# The True Multiplier

I ended “The Keynesian Multiplier: Phony Math” on this note:

If there is a multiplier on government spending, it’s bound to be negative. Stay tuned for more about the effect of government spending on economic output.

Before I get to my estimate of the true multiplier — the one that does lasting damage to the economy — I must say more about the multiplier of Keynesian mythology.

As shown in “The Keynesian Multiplier: Phony Math,” the Keynesian multiplier rests on a mathematical illusion. It is nevertheless possible that an exogenous increase in spending really does yield a short-term, temporary increase in GDP.

How would it work? The following example goes beyond the bare theory of the Keynesian multiplier, and addresses several practical and theoretical reservations about it (some which I discuss in “A Keynesian Fantasy Land” and “The Keynesian Fallacy and Regime Uncertainty“):

1. Annualized real GDP, denoted as Y, drops from \$16.5 trillion a year to \$14 trillion a year because of the unemployment of resources. (How that happens is a different subject.)
2. Government spending (G) is temporarily and quickly increased by an annual rate of \$500 billion; that is, ∆G = \$0.5 trillion. The idea is to restore Y to \$16 trillion, given a multiplier of 5 (In standard multiplier math: ∆Y = (k)(∆G), where k = 1/(1 – MPC); k = 5, where MPC = 0.8.)
3. The ∆G is financed in a way that doesn’t reduce private-sector spending. (This is almost impossible, given Ricardian equivalence — the tendency of private actors to take into account the long-term, crowding-out effects of government spending as they make their own spending decisions. The closest approximation to neutrality can be attained by financing additional G through money creation, rather than additional taxes or borrowing that crowds out the financing of private-sector consumption and investment spending.)
4. To have the greatest leverage, ∆G must be directed so that it employs only those resources that are idle, which then acquire purchasing power that they didn’t have before. (This, too, is almost impossible, given the clumsiness of government.)
5. A fraction of the new purchasing power flows, through consumption spending (C), to the employment of other idle resources. That fraction is called the marginal propensity to consume (MPC), which is the rate at which the owners of idle resources spend additional income on so-called consumption goods. (As many economists have pointed out, the effect could also occur as a result of investment spending. A dollar spent is a dollar spent, and investment  spending has the advantage of laying the groundwork for economic growth, unlike consumption spending.)
6. A remainder goes to saving (S) and is therefore available for investment (I) in future production capacity. But S and I are ignored in the multiplier equation: One story goes like this: S doesn’t elicit I because savers hoard cash and investment is discouraged by the bleak economic outlook. This is probably closer to the mark: The multiplier would be infinite (and therefore embarrassingly inexplicable) if S generated an equivalent amount of I, because the marginal propensity to spend (MPS) would be equal to 1, and the multiplier equation would look like this: k = 1/(1 – MPS) = ∞, where MPS = 1.
7. In any event, the initial increment of C (∆C) brings forth a new “round” of production, which yields another increment of C, and so on, ad infinitum. If MPC = 0.8, then assuming away “leakage” to taxes and imports, the multiplier = k = 1/(1 – MPC), or k = 5 in this example.  (The multiplier rises with MPC and reaches infinity if MPC = 1. This suggests that a very high MPC is economically beneficial, even though a very high MPC implies a very low rate of saving and therefore a very low rate of growth-producing investment.)
8. Given k = 5,  ∆G = \$0.5T would cause an eventual increase in real output of \$2.5 trillion (assuming no “leakage” or offsetting reductions in private consumption and investment); that is, ∆Y = [k][∆G]= \$2.5 trillion. However, because G and Y usually refer to annual rates, this result is mathematically incoherent; ∆G = \$0.5 trillion does not restore Y to \$16.5 trillion.
9. In any event, the increase in Y isn’t permanent; the multiplier effect disappears after the “rounds” resulting from ∆G have played out. If the theoretical multiplier is 5, and if transactional velocity is 4 (i.e., 4 “rounds” of spending in a year), more than half of the multiplier effect would be felt within a year from each injection of spending, and about two-thirds would be felt within two years of each injection. It seems unlikely, however, that the multiplier effect would be felt for much longer, because of changing conditions (e.g., an exogenous boost in private investment, private reemployment of resources, discouraged workers leaving the labor force, shifts in expectations about inflation and returns on investment).
10. All of this ignores that fact that the likely cause of the drop in Y is not insufficient “aggregate demand,” but a “credit crunch” (Michael D. Bordo and Joseph G. Haubrich in “Credit Crises, Money, and Contractions: A Historical View,” Federal Reserve Bank of Cleveland, Working Paper 09-08, September 2009), “Aggregate demand” doesn’t exist, except as an after-the-fact measurement of the money value of goods and services comprised in Y. “Aggregate demand,” in other words, is merely the sum of millions of individual transactions, the rate and total money value of which decline for specific reasons, “credit crunch” being chief among them. Given that, an exogenous increase in G is likely to yield a real increase in Y only if the increase in G leads to an increase in the money supply (as it is bound to do when the Fed, in effect, prints money to finance it). But because of cash hoarding and a bleak investment outlook, the increase in the money supply is unlikely to generate much additional economic activity.

To top it off, a somewhat more realistic version of multiplier math — as opposed to the version addressed in “The Keynesian Multiplier: Phony Math” — yields a maximum value of k = 1:

How did I do that? In step 3, I made C a function of P (private-sector GDP) instead of Y (usually taken as the independent variable). Why? For the years 1929-2012 (excluding 1941-46, when the massive war effort and its aftermath drastically reduced C), C was more closely linked to P than to Y. (The true consumption function turns out to be C = – \$148 trillion in 2012 \$ + 0.838P.)

Math trickery aside, there is evidence that the Keynesian multiplier is less than 1. Robert J. Barro of Harvard University opens an article in The Wall Street Journal with the statement that “economists have not come up with explanations … for multipliers above one.”[1]

Barro continues:

A much more plausible starting point is a multiplier of zero. In this case, the GDP is given, and a rise in government purchases requires an equal fall in the total of other parts of GDP — consumption, investment and net exports….

What do the data show about multipliers? Because it is not easy to separate movements in government purchases from overall business fluctuations, the best evidence comes from large changes in military purchases that are driven by shifts in war and peace. A particularly good experiment is the massive expansion of U.S. defense expenditures during World War II. The usual Keynesian view is that the World War II fiscal expansion provided the stimulus that finally got us out of the Great Depression. Thus, I think that most macroeconomists would regard this case as a fair one for seeing whether a large multiplier ever exists.

I have estimated that World War II raised U.S. defense expenditures by \$540 billion (1996 dollars) per year at the peak in 1943-44, amounting to 44% of real GDP. I also estimated that the war raised real GDP by \$430 billion per year in 1943-44. Thus, the multiplier was 0.8 (430/540). The other way to put this is that the war lowered components of GDP aside from military purchases. The main declines were in private investment, nonmilitary parts of government purchases, and net exports — personal consumer expenditure changed little. Wartime production siphoned off resources from other economic uses — there was a dampener, rather than a multiplier….

There are reasons to believe that the war-based multiplier of 0.8 substantially overstates the multiplier that applies to peacetime government purchases. For one thing, people would expect the added wartime outlays to be partly temporary (so that consumer demand would not fall a lot). Second, the use of the military draft in wartime has a direct, coercive effect on total employment. Finally, the U.S. economy was already growing rapidly after 1933 (aside from the 1938 recession), and it is probably unfair to ascribe all of the rapid GDP growth from 1941 to 1945 to the added military outlays. (“Government Spending Is No Free Lunch,” The Wall Street Journal (online.WSJ.com), January 22, 2009)

This is from Valerie A. Ramsey of  the University of California-San Diego and the National Bureau of Economic Research:

…[I]t appears that a rise in government spending does not stimulate private spending; most estimates suggest that it significantly lowers private spending. These results imply that the government spending multiplier is below unity. Adjusting the implied multiplier for increases in tax rates has only a small effect. The results imply a multiplier on total GDP of around 0.5. (“Government Spending and Private Activity,” January 2012)

The price of the demonstrably small Keynesian multiplier is a “temporary” increase in G — an increase that is likely to be permanent and therefore harmful to economic growth.

If that is the case, whence the continuing clamor for “temporary” increases in government spending? It’s because the Keynesian multiplier isn’t just a phony theory; it’s a “religious” tenet shared by economists, pundits, and policy-makers who are true believers in big government. True believers aren’t swayed by such considerations as slower growth and the loss of freedom that accompanies government interventions in private affairs. True believers — Paul Krugman, Brad DeLong, Joseph Stiglitz, and their ilk — always claim that government should spend more, not just in recessionary times. Their preachings bolster the pro-government-spending biases of most pundits and a large fraction of politicians.

As for “temporary” increases in government spending, they usually are as temporary as the infamous “temporary government buildings” in Washington, D.C. Consider this:

Sources: See footnote 3.

Look at defense spending, which actually fluctuates noticeably. Then look at the two lines for government spending, especially the top line. What do you see? An almost unbroken rise in total government spending (including transfer payments). There’s no give-back of any significance. When government officials latch onto your money, they find a way to keep it. If a reduction in defense spending seems to be in order, the money is shifted to other government programs. If there’s a cut in government programs that don’t provide “social insurance,” the money is shifted to government programs that do provide “social insurance” (mainly Social Security, Medicare, and Medicaid). In other words, our rulers consider our money to be their money, and they find ways to keep it, and to grab more and more of it. That’s why the private sector’s share of GDP — the gap between GDP and top-line government spending — shrank almost steadily from 1947 (the first year of full demobilization after World War II) through 2012.

Let’s now talk about the true multiplier on government spending, which I denote as K. Before I spring some equations on you, I want to take a brief tour of the economy’s performance since World War II. Consider the long, upward trend in government spending (G)[2] as a fraction of GDP:

Sources: See footnote 3.

The decline of G/GDP in the 1990s can be attributed to the “peace dividend” — the accelerated reduction of defense spending following the end of the Cold War and the Gulf War — and to the overrated “Clinton boom.” (This so-called boom featured a real growth rate of 3.4 percent from 1993 to 2001, which is unimpressive by historical standards. For example, the overall rate of growth from the first quarter of 1947 to the first quarter of 1993 — recessions and all — was 3.4 percent.)

In any event, the cumulative effect of rising G/GDP on the rate of growth is evident here:

Derived from a spreadsheet published by the Bureau of Economic Analysis, Current Dollar and “Real” Gross Domestic Product.

This graph tells the same story in a different way:

Derived from the same source as the preceding graph. My definition of a recession is given here.

Putting it all together, for the period 1947-2012 I estimated[3] the year-over-year percentage change in GDP (denoted as Y%) as a function of G/GDP (denoted as G/Y):

Y% = 0.09 – 0.17(G/Y)

Solving for Y% = 0 yields G/Y = 0.53; that is, Y% will drop to zero if G/Y rises to 0.53 (or thereabouts)[4]. At the present level of G/Y (about 0.4), Y% will hover just above 2 percent, as it has done in recent years. (See the graph immediately above.)

If G/Y had remained at 0.234, its value in 1947:

• Real growth would have been about 5 percent a year, instead of 3.2 percent (the actual value for 1947-2012).
• The total value of Y for 1947-2012 would have been higher by \$500 trillion (98 percent).
• The total value of G would have been lower by \$61 trillion (34 percent).

The last two points, taken together, imply a cumulative government-spending multiplier (K) for 1947-2012 of about -8. That is, aggregate output in 1947-2012 declined by 8 dollars for every dollar of government spending above the amount represented by G/Y = 0.234.

But -8 is only an average value for 1947-2012. It gets worse. The reduction in Y is cumulative; that is, every extra dollar of G reduces the amount of Y that is available for growth-producing investment, which leads to a further reduction in Y, which leads to a further reduction in growth-producing investment, and on and on. (Think of the phenomenon as negative compounding; take a dollar from your savings account today, and the value of the savings account years from now will be lower than it would have been by a multiple of that dollar: [1 + interest rate] raised to nth power, where n = number of years.) Because of this cumulative effect, the effective value of K in 2012 was about -14.

For this, the U.S. government should “stimulate” the economy with a burst of “temporary” spending? Think again.

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Footnotes:

[1] Theoretical estimates of the Keynesian multiplier [k = 1/(1 – b)] are always greater than 1. How much greater depends only on the value assigned to b, the marginal propensity to consume. The story about “rounds” of additional consumption spending, the sum of which asymptotically approach the value of the multiplier, is just that — a story, a rationalization of phony multiplier math:

The phony math and phony story led Keynes’s intellectual heirs and their followers to believe that the multiplier is greater than 1 — significantly greater, in the minds of true believers. And when people believe in something, it’s easy to find numbers to support the belief. This is especially true of macroeconomic aggregates, which reflect the influence of so many variables that it’s hard to pinpoint what causes what.

Why is 1 the true upper limit of the Keynesian multiplier? I offer the following explanation by way of a thought experiment.

Consider a simple economy with two producers who trade with each other. One (the baker) makes bread; the other (the dairyman) makes butter. With fixed capital, which is kept in repair but never improved or expanded, the output and consumption of bread and butter will change for any or all of four reasons: (1) changes in the tastes and preferences of the producers (as consumers); (2) changes in the availability of resources because of ambient conditions (e.g., a flood that disruptions production, weather conditions that affect the yield of wheat, the health of the baker and the dairyman); (3) innovations that lead to an increase the quality or quantity of output, without requiring additional inputs; and (4) a disruption of credit.

None of these conditions can be remedied at zero cost, that is, simply by printing money in the hope of re-employing the unemployed resources. The fourth condition warrants elaboration. Suppose that the baker had been relying on advances of butter from the dairyman. Then the dairyman cuts off those advances — perhaps because his churn is being repaired., or because he has less tolerance for risk. The baker’s resulting loss of energy causes him to produce less bread, which reduces the rate at which the baker and dairyman exchange bread and butter, which exacerbates the baker’s loss of energy and initiates a decline in the dairyman’s energy, and so on. (You should recognize this as an analog of the process by which an economy is thought to fall into recession or depression. The pervasiveness of the “credit crunch” as a cause of or major factor in recessions and depressions is documented by Michael D. Bordo and Joseph G. Haubrich in “Credit Crises, Money, and Contractions: A Historical View,” Federal Reserve Bank of Cleveland, Working Paper 09-08, September 2009.) No amount of “stimulus” will cause the dairyman to restore credit to the baker, unless and until the dairyman is convinced of the baker’s creditworthiness. (We’re in a barter economy, so throwing money at the baker won’t make him any more credit-worthy or lead to a rise in real output; it will just spread the pain. Nor does throwing money around do much to help in a money-based economy; it doesn’t (a) fix the underlying problem (e.g., a badly managed business in a highly competitive industry) or (b) yield a one-for-one increase in output, inasmuch as the thrown money is inevitably misdirected and must therefore cause some degree of price inflation instead of spurring real output.)

In the absence of any of the kinds of change discussed above, the simple baker-dairyman economy can be characterized as a static circular flow: the same inputs yield the same kinds of outputs, which are consumed at the same rate, year after year. Specifically, the baker keeps some of his output and trades some of it for butter; the dairyman keeps some of his output and trades some of it for bread. The two producers, acting as consumers, use all of the bread and butter that they produce. As a result, they produce the same amount of bread and butter in the next year, which they consume. And so on.

A heretofore unemployed third party enters: a maker of jam, who also wants to consume bread and butter. Where did he come from? Perhaps he’s a son of the baker or the dairyman who has just become old enough to strike out on his own. In any event, his production of jam doesn’t reduce the output of bread and butter; he is drawing on heretofore unused resources that the baker and dairyman couldn’t employ because they are fully engaged in their respective activities.

The producers of bread, butter, and jam decide to engage in three-way trade, so that every one of them becomes a consumer of all three items. The producers of bread and butter willingly consume less bread and butter than before in order to have jam. The producer of jam, of course, trades some of his output for some bread and butter.  As a result of these voluntary trades, all three producers are better off than they were before. (If they weren’t, they wouldn’t trade with each other.)

Because the employment of previously unemployed resources makes everyone better off, those previously unemployed resources will continue to be employed, barring changes of the kind discussed above. That is, the circular flow will continue, but at a higher level of output and consumption. But it won’t expand beyond the level attained when the jam-maker entered the scene and entered into three-way trade with the baker and dairyman.

In sum, the initial “burst” of new employment and output, represented by the jam-maker’s production, doesn’t cause a “ripple effect” that leads to further expansion of output and consumption. Any further expansion would have to be caused by (and limited to) the employment of yet another heretofore unemployed resource; that is, yet another shot of “stimulus.”

Conclusion: The maximum multiplier on the employment of a previously unemployed resource is 1. But it can be (and probably will be) less than 1 if a fourth party (government) tries to entice additional output by issuing directives (spending money) without perfect knowledge of current economic variables (including, but not limited to, knowledge of tastes and preferences, states of health, and producers’ and consumers’ plans and expectations). A good example of government failure: directing (issuing money to) the fully employed baker and dairyman to produce more bread and butter,  while failing to direct (issue money to) the jam-maker to make enough jam to fully employ himself.

[2] G, as I use it here, stands for all government spending, including so-called transfer payments. A transfer payment (usually “social insurance“) is just another way of moving claims on resources from those who earned such claims to those who didn’t earn them. In this respect, transfer payments are no different than other government programs, which involve the coercion of taxpayers to compensate government employees and contractors who do unproductive and counterproductive work (e.g., writing and enforcing regulations). Transfer payments, like other government programs, require administration by vast, costly bureaucracies. In sum, there is no substantive difference between transfer payments and other kinds of government spending; transfer payments are therefore properly considered government spending, arbitrary national-income accounting flim-flam to the contrary notwithstanding.

[3] This equation is based on estimates of GDP and government spending  for 1946-2012. The equation, the intercept, and the coefficient on G/GDP are significant at the 0.05 level and better. The standard error of the estimate is 0.024 percentage points; there is a 95-percent probability that the zero growth point lies between G/Y = 0.41 and 0.75. To derive the equation, I obtained current-dollar estimates of GDP and G from the Bureau of Economic Analysis, GDP and the National Income and Product Accounts (NIPA) Historical Tables, 1.1.5 Gross Domestic Product, line 1, and 3.1 Government Current Receipts and Expenditures, lines 33 and 34. I deflated the current-dollar values using the GDP deflator published at MeasuringWorth.com.

[4] This is is remarkably close to the zero-growth estimate of 0.55 that I derived in “Estimating the Rahn Curve: Or How Government Inhibits Economic Growth.” The equation given in that post is based on a longer view of the effects of government spending on growth. In retrospect, that longer view gives too much weight to the bygone era of low government spending, an era that ended with the Great Depression. I stand by the equation in this post as indicative of reality in the post-World War II era of rampant growth in government spending.

# The Keynesian Multiplier: Phony Math

Much is wrong with the Keynesian multiplier. The arguments for it and explanations of it range from incoherent to inconsistent. In time, I’ll address those arguments and explanations. Today, however, I’ll focus on the phony math at the heart of the multiplier.

The bottom line: The Keynesian multiplier is a tautology that explains nothing. To see why, read on.

THE MULTIPLIER: AN IDEA THAT WON’T DIE

Why worry about the Keynesian multiplier, when old-style Keynesian economics has been supplanted — in the academy — by new Keynesianism, new classical macroeconomics, and the new neoclassical synthesis? Economist John Cochrane has the answer:

Many Keynesian commentators have been arguing for much more stimulus.  They like to write the nice story, how we put money in people’s pockets, and then they go and spend, and that puts more money in other people’s pockets, and so on.

But, alas, the old-Keynesian model of that story is wrong. It’s just not economics. A 40 year quest for “microfoundations” came up with nothing. How many Nobel prizes have they given for demolishing the old-Keynesian model? At least Friedman, Lucas, Prescott, Kydland, Sargent and Sims. Since about 1980, if you send a paper with this model to any half respectable journal, they will reject it instantly.

But people love the story. Policy makers love the story.  Most of Washington loves the story. Most of Washington policy analysis uses Keynesian models or Keynesian thinking. This is really curious. Our whole policy establishment uses a model that cannot be published in a peer-reviewed journal. Imagine if the climate scientists were telling us to spend a trillion dollars on carbon dioxide mitigation — but they had not been able to publish any of their models in peer-reviewed journals for 35 years. (“New vs. Old Keynesian Stimulus,” The Grumpy Economist, November 8, 2013)

People — in the academy, the media, and politics — love the story so much that Obama’s “stimulus package” was predicated on a multiplier of about 1.6.  That estimate was produced in January 2009 by Christina Romer, who was then chairwoman-designate of Obama’s Council of Economic Advisers. Another prominent economist, Alan Blinder (a member of the CEA under Clinton and former vice chairman of the Fed’s Board of Governors), cites a multiplier of 1.5.

Those of you who have at least a passing familiarity with the multiplier will ask what’s wrong with a multiplier of 1.5, or 1.6 — or even a multiplier of 5. That is, if government spends an extra \$1 to employ previously unemployed resources, why won’t that \$1 multiply and become \$1.50, \$1.60, or even \$5 worth of additional output?

The answer, my friends, is found in the phony math by which the multiplier is derived, and in the phony story that was long ago concocted to explain the operation of the multiplier. The phony math and phony story led Keynes’s intellectual heirs and their followers to believe that the multiplier is greater than 1 — significantly greater, in the minds of true believers. And when people believe in something, it’s easy to find numbers to support the belief. This is especially true of macroeconomic aggregates, which reflect the influence of so many variables that it’s hard to pinpoint what causes what.

MULTIPLIER MATH

I’ll deal with the phony story in a future post. Today’s lesson is about the phony math. To show you why the math is phony, I’ll start with a derivation of the multiplier. That derivation begins with the accounting identity  Y = C + I + G, which means that  total output (Y) = consumption (C) + investment (I) + government spending (G). I could have used  a more complex identity that involves taxes, exports, and imports. But no matter; the bottom line remains the same, so I’ll keep it simple and use Y = C + I  + G.

Keep in mind that the aggregates that I’m writing about here — Y , C , I , G, and later S  — are supposed to represent real quantities of goods and services, not mere money.

Now for the derivation:

So far, so good. Now, let’s say that b = 0.8. This means that income-earners, on average, will spend 80 percent of their additional income on consumption goods (C), while holding back (saving, S) 20 percent of their additional income. With b = 0.8, k = 1/(1 – 0.8) = 1/0.2 = 5.  That is, every \$1 of additional spending — let us say additional government spending (∆G) rather than investment spending (∆I) — will yield ∆Y = \$5. In short, ∆Y = k(∆G), as a theoretical maximum. (There are many reasons for the multiplier, even if it were real, to fall short of its theoretical maximum; see this post.)

How is it supposed to work? The initial stimulus (∆G) creates income (don’t ask how), a fraction of which (b) goes to C. That spending creates new income, a fraction of which goes to C. And so on. Thus the first round = ∆G, the second round = b(∆G), the third round = b(b)(∆G) , and so on. The sum of the “rounds” asymptotically approaches k(∆G). (What happens to S, the portion of income that isn’t spent? That’s part of the complicated phony story that I’ll examine in a future post.)

Note well, however, that the resulting ∆Y isn’t properly an increase in Y, which is an annual rate of output; rather, it’s the cumulative increase in total output over an indefinite number and duration of ever-smaller “rounds” of consumption spending.

The cumulative effect of a sustained increase in government spending might, after several years, yield a new Y — call it Y’ = Y + ∆Y. But it would do so only if ∆G persisted for several years. To put it another way, ∆Y persists only for as long as the effects of ∆G persist. The multiplier effect disappears after the “rounds” of spending that follow ∆G have played out.

The multiplier effect is therefore (at most) temporary; it vanishes after the withdrawal of the “stimulus” (∆G). (A permanent increase in G would adversely affect GDP in the longer term by diverting resources from more productive private uses and discouraging growth-producing investment spending.) The idea is that ∆Y should be temporary because a downturn will be followed by a recovery — weak or strong, later or sooner. (I can’t resist the observation that enthusiasts of big government relish the thought of any increase in G, hoping that it will become permanent.)

WHY MULTIPLIER MATH IS PHONY MATH

Now for my exposé of the phony math. I begin with Steve Landsburg, who borrows from the late Murray Rothbard:

. . . We start with an accounting identity, which nobody can deny:

Y = C + I + G. . . Since all output ends up somewhere, and since households, firms and government exhaust the possibilities, this equation must be true.

Next, we notice that people tend to spend, oh, say about 80 percent of their incomes. What they spend is equal to the value of what ends up in their households, which we’ve already called C. So we have

C = .8YNow we use a little algebra to combine our two equations and quickly derive a new equation:

Y = 5(I+G)That 5 is the famous Keynesian multiplier. In this case, it tells you that if you increase government spending by one dollar, then economy-wide output (and hence economy-wide income) will increase by a whopping five dollars. What a deal!

. . . [I]t was Murray Rothbard who observed that the really neat thing about this argument is that you can do exactly the same thing with any accounting identity. Let’s start with this one:

Y = L + E

Here Y is economy-wide income, L is Landsburg’s income, and E is everyone else’s income. No disputing that one.

Next we observe that everyone else’s share of the income tends to be about 99.999999% of the total. In symbols, we have:

E = .99999999 Y

Combine these two equations, do your algebra, and voila:

Y = 100,000,000 LThat 100,000,000 there is the soon-to-be-famous “Landsburg multiplier”. Our equation proves that if you send Landsburg a dollar, you’ll generate \$100,000,000 worth of income for everyone else.

The policy implications are unmistakable. It’s just Eco 101!! (“The Landsburg Multiplier: How to Make Everyone Rich,” The Big Questions blog, June 25, 2013)

Landsburg attributes the nonsensical result to the assumption that

equations describing behavior would remain valid after a policy change. Lucas made the simple but pointed observation that this assumption is almost never justified.

. . . None of this means that you can’t write down [a] sensible Keynesian model with a multiplier; it does mean that the Eco 101 version of the Keynesian cross is not an example of such. This in turn calls into question the wisdom of the occasional pundit [Paul Krugman] who repeatedly admonishes us to be guided in our policy choices by the lessons of Eco 101. (“Multiple Comments,” op. cit,, June 26, 2013)

It’s worse than that, as Landsburg almost acknowledges, when he observes (correctly) that Y = C + I + G is an accounting identity. That is to say, it isn’t a functional representation — a model — of the dynamics of economic exchange. Assigning a value to b (the marginal propensity to consume) — even if it’s an empirical value — doesn’t alter that fact that the derivation is nothing more than the manipulation of a non-functional relationship.

Consider the equation for converting temperature Celsius (C) to temperature Fahrenheit (F): F = 32 + 1.8C. It follows that an increase of 10 degrees C implies an increase of 18 degrees F. This could be expressed as ∆F/C = k* , where k* represents the “Celsius multiplier.” There is no mathematical difference between the derivation of the investment/government-spending multiplier (k) and the derivation of the Celsius multiplier (k*). And yet we know that the Celsius multiplier is nothing more than a tautology; it tells us nothing about how the temperature rises by 10 degrees C or 18 degrees F. It simply tells us that when the temperature rises by 10 degrees C, the equivalent rise in temperature F is 18 degrees. The rise of 10 degrees C doesn’t cause the rise of 18 degrees F.

Similarly, the Keynesian investment/government-spending multiplier simply tells us that if ∆Y = \$5 trillion, and if b = 0.8, then it is a matter of mathematical necessity that ∆C = \$4 trillion and ∆I + ∆G = \$1 trillion. In other words, a rise in I + G of \$1 trillion doesn’t cause a rise in Y of \$5 trillion; rather, Y must rise by \$5 trillion for C to rise by \$4 trillion and I + G to rise by \$1 trillion. If there’s a causal relationship between ∆G and ∆Y, the multiplier doesn’t portray it.

And that’s that.

Well, that’s almost that. I couldn’t resist another jab at the multiplier.

Recall the story that’s supposed to explain how the multiplier works: The initial stimulus (∆G) creates income, a fraction of which (b) goes to C. That spending creates new income, a fraction of which goes to C. And so on. Thus the first round = ∆G, the second round = b(∆G), the third round = b(b)(∆G) , and so on. The sum of the “rounds” asymptotically approaches k(∆G). So, if b = 0.8, k = 5, and ∆G = \$1 trillion, the resulting cumulative ∆Y = \$5 trillion (in the limit). And it’s all in addition to the output that would have been generated in the absence of ∆G, as long as many conditions are met. Chief among them is the condition that the additional output in each round is generated by resources that had been unemployed.

In addition to the fact that the math behind the multiplier is phony, as explained above, it also yields contradictory results. If one can derive an investment/government-spending multiplier, one can also derive a “consumption multiplier”:

Taking b = 0.8, as before, the resulting value of k-sub-c is 1.25. Suppose the initial round of spending is generated by C instead of G. (I won’t bother with a story to explain it; you can easily imagine one involving underemployed factories and unemployed persons.) If ∆C = \$1 trillion, shouldn’t cumulative ∆Y = \$5 trillion? After, there’s no essential difference between spending \$1 trillion on a government project and \$1 trillion on factory output, as long as both bursts of spending result in the employment of underemployed and unemployed resources (among other things).

But with k-sub-c = 1.25, the initial \$1 trillion burst of spending (in theory) results in additional output of only \$1.25 trillion. Where’s the other \$3.75 trillion? Nowhere. The \$5 trillion is phony. What about the \$1.25 trillion? It’s phony, too. The “consumption multiplier” of 1.25 is simply the inverse of b, where b = 0.8. In other words, Y must rise by \$1.25 trillion if C is to rise by \$1 trillion. More phony math.

If there is a multiplier on government spending, it’s bound to be negative. Stay tuned for more about the effect of government spending on economic output.

The sequel is here.

# Vulgar Keynesianism and Capitalism

A REISSUE (WITHOUT UPDATES) OF THE ORIGINAL POST DATED DECEMBER 4, 2011

Robert Higgs quite rightly disparages “vulgar Keynesianism”:

Most of the people who purport to possess expertise about the economy rely on a common set of presuppositions and modes of thinking. I call this pseudo-intellectual mishmash vulgar Keynesianism. It’s the same claptrap that has passed for economic wisdom in this country for more than fifty years and seems to have originated in the first edition of Paul Samuelson’s Economics (1948), the best-selling economics textbook of all time and the one from which a plurality of several generations of college students acquired whatever they knew about economic analysis. Long ago, this view seeped into educated discourse and writing in the news media and in politics and established itself as an orthodoxy.

Unfortunately, this way of thinking about the economy’s operation, particularly its overall fluctuations, is a tissue of errors of both commission and omission. Most unfortunate have been the policy implications derived from this mode of thinking, above all the notion that the government can and should use fiscal and monetary policies to control the macroeconomy and stabilize its fluctuations. Despite having originated more than half a century ago, this view seems to be as vital in 2009 as it was in 1949.

Higgs then dissects “the six most egregious aspects of this unfortunate approach to understanding and dealing with economic booms and busts.” These are the aggregation of myriad and disparate economic actions, failure to take into account changes in relative prices, misunderstanding of the meaning and economic role of interest rates, disregard for the importance of capital, blind “money pumping” as a “solution” to recessions, and disregard for the disincentivizing effects of government activism on the private sector.

I agree with everything said by Higgs, and I have said many of the same things (in my own way) at this blog and its predecessor.  However, GDP — an aggregate measure of economic activity — is a useful construct, as flawed as it may be. It is an indicator of the general direction and magnitude of economic activity. Other aggregate measures — such as employment, jobs added and lost, unemployment rate — are also useful in that regard. If, for example, constant-dollar GDP per capita was twice as high in 2010 than it was 40 years earlier, in 1970 (computed here), it indicates that most Americans enjoyed a significantly higher standard of living in 2010 than they and their predecessors did in 1970. Further, the difference is so significant that it overshadows the difficulty of aggregating the value of billions of disparate transactions and separating the effects of price inflation from quality improvements.

What is special about 1970? It marks a turning point in the economic history of the U.S., which I discussed in a post that is now two-and-a-half years old:

Can we measure the price of government intervention [in the economy]? I believe that we can do so, and quite easily. The tale can be told in three graphs, all derived from constant-dollar GDP estimates available here. The numbers plotted in each graph exclude GDP estimates for the years in which the U.S. was involved in or demobilizing from major wars, namely, 1861-65, 1918-19, and 1941-46. GDP values for those years — especially for the peak years of World War II — present a distorted picture of economic output….

The trend line in the first graph indicates annual growth of about 3.7 percent over the long run, with obviously large deviations around the trend. The second graph contrasts economic growth through 1907 with economic growth since: 4.2 percent vs. 3.6 percent. But lest you believe that the economy of the U.S. somehow began to “age” in the early 1900s, consider the story implicit in the third graph:

• 1790-1861 — annual growth of 4.1 percent — a booming young economy, probably at its freest
• 1866-1907 — annual growth of 4.3 percent — a robust economy, fueled by (mostly) laissez-faire policies and the concomitant rise of technological innovation and entrepreneurship
• 1908-1929 — annual growth of 2.2 percent — a dispirited economy, shackled by the fruits of “progressivism” (e.g., trust-busting, regulation, the income tax, the Fed) and the government interventions that provoked and prolonged the Great Depression (see links in third paragraph)
• 1970-2008 — annual growth of 3.1 percent –  [2.8 percent for 1970-2010] an economy sagging under the cumulative weight of “progressivism,” New Deal legislation, LBJ’s “Great Society” (with its legacy of the ever-expanding and oppressive welfare/transfer-payment schemes: Medicare, Medicaid, a more generous package of Social Security benefits), and an ever-growing mountain of regulatory restrictions.

Taking the period 1970-2010 as a distinctive era — that of the full-fledged regulatory-welfare state — it may be possible to discern some aggregate relationships that were stable during that era (and may well continue to hold). The relationship that I want to explore is suggested by Higgs’s discussion of the vulgar Keynesian view of aggregate demand and the role of capital in economic production:

Because the vulgar Keynesian has no conception of the economy’s structure of output, he cannot conceive of how an expansion of demand along certain lines but not along others might be problematic. In his view, one cannot have, say, too many houses and apartments. Increasing the spending for houses and apartments is, he thinks, always good whenever the economy has unemployed resources, regardless of how many houses and apartments now stand vacant and regardless of what specific kinds of resources are unemployed and where they are located in this vast land. Although the unemployed laborers may be skilled silver miners in Idaho, it is supposedly still a good thing if somehow the demand for condos is increased in Palm Beach, because for the vulgar Keynesian, there are no individual classes of laborers or separate labor markets: labor is labor is labor. If someone, whatever his skills, preferences, or location, is unemployed, then, in this framework of thought, we may expect to put him back to work by increasing aggregate demand, regardless of what we happen to spend the money for, whether it be cosmetics or computers.

This stark simplicity exists, you see, because aggregate output is a simple increasing function of aggregate labor employed:

Q = f (L), where dQ/dL > 0.

Note that this “aggregate production function” has only one input, aggregate labor. The workers seemingly produce without the aid of capital! If pressed, the vulgar Keynesian admits that the workers use capital, but he insists that the capital stock may be taken as “given” and fixed in the short run. And ― which is highly important ― his whole apparatus of thought is intended exclusively to help him understand this short run. In the long run, he may insist, we are, as Keynes quipped, “all dead”; or he may simply deny that the long run is what we get when we place a series of short runs back to back. The vulgar Keynesian in effect treats living for the moment, and only for it, as a major virtue. At any given time, the future may safely be left to take care of itself.

In fact, the Keynesian-Marxian view of capital is about 180 degrees from the truth:

1. A broad array of capital goods (e.g., metal presses and railroad cars) will produce the same outputs (e.g., auto body parts of a certain quality and a certain number of passenger-miles) despite wide variations in the intelligence, education, and motor skills of their operators.

2. That is to say, capital leverages labor (especially unskilled labor).

3. Rewards justifiably — if unpredictably — flow to those who invent capital goods, innovate improvements in capital goods, invest in the production of such goods, and take the risk of owning businesses that use such goods in the production of consumer goods and services.

4. The activities of those inventors, innovators, investors, and entrepreneurs constitute a form of labor, but it is a very special form. It is not the brute force kind of labor envisaged by Marx and his intellectual progeny. It is a kind of labor that involves mental acuity, special knowledge, a penchant for risk-taking, and — yes, at times — hard work.

Without capital, labor would produce far less than it does. Capital, by the same token, enables labor of a given quality to produce more than it otherwise would.

(By “invest in the production of capital goods,” I mean to include individuals whose saving — whether or not it goes directly into the purchases of stocks and corporate bonds — helps to fund the purchases of capital goods by businesses.)

With that in mind, look at the aggregate relationship between the stock of private non-residential capital and private-sector GDP (GDP – G) for the period 1970-2010:

Notes:  Current-dollar values for GDP and G are from Bureau of Economic Analysis, Table 1.1.5. Gross Domestic Product (available here). Capital stock estimates are from Bureau of Economic Analysis, Table 4.1. Current-Cost Net Stock of Private Nonresidential Fixed Assets by Industry Group and Legal Form of Organization (available here). Current-dollar values for GDP – G and capital stock were adjusted to 1982-84 dollars by constructing and applying deflators from CPI-U statistics for 1913-present (available here).

Variations around the trend line indicate fluctuations in economic activity. I treat the difference between “actual” GDP and the trend line as a residual to be explained by factors other than the aggregate value of the private, nonresidential capital stock. Measures of employment or unemployment will not do the job; they are simply proxies for aggregate output. The best measure that I have found is the value of new investment in the current year, relative to the value of the capital stock at the end of the prior year:

Notes: Residual GDP – G derived from Fig. 1, as discussed in text. Estimates of new investment in private capital stock are from Bureau of Economic Analysis, Table 4.7. Investment in Private Nonresidential Fixed Assets by Industry Group and Legal Form of Organization (available here); adjusted for inflation as discussed in notes for Fig. 1.

Using the trendline equation from Fig. 2, I adjusted the estimates derived from the trendline equation of Fig. 1, with this result:

There is precious little for labor to do but to show up for work and apply itself to the tools provided by capitalism:

*   *   *

Knowledgeable readers will understand that I have taken some statistical liberties. And I have done so as a way of satirizing the view that prosperity depends on labor and its correlate, consumption spending. But my point is a serious one: Capital should not be denigrated. Those who denigrate it give aid and comfort to the enemies of economic growth, that is, to the “progressives” who are the real enemies of the poor, of labor, and of liberty.

# Making a Worse “Mess”

Obama and his pet grinning baboon VP like to claim that the economy is still in bad shape because of the “horrific mess” that they inherited from Bush. That the mess wasn’t Bush’s is lie number 1. That Obama’s policies would have “worked” but for Republican intransigence is lie number 2. There are many more lies lying around the Obama White House, but a distaste for nausea prevents me from detailing them.

I will give Obama the benefit of the doubt by measuring the effectiveness of his “stimulus” not by the current state of the economy, but by how far it has advanced the economy since the depth of the Great Recession. As it happens, the Great Recession bottomed in the second quarter of 2009. The latest estimates of real GDP, 12 quarters later, indicate real growth since the bottom of 2.2 percent a year. How does that stack up against previous post-WWII recessions? Here’s how:

Even the short-lived recoveries from the 1958 and 1980 recessions were more robust than the Obama recovery of 2009-2012. Enough said.

# Where We Are, Economically

UPDATED (10/26/12)

The advance estimate of GDP for the third quarter of 2012 has been released. Real growth continues to slog along at about 2 percent. I have updated the graph, but the text needs no revision.

*  *   *

It occurred to me that the trend line in the second graph of “The Economy Slogs Along” is misleading. It is linear, when it should be curvilinear. Here is a better version:

Derived from the October 26, 2012 release of GDP estimates by the Bureau of Economic Analysis. (Contrary to the position of the National Bureau of Economic Research, there was no recession in 2000-2001. For my definition of a recession, see “Economic Growth Since World War II.”)

The more descriptive regression line underscores the moral of “Obama’s Economic Record in Perspective,” which is this:

The claims by Obama and his retinue about O’s supposed “rescue” of the economy from the abyss of depression are ludicrous. (See, for example, “A Keynesian Fantasy Land,” “The Keynesian Fallacy and Regime Uncertainty,” “Why the “Stimulus” Failed to Stimulate,” “Regime Uncertainty and the Great Recession,” The Real Multiplier,” “The Real Multiplier (II),”The Economy Slogs Along,” and “The Obama Effect: Disguised Unemployment.”) Nevertheless our flannel-mouthed president his sycophants insist that he has done great things for the country, though the only great thing that he could do is to leave it alone.

Obama is not to blame for the Great Recession, but the sluggish recovery is due to his anti-business rhetoric and policies (including Obamacare, among others). All that Obama can rightly take “credit” for is an acceleration of the downward trend of economic growth.

# Economic Growth Since World War II

As we await (probably in vain) the resumption of robust economic growth, let us see what we can learn from the record since World War II (from 1947, to be precise). The  Bureau of Economic Analysis (BEA) provides  in spreadsheet form (here) quarterly and annual estimates of current- and constant-dollar (year 2005) GDP from 1947 to the present. BEA’s numbers yield several insights about the course of economic growth in the U.S.

I begin with this graph:

The exponential trend line indicates a constant-dollar (real) growth rate for the entire period of 0.81 percent quarterly, or 3.3 percent annually. The actual beginning-to-end annual growth rate is 3.2 percent.

The red bands parallel to the trend line delineate the 99.7% (3-sigma) confidence interval around the trend. GDP has been running at the lower edge of the confidence interval since the first quarter of 2009, that is, since the ascendancy of Barack Obama.

The vertical gray bars represent recessions, which do not correspond precisely to the periods defined as such by the National Bureau of Economic Research (NBER). I define a recession as:

• two or more consecutive quarters in which real GDP (annualized) is below real GDP (annualized) for an earlier quarter, during which
• the annual (year-over-year) change in real GDP is negative, in at least one quarter.

For example:

Annualized real GDP in the second quarter of 1953 was \$2,366.2 billion (i.e., about \$2.4 trillion in year 2005 dollars). Annualized GDP for the next  five quarters: \$2,358.1, \$2,314.6, \$2,303.5, \$2,306.4, and \$2,332.4 billion, respectively. The U.S. was still in recession (by my definition) even as GDP began to rise from \$2,303.5 billion because GDP remained below \$2,366.2 billion. The recession (i.e., drop in output) did not end until the fourth quarter of 1954, when annualized GDP reached \$2,379.1 billion, thus surpassing the value for the second quarter of 1953. Moreover, the year-over-year change in GDP was negative in the first three quarters of the recession.

Unlike the NBER, I do not locate a recession in 2001. Real GDP, measured quarterly, dropped in the first and third quarters of 2001, but each decline lasted only a quarter. But, whereas the NBER places the Great Recession from December 2007 to June 2009, I date it from the first quarter of 2008 through the third quarter of 2011 (at least).

My method of identifying a recession is more objective and consistent than the NBER’s method, which one economist describes as “The NBER will know it when it sees it.” Moreover, unlike the NBER, I would not presume to pinpoint the first and last months of a recession, given the volatility of GDP estimates:

This graph suggests three things: (1) the uncertainty of quarterly estimates, (2) a declining rate of growth since 1947, and (3) some degree of periodicity in economic growth.

The periodicity, though irregular, can be seen more clearly in the following graph, where the vertical gray bars indicate quarters in which growth is below the declining trend line shown in the preceding graph.

The two preceding graphs lead to two observations:

The following statistics underscore the first point:

 Inter-recessionary period Annual  growth rate 1947q4 – 1948q4 4.6% 1950q1 – 1953q2 7.5% 1954q4 – 1957q3 3.9% 1958q4 – 1960q1 3.7% 1961q2 – 1969q3 5.1% 1970q3 – 1973q4 4.4% 1975q4 – 1980q1 4.2% 1981q1 – 1981q3 3.3% 1983q2 – 1990q3 4.2% 1991q4 – 2007q4 3.1%

To put a point on it, here are the rates of growth during the three longest periods of above-trend growth since World War II:

• 1963q1 – 1966q1 — 6.6%
• 1983q1 – 1986q1 — 5.1%
• 1995q3 – 1999q4 — 4.5%

It is hard to deny the almost-constant deceleration of growth in the post-war era — especially the sharper deceleration after 1970 — a deceleration that is embedded in the longer downward trend that began in the early 1900s.

In this connection, I note that the “Clinton boom“ — 3.4 percent real growth from 1993 to 2001 — was nothing to write home about, being mainly the product of Clinton’s self-promotion and the average citizen’s ahistorical (if not anti-historical) perspective. The boomlet of the 1990s, whatever its causes, was less impressive than several earlier post-war expansions. In fact, the overall rate of growth from the first quarter of 1947 to the first quarter of 1993 — recessions and all — was 3.4 percent.

What about the lingering Great Recession? It lingers mainly because it has been used — first by Bush, then by Obama — as an excuse for eve more disastrous expansions of the cost and reach of government.

# The Great Recession Is Barely Over … Maybe

UPDATED 12/22/11

The third estimate of real GDP for the third quarter of 2011 (3Q2011) is \$15 billion lower than last month’s advance estimate. The annualized rate of \$13,331.6 billion (in chained 2005 dollars) is only \$5.6 billion above the estimate for the fourth quarter of 2007 (4Q2007), the last pre-recession quarter.

Based on the third estimate, real GDP grew at an annual rate of 0.011 percent — 11/1000 of one percent — between 4Q2007 and 3Q2011. In other words, real GDP in 3Q2011 is the same as it was in 4Q2007. Whether or not the Great Recession has ended is still up in the air and will not be known (possibly) until the release of GDP estimates for 4Q2011.

# The Real Multiplier

In truth, the Keynesian multiplier is a mathematical fiction, as explained here, and government spending is in fact destructive of economic growth, as discussed here and in some of the posts listed at the end.

GRAPH UPDATED 12/01/13

The Keynesian multiplier is bogus, for reasons spelled out in “A Keynesian Fantasy Land.” By bogus, I do not mean that government spending (G) has no effect on gross domestic product (GDP). What I mean is that the effect of G on GDP is (1) overrated and (2) irrelevant.

The effect of G on GDP is overrated because, contrary to the assertions of quacks like Paul Krugman, an increase in G does not cause an increase in GDP. For example, Robert Barro writes:

For annual data that start in 1939 or earlier (and, thereby, include World War II), the defense-spending multiplier that applies at the average unemployment rate of 5.6% is in a range of 0.6-0.7. A multiplier less than one means that, overall, other components of GDP fell when defense spending rose.

My own analysis of post-WWII statistics (for 1947-2010) yields a multiplier for G of 0.8. [UPDATE: A more authoritative estimate is 0.5.] That is to say, every additional dollar of government spending has led to a 20-cent reduction in non-government spending. To put it another way, the real effect of additional government spending is the shrinkage of the private sector. (Which makes sense, when you stop to think about it.) Thus the irrelevance of the multiplier: What good is more government spending if it shrinks the private sector, where real products and services are produced?

It is quite true that private investment in business capital (buildings, equipment, technology, etc.) rises and falls with the business cycle. The elasticity of new investment with respect to private-sector GDP (GDP – G) during the period 1947-2010 was about 3.3; that is, every 1-percent change in private-sector GDP resulted in a 3.3-percent change (in the same direction) in new investment. (Kevin Hassett clearly discusses the causes and effects of these fluctuations in “Investment,” at the Library of Economics and Liberty.)

But no matter the level of investment, it yields positive returns in the aggregate and most of the time. That is the reason for positive, real interest rates on corporate debt, and for the rising real value of stock prices over the long run. The average rate of return on net capital investment (i.e., after depreciation) for 1947-2010 was about 10 percent. However, there was a marked downward trend until the early 1980s, followed by what seems to be a leveling off. The average since the “Reagan recovery” of the mid-1980s has hovered below 8 percent.

Source: Derived from BEA Table 4.1 Current-Cost Net Stock of Private Nonresidential Fixed Assets by Industry Group and Legal Form of Organization, Table 1.3.5. Gross Value Added by Sector, and Table 1.15. Price, Costs, and Profit Per Unit of Real Gross Value Added of Nonfinancial Domestic Corporate Business.

In sum, the real multiplier on government activity is markedly negative. Government activity has resulted in an ever-deepening Mega-Depression.

# Why the “Stimulus” Failed to Stimulate

This post examines practical reasons for the failure of “stimulus” to stimulate and the “multiplier” to multiply. The deeper truth is that the Keynesian multiplier is a mathematical fiction, as explained here, and government spending is in fact destructive of economic growth, as discussed here and in some of the posts listed at the end.

I spell out the reasons in “A Keynesian Fantasy Land.” There are six of them, including the timing-targeting problem (number 3).

[In an earlier version of this post, I also mentioned Ricardian equivalence, which is an aspect of reason number 2, the disincentivizing aspects of government borrowing and spending. I referred to a post by Steven Landsburg, which I had read hastily and misinterpreted as a discussion of Ricardian equivalence. When Dr. Landsburg graciously pointed out that I had the wrong end of the stick, I deleted the brief discussion of Ricardian equivalence from this post.]

A key component of the timing-targeting problem is the strong possibility that “stimulus” money will be spent on already-employed resources, thus bidding up their prices but doing little or nothing to stimulate real economic activity. Tyler Cowen recaps two papers that document the misdirection of “stimulus” money:

My colleagues Garett Jones and Daniel Rothschild conducted extensive field research (interviewing 85 organizations receiving stimulus funds, in five regions), asking simple questions such as whether the hired project workers already had had jobs.  There are lots of relevant details in the paper but here is one punchline:

…hiring people from unemployment was more the exception than the rule in our interviews.

In a related paper by the same authors (read them both), here is more:

Hiring isn’t the same as net job creation. In our survey, just 42.1 percent of the workers hired at ARRA-receiving organizations after January 31, 2009, were unemployed at the time they were hired (Appendix C). More were hired directly from other organizations (47.3 percent of post-ARRA workers), while a handful came from school (6.5%) or from outside the labor force (4.1%)(Figure 2).

One major problem with ARRA was not the crowding out of financial capital but rather the crowding out of labor.  In the first paper there is also a discussion of how the stimulus job numbers were generated, how unreliable they are, and how stimulus recipients sometimes had an incentive to claim job creation where none was present.  Many of the created jobs involved hiring people back from retirement.  You can tell a story about how hiring the already employed opened up other jobs for the unemployed, but it’s just that — a story.  I don’t think it is what happened in most cases, rather firms ended up getting by with fewer workers.

There’s also evidence of government funds chasing after the same set of skilled and already busy firms.  For at least a third of the surveyed firms receiving stimulus funds, their experience failed to fit important aspects of the Keynesian model.

The Keynesian model is deeply flawed because it is a simplistic model based on simplistic assumptions about the behavior of human beings and human institutions. I say in “A Keynesian Fantasy Land,” models are supposed to mirror reality, not the other way around. The Keynesian model — or the version embraced by Paul Krugman and his fellow leftists — is a version of the reality that they would prefer: a reality in which government runs the economy.

# Does “Pent Up” Demand Explain the Post-War Recovery?

Russ Roberts wonders about the meaning of “pent up” demand:

The usual way that Keynesians explain the post-[World War II] expansion despite the huge cut in government spending is to say, well of course the economy boomed, there was a lot of pent-up demand. What does that mean? There is always pent-up demand in the sense there is a stuff I wish I could have but can’t. But the standard story is that people couldn’t buy washing machines or cars during the war–they were rationed or simply unavailable or unaffordable. So when the war ended, and rationing and price controls ended, people were eager to buy these things. But the reason these consumer goods were rationed or unavailable is because all the steel went into the tanks and planes during the war. So when the war ended, there was steel available to the private sector. That’s why cutting government activity can stimulate the private sector. Fewer resources are being commandeered by the public sector.

Roberts refers to an earlier post of his, in which he rightly ridicules Keynesians for believing in the magical multiplier:

One of the most mindless aspects of the multiplier is to treat is as a constant, such as 1.52. It can’t be a constant, not in any meaningful way. If the government conscripted half of the US population to dig holes all day and conscripted the other half to fill them back in, and paid each of us a billion dollars a day for the task, and valued holes that were dug and holes that were filled in at a trillion dollars a hole, then GDP would be very very large, unemployment would be zero and there would be no stimulating effect and we would soon be dead from starvation.

Priceless.

I share Roberts’s disdain for the multiplier. (See this and this.)

Nevertheless, the availability of resources for private use after the war ended is only half the story. Consumers and businesses had to demand things — not just want them, but demand them with money in hand. That is where pent-up demand comes into play, as I explain here:

Conventional wisdom has it that the entry of the United States into World War II caused the end of the Great Depression in this country. My variant is that World War II led to a “glut” of private saving because (1) government spending caused full employment, but (2) workers and businesses were forced to save much of their income because the massive shift of output toward the war effort forestalled spending on private consumption and investment goods. The resulting cash “glut” fueled post-war consumption and investment spending.

Robert Higgs, research director of the Independent Institute, has a different theory, which he spells out in “Regime Uncertainty: Why the Great Depression Lasted So Long and Why Prosperity Resumed After the War” (available here), the first chapter his new book, Depression, War, and Cold War. (Thanks to Don Boudreaux of Cafe Hayek for the pointer.) Here, from “Regime Change . . . ” is Higgs’s summary of his thesis:

I shall argue here that the economy remained in the depression as late as 1940 because private investment had never recovered sufficiently after its collapse during the Great Contraction. During the war, private investment fell to much lower levels, and the federal government itself became the chief investor, directing investment into building up the nation’s capacity to produce munitions. After the war ended, private investment, for the first time since the 1920s, rose to and remained at levels sufficient to create a prosperous and normally growing economy.

I shall argue further that the insufficiency of private investment from 1935 through 1940 reflected a pervasive uncertainty among investors about the security of their property rights in their capital and its prospective returns. This uncertainty arose, especially though not exclusively, from the character of federal government actions and the nature of the Roosevelt administration during the so-called Second New Deal from 1935 to 1940. Starting in 1940 the makeup of FDR’s administration changed substantially as probusiness men began to replace dedicated New Dealers in many positions, including most of the offices of high authority in the war-command economy. Congressional changes in the elections from 1938 onward reinforced the movement away from the New Deal, strengthening the so-called Conservative Coalition.

From 1941 through 1945, however, the less hostile character of the administration expressed itself in decisions about how to manage the warcommand economy; therefore, with private investment replaced by direct government investment, the diminished fears of investors could not give rise to a revival of private investment spending. In 1945 the death of Roosevelt and the succession of Harry S Truman and his administration completed the shift from a political regime investors perceived as full of uncertainty to one in which they felt much more confident about the security of their private property rights. Sufficiently sanguine for the first time since 1929, and finally freed from government restraints on private investment for civilian purposes, investors set in motion the postwar investment boom that powered the economy’s return to sustained prosperity notwithstanding the drastic reduction of federal government spending from its extraordinarily elevated wartime levels.

Higgs’s explanation isn’t inconsistent with mine, but it’s incomplete. Higgs overlooks the powerful influence of the large cash balances that individuals and corporations had accumulated during the war years. It’s true that because the war was a massive resource “sink” those cash balances didn’t represent real assets. But the cash was there, nevertheless, waiting to be spent on consumption goods and to be made available for capital investments through purchases of equities and debt.

It helped that the war dampened FDR’s hostility to business, and that FDR’s death ushered in a somewhat less radical regime. Those developments certainly fostered capital investment. But the capital investment couldn’t have taken place (or not nearly as much of it) without the “glut” of private saving during World War II. The relative size of that “glut” can be seen here:

Derived from Bureau of Economic Analysis, National Income and Product Accounts Tables: 5.1, Saving and Investment. Gross private saving is analagous to cash flow; net private saving is analagous to cash flow less an allowance for depreciation. The bulge in gross private saving represents pent-up demand for consumption and investment spending, which was released after the war.

World War II did bring about the end of the Great Depression, not directly by full employment during the war but because that full employment created a “glut” of saving. After the war that “glut” jump-started

• capital spending by businesses, which — because of FDR’s demise — invested more than they otherwise would have; and
• private consumption spending, which — because of the privations of the Great Depression and the war years — would have risen sharply regardless of the political climate.

The post continues with an exchange between Higgs and me. The bottom line is the same.

What is the answer to the title question, then? It is that a period of forced, nominal saving can create pent-up demand, which can result in the employment of resources that had theretofore been unavailable. The pent-up demand at the end of World War II was, in great measure, responsible for the post-war recovery.

This rare phenomenon has nothing to do with the multiplier, and probably has nothing to do with the current economic situation. Government has commandeered a large chunk of the American economy, but so gradually that Americans have not acquire a “glut” of nominal savings, as they did in World War II.

# The Keynesian Fallacy and Regime Uncertainty

In “A Keynesian Fantasy Land,” I gave six reasons for the failure of “stimulus” spending to stimulate the economy, despite the insistence of leftists and left-wing economists that economic salvation is to be found in bigger government. The reasons, which I elaborate in the earlier post, are these:

1. “leakage” to imports

2. disincentivizing effects of government borrowing and spending (regime uncertainty)

3. timing and targeting problems (spending that is too late and misdirected)

4. reversed causality (lower aggregate demand as symptom, not cause)

5. the negative consequences of bail-outs

6. the unaccounted for complexity of human behavior

An article by Casey B. Mulligan, “Simple Analytics and Empirics of the Government Spending Multiplier and Other ‘Keynesian’ Paradoxes,” underscores the futility of “stimulus” spending. These are among Mulligan’s conclusions:

From a partial equilibrium perspective, it would be surprising if government purchases did not crowd out at least some private consumption, and that a reduction in factor supply did not result in less output. Yet some “New Keynesian” models, not to mention much public policy commentary, claim that today’s economy has turned this partial equilibrium reasoning on its head, even while it might have been historically valid. Among other things, individual firms and the aggregate private sector are alleged to leave their production invariant to changes in factor supply conditions during this recession. This paper shows how the government spending multiplier and the “paradox of toil” are related in theory, and examines evidence from this recession on the output effects of factor supply…

This paper does not contain a numerical estimate of the government purchases multiplier. However, its examination of data exclusively from the 2008-9 recession suggests that sectoral and aggregate employment and output vary with supply conditions in much the same way they did before the recession. The results contradict Keynesian claims that the government purchases multiplier would be significantly greater during the recession than it was before 2008, suggesting instead that historical estimates of the effects of fiscal policies are informative about fiscal policy effects in more recent years. Moreover, the supply incentives created by government spending cannot be ignored merely because 2008 and 2009 were recession years; rather incentives mattered as much as ever. Government purchases likely moved factors away from activities that would have supported private purchases. Unemployment insurance, food stamps, and other expanding means-tested government programs likely reduced employment and output during this recession, in much the same way they did in years past.

Compounding the futility of “stimulus” spending is the general climate of economic fear that Obama’s policies have engendered; for example:

As John Steele Gordon points out,

[t]he greatest periods of American economic growth came when taxes were very low—such as in the 19th century—or being lowered and simplified, as in the 1920s, 60s, and 80s. Inescapably, to tax wealth creation is to discourage it. But there is a large and politically potent segment of the population that, because its interests are now aligned with those of the government, seek to promote dependency through entitlements. This segment favors ever higher taxes (although they disguise the fact by demanding that only “the rich” pay their “fair share.”) But, as with regulation, high taxes inevitably produce low growth—and low growth threatens entitlements in the long term. If the United States remains in the doldrums for several more years without hope of a real turnaround, Medicare as it is currently constituted will go bankrupt in 2019. Raising taxes to prevent that will only slow overall growth, and that will actually defeat the purpose of saving Medicare.

So there is really no alternative to pursuing policies that encourage economic growth through private action by liberating the forces of the free market. A presidential candidate who finds a way to ground his economic policies in this core truth—and harnesses the idea to a larger and more optimistic understanding of the United States, both past and future, and resists the take-your-medicine tone that dominates the conservative policy discussion of the present moment—will be able to draw a sharp and effective contrast with the failures of the Obama years. (“Growth: The Only Way out of This Mess,” Commentary, July 2011)

But there is no point in cutting taxes unless government spending is cut — and cut drastically — for government spending, along with regulation, is the real drag on the economy. Only in the left’s magical thinking is government spending a good thing. In reality, it is a destructive force — even during recessions and depressions.

# A Keynesian Fantasy Land

This post examines practical reasons for the failure of “stimulus” to stimulate and the “multiplier” to multiply. The deeper truth is that the Keynesian multiplier is a mathematical fiction, as explained here, and government spending is in fact destructive of economic growth, as discussed here and in some of the posts listed at the end.

“Liberal” economists and pundits complain incessantly that the recovery from the Great Recession is weak, and in jeopardy, because the federal government hasn’t spent “enough” money. (See this for some examples of the “liberal” view.) How much is “enough” for Paul Krugman et al.? It is always more than the government spends, of course.

Why should that be? The blindingly obvious answer — but not obvious to Krugman and company — is that demand-side fiscal policy (i.e., government “stimulus” spending) is ineffective. If the economy depends on government spending, how does one explain the decades after the Civil War, when government spent less than 10 percent of GDP (vs. today’s 40 percent), while America’s economy grew faster than at any time in its history? It took World War II and regime change (the disruption of the New Deal by the war) to end the Great Depression. Mr. Roosevelt’s adoption of Mr. Keynes’s hole-digging prescription (the Civilian Conservation Corps and similar make-work projects) had nothing to do with it. Mr. Roosevelt may have been an excellent marketeer, but he was a dismal economic engineer.

This is not to reject supply-side fiscal policy: tax-rate reductions. When tax-rate reductions are prospectively permanent — as opposed to one-time tax rebates and “holidays” — they can and do spur economic growth. Christina Romer, former chair of Obama’s Council of Economic Advisers, once proved it — though she developed a convenient case of amnesia when she became a proponent of “stimulus.”

As any reputable economist will tell you, however, the best that one can expect of a temporary increase in government spending is a temporary increase in economic activity; it is a stop-gap until the economy recovers on its own. (And a reputable economist, unlike Krugman, will also tell you that a permanent increase in government spending diverts resources from productive uses — uses that yield economic growth and satisfy actual economic wants — toward less-productive and counter-productive ones, including the creation of paper-shuffling, regulatory bureaucracies.)

Despite the promises of Obama, Romer, and company, the “stimulus” has evidently failed to do much — if anything — to alleviate the Great Recession and its lingering aftermath. (See this, this, and this, for example.) Thus the wailing and gnashing of teeth by Krugman and company — who want to replicate the failure on a grander scale.

WHY THE “STIMULUS” FAILED TO STIMULATE: GENERAL OBSERVATIONS

What went wrong? Anthony de Jasay offers a piece of the explanation:

…In Keynesian parlance there is the multiplier effect and it is greater than 1. As long as there is spare capacity (unemployment) in the economy, the government ought to go on spending more, working through the multiplier, because the extra private saving takes care of the government dissaving and the extra consumption is, so to speak, a welcome windfall gain. Timidly refusing to generate it is criminal waste.

Despite truculent voices to the contrary, the Keynesian logic is faultless in that the conclusions do follow from the assumptions. Why it does not really work and why it singularly failed to work in 2009-2010 and maybe beyond, is that other things do not remain equal. Part of the extra spending stimulus fails to stimulate domestic income because as much as 0.3 of the multiplier might leak out through extra imports. Much of the rest may be offset by industry taking fright of the rising budget deficit and reducing investment, and consumers striving to reduce their indebtedness producing some saving to balance the government’s dissaving. The total effect of higher imports and lower investment might be a multiplier barely higher, or maybe even lower, than 1 and the stimulus stimulating nothing except the national debt. This is not the fault of Keynes but of those whose macro-economics exist in a fantasy land. (Library of Economics and Liberty, “Micro, Macro, and Fantasy Economics,” December 6, 2010)

Generally,

[t]he available empirical evidence does not support the idea that spending multipliers typically exceed one, and thus spending stimulus programs will likely raise GDP by less than the increase in government spending. (Robert J. Barro and Charles J. Redlick, “Stimulus Spending Doesn’t Work,” WSJ Online, October 1, 2009)

(For more on the subject see Barro’s “Government Spending Is No Free Lunch,” WSJ Online, January 22, 2009.)

WHY “STIMULUS” FAILS: SPECIFIC REASONS

Altogether, there are six reasons for the ineffectiveness of Keynsesian “stimulus.”

1. The “leakage” to imports, as indicated by de Jasay.

2. The disincentivizing effects of government borrowing and spending, to which de Jasay alludes.

As de Jasay suggests, industry (and the high-income earners who finance it) are being cautious about the implications of additional government debt. As I say here,

the sophisticat[ed] … institutions and persons who have the greatest interest in government’s actions [are] large corporations and persons in high-income brackets. They will react to government borrowing as if it would affect them and their heirs (corporate and individual).

That is to say, even if additional debt does not crowd out private-sector borrowing to finance business expansion, it will nevertheless inhibit investments in business expansion. This inhibiting effect is compounded by the reasonable expectation that many items in a “stimulus” package will become permanent fixtures in the government’s budget.

3. The timing-targeting problem.

The lag between the initial agitation for “stimulus” and its realization. In the extreme, the lag can be so great as to have no effect other than to divert employed resources from private to government uses. But even where there is a relatively brief lag, “stimulus” spending is essentially wasted if the result is simply to divert already employed resources from private to government uses.

The timing-targeting problem is one that strident Keynesians and their unsophisticated disciples in the media seem not to understand or care about. (They are happy as long as government “does something,” regardless of the cost.) The problem arises from the fundamental flaw in the Keynesian analysis: Economic output is portrayed as a homogeneous commodity, one that can be characterized  in terms of aggregate demand (AD) and aggregate supply (AS). Accordingly, in the Keynesian orthodoxy, all it takes to stimulate AD is to pump in some additional government spending (dG), and the rest takes care of itself.

Arnold Kling calls it “hydraulic” macroeconomics:

Once upon a time, Joe lived in Keynesiana, where he was a representative agent.

Joe worked in a GDP factory, making GDP. Every Monday morning, he went to work, and he worked five days a week. He was paid \$1 for every 24-minute segment he worked, and he worked 100 segments (40 hours), so he earned \$100 a week. Every Friday afternoon, Joe cashed his paycheck and went to the GDP factory outlet, where he spent it all on GDP.

One day, Joe decided that he needed to accumulate some savings. He made up a rule for himself. Knowing that he needed to consume at least \$40 of GDP each week, he decided that his rule would be to save 20 percent of everything he earned over and above that \$40. So the first week, that meant saving 20 percent of \$60, or \$12. So he cashed his \$100 paycheck, but that Friday afternoon he only spent \$88.

Next Monday, morning, Joe’s boss had some news. “A funny thing happened last week. We sold 12 percent less GDP than usual. So this week, we’re gonna put you on a short week. You work 88 segments, instead of 100.”

Joe was disappointed, because this meant he would only be paid \$88 this week. Sticking to his new rule, he resolved to save 20 percent of \$48, or \$9.60. So that Friday afternoon, he cashed his \$88 paycheck and spent \$78.40.

Next Monday morning, Joe’s boss said. “Well, golly, it looks like we sold even less GDP last week. I’m afraid we’ll have to cut you back to 78.40 segments this week.” Still following his rule, Joe resolved to save 20 percent of \$38.40, or \$7.68. So he spent only \$70.72 at the GDP factory outlet that Friday.

Seeing where this was going, the country asked Krug Paulman, the famous economist, what to do. He said, “The stupid people are saving too much. We need government to spend what the idiots are not spending.” So the government borrowed \$29.28 from Joe and spent it at the GDP factory outlet.

Now, when Joe came to work on Monday morning, his boss said, “Good news, we sold 100 percent of what we used to sell, so you can work 100 segments this week.” Sticking to his rule, Joe saved \$12 on Friday afternoon. But the government borrowed the \$12 and spent it at the GDP factory outlet. They all lived happily ever after. (Library of Economics and Liberty, “Hydraulic Macro: A Fable,” August 30, 2009)

But in reality, economic activity is far more complex than that. One very important part of that reality the vast variety of goods and services changing hands, in response to constantly shifting tastes, preferences, technologies, and costs. The real economy bears no resemblance to the “hydraulic” one in which the homogeneous “fluid” is units of GDP. For “stimulus” — an increase in government spending (dG) — to generate an real increase GDP significantly greater than dG, several stringent conditions must be met:

a. dG must lead directly to the employment of resources that had been idled by a downturn in economic activity (or newly available resources that otherwise would lay idle), therefore eliciting the production of additional goods for delivery to consumers and businesses.

b. Accordingly, government functionaries must be able to distinguish between unemployment that occurs as a result of normal (and continuous) structural changes in the economy and unemployment that occurs because of a general slowdown in economic activity.

c. To the extent that the preceding conditions are satisfied, dG may be used to restore employment if government functionaries do the following things:

• Ensure that dG is used to purchase goods and services that would have been produced in the absence of a general slowdown in economic activity.
• Ensure that dG is used by those persons, businesses, and governmental units that have become unable to buy those goods and services because of a general slowdown in economic activity.
• Allowing for shifts in tastes, preferences, technologies, etc., adjust the issuance, allocation, and use of dG so that goods and services are produced in accordance with those shifts in taste, etc.
• Reduce dG as the demand for unemployed resources rises, in order to avoid the distorting and disincentivizing effects of inflation.

To the extent that dG is less than on-time and on-target, there is “leakage,” which causes the multiplier to recede toward a value of 1. It can easily slide below 1 — as Barro has found — because of the “leakage” to imports and the disincentivizing effects of government borrowing and spending.

The fourth reason for the failure of the “stimulus” to stimulate is that it is does not address the cause of the drop in AD. A drop in AD usually is caused by an exogenous event, and that exogenous event usually is a credit crisis. Pumping money into the economy — especially when it results in the bidding up the prices of already employed resources — does not reinflate the punctured credit bubble that caused the slowdown.

If a credit crunch arises from a sharp rise in the rate of home-mortgage defaults — as in the case of the Great Recession — the obvious way to “solve” the problem is to prop up the defaulting borrowers and their lenders, and to do so quickly.

But, in practice, the propping up is hit-and-miss, and the misses have drastic consequences. Consider, for example, the decision not to bail out Lehman Brothers and the effects of that decision on financial markets.

Which leads into the fifth reason…

5. Inequity, moral hazard, and their consequences.

Any kind of “stimulus” that targets particular individuals and firms, in an effort to rectify their failures of judgment, has adverse political and economic effects.

Favorable treatment of defaulters and failing companies generates considerable popular resentment, which — in the present instance — has found a vocal and politically potent outlet in the Tea Party movement. Favorable treatment of defaulters and failing companies also creates moral hazard; that is, it encourage unwise risk-taking that can (and probably will) spark future crises, leading the government to assume more obligations and impose more regulations, in a futile effort to change human nature.

All of this adds up to a climate of political contention and financial pessimism — conditions that militate against consumer confidence and business expansion.

6. The human factor.

The preceding five reasons for the ineffectiveness of Keynesian “stimulus” point to a sixth, fundamental reason: the human factor.

Models are supposed to mirror reality, not the other way around. Those who cling to the Keynesian multiplier would like the world to comply with it. But the world does not because it is filled with people, whose behavior is not determined (or described) by a simplistic model but by their responses to incentives, their political predispositions, their informed and reasonable skepticism about the consequences of government intervention in economic matters, and — above all else — their fallibility. And, believe or not, government officials and bureaucrats are no less fallible than the “ordinary” citizens whose lives they would like to organize.

The human factor is an inconvenient truth. But “liberals,” in their usual arrogance and ignorance prefer magical thinking to reality. Belief in the Keynesian multiplier is a prime example of magical thinking.

# Does World War II “Prove” Keynesianism?

In “How the Great Depression Ended,” I say that

World War II did bring about the end of the Great Depression, not directly by full employment during the war but because that full employment created a “glut” of saving. After the war that “glut” jump-started

• capital spending by businesses, which — because of FDR’s demise — invested more than they otherwise would have; and
• private consumption spending, which — because of the privations of the Great Depression and the war years — would have risen sharply regardless of the political climate.

That analysis is by no means an endorsement of simple-minded Keynesianism (as propounded by Paul Krugman, for example), which holds that the government can spend the economy out of a recession or depression, if only it spends “enough” (which is always more than it actually spends). But there is no point in pumping additional money into an economy unless the money elicits productive endeavors: business creation and expansion, leading to net capital formation and job creation.

Pumping additional money into government programs results in the misdirection of resources, at best, and in the discouragement of productive private activity, at worst. Discouragement takes two forms: crowding-out and active interference (usually through regulatory inhibitions).

The answer to the question of this post’s title is that World War II has nothing to do with Keynes or Keynesianism, as it is widely understood. Employment and output (measured in dollars) rose sharply during World War II, but most of the additional output was devoted to the war effort. Huge increases in government spending did not lead to huge increases in the material well-being of Americans, most of whom were working harder while being deprived of the fruits of their labors, through rationing.

If anything, the post-war recovery “proves” the folly and wastefulness of efforts to stimulate an economy through government spending. It was not government spending that re-started the U.S. economy after World War II, it was private spending on capital investments and consumer goods. Some of that private spending was encouraged by the end of regime uncertainty. That end was brought about by the curtailment of New Deal initiatives (until the 1960s) because of the war and FDR’s death. Private spending — which was boosted by wartime saving — would have been purely inflationary had businesses not been willing and able to create jobs and expand output.