Mainly for economists
Ever since I started blogging I have written posts on macroeconomic methodology. One objective was to try and convince fellow macroeconomists that Structural Econometric Models (SEMs), with their ad hoc blend of theory and data fitting, were not some old fashioned dinosaur, but a perfectly viable way to do macroeconomics and macroeconomic policy. I wrote this with the experience of having built and published papers with both SEMs and DSGE models.
Olivier Blanchard’s third post on DSGE models does exactly the same thing. The only slight confusion is that he calls them ‘policy models’, but when he writes
“Models in this class should fit the main characteristics of the data, including dynamics, and allow for policy analysis and counterfactuals.”
he can only mean SEMs.  I prefer SEMs to policy models because SEMs describe what is in the tin: structural because they utilise lots of theory, but econometric because they try and match the data.
In a tweet, Noah Smith says he is puzzled. “What else is the point of DSGEs??” besides advising policy he asks? This post tries to help him and others see how the two classes of model can work together.
The way I would estimate a SEM today (but not necessarily the only valid way) would be to start with an elaborate DSGE model. But rather than estimate this model using Bayesian methods, I would use it as a theoretical template with which to start econometric work, either on an equation by equation basis or as a set of sub-systems. Where lag structures or cross equation restrictions were clearly rejected by the data, I would change the model to more closely match the data. If some variables had strong power in explaining others but were not in the DSGE specification, but I could think of reasons for a causal relationship (i.e. why the DSGE specification was inadequate), I would include them in the model. That would become the SEM. 
If that sounds terribly ad hoc to you, that is right. SEMs are an eclectic mix of theory and data. But SEMs will still be useful to academics and policymakers who want to work with a model that is reasonably close to the data. What those I call DSGE purists have to admit is that because DSGE models do not match the data in many respects, they are misspecified and therefore any policy advice from them is invalid. The fact that you can be sure they satisfy the Lucas critique is not sufficient compensation for this misspecification.
By setting the relationship between a DSGE and a SEM in the way I have, it makes it clear why both types of model will continue to be used, and how SEMs can take their theoretical lead from DSGE models. SEMs are also useful for DSGE model development because their departures from DSGEs provide a whole list of potential puzzles for DSGE theorists to investigate. Maybe one day DSGE will get so good at matching the data that we no longer need SEMs, but we are a long way from that.
Will what Blanchard and I call for happen? It already does to a large extent at the Fed: as Blanchard says what is effectively their main model is a SEM. The Bank of England uses a DSGE model, and the MPC would get more useful advice from its staff if this was replaced by a SEM. The real problem is with academics, and in particular (as Blanchard again identified in an earlier post) journal editors. Of course most academics will go on using DSGE, and I have no problem with that. But the few who do instead decide to use a SEM should not be automatically shut out from the pages of the top journals. They would be at present, and I’m not confident - even with Blanchard’s intervention - that this is going to change anytime soon.
 What Ray Fair, longtime builder and user of his own SEM, calls Cowles Commission models.
 Something like this could have happened when the Bank of England built BEQM, a model I was consultant on. Instead the Bank chose a core/periphery structure which was interesting, but ultimately too complex even for the economists at the Bank.