Tuesday, July 22, 2014

Halbig fictions

If you haven't heard, a three-judge panel of the DC circuit court just ruled that individuals who bought health insurance on the Obamcare exchange in any of the 36 states that refused to set up their own exchanges are ineligible for subsidies. The case stems from a typo in the section of the ACA that lays out formulas for calculating subsidies, which refers to "state" exchanges rather than to both state and federally set up exchanges. Proponents argue that the typo was a deliberate: congress intended to deny subsidies to residents of states that refused to create their own exchange.

Mike Konczal points out the fundamental problem with the Halbig proponent's position. They are arguing specifically that the statutory language isn't a typo at all, and that theirs is the intended interpretation of the statute. Halbig and its proponents claim that the authors of the ACA intended to apply subsidies only to state implemented exchanges in order to coerce states into implementing exchanges so that the federal government wouldn't have to. As Konczal says, the proponents claim that it wasn't an ambiguous typo, but a secret doomsday device. The problem with that, of course, is you can't threaten people into submission if they aren't aware of your doomsday device--if this was intended to be threatening, then where is the threat?

Michael F. Cannon has done his best to dig up actual evidence of the Halbig threat:I will add the same disclaimer as Cannon did: this is the only evidence, anywhere, ever, that has been offered as support for Halbig's claim. Cannon states the proponent's case:
"Baucus’s response is hardly a model of clarity. But I can see no possible interpretation other than Baucus is admitting that (A) the statute makes tax credits conditional on states establishing an Exchange, and therefore does not authorize tax credits through federal Exchanges, and (B) that this feature was essential for the Senate’s tax-writing committee to have jurisdiction to legislate in the area of health insurance."
I want to point out that Cannon's point (B) doesn't really follow. This was an impromptu remark offering tax subsidies as one example of why the Senate Finance Committee has jurisdiction over the ACA. Indeed, the subsidies aren't even the only reason the Baucus offers--he starts by noting that the ACA is largely about medicaid regulations, which are indisputably exclusive jurisdiction of the committee. But this is a moot point--jurisdiction and parliamentary procedure are not disputed in the Halbig case.

As to point (A) I think you really have to twist the words to make them say that subsidies don't apply to federal exchanges. Here's the transcript of the video starting at 1:54 minutes in:
Ensign: "How do we have jurisdiction on changing state laws on coverage? [outside of Medicaid]"

Baucus: "there are conditions to participate in the exchange"

Ensign: "that's right"

Baucus: "for setting up an exchange"

Ensign: "these would be conditions to participate"

Baucus: "and states, an exchange is essentially is tax credits"
The last line reveals the full extent of Baucus's argument: "Senate Finance Committee because tax credits." Baucus was arguing that Senate Finance Committee can promulgate insurance regulations for plans offered on exchanges because plans on the exchanges are eligible for tax credits--at no point anywhere in the video is any contrast made between exchanges created by states versus HHS. In fact, adopting Cannon's interpretation that states can opt out of the tax subsidies actually contradicts Baucus's point because the bill does not allow states to opt out of the insurance regulations promulgated by the Senate Finance Committee (this is not disputed in Halbig). Had it been made clear, at any point during this hearing, that states opting not to set up their own exchange would be ineligible for tax subsidies, Senator Ensign would have attacked the validity of the committee's regulations on non-subsidized exchanges. He didn't do that, because it was clear to everyone in that room that non-cooperating states would still be eligible for tax subsidies. CASE CLOSED.

Besides, I don't accept this kind of evidence as valid. It gives individual congressmen way too much power. If Baucus had casually said in committee that section 1312 should be interpreted as requiring everyone to make him a sandwich, would we all be legally required to give him a sandwich? It was his intention, and there's nothing in the legislative record that says otherwise!

[update: Here's an amicus brief, signed by Max Baucus, stating that
"Congress always intended that the tax credits be available to all Americans, regardless of whether they purchased their health insurance on a state-run or federally-facilitated Exchange."

Monday, July 21, 2014

On Malinvestment

Why can't we have nice things?
I stopped following Noah Smith's debate with the so-called "Austrian Economists" (which I will refer to as "Austrianists" to distinguish them from economists actually from Austria) when Bob Murphy said this:
"Austrian economics per se doesn’t make empirical predictions–that’s either its virtue or its vice, depending on your methodological views."
Ok, whatever. But the fact that Austrianism is a load of crap doesn't mean that everything any of them have said is totally useless. A lot of Austrianist writings talk about one concept in particular, called "malinvestment," that causes the business cycle. Although many mainstream models include risky investments (not exactly mainstream, but here's one!), few of them contain anything resembling "malinvestment." Yet, I suspect that most people, even most economists, secretly believe something like malinvestment is closer to the truth. Let's leave the models behind for a moment, and examine something that happened in the real world.

I live in a small-town suburb of a big city. In the mid-2000s we got a coffee shop, and it was always busy. A couple years later we got a second coffee shop, and it did decent business as well. Then we got a third coffee shop, a second location of the first coffee shop, a drive-through coffee shop stand, then a coffee-shop/book-store combo, then the national chains took notice and we got a starbucks, then a coffee-shop/church combo (you really can't make this stuff up). Now, the residents of this town are fairly wealthy, but remember this is a small town populated by people who commute down to the big city everyday, and who therefore consume most of their coffee outside of town. Needless to say, we simply couldn't sustain the coffee-shop boom. And because they competed against eachother, we didn't just watch the newcommers go out of business--they all went out of business, more or less at the same time. Not even the original coffee-shop, the one that had been thriving alone, could survive the debt it accumulated while competing against the entrants. But here's the thing: it's pretty clear that this town can support at least one permanent coffee shop.

This looks a lot more like malinvestment than any mainstream theory of business cycles I've ever seen. New Keynesian theory doesn't apply because there was no demand shock--aggregate demand for coffee remained constant the whole time. Real Business Cycle theory doesn't apply because there wasn't any collapse in our ability to produce coffee, we simply tried to produce more than people wanted. It looks superficially like a news-shock model in which hypothetical coffee-shop investors heard that coffee shops in my small-town suburb were the next facebook, but I think even the peddlers of these models secretly know that's not what's happening--no one was predicting that our-town's coffee consumption was booming, just that they would be able to steal enough of the market to make it as the One True Coffee Shop for this town.

If I had to coerce the reality into a neoclassical model, I'd say our coffee shop cycle was a case of failure to converge to equilibrium. Equilibrium models assume not that unprofitable business will be driven out of the market, but that there are no unprofitable businesses in the market. A problem with the standard equilibrium modelling is that they ignore the possibility that unprofitable entrants in a market can stay in business long enough to drive both themselves and profitable incumbents into bankruptcy. Consider a model (I promise, hardly any calculus!) of a coffee shop in a small town. It's a very small town actually--they only demand 10 cups of coffee every month. But that's ok because the shop earns 1 unit of net revenue after paying labor and materials on each cup, and their fixed costs come to 8 units a month. They're earning 2 units of profit every month and, like a good little corporation, remit this profit immediately to shareholders (so that the corporation has zero cash on hand). Now an upstart little cretin from the big city moves in and sees that this coffee shop model is profitable, and sets up an identical replica of it right across the street. Coffee drinkers are indifferent between these two identical shops, so they go to each half the time. This means that both shops are selling only 5 cups a month, accumulating debt at a rate of 3 units a month to cover fixed costs.

Of course, they cannot go into debt for ever. A bit of math reveals that at 5 percent interest the companies become permanently unprofitable after 10 months of competition: The coffee shop needs to borrow 3 units each period for T periods at 5 percent interest, so the real present value of the debts that the coffee shop will accumulate is a geometric series given by [$$]Debt=\sum_{t=o}^T\frac{3}{1.05^t}=63\left(1-\frac{1}{1.05^T}\right).[$$] After date T, the coffee shop will begin earning 2 units of profit for ever after, which it can use to repay the loans. The total real present value of all future profits--the maximum amount of debt the coffee shop could possibly repay--is [$$]Profits=\sum_{t=T}^\infty\frac{2}{1.05^t}=\frac{42}{1.05^T}.[$$] Thus, the loans cab be repaid only if [$$]\frac{42}{1.05^T} \geq 63\left(1-\frac{1}{1.05^T}\right).[$$] Solving reveals that the maximum financing possible is T=10 months. At the 11th month, the coffee shop will default because the size of it's debts exceeds the total sum it will earn over all future periods. At 11 months, both the incumbent and the entrant are rendered permanently, irretrievably unprofitable.

I only do that bit of math so that we can talk about monetary policy. Austrianists see a malinvestment as a story about optimal monetary policy. That's pretty hard to follow, because the connection is pretty ambiguous. Monetary policy affects the above only to the extent that changing the nominal interest rate target temporarily changes the real interest rate in the inequality above--as the real interest rate falls, the T date increases. This, of course, ignores all the demand-side effects that money supply, prices, and interest rates have on the demand for coffee, and even then it is unclear how a lower real rate would actually affect the coffee shop market--regardless of the T date, it is only profitable for at most one of the two companies to borrow at all.

Strictly speaking, the coffee shop situation above shouldn't happen in neoclassical models--such models assume we've already reached a situation where all unprofitable entrants have been driven out of business, without addressing the question of whether profitable businesses can remain in business long enough to outlast unprofitable new entrants. Yet we see it happening all the time in real life--an explosion of new entrants render formerly profitable markets unprofitable for both the new and incumbent firms, with the resulting bust leaving us with fewer firms than the market can profitably sustain. (side note: the last coffee-shop bust happened years ago; since then my small town has had several other boom-bust cycles, most recently involving dance studios.) My suspicion is that something like this coffee-shop malinvestment cycle is what causes macroeconomic business cycles. It's not that businesses are expecting demand to surge in particular markets and turn out to be wrong, but that misguided investors think they can make it in already saturated markets, driving both themselves and the incumbents out of business.

What are the policy implications of malinvestment? It's hard to say without an empirically grounded mathematical model. But my intuition suggests a few things: 1) counter-cyclical monetary policy, tightening access to finance when entrants are upsetting markets and loosening it when incumbents are collapsing, 2) macroprudential regulations that prevent stupid entrepreneurial decisions like entering an already saturated market with a lackluster business model, 3) bankruptcy protections that allow once-profitable incumbents to discharge debts accumulated while competing with insane market entrants. In otherwords, if you think markets are plagued by malinvestment that chases good investment out of business, the policy implications would seem to be much closer to standard Monetarist and Keynesian views than Austrianist free-market liquidationism.

Monday, July 14, 2014

Monday Morning Music

You may have noticed that I haven't actually been posting music every Monday. That's simply because I've realized that I only write a couple of actual posts a week, so a weekly music post would shift the focus of this blog too far away from economics. But I still plan on posting music every once in a while (this is, after all, an easy way for me to keep track of youtube music that I like).

Today's piece is the death scene from Mussorgsky's Boris Godunov:It's actually surprisingly hard to find a good version of this aria, considering that Boris Godunov is the most-played Russian opera of all time--even more than Tchaikovsky's Eugene Onegin--and this is the most famous scene from the opera. The version from the Bayeriche Staatsoper is absolute perfection, but has unfortunately been removed from youtube.

Now, Boris Godunov is not in it's original Mussorgsky form. The opera's musical style has always been controversial, prompting several revisions over the centuries, most notably by Rimsky-Korsakov who "fixed" what he believed were "structural flaws" in several of the opera's arias. Lately it has become fashionable to play the restored opera without Rimsky-Korsakov's revisions, though "restored" by no means implies "original." However, I have no clue which version the above video is.

Thursday, July 10, 2014

When is moral hazard adverse selection?

The fact that the insurance will pay your fines does not actually mean you can afford the insurance, even if it is actuarially fair.
[Update 7/15/2014: this post has been edited to fix an error. See explanation below.]

Much of the debate surrounding Obamacare has been about how to minimize moral hazard and adverse selection, while decreasing the inequalities in the system that, for example, lead to higher costs for women than for men, and higher costs for those with higher health risk than those with lower risks. Moral hazard is the effect by which providing insurance increases total health expenditure. While this is often viewed as a type of inefficiency, I explained previously why this is actually often a good thing (which it turns out is closely related to John Nyman's research). Adverse selection is the effect by which individuals with lower health risks get priced out of the insurance market because their low risk reduces their willingness to pay for insurance.

Einav and Finkelstein (2011) laid out the textbook methods for detecting and quantifying these effects, and note that the "positive correlation test" which tests whether those who opt to buy insurance have higher average costs than those who do not, cannot discern between moral hazard and adverse selection, as both lead to higher expenditures for those who have insurance than those who don't. They then summarize how one might distinguish between the two: you need a dataset with exogenous variation in premiums, so you can see whether lowering premiums--inducing more people to buy insurance--causes average costs to decline. If it does, the theory goes, you have adverse selection in the market. This, in turn, comes with a couple possible policy recommendations: either risk-rate the insurance premiums, if possible, or enforce a mandate requiring that everyone buy insurance plans that provide some mandatory (relatively high) minimum amount of coverage, or even prohibiting heterogeneity of plan types. Kifmann (2002) and others (myself included) have also argued that a tax-and-subsidy scheme could achieve our policy objectives more effectively than command-and-control approaches to plan coverage requirements.

In my own simulations of the health insurance market, I keep coming across a problem in the above analysis. Even using the revised methodology from Einav and Finkelstein--using identifying variations in premiums to differentiate between moral hazard and adverse selection--doesn't always work. Despite having drastically different policy implications, moral hazard and adverse selection aren't always distinguishable from each other in reduced-form estimators. For illustration let's return to the healthcare model discussed in my moral hazard post, originally taken from Blomqvist (1997) and calibrated to the RAND health insurance experiment data: [$$]U_i=E_i\left[\frac{1}{-c_i}+\frac{0.001098}{-\left(h_i-\theta \right)}\right][$$] where [$]h_i[$] is spending on healthcare, [$]c_i[$] is spending on all other goods and services, and [$]\theta[$] is a two-state random that takes the value [$]\theta=4.86[$] when the individual is healthy, and [$]\theta_H=61.07[$] when he is sick. Sickness occurs with probability [$]p_i[$], which varies across individuals. There is insurance available with no deductibles and a 15 percent coinsurance rate, but insurers can perfectly observe risk types, so that the insurance plans are perfectly risk-rated so that for each individual [$]i[$], [$$]m_i=0.85E_i\left[h_i\right][$$] where [$]m_i[$] is the insurance premium. As in Blomqvist, we'll assume individuals have income of 150 (measured in hundreds of dollars), so that the budget constraints are given by [$$]c_{i,\theta}+m_i+0.15h_{i,\theta}\leq 150[$$] if they buy insurance, or [$$]c_{i,\theta}+h_{i,\theta}\leq 150[$$] if they do not buy insurance.

Now, it is clearly efficient for everyone to buy insurance. Insurance itself has no loading costs and are risk rated, while all individuals are strictly risk-averse and have health risk--that is, we can costlessly make everyone of these individuals better off by reducing their risk. Yet, when you do the math, it turns out that all individuals with [$]p_i<0.1[$] (including the benchmark case in my previous post with p=0.086!) will opt out of this insurance despite the fact that plans are perfectly risk rated. These individuals are selecting out of the insurance market even though the number of higher-risk individuals in the market has absolutely no impact on their own premiums!

The reduced-form methodology described in Einav and Finklestein would indicate the presence of adverse selection in our fully-risk rated insurance market, because exogenously lowering premiums would induce lower risk types to buy insurance, thereby reducing the average costs of those who have insurance. Here's a graph of the relationship between risk type [$]p_i[$] and the minimum coinsurance rate at which individuals are willing to buy insurance:
When coinsurance rates are too low, individuals with low health risks get priced out of the market due to excessive moral hazard. The minimum coinsurance rate at which individuals will buy insurance (vertical axis) is highest for the lowest risk types (horizontal axis).
But what's actually happening in our market is not adverse selection as we typically think of it, but rather a problem of moral hazard: the 15 percent coinsurance rate would induce individuals to buy a lot more healthcare than they would if they had to pay for a larger share of it, which in turn drives up the premium insurers have to charge. In this way, the excessively generous benefits of insurance actually drives up spending so much as to drive the individual out of the market.

So when does moral hazard cause adverse selection? This is an important question because, especially post-Obamacare, many individuals face essentially near-zero coinsurance rates for large medical bills above the out-of-pocket maximums, which could be pricing some of them out of the market if their preferences resemble the utility function above. Intuitively, in the utility function above, we are guaranteed to have some minimum coinsurance threshold because the additional utility from more health spending is always strictly positive, meaning that the choice of how much to consume explodes as coinsurance drops to zero, which drives up premiums and therefore drives down total utility, eventually so much that it is less than without insurance at all. This is probably not a reasonable assumption, as I'd be willing to bet that people wouldn't consume an infinite amount of healthcare if it was totally free--while moral hazard certainly exists to some extent, people don't generally want more healthcare than they feel that they need. Obviously, when the coinsurance rate is 100 percent (the insurer pays zero percent) expected utility without insurance and expected utility with insurance are equal. If expected utility with insurance remains higher than without insurance for all coinsurance rates less than that (when insurers pay more than zero percent), then we can say that moral hazard never causes selection effects; otherwise, there exists some coinsurance rate low enough so that some individuals will select out of the market.

It turns out that mathematicians already have a name for exactly this condition: it's called "single-crossing," which you may recall from the Topkis Theorem, or the optimal tax literature, or as that thing your microeconomics professor mentioned while you weren't paying attention. Our case is a rather trivial application: if we define [$]z[$] as the percentage of health costs that the insurer pays, [$]F\left(z\right)[$] as the expected utility with insurance, and [$]G\left(z\right)[$] as expected utility without insurance (which is a constant function over [$]z[$]), then single-crossing as applied here says simply that there exists [$]x \in \left[0,1\right][$] such that for all [$]z\in \left[0,1\right][$], [$]z\geq x[$] implies [$]F\left(z\right) \geq G\left(z\right)[$] and for all [$]z[$], [$]z\leq x[$] implies [$]F\left(z\right) \leq G\left(z\right)[$]. We all ready have established that the two functions intersect at [$]z=0[$], which implies that [$]x=0[$]. Graphically, we can easily see that this is not true of the utility functions specified above:
The black line shows expected utility,[$]F\left(z\right)[$], for individuals that buy insurance, while the horizontal red line shows expected utility without insurance, [$]G\left(z\right)[$]; both derived from the utility function specified above with [$]p_i=0.086[$].
So when might the single crossing condition be satisfied? In our case, the answer is basically only if utility from health spending is bounded, and if that bound is sufficiently low as to avoid too much moral hazard.

The point of all this is to say that moral hazard and adverse selection are not as distinct from each other as we might think, and that it can be empirically difficult to disentangle. In fact, under the right conditions--low cost-sharing with non-single crossing utility functions--the two concepts actually merge into one, a condition which will not show up in reduced-form econometric modeling. And because the policy implications differ, this points to a need to supplement our reduced form estimates with fully estimated structural models before making policy recommendations.

Feel free to check my math or play with the model here.

[Update explanation: the original code I used for this post miscalculated the insurance premiums. It had [$]m_i=E_i\left[h^*_i\right][$] instead of [$]m_i=zE_i\left[h^*_i\right][$]. The result of this error was an overestimation of the optimal insurance rates and, consequently significantly underestimating the thresholds at which individuals would drop out of the market. For the benchmark case with p=0.086, the actual threshold below which he will drop out of the market is 17 percent out-of-pocket costs, which is a lot higher than the 2.5 percent mentioned in the original version of this post.]

Thursday, July 3, 2014

Is the stock market due for a correction?

Does it even make sense to ask?

A friend of mine is worried that the stock market might have a "correction" soon, and is thinking about selling off his stocks in anticipation. Looking at the Dow Jones Industrial Average (DJIA). It's easy to see where this talk is coming from:
Graph of the Dow Jones Industrial Average, monthly, January 1985 to present.
From this graph, it appears that we are currently well above the historical trend, and therefore due for a correction. On twitter, Seth Trueger said what I think most people are thinking:
Indeed, if there is a tendency for the stock market to regress to the mean ("mean," in this case, meaning the trend line in red), then the fact that we are currently above the trend line implies we should expect a higher than average probability of a downward movement in the stock market--that is, a "correction" that returns us to the true, underlying time-trend. We'll call this the One True Trend theory of the stock market.

But time series are much trickier than that. Series that don't have regression towards the mean can look quite a bit like series that do. Consider, for example, a random walk with drift:[$$]y_t=y_{t-1}+\alpha+\epsilon_t,[$$]where [$]y_t[$] is this month's stock index, [$]y_{t-1}[$] is last month's index value (a coefficient of 1 means this is a random walk), [$]\alpha[$] is a constant (the "drift" term), and [$]\epsilon_t[$] is this month's random shock, which is normally distributed with mean zero. This process will produce a graph that looks a lot like the stock market with a clear, unambiguous time trend caused by the drift term, and will appear prima facie to exhibit reversion to the mean, because the error term is symmetric--negative shocks are as common and as large as positive shocks, so the index will appear to bounce around a common time trend, on average. But there actually is no One True Trend in this process--all shocks are permanent, being above trend in one period has absolutely no effect on the probability of the index rising or falling in the next period. If, on the other hand, the coefficient on [$]y_{t-1}[$] is less than 1, then the impact of random shocks would diminish over time, resulting in reversion to the mean--maintaining an above-trend index value would require a sequence of increasingly extreme, and thus decreasingly likely, random shocks. That is, when shocks are transitory rather than permanent, being above trend increases the likelihood of a decrease in the stock price--a "correction," if you will.

The question above is just a restatement of what is more formally known as the unit root hypothesis. The autoregressive process above, with a coefficient of 1
on [$]y_{t-1}[$], has a unit root, which implies that each realization of [$]\epsilon_t[$] actually shifts the entire time-trend permanently. With a unit root, there is no One True Trend--the observed time trend is actually variable, dependent on the entire history of realizations of [$]\epsilon_t[$] since the beginning of time. And since the next realization will also shift the time trend permanently, whether we are above or below "trend" cannot possibly predict the future direction of the index, ever. It turns out that the (stationary) ARIMA model that minimizes the Akaike information criterion (in a sense, the best-fitting valid model) is an ARIMA(0,1,0) with drift. That corresponds to exactly the equation above, and yes, it has a unit root:[$$]y_t=y_{t-1}+43.7+\epsilon_t.[$$]Sorry folks, but as best we can tell from this one series, the One True Trend is apocryphal, and there is no such thing as a "correction." What we perceive as corrections are actually just totally random shocks. I've plotted the forecast below, and as you can see it does not predict a "correction." In fact, an increase in the DJIA remains slightly more likely than a decrease, despite the fact that we are way above the apparent trend:
Forecast of the DJIA

To drive home the point, I did a few simulations calibrated to the exact ARIMA process estimated above. Out of slightly more than 100 simulations, here are a few that looked interesting:
Prima facie, this graph would appear to suggesst a tendency for reversion to the mean. But if you're predicting a future of rapid growth because we're below trend, you'd be quite mistaken.
This looks a lot like the stock market, and many other macro time series. But as in the other simulations, being currently below trend conveys no information whatsoever.
Nope, this graph does not imply we are in the midst of a massive bubble.
While the graph strongly suggests a tendency to return to trend, this is actually not true of the process that generated it.
As these simulations show, random walks with drift often do seem to bounce around a One True Trend, but this is entirely an illusion: these are all simulations from a process in which distance from trend contains absolutely no information about the likely direction of future stock movements.

But then again, I did mention that time series are tricky. We must avoid committing the Mankiw Unit Root Fallacy--the fact that our data is empirically consistent with a unit root does not actually imply that all shocks are necessarily permanent and inevitable. A bivariate analysis may detect a combination of transitory and permanent shocks and, either way, there's no reason to suppose that policies can't affect stock values, or that insider information isn't predictive of stock prices. But, what I can say is that if you are one of the many people worrying that stock prices are above trend, stop--your fears are empirically unfounded. Perhaps Bill Gardner said it best:Indeed. Empirically, the history of stock prices adds nothing to your priors.

As always, you can review my data and script file.