Dynamic Stochastic General Equilibrium Models in Macroeconomics (DSGEs)

Pretend that the national economy consists of a single person, the "representative agent". This agent owns all the goods, especially all the capital goods, and does all the work in the economy. The agent is greedy for material consumption, and lazy. To consume, which it likes, it must produce, which is a matter of indifference, except that to produce it must work, which it dislikes. If it produces more now than it consumes, it can save the difference as capital goods, which make its future labor more productive. There are also shocks to "technology", i.e., to how effectively it can use capital to turn labor into consumption goods; rather bizarrely, these shocks are both negative and positive, which means that it regularly forgets productive technologies, and not because better replacements have come along.

In addition to being greedy and lazy, the agent is is determined to act now so as to maximize not present utility, but the discounted future stream of utility at all times (since it is also immortal). Fortunately, it is incredibly foresighted, and knows the exact distribution of future shocks to technology. (This distribution is not changed by anything the agent does; or, if you like, it always acts in such a way that its expectations are exactly fulfilled.) Possessing unlimited cognitive resources, it is easy for the agent to solve the resulting dynamic programming problem optimally. This will not lead to a smooth pattern of production, investment and consumption; if, for instance, there is a big negative shock to technology, and shocks are persistent, it becomes rational to slack off now, and enjoy leisure; extra work will be more rewarded later when the agent will have remembered how to do stuff. These fluctuations are, supposedly, the fluctuations of the macroeconomy, the business cycle.

I have sketched this sort of model in a deliberately hostile way, because I think such things are remarkably silly. But many very eminent economists regard them very highly indeed. Mostly I think this reflects badly on the discipline of macroeconomics, but it does raise some interesting technical problems, like:

How do people evaluate the fit of these models?
Do those evaluation methods make any sense?
How many of the parameters of these models are actually identifiable?
How much data would it take to estimate one of these models to a given degree of precision?
How much data would it take to detect that one of these models was wrong?
How well would these models fit in-sample if they were wrong about the structure of the economy?

(You might well ask "where is the equilibrium, let alone the general equilibrium, in a model with one agent and no trade?" You might very well ask that.)

Bent Jesper Christensen and Nicholas M. Kiefer, Economic Modeling and Inference [Review: An Optimal Path to a Dead End.]
David N. DeJong and Chetan Dave, Structural Macroeconometrics [Review]
Finn E. Kydland and Edward C. Prescott, "Time to Build and Aggregate Fluctuations", Econometrica 50 (1982): 1345--1370 [JSTOR. Pretty much the origins of the approach, and of "real business cycle theory".]
Frank Smets and Rafael Wouters, "Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach", American Economic Review 97 (2007): 586--606 [Perhaps the best-regarded current DSGE of the US economy. Preprint version]

Marco Del Negro, Frank Schorfheie, Frank Smets and Rafael Wouters, "On the Fit of New Keynesian Models", Journal of Business and Economic Statistics 25 (2007): 123--162 [Including discussion and reply]
Rochelle M. Edge and Refet S. Gurkaynak, "How Useful are Estimated DSGE Model Forecasts?", ssrn/1810075 [Recommended for actually going through the exercise of comparing out-of-sample forecasts, and including simple baseline models. But the methodological ideas here are suspect. It is true that there is not much to predict about an in-control system, and what is happening is largely random and so unpredictable, so that even the true model would show low forecasting ability. The question however is why we are supposed to think that the DSGE does give us good information about counterfactuals. If you could show that it had much better predictive performance than baselines like constants or random walks during out-of-control periods, that would be something; but they don't.]
Lars Peter Hansen and James J. Heckman, "The Empirical Foundations of Calibration", Journal of Economic Perspectives 10 (1996): 87--104 [Or, rather, the lack thereof. JSTOR]
Katarina Juselius and Massimo Franchi, "Taking a DSGE Model to the Data Meaningfully", Economics 1 (2007): 4 [There are places where Juselius and Franchi write as though a VAR, or co-integrated VAR, were automatically a sufficient statistic for any time series. This I think is mere minor carelessness; the general strategy here, of seeing what implications the generative model has for phenomenological models, and testing those implications, is quite sound (it's obviously close to indirect inference). It is particularly interesting to try to translate specific pieces of the generative model to specific observable hypotheses. — The fact that the DSGE model is a miserable failure at matching the data is, of course, just a bonus.]
Ivana Komunjer and Serena Ng, "Dynamic Identification of DSGE Models" [Preprint available via Prof. Komunjer]
Mark Watson, "Measures of Fit for Calibrated Models", Journal of Political Economy 101 (1993): 1011--1041

Willem Buiter, "The unfortunate uselessness of most `state of the art' academic monetary economics", Financial Times 3 March 2009 [The point about needing to impose the transversality condition is particularly interesting]
Ricardo J. Caballero, "Macroeconomics after the Crisis: Time to Deal with the Pretense-of-Knowledge Syndrome", SSRN/1683617
David Colander, Peter Howitt, Alan Kirman, Axel Leijonhufvud and Perry Mehrling, "Beyond DSGE Models: Towards an Empirically-Based Macroeconomics" [PDF preprint]
Alan Kirman, "Whom or What Does the Representative Individual Represent?", Journal of Economic Perspectives 6 (1992): 117--136 [Answer: No one and nothing; accordingly it "deserves to be buried". JSTOR]
James Morley, "The Emperor Has No Clothes", Macro Focus 5:2 (March 2010) [PDF]
Robert Solow, "The State of Macroeconomics", Journal of Economic Perspectives 22 (2008): 243--249 ["the claim that `modern macro' somehow has the special virtue of following the principles of economic theory is tendentious and misleading... The other possible defense of modern macro is that, however special it may seem, it is justified empirically. This too strikes me as a delusion."]
Lawrence H. Summers, "Some Skeptical Observations on Real Business Cycle Theory" [1986; PDF]

James K. Galbraith, Olivier Giovanni and Ann J. Russo, "The Fed's Real Reaction Function: Monetary Policy, Inflation, Unemployment, Inequality — and Presidential Politics" [Not directly about DSGEs, but since so many of them incorporate some version of the Taylor rule, it amuses me to think about writing one using this instead. University of Texas Inequality Project working paper 42, 2007]
Herbert Gintis, "The Dynamics of General Equilibrium", The Economic Journal 117 (2007): 1280--1309 [PDF reprint courtesy of Prof. Gintis]
Aapo Hyvärinen, Kun Zhang, Shohei Shimizu, Patrik O. Hoyer, "Estimation of a Structural Vector Autoregression Model Using Non-Gaussianity", Journal of Machine Learning Research 11 (2010): 1709--1731
James Morley and Jeremy Piger, "The Asymmetric Business Cycle", The Review of Economics and Statistics 94 (2012): 208--221

George-Marios Angeletos and Jennifer La'O, "Animal Spirits" [PDF. From a quick examination, epi-cycle adding --- or, rather, shock-adding.]
Jean Boivin and Marc P. Giannoni, "DSGE Models in a Data-Rich Environment" [PDF preprint]
Fabio Canova and Luca Sala, "Back to square one: identification issues in DSGE models" [PDF preprint]
David Colander (ed.), Post Walrasian Macroeconomics: Beyond the Dynamic Stochastic General Equilibrium Model [blurb]
Olivier Coibion and Yuriy Gorodnichenko, "Strategic Interaction among Heterogeneous Price-Setters in an Estimated DSGE Model", The Review of Economics and Statistics 93 (2011): 920--940
Roger E. A. Farmer, Expectations, Employment and Prices []
Lance Taylor, Maynard's Revenge: The Collapse of Free Market Macroeconomics [Blurb]

Co-conspirators to be named later + CRS, "Your Favorite DSGE Sucks"

Notebooks

Dynamic Stochastic General Equilibrium Models in Macroeconomics (DSGEs)