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INFERENCE IN PARTIALLY IDENTIFIED PANEL DATA MODELS WITH INTERACTIVE FIXED EFFECTS

Published online by Cambridge University Press:  19 January 2024

Shengjie Hong Open the ORCID record for Shengjie Hong [Opens in a new window] ,
Liangjun Su Open the ORCID record for Liangjun Su [Opens in a new window]  and
Yaqi Wang Open the ORCID record for Yaqi Wang [Opens in a new window]
Shengjie Hong
Affiliation:
Renmin University of China
Liangjun Su*
Affiliation:
Tsinghua University
Yaqi Wang
Affiliation:
Central University of Finance and Economics
*
Address correspondence to Liangjun Su, School of Economics and Management, Tsinghua University, Beijing, China; e-mail: sulj@sem.tsinghua.edu.cn. Address correspondence to Liangjun Su, Tsinghua University; e-mail: sulj@sem.tsinghua.edu.cn
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Abstract

In this paper, we develop methods for statistical inferences in a partially identified nonparametric panel data model with endogeneity and interactive fixed effects. Under some normalization rules, we can concentrate out the large-dimensional parameter vector of factor loadings and specify a set of conditional moment restrictions that are involved with only the finite-dimensional factor parameters along with the infinite-dimensional nonparametric component. For a conjectured restriction on the parameter, we consider testing the null hypothesis that the restriction is satisfied by at least one element in the identified set and propose a test statistic based on a novel martingale difference divergence measure for the distance between a conditional expectation object and zero. We derive a tight asymptotic distributional upper bound for the resultant test statistic under the null and show that it is divergent at rate-N under the global alternative. To obtain the critical values for our test, we propose a version of multiplier bootstrap and establish its asymptotic validity. Simulations demonstrate the finite sample properties of our inference procedure. We apply our method to study Engel curves for major nondurable expenditures in China by using a panel dataset from the China Family Panel Studies.

Type
ARTICLES
Information
Econometric Theory , First View , pp. 1 - 62
Copyright
© The Author(s), 2024. Published by Cambridge University Press

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Footnotes

The authors thank Iván Fernández-Val and two anonymous referees for their constructive comments. They also thank Xiaohong Chen, Jack Porter, Andres Santos, and Yu Zhu for very helpful comments and suggestions. Hong, Su, and Wang thank the National Natural Science Foundation of China (NSFC) for financial support under the Grant numbers 72373175, 72133002, and 72273164, respectively.

References

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