Tony Yates forgot who Hendry is. Come on Tony, do you really think he never estimated a DSGE model? You should read the paper before bulls**tting around. As everyone who have actually estimate something resembling a DSGE, adding breaks is basically adding infinitely many parameters. Hendry and Mizon are showing something different in the paper, but if you like it keep going.
Hendry and Mizon summarised a recent paper of theirs on VoxEU explaining that DSGE models break down in crises because these events involve shifts in the distribution of observeables that fixed-parameter, fixed-variance DSGE models can’t articulate. They tell the story in a way that a lay reader might conclude is catastrophic for microfounded, dynamic macroeconomics, and/or rational expectations.
But it isn’t.
Several papers have taken steps to articulate models that have time-varying propagation parameters, and time-varying variances. And there is a literature connecting these models to empirical macro models that estimate time-varying econometric counterparts. None of these papers make it into the citations of the VoxEU post, or the original academic paper.
Part of the discussion is about how the equilibrium laws of motion of the economy, got by invoking the law of iterated expectations, in some cases, aren’t derivable by these same means with time-varying parameters. This is well-known. But DSGE modellers who use time-varying parameters, or time-varying variances, know how to solve such models, at least in cases where there aren’t too many things moving around all at once. Finding expectations that, when used, generate laws of motion whose expectations are equal to what you started with is neat and easy with time-invariant parameters. But though difficult when they vary, the process of searching for this ‘fixed point’ as it’s called is conceptually the same, and often achievable.
Some examples of time-varying DSGE models: (i) Models with ‘stochastic volatility’ [variances of shocks that move around in continuous and random small steps over time], including Caldera et al, and Fernandez-Villaverde and Rubio-Ramirez. (ii) Or Markov-regime-switching models [models in which parameters like price-stickiness, or policy parameters, move around randomly through a small set of possibilities]. including Foerster et al.
All these models rest on a degree of time-invariance; in a stochastic volatility model, the shocks to variances are themselves drawn from a fixed variance. In a Markov-Switching model, the switches occur with fixed probabilities. But in principle we could push the time-variation one step further if we really wanted to. [In fact in the case of Markov-Switching I believe there are examples that do this, though I can't lay my hands on one now].
The article dwells on the notion that from the perspective of agents the mean and the variance of relevant distributions won’t be known ahead of time. But expectations can be calculated provided that the distributions from which this means and variances are drawn are known.
At any rate, the critique is somewhat academic, because many authors have pushed the boundaries of DSGE models by dropping the notion of rational expectations. Sargent and coauthors have worked out the equilibria for agents who are Bayesian learners, yet doubt the distributions for relevant concepts implied by their models. Ilut has figured out a simple DSGE model in which agents respond to changes in the degree of ambiguity about the distribution of technology over time. Models with learning can be simulated recursi...See full post