Whether we need to control for firm fixed effect when the law is at country level?

Question

From the discussion of @Thomas Bilach here,

The "group" fixed effects is technically referring to the panel unit. If the panel unit is firms observed over time and the policy impacts some firms and not others, then it is customary to estimate firm fixed effects.

Normally, in many papers, I saw that they mostly control for firm-fixed effects, for example, Dasgupta, 2019, when examining the impact of laws on countries also use the firm-fixed effects.

However, I am curious about why we must use firm-fixed effects in Dasgupta's case? Because the laws have an impact at national levels rather than specific firm levels. I mean, from my understanding, when we examine the impact of law on firms' asset growth, we must do country-fixed effect, the firm-fixed effect is an option, not a must. I am wondering if I fell into any fallacy.

I will rewrite the statement of Thomas Bilach based on my understanding if the panel unit is "country"

The "group" fixed effects is technically referring to the panel unit. If the panel unit is countries observed over time and the policy impacts some countries and not others, then it is customary to estimate countries fixed effects.

Answer 1

In most difference-in-differences (DD) applications, the unit fixed effect is specified at some aggregate level (e.g., city, county, state, or country level etc.). For example, if we're investigating the effects of a state level intervention on some outcome of interest, then we often estimate state fixed effects. Likewise, if we're examining the impact of a country level policy, then we typically estimate country fixed effects.

Similar to the referenced research, say we observe firms within countries. Anti-collusion laws may be adopted by some countries but not others, though they're designed to affect the firms within those treated jurisdictions. In other words, a firm is "treated" if it's nested within a country that passed a leniency law. Now assuming we observe the same firms before and after the law change, then we can estimate the DD coefficient with firm or country fixed effects. Again, it's important to highlight that we must observe firms in all pre- and post-adoption periods.

In the paper you cite, the law change is at the country level, yet it affects all firms within treated countries. Since the authors observe the same firms over time, before and after the enactment of a leniency law, then estimating firm and year fixed effects is appropriate. Why did they estimate firm instead of country fixed effects? A few justifications come to mind. The first is to account for the differences across firms. Note how the firm fixed effects removed all time-invariant firm level heterogeneity. The second involves inference. They seem particularly interested in identifying the effects of less collusion on firms’ financing decisions. Thus, the "firm" is the target of their inferences. Lastly, firm fixed effects may absorb more variation and likely reduced the size of their standard errors.

Peruse this answer for more detail on when it's appropriate to estimate fixed effects at a lower level.