# Government Spending: The Zero Multiplier Model

by: Casey Mulligan

On Tuesday, Professor Krugman claimed that there is no model saying that "fiscal expansion does nothing but shift money around."

He is incorrect about the existence of such a model. In fact, the model has been featured for 25 years in various undergrad editions of Macroeconomics by Robert Barro (Professor Barro is the world expert on government multipliers -- funny how Professor Krugman neglected to check there).

Here's how it works. Citizens have preferences u for working (n is the amount of time they work), consuming private goods c, and consuming goods g provided by the government. More goods c + g are produced when the citizens work more according to the production function F(n). The governments gets its revenue from lump sum taxation.

The marketplace sets wages and prices to provide the efficient amount of work and private consumption, taking as given the amount spent by the government. In mathematical terms, (c,n) solve max u(c,g,n) subject to c + g = F(n).

When the government is purchasing things (say, health care, or schooling) that citizens would have purchased themselves, then the public spending g is a "perfect substitute" for private consumption c, and the effect of g is just to reduce private spending dollar-for-dollar. In other words, the multiplier in the perfect substitute model is zero: fiscal expansion does nothing but shift money around.

Of course, reality is more complicated than this. But (a) by definition, a model is not reality -- and my claim so far is just that (contrary to Krugman) a well-known model does exist that says the multiplier is zero, and (b) "realistic" deviations from this model could well give you a negative multiplier -- that is, government spending reduces private spending more than dollar-for-dollar, thereby reducing total spending. Thus the zero multiplier is one natural place to start, which is why Professor Barro started there in his famous WSJ oped (for rhetorical reasons, my macro courses start with a positive multiplier model: Professor Cochrane ignored my advice on this).

Of course, one can argue which model is more appropriate for application to our economy (guess what -- I will not agree with Professor Krugman there either -- more on that in the next few weeks. See also a fancier version of the perfect substitutes model that explains well what has happened our economy so far, and offers a forecast of where it is headed), but you have to understand that Professor Krugman's macroeconomics commentary deliberately treats mainstream macroeconomics as if it never existed, hoping that his faithful readers will not fact check him.

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The great irony here is that the model above also appears in a paper by Professor Woodford, and adored by Professor Krugman, with one deviation: Professor Woodford's model assumes that government spending is intrinsically worthless whereas the Barro model (above) assumes that citizens actually like government spending, perhaps as much as their own spending! Thus, in addition to misleading you about the macroeconomics literature, Professor Krugman's case for the multiplier secretly rests on an economic logic that requires his beloved government spending to be intrinsically useless!