Legislative Term Limits and Ideological Representation

Abstract

How do term limits affect dyadic ideological representation? Despite reformers’ claims that term limits should improve legislators’ connections to their constituents, much empirical political science research suggests that term limits actually break that electoral connection. In this study, I use a regression discontinuity design to measure the ideological gap in how Democrats and Republicans represent evenly matched districts and then explore how this gap varies across settings with and without state legislative term limits in effect. Across a number of specifications, my results are consistent with term limits exacerbating rather than improving dyadic representation. This study contributes to a growing scholarly consensus that term limits do not improve, and may worsen, state legislative representation.

States are often described as “laboratories of democracy” ¹ and have routinely throughout their history experimented with their governmental institutions in an effort to improve representation. Such changes include the adoption of an elected judiciary, ² changes to state legislatures’ sizes, ³ separate election of executive offices, ⁴ institutionalization and professionalization of state legislatures, ⁵ implementation of executive term limits, ⁶ and the adoption of direct primary elections. ⁷ Coexisting with this spirit of experimentation in American political history is an individualistic and antiestablishment streak. Hofstadter, for example, argues that from the earliest years of American politics, the voting public was “proud of its rights, alert to violations of them, and suspicious of authority.” ⁸ Tocqueville identified an aversion to authority as intrinsic to the American spirit: “The citizen of the United States is taught from his earliest infancy to rely upon his own exertions in order to resist the evils and the difficulties of life; he looks upon social authority with an eye of mistrust and anxiety.” ⁹ Antiestablishment mores inspired many of the institutional innovations above: primary elections represented a more-democratic alternative to the “smoke-filled back room”; ¹⁰ an elected judiciary guarded against the appointment of “incompetent and arrogant judges”; ¹¹ smaller legislatures were supposed to be more efficient. ¹² Today, this antiestablishment streak manifests in support for outsider candidates, ¹³ including President Donald Trump. ¹⁴

Around the turn of the twenty-first century, these American traditions of state-level institutional experimentation and antiestablishmentarianism collided in the widespread adoption and implementation of state legislative term limits. Nearly half of all states (22) attempted to implement term limits, and legislative term limits are currently in effect in 16 states. ¹⁵ Supporters of term limits consistently appeal to the notion that term limits facilitate representation by inhibiting legislators from becoming entrenched in the political establishment. Advocating for term limits in Maryland, then-Governor Larry Hogan stated that “Most people feel like staying here forever makes you more susceptible to influence from lobbyists and makes you more trapped inside Annapolis.” ¹⁶ Others argue that term limits would liberate legislators from partisan and ideological pressures: US Representative Dean Phillips, for example, argues that “When one feels liberated to speak the truth, to say the quiet part out loud, to vote the way that their conscience dictates, that might be in the best interests of the country, not for a re-election…That is a very powerful antidote to the disease facing our Congress.” ¹⁷ Although the public has been broadly supportive of term limits, ¹⁸ elite proponents of term limits were also likely motivated by partisanship and ideology. In addition to aligning with traditional small-government conservatism, term limits represented an opportunity in some states for Republicans, facing an uphill climb against Democratic incumbents, to eliminate that advantage. ¹⁹ In California, for example, Speaker of the House Willie Brown’s “strong-arm tactics, his links to rich interest groups, and the growing atmosphere of partisanship in his assembly made the house vulnerable to a reform initiative.” ²⁰

Most political science research, on the other hand, suggests that state legislative term limits were an experiment gone wrong. Mounting scholarly evidence suggests that term limits reduce legislator effort, ²¹ inhibit bipartisan relationships, ²² increase legislative polarization, ²³ increase the perceived influence of interest groups and the executive branch, ²⁴ and induce a “Burkean shift” among legislators that leads to less focus on their constituents. ²⁵ Some literature pushes back on these claims, showing that legislators’ effort changes little absent reelection incentives ²⁶ or that term limits are associated with lower levels of “multiclient lobbying.” ²⁷ Although the balance of evidence suggests that term limits generate at least some negative side effects, they appear to do so while more or less failing to introduce new types of legislators—in terms of gender and race—into the chambers. ²⁸ In short, term limits have been either inconsequential or consequential in ways that are largely inconsistent with advocates’ goals.

Despite this, little scholarship has directly interrogated the relationship between legislative term limits and dyadic substantive representation, ²⁹ possibly due to the difficulty of measuring constituent preferences and legislator behavior on the same scale. ³⁰ Closely related are studies showing that term limit adoption is associated with increased state legislative polarization ³¹ and polarization of the broader candidate pool. ³² Various theoretical perspectives, however, suggest that dyadic representation should suffer as a result of adopting term limits. Shortened time horizons inhibit the ability to socialize across the aisle, increasing the partisanness of legislators’ networks. ³³ The reduced appeal of officeholding with a finite time horizon devalues officeholding, thereby increasing the share of intrinsically motivated extremists seeking office ³⁴ as well as the role of parties in the electoral process. ³⁵ Finally, the absence of an electoral connection in legislators’ final terms may facilitate shirking or rent-seeking behavior. ³⁶

In this article, I explore the relationship between legislative term limits and dyadic ideological representation using a regression discontinuity design (RDD). My outcome variable is estimates of state legislator ideology based on roll call voting. ³⁷ My independent, or running, variable is the Democratic share of the two-party vote in state legislative elections. ³⁸ My main quantity of interest is the jump in ideology at 50%, when a district is evenly split between Democrats and Republicans. What difference in ideological representation does barely electing a Republican versus barely electing a Democrat produce? In this context, one of the core limitations of the RDD—that the estimates it produces are “local” in nature and apply only at the discontinuity—is potentially a feature, in two respects. First, in a district that is evenly split between Democrats and Republicans, the median voter will likely lie between the right-most Democrat and the left-most Republican and should therefore be quite moderate. Second, any gap between how the two parties represent such a district represents a failure of Downsian convergence to the preferences of the district’s median voter. The RDD provides a credible estimate of the degree of convergence for a district—evenly split—where the counterfactual of either party representing it is especially relevant. By comparing the RDD estimates from settings with and without state legislative term limits, I can evaluate how ideological convergence varies across settings with and without term limits in these evenly split districts.

My results point to term limits’ limitations for strengthening representation. Across a variety of comparisons, I find consistent evidence that term limits either do not improve or, more commonly, decrease ideological convergence in evenly split districts. The average ideological gap between Democrats and Republicans is consistently higher for these districts when term limits are in place than when they are not, and this relationship holds even when controlling for a variety of unobservable geographic and temporal factors. Although my conclusions are limited to the evenly split districts for which the RDD yields estimates, my results nevertheless constitute some of the most direct evidence to date that legislative term limits worsen dyadic ideological representation.

Term Limits and Representation

Effects of Term Limits

Much scholarship on term limits in their immediate aftermath was focused on the turnover that they would generate with respect to legislator demographic and socioeconomic diversity, generally finding few such effects. ³⁹ The forced turnover created by term limits may, however, have disproportionately replaced more-moderate with more-extreme legislators. This pattern could arise through a number of theoretical mechanisms with distinct normative implications.

First, term limits could produce a more extreme pool of candidates and set of elected legislators by simply accelerating turnover amidst increasing elite polarization. Party elites were increasingly ideologically polarized in the period when state legislative term limits were being implemented. ⁴⁰ State legislators, like other state and federal offices, ⁴¹ enjoy a significant incumbency advantage. ⁴² As a result, it is possible that the ideological distribution of sitting state legislators at any given time lags behind the ideological distribution of potential state legislators, as incumbency helps to entrench the ideological preferences of yesteryear. Term limits, by artificially truncating careers and removing incumbents, may bring the preferences of those elected into closer alignment with contemporary elite preferences. In a setting where elites are polarizing, one effect of term limits could therefore be to remove more-moderate legislators from office and inject more-extreme legislators into office.

Term limits could also exert a direct effect on the composition of the potential candidate pool. For example, existing scholarship shows that term limits are associated with the creation of a more-extreme candidate pool as a result of declining newspaper coverage of state legislative politics. ⁴³ By imposing a limited time horizon on state legislative service, term limits may also decrease extrinsic motivations to serve, thereby increasing the importance of intrinsic—possibly ideological—motivations in candidate emergence. ⁴⁴

The truncated time horizon on legislative service that is generated by term limits may not just induce worsened representation through selection effects; it might also change legislators’ behavior in the chamber. Although existing scholarship fails to find evidence that legislators systematically change their roll call voting in their final term before being term-limited, ⁴⁵ it may also be the case that the presence of term limits devalues reelection from the start of legislators’ careers. If that is the case, new legislators not only may be drawn from a more-extreme pool but also may be comfortable acting out of step with their constituents and risking their retribution, ⁴⁶ particularly if news coverage is not robust. ⁴⁷

Dyadic representation at the congressional level—and likely in state legislatures as well—is characterized by what Bafumi and Herron call “leapfrog representation.” ⁴⁸ This describes a state of affairs in which voters suffer from “a distinct lack of congruence … due to the fact that [legislators] are politically extreme compared with the voters who put them in office” ⁴⁹ and voters who choose to replace their incumbent legislator are leapfrogged and end up represented by an extremist on the other end of the ideological spectrum. If term limits generate a more-extreme, more-ideological pool of candidates or a group of legislators who are less concerned with reelection and the electoral connection between them and their constituents, then term limits are likely to exacerbate leapfrog representation and worsen ideological congruence between constituents and state legislative representatives.

Representation in Closely Matched Districts

To explore the consequences of electing a Democrat relative to a Republican, I use a RDD, described in more detail below. This design produces an estimate of the average effect of electing a Democrat, relative to a Republican, in an evenly matched (50-50 district). Normally, this “local average treatment effect” is viewed as a limitation of the RDD because the design’s estimates do not necessarily generalize beyond these evenly matched places. ⁵⁰ However, in my setting this quantity of interest provides a unique opportunity to learn about the representational consequences of term limits.

In most studies of substantive ideological representation, it is not possible to measure the preferences of constituents and elites on the same scale. For example, constituent preferences might be measured by using survey questions and legislators’ preferences by using roll call votes. Although these can certainly tap into the same underlying beliefs, it is not possible to say that an average of 4.8 on a 7-point Likert-type scale corresponds to a legislative ideal point estimate of 1.2, for example. Although some studies turn to creative solutions, such as tailor-made survey questions ⁵¹ or using referendums, ⁵² many studies eschew studying the ideological congruence between constituents and representatives altogether and instead focus on “responsiveness,” whether legislators’ and constituents’ preferences or actions tend to move in the same (or opposite) directions. ⁵³ Although responsiveness may capture substantively important relationships, it is generally less conceptually satisfying than congruence, ⁵⁴ which more succinctly captures whether constituents are or are not having their preferences reflected in their legislative representation.

In this article, I explore congruence by focusing on districts that are evenly split between Democrats and Republicans in a given election. There are two possible interpretations of the RDD that support this interpretation. First, it is possible that evenly matched districts are more ideologically moderate than those that are lopsidedly partisan. Members of Congress, for example, are systematically more extreme even than their own copartisans in the electorate, let alone the median voter in the district. ⁵⁵

Though potentially compelling, however, that interpretation of the RDD’s value still lies in an empirical leap from “close election” to “ideologically moderate district.” Though plausible, this relationship need not be mechanically true. Another way to interpret the RDD in this context is to interpret it as a failure of Downsian convergence. ⁵⁶ Although it is well-established that America’s two major parties do not fully converge to the preferences of district-level median voters, ⁵⁷ it is nevertheless the case that, in theory, full convergence would equate to ideologically congruent representation, at least on average. That representatives in marginal districts do seem to be at least slightly more moderate suggests that these representatives are at least somewhat cognizant of their ideological mismatch with voters and fear electoral consequences for it. ⁵⁸

Although in more-extreme districts congruence could be achieved through electing a congruent Democrat or Republican, in a perfectly split district a failure by Democrats and Republicans to converge to the median voter’s preferences likely indicates that the representative will be incongruent. In the analyses that follow, I explore whether term limits shrink (no) or increase (yes) the average gap between Democrats and Republicans in these evenly split districts. Specifically, because the RDD estimand applies to these evenly split districts, under reasonable distributions of voter preferences this analysis portrays representation and congruence in these districts. More succinctly, the design captures the degree of polarization between the parties in the districts where the electoral pressures to converge are the strongest. By showing that polarization occurs even in these places, my results help refine understanding of the representational consequences of the polarization that term limits seem to induce. ⁵⁹

Data and Empirical Design

Data on State Legislative Roll Call Voting, Elections, and Term Limits

My analysis relies on two types of data. My outcome variable is state legislator ideal point estimates—estimates of state legislators’ ideologies on a liberal-to-conservative spectrum. My main independent variables are based on state legislative election returns; specifically, I use the Democratic share of the two-party vote and an indicator variable for “Democrat won” that takes on a value of “1” for all elections where the Democratic share of the two-party vote is greater than 0.5 and 0 otherwise. My unit of analysis is the legislative district–election; for example, District 1 of the Alabama House of Representatives in 2010.

For my dependent variable, I use state legislator ideal point estimates from Shor and McCarty. ⁶⁰ These estimates of legislators’ ideologies are based on roll call voting within each state legislature and are then made comparable across states by using survey questions that are answered by state legislators across the United States to bridge states together and put them on a common scale. These data range from 1993 to 2020, with data availability improving over the course of the 1990s. Each legislator receives a single score for the duration of their career. Although the scores range from approximately -3.5 to 3.5, most of the observations (approximately 95% in my sample) fall between -1.5 and 1.5 and the median Democrat and Republican have scores of -0.84 and 0.77, respectively. As this suggests, the two major parties were meaningfully polarized in state legislatures over this period. ⁶¹

I merge each legislator’s ideal point estimate with their election results in the previous election. I use state legislative election data compiled and made available by Carl Klarner, ⁶² which ends in 2016. Therefore, my sample runs from (election years) 1992 to 2016. Because of the demands of the RDD and to ensure accurate merging between state legislative roll call records and elections, I limit my sample in a variety of ways. I focus only on on-cycle general elections in single-winner seats; this includes multimember districts with posts or staggering, but it excludes some multimember districts. I also limit my focus to elections that did not feature significant third-party or independent involvement; I drop elections where the two major parties garnered less than 85% of the combined vote. Fortunately, most of the American state legislative elections during this period are single-winner, two-party affairs. To prepare the data for analysis, I merge each election to the legislator who served in that seat the next year. ^{63 , 64}

My final variable of interest is whether term limits are implemented in a state at the time of an election. I specifically focus on whether term limits have already “bit”—that is, whether they are affecting candidates’ ability to seek reelection—rather than whether they have been adopted. Although some legislators or candidates may adapt their behavior in anticipation of term limits, ⁶⁵ most theoretical perspectives on term limits’ effects emphasize the replacement of term-limited legislators with new, different legislators. ⁶⁶ A second reason for this choice is practical. The timing of term-limit adoption is too early to have reasonable pre or postadoption data on state legislative roll call voting, as many states’ adoption of term limits in the early 1990s precedes the earliest available years of Shor and McCarty’s ideal point estimates. ⁶⁷ Table A.1 in the Supplementary Materials summarizes the years after which I consider each term-limited state to be treated. If a state chamber has term limits in effect, I code term limits as a “1”; if not, I code it as a “0.” Below, I also present estimates using a measure of “term limitedness” that incorporates information on how much term limits increase legislative turnover and whether a particular state’s term limits allow cycling between offices. ⁶⁸

Electoral Regression Discontinuity Design

My core empirical strategy is the RDD. This design is useful in contexts where treatment assignment is a function of a threshold in a variable value—for example, a scholarship that is awarded above a certain test score ⁶⁹ or, in my application, a Democratic victory when a Democrat receives more than 50% of the vote in a two-party contest. Intuitively, districts that give Democrats 49% of the vote and 51% of the vote are likely to be quite similar, holding many potential confounders constant, but they will be represented by a different party. The design produces causal estimates of the treatment under either a “local randomization” assumption, which stipulates that within a narrow bandwidth around the treatment threshold treatment is as good as randomized, or the less-strong “continuity” assumption, which requires only that potential outcomes under treatment and control continue smoothly across the threshold. ⁷⁰ In part because these assumptions are plausible in many settings, the RDD is one of the most credible research designs for drawing causal inferences with observational data. ⁷¹ The credibility of the design, however, comes at a cost—the estimand of the design is a “local average treatment effect” that applies only at the discontinuity. In the context of my application of the design, this means that I can recover the average effect of electing a Democrat relative to a Republican on ideological representation for evenly split districts or, if relying on a local randomization assumption, for districts very close to the threshold. I cannot estimate a broadly generalizable estimate of the effect of electing a Democrat relative to a Republican. As I note above, in the context of my study this limitation is possibly conceptually helpful.

A significant concern with the RDD is that units may be able to manipulate their value of the running variable, which would pose a threat to identification assumptions. This is unlikely to be a meaningful concern in my setting. Although previous work on election RDDs finds some evidence of manipulation of vote shares, ⁷² this has been in studies where the running variable of interest was incumbent vote share, not partisan vote share. In the case of using Democratic (or, symmetrically, Republican) vote share as a running variable, the very presence of two opposed candidates and campaigns, engaged in free and fair elections, should assuage concerns about the running variable being directly manipulable by any actors involved.

In Figure 1 I empirically explore the credibility of the research design. In the top panel, I present a histogram of the density of the running variable; if the running variable was manipulated, one might expect to see “bunching” on one side of the discontinuity. ⁷³ No such bunching is apparent in this figure. In the bottom panel, I visualize the RDD but use a one-period lag of the outcome variable. By exploring an outcome that mechanically cannot be affected by the treatment—because it happened in the past—and showing that it is similar on both sides of the discontinuity, I help to rule out that units on either side of the discontinuity are systematically different in ways that are unrelated to the treatment. In this figure, the smooth fits on either side of the discontinuity continue almost perfectly across the discontinuity. This provides further suggestion that the RDD assumptions are likely to be met in this context.

Figure 1. Exploring the Validity of the Regression Discontinuity Design.

Note: The top panel plots the density of two-party Democratic vote share over the support of the data, and the vertical line at 0.5 separates races won by Republicans (on the left) and those won by Democrats (on the right). The bottom panel plots a smooth fit of legislators’ ideal points, lagged by one election within district, as a function of two-party Democratic vote share. Smooth curves are fit separately on both sides of the discontinuity. In both plots, state-chamber-years with and without term limits are plotted separately; histograms are stacked in the left panel.

Heterogeneity across Term Limit Usage

Although it may be descriptively interesting to know whether and to what extent Democrats and Republicans differ in their representation of evenly split districts, previous scholarship establishes that Democrats and Republicans broadly fail to converge and, therefore, represent ideologically similar districts differently. ⁷⁴ My particular interest is in understanding whether the difference in how Democrats and Republicans represent evenly split districts differs by whether a legislator was elected under term limits. Put another way, I want to know whether the ideological gap between Republicans who just won and Democrats who just won is the same, bigger, or smaller in state chambers with term limits than in those without. To estimate this quantity of interest, I rely on two complementary empirical approaches.

First, I simply apply the RDD to state-chamber-years with term limits and those without term limits, separately, and compare the estimates. This approach has as strengths straightforward interpretation and the ability to apply best practices in regression discontinuity estimation, such as the use of local linear regression ⁷⁵ using data in a narrow, data-driven bandwidth. ⁷⁶ The primary limitation of this design, however, is that it cannot control for potential systematic differences between states that do and do not adopt state legislative term limits. Because term limits were adopted by strategic political actors with policy objectives in mind, it is unlikely that states that adopt and fail to adopt term limits are otherwise comparable. To address these shortcomings, I also turn to panel models that control for a variety of potential geographic and temporal unobservable confounders, in the spirit of a difference-in-differences design. Specifically, I estimate models of the following form:

$ {\displaystyle \begin{array}{c} Ideal\;{Point}_{ist}={\unicode{x03B2}}_1{Running}_{ist}\times Dem.{Wins}_{ist}\times Term\;{Limits}_{st}\\ {} + {\unicode{x03B2}}_2{Running}_{ist}\times Dem.{Wins}_{ist}\\ {}\hskip0.9em + {\unicode{x03B2}}_3{Running}_{ist}\times Term\;{Limits}_{st}\\ {}\hskip1.9em + {\unicode{x03B2}}_4 Dem.{Wins}_{ist}\times Term\;{Limits}_{st}\\ {}\hskip13.12em +\hskip0.3em {\unicode{x03B2}}_5{Running}_{ist} + {\unicode{x03B2}}_6 Dem.{Wins}_{ist}+{\unicode{x03B2}}_7 Term\;{Limits}_{st}\\ {}\hskip-8em +\hskip0.4em {\unicode{x03B1}}_i+{\unicode{x03C4}}_t+{\in}_{st},\end{array}} $

where i indexes districts defined within redistricting cycles, s indexes state-chambers, and t indexes election years; Running is Democratic two-party vote share, centered at 0, α is a district fixed effect, and τ is a year fixed effect. The traditional least-squares regression discontinuity estimator would include the interaction between Running and Dem. Wins and the base terms and interpret the coefficient on Dem. Wins as the effect at the threshold of a Democrat being elected in lieu of a Republican. To that base specification I add both (1) unit and time fixed effects to control for potential unobservable confounders ⁷⁷ and (2) an additional interaction with Term Limits (and relevant lower-order interactions and base terms). These features allow me to increase the likelihood of making an all-else-equal comparison and to conduct inference directly on my main quantity of interest, the difference in the effect of electing a Democrat in places with and without term limits (β₄).

Importantly, credibly identifying the causal effect of a moderator for the regression discontinuity design is difficult. ⁷⁸ Although my variety of fixed effects specifications are intended to control for potential confounders to make the claim that term limits cause decreased convergence more credible, even in such models that comparison requires strong, possibly unrealistic assumptions. ⁷⁹ In addition, my design assumes that term limits do not systematically affect which districts have close elections and relies on a familiar “parallel trends” assumption. By presenting a number of estimation approaches I hope to bring to bear a variety of evidence with different strengths and weaknesses that all suggests broadly consistent results, but an unqualified causal interpretation of the moderating effect of term limits on ideological convergence is perhaps not warranted.

Term Limits Exacerbate Leapfrog Representation

I begin my exploration of term limits’ effects on dyadic representation by visualizing the relationship between electing a Democrat and ideological representation. Figure 2 is analogous to the bottom panel of Figure 1 above but uses a nonlagged ideal point estimate. To create this figure, I simply plot a smooth fit of state legislator ideal point estimates as a function of Democratic two-party vote share, fit separately on both sides of the discontinuity at 50%. These fits are also done separately for state-chamber-years with and without term limits in effect. The effect of electing a Democrat relative to a Republican is captured by the difference in the value of the smooth fit as it approaches the discontinuity from the left and the value as it approaches from the right.

Figure 2. Regression Discontinuity Visualization.

As Figure 2 indicates, narrowly electing a Democrat is associated with a substantial negative (liberal) change in the ideal point estimate of that district’s representative. This plot suggests that in a tied district that selects a Democrat via a coin flip, that Democrat would on average have an ideal point estimate between -0.5 and -1; if that coin flip selected a Republican, that Republican would represent that same district with an average ideal point between 0.5 and 1. This dramatic qualitative difference exists in states that both do and do not use term limits and indicates that Republicans and Democrats do not converge to the preferences of the median voter in their representation of even closely matched districts.

For understanding the consequences of term limits, this plot yields an important preliminary conclusion: term limits are associated with a greater gap between Democrats and Republicans’ representation of the same district and reduced convergence. This conclusion is apparent because the black fits, which correspond to term-limited state-chamber-years, are farther apart at the discontinuity than the gray fits, corresponding to times and places without term limits in effect. Moreover, this difference is approximately symmetrical: Republicans in term-limited places are more conservative and Democrats more liberal than are their counterparts in non-term-limited places.

I now turn to more-formal exploration of the effects of electing a Democrat over a Republican and how this effect differs across term-limited and non-term-limited settings. I begin, as I describe above, by using local linear regression. Estimation is undertaken with the rdrobust package in R. ⁸⁰ The bandwidth of data used for estimation is selected through a data-driven procedure, ⁸¹ and I report bias-corrected estimates with standard errors clustered by state-chamber. The results are presented in Table 1. Looking within the two columns, we find unambiguous evidence that Democrats and Republicans represent the same district differently. Looking across the columns suggests a meaningful difference in that relationship depending on whether term limits are in use. Specifically, the gap between Democrats and Republicans when a Democrat wins is larger by more than 0.2 in places using term limits. This difference is more than one-fifth of a standard deviation of the distribution of ideal point estimates in my sample (0.90). This therefore represents a substantively meaningful difference in the consequences of elections in marginal seats.

Table 1. Local Linear RD Results

Note: Entries are local linear regression coefficients with standard errors clustered by state-chamber in parentheses. Observations are at the election level. Estimated using the rdrobust package in R.

^∗p < 0.10; ^∗∗p < 0.05 (two-tailed).

Although the results in Table 1 rely on best practices in regression discontinuity estimation, they do not directly establish whether there is a statistically significant difference in convergence in places with and without term limits, nor do they control for potential factors that could confound the relationship between term limits and ideology. To address these shortcomings, I now turn to a series of panel models, each of which controls for time- and place-specific unobservable characteristics. These results are presented in Table 2. The left-most column represents a straightforward baseline on which to build subsequent models: this is simply a global linear fit—all observations of the running variable, not only those close to the discontinuity, are included—with no fixed effects. The reported coefficient is the difference in the effect of electing a Democrat in places with and without term limits. The negative estimated coefficient suggests that term limits are associated with a bigger gap between the two parties—recall that more-liberal ideal points are negative. Possibly due to the use of a global linear fit, the estimated coefficient is nearly twice as large as that suggested by the results in Table 1.

Table 2. Adoption of Term Limits and Leapfrog Representation

Note: Table presents linear regression coefficients, with standard errors, clustered by state-chamber, in parentheses. Lower-order terms are suppressed (see Table B.1 in the Supplementary Materials).

^∗ p < 0.10; ^∗∗p < 0.05 (two-tailed).

In the right-most four columns of Table 2, I add to the base specification a variety of fixed effects. In the second column, I add state-chamber and year fixed effects. The former accounts for time-invariant characteristics of a state-chamber that shape its mean liberalism; the second accounts for year-specific shocks shaping aggregate liberalism or conservatism. The fourth model is substantively similar; it replaces state-chamber fixed effects with district fixed effects. ⁸² This accounts for the overall liberalism or conservatism of a particular district. The third and fifth columns further interact party with the fixed effects from the second and fourth, respectively; these models account for the mean liberalism of parties within states or districts as well as overtime shifts in the liberalism or conservatism of Democrats and Republicans nationally. Across all models, term limits are associated with larger gaps between Democrats and Republicans in evenly split districts. Although this effect fails to achieve statistical significance in the model with state-chamber-party fixed effects, it is statistically significant at the p < 0.05 level in all other models.

To further clarify the interpretation of these models, consider the second model from the right, with district and year fixed effects. The year fixed effects in this model account for aggregate year-to-year changes in liberalism. The district fixed effects offer a “within-district” interpretation; in short, this suggests that over time, within a particular district, the adoption of term limits increases the effect of electing a Democrat by nearly one-fifth of a standard deviation and more than one within-district standard deviation (0.16). Even after accounting for the average ideological orientation of every district in the data, I continue to find evidence that term limit implementation exacerbated nonconvergence in the most moderate districts. Of course, this design still relies on a parallel trends assumption for identification. If, for example, primary electorates in term-limited states polarized over time more than those in non-term-limited states, this could result in the nomination of more-extreme candidates and produce the patterns seen here.

Additional Results and Robustness Checks

In this section, I expand on my base results to explore a variety of alternative specifications. For some, I examine whether the relationship between term limits and ideological convergence reflects heterogeneity along a number of dimensions. These results provide important additional context and support for my main findings, suggest their generalizability to a variety of subsets of the data, and help to adjudicate between the different theoretical mechanisms proposed above. To perform these tests, I simply reestimate my local linear regression procedure (Table 1) while splitting the sample as appropriate based on values of the hypothesized moderator. I also present fixed-effects estimates in the Supplementary Materials. I then describe some robustness checks undertaken to examine the sensitivity of my results to the specific modeling choices I have made.

Heterogeneity by Professionalism

Above I suggested that one mechanism through which term limits might affect dyadic representation is by devaluing officeholding—if the office provides fewer extrinsic inducements for a legislator, they may be less inclined to heed constituent preferences in order to secure reelection or may be more intrinsically motivated to begin with. One implication of this theoretical pathway is that the effects of term limits on dyadic representation should vary systematically with the baseline value of the office: in a place where legislating is a full-time, desirable job with good pay and support, the introduction of term limits might have a substantial effect; in a place with a part-time, low-paying legislature, on the other hand, the office may not have been especially desirable to begin with. ⁸³ To explore this, I first examine whether my estimates vary across legislative professionalism. To measure professionalism, I use the first dimension of professionalism from work by Bowen and Greene. ⁸⁴ This measure is desirable because it incorporates information on legislative session length, pay, and expenditures, and it is available for each session, unlike the commonly used Squire Index. ⁸⁵ Although obviously intended primarily to explain the “professionalism” of state legislatures, it also taps into the nature of the job in different states and the potential value and desirability of the job.

Figure 3 presents the results of a simple split-sample test using the local linear estimation strategy described above. ⁸⁶ For presentational simplicity, I simply divide states into those that are above the median average professionalism for the period of my study and those that are below. The figure suggests that in both more- and less-professional states the gap between Democrats and Republicans is greater with than it is without term limits, although this gap appears to be smaller among less-professional states. In Table B.2 in the Supplementary Materials, I expand on this analysis by incorporating Bowen and Greene’s annual, continuous measure in my panel analysis. ⁸⁷ Models with fewer fixed effects generally suggest that term limits’ effects were greater in more-professional places, but this finding is not robust to the inclusion of party-specific or district fixed effects. Therefore, these findings do not provide dispositive evidence in favor of the “devaluing of office” mechanism proposed above. Although there is some suggestion that the effects of term limits may be greater in more-professional state legislatures, the mixed evidence here also leaves open the possibility that term limits’ effects are due to increased turnover amidst a polarizing elite.

Figure 3. Legislative Professionalism Local Linear Estimates.

Note: Figure presents local linear regression estimates, with sample split by legislative professionalism and use of term limits (95% confidence intervals based on state-chamber-clustered standard errors).

Heterogeneity by Chamber

I next consider whether term limits affected convergence differently in state legislative upper and lower chambers. Previous work demonstrates that candidates approach term limits strategically ⁸⁸ and that term limits can force lower-chamber legislators to pursue higher offices in hopes of remaining in government. ⁸⁹ As a result, one might expect the effects of term limits to be less pronounced in upper chambers, for which lower chambers may provide a ready-made group of political insiders to step up after term limits take effect.

To explore this, I simply split my sample by chamber and reestimate the local linear specifications described above. The results are presented in Figure 4. As the figure indicates, for both upper and lower chambers term limits are associated with a bigger ideological gap between Democrats and Republicans in evenly split districts, with few differences to speak of. These results suggest that term limits’ effects were broadly similar across chambers.

Figure 4. Chamber-Specific Local Linear Estimates.

Note: Figure presents local linear regression estimates, with sample split by chamber and use of term limits (95% confidence intervals based on state-chamber-clustered standard errors).

In Table B.3 in the Supplementary Materials, I present the results for models that are analogous to those presented in Table 2 above but include an additional interaction with a chamber indicator variable. My results for Dem. Wins × Term Limits are substantively similar to those reported above. The further interaction between those regressors and the indicator for Senate are substantively small and fail to achieve statistical significance. These results are therefore consistent with those in Figure 4.

Heterogeneity by Region

Finally, I ask whether the relationship between term limits and ideological convergence differs in the states of the US South compared with states outside the South. Although the basic theoretical mechanisms described above are unlikely to vary in their application across regions, there is reason to suspect that the ideological polarization between parties might differ in the South, possibly changing term limits’ effects. Although the realignment of white southerners to the Republican Party began in the 1960s, ⁹⁰ many southern conservatives continued to participate in Democratic primaries into the 1990s ⁹¹ and some state legislatures—such as those in Alabama, Arkansas, Louisiana, and Mississippi—did not reliably flip to Republican control until 2010 or later. As a result, one might expect the ideological gap between Democrats and Republicans to be smaller in Southern states and Democrats’ ideologies to be more variable and, possibly, malleable than they are in non-Southern states.

I again repeat my analysis above, simply splitting the sample into Southern versus non-Southern states and repeating my local linear regression estimation procedure. I use an expansive definition of the South, including not only the eleven states of the former Confederacy but also Oklahoma, Missouri, Kentucky, West Virginia, Maryland, and Delaware. ⁹² The results, presented in Figure 5, suggest that both partisan nonconvergence and the effects of term limits thereon are more muted in the South than they are outside the South. In both places with and without term limits, the effect of electing a Democrat is smaller in the South than the non-South; moreover, the difference across those places is nearly 0.3 for the non-South, but it is about half that in the South. This suggests that the unique relationship between ideology and party in the South limited term limits’ influence in those states. As with chamber above, I again estimate fixed effects models that interact my main quantity of interest, the interaction between Dem. Wins and Term Limits, with an indicator variable, this time for whether a state is in the South. As with Figure 5, the results (Table B.4 in the Supplementary Materials) suggest that the effects of term limits may be more muted in the South, but the relationship between term limits and convergence across regions is not statistically distinguishable.

Figure 5. Region-Specific Local Linear Estimates.

Note: Figure presents local linear regression estimates, with sample split by region and use of term limits (95% confidence intervals based on state-chamber-clustered standard errors).

Robustness Checks

Finally, I conduct a number of additional analyses to probe the robustness of my results. In Table C.1 in the Supplementary Materials, I present fixed-effects models analogous to those in Table 2 above but that fit a third-order polynomial of the running variable (rather than the linear one in Table 2). In Table C.2, I replace my various unit fixed effects with a within-district lag of the dependent variable, which controls for unobservables under an altogether different set of assumptions than the fixed-effects models. In Tables C.3 and C.4, I present both local linear and fixed-effects regression results estimated while limiting my sample to contested elections. In Table C.5, ⁹³ I present results from models where I replace my binary term-limits measure with a more-refined measure of “term limitedness” from Sarbaugh-Thompson. ⁹⁴ Specifically, I use chamber-specific measures of “term limitedness adjusted for recycling potential,” which not only incorporates information on term limits’ effects on legislative turnover but also accounts for variation across states in the ability to cycle between chambers when term limited from one. ⁹⁵ Finally, I also estimate my local linear and fixed-effects specification on a matched sample of states, designed to ensure comparability between the treated and control groups. I match a sample of states, ⁹⁶ without replacement, ⁹⁷ to the treated states based on population, percentage Black and Latinx, Democratic state house seat share and overall partisan control of state government, ⁹⁸ and social and economic liberalism in both the public and policy. ⁹⁹ I then estimate my models on this sample of states. The results are presented in Tables C.6 and C.7 in the Supplementary Materials. ¹⁰⁰ Although across the various robustness checks the estimated coefficients vary somewhat in size and significance, the overall pattern of results remains similar to that of the in-text results.

Conclusion

Advocates of legislative term limits in the United States have repeatedly touted that institution’s ability to bring legislators closer to the constituents they serve and to preclude legislators from growing insulated from constituent opinion. In this way, they reflect an institutional continuation of various efforts to avoid elite entrenchment in American politics. Previous scholarship in political science suggests that these goals have not been met, but this has been limited by types of available data in drawing firm conclusions about term limits’ representational consequences.

In this article, I use a regression discontinuity design, which necessarily limits my focus to evenly split districts, to explore term limits’ representational consequences. Under assumptions about constituent preferences, the RDD perhaps comes closer than previous scholarship to examining a critcal relationship of interest: that between term limit adoption and legislators’ ideological congruence with their constituents.

My results contribute to a growing scholarly consensus that artificially limiting voters’ choices at the ballot box has pernicious effects on legislative politics in the American states, but they also reveal the need for future scholarship to address additional unanswered questions in the study of state legislative politics. Future scholarship might extend work on the state legislative candidate pool ¹⁰¹ and on the effects of term-limit-induced turnover ¹⁰² to explore whether and how legislator-level tenure serves as a mechanism for term limits’ effects. Further work might also extend this and other works’ suggestion that term limits’ effects were greatest in more-professional legislatures to consider how term limits combine with features like low legislator pay to devalue legislative service. ¹⁰³ Finally, future work might do more to interrogate how the particular states that adopted and districts that have been affected by legislative term limits have shaped scholarly conclusions. As heterogeneity by professionalism suggests, aggregate conclusions about term limits’ effects are a function of the particular times and places in which they were adopted. Expanded data collection efforts along the lines of Tausanovitch and Warshaw’s estimates of district ideology ¹⁰⁴ might provide the opportunity to further explore whether districts that are affected by term limits were ideologically distinctive and what direct effects term limits may have had on them. Moreover, recent and future institutional innovations such as North Dakota’s 2022 adoption of term limits might provide an opportunity for scholars to further interrogate how the particular set of states that adopted term limits has shaped scholarly conclusions about their effects.