Various non Keynesians have argued that the pattern of public spending and GDP in the USA during the current recovery (that is since June 2009) undermines the Keynesian hypothesis that the Government spending multiplier is positive. In particular JOhn Cochrane and Tyler Cowen argue that, if Keynesians were right, sequestration should have caused at least a decline in GDP growth rates.Waldmann shows us a chart, calculates a correlation coefficient (complete with standard error and t-statistic), showing that, for the last 19 quarters, quarterly growth in real government spending and growth in real GDP are positively correlated, and concludes:

...19 data points can’t prove anything, but the few data support the Keynesian hypothesis about as strongly as could be imagined. I am impressed by the unreliability of casual empiricism conducted by idealogues. Some people look at this period and see the opposite of what I see. Even now, I am shocked that economists didn’t bother to look up the data on FRED before making nonsensical claims of fact.First, I think Christian Zimmerman will be very pleased to learn that FRED has become so user-friendly that failure to consult it has become proof that one is a dim-wit. In fact, my cat was using FRED the other day to sort out some empirical facts. Apparently she's been getting tips from FRED Blog. Second, I'll go Waldmann one better, and include two more observations, so that I can include the whole post-recession time series. Then, the scatter plot of output growth vs. growth in government spending looks like this: From Waldmann's standpoint, this is even better - a correlation coefficient of 0.50 to his 0.34.

I can see why Waldmann is worried that 19 observations might be too skimpy, though. If you include all the data from 2008Q1 to 2014Q3, you get this: That doesn't look so great. In that scatter plot, the correlation coefficient is -0.12 which, by Waldmann's criteria, would be a win for the non-Keynesians. But, my cat is is looking over my shoulder and telling me "not so fast." My cat, in addition to knowing FRED, also took an intro-to-macro course, and knows all about the Keynesian Cross. She's a big Paul Krugman fan too.

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. We can solve for

*C*and

*Y*as follows (my cat checked my algebra):

(3) C = [A + c(I + G)]/(1-c)

(4) Y = (A + I + G)/(1-c)

Here, 1/(1-c) is the multiplier. Krugman, with whom Waldmann appears to be quite sympathetic, has told us that IS/LM is truth, truth is IS/LM - that is all we know on earth, and all we need to know. Better than that, since late 2008, when we entered the liquidity trap and the LM curve became flat, Keynesian Cross has become our even simpler truth. My cat agrees that (3) and (4) are rich with implications and policy conclusions. She has also pointed out that it's not quite fair to be drawing conclusions from the last chart above. Suppose, says my cat, that

*A*and

*I*are random variables, that the government sees the realizations of

*A*and

*I*before choosing

*G*, and that the government has a target level of output,

*Y**. Then,

*Y = Y**and

*Y*and

*G*would be uncorrelated. Alternatively, suppose that the government is constrained, so that it can only close a fraction of the output gap, under any circumstances. Then, we could observe something like the last chart. There was a big demand shock in 2008, the government didn't do enough, and so we see government spending going up when output is going down during 2008.

So, my cat reasons, maybe Waldmann has the right idea. After the end of the recession in mid-2009, the demand shock is long gone, and the government has been behaving in a random fashion. Then, if we see a positive correlation between output growth and growth in government spending post-recession, that's consistent with Keynesian Cross. My cat has an inquiring mind though, and she's thinking about equation (3). She understands that the Keynesian multiplier works through consumption, and that (3) implies that we should see a positive correlation between consumption growth and government expenditure growth over the period Waldmann looks at, if Keynesian Cross actually describes the data. No such luck though: I showed my cat how to use Matlab to compute the correlation coefficient for the data in the chart, and she gets -0.07. Now she's pissed, and is hiding under the sofa.

Obviously, my cat has a lot to learn. I'll have her read Hal Cole's post on the aggregate effects of government spending, for starters. It's also important that my cat understand that there are few economic policy problems that can be solved in a blog post. We're very lucky if looking at raw correlations helps us to discriminate among economic models, or to draw policy conclusions. Indeed, normal economics tells us that there are various mechanisms by which increases in government spending can cause aggregate output to increase. Government spending could be totally unproductive, but lead to an increase in output because of a wealth effect on labor supply. Government spending could be complementary to private consumption, and if the complementarities are large enough, there could be large multipliers. There could be multiple equilibria. But, when we start to think in terms of normal economics, it becomes clear that the effects of government spending depend on what the government spends on, how the spending is financed, etc. And we start asking more questions - interesting ones. Indeed, I think my cat would quickly go back to watching squirrels, if (1)-(4) were all the economics she had to think about.