Detecting neglected parameter heterogeneity with Chow tests

Abstract

The paper demonstrates through a number of Monte Carlo experiments that, for the type of cross-section data sets typically encountered in applied economics, Chow tests on sorted variations of the data matrix can detect neglected parameter heterogeneity. The paper focuses on heterogeneity in the behavioural responses of economic actors that belong to different economically meaningful groups, such as the young, middle-aged, and old. Since the suggested methodology is easy to implement yet powerful, its routine use by applied economists would be desirable given the very significant estimation bias that can result from neglecting parameter heterogeneity.

Acknowledgements

The author would like to thank Jonathan Temple for numerous helpful comments. This research was partially funded by a summer research grant of the faculty research and creative activity program at Middle Tennesse State University.

Notes

¹ Chesher and Spady (1991), Davidson and MacKinnon (1992), and Godfrey and Orme (1994) are some of the more recent studies.

² A significant amount of work on parameter heterogeneity exists in the literature dealing with panel data. Tests for varying parameters are also routinely applied in time series applications.

³ Group-wise parameter heterogeneity could arise, for example, across the saving behaviour of the young, middle-aged, and old, or across firms belonging to the manufacturing as opposed to the service sector.

⁴ For example, the coefficients describing firm's R&D expenditures may vary by size category or saving behavior may be different by age group.

⁵ Since the Chow tests are not used for a constructive specification search, the tests are independent and require no adjustment of significance levels.

⁶ A more elaborate test strategy could involve splitting the sample at different points, such as, the 33rd quantile, the 50th quantile, and the 67th quantile, as measured by the marginal distribution of the regressor variable that is used to sort the data matrix.

⁷ Zietz (2001) has recently re-emphasized the link between heteroscedasticity and parameter heterogeneity.

⁸ If one decided to divide the data set into three rather than two segments for the Chow test, the number of variables would triple; and so forth.

⁹ The calculations use the gmac2 version as made available on the TSP web site: http://www.stanford.edu/~clint/tspex/gmac2.tsp