Friday, December 28, 2012

Number of laws passed as a measure of Congress' productivity?

From the WSJ today:

Following the tea-party wave in the 2010 election, the 112th Congress looks set to be the least productive in recent history. By the end of November, the House had passed 146 bills over the previous two years, by far the smallest number for any Congress since 1948. The Senate passed fewer bills in 2012 than in any year since at least 1992.

 Damn, only 146 bills.

And the fat lady hasn't begun to sing quite yet.  We might yet get a tax increase without any spending cuts.  Imagine, the automatic spending cuts set to kick in are $110 billion...on a GDP of $15 trillion.  I will save you the math...that is less than 1%.

Note added:  The cuts of $110 billion are only 1% of GDP, which is relevant when thinking about the (possible!) impact on spending and hence GDP.  The cuts are a bit more than 4% of the total Federal budget, and of course more than 4% of discretionary spending.  Still, to refer to the cuts as "draconian" as is customary, seems a bit of an exaggeration...especially when the Federal government is clearly living beyond its mean.

Wednesday, December 26, 2012

The optimal safety net depends on the heterogeneity of the population?

Comparisons between heterogeneous countries like the US versus Sweden or Finland have always bothered me.  It seems intuitive that all kinds of public policy should optimally depend on the degree of heterogeneity in the underlying population.  A more homogeneous population should be able to provide a better safety net, for example, because there will be less of an incentive problem in providing a minimum level of welfare.   Here is an attempt to formalize that intuition.  I suppose this has been done before.  I don't have the math worked out entirely but it seems right...

Let individuals in the population be defined by a parameter a, which we will think of the individual's ability to create wealth in the market economy. (I do not presume a negative connotation here. This is a very narrow definition of ability -- the ability to create wealth in the market economy.  Great artists might not have much ability by this definition!)  More precisely, each individual has a function

     W = W(E | a)

where W is wealth, a is an individual-specific parameter, and E is effort.

We will assume that dW/dE = a

and let a be normally distributed.

Every individual will have an increasing disutility of effort, but this is the same for everyone.

Each individual will in the market economy choose her optimal level of effort and therefore her optimal level of wealth.  The optimum occurs where the marginal disutility of effort equals the marginal effect of effort on wealth, which is given by a.  With marginal disutility of effort increasing, it will be the case that individuals with higher a choose higher levels of wealth.  This makes sense.  If an individual has the capability to create more wealth, they will choose to do so.  This is the essential heterogeneity I am dealing with.

Now bring in public policy in the sense of a minimum safety net level of wealth, S, or a subsidy that would be available to anyone who has less wealth than S.

If there is no disutility associated with receiving the safety net subsidy, then a rational individual should compare the wealth less disutility they would achieve in the market economy to S and choose whatever is greater.  Since individuals with higher a choose higher wealth, there will be some critical level of the ability parameter, let's denote it a*, below which it will be optimal to elect the subsidy and above which it will be optimal to engage in the market economy.

The final step is to think about how public policy sets S.  There must be some value associated with equity, letting the less able achieve a minimum level of net wealth.  The cost of achieving equity, however, is the loss of effort from individuals who choose the subsidy.  As the base subsidy S increases, several marginal effects occur:  One, the marginal value of increased equity falls, because individuals getting the subsidy are increasingly well off.  Two, the marginal wealth loss increases as more-able individuals drop out of the market economy.  Wealth loss has to be a negative.  And third, as S increases, we move along the normal curve and experience an increasing slope of that density.  This last point is critical, as it addresses the issue of heterogeneity.  I assume that S is further than one standard deviation less than the mean of a.  Since the inflection point of the normal is at one SD away from the mean, that means we are in the range of increasing slope.  So as S increases in that range, more individuals are caught up, and more wealth is lost even if marginal ability were not increasing.

The optimal S, S*, has to balance the marginal benefits of greater equity against the marginal cost of wealth loss.  Remember that with S* there is also an implied a*.  Individuals with ability below a* take the subsidy; individuals above  a* participate in the market economy.

Here is a picture of two normals.  The tighter one represents a more homogeneous society to begin with (Finland, Sweden).  The less tight one we can think of the US.

Now remember we are far to the left on these densities, where the slope is increasing in a (which is on the horizontal axis).

Here is where it starts getting a little tricky, and I will have to check the math by getting the derivative of the normal density as a function of the standard deviation.

But suppose that S* for the tighter distribution, the more homogeneous population, implies an  a* right about where the density curve in the picture above ends.  Then go up to the density for the less homogeneous population, the wider normal curve.  Note that the slope of that curve will be greater than for the other curve -- essentially we are closer to the inflection point, where the slope reaches a maximum.

If the slope of the density for the more heterogeneous population is greater, that means that the marginal cost of increasing S is also greater, for we are picking up more of the population.

All the other marginal effects are the same, for we are at the same level of a.

A higher marginal cost of S means that the more heterogeneous population would optimally choose an S*, and an  a*, less than that of the more homogeneous population.

The optimal safety net depends on the heterogeneity of the population?

Tuesday, December 25, 2012

Medicare Advantage auctions: Asking too much?

When I teach about auctions, I like to ask students:  What does an auction accomplish, or put differently, what social roles does an auction play?

I point to two major roles:  An auction determines an allocation -- who gets the good being sold, or who is chosen to produce -- and it also determines a price.  Two very important things:  allocation and price.

In Medicare -- a confused and confusing policy area if there ever was one!-- auctions are used in both Medicare Part D (prescription drug coverage) and Medicare Advantage (private Medicare plans).

I am concerned that some policy proposals for Medicare Advantage (MA) are asking too much from an auction, for they add a third role:  determining the subsidy level for subscibers.  This is a complicated issue, requiring auction theory that is at the frontier.  But I think the intuition is pretty clear.  Also, while I will focus on MA here, similar issues arise with Part D plans, albeit somewhat less so because of the way those rules are set.

In a nutshell, here is the way MA plans work now.  Private insurers submit bids to provide health coverage for those over 65, with bids submitted on a county basis.  Folks who qualify for Medicare can either take the standard government-issue Medicare or opt into one of the private MA plans. The private plans are paid by the government a subsidy amount equal to the average per person cost of that county's standard Medicare plan.  If the plan bids more than that, the enrollees in that plan pay the difference between the subsidy and the bid.  If a plan bids less than the subsidy, then enrollees don't pay anything but the plan has to rebate the difference to enrollees as either cash or extra benefits (I do need to verify the specifics of this, but for now I don't think it is crucial).  Importantly, enrollees select which MA plan they want, so choice is a key part of the process.

So this is fine.  The auctions do two things, as above.  They determine which of the private plans provide service (allocation) and they determine a price (the price paid by enrollees).

Note that the subsidy is determined exogenously from the auction -- the average per person cost of standard Medicare.  Granted, there might be some endogeneity here, as the cost of the local Medicare plan depends on who opts into MA plans...but that seems of second order importance.

However, some policy proposals (see Alice Rivlin, for example) will add a third role to MA auctions, that of determining the subsidy.  The typical idea is to set the subsidy at the second-lowest bid of the private insurers.

The first order logic of this is great.  Set the subsidy at that level, and you can be sure that at least two plans will be willing to offer coverage at that subsidy amount.  Even more important, instead of having the MA subsidy set through a political process, it is set in a market mechanism.  What could sound better than that?

Here is my concern, arising from the effect that setting the subsidy in the auction will have on strategic bidding behavior. (Let's be clear that strategic bidding behavior should be expected, that is, insurers will not just put bids in that equal their expected cost, even if that is what the government asks for.  Insurers will put in bids that maximize their expected profit.)

The issue is that by putting in a higher bid, an insurer has a reasonable expectation that it will increase the subsidy (if the bidder happens to be the second lowest bid).  This will increase the subsidy to enrollees and make it less likely that the insurer's bid will result in a net payment by the enrollees.  Also, as the subsidy increases, more people will opt into the MA plan arena.  Seems pretty clear to me that this will result in higher bids.

Amplification of this problem arises because is in MA plans, there is not a standard package of benefits.  By adding benefits, and putting in a higher bid reflecting the higher cost of that expanded package, an insurer minimizes any competitive effect of being a high bidder in the auction while still having a reasonable expectation that the subsidy will be increased.

As all bidders do this, the entire distribution of bids shifts higher.  Studies that have been done on the cost savings from basing the subsidy on the second lowest bid are obviously wrong, as that second lowest bid is going to be higher.

The idea is not that different from shifting from a second-price sealed bid auction to a first-price selaed bid auction (standard auction where something is being SOLD to bidders).  It would seem that taking the highest bid as the price in an auction would clearly be better than taking the second highest.  But as the rules change from second-highest to highest, we have to expect that bidders will lower their bids.  I always ask students:  What do you think is greater -- the second highest out of a distribution, or the first highest out of a lower distribution?

Friday, December 21, 2012

Just for the record: Federal spending

Sorry for the small font on this -- the table is from here if you want to see original.  I added the last line, percent growth year on year.

Three main points to note:  First, the 18% increase in total federal outlays from 2008 to 2009, on top of a 9% increase 2007 to 2008, both of which were stimulus to a great extent.  Second, since then, there is only one year when nominal spending went down, by 2% from 2009 to 2010.  And third, overall between 2007 and 2012, nominal Federal outlays are up 39%.

In previous posts, I noted my fear that stimulus spending would become permanent.  Here is a quick graph of the outlays from 2007-12.

House Republicans Deal a Bad Hand to Democrats?

Speaker Boehner pulled his "Plan B" bill from the House Thursday evening, saying there were not enough votes to pass it.  This bill would have preserved the current tax rates for those under $1 million in income, allowing tax rates to rise on those above.

Pundits are crying the end of the world, which coincidentally coincides with the predictions of the ancient Mayans.

The end of the world as we know it is not nigh.  I actually give the advantage now to the forces in favor of smaller government, as in less spending and lower taxes.

Look at it this way.  Any deal has to win approval of a majority in the House.  My working assumption  is that the Republicans will hold together (but see the * endnote below).  Thus, any deal needs approval of almost all Republicans.  Think of the Republicans as being lined up on a continuum, from very conservative (lower taxes, lower spending) to more moderate (willing to accept higher taxes, higher spending).  Boehner's failure defines the conservative side of the spectrum in regard to the minimum deal it is willing to accept and the risks it is willing to endure.  With this clarity, the center of gravity in the Republican continuum has shifted to the conservative side.

Suppose I was negotiating with two people, one very demanding and one less so. The more demanding person just committed himself to blowing his head off if he doesn't get his way.  I would say that the center of gravity shifted to the very demanding side of the spectrum.

The conservative Republicans are willing to risk going over the cliff, and I think they are correct in accepting that risk.  My belief is that "the cliff" is not anything like truly going over a cliff.  There will be some unfortunate consequences, especially in regard to the Alternative Minimum Tax and Medicare rates for doctors (the media are not focusing on the Medicare implications, but the so-called Doc Fix needs to be voted this year or Medicare payments to docs will fall).  Taxes will go up, which to be honest I don't see as a disaster either.

If I am right in that the cliff is not a disaster, the Democrats lose much of their negotiating power in the new year.  That power right now is fueled by media-supported claims of economic apocalypse.  If Jan. 1 comes with no deal, and life goes on, how does the Democrat position look?  There will be some cries of pain, yes, but blame will be equally spread -- and if there is any justice, most folks will blame the leader, ie., President Obama, for failing to negotiate a deal.  Thus, in the new year, the balance of power shifts to the conservative side, with a better prospect of getting more spending cuts and a better mix on the revenue side.

*Endnote.  It is possible that the Republicans will not hold together in the House.  If Obama and Reid craft a deal in the Senate, could that attract all the Democrats in the House and just enough Republicans to pass?  Possible, but unlikely...unless the deal is attractive enough on the "less spending and taxes" dimension.