds
Risk-Free Rate
mean 0.84 0.88 0.42
sd 2.42 1.91 0.21
skewness 0.22 0.52 0.43
kurtosis 3.75 5.54 3.22
min -6.94 -4.73 0.02
max 8.64 8.55 1.13
p25 -0.65 -0.13 0.28
p75 2.35 1.87 0.54 Table 2: Bond monthly nominal returns (%, continuous log basis)
Equity class
Market Health Health
services
Medical
equipment
Drugs
mean 0.91 1.12 0.83 1.05 1.21
sd 4.48 4.83 6.92 5.29 5.01
skewness -0.91 -0.19 -0.36 -0.50 -0.10
kurtosis 6.21 4.24 4.75 4.85 3.84
min -22.54 -20.47 -31.50 -20.56 -19.10
max 12.85 16.54 20.49 16.31 16.37
p25 -1.70 -2.03 -3.51 -1.82 -1.89
p75 3.91 4.00 5.11 4.46 4.38 Table 3: Stock monthly nominal returns, 1982-2008 (%, continuous log basis)
Results
Modeling of spending growth
Both total spending and insurance premium growth are strongly serially
correlated. The growth rate in total medical spending is correlated from year to year in a
way that GDP growth is not (see Figure 1). Premium growth per enrollee in private plans
is also serially correlated. Using prior year trend alone explains 51% of the variation in
the next year's spending, using only data from 1970-2008, as shown in Figure 2. The
predictability in annual data suggests that it may be possible to forecast future medical
spending growth. If the data were predictable enough, a hedge would not be needed.
Figure 1: Growth rate of nominal GDP and nominal medical spending per capita
Hedging growth with asset returns requires a separating medical trend from
prediction errors. To the extent that growth predictably increases, insurers prefund future
medical losses with actuarially fair premiums. Simple correlations of nominal asset
returns and total medical inflation are instructive. In Table 6, I show the correlations for
the high frequency time series and securities returns over the 1982--2008 period. The
correlations show that medical inflation is most correlated with the risk-free rate (short-
term Treasury bills), general inflation, and health care services companies. It also shows
that stocks are not highly correlated with inflation, despite stocks‘ known relationship
with inflation (Bodie, 1976). This analysis shows the finding a hedge with the proper
relationship. By partialling out the predictable portion of medical spending growth, the
forecast errors, or surprises, remain. It is buffering against these surprises that hedging is
important. For that reason, I analyze regression results in addition to raw correlations.
The time series properties of medical spending growth suggest that there is not
one consistent trend rate1. For example, a unit root test for the period 1971-2008 shows
that there is almost certainly a unit root in the insured spending data, while there may or
may not be a unit root in the change in spending time series (see Table 4 and Table 5). A
unit root test for the period 1982-2008 shows that there is almost certainly a unit root in
the total spending data. This may be because of U.S. specific factors, such as the
managed care revolution (Strunk et al., 2002), or a common factor across developed
countries such as Baumol‘s ―cost disease‖ (Hartwig, 2008). While I can reject the
possibility of a unit root in the Medicare change series, I cannot strongly reject the
possibility of a unit root in the private spending change series. As a result, I will use the
errors in forecasting the change in privately insured spending as the goal for hedging.
1 That would make a hedge more valuable if the nonstationarity in medical trend matched the
nonstationarity in asset returns, but that is a consideration beyond the scope of this study.
Figure 2: Nominal insured medical spending per capita, year on year rate of change
Time series Test statistic p-value
Spending per enrollee
Medicare
All benefits 5.97 >0.99
Common benefits 5.60 >0.99
Private insurance
All benefits 7.96 >0.99
Common benefits 8.65 >0.99
Change in spending
Medicare
All benefits -3.08 0.03
Common benefits -2.37 0.15
Private insurance
All benefits -2.34 0.16
Common benefits -2.11 0.24 Table 4: Unit root test of per capita nominal insurer expenditures, 1971-2008
Time series Test statistic p-value
Spending per enrollee
Medicare
All benefits 3.79 >0.99
Common benefits 2.69 >0.99
Private insurance
All benefits 4.34 >0.99
Common benefits 5.04 >0.99
Change in spending
Medicare
All benefits -3.63 <0.01
Common benefits -3.54 <0.01
Private insurance
All benefits -2.56 0.10
Common benefits -2.34 0.15 Table 5: Unit root test of per capita nominal insurer expenditures, 1982-2008
Variables Stock
market
Health
stocks
Health
services
stocks
Health
equipment
stocks
Drug
stocks
1 month
govt
bonds
10 year
govt
bonds
AAA
corp
bonds
General
inflation
Medical
inflation
Stock
market
1.000
Health
stocks
0.805 1.000
Health
services
stocks
0.032 0.032 1.000
Health
equipment
stocks
0.719 0.772 0.024 1.000
Drug
stocks
0.781 0.993 0.030 0.714 1.000
1 month
govt
bonds
-0.012 0.012 0.654 0.003 0.014 1.000
10 year
govt
bonds
0.105 0.146 0.136 0.119 0.146 0.126 1.000
AAA corp
bonds
0.188 0.171 0.150 0.148 0.168 0.102 0.595 1.000
General
inflation
0.009 -0.034 0.204 -0.007 -0.037 0.259 -0.069 -0.108 1.000
Medical
inflation
-0.036 -0.087 0.263 -0.074 -0.087 0.431 0.032 0.035 0.342 1.000
Table 6: Correlations of monthly inflation and nominal returns, 1982-2008
First, I examine the amount of spending growth I can explain. Over the entire
period my data covers, 1971-2008, one year lagged spending growth explains roughly
half of the variation in current year's spending growth. Over the more recent period 1982-
2008, prior growth is less predictive of current growth, with an adjusted R2 of 39% (see
Table 7 and Table 8). The lower predictability is not a function of the variance of
spending growth, which has remained constant relative to the rate of spending growth
(which has fallen constantly over the last 40 years). However, for the more recent period
adding spending growth from two years ago improves the prediction of recent spending
growth (adjusted R2 of 43%) while slightly reducing the adjusted R
2 for the entire time
horizon. Dropping lagged spending growth leads to much less predictability. This
suggests that a large portion of the annual growth in medical spending cannot be forecast.
With multiple years of trend necessary for guaranteed renewable health insurance,
accurate forecasts beyond the long run require additional political or social factors or
general equilibrium models2.
Variable Coefficient SE t-statistic p-value 95% CI
min
95% CI
max
constant 2.50 1.30 1.92 0.06 -0.14 5.14
Spending
lag 1
0.72 0.12 6.07 <0.01 0.48 0.96
N 38
F-test <0.01
Adj R2 0.49
Root MSE 3.26 Table 7: Per capita nominal insurer expenditures regressed on lagged expenditures, 1971-2008
2 For examples of how to produce longer term forecasts, see thee Society of Actuaries technique for
modeling long run healthcare cost trends (Getzen, 2007), or the estimates produced by the CBO for their
budgeting purposes (Congressional Budget Office, 2010).
Variable Coefficient SE t-statistic p-value 95% CI
min
95% CI
max
constant 2.58 1.29 2.00 0.06 -0.08 5.24
Spending
lag 1 0.64 0.14 4.50 <0.01 0.35 0.93
N 27
F-test <0.01
Adj R2 0.43
Root MSE 2.70 Table 8: Per capita nominal insurer expenditures regressed on lagged expenditures, 1982-2008
I can improve the prediction of current spending by using lagged medical inflation
and physician office employment. Using either variable in concert with two lags of
medical spending produces an adjusted R2 of 49% in the recent period. The coefficients
on lagged employment growth and inflation also have lower p-values. The best model for
predicting spending growth for the entire period is the model with two lags of spending
growth and current medical inflation and physician office employment growth. While
physician office employment is not significant, it improves the fit of the model, so I
chose to continue to include it as a predictor. The best model in the more recent 1982-
2008 period is the one with two lags of spending growth and lagged physician office
employment growth (see Table 9). There is a substantial remaining error term to be
hedged using this model.
Variable Coefficient SE t-statistic p-value 95% CI
min
95% CI
max
constant -0.09 1.57 -0.06 0.96 -3.35 3.17
Inflation 1.10 0.40 2.73 0.01 0.26 1.93
Premium growth
Lag 1 0.62 0.16 3.84 <0.01 0.29 0.95
Lag 2 -0.35 0.15 -2.26 0.03 -0.67 -0.03
MD office
Lag 1 0.66 0.42 1.59 0.13 -0.20 1.53
N 27
F-test <0.01
Adj R2 0.63
Root MSE 2.16 Table 9: Per capita nominal insurer expenditures regressed on multiple variables
As a first pass approach, I added asset returns to try to improve the fit of these
models as part of vector B in Equation 2. Asset returns do not improve the prediction of
current spending growth. Adding the risk free, the market return, health sector and
subsector returns, one or two period lagged asset returns do not improve on the prediction
of spending growth. The results hold across all of the asset classes I use for the recent
period 1982-2008. There are two asset classes with significant results (p-values between
0.01 and 0.05) with lags: drugs and medical equipment. The results are insignificant over
the longer 1973-2008 time horizon. All of these results point to the need for more
sophisticated methods that focus on errors to try to hedge aggregate medical spending
growth.
There are two main takeaways from this approach. One is that, significant work
has been done to identify predictors of medical spending growth. My work builds on that
prior literature, and finds that these previously identified predictors, and models, produce
potentially useful forecasts of medical spending growth. The second takeaway is that
securities market returns do not contain additional information that is not already
included in other macroeconomic regressors for predicting medical spending growth.
Reasons to expect that securities market data might be informative include the unique
incentives that traders have to find and utilize information that is predictive of future
economic trends, especially given the large share of the economic consumption for
healthcare. Reasons to doubt that securities market data might be informative include
prior results that show that the stock and bond markets may not reflect the real economy,
or may not do so in a way that is predictive (Harvey, 1989). It may also be that while the
securities market does not explain the growth rate, it explains unexpected changes in the
growth rate. This motivates my use of an adaptive expectations model in the next section.
Adaptive expectations results
The adaptive expectation results for a grid of updating coefficients ranging from
0.10-1.00 are in Table 10 and Table 11, and I summarize the prediction errors in Table
12. The expectation of long-term medical spending growth has come down as the rate of
growth in spending has decreased. For 2009, the predicted spending growth rates range
from 3-7% depending on the updating parameter θ3. The reason is the strong moderation
in spending increase rates from over 11% in 2002 to 4.5% in 2008. The smallest updating
parameter (θ=0.1) gives the smallest proportional variance.
3 The actual figure for 2009 was 6.9% (see
https://www.cms.gov/NationalHealthExpendData/downloads/tables.pdf).
θ
Statistics 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
mean 10.53 9.47 9.03 8.80 8.65 8.55 8.48 8.42 8.38 8.35
sd 2.19 2.57 2.72 2.85 3.01 3.16 3.32 3.46 3.60 3.73
skewness 0.22 0.42 0.42 0.36 0.33 0.32 0.33 0.34 0.34 0.33
kurtosis 1.59 1.86 1.97 1.89 1.80 1.76 1.79 1.88 2.02 2.19
min 7.52 6.32 5.49 4.98 4.64 4.47 4.38 3.50 2.66 1.87
max 14.19 14.35 14.37 14.34 14.35 14.44 14.62 14.86 15.16 15.49
p25 8.40 7.19 6.74 6.33 6.05 5.46 4.99 5.07 5.06 4.98
p75 12.22 11.61 11.71 11.21 11.28 11.63 11.29 10.96 10.66 10.57 Table 10: Adaptive expectations average rates for per capita nominal insurer expenditures, 1982-2008
θ
Statistics 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
prediction 7.12 5.88 5.24 4.72 4.32 4.04 3.84 3.7 3.6 3.53 Table 11: Adaptive expectations forecast rates for per capita nominal insurer expenditures, 2009
θ
Statistics 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
mean -2.62 -1.57 -1.13 -0.89 -0.74 -0.64 -0.57 -0.52 -0.48 -0.44
sd 3.21 3.29 3.27 3.22 3.16 3.10 3.05 3.01 2.99 2.97
skewness -0.23 -0.13 0.02 0.14 0.22 0.28 0.33 0.36 0.38 0.41
kurtosis 3.65 3.91 4.10 4.41 4.75 5.01 5.10 4.99 4.76 4.48
min -11.27 -10.51 -9.86 -9.34 -8.96 -8.66 -8.41 -8.19 -7.97 -7.73
max 3.70 5.48 6.76 7.60 8.10 8.33 8.33 8.13 7.76 7.21
p25 -3.94 -3.23 -2.64 -2.69 -2.45 -2.32 -2.27 -2.01 -2.31 -2.46
p75 -0.56 0.81 0.71 0.89 1.03 1.04 0.99 0.92 0.96 0.99 Table 12: Adaptive expectations errors for per capita nominal insurer expenditures, 1982{2008
I regress excess returns to the overall market, health care, and health care
subindustries on the error term for the entire and recent periods (see Equation 4). I used
the full range of updating factors from 0.1 to 1.0. I searched over ten possible updating
factors across eight asset classes (nine counting general inflation, which can be an asset
class via TIPS bonds). None of the coefficients were statistically significant when
factoring in multiple comparisons. The results show that unanticipated shocks in medical
spending either do not feed through into contemporaneous nominal asset returns, or these
effects cannot be detected using this data. I discuss the implications in the final section of
this paper.
I also used lagged asset returns, which are generally insignificant as well. Total
and excess returns to the market lagged one year for small θ (0.1 or 0.2) are both
correlated with errors, as are corporate bond returns both in total (all θ) and excess
returns (θ≤0.6). Excess returns to short-term government bonds (θ=0.1, 0.9, 1.0) and long
government bonds (θ=0.1, 0.2, 0.3) are also correlated with the shocks I generated for the
spending growth time series. All the correlations are also negative. This suggests that, as
in Bodie, 1976, above average medical spending growth may be bad for stock market
returns but with some lag. The results would also indicate that stock returns are a leading
indicator of the unpredictable portion of medical spending growth, which is important for
policy but does not make for a useful hedge.
There are two main takeaways from this approach. One is that, significant work
has been done to identify deviations from trend in medical spending growth. Finding
when the trend will change, especially in an autoregressive time series, is important. It
may also be that a more complex, forward looking expectations setting process is needed
in order to admit data from securities returns. It may also be that the correct variables for
finding unexpected changes in medical spending growth are as difficult to model as
medical spending growth itself, such as unexpected changes in GDP growth, or difficult
to model entities such as the ―resistance point‖, when individuals in aggregate wish for
medical spending growth to stop (Getzen, 2007). In either case, securities returns will not
contain the information needed, and may even be lagging indicators of certain types of
macroeconomic variables.
Discussion If there are no good hedging assets for medical spending growth, then the ideal
investment allocation is a diversified portfolio. The portfolio would not differ from that
of any line of insurance where there is no available hedging asset, as is the case with
longevity hedges for annuities (Bauer et al., 2010).The characteristics of the investments
would then be determined only by the duration and convexity of the guaranteed
renewable liability. The timing of payments for guaranteed renewable insurance has not
been extensively studied (for an initial investigation, see chapter 4 of Lieberthal, 2011 or
Lieberthal, 2012). The basic actuarial idea is that expected payments will be made more
quickly for less healthy populations, while expected payments are more likely to be in the
future for more healthy populations. Otherwise, guaranteed renewable health insurance
looks like other lines of multiyear insurance; for example, lower interest rates increase
the duration of the liability. Financial arrangements should be used to match the timing of
premiums from the contract, which are generally frontloaded, with the claims, which are
generally back loaded.
The other general principle to consider is the risk appetite of the insurance
company. Insurers that are more risk averse may hold safer assets and have safer
portfolios, while other insurers may have riskier investment strategies. Guaranteed
renewable insurance as a particular product should not change that broad strategy. One
potential future implication of the Patient Protection and Accountable Care Act is to draw
more people into the insurance pool and induce less switching, or churn, in health
insurance. If that takes place, insurers may be able to increase their exposure to riskier
assets, whether through longer duration bonds or through equities in order to finance
guaranteed renewable health insurance.
Conclusion The newly enacted health reform law will have two effects that will change the
applicability of my results. First, the law may change the ability of insurers to create
underwritten pools of lives for the purposes of guaranteed renewability. It will also affect
the ability of insurers to price their premiums consistent with guaranteed renewable
principles. Other systems that have moved to a similar mandate based insurance scheme,
like Germany, have a significant, stable, market for guaranteed renewable health
insurance (Hofmann, Browne, 2010).
There is a second, indirect, potential effect of health reform. The law may change
the time series properties of spending growth, returns on financial assets, and the
relationship between these variables. Bending the cost curve was an explicit goal of
health reform, so the effect of the PPACA on future spending growth is an intended
consequence of the law. The effect of the law on healthcare asset returns is an anticipated
consequence, but there could be an indirect effect on other financial asset returns given
that healthcare is such a large segment of the entire economy. Finally, the relationship
between spending growth and asset returns is another unintended consequence of health
reform. It is possible that the PPACA will cause financial asset returns to become more
tied to the growth in medical spending. I consider the possibility a starting point for
future research in this area. Any new expansion by health insurers into the nongroup
market will have to consider this possibility, and set their investment policy for contract
reserves accordingly. Any required contract reserves may still be limited by new medical
loss ratio rules, which are still being developed.
Finally, I conclude that there is no ideal hedge for medical trend, because there is
no negatively, or positively, correlated asset. My next step, in future work, will be to
measure the gap between a diversified investment portfolio and the unpredictable
component of medical spending growth. One consideration I have not considered in this
paper is what the beta of that portfolio should be. In related work, I consider the effect of
the health of the population on the duration and convexity of claims (Lieberthal, 2012).
That work suggests that, for less healthy populations, the portfolio duration should be
lower in order to match the timing of claims, which would likely correspond to a lower
beta portfolio. Health insurers that wish to manage front loaded contracts, such as
guaranteed renewability and long-term care insurance, or have aging populations with a
higher spending profile, will be exposed to stochastic medical spending growth. They
will need to consider the effect of medical trend, asset returns, and the interaction with
population health variables such as the health of their insured populations in order to set
their investment policy.
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