Sunday, December 28, 2014

Where's the Multiplier?

Robert Waldmann thinks there are "non-Keynesians" who are excessively dismissive of the Keynesian multiplier:
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.


  1. Why don't you use scatter plots from FRED if you are so proud of it? So who is the dim-wit?

    1. Stupid cat didn't show me that. Seriously, though, I have never used FRED to construct a scatter plot, and had no idea the capability was there, though of course it seems natural that it would go beyond time series plots. But, I saw that Waldmann had what looked like a FRED scatterplot, so I looked around to see how that might be done, but with no success. If I was at work, I'd just ask Zimmerman, but I wasn't, so I thought, screw that. It takes a few clicks to import the data into Matlab and do it there. By the way, you seem to have an attitude. Not nice to call people dim-wits.

    2. Christian Zimmermann wrote with two complaints:

      1. As mentioned above, FRED delivers scatter plots.
      2. It's Zimmermann, not Zimmerman.

  2. Purely for historical interest: Old Keynesian Maurice Peston making the point about correlation between target and instrument:

    1. Yes, it's a standard, and maybe obvious point. Endogenous policy makes inference difficult. I like to give undergraduate students an example of an active central bank in a sticky price world vs. a price-stabilizing central bank in a world where money is neutral. The time series are identical.

    2. It's one of those things that's only obvious when you've seen it. And we seem to keep forgetting it, especially in new contexts.

  3. Replies
    1. My cat actually liked it too, after she settled down a bit

    2. I tried showing it to my friend's cat, but he decided he'd rather just rub his face on my face. So it goes...

  4. There are, thankfully, rarely clear-cut experiments in economics outside of the lab. But Europe has just conducted an experiment and the result is that Macro 101 is correct, contractionary fiscal policy during a recession in which interest rates are close to zero is indeed contractionary.
    If you wanna read serious stuff on it, there are some decent IMF papers and they all estimate a multiplier above one.
    This is hardly surprising, we are in a liquidity trap so fiscal policy is the only game in town. During "ordinary" recessions it is most likely far lower.

    Of course New Classicals like Williamson are ignorant of Econ 101 (gee, the monetary "model" of this guy is basically just the Fisher relation with the implicit assumption that the real rate is fixed or not impacted by monetary policy which is obvious nonsense) and anti-Keynesian by nature (the usual riggt-wing stuff: not caring about the unemployed, caring about rentiers, dismissing that government could ever do something useful and so on).

  5. "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."

    People have been asking these questions for centuries. I am not sure that the New-classical revolution and the digging up out of Ricardian Equivalence - which was already trashed by nineteenth century economists - has helped us answer however whether bond financed or tax increase - financed bond expenditure expansion is good or bad. (Of course it depends on the context, something neo-classical models ignore.)

    Pity, because we have so much historical investigation (which is not just numbers) to look at, and so much work done by historians and others on the actual long term consequences of large increases in government expenditure, inflation and debt.

    1. Not sure what you're getting at. Theory is bunk, and historians have all the answers? Is that it?

    2. No. I am just saying sometimes a lot of theorizing seems to go on with assumptions like rational expectations when we can get some answers from historians who have been looking at case studies that have actually happened in the real world. We know from the beginning to the end what happened.

      I am not saying everyone does it, but a lot of abstraction seems to go on so we can get a mathematical model. Another thing that happens is that people run huge amounts of data through a computer programmes with very little historical context (I accuse Rogoff and Reinhart of doing this to some extent although I do not say that their work was totally useless).

      Want to know what happens when central banks purchase large amounts of government debt? Does it lead to recovery or inflation? What about credit policy (and the monetising of private securities). Yep, we have examples of that too. Did it end Western Civilisation as we know it through hyper-inflation? In one case it was almost accompanied by something like that, but the credit policy or the massive issuance of government debt was not the cause.

      What I would like to see when I open the JME is lots of factual and contextual detail, and an abstraction only when really needed.

    3. You are not smart.

    4. I don't think any serious economist would argue that we should ignore data, and that necessitates digging into the historical record. But you can't make sense of the historical record without theory to organize how you think about the data. Tom Sargent is a good example of an economist who has respect for the theory (including rational expectations, which you seem to think is some goofy kind of fooling about) and for history.

    5. I am relieved to hear that Stephen, perhaps what I have seen is not properly representative. I have, however, read some Sargent, and I have to confess, he does not impress. In many ways this is an extreme case of the bad practice I am talking about. One thing he looked at was the stabilisation of inflation in the interwar period. In this study he basically sets out the case for rational expectations theory (which is not the correct way you do history). His basic conclusion was that inflation was stabilised in Germany, Czechoslovakia, Austria and Poland once the money supply was tied to commodity money (ie reduce the guaranteed reserve component in your reserve for money supply) because it established "policy credibility". To an historian that is likely to be absolutely ridiculous. The cause of inflation all historians would agree (with their own independent investigations) was a result of the disfunction these economies faced brought upon by events during WWI. They had either lost the War or came out of them as failed states. Their currency did not have "currency". A barter system had taken over. Inflation was stabilised once law and order and institutional control and authority had been restabilished. To the extent that the restoration of the Gold Standard helped was only in so far as being icing on the cake. The critical condition was the re-establishment of government authority.

      Power is a big variable missing in neo-classical analysis and is why you need to consult other schools of thought sometimes, including Marxian analysis. Otherwise you get people who think that inflation or currency collapse is only caused by monetary factors or never caused by monetary factors. Ask a Classicist. He will tell you that during the Roman Empire the currency was continually debased (literally the silver content reduced in the coins). It did not matter as long as Ceasar's head was on the coin and he had the political authority to say it was worth what he said it was. The Gold Standard could work until 1914 as long as Britain had the authority to ensure its enforcement. In the interwar period that was no longer the case. We had to wait until 1945 and a decisive war to sort out new power arrangements for a new monetary system based around the US dollar.

      Such an oversight by Sargent is tolerable, as huge as it is. But the unforgivable thing was starting with his Model, using data which does not give you a big enough picture (ie money supply, currency and price data) and then going out to prove it. You look at the historical evidence first (which must be wide in scope and include as much primary material as possible), then you make your conclusions - which may include a model. But the model must not come first because it will dictate the analysis and therefore the conclusion.

    6. Sargent wasn't trying to "do history". He was trying to "do economics" or, more ambitiously "do science". The scientific method is:
      1/ Write down your theory/hypothesis
      2/ Go to the data
      3/ Check if the data is consistent with your theory. If yes, great! Do some further tests. If no, go back to step 1 and try again.

      I have a lot of time for using historical episodes to better understand economics. But the reverse methodology you describe sounds a lot like data mining. Sure, you can identify correlations in the data. But how do you test whether those correlations are spurious or telling us something systematic about the world?

  6. Good Lord Steve, why give a crackpot like Waldmann free advertising? There is enough bad crap out there without making it easier for dumb people to find it.

    1. People will have no trouble finding bad crap. The hope is that, in sometimes addressing bad crap, some people are convinced who otherwise would not be.

  7. Two 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

    1. "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."

      Fama is, to my knowledge, a finance guy, and has not done any research in modern macro. Cochrane has said some stuff in blogs, and the WSJ about multipliers. With regard to Lucas, I think you're referring to some stuff he said in public forums. Why don't you go to the published research on the effects of government spending? There is plenty of it, and it doesn't come down to: Keynesians > 1, others = 0.

      "Can you give an argument for excusing failure to FRED ?"

      Can you give me an argument for excusing failure to read?

      "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."

      Yes, I agree that "paleo-Keynesian" is a good label for this sort of thinking. I hope you understand that there are actual theories that explain why investment and output are positively correlated.

    2. This post is spectacularly uninformed. Good job, Robert, you have really managed to bring incoherence to a new level.

  8. It seems to me like we can look at a base case where the private economy (PE) is the unknown variable. This would be a simple two sector division of the economy. We could begin with your equations 1 and 2 to write

    (1) C = A + cY,

    (2) Y = C + I + G,

    Then we would set C - A = C + I = PE.

    Substitute into equation 1 to get

    (3) PE = cY

    and into equation 2 to get

    (4) Y = PE + G.

    These are all trivial equations no one should dispute.

    Substitute equation 4 into equation 3 to get

    (5) PE = c*PE + c*G.

    Rearrange equation 5 to write

    (6) PE = c* G / (1 - c)

    Substitute equation 3 into equation 4 to get

    (7) Y = c* Y + G.

    Rearrange equation 7 to write

    (8) Y = G / (1 - c)

    Rearrange equation 8 to find c and write

    (9) c = 1 - G / Y

    There is nothing spectacular here but we could call it a base case. A base case that we can test and expand with more sectors.

    I think we should notice that when the G term is defined as government expenses, then any effects of borrowing to pay these expenses has been included in both the Y and G terms. That is an inherent contamination of the terms by the creation of money (at worse) or investment borrowing (at best).

    So far as I can determine, this contamination can not be teased out of the Y term. I think the best analysis that can be done is to trace any new money or borrowed money by the anticipated spending sequence. The easiest analysis is to observe that the new money is first spent by government and then assume that new money is immediately re-spent in patterns identical to patterns of old money.

    Thanks for the thoughtful post. Happy New Year!

    1. You are in desperate need of a principles of economics class. Preferably one I don't teach.