Bryan Caplan  

The Sophistry of the Balanced Budget Multiplier

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Collected Macro Lectures... Critical Review Symposium on M...
If you go to an old-fashioned Keynesian macro text, it will explain that raising taxes and spending by equal amounts increases total spending.  How is this possible?  Well, if the Marginal Propensity to Consume=a, then the gross positive effect on nominal GDP of spending G equals:

G+aG+a^2G+a^3G+...=G/(1-a)

The gross negative effect of raising taxes, however, equals:

aG+a^2G+a^3G+...=aG/(1-a)

If you subtract the first expression from the second, you find that increasing spending and taxes by G raises nominal GDP by G.  Hence the famous result: The Balanced Budget Multiplier equals 1.  This reasoning implies, in turn, that dollar-for-dollar, spending has a bigger stimulative effect than a tax cut of equal size.

Unfortunately, this argument is sleight of hand.  How so?  It assumes that government agencies automatically spend 100% of any new funds allocated to them.  And strange as it seems, that assumption is often false.  It takes time and effort to figure out how to spend new money, you often need the approval of multiple levels of supervision to get started, etc.  The standard Keynesian analysis essentially compares a conditional effect of government spending to an unconditional effect of tax cuts.  Even within the confines of the textbook Keynesian model, this is a clear case of stacking the deck in favor of spending.


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COMMENTS (8 to date)
Brian writes:

I actually made a very similar point at my old job, which was full of UPenn Keynesians, and I was branded a libertarian kook. At least they got the libertarian part correct, but I digress.

Jacob Miller writes:

I always wondered where "deadweight social loss" was supposed to be factored in this equation. Lost productivity transferring money and the effects on incentives are not free.

Oliver writes:

The same can then also be said about consumer spending after lowering of taxes: many consumers will first invest time and effort to figure out how to spend their additional income.

Marcus writes:

Oliver, maybe if we gave an individual a trillion dollars to spend but we're not. A tax cut is literally placing millions of more minds on to solving the problem.

MattYoung writes:

a, the propensity to spend, is not really a scalar and the equations above apply only to the average.

'a' really is a distribution of relative elasticities, not a problem as long as the distribution is relatively bell shaped, then 'a' becomes a stochastic matrix, A, and the equations still work.

But the matrix A, representing the distribution is very different in 2010 than in 2008, that is the problem. A, the distribution is not likely even bell shaped at this particular moment.

Further, government, and the rest of the economic sectors, cannot refine their knowledge of A until they experiment with small trials, they have to perform marketing studies.

To understand a distribution of relative elasticities imagine two distributions, one distribution tells us where goods are in space and time; the other tells us where we want goods arranged. The difference is the relative elasticity distribution.

That distribution is heteroskedatic at the moment, as Jim Hamilton would say. This is equivalent to having an inverted yields curve, things are not bell shaped; hence the equations are temporarily invalid, the series does not converge.


liberty writes:

Someone please correct me if I'm wrong, but to me there is an even graver error.

The Marginal Propensity to Consume concept itself is assuming that only spending and not saving is going to increase GDP. Why would we assume this? If the consumer (the recipient of a personal income tax cut) saves his money in a bank, instead of under his mattress, then his savings automatically increase available funds for loans and investment. Won't this increase output too?

More funds to lend mean that the marginal borrower has a better chance of getting a loan, and is now able to expand operations and hire more workers, right? Isn't this very much the same as the same firm getting more revenue from the higher purchases that result from consumption?

To me it seems that savings and consumption are both good - and that the main difference between tax cuts and government spending is that one happens centrally, with a central mind spending money which is not his own, and one happens in a private decentralized way.

wally in miami writes:

Our cities have fallen into disrepair while other developed Nations have invested trillions in infrastructure. Our public schools and universities struggle to make ends meet, failing to keep up with the need to turn out minds able to compete in a rapidly changing world. We subsidize the consumption of oil by paying for "defense" of the oil pipeline with income tax dolllars rather than Mideast oil taxes, thereby tilting the playing field in favor of oil over preferable energy sources that are less poluting and do not reward cultures who want us dead. We burden manufacturing in the US with environmental costs while encouraging trade agreements to bring goods to us unburdened by that critical social policy. We place the burden of health care on employers who then try to compete with foreign manufacturers whose governments deliver universal health care. And the "conservatives" continue to argue for lower taxes as if the tooth fairy will provide for public needs. The Reagan Revolution is destroying our country. Greed is a short term strategy.

Ian writes:

I would agree with Liberty's comment above. The fundamental problem is the assumption that savings do not enter the economy. If the money is lent, the borrower introduces it to the money supply. Only if the money is hoarded does the Keynesian have a point under his own assumptions (that price levels are sticky). Assuming that actual hoarding is very small, the actual MPC is 1, or nearly so.

This immediately questions the entire model, for if the MPC is 1, this model predicts an infinite increase in consumer spending. The solution is time: this model somewhat arbitrarily assumes infinite velocity. Using a finite velocity, we get a much more realistic interpretation: new money stays in the system, not exhausting itself over time, and the magnification is not a function of the money multiplier (which is nearly infinite) but velocity.

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