David F. Hendry and Grayham E. Mizon — Why DSGEs fail in crises

Everything you wanted to know about DSGE.

Unfortunately, in most economies, the underlying distributions can shift unexpectedly. This vitiates any assumption of stationarity. The consequences for DSGEs are profound. As we explain below, the mathematical basis of a DSGE model fails when distributions shift (Hendry and Mizon 2014). This would be like a fire station automatically burning down at every outbreak of a fire. Economic agents are affected by, and notice such shifts. They consequently change their plans, and perhaps the way they form their expectations. When they do so, they violate the key assumptions on which DSGEs are built.

The key is the difference between intrinsic and extrinsic unpredictability. Intrinsic unpredictability is the standard economic randomness – a random draw from a known distribution. Extrinsic unpredictability is an ‘unknown unknown’ so that the conditional and unconditional probabilities of outcomes cannot be accurately calculated in advance.

Extrinsic unpredictability derives from unanticipated shifts of the distributions of economic variables at unpredicted times. Of these, location shifts (changes in the means of distributions) have the most pernicious effects. The reason is that they lead to systematically biased expectations and forecast failure....

Most macroeconomic variables have experienced abrupt shifts, of which the Financial Crisis and Great Recession are just the latest exemplars.

The basic point is simple. We say an error term is intrinsically unpredictable if it is drawn from, for example, a normal distribution with mean µt and a known variance. If the mean of the distribution cannot be established in advance, then we say the error is also extrinsically unpredictable. In this case, the conditional expectation of the shock needs not have mean zero for the outcome at t+1. The forecast is being made with the ‘wrong’ distribution – a distribution with mean µt, when in fact the mean is µt+1. Naturally, the conditional expectation formed at t is not an unbiased predictor of the outcome at t +1.

It seems unlikely that economic agents are any more successful than professional economists in foreseeing when breaks will occur, or divining their properties from one or two observations after they have happened. That link with forecast failure has important implications for economic theories about agents’ expectations formation in a world with extrinsic unpredictability. General equilibrium theories rely heavily on ceteris paribus assumptions – especially the assumption that equilibria do not shift unexpectedly. The standard response to this is called the law of iterated expectations. Unfortunately, as we now show, the law of iterated expectations does not apply inter-temporally when the distributions on which the expectations are based change over time. ...

Much of the economics literature (e.g. Campbell and Shiller 1987) assumes that such shifts are intrinsically unpredictable since they depend upon the random innovation to information that becomes known only one period later...

The point is that the new distributional form has to be learned over time, and may have shifted again in the meantime.4 The mean of the current and future distributions (µt and µt+1) need to be estimated. This is a nearly intractable task for agents – or econometricians – when distributions are shifting....

Unanticipated changes in underlying probability distributions – so-called location shifts – have long been the source of forecast failure. Here, we have established their detrimental impact on economic analyses involving conditional expectations and inter-temporal derivations. As a consequence, dynamic stochastic general equilibrium models are inherently non-structural; their mathematical basis fails when substantive distributional shifts occur.

Like Keynes said, who after all wrote a Treatise on Probability.

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Why DSGEs fail in crises
David F. Hendry, Professor of Economics and Fellow of Nuffield College, University of Oxford, and Grayham E. Mizon, Institute for New Economic Thinking at the Oxford Martin School, Oxford University; Economics Department, University of Southampton