The contingent value of connections: legislative turnover and revolving-door lobbyists

Abstract Former legislators who lobby exacerbate the effects of financial resources on the relative political influence that various organized interests achieve. These lobbyists receive more income and achieve favorable policy outcomes more often than other lobbyists. The value of these revolving-door lobbyists, however, is contingent on the continued presence of former colleagues in legislatures. Former legislators achieve influence because of their insider connections, and membership turnover among incumbents decreases the value of this asset for interest groups. I examine the incomes and clienteles of former legislators who lobbied in the American states over seven decades. Turnover is a consistent, negative predictor of revolver value. This effect is enhanced by the presence of legislative staff support. This study is the first to examine the value of revolving-door lobbyists in the state legislatures. My findings imply that reforms that induce turnover help to level playing fields of political advocacy among interests with different levels of financial resources.


Introduction
Revolving-door lobbyists include legislators who become lobbyists to capitalize on their insider connections and political knowledge. While working in the assembly, legislators form connections or relationships with each other. When theyretire, their connections allow for effective lobbying because the remaining incumbents grant them access or meetings, and former legislators know how to appeal to incumbents' interests. Empirical patterns support these claims. Former members of Congress deliver policy results for their clients more often than other lobbyists. 1 Perhaps as a result, these lobbyists are among the best-paid and represent the most clients in Washington. 2 Given that revolvers are paid handsomely and deliver policy results for their clients, social scientists raise concerns over their role in exacerbating the effects of resource inequalities on the relative political influence that different groups exercise. Organized interests have access to unequal levels of monetary support. Most interests active in legislatures are narrow, special interests seeking particularistic benefits. These organizations typically have access to more resources than those that claim to represent dispersed interests and seek collective benefits. 3 Hence, it is argued that the use of revolving-door lobbyists by wealthy interests allows for more upper-class bias in the kinds of interests that exercise influence. 4 Despite these arguments, little remains known about the conditions under which revolving-door lobbyists are more or less valuable. From existing research, revolvers achieve influence in government because of their connections. These assets are undermined when allied incumbents move out of legislatures. Moreover, revolvers with fewer years of legislative experience have weaker connections than those with more years of experience. Turnover among legislators therefore reduces the value of prior legislative experience and makes former legislators, as advocates, similarly attractive as other lobbyists. Existing research provides evidence of a contingent value of revolving-door lobbyists. Former staffers for senators attract less money in lobby contracts whenever their former bosses retire from the Senate, 5 and former staffers with more connections on the Hill attract more lobby contract revenue. 6 Both findings provide valuable insight into the revolving door but both of the relevant studies examine staff revolvers in the same political system (i.e., Congress) for short periods. Little remains known about how the value of legislator revolvers changes across political systems and decades in response to large shifts in membership stability.
Using original data sets, I build on others' findings and provide significantly more insight into the contingent value of revolving-door lobbyists. With directories of legislators and lobbyists retrieved from archives across the United States, I identify the former legislators who became lobbyists in the states over seven decades. I then compare the client numbers of revolvers to those of nonrevolvers over the same period. Using this information, I examine changes in the clientele premium associated with legislative experience. I find consistent evidence that the premium increased in most states over time but did so discernibly less quickly where turnover among incumbents escalated or remained elevated. Importantly, this effect was not tempered or enhanced by changes in session lengths, party control of state legislatures, or levels of party competition. Instead, the negative effect of turnover on revolver premiums was greatest in states that added legislative staff who could, presumably, also quit and work as lobbyists. My findings align well with those of recently published studies that rely on access-driven accounts of lobbyist value.
My findings also provide important contributions to the study of interest representation and political reform. This study is the first to identify revolvers active before the 1980s, and the first to examine the clienteles or incomes of state revolvers at any point. Apart from the development of original data, however, this study has significant implications for representation and reform. State legislatures have professionalized over the past several decades. Likely as a result, member turnover has declined as well. 7 Former legislators came to benefit from reductions in member turnover because their personal acquaintances remained in office longer, on average. This suggests a paradox: while legislative professionalization in the 1960s and 1970s was intended to improve representation, it allowed for the emergence of gatekeeping, revolving-door lobbyists. Moreover, the turnover induced by term limits implemented decades after professionalization may have weakened somewhat the ties that bind groups to their advocates. While professionalization improved the lawmaking capacities of legislatures and term limits weakened legislative capaciies the presence of gatekeeping lobbyists, whether revolvers or not, raises normative concerns about political equality and how the characteristics of legislatures help determine which interests achieve influence. 8 Legislative turnover and revolver value To LaPira and Thomas, lobbyists rely on two assets or personal qualities to achieve access and influence: personal relationships and knowledge. 9 Relative to other lobbyists, former legislators acting as lobbyists benefit more from their relationships with prior colleagues. While working together, legislators form professional relationships with one another. Staffers develop similar ties among themselves and with legislators. These relationships endure beyond members' or staffers' retirements from the assembly. The findings from Jordi Blanes i Vidal, Mirko Fons-Rosen, and Christian Draca indicate that relationships matter to organized interests. 10 They argue that the value of a relationship is revealed through lost lobby revenue whenever the former boss of a staffer who became a lobbyist retires from Congress. In addition to relationships, lobbyists might also rely on different forms of knowledge to achieve influence. A type of knowledge that is exclusive to those with legislative experience is personal familiarity with incumbents' interests or priorities. 11 Having this knowledge enables former legislators to lobby more effectively. Former legislators understand or recall the political interests or priorities of former colleagues, as privately expressed, and this allows them to lobby their colleagues more effectively than could other lobbyists. A former staffer in Congress, Joe Cirincione, describes this exclusive information somewhat: "[w]hat I knew [as a staffer] was how a bill becomes a law…how you get it through the committees, what members' interests were. You can take that knowledge and sell it." 12 Importantly, such personal familiarity with members' interests is different from the sheer policy expertise that all lobbyists, revolvers or not, may acquire.
Legislative turnover occurs whenever there is member replacement, whether due to voluntary retirements, term limits, reelection loses, or even deaths. In the United States, turnover has been shown to respond to term limits, 13 opportunities for higher office and member pay, 14 national economic conditions, 15 and interbranch bargaining, 16 but not respond to factors more closely related to lobby activities: legislative gridlock, 17 campaign contribution limits, or public campaign funding generally. 18 Turnover affects the value of revolving-door lobbyists' assets or personal qualities. To date, researchers have focused on how turnover reduces numbers of incumbents with whom revolvers have connections and familiarity. In this narrative, the value of legislative experience is contingent on whether acquaintances continue to serve in office and have influence over policy. In cases in which legislators are replaced, revolving-door lobbyists lose valuable connections in the assembly. Other lobbyists lack legislative experience and likewise lack similarly close connections and insider knowledge, although they may be affected negatively by turnover somewhat. Any effect of turnover on revolver premiums therefore depends on the disproportionate value of personal connections for revolvers versus for other lobbyists. If these assets were of equal value to all lobbyists, then changes in turnover would not affect the premiums that revolvers enjoy. 19 Indeed, businesses appear to hire former members of Congress specifically more often during times of uncertainty because of their connections with incumbents. 20 The connection between legislative turnover and the value of legislative experience for lobbyists relies on the assumption that organized interests can gauge somewhat the value of former legislators before or after hiring them. While Lee Drutman argues that organized interests have less information than their lobbyists about political environments, including about the lobbyists' connections, others' findings suggest strongly that groups can determine at least somewhat the value of their lobbyists' connections. 21 The findings show that groups hire former Senate staffers to take advantage of their ties to specific senators, and then pay the former staffers less after the senators retire. At least some groups in Congress therefore hire staff revolvers for their ties to specific incumbents. If organized interests hire former legislators to solicit incumbents and can gauge somewhat the abilities of 11 Strickland (2020). 12 Citizens for Responsibility and Ethics in Washington (2012). 13 Moncrief et al. (2004). 14 Rosenthal (1974). 15 Berry et al. (2000). 16 Krupnikov and Shipan (2020). 17 Squire (1998). 18 Butcher and Milyo (2020). 19 Previous research (e.g., Carey et al. 2000, 83;Moncrief and Thompson 2001;Sarbaugh-Thompson et al. 2004;and Powell 2012) on legislative turnover and lobbying suggests that newer legislators tend to have less policy expertise and accordingly rely more on lobbyists and bureaucrats for expertise. For this reason, turnover is said to empower lobbyists and governors (Mooney 2007;. These studies do not examine the difference in value between different kinds of lobbyists, however, and they all rely on information-based narratives of how lobbyists achieve influence. 20 Liu (2020). former legislators to achieve access and influence, then turnover among incumbents should be negatively correlated with the lobby value of former legislators, on average.

Other determinants of revolver value
Congress and various state legislatures have implemented restrictions on postgovernmental employment (PGE), also known as cooling-off laws. These laws require retiring lawmakers to wait some amount of time before lobbying. These laws are intended to limit conflicts of interest in which soonretiring lawmakers may change their legislative decisions to cater to the interests of future employers. 22 The laws appear to discourage lobbying by former officials. In Congress, the Honest Leadership and Open Government Act of 2007 imposed a cooling-off period on members and staff, and fewer staff subsequently became lobbyists. 23 In the state legislatures, for every additional year former lawmakers are required to wait, roughly three fewer former legislators register to lobby. 24 Besides affecting revolver totals, restrictions on PGE may depress the value of revolvers. Former legislators become lobbyists to capitalize on their relationships and political knowledge, and those assets may lose value during the period when former legislators cannot lobby. Also, revolvers lose the ability to build their lobbying skills during that period. Cooling-off periods are similar to other kinds of labor sabbaticals that are associated with decreased wages. A prominent example is motherhood: mothers tend to be paid less than their nonmother female coworkers. The unfortunate wage losses associated with motherhood tend to last for years, 25 and similar wage effects might be found for revolving-door lobbyists due to lost connections or skills.
Former legislators are not the only people in capital cities who may offer legislative experience to potential clients. Legislative institutions vary in their numbers of full-and part-time support staff. In Congress, these individuals often retire and become lobbyists. 26 Due to their greater numbers, more former congressional staffers regularly serve as lobbyists than former members. 27 These lobbyists are typically subjected to the same PGE restrictions as legislators. 28 If a legislature contains numerous staffers who sometimes become lobbyists, then this threatens the exclusivity of revolver assets among former legislators. 29 As a result, former legislators acting as lobbyists may have fewer clients in states with historically higher levels of legislative staffing.
Finally, apart from the effects of turnover, the value of legislative experience might also be determined by how much competition there is for political access. Political systems differ in how many members serve in legislatures. Kyle Kattelman argues that it is easier for lobbyists to achieve access in large assemblies versus small assemblies simply because there are more potential points of access in large assemblies. 30 Moreover, Robert McCormick and Robert Tollison also argue that access is more valuable in small assemblies given that individual legislators have more proportional influence over legislative outcomes. 31 Organized interests may be more likely to hire former legislators to lobby in small assemblies given that other lobbyists fail to achieve as much access or if personal access to individual legislators is perceived to be more desirable. This effect on the value of legislative experience might be particularly pronounced in political systems also with many organized interests 22 Barro (1973). 23 Cain and Drutman (2014). 24 Strickland (2020). 25 Kahn et al. (2014).  LaPira and Thomas (2017). 28 Holman and Reddy (2011). 29 While Berkman (2001) argues that staffers serve as substitutes for lobbyists and therefore reduce interest mobilization, this argument does not explain the value differential between different kinds of lobbyists. Legislators with more staff may rely on lobbyists generally (revolvers and others) less often, with the premium for legislative experience remaining stable. Moreover, Berkman's argument is information-based in that legislators with staff are said not to rely on lobbyists for policy expertise. I argue, however, that the source of revolvers' value is personal connections and insider knowledge (i.e., not policy expertise). 30 Kattelman (2015). 31 McCormick and Tollison (1981). competing for access. Numbers of organized interests vary remarkably across systems. 32 While there may be more competition for access in systems with more organized interests, this relationship may be moderated or enhanced by legislature size.
I controlled for the effects of similar confounders in an analysis of revolver totals in the states. 33 That study found that totals of revolvers changed in response to legislative turnover, restrictions on PGE, and numbers of organized interests in the states. I argued that the value of state revolvers declined in response to turnover, but did not observe revolver values directly. Instead, I examined totals of former legislators who lobbied. The present study, in contrast, tests for whether changes in revolver value, when observed directly, may be detected and predicted successfully despite the possibility that some former legislators fail to become lobbyists because of low premiums for their legislative experience.

Identifying revolvers
To determine if turnover and other factors are correlated with revolver value, I turn to the American states. The states were the first democracies to register lobbyists on a permanent basis. 34 The first of these laws emerged in Massachusetts in 1891, and all states required lobbyists to register by 1975. 35 As a result, the states offer a wealth of information regarding how lobbying has changed over time. Importantly, they also vary in significant ways institutionally. Legislative turnover has historically declined within the states overall but continues to vary across states. Fifteen legislatures now enforce term limits but even beyond those assemblies members serve varying lengths of time on average depending on legislature professionalization and the other factors listed earlier. 36 To measure the value of revolving-door lobbyists, one must first identify which lobbyists served as government officials. Using directories of legislators and lobbyists dating back several decades, I identify revolving-door lobbyists by matching names across lists within states. I first gathered lists of registered lobbyists and clients. All lists from before the 1970s were found in state archives, libraries, or newspapers. 37 Lists from after those decades were found in archives and libraries (also), compilations of lobbyist lists, 38 or were provided by the National Institute on Money in Politics (now part of OpenSecrets). I then gathered lists of legislators published by the Council of State Governments. Beginning in 1937, the council began to publish legislator directories as appendices to its biennial Book of the States, a compendium of state government statistics. For legislators active after 1970, I turned to a directory of election winners produced by Carl Klarner and others. 39 Assistants transcribed the names of lobbyists and former legislators into separate spreadsheets. Combinations of first and last names that appeared among lobbyists and former legislators were identified. 40 I previously demonstrated that this method of identifying former legislators who lobby is accurate because it produces few false matches based on lists from different states. 41 Using the directories, I identified former legislators registered to lobby in the states for years around 1949, 1959, 1973, 1989, and 2009. Because some states did not register lobbyists until the 1970s, complete waves of observations are not available for all periods. Nineteen states have observations of 32 Mueller and Murrell (1986); Gray and Lowery (1996). 33 Strickland (2020). 34 Opheim (1991). 35 Strickland ( Reitman and Bettelheim (1973); Marquis Academic Media (1975); Wilson (1990). 39 Klarner et al. (2013). 40 While the council's directories were not published regularly, they were published regularly enough to allow me to identify former legislators who registered to lobby. For each wave of observations in my collection of lobbyist lists, I identified former legislators who had served in office at some point during the preceding two decades or so, depending on the year of the lobbyist list. Unfortunately, there are no directories of legislative staff readily available in a usable format, so this study examines only legislator revolvers. 41 Strickland (2020). revolving-door lobbyists for all five waves. 42 Nine more states have observations for four waves only. 43 There are three observations for each of the remaining states, except Hawai'i. 44 Ultimately, 193 stateyear observations of revolver totals are available. This sample, which spans seven decades, exceeds in scope previous studies of state revolving-doors. 45 Once former legislators were identified within my lists of registered lobbyists, I counted their totals to get an initial sense of how the overall size of the revolving door has changed in the states. For the first time, state revolver totals from before the 1980s are produced: figure 1 reports a box-and-whisker plot of total revolvers in the states for each wave of observations under study. Revolver totals have increased, and most of these increases occurred since the 1970s when states saw large increases in numbers of organized interests that registered lobbyists. 46 In general, increases in revolver numbers occurred despite the fact that turnover declined over these decades and, as a result, numbers of former legislators available to lobby also declined. Figure 2 presents the totals for each state individually.

Measuring revolver value
Ideally, to measure the value of legislative experience, one would not observe revolver totals but instead the compensation that lobbyists receive. For studies based on Congress, scholars examined the lobby contract revenue that revolvers drew to their firms. 47 Unfortunately, in the states, lobbyist incomes or revenues are not widely available because only a few states require that lobbyists report these statistics No lists of lobbyists from the 1970s for this state could be located by archive or library staff in multiple facilities. Also, Michigan's observation from 1989 is omitted given that lobbyist registrations in that state were permanent and the list included inactive entries. The more recent list produced by the National Institute for the state includes active lobbyists only.  in readily usable formats. Because direct observations of revolver and nonrevolver value are not available in most states, I examine the clientele premium. 48 Using the lobbyist lists, acquiring clientele size for each lobbyist is straightforward. All registration laws require that lobbyists name the clients they represent or the firms they work for, which in turn name the clients the firms represent. Table 1 presents average clientele totals for both revolvers and nonrevolvers in all available states for each of the five periods under observation in my sample. The table also reports the results of simple difference-of-means tests. During all five periods, revolvers across the nation represented more clients than nonrevolvers, on average. Growth in revolver clienteles truly increased during the 1980s, with revolvers representing more than twice as many clients as nonrevolvers by the end of that decade, on average. Generating averages across various state-level averages gives more weight to states with smaller numbers of revolvers than others, however, so table 2 reports similar statistics at the level of the individual lobbyists who registered during each wave of observations. The results are similar across the tables: former legislators who became lobbyists represented discernibly more clients than their counterparts for each of the five periods. The revolver premium appears to have grown especially throughout the 1980s and subsequent decades. This is unsurprising given the sharp growth in interest groups lobbying state officials during these decades. 49 The test results from both tables indicate that the chances of the revolver premiums in nearly all periods being due to random chance are remarkably low. These findings reflect trends in Congress but, of course, mask differences in revolver premiums across states. 50 Figure 3 presents the revolver clientele premium (difference between average clientele size of revolvers and that of nonrevolvers) across states and observation waves. 51 For most observations, revolving-door lobbyists represented more clients than other lobbyists (i.e., the premium is above zero). The figure excludes two observations with values greater than ten. In general, the clientele premiums of former legislators have grown over time. Trends in California, Vermont, and Washington are prominent exceptions.

Explanatory variables
One of the biggest changes in state legislatures during the twentieth century was reduced turnover among members. At the beginning of the century, memberships were "shockingly unstable." 52 The In the appendix, I use lobbyist income statistics from five states to show that clientele premiums are a good proxy for the value of legislative experience. In particular, because former legislators are shown to be paid more in total but not on a per client basis, their clienteles are reliable proxies for how much additional income they receive in comparison to nonrevolvers. In other words, revolving-door lobbyists take home more compensation due to having larger clienteles than nonrevolvers, and not because they receive discernibly more from each client on average. 49 Strickland (2021). 50 LaPira and Thomas (2017). 51 In states with zero revolvers, revolvers were indicated to represent zero clients and the premium would likewise be a negative number.
legislative professionalization movement of the 1960s and 1970s sought partially to lower turnover by paying legislators more. 53 Today, more professionalized legislatures have lower member turnover; but these trends were disrupted somewhat in the 1990s by the implementation of legislative term limits, which are now in effect in fifteen states. 54 To estimate the effects of legislative turnover, I turn to measures provided by Kwang Shin and John Jackson, and Gary Moncrief,Richard Niemi,and Lynda Powell. 55 These authors provided turnover rates for either decadal or biennial periods. Biennial rates are averaged for each decade where needed. House and Senate assemblies often display different turnover rates but lobbyist lists do not indicate which individuals lobby representatives, senators, or both. I weighted the turnover rates of Houses and Senates based on their membership sizes to generate single turnover measures for each legislature. This variable therefore captures the percentage of new members who entered assemblies every two years, averaged over the ten-year periods preceding each wave of observations. According to my expectations, turnover should be negatively correlated with revolver premiums.
Throughout the latter twentieth century, state legislatures began to impose restrictions on the PGE of former members. This variable is measured in numbers of months that former members had to wait before registering to lobby. Cooling-off period lengths were collected from a previous study for my fourth and fifth waves of observations. 56 For earlier waves, I reviewed the lobby statutes of all states, included in Marquis Academic Media (1975). No state had enacted any PGE restriction by then. Since I found previously that states never eliminated or shortened their cooling-off periods once enacted, no restrictions were assumed to be in effect in any state during the first three waves of observations. 57 Longer cooling-off periods should be negatively correlated with revolver premiums.
Measuring legislative staff is challenging given the timing of some of my observations. Measures of legislative staff are available from Daniel Bowen and Zachary Greene, and the National Conference of State Legislatures, 58 but those observations date back only to the early 1970s. I control for the effects of staffing by including a less precise measure of legislative staff support in regression models: total spending on the legislature in millions of real dollars. This measure is imperfect because it also captures legislator salaries, but such salaries tend to be a small portion of total spending. These spending statistics were produced by the Census Bureau's Governments Division and provided by Carl Klarner. 59 To measure competition for legislator attention, I turn to numbers of legislators and interest groups. Personal access is expected to be more difficult to achieve yet more valuable in small assemblies, so  Moncrief et al. (2004); . 55 Shin and Jackson (1979); Moncrief, Niemi, and Powell (2004). I thank Gary Moncrief for providing updated turnover data for the states. 56 Strickland (2020). 57 Strickland (2020). 58 Bowen and Greene (2014); National Conference of State Legislatures (2016). 59 Klarner (2015). organized interests may be more prone to hire former legislators to target members of small assemblies. Yet, numbers of organized interests vary widely by state such that levels of intergroup competition may differ. These numbers were collected from the lists of registered lobbyists. Hence, while I incorporate numbers of legislators and interest groups with registered lobbyists into my models, I also construct an interactive term to help indicate if numbers of groups (legislators) moderate or enhance the effect of legislator (group) numbers on revolver premiums. Because no states had zero legislators or interest groups, only the coefficient reporting the interactive effect between these two variables is of interest.
As for a final explanatory variable, I control for the effects of a prominent yet idiosyncratic lobbyist registration procedure used in a small number of states. In California, New Jersey, and New York, lobbyists, interest organizations, and lobby firms may all register separately. This procedure was not used prior to the 1990s. In compiling lists of lobbyist-client pairings from these states, the National Institute on Money in State Politics appears to have assigned all lobbyists active with lobby firms to all of the clients registered for each firm. As a result, the lists of lobbyist-client pairings from these states likely include numerous lobbyist-client pairings that may not be active (as members of lobby firms may divide clients among themselves). This has the potential to inflate artificially the revolver premium because, if former legislators are more likely to be members of firms than other kinds of lobbyists, then their clienteles will merely appear larger in states with firm-level registration procedure. The idiosyncratic registration procedure is measured using a dichotomous indicator for observations in my last wave only from California, New Jersey, and New York.

Estimation method and results
To determine if turnover and other explanatory variables are correlated with the value of legislative experience, I estimate a series of least-squares regression models. In each model, the dependent variable is the difference between the average clientele size for revolvers and that for nonrevolvers. The variable assumes positive, negative, and noninteger values. Because I am working with repeated observations of states and am interested in how changes within each explanatory variable align with changes in my dependent variable, I include fixed effects of all states and periods in my models. 60 The fixed effects help to ensure that the coefficients produce estimates based only on changes that occurred within individual states over time. 61 I also estimate different specifications of my initial model to test the robustness of the hypothesized relationships. Among the four models presented in table 3, the first model uses all available observations, the second model excludes observations generated with the idiosyncratic registration procedure, the third model is estimated using only observations from the last three waves of observations, and the fourth model is calculated using only observations that appeared in all earlier models.
The coefficients listed in table 3 show strong support for the contingent value of legislative experience. The coefficients for turnover have negative values in every model. According to model 1, every one-unit increase in turnover percentage is associated with a reduced revolver premium of 0.09 clients on average, ceteris paribus. This effect is reduced to 0.04 clients in the second model, which excludes observations from states where lobby firms also register with state authorities. Nevertheless, because turnover decreased by 40 percent or more in some states, the predicted effects on revolver premiums from all models are substantively meaningful. The first model indicates that, with such a shift in turnover, the revolver premium would increase by 3.6 clients on average, ceteris paribus.
The implementation or lengthening of restrictions on PGE do not appear to affect the revolver premium. Although all four coefficients have negative values as expected, none of the effects are statistically discernible. This finding seemingly contradicts those of Bruce Cain and Lee Drutman, and my own findings, but some former legislators may simply not follow the laws. 62 Former legislators may not register yet lobby during their cooling-off periods or serve as consultants in lobby firms as did 60 The results remain substantively unchanged if I use effects for states and years. 61 Mummolo and Peterson (2018). 62 Cain and Lee (2014); Strickland (2020). former members of Congress Tom Dashcle and Newt Gingrich. 63 If these revolvers are failing to register while lobbying, then PGE laws may be correlated with depressed revolver numbers but not with revolver premiums since the clients would also not be registered under those revolver names. Such shadow lobbying is difficult to detect, particularly in the state legislatures where research on registered revolvers is limited. It may also be the case that PGE laws lead some former legislators not to lobby at all. In which case, revolver totals may decrease while clientele premiums (among those that remain as lobbyists) remain unaffected.
As for my remaining explanatory variables, I find little evidence that they explain revolver premiums consistently. While changes in legislature support are correlated negatively with changes in revolver premiums in two models, this variable is not correlated with premium changes in the two models that exclude states with firm registration suggest. This suggests that observations from California, New Jersey, and New York exercise significant leverage in models 1 and 3. Relatedly, these states have some of the most professionalized assemblies in the country. 64 Interestingly, there appear to be no correlations between changes in revolver premiums and changes in legislator numbers, group numbers, or the interactive term. As for firm registration, two models suggest that revolver premiums began to larger in states that implemented firm registration. This result suggests that former  1946-2011 1946-2011 1971-2011 1971-2011 Note: Standard errors in parentheses. *p < 0.05; **p < 0.01 on two-tailed tests.
legislators in those states were more often than other lobbyists members of lobby firms. The estimated turnover effect is reduced in size somewhat but continues to achieve statistical significance when I exclude observations from these states in the second and fourth models. Curiously, in no model is the constant statistically different from zero. This suggests that revolver premiums are expected to remain unchanged whenever turnover and other variables do not change. (Recall that the models include fixed effects for states and periods.)

Context and contingent connections
The preceding analyses examined the direct effect of turnover on revolver clientele premiums, but former legislators who lobby may be more valuable to interest groups depending on institutional context. Importantly, some explanatory variables not included in the previous analyses may interact with turnover to moderate or magnify its effects on the value of former legislators acting as lobbyists. Recall that the source of value for former legislators acting as lobbyists was said to be their personal connections to and familiarity with incumbent officials. Both legislature-and party-related factors may affect the link between turnover and revolver premiums. Legislatures in the states differ in terms of session length. Whereas some legislatures convene during most months every year, others have sessions of limited length (often sixty days) or convene biennially. 65 In legislatures with longer session lengths, members may form closer ties to each other such that turnover has less of an effect on the value of former legislators. Also, legislatures differ in staff resources. Some employ thousands of staff persons whereas others employ only a few dozen. 66 In legislatures with low levels of staff persons, former legislators may also not be affected as much by turnover given that there are fewer credible substitutes (former staff) and few access points in general.
With regard to party, shifts in partisan balance may upset the relationship between turnover and revolver premiums. Timothy LaPira and Herschel Thomas find that both Republican and Democratic former members of Congress become well-paid lobbyists but shifts in a legislature's partisan balance may jeopardize the value of some revolvers but not others. 67 In Congress, Democratic lobbyists took a hit when Republicans assumed a majority in Congress in 2011. 68 In the states, partisan shifts also occur on occasion and may affect the link between turnover and revolver premiums. If a legislature transitions from a highly competitive environment to being dominated by members of a single party, then former legislators who were members of the minority party presumably lose value as lobbyists. More generally, if partisan control of a legislature shifts at all, then also members of the new minority party lose value. This all matters for the link between turnover and revolver value since significant shifts in partisan control may sharpen or enhance the negative effect of turnover on revolver premiums. Every legislature has turnover such that if partisan control is constant, then the value of former legislators attributable to having connections in the majority party remains stable. If partisan control shifts, then the value of former legislators based on shared party affiliations with incumbents also is jeopardized.
The eight models presented in table 4 are specified similarly to the models presented in table 3. The dependent variable remains unchanged: the difference in average clientele sizes between revolvers and nonrevolvers. All eight models are estimated with observations that exclude firm registration and that occurred during one of the three most recent waves of observations. All models include fixed effects for states and periods, and those coefficients are not reported. The models differ from those in table 3, however, in that they include different explanatory variables besides turnover, including session length in hundreds of days, numbers of permanent staff, a folded index to reflect party competition, and an indicator for whether party control of a legislature flipped at some point during the preceding decade. 69 In the first four models, I estimate the direct effects of legislative turnover and the various 65 Squire (2012).    1971-2011 1971-2011 1971-2011 1971-2011 1971-2011 1971-2011 1971-2011 1971-2011 Note: Standard errors in parentheses. *p < 0.05; **p < 0.01 on two-tailed tests.
institutional variables on revolver premiums. These are intended to test for the robustness of the relationship between turnover and revolver clientele premiums discovered earlier. In the last four models presented in table 4, I report the results of regressions that include interactive terms. These additional variables serve to indicate if any of the institutional variables moderate or magnify the direct effects of turnover on revolver clienteles. Observations from Nebraska's nonpartisan legislature are excluded from models that examine party effects. From the first four models, the unconditional, direct effect of legislative turnover on revolver clienteles appears robust. In the only model (3) in which an effect in not detected, turnover falls just short of the traditional level of statistical significance ( p = 0.054). Regarding the four remaining models: in all but one of the models is no interactive effect detected between turnover and another institutional variable. From model 6, it appears that the presence of additional permanent legislative staff helps to magnify the negative effect of turnover on revolver clientele premiums. Figure 4 helps to illustrate this point by charting the predicted changes in clientele sizes between revolvers and nonrevolvers across different changes in turnover, for different levels (tenth, fiftieth, and ninetieth percentiles) of permanent legislative staff, while holding all state and period effects at their means. The legislature at the tenth percentile had fifty-five permanent staff whereas the legislature at the ninetieth percentile had 1,047 staff members. As staff resources increase, the negative effect between legislative turnover and revolver premiums for former legislators is more pronounced. Whereas revolver premiums are predicted to increase regardless of changes in turnover in states with low staff numbers, increases are muted by turnover in states with high numbers. The magnifying effect of staff on the connection between turnover and revolver premiums is robust to the inclusion of the three observations with firm registration. Moreover, in results not presented, similar trends can be found for all staff (both permanent and temporary), only temporary staff, total spending on the legislature (the variable employed in earlier regressions), and Squire's index of overall professionalization. 70 All these variables help to enhance the negative link between turnover and revolver clientele premiums.
What might explain the role of legislative staff resources in magnifying the negative effects of turnover on revolver premiums? Recall that the dependent variable measures the difference in clientele sizes between former legislators and all other lobbyists. Yet, former staffers in Congress often become lobbyists and former legislative staffers may also lobby in the states. 71 It may be the case that, in states with low legislative staff, turnover does not affect interest groups' propensities to hire former legislators since there are limited potential staff revolvers and few access points. In other words, with few staff members becoming lobbyists and few staff members in office to lobby, former legislators (including inexperienced ones) may remain among the best options for interest groups looking to capitalize on legislative experience. 72 In states with abundant staff, however, there are many possible staffers who This trend might also be related to low turnover among staff because low turnover would result in fewer potential staffers available to lobby. Staff turnover in Congress may be high compared to that of the legislators (Marcos 2022), but it is unknown how turnover rates for staff persons and legislators differ in the states generally. Anderson (1990) found higher turnover rates may lobby, and many points of access or current staffers whom they know personally. Interest groups may be more likely to hire former staffers in these states if turnover is high among legislators. Unfortunately, it is impossible to compare the sizes of clienteles between staff and legislator revolvers because it is unknown how many or which staffers became lobbyists in the states. In Congress, where there are abundant staff members but low turnover among members, it is unsurprising that former members are among the most popular lobbyists around. 73 Members of Congress likely are particularly susceptible to turnover's effects given the abundance of congressional staffers relative to in the state legislatures.

Analysis of lobbyist data
In an additional set of analyses, I seek to estimate the effect of turnover on revolver value using observations of individual lobbyists. These analyses are not intended to measure the effects of individual characteristics but rather to provide more specificity of turnover's effect on revolvers. Moreover, while the analyses of state-level observations provide evidence that turnover affects revolver value, observations for small and large states are weighted equally in those analyses. Analyses of lobbyist-level data instead result in more weight being given to observations from states where there are numerous lobbyists. Ideally, the two sets of analyses should produce substantively similar results.
To begin, I produced a data set consisting of more than 102,000 rows that each represented a single lobbyist who registered in a particular state and year. These observations were collected from the lobbyist lists used to produce my state-level observations of revolver premiums. In the data, each registrant was marked as a revolver or not, and a number of unique clients was generated for each registrant. I estimated a series of regression analyses that predicted the number of clients each lobbyist represented, but with some changes to the base specification used in previous analyses. First, while the direct effect of turnover is included in the models to help capture the effect on all lobbyists, this variable is interacted with each lobbyist's revolver status to determine if revolvers' clientele sizes are affected more severely by turnover than those of other lobbyists. Second, if revolvers are more likely than other lobbyists to join firms, then revolvers' clienteles are expected to be particularly large in states with firm registration. This variable is also interacted with each lobbyists' revolver status. Third, while each regression predicts numbers of clients represented, I control for the total clients within each state. Finally, while state and period effects are estimated but not reported, standard errors are also clustered by state-period combination because lobbyists' clienteles within each state and year likely affected each other (i.e., lobbyists competed for limited sets of clients within each state).
From table 5 the first regression model excludes any interactive effects, the second model includes both kinds of interaction effects, and the last two models examine the direct effects of variables on the client numbers of revolvers only (i.e., other lobbyists are excluded). The results of the first model are not surprising: revolving-door lobbyists represented roughly 2.6 more clients, on average, than nonrevolvers; and lobbyists in states with firm registration had more clients (roughly 6.8) than those elsewhere. Turnover is not correlated with how many clients all lobbyists represented. The number of groups in each state also is not correlated with clientele sizes. From model 2, the two interactive terms are discernibly correlated with clientele sizes. Whereas there is no relationship between clienteles and turnover for nonrevolvers (the state-level coefficients summarize these results since all lobbyist-level coefficients assume a value of zero for nonrevolvers), this relationship is negative for revolvers. From this model, for every additional percentage point of legislators who turned over, revolvers represented about 0.1 fewer clients. This finding is close to that estimated in the first model of table 3. Also, revolvers in states with firm registration represented about 23.5 more clients, on average, than nonrevolvers in those states.
For the last two models in table 5, I test earlier hypotheses regarding turnover and staff resources but use lobbyist-level data. Both models, like the others in the table, are estimated using state and among staff than legislators in Nebraska and Ohio; Brant (2020) found slightly lower rates for staff in California, Missouri, and South Dakota. period effects, and clustered standard errors. 74 The models examine observations only among the 2,874 revolving-door lobbyists in my data set. From models 3 and 4: two trends are particularly noteworthy. First, legislative turnover is correlated negatively with numbers of clients represented by former legislators across states. From model 3, for every one-point percentage increase in turnover, revolvers  1946-2011 1946-2011 1946-2011 1946-2011 Note: Clustered standard errors in parentheses. *p < 0.05; **p < 0.01 on two-tailed tests.

74
The number of clusters is lower in these two latter models because two states had no revolvers during one period each.
represented about 0.119 fewer clients on average. This effect is enhanced somewhat by the absence of staff resources. The interactive term in my fourth model (reported immediately above the constant) reports that there is a more negative relationship between turnover and revolver clients in states with more legislative support. This finding aligns with results presented earlier and is illustrated in figure 5. The figure shows the marginal effect of turnover on revolver clients across different levels of legislative support, and when all other variables are held at their means except firm registration, which is set to zero. Hence, the interactive effect of staff and turnover appears at the level of individual lobbyists.

Implications and extensions
Social scientists have known for decades that organized interests do not represent all interests latent in society equally or achieve equal amounts of political influence. Such inequalities have at least two sources. While broad interests must overcome issues of free-riding, the most educated and wealthy individuals also tend to participate in groups and politics generally the most often. 75 Revolving-door lobbyists are argued to contribute to or embody inequalities in representation and influence. Revolving-door lobbyists are often among the most influential lobbyists in Congress, 76 and clients pay handsomely for their services. Invoking Elmer Schattschneider, some even argue that revolving-door lobbyists are the "unheavenly chorus" of American politics: they get paid by wealthy interests to skew policy toward the preferences of the wealthy. 77 Concerns over representation and equality are the foundation of these concerns over revolvers.
Only recently have social scientists begun to examine the relationship between revolvers' influence and legislative institutions, and the findings presented in this study add to a small but growing literature. Increasingly, studies suggest that turnover among officials harms lobbyists by reducing the number or quality of relationships they have within government. Specifically, others suggest that organized interests can, at least on average, measure the value of lobbyists and adjust their compensation or hiring decisions in response to turnover. 78 The present study provided substantially more insight into lobbyist value and turnover by quantifying the relationship between these two variables and finding that the relationship is most noticeable in legislatures with high levels of staff support.
My findings have several implications for representation and reform. Since the 1960s, state legislatures have become more professional assemblies in terms of member incomes, staff resources, and session length. 79 These improvements are associated with reduced turnover among members. 80 My findings suggest that professionalization and the resulting reductions in turnover likely contributed to the growth of the revolving door. While more interests mobilized throughout the 1980s than ever before, former legislators from low-turnover assemblies benefited from this growth more than former   Olson (1965); Brady et al. (1995). 76 Baumgartner et al. (2009, 208); Makse (2017). legislators who served elsewhere. 81 The possible entrenchment of well-connected lobbyists and their role in exacerbating the effects of resource inequalities on political influence suggests a paradox of professionalization: while such professionalization was intended to reduce corruption in legislatures and equalize power among branches of government so as to improve representation, it made access more difficult to achieve than ever in some states. 82 It remains unknown if the concurrent rise in campaign contributions and spending in the states is related to the entrenchment of allied legislators and lobbyists.
The implementation of legislative term limits has proven a controversial solution for entrenchment, and my findings have implications for this reform as well. Political scientists tend to critique term limits because the resulting turnover reduces policy work among legislators, 83 empowers governors and lobbyists, 84 and contributes to political polarization. 85 I do not dispute any of these findings but previous studies of turnover and lobbying employ information-based accounts of influence and do not distinguish between different kinds of lobbyists. With high turnover, it is possible for all lobbyists to achieve more influence through policy expertise while revolving-door lobbyists also lose special connections. Given revolvers' comparatively high salaries and exclusive clienteles, such an outcome seems normatively desirable but appears contingent on the presence of legislative staff support.
What additional questions might scholars answer so as to determine how severely revolvers undermine the equal representation of interests in the states? A large study of the revolving door in Congress provides rich detail into the value differentials associated with years of experience, service in different chambers, client types, and lobbyists' descriptive characteristics (e.g., race and gender). 86 Such differentials may be examined in the states using the data set of individual lobbyists developed here and data released in the last decade. 87 These new data allow scholars to answer new and old research questions definitively, and the American states, with their numerous institutional variations, will likely prove to be ideal test cases. Moreover, the information available in the states allow scholars to examine in a straightforward manner the kinds of interests former legislators represent and-provided the resources-the legislative outcomes associated with their lobbying efforts. It remains to be seen if former legislators truly represent fewer well-paying clients in states with high turnover or if their lobbying efforts more often fall on deaf ears in high-turnover assemblies. At present, I leave these questions for others to examine.