# Local analysis in macroeconomics

The substantive piece of John Quiggen’s criticism of New Keyensian macro is that the analysis is limited to looking at deviations of the economy around some set point. If the economy gets far away from that point, the analysis may not apply. His mistake was assuming the set point was the Smithian or neoclassical ideal, but in the NK models this isn’t the set point.

Nevertheless, to analyize these models, we do local analysis. Everybody does local analysis, so this criticism actually applies not just to New Keyensian macro but to most modern macro. I’ve actually been worried about this problem sense I realized this is what I was doing when I solved those models.

Ken Judd — Stanford’s computational economics god — gave a seminar at Davis yesterday and he made me feel much better about these techniques. While discussing this paper, he defended so-called perterbation methods by appealing to the authority of physics. They do it, so its ok for us to do it. Apparently, to solve the equations of general relativity, physicists perterb the system around the no mass solution. In other words, the set point that they do local analysis around is a universe with no mass in it! Not only that, because they’re doing local analysis (and like in economics “local” is undefined), their analysis suggests the universe is stable only up to an undetermined point of time. Outside that time interval, the local area of analysis, the results of general relativity may not apply ((BTW, IANAP (physicist) and neither is Judd, but he’s a smart guy and as long as I didn’t misunderstand him, I believe what he told us. Corrections are welcome.)). Yike!

That said, there are still problems with the way most macro folks do local analysis — we linearize when we probably should use higher order local approximations ((Although, a professor told me there’s very few cases where linearization can lead you astray. Unless you’re studying precautionary motives or other behaviors that depend on second moments, linearization should be ok.)) — and if all of us picked up a copy of Judd’s textbook (and read it!) we’d be better off.

## 5 thoughts on “Local analysis in macroeconomics”

1. Quentin says:

Unfortunately, “It works in physics therefore it must work in economics ” is not a convincing argument at all.
In physics, one is dealing with physical systems, in economics one is dealing with social systems. There is no reason to believe, a priori, that what works in one wll work in the other.
Physicists have very rigorous falsifiability criterea for testing their theories. Economists don’t. We have mountains of evidence that General Relativity works, ie it has not been falsified -going back to Eddington’s expedition in 1919. There is no comparable evidence for the models Judd is using.

2. Quentin says:

A brief addendum to by previous post:
Judd seems to be confusing the properties of a formal system with the properties of the real world to which he is applying that formal system.

3. Absolutely, economics and physics are talking about different things. What specific argument is there that says local analysis doesn’t work in economics but does work in physics? What justifications of its use in physics don’t apply to economics?

These different systems of equations describe different phenomenon, sure, but there’s nothing a priori that says analyzing economic-flavored equations should be different from analyzing physics-flavored ones.

I disagree about falsifiability in economics but its beside the point of this post. BTW, GR hasn’t been falsified under the assumption that the actual universe isn’t far away from the no mass equilibrium.

Also, Judd is not confused in the way you say he is. He’s only talking about formal systems and in any case, how does one do “local analysis” (in the sense of this post) on the actual economy?

4. Quentin says:

( Perhaps my comments were more suited to your previous post http://www.ambrosini.us/wordpress/2009/05/was-newtonian-physics-refuted/ )

“… he defended so-called perterbation methods by appealing to the authority of physics. They do it, so its ok for us to do it.”

He may well be right, but this is a silly defense.

“What justifications of its use in physics don’t apply to economics?”

Not talking about local analysis in particular, but about formal systems in general.
Actually there is no logical justification for its use in physics either. It is the ‘unreasonable effectiveness of mathematics in the natural sciences’ (Wigner). Physicists use it because it works.
That it works is a purely empirical justification. It clearly applies to physics but so far no one has provided any evidence that it can be consistently applied to human behaviour – even behaviour of groups.

“I disagree about falsifiability in economics but its beside the point of this post. BTW, GR hasn’t been falsified under the assumption that the actual universe isn’t far away from the no mass equilibrium ”

How do you define falsifiability? I am using it in the sense of Popper. ie to be falsifiable, a theory has to make risky predictions. It should predict things, that in the absence of that theory we would not have expected. In case of GR one such prediction involved the bending of light.

“These different systems of equations describe different phenomenon, sure, but there’s nothing a priori that says analyzing economic-flavored equations should be different from analyzing physics-flavored ones.”

True. It doesn’t matter what flavor a formal system has. It would be useful to recall Russell’s definition of a formal system as one “in which we do not not know what we are talking about, nor whether what we are saying is true”.

My point was that these equations may not apply to the real world economy. Just because you give the equations an economic ‘flavor’ doesn’t mean anything at all. Therefore doing local analysis and extrapolating becomes meaning less. Is economics an independent discipline or is it a poor man’s physics? Can economic systems be modelled as dynamic physical systems ? The burden of proof lies with economists. They are yet to provide any convincing evidence. Of course this is not a criticism of just New Keynesian Economics but of much of modern macro.

5. I wouldn’t argue that the equations economists study perfectly describe the economy and I agree arguments from authority are silly (but this one was funny).

That said, as an economist I find formal systems useful for my study of economics. I write down equations and see if actual behavior matches predicted behavior. That to me, is the point of writing down such equations. Has there been a general proof that formal systems can’t be used in this way?