Research

Recent research has pointed out several pitfalls to the two-way fixed effects (TWFE) estimator when the adoption of treatment is staggered and the effect of treatment is heterogeneous. For example, it is biased and does not identify an interpretable measure of treatment effects. On the other hand, new literature proposes an extended TWFE estimator that is more flexible to model heterogeneous treatment effects. The criticisms of the TWFE estimator raise the question if the extended two-way fixed effects estimator suffers the same problems as restricted TWFE specifications. This paper finds an equivalence between the extended TWFE estimator and a difference-in-difference estimator. This equivalence deepens our understanding of the structure of the TWFE estimator. Using this difference-in-difference decomposition, we evaluate the statistical properties of the extended TWFE estimator, and we list the required assumptions to identify treatment effects. The paper clarifies that most of the pitfalls of the TWFE estimator are restricted to particular TWFE specifications. The paper shows that the extended TWFE estimator can identify interpretable measures of treatment effects.

We develop a procedure to identify latent group structures in linear panel data models that exploits a grouping in the error variances of cross-sectional units. To accommodate such grouping, we introduce an objective function that avoids a singularity that arises in a pseudo-likelihood approach. We provide theoretical and numerical evidence showing when allowing for variance groups improves classification. The developed procedure provides new evidence on the relation between firm-level R&D investments and the business cycle. We find a well-defined group structure in the variances that ex-post can be related to firm size. Our estimates indicate stronger procyclical investment patterns at medium-size firms compared to large firms.