Oracle Efficient Estimation of Heterogeneous Dynamic Panel Data Models with Interactive Fixed Effects

Abstract

We propose a two-step procedure to estimate a heterogeneous dynamic panel data model with interactive fixed effects. We establish the asymptotic properties of the estimators and show that the final estimator is oracle efficient. We also propose a specification test for the null hypothesis of homogeneous slopes and study the asymptotic properties of the test statistic under both local and global alternatives. Simulations demonstrate the fine performance of the estimator and test statistic. The new estimation and inference methods are applied to study the heterogeneous effects of minimum wage on employment across different counties in the United States. Our dynamic model suggests that the changes of employment range from about–1% to 1% when the minimum wage increases by 1%.

KEYWORDS:

• Cross-sectional dependence
• Dynamic panel
• Heterogeneity
• Minimum wage
• principal component analysis

Supplementary Materials

The online supplement contains the proofs of the main results, some discussions on the specification tests for IFEs, and the second empirical application.

Acknowledgments

The authors thank the coeditor, associate editor and two anonymous referees for their constructive comments.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Notes

1 Specifically, when x_it and y_it contain different factors, the factors defined in Li, Cui, and Lu’s (2020) framework should be the union of all factors. Then some columns of the factor loadings are zero. This violates their Assumption C.2, which requires positive definiteness of their factor loading matrix Q.

2 Please see Section A of the online supplement for the technical details.

3 Please see Section A of the online supplement for the technical details.

4 A rigorous proof of this result is beyond the scope of this article and we leave it for future research.

5 In dynamic panels one typically makes the m.d.s. assumption on the error term. Nevertheless, without such an m.d.s. assumption, it is possible to have both $E(z_{it}^{†}{u}_{it})=0$ and that $\left\{z_{it}^{†}{u}_{it}\right\}$ is serially correlated.

6 In Section D of the online supplement, we discuss several tests for the specification of IFEs.

7 The tests of Castagnetti, Rossi, and Trapani (2015) are directly applicable to the residuals from the CCE estimation of heterogeneous static panels with IFEs. It is easy to see that their tests are also applicable to the residuals obtained from the PCA-type estimation for heterogeneous dynamic and static panels with IFEs. See the discussion in Section D.1 of the online supplement.

Additional information

Funding

Cao thanks the support from the China Postdoctoral Science Foundation under the grant number 043203013. Lu acknowledges support from the Hong Kong Research Grants Council (RGC) under grant number 14501323 and Chinese University of Hong Kong for the startup fund. Su thanks the National Natural Science Foundation of China (NSFC) for financial support under the grant number 72133002.