Rules Universe and Raters

Specifically, our IRT approach synthesizes 15 raters to generate significance measures for a rules universe of 39,311 federal regulations published in the Unified Agenda of Federal Regulatory and Deregulatory Actions between Spring 1995 and Spring 2019, inclusive (Chiou and Klingler Reference Chiou and Klingler2023).Footnote ⁴ Pursuing the argument and practice of O’Connell (Reference O’Connell2008) and Potter (Reference Potter2017), we use data from an RIN’s final UA entry for our measure as we agree that data captured at promulgation (or the end of development) best characterize the noteworthiness of the entire package represented by an RIN during its development.Footnote ⁵ Our justification for using this data source and additional information on our rules universe may be found in Appendix A of the Supplementary Material.

The scope of this rules universe substantially expands on prior efforts (e.g., Carey Reference Carey2019; Haeder and Yackee Reference Haeder and Yackee2015; O’Connell Reference O’Connell2008; Reference O’Connell2011; Potter Reference Potter2017; Yackee and Yackee Reference Yackee and Yackee2009a) by incorporating all rules considered by both executive and independent agencies, including rules with or without NPRMs. “Rules without NPRMs” refers to rules for which a proposed rule was never published, as well as direct final rules, and interim final rules.Footnote ⁶

As mentioned above, we propose 15 raters for rule significance. Drawing from and substantially expanding on previous efforts for measuring legislative and rule significance, we collected data for many more raters. We employed only the most theoretically and empirically justifiable raters related to the concept of rule significance defined above, safeguarding that the uncovered latent variable reflects that concept. In addition, we omitted raters that could reflect potential veto players’ reactions to agency rulemaking activities. These criteria facilitate interpretation of our estimates and allow our measure to be invaluable to other scholars seeking to apply them to address theoretical and empirical questions. The rest of this subsection is devoted to describing our justifications for each of these raters, leaving the discussion of how each rater is coded in Appendix B of the Supplementary Material.

Rule mentions in major newspapers reflect judgments of rule consequence and noteworthiness by contemporary chroniclers, and we count such mentions in The New York Times (NYT) and The Washington Post. NYT indicates whether an RIN was published as a proposed rule and covered in the NYT’s “National Desk” section. These data were used in Potter (Reference Potter2017) and were furnished by the author. We create the Washington Post Total rater with a Washington Post ProQuest search through a count of articles discussing an RIN during its development reported and shown in the UA. We measure editorial priorities by counting front page mentions of rules in The Washington Post to create Washington Post Front Page, following the same procedure as Washington Post Total. The length of each rule’s development varies, and journalists tend to be aware of rules while they appear in the UA. Thus, a rule with a longer development period may receive more news coverage than an equally notable rule which was developed quickly. To account for this confounder, we incorporate the number of UA issues including a rule as a control variable for these two raters.

Unfortunately, media resources are too constrained to cover the thousands of rules on the UA. As reported in Table A.5 in Appendix B of the Supplementary Material, there are, in total, fewer than two-thousand rules covered by these three newspaper raters, occupying less than 5% of the rule universe. Relying on media raters alone would lead us to fail to distinguish the significance of the rest of the rules. Building on prior efforts on legislative significance (Clinton and Lapinski Reference Clinton and Lapinski2006), we incorporate data on general regulatory activity in order to further refine highly significant rules and differentiate between moderately significant rules.

Regulatory agencies generate copious data on rules under development, reporting biannually on considered rules in the UA. UA entries identify RINs classified as “major”—judged by agencies to have an annual economic effect of $100 million or more, or to meet other criteria set by the Congressional Review Act. O’Connell (Reference O’Connell2008) uses this dichotomous indicator to determine a significant rule. We label this rater as Major. Further actions reveal agency beliefs that a rule is notable to the public. NPRMs are required by the Administrative Procedure Act to allow public comment on rules (with exceptions). Furthermore, advance notices of proposed rulemaking (ANPRMs) may be issued to gauge public opinion at earlier stages at agency discretion. The number of ANPRMs and NPRMs published for an RIN were included through the raters ANPRM Count and NPRM Count, and Hearing indicates a hearing/meeting was held on the rule.

Agencies report a rule’s priority, influenced by the RIN’s economic impact, but also determined by whether agency leaders seek action on an RIN. We identify if an RIN’s reported priority category in the UA was either “Economically Significant” or “Other Significant” as an indicator for significant rules.Footnote ⁷ Yackee and Yackee (Reference Yackee, Yackee, Provost and Teske2009b), Lavertu and Yackee (Reference Lavertu and Yackee2014), and Potter and Shipan (Reference Potter and Shipan2019) employ this binary indicator to determine which rule is significant.Footnote ⁸ Agencies also report an RIN’s inclusion in an agency’s Regulatory Plan, reflecting the most important regulatory actions expected to be proposed by an agency in a fiscal year. We label these raters as Priority and Regulatory Plan, respectively.Footnote ⁹

A rulemaking project’s noteworthiness may manifest itself in the legal or anticipated public response to the text of the regulation. We capture this in two ways, starting with regulation length, which arguably captures the noteworthiness of a rule through the agency’s preemptive defense of the policy. Page Count is the count of pages used by the first NPRM, direct final rule, or interim final rule published in the Federal Register for each RIN.Footnote ¹⁰ Assuming texts with the force of law which are cited more often in scholarly research are more likely to be substantively important (see Haeder and Yackee Reference Haeder and Yackee2022; Yackee and Yackee Reference Yackee and Yackee2016), we include Legal Citations, which captures the number of times an RIN is cited as visible in Hein Online’s Law Journal Library search.Footnote ¹¹

Demands from the legislative and judicial branch for an agency to act in a policy area provide a signal of noteworthiness for a rulemaking project before it begins. We incorporate whether congressional statute set a deadline for regulatory action on the RIN (i.e., indicating somewhat urgent or intensive attention to a policy) as the rater Statutory Deadline (Lavertu and Yackee Reference Lavertu and Yackee2014). We leverage analogous information from the UA on the presence of a court-imposed deadline for action as the rater Judicial Deadline.

Finally, the procedures of notice-and-comment rulemaking generate data from the public and interest groups which captures the significance of regulations. OMB Lobbying captures the number of recorded lobbying meetings with OMB officials on the subject of a rule, as required by EO 12866. Our final rater, Public Comments, is a count variable measuring the total number of public comments attached to a rule’s docket on Regulations.gov. Table A.5 in Appendix B of the Supplementary Material provides descriptive statistics on these seven dichotomous and eight count raters. Footnote ¹²

New Measurement and Validation

Having introduced the raters for measuring rule significance, we will turn to present our estimates of rule significance, with the model and its estimation detailed in Appendix C of the Supplementary Material. All of the raters included in our model can discriminate rule significance, to a varying degree. The discrimination parameter of each rater is far away from zero, as displayed in Table 1. Among the raters with binary outcomes (i.e., the first seven raters in Table 1), the rater of Major performs the best, followed by the raters of Priority and Regulatory. NYT can also discriminate significance well. However, it only mentions 122 rules and covers only rules with NPRMs that were issued by executive agencies up to 2014, limiting its discriminate power. Among the raters with count outcomes, the discrimination parameters of OMB Lobbying and Washington Post Front Page are the largest.Footnote ¹³ The mean of these raters is not particularly larger or smaller among count raters, suggesting that these two raters are responsive to the underlying latent significance.Footnote ¹⁴

Table 1.

Raters’ Discrimination and Difficulty Parameter Estimates

For a broad overview of regulatory significance across agencies, Figure 1 displays the distribution of all significance scores, and Figure 2 displays the distribution of significance scores for each of the various agencies in the dataset. There is substantial variation in the median significance across agencies as well as in the number and variation in significance scores. For example, the Department of Health and Human Services and the Department of Labor tend to work on rules which are rather noteworthy, with median significance scores of 0.419 and 0.426 (respectively), whereas the National Credit Union Administration and NASA tend to work on rules which are less significant, with median regulatory significance scores of−0.441 and−0.441. Beyond agency structure, agencies which propose fewer rules or whose regulations pertain to management practices out of public view (such as NASA) appear less likely to produce highly significant regulations.

Figure 1.

Significance Distribution of Rules, 1995–2019

Figure 2.

Distribution of Agency Significance Scores

Notes: Boxplots describe the distribution of significance scores for each agency in the dataset, sorted by median. The bounds of the box are defined by the interquartile range, and the whiskers extend from the ends of the IQR on both sides to 1.5x the IQR, or the maximum/minimum, whichever is closer. All points extending beyond 1.5x the IQR from the ends of the IQR are outliers depicted as dots. Agency abbreviations may be referenced in Table A.3 in Appendix A of the Supplementary Material.

O’Connell (Reference O’Connell2008) suggests that there may be some differences in the significance of the rules produced by independent and executive agencies. Figure 2 illustrates the distribution of regulatory significance across both executive and independent agencies. A two-tailed t-test of agency median significance during the study period by agency type reveals that the difference is not significant.

Our validity checks on our measure start with examining the correlation between our measure and existing ones. Our significance scores are particularly correlated with each agency’s reporting whether a rule is major or is rated as a priority (i.e., with a status of “Economically Significant” or “Other Significant”), with the correlation coefficients of 0.544 and 0.671, respectively.Footnote ¹⁵ When a rule is determined to be major or a priority, this does not guarantee that this rule would have high-significance scores unless some other raters simultaneously mention it or have a higher number. For example, as displayed in Figure A.1 in Appendix C of the Supplementary Material, when a rule is rated as a priority, which is employed by Yackee and Yackee (Reference Yackee, Yackee, Provost and Teske2009b) and Potter and Shipan (Reference Potter and Shipan2019) as the only indicator to determine a significant rule, our estimated significance can range from −0.435 to 3.483. This implies that when a rule is rated as a priority, we can further differentiate its significance. On the other hand, a rule not rated to be a priority can be assigned virtually any significance score.Footnote ¹⁶

Likewise, our scores are correlated with Potter’s (Reference Potter2017) impact scores by 0.487. This is not surprising, as her impact scores are obtained from four raters, two of which are incorporated into our IRT model. Our measure seems to improve on hers as the former further distinguishes rules with impact scores less than 0.6. These occupy approximately 99% of the rules included in her measure, as shown in Figure A.2 in Appendix C of the Supplementary Material. For instance, rules with impact scores around 0.3 are now stretched and can have significance scores ranging from 0 to 0.9, with evidence of clustering between 0 and 0.5.Footnote ¹⁷

In Appendix C of the Supplementary Material, we consider the most and least significant rules in our dataset, building on the convergent construct validity established in this section to provide substantial confidence in the validity of our rule significance measures.

Theoretical Model and Hypothesis

As mentioned, we adapt Romer and Rosenthal’s (Reference Romer and Rosenthal1979) and Tsebelis’s (Reference Tsebelis2002) theoretical work to generate competing models of rulemaking. We first describe common elements in these models. Under our theoretical framework, a game is composed of one agenda setter and one or more veto players. A government agency serves as the agenda setter (A) and proposes a rule $ {y}_j\in R $ to possibly alter the status quo $ {q}_j\in R $ in a unidimensional policy space (if $ {y}_j={q}_j $ , that means that A decides not to change the status quo), subject to a vetoing decision sequentially made by each of veto players, $ {V}_1,\dots, {V}_N, $ where N is a positive integer.Footnote ¹⁸ Each player has symmetric, single-peaked preferences. The agenda setter and veto players, respectively, have ideal points of $ {x}_A\in R $ and $ {x}_1,\dots, {x}_N\in R $ . Denote $ {x}_V=\{{x}_1,\dots, {x}_N\} $ . A proposed rule ( $ {y}_j\ne {q}_j $ ) will be finalized and replace $ {q}_j $ if none of the veto players blocks the proposed rule. Otherwise, $ {q}_j $ will be sustained.

To examine the relative influence of the two branches in rulemaking processes, we generate three competing models (they differ only in the set of veto players) from this theoretical framework as follows:Footnote ¹⁹

1. 1. Congress (i.e., the medians of the House and Senate) acts as the only veto players (labeled as Model C).Footnote ²⁰

2. 2. The president constitutes the only veto player (Model P).

3. 3. Congress and the president jointly function as the only veto players (Model CP).

For each status quo j, we solve for its subgame perfection equilibrium under each of the three models. Assume that $ {q}_j $ is drawn from a continuous distribution with the support large enough to cover the ideal points of the most conservative and liberal players. Denoting $ {y}_j^{*}({x}_V,{x}_A,{q}_j) $ as the policy in equilibrium, we can define the set of status quos that will be sustained in equilibrium as follows.

With the assumptions and definition above, we can obtain our main theoretical result laid out in the following proposition.

This proposition crucially implies that more veto players do not necessarily expand the boundaries of the agency gridlock set, a well-established result from Tsebelis (Reference Tsebelis2002). Another implication is that the boundaries depend on the relative location of the agenda setters and veto players (Krehbiel Reference Krehbiel1998).

These implications are illustrated in Figure 3, where the president is assumed to be a Democrat and the median of Congress is more conservative than the president. Unicameralism is assumed in this figure for the purpose of illustration, but we remind the reader that in our empirical analysis, we consistently assume that each chamber constitutes a veto pivot. There are three scenarios for the agency’s preferences to discuss in this simplified illustration: (i) the agency is even more liberal than the president; (ii) the agency is moderate; and (iii) the agency is an outlier and even more conservative than the median of Congress. Under the first scenario, the agency is closest to and more extreme than the president, compared with the two veto players, making the AGI of Model P shortest among the three competing models. The AGI of Models C and CP is identical and larger, although the latter model has an additional veto player. When the agency is moderate (i.e., scenario (ii) in the figure), the AGI of Model C shrinks, whereas that of the other models remains similar. Under scenario (iii), where the agency is located to the right of Congress and an outlier to the president and Congress, the AGI of Model P is expanded and has the same length as Model CP. Overall, the shift in the ideology of the agency may or may not alter the AGI of a model, depending both on the set of its veto players and on their relative locations.

Figure 3.

The Illustration of Agency Gridlock Interval (AGI) for Each of the Competing Models Under Different Preference Configurations

Notes: The bolded line to the left of a model label indicates the model’s AGI.

It is important to note that our theoretical framework does not require the control exercised by these veto players to be zero-sum. In a wide variety of preference configurations, action taken by one branch to constrain an agency may also benefit another branch. For example, in Model CP, a right-leaning Congress and President would be both better off by preventing a left-leaning agency from promulgating rules which would move policy further away from them. Additionally, there are a wide array of process controls (reporting mandates, impact analyses, and other procedural requirements) which may be imposed by a branch on agencies without forcing in a substantive change in policy (Rosenbloom, Newbold, and Doughty Reference Rosenbloom, Newbold and Doughty2018).

Like previous studies on legislative productivity and unilateral action (e.g., Chiou and Rothenberg Reference Chiou and Rothenberg2014; Howell Reference Howell2003; Krehbiel Reference Krehbiel1998), we assume that status quos are uniformly distributed.Footnote ²² This assumption implies that an agency facing political environment entailing a more lengthy AGI will be less productive in a Congress (i.e., the lengthier the AGI, the less productive the agency). We will concentrate our empirical analysis on this hypothesis.

These competing models are related to hypotheses proposed by previous studies in several ways. For example, Potter and Shipan (Reference Potter and Shipan2019) hypothesize that an agency is more productive when it is ideologically aligned with the president, which is quite consistent with Model P. Additionally, their congressional influence hypothesis (i.e., agency productivity would be lower when Congress is an agency’s strong opponent) can be derived from Model C.Footnote ²³ On the other hand, the hypothesis proposed by Yackee and Yackee (Reference Yackee and Yackee2009a) on divided government cannot be derived from any of these models. These hypotheses assume that implicit vetoes are exercised by both Congress and the president. One of the important advantages from our theoretical framework is that we more systematically and explicitly evaluate potential models and improve theoretical clarity.

Method and Data

We examine the hypothesis derived from Proposition 1 using a dataset of 442 parent agency-Congress observations, covering 55 parent agencies (hereafter referred to as agencies) from 1995 to 2012, as detailed in Appendix A of the Supplementary Material. Our analysis focuses on this period and these agencies because agency ideal point estimates comparable with those of veto players we employ are available only for this period and these agencies. The unit of observation was tied to a 2-year Congress rather than alternatives such as quarters or months, which have been used by other studies (Potter and Shipan Reference Potter and Shipan2019; Yackee and Yackee Reference Yackee and Yackee2009a). We make this choice because each agency and corresponding veto players, including Congress and the president, have constant measured preferences (i.e., common-space scores) within a Congress, and a Congress captures the period between which the elected branches may act without clear signals of public preferences. Put differently, our key theoretical predictor, AGI, varies little for an agency within a Congress during the period, justifying our unit of analysis. This periodicity also follows convention in well-developed literature on legislative productivity (Binder Reference Binder1999; Krehbiel Reference Krehbiel1998) and executive orders (Chiou and Rothenberg Reference Chiou and Rothenberg2014; Howell Reference Howell2003).

Calculating agency productivity by focusing on promulgation of RINs from our rules universe for which an NPRM was published requires several noticeable choices worth highlighting and defending. We exclude interim final rules and final rules with statutory or judicial deadlines, consistent with Potter and Shipan (Reference Potter and Shipan2019), because the former types of final rules are intended to have only a temporary impact on public policy and are not consistent with our theoretical model. Similarly, Congress or the courts act as the agenda setter under the latter types of final rules. Although our theoretical model does not depend on whether or not an NPRM was issued for a rule before it was finalized, we focus on rules with NPRMs in our primary analysis to be consistent with prior scholarship on regulatory productivity (Potter and Shipan Reference Potter and Shipan2019; Yackee and Yackee Reference Yackee and Yackee2009a). Later, we extend our empirical analysis by including these final rules without NPRMs.

To examine agency rule productivity, our dependent variables are the number of final rules with at least one NPRM whose significance scores are at least as high as a given significance threshold and promulgated by an agency in a Congress. For each agency-Congress observation, data on agency regulatory productivity in that biennium were drawn from our rules universe (described in Appendix A of the Supplementary Material). Given that estimated scores of rule significance range from −1.276 to 3.483, as shown in Figure 1, that rules with NPRMs share this range of scores, and that rules without mentions of all raters tend to have scores between −1.276 and −0.3, we start our minimum significance threshold at −0.25 and incrementally increase the threshold of 0.25 until 2.25, as Chiou and Rothenberg (Reference Chiou and Rothenberg2014) conduct.Footnote ²⁴ In other words, there are 11 dependent variables, each of which corresponds to a significance threshold. In addition, the number of all of the final rules with NPRMs promulgated by an agency within a Congress is included as the 12th dependent variable, allowing us to examine rule productivity without holding any significance thresholds. Accounting for the nature of count data (e.g., overdispersion) and the importance of controlling for idiosyncratic characteristics of individual agencies for regulatory affairs productivity, we follow Potter and Shipan (Reference Potter and Shipan2019) decision of employing a negative binomial regression model with random effects at the agency level and standard errors clustered on the agency.Footnote ²⁵

In order to test our hypotheses, our primary independent variable of interest is AGI. According to the theoretical results of the “Theoretical Model and Hypothesis” section, AGI characterizes the location of the rule promulgating agency in relation to the relevant political actors in policy space.Footnote ²⁶ As a starting point, for each agency in the dataset, we use the ideal points estimated by Chen and Johnson (Reference Chen and Johnson2015) to place the agency in Common Space with the president and members of Congress (McCarty, Poole, and Rosenthal Reference McCarty, Poole and Rosenthal2006).Footnote ²⁷ The agency ideal points generated by Chen and Johnson (Reference Chen and Johnson2015) are estimated for 79 agencies using the political contribution data of individuals identified as working for the agency in those data.Footnote ²⁸ The AGI for each of the three models is calculated according to Proposition 1, the interval bounded by the ideal point of an agency and the veto players stipulated in each of the three competing models in the last subsection. For instance, an agency’s gridlock interval of model CP for a Congress is the distance between ideal points of this agency, the chamber medians of the House and Senate, and the president during this given Congress. For each of the three models, we calculate the AGI for each Congress from the 104th to 112th.

We also include several control variables to account for important predictors already identified in the literature, or expected to be theoretically relevant. Prior research has suggested that divided government may pose additional barriers to agency productivity in the form of conflicting demands (Yackee and Yackee Reference Yackee and Yackee2009a). In order to account for this possibility, we include a dummy variable for Divided Government, which is coded 1 for agency-Congress observations for which the president and at least one house of Congress were controlled by different parties the majority of the time, and 0 otherwise.

We control for the workload capacity of agencies with Employment, the logged average yearly number of employees at each agency, as this influences productivity (Potter Reference Potter2017). Prior scholars have suggested that independent agencies may be less productive (Potter and Shipan Reference Potter and Shipan2019), so we include an indicator variable for Independent Agency. Footnote ²⁹ We include a time trend variable in the form of Congress and Congress Squared following the approaches of Carter and Signorino (Reference Carter and Signorino2010).Footnote ³⁰

Empirical Results

We present our empirical results from testing our hypotheses for our three competing models. We start with our results from testing Model P, where the president constitutes the only veto player. As displayed in Table 2, the dependent variable of the first equation is the total number of final rules with NPRMs promulgated by an agency within a Congress. The dependent variable of the second equation is the total number of final rules with NPRMs and significance scores at least as high as $ -0.25 $ . The last equation has the total number of final rules with NPRMs and scores equal to or higher than $ 2.25 $ as the dependent variable. As shown in this table, the coefficient of the AGI, our key independent variable, is negative, as predicted, and statistically significant under a wide range of significance thresholds, that is, from 1 to 1.75. The average marginal effect of this variable is $ -1.858,-2.122,-1.445 $ , and $ -0.626 $ under each of these four significance thresholds, respectively. The substantive importance of the AGI effect is evident, given the mean of the associated dependent variables (see Table A.8 in Appendix D of the Supplementary Material). These results suggest that the empirical support for Model P is obtained under moderate- or high-significance thresholds.

Table 2.

The President as the Only Veto Player (Lowest to High Thresholds)

Note: Standard errors are in parentheses. Each model’s dependent variable is the number of eligible final rules with NPRMs and a significance score of at least T (defined in the column labels), promulgated by an agency within a Congress. Models include agency-level random effects and agency-clustered SEs. BIC = Bayesian information criterion. One-tailed test: $ {}^{*}p<0.05 $ , $ {}^{**}p<0.01 $ , $ {}^{***}p<0.001 $ .

The results for testing Model C (Congress functions as the only veto player) are shown in Table 3. The results for our key independent variable diverge: the AGI is negative and statistically significant only under the thresholds equaling to 1.50 or higher. The average marginal effect of this variable is $ -3.912,-2.008 $ , and $ -1.346 $ under the thresholds of 1.50, 1.75, and 2. These are pronounced and even stronger than under Model P, given the mean of the dependent variable under these thresholds. Likewise, the coefficient of the AGI of Model CP is statistically significant under the thresholds of 1, 1.25, 1.50, 1.75, and 2, with the average marginal effect of $ -1.788,-2.852,-2.758,-1.265 $ , and $ -0.470 $ (see Appendix F of the Supplementary Material).

Table 3.

Congress as the Only Veto Player (Lowest to High Thresholds)

Note: Standard errors are in parentheses. Each model’s dependent variable is the number of eligible final rules with NPRMs and a significance score of at least T (defined in the column labels), promulgated by an agency within a Congress. Models include agency-level random effects and agency-clustered SEs. BIC = Bayesian information criterion. One-tailed test: $ {}^{*}p<0.05 $ , $ {}^{**}p<0.01 $ , $ {}^{***}p<0.001 $ .

While previous studies tend to find the effect of divided government is negative and statistically significant, we uncover more systematic evidence for this effect only with very low-significance thresholds under Model CP.Footnote ³¹ This implies that agencies do not produce a lower number of moderately or highly significant final rules under divided government.Footnote ³² However, consistent with previous findings, the effect of agency employment size is always positive and statistically significant under various significance thresholds. Furthermore, rule productivity does not hinge on whether an agency is an executive or independent one, regardless of the thresholds. We also find an upward trend (i.e., more final rules with NPRMs were promulgated during Bush’s second term and Obama’s first term) under moderate or high-significance thresholds.Footnote ³³

As summarized in Table 4, when the significance threshold is less than 1, none of the three models receive empirical support. With the thresholds of $ 1 $ and $ 1.25 $ , the main hypothesis is supported for Models P and CP. The Bayesian information criterion (BIC) of these two models are about the same, so it is difficult to use the BIC to distinguish which performs the best. Following the principle of theoretical parsimony, however, Model P appears superior, as adding more veto players does not improve model fit. The AGIs of Models P, C, and CP all receive empirical support with the threshold of 1.50, but the second model has slightly lower BIC. When the threshold is 1.75, Models C and CP perform similarly and clearly outperform Model P. With the significance threshold of $ 2 $ , the AGI coefficients of Models C and CP are both significant, but the BIC of the former is clearly smaller than that of the latter.

Table 4.

Model Comparison: Rules Only with NPRMs

Note: The blank cells indicate that a particular model found no significant relationship between agency gridlock interval (AGI) and rule productivity using a one-tailed test for $ \alpha =0.05 $ , drawing from a rules universe with only RINs scoring above the row’s listed significance threshold. If the coefficient on AGI is significant for a model (with expected sign) under a significance threshold, the Bayesian information criterion of the model is listed.

We conduct several robustness checks (and extensions of our analysis). First, we explore alternative actors in Congress that may play a crucial role in constraining agency rulemaking activities. Although chamber medians are considered the most critical actors by nonpartisan (Krehbiel Reference Krehbiel1992) and partisan theories (Cox and McCubbins Reference Cox and McCubbins2005), we examine majority party medians and leaders to examine whether partisan force is an essential element in rulemaking productivity. For majority medians, we evaluate three competing models: (1) majority medians constitute the only veto players; (2) the president and majority medians act as veto players; and (3) majority medians, chamber medians, and the president are veto players. We do not find strong support for the first model (the coefficient of AGI is at best marginally significant under high-significance thresholds), but the results for the second and third models are qualitatively akin to those of our Model CP (see Table 4), with slightly higher BIC scores.Footnote ³⁴ However, the models where chamber medians act as veto players always perform better than those models where we do not alter the set of veto players, except that we replace chamber medians with majority medians. Since the ideologies of majority medians and majority party leaders are highly correlated, unsurprisingly, our results for majority party leaders are almost qualitatively identical to those for majority medians.Footnote ³⁵ This suggests that chamber medians are the most important actors in Congress and that their role cannot be replaced by majority medians or leaders. Our conclusions drawn from our results in Table 4 are robust.

In addition, we examine whether our primary results still hold up if we add final rules without NPRMs (excluding interim final rules and rules with legal deadlines). There exists a sizable number of rules which are finalized without being designated by an agency as a direct final rule or generating an NPRM (see Appendix A of the Supplementary Material). As displayed in Table 5, the overall results continue to hold. This means that the president and Congress seem to exercise influence over rules with or without NPRMs similarly. Moreover, the implicit veto held by the two branches over a rule is not mediated by the formal procedures of the standard notice-and-comment process.

Table 5.

Model Comparison: Final Rules With or Without NPRMs

Note: The blank cells indicate that a particular model found no significant relationship between agency gridlock interval (AGI) and rule productivity using a one-tailed test for $ \alpha =0.05 $ , drawing from a rules universe with only RINs scoring above the row’s listed significance threshold. If the coefficient on AGI is significant for a model (with expected sign) under a significance threshold, the Bayesian information criterion of the model is listed.