July 2007

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Cavalcade of Risk #31

July 31, 2007 in Carnivals | Permalink

I am honored to host the 31st edition of the world-renowned Cavalcade of Risk. In a departure from some prior carnivals, I have tried to make this a more concise edition, highlighting the truly best articles of the past two weeks. Using this method, I intended to eliminate minimize the risk that you will choose an uninteresting article to read. Enjoy!

POLICY

Currently, the government is debating about whether or not to renew SCHIP. SCHIP was created in 1997 and gives government provided health insurance to children in households typically below 200% of the federal poverty line. Should this program be renewed? Congress generally says yes; the president says no. Paul Krugman of the N.Y. Times says yes; Michael Cannon of Cato-at-Liberty says no.

Jon Coppelman of Workers Comp Insider notes in “Trouble in Trucking” that when he is driving 70 miles per hour down an interstate, sandwiched between two rigs, he is hoping the other guys are tenaciously awake. The odds are a little more in his favor since the federal appeals court recently struck down a rule that increased the number of hours a trucker can spend behind the wheel.

Those of the political left often cite the need for government intervention in order to redistribute income from rich to poor. In “The new world of risk,” Leon Gettler of Sox First discusses a John Quiggin’s policy paper which claims that “the primary role of the welfare state is managing risk, not redistributing income.”

INSURANCE

Private health insurance companies are more streamlined, more efficient versions of their public sector counterparts…right? Over at InsureBlog, Bob Vineyard presents “Stupid Carrier Tricks,” demonstrating the private market isn’t always perfect (this is tough for an economist, like me, to admit).

David Williams of the Health Business Blog worries that rapidly rising premiums pose a risk to Massachusetts’ health reform plans.

Will businesses be able to charge employees different health insurance premiums based on their DNA? Shaheen Lakhan of GNIF Brain Blogger discusses whether this is a possibility in “Genetic Discrimination: A Real Threat?”

In his Personal Injury Law Round-Up, Eric Turkewitz of NY Personal Injury Law Blog reviews some risk related news. More interestingly, Mr. Turkewitz attempts to explain in another post why NY medical malpractice insurance jumped 14%” (hint: it’s not due to a huge increase in the number malpractice lawsuits or the amount of money awarded in these cases).

DATA RISK and Barry BONDS

Veterans Administration. TJ Maxx. ChoicePoint. What do these entities have in common? They have all experienced breaches of their customer’s personal data. Jimmy Atkinson analyzes the risk of data breaches in his article “How Many Times Has Your Personal Data Been Stolen This Year?” posted at Ask the Advisor.

Over at IowaBiz , Joe Kristan‘s article on surety bonds wins the award for the most clever title: “Bonds – and I’m not talking Barry!”

ECONOMICS and FINANCE

Why did the vice-president of your company sell some of his vested options even though he expects the company to continue its success in the future? Learn why at The Digerati Life‘s post “8 Different Ways To Diversify And Manage Risk.”

How do people make decisions when faced with risky alternatives? Typically economists rely on expected utility theory to explain an individual decision-making. Jason Shafrin of Healthcare Economist discusses “Prospect Theory,” proposed by Nobel laureate Daniel Kahneman and Amos Tversky. Prospect Theory claims that people value money not in terms of its absolute value, but measured as gains and losses from a reference point.

Prospect Theory

July 31, 2007 in Economics - General, Experimental | Permalink

Yesterday, I talked about expected utility theory (EUT). Today I will write about one on the major departures from EUT: Prospect Theory. This theory was developed by Nobel laureate Daniel Kahneman and Amos Tversky (Econometrica 1979). The four key characteristics of prospect theory are:

  1. Individuals use decision weights, π(p), rather than probabilities, p, when making decisions.
  2. The value function is defined as deviations from a reference point. Thus, earning $100,000 this year is perceived differently for an individual earning $50,000 last year compared to one making $1 million last year.
  3. Individuals are risk averse with respect to gains but risk loving with respect to losses. This implies that the value function is concave for gains, but convex for losses.
  4. The value function is steeper for losses than for gains . This means that losses of $1000, hurt more than gains of $1000.

Why is there a need for prospect theory?

Much experimental evidence has shown that EUT does not only hold. Consider the Allais paradox. Which of the following lotteries would you choose:

  • A: ($1m, 1) vs. B: ($1m, .89; 0, .01; $5m .10)
  • C: (0, .89; $1m, .11) vs. D: (0,.90; $5m, .10)

Most people choose A and D. Yet it can be shown that under the EUT, these lotteries are mathematically equivalent and this leads to a preference reversal.

Another example is the following:

  • A: (6000, .45; 0, .55) vs. B: (3000, .90; 0, .10)
  • C: (6000, .001; 0, .999) vs. D: (3000,.02; 0, .998)

The majority of people surveyed here chose B and C. Again these A and C are two are equivalent lotteries as are B and D. The probability of winning in the latter pair is simply dived by 450. Thus, we see a preference reversal according to traditional EUT theory.

Also we see that people treat losses and gains differently.

  • A: (6000, .25; 0, .75) vs. B: (4000, .25; 2000, .25; 0, .5)
  • C: (-6000, .25; 0, .75) vs. D: (-4000, .25; -2000, .25; 0, .5)

Kahneman and Tversky find that 82% of people choose B over A, but 70% of people choose C over D. This implies that individuals are risk averse with respect to gains and risk loving with respect to losses.

Editing

Before utility functions are evaluated, Kahneman and Tversky say that choices are “edited.” The reason for this is 1) it helps to prevent obvious contradictions in which would occur if editing was not included, and 2) the editing process may more accurately reflect the process by which individuals make choices. Here are some of the ways which individuals edit:

  • Coding: Outcomes are perceived as gains and losses with respect to a reference point. The reference point may be the status quo or it may be an expectation. For instance, if my monthly before-tax earnings are $2000 but my after-tax earnings are $1500, I may perceive this as a $500 loss from my expected income rather than a simple $1500 gain.
  • Combination: Identical outcomes are simplified so that (100, .25; 100, .25; 0 .50) = (100, .50; 0 .50).
  • Segregation: Risky components are separated from non-risky components. For instance, (500, .7; 100, .3) is decomposed into a sure gain of $100 and a lottery of (400, .7; 0, .3).
  • Cancellation. This implies that when lotteries are compared, common outcomes are eliminated. “For example, the choice between (200, .20; 100, .50; -50, .30) and (200, .20; 150, .50; -100, .30) can be reduced by cancellation to a choice between (100, .50;-50, .30) and (150, .50; -100, .30).”

Evaluation

After editing, individuals make decisions according to the following utility function:

  • Σ π(p)v(x)

Tversky and Kahneman (J Risk Uncert 1992) show that empirically, the function gives an inverted-S shape (see graph). “…for both positive and negative prospects, people overweight low probabilities and underweight moderate and high probabilities. As a consequence, people are relatively insensitive to probability difference in the middle of the range.” As mentioned earlier, the value x is evaluated with respect to a reference point. It is either a gain or a loss. For gains, v”<0 but for losses v”>0. Also, because the utility function is steeper for losses than gains, v(x)<-v(-x). For a graphical display of a prospect theory value function, see a picture from the U of RI economics website.

Another lottery experiment to support prospect theory is the following:

  • A: (5000, .001; 0, .999) vs. B: 5
  • C: (-5000, .001; 0, .999) vs. D: -5

Of those surveyed, 72% of people choose A over B, but 83% of people chose C over D. This would seem to imply that individuals are risk loving for gains and risk averse to losses. However, the bulk of the evidence has shown that this is not the case. As mentioned above, it seems more likely that people tend to overweight low probability events and underweight high probability events.

While Prospect Theory still is not as popular in mainstream economics as Expected Utility Theory. This is likely due to the added data needed regarding how an individual is editing, and what the individual’s reference point would be. Further, one wonders whether or not individuals become more ‘rational’ in the expected utility sense if they receive feedback from repeated games. Nevertheless, Prospect Theory seems to very accurately explain many of the findings in experimental economics and more work in this area is needed.

CoR Sumbissions Due

July 30, 2007 in Current Events | Permalink

If you want to participate in this week’s edition of the Cavalcade of Risk, please submit your post to me today (Monday, July 30th).  Here are instructions.

Four Axioms needed for Expected Utility Theory

July 30, 2007 in Economics - General | Permalink

How do economists understand individuals preferences when there is risk? Without risk, economists generally believe that individuals have a utility function which can convert ordinal preferences into a real-valued function. This real valued function is the utility function.

When risk enters into the picture, the expected utility theory (EUT) is used. This theory was developed by Daniel Bernoulli (1738) and expanded by John von Neumann and Oskar Morgenstern (1947). The EUT implies that utility functions have the following functional form:

  • U=Σi piu(xi)

Here there are i states of the world. In each state of the world, i, the individual receives xi dollars. The probability of receiving xi is pi. An individual will prefer one risky lottery over another if their utility is higher in the first lottery compared to the second.

For example, let us assume that there are two lotteries. In lottery A you receive $100 for sure. In lottery B you have a 60% chance of receiving $200 and a 40% chance of receiving $0. Thus your utility in each case would be:

  • UA= 1*u(100)
  • UB= .6*u(200)+.4*u(0)

The lottery you choose will be based on your expected utility. Risk neutral individuals have linear utility functions, risk averse individuals have concave utility functions (u”<0) and risk loving individuals have convex utility functions (u”>0).
Do people actually make decisions according to these rules?

4 axioms

In order for people to make decisions according to the EUT framework, 4 axioms must hold. Let q, r, and s, be defined as the following lotteries: q=(x1,p1; x2,p2;…xn,pn), r=(y1,q1; y2,q2;…yn,qn) and s=(z1,w1; z2,w2;…zn,wn). Also, define aWb to mean that ‘a’ is weakly preferred to ‘b’.

  1. Completeness. This entails that for all q, r: either qWr or rWq or both. If the answer is both, then I am indifferent between q and r.
  2. Transitivity. If qWr, rWs then qWs.
  3. Continuity. If qWr, rWs then there exists some p such that (q,p; s,1-p)~r.
  4. Independence. This requires that if qWr, then (q,p; s,1-p)W(r,p; s,1-p) This means that I prefer tacos to hamburgers for lunch, I will not change my preferences between tacos and hamburgers if I am offered a salad as well. This is the axiom most commonly relaxed when alternatives to EUT are examined.

Are these axioms realistic? In the next post, I will review an article which describes “Developments in Non-Expected Utility Theory” where some of these axioms are violated.

ESD: Han Bleichrodt

July 27, 2007 in Uncategorized | Permalink

This post will review Han Bleichrodt‘s lecture regarding the micro foundations of using QALY based utility functions.

QALYs

Many health economists use a QALY model to describe a person’s preference over health states. For instance let (q1,…qτ) be an individuals health profile from year 1 to year τ. The QALY model assumes that utility is additive so that U(q1,…qτ)=ΣV(qt). For chronic health conditions where health states do not vary from year to year, one can further simplify the formulation so that U(Q,T)=V(Q)*T.

Standard Gamble

Calculating V(Q) is not as easy as it seems. One way to elicit the individuals preferences is to use the standard gamble and to assume that V(Death)=0 and V(Full Health)=1. Let us look at an example.

You currently have severe back pain. You are offered a surgery that with probability p will make you completely healthy for the next 30 years, but with probability 1-p you will die. If you do not preform the surgery, then you will have chronic back pain for the next 30 years.

One can ask the individual to choose whether or not they want to surgery and the experimenter can adjust the probabilities until the individual is indifferent between both states. In this case, we know that the QALY utility weight is equal to p:

  • U(Back Pain, 30 yrs)=p*U(Health, 30 yrs) + (1-p)U(Death) = p*1+(1-p)0 = p

The total number of QALYs is p*T=p*30.

Time Trade-off

Another means of eliciting patient preference is to use the time trade-off. For instance, one is asked if they prefer to live 40 years with back pain, or 30 years in full health. The number of years in full health can be adjusted until the patient is indifferent between the two states. Thus, mathematically we can calculate the utility weight of the QALY as :

  • (Q1,T1)~(Q2,T2)–>(Back pain, 40 yrs)~(Health, 30 yrs) –>
  • U(Back Pain)*40=U(Health)*30 –>
  • U(Back Pain)=1*30/40=0.75

Rating Scale

The final method to elicit QALY is to simply ask the person. One asks simply describes a disease and asks a person to rate it between 0 and 100, where 100 is perfect health and 0 is death. The QALY is the stated rating divided by 100.

Microeconomic Theoretical Foundations

What assumptions need to be satisfied in order for the QALY model to be an accurate depiction of reality? An article by Pliskin, Shepard and Weinstein (Operations Research 1980) derives 3 conditions in order for the QALY model to hold:

  1. Mutual Utility Independence. This states that the utility function must be separable between quality of life and years of life. Mathematically U(Q,T)=V(Q)+W(T) or U(Q,T)=V(Q)*W(T).
  2. Constant Proportional Tradeoff. This means that (Q1,T1)~(Q2,T2) if and only if (Q1,αT1)~(Q2,αT2), where α is non-negative.
  3. Risk Neutrality with respect to life-years. This is probably the key assumption. One must assume that W(T)=T.

Empirical Findings

Does the QALY model hold empirically? Bleichrodt states that empirical evidence shows that people are not risk neutral with respect to life years. If a less restrictive model of the form U(Q,T)=V(Q)Tr were adopted, then empirically r ≈0.75.

Miyamoto and Eraker (1988) try to test utility independence. They find support for utility independence of life duration from health quality, but also found that for short life durations, about 25% of their subjects were not willing to give up any life years to improve their health status.

Bleichrodt, Pinto and Abellan-Perpiña (JHE 2003) test for constant proportional trade-offs using life durations of 13, 19, 24, 31 and 38 years. There was some support that constant proportional trade-offs holds, but the evidence was not overwhelming.

Bleichrodt claims that the Time trade-off QALY solicitation is the least biased while the ranting scale is the least accurate. Evidence for this comes from the Bleichrodt and Johannesson (JHE 1997) paper, but I believe that between the standard gamble and time trade-off there is no clear cut optimal method. In my opinion, the rating scale seems to be the worst method, with the least grounding in microeconomic traditions.

Bleichrodt also briefly discusses prospect theory, which claims that people do not weight probabilities accurately. For instance, people care much more about an increased probability of dying from 1% to 2% then an increase from 51% to 52%. To take this into account, prospect theory uses a weighting function. Let us give an example:

  • {(Q1,T1),p; (Q2,T2),1-p}=w(p)U(Q1,T1) + (1-w(p))U(Q2,T2)

The function w(p) weights the probability to take into account the fact that individuals do not perceive probabilities accurately.

ESD: Willard Manning

July 26, 2007 in Econometrics | Permalink

Today I will review the insightful lecture of Willard Manning at European Science Days. Manning is most famous for his work with the RAND Health Insurance Experiment.

Problems with Healthcare Data

There are 4 major econometric problems one must consider when trying to analyze health care cost and utilization data:

  1. There is a large mass of individuals with zero utilization (or expenditures) during a given time period,
  2. Consumption among those with any care is very skewed (e.g.: visits, hospitalizations, expenditures),
  3. The dependent variable often responds in a non-linear manner to many covariates,
  4. demand response to covariates may change by the level of demand (e.g.: outpatient to inpatient, or low to high levels)

Log or Box-Cox Transformations

While using OLS is easy, it can often produce out-of-range predictions (i.e.: yhat=xβhat<0). Since health care data is skewed, many researchers decide to log the dependent variable in order to have a more symetric distribution of errors. The tradeoff of using logs is that although one gains precision and robustness, no one is interested in log-scale results per se.

The Box-Cox transformation of y is as follows:

  • [(yλ-1)/λ]=xβ+ε, if λ≠0
  • log(y)=xβ+ε, if λ=0

One estimates λ using MLE in order to minimize the skewness in the residuals.

Log Example

Using a log transformation implies that second moments often matter. For instance, let us assume log(y|g)~N(μg,σg), where treatment g=A, B. Then we know

  • E(y|g=A) = exp[μa+ 0.5(σa)2].
  • E(y|g=A)/E(y|g=B) = exp[(μa-μb)+ 0.5{(σa)2-(σb)2}]

We can see from the second equation above, that the second moment of the distributions matters if there is heteroskedasticity, but not if there is homoskedasticity (i.e.: σa=σb=σ)

Marginal Effects with log transformation

Calculating marginal effects with non-linear econometric formulations is often difficult.  For instance, we know that E(y)= exp(xβ)E{exp(ε)|x}. This implies that the marginal effect is equal to:

  • dE(y)/d(xk)=exp(xβ)[βkE{exp(ε)|x}+ d E{exp(ε)|x}/d(xk)]

This is much more complicated that the incorrect formulation that: dE(y)/d(xk)=exp(xβ)βk.

Generalized Linear Model Approach

In this method, one searches for the appropriate β’s to solve the following function:

  • Σ dμ(xβ)/dβ*V(x)-1*(y-μ(xβ))=0

In practice, one usually assumes that μ(xβ)=exp[xβ]. A variance structure is assumed so that Var(y|x)=α[E(y|x)]γ. The γ’s correspond to some standard parametric distributions:

  • Gaussian NLS: γ=0
  • Poisson: γ=1
  • Gamma: γ=2
  • Wald or inverse Gamma: γ=3.

Two Part Models

To this point, we have been focusing on the skewness problem and been ignoring the fact that many of the observations also clump at zero. We can decompose the expected value as follows:

  • E(y|x) = P(y>0)*E{y|y>0} + P(y=0)*0 = P(y>0)*E{y|y>0}

Now we must estimate P(y>0) and E(y|y>0) separately. The first part term we can estimate with a probit model [P(y>0)=Φ(xα). The second part one can log the y term to take into account skewness.

If the log-scale error term is normally distributed, then:

  • yhat= Φ(xα)*exp(xβ + .5σ2), where β, σ are estimated from the data.

If the log-scale error term is not normally distributed, than one can use the following formulation:

  • yhat= Φ(xα)*exp(xβ)*D
  • D is Duan's (JASA 1983) smearing estimator:
  • D=N-1Σexp[ε]=N-1Σexp[ln(y|y>0)-xβols]

Count Data

Count data in health economics is very common. The number of doctor visits, hospitalizations and ER visits all are types of count data. Poisson and Negative Binomial regressions are frequently recommended for these types of data.

The latest Health Wonk Review is up

July 26, 2007 in Carnivals | Permalink

The July 26, 2007 edition of the Health Wonk Review has been posted at Robert Laszewski’s Health Care Policy and Marketplace Review.

Primary Care vs. Specialists

July 25, 2007 in Current Events | Permalink

The Wall Street Journal (“Doctor Shortage…“) reports that the percentage of medical residents choosing to practice in the primary care arena is falling.  This is likely due to the fact that specialists make significantly more money the primary care doctors. 

Arnold Kling of EconLog has an interesting point as primary care physicians shortages and primary care doctors’ low pay:

  • “The focus of the story is on how the reduction in primary care doctors hurts the Massachusetts health plan. I think that is almost beside the point. My guess is that this is another instance in which American medical care is allocated at the margin in a cost-ineffective way. If insurance companies were not paying so much of the bill, people would not see so many specialists. Specialist income would decline, and more physicians would stay in primary care.”

More growth in Convenience Clinics

July 25, 2007 in Nonphysician Clinicians, Supply of Medical Services | Permalink

Earlier this month, VentureBeat reported that QuickHealth, a Burlingame, Calf. company that operates walk-in medical clinics, said it has raised an $8.5 million in a second round of financing.  The company’s report states the following:

Take Care Health Systems LLC, an operator of retail clinics predominantly in the Midwest, completed its sale to Walgreen Co. in May for undisclosed terms…CVS Corp. completed the acquisition of MinuteClinic in September 2006 for undisclosed terms….America Online Inc. founder Steve Case, through Revolution Health, has backed InterFit Health Inc.’s RediClinics chain. Wal-Mart Stores Inc. formed an agreement with SmartCare Family Medical Centers in 2006 to include its retail clinics in stores in Colorado, Nevada and Arizona. SmartCare is backed by the Colorado Fund I and individual investors.

It looks like investors see lots of potential for these convenience clinics.

ESD: Don Kenkel

July 25, 2007 in Uncategorized | Permalink

Below is a summary of Don Kenkel‘s lecture regarding the Economics of Substance Abuse Use.

General

The World Health Organization and the United Nations International Drug Control Programme (UNDCP) have statistics on the number of drug users around the world. They claim that in 2002 there were 2 billion alcohol users, 1.3 billion smokers, and 185 million illicit drug users.  These number represent 32%, 21% and 3% of the world’s population.  Of illegal drug users, 69% use cannabis, 16% amphetamines, 6% cocaine, 4% heroin, 3% ecstasy and the rest other opiates.

Defining what the term ‘substance’ is also difficult.  Alcohol and marijuana have been legal and illegal in different times and places.  Is caffeine a substance?  What about prescription drugs?  Are betel or khat substances?

Rational Addiction Model

Kenkel briefly discusses a model of a rational addict.  The rational addict is forward looking and takes into account that choice of consumption today will affect the marginal utility of consuming the substance in the next period.  A rational addict may have the following utility function:

  • Σβt-1 U(Ct,Ct-1, Yt, et)
  • s.t.: It=Yt+pCt
  • C: number of cigarettes, Y: other consumption goods, I: Income

Assuming a quadratic utility function, one can show that the structural demand equation is:

  • Ct=θCt-1+βθCt+1+θ1Pt+θ2et+θ3et+1

This can be estimated using 2SLS with Pt-1, Pt+1 as instruments for Ct-1, Ct+1.

The rational addiction model is appealing for a number of reasons.  It explains many features of addictive consumption and features two unstable steady states: one with low and one with high consumption of cigarettes.  Life cycles shocks can move consumers from the low to high cigarette consumption states.  The model also explains why quitting cold turkey can be optimal.

Quasi Hyperbolic Discounting

This was developed by Laibson (1997).  The utility function is time-inconsistent in that the future is discounted by more than the present.  For instance:

  • Ut=ut + δΣβτ-1 uτ

The term δ represents the taste for immediate gratification. Psychological experiments tend to confirm quasi-hyperbolic discounting. Undergraduates given choices between a delayed reward of $1000 and immediate rewards ranging from $1 to $1000 revealed a year 1 discount rate of 60%, but a 16% discount rate for years 2-5. Also, this model would explain the existence of commitment devices (e.g.: former smokers supporting restaurant smoking bans as a commitment device).

Cue triggered addiction

The seminal work here is Berheim and Rangel (AER 2004).  The paper claims that individuals operate in either a ‘cold’ mode where decision processes are made rationally, and a ‘hot’ mode where decisions and preferences diverge and this results in substance use.  Addicts know they make bad decisions while in hot mode and can choose their lifestyle to alter the probability of being in the hot mode.  The Neuroeconomics blog from George Mason University has some commentary on this paper.

Quotation.
Entertaining quotation regarding the 1998 Master Settlement Agreement.

Q: Could you please explain the recent historic tobacco settlement?
A: Sure. Basically, the tobacco industry has admitted that it is killing people by the millions, and has agreed that from now on it will do this under the strict supervision of the federal government.
-Dave Barry

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