Saturday, April 21, 2012

Is the Rural Hospital Problem Really a Problem?

Many medical markets use a version of the deferred acceptance algorithm (Gale Shapley (1962)) to match doctors to residencies or internships (e.g. Roth (1984), Roth and Peranson (1999)). The deferred acceptance algorithm takes in rank order lists of preferences of doctors (over hospitals) and hospitals (over doctors) and outputs a stable match that assigns doctors to hospitals.

It is possible that in a given stable match, some positions (say at undesirable rural hospitals) go unfilled. Because of this, it is sometimes argued that there is a “problem” with rural hospitals being understaffed and thus under-serving rural areas. Maybe there is another stable match that, while worse for some doctors, is better for rural hospitals? It turns out that the answer to that question is no. In a stable match, if a hospital is matched to a set of doctors that does not fill all of its positions, the hospital is matched to the same set of doctors in every stable match (e.g. Roth (1986)). Is there another way to increase the number of doctors that are assigned to rural hospitals? Or, is this even a question worth asking?

Japan recently implemented a program of “regional caps” which restrict the total number of applicants which are allowed to be matched with hospitals in each region. This is an attempt to “match” more doctors to rural areas by limiting the number that can be matched in urban areas. Kamada and Kojima (2011) construct a new mechanism that is stable, strategy-proof and more efficient (from the doctor’s perspective) than the currently implemented one. Basically, they are more flexible in determining which hospitals receive fewer doctors if hospitals in a region exceed the cap (the mechanism in place reduced the number of doctors at each hospital proportionally if the region exceeded the cap).

But is this really better than the original uncapped deferred acceptance algorithm? By entertaining the notation that regional caps are a hard and fast political constraint and calling their solution (constrained) efficient even when the outcome could on net hurt the hospitals (profits, the level of care they provide, etc.) which could lead to an overall socially worse outcome, Kamada and Kojima give the impression that by adopting their solution, the Japanese medical residency market will be “fixed.” In fact, the outcome may be strictly worse than before the regional caps policy was implemented since regional caps are just a type of quota system, and quotas are inefficient. Even if the hospitals are not hurt, doctors that are assigned to less preferable hospitals because of the regional caps bear the costs of the policy. It is hard to tell what the costs are, though. Rank order lists contain only ordinal information, so we don’t know how much doctors and urban hospitals are hurt or how much rural hospitals are helped (welfare comparisons are generally more difficult in matching than standard price theory). 

A contract between a hospital and an applicant usually includes some kind of wage or other benefit. It seems like if a rural hospital is truly underserved it should increase its wage (if the marginal benefit of having the position filled exceeds its cost, then it would be beneficial to the hospital to increase its wage offered with the position in hopes of encouraging more doctors to rate its positions higher). However, year after year, these hospitals seem to prefer to leave the position left unfilled than to increase the wage or any other benefits that would make the position more attractive to potential applicants.

This begs the question, is there even a real problem? If there is, it would have to be because paying more is infeasible or there are externalities not being taken into account. But it may be that the rural hospital problem is just an example of one group extracting rents from another by successfully complaining to a centralized authority. 

Market designers typically take constraints like caps as given and then see how well we can do given the constraints. But I think sometimes it is more important to really question whether these constraints really deserve lexicographic preference over other objectives. What are the real or important constraints is itself an interesting question relevant to design.

Health Insurance and the Supreme Court

Alan Blinder (an economist at Princeton) wrote an op-ed which appeared in the Wall Street Journal on Friday: Life, Liberty, and the Pursuit of Insurance. He argues forcefully for keeping the Affordable Care Act in place as is because it represents a "bargain made in 2010." In particular, he does not want the Supreme Court to overturn the law nor Republicans to repeal it in the future.

Professor Blinder makes some important points about the horribleness of the previous health care system:
For one, the tax code incents employers to pay part of workers' wages in the form of health insurance, which is why insurance became tied to employment in the first place. For another, we have somehow decided that the state should provide anyone age 65 or older with health insurance, while everyone younger should fend for themselves.
He also points out there is adverse selection in the insurance market and rightly points out that the individual mandate (if actually correctly enforced) would eliminate this particular problem. The ability to purchase "insurance" for pre-existing conditions also is tied to the mandate (insurance is in scare quotes because it isn't really insurance if there is no uncertainty). However, he does not address the fact that even if the law were to survive, the mandate isn't sufficiently enforced. The penalty is so low that it remains optimal for young, healthy people to remain uninsured and buy insurance at a low rate only when something happens (the low rate is guaranteed by the no pre-existing conditions clause) which still leads to the unraveling Professor Blinder hopes to avoid. In addition, he does not discuss how moral hazard plays into the insurance market and how these concerns would be increased relative to the old system if the mandate remains (when people are perfectly insured, they demand more goods and health services than is socially optimal, or they may fail to take costly preventative care measures that result in large health costs (for others, since the individual doesn't pay them) down the line, etc.).

He also goes on and on about how the Supreme Court should not "decide what sort of health-care payment system the nation should have" and we should all accept the "bargain" Congress struck. This strikes me as a strange argument. First, there are clearly more than two choices (the ACA or the old system) so it is hard to see how striking the law down is the same as "judges making economic policy." In addition, while I agree law and economics are different, I think constitutionality, separation of powers, etc. matter in economically important ways (hopefully more on this in the future), and saying the Supreme Court shouldn't have the power to undo unconstitutional acts of Congress is a very strong claim and should be more carefully thought through.

Monday, April 16, 2012

Strategic Voting (Reality TV Edition)

From Cheap Talk:
The problem in a nutshell is that American Idol voters are deciding whom to eliminate but instead of directly voting for the one they want to eliminate, they are asked to vote for the person they don’t want eliminated.  This creates highly problematic strategic incentives which can easily lead to a strong favorite being eliminated.
 I am sure the producers of American Idol simply thought viewers would vote honestly. But if a question has actual consequences (seemingly no matter how trivial), the answers people give can depend more on the reason for asking a question than the question actually being asked. Also,
Jessica Sanchez was “voted off” and only survived because the judges kept her alive by using their one intervention of the season
If the clear favorite can be saved by the judges, you have less incentive to vote for her, further increasing the element of strategic voting. From what I understand, the judges save is a recent addition to the show which may be why there wasn't as much strategic voting in earlier seasons of the show.

Saturday, April 14, 2012

The Milwaukee Voucher Program

In the last post, I noted that what we really care about when evaluating the effectiveness of voucher programs is how the voucher students would have done if they had remained in public schools, and how public school students would have done if the voucher students had remained in public schools. One can make a stab at this first counter-factual by exploiting the mechanism in which vouchers are awarded: by lottery (a random assignment). Some students of similar backgrounds and schools get vouchers while others must remain in public schools. By comparing the outcomes of the students who got the vouchers to those who applied but did not get the vouchers, we can get an estimate of how the voucher students would have done had they remained in public schools.

The real debate over the effectiveness of the Milwaukee program (esp. on math and reading test scores) looked something like this:
  • 1991: Milwaukee program adopted
  • 1994/5: John Witte of Wisconsin's political science department publishes the first official review using basic techniques; finds zero or small negative effects of the voucher program (Witte publishes updates on the program regularly and generally finds mixed results).
  • 1995: Paul Peterson of Harvard reanalyzes Witte's data and compares attenders of voucher schools to other applicants and finds big, positive effects. A problem with his analysis is that the attenders are not a random sample of the winners of the vouchers which may bias results in the positive direction. Peterson's research objectivity does come into question in subsequent years as he keeps publishing -- he only publishes when he finds large positive effects and others do not, and not always in refereed venues. Witte begins to call attention to "characteristics of pseudo-scientific right-wing trash" in some of his presentations.
  • 1998: Cecilia Rouse publishes a more correct analysis in the QJE. She compares those selected to attend a private school to those who were not selected (which I posited was the correct way, above), which avoids the potential bias in Peterson's work. She finds positive effects for math and no effect for reading.

There are similar papers for just about every other voucher program out there (Cleveland, Michigan, NYC, DC, Columbia, Chile, etc.), and papers that look at effects outside of math and reading scores (increase in years of schooling/graduation rates, college attendance rates, cohabitation/pregnancy rates, etc.), but these are topics for other posts.

The general consensus is that voucher students do slightly better (or in some cases no worse) on various measures of short term achievement than their public school counterparts.

But what about that other question: how do the public school students do when there are voucher programs? Because voucher programs are usually tied with the implementation of charter schools, this also raises the question of how competition affects education outcomes. If competition improves education all around, then the "no difference" effects we see in the above papers can be explained by the charter schools and threat of vouchers forcing public schools to improve and lifting all boats, so to speak. And this has sparked even hotter debates than the one cited above, in particular, in relation to Hoxby's "rivers" paper, but that's another post.

You don't want to read the papers? That's fine. You can watch the movie (it's also on Netflix). It's good and worth watching, but be warned: the movie is almost never as good as the book. "Waiting for Superman" focuses on the plight of a few select students, how problematic/prevalent failing schools really are, the difference between teachers and teachers' unions, and the lottery system. It is very light on actual numbers and why vouchers and charters actually would fix the problem of failing schools.

Vouchers in the South

The Wall Street Journal printed an article ("School Vouchers Gain Ground") on Thursday noting that Louisiana is going to expand its voucher program to include the ability to pay for apprenticeships at local businesses, college courses, and online classes. The state is also planning on expanding charter schools and introducing "parent triggers" which allow parents to effectively convert the schools to charters. This in interesting because voucher programs are usually (always?) targeted at disadvantaged, low-income students, but by paying for college classes and online classes for public school children, it is opened up to be used by more middle class/wealthy students who are doing just fine in school, as well. It will be interesting to see what the effects of this program are. At the very least, the program is going to be more popular if more people can use the government's money to improve their children's education.

The article is pretty good, but the WSJ really falls down when it cites conflicting evidence on the benefits of voucher programs:
In Milwaukee, the nation's oldest voucher program, results from the 2010 state exam showed voucher students performed worse in math and reading than students in the city's public schools. But a study by Patrick Wolf, a professor at the Department of Education Reform at the University of Arkansas, found voucher students made more progress in reading than counterparts in the Milwaukee system over a four-year period. There was no difference in math.
Well, of course if you look at the test scores of the average voucher student versus the test scores of the average public school student, the voucher student will do worse: the whole reason they are voucher eligible is because they have a disadvantaged background and are in failing schools, thus are likely to do very poorly. What we really care about is how the voucher students would have done if they had remained in public schools, and maybe how public school students would have done if the voucher students had remained in public schools (sometimes it is argued that giving some students vouchers hurts those they leave behind).

In my next post I will relate what I know about the history of the evidence on the effectiveness of the Milwaukee program and voucher programs in general.

Sunday, April 8, 2012

Happy Easter

For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life. (John 3:16, NIV)
Martin Luther called this verse the Gospel in miniature. Happy Easter!

Saturday, April 7, 2012

Strategic Voting

Given that a person votes, will he vote honestly or strategically? It seems like in one corner of the dating world, people vote strategically: the procedure the dating site uses to decide whether to allow a person to join had to be adapted to better prevent strategic voting (via PRNewswire):
Entry to is only possible after passing a democratic rating process, where existing members of the opposite sex vote on new applicants based on photographs and a brief profile submitted by new applicants.
The community only allows opposite sex voting, as it was quickly realized on first launching the site in 2002, that members voting on same sex applicants would vote strategically and vote other beautiful applicants out. This strategic voting was most prevalent amongst the women.

Monday, April 2, 2012

When do Incentives Coerce?

The current mantra among economists is that incentives matter. Incentives matter a lot. But, can incentives matter so much that using them to nudge behavior actually becomes unconstitutional? That seems to be the question the states wanted the Supreme Court to consider when they presented their argument against the Medicaid expansion contained in the health care law.

Consider the following situation (model follows the break): 

Sunday, April 1, 2012

Enumerated Powers & the Commerce Clause

The health care law debate in front of the Supreme Court was a treasure trove of interesting things to think about from health care economics to political economy and politics and even ethics. Economists have been posting their thoughts on other blogs recently, and its interesting to see where other economists come down on certain issues.

In this post on Cheap Talk, Sandeep Baliga argues:
... Justice Scalia, Roberts etc can be forced to buy broccoli by law.
What is then the limiting principle? The commerce clause has no limiting principle, according to me, a non-lawyer. The limiting principle is the imposed by politics: any politician who seeks to regulate the broccoli market must run for election. This politician will reach the limit of his political career.
There are two issues in this statement, and in this post I want to deal with the first: Does the commerce clause give Congress unlimited power? I disagree with Sandeep and think that only a lawyer can come to the conclusion that the answer to this question is yes.

When reading a book, article, etc., one always keeps in mind the main message or point. Language is limited and it cannot be that one unclear phrase or part of a sentence can rewrite the entire meaning of the text when many clear sentences and phrases are present elsewhere (for clarification of this principle, see How to Read a Book: The Classic Guide to Intelligent Reading by M.J. Adler and C. Van Doren). For some reason this general "reading principle" seems to be most ignored by people when reading important texts. In the Constitution's case, the whole point is to give the central government limited powers which are then enumerated. Any reading of any particular clause to mean "the central government can do anything" must be incorrect. 

Madison even argues this point in Federalist 41 in response to a similar criticism of the Constitution in his day: that the taxing power of Article I Section 8 gives the government unlimited power:
It has been urged and echoed that the power "to lay and collect taxes, duties, imposts, and excises, to pay the debts, and provide for the common defense and general welfare of the United States," amounts to an unlimited commission to exercise every power which may be alleged to be necessary ... If the different parts of the same instrument ought to be so expounded as to give meaning to every part which will bear it, shall one part of the same sentence be excluded altogether from a share in the meaning; and shall the more doubtful and indefinite terms be retained in their full extent, and the clear and precise expressions be denied any signification whatsoever? For what purpose could the enumeration of particular powers be inserted, if these and all others were meant to be included in the preceding general power?
Madison goes on to note the particular phrase "their common defense, security of their liberties, and mutual and general welfare" appeared in the Articles of Confederation, and no one was arguing that the central government was all-powerful there. 

In commenting on the commerce clause specifically, Madison in Federalist 42 clearly states that the phrase "and among the several States" was included just to make the power of regulating commerce between nations complete by protecting states from "improper contributions levied" on goods passing through other states on its way to the world market. In some sense, it was just meant to be a free trade agreement among the States. Unfortunately, the Supreme Court in the past has expanded the commerce clause way beyond this original intent. I am with John Cochrane in hoping the ruling on the health care law reigns in this over-reading of the commerce clause.

Supreme Court & the Health Care Law

On Monday, Tuesday, and Wednesday of last week, the Supreme Court held oral arguments on the constitutionality of several parts of the Patient Protection and Affordable Care Act.

The oral arguments can be found on C-SPAN here. The video links are on the right hand side of the page. The briefs can be found here. The merit briefs lay out each side's case in full.

Believe it or not, it was riveting stuff! Take the time to listen to the second day (individual mandate) and third day (esp. Medicaid) since they seemed to be the core of the case. The oral arguments themselves were basically the Justices "asking questions" rather than each side presenting its argument in full, which I found entertaining.

In the next couple of posts, I will share some thoughts relating to this case.