The Canadian government decides to run an experiment to see if fiscal policy works. It throws 100 darts at a map of Canada. One dart lands on Wawa Ontario, so it spends an extra $1 million in Wawa. Local GDP in Wawa, and local GDP in all the other 99 places where the darts land, increases by $2 million relative to the control group of the Rest of Canada. The experiment clearly shows there's a government expenditure multiplier of 2.0.
Does that mean there's a government expenditure multiplier of 2.0 in the whole of Canada?
You should be able to see the underlying fallacy of composition. "Government spending has a multiplier of 2.0 in each part of Canada, therefore government spending has a multiplier of 2.0 in the whole of Canada."
I can immediately think of three reasons why the whole might be less than the sum of the parts:
- Taxes. Wawa will pay only a tiny fraction of the present and future taxes used to finance the extra $1 million expenditure in Wawa, but the higher taxes might reduce GDP in the Rest of Canada.
- Monetary Offset. Wawa does not have its own central bank, money, and exchange rate. But Canada does. Increasing government spending in Canada as a whole might lead to an appreciation of the exchange rate and a fall in net exports.
- The supply side. Resources like labour can more easily move within Canada in search of better jobs than resources can move to Canada from outside.
And I can immediately think of one reason why the whole might be more than the sum of the parts:
- Propensity to import. People living in Wawa probably spend a much smaller fraction of their income on goods produced in Wawa (unless they are addicted to the excellent Wawa summer sausage) than people living in Canada spend on goods produced in Canada. In a simple Old Keyensian model that would mean the Wawa multiplier is smaller than the Canadian multiplier.
And I can immediately think that the whole purpose of running an experiment would be to test whether there might be something that makes fiscal policy for the whole different from the sum of the parts that I can't immediately think of. Experiments are supposed to tell us whether there might be unknown unknowns. (Does anybody remember all the clever people laughing at Donald Rumsfeld when he first said "unknown unknowns"?)
Yesterday I read my colleague Vivek Dehejia on randomised control trials in economics, worrying about external validity of experiments. Today I read (H/T Mark Thoma) Price Fishback's survey paper on the microeconomic effects of Roosevelt's New Deal (as micro it looks legit to me, but we have to be very careful before drawing any macro conclusions from these micro results).
I don't have any good easy answers either. But this is why we need theory. Experiments alone aren't enough. If you do a drug trial in Wawa, the external validity of the experiment will depend on whether it's a communicable disease.
Update: Kevin Milligan tweets that I am saying that local macroeconomic multiplier experiments almost surely violate the Stable Unit Treatment Value Assumption. I hadn't heard of SUTVA before, but after reading the Wikipedia, that sounds right to me.
Update2: see Ryan Murphy's working paper on the sheer number of papers that ignore the basics like monetary offset by the central bank.
Worthwhile Canadian Initiative 
“Does anybody remember all the clever people laughing at Donald Rumsfeld when he first said “unknown unknowns”?”
At least some people were darkly laughing at Rumsfeld because his “knowns” were known to be not what was known.
Speaking of fallacies of composition…
Regarding “the whole of Canada” as a closed system commits a fallacy of composition relative to the whole of Canada as an open system. This is why we need systems theory.
A useful concept here is the Stable Unit Treatment Value Assumption (SUTVA) of the Rubin Causal Model
https://en.wikipedia.org/wiki/Rubin_causal_model#Stable_unit_treatment_value_assumption_.28SUTVA.29
Basic idea is that outcome of unit ‘i’ is unaffected by the treatment status of all other units not/i. This rules out externalities of the type Nick describes here.
Kevin: thanks. I saw your tweet, read the Wiki, and updated the post, because I think you are right. Interesting perspective, linking it all together.
Sandwichman: Yep. I would say it this way: what is true for each country may not be true for the world as a whole.
I have a working paper on this topic: [ Link Here NR]
Ryan: Spot on! Good paper, with emphasis on the monetary offset argument.
It’s amazing that all those papers get away with it!
Re: Ryan Murphy’s working paper:
As an addendum to my comment from yesterday, this point is also related to the usefulness of fiscal transfers in a monetary union: there is a free lunch to be had, in aggregate, by balancing aggregate demand among constituent units.
I apologize for the lateness of my reply but I do have a question/disagreement regarding part of the post.
Why would monetary offset be a relevant reason for believing that the fiscal multiplier is smaller for the whole of Canada? Developing countries today only ever apply national fiscal stimulus when monetary policy has become either unable or unwilling to close the output gap and keep inflation steady. In a sense the fiscal stimulus is seen as a way to bail out monetary policy. When economists try to measure the national multiplier they are looking at how effective fiscal policy will be in helping the central bank meet its goals. I.e. how much fiscal stimulus will be necessary for monetary policy to regain traction with the economy. What use would it be to calculate multipliers when the central bank is unconstrained? Assuming a competent central bank the multiplier will always be fully offset by monetary policy.
A case in point is the specific example used in the blogpost. The new deal was accompanied by expectations of monetary easing since Roosevelt advocated taking the dollar off gold. If anything I think monetary offset should be included as a reason why the whole may be more than the sum of its parts since stimulus that only occurs in some localities will be partly offset by monetary tightening and is (AFAIK) never done in co-ordination with national monetary policy.
Note that none of this criticism applies to Ryan Murphy’s (good) paper which focuses on monetary offset in the context of local and state level fiscal policy.