The False Promise of the Fiscal Multiplier

With a bit of trickery that is hard to spot, it is possible to “prove” that 1 + 1 = 3. (Watch this video and look carefully at the fourth and fifth lines of the “proof”, neither of which follows from the preceding line.)

Building on the logical and empirical analyses of some notable economists, I (and many others) have found the trickery in the “proof” that there is a fiscal multiplier: an additional dollar of government spending, not financed by borrowing or taxes) generates more than a dollar’s worth of additional GDP. The multiplier is both logically unsound and empirically invalid.

I urge you to read my page, “Keynesian Multiplier: Fiction vs. Fact“, for the details of my disproof. (For a recent discussion of the empirical invalidity of the multiplier, see this post by Veronique de Rugy.) I won’t repeat the details here, but I will focus on a particular aspect of the disproof. It exposes the logical trickery that underlies belief in the multiplier.

It used to be (and perhaps still is) the case that courses in the principles of macroeconomics began with a circular-flow model of a static economy. If everyone did the same thing, year after year, the same economic units would produce the same things. Each economic unit’s output would be valued in the marketplace, and that value would give the economic unit a claim on a slice of the total production of goods and services. The division of output between consumption (goods and services enjoyed here and now) and investment (replacement of the stock of capital as it deteriorates) would be determined by the willingness of producers (earners of income) to forgo consumption in favor of saving. (It is saving, non-consumption, that allows the diversion of resources to the production of capital goods.) The rate of investment would be just enough to sustain the output of goods and services at constant rates.

The circular flow could be perturbed for many reasons (e.g., population growth, a natural disaster, technological innovation). But what would happen to the circular flow in the event of such a perturbation? The output of goods and services would be increased or decreased by the immediate effect of the perturbation and by its secondary effects on the economy.

Take a simple two-producer economy, for example, where Joan makes guns and Ralph makes butter. Joan and Ralph exchange some of their output of guns and butter, so that during the year each of them earns a combination of guns and butter. If Ralph dies, and Joan is unable to make guns, the only output will be butter. And if Joan doesn’t need as much butter as she used to produce (some of which she traded to Ralph for guns), she will produce less butter — just enough for her own consumption. So there is the immediate effect of Ralph’s death (no guns) and the secondary effect of Ralph’s death (Joan produces less butter but consumes the same amount as before).

The multiplier doesn’t work that way. According to the multiplier, the reduction in Ralph’s spending on butter would affect Joan’s spending according to her marginal propensity to consume (the rate at which each increment of her income is translated into more or less spending on consumption goods). But it doesn’t. Joan, quite sensibly, simply consumes as much butter as before, though she produces less of it. There is no multiplier effect. There is just a reduction in the economy’s total output: no guns, and just enough butter for Joan’s needs.

A defender of the multiplier would respond that my economy doesn’t represent an advanced economy like that of the United States, in which most transactions don’t take place at arms length (through barter) but, rather, through a medium of exchange (U.S. dollars). In such an economy, the defenders would argue, an exogenous reduction or increase in the demand for goods and services would cascade through the economy. Less demand for A would reduce the income of the producer of A, who would spend less on B through Z; the producer of B would spend less on A and C through Z; etc. In the end, the economy would shrink by the sum of each producer’s reduced spending — the multiplier effect. Here is the standard derivation of that effect, which I explain here:

Derivation of investment-govt spending multiplier

Y is GDP, C is consumption spending, I is investment spending, G is government spending (all in “real” terms), and b (as stated) is the marginal propensity to consume.)

Because b is less than 1, the expression 1/(1-b) must be greater than 1 — thus the “multiplier” on an exogenous change in spending. And despite the heading, the multiplier effect, in theory, applies to any exogenous change in the amount or rate of spending or saving. It could be a consumption or saving multiplier, for example. That is one of the tricks of the multiplier: If it exists, it isn’t just a government-spending multiplier, much as the proponents of bigger government would like you to believe.

Another trick is the mysterious mechanism by which an exogenous change in the rate of spending results in even more spending. It’s time to expose the mechanism.

What is Y but the sum of the dollar values (adjusted for inflation) of the output of all “final” goods and services (including changes in inventory) during a given period? What does Y therefore represent? As long as we’re using the terminology of macroeconomics, in which everything is implicitly homogeneous, Y represents the familiar (to some) equation of exchange:

MV = PQ, where, for a given period,

M is the total nominal amount of money supply in circulation on average in an economy.

V is the velocity of money, that is the average frequency with which a unit of money is spent.

P is the price level.

Q is an index of real expenditures (on newly produced goods and services).

The multiplier implies that, everything else being the same, a change in Q will result in proportional changes in PQ and MV. If there are unemployed resources and an exogenous increase in government spending employs them (and does nothing to prices), an increase in M (deficit spending) is exactly matched by an increase in Q (real output), so that the equation MV = PQ isn’t violated.

But how does an increase in Q (the initial burst of additional output) result in further additions to Q, as the multiplier implies? If P doesn’t increase (and it shouldn’t if the multiplier is “real”), then MV must rise. There is an increase in M — the jolt of exogenous government spending. But there is no further increase in M. So MV must rise because V increases as a result of the initial jolt of government spending. The multiplier, however, says nothing about V, unless increases in spending that result from the initial jolt in Q can be construed as increases in V and Q.

Let’s step back from this conundrum and consider the situation of a static economy with unemployed resources. An increase in M (deficit spending), of targeted perfectly, resulting in a proportional increase in Q. The persons who earn income from that increase spend some of it (that is, their rate of spending rises temporarily). There is no new M, but V rises (that is, the rate of spending rises) in proportion to the rise Q. So, temporarily, MV’ = PQ’.

This is the only sensible way of explaining the multiplier. But look at how many things must happen if an exogenous increase in government spending is to result in an actual increase real output:

The additional spending must be targeted so that it elicits additional production from unemployed resources.

The addition production must, somehow, be delivered to persons who actually benefit from it.

The recipients of additional spending must at least some of their new income into spending that results in the employment of hitherto unemployed resources, and the result must be the production of additional things that are delivered to persons who benefit from the production.

And so on and so forth.

What happens in practice, of course, is that deficit spending results in the production of things that politicians and bureaucrats favor (e.g., economically useless bullet trains and bridges to nowhere). but which have little or no economic value. And the spending often crowds out the production of other things because many (most?) of the resources involved are already in use (e.g., engineers and trained mechanics, not unemployed high-school dropouts from inner cities). Those are among that many things that are skipped over in the “proof” that the multiplier is real and positive. (See my page about the multiplier for much more.)

The bottom line is that the multiplier might well be positive, in nominal terms. That is, GDP might seem to rise, at least temporarily, but real GDP — the actual output of things valued by consumers — is another matter entirely. As I suggest here — and as is pointed out in my page about the multiplier and the article by Veronique de Rugy — the actual output of things valued by consumers may not rise at all, and probably will be crowded out by additional government spending.

Things valued by consumers certainly will be crowded out by additional government spending, because — in the long run — temporary additions usually become permanent ones. Which is just what the proponents of the multiplier want to happen. The multiplier isn’t just phony, it’s an excuse to boost government spending, that is, the share of the economy that is directly controlled by government.

Have you noticed lately what a great job government is doing for the citizenry, especially in Blue States and cities?

Further Reflections on the Keynesian Multiplier

In “Keynesian Multiplier: Fiction vs. Fact“, I piggyback on the insights of Murray Rothbard and Steven Landsburg to show that the fiscal multiplier is fool’s gold. In addition to showing this mathematically and empirically, I address the mechanics of the multiplier:

How is it supposed to work? The initial stimulus (∆G) [an exogenous — unfunded — increase in government spending] creates income (don’t ask how), a fraction of which (b) [the marginal propensity to consume] goes to C [consumption spending]. 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) [where k is the multiplier]….

Note well, however, that the resulting ∆Y [change in real, inflation-adjusted GDP] 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). The idea is that ∆Y should be temporary because a downturn will be followed by a recovery — weak or strong, later or sooner.


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 the clincher:

Taking b = 0.8, as before, the resulting value of kc 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 all, 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 kc = 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.

The essential falsity of the multiplier can be found by consulting the equation of exchange:

In monetary economics, the equation of exchange is the relation:


where, for a given period,

M is the total nominal amount of money supply in circulation on average in an economy.

V is the velocity of money, that is the average frequency with which a unit of money is spent.

P is the price level.

Q is an index of real expenditures (on newly produced goods and services).

Thus PQ is the level of nominal expenditures. This equation is a rearrangement of the definition of velocity: V = PQ/M. As such, without the introduction of any assumptions, it is a tautology. The quantity theory of money adds assumptions about the money supply, the price level, and the effect of interest rates on velocity to create a theory about the causes of inflation and the effects of monetary policy.

In earlier analysis before the wide availability of the national income and product accounts, the equation of exchange was more frequently expressed in transactions form:



VT is the transactions velocity of money, that is the average frequency across all transactions with which a unit of money is spent (including not just expenditures on newly produced goods and services, but also purchases of used goods, financial transactions involving money, etc.).

T is an index of the real value of aggregate transactions.

(Note the careful — but easily overlooked — qualification that quantities are for “a given period”, as I point out in the first block-quoted passage. One cannot simply add imaginary increases in real output over an unspecified span of time to an annual rate of output and obtain a new, annual rate of output.)

If the values for M, V, P, and Q are annual rates or averages, then MV = PQ = Y, the last of which I am using here to represent real GDP.

If the central government “prints” money and spends it on things (i.e., engages in deficit spending financed by the Federal Reserve’s open-market operations), then ∆G (the addition to the rate of G) = ∆M (the average annual increase in the money supply). What happens as a result of ∆M depends on the actual relationships between M and V, P, and Q. They are complex relationships, and they vary constantly with the state of economic activity and consumers’ and producers’ expectations. Even a die-hard Keynesian would admit as much.

If new economic activity (Y) is relatively insensitive to  ∆G, as it is for the many reasons detailed here, it is equally insensitive to ∆M. For one thing — one very important thing — ∆M may be absorbed almost entirely by an increase in VT without a concomitant increase in Q. That is to say, ∆G necessarily implies (in the short run) an increase in transactions velocity (VT) and it is most likely to be spent on resources that are already employed (i.e, either on things that were already being produced or by displacing private purchases of things that were already being produced).

The equality MV = PQ long predates Keynes’s General Theory, in which he introduces the multiplier, and so it was well known to Keynes. As it happens, the equality is at the heart of his multiplier:

The state of the economy, according to Keynes, is determined by four parameters: the money supply, the demand functions for consumption (or equivalently for saving) and for liquidity, and the schedule of the marginal efficiency of capital determined by ‘the existing quantity of equipment’ and ‘the state of long-term expectation’ (p 246).

Adjusting the money supply is the domain of monetary policy. The effect of a change in the quantity of money is considered at p. 298. The change is effected in the first place in money units. According to Keynes’s account on p. 295, wages will not change if there is any unemployment, with the result that the money supply will change to the same extent in wage units.

We can then analyse its effect from the diagram [reproduced below], in which we see that an increase in M̂ shifts r̂ to the left, pushing Î upwards and leading to an increase in total income (and employment) whose size depends on the gradients of all 3 demand functions. If we look at the change in income as a function of the upwards shift of the schedule of the marginal efficiency of capital (blue curve), we see that as the level of investment is increased by one unit, the income must adjust so that the level of saving (red curve) is one unit greater, and hence the increase in income must be 1/S'(Y) units, i.e. k units. This is the explanation of Keynes’s multiplier.

Here’s the diagram:

If that is the explanation of Keynes’s multiplier, it is even more backward than the usual explanation that I shredded earlier. All it says is that if the real money supply (M̂) is increased (i.e., not translated into higher prices) due to an exogenous increase in government spending, the real interest rate (r̂) decreases. And if the decrease in the real interest rate leads to an increase in investment, Y must rise by enough to preserve the theoretical relationship between Y and saving (S) and investment (I).

In this case, Keynes depicts the multiplier as the effect of an increase in I resulting from an increase in M, which is really an increase in G (∆G) under the condition of less than full employment (whatever that is). The increase in I is made possible by the decrease in the real rate of interest. That’s odd, because the popular view of the multiplier is that it is the rise in real GDP that is directly attributable to a rise in government spending. Will the real multiplier please stand up?

Regardless, the relationship between the increase in I and the increase in Y is no less tautologous than it is in the usual explanation of the multiplier.Simply put, the increase in I is the increase that must result if Y increases, given an ex-post relationship between I and Y. There is no causality, except in the imagination of the proponent of increased government spending.

We are back where we started, with a mythical multiplier that explains nothing.

New Pages

In case you haven’t noticed the list in the right sidebar, I have converted several classic posts to pages, for ease of access. Some have new names; many combine several posts on the same subject:

Abortion Q & A

Climate Change

Constitution: Myths and Realities

Economic Growth Since World War II


Keynesian Multiplier: Fiction vs. Fact




Multiplicative Hogwash

The Economist offers an almost-balanced view of the Keynesian multiplier, starting with its inception in Keynes’s General Theory, its theoretical refinement by Alvin Hansen and Paul Samuelson, and subsequent theoretical and empirical work. This sums it up: “Decades after its conception, Keynes’s multiplier remains as relevant, and as controversial, as ever.” It’s relevant only in the sense that a lot of economists and policy-makers still believe in it. What it is is hogwash:

The Keynesian Multiplier: Phony Math
The True Multiplier
Further Thoughts about the Keynesian Multiplier