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In any multiperiod panel, a two-way fixed effects (TWFE) regression is numerically equivalent to a first-difference (FD) regression that pools all possible between-period gaps. Building on this observation, this paper develops numerical and causal interpretations of the TWFE coefficient. At the sample level, the TWFE coefficient is a weighted average of FD coefficients with different between-period gaps. This decomposition is useful for assessing the source of identifying variation for the TWFE coefficient. At the population level, a causal interpretation of the TWFE coefficient requires a common trends assumption for any between-period gap, and the assumption has to be conditional on changes in time-varying covariates. I propose a natural generalization of the TWFE estimator that can relax these requirements. I illustrate the practical importance of these insights by examining the TWFE estimates of the minimum wage effect on employment outcomes in the U.S. state–year panel.

Uncertainty faced by individual firms appears to be heterogeneous. In this paper, I construct a new set of empirical measures of firm-level uncertainty using data such as the IBES and Compustat. The panel data that I construct reveals persistent differences in the degree of uncertainty facing individual firms not reflected by existing measures. Consistent with existing measures, I find that the average level of uncertainty across firms is countercyclical, and that it rose sharply at the start of the Great Recession. I next develop a heterogeneous firm model in a setting wherein each firm gradually learns about its own productivity, and each occasionally experiences a shock forcing it to start learning afresh. Uncertainty is gradually resolved as firms operate longer and get better informed. When calibrated to reproduce the level and cyclicality of the cross-sectional dispersion of sales growth, I show that an uncertainty shock can explain 18 percent of the observed output volatility and 29 percent of the investment volatility in the data. ​

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