GMM estimation of panel data models with time-varying slope coefficients

ABSTRACT

A difference/system generalized method of moments (GMM) model that imposes time-constant coefficients is common in empirical studies using panel data. However, a rejection by the Sargan–Hansen test is sometimes a serious concern for researchers. We highlight the fact that the Sargan–Hansen test for GMM estimators applied to panel data is a joint test of valid orthogonality conditions and coefficient stability over time. A possible reason for a rejection is therefore that the slope coefficients vary over time. One solution is to estimate an empirical model in which the coefficients are time specific. We apply this solution to the system GMM estimator of simple nondynamic Cobb–Douglas production functions for a selection of Swedish industries and find that relaxing the assumption of constant slope coefficients results in more satisfactory outcomes of the Sargan–Hansen test.

KEYWORDS:

• Panel data
• generalized method of moments
• overidentification test
• time-varying coefficient
• production function

JEL CLASSIFICATION:

• C13
• C33
• D21

Acknowledgement

We thank Steve Bond for very helpful comments on an earlier draft of the article.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ Stata code for estimation of the TVC model, and an example, can be found in Appendix 2 in Sato and Söderbom (2013).

² Because of the two-step procedure, the Hansen test, instead of the Sargan test, is an appropriate test for the overidentifying restrictions.

³ The average is taken from .

⁴ The averages are taken from and . The SEs of the time average of the estimated are obtained by the delta method based on the covariance matrix.

⁵ The data are obtained from the Structural Business Statistics at Statistics Sweden. The original database contains detailed information on the income statements, balance sheets and physical investment of all firms active in Sweden, including private and public firms but not financial firms. Most of the data are obtained from registers at the Swedish National Tax Agency.

⁶ t is defined as .

⁷ The SEs are obtained by the delta method using the covariance matrix.

Additional information

Funding

Funding from the Jan Wallanders och Tom Hedelius Stiftelse samt Tore Browaldhs Stiftelse is gratefully acknowledged.