D S G E — What’s Not to Like?

Matthew of Separating Hyperplanes recently tweeted “When folks dismiss DSGE as a class, I wonder which of D, S, G, or E they think is wrong”. It’s an argument I’ve seen before — I think Simon Wren-Lewis has made it, though I cannot find the post — are critics unhappy with the Dynamic, Stochastic, General or Equilibrium part of DSGE? The implication is that any macroeconomic model worth its salt would include most or all of these. On its surface, it’s an entirely reasonable point — but it’s also completely misleading.

At a basic level, just because a model is labelled a ‘Dynamic Stochastic General Equilibrium’ model, that doesn’t mean it deals with any of these components satisfactorily. We need to ask what dynamics, stochastics and general equilibrium actually mean in the models. I’ll do this part by part to illustrate some of the main points made by critics more thoroughly. I stress that I am not talking about absolutely every DSGE model here — I’m sure some don’t fit my characterisation. But most do, as do the main models which form the basis of teaching, research and policy.

Dynamic. In DSGE models, a representative agent solves a dynamic optimisation problem over an infinite time horizon (this can be in discrete or continuous time). In this sense, the models are obviously ‘dynamic’ — there’s time, right? But the dynamics in DSGE models are usually quite superficial. Time only enters the problem through the discount function, which is used to reduce the weight of utility in future periods. Mathematically, the resultant problem is of limited complexity, resulting (in the case of continuous time) at worst in a class of problems called ‘autonomous second order differential equations’ — the kind of things qualified mathematicians can do in their sleep (even I can solve them!).

The kind of solutions you get for these differential equations are usually glorified exponential functions, which either tend to a steady-state equilibrium state or else completely break down in either direction (runaway growth or zero employment). Often you end up with the kind of nice looking monotonic curve which economists love. More modern DSGE models sometimes need to be solved numerically, but the result usually looks similar. In other words, you don’t see the kind of cyclical, or crash-prone behaviour we observe in the real macroeconomy. To get that kind of behaviour you need to start looking at things like non-autonomous differential equations and beyond (or else impose a ‘crash’ by shocking the model from without).

There’s more. Since DSGE models are simple enough that they usually tend towards a steady-state equilibrium, they are often simply solved for this equilibrium when comparing the effects of parameter value or policy regime changes, rather than looking at the path of the entire economy. Similarly, when some ‘shock’ hits a model, the transition path is modelled between the steady state equilibria before and after the shock. In other words, what limited dynamics exist in DSGE models are omitted when discussing the main implications of the models, taking us back to the world of comparative statics.

Stochastic. As with dynamics, DSGE models only deal with stochastic behaviour in a stylised sense: by imposing terms which are stochastic — usually normally distributed — into the rest of the model. At worst these are just additive error terms with mean zero which barely even affect the main predictions of the model. At best, they are things like stochastic productivity, which has more significant implications but still just takes an existing parameter and makes it stochastic. The main conclusions of the model will generally still follow, albeit with more uncertainty and volatility. For example, in the Euler equation — which (assuming discrete time) takes consumption at period t and gives you consumption at period t+1 — you just need to replace future consumption with the expected value of future consumption when you go from the deterministic to the stochastic version of the model.

This contrasts with the kind of stochastic calculus used in mathematics, physics and indeed in other areas of economics such as finance. Here it assumed that changes in a variable are stochastic, depending on the random incremental behaviour of other variables (including time — stochastic calculus ties in well with more substantive dynamics). Once more, the behaviour of the system becomes much more complex and interdependent. It’s not guaranteed that the qualitative behaviour of key variables will remain the same when this kind of stochasticity is introduced.

General. In economics, ‘general’ means ‘including the whole system’ so that interactions between different parts of the economy can be modelled. Again, while I don’t have any problem with this in principle, economic models almost always (always?) only model interactions through the price mechanism. Non-price communication is ruled out, which is something that everyone from Keynes to network sociologists to modern Agent-Based Modellers consider of utmost importance for understand trends, financial panics, peer comparisons/influence and so forth. To be truly general, models must assume people act based on more information than price signals.

Equilibrium. Equilibrium gets a fair amount of attention from critics of economics, and there have been attempts in the blogosphere to push back against this, since ‘equilibrium’ can mean something broader than what the critics have in mind. In particular, the ‘equilibrium’ in a DSGE model refers to the entire time path of the economy, while the ‘steady-state equilibrium’ is the unchanging outcome most people would think of as an equilibrium (one could be forgiven for thinking economists are trying to confuse people).

However, we should be careful not to define equilibrium so broadly that it is meaningless, as the term still carries with it some implications. My interpretation is that for a situation to be an equilibrium, something must not be changing. In a steady-state equilibrium-or an object at rest-nothing relevant is changing. In the time-path equilibrium of a DSGE model what isn’t changing is the relationship between key variables. Consumption, for example, might be growing steadily or even fluctuate as time goes on, but no matter what point we’re at in time it will be governed by the same Euler equation.

The implication of this is that there’s no real path dependence in DSGE models. Everything is malleable, reversible and generally shocks will only cause temporary disruption. The kind of qualitative changes you can get from a tiny change in initial conditions in more chaotic models is ruled out completely. Tractability permitting, the functions which govern the behaviour of key variables can be specified at the outset and come what may, these functions will not change. This much is guaranteed by the imposition of optimal solutions and market-clearing conditions, which create strong tendencies towards stability even in the presence of frictions.

I think this point about superficial use of terms could be broadened to other areas of economics, but I will stop here for now. This argument seems relevant in the context of Roger Farmer’s call for post-Keynesians to embrace DSGE (and yes I am aware of his counterargument, but I’m not convinced a lack of evidence is reason to favour DSGE in particular). In my opinion and despite their fancy name, below the surface DSGE models do not do what they say on the tin.



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