Dynamic Regulation with Firm Linkages: Evidence from Texas

This paper evaluates the efficiency of linked environmental regulation, a targeting mechanism whereby inspectors who discover violations at one plant can increase enforcement pressure on other plants sharing the same owner. The central research question is whether linking inspection decisions across co-owned plants adds value over unlinked, plant-level targeting and over random enforcement. The paper develops a new empirical framework of dynamic moral hazard under linked regulation, applies it to Texas environmental enforcement data, and uses the estimated model to evaluate counterfactual regulatory designs.

The empirical setting is the Texas Commission on Environmental Quality (TCEQ), which enforces the Resource Conservation and Recovery Act (RCRA, governing hazardous waste) and the Clean Water Act using a two-dimensional scoring system. A plant-level “site rating” score captures the individual plant’s compliance history, while a firm-wide “person rating” score aggregates the weighted average of plant scores across all plants under the same manager. Both scores feed into a multiplicative penalty escalation rule and a logit-form inspection probability function. The data are an unbalanced panel of 9,792 plants from 2012–2020, with detailed records of inspections, violations, penalties, scores, and ownership. The average plant is inspected with probability 0.289 per year and is linked with approximately 2 other plants through common ownership, though some firms own portfolios exceeding 50 plants.

The model features firms endowed with private types (abatement cost parameters) that may be affiliated within a firm’s portfolio, choosing continuous pollution actions to maximize discounted payoffs net of expected penalties. The regulator observes only scores and minimizes social costs subject to a binding inspection budget. A key computational innovation is “continuation value sufficiency”: because fully solving the portfolio optimization over large plant sets is infeasible due to the curse of dimensionality, each plant’s decision is approximated using three state variables — its own plant score, the firm-wide score, and a scalar summarizing other co-owned plants’ continuation values — governed by an AR(1) transition process. Estimation proceeds in three stages: OLS/logit for inspection and penalty parameters, simulated method of moments for type distribution and curvature parameters, and inversion of the regulator’s first-order conditions to recover sector-specific marginal social harms.

Descriptive evidence confirms three preconditions for linked regulation to add value: violations are positively correlated within firm portfolios, inspections are targeted toward higher-scoring plants on both dimensions, and higher inspection probabilities (instrumented by scores) are associated with fewer violations conditional on plant fixed effects. The coefficient on predicted inspection probability in the deterrence regression (specification 3, plant fixed effects, inspected years only) is −3.920, and an increase in log scores from 0 to 1.5 (roughly the interquartile range) reduces expected violations by approximately 0.5.

Structural estimates show that plant-level and firm-level type variance are similar (σ²_J = 0.209, σ²_F = 0.275), indicating moderate within-firm cost correlation. The curvature parameter y = 0.403 governs diminishing returns to negligence. In counterfactual experiments centered on a 30% budget increase (approximately 10 percentage point rise in per-plant inspection probability), unlinked plant-score-based escalations reduce social costs by 31.9% relative to random inspections. Linked firm-score-based escalations reduce social costs by 41.8% relative to random. The optimal mix — approximately 40% unlinked and 60% linked — reduces social costs by 42.2% relative to random. A back-of-the-envelope cost-benefit calculation calibrating utility-sector violation costs at $3,157 per violation and inspection costs at $740 finds a return of $11.77 in avoided social costs per additional dollar spent on inspections under the optimal mixed regime, versus $8.28 under random inspections.

The scope conditions are specific: the framework applies to RCRA and Clean Water Act plants in Texas, which typically cannot reallocate production across facilities (unlike Clean Air Act firms), so the pollution-substitution channel documented for multi-plant Clean Air Act firms is not modeled. The penalty schedule is taken as fixed; only inspection allocation is treated as a policy choice.

Q: What is linked regulation and why might it improve on unlinked enforcement? A: Linked regulation allows the regulator to increase inspection and penalty pressure on all plants owned by a firm when any one plant accumulates violations. It is efficient when compliance costs (types) are correlated within firms — e.g., due to managerial practices — because a violation at one plant is informative about likely violations at co-owned plants. This correlation means the regulator can target scarce inspection resources toward portfolios that are likely to harbor multiple bad actors, rather than inspecting each plant independently.

Q: How does Texas implement linked regulation in practice? A: Texas uses a two-dimensional scoring system. The plant score (“site rating”) summarizes the individual plant’s violation history over the past five years, normalized by complexity points. The firm score (“person rating”) is the complexity-weighted average of plant scores across all plants under the same manager. Penalties are then multiplied by escalation factors based on both scores: a firm in the “unsatisfactory performer” tier (firm score ≥ 55) faces a 1.1× firm escalation, while a “high performer” (firm score < 0.1) faces a 0.9× multiplier. Because the firm escalation applies to all plants in the portfolio simultaneously, even a small change in firm score can produce large aggregate deterrence effects across a large portfolio.

Q: What descriptive evidence supports the preconditions for linked regulation to add value? A: Three pieces of evidence are presented. First, a scatterplot (Figure 1) shows a positive cross-sectional correlation between a plant’s average violations per inspection and the leave-one-out average violations per inspection of its co-owned plants, indicating within-firm cost correlation. Second, Table 2 logit regressions show that both plant score (coefficient 0.121) and firm score (coefficient 0.062) significantly predict inspection probability, conditional on year and NAICS fixed effects. Third, Table 3 shows that conditional on plant fixed effects, predicted inspection probability is negatively associated with violations (coefficient −3.246 in specification 2, rising to −3.920 in specification 3 restricted to inspected plant-years), confirming dynamic deterrence.

Q: What is the curse of dimensionality problem and how is it resolved? A: In a multi-plant firm, each plant’s optimal action depends on the scores of every other co-owned plant, producing a state space of dimension n_plants + 1. For firms with portfolios of 50+ plants this is computationally infeasible. The paper introduces “continuation value sufficiency”: each plant’s decision is reduced to three state variables — its own score s_j, the firm score s_f, and a scalar W_j aggregating other co-owned plants’ continuation values. Transitions are approximated by plant-specific AR(1) processes. This reduces the portfolio problem from one high-dimensional value function to n_plant separate three-dimensional value functions, each solved independently within an inner fixed-point loop.

Q: How are the type distribution parameters identified? A: The mean type for each NAICS sector θ̄_g is identified by average violations per inspection within that sector — a higher mean type implies more violations conditional on inspection. The plant-level type variance σ²_J is identified by the share of total violation variance occurring across plants within the same firm. The firm-level type variance σ²_F is identified by the share of total violation variance occurring across firms. The curvature parameter y is identified by the responsiveness of violations to changes in predicted inspection probability (the coefficient from specification 3 of Table 3, which equals −3.920 empirically and −6.095 in simulation moments).

Q: What are the main counterfactual results? A: A 30% increase in the inspection budget (approximately +10 percentage points in per-plant inspection probability) is allocated under four regimes. Random inspections reduce violations per plant by 0.31 from a baseline of 0.98. Unlinked (plant-score) escalations reduce social costs by 31.9% more than random. Linked (firm-score) escalations reduce social costs by 41.8% more than random. The optimal mix (approximately 40% unlinked, 60% linked) reduces social costs by 42.2% more than random. In detected violations, all three targeted regimes perform similarly (+0.7% detected violations versus random), meaning the social cost advantage of linked regulation comes through greater undiscovered deterrence rather than through detection rates.

Q: How does the decomposition into static, own-plant, and cross-plant effects clarify the mechanism? A: For unlinked escalations: the static effect accounts for −5.4% of social cost relative to random, own-plant dynamic deterrence accounts for −30.6%, and the cross-plant effect is +4.1% (slightly adverse, because unlinked escalations do not account for portfolio-level incentives). For linked escalations: the static effect is −2.4%, own-plant deterrence is −24.5% (smaller than unlinked because linked escalations are less precisely targeted to individual plant histories), and cross-plant deterrence is −14.9% (large and beneficial). The dominance of cross-plant deterrence under linked escalations is the key mechanism explaining why linking outperforms unlinked targeting.

Q: What does the cost-benefit calculation find? A: Calibrating utility-sector violation social costs at $3,157 per violation (from Kang and Silveira 2021 for California water utilities post-2006) and inspection costs at $740, the paper finds a return of $11.77 in avoided social costs per additional dollar spent on inspections under the optimal linked/unlinked mix, versus $8.28 under random inspections. This suggests a large return to expanding enforcement budgets, with the gain amplified substantially by optimal targeting design.

Q: What are the scope conditions and limitations acknowledged? A: The framework applies to RCRA and Clean Water Act plants in Texas, where firms (e.g., gas station chains) typically cannot reallocate production across facilities, so the pollution-substitution channel documented by Gibson (2019) for Clean Air Act firms is not modeled. The penalty schedule is taken as fixed — only inspection allocation is treated as a policy choice — because Texas’s bylaws are prescriptive about how violations translate into penalties while leaving inspection targeting largely to regulator discretion. Social harm parameters h_g are identified only up to a scale normalization. The paper also does not model why types are correlated within firms (bad managers versus specialization), as the counterfactual results depend only on the degree of correlation, not its source.

Q: How well does the model fit the data? A: The model matches the targeted moments well (Table 5). Mean violations by NAICS sector are closely reproduced (e.g., utility: 0.201 empirical vs. 0.184 simulated; trade: 0.252 vs. 0.236). Responsiveness of violations to inspection probability matches closely (−6.398 empirical vs. −6.095 simulated). A non-targeted fit statistic — the correlation between a plant’s own violation rate and its co-owned plants’ violation rates — is 0.32 in simulation versus 0.26 in the data, which the authors characterize as a good out-of-sample fit given it was not directly targeted in estimation.

Q: How do heterogeneous effects shed light on the distributional consequences of regulation? A: The own-plant deterrence effect is positive for all plants including those with low types that are unlikely to be targeted, but is especially pronounced for high-type plants under unlinked escalations. Under linked escalations, high-type plants are deterred less to the extent they are co-owned with lower-type plants, because firm-score-based targeting aggregates across the portfolio. Cross-plant effects are predictably small under unlinked escalations and larger under linked escalations, especially for firms with high-type portfolios, since those are the firms whose firm scores respond most to individual violations.

Linked regulation: An enforcement mechanism in which the discovery of violations at one plant triggers increased inspection and penalty pressure on all other plants under the same owner. It exploits within-firm correlation in compliance costs to target scarce regulatory resources more efficiently than plant-by-plant escalation alone.

Escalation mechanism: A penalty and inspection design in which plants with worse compliance records — measured by accumulated compliance scores — face disproportionately greater scrutiny and higher penalties per additional violation. The TCEQ’s two-dimensional scoring system is an escalation mechanism operating simultaneously at the individual plant and firm portfolio level.

Plant score / firm score: The plant score (“site rating”) is a normalized index of a single facility’s violation history over the past five years, divided by investigation count and complexity points; the firm score (“person rating”) is the complexity-weighted average of all plant scores across the firm’s portfolio. Higher scores indicate worse compliance records and trigger both higher penalties and higher inspection probabilities.

Continuation value sufficiency: The paper’s solution to the curse of dimensionality in large plant portfolios. Rather than tracking the full joint score state across all co-owned plants, each plant’s optimal action is approximated using three variables — its own score, the aggregate firm score, and a scalar W_j summarizing co-owned plants’ continuation values — with state transitions governed by a plant-specific AR(1) process.

Dynamic moral hazard under linked regulation: The firm’s problem of choosing how much to invest in pollution mitigation at each plant over time, given that current actions affect future scores, future penalties, and — through the firm-wide score — future scrutiny of all co-owned plants. The moral hazard arises because abatement costs are private information not directly observable by the regulator.

Complexity points: A normalization factor in the TCEQ scoring system that adjusts raw violation counts for plant size and sector, enabling comparable compliance histories across heterogeneous facilities. They were introduced in 2012 specifically to prevent mechanically larger facilities from appearing riskier simply due to their scale.

Cross-plant deterrence effect: The reduction in pollution actions at co-owned plants induced by increases in the firm-wide score following a violation at one plant in the portfolio. In the counterfactual decomposition, this effect accounts for −14.9 percentage points of social cost reduction under linked escalations and is the primary mechanism by which linked regulation outperforms unlinked plant-level escalation.