Posts Tagged DSGE

The DSGE Dance

Something about the way economists construct their models doesn’t sit right.

Economic models are often acknowledged to be unrealistic, and Friedmanite ‘assumptions don’t matter‘ style arguments are used to justify this approach. The result is that internal mechanics aren’t really closely examined. However, when it suits them, economists are prepared to hold up internal mechanics to empirical verification – usually in order to preserve key properties and mathematical relevance. The result is that models are constructed in such a way that, instead of trying to explain how the economy works, they deliberately avoid both difficult empirical and difficult logical questions. This is particularly noticeable with the Dynamic Stochastic General Equilibrium (DSGE) models that are commonly employed in macroeconomics.

Here’s a brief overview of how DSGE models work: the economy is assumed to consist of various optimising agents: firms, households, a central bank and so forth. The behaviour of these agents is specified by a system of equations, which is then solved to give the time path of the economy: inflation, unemployment, growth and so forth. Agents usually have rational expectations, and goods markets tend to clear (supply equals demand), though various ‘frictions’ may get in the way of this. Each DSGE model will usually focus on one or two ‘frictions’ to try and isolate key causal links in the economy.

Let me also say that I am approaching this issue tentatively, as I in no way claim to have an in depth understanding of the mathematics used in DSGE models. But then, this isn’t really the issue: if somebody objects to utility as a concept, they don’t need to be able to solve a consumer optimisation problem; if someone objects to the idea that technology shocks cause recessions, they don’t need to be able to solve an RBC model. To use a tired analogy, I know nothing of the maths of epicycles, but I know it is an inaccurate description of planetary rotation. While there is every possibility I’m wrong about the DSGE approach, that possibility doesn’t rest on the mathematics.

Perverse properties?

DSGE has been around for a while, and along the line several ‘conundrums’ or inconsistencies have been discovered that could potentially undermine the approach. There are two main examples of this, both of which have similar implications: the possibility of multiple equilibria and therefore indeterminacy. I’ll go over them briefly, although won’t get into the details.

The first example is the Sonnenschein-Mandel-Debreu (SMD) Theorem. Broadly speaking, this states that although we can derive strictly downward sloping demand curves from individually optimising agents, once we aggregate up to the whole economy, the interaction between agents and resultant emergent properties mean that demand curves could have any shape. This creates the possibility of multiple equilibria, so logically the system could end up in any number of places. The SMD condition is sometimes known as the ‘anything goes’ theorem, as it implies that an economy in general equilibrium could potentially exhibit all sorts of behaviour.

The second example is capital reswitching, the possibility of which was demonstrated by Piero Sraffa in his Magnum opus Production of Commodities by Means of CommoditiesThe basic lesson is that the value of capital changes as the distribution (between profits and wages) changes, which means that one method of production can be profitable at both low and high rates of interest, while another is profitable in between. This is in contrast to the neoclassical approach, which suggests that the capital invested will increase (decrease) as the interest rate decreases (increases). The result is a non-linear relationship, and therefore the possibility of multiple equilibria.

That these issues could potentially cause problems is well known, but economists don’t see it as a problem. Here is an anonymous quote on the matter:

We’ve known for a long time one can construct GE models with perverse properties, but the logical possibility speaks nothing about empirical relevance. All these criticisms prove is that we cannot guarantee some properties hold a priori – but that’s not what we claim anyway, since we’re real economists, not austrian charlatans. Chanting that sole logical possibility of counterexamples by itself destroys large portions of economic theory is just idiotic.

As it happens, I agree: based on available evidence, neither reswitching nor the SMD theorem are empirically relevant. For everyday goods, it is reasonable to suppose that demand will rise as price falls, and vice versa.  Firms also rarely switch their techniques in the real world (though reswitching isn’t the main takeaway of the capital debates). So the perspective expressed above seems reasonable – that is, until we stop and consider the nature of DSGE models as a whole.

For the fact is that DSGE models themselves are not “empirically relevant”. They assume that agents are optimising, that markets tend to clear, that the economy is an equilibrium time path. They use ‘log linearisation’, a method which doesn’t even pretend to do anything other make the equations easier to solve by forcibly eliminating the possibility of multiple equilibria. On top of this, they generally display poor empirical corroboration. Overall, the DSGE approach is structured toward preserving the use of microfoundations, while at the same time invoking various – often unrealistic – processes in order to generate something resembling dynamic behaviour.

Economists tacitly acknowledge this, as they will usually say that they use this type of model to highlight one or two key mechanics, rather than to attempt to build a comprehensive model of the economy. Ask an economist if people really maximise utility; if the economy is in equilibrium; if markets clear, and they will likely answer “no, but it’s a simplification, designed to highlight problem x”. Yet when questioned about some of the more surreal logical consequences of all of the ‘simplifications’ made, economists will appeal to the real world. This is not a coherent perspective.

Some methodology

Neoclassical economics uses an ‘axiomatic deductive‘ approach, attempting to logically deduce theories from basic axioms about individual choice under scarcity. Economists have a stock of reasons to do this: it is ‘rigorous’; it bases models on policy invariant parameters; it incorporates the fact that the economy ultimately consists of agents consciously making decisions, etc. If you were to suggest internal mechanics based on simple empirical observations, conventional macroeconomists would likely reject your approach.

Modern DSGE models are constructed using these types of axioms, in such a way that they avoid logical conundrums like SMD conditions and reswitching. This allows macroeconomists to draw clear mathematical implications from their models, while the assumptions are justified on the grounds of empiricism: crazily shaped demand curves and technique switching are not often observed, so we’ll leave them out. Yet the model as a whole has very little to do with empiricism, and economists rarely claim otherwise. What we end up with is a clearly unrealistic model, constructed not in the name of empirical relevance or logical consistency, but in the name of preserving key conclusions and mathematical tractability. How exactly can we say this type of modelling informs us about how the economy works? This selective methodology has all the marks of Imre Lakatos’ degenerative research program.

A consequence of this methodological ‘dance’ is that it can be difficult to draw conclusions about which DSGE models are potentially sound. One example of this came from the blogosphere, via Noah Smith. Though Noah has previously criticised DSGE models, he recently noted – approvingly – that there exists a DSGE model that is quite consistent with the behaviour of key economic variables during the financial crisis. This increased my respect for DSGE somewhat, but my immediate conclusion still wasn’t “great! That model is my new mainstay”. After all, so many DSGE models exist that it’s highly probable that some simplistic curve fitting would make one seem plausible. Instead, I was concerned with what’s going on under the bonnet of the model – is it representative of the actual behaviour of the economy?

Sadly, the answer is no. Said DSGE model includes many unrealistic mechanics: most of the key behaviour appears to be determined by exogenous ‘shocks’  to risk, investment, productivity etc without any explanation. This includes the oft-mocked ‘Calvo fairy’, which imitates sticky prices by assigning a probability to firms randomly changing their prices at any given point. Presumably, this behaviour is justified on the grounds that all models are unrealistic in one way or another. But if we have constructed the model to avoid key problems – such as SMD and reswitching, or by log-linearising it – on the grounds that the problems are unrealistic, how can we justify using something as blatantly unrealistic as the Calvo fairy? Either we shed a harsh light on all internal mechanics, or on none.

Hence, even though the shoe superficially fits this DSGE model, I know that I’d be incredibly reluctant to use it if I were working at a Central Bank. This is one of the reasons why I think Steve Keen’s model – which Noah Smith has chastised – is superior: it may not exhibit behaviour that closely mirrors the path of the global economy from 2008-12, but it exhibits similar volatility, and the internal mechanics match up far more nicely than many (every?) neoclassical model. It seems to me that understanding key indicators and causal mechanisms is a far more modest, and credible, claim than being able to predict the quarter-by-quarter movement of GDP. Again, if I were ‘in charge’, I’d take the basic Keensian lesson that private debt is key to understanding crises over DSGE any day.

I am aware that DSGE and macro are only a small part of economics, and many economists agree that DSGE – at least in its current form – is yielding no fruit (although these same economists may still be hostile to outside criticism). Nevertheless, I wonder if this problem extends to other areas of economics, as economists can sometimes seem less concerned with explaining economic phenomena than with utilising their preferred approach. I believe internal mechanics are important, and if economists agree, they should expose every aspect of their theories to empirical verification, rather merely those areas which will protect their core conclusions.

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Dynamics and Equilibrium




Keen’s Models








Labour Theory of Value














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Debunking Economics, Part VIII: Macroeconomics, or Applied Microeconomics?


Say’s Law














Macroeconomics after IS/LM









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DSGE, Epicycles and Neoclassical Methodology

Daniel Kuehn asks me to define the difference between incorporating something into a model and ‘adding epicycles‘, as Keen and others so often put it.

As it happens, an essay by Christian Arnsperger & Yanis Varoufakis may provide us with the answer. In this essay, Arnsperger and Varoufakis attempt to define neoclassical methodology, hoping to nullify its lizard-like ability to dispose of certain parts in order to evade criticism. Personally, I think they hit the nail on the head.

They provide three axioms which define neoclassical methodology:

(1) Methodological individualism – the economy is modeled on the basis of the behaviour of individual agents.

(2) Methodological instrumentalism – individuals act in accordance with certain preferences rankings, to attain some end goal that they deem desirable.

(3) Methodological equilibration – given the above two, macroeconomics asks what will happen if we assume equilibrium. Note that this doesn’t  necessarily posit that the system will end up in equilibrium (although that is often the case), but rather seeks to find out what will happen if we use equilibrium as an epistemological starting point.

I will not criticise the axioms here, but suffice to say that this gets to the crux of what the arguments have been about. This methodological core underlies everything from demand-supply to game theory to DSGE.

Much like the assumption of circular orbit, the methodological core of neoclassicism is at all times protected as it develops. Most neoclassical economists don’t think twice about the axioms, and this helps them deny that they are, in fact, ‘neoclassical’, seeing it only as a buzz word used by their enemies.

In fact, neoclassical economics has a habit of preserving not only these three axioms, but also many other assumptions it introduces. For example, take the case of Krugman and Eggertson versus Keen. Keen models the banks as explicit agents and creators of purchasing power, whilst Krugman and Eggertson preserve the ‘banks as intermediaries between savers and borrowers’ line, abstracting them out the economy, and ad-hocing a role for private debt.

You can also see these axioms in criticisms of Keen’s models. Krugman says that there is ‘a lot of implicit theorising’ going on in Keen’s paper. Perhaps this is true and maybe Keen needs to clarify his epistemology, but what Krugman really means – unknowingly, perhaps – is that Keen doesn’t start from the three axioms: he isn’t looking at individual behaviour, instead at the flow of money between agents; nobody is acting in accordance with attaining certain preferences; equilibrium is not used as a starting point. From my experience, I strongly suspect that most mainstream economists feel a similar skepticism when reading Keen’s paper.

I believe that in order for the debate to move forward, these 3 axioms – and others that are protected by the ad hoc style of DSGE – must be focused on and criticised. Otherwise critics will never land a convincing blow, and will be forever accused of straw manning.

* As a note, Austrians, this is why I link you with neoclassicism. The first two certainly define all of Austrian economics, and, at least in the case of Hayek, you also use equilibrium as an epistemological starting point.

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