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Stephen: "is that the lack of analytical solutions to DSGE models made it hard/impossible to use in empirical work and forecasting."

I'm thinking about your experience in light of my recent post on methodology, which talked about the virtues of models with predictions. Now there you were, realizing that there was a practical problem with the models you were working with, and you had two alternatives. One was to do brutally difficult and technical work that might solve the problem, but was hard to get people to read or publish. The other was to blog instead. You've certainly had way more impact taking the latter route. I'm wondering what it would have taken for the former route to work out for you?

I guess that's in some ways a sociology-of-economics question - what would it have taken for your answer to gain traction?


Thanks for this interesting post. You certainly know more than me about DSGE models, and I found this very informative.

I'd like to comment on one thing you've said. In an environment with inter-temporal maximization, general equilibrium has much stronger implications than simply ensuring that "things add up". That makes it sound innocuous, as though it were simply an accounting identity. In fact, it is a far stronger assertion that requires solving for a unique equilibrium time path across all periods (Samuelson, 1958).

As you said, reasonable people can disagree about modeling choices. I am neither for, nor against, general equilibrium in principle. However, it is more than a simple accounting identity, and it certainly does not come for free. While general equilibrium is an important tool, I suspect we may be miss many insights about the real-world economy by taking for granted the need for such a strong notion of equilibrium.

I'm sure you were well aware of all this, and I hope this doesn't seem too picky. Just thought it added to the discussion. Again, great post!

You, or your professor, have re-discovered Pontryagin's minimum principle, which I agree is brilliant. It is also well known that it is much harder to find stochastic solutions to a global approach such as this versus Bellman's iterative approach. However, it has been done and there are papers on stochastic pontryagin solutions that the budding grad student may wish to consult.

I don't think this has much to do with whether DSGE approach is a "dead end" as declared by Axel Leijonhufvud and many others, or how much insight can be gained from them. The problem is not the well-behavedness of the solutions to linear approximation but the well-behavedness of the model to deformations as well as the aggregation problem when many individuals with different endowments are each optimizing a different value function, each possibly using different approximation techniques.

In physics, there is one decision maker -- "nature" -- and one value function. But in economics, you may have 2 actors with mutually inconsistent expectations of future prices, different value functions, and each using a different approximation to determine their present day consumption. Even if there were complete markets for every possible opinion that someone may have about the future, nothing mandates participation in these expectations markets.

But the two aggregate solutions [(c_1(t), l_1(t)), (c_2(t), l_2(t))] of two optimization problems with two different expectations of future prices is not in general, the solution of a single multi-period optimization problem with a single expectation of future prices. Add in a hundred million decision makers, and it is easy to see why some people don't see a lot of value in this approach, and prefer to just look at known patterns in aggregate behavior.

Moreover, as every model is only an approximation to the underlying behavior being modelled, there is no point in considering models whose conclusions are reversed when small terms are added to the value function, or whose solutions differ discontinuously when they are calculated by optimizing over a truncated number of periods versus over all periods.

But dynamic optimization problems famously do not have this property in general. Other disciplines, such as physics, do restrict themselves to only considering certain functional forms in their Lagrangians for this reason.

rsj: No, that's not Pontryagin's minimum principle. The minimization is with respect to the *exogenous* variable p, not the control variable.

Dan: To the extent that equilibrium paths must be consistent with the laws of motion, GE still amounts to making sure that things add up.

Frances: That really is - as they say around these parts - la question qui tue. Maybe I should have gone to a higher-profile school for my PhD.

It is interesting to note that economists assume unbounded rationality, but in fact the Taylor approx implies some kind of bounded rationality of the model builder.

Interesting article. In fact, we face the exact same problem with economic growth models, endogenous or not. Indirect methods (Pontyagrin's Maximum Principle) that solve the underlying optimal control problem are somewhat limited due to the linearization/log-linearization and the numerical tools available boil down to solving ordinary differential equations derived from the necessary optimality conditions.

We are about to publish an article on the Journal of Economic Dynamics and Control that allows one to use a direct method to solve infinite-horizon nonlinear growth models without having to linearize. The NLP problem is fully nonlinear, with all its multiple-equilibria nuisances. But still, a fairer approximation of reality. Anyway, this allows for such interesting things as studying multiple sequential shocks or time-invariant tax policies (which in the analytical version are intractable problems).

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