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for specific deterrence models is lagged EPA/state enforcement activities directed at that facility. For example, the key specific deterrence explanatory variable may be the number of inspections directed at the given facility over the past year. The key explanatory variable for general deterrence models is lagged EPA/state enforcement activities directed at other facilities in the same state and sector. For example, the key general deterrence explanatory variable may be the presence of a fine directed at another facility in the same state and sector in the past year. Other explanatory variables are included in the simplified models to capture confounding factors.

For the more mathematically and statistically inclined reader, the basic regression model is yit = αi + γt + Ditδ + Xitβ + εit, where i indexes the unit of observation (a facility) and t indexes time (months or years). yit represents facility i’s compliance status or scaled pollution discharges in period t. αi is typically a facility-specific indicator that represents unobserved time invariant facility characteristics like size, capacity, industrial sub- category, and profitability. The basic idea here is that different facilities have different regression intercepts. γt is a year-specific indicator that represents unobserved time effects common to all facilities like technological change, sector maturation, and economic fluctuations over time. Dit is the key explanatory variable and represents the presence or count of lagged EPA/state enforcement or monitoring activities. In the specific deterrence model, Dit is the presence or count of lagged EPA/state enforcement or monitoring activities directed at facility i in the recent past. In the general deterrence model, Dit is the presence or count of lagged EPA/state enforcement activities directed at other plants in plant i’s state and sector in the recent past. Xit represents other control variables, including seasonality indicators to control for within-year variation and state- specific indicators to control for average differences in regulatory activity across states. εit is the usual regression error term. 2

The basic intuition of the empirical models is quasi-experimental. Essentially, the simplified models compare observations in which there was an agency action in the recent past to observations in which there was no agency action in the recent past. For example, in the specific deterrence models, we might compare facility/time combinations with an inspection in the past year with facility/time combinations without an inspection in the past year. The difference between these two average levels represents the average deterrence effect of an inspection in the recent past. For some of the models, the actual statistical identification of deterrence effects is more subtle, but the basic intuition still holds. 3,4

2 As a technical note, in models that actually contain facility specific fixed effects, these state level fixed effects are omitted since they are redundant.

3 Note that this intuition implies that any concerns about regression to the mean are minimized. The regression to the mean concern is that periods that triggered regulator actions may reflect abnormally high pollution levels and therefore post-action periods may inherently display lower pollution levels than pre- action periods. However, note that the relevant comparison is not pre-action vs. post-action performance. The relevant comparison is performance (or changes in performance) for those observations with actions vs. performance (or changes in performance) for those observations without actions, and so the comparison is relative to all non-sanction periods (not just the pre-action period).

4 Also note that this intuition implies that historically-derived baseline data is not necessary to achieve useful results. Results still show the impact of inspections or enforcement activity on pollution and

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