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Blogs review: Getting rid of the Euler equation

What’s at stake: There has been a new round of discussions on the limits of DSGE models over the past two weeks in the econblogosphere. What started as a general conversation on whether DSGE models (see last section) have failed the market test – in the sense that they are barely used by investors – have turned into a specific discussion on the problems associated with what Noah Smith calls “the equation at the core of modern macro”: the Euler equation. 

By: Date: February 13, 2014 Topic: Global Economics & Governance

What’s at stake: There has been a new round of discussions on the limits of DSGE models over the past two weeks in the econblogosphere. What started as a general conversation on whether DSGE models (see last section) have failed the market test – in the sense that they are barely used by investors – have turned into a specific discussion on the problems associated with what Noah Smith calls “the equation at the core of modern macro”: the Euler equation. 

The equation at the core of modern macro

Noah Smith reports that Martin Eichenbaum (of the Christiano-Eichenbaum-Evans model, which was the basis for the later Smets-Wouters model that has become the standard at central banks) said that “maybe next time [we update our model], we can finally get rid of the … Euler Equation." This equation underlies every DSGE model you’ll ever see, and drives much of modern macro’s idea of how the economy works. So why is Eichenbaum, one of the deans of modern macro, pooh-poohing it? Simple: Because it doesn’t fit the data. Eichenbaum uses Euler Equations in his models because they’re the only game in town, but he hopes to replace them someday, because they just don’t seem to fit the facts.

Noah Smith reports explains the Consumption Euler (pronounced "oiler") Equation is sort of like the Flux Capacitor that powers all modern "DSGE" macro models. Here’s a simple two-period version of it:

Basically, it says that how much you decide to consume today vs. tomorrow is determined by the interest rate (which is how much you get paid to put off your consumption till tomorrow), the time preference rate (which is how impatient you are) and your expected marginal utility of consumption (which is your desire to consume in the first place). When the equation appears in a macro model, "you" typically means "the entire economy".

Carola Binder writes that it is really the D of DSGE that brings in the Euler equations. Optimization problems whether deterministic or stochastic, whether partial or general equilibrium, have first-order conditions. Dynamic optimization problems have more than one time period, so you can have first-order conditions in consumption in different time periods. Combine these first-order conditions in consumption with a budget constraint and you get an Euler equation – whether or not you are writing down a DSGE model. The most obvious ways to get rid of the Euler equation are to get rid of optimization (a la Campbell and Mankiw 1991), add other constraints (liquidity constraints, incomplete markets), or pick weird preference relations that make utility non-time-separable (a la Campbell Cochrane 1999). 

The empirical literature on the Euler equation

Christopher D. Carroll writes that estimation of Euler equations has occupied a central place in consumption research over the more than twenty years since Hall (1978) first derived and tested the consumption Euler equation. Unfortunately, despite scores of careful empirical studies using household data, Euler equation estimation has not fulfilled its early promise to reliably uncover preference parameters like the intertemporal elasticity of substitution. Even more frustrating, the model does not even seem to fail in a consistent way: Some studies find strong evidence of ‘excess sensitivity’ of consumption to predictable income growth, while others find little or no excess sensitivity.

Matthew B. Canzoneri, Robert E. Cumby and Behzad T. Diba write that interest rates implied by combining the dynamics of consumption and inflation observed in U.S. data with Euler equations derived from several specifications for preferences exhibit behavior that differs strikingly from that of money market interest rates. The authors show that the rates implied by consumption Euler equations and the money market rate are not highly correlated. This result raises a problem for standard macroeconomic models, which equate the Euler equation rate with the money market rate.

Andy Harless writes that these studies make (implicitly or explicitly) the identifying assumption that preferences are constant over time. But if shocks to preferences (and specifically to the time preference parameter) are driving the data, then you would expect interest rates to be higher exactly when people want to consume more. In that case, the Euler equation isn’t wrong; it’s just not being used properly. Of course economists who want to keep clear of the Lucas critique have an incentive to assume constant preferences, because once you admit that preferences can change, you must start to worry that they can be influenced by policy, and probably technology can too, so the prospect for ever having robust structural models starts to diminish.

DSGE models and the market test

Noah Smith writes that DSGE models have failed the market test since private-sector firms don’t hire anyone to make DSGE models, implement DSGE models, or even scan the DSGE literature. There are a lot of firms that make macro bets in the finance industry – investment banks, macro hedge funds, bond funds. To my knowledge, none of these firms spends one thin dime on DSGE. I’ve called and emailed everyone I could think of who knows what financial-industry macroeconomists do, and they’re all unanimous – they’ve never heard of anyone in finance using a DSGE model. DSGE models (not just "Freshwater" models, I mean the whole kit & caboodle) have failed a key test of usefulness. Their main selling point – satisfying the Lucas critique – should

make them very valuable to industry. But industry shuns them. Many economic technologies pass the industry test. Companies pay people lots of money to use auction theory. Companies pay people lots of money to use vector autoregressions. Companies pay people lots of money to use matching models. But companies do not, as far as I can tell, pay people lots of money to use DSGE to predict the effects of government policy. Maybe this will change someday, but it’s been 32 years, and no one’s touching these things.

Tony Yates writes that there are quite a few private sector people doing DSGE modeling and the reason these people are doing it is because they know central banks are doing it.  And if everybody in the central banking community is doing it, you can see why it might pay the private sector economist to be doing it.  If they think that central banks are actually using those critters to set policy, they might be able to get their clients an edge by figuring out what those DSGE models will be telling central banks. 


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