## Economics textbooks — when the model becomes the message

14 October, 2015 at 10:43 | Posted in Economics | Leave a commentWendy Carlin and David Soskice have a new intermediate macroeonomics textbook — *Macroeconomics: Institutions, Instability, and the Financial System* (Oxford University Press 2015) — out on the market. It builds more than most other intermediate macroeconomics textbooks on supplying the student with a “systematic way of thinking through problems” with the help of formal-mathematical models.

Carlin and Soskice explicitly adapts a ‘New Keynesian’ framework including price rigidities and adding a financial system to the usual neoclassical macroeconomic set-up. But although I find things like the latter amendment an improvement, it’s definitely more difficult to swallow their methodological stance, and especially their non-problematized acceptance of the need for macroeconomic microfoundations.

Some months ago, another sorta-kinda ‘New Keynesian’, Paul Krugman, argued on his blog that the problem with the academic profession is that some macroeconomists aren’t “bothered to actually figure out” how the New Keynesian model with its Euler conditions — “based on the assumption that people have perfect access to capital markets, so that they can borrow and lend at the same rate” — really works. According to Krugman, this shouldn’t be hard at all — “at least it shouldn’t be for anyone with a graduate training in economics.”

Carlin & Soskice seem to share Krugman’s attitude. From the first page of the book they start to elaborate their preferred 3-equations ‘New Keynesian’ macromodel. And after twenty-two pages they have already come to specifying the demand side with the help of the Permanent Income Hypothesis and its Euler equations.

But if people — not the representative agent — at least sometimes can’t help being off their labour supply curve — as in the real world — then what are these hordes of Euler equations that you find *ad nauseam *in these ‘New Keynesian’ macromodels gonna help us?

It is clear that the New Keynesian model, even extended to allow, say, for presence of investment and capital accumulation, or for the presence of both discrete price and nominal wage setting, is still just a toy model, and that it lacks many of the details which might be needed to understand fluctuations …

One striking (and unpleasant) characteristic of the basic New Keynesian model is that there is no unemployment! Movements take place along a labor supply curve, either at the intensive margin (with workers varying hours) or at the extensive margin (with workers deciding whether or not to participate). One has a sense, however, that this may give a misleading description of fluctuations, in positive terms, and, even more so, in normative terms: The welfare cost of fluctuations is often thought to fall disproportionately on the unemployed.

Yours truly’s doubts regarding the ‘New Keynesian’ modelers’ obsession with Euler equations is basically that, as with so many other assumptions in ‘modern’ macroeconomics, the Euler equations don’t fit reality.

For the uninitiated, the Consumption Euler Equation is sort of like the Flux Capacitor that powers all modern “DSGE” macro models … 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 til 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”.

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. The thing is, we can measure people’s consumption, and we can measure interest rates. If we make an assumption about people’s preferences, we can just go see if the Euler Equation is right or not!

[Martin] Eichenbaum was kind enough to refer me to the literature that tries to compare the Euler Equation to the data. The classic paper is Hansen and Singleton (1982), which found little support for the equation. But Eichenbaum also pointed me to this 2006 paper by Canzoneri, Cumby, and Diba of Georgetown (published version here), which provides simpler but more damning evidence against the Euler Equation …

[T]he Euler Equation says that if interest rates are high, you put off consumption more. That makes sense, right? Money markets basically pay you not to consume today. The more they pay you, the more you should keep your money in the money market and wait to consume until tomorrow.

But what Canzoneri et al. show is that this is not how people behave. The times when interest rates are high are times when people tend to be consuming more, not less.

OK, but what about that little assumption that we know people’s preferences? What if we’ve simply put the wrong utility function into the Euler Equation? Could this explain why people consume more during times when interest rates are high?

Well, Canzoneri et al. try out other utility functions that have become popular in recent years. The most popular alternative is habit formation … But when Canzoneri et al. put in habit formation, they find that the Euler Equation still contradicts the data …

Canzoneri et al. experiment with other types of preferences, including the other most popular alternative … No matter what we assume that people want, their behavior is not consistent with the Euler Equation …

If this paper is right … then essentially all modern DSGE-type macro models currently in use are suspect. The consumption Euler Equation is an important part of nearly any such model, and if it’s just wrong, it’s hard to see how those models will work.

In the standard neoclassical consumption model — underpinning Carlin’s and Soskice’s microfounded macroeconomic modeling — people are basically portrayed as treating time as a dichotomous phenomenon – *today* and the *future — *when contemplating making decisions and acting. How much should one consume today and how much in the future? Facing an intertemporal budget constraint of the form

*c _{t} + c_{f}/(1+r) = f_{t} + y_{t} + y_{f}/(1+r),*

where c_{t} is consumption today, c_{f} is consumption in the future, f_{t} is holdings of financial assets today, y_{t} is labour incomes today, y_{f} is labour incomes in the future, and r is the real interest rate, and having a lifetime utility function of the form

*U = u(c _{t}) + au(c_{f}),*

where a is the time discounting parameter, the representative agent (consumer) maximizes his utility when

*u´(c _{t}) = a(1+r)u´(c_{f}).*

This expression – the Euler equation – implies that the representative agent (consumer) is indifferent between consuming one more unit today or instead consuming it tomorrow. Typically using a logarithmic function form – u(c) = log c – which gives u´(c) = 1/c, the Euler equation can be rewritten as

*1/c _{t} = a(1+r)(1/c_{f}),*

or

*c _{f}/c_{t} = a(1+r).*

This importantly implies that according to the neoclassical consumption model that changes in the (real) interest rate and the ratio between future and present consumption move in the same direction.

So good, so far. But how about the real world? Is the neoclassical consumption as described in this kind of models in tune with the empirical facts? Not at all — the data and models are as a rule insconsistent!

In the Euler equation we only have one interest rate, equated to the money market rate as set by the central bank. The crux is that — given almost any specification of the utility function – the two rates are actually often found to be strongly *negatively* correlated in the empirical literature:

In this paper, we use U.S. data to calculate the interest rate implied by the Euler equation, and we compare this Euler equation rate with a money market rate. We find the behavior of the money market rate differs significantly from the implied Euler equation rate. This poses a fundamental challenge for models that equate the two rates.

The fact that the two interest rate series do not coincide – and that the spread between the Euler equation rate and the money market rate is generally positive – comes as no surprise; these anomalies have been well documented in the literature on the “equity premium puzzle” and the “risk free rate puzzle.” And the failure of consumption Euler equation models should come as no surprise; there is a sizable literature that tries to fit Euler equations, and generally finds that the data on returns and aggregate consumption are not consistent with the model.

If the spread between the two rates were simply a constant, or a constant plus a little statistical noise, then the problem might not be thought to be very serious. The purpose of this paper is to document something more fundamental – and more problematic – in the relationship between the Euler equation rate and observed money market rates … We compute the implied Euler equation rates for a number of specifications of preferences and find that they are strongly negatively correlated with money market rates …

Our results suggest that the problem is fundamental: alternative specifications of preferences can eliminate the excessive volatility, but they yield an Euler equation rate that is strongly negatively correlated with the money market rate.

All empirical sciences use simplifying or unrealistic assumptions in their modeling activities. That is not the issue – *as long as the assumptions made are not unrealistic in the wrong way or for the wrong reasons*.

Theories are difficult to directly confront with reality. Economists therefore build models of their theories. Those models are *representations* that are *directly* examined and manipulated to *indirectly* say something about the target systems.

But models do not only face theory. They also have to look to the world. Being able to model a “credible world,” a world that somehow could be considered real or *similar* to the real world, is not the same as investigating the real world. Even though all theories are false, since they simplify, they may still possibly serve our pursuit of truth. But then they cannot be unrealistic or false in *any* way. The falsehood or unrealisticness has to be* qualified*.

Some of the standard assumptions made in neoclassical economic theory – on rationality, information handling and types of uncertainty – are not possible to make more realistic by “de-idealization” or “successive approximations” without altering the theory and its models fundamentally.

If we cannot show that the mechanisms or causes we isolate and handle in our models are stable, in the sense that what when we export them from are models to our target systems they do not change from one situation to another, then they only hold under *ceteris paribus* conditions and *a fortiori* are of limited value for our understanding, explanation and prediction of our real world target system.

No matter how many convoluted refinements of concepts made in the model, if the “successive approximations” do not result in models similar to reality in the appropriate respects (such as structure, isomorphism etc), the surrogate system becomes a *substitute *system that does not bridge to the world but rather misses its target.

From this methodological pespective yours truly has to conclude that Carlin’s and Soskice’s microfounded macroeconomic model is a rather unimpressive attempt at legitimizing using fictitious idealizations — such as Euler equations — for reasons more to do with model tractability than with a genuine interest of understanding and explaining features of real economies.

As May Brodbeck once had it:

Model ships appear frequently in bottles; model boys in heaven only.

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