If a commodity is in "backwardization", that is, if futures prices are lower than current prices, does that imply that futures markets are discouraging storage (encouraging disgorgement)? Paul Krugman makes the case, here and here.

I'm going to challenge him with a low-down, dastardly kind of argument. The gentleman keeps asking for evidence, evidence, and in response I'm going to offer an unfalsifiable hypothesis. Krugman says that futures prices are too low to cause people to withhold physical oil and sell forward, as required to affect spot prices. But whatever forward price curve he shows me, I can posit an invisible "convenience yield" large enough to make hoarding oil worthwhile. I don't even have to be unreasonable about it. Extrapolating from historical data, we see that gently "backwardized" futures prices might be quite sufficient to encourage storage when convenience yields are taken into account.

Despite all of this, I agree with Krugman that futures markets can't explain the recent skyrocketing oil prices. Not unusually, he's been a voice of sanity and reason. But just as speculation in futures need not affect spot prices (if it is balanced long and short), speculative withdrawal of physical supply need not affect the shape of the future price curve. Futures market "signatures" can't be relied upon to distinguish speculative from fundamental demand, and inventory may be unmeasurable, especially if it is offshore or takes the form of withheld production. Further, both futures in contango and measured inventory build can signify known fundamental demand as well as speculation. (Suppose entrepreneurs are planning to fire up many new factories over the next few months. If they buy forward to hedge their exposure to energy prices, that would push futures into contango and promote storage with no one speculating on anything.)

But this isn't about that. This is a disquisition, and ode, a homage and a tribute to the marvelous, mysterious, misunderstood and maligned convenience yield:

The bedrock principle of futures markets is "no arbitrage", that is prices should be set such that there is no investment strategy that yields a risk-free profit higher than the risk-free rate of interest. For a physical commodity, this seems to imply that the forward price should equal the present price plus the risk-free rate of interest and any storage costs. Interest rates are never negative, and storing stuff always costs something, so you'd expect future prices of storable commodities to always be higher than current ("spot") prices. But check out the following graph of the four month "forward yield" of crude oil. (Data courtesy of the EIA, hat tip Krugman, calculations and errors are mine, click for a bigger version).

The "forward yield" is just the percentage by which the future price is higher than the spot price. I'm using four month futures, but I've converted the yield an annual rate. If the forward yield is 10% and the interest rate is 4%, an oil man would profit from buying oil now and selling it forward, as long as his storage costs are less than 6% per year. Tycoons would start buying spot and selling forward until yield dropped to interest + storage.

But didn't we say future prices should be higher than spot prices? Look at the average (the yellow line in the graph). It at -3.4%, well below zero! The yield is negative more often than it is positive. Whenever the yield is anything less than interest + storage, you'd expect oilmen to sell crude from storage and buy it back forward. He earns interest on his cash and saves the storage costs that way, which is better than the profit he'd make storing and selling forward. When the forward yield is negative, Texans should be selling physical and buying forward like mad. By doing so, they earn interest on cash, save storage costs, and lock-in an easy profit buying back their oil for less than than what they sold it for. Very quickly, all the selling should create a glut of physical oil, driving down spot prices, while the buying forward drives up future prices, until the yield is positive and sanity is restored. But negative forward yields for oil have persisted, sometimes for years at a time! We must be missing something. Hmmm...

Suppose someone offered to buy your vacuum cleaner today for $100, and sell it back to you next week for $80, with no risk of wear or breakage. Would you? It would depend how much you value the use of your snorter. If you refuse, we might infer that a week's access to the pleasures of vacuuming is worth 20 bucks to you. We call that value of temporary use a "convenience yield". It's as if having the vacuum cleaner around pays you $20, even if no cash changes hands. Maybe we observe negative forward yields on oil because the smell of oil in the morning is priceless to guys in cowboy hats. (Or not... see below for a more plausible account of oil's "convenience yield".)

Let's eliminate wandering interest rates, and take a look at the storage cost / convenience yield of oil historically. Below is a graph of a three-month forward yield (calculated from the first to the fourth month forward, because futures prices are more trustworthy than spot) with the concurrent 3-month T-bill rate backed out of it, leaving only storage costs. When storage costs are negative, that reflects, by definition, a convenience yield. (Again EIA monthly data, T-bill rates courtesy of FRED, my calculations)

From Jan 1986 through May 2008, oil futures have reflected a convenience yield of 8% per year on average. (This is in rough agreement with the overall mean of 0.021% per day calculated here by Milonas and Henker, see Table 3.)

Suppose that the current convenience yield is about 8% and three month interest rates are about 2%. Then a one-year futures contract should be about 6% cheaper than spot, and a four-month-out contract should be about 1.4% cheaper than a one-month-out contract (reflecting 3 months of storage). At the end of May, the 4-month-out contract was in "backwardation", but was only 0.5% cheaper than the 1-month, still too expensive given the convenience yield. Oil dudes could have earned (on an annualized basis) about 3.6% more than the risk free rate (about 5.6% overall) buying high and selling low, but enjoying the privilege of storage. Now that oil is in gentle contango (as of June 17, the 4 month contract costs about 1% more than the 1 month), buying forward and storing looks like a really fantastic deal.

What is this "convenience yield"? Is it real? It seems like it must be, the economics of an 8% return aren't subtle in the data. But when I first encountered this idea, it baffled me. So instead of talking oil, let's talk hotels.

Suppose you have a hotel, it's morning, and you've got a room that isn't yet booked for tonight. Empty rooms end up costing you about $10 a night, considering your rent, maintenance, utilities, etc. But, you estimate there's about a 50% chance that a weary last-minute traveler will come by and pay your walk-in rate of $150 for the room. So, the risk-neutral expected value of your empty room is $65 [(150 ÷ 2) - 10]. You're risk-averse, not risk neutral, though. You'd accept a certain $60 rather than a 50-50 chance of losing $10 or earning $140. That $60 is the "convenience yield" on your empty room, it's what having a room empty, in case opportunity strikes, is worth to you.

Oil is a "spiky" commodity. Every once in a while, someone really needs it, now, and will pay a premium for immediacy. The market for oil in Cushing, Oklahoma might be reasonably efficient, but what happens when someone in Peoria needs oil today? Opportunity! Instead of running a hotel, you build an oil tank in Peoria. Suppose that every month, there's a 10% chance a desperate client will offer a 5% premium for immediate delivery of all your oil, and that interest and storage cost you 0.2% per month. Then on average, you'd earn 0.5% (10% x 5%) each month from desperate clients, and pay 0.2% in expenses. You don't want to bear the risk of fluctuating oil prices, so you sell your oil forward. If you were risk neutral, you'd be willing to sell it for a discount of up to 0.3% less than you bought it for at the beginning of the month, at which price you'd just break even. But you're not risk-neutral: You attach a "certainty-equivalent" value of only 0.4% to the unpredictable income from needy customers, and would offer no more than a 0.2% discount on month-forward oil sales. In the end, you earn a risk-adjusted 0.4% per month "convenience yield" from desperate polluters, and pay 0.2% in interest and expenses, and 0.2% in hedging costs. If one-month oil futures pay more than 0.2%-less-than-spot, or (golden days!) if they are in contango, you'd buy as much oil as you could and sell it all forward, because every new barrel that you promise to buy high and sell not-so-low represents certain (well, "certainty equivalent") profit.

Putting aside Peoria and our artificial needy customer, sometimes oil spikes even on the wider market, so that anybody with physical oil can sell at a high price and while locking in low-priced near future purchases to replenish their stock quickly enough to meet any other contractual obligation to sell. If you estimate the profit you'd to earn from these occasional opportunities, and subtract a bit to come up with a "certainty-equivalent" value for this uncertain income stream, you'll have determined a convenience yield. It shouldn't be surprising that convenience yields are especially high for volatile commodities subject to frequent shortages and price spikes.

When futures markets are well-arbitraged (which might not always be the case!), the future price of a storable commodity is determined by the spot price plus the total cost of storage, defined as foregone interest, plus storage costs, minus any benefit of temporary ownership &mdash the convenience yield! When a storable commodity like oil is in backwardation, that doesn't mean that the markets are predicting that its price will fall. It means there is a convenience yield. And in order to decide whether futures markets are creating incentives to store or to sell physical stuff, you have to estimate the convenience yield.

Postscript: While I was writing...

Mark Thoma offers a nice extension of Krugman's model, showing how monetary policy, by affecting interest rates, would be expected to affect storage.

Yves Smith offers very pointed commentary on futures markets, speculation, and inventory (here and here).

If policymakers want to "do something" about commodity speculation, they should really start investigating passivity on the short side of the market rather than enthusiasm on the long. Given what's before them, I hope they ignore Michael Masters (ugh!) and Thomas Palley (whom I often like, but yuk), and go with Dean Baker's suggestion of a Tobin Tax (ht Mark Thoma).

In response to a (somewhat ridiculous) proposal that we "sue OPEC" over high oil prices, Mark Thoma writes:

[I]t's unlikely that [monopoly power] is the factor behind the run-up in prices. Monopoly power explains the level of prices, i.e. why price is $8 rather than $5, but it doesn't explain the change in prices, i.e. why the price would change from $8 to $12. There are ways to tell this story, e.g. a war or some other event giving a cartel the cover it needs to raise prices and blame it on external factors, but I don't think that's what's going on in oil markets today, at least I don't think this is a significant factor behind the oil price increases.

I think there may have been a change over the last few years in the market power of oil producers, for structural reasons. Traditionally, OPEC has suffered from the usual problem that makes large cartels unwieldy: Under agreements to restrain production, members individually have an incentive to cheat and sell larger-than-agreed upon quantities at still artificially high prices. But that assumes that the production quotas are significantly beneath the capacity of most members to produce. More subtly, it also assumes that each country gains by producing more rather than less oil, if cartel prices are maintained. Both of those assumptions may no longer hold.

As the global oil market has grown, demand may have outpaced individual countries' capacity to supply, either because investment in new projects has not kept pace, or because nations have hit domestic "peak oil". (See Indonesia for an extreme example.) Other countries may desperately need money in order to fund current spending, so it is widely known they will produce as much as they can, regardless of quotas. Ironically, as long as the total capacity of sure-fire cheaters and constrained suppliers is well below global demand at the cartel's target price, the certainty of their output may enhance the ability of discretionary producers to control the quantity produced.

It'd always be easier for a cartel of five or six producers to exercise market power than a cartel of, say, thirteen. But that's especially true when cartel members have little incentive to cheat. Normally, we think of governments as spendthrifts, always eager to spend an extra dime unless constrained by tax revenues or debt markets. That's obviously a mischaracterization of today's most important oil producers, whose governments spend far less than the oil revenue they receive. For Saudi Arabia, selling a barrel more of oil is a portfolio choice: revenue from the marginal barrel will be saved, not spent, so the question becomes whether it is wise to shift some of the Kingdom's current allocation out of oil and into some asset that can be purchased with currency. For countries that have very little non-oil savings, mere diversification would encourage oil sales. It is unwise to have all ones eggs in one basket, and oil producers remember all too well that world prices can go down as well as up. They'd want to store their national wealth in an "efficient portfolio", one that maximizes their return on risk by including a variety of investments.

But as oil producing nations have accumulated vast reserves of financial assets, switching from oil-in-the ground to stocks, bonds, or bank accounts is no longer so sure a bet. Real interest rates on "safe" dollar assets are currently negative, both in US and home country terms, and the outlook for safe euro assets is uncertain at best. Central banks and sovereign wealth funds of oil-producing nations already hold hundreds of billions of dollars worth of Western financial assets. They might already have reached or exceeded what they view as an optimal allocation of their national wealth into these securities. Of course, producers are still not well diversified, and it's pretty clear that sovereign wealth funds are looking for alternative assets that might hedge their exposure both to oil and Western paper. But allocating into less liquid, unfamiliar categories of assets is slow work if you want to do it well. Perhaps current oil revenues outstrip oil producers' capacity to find good investment opportunities, and they view oil-in-the-ground as a better second-best asset than dollars in the bank.

Ten years ago, oil producers did not have vast hoards of dollars and euros, and required oil revenue to meet budgetary needs. World demand was low enough that cheating by OPEC members could corrode producer pricing. It was hard to exercise market power. Now, cheaters don't matter, and discretionary producers may be indifferent or worse to the prospect of selling a barrel more of oil at current prices.

(In a sense you might not call this market power at all, as price equals marginal cost, that is to oil producers, the assets they can buy for the dollar price of a barrel of oil are worth no more to them than a barrel of oil left in the ground.)

Brad Setser recently noted that...

[T]here are two clear paths that could end the current “oil up, dollar down” pattern.

Weakness in the US economy could drag down global oil demand, pulling both the dollar and oil down. Asia’s 1997-98 crisis led both Asian currencies and the price of oil.

Or a rebound in the US economy could push up the dollar while adding to oil demand. In 2000, a booming US pushed up oil prices and the dollar.

Ironically, a strong, healthy US economy might also push oil prices down, even while increasing US and world demand for oil! The price of oil to discretionary producers is not measured in dollars, but in the future purchasing power of the assets dollars can buy. If oil producers expected US financial assets to appreciate in value more quickly than oil (in terms of what they want to buy), President Bush wouldn't have to look anyone in they eye to get the producers to invest in new wells. However, if that's not the case, then the rate of production might be determined more by the political costs of failing to produce than by world demand or current-dollar prices.

But... for US dollar assets to appreciate faster in oil-producer purchasing power than oil itself, those assets would have to represent claims (direct or indirect) on future goods that producers want to buy, that is investment in tradable goods and services. Unfortunately, Brad is probably right to suggest that a "rebound" in the US economy would drive oil prices up, since we've come to believe that more GDP is always better, sectoral composition doesn't matter, and producing tradables is for the little people. Federal stimulus checks might give a zetz to GDP, but in and of themselves they do nothing to make claims on American assets worth buying.

What distinguishes a speculator from a hedger? Here's the New York Times:

Unlike hedgers — the farmers, miners, refineries and other commercial interests that actually make or use the commodities themselves — the speculators, like day traders in the stock market, are simply trying to profit from changing prices.

But that's not really right. Conceptually, a hedger is a party trying to shed risk, usually accepting some cost to do so, while a speculator willingly takes on risk, hoping to profit.

If we take nominal dollars as investors' unit-of-account, then all noncommercial interest in commodities is "speculation", as the Times implies. People are pouring money into commodities because they believe commodity prices will rise in US dollar terms. Since holding cash is risk-free (in nominal dollar terms), all investment is speculation unless it's offsetting some commercial risk.

But if we more realistically view investors' planned consumption bundles as their unit-of-account, the recent interest in commodities is better characterized as hedging than speculation. Investors perceive the value of currency to be more volatile than stored commodities, relative to the goods and services they hope to consume. It would be inefficient for investors to store commodities directly, so they hire professionals to store on their behalf by purchasing financial futures. (In properly functioning futures markets, when more money wants to go long than short, an invisible hand seeks out those capable of efficient storage, and compels them to fill warehouses in order to meet the excess demand.)

What Joe Lieberman proposes to do, then, is best understood not as barring speculation by institutional investors, but as barring hedging, as forcing investors to accept risks that they would prefer to shed.

Yves Smith writes that Senator Lieberman's proposal is "a Nixon-goes-to-China moment". I am wrong far more often than Yves Smith is, but I'm gonna go out on a limb here and say she's mistaken. The Senator fron Hedgefundistan is acting very much on behalf of his constituents. Smith writes:

Opponents may argue that this will simply drive investing in commodities overseas. Perhaps, but funds regulated under the Investment Company Act of 1940 (most US fund managers) don't have that sort of latitude, and ERISA investments could similarly be reined in quite easily. And it's US investors, plagued by (until recently) an ever falling dollar who have had particularly strong reasons to look to a hedge like commodities.

As a move to drive any speculative froth out of commodities, this one isn't bad (but one wonders how all those commodities index funds get unwound). Although some have called for increases on margins at commodities exchanges, that hurts commercial actors as well as speculators. A move like this focuses on the underlying issue more directly.

Goldman in particular would suffer, since as the biggest manager of commodities funds based on its index, GSCI, it not only earns fees, but as we have discussed elsewhere, earns even more from an unsavory but hugely profitable practice called "date rape" around the monthly futures contract roll.

Now before the wealth-holding class howls that they've just been done a dirty by being deprived of inflation protection, there is an asset class that, unlike commodities, supports productive investment. and provides inflation protection, namely, infrastructure investments. The cash flow from infrastructure projects (toll roads, airports) goes up over time, as do the payouts, so they have fairly secure cash flow that increases over time. Although there is some debate about how to view them, they seem closest to an inflation-indexed bond (although any investor would need to study the ability of the enterprise to increase charges versus the drivers of operating expenses).

Many investment funds may be prohibited by charter or regulation from participating in overseas commodity markets, but Senator Lieberman's hedge fund constituents and their wealthy accredited investors are not. The "wealth-holding class" would evade these restrictions quite easily, by funneling money through Connecticut businesses. This would be a growth-enhancing regulation for Stamford.

Meanwhile, retirement funds and retail ETF investors would be stuck with currency-denominated securities, and forced to bear any loss of purchasing power. Infrastructure as an asset class might or might not be a reasonable inflation hedge, as might stock (in the long run, equities are said to pass through inflation), TIPS, or any number of other assets. But that's fundamentally a decision for individuals to make. If infrastructure is a good choice, let the hedge funds buy it. But so long accredited investors (and savvy individuals with direct futures market accounts) have access to commodity exposure, it is inequitable to prevent the beneficiaries of ordinary investment funds from enjoying the same.

The United States economy is suffering the aftermath of poor aggregate investment decisions over a period of many years. Losses will have to be taken on those investments. The "wealth-holding class" responsible for the misdirection of capital will do what it can to shift losses to dispersed and relatively powerless little guys. I'd be glad to see the government take a more active role in addressing America's economic crisis. But most of the proposals out of Washington so far, including this idea from Senator Lieberman, give options to banks and wealthy investors while shoving costs and constraints onto everyone else. Trying to address the "commodity bubble" by restricting so-called speculation is a fool's game. If it's a bubble pop it, if it's a response to real risks, address those. Blaming speculators is like combating global warming by banning thermometers.

FD: I'm an evil speculator, but as an individual who trades futures directly, Senator Lieberman's proposal wouldn't prevent me from escaping the little people's inflation. That said, the only commodities I'm long are precious metals. I'm short Ag comodities via a retail ETF. I lose money all the time, so taking anything I say as investment advice is just dumb.

If you think $135 oil is a speculative bubble, that the only basis for current prices is want of a pin, here's a plan. If you're right, there's a market failure. Those with access to physical oil are accommodating the bubble for some reason, when they could, should in theory, sell forward in quantity and insist upon delivery, forcing speculators who cannot accept physical oil to close their positions at desperation prices. Note you don't have to overwhelm all the specs. Prices are set at the margin. You just have to sell with intent to deliver contracts representing somewhat more than demand for actual delivery to force oil off a cliff and crush the specs like bugs. If private arbitrageurs won't do this — perhaps those who can, don't, because they benefit more from high headline oil prices than they lose from foregoing a one-time arb &mdash then perhaps government should step in.

The US Strategic Petroleum Reserve could sell $135 oil forward in very large quantities, and refuse to close its contracts prior to delivery.

If you are right, and oil is an ordinary speculative bubble, then prices will fall sharply, and the petroleum reserve will be able to recover all the oil it sold cheaply, turning a profit for taxpayers.

But, if you are wrong, and oil prices are due to either current fundamentals or informed speculation on future supply and demand, then players interested in consuming or storing the product will step in as prices begin to fall and start buying. Prices would fall a little, but the drop would be transient, and the petroleum reserve would take a loss when it eventually repurchases to replenish.

It'd be a gamble. But if you think this is a bubble, a quick Federal pricking would be far less damaging public policy than curtailing unleveraged speculation. If you're not so sure it's a bubble, if you think it's possible that current or future supply and demand justify current prices, then you should definitely not be banning speculators, who are doing the good work dissuading us from squandering what is precious. If you think current prices are a monetary phenomenon, that selling oil forward trades a valuable commodity for depreciating paper, then you don't think this is a bubble at all, and limiting speculation is just a way of preventing would-be speculators from evading an inflation tax and spreading disquieting news.

I don't know whether current oil prices a speculative bubble or not. Maybe, maybe not. Maybe the best way to find out is with the help of a nice long pin.

While chatting with a commenter on the previous post, I went back to the Mathematica notebook where I had played with the numbers, and found an error in my arithmetic that is, as they say, "material". I erroneously used 68%, rather than 67%, as the late 90s participation rate, when I asserted that unemployment would be 8% today if participation returned to previous levels. The correct value is 6.6%.

That is, if an additional 0.8% of the "civilian noninstutional population" became active job seekers, but no net new jobs were created, the reported unemployment rate would be 6.6%. (The numbers, which hopefully I've correctly transcribed for a change, are May 2008 data from the June 6 release of BLS employment situation, Table A-1.) That's still a big jump from 5.5%, but it's a far cry from 8%, which sounds like a nasty recession.

To say I regret the error would understate the red-faced heart-thumpingness of the thing. Sorry!

Much of the chatter surrounding the latest BLS release has focused on a spike in the denominator of the unemployment statistic, the fraction of the population either working or actively looking for work. Courtesy of the indispensible FRED...

About a year ago, David Altig (whose macroblogging I miss very much) wrote the following:

[Since 2000] you would be justified in claiming a broad-based decline in the number of people choosing to participate in U.S. labor markets. But I use the word "choosing" intentionally, as I'm convinced that the post-2000 changes in labor force participation rates (or employment-to-population ratios, if you like) reflect trends that are largely independent of the business cycle.

Much turns on the question of why people chose not to participate in the labor force this decade. A "business cycle" explanation, as I read Altig, would mean that people left the labor force because there weren't employment opportunities. They couldn't find a job, and became "discouraged workers", in the lingo. I agree with Altig that this is unlikely. However, unemployment statistics (very uneconomically) ignore price, and stagnant real wages over the period undoubtedly had something to do with the decline in participation. People chose not to work because they decided the money wasn't worth their time.

But it's also important to consider a credit cycle explanation for why people left the workforce. One has the luxury of choice when one can afford to do without employment. During a credit expansion, many people have that luxury, because one can live off of borrowing and asset appreciation. You can quit your shitty job and withdraw some home equity while you write the great American novel, focus on your music, or raise your children. You can go to school, even though you lack savings, because student loans are plentiful.

But when credit conditions tighten and asset prices fall, work becomes less optional. Quitting the rat race and pursuing your passion starts to recall the phrase "starving artist", and not in a charming way. Dad might decide he needs a job to make ends meet, even if that means putting the kids in day care.

Some argue that the US economy is structurally immune from the wrenching spikes in unemployment that used to accompany recessions, because employment has transitioned from volatile manufacturing to more mellow services. See, for example, this excellent analysis from Calculated Risk. CR chooses 8% unemployment as his threshold for a "severe" recession. But the US economy need not lose a single job more to bring unemployment to that level. If participation rose back to the levels of the late 90s without a commensurate increase in new jobs, we'd be there already we'd be at 6.6% unemployment right now. [Note: In my original calculations, I mistakenly entered 68%, rather than 67%, as the late 90s participation rate, significantly exaggerating the effect. My apologies for the error!]

When we ended welfare as we know it, back in the nineties, the slogan "Choose to work" might have captured the spirit of the times. It's ironic that more than a decade later, the apparent health of the American economy depends largely on how many people continue to choose not to work, now that the credit spigot has dried up.

Greg Mankiw offers a strong endorsement of a proposal to cut the corporate income tax from 35 to 25 percent, claiming "It is perhaps the best simple recipe for promoting long-run growth in American living standards." (Hat tip Mark Thoma.) A good case can be made for cutting or even eliminating the corporate income tax. But Mankiw's argument does not cohere.

Let's start positive. Mankiw is right to point out that the "incidence" of the corporate income tax might not in fact be as progressive as its proponents would wish. He quotes studies suggesting that workers end up paying 70% to 92% of the taxes in the form of lower wages. I'm skeptical of those numbers, but it is surely true that some fraction, perhaps even a large fraction, of the corporate tax burden falls on workers and customers rather than presumptively wealthier investors. Mankiw does us all a service by reminding us of this.

Then he tells us a fairy tale:

A cut in the corporate tax... would initially give a boost to after-tax profits and stock prices, but the results would not end there. A stronger stock market would lead to more capital investment. More investment would lead to greater productivity. Greater productivity would lead to higher wages for workers and lower prices for customers.

First, if as Mankiw has argued, the lion's share of tax burden falls on workers, the "boost to after-tax profits and stock prices" would have to be correspondingly small. You can't have it both ways — either investors pay the tax, and stocks would be more valuable without them, or workers pay the tax, and stockholders are mostly indifferent. Perhaps Mankiw doesn't think that workers pay the tax after all.

Suppose there would be a surge in profits and stock prices, either because the corporate tax does burden stockholders, or out of irrational exuberance by cigar-smoking plutocrats. What then? Would "a stronger stock market... lead to more capital investment"? The tax change can't affect the economic opportunities available to firms. It can only affect investment decisions by reducing firms' cost of capital. As long as firms are correctly valued, the cost of equity depends on investor expectations going forward, not the level of the stock market today. Counterintuitively, if investors expect high future stock returns, that implies an increase in the cost of equity, and less corporate investment as existing opportunities face a higher "hurdle rate". Steepening return expectations only lead to more capital investment if they reflect an improvement in the opportunities available to firms. That is beyond the power of a tax cut.

Unreasonably high stock prices can, of course, encourage capital investment, as managers try to exchange overpriced paper for valuable projects, but the quality of investments under those circumstances is questionable at best. Surely, Mankiw does not think we should jolt stock markets into a bubble, because then firms will invest willy-nilly to preserve value before investors come to their senses?

A more charitable interpretation would be that Mankiw meant that investors' required return for stock investments wouldn't increase as much as the after-tax value of investment opportunities would, effectively reducing the equity cost of existing opportunities. But if the after-tax opportunity values would improve (they wouldn't, if workers bore the tax), there's no reason to think investor return requirements wouldn't increase as well. Just as it's hard to say who a tax will ultimately fall on, it's hard to know a priori how the proceeds of an investment tax break will be split between reinvestment, consumption, and safety. Some of the tax windfall would (thank goodness!) go towards delevering to reduce risk, and some would be withdrawn and spent by investors. How much actually goes to new capital investment would depend upon investor preferences, credit markets (which set the cost of safety), and the quality of potential new projects.

In theory, when firms do not have productivity-enhancing new projects at the ready, they return funds to investors. But, in the aftermath of first the dot-com bubble, and then a massive credit & housing bubble, it's worth asking what actually happens when the economy experiences positive shocks to the supply of capital. Perhaps, in a world where agents are informationally limited and distinct from the owners of capital they deploy, it is not always optimal to increase the rate at which capital is made available to firms and investment professionals, when the same wealth might otherwise be consumed or held for future use. We might illustrate this to supply-siders as a "Laffer Curve", with an optimal cost of capital above which productivity-enhancing investments are foregone, but below which wealth-destroying projects are funded. I think we've been on the wrong side of that curve for much of the past decade, so before I get excited about policies that purport to deliver growth by increasing incentives to save and invest, I'd like to see evidence that if we had more capital at hand, we'd use it well rather than employing well-paid intermediaries to destroy stuff in crazy schemes.

Supply side economics is a nice story, a hopeful story. It offers a clean, plausible policy framework: encourage investment, always and everywhere, and prosperity is sure to follow. But this decade has been about a pure a test of that idea as we could hope for. Capital in the United States was incredibly cheap, and what did we do? We destroyed a lot of wealth. We don't need more capital (although we might soon, if our foreign backers get skittish). We need more discriminating capital. In the meantime, the only thing I'm sure "works" about the supply side story is that it shifts the tax burden from richer to poorer. I'd rather that stop working so well.

Postscript: It is always deflating to see good ideas supported by poor arguments. I'd enthusiastically support eliminating the corporate income tax entirely, if the change were paid for by new taxes at least as progressive as the corporate income tax was intended to be. But my reasons are different from Mankiw's. Currently, the portion of corporate earnings payable to shareholders is taxed as corporate income, while the portion of earnings payable to debt holders is not taxed at all at the corporate level. (The accountants don't call the latter earnings at all, but that is semantics.) This differential tax treatment effectively pays firms to borrow funds rather than raise new equity when they need cash, which is bad public policy. Corporate leverage has social costs, "negative externalities", in terms of financial stability. To the degree government interferes in the capital structure decision at all (and I'm not arguing that it should), policy should favor equity financing since equity-funded firms are better able to internalize the costs of their misfortunes than are highly leveraged firms. So, three cheers for a progressively funded abolishment of the corporate income tax!

Alas, Mankiw proposes increasing gasoline taxes to replace the lost revenue. While there is much to be said for a higher gas tax, it fails the progressivity test. (Poorer people spend a much larger share of their income on fuel than do the affluent. Surely a Pigouvian would delight in redistributing the proceeds of a carbon tax as a flat transfer back to citizens to offset that unfair burden. A rebated carbon tax could be wildly popular, and help save the planet too.)

If, instead, we funded the change by increasing the highest marginal tax rate, or better yet, by creating a new top tax bracket, eliminating the corporate income tax would be a grand idea.