September 2006

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Information asymmetry, insurance and the decision to hospitalize

September 21, 2006 in Academic Articles, Health Insurance, Supply of Medical Services | Permalink

There is a dynamic relationship between generalists and specialists.  Currently, 4.5% of visits to PCPs result in a referral.  A RAND study and my own investigation of the 1998-1999 Community Tracking Survey show that about 10% of individuals are hospitalized at least once each year.  How should we model the decision patients face between generalist and specialist care.

Model with perfect information 

This is the problem tackled by Blomqvist and Léger in their 2005 paper in the Journal of Health Economics.  They have a simple model:

  • max_{q,J} U(X,H); J=G or S
    • X=I-Cj(q)-
    • H=q-

Consumption is represented by ‘X‘, which depends on income ‘I’; the copay rate , the cost of the procedure Cj(q) and the insurance premium . Health (‘H’) is a function of the amount of medical services chosen (‘q‘) and the underlying health of the person ().  This variable is unknown ex ante, but its distribution F() is known.  The cost of the procedure depends on whether the patient chooses a generalist (j=G) or a specialist (j=S).  For each provider type, we have the following first order condition:

  • U_x*(-C’j(q)) + U_h=0

The authors go on to show that there is a critical value * above which the individual chooses a specialist and below which the individual chooses a generalist.  This critical value will increase when the coinsurance rate () increases, since the individual as the individual bears more and more of the cost, they will prefer less dear services.  In proposition 3, the authors claim that consumers will choose an inefficiently small * if they are insured.  In other words, they will demand too much specialist relative to generalist care.  The expected value of the utility function ex ante is:

  • EU=Int_{} U[I-Cj(q())-,q()-]dF()

If the consumer increases the critical value ex post, we see that:

  • dE/d* = V_S(*,)-V_G(*,)+(dE/d)(d/d*)
  •            = 0 +(dE/d)[C_G(q)-C_s(q)](1-)>0

Since dE/d<0 (since increasing the insurance premium ceteris paribus will decrease utility) and [C_G(q)-C_s(q)]<0 (since it is assumed that specialist services are more expensive than generalists services, we can show that the equation above is positive as long as the copay rate is less than 100%.  This is the mathematical representation of moral hazard. 

Model with imperfect information

The new model Blomvqist and Léger derive assumes that patients know approximately how sick they are, but only the doctors can know  with certainty.  From the paper:

“…assume that the distribution F() from which illness severity is drawn is bounded by _o and _L and is subdivided into L intervals [_{l-1},_l] l=1,…L.  Although the patient does not observe the exact value of , we assume that he or she can distinguish between these classes of illnesses; that is, the patient knows in which interval his or her true  is located.”

A doctor must offer an amount of treatment so that for q(_{l-1})>q>q(_{l}).  If the doctor does not offer services within this range, the patient will know the doctor is defrauding them by under- or over-providing services.  Fee for service doctors still have an incentive to choose the maximum amount of services within the interval, q(_{l}), and capitation/salaried doctors still have an incentive to provide the minimum amount of services within the interval, q(_{l-1}).  The paper continues stating that a managed care contract which specifies different cost sharing parameters _l for each interval will yield a higher expected utility than the optimal conventional contract of the form  (,()).

Analysis

This paper gives very intuitive conclusions and has straight-forward models.  Like most health economics models, this one greatly simplifies how medical service provision works.  There is only on dimension upon which health can vary and the degree of physician specialization divided into only two discrete categories (i.e.: specialists and generalists).  The model claims that appropriately written managed care dominate traditional contracts, but the model does not take into account the cost of information collection needed to correctly establish the copay rate for each of the L subintervals.  While this paper will not solve the problems of the medical field, it does put another simple yet insightful model into the healthcare economist’s toolbox. 

Blomqvist, Åke; Léger, Pierre Thomas (2005) “Information asymmetry, insurance and the decision to hospitalize” Journal of Health Economics, Vol 24(4), pp. 775-793.

Genius: A non-profit drug company wins a MacArthur Foundation Award

September 20, 2006 in Current Events, Pharmaceuticals | Permalink

The so-called genius awards (actually called the MacArthur Foundation fellows) are given to 25 individuals based on “their creativity, originality, and potential to be significant contributors in their fields.”  Recipients receive $500,000 over five years with no strings attached.  One of the recipients which interests this blog is Victoria Hale (bio).  She is a pharmaceutical entrepreneur who started a non-profit drug company to treat third world diseases.  NPR’s Marketplace ran an interview with Ms. Hale yesterday and below is an excerpt:

Hale: We have been funded very generously by the Bill and Melinda Gates Foundation to date. And how will we keep it going is the question. We have a challenge because of the budget size of our Research and Development program. So we have a couple of different approaches. One is to continue with philanthropy, revenues on products that are sold in private markets in the developing world, or to travelers in the West, let’s say for diarrhea or malaria. And we also are speaking with financial advisers, friends and colleagues about some creative ways to fund a nonprofit organization.

Ryssdal: What has the reaction of the more-established pharmaceutical industry been to your work? 

Hale: Early on, if we go back to the year 2000, we heard concepts and phrases like, “What is this about? What are you trying to do? And what markets are you going after? And how can you develop drugs with few people and with philanthropy? We don’t understand.” Then slowly, over time, as we began to do our work, and as the word spread that there really needs to be another organization, another set of organizations that address diseases of people who are at the bottom of the pyramid, slowly we’ve become quite accepted and are currently negotiating partnerships with a large number of large pharmaceutical companies.

Ms. Hale’s company–named the Institute for OneWorld Health–has worked primarily in India to date.  If you would like more information on her company or have an inclination to donate to their organization, visit the OneWorld Health website.

Disproportionate Stratified Sampling

September 19, 2006 in Econometrics | Permalink

Many data sets that social scientists come across use disproportionate stratified sampling. If a subpopulation is small, the survey designers may want to oversample this group. For example, in the Survey of Income and Program Participation (SIPP) poor individuals are oversampled and in the Community Tracking Study (CTS) uninsured individuals are oversampled in order to give more precision to the estimates made for these groups with a smaller population. Below, is a brief explanation of how to work with a disproportionate stratified data set.

Simple Example (from a Napier University website)

Lets us imagine a town which has 1200 rich people and 2500 poor people. Due to budget constraints, the survey designer samples 100 people from each of the two strata (200 people total). The sampling fraction for the rich is .08333 (100/1200) and for the poor is .04 (100/2500). The weights to be placed on each observation is simple just the inverse of the sampling fraction; thus the weights are 12 for the rich and 25 for the poor.

In the example above, suppose the mean household income in the poor areas was £12,000 and that in the rich areas was £25,000, then the weighted mean would be

[100x £12,000 x (w=25) +100 x £25,000 x(w=12)] ÷ (100×25+100 x 12) = £16,216.20.

An unweighted mean here would just be £18,500, so we can see that the weighting has corrected the fact that the sample has too many rich households.

Econometrics (see Wooldridge pp. 590-598)

Here is how Wooldridge explains variable probability sampling:

  1. Draw an observation w_i at random from the population
  2. If w_i is in stratum j, toss a (biased) coin with probability ‘p_j‘ of turning up heads. Let h_{ij}=1 if the coin turns up heads and zero otherwise.
  3. Keep observation i if h_{ij}=1; otherwise leave out of the sample.

A weighted M-estimator would be:

  • min _{β} SUM_{i=1 to N} [p_{j_i}]^{-1}*q(w_i,β)

Here q(w,β) is the objective function that is chosen to identify the population parameters β_o. In the OLS case, q(w_i,β)=x*(y-xβ). The asymptotic variance matrix for the linear model is:

  • [SUM_i p^{-1}x'x]^{-1} [SUM_i p^{-2}(u^2)x'x] [SUM_i p^{-1}x'x]^{-1}

where all variables are to have subscript i‘s except p, since p=p_{j_i}.

Stata

A simple and clear example of how to use weights in a stratified sample can be found at the UCLA Academic Technology Services website (Stata FAQ: How do I use the Stata survey (svy) commands?“). There are three main variables which need to be definied.

  1. The primary sampling unit (psu) is the lowest unit of observation, usually either an individual or a household identification number. In the econometric section above, psu’s are indexed by the letter i.
  2. The strata are the groups into which the data set is divided. The strata are indexed by the letter j. In the first example above, there are two strata: rich households and poor households.
  3. The sampling weight is defined as the inverse of the psu’s probability of selection.

To program this into stata, if the we would write:

  • svyset [pweigh=wt], psu(house) strata(eth)

Here the psu is the variable house, the strata are categorized by eth (a variable for the ethnic group) and the weight is the variable wt. To run a weighted least squares regression (WLS), you would simply type:

  • svy: regress y x1 x2 x3

and the appropriate weighting will occur.

The upcoming stock market crash?

September 18, 2006 in Economics - General | Permalink

In 5 years, the oldest baby boomers will hit 65 years old.  As the boomers begin to retire, this enormous cohort will start to sell off their financial assets in order to finance consumption in their non-working years.  One begins to wonder if there will be a stock market crash since equities demand may drop significantly. 

Stock Market crash: YES

  • Lower demand for equities will depress the price.  The U.S., EU and Japan make up about 50% of the world economy in purchasing power parity terms and almost 80% of the world economy in official foreign exchange terms.  All of these countries are facing an aging population.  It is unlikely that the developing world will be able to save the necessary capital to keep equity prices propped up.
  • Brooks (2002) believes that as people age, they will seek less risky investments.  Thus they will shift from stocks to bonds.  If this were to occur on a large scale, the phenomenon would drive down the price of equity.
  • Because of less efficient capital markets, money from economic growth in Latin America and Asia will not be invested in U.S. and European stocks on a large scale.  Higher transaction costs may convince developing world investors to keep their money invested at home. 

Stock Market crash: NO

  • In open economies, stock market returns should equalize across countries.  If investors are foresighted, then any future decrease in equity demand is already priced into the current stock valuations. 
  • Capital from economic growth in Latin America and Asia will be invested in U.S. and European stocks, thus keeping their prices high. 
  • Most people do not sell off their assets during retirement:
    • Poterba (2001, 2004) analyzes the empirical relationship between an aging population and the prices/returns for US stocks using the Survey of Consumer Finances (SCF).  He finds that financial assets peak to $32,000 at age 55 and fall to $25,000 by age 75. This means the average investor sells $350 of financial assets per year, a small amount.
    • According to Mitchell, et al. (2006), median retirement wealth in the US was about $340,000 in 1992.  Of this amount, however, 40% comes from owner-occupied housing and defined benefit pension, and another 40% comes from Social Security benefits.  We see that little of the savings of the majority of individuals comes in the form of financial assets. 

Mitchell, Olivia; Piggott, John; Sherris, Michael; and Yow, Shaun; (2006); “Financial innovation for an aging world” NBER Working Paper No. 12444.

Brooks, Robin (2002); “Asset-market effects of the baby boom and Social-Security reform,” American Economic Review, Vol 92(2), pp. 402-406.

Poterba, James (2001) “Demographic Structure and Asset Returns,” The Review of Economics and Statistics Vol 83(4), pp. 565-584.

Poterba, James (2004); “The impact of popluation aging and financial markets,” NBER Working Paper, MIT.

 

Phree Trade for Pharmaceuticals

September 15, 2006 in Current Events, Pharmaceuticals | Permalink

The Envisioning 2.0 (“Drug Importation“) speaks to the fact that the FDA has consistently tried to prohibit the importation of drugs from abroad, despite the fact that drug importation has broad popular support.  Further the post cites a USA Today report which says that the US (but not Canada) has a serious drug counterfeiting problem. 

Moral hazard, adverse selection and health expenditures: A semiparametric analysis

September 15, 2006 in Academic Articles, Health Insurance | Permalink

Moral hazard and adverse selection are ever-present problems in the health insurance market.  Identifying their existence and their magnitudes is difficult.  Most of the papers presented in this blog have used a reduced form approach [see Finkelstein, McGarry (2003) and Bhattacharya, Vogt (2006)].  Today we will look at a paper by Bajari, Hong and Khwaja where the authors use a structural approach.

Model

The authors set up a two period model.  In the first time period the individuals choose the level of insurance; in the second period they choose a level of medical expenditures ‘m‘.  The individuals are assumed to have a separable utility function as follows:

  • U(c,m-q;g)=(1-g1)^{-1}*c^(1-g1) + g2(1-g3)^{-1}*(m-q)^{1-g3}
  • c=y-p-z(m)

The variables g1, g2, and g3 are parameters characterizing the consumer’s utility function; c is a consumption of non-medical goods; q is the consumers latent health status; y is an exogenous income measure, p is the insurance premium, z(m) is the copayment schedule.  The first order condition is:

  • g2(m-q)^{-g3}=c^{-g1} * [z'(m)]

This first order condition will be the cornerstone of all subsequent empirical analysis.

Methodology 

The authors use data from the 1996 (wave 3) Health and Retirement Study (HRS).  The HRS is a panel study which tracks individuals over age 50 for a period of 2 years.  The first step in the analysis is estimate the health insurance co-payment schedule (z(m))using data on out of pocket medical expenditures and insurance choices.  The reimbursement schedule is unique for each insurance group (eg: employer, Medicare, etc.), but not for each individual.  Since c, y, p, m are known, and z(m) is estimated, we can now try to recover the g‘s and the q variable.  The authors assume ‘y’ is exogenous.  This is unlikely since those with a poor health (high q) are unlikely to earn much money if they are continually sick.  Nevertheless, if y were to be exogenous, we can solve the FOC for q so that q_i=r(m_i,p_i,y_i,z(m_i),g). 

The authors then use three instrumental variables (x_i) to formulate a method of moments estimator where the median latent health status u_q, as well as the parameters g are estimated.  The median moment condition below is wisely employed since it is more robust to censoring at the upper and lower tails of the conditional distribution of the observables. 

  • (u_q,g)=argmin || n^{-1} SUM_i [f(x_i)*{1{r()}-0.5}] ||

The brackets “|| ||” represent the quadratic norm, ie: ||x||=x’Wx.   If the instruments are truly valid, then f(x_i) should be orthogonal to r() when r is evaluated at the true vetor g.  The instruments used are as follows:

  1. State level housing price index
  2. County level malpractice insurance component of the Geographic Practice Cost Index (GPCI)
  3. Number of establishments in a county

In order for these to be good instruments, the variables chosen must provide variation in the price of providing medical goods but be uncorrelated with the latent health distribution.  Each of these three seems to fulfill this requirement, but there could be some problems.  While higher rental prices should increase the cost of living and thus the cost of medical services, it is also possible that only healthier people are able to make sufficient income to be able to afford houses in high rent areas.  Malpractice insurance certainly effects the price of medical services and likely does not significantly effect health status.  The author mentions that any defensive medicine caused by higher malpractice insurance rates should be reflected in the price consumers pay for health insurance.  The number of establishments in a county may effect prices, but the direction is unclear.  This is likely a weak instrument. 

Results

The authors find that the coefficient of relative risk aversion for aggregate consumption (g1) is 0.85, while the same parameter for consumption of health services (g3) is 1.52.  This shows that individuals are more risk averse with respect to health status than the aggregate consumption commodity.  The authors find that the utility weight on the consumption of health services relative to the composite good (g2) is 1.37.  Thus the medical services good is more highly valued than the composite good. The authors’ estimate of the median value of latent health status (u_q) is $4063.  For the 25th percentile, u_q has a value of $708 and for the 75th percentile the value is $11,653.  We see how the latent health variable has a significant effect on healthcare costs.

The authors can also estimate the medical expenditure elasticity at different expenditure percentiles.  The median elasticity is -0.21, but is -0.47 at the 25th percentile and -0.01 at the 75th percentile.  Bajari, et al. also subdivide the elasticities by insurance type.  They find no significant difference in elasticities between insurance groups, except for the self employed who have a higher elasticity, likely because as a group they are healthier than the other categories.  The variation in the elasticity of demand for health care occurs within plans, not between them.  

To estimate the moral hazard phenomenon, the authors examine the correlation between estimated elasticities and various individual characteristics.  The authors find that elasticity monotonically increases as self reported health status improves.  This implies that younger and healthier individuals have a more elastic response to price incentive. 

At first glance, it seems that adverse selection is a problem since we find that those who are uninsured have the best latent health status at the median.  The authors use a Kolmogorov-Smirnov test statistic to see if the uninsured are truly different than the insured.  The K-S test cannot reject the equality of the distributions across the insurance categories.  So there is no adverse selection?  The authors wisely note that this could simply be due to the fact that the categories chosen (ie: Medicare, VA/CHAMPUS, employer-provided, etc.) are too broad and that there is adverse selection present, but it is within each insurance category.  Further, since the HRS deals with individuals above age 50, it is likely that adverse selection is less of a problem since many of these individuals are eligible for public insurance (Medicare for those over 65).

Mandatory Vaccines in Michigan

September 14, 2006 in Current Events | Permalink

Seven hundred twenty million dollars.  This would the the annual cost to immunize all girls against the human papilloma virus (HPV).  According to the Detroit Free Press (“Law…“), the state of Michigan is considering requiring all girls entering the sixth grade to receive the HPV vaccine.  Is this good policy?

Cervical cancer affects 9,700 women per year in the U.S.; 3,700 women die from the disease each year.  According to WebMD, “Abnormal cervical cell changes are often the result of high-risk sexual behaviors years earlier.”  CNN wisely notes “Although the vaccine could prevent up to 70 percent of cervical cancer cases, it can’t prevent infection with every virus that causes cervical cancer.“ 

What is the cost per life saved?  Using a quick back of the envelope calculations, we see that there are approximately 2 million twelve year old girls in the U.S.  Thus, the total cost to immunize the population (in the long term) is $720m.  If there are 3900 lives saved each year, then the cost per life saved is approximately $195,000.  This does not take into account any side effects from the vaccine on the one hand, and on the other does not calculate any benefits from lower morbidity.  This analysis seems to justify, prima facie, paying the high cost for the vaccine. 

A question remains: if the benefits to this immunization are so large, why require it?  Libertarians would say that parents likely have their child’s best interest at heart and would give the child the treatment if it was beneficial for them.  Why mandate something people should do on their own.  There are a few justifications for this legislation:

  1. Externalities: Parents will only take into account the benefit the HPV vaccine will have on their children and won’t take into account the fact that the vaccine will lower the probability that another child will contract the disease.   
  2. Excessive optimism: Parents may feel that their daughter is not of the promiscuous type.  Thus, they may incorrectly estimate the probability that their offspring will be infected and undervalue the infection. 

If unprotected teenage sexual activity becomes more safe, some may argue that the vaccine will increase the amount of underage sex in America.  I find this unlikely given the fact that we still face the enormous problem of AIDS and other STDs.  Thus, requiring the immunizations does seem to me to be sound policy.

Hospitals Negotiating Leverage

September 14, 2006 in Academic Articles, Supply of Medical Services | Permalink

In the early- and mid- 1990s, hospitals were under pressure.  Managed care was taking off and forcing hospitals to reduce prices.  These managed care plans had the upper hand because:

  1. Competition between hospitals was intense.  Each hospital had to fight to secure contracts from managed plans in order to direct large chunks of patients to their hospital.
  2. Managed Care plans are more price sensitive than consumers because they pay a larger portion of the health care cost.
  3. When managed care instituted utilization review, the amount of hospital services demanded by patients decrease.

In the late 1990s, however, it seems that hospitals began winning back some bargaining power.  A paper by Devers, et al (2003) employs a mix of interviews and quantitative data in order to demonstrate that hospital bargaining power did increase in the late 1990s.  The authors give seven reasons why the hospitals bargaining power increased in this time period.

  1. Legislation – Congress passed acts (such as the Patient’s Bill of Rights in 1998) which gave patients more freedoms in their choice of providers and thus reduced the credibility managed care’s threats to entirely drop contracts with hospitals.
  2. Employer response – The late 1990s was one of a backlash from managed care.  In a time of an economic boom, employers began choosing more generous health plans to attract skilled employees.  More generous health plans give more money to hospitals thus increasing their bargaining position.
  3. Medicare/Medicaid managed care enrollment – Medicaid and Medicare managed care enrollment was lower then anticipated, thus weakening managed care’s bargaining power.
  4. Hospital Mergers – In this time period we see a spate of hospital mergers.  As proof of this phenomenon, data from the CTS in 12 markets show that the HHI increased on average 34% between 1996 and 2000. 
  5. Broader Provider Network – In order to attract more enrollees, managed care began to offer broader provider networks, thus reducing the credibility of a threat to remove all patients from a hospital’s rolls.
  6. Must have services – Hospitals increased their purchases of advanced technological equipment and added to their marketing budgets.  Through these two avenues, the hospital tried to convince consumers that their hospital provided essential services which could not be found elsewhere.
  7. Capacity Constraints – In the late 1990s, hospitals began to experience capacity constraints, and thus did not fear the loss of a moderate amount of patients.

One other interesting point made by the article centers on what happens when a managed care plan makes up a large percentage of a hospital patients.  On the one hand, the plan has significant power since moving the patients to another hospital would devastate the revenue of the original hospital.  On the other hand, we see diminishing returns in this bargaining power.  As the number of patients who are served at the original hospital increases, it will be more and more difficult for the plan to switch hospitals without upsetting their enrollee base.

Devers, Casalino; Rudell; Stoddard; Brewster; Lake; (2003) “Hospitals’ Negotiating Leverage with Health Plans: How and why has it changed?” Health Services Research, Vol 38(1), pp. 419-446.

Poisson Distribution Estimation

September 13, 2006 in Econometrics | Permalink

The Poisson distribution is one that is often used in health economics.  Wikipedia has a nice basic summary of the Poisson distribution; Wolfram MathWorld gives a more sophisticated analysis.  The distribution is

f(k;\lambda)=\frac{e^{-\lambda} \lambda^k}{k!},\,\!

where ‘λ‘ is equal to the number of expected occurrences in a period.  The distribution expresses the probability of a number of events (‘k‘) occurring in a fixed period of time if these events occur with a known average rate, and are independent of the time since the last event.  The variance and the mean for a Poisson distribution are the same.  Healthcare economists can use the distribution to determine how different variables (eg: income, smoking, medical treatments) affect the probability of observing the occurrence of a certain number of events (eg: illnesses, deaths, etc.). 

Let’s look at an example:

In the US in 2000, there were approximately 15 million people aged 55-59 years of age.  The death rate for this age group was approximately 750 deaths per year per 100,000 individuals.  Thus, the expected number of deaths (‘λ‘) per year is 112,500.  What factors impact the lambda term?  An economists may be interested in whether increasing average real income for the cohort would increase or decrease the death rate.  We can model lambda as a function of other covariates (‘x‘) such as the whether or not the individual has health insurance, if they are a smoker, and their income level and their corresponding coefficients (‘β‘).  Thus our new equation is:

  • f(k;x)=exp[-λ(x;β)] * [λ(x;β)]^k / k!

If we have observations from multiple census years (and if we assume that the 55-59 age cohort is of the same size each year), we can estimate this coefficients (β) using a log likelihood function:

  • l_i(β)=k_i *log [λ(x;β)] - [λ(x;β)]

The ‘k!‘ term drops out because it does not depend on the parameter β. Each observation (‘i‘) corresponds to data from each census year in the sample.  The most common form for λ(x;β) to take is λ(x;β)=exp(xβ).  If the variable x_j is continuous and we assume λ(x;β)=exp(x;β), then we can show:

  • ∂{E(k|x)} / ∂{x_j} = exp(xβ)*β_j
  • β_j = ∂{log [E(k|x)]} / ∂{x_j}

Now that we know β_j, the economists knows the impact that any covariate ‘x‘ (such income or smoking, or health insurance) will have on the average death rate (λ).

Empirical Research: Wine and longevity

September 9, 2006 in Miscellaneous | Permalink

In January of this year, I wrote (“Does drinking wine truly increase longevity“) that I was doubtful that wine has a large impact on longevity.  As a dedicated social scientist, I have decided not to simply accept the findings of other experts, but instead to do some of my own empirical research.  Monday and Tuesday I will be in Santa Barbara with my girlfriend to sample a variety of this nation’s finest wines.  Healthcare Economist will return on Wednesday.

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