The Statistical Truth Nonrandom Thoughts and Data 

by Matt Carlson

March 14, 2009
Economics: A Theoretical Divide

In recent weeks there’s been a curious controversy among some of the leading lights in the economics profession over the fiscal stimulus. Here’s University of Chicago economist Eugene Fama’s synopsis of his argument about why President Obama’s stimulus plan may fail to stimulate:

“1. Bailouts and stimulus plans must be financed.
2. If the financing takes the form of additional government debt, the added debt displaces other uses of the same funds.
3. Thus, stimulus plans only enhance incomes when they move resources from less productive to more productive uses.”

Point 2 suggests that the stimulus won’t result in any more spending than would occur if the government did nothing at all. Point 3 seals the deal: since the private sector is supposedly much better at finding productive uses for resources than the government is, the stimulus would likely be a net loss for the economy, which of course is the very opposite of what we want from the stimulus.

Point 1 is uncontroversial. Point 2, most economists would agree, is simply wrong. It assumes a constant velocity of money. The velocity of money (nominal GDP divided by the quantity of money in circulation) tells us how many dollars worth of transactions a given quantity of money accomplishes in a given period of time. Velocity isn’t just a technical variable or a constant determined exogenously to economic activity, as Fama implicitly assumes. It’s an economic variable, determined in part endogenously, by the volume of economic activity. The historical data on this are clear: the velocity of money tends to fall during recessions and rise during upturns. (See diagram.) So “the added debt” from government borrowing will not displace “other uses of the same funds.” It will merely set those funds in motion, raising the velocity of money, and raising GDP by the dollar value of the transactions that the increased velocity of money enables the money supply to support.



Fama’s point 3 is more complex than many realize. Whether it’s the private sector or the government that puts resources to their “most productive uses” depends on what uses we’re talking about. For the production of everyday goods and services, undoubtedly it’s the private sector, which has the incentives and specialized knowledge to cater most effectively to consumer and business demands. But for large-scale investments in technology, education and infrastructure—which add greatly to productivity, yet lack the financial returns needed to make them worthwhile undertakings for the private sector—the government is the crucial agent.

But since point 2 is wrong, point 3 is actually moot. The issue, in a depressed economy, isn’t whether savings will be more productively invested by the government or by the private sector, but whether savings will be invested at all. Absent the stimulus, they won’t.

Fama’s argument and a similar one by University of Chicago economist John Cochrane have been widely ridiculed in the blogosphere. U.C. Berkeley economist Brad DeLong, for instance, noted the implicit constant-velocity-of-money assumption and accused Fama and Cochrane of making the “freshman error” of confusing an accounting identify (whereby savings and investment are always equal by definition, in accounting terms) with an equilibrium relationship (whereby savings and investment tend to move toward equality with each other through normal economic processes). Princeton economist and New York Times columnist Paul Krugman similarly noted that in a depressed economy saving is endogenous, not exogenous, determined by the level of income. We see this in textbook diagrams of the Keynesian multiplier where investment increases “autonomously,” and then through the rounds of the multiplier savings rises (because income is rising) until it equals the initial investment, at which point equilibrium (savings equal to investment) has been restored.

Since in Fama’s and Cochrane’s analysis the government can’t borrow without causing an equivalent, simultaneous drop in private spending, they implicitly assume, as Krugman observed, that all savings are invested—a doctrine called Say’s Law. Attributed to the French economist Jean-Baptiste Say (1776-1832), Say’s Law asserts that people supply goods and services only for the sake of demanding other goods and services—money being a mere “conduit.” Supply thus creates its own demand, all savings are automatically spent, and there’s no possibility of a recession caused by an overall demand deficiency.

Many economists had thought Say’s Law long discredited, if not by the Great Depression, then by John Maynard Keynes’s General Theory of Employment, Interest, and Money, which made a theoretical argument for the possibility of just such a recession. Yet Say’s Law is exactly what the work of a prominent group of macroeconomic theorists—the New Classical school, which includes Fama and Cochrane—has converged upon in recent decades. In their models hyper-rational consumers and businesses optimize their spending and savings decisions; prices adjust to clear all markets; and recessions occur, not because of an overall demand deficiency, but as an efficient response to exogenous supply shocks, e.g., technological changes. The current crisis might then be explained, not as the result of a fall in aggregate demand occasioned by the bursting of a housing bubble, but of a breakdown in our “financial technology,” specifically securitization, causing the flow of savings into the economy to become temporarily blocked. The solution would then be to fix the financial system (or allow it to fix itself), rather than
filling a nonexistent “hole” in aggregate demand.

Fama’s and Cochrane’s argument is actually an extreme statement of a perspective expressed in recent weeks by other conservative economists, for example, Robert Barro, Gary Becker, Kevin Murphy, Michele Boldrin and David Levine. Though few would take the extreme view that there’s 100 percent crowding out, with no net increase in spending as a result of the stimulus, such economists view markets as inherently highly efficient. Thus they tend to see “crowding out” effects as large, which makes the value of the multiplier, on which the stimulus is based, small.

What’s curious about this controversy—among economists like Fama, Cochrane, DeLong, Krugman, and others, who’ve built careers writing academic papers few paragraphs of which a layperson can read—is that it concerns textbook issues. The debate is about the multiplier, “crowding out,” Say’s Law, accounting identities, the velocity of money, etc., all concepts commonly found in introductory economics textbooks. The fact that the debate concerns textbook issues suggests that the fissure in the profession is large and basic.

Will the Stimulus Work?

To answer the conservative critics, let’s examine why anyone would think the stimulus should work in the first place. The theoretical basis for the stimulus is the Keynesian multiplier, a staple of macroeconomics textbooks, that shows how income can expand when “idle savings” are set to work.

In the following table we assume a closed economy (i.e., no foreign trade) and a “depressed economy,” i.e., that there are “idle savings” so that government spending doesn’t entail a corresponding diminution in private sector spending. (Concretely “idle savings” means the velocity of money is less than it could be, given the development of the financial system.) Suppose there’s an initial increase in government spending, G, of $300 and that the marginal propensity to consume is 0.33, i.e., people spend one-third of each additional dollar of income and save two-thirds. (In reality people spend much more on consumption, but no matter.) The initial spending of $300 is income, Y, for the recipients of that spending. And with a marginal propensity to consumer of 0.33, that means that $100 of that goes to consumption, C, and $200 goes to savings, S. The $100 of consumption spending is in turn income for the recipients of that expenditure in the next “round.” That is then apportioned between consumption and savings, as before, and so on. Income rises in each round of the multiplier by the amount of additional consumption expenditure.


The value of multiplier here is 1.5 (the approximate value of the multiplier assumed by the Obama administration). That is, for an increase in spending (increase in G) of $300, the total increase in income or GDP (Y) is $450. Or more precisely, the multiplier is (increase in Y) ÷ (increase in G) = $450/$300 = 1.5.

In strict accounting terms, this works. The initial increase in government spending of $300 is borrowed (through issuance of Treasury bonds), so debt, D, rises by $300. But savings, S, has, by the end of the process, risen by $300, and so is available, in principle, to retire the debt used to finance the initial spending. I say “in principle” because this is the thorny part: taxing savings, now dispersed through the economy, to pay off the government debt incurred in financing the initial spending. In a frictionless political environment, this could be done. And with justification, since the accumulated savings wouldn’t exist but for the initial government spending. However, the politics of taxation are anything but frictionless, and, as noted below, this does present a problem. (It should be noted, however, that it’s estimated that about a third of the cost of the stimulus will be covered by tax receipts that will be higher because of an improved economy.)

But note the end-result. The economy has grown. We have $450 more worth of stuff. There’s nothing “magical” about this, as Robert Barro seems to believe Keynesian economists believe. The multiplier simply captures, mathematically, a key relationship that obtains at the macro level between spending and income. And note that it applies to any spending whatever—not just government spending, but investment and consumption as well. The multiplier describes how spending radiates through the economy and helps explain why the economy, rather than following a stable growth path, rises and falls in waves of activity.

This result was admittedly obtained using idealized assumptions, in particular, that of a depressed economy (an economy with idle savings so that an increase in government spending causes no diminution in private spending). Probably even in a depressed economy, a government stimulus will entail some fall-off in private spending. But few economists believe, like Fama and Cochrane, that there will be one-for-one crowding-out, i.e., no net increase in overall spending as a result of the stimulus.

Unfortunately, the multiplier process also works in reverse. If net spending falls by, say, $300, then income will fall by that amount. And consumption will fall, not by the full amount of the fall in income but by a portion of it, say, one-third, or $100. That will mean an additional fall in income of $100 in the next “round” of a reverse multiplier process that can be captured mathematically by putting minus signs in front of each number in the above table.

The fact that this process, once set off, has a momentum of its own means the authorities must intervene from time to time to stabilize the economy. Normally in a downturn the Fed can lower interest rates sufficiently to raise the return on capital enough to motivate new investment, which through the macroeconomic interactions described above (plus the “accelerator”—a relation between income and purchases of capital goods—that we needn’t get into) propels the economy back upward. Our current situation is different.

The current crisis arises from two separate phenomena that, conjoined, feed off of each other in a most destructive way. What set off the crisis was a combination of falling asset prices and high indebtedness—i.e., the bursting of a highly leveraged asset bubble. The ensuing deleveraging (i.e., selling off of assets) then caused asset prices across the board (not just of houses and mortgage-backed securities) to plummet, further worsening balance sheets and systematically siphoning spending out of the economy. The latter then, through reverse multiplier effects, has caused incomes to fall and indebtedness to rise still further, further worsening balance sheets and causing spending to contract still more, etc.—basically a downward vicious spiral.

The revised Bureau of Economic Analysis report that GDP fell at an annualized rate of 6.2 percent in the fourth quarter of 2008 and the Bureau of Labor Statistics report that unemployment is now 8.1 percent are startling, but perhaps shouldn’t be surprising. Perverse feedback effects have been set in motion, and unless something quite aggressive is done to stop them, they will continue. Obviously these processes have slipped well beyond the Fed’s capacity to affect them by lowering interest rates.

So what could arrest these processes? Certainly aggressive action must be taken to clean up the balance sheets of consumers and banks. Politically this is difficult since, whether it’s buying toxic assets or injecting capital into banks or modifying mortgages, it necessarily involves bailouts, i.e., taking money from some taxpayers and giving it to other parties, many of them deemed victims of their own errors. Of course, as the downturn proceeds many who are blameless for their predicament get sucked into the vortex. If people are rational, sheer self-defense should compel them to support bailouts, regardless of how “worthy” are the recipients of bailout money.

Also crucial is a massive fiscal stimulus, for two reasons. First, because if large enough it will temporarily halt the deflationary spiral in its tracks, saving many jobs and preventing capacity from being wasted. Second, because it will contribute in some degree to the cleaning-up of balance sheets, since higher incomes will enable people and businesses to retire more debt. In effect, since the government is taking on debt to enable homeowners and businesses to retire debt, the stimulus will transfer debt from insolvent homeowners and businesses to the government. This, of course, is the objective of the bailouts, but here it’s done by less direct (and, one might think, politically less objectionable) means.

In sorting through the objections of conservative economists to the stimulus, it’s important to distinguish between two kinds of objection: economic objections, on the one hand, and political or practical ones, on the other. The economic objections are two in number, one bogus, the other real but addressable.

The bogus one is that the multiplier smacks of a “free lunch”—i.e., getting something for nothing. But an examination of the table above shows that this isn’t the case. Everything is paid for at cost, whether it’s the initial government spending, which must be taxed, or the goods and services purchased as a result of the expansion of income, all of which are bought at prices that presumably cover costs of production. (It’s only if one assumes a constant velocity of money that the multiplier looks like a “free lunch”; in fact, if money isn’t created to pay for the stimulus, a constant velocity of money means there’s no multiplier.)

The more serious economic objection concerns financing constraints. As noted, the stimulus will need to be financed by future savings. Though Fama and Cochrane are wrong that “crowding out” of private expenditure is immediate and one-for-one, “crowding out” is real and will likely bite in the long run when the economy returns to form and private sector investment really does compete with taxation for scarce savings. Interest rates will then rise; and interest on the debt will be a drag on the economy.

One point to note, however: that if this occurs, the stimulus will be partly a victim of its own success. For it’s the recovery that the stimulus helps generate that makes financial resources scarcer than they otherwise would be. So the “crowding out” effect is not really a strong argument against the stimulus. We would be lucky to have an economy in which government spending “crowds out” private investment.

More importantly, the solution to the “crowding out” problem is to spend a portion of the stimulus money on assets, i.e., on infrastructure, education and technology—investments that could be sufficiently productivity-enhancing and income-generating to more than offset private investment lost through “crowding out.” Such investments, in any case, are vital to an advanced industrialized economy.
Where would we be without the highway system, the public education system, key aspects of airplane technology, computers, the Internet, etc., all built or developed with crucial government support? And if we are to undertake such projects, now’s the time, since the opportunity cost of such investments in terms of lost private sector investment is now low.

The real question about the effectiveness of the stimulus is how big the multiplier is, i.e., given the stimulus money, how much will consumers spend? One could argue that, with the credit system impaired, credit-based spending (i.e., investment spending and consumer spending on, e.g., cars and houses) isn’t likely to rise much. That would diminish the value of the multiplier. One could also argue, as President Obama’s Chair of the Council of Economic Advisors Christina Romer has, that liquidity constraints arising from the credit crisis have caused a surfeit of pent-up consumer demand to build up, waiting to be released by the stimulus. That would make the multiplier larger than the usual empirical estimates, which range from 1.5 to 2 for spending and 0.5 to 1 for tax cuts.

Another question is how much Americans will spend on American products. In the above table we assumed no foreign trade. But the biggest threat to the effectiveness of the stimulus may be that Americans spend much of their stimulus money on foreign products, thus, to some extent, exporting our multiplier. If Japan and Western European countries fail to stimulate their economies to the extent that the U.S. has its economy, as seems likely, this is a real threat. American consumers will buy more products in general, including more foreign products. European and Japanese consumers will buy fewer products in general, including fewer American products. Hence the need, as the IMF advocates, for a coordinated global fiscal stimulus.

Among the political/practical objections made by conservatives, there’s this: that once government spending programs are established, they have a way of hanging around, as self-interested bureaucrats lobby to keep them alive. This is a very conservative concern. But it’s probably a non-issue. The people in charge of economic policy are actually hard-line Clintonite fiscal hawks who balanced budgets (of all things) in the 1990s and even ran surpluses in the latter part of the decade. By the Obama team’s (admittedly probably rosy) calculations, government spending will be 22.2 percent of GDP in 2013, just less than two percentage points higher than it was last year. (So is the crossover point into socialism going from a 20.4 percent government share of GDP, as in 2008, to a 22.2 percent share, as projected for 2013?)

Think of the contrast between that and the fiscal profligacy the Republicans have embraced in the last three decades. Latest evidence: the DeMint amendment, supported by all but six Senate Republicans, which would have massively and permanently cut a host of taxes, costing the Treasury $3.1 trillion dollars over ten years (according to Paul Krugman). That’s four times the size of Obama’s $787 billion stimulus, less stimulative (since it’s tax cuts), and, unlike the Obama plan, lacking in any strategy to recoup the losses. (And John McCain talks of “generational theft”?)

No one thinks the stimulus is itself a solution to the crisis. Primarily it would save jobs and capacity and buy time to address the real source of the problem, the troubled assets of banks and homeowners. And few are blithely unaware of the political problems the stimulus poses, above all, the thorny question of how to tax future savings to cover the debt incurred by the stimulus spending.

Indeed, given the politics, the stimulus and the bailouts may be the worst possible solutions to the crisis, except for the alternatives. In denouncing stimulus spending the conservative economists are in effect counseling that we junk a portion of our capital stock (and sacrifice many jobs and goods and services as well). In the long run, if the credit crisis persists, this actually is a solution to the crisis. As the capital stock obsolesces, the “marginal efficiency of capital” (to use Keynes’s term for the return on an additional dollar of investment) will rise, and ultimately it will rise just enough to make investment in capital goods profitable. More workers will then be hired, incomes will rise, and spending will increase, etc., propelling the economy back upward. The problem is that if we have to wait for our capital stock to obsolesce, we’re talking Great Depression II in the meantime. A more apt application of the “lunch” metaphor would be that through the stimulus we get the “lunch” we’ve already paid for, rather than letting it go to waste.

Economists, conservative ones especially, with their strong faith in markets, usually counsel that we let market forces play themselves out. In normal times that might be sound advice. These aren’t normal times. The problem now is that processes have been set in motion that, if allowed to play themselves out, will drive the economy (and ourselves) right into a ditch. And we may be but a small way into the crisis, given the scale of the deleveraging seemingly still in store. NYU economist Nouriel Roubini, who predicted the disaster, writes not just of a housing bubble, but of “an equity bubble, a bond bubble, a credit bubble, a commodity bubble, a private equity bubble, a hedge funds bubble… all now bursting at once in the biggest real sector and financial sector deleveraging since the Great Depression.” The massive indebtedness behind the insolvencies systematically siphoning spending out of the economy must somehow be unwound. It can be unwound the “easy” way, through stimulus spending and bailouts, or the hard way, through a Japanese-style “lost decade” or by revisiting the 1930s.

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Where the Economy is and Where It's (Apparently) Going
Some Reality about Deficits

Armageddon: The Aftermath
The Hype

How to Explain It 
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The Point of the Public Plan
The Context of Health Care Reform
Addendum
Is Low Life Expectancy the Fault of Our Health Care System?
What Americans Believe
American Health Care: Best in the World?
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Inside the Asylum
More About Bubbles
Why Did Economists Miss the Housing Bubble?
Why Has Monetary Policy Been so Ineffective?

The Geithner Plan
Is 22.2 Large?
The New Deal and the Great Depression
Stimulus By the Skin of Our Teeth
The Interregnum
Postmortem
Obama and McCain on Tax Cuts and Health Care
Religion and the New Atheism
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