Journal
ECONOMETRICA
Volume 83, Issue 4, Pages 1543-1579Publisher
WILEY
DOI: 10.3982/ECTA9382
Keywords
Panel data; interactive fixed effects; factor models; perturbation theory of linear operators; random matrix theory
Categories
Funding
- NSF [SES-0920903]
- USC
- Economic and Social Research Council through ESRC Centre for Microdata Methods and Practice [RES-589-28-0001]
- ESRC [ES/I034021/1] Funding Source: UKRI
- Economic and Social Research Council [ES/I034021/1] Funding Source: researchfish
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In this paper, we study the least squares (LS) estimator in a linear panel regression model with unknown number of factors appearing as interactive fixed effects. Assuming that the number of factors used in estimation is larger than the true number of factors in the data, we establish the limiting distribution of the LS estimator for the regression coefficients as the number of time periods and the number of cross-sectional units jointly go to infinity. The main result of the paper is that under certain assumptions, the limiting distribution of the LS estimator is independent of the number of factors used in the estimation as long as this number is not underestimated. The important practical implication of this result is that for inference on the regression coefficients, one does not necessarily need to estimate the number of interactive fixed effects consistently.
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