David R. Henderson  

The Balanced-Budget Multiplier

Poverty, Conscientiousness, an... A High-Yielding Investment?...

In the "Letters" section of the Wall Street Journal today, Ball State University economics professor T. Norman Van Cott, in praising a recent WSJ critique of Keynesian economics by Allan H. Meltzer, adds to the critique, writing:

Particularly egregious is something labeled "the balanced budget multiplier." To wit, an equal increase in government expenditures and taxes leads to an increase in national output equal to the additional government expenditures and taxes. Mr. Samuelson, et al., gives the notion a scientific aura by packaging it in equations and graphs.
Economic surrealism? You bet. Note that national output and taxes rising by the same amount means producers' after-tax incomes are unchanged. How or why would producers produce more for no increase in after-tax income? Hint: They won't. Never mind the smoke screen of graphs and equations.

I had never heard Van Cott's particular criticism of the balanced-budget multiplier. It got me thinking and I'm genuinely not sure.

So my question for Keynesians and non-Keynesians alike. Is Professor Van Cott's criticism correct? As co-blogger Bryan would say, please show your work.

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CATEGORIES: Fiscal Policy

COMMENTS (13 to date)
Kevin L writes:

I suppose a case could be made for it by assuming that the government will expend the tax dollars in ways that increase overall value more than those from whom the money was taxed would have. That is, if the person who was taxed had planned on consuming or investing in exchanges with little value creation, and the government instead consumed it in a more productive manner, that would be a net benefit.

Unfortunately, since government lacks the profit-loss signals of individuals and companies under the market, knowing whether an expenditure by the government is better than the alternative is difficult. Even under very good conditions and assuming government decisions are very well made, I would expect the multiplier to be between 1.0 and 1.1. Of course, since government expenditures are usually more about political expediency than financial judiciousness, it is not hard to imagine that the multiplier would be significantly less than 1.0. It is also common for ideological proponents of government spending to assume - against all historical and theoretical logic - that savings and investment are inherently less productive than current consumption, which thinking would cancel out any positive short term multiplier when viewed in the long term.

I approached this not from incentives, as does Van Cott, but rather consequences, and the logic comes out the same. Belief in a balanced budget multiplier relies on the same assumptions that are used to promote technocratic central planning, and those assumptions have historically been incorrect.

david writes:

If I understand T. Norman Van Cott correctly, he is referring to the "Keynesian cross" analysis still seen in older undergraduate textbooks, as per this worked example on Wikipedia.

As Van Cott notes, it is indeed the case that ΔY = ΔT = ΔG. The latter two are the balanced budget. And, yes, national income rises no more than taxes.

It is indeed the case that after-tax producer income is wholly unchanged (ΔY - ΔT = 0); the nonzero multiplier arises in that ΔG has been apparently funded "for free", without reducing after-tax producer income: ΔY = ΔG. So where is the rise in national output coming from? G, of course.

Think about it: if you could miraculously tax someone without affecting their aftertax income, wouldn't your government be able to spend much more and thus your national output would rise? Is this so surprising?

Of course, nobody should pay attention to the Keynesian cross after first year. For one thing, there's no money, which is model is confusing when you try to 'follow the money' - we have increased national current consumption and thus reduced national saving (to fund ΔG) without reducing national investment. For this to be the case, the central bank must have implicitly intervened to maintain the level of I.

Thus the BBM is a well-hidden monetary policy model - the mint issues $100, hands it to producers, the Treasury taxes it away, and then spends it. Lo and behold: NGDP increases by $100. RGDP increases insofar as money illusion exists. Or nominal rigidities, for a more modern flavor.

david writes:

For more on the "it's really the missing money market" answer, note that if you plug the balanced-budget model into ISLM instead of just IS, you get a BBM less than one. It is still nonzero but it is now obvious where the multiplier effect on national income is coming from (namely, savings - the interest rate rises in response. I declines, but less than C and G increases).

mobile writes:

Sounds like a Laffer curve for progressives.

Bill writes:

Isn't the whole notion of the balanced budget multiplier anchored in the supposition that the tax payments that come from reduced saving would have leaked out of the expenditure stream had these savings stayed in private hands? Seems to me it's a relic of the "hoarding" notion of savings from the 1930s.

Glen writes:

David is right: Van Cott is channeling the old Keynesian cross model. The idea is that a balanced-budget rise in government spending will increase national output by the same amount.

I'm having to reach waaay back in memory (because they don't teach you the Keynesian cross in grad school), but as I recall, the effect is driven by the fact that marginal propensity to consume (MPC) is less than one. So when a dollar goes to the private sector, less than a dollar is spent. But when the same dollar goes to the government, the whole dollar gets spent. The difference in spending (equal to [1 - MPC]) then goes through the standard Keynesian multiplier process.

Hey, look, Wikipedia does the math for us: http://en.wikipedia.org/wiki/Balanced_budget#Balanced_budget_multiplier
The MPC is represented by C1.

Of course, what this model is missing (among many other things) is that the money consumers don't spend doesn't just disappear from the economy. Unless people stick it in their mattresses, it goes into the banking system and affects investment.

Bill writes:

Glen, your explanation of my point is better than my own. Thanks.

David R. Henderson writes:

You stated the standard analysis of the BBM--at least the Keynesian Cross analysis I remember from waaay back--well.
@Bill and Glen,
You made relevant and good criticisms.

Here’s my problem, though. Van Cott states that producers’ after-tax income can’t rise. Is that true?

david writes:

Well, in any Keynesian-type recession there is in principle exactly nothing preventing animal spirits/etc. from propelling the economy to a different equilibrium. So there is no prohibition on what producer's after-tax income would be. We are merely specifying what effect we would expect from a given balanced-budget fiscal stimulus.

In an IS, 'Keynesian Cross' analysis, we expect no effect on producer's after-tax income (ΔY - ΔT = 0) but there is nothing in the model that relies on this to be true. We can easily extend the model (into IS/LM, say) - for a fixed price level, producer's after-tax income decreases. Or we could have taxes as a function of income rather than a lump sum, which is much more plausible (and also changes the result).

As long as Ricardian equivalence does not hold, or the money supply turns out to be non-constant, one can obtain a nonzero balanced-budget multiplier.

David R. Henderson writes:

Thanks. So your bottom line is that Van Cott stated it with too much certainty, right?

david writes:

In context, Van Cott is launching his salvos at Samuelson and Nordhaus' 1948 textbook. While I have not read Economics, I would be be surprised if the simple Keynesian Cross analysis appears or used to appear in it and it is the specified model that presents this certain result, which Van Cott is quoting and criticizing.

The criticism of the model is fair, but how relevant is an undergraduate pedagogical model anyway? As far as bottom lines go, I would say that Van Cott is very successfully spearing a strawman with no resemblance to New Keynesianism as is practiced or advocated.

david writes:

edit: *not be surprised.

David Glasner writes:

David, Just saw a link to your question on Scott Sumner's blog. I think that the simple answer is that the balanced-budget multiplier presumes that there is involuntary unemployment. The additional output is produced by the employment of those previously unemployed; those previously employed experience a reduction in their real wage. I am not necessarily endorsing the analysis, but I think that is logic behind it.

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