The shaky mathematical basis of DSGE models

28 Mar, 2016 at 14:14 | Posted in Economics | 1 Comment

In most aspects of their lives humans must plan forwards. They take decisions today that affect their future in complex interactions with the decisions of others. When taking such decisions, the available information is only ever a subset of the universe of past and present information, as no individual or group of individuals can be aware of all the relevant information. Hence, views or expectations about the future, relevant for their decisions, use a partial information set, formally expressed as a conditional expectation given the available information.

Moreover, all such views are predicated on there being no un-anticipated future changes in the environment pertinent to the decision. This is formally captured in the concept of ‘stationarity’. Without stationarity, good outcomes based on conditional expectations could not be achieved consistently. Fortunately, there are periods of stability when insights into the way that past events unfolded can assist in planning for the future.

The world, however, is far from completely stationary. Unanticipated events occur, and they cannot be dealt with using standard data-transformation techniques such as differencing, or by taking linear combinations, or ratios. In particular, ‘extrinsic unpredictability’ – unpredicted shifts of the distributions of economic variables at unanticipated times – is common. As we shall illustrate, extrinsic unpredictability has dramatic consequences for the standard macroeconomic forecasting models used by governments around the world – models known as ‘dynamic stochastic general equilibrium’ models – or DSGE models …

Many of the theoretical equations in DSGE models take a form in which a variable today, say incomes (denoted as yt) depends inter alia on its ‘expected future value’… For example, yt may be the log-difference between a de-trended level and its steady-state value. Implicitly, such a formulation assumes some form of stationarity is achieved by de-trending.

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 … 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.

David Hendry & Grayham Mizon

A great article, not only showing on what shaky mathematical basis DSGE models are built, but also confirming much of Keynes’s critique of econometrics, underlining that to understand real world ”non-routine” decisions and unforeseeable changes in behaviour, stationary probability distributions are of no avail. In a world full of genuine uncertainty — where real historical time rules the roost — the probabilities that ruled the past are not those that will rule the future.

Advocates of DSGE modeling want to have deductively automated answers to fundamental causal questions. But to apply “thin” methods we have to have “thick” background knowledge of what’s going on in the real world, and not in idealized models. Conclusions can only be as certain as their premises — and that also applies to the quest for causality and forecasting predictability in DSGE models.