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why conditional random effect regression specifications are ever preferred to fixed effect regression specifications. For reasons beyond the scope of this report, fixed effects lead to biased (wrong, on average) estimates for the non-linear models necessary when the dependent variable is discrete like a 0/1 compliance indicator.

Correlation vs. Causality

The first lesson of basic statistics is that correlation is not causality. However, the simplified, cost-effective regression models developed in this report do attempt to isolate causality and do intend to attribute deterrence directly to average regulatory actions. First, the panel data techniques discussed in the preceding sub-section are explicitly designed to minimize bias from omitted variables (important confounding factors not explicitly included in the data and models). Second, and more importantly, the models account for reverse causality. The concern here is that correlations between monitoring and enforcement activities and compliance and emissions may reflect the causal effect of compliance or emissions on monitoring and enforcement due to regulator targeting. However, this reverse causality is minimized in two ways. First, all monitoring and enforcement variables in the analysis are lagged. While it is possible that contemporaneous pollution or compliance may induce regulator actions, it is unlikely that current pollution or compliance induced regulator actions in the past. Only past pollution or compliance is likely to have induced past regulator actions. Second, two of the panel data techniques (fixed effects and conditional random effects) discussed in the preceding sub-section provide unbiased (accurate, on average) estimates of deterrence impacts in the presence of correlations between the facility specific control and the standard error term. In other words, these models isolate the direction of causality, even if enforcement or inspection targeting is based upon a plant’s overall environmental performance. 5

3. Simplified Methods for Measuring Specific Deterrence

The state-of-science white paper prepared for Task 1 of this ORD/OECA deterrence research project reveals that significant reductions in non-compliance and emissions are obtainable with traditional monitoring and enforcement. The environmental regulation literature indicates that inspections and enforcement actions consistently produce improved future environmental performance at the evaluated or sanctioned facility. Results hold both historically and currently.

Consequently, the Task 1 state-of-science white paper recommended that OECA should consider closely replicating statistical database analyses for measuring the specific deterrence effects of monitoring and enforcement. This section presents simplified, cost- effective quantitative methods for this purpose. In this context, specific deterrence refers to the effects of regulatory actions on the evaluated or sanctioned firm itself.

5 A complete proof of this statement is beyond the scope of this report, but the well known econometric advantage of fixed effect and conditional random effect models over other techniques is unbiased estimates in the presence of such a correlation. See any introductory econometrics textbook for a more complete discussion.

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