THE ECONOMETRICS OF MACROECONOMIC MODELLING
Testing the Lucas critique
While it is logically possible that conventional Phillips curves are ‘really’ Lucas supply functions in reverse, that claim can be tested for specific models. Finding that the Phillips curve is stable over sample periods that included regime shifts and changes in the correlation structures is sufficient for refuting inversion. Likewise, the Lucas critique is a possibility theorem, not a truism (see Ericsson and Irons 1995), and its assumptions have testable implications. For example, the Lucas critique implies (1) that /ols is non constant as a changes (inside the unit circle), and (2) that determinants of a (if identifiable in practice) should affect /ols if included in the conditional model of yt. Conversely, the Lucas critique is inconsistent with the joint finding of a stable conditional relationship and a regime shift occurring in the process which
drives the explanatory variable; see Ericsson and Hendry (1999). Based on this logic methods of testing the Lucas critique have been developed: see, for example, Hendry (1988), Engle and Hendry (1993), and Favero and Hendry (1992).
Surveys of the empirical evidence for the Lucas critique are found in Ericsson and Irons (1995) and Stanley (2000). Though very different in methodology, the two studies conclude in a similar fashion, namely that there is little firm evidence supporting the empirical applicability of the Lucas critique. In Section 4.6 we review the applicability of the Lucas critique to the Norwegian Phillips curve. As an alternative to rational expectations, we note as a possibility that agents form expectations on the basis of observed properties of the data itself. Interestingly, there is a close relationship between data-based forecasting rules that agents may pick up, and the time-series models that have been successful in macroeconomic forecasting.
