December 2008

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Economists have generally found that rich people are happier.  People who are wealthy are likely to be happier than those who have trouble affording food, clothes, or shelter.  What is driving this happiness differential?  Is the additional happiness from additional wealth due to the fact that you can more easily fulfill basic needs, or is it because people with fancier cars and more iPhones are actually happier?

A paper by  Di Tella and MacCulloch (2008) examines what happens to individuals in developed countries when they become wealthier.  They find that increased wealth does increase happiness, but only temporarily.

“We find evidence that for wealthy Germans, and for the rich half of European nations, higher levels of per capita income don’t buy greater happiness. The reason appears to be adaptation. However even for the rich half of European nations such habituation may take over 5 years so the happiness gains that they experience, whilst not permanent, can still be relatively long-lasting. Finally we study a cross section of nations in 2005 from the World Gallup Poll and find that the past 45 years of economic growth (from 1960-2005) in the rich half of nations has not brought happiness gains above those that were already in place once the 1960s standard of living had been achieved. However in the poorest half of nations we cannot reject the null hypothesis that the happiness gains they have experienced from the past 45 years of growth have been the same as the gains that they experienced from growth prior to the 1960s.

As Thomas Jefferson once said: “It is neither wealth nor splendor, but tranquillity and occupation, which give happiness.”

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Should breast feeding be mandatory?  Find out in the New Year’s Eve edition of the Cavalcade of Risk at the Colorado Health Insurance Insider.

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CBO Papers

In the Health Care Blog, Robert Laszewski suberbly analyzes Congressional Budget Office (CBO)’s two papers.  His key points are that 1) there is no silver bullet and 2) “really controlling costs will be very hard and will require some courageous and politically problematic actions.”

I would point out other highlights, but the post is so good I highly recommend reading it yourself.

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I am taking a break from blogging about health care and focusing on the health of the Green Bay Packers.  For those appreciate the quantitative focus of this blog, do not dispair, there will be lots of numbers.

Rodgers vs. Favre

At the beginning of the NFL season, the Packers jettisoned their hall of fame quarterback in favor of a young quarterback who had never started a profession game.  Did the Packers choose wisely?  A statistical comparison of the two quarterbacks clearly shows that Aaron Rodgers has a superior season to Brett Favre.  As shown in this table, Rodgers surpassed Favre in every statistical category except completion percetage.  Most importantly, Rodgers is 25 and Favre is 39.

The Packers Season: Talent without execution

Despite the superior play of Aaron Rodgers, the Packers were only 6-10.  Should Packers fans expect another poor season next year?  I don’t believe so.

In baseball, statisticians use Bill James’ Pythagorean Record to measure how many games a team should have won according to their talent.  According to Pro-football Reference, a team’s Pythagorean Record in the NFL is:

  • (Points For)2.37/[(Points For)2.37 + (Points Against)2.37].  

According to actual Wins and Losses, the Packers had the 24th best team in the NFL.  According to my Pythagorean Record calculations, however, the Packers had the 15th best team.  In fact, the Packers were the most under-preforming team in the NFL.  This table shows that the Packers should have expected a win percentage of .558 (8.9 wins), but they only won 6 games.  This means that either 1) the Packers were very unlucky or 2) the Packers lost a large portion of close games.  

Better luck next year for the green and gold.

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Many pundits are calling for Barack Obama to fund massive infrastructure projects.  UC-San Diego economist Jim Hamilton of  believes that increased block grants to states will not only stimulate the economy, but also permit states the flexibility they need to spend these fund efficiently.

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ANOVA

Let us say that you are a hospital administrator.  You are very clever and have come up with a system to score the quality of the work done by the physicians at your hospital.  To simplify things, lets assume that you only have 3 physicians who work at your hospital.  The physician’s scores are as follows:

  • Dr. Albert: 76, 85, 91, 67, 73 
  • Dr. Burns: 92, 90, 60, 79, 75
  • Dr. Collin: 50, 80, 83, 80, 74

The average score for Dr. Albert is 78.4, for Dr. Burns is 79.2 and for Dr. Collin is 73.4.  As the hospital administrator, you want to know whether these differences are due to differences in doctor quality or likely from random chance.  If there were only two doctor’s a t-test would suffice, but what tests can you use in the case of multiple doctors?

The solution to this is to run an ANOVA test.  How do we do this?  Follow these easy steps.

  1. Let j be the group number (j=a, b, c) and i be the number obervation within each group (i=1, 2,…,5)
  2. Calculate the mean of each group (μj): μa= 78.4; μb 79.2; μc= 73.4.
  3. Also calculate the mean of the entire sample. μ=77
  4. Now calculate the Sum of Squares within each group [SSwithin = ΣΣ (Xij - μj)2].  This shows how much variation there is for each doctor.
    • SSa = (76 – 78.4)2 + (85 - 78.4)2 + (91 - 78.4)2 (67 – 78.4)2 + (73.4 – 78.4)2 = 367.2 
    • SSb = 666.8
    • SSc = 727.2
    • SSwithin  = SSa + SSb +  SSc = 1761.2
  5. Now calculate the Sum of Squares between each group. [SSbetween =Σ njj - μ)2].  This shows how much variation there is across each of the doctor’s average score.
    • SSbetween = 5*(78.4 -77)2 + 5*(79.2 – 77)2 + 5*(73.4 – 77)2 = 98.8
  6. The F-statistic is calculated as the mean square (MS) statistic for the between and within sum of squares (SS).  How do we go from the SS to the MS?  That’s easy, we just divide both by the degrees of freedom.
    • MSwithin  = SSwithin/(N-J) = SSwithin/13.  This is because there are 15 observations and 3 doctors so 15-3=12.  Our answer here is: 1761.2/12 = 146.77
    • MSbetween = SSbetween/(J-1) = SSwithin/2. This is because there are 3 doctors, we have 3-2=4. Our answer here is: 98.8/2 = 49.4.
  7. Now we can calculate the F statistic as: F = MSbetween/MSwithin = 49.4/166.77 = .337
  8. If we look this up on an chart for F-statistics, we see that the probability that all 3 doctors are equally good is .721.  Thus, we fail to reject the null that all three doctors are equally good.

STATA

Is there an easier way to do this?  Yes.  If you have Stata, you could just use the score as the dependent variable and have dummy variables for Drs. A, B, an C. The you can run a statistical test that the coefficient estimate for Dr. A = the coefficient estimate for Dr. B = the coefficient estimate for Dr. C.  This will give you the same probability that the three doctors are equally skilled that we calculated manually above.

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To stimulate the economy, expand government health insurance.

To stimulate the economy, defeat government health insurance expansions.

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In the U.S., 2.9% of individuals who enter a hospital are actually harmed by the medical care they receive.  Reducing these preventable iatrogenic injuries is one of the goals of any hospital administrator.  Paul Levy of Running a Hospital lists 3 goals to achieve in the new year which will help reduce these adverse events.

  1. Eliminating central line infections [Metric: The number of CLIs, as defined by the CDC. Goal = 0]
  2. Adopting the IHI bundle to help avoid ventilator associated pneumonia [Metric: Percent compliance with the bundle. Goal = 100%]
  3. Adopting the WHO protocol developed by Brigham and Women’s Hospital’s Atul Gawande for surgical procedures [Metric: Percent of surgical cases in which the pre-op, time-out, post-op checklist has been followed. Goal = 100%]

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“When goods do not cross borders, soldiers will.”

  • Frédéric Bastiat

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This blog has repeated reported on microfinance programs in the developing world which give loans to poor individuals.  This model has been extended to work even in the U.S.  Ways to Work provides loans to poor Americans, often to purchase or repair an automobile.  After welfare reform acts in the 1990s, many states required individuals to work in order to be eligible for welfare.  However, working involves significant fixed cost.  An individual who wants to have a full-time job must be able to purchase work clothes, pay for child care, and most–importantly–find a form of transportation to an from work.

In order to help the poor be able to afford the fixed costs associated with car ownership, Ways to Work provides low interest loans (around 8%) that make purchasing and maintaining a car fit within the family budget.  Client repayment rate was 87% between 1996-2007.

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