Dollars and Jens
Saturday, April 25, 2020
reopening the economy
Most of the cost-benefit analysis I've seen of non-medical measures to reduce the contagion of covid have been treating them as an all-or-nothing deal.[1]  I want to think more granularly: independent of why a particular level of contact takes place, consider the incremental cost of a small change in contact.  What are the costs of higher contact?

And the answer leans heavily on the nature of exponential processes, with which people may be more familiar than a month and a half ago.  First, note that the reproduction number of the virus depends on the amount of time an infected person is contagious, in addition to other stuff.[2]  In the fastest exponential growth phase of this disease, cases seemed to increase by a factor of the basic reproduction number about twice per week; I'm going to use "half a week" as the effective infectious time here.  Okay, then, consider some scenario as a baseline, and let's consider a small change from it.  If we eliminate 1% of contacts in a half-week period, and other than that half-week change nothing — go back to the baseline — then in expectation we should have 1% fewer people infected than we would otherwise.  Forever.  Whatever your exponential growth and decrease do after that period, that 1% is locked in.  [3]

Let's suppose the optimal number of QALY that we expect to lose from covid is 2 million; this proceeds from an estimate I've seen of 8.6 per fatality (because they skew older), a guess that we're aiming at close to 100,000 deaths, and a rough factor of a bit over 2 to account for morbidity injuries to patients who recover.  Let's call that $400 billion.  Note that, as opponents of shut-downs like to observe, this is much smaller than the economic costs incurred from shut-downs, but note, as they do not like to observe, that that fact is basically irrelevant because the correct comparison is how much worse things would be, health-wise, if we relax restrictions, compared to how much better the economy would be doing.[4]  So if opening up restaurants of a certain type in a certain manner increases "contacts" by 1%, the cost isn't $4 billion — it's $8 billion per week.  In recent years, the United States economy has produced about $400 billion per week, so if those contacts represent more than 2% of the US productive economy, we should do them; if they represent less, they aren't worth the added health risks.

That first $400 billion number is very rough; you could reasonably suppose that the mortality/morbidity cost is $700 billion or $250 billion.  The other numbers are more reasonably precise, though, and the primary point I want to make is that the optimal response will be one with a lot more economic costs than health outcome costs.

[1] The most egregious versions seem to assume, in fact, that if there is no government response, individuals will blithely behave as usual; in fact, restaurant attendance seems to have dropped about 70% before government action took place, so many of the costs and benefits of "closing down the economy" are independent of government policy actions.  It won't matter whether changes considered here are driven by policy or not.

[2] If you're more infectious at some times than others, we're going to end up with an average of sorts.

[3] This supposes that we aren't going to end up acquiring herd immunity by burning through a large fraction of the population.  If that is in fact what we're going to do, then things change a lot; in fact, the benefit of shutting down is very small once we keep the disease from overwhelming the health care system, and possibly even then if treatment doesn't actually do very much good.

[4] The ratio between "cost/benefit" and "change in cost/change in benefit" is what we call, in economics, an "elasticity", and in most contexts it's on the order of 1 or 2, but boy is it not in this context.

Wednesday, April 01, 2020
total stimulus
The recent COVID relief bill that passed congress has been reported, variously, as being $2.2 trillion in size, or, in some cases, as being $6 trillion, as part of the money is to be leveraged by borrowing $4 trillion from the federal reserve.  There are various people who want to report a big number — journalists like a big number in a headline because it gets attention, some politicians like it because it looks like they're doing a lot, and some populist opponents of the bill trumpet it as an enormity, another massive debt that we are thrusting on the shoulders of future generations.

I view it as a bunch of numbers that are added together.

There are three different kinds of things in the bill, and I would really like to see them broken out separately.  Now, there are two kinds of people these days: people with more free time than a month ago, and people with less.  I'm in the latter camp, so this will not be particularly researched or detailed, but here's a taxonomy of dollar figures:

Finally, I'll note that I've largely joined some prominent economists in avoiding calling it a "stimulus" bill; to the extent that it has similar goals to a stimulus bill, it actually feels more to me like a monetary stimulus than a fiscal stimulus.  The loans in particular have that feel; they're intended not to affect wealth distribution, but to get literal cash to economic agents who suddenly need more cash than they had provisioned for.  This is less true, but still fairly true, of the cash being handed out to individuals; of course, this does involve some wealth redistribution, but the scale of the cash payments is a couple of weeks' spending for many people without savings, or a modest increase in savings for those who suddenly wish they'd been saving more; it is on the scale of short-term spending needs, not on the scale of life-time income or wealth, and is much more attuned to alleviating financing constraints than solvency constraints on economic decision-makers.

Wednesday, July 11, 2018
Roth vs. traditional retirement plans
I have a lot of work I should be doing, but someone is wrong on the internet:
The chart makes a lot of assumptions, including that each investor contributes $1,000 to either the Roth or traditional IRA, that they are in the 25 percent tax bracket and that there is a seven percent annualized return. And in almost every case, the Roth does better than the traditional, even for older workers.
Okay, this is correct: if you give up $1,000 per year now to put into a retirement account that won't be taxed in the future, you will have more retirement savings than if you give up $750 per year now to put $1,000 into a retirement account that will be taxed in the future, at least if you assume the growth rate of the money exceeds the rate at which you discount your marginal consumption spending. (And boy do they seem to assume that, but that's a harder quibble than the apples-to-oranges comparison they're making here.)

They would be on somewhat firmer ground if, instead of supposing each investor contributed $1,000, they supposed that each investor contributed $5,500: because the dollar amounts of the contribution caps are the same, the effective cap on the Roth is higher than the traditional IRA: you can forego up to $5,500 to a Roth, versus (using the 25% rate) $4,125 for a traditional IRA.  Similarly, if you're going to max out a 401(k), even if you think your tax rate in retirement will be somewhat lower than it is now, it may be worth paying the extra taxes now to avoid not just taxes in retirement but compounding taxes along the way.  Furthermore, if you are likely to save more money using one kind of account than the other (perhaps because of the salience of taxes), there may be behavioral reasons to use the one that will incline you toward better behavior.  If you aren't hitting the caps, though, and you think your tax rate in retirement will be lower than today's, and you compare apples to apples, the Roth is your better bet.

Thursday, February 09, 2017
game theory
This might be in part because I'm teaching game theory this semester, but I look at this working paper suggesting that investment has gone down in industries that have become less competitive, and I'm struck by the idea that not only does the optimal level of capital go down if a tacit cartel forms (as production goes down), but that publicly maintaining a low level of capital could be useful in keeping a tacit cartel together; underinvesting is a commitment device, making it hard and costly to ramp up production should there be an otherwise profitable opportunity to deviate from the arrangement.

Friday, June 10, 2016
If you don't read Matt Levine, I don't understand why not; if you do, then you probably have some awareness of Saudi Arabia's build-up to doing an IPO on its massive state oil company, even if you haven't yet read today's column.
A $150 billion initial public offering would be by far the biggest ever; Bloomberg's league tables show about $176 billion in total global equity offerings so far in 2016. And if Saudi Arabia is selling oil shares, who is buying? "There is no guarantee there will be sufficient demand from investors to soak up all the shares," and messing this one up would be many times more embarrassing than messing up, say, the Facebook IPO.
Note that the $150 billion figure itself is only for 5% of the company; the expectation is that Saudi Arabia could retain a 95% share and get $150 billion for the rest of it.  The purpose of the funds is diversification; the plan is to take the $150 billion and turn around and invest it in like Baidu or niobium mines or Caterpillar or something.

I expect that the plan would also be to later sell more of the company, and I kind of wonder whether they picked 5% because $150 billion is the very largest initial deal they think could get pulled off.  I kind of think, though, that they ought to halve it, or maybe even go to 1% or something.  You really only need it to be large enough to create a liquid market in the shares, at which point you can sell more shares into that market later or even directly swap shares for other investments.  You want the initial float to be big enough that you can do those later deals (and maybe $30 billion would leave the market too thin to absorb what you're planning to do later), but it seems like trying to find that much cash among IPO investors when you're not really looking for cash so much as to create your own currency (viz. the shares with which you will purchase other investments) creates a difficulty that at least in principle could be avoided.

Thursday, December 17, 2015
FOMC plumbing
The FOMC yesterday asserted that it will be raising interest rates today. I mean, probably they will; the first place to watch the progress of the implementation is where they post gross statistics of the reverse repo facility; I think the auction ends around 1:15 Eastern Time, and don't know how long it will take for the results to be posted there. What everyone then wants to see is whether the actual Fed Funds rate overnight falls in that target 25–50 bp range, and, if not, how far on which side. Tomorrow's reverse repo operations will be that much more interesting if they miss the range tonight.

Thursday, October 15, 2015
positive interest rates
Traditionally the reason a central bank raises interest rates is to reduce financing activity that supports "aggregate demand" that might lead to inflation. Inflation and its expectations seem to be low — below the official 2% target for quite a while — which makes me at least cautious about this, and yet I support an interest rate hike at the next FOMC meeting. Here is a smattering of reasons why:
The recurring theme is mostly that moving away from zero when we aren't in a hurry to raise rates leaves more flexibility to handle the unexpected than raising rates when we are in a hurry would.  It should be clear from the reasons that I'm not proposing or expecting that we begin an unbroken string of 25 bp hikes at each meeting for the next two years; if we had two such hikes and saw a slight uptick in inflation and the participation rate, I would support holding rates there for a while until we got a stronger signal that more sustained inflation was coming, even if it might allow some corners of the market to collect risky securities at unsafe leverage.

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