sales tax as monetary policy

 This falls well in the half-baked (or less) wheelhouse of this blog: to help assist monetary policy, we should have a national sales tax that follows the short-term interest rate.  If short-term rates are 0, the sales tax goes away; if they're around a 5% annual rate, we have a tax of 2.5%, if it's an 8% annual rate the tax is 4%, etc.

I came to this idea, such as it is, from thinking about "Modern Monetary Theory", the advocates of which want to use fiscal policy to control inflation to a much greater extent than we do now; in particular, if inflation got too high, we would raise taxes to take money out of circulation to cool it down.  What I haven't heard noted in my consumption of their material is that what you would need to tax would be consumption, not income.  In particular, if you had a class of subsistence-plus farmers who had income but never spent it, taxing them would do no good whatsoever for reining in inflation; the money they're sitting on is economically inert.  If demand for the quantity of goods and services being produced is high enough to push up prices, the only way to prevent that is to somehow effectively reduce that demand, and the way you would do that in anything like this framework would be a combination of reducing the ability of people who want to spend money to do so and of encouraging those people to delay their spending.  To the extent that you get people to save their money, that addresses the problem.

An important thing to note about encouraging people to save money rather than spend is that it depends on real interest rates, not nominal ones; "real" in this context means "inflation-adjusted", except that what actually matters is not realized inflation, but expected inflation.  For a given interest rate, people will generally be more willing to save if they think inflation will be low (so they can buy more stuff in the future if the save now) than if they think inflation will be high; by the time we know what actual inflation is over a time period, it's well after the decision was made.  Another important thing to note is that, if the sales tax is changing with time, your actual purchasing power at a given time depends on after-tax prices.  In the short-run, a tax response to inflation means that you're responding to an erosion in purchasing power by further eroding people's purchasing power.  If you link it to interest rates (or something else in the economy that's likely to be low in recessions and high in inflationary expansions), though, that higher tax is at least expected to be temporary — the expected after-tax inflation rate is lower than the expected before-tax inflation rate.  (Or, if you prefer, there's a tax incentive for deferring spending to a time when the tax has come down.)

I find this easier to discuss in terms of periods of high inflation, but it should work the other way, too; if people think a sales tax is going to kick in in two years, spending more now becomes comparatively more attractive, and the after-tax real interest rate is lower even before taking account of the result that we're hoping this has on inflation.  If you can make this credible — if you can make people really believe that there will be a sales tax in two years — then this should enhance the ability of low nominal interest rates to get people spending money now, while avoiding some of the mechanical and psychological difficulties associated with negative nominal interest rates.

If we could ignore mechanical difficulties, of course, negative interest rates would be more attractive, but so would a negative sales tax; note that what's important for the substitution effect is not the level of the tax, but its expected change, and to the extent that we're trying to affect the amount of money in the system and expect that to do some work for us, a tax that's actually negative when we're trying to stimulate spending is in fact what we'd want.  (While the primary logic of mailing out checks this past spring was straightforward relief rather than stimulus, it provided some nominal stimulus by enabling spending.)  To some extent you could get the money-balance effect by lowering other taxes instead — even with this sales-tax scheme, funding the government probably requires positive income tax rates, but they could be lower if some of the revenue comes from the sales tax instead — but maybe a negative sales tax would be easier than some other negative taxes.  The idea of a negative income tax has gotten more attention, and to some extent, with the EITC, we have that.  It may also be, though, that "the sales tax" would be better implemented through the income tax, where it might look more like a savings incentive — instead of a 5% sales tax, you would increase income tax rates 5 percentage points above their baseline level, but with a 5% credit for new savings, making clear that part of the point is encouraging people to save the money to spend later instead of now, and instead of a -5% sales tax you could have temporarily lower income tax rates, but with a similarly temporary savings tax to encourage spending now.  One problem with doing it this way is also a problem with using a value-added tax, which is sometimes said to be equivalent to a consumption tax; that problem is one of timing.  I envision the tax changing in the middle of a year, rather than having a constant value for each tax year; maybe that's unnecessary.  A value-added tax takes time to bubble its way up through the supply chain.  In either case, though, a delay in implementation causes the tax to trip over its own feet a bit; remember that a significant part of the effect is to come from the expected mean-reversion, that is that raising the tax should lead to the expectation that it will be lower in the future than it is now, and saying "we're going to raise, you'll feel the rise in six months" encourages exactly the opposite of what we want in the near-term.

errata and addenda

I have a couple of what should be edits to previous posts, but I've had issues with blogspot editing in the past, so I'm going to record them here and hope that's adequate.

• About 7 weeks ago I wrote about the foreign exchange market; apparently the market has become less decentralized than I had realized.  The CME group ("Chicago Mercantile Exchange") owns a platform called EBS, and Refinitiv has a platform called Matching; these account for something like 30% of foreign exchange trading.  There are other smaller exchanges, and Cboe Global Markets ("Chicago Board Options Exchange") is launching a new market called Cboe FX Central.
  
• About 3.5 weeks ago I wrote a post with the term "Fair Value" in the title.  I sort of regret calling it that, because it's not the "Fair Value" that Warren Buffett and Benjamin Graham are talking about, even if that's what I meant to invoke.  The measure I described will have a bit of a "Fair Value" feel to a CFO, in that it calculates a value for the company independent of any price data from securities markets, and recommends that the company buy its stock if it's cheaper than that and sell if it's more expensive.  If companies reported such a thing, they really shouldn't call it "fair value", and if I'm going to allude to the term, I should give more emphasis than I did to the last two sentences of that post, which basically describe how it differs from the investor's notion of "fair value".  It's a summary statistic about internal investment opportunities that leaves to the shareholders the decision as to whether (or how much) internal investment is actually attractive; whether the stock is actually worth that amount is up to the shareholders to decide.

stock-market wealth

A lot of the people in Jane Austen novels seem to "have" an income.  I don't quite understand this; they don't seem to have jobs, exactly, and my least bad guess is that they own estates that have much more regular cash flows than I would expect manorial estates to have.  Let's suppose, though, that one "has" an income of $1 million per year, coming from such an estate.  What is the "wealth" value[1] of the estate?  Well, if comparably safe investments generally pay a 5% interest rate, a prospective buyer would be indifferent between paying $20 million for the estate versus investing that elsewhere, so the estate is worth $20 million.  If interest rates were instead 4%, the estate would be worth $25 million.

One of the things I've been hearing lately is that many billionaires have "made" billions of more dollars since March  23, or (less incorrectly) that their wealth has gone up billions of more dollars since then.  In a few cases, company profits (or prospect of future corporate profits) have gone up, but mostly they have not; since Feb  23, in fact, most company's prospects, especially in the near term, have gone down considerably.  Interest rates, however, have also gone down.  Mr. Darcy's income has gone down, but so has the income associated with any means of saving for the future, and indeed the latter has dropped sufficiently that, if Darcy were willing and able to sell his estate to someone else, he could get a higher price for it than before.

Does this mean he's richer than before?  To reiterate, other forms of saving have gone down, too; he can't take the money and put it somewhere where it will allow him to spend more on an ongoing basis.  If he has always wanted to blow all of his prospects on a bacchanal, followed by a life of penury after that, then his wealth has gone up, but if he was uninterested in selling before and is uninterested in selling now, as seems quite likely, his best allocation of his wealth over time results in a lower consumption path, not a higher one — it follows the income, not the capitalized wealth.

In what senses can we say that he is richer, or even more daringly turn the change in the capitalized value of his wealth into something like an income?  Especially for this latter step, it seems most reasonable if Darcy has been, is now, and expects to continue to be a trader, timing the market, buying low and selling high.  If he had a cash endowment at the beginning of the year, he would be better off having bought the estate in March than he would be buying it now.  If the continued value of his trading prowess is unaffected by the drop in interest rates, his ability to consume may be higher than it was before.  Conversely, it seems most obviously the case that his wealth has gone, not up, if his asset is entirely illiquid, he has no way of knowing what its capitalized value is, and he has simply been informed by his foreman that the income will be lower for the foreseeable future.

A lot of this is entailed[2] in the standard economic principle that the best measure of a person's wealth, in the long-run, is likely to be his or her level of consumption, or in any case that that's a better measure than that person's income or the total value we can assign to those of the person's tangible assets to which we can assign value.  If the stream of value that you had expected to consume is no longer one you can afford, you have gotten poorer, not richer, regardless of how that's measured in today's dollars.

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[1] We would often call this a "capitalized" value.

[2] Not in the real-estate sense of Jane Austen's world.

A simplistic guide to Fair Value for CFOs

Suppose a company can reasonably determine that if it made $300 million in new investment, its earnings (perhaps before interest and taxes) would be about 5% higher, in the long-run, than if it didn't.[1]  That basically means that the company's market cap (perhaps enterprise value) should be $6 billion[2] — independent of your cost of capital.  If you're trading at $3 billion, that means your cost of capital is high, and in fact is higher than your marginal internal rate of return; if you have cash that you're looking to deploy, you should return it to shareholders, perhaps by buying back stock.[3]  If you're trading at $10 billion, your cost of capital is lower than your marginal internal rate of return, and you should invest that $300 million internally, issuing new stock if necessary (and possible) to do so.

I've never been a CFO, and may be all wrong here, but the way schools present corporate finance the process is often sketched out as, well, you figure out your weighted average cost of capital, and your internal rate of return, and there are strategies for trying to do these things, but cost of equity in particular is pretty slippery.  And it seems to me that it frequently doesn't matter; there's a simpler approach that avoids the questions that are hard, the answers to which largely cancel out by the time you get to the part that's actionable.  So it seems to me that a lot of companies should often issue, somewhere in their quarterly or annual reports, ranges of what they think their "fair value" is, with the understanding that they're likely to buy below that range and sell above it.  If they did, I'm sure some people would misunderstand and complain, not least because so many people seem to make those two things their primary hobbies; that his has, as a side-effect, some tendency to stabilize the stock price and to make money trading the company's own stock (if you hit both ends of the range in the same period) will probably be called "manipulation" or, I don't know, "profiteering" or something — the people I have in mind aren't careful about language.  Some people might also imagine that the company is trying to tell stock traders that its price should stay in that range, which is not at all the point; certainly the company's buying and selling would not, in the face of big macroeconomic news, be expected to create hard price barriers.  The range is an indication of internal rates of return of new investment, but in a non-traditional language; if shareholders decide the demand a higher rate of return than they'd been expecting, the price of the stock can go down and the company accepts that verdict.

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[1] This is intended to be "in expectation", using a risk-neutral measure, but is still subject to supposing, for example, that you can reasonably estimate an expected glide-path that follows the otherwise expected glide-path, just some multiple higher.  I mean, you don't need the glide-paths, which is part of the point of the post; you only need the multiple.  And so I think that it's likely that there are a lot of environments in which a CFO could reasonably say that it's between 4% and 6%, in some reasonable expected sense, meaning, again, that it could end up outside that range, but that you can justify that reasonably well in the light of what should be reasonably known now.

[2] Or, continuing the previous footnote, maybe $5 billion or $7.5 billion.

[3] Ignoring other capital structure issues, which I think should be largely independent of this.

Reopening the economy; cost benefit analysis

Elsewhere I provide a back-of-the-envelope cost-benefit statistic to guide reopening the economy from the covid shutdowns; here I want to extend the model a bit.  In that post I work in terms of the sort of model in which we use a reproduction number — in particular, a fairly homogeneous model.  There I look at assessing the cost of creating opportunities for the disease to spread, and here I want to allow at least some variation in that.

For at least the past month I have been largely thinking about the epidemiology of the disease in terms of multiple populations; these could be counties or states, and it was county and state data that moved me toward this framework, but I've occasionally thought in terms of multiple populations in the same area, one of which engages in much more "social distancing" than the other.  I think the following crude model will be sufficient for my purposes: suppose time is discrete, and consider a vector v at each time, with each component indicating infectious cases in a particular area, and v_t+1=Rv_t, where the reproduction number R is now a matrix instead of a number.  I don't suppose that it's constant with time, but I am going to consider changing one element R_ij at a single moment in time with R unchanged at all other times; to be clear, it may be changing over time, but the counterfactual follows the same path as the baseline scenario except for a single element of the matrix at a single time.

For T>t+1 let M_T be the product of the transition matrices from time t+1 to time T-1, such that v_T=M_TRv_t. The change in v_T,l due to a change in R_ij is the amount of that change times M_T,li v_t,j. If you can place a cost on each exposure — a cost that may be different at different times and different for different populations — and multiply each row of each M_T by the relevant cost and then add up the M, you get a matrix C; the associated marginal cost of an increase in R_ij is C_liv_t,j, i.e. the relevant cost from the C matrix times the current prevalence in the population from which we're increasing the spread.[1]  The real question, now, is how to get any kind of bead on C.  In parallel with the earlier post, I'll note that the sum over rows of CRv is the total cost of all future infections; this will allow us to make contact with other attempts to do a cost benefit analysis on the entire crisis.

I'm not sure there's benefit in producing more formulas by imposing more structure on C; I could note that, if R were constant (and all of its eigenvalues below 1) and the costs were constant or exponentially declining, then we would basically have C=(1-R)^-1, and even with varying R we can maybe read something off of that. It's worse to transmit infections to places that tend to transmit more infections; it's worse to transmit infections to places that do so, and so on.

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[1] This may seem on some level obvious; I would kind of hope it does.  Note an implication, though: there is substantial benefit in cutting transmission from a hotspot, and that benefit is largely independent of whether it's to a hotspot or seeding a new location.  In conversation I sometimes get the impression that people think that, well, if we're trading people between hotspots, that doesn't matter, but if each infected person in each place transmits the disease, on average, to 0.8 people in their hotspot and 0.4 in the other, you will get exponential growth that could be eliminated by stopping the interchange.

batch auctions for foreign exchange

The foreign exchange market is quite decentralized, and I've been thinking recently that it might be convenient for some players in the market for there to be a daily batch auction, perhaps early in the morning in NYC, late morning in London, and evening in Tokyo.  Academics often seem to like batch auctions for the thickness (liquidity) they offer, but one of my motivations was the existence of currency derivatives and indexes; there are traders who may be trying to hedge in the spot market against an "end-of-day" risk, and I thought having a batch auction that provided fixes for derivatives would make it easier to avoid some basis risk.

Foreign exchange markets can feel a bit like barter in some ways; if I'm buying pounds from a trader in London, we'll both think of ourselves as the buyer, and if someone in Europe wants to trade dollars for yen, it's not clear whether that's a purchase or a sale.[1]  In some ways, a centralized auction alleviates the double-coincidence-of-wants problem and makes barter feasible and even makes money (or, in this case, a vehicle currency) redundant, but there is a complication: consider a trader who enters, into the auction, an order expressing a desire to exchange 10 euros for 900 yen, and suppose the auction determines that the clearing price is 100 yen per euro.  A European entering an order to buy 900 yen expects to end up exchanging 9 euros for 900 yen, while a Japanese person entering an order to sell 10 euros expects to exchange 10 euros for 1000 yen.  An American may wish to hand over 10 euros and receive 900 yen and to receive the gains from trade in US dollars.  An order now should specify the currency of the order, which may be the currency the trader wants to buy, or sell, or something else.  In more generality, the trader may express three baskets of currencies, expecting that, if the trade is executed, the trader will give up basket A and receive basket B and some multiple of basket C such that the currency received and the currency provided have the same value at the clearing prices.

Actually determining how to clear the markets turns out to be equivalent to solving a convex optimization problem, at least if currencies are arbitrarily divisible and orders can be partially executed, at least provided that, for each order that executes, the currency associated with that order is provided by some combination of other orders that execute.  The solution technique is likely to involve iteratively finding the excess demand for different currencies given different price vectors, and it seems likely that in a practical distributed setting you would want to group orders by currency, where you would first figure out, given the proposed price, which orders execute, the total gains from trade those orders, and how much currency that adds to the demand vector.  One potential complication here is created by orders that clear exactly, with no gains from trade, which may end up partially executing; when excess demand of different groups of orders is being aggregated it may be necessary, especially late in the process of finding the execution price, to retain a lot of possible excess demand vectors to aggregate the partial calculations.

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[1] This is the source of some confusion regarding options at times; the terms "put" and "call" are similarly poorly defined.  In some ways, though, this is clarifying, though I think I should let go of this particular tangent at this point.

A quick thought on the size of the firm

In times of war, pandemic, or other emergency, particularly when there are quick shifts in the environment, it seems that the sorts of coordination that are amenable to top-down approaches on a large scale become more significant, while the sorts of coordination that they're bad at, or that lower-level coordination is good at, don't change.  In Coase's framework, this suggests that the optimal firm size has suddenly gotten larger.  (It obviously has other, more political/legal implications as well.)

how fed policy works

This post is perhaps on the wrong blog; there's little if anything in this post that I intend to be speculative or even novel.  I've been hearing some talk from laymen about fed policy that makes me think that they are thinking about some things very differently from how I, and I think most economists, do, and I'm writing this post as a guide to a framework that's more in the realm of mainstream economics.

Suppose you're in a car on a stunt track, and you're supposed to go up a ramp and jump over a ravine; you need to be going at least some minimum speed when you get to the top of the ramp or you won't make it across.  One thing you would want to do, if you're well below that speed, is to start accelerating well before you get to the ramp.  If you put the pedal to the metal hundreds of yards out, and someone criticized this decision on the grounds that if you push the gas pedal as hard as you can now, you won't be able to push it any harder when you close within a hundred yards of the ramp, you would think that criticism was nuts.[1]  It would sound exactly as nuts as the complaint that cutting the federal reserve policy interest rate in response to a small slowdown in the economy "uses up ammunition", and that the fed should instead "save up ammunition" for if there's a full-blown recession.

Certainly in every economics model I've seen — and (not quite the same thing), I'm pretty sure that almost[2] every economist is quite confident that this is true — it is not the rate cut that is stimulative; it is the low rate that is stimulative.  "Low" will depend on context — indeed, a low rate is typically a sign that policy hasn't been stimulative recently — but from a given starting point, lowering the rate sooner will allow stimulation to accumulate longer; trying to postpone the cut will increase the need for stimulus in the future.

The simplest model, then, with the fewest possible explicit moving parts, is that there is some "neutral interest rate", not known with full precision and subject to influence from noisy external factors, and that policy is contractionary if the policy rate is higher than it and stimulative if the policy rate is lower than it.[3]  If policy is stimulative, that will tend to raise the future neutral interest rate, and if it's contractionary it will tend to lower it.  Note that the system — at least parameterized this way — is unstable; if you keep the policy rate fixed forever, the natural rate will either find itself above the policy rate, and will then be pushed higher (by inflationary expectations as aggregate demand picks up), making the policy rate even more stimulative, making it move higher even faster, or the natural rate will find itself below the policy rate, and will similarly move ever lower as a deflationary spiral takes hold.  If you're making monetary policy by controlling an interest rate, then, you need to move it in response to noise, pushing it above the natural rate when the natural rate gets high and below it when the natural rate gets low.

And this, then, gets me closer to another comment I hear, which is that long-term interest rates are driven entirely by expectations for future short-term rates, which may in some sense be true, and that therefore the fed has complete control of long-term rates, which is in important ways false, at least where we're talking about real interest rates.[4]  I recently mentioned to my class that if you want to know how many jobs there will be in the economy next year, ask an economist, but if you want to know how many jobs there will be in thirty years, you should ask a demographer; similarly, in the short run the fed may have a fair amount of latitude, but if it's avoiding both hyperinflation and depression, an interest rate that's too high now implies a lower range of reasonable policy rate options in the future.  Expectations about long-term average future real rates should be formulated (almost) entirely on the basis of economic phenomena, and not on some institutional analysis of the fed or psychological analysis of its governors.

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[1] You'd be right.

[2] This is the "Dean almost", wherein I have an excessive aversion to making categorical statements about large groups of people; you can probably drop the "almost".

[3] To be clear, all the standard models could be reduced to this sort of model; they would differ in how (much) outside factors affect the neutral rate, and how stimulative or contractionary deviation from that rate is.

[4] If the fed has a credible inflation target, then control of long-term real rates and control of long-term nominal rates are basically the same.