The Effect of Government Spending on GNP in the Classical Model

Robert Waldmann

Brad DeLong has been denouncing Eugene Fama for arguing that an identity proves that the stimulus won’t work as advertised. Greg Mankiw attempts to defend Fama by arguing that Fama was assuming that the classical model, in which all markets including the labor market clear, holds. Brad DeLong notes that Fama made it very clear that he was not discussing the classical model. I don’t have much to add, but I would like to note that Fama’s argument would be false if the world corresponded to a Real Business Cycle Model — that is the only type of classical model that any economist takes seriously as a model of short term fluctuations.

Before getting to my thoughts, this post got to be very long so I am banishing all of my summary of the debate so far past the jump. Up here, just make the assumption that all markets clear so, among other things, labor demand equals labor supply and ask if Government deficit spending can cause an increase in measured GDP assuming that the product of public investment is no more productive than the products of private investment. The answer, according to the classical model is clearly yes, so Mankiw’s defence of Fama fails on its own terms even if one overlooks the fact that Fama made it perfectly clear that he wasn’t assuming that the classical model describes reality.

The model in which Fama’s conclusion would be valid is the classical model with exogenous labor supply. If capital is a state variable and labor supply is exogenous and all markets clear, then output is determined by the aggregate production function and can’t be affected by Government spending or anything else. However, the question of whether it is reasonable to assume the classical model and fixed labor supply when discussing short term fluctuations is *not* a judgment call even under Mankiw’s very broad apparent definition as an issue with prominent economists on both sides. Economists have noticed that aggregate hours worked fluctuate and that such fluctuations are correlated with other economic variables. There are, amazing but true, two schools of thought on what is going on. Some economists do indeed argue that the labor market always clears and that labor supply and demand are both fluctuating in response to other variables. Others believe that there is such a thing as unemployment. No one believes that it is a coincidence and that labor supply has nothing to do with anything else in the economy and is equal to labor demand. No one.

The classical model as it appears in current research assumes endogenous labor supply. It quickly becomes complicated, but has a clear implication that a temporary increase in wages causes an increase in labor supply (the temporary is needed to keep income effects small enough and how temporary is temporary enough depends on the shape of utility functions). In particular if the increase in wages is brief enough, the response of labor supply goes to the compensated elasticity which, according to the model must be positive. Sometimes it is assumed to be infinite. In modern market clearing macro models it is always very high.

The elasticity of labor demand is also very high in such models, but this doesn’t matter.

What happens when the government spends more ? Well to hire workers in the classical model they have to offer higher than prevailing wages. The increase in wages causes labor supply to increase and private employment to decline. Total employment increases because labor supply has increased. Assuming that public capital spending is exactly as efficient as private capital spending the capital stock is higher than it would be if the Government hadn’t invested in infrastructure.

Fama’s conclusion is false if one assumes the classical model unless one assumes that labor supply is exogenous. Now I’m sure the classical model with exogenous labor supply is exactly the classical model to which Mankiw refers. However, no economist considers it a reasonable approximation to reality.

There is an identity in macroeconomics. It says that in any given year private investment must equal the sum of private savings, corporate savings (retained earnings), and government savings (the government surplus, which is more likely negative, that is, a deficit),
PI = PS + CS + GS

In a global economy the quantities in the equation are global. This means the equation need not hold in a particular country, but it must hold in the world as a whole. For example, in recent years private investment in the US has been greater than the sum of private, corporate, and government savings in the US. This means the US has been importing savings from the rest of the world (by selling US securities to the rest of the world). But the equation always holds for the world as whole.

The quantities in the equation are not predetermined from year to year, and government actions affect them. The goal of government policy is to expand current and future incomes. When I analyze the auto bailout and the stimulus plan below, I judge them on whether they are likely to achieve this goal.

Government bailouts and stimulus plans seem attractive when there are idle resources – unemployment. Unfortunately, bailouts and stimulus plans are not a cure. The problem is simple: bailouts and stimulus plans are funded by issuing more government debt. (The money must come from somewhere!) The added debt absorbs savings that would otherwise go to private investment. In the end, despite the existence of idle resources, bailouts and stimulus plans do not add to current resources in use. They just move resources from one use to another


Brad now has a very readable pdf up.

N Greg. Mankiw has attempted to defend Eugene Fama writing

In the case at hand, I think Fama’s arguments make sense in the context of the classical model, the model presented in Chapter 3 of my intermediate macro textbook, even if Fama in his brief essay does not spell out all the details of that model. Unlike Fama, and like Brad, I would not stop at that model. To understand the present situation, I would go on to the Keynesian model presented in Chapter 9 to 11. But whether one leaves the classical model behind to embrace the Keynesian model is a judgment call. On this particular judgment call, Brad and I agree, but I am not eager to castigate those like Fama who reach differing judgments.

DeLong replies by noting that Fama made it perfectly clear that he was *not* talking about the classical model at all, since he assumed that there are “idle resources” which don’t exist in the classical model. Obviously he is right.

I personally am more displeased by Mankiw’s insistence that “whether one leaves the classical model behind to embrace the Keynesian model is a judgment call.” I think he means that prominent economists have made a different call than he and Brad have. I believe (I admit I base this on brief contact with Mankiw long ago) that Mankiw decides that assertions about economics are worthy of castigation or not depending on whether they have been stated by a proiminent economist (a Nobel laureate is automatically so prominent that Mankiw thinks that his views must not be castigated but I think Mankiw believes that there is a much larger set of uncastigatable economists). On the other hand, views which are not held by anyone in that club should sometimes be castigated.

Now I admit again that I am just guessing about Mankiw’s decision rule (and I admit that I have no doubt at all that my guess is correct). But if there were an agent whose decision rule was that which I ascribe to Mankiw, that agent would be a menace. The rule has nothing to do with evidence, data, or reality. It can’t have any place in any field which aims to be a science. I note that Brad didn’t use profanity or insult Fama’s character intellect or mother. He the text of Fama’s post. Only his conclusion — that Fama made an error not a judgment call — is unacceptable to Mankiw.

For completeness an edited version of my comment on Brad’s post.

Notice he didn’t say anything about the elasticity of labor supply. One can have the labor market clearing a postitive elasticity of labor supply and have Government spending drive labor supply up (above the socially optimal level). For Fama to be right one has to assume that markets clear *and* that labor supply is exogenouse, that it doesn’t depend on wges and prices. Now even using Mankiw’s definition of “judgment call” which I interpret as meaning “prominent economists make different calls,” this is just not a judgment call. People write down models with exogenous labor supply when they are focusing on long run growth, but, as far as I know, no economist has ever argued that, when discussing economic fluctuations, it is reasonable to assume both that the labor market clears and that labor supply is exogenous.