Fixed effects demeaning in the presence of interactive effects in treatment effects regressions and elsewhere

Abstract

The present paper shows that cross-section demeaning with respect to time fixed effects is more useful than commonly appreciated, in that it enables consistent and asymptotically normal estimation of interactive effects models with heterogeneous slope coefficients when the number of time periods, T, is small and only the number of cross-sectional units, N, is large. This is important when using OLS but also when using more sophisticated estimators of interactive effects models whose validity does not require demeaning, a point that to the best of our knowledge has not been made before in the literature. As an illustration, we consider the problem of estimating the average treatment effect in the presence of unobserved time-varying heterogeneity. Gobillon and Magnac (2016) recently considered this problem. They employed a principal components-based approach designed to deal with general unobserved heterogeneity, which does not require fixed effects demeaning. The approach does, however, require that T is large, which is typically not the case in practice, and the results reported here confirm that the performance can be extremely poor in small-T samples. The exception is when the approach is applied to data that have been demeaned with respect to fixed effects. 1 While the results reported in the present paper are not restricted to the treatment effects case, we will use it as a motivating example. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

A regularization approach to common correlated effects estimation

“…In the remainder of this section we briefly compare the (pooled) empirical results based on the rCCE estimator with those of the IFE/PC estimator Bai (2009). We follow the suggestion of Petrova and Westerlund (2020) and implement this estimator after double de-meaning the data (i.e., after the two-way fixed effects transformation). 22 structive comments and suggestions.…”

“… Note : The iterative optimization procedure is initialized using the rCCEP estimator. All variables are double de‐meaned prior to estimation as in Petrova and Westerlund (2020). See Table 6 for a detailed description of the regressors.…”

DNA-based quantification and counting of transmission stages provides different but complementary parasite load estimates: an example from rodent coccidia (Eimeria)

“…With the second approach, we used a linear model after transformation in which the within-individual mean and within-dpi mean were subtracted from all observations (time and subject demeaned). This approach allows elimination of within-subject effects (changes associated with each individual that are time-invariant) and within-time effects (changes over time that affect all observations in the same way; time-variant variability) [ 29 – 31 ].…”

Assessing the Impact of Digital Technologies on Energy Efficiency: The Role of OFDI and Virtual Agglomeration

“…The main observation is whether the coefficients and significance of the core explanatory variables in the second part of the equation meet the expectations. Compared with the classical panel fixed effect model, the interactive panel fixed effect can better fit the data and fully consider the impacts of various uncertain factors on the real economy and society (Bai et al, 2009; Petrova and Westerlund, 2020). This method has important applications in controlling for missing variables, capturing time-varying features, and improving goodness of fit.…”