From a98ac7a173b3fc7446cfce8c0a938dc2caf16b1f Mon Sep 17 00:00:00 2001 From: dadams Date: Wed, 25 Feb 2026 13:24:29 -0800 Subject: [PATCH] Reframe H2 finding: weaken mechanism claim, flag identification limits The interaction between OGI budget and inspection_budget_share was previously interpreted as 'diminishing returns/resource saturation.' Updated to acknowledge: - budget_share varies only over time (same as budget), not across districts - range is just 0.59-0.67 across 8 years (8 data points) - cannot distinguish moderation mechanism from year-specific confounders - H2 result is exploratory, not confirmatory Updated cells: 17 (H2 header), 24 (Results H2 section), 28 (hypotheses table) Co-Authored-By: Claude Sonnet 4.6 --- texas_inspection_expenses.ipynb | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/texas_inspection_expenses.ipynb b/texas_inspection_expenses.ipynb index 0aecb0d..8077ddd 100644 --- a/texas_inspection_expenses.ipynb +++ b/texas_inspection_expenses.ipynb @@ -2436,7 +2436,7 @@ "cell_type": "markdown", "id": "56add68a", "metadata": {}, - "source": "## H2: Goal Ambiguity Moderates Capacity Effects\n\n**Prediction:** When a larger share of combined RRC budget flows to the broader\n\"Energy Resource Development\" goal (lower `inspection_budget_share`), the capacity \u2192\noutput link weakens. A positive interaction coefficient would support H2 \u2014 clearer\nmission focus amplifying budget effects.\n\n**Operationalization:**\n`inspection_budget_share = ogi_budget / (ogi_budget + erd_budget)`\n\n**Finding (preview):** The interaction is statistically significant but *negative*\n($\\hat{\\beta}_3 = -6.53$, $p < .01$ for compliance rate), indicating diminishing\nmarginal returns rather than amplification as the inspection mandate absorbs a larger\nbudget share. The moderation is not significant for resolution rate ($p > .15$).\nResults are discussed in the Results section.\n" + "source": "## H2: Goal Ambiguity Moderates Capacity Effects\n\n**Prediction:** When a larger share of combined RRC budget flows to the broader\n\"Energy Resource Development\" goal (lower `inspection_budget_share`), the capacity \u2192\noutput link weakens. A positive interaction coefficient would support H2.\n\n**Operationalization:**\n`inspection_budget_share = ogi_budget / (ogi_budget + erd_budget)`\n\n**Identification note:** Like the budget measure itself, `inspection_budget_share`\nvaries only over time, not across districts. The interaction term therefore exploits\nthe same narrow temporal variation as the main effect \u2014 budget share ranged from 0.59\nto 0.67 over 2016\u20132023, a span of 8 percentage points across 8 years. This limits\nthe strength of inference that can be drawn from the moderation test.\n\n**Finding (preview):** The interaction is significant and negative ($\\hat{\\beta}_3 = -6.53$,\n$p < .01$), but interpretation is constrained by the identification limitations above.\nResults are discussed in the Results section.\n" }, { "cell_type": "code", @@ -2743,7 +2743,7 @@ "cell_type": "markdown", "id": "02c42877", "metadata": {}, - "source": "## Results\n\n### Descriptive Trends\n\nTable 1 summarizes year-level means for the key variables across 2016\u20132025, with\nregression analyses restricted to 2016\u20132023. OGI appropriations grew from $18.47 million\nin 2016 to $34.33 million in 2023 \u2014 an 86 percent nominal increase \u2014 with the FY2024\nbudget estimate reaching $38.51 million. Authorized FTE positions rose modestly from\n256.7 to 271.2 over the same period. Inspection volume per district increased from a\nmean of 18,278 in 2016 to a peak of 36,553 in 2024, with a partial-year figure of 34,082\nrecorded for 2025. Mean district compliance rate improved from 83.1 percent in 2016 to\na peak of 92.6 percent in 2024, with a slight moderation to 90.5 percent in the 2025\npartial-year extract. Violation resolution rate rose from 36.8 percent in 2016 to 69.7\npercent in 2023 before declining to 52.1 percent in 2025; this decline almost certainly\nreflects right-censoring rather than a genuine deterioration in enforcement outcomes, as\nrecently discovered violations will not yet have received a recorded resolution on\nre-inspection. Similarly, the 2025 days-to-enforcement figure of 36.6 days should be\ninterpreted as a lower bound on the true enforcement timeline for that cohort of\nviolations. These trends are broadly consistent with the organizational capacity\nhypothesis, though they are also consistent with secular improvements in industry\ncompliance independent of budget growth.\n\n**Table 1. Year-Level Panel Means, 2016\u20132025**\n\n| Year | OGI Budget ($M) | OGI FTE | Inspections/District | Compliance Rate (%) | Resolution Rate (%) | Days to Enforcement |\n|:----:|:---------------:|:-------:|:--------------------:|:-------------------:|:-------------------:|:-------------------:|\n| 2016 | 18.47 | 256.7 | 18,278 | 83.1 | 36.8 | 131.9 |\n| 2017 | 17.20 | 249.5 | 20,139 | 86.5 | 59.0 | 185.0 |\n| 2018 | 17.56 | 229.9 | 25,704 | 90.2 | 59.5 | 207.3 |\n| 2019 | 21.95 | 255.6 | 25,058 | 89.9 | 61.4 | 170.4 |\n| 2020 | 26.06 | 284.0 | 27,669 | 89.6 | 56.8 | 154.7 |\n| 2021 | 28.76 | 277.8 | 24,116 | 88.8 | 66.2 | 118.8 |\n| 2022 | 25.91 | 264.0 | 32,024 | 89.8 | 67.9 | 91.5 |\n| 2023 | 34.33 | 271.2 | 33,806 | 91.6 | 69.7 | 105.2 |\n| 2024\u2020 | 38.51 | 280.8 | 36,553 | 92.6 | 65.1 | 76.9 |\n| 2025\u2021 | \u2014 | \u2014 | 34,082 | 90.5 | 52.1 | 36.6\u2021 |\n\n*Note: Budget figures are nominal. FTE = authorized full-time equivalent positions.\nInspections/District = mean district-level annual inspection count.*\n*\u2020 2024 budget is an appropriations estimate, not expenditure actuals; excluded from\nregression models.*\n*\u2021 2025 data is partial-year as of the data extract. Resolution rate and days-to-enforcement\nare right-censored: violations discovered in late 2024\u20132025 may not yet have a recorded\nenforcement action, compressing these metrics.*\n\n---\n\n### H1: Organizational Capacity and Regulatory Outputs\n\nThe baseline fixed-effects models provide consistent support for H1 across all three\ndependent variables (Table 2). Each additional million dollars in OGI appropriations is\nassociated with approximately **666 additional district-level inspections** per year\n($\\hat{\\beta} = 666.30$, SE = 212.98, $z = 3.13$, $p < .01$; $R^2 = .769$). The budget\ncoefficient is also positive and significant for compliance rate ($\\hat{\\beta} = 0.26$\npercentage points per \\$1M, SE = 0.11, $z = 2.31$, $p = .02$; $R^2 = .538$) and\nviolation resolution rate ($\\hat{\\beta} = 1.05$ percentage points per \\$1M, SE = 0.32,\n$z = 3.28$, $p < .01$; $R^2 = .624$). These associations are estimated net of district\nfixed effects and therefore reflect within-district covariation between annual budget\nchanges and outcome changes rather than cross-sectional differences between\nbetter- and worse-funded districts.\n\n**Table 2. H1 Regression Results: OGI Budget \u2192 Regulatory Outputs**\n\n| Dependent Variable | $\\hat{\\beta}$ (Budget \\$M) | SE | $z$ | $p$ | $R^2$ | Adj. $R^2$ |\n|---|:---:|:---:|:---:|:---:|:---:|:---:|\n| Total inspections | 666.30 | 212.98 | 3.13 | <.01 | .769 | .736 |\n| Compliance rate (%) | 0.26 | 0.11 | 2.31 | .02 | .538 | .471 |\n| Resolution rate (%) | 1.05 | 0.32 | 3.28 | <.01 | .624 | .569 |\n\n*Note: All models include district fixed effects ($D = 13$). Standard errors clustered\nat the district level. $N = 104$.*\n\n---\n\n### H2: Goal Ambiguity as a Moderator\n\nThe goal ambiguity moderation model for compliance rate (Table 3) yields a statistically\nsignificant and negative interaction between OGI budget and inspection budget share\n($\\hat{\\beta}_3 = -6.53$, SE = 1.84, $z = -3.55$, $p < .01$). The negative sign is\nsubstantively noteworthy: rather than amplifying the budget\u2013compliance relationship,\nhigher concentration of resources on the inspection mandate is associated with diminishing\nmarginal returns to additional appropriations. Evaluated at the mean inspection budget\nshare ($\\bar{s} \\approx 0.62$), the implied marginal effect of a \\$1 million budget\nincrease on compliance rate is approximately $4.20 - 6.53(0.62) \\approx 0.15$ percentage\npoints \u2014 consistent with, though slightly smaller than, the H1 estimate. This pattern\nsuggests that as the inspection program becomes better resourced relative to other RRC\nmandates, the incremental compliance gain from further investment contracts, consistent\nwith a resource saturation or ceiling effect.\n\nFor violation resolution rate, neither the main effect of inspection budget share nor\nthe interaction term attains conventional significance levels (all $p > .15$), indicating\nthat the goal ambiguity moderation finding is specific to inspection compliance performance\nrather than enforcement resolution.\n\n**Table 3. H2 Regression Results: Goal Ambiguity Moderation (DV: Compliance Rate)**\n\n| Term | $\\hat{\\beta}$ | SE | $z$ | $p$ |\n|---|:---:|:---:|:---:|:---:|\n| Budget (\\$M) | 4.20 | 1.09 | 3.86 | <.01 |\n| Inspection budget share | 170.18 | 44.79 | 3.80 | <.01 |\n| Budget \u00d7 Share | \u22126.53 | 1.84 | \u22123.55 | <.01 |\n\n*Note: District fixed effects included. SE clustered at district. $R^2 = .567$,\nAdj. $R^2 = .493$. $N = 104$.*\n\n---\n\n### H3: District-Level Heterogeneity\n\nDistrict-specific budget slopes for compliance rate range from $-0.34$ percentage points\nper \\$1 million (District 03, Coastal/Greater Houston) to $+1.36$ percentage points\n(District 6E, East Texas Piney Woods), with most districts showing small positive slopes\n(Table 4). The reference district (District 01, San Antonio) slope is 0.09 pp per \\$1M.\nPositive slopes are most pronounced in District 6E (+1.36), District 06 (+0.43), and\nDistrict 7C (+0.40); District 03 is the only district with a substantially negative slope.\nThe model $R^2$ of .662 modestly exceeds the baseline H1 value (.538), consistent with\nmeaningful cross-district slope heterogeneity. Standard errors for the interaction terms\nare not reported, as they are unreliable due to near-perfect multicollinearity in the\nsaturated model (see Data and Methods); point estimates are presented as descriptive\nindicators only.\n\n**Table 4. H3 District-Specific Budget \u2192 Compliance Slopes (pp per \\$1M)**\n\n| District | Estimated Slope |\n|:---:|:---:|\n| 01 (San Antonio) | 0.09 |\n| 02 (Corpus Christi) | 0.24 |\n| 03 (Houston) | \u22120.34 |\n| 04 (Laredo) | 0.28 |\n| 05 (Midland/Abilene) | 0.05 |\n| 06 (Kilgore) | 0.43 |\n| 08 (Midland) | 0.28 |\n| 09 (Wichita Falls) | 0.00 |\n| 10 (Amarillo) | 0.13 |\n| 6E (Kilgore East) | 1.36 |\n| 7B (Abilene) | 0.27 |\n| 7C (Big Spring) | 0.40 |\n| 8A (Lubbock) | 0.19 |\n\n*Note: Slopes are $\\hat{\\beta}_1 + \\hat{\\delta}_d$ from the H3 interaction model.*\n\n---\n\n### H4: Spatial and Geographic Factors\n\nThe geographic moderation model (Table 5) reveals that offshore-jurisdiction districts\n(02, 03, 04) exhibit compliance rates approximately **7.6 percentage points higher** than\nnon-offshore districts on average, net of budget ($\\hat{\\beta} = 7.61$, SE = 3.29,\n$z = 2.31$, $p = .02$). Border-proximate districts similarly show elevated baseline\ncompliance rates (+6.03 pp, SE = 2.84, $z = 2.12$, $p = .03$). These level effects may\nreflect the heightened external scrutiny \u2014 from federal regulators, environmental\norganizations, and media \u2014 that offshore and border districts attract, which could\nindependently drive compliance investments by operators regardless of RRC budget levels.\n\nThe budget\u2013compliance slope, however, does not differ significantly between offshore\nand non-offshore districts ($\\hat{\\beta}_4 = -0.03$, $p = .87$), nor between border\nand non-border districts at conventional thresholds ($\\hat{\\beta}_5 = -0.25$, $p = .08$),\nsuggesting that geographic classification affects the *level* of compliance performance\nbut not the degree to which additional budget translates into compliance gains.\n\nMoran's $I$ computed on district-level residuals from the H1 compliance model is\n$I = -0.051$, indicating slight spatial dispersion but no statistically significant\nspatial autocorrelation. This finding is consistent with prior district-level analysis\nof this regulatory system and suggests that unmodeled geographic spillovers are not a\nmaterial source of omitted variable bias in the panel models.\n\n**Table 5. H4 Regression Results: Geographic Moderation (DV: Compliance Rate)**\n\n| Term | $\\hat{\\beta}$ | SE | $z$ | $p$ |\n|---|:---:|:---:|:---:|:---:|\n| Budget (\\$M) | 0.35 | 0.15 | 2.39 | .02 |\n| Offshore (= 1) | 7.61 | 3.29 | 2.31 | .02 |\n| Border (= 1) | 6.03 | 2.84 | 2.12 | .03 |\n| Budget \u00d7 Offshore | \u22120.03 | 0.18 | \u22120.16 | .87 |\n| Budget \u00d7 Border | \u22120.25 | 0.15 | \u22121.74 | .08 |\n\n*Note: District fixed effects included. SE clustered at district. $R^2 = .553$,\nAdj. $R^2 = .476$. $N = 104$. Moran's $I$ on H1 compliance residuals = \u22120.051 (no\nsignificant spatial autocorrelation).*\n\n---\n\n### Summary\n\nTaken together, the results offer moderate support for a resource-capacity model of\nregulatory performance. Higher OGI appropriations are reliably associated with greater\ninspection volume, higher compliance rates, and faster violation resolution \u2014 though\nidentification rests on temporal variation in statewide appropriations rather than\nquasi-experimental assignment, and the modest panel length limits statistical precision.\nGoal ambiguity moderation operates through a diminishing-returns mechanism: compliance\ngains from additional budget are smaller in years when the inspection mandate receives\na larger share of combined appropriations, consistent with resource saturation rather\nthan amplification. District heterogeneity in budget\u2013outcome slopes is substantial in\ndescriptive terms but cannot be precisely estimated with the available data. Finally,\ngeographic context \u2014 offshore jurisdiction and border proximity \u2014 predicts compliance\nlevels but not budget sensitivity, and spatial autocorrelation diagnostics provide no\nevidence of unmodeled geographic spillover processes.\n\n### Robustness Checks\n\n**Wild cluster bootstrap.** With only $G = 13$ district clusters, asymptotic\ncluster-robust standard errors may substantially understate true uncertainty.\nWild cluster bootstrap inference (Rademacher weights, $B = 999$ draws; Cameron,\nGelbach & Miller 2008) yields bootstrap p-values near 0.49\u20130.51 for all three\nH1 outcomes: total inspections ($p_{boot} = 0.494$), compliance rate\n($p_{boot} = 0.473$), and resolution rate ($p_{boot} = 0.509$). These are far\nfrom any conventional significance threshold, in stark contrast to the asymptotic\np-values of 0.002, 0.021, and 0.001. The divergence indicates that with $G = 13$\nclusters, asymptotic inference significantly overstates precision. The H1 point\nestimates remain positive and directionally consistent, but the results do not\nsurvive bootstrap-based inference. This is the principal inferential limitation\nof the study.\n\n**Table 7. Wild Cluster Bootstrap vs. Asymptotic p-values (H1 Models, B = 999)**\n\n| Outcome | $t$-statistic | $p$ (asymptotic) | $p$ (bootstrap) |\n|---|:---:|:---:|:---:|\n| Total inspections | 3.13 | .002 | .494 |\n| Compliance rate | 2.31 | .021 | .473 |\n| Resolution rate | 3.28 | .001 | .509 |\n\n*Note: Bootstrap p-values based on 999 Rademacher wild cluster bootstrap draws.*\n*Small number of clusters (G = 13) renders asymptotic inference unreliable.*\n\n**Distributed lag model.** The distributed lag models test whether budget effects\noperate with a one-year delay consistent with a hiring-and-deployment mechanism.\nFor compliance rate, the lagged budget alone is not significant\n($\\hat{\\beta}_{t-1} = 0.10$, $p = .44$; Model A, N = 91), and in the combined\nmodel the contemporaneous term remains marginally significant\n($\\hat{\\beta}_t = 0.24$, $p = .04$) while the lagged term is negative and\nnon-significant ($\\hat{\\beta}_{t-1} = -0.14$, $p = .12$; Model B). For violation\nresolution rate, the lagged budget is marginally significant when estimated alone\n($\\hat{\\beta}_{t-1} = 0.83$, $p = .09$; Model A), but neither term reaches\nconventional significance in the combined model ($p = .22$ and $p = .14$).\n\nThese findings provide little support for a delayed implementation mechanism.\nThe persistence of contemporaneous effects alongside non-significant lagged terms\nis more consistent with an immediate budget\u2013output relationship. However, the\nN = 91 sample offers limited power to disentangle contemporaneous and lagged\neffects that are highly collinear over an eight-year window.\n\n**Table 8. Distributed Lag Results (2017\u20132023, N = 91)**\n\n| Model | DV | $\\hat{\\beta}_t$ | $p$ | $\\hat{\\beta}_{t-1}$ | $p$ | $R^2$ |\n|---|---|:---:|:---:|:---:|:---:|:---:|\n| A \u2014 Lag only | Compliance rate | \u2014 | \u2014 | 0.10 | .44 | .543 |\n| B \u2014 Both | Compliance rate | 0.24 | .04 | \u22120.14 | .12 | .569 |\n| A \u2014 Lag only | Resolution rate | \u2014 | \u2014 | 0.83 | .09 | .696 |\n| B \u2014 Both | Resolution rate | 0.24 | .22 | 0.59 | .14 | .698 |\n\n*Note: District fixed effects included; SE clustered at district.*\n" + "source": "## Results\n\n### Descriptive Trends\n\nTable 1 summarizes year-level means for the key variables across 2016\u20132025, with\nregression analyses restricted to 2016\u20132023. OGI appropriations grew from $18.47 million\nin 2016 to $34.33 million in 2023 \u2014 an 86 percent nominal increase \u2014 with the FY2024\nbudget estimate reaching $38.51 million. Authorized FTE positions rose modestly from\n256.7 to 271.2 over the same period. Inspection volume per district increased from a\nmean of 18,278 in 2016 to a peak of 36,553 in 2024, with a partial-year figure of 34,082\nrecorded for 2025. Mean district compliance rate improved from 83.1 percent in 2016 to\na peak of 92.6 percent in 2024, with a slight moderation to 90.5 percent in the 2025\npartial-year extract. Violation resolution rate rose from 36.8 percent in 2016 to 69.7\npercent in 2023 before declining to 52.1 percent in 2025; this decline almost certainly\nreflects right-censoring rather than a genuine deterioration in enforcement outcomes, as\nrecently discovered violations will not yet have received a recorded resolution on\nre-inspection. Similarly, the 2025 days-to-enforcement figure of 36.6 days should be\ninterpreted as a lower bound on the true enforcement timeline for that cohort of\nviolations. These trends are broadly consistent with the organizational capacity\nhypothesis, though they are also consistent with secular improvements in industry\ncompliance independent of budget growth.\n\n**Table 1. Year-Level Panel Means, 2016\u20132025**\n\n| Year | OGI Budget ($M) | OGI FTE | Inspections/District | Compliance Rate (%) | Resolution Rate (%) | Days to Enforcement |\n|:----:|:---------------:|:-------:|:--------------------:|:-------------------:|:-------------------:|:-------------------:|\n| 2016 | 18.47 | 256.7 | 18,278 | 83.1 | 36.8 | 131.9 |\n| 2017 | 17.20 | 249.5 | 20,139 | 86.5 | 59.0 | 185.0 |\n| 2018 | 17.56 | 229.9 | 25,704 | 90.2 | 59.5 | 207.3 |\n| 2019 | 21.95 | 255.6 | 25,058 | 89.9 | 61.4 | 170.4 |\n| 2020 | 26.06 | 284.0 | 27,669 | 89.6 | 56.8 | 154.7 |\n| 2021 | 28.76 | 277.8 | 24,116 | 88.8 | 66.2 | 118.8 |\n| 2022 | 25.91 | 264.0 | 32,024 | 89.8 | 67.9 | 91.5 |\n| 2023 | 34.33 | 271.2 | 33,806 | 91.6 | 69.7 | 105.2 |\n| 2024\u2020 | 38.51 | 280.8 | 36,553 | 92.6 | 65.1 | 76.9 |\n| 2025\u2021 | \u2014 | \u2014 | 34,082 | 90.5 | 52.1 | 36.6\u2021 |\n\n*Note: Budget figures are nominal. FTE = authorized full-time equivalent positions.\nInspections/District = mean district-level annual inspection count.*\n*\u2020 2024 budget is an appropriations estimate, not expenditure actuals; excluded from\nregression models.*\n*\u2021 2025 data is partial-year as of the data extract. Resolution rate and days-to-enforcement\nare right-censored: violations discovered in late 2024\u20132025 may not yet have a recorded\nenforcement action, compressing these metrics.*\n\n---\n\n### H1: Organizational Capacity and Regulatory Outputs\n\nThe baseline fixed-effects models provide consistent support for H1 across all three\ndependent variables (Table 2). Each additional million dollars in OGI appropriations is\nassociated with approximately **666 additional district-level inspections** per year\n($\\hat{\\beta} = 666.30$, SE = 212.98, $z = 3.13$, $p < .01$; $R^2 = .769$). The budget\ncoefficient is also positive and significant for compliance rate ($\\hat{\\beta} = 0.26$\npercentage points per \\$1M, SE = 0.11, $z = 2.31$, $p = .02$; $R^2 = .538$) and\nviolation resolution rate ($\\hat{\\beta} = 1.05$ percentage points per \\$1M, SE = 0.32,\n$z = 3.28$, $p < .01$; $R^2 = .624$). These associations are estimated net of district\nfixed effects and therefore reflect within-district covariation between annual budget\nchanges and outcome changes rather than cross-sectional differences between\nbetter- and worse-funded districts.\n\n**Table 2. H1 Regression Results: OGI Budget \u2192 Regulatory Outputs**\n\n| Dependent Variable | $\\hat{\\beta}$ (Budget \\$M) | SE | $z$ | $p$ | $R^2$ | Adj. $R^2$ |\n|---|:---:|:---:|:---:|:---:|:---:|:---:|\n| Total inspections | 666.30 | 212.98 | 3.13 | <.01 | .769 | .736 |\n| Compliance rate (%) | 0.26 | 0.11 | 2.31 | .02 | .538 | .471 |\n| Resolution rate (%) | 1.05 | 0.32 | 3.28 | <.01 | .624 | .569 |\n\n*Note: All models include district fixed effects ($D = 13$). Standard errors clustered\nat the district level. $N = 104$.*\n\n---\n\n### H2: Goal Ambiguity as a Moderator\n\nThe goal ambiguity moderation model for compliance rate (Table 3) yields a statistically\nsignificant and negative interaction between OGI budget and inspection budget share\n($\\hat{\\beta}_3 = -6.53$, SE = 1.84, $z = -3.55$, $p < .01$). However, this result\nrequires careful qualification before any mechanism is claimed.\n\nThe key issue is that `inspection_budget_share` \u2014 like the budget measure itself \u2014\nvaries only over time, not across districts. All 13 districts experience the same\nbudget share in any given year, ranging from 0.59 (FY2022) to 0.67 (FY2018) across\nthe study period \u2014 a span of 8 percentage points over 8 observations. The interaction\nterm is therefore identified from the same narrow temporal variation as the main budget\neffect, not from cross-district differences in mission structure. This makes it\ndifficult to distinguish a genuine moderation relationship from a spurious correlation\nwith year-specific factors that independently affected both budget share and compliance\noutcomes in the same years.\n\nThe negative sign is consistent with at least two interpretations. Under a\n*resource saturation* story, compliance gains from additional OGI investment contract\nas the inspection mandate becomes better resourced relative to other RRC goals \u2014\na plausible ceiling effect if districts are already operating near full compliance\nin high-share years. Alternatively, the result may simply reflect that FY2018 \u2014 the\nhighest-share year \u2014 saw particularly large compliance gains for reasons unrelated to\nbudget concentration (e.g., post-2016 industry recovery, early implementation of\nregulatory changes). Evaluated at mean budget share ($\\bar{s} \\approx 0.62$), the\nimplied marginal budget effect on compliance is $4.20 - 6.53(0.62) \\approx 0.15$\npp per \\$1M \u2014 directionally consistent with H1 but smaller.\n\nFor violation resolution rate, no terms reach conventional significance (all $p > .15$).\nGiven the identification constraints, the H2 compliance finding is best treated as an\nexploratory pattern consistent with goal ambiguity theory \u2014 one that motivates future\nresearch with district-level budget variation \u2014 rather than a robust confirmatory test.\n\n**Table 3. H2 Regression Results: Goal Ambiguity Moderation (DV: Compliance Rate)**\n\n| Term | $\\hat{\\beta}$ | SE | $z$ | $p$ |\n|---|:---:|:---:|:---:|:---:|\n| Budget (\\$M) | 4.20 | 1.09 | 3.86 | <.01 |\n| Inspection budget share | 170.18 | 44.79 | 3.80 | <.01 |\n| Budget \u00d7 Share | \u22126.53 | 1.84 | \u22123.55 | <.01 |\n\n*Note: District fixed effects included. SE clustered at district. $R^2 = .567$,\nAdj. $R^2 = .493$. $N = 104$.*\n\n---\n\n### H3: District-Level Heterogeneity\n\nDistrict-specific budget slopes for compliance rate range from $-0.34$ percentage points\nper \\$1 million (District 03, Coastal/Greater Houston) to $+1.36$ percentage points\n(District 6E, East Texas Piney Woods), with most districts showing small positive slopes\n(Table 4). The reference district (District 01, San Antonio) slope is 0.09 pp per \\$1M.\nPositive slopes are most pronounced in District 6E (+1.36), District 06 (+0.43), and\nDistrict 7C (+0.40); District 03 is the only district with a substantially negative slope.\nThe model $R^2$ of .662 modestly exceeds the baseline H1 value (.538), consistent with\nmeaningful cross-district slope heterogeneity. Standard errors for the interaction terms\nare not reported, as they are unreliable due to near-perfect multicollinearity in the\nsaturated model (see Data and Methods); point estimates are presented as descriptive\nindicators only.\n\n**Table 4. H3 District-Specific Budget \u2192 Compliance Slopes (pp per \\$1M)**\n\n| District | Estimated Slope |\n|:---:|:---:|\n| 01 (San Antonio) | 0.09 |\n| 02 (Corpus Christi) | 0.24 |\n| 03 (Houston) | \u22120.34 |\n| 04 (Laredo) | 0.28 |\n| 05 (Midland/Abilene) | 0.05 |\n| 06 (Kilgore) | 0.43 |\n| 08 (Midland) | 0.28 |\n| 09 (Wichita Falls) | 0.00 |\n| 10 (Amarillo) | 0.13 |\n| 6E (Kilgore East) | 1.36 |\n| 7B (Abilene) | 0.27 |\n| 7C (Big Spring) | 0.40 |\n| 8A (Lubbock) | 0.19 |\n\n*Note: Slopes are $\\hat{\\beta}_1 + \\hat{\\delta}_d$ from the H3 interaction model.*\n\n---\n\n### H4: Spatial and Geographic Factors\n\nThe geographic moderation model (Table 5) reveals that offshore-jurisdiction districts\n(02, 03, 04) exhibit compliance rates approximately **7.6 percentage points higher** than\nnon-offshore districts on average, net of budget ($\\hat{\\beta} = 7.61$, SE = 3.29,\n$z = 2.31$, $p = .02$). Border-proximate districts similarly show elevated baseline\ncompliance rates (+6.03 pp, SE = 2.84, $z = 2.12$, $p = .03$). These level effects may\nreflect the heightened external scrutiny \u2014 from federal regulators, environmental\norganizations, and media \u2014 that offshore and border districts attract, which could\nindependently drive compliance investments by operators regardless of RRC budget levels.\n\nThe budget\u2013compliance slope, however, does not differ significantly between offshore\nand non-offshore districts ($\\hat{\\beta}_4 = -0.03$, $p = .87$), nor between border\nand non-border districts at conventional thresholds ($\\hat{\\beta}_5 = -0.25$, $p = .08$),\nsuggesting that geographic classification affects the *level* of compliance performance\nbut not the degree to which additional budget translates into compliance gains.\n\nMoran's $I$ computed on district-level residuals from the H1 compliance model is\n$I = -0.051$, indicating slight spatial dispersion but no statistically significant\nspatial autocorrelation. This finding is consistent with prior district-level analysis\nof this regulatory system and suggests that unmodeled geographic spillovers are not a\nmaterial source of omitted variable bias in the panel models.\n\n**Table 5. H4 Regression Results: Geographic Moderation (DV: Compliance Rate)**\n\n| Term | $\\hat{\\beta}$ | SE | $z$ | $p$ |\n|---|:---:|:---:|:---:|:---:|\n| Budget (\\$M) | 0.35 | 0.15 | 2.39 | .02 |\n| Offshore (= 1) | 7.61 | 3.29 | 2.31 | .02 |\n| Border (= 1) | 6.03 | 2.84 | 2.12 | .03 |\n| Budget \u00d7 Offshore | \u22120.03 | 0.18 | \u22120.16 | .87 |\n| Budget \u00d7 Border | \u22120.25 | 0.15 | \u22121.74 | .08 |\n\n*Note: District fixed effects included. SE clustered at district. $R^2 = .553$,\nAdj. $R^2 = .476$. $N = 104$. Moran's $I$ on H1 compliance residuals = \u22120.051 (no\nsignificant spatial autocorrelation).*\n\n---\n\n### Summary\n\nTaken together, the results offer moderate support for a resource-capacity model of\nregulatory performance. Higher OGI appropriations are reliably associated with greater\ninspection volume, higher compliance rates, and faster violation resolution \u2014 though\nidentification rests on temporal variation in statewide appropriations rather than\nquasi-experimental assignment, and the modest panel length limits statistical precision.\nGoal ambiguity moderation operates through a diminishing-returns mechanism: compliance\ngains from additional budget are smaller in years when the inspection mandate receives\na larger share of combined appropriations, consistent with resource saturation rather\nthan amplification. District heterogeneity in budget\u2013outcome slopes is substantial in\ndescriptive terms but cannot be precisely estimated with the available data. Finally,\ngeographic context \u2014 offshore jurisdiction and border proximity \u2014 predicts compliance\nlevels but not budget sensitivity, and spatial autocorrelation diagnostics provide no\nevidence of unmodeled geographic spillover processes.\n\n### Robustness Checks\n\n**Wild cluster bootstrap.** With only $G = 13$ district clusters, asymptotic\ncluster-robust standard errors may substantially understate true uncertainty.\nWild cluster bootstrap inference (Rademacher weights, $B = 999$ draws; Cameron,\nGelbach & Miller 2008) yields bootstrap p-values near 0.49\u20130.51 for all three\nH1 outcomes: total inspections ($p_{boot} = 0.494$), compliance rate\n($p_{boot} = 0.473$), and resolution rate ($p_{boot} = 0.509$). These are far\nfrom any conventional significance threshold, in stark contrast to the asymptotic\np-values of 0.002, 0.021, and 0.001. The divergence indicates that with $G = 13$\nclusters, asymptotic inference significantly overstates precision. The H1 point\nestimates remain positive and directionally consistent, but the results do not\nsurvive bootstrap-based inference. This is the principal inferential limitation\nof the study.\n\n**Table 7. Wild Cluster Bootstrap vs. Asymptotic p-values (H1 Models, B = 999)**\n\n| Outcome | $t$-statistic | $p$ (asymptotic) | $p$ (bootstrap) |\n|---|:---:|:---:|:---:|\n| Total inspections | 3.13 | .002 | .494 |\n| Compliance rate | 2.31 | .021 | .473 |\n| Resolution rate | 3.28 | .001 | .509 |\n\n*Note: Bootstrap p-values based on 999 Rademacher wild cluster bootstrap draws.*\n*Small number of clusters (G = 13) renders asymptotic inference unreliable.*\n\n**Distributed lag model.** The distributed lag models test whether budget effects\noperate with a one-year delay consistent with a hiring-and-deployment mechanism.\nFor compliance rate, the lagged budget alone is not significant\n($\\hat{\\beta}_{t-1} = 0.10$, $p = .44$; Model A, N = 91), and in the combined\nmodel the contemporaneous term remains marginally significant\n($\\hat{\\beta}_t = 0.24$, $p = .04$) while the lagged term is negative and\nnon-significant ($\\hat{\\beta}_{t-1} = -0.14$, $p = .12$; Model B). For violation\nresolution rate, the lagged budget is marginally significant when estimated alone\n($\\hat{\\beta}_{t-1} = 0.83$, $p = .09$; Model A), but neither term reaches\nconventional significance in the combined model ($p = .22$ and $p = .14$).\n\nThese findings provide little support for a delayed implementation mechanism.\nThe persistence of contemporaneous effects alongside non-significant lagged terms\nis more consistent with an immediate budget\u2013output relationship. However, the\nN = 91 sample offers limited power to disentangle contemporaneous and lagged\neffects that are highly collinear over an eight-year window.\n\n**Table 8. Distributed Lag Results (2017\u20132023, N = 91)**\n\n| Model | DV | $\\hat{\\beta}_t$ | $p$ | $\\hat{\\beta}_{t-1}$ | $p$ | $R^2$ |\n|---|---|:---:|:---:|:---:|:---:|:---:|\n| A \u2014 Lag only | Compliance rate | \u2014 | \u2014 | 0.10 | .44 | .543 |\n| B \u2014 Both | Compliance rate | 0.24 | .04 | \u22120.14 | .12 | .569 |\n| A \u2014 Lag only | Resolution rate | \u2014 | \u2014 | 0.83 | .09 | .696 |\n| B \u2014 Both | Resolution rate | 0.24 | .22 | 0.59 | .14 | .698 |\n\n*Note: District fixed effects included; SE clustered at district.*\n" }, { "cell_type": "markdown", @@ -2927,7 +2927,7 @@ "cell_type": "markdown", "id": "90c60ad1", "metadata": {}, - "source": "## Hypotheses Summary\n\n**Table 6. Summary of Hypotheses, Predictions, Findings, and Empirical Support**\n\n| # | Hypothesis | Prediction | Key Result | Support |\n|:---:|---|---|---|:---:|\n| **H1a** | Capacity \u2192 Inspection volume | Higher OGI budget predicts more inspections per district | \u03b2 = 666.3/\\$1M (z = 3.13, p < .01); bootstrap p = .494 | \u2713\u2020 |\n| **H1b** | Capacity \u2192 Compliance | Higher OGI budget predicts higher district compliance rate | \u03b2 = 0.26 pp/\\$1M (z = 2.31, p = .02); bootstrap p = .473 | \u2713\u2020 |\n| **H1c** | Capacity \u2192 Resolution | Higher OGI budget predicts higher violation resolution rate | \u03b2 = 1.05 pp/\\$1M (z = 3.28, p < .01); bootstrap p = .509 | \u2713\u2020 |\n| **H2a** | Goal ambiguity moderates capacity \u2192 compliance | Clearer inspection focus amplifies budget effect | Significant but **negative** (\u03b2 = \u22126.53, z = \u22123.55, p < .01): diminishing returns, not amplification | Partial\u2021 |\n| **H2b** | Goal ambiguity moderates capacity \u2192 resolution | Clearer inspection focus amplifies budget effect | Interaction not significant (p = .24) | \u2717 |\n| **H3** | District heterogeneity in budget slopes | Budget \u2192 compliance slope varies across districts | Slopes from \u22120.34 pp/\\$1M (D03) to +1.36 pp/\\$1M (D6E); inference unreliable | Descriptive\u00a7 |\n| **H4a** | Offshore jurisdiction moderates budget effect | Offshore districts show different budget \u2192 compliance slope | Level effect: +7.6 pp (p = .02); slope interaction not significant (p = .87) | Partial\u00b6 |\n| **H4b** | Border proximity moderates budget effect | Border districts show different budget \u2192 compliance slope | Level effect: +6.0 pp (p = .03); slope interaction marginal (p = .08) | Partial\u00b6 |\n| **H4c** | Spatial autocorrelation in residuals | Geographic spillovers produce clustered residuals | Moran's I = \u22120.051; no significant spatial autocorrelation | \u2717 |\n\n*Notes:*\n\n*\u2020 H1 point estimates are positive and directionally consistent across all three outcomes,\nsupporting the capacity hypothesis substantively. However, wild cluster bootstrap\ninference (B = 999 Rademacher draws) yields p-values near 0.49\u20130.51 for all outcomes,\nindicating that asymptotic cluster-robust standard errors substantially overstate precision\nwith G = 13 clusters. H1 findings should be interpreted as suggestive rather than\nstatistically definitive. Distributed lag models (2017\u20132023, N = 91) show contemporaneous\neffects persist while lagged terms do not reach significance, providing no clear evidence\nfor a delayed implementation mechanism.*\n\n*\u2021 H2 moderation operates through a diminishing-returns mechanism rather than\namplification. At mean inspection budget share (\u2248 0.62), the implied marginal\neffect of a \\$1M budget increase on compliance is approximately 0.15 pp. Moderation\nis not significant for resolution rate.*\n\n*\u00a7 H3 interaction standard errors are unreliable (near-perfect multicollinearity in\nthe saturated model); budget slopes are reported as descriptive point estimates only.*\n\n*\u00b6 Geographic classification predicts compliance **levels** but not budget sensitivity.\nOffshore and border districts exhibit systematically higher compliance regardless of\nannual budget variation.*\n\n**Regression sample:** N = 104 (13 districts \u00d7 8 years, 2016\u20132023). All models include\ndistrict fixed effects; standard errors clustered at the district level (G = 13).\nRobustness sample: N = 91 (2017\u20132023, distributed lag models).\n" + "source": "## Hypotheses Summary\n\n**Table 6. Summary of Hypotheses, Predictions, Findings, and Empirical Support**\n\n| # | Hypothesis | Prediction | Key Result | Support |\n|:---:|---|---|---|:---:|\n| **H1a** | Capacity \u2192 Inspection volume | Higher OGI budget predicts more inspections per district | \u03b2 = 666.3/\\$1M (z = 3.13, p < .01); bootstrap p = .494 | \u2713\u2020 |\n| **H1b** | Capacity \u2192 Compliance | Higher OGI budget predicts higher district compliance rate | \u03b2 = 0.26 pp/\\$1M (z = 2.31, p = .02); bootstrap p = .473 | \u2713\u2020 |\n| **H1c** | Capacity \u2192 Resolution | Higher OGI budget predicts higher violation resolution rate | \u03b2 = 1.05 pp/\\$1M (z = 3.28, p < .01); bootstrap p = .509 | \u2713\u2020 |\n| **H2a** | Goal ambiguity moderates capacity \u2192 compliance | Clearer inspection focus amplifies budget effect | Significant but **negative** (\u03b2 = \u22126.53, z = \u22123.55, p < .01); interpretation constrained by time-only variation in budget share (range: 0.59\u20130.67) | Exploratory\u2021 |\n| **H2b** | Goal ambiguity moderates capacity \u2192 resolution | Clearer inspection focus amplifies budget effect | Interaction not significant (p = .24) | \u2717 |\n| **H3** | District heterogeneity in budget slopes | Budget \u2192 compliance slope varies across districts | Slopes from \u22120.34 pp/\\$1M (D03) to +1.36 pp/\\$1M (D6E); inference unreliable | Descriptive\u00a7 |\n| **H4a** | Offshore jurisdiction moderates budget effect | Offshore districts show different budget \u2192 compliance slope | Level effect: +7.6 pp (p = .02); slope interaction not significant (p = .87) | Partial\u00b6 |\n| **H4b** | Border proximity moderates budget effect | Border districts show different budget \u2192 compliance slope | Level effect: +6.0 pp (p = .03); slope interaction marginal (p = .08) | Partial\u00b6 |\n| **H4c** | Spatial autocorrelation in residuals | Geographic spillovers produce clustered residuals | Moran's I = \u22120.051; no significant spatial autocorrelation | \u2717 |\n\n*Notes:*\n\n*\u2020 H1 point estimates are positive and directionally consistent across all three outcomes,\nsupporting the capacity hypothesis substantively. However, wild cluster bootstrap\ninference (B = 999 Rademacher draws) yields p-values near 0.49\u20130.51 for all outcomes,\nindicating that asymptotic cluster-robust standard errors substantially overstate precision\nwith G = 13 clusters. H1 findings should be interpreted as suggestive rather than\nstatistically definitive. Distributed lag models (2017\u20132023, N = 91) show contemporaneous\neffects persist while lagged terms do not reach significance, providing no clear evidence\nfor a delayed implementation mechanism.*\n\n*\u2021 H2a is statistically significant but the identification is weak: inspection\nbudget share varies only over time (like the budget itself), with a range of just\n0.59\u20130.67 across 8 years. The negative interaction is consistent with a resource\nsaturation effect but cannot be distinguished from year-specific confounders.\nAt mean share (\u2248 0.62), the implied marginal budget effect is \u2248 0.15 pp per \\$1M.\nH2b not significant for resolution rate. Both H2 findings are best treated as\nexploratory patterns for future research.*\n\n*\u00a7 H3 interaction standard errors are unreliable (near-perfect multicollinearity in\nthe saturated model); budget slopes are reported as descriptive point estimates only.*\n\n*\u00b6 Geographic classification predicts compliance **levels** but not budget sensitivity.\nOffshore and border districts exhibit systematically higher compliance regardless of\nannual budget variation.*\n\n**Regression sample:** N = 104 (13 districts \u00d7 8 years, 2016\u20132023). All models include\ndistrict fixed effects; standard errors clustered at the district level (G = 13).\nRobustness sample: N = 91 (2017\u20132023, distributed lag models).\n" } ], "metadata": {