## On Williamson on Waldmann

Stephen Williamson wrote a critique of this post which critique was praised by David Andolfato and Noah Smith.

Williamson critiques the Keynesianism defined as

So, as I learned from Dick Lipsey in 1975, and my cat learned last fall, Keynesian Cross is

(1) C = A + cY,

(2) Y = C + I + G,

where C is consumption, Y is output, I is investment, and G is government expenditures, with 0 < c < 1 and A > 0. Y and C are endogenous, and A, I, and G are exogenous.

This is not Keynesianism as presented in “The General Theory of Employment, Interest and Money” nor is it Keynesianism as practiced just before the rational expectations revolution.

Williamson notes that, unlike GDP consumption was not correlated with G during the recovery.

Importantly, Williamson and I agree that simple raw correlations tell us almost nothing especially when there are very few data points. As always, I stress that, to me, the interesting thing is the difference between statistical calculations however simple and crude (people agree on what they are if not what they mean) and impressions based on reading newspapers where people perceive very different supposed facts.

My reply.

Three things. First the phrase “Keynesian multiplier effects” really needs an agreed definition. Economists including Fama, Cochrane and Lucas assert that the multiplier must be zero. But as soon as data is consulted the Keynesian claim becomes that it is greater than one. 1>0.

Second, I have the impression that your comment on how failure to FRED is inexcusable is ironic. Can you give an argument for excusing failure to FRED ?

Third, contemporary paleo Keynesians (we do still exist) believe in the accelerator. In FRED there is a strong correlation between delta ln(Y-I) and delta ln(i)

This means that G works through Investment too. Consumption has not such a very special role in 1960s era Keynesianism.

This is for non residential fixed investment (also subtracted from GDP). If one were to pretend that this absurd regression is the estimate of the true causal effect of anything which affects GDP on investment, then one gets a multiplier greater than one without any effect on consumption (there is also an effect on consumption in the data, but as of say 1965 consumption no longer had a very special role in explaining why the multiplier is greater than one.

. reg dlrinv dlrgdpmi

Number of obs = 267

R-squared = 0.0384

dlrinv | Coef. Std. Err. t

dlrgdpmi | 1.381569 .424611 3.25

_cons | -.0013458 .004415 -0.30

Hi Robert:

Been reading the exchange between you and the others. I think you pretty much said it back in the beginning:

“19 data points can’t prove anything, but the few data support the Keynesian hypothesis about as strongly as could be imagined.”I would not change much on a shop floor with so little data although it point in a positive direction. I would pursue it further by finding and analyzing more data.

actually more data have been analysed. The include US state level data where the interaction of the ARRA and state medicaid programs implied different stimulus in different states. This yields a positive multiplier (less than 1 IIIRC). Also international data. Olivier Blanchard and Daniel Leigh wrote an excellent paper in which they looked at actual gdp growth minus gdp growth forecast by the IMF model. Here lots of variables are already included in the IMF model which worked pretty well before economies fell into liquidity traps. They regressed that difference on an estimate of the change in G. They got a coefficient of 1. This means that, iff the IMF model were otherwise perfect, it would be wrong because it assumed a multiplier smaller than the true multiplier by 1. The IMF model implies a multiplier of about 0.5 so the Blanchard and Leigh is 1.5.

http://www.imf.org/external/pubs/ft/wp/2013/wp1301.pdf

Oddly my pointless analysis of a few US data points and my analysis of all available US data points with no other variables at all yields extremely similar estimates. 0.5 if the economy is not in a liquidity trap and about 1.5 if it is.

My posts aim to be about psychology and confirmation bias. They add almost exactly nothing to the literature on multipliers.

Stephen Williamson admits he lets his cat use FRED to do empirical analysis? This is what passes for econometrics at the University of Washington these days?