Monday, November 12, 2012

Where DSGE Modeling Needs to Go Next: Away from the Taylor Rule

In September I had grand plans to post something interesting at least once a week, but as you can see from my archives, those plans have not been carried out. 

I'm blaming Paul Krugman (he gets blamed for everything anyway), Gauti Eggertson, and a paper they wrote called "Debt, Deleveraging and the Liquidity Crisis: A Fisher-Minksy-Koo Approach." I stumbled upon it when Krugman casually linked to it in one of his NYT blog posts.

As an economics undergrad I read enough formal economic papers to become familiar with the standard progression: 
  1. Setup the problem by defining one or two "agents"with utility functions, budget constraints, and possibly production functions that incorporate a fair shake of "simplifying assumptions"
  2. Introduce a "trick," some specific item like a price or a new technology that makes the whole thing a little bit closer to reality than the setup
  3. Do some math and work out some relationships ("The second derivative shows that when this increases, this increases also! Whoohoo!") 
  4. Get some data from somewhere, do some statistical analysis and show that the relationships suggested by theory do in fact hold in reality 

But I had only heard about what economists call a "Dynamic Stochastic General Equilibrium" or "DSGE" model when I read Krugman and Eggertson's paper.  As it turns out, it's really not that different; a DSGE paper follows the same basic setup as above, but leaves off  4. and tries to take away as many "simplifying assumptions" in 1. and incorporate as many "tricks" in 2. before self-destructing due to (as Bennett McCallum put it) "blizzards of notation."

I often think of modern macroeconomics as a collective attempt to create the perfect DSGE model. "Tricks" that gain critical acceptance contribute to a living standard that is carried by the academic consciousness to the next generation of critics and contributors. The living DSGE model is important, because economists supposedly consult it to make policy recommendations, but in fact most find the blizzards of notation so difficult to navigate that for many questions they refer either to a handful of basic principles that are right in theory but grossly oversimplified and almost always wrong in practice, or to a handful of old models that have been proven quite wrong in theory but are still somehow mostly right in practice.  

What's worse, while the living DSGE model has grown far enough away from the handful of principles right in theory to be complicated, it has not grown close enough to the handful of old models to be entirely correct, so those who manage to fight their way thought the storm end up with predictions that are neither easy to obtain nor particularly useful.  The volume of criticism in this vein in the economics blogosphere is overwhelming; you can find some examples here, here and here.

"A Fisher-Minsky-Koo Approach" is Krugman & Eggertson's 2010 attempt to incorporate debt a little more realistically into the standard DSGE model. It's not a full model by any means; they don't include many accepted "tricks" in an effort to keep their paper comprehensible, but as far as I can tell, it's one of the only serious attempts to do so by a mainstream macroeconomist after the financial crisis, a fact that I find incredibly depressing.

Krugman wrote a little on Vox about why he & Eggertson embarked on a Fisher-Minsky-Koo and what "tricks" they tried to incorporate. I've color coded it for emphasis:

The current preoccupation with debt harks back to a long tradition in economic analysis, from Fisher’s (1933) theory of debt deflation to Minsky’s (1986) back-in-vogue work on financial instability to Koo’s (2008) concept of balance-sheet recessions. Yet despite the prominence of debt in popular discussion of our current economic difficulties and the long tradition of invoking debt as a key factor in major economic contractions, there is a surprising lack of models – especially models of monetary and fiscal policy – of economic policy that correspond at all closely to the concerns about debt that dominate practical discourse. Even now, much analysis (including my own) is done in terms of representative-agent models, which by definition can’t deal with the consequences of the fact that some people are debtors while others are creditors.

I really admire Krugman & Eggertson's work. (I also admire Minksy. I have mixed feelings about Fisher and Koo. A longer story).  But there are still some problems. Here are three
  1. It's still horribly complicatedI still don't understand it completely (that said, you might want to disregard this entire post).  With some effort the authors could probably translate it down into usable parcels, but it would still be unwieldy and Krugman himself uses the good old IS-LM model for much of his analysis. 
  2. They rely on two representative agents who don't represent reality, a "borrower" who always borrows up to an exogenous limit, and a "saver" who always lends up to the same limit. The authors are conscious of this weakness, and say: "We have not tried to model the sources of the debt limit, nor will we try to in this paper. Clearly, however, we should think of this limit as a proxy for general views about what level of leverage on the part of borrowers is “safe”, posing an acceptable risk either of unintentional default or of creating some kind of moral hazard."
  3. They rely on a Taylor rule.  Ever since Michael Woodford published Interest and Prices in 2003, standard DSGE models have been constructed to solve for three variables, the price level, the interest rate, and the output gap or unemployment, from three equations, the household consumption function that approximates aggregate demand and usually takes the form of a Euler Equation, the firm production function that approximates aggregate supply and usually takes the form of a New Keynsian Phillips Curve, and the central bank reaction function that sets the interest rate and usually takes the form of a Taylor rule.   I take issue with the Taylor rule for three reasons:
    1. First, because not all economies have central banks, a truly general solution shouldn't require one; supply and demand should be enough. I think most macroeconomists would feel similarly if they honestly examined their feelings, but the problem is math: there are three unknowns, so the model needs three equations.  (150 years later we're still not that much further than Walrasian counting-- this comment is unjustly snide)
    2. Second, the inclusion of the Taylor rule necessarily excludes the influence of other financial institutions-ie the 1.3 trillion dollar US financial sector-on interest rates, and therefore also on the other two variables, the price level and the output gap. Perhaps that's why macroeconomic models of the crisis have been so slow to come out; because an essential assumption of the living model implies it didn't happen.  
    3. Third, in an international world, there are many central banks, not one, and unless they are coordinated by a binding international body (which has been proposed many times but never successfully enacted), the living model can not explain international macro phenomena.
Now the question is, can macroeconomists fix these three problems before I'm too old?  Maybe. Maybe not. Maybe I just don't understand the problems yet. 

Unintentionally, I've spent the last two months trying to address these problems by building a DSGE model of my own. I say unintentionally, because as I mentioned earlier, I had never seen a DSGE model when I first downloaded A Fisher-Minsky Koo, and I literally didn't know what I was trying to do, until after I had been thinking about it for about a week and was hooked.  It's probably compeletely wrong, but I'll try to post what I have so far to this blog in the next month, if only to keep myself accountable.