Modelling our Changing World by Jennifer L. Castle & David F. Hendry

Author:Jennifer L. Castle & David F. Hendry
Language: eng
Format: epub
ISBN: 9783030214326
Publisher: Springer International Publishing

4.4 Dynamic-Stochastic General Equilibrium (DSGE) Models

Everyone has to take decisions at some point in time that will affect their future in important ways: marrying, purchasing a house with a mortgage, making an investment in a risky asset, starting a pension or life insurance, and so on. The information available at the time reflects the past and present but obviously does not include knowledge of the future. Consequently, a view has to be taken about possible futures that might affect the outcomes.

All too often, such views are predicated on there being no unanticipated future changes relevant to that decision, namely the environment is assumed to be relatively stationary. Certainly, there are periods of reasonable stability when observing how past events unfolded can assist in planning for the future. But as this book has stressed, unexpected events occur, especially unpredicted shifts in the distributions of relevant variables at unanticipated times. Hendry and Mizon (2014) show that the intermittent occurrence of ‘extrinsic unpredictability’ has dramatic consequences for any theory analyses of time-dependent behaviour, empirical modelling of time series, forecasting, and policy interventions. In particular, the mathematical basis of the class of models widely used by central banks, namely DSGE models, ceases to be valid as DSGEs are based on an inter-temporal optimization calculus that requires the absence of distributional shifts.

This is not an ‘academic’ critique: the supposedly ‘structural’ Bank of England Quarterly Model (BEQM) broke down during the Financial Crisis, and has since been replaced by another DSGE called COMPASS, which may be pointing in the wrong direction: see Hendry and Muellbauer (2018).

DSGE Models

Many of the theoretical equations in DSGE models take a form in which a variable today, denoted , depends on its ‘expected future value’ often written as , where indicates the date at which the expectation is formed about the variable in the . Such expectations are conditional on what information is available, which we denoted by , so are naturally called conditional expectations, and are defined to be the average over the relevant conditional distribution. If the relation between and shifts as in Fig. 4.5, could be far from what was expected.

As we noted above, in a stationary world, a ‘classic’ proof in elementary statistics courses is that the conditional expectation has the smallest variance of all unbiased predictors of the mean of their distribution. By basing their expectations for tomorrow on today’s distribution, DSGE formulations assume stationarity, possibly after ‘removing’ stochastic trends by some method of de-trending. From Fig. 4.5 it is rather obvious that the previous mean, and hence the previous conditional expectation, is not an unbiased predictor of the outcome after a location shift.

As we have emphasized, underlying distributions can and do shift unexpectedly. Of course, we are all affected to some extent by unanticipated shifts of the distributions relevant to our lives, such as unexpectedly being made redundant, sudden increases in mortgage costs or tax rates, or reduced pension values after a stock market crash. However, we then usually change our plans, and perhaps also our views of the future.

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