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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: [email protected]. Address correspondence to Liangjun Su, Tsinghua University; e-mail: [email protected]
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Abstract

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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

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

REFERENCES

Adams, R. A., & Fournier, J. J. (2003). Sobolev space . Elsevier.Google Scholar
Aguiar, M., & Bils, M. (2015). Has consumption inequality mirrored income inequality? American Economic Review , 105(9), 2725–2756.Google Scholar
Ahn, S., & Horenstein, A. (2013). Eigenvalue ratio test for the number of factors. Econometrica , 81, 1203–1227.Google Scholar
Ahn, S. C., Lee, Y. H., & Schmidt, P. (2001). GMM estimation of linear panel data models with time-varying individual effects. Journal of Econometrics , 101, 219–255.Google Scholar
Ahn, S. C., Lee, Y. H., & Schmidt, P. (2013). Panel data models with multiple time-varying individual effects. Journal of Econometrics , 174, 1–14.Google Scholar
Ai, C., & Chen, X. (2003). Efficient estimation of models with conditional moment restrictions containing unknown functions. Econometrica , 71, 1795–1843.Google Scholar
Andrews, D. W. (1994). Empirical process methods in econometrics. In Engle, R. F. and McFadden, D. L. (Eds.), Handbook of econometrics , vol. 4, (pp. 2248–2294), Elsevier.Google Scholar
Andrews, D. W., & Shi, X. (2013). Inference based on conditional moment inequalities. Econometrica , 81, 609–666.Google Scholar
Andrews, D. W., & Shi, X. (2014). Nonparametric inference based on conditional moment inequalities. Journal of Econometrics , 179, 31–45.CrossRefGoogle Scholar
Arcones, M. A., & Giné, E. (1993). Limit theorems for $\mathrm{U}$ -processes . Annals of Probability , 21, 1494–1542.Google Scholar
Bai, J. (2009). Panel data models with interactive fixed effects. Econometrica , 77(4), 1229–1279. Google Scholar
Bai, J., & Ng, S. (2002). Determining the number of factors in approximate factor models. Econometrica , 70, 191–221.Google Scholar
Banks, J., Blundell, R., & Lewbel, A. (1997). Quadratic Engel curves and consumer demand. Review of Economics and Statistics , 79, 527–539.CrossRefGoogle Scholar
Benjamini, Y., & Hochberg, Y. (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society: Series B (Methodological) , 57, 289–300.Google Scholar
Bierens, H. (1982). Consistent model specification tests. Journal of Econometrics , 20, 105–134.Google Scholar
Blundell, R. W., Browning, M., & Crawford, I. A. (2003). Nonparametric Engel curves and revealed preference. Econometrica , 71(1), 205–240.CrossRefGoogle Scholar
Blundell, R. W., Chen, X., & Kristensen, D. (2007). Semi-nonparametric IV estimation of shape-invariant Engel curves. Econometrica , 75(6), 1613–1669.CrossRefGoogle Scholar
Browning, M., & Crossly, T. (2009). Are two cheap, noisy measures better than one expensive, accurate one? American Economic Review , 99(2), 99–103.Google Scholar
Bücher, A., & Kojadinovic, I. (2009). A note on conditional versus joint unconditional weak convergence in bootstrap consistency results. Journal of Theoretical Probability , 32, 1145–1165.CrossRefGoogle Scholar
Chen, X., & Pouzo, D. (2012). Estimation of nonparametric conditional moment models with possibly nonsmooth moments. Econometrica , 80, 277–321.Google Scholar
Chernozhukov, V., Newey, W., & Santos, A. (2023). Constrained conditional moment restriction models. Econometrica , 91(2), 709–736.CrossRefGoogle Scholar
Coakley, J., Fuertes, A., & Smith, R. (2002). A principal components approach to cross-section dependence in panels. Working paper, Birkbeck College, University of London.Google Scholar
de la Peña, V. H., & Giné, E. (1999). Decoupling: From dependence to independence . Springer.CrossRefGoogle Scholar
Deaton, A. S., & Muellbauer, J. (1980). An almost ideal demand system. American Economic Review , 70(3), 312–326.Google Scholar
Dehling, H., Durieu, O., & Volny, D. (2009). New techniques for empirical processes of dependent data. Stochastic Processes and Iheir Applications , 119, 3699–3718.CrossRefGoogle Scholar
Dominguez, M. A., & Lobato, I. N. (2004). Consistent estimation of models defined by conditional moment restrictions. Econometrica , 72, 1601–1615.Google Scholar
Dong, C., Gao, J., & Peng, B. (2020). Varying–coefficient panel data models with nonstationarity and partially observed factor structure. Journal of Business & Economic Statistics , 39(3), 700–711.CrossRefGoogle Scholar
Freyberger, J. (2018). Non-parametric panel data models with interactive fixed effects. Review of Economic Studies , 85(3), 1824–1851.CrossRefGoogle Scholar
Freyberger, J., & Masten, M. A. (2019). A practical guide to compact infinite dimensional parameter spaces. Econometric Reviews , 38(9), 979–1006.CrossRefGoogle Scholar
Greenaway-McGrevy, R., Han, C., & Sul, D. (2008). Estimating and testing idiosyncratic equations using cross-section dependent panel data. Working Paper, Department of Economics, University of Auckland.Google Scholar
Hamilton, B. W. (2001). Using Engel’s law to estimate CPI bias. American Economic Review , 91(3), 619–630.Google Scholar
Holz-Eakin, D., Newey, W., & Rosen, H. (1988). Estimating vector autoregressions with panel data. Econometrica , 56, 1371–1395.CrossRefGoogle Scholar
Hong, S. (2017). Inference in semiparametric conditional moment models with partial identification. Journal of Econometrics , 196, 156–179.Google Scholar
Hurst, E., Li, G., & Pugsley, B. (2014). Are household surveys like tax forms? Evidence from income underreporting of the self-employed. Review of Economics and Statistics , 96, 19–33.Google Scholar
Jin, S., Miao, K., & Su, L. (2021). On factor models with random missing: EM estimation, inference, and cross validation. Journal of Econometrics , 222, 745–777.Google Scholar
Kapetanios, G., & Pesaran, M. H. (2007). Alternative approaches to estimation and inference in large multifactor panels: Small sample results with an application to modelling of asset returns. In G.Phillips and E. Tzavalis (eds.), The refinement of econometric estimation and test procedures: Finite sample and asymptotic analysis . Cambridge University Press.Google Scholar
Kororok, M. R. (2008). Introduction to empirical processes and semiparametric inference . Springer.Google Scholar
Lee, A. J. (1990). U-statistics: Theory and practice . CRC Press.Google Scholar
Leucht, A., & Neumann, M. H. (2013). Dependent wild bootstrap for degenerate U- and V-statistics. Journal of Multivariate Analysis , 117, 257–280.CrossRefGoogle Scholar
Lu, X., & Su, L. (2016). Shrinkage estimation of dynamic panel data models with interactive fixed effects. Journal of Econometrics , 190, 148–175.CrossRefGoogle Scholar
Manski, C. F. (2003). Partial identification of probability distributions . Springer.Google Scholar
Moon, H. R., & Weidner, M. (2015). Linear regression for panel with unknown number of factors as interactive fixed effects. Econometrica , 83, 1543–1579.CrossRefGoogle Scholar
Moon, H. R., & Weidner, M. (2017). Dynamic linear panel regression models with interactive fixed effects. Econometric Theory , 33, 158–195.Google Scholar
Nakamura, E., Steinsson, J., & Liu, M. (2016). Are Chinese growth and inflation too smooth? Evidence from Engel curves. American Economic Journal: Macroeconomics , 8, 113–144.Google Scholar
Newey, W. K., & Powell, J. L. (2003). Instrumental variable estimation of nonparametric models. Econometrica , 71, 1565–1578.Google Scholar
Onatski, A. (2010). Determining the number of factors from empirical distribution of eigenvalues. Review of Economics and Statistics , 92, 1004–1016.CrossRefGoogle Scholar
Pesaran, M. H. (2006). Estimation and inference in large heterogenous panels with multifactor error. Econometrica , 74, 967–1012.Google Scholar
Pesaran, M. H., & Tosetti, E. (2007). Large panels with common factors and spatial correlation. Journal of Econometrics , 161, 182–202.Google Scholar
Phillips, P. C. B., & Sul, D. (2003). Dynamic panel estimation and homogeneity testing under cross sectional dependence. Econometrics Journal , 6, 217–259.Google Scholar
Phillips, P. C. B., & Sul, D. (2007). Bias in dynamic panel estimation with fixed effects, incidental trends and cross section dependence. Journal of Econometrics , 137, 162–188.Google Scholar
Pissarides, C. A., & Weber, G. (1989). An expenditure-based estimate of Britain’s black economy. Journal of Public Economics , 39, 17–32.CrossRefGoogle Scholar
Santos, A. (2012). Inference in nonparametric instrumental variables with partial identification. Econometrica , 80, 213–275.Google Scholar
Schumaker, L. (2007). Spline functions: Basic theory . Cambridge University Press.Google Scholar
Shao, X., & Zhang, J. (2014). Martingale divergence correlation and its use in high dimensional variable screening. Journal of the American Statistical Association , 109, 1302–1318.CrossRefGoogle Scholar
Stinchcombe, M. B., & White, H. (1998). Consistent specification testing with nuisance parameters present only under the alternative. Econometric Theory , 14, 295–325.CrossRefGoogle Scholar
Su, L., & Jin, S. (2012). Sieve estimation of panel data models with cross section dependence. Journal of Econometrics , 169, 34–47.Google Scholar
Su, L., Jin, S., & Zhang, Y. (2015). Specification test for panel data models with interactive fixed effects. Journal of Econometrics , 186, 222–244.CrossRefGoogle Scholar
Su, L., & Zhang, Y. (2018). Nonparametric dynamic panel data models with interactive fixed effects: Sieve estimation and specification testing. Working Paper, Singapore Management University.Google Scholar
Su, L., & Zheng, X. (2017). A Martingale-difference-divergence-based test for specification. Economics Letters , 156, 162–167.Google Scholar
Sun, H. (2005). Mercer theorem for RKHS on noncompact sets. Journal of Complexity , 21, 337–349.CrossRefGoogle Scholar
van der Vaart, A. W., & Wellner, J. (1996). Weak convergence and empirical processes: With applications to statistics . Springer.CrossRefGoogle Scholar
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