## Over at Equitable Growth: Yes, the Past Four Years Are Powerful Evidence for the Keynesian View of What Happens at the Zero Lower Bound. Why Do You Ask?: Daily Focus

**Over at Equitable Growth**: He whom we all disagree with at our grave peril writes:

**:
The Record of Austerity - NYTimes.com:
"How many people, I wonder--even among economists who have eagerly taken sides in the austerity debate...**

...have a sense of what the overall picture looks like since the great turn to austerity in 2010... [not] what happened in country X in year Y, which you imagine supports your position... [but] the overall shape...[?] Annual data on the growth of real GDP and of government purchases from Eurostat.... 33 countries for 4 years, 132 observations.... Does this picture make you think that Keynesian economics is nonsense?... The raw observations are consistent with the view that in depressed economies, cutting government spending hurts growth.

Of course, the fit isn’t perfect. In fact, the R-squared is only 0.31. That’s because... stuff happens. And that is why we have statistics.... You can, if you like, try to argue that this relationship is spurious.... But one form of argument that is really illegitimate is to... pick out outliers... claiming that the... outliers--because stuff does, in fact, happen--disproves Keynesian logic. Unfortunately, you see a lot of that, including from economists who really should know better."

If you assume that all of the correlation reflects a causal connection running from fiscal austerity to slower GDP growth, the associated multiplier μ is 2.3. This is an open-economy multiplier, and the typical country in Eurostat is very open indeed. An open-economy multiplier of 2.3 corresponds to the closed economy multiplier of 4.

What I want to add to Paul's discussion here is what I see as the absurdity of the arithmetic underlying the reverse-causation argument:

Write "Δ" for "change", "Y" for "GDP", "μ" for the fiscal multiplier, "G" for "government purchases", "ε" for "other things than government purchases that affect GDP", "λ" for "reverse causation in which falling GDP leads to cuts in government purchases", "η" for "other things besides GDP that affect government purchases":

ΔY = μΔG + ε

ΔG = λΔY + η

Make the truly heroic assumption that ε and η are uncorrelated. Define the ratio σ of the variances of ε and η:

V(ε) = σV(η)

The estimated slope from a regression of ΔY on ΔG is then a weighted average of the true fiscal multiplier μ and the inverse of the reverse-causation effect of falling GDP on government spending:

s = ρ(μ) + (1-ρ)(1/λ)

with the weight ρ given by:

ρ = [1/(λ

^{2}σ + 1)]

In order to get a high estimated slope out of reverse causation, the value of the parameter λ has to be small--there has to be relatively little influence of falling GDP on government purchases. But if that is the case, then the weighted average that is the slope will put most of its weight on the true multiplier μ. A high estimated slope--on the order of 4 for the closed-economy case--can only be consistent with a small true multiplier μ for a truly absurdly large value of the variance ratio σ: the level of government purchases then has to be a function of GDP *and of GDP alone* for the arithmetic to work. And that is simply not the case.

See for yourself (always assuming I have not gotten the arithmetic of the spreadsheet wrong):

556 words