## 1 Introduction

Numerous studies have shown that institutional designs affect policy choices by constraining the actions of elected officials. Some research highlights the importance of term limits on elected officials. Besley and Case (1995) report that US governors facing a binding term limit tend to increase taxes and expenditures because executive term limits deemphasize the importance of political reputation for chief executives who are ineligible for reelection; thus, they have fewer incentives to serve the interests of voters in their last term; see also Alt, de Mesquita, and Rose (2011).

Less is known about the impact of *legislative* term limits on policy choices.
^{1} Scholars and political observers have debated the fiscal consequences of legislative term limits in the United States, where, as of November 2014, term limits are imposed on the legislatures of 15 states. Supporters of term limits claim that term limits should end pork-barrel politics and ultimately decrease the total amount of government expenditures because long-serving incumbents who are fiscally liberal or more experienced in pork-barrel politics would be replaced with freshmen who are considered to be fiscally conservative or more “clean” (e. g. Payne 1992).
^{2} Similarly, Herron and Shotts (2006) argue that the adoption of term limits reduces pork-barrel spending if it is somewhat wasteful because term limits restrict voters’ ability to select representatives who deliver particularistic benefits.
^{3}

However, empirical analysis with data from US states reports a result contrary to the expectation. Erler (2007) shows that the amount of total government spending increases after legislative term limits are introduced. Similarly, Uppal and Glazer (2015) find that the adoption of term limits increases the amount of spending for capital-intensive projects (e. g. constructing a rail line). Further, Keele, Malhotra, and McCubbins (2013) find little evidence that term limits affect state government spending by applying a case-synthetic method. In short, the literature on legislative term limits leaves us with an important puzzle: How and why does the adoption of legislative term limits affect government spending?

To address the above question, we develop a new theory on the role of term limits and seniority in legislative organizations. Past research (Dick and Lott 1993; Levitt and Poterba 1999; McKelvey and Riezman,1992; Payne 1992) suggests that legislators’ political views and skills change as they gain seniority, implying that the change in average seniority of a legislature generates a shift in the aggregate policy preference or experiences in pork-barrel politics. Thus, the adoption of term limits reduces the amount of spending because it reduces the average seniority of the legislature. In contrast to this perspective, we argue that the adoption of term limits affects government spending because it changes how legislators bargain over distributive benefits. Our theory highlights the importance of the distribution of legislators with different levels of seniority within a legislature, both in the presence and absence of term limits.

More specifically, we develop a model of legislative bargaining over distributive benefits among legislators with three levels of seniority. We consider a legislature that is composed of senior, intermediate, and junior legislators. We assume that (1) legislators with higher levels of seniority are more likely to be agenda setters because of a seniority system in the legislature; and (2) an agenda setter with higher levels of seniority possesses the power to control the amount of distributions allocated to legislators with lower levels of seniority, while legislators with the same level of seniority possesses the limited power to influence each other. Building on these assumptions, our model begins by considering the bargaining process that determines the amount of distributions allocated to legislators. Legislators are supposed to maximize payoffs to their districts by obtaining more projects and reducing the costs imposed on them. The model then examines the electoral process where a representative voter of the district chooses a legislator in the presence (and absence) of term limits. In our model, we examine the influence of strict and moderate term limits, where the former forces legislators to retire earlier than the latter.

Our model predicts the following. In the absence of term limits where voters have a choice of senior, intermediate, and junior candidates, voters are likely to elect either senior or intermediate legislators who produce the same payoff in equilibrium. However, if a senior agenda setter has very strong power to control the behavior of other legislators with the lower level of seniority, voters maximize the payoff by electing senior legislators. In the presence of moderate term limits when voters have a choice of intermediate or junior candidates, the similar equilibria as described above emerge where senior legislators are replaced by intermediate legislators. In the presence of strict term limits, voters have no choice but to elect a junior legislator.

When the legislature is occupied by legislators with same levels of seniority (e. g. all senior, intermediate, or junior legislators), their capability to influence others’ behavior is limited in the bargaining process. As a result, the legislature allocates more projects to the districts, increasing the total amount of government expenditures. In contrast, when the legislature is composed of a mix of legislators with differing levels of seniority, the agenda setter with the higher level of seniority reduces the total amount of expenditures by cutting projects allocated to legislators with the lower levels of seniority who are a part of the majority. As a result, the legislature allocates fewer projects to the districts, decreasing the total amount of expenditures.

Building upon these predictions from the model, we develop two hypotheses for empirical testing. First, the adoption of term limits that results in a larger reduction in the variance of seniority (i. e. a change from a legislature comprising legislators with different levels of seniority to one comprising legislators with similar levels of seniority) increases the amount of government spending. Second, legislatures that adopt stricter term limits have increased amounts of government spending, while legislatures that adopt moderate term limits show no changes in the amount. We provide evidence for these hypotheses using panel data for 49 US state legislatures between 1980 and 2010.

This paper contributes to the literature on legislative studies in two major ways. We show theoretically and empirically that term limits are another institutional determinant of the electoral and legislative process, ultimately affecting economic policies. In consistent with previous studies that show that government spending always expands as a result of term limits (Alt, de Mesquita, and Rose 2011; Besley and Case 1995; Erler 2007; Uppal and Glazer 2015), we demonstrate that the impact of legislative term limits is positive, but the effect depends on the types of term limits to be implemented. Substantively, our findings offer an important implication for states and nations that are considering adopting term limits.

The paper proceeds as follows. The next section develops a model of government spending as a result of bargaining among legislators with different levels of seniority and electoral choices of voters, then presents two hypotheses regarding the effect of term limits on the amount of spending. The third section describes our data and present empirical findings. The final section offers concluding remarks.

## 2 The Model

Our model considers a single legislative session where (i) a representative voter in each district chooses a legislator before the session begins and (ii) elected legislators negotiate and determine the amount of distributive projects allocated to their districts. Below we begin by describing the settings of our model and discussing the bargaining process among legislators at period (ii). Next, we consider the electoral process at period (i). We apply a pure-strategy subgame-perfect equilibrium to find the policy outcome. At the end of this section, we derive two hypotheses from our model that predict the effect of term limits on government spending.

### 2.1 Settings

Suppose that the legislature consists of odd *senior*, *intermediate*, and *junior*. The length of service is assumed to be *senior* *intermediate* *junior*.

The elected legislators negotiate over the allocation of distributive projects to their districts. The distributive projects in our model are continuous units with several possible projects for each district. The amount of distributions for each project is defined as ^{4} That is, we focus on the proportion of projects,

The legislators determine the amount of the distributions to their districts in the following way.
^{5} One of the *agenda setter*, who proposes the amount of distributions to each district. If the majority of legislators (i. e. ^{6}

The selection of an agenda setter is determined by seniority. As discussed by McKelvey and Riezman (1992), legislators with a higher level of seniority are more likely to be an agenda setter because their lengthy career allows them to accumulate legislative skills and receive better committee assignments.
^{7} Our model assumes that the legislator with the highest level of seniority in the legislature becomes the agenda setter. If there are multiple legislators with the highest level of seniority, then each of those legislators has the same probability of being an agenda setter.

To maximize the payoff, the agenda setter proposes *majority coalition*. We assume that ^{8} Formally,

^{9}

Furthermore, the agenda setter maximizes the payoffs by manipulating

This assumption is justifiable because party or committee leaders, who are the typical agenda setters in the federal and state legislatures, possess the formal and informal power to control the behavior of other members by promising future benefits in exchange for loyalty or by disciplining (Clucas 2001; Cox and McCubbins 1993, 2005; Squire and Moncrief 2010). A legislature with a seniority system has a hierarchical structure, which means that the bargaining process is centralized such that a senior leader can control other members in a variety of ways. In contrast, if all legislators have similar levels of seniority and the legislature has no hierarchical structure, then the power that party leaders and committee chairs can exercise against other members is weak. As a result, the bargaining process is likely to be decentralized.

The senior agenda setter, who is typically a party leader, does not allow members with lower levels of seniority in the majority coalition to spend as much as they want for their reelections because the agenda setter is expected to keep the value of party brand names. According to the literature on political parties and legislatures in political science, party members including junior legislators try to keep party labels as informative as possible by allowing party leaders to coordinate legislative activities (Cox and McCubbins 1993; Primo and Snyder 2010). Party labels are a low-cost method to inform constituents about their issue positions. Thus, those labels help (especially junior) legislators secure support from voters who share similar political views. If party leaders let junior legislators to spend as much as possible, it would damage party’s brand names and result in a bad reputation. In short, agenda setters and party leaders allocate some distributions to junior legislators, but the amount is limited so that junior legislators are benefited from both distributive projects and party brand names for future elections.

If the agenda setter can exercise influences on some members of the majority coalition with lower levels of seniority, we call those members who are subject to the control of the agenda setter *followers*. We suppose that the agenda setter allocates the proportions of projects (i. e.

### 2.2 Distributions

Denote

The agenda setter sets

The payoff of the agenda setter and the other members in the majority coalition is

The total amount of distributions allocated to the majority coalition is

### 2.3 Elections and Term Limits

Drawing on the above discussion, we examine the electoral process in period (i). Suppose that each district has a representative voter (e. g. the median voter in the Downsian model) who prefers a higher payoff for the district. Consider two types of term limits: moderate and strict term limits. The latter forces legislators to retire earlier than the former does. The type of term limits imposed on the legislature constrains the choice of the representative voter in the election in the following way:

- –In the absence of term limits, the representative voter has a choice of candidates who are either senior, intermediate, or junior.
- –With the adoption of moderate term limits, the representative voter has a choice of candidates who are either intermediate or junior.
- –With the adoption of strict term limits, the representative voter can only elect a junior candidate.

We derive the following equilibria regarding the types of legislators elected in the absence and presence of strict and moderate term limits:

- (i)
*In the absence of term limits, two types of equilibria emerge*:*(a)***Equilibrium I**: If and only if , the legislature consists of$p<({n}^{2}-1)/({n}^{2}+1)$ senior legislators and$\stackrel{\u203e}{n}$ intermediate legislators where$n-\stackrel{\u203e}{n}$ $\stackrel{\u203e}{n}\equiv \frac{n}{n+1}\left(\frac{2(n+1)-p(n-1)}{(n+1)-p(n-1)}\right).$ *The majority coalition includes intermediate legislators and a single senior legislator, who is an agenda setter. The total amount of distributions is*$\stackrel{\u203e}{D}$ *, where*$\stackrel{\u203e}{D}\equiv \frac{n}{2}\left(1-\frac{p(n-1)}{2(n+1)-p(n-1)}\right)<\frac{n}{2}.$ *(b)*.**Equilibrium II**: If and only if , the legislature consists of all senior legislators. The total amount of distributions is$p\ge (n-1)/n$ $n/2$

- (ii)
*In the presence of moderate term limits, two types of equilibria emerge*:*(a)*.**Equilibrium I′**: If and only if , the legislature consists of$p<({n}^{2}-1)/({n}^{2}+1)$ intermediate legislators and$\stackrel{\u203e}{n}$ junior legislators. The majority coalition includes junior legislators and a single intermediate legislator, who is an agenda setter. The total amount of distributions is$n-\stackrel{\u203e}{n}$ $\stackrel{\u203e}{D}$ *(b)*.**Equilibrium II′**: If and only if , the legislature consists of all intermediate legislators. The total amount of distributions is$p\ge (n-1)/n$ $n/2$

- (iii)
**Equilibrium III**: In the presence of strict term limits, the legislature consists of all junior legislators. The total amount of distributions is$n/2$

See the Appendix.

This proposition can be described by the following intuition. Consider a legislature in the absence of term limits. First, suppose that the legislature includes some junior legislators. They always have a nonpositive expected payoff because they receive zero payoff even if they become a member of the majority coalition. On the other hand, senior and intermediate legislators have a positive expected payoff.
^{10} Accordingly, the representative voter who chooses a junior candidate will deviate to choose a senior or intermediate legislator. Thus, in the absence of term limits, the legislature includes no junior legislators in the equilibrium. If no senior legislator is present in the legislature, then the representative voter will deviate to choose a senior candidate who will be an agenda setter with certainty.

Second, suppose that the legislature consists of all intermediate legislators. Then, the representative voter will deviate to choose a senior candidate because the voter will enjoy the comparative advantages in legislative bargaining by electing a legislator with a higher level of seniority. Hence, senior legislators are elected from at least some districts. As the number of senior legislators increases, the expected payoffs for senior legislators decreases because the probability of being an agenda setter decreases. On the other hand, the expected payoff for intermediate legislators increases because the probability of being included in the majority coalition increases.
^{11} When the number of senior legislators equals ^{12} Then, no voter has an incentive to deviate. Thus, Equilibrium I exists. However, if

Third, suppose that all legislators are senior. They have no comparative advantage, and

The same equilibrium outcomes are extended to legislatures with moderate term limits. In that legislature, intermediate legislators play the same role as senior legislators in the absence of term limits.

Note that our model assumes that, in the absence of term limits, voters always have a choice of all three types of candidates who differ in their level of seniority. However, voters seldom participate in electoral contests between a senior and an intermediate candidate. In reality, they often make a choice between a senior or intermediate incumbent and a junior challenger or between two junior candidates, which is not always consistent with our discussion. However, the most important implication of the equilibria is that the representative voter has no incentive to choose a junior candidate, which then means that a legislature is unlikely to include many junior legislators in the absence of term limits. To be precise, Proposition 1 indicates that all other situations beyond the equilibria are unlikely to be stable. For example, suppose that the legislature without term limits contains two junior candidates. In this case, even though voters cannot deviate to choose either an intermediate or senior legislator immediately, voters may wait until this elected junior legislator will be an intermediate (or a senior) legislator in the long run. Thus, even though the components of the legislatures are not exactly same as the components in the equilibria, they will change and approximate the components in Equilibrium I (if

Note also that our model considers only legislators of one chamber, but there are two possible other political actors who may have a power to approve the bill; a governor and the other chamber. In some states, a governor has a line-item veto, so even if the majority of legislators approve a bill proposed by an agenda setter, a governor may reject it. Moreover, if the state employs bicameralism, another chamber may also be able to reject a bill. In this case, these political actors (governor and/or the majority of the other chamber) become members of the majority coalition of an agenda setter. That is, an agenda setter needs to provide some distributions to policies favored by a governor and/or the majority members of the other chamber. However, the theoretical implications (Proposition 1) do not change so much since some players are just added as the coalition members, so our model does not include their effects explicitly.

### 2.4 Predicting the Effect of Term Limits

Building on Proposition 1, we now derive two hypotheses regarding the effects of term limits on government spending. A serious challenge for an empirical test is that we cannot directly observe the type of equilibrium (i. e. either equilibrium I or II, or either equilibrium I′ or II′) in the legislature. However, if Equilibrium II changes to II′ or III, both the variance in the level of seniority and the total amount of government spending will show no change. Similarly, if Equilibrium I changes to Equilibrium I′, both the variance and the amount of spending will show no change. In contrast, if Equilibrium I changes to II′ or III, the variance in the level of seniority decreases, and the amount of government spending increases. On the other hand, if Equilibrium II changes to I′, the variance in the level of seniority increases, and the amount of government spending decreases. We summarize these relationships in Table 1.

Summary of our predictions.

Equilibrium I′ | Equilibrium II′ | Equilibrium III | |
---|---|---|---|

Variance | Variance | Variance | |

Equilibrium I | Distribution | Distribution | Distribution |

Average | Average | Average | |

Variance | Variance | Variance | |

Equilibrium II | Distribution | Distribution | Distribution |

Average | Average | Average |

Note: Each column shows an equilibrium before term limits are adopted (i. e. Equilibrium I or II), while each row shows an equilibrium after term limits are adopted (i. e. Equilibrium I, II, or III). Each box indicates how the variance of seniority (Variance), the total amount of distributions (Distributions), and the average level of seniority (Average) change as a result of the adoption of term limits.

H1: The adoption of term limits that results in a larger reduction in the variance of seniority will increase the amount of government spending.

Note that for all changes in the equilibria, the average level of seniority decreases in the legislature. This means that the change in the average level of seniority is not an important determinant of the total amount of distributions. Thus, the empirical test for H1 requires us to examine how the change in the variance of seniority affects the amount of government spending.
^{13}

H2: The adoption of stricter term limits will increase the amount of government spending, while the adoption of moderate term limits will show no change in the amount.

## 3 Empirical Analysis

To test the hypotheses, we develop a panel data set of 49 US states between 1980 and 2010. States and years were chosen on the basis of data availability. The total number of observations included in our analysis is 1,519. We exclude Nebraska from our analysis because Nebraska’s legislature is unicameral and nonpartisan.

### 3.1 Data and Methods

We use the following model:

^{14}

All time-invariant characteristics of state

Any time-specific shock is captured by the year-fixed effect,

The outcome variable, ^{15}

In eq. [8],

The size of the reduction in the variance of seniority within the legislature is measured by comparing the variance before and after the adoption of term limits. More specifically, for each state with term limits, we compute the average variance in the level of seniority before and after the adoption of term limits. To compute the average variance before the adoption of term limits, we include the years after 1990, so that we could compare the change in the variance of seniority just before the adoption of term limits. For Maine where term limits were adopted in 1996, for example, we compute the average variance in seniority between 1990 and 1995 and the average variance between 1996 and 2010, and then took a difference in the averages. The changes in the average variance of seniority before and after the adoption of term limits are reported in Table 2.
^{16} All states but Oregon showed a positive value, which means that the variance of seniority in the house and the senate is larger before the adoption of term limits than after that.

States with term limits.

House | Senate | |||||
---|---|---|---|---|---|---|

Year | Change | Limit | Year | Change | Limit | |

Maine | 1996 | 0.75 | 8 | 1996 | 0.59 | 8 |

California | 1996 | 1.77 | 6 | 1998 | 1.23 | 8 |

Colorado | 1998 | 1.22 | 8 | 1998 | 0.83 | 8 |

Arkansas | 1998 | 3.10 | 6 | 2000 | 0.88 | 8 |

Michigan | 1998 | 2.19 | 6 | 2002 | 0.94 | 8 |

Florida | 2000 | 1.34 | 8 | 2000 | 0.69 | 8 |

Ohio | 2000 | 1.72 | 8 | 2000 | 0.83 | 8 |

Oregon | 1998–2002 | 1.82 | 6 | 1998–2002 | –0.33 | 8 |

South Dakota | 2000 | 0.67 | 8 | 2000 | 1.36 | 8 |

Montana | 2000 | 1.60 | 8 | 2000 | 0.76 | 8 |

Arizona | 2000 | 0.99 | 8 | 2000 | 1.00 | 8 |

Missouri | 2002 | 1.56 | 8 | 2002 | 1.04 | 8 |

Oklahoma | 2004 | 0.84 | 12 | 2004 | 0.66 | 12 |

Louisiana | 2007 | 1.08 | 12 | 2007 | 0.53 | 12 |

Note: “Year” denotes the first year when term limits became effective. “Change” denotes a change in the variance of seniority before and after the adoption of term limits. “Limit” denotes the maximum years of service. Term limits became effective in Nevada in 2010, yet this information is not reflected in our analysis because our analysis focuses on years from 1980 to 2010 and we take the lag of the adoption of term limits.

We use the size of the reduction of seniority, as shown in Table 2, to test whether the adoption of term limits that results in a larger reduction in the variance of seniority tends to increase the amount of government spending. We create a continuous scale of the reduction in the variance of seniority for the states that adopted term limits. The positive values of the scale indicate the larger reduction in the variance after term limits became effective. The remaining states (including the states without term limits) and years were coded zero. In the case of Maine, for example,

For the second hypothesis which focuses on the effects of strict and moderate term limits, we categorize states that adopted term limits by using the difference in the maximum years of service. Of the 14 states that adopted term limits for the house before 2010, four states (AR, CA, MI, and OR) set the limit at 6 years, while eight states (AZ, CO, FL, ME, MO, MT, OH, and SD) set the limit at 8 years.
^{17} The remaining two states (LA and OK) set the limit at 12 years. Similarly, of the 13 states that adopted term limits for the senate before 2010, eleven states (AR, AZ, CA, CO, FL, ME, MI, MO, MT, OH, OR, SD) set the limit at 8 years, while two states (LA and OK) set the limit at 12 years. No state adopted a 6-year limit for the senate.

We assume that term limits allowing legislators to stay for less time in the legislature (i. e. equal to 6 years) were stricter than those allowing them to stay longer (i. e. 8–12 years). For estimation, we create three indicator variables for the 6-year, 8-year, and 12-year term limits for the house. while we create two indicator variables for the 8-year or 12-year term limits for the senate. They equal 1 in the subsequent years after term limits became effective in state ^{18}

Importantly, our measure of term limits improves upon the existing binary variable that equals 1 if term limits are adopted and 0 otherwise. Similarly to Sarbaugh-Thompson’s (2010) study, we argue that the binary measure is not sufficient to capture the characteristics of different term limit rules across the states and thus able to examine their impacts on political and economic outcomes.

The vectors

The vectors

Summary statistics.

Mean | SD | Min | Max | |
---|---|---|---|---|

Total expenditures per capita | 1,935.307 | 813.910 | 833.820 | 8,038.160 |

Total expenditures as a percent of personal income | 12.694 | 4.104 | 6.392 | 43.022 |

Six-year limit in the house | 0.026 | 0.158 | 0.000 | 1.000 |

Eight-year limit in the house | 0.050 | 0.218 | 0.000 | 1.000 |

Twelve-year limit in the house | 0.005 | 0.068 | 0.000 | 1.000 |

Eight-year limit in the senate | 0.076 | 0.265 | 0.000 | 1.000 |

Twelve-year limit in the senate | 0.005 | 0.068 | 0.000 | 1.000 |

Change in variance by term limits in the house | 0.122 | 0.453 | 0.000 | 3.062 |

Change in variance by term limits in the senate | 0.064 | 0.241 | –0.334 | 1.385 |

Legislative professionalism | 0.196 | 0.124 | 0.020 | 0.682 |

Gubernatorial term limits | 0.652 | 0.477 | 0.000 | 1.000 |

Divided government | 0.548 | 0.498 | 0.000 | 1.000 |

Percent Democratic legislators in the senate | 56.550 | 18.236 | 8.571 | 100.000 |

Percent Democratic legislators | 56.231 | 17.481 | 12.857 | 98.095 |

Democratic governor | 0.523 | 0.500 | 0.000 | 1.000 |

Percent unemployed | 5.991 | 2.108 | 2.300 | 17.400 |

Personal income per capita (log) | 9.607 | 0.201 | 9.048 | 10.197 |

Population size (log) | 15.013 | 1.018 | 12.912 | 17.435 |

Percent under 15 years old | 22.028 | 2.067 | 16.584 | 32.703 |

Percent over 65 years old | 12.343 | 2.075 | 2.898 | 18.550 |

Number of observations | 1,519 |

Note: Data are based on 49 US states between 1980 and 2010.

### 3.2 Results

We estimate eq. [8] to find numerical estimates of the effects of term limits. Table 4 presents the estimation results when using the amount of government expenditures per capita as an outcome variable. To test H1, we use the size of the changes in the variance of seniority within the legislatures as a predictor of the per capita spending. Column (1) of Table 4 presents the estimation results for houses. As predicted, larger reductions in the variance of seniority has a positive and statistically significant effect on the amount of per-capita spending. The coefficient indicates that the amount of spending increases by $56 as term limits reduce the variance of seniority by 1. Note that Table 2 indicates that the size of the reduction in the variance varies from 0.67 to 3.10. In contrast, column (2) shows that the same variable for the senate has little effect on the amount of spending.

Term limits and government expenditures per capita.

(1) | (2) | (3) | (4) | |
---|---|---|---|---|

House | Senate | House | Senate | |

Change in variance by term limits | 55.789^{**} | –13.178 | ||

(22.239) | (71.047) | |||

Six-year limits | 175.904^{**} | |||

(47.588) | ||||

Eight-year limits | –17.047 | 38.177 | ||

(67.821) | (54.888) | |||

Twelve-year limits | 57.996 | 50.559 | ||

(100.493) | (99.936) | |||

Percent Democratic legislators | 0.731 | 0.670 | 0.689 | 0.681 |

(1.374) | (1.418) | (1.346) | (1.440) | |

Democratic governor | 23.753 | 23.905 | 19.951 | 23.334 |

(19.079) | (18.711) | (19.114) | (18.841) | |

Divided government | 36.370^{**} | 36.555^{**} | 31.462^{*} | 37.505^{**} |

(17.109) | (17.647) | (17.338) | (17.711) | |

Legislative professionalism | 477.207 | 363.863 | 468.392^{*} | 414.150 |

(276.393) | (300.719) | (254.898) | (290.292) | |

Gubernatorial term limits | 29.864 | 63.823 | 26.366 | 50.211 |

(67.364) | (78.288) | (68.869) | (74.757) | |

Percent unemployed | 23.279^{**} | 21.316^{*} | 23.415^{**} | 21.653^{*} |

(11.296) | (11.082) | (11.064) | (11.001) | |

Personal income per capita (log) | 2,489.424^{**} | 2,444.656^{**} | 2,493.367^{**} | 2,451.448^{**} |

(758.297) | (767.218) | (756.149) | (767.714) | |

Population size (log) | –545.510^{**} | –542.526^{**} | –524.464^{**} | –546.578^{**} |

(132.197) | (139.283) | (140.053) | (137.254) | |

Percent under 15 years old | 25.793 | 26.824 | 23.208 | 27.279 |

(20.119) | (19.605) | (20.163) | (19.713) | |

Percent over 65 years old | 79.325^{**} | 70.857^{**} | 76.225^{**} | 74.291^{**} |

(31.325) | (29.935) | (30.863) | (29.916) | |

0.962 | 0.962 | 0.963 | 0.962 |

^{*}

Note: Table entities are fixed effects regression estimates and standard errors in parentheses. Standard errors are clustered by the state. Estimates are based on data from 49 states between 1980 and 2010. The dependent variable is the amount of total government expenditures per capita in dollars. State- and year-fixed effects are included in the models. The number of observations is 1,519. *p**p*

Next, we test H2 by exploiting the different types of term limits. Column (3) of Table 4 shows that the coefficient associated with the 6-year limit for the house was positive and statistically significant. The coefficient indicates that the amount of government expenditures per capita increased by $176 after states adopted 6-year (i. e. stricter) term limits. The coefficients associated with 8- and 12-year term limits indicate that their adoption had no statistically significant effect on government expenditures. Column (4) shows that coefficients associated with the 8-year and 12-year term limits for senates had a positive but statistically insignificant association with the outcome variable.

Some control variables in Table 4 show consistent patterns to explain the amount of spending. Among the political variables, divided government was the only predictor with a significant coefficient. When the government was controlled by two parties, the amount of expenditures tended to increase by $30–$40. The demographic variables showed that the amount of expenditures increased as the percent of the population who were unemployed or under 15 years old, and per capita personal income increased, while it decreased as the log size of population size increased.

The results in Table 4 are replicated by using the share of government expenditures in state personal income as an outcome variable. Table 5 reports the estimation results. For the houses, larger drops in the variance of seniority as a result of term limits in the house in column (1) increase the share of state government expenditures. Similarly, the adoption of 6-year term limits in column (3) increases the share by 1.1 percentage points. On the other hand, the 8-year and 12-year term limits in the house have no statistically significant relationship with the outcome variable. Similarly, the adoption of term limits in the senate has no significant effect on the share of government spending. With respect to the control variables, the share of government expenditures increased in the presence of divided government and as the population size decreased.

Term limits and government expenditures as a percent of state personal income.

(1) | (2) | (3) | (4) | |
---|---|---|---|---|

House | Senate | House | Senate | |

Change in variance by term limits | 0.482^{**} | 0.231 | ||

(0.171) | (0.446) | |||

Six-year limits | 1.125^{**} | |||

(0.485) | ||||

Eight-year limits | 0.230 | 0.512 | ||

(0.421) | (0.363) | |||

Twelve-year limits | 0.384 | 0.463 | ||

(0.550) | (0.547) | |||

Percent Democratic legislators | –0.009 | –0.009 | –0.010 | –0.009 |

(0.009) | (0.009) | (0.009) | (0.010) | |

Democratic governor | 0.191^{*} | 0.201^{*} | 0.175^{*} | 0.198^{*} |

(0.102) | (0.104) | (0.103) | (0.105) | |

Divided government | 0.241^{**} | 0.243^{*} | 0.226^{*} | 0.249^{*} |

(0.120) | (0.125) | (0.124) | (0.124) | |

Legislative professionalism | 2.336 | 1.598 | 2.196 | 1.987 |

(2.047) | (2.091) | (2.031) | (2.078) | |

Gubernatorial term limits | –0.109 | 0.159 | –0.073 | 0.069 |

(0.537) | (0.618) | (0.556) | (0.594) | |

Percent unemployed | 0.077 | 0.075 | 0.074 | 0.078 |

(0.080) | (0.081) | (0.079) | (0.080) | |

Personal income per capita (log) | 1.178 | 0.840 | 1.090 | 0.892 |

(4.761) | (4.816) | (4.761) | (4.796) | |

Population size (log) | –2.278^{**} | –2.464^{**} | –2.247^{**} | –2.493^{**} |

(0.962) | (1.023) | (1.013) | (1.013) | |

Percent under 15 years old | 0.107 | 0.096 | 0.100 | 0.100 |

(0.141) | (0.141) | (0.144) | (0.142) | |

Percent over 65 years old | 0.088 | 0.049 | 0.066 | 0.071 |

(0.222) | (0.225) | (0.222) | (0.222) | |

0.943 | 0.941 | 0.942 | 0.942 |

^{*}

Note: Table entities are fixed effects regression estimates and standard errors in parentheses. Standard errors are clustered by the state. Estimates are based on data from 49 states between 1980 and 2010. The dependent variable is the amount of total expenditure as a percent of state personal income. State- and year-fixed effects are included in the models. The number of observations is 1,519. *p**p*

Tables 4 and 5 show the consistent results that the effects of term limits for the house are larger than the senate. We speculate that this is because the adoption of term limits resulted in a smaller change in the variance of seniority in the senate than in the house across the states. The average reduction in the variance in the senate is by 0.83, while the average reduction in the house is 1.45. Thus, the variance of seniority changes to the larger extent in the house as a result of term limits, resulting in the increase in government spending.

Taken together, according to our results, term limits that cause a large change in the distribution of seniority have a larger positive effect on the amount of government expenditures than those that cause a small change. These findings offer evidence that more restrictive term limits that greatly change the distribution of seniority within the legislature increase the amount of spending, while less restrictive term limits that slightly change the distribution of seniority have little effect on the amount of spending. One may argue that our estimation results could be potentially biased because of a potential reverse causation between the adoption of legislative term limits and government spending. In other words, stricter term limits might be more likely to be adopted by the states with the higher levels of spending. However, Erler (2007) and Mooney (2009) suggest that major political and demographic characteristics of states have no strong relationship with the adoption of legislative term limits. Thus, this implies that the reverse causality is unlikely to have a significant influence on our estimation results.

## 4 Conclusion

This study revisits the enduring question of how the adoption of term limits affects the amount of government expenditures. We developed a model that consists of two parts. In the bargaining process, legislators determine the amount of distributions allocated to their districts. In the electoral process, a representative voter of the district chooses a legislator in the presence (and absence) of term limits that differ in the level of strictness. Drawing from the model, we hypothesized that the adoption of term limits that caused a large change in the distribution of seniority would have a larger positive effect on the amount of government expenditures than those that caused a small change. Our analysis using the panel data for 49 US states between 1980 and 2010 offered supportive evidence for our hypotheses.

Our findings are consistent with Erler’s (2007) and Uppal and Glazer’s (2015) findings, yet our model now explains why the adoption of strict term limits increases government spending, while the adoption of moderate term limits has no such effect. We show formally that the relationship between term limits and the amount of government spending depends crucially on the distribution of seniority in a legislature. Our study also helps us to show the role of overall seniority in a legislature.

In addition, our findings can be reconciled with the findings of previous research showing that senior legislators tend to be more pro-spending (Garand, Myers, and Renegar 2011; Payne 1992). Our model and empirical analysis indicate that the amount of government spending increases when a legislature consists of legislators with similar levels of seniority. Thus, the distribution of seniority, not the average level, plays a more important role as a determinant of government expenditures.

This study suggests that the adoption of strict term limits may have an undesirable consequence (i. e. an increase in the amount of spending). In contrast, the adoption of moderate term limits is likely to have no such consequence. Thus, if voters and legislators wish to adopt any forms of term limits to increase electoral competitiveness and turnover without increasing government spending, for example, they may view the adoption of moderate term limits as an appealing choice.

This study involves an important limitation. The model we developed is static, but politicians in the presence of term limits may produce policies that bind policy decisions in the future, as suggested by prior studies (e. g. Alesina and Tabellini 1990). When legislators expect that they will be replaced with legislators of different ideological preferences, they will seek to tie the hands of new legislators by creating policies that are not readily adjustable. Our model does not consider the dynamic effect of term limits on policies. Though this is beyond the scope of our analysis, future research should consider the implications of this dynamic process.

The authors wish to thank Peter Berck, Shunichiro Bessho, Hirokazu Ishise, Gary Moncrief, and the participants of the 2012 annual meeting of the American Economic Association, and the Models and Data Group of the Department of Political Science at the University of Wisconsin-Madison for their valuable comments. We would also like to thank Carl Klarner for graciously providing us his updated state legislative election returns data.

Denote

## 1 Without Term Limits (Proposition 1 (i))

In the absence of term limits, the legislature can include one of the following five sets of legislators:

- –Case 1: Legislature with senior and intermediate legislators (
,$s>0$ , and$m>0$ ).$n-s-m=0$ - –Case 2: Legislature with only senior legislators (
).$s=n$ - –Case 3: Legislature without senior legislators (
).$s=0$ ^{19} - –Case 4: Legislature with senior and junior legislators (
and$m=0$ ).$s\in (0,n)$ - –Case 5: Legislature with all three types of legislators (
,$s>0$ , and$m>0$ ).$n-s-m>0$

Below, we consider whether each case emerges as an equilibrium.

### 1.1 Case 1: $s>0$ , $m>0$ , and $n-s-m=0$

First, suppose that the legislature includes senior and intermediate legislators but no junior legislators. A senior legislator will be an agenda setter.

**Case 1-a** (^{20}

The expected payoff for senior legislators and their districts before an agenda setter is chosen is

The expected payoff for intermediate legislators and their districts is

Among

In equilibrium, these two expected payoffs must be identical. This is because, if a senior legislator has a higher expected payoff than an intermediate one, then the representative voter who chooses an intermediate candidate will deviate to choose a senior candidate. Similarly, if an intermediate legislator has a higher expected payoff, then the representative voter who chooses a senior candidate will deviate to choose an intermediate candidate. The expected payoffs for senior and intermediate legislators become identical when

If

If

Next, suppose

If the expected payoff from choosing a senior or intermediate legislator at

Note that, when

In addition, the above result is true only if ^{21}

**Case 1-b** (

The expected payoff for intermediate legislators is

*In Case 1-b, as *.

Differentiate eq. [10] by

*In Case 1-b, as *.

Differentiate eq. [11] by

Then, the following lemma is also obtained.

*Suppose Case 1-b and for all *.

If

Thus, if

Finally, suppose

### 1.2 Case 2: $s=n$

Suppose that the legislature consists of all senior legislators. Then,

### 1.3 Case 3: $s=0$

Suppose that the legislature consists of intermediate and/or junior legislators. Either an intermediate (if

### 1.4 Case 4: $m=0$ and $s<n$

Suppose that the legislature consists of senior and junior legislators but no intermediate legislator. A senior legislator will be an agenda setter.

**Case 4-a** (

**Case 4-b** (

### 1.5 Case 5: $s>0$ , $m>0$ , and $n-s-m>0$

Suppose the legislature has all types of legislators. A senior legislator will be an agenda setter. Denote

**Case 5-a** (

**Case 5-b** (

**Case 5-c** (

The expected payoff for senior legislators before an agenda setter is chosen is

From the same reasons as the proof in Case 1-a, these expected payoffs that senior and intermediate legislators receive must be identical. This means

In Case 5-c, at

The expected payoff of junior legislators is

Accordingly, the representative voter who chooses a junior legislator will deviate to choose a senior or intermediate legislator, suggesting that Case 5-c is not an equilibrium.

## 2 With Term Limits (Proposition 1 (ii) and (iii))

In the presence of moderate term limits (Proposition 1 (ii)), there are three possible cases:

- –Case 1′: Legislature with intermediate and junior legislators (
).$m\in (0,n)$ - –Case 2′: Legislature with only intermediate legislators (
).$m=n$ - –Case 3′: Legislature with only junior legislators (
).$m=0$

Because we suppose that the proportion of junior members controlled by an intermediate agenda setter is

Proposition 1 (iii) is obvious. ☐

In this section, we show that the main results drawn from our one-shot game hold even when we consider an infinitely repeated game, as long as we suppose stationary equilibria where an agenda setter makes the same proposal in all periods.

The amount of distributions,

Denote

Suppose that all followers in the majority coalition have the same level of seniority. Then, when a legislator becomes a follower and approves the proposal, the payoff is

If this legislator deviates by rejecting the proposal, the bargaining will be concluded in the next period, so his/her expected payoff is

From the one-shot deviation principle, the follower is indifferent between accepting and rejecting the proposal when the above two expected payoffs are equal, i. e.

Thus, the agenda setter proposes

which is identical to eq. [3] in the main text. The agenda setter allocates less to the followers in a repeated game than in a one-shot game, i. e.

The right-hand side is less than 1 if

Note that if an agenda setter is senior and the followers include both intermediate and junior legislators, the value of

From the above analyses, the following corollary is immediately derived.

*In a repeated game: (i) In the absence of term limits, the representative voter does not choose a junior legislator. (ii) The equilibrium outcomes are identical in the absence of term limits and with a moderate term limits*.

(i) From the same reasons as Proposition 1, the voter prefers to choose a senior legislator if none is in a legislature. Suppose a legislature with at least one senior legislator. In the absence of term limits, the junior legislator has a nonpositive expected payoff in a repeated game and zero payoff in a one-shot game. The representative voter does not choose a junior legislator in a one-shot game from Proposition 1-(i). The same logic applies to the repeated game. (ii) The probability

Moreover, in a repeated game, the equilibrium where both senior and intermediate legislators are elected (i. e. similar to Equilibrium I in Proposition 1) exists in the absence of term limits.

*In a repeated game without term limits, if*

*there exists an equilibrium where the legislature consists of *

See the next section. ☐

From Corollary 1-(ii), the equilibrium outcomes do not change even if moderate term limits are introduced. An equilibrium where both senior and intermediate legislators exist in a legislature (Corollary 2) is associated with the smaller amount of distributions than the equilibrium where only junior legislators exist in the legislature (since

Needless to say, the repeated setting we considered above suffers from the problem of multiple equilibria. The above equilibrium is just one of (stationary) equilibria. Moreover, we face two additional challenges. First, a one-shot bargaining in a repeated game is typically interpreted as bargaining between elections, and the discount factor includes the probability of winning in the next election (see, e. g. Gehlbach 2012). Our model considers the electoral choices by voters endogenously, so we have to analyze voters’ decisions and the endogenous probability of winning simultaneously in a dynamic setting. Second, when considering dynamic games, a junior legislator becomes no longer junior after several periods. That is, we need to take into account the change in the level of seniority for each legislator in the repeated setting. These two challenges complicate our model to the great extent. As a result, to simplify our discussion, we use a one-shot game in the main text.

Suppose that there are

In equilibrium, these two expected payoffs must be identical, so it must be

From the same reason as Proposition 1, it must be

If the expected payoff from choosing a senior or intermediate legislator at

Our model assumes that all members of the majority coalition can perfectly coordinate to circumvent a common pool problem. This appendix shows that our conclusion holds even if this assumption is relaxed.

Suppose that members of the majority coalition partially care about the amount of the costs incurred by all members in the majority coalition. Formally, the maximization problem of

As

Moreover, even if

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## Footnotes

^{1}

Numerous studies have investigated the impact of term limits. See Carey et al. (2006) and Mooney (2009). A recent study by Lewis (2012) found the negative impact of legislative term limits on state fiscal performance using state bond ratings, while Elder and Wagner (2015) showed that the legislative term limits lead to more pension underfunding.

^{2}

Senior members of Congress are more likely to support greater spending than their junior colleagues (Garand, Myers, and Renegar 2011), while being known to deliver more distributive benefits to their own constituents (Lazarus 2010).

^{3}

Herron and Shotts (2006) predict that the adoption of term limits *increases* pork-barrel spending if it is highly wasteful because term limits remove legislators who seek to avoid imposing the cost of wasteful pork projects on their constituents.

^{4}

When

^{5}

This model is a modified version of the simple ultimatum legislative-bargaining model developed by Baron and Ferejohn (1989).

^{6}

To simplify the model, we suppose the ultimatum game because a repeated game has the problem of multiple equilibria. The main results shown below hold even when we consider an infinitely repeated game, as long as we suppose stationary equilibria where an agenda setter makes the same proposal in all periods. The supplementary analyses are shown in Appendix 2.

^{7}

Squire and Moncrief (2010) note that seniority plays an important role in the selection of leaders and committee chairs in US state legislatures.

^{8}

They act as if they are the members of the government party or coalition government.

^{9}

Our conclusion described below holds when all members coordinate not perfectly but with sufficiently a high degree. See Appendix 3 for more details.

^{10}

When the number of senior legislators is large, then intermediate legislators have a positive expected payoff. When the number of senior legislators is small, then senior legislators have a positive expected payoff. See the Appendix for more details.

^{11}

To be precise, these comparative statics are true when the number of senior legislators is lower than

^{12}

Here, we assume that

^{13}

In addition to H1, we can draw another hypothesis from the model and Table 1 that the adoption of term limits that results in an increase in the variance will decrease the amount of government spending. We are not able to test this hypothesis in our empirical analysis because no state experienced an increase in the variance of seniority after the adoption of term limits. The senate in Oregon showed a small increase in the variance after the adoption, but this change was temporal because the Oregon Supreme Court struck down the law in 2002.

^{14}

For example, legislators who won the 1998 election are expected to influence the budget year beginning July 1999.

^{15}

The data were obtained from http://www.census.gov/govs/state/.

^{16}

In Oregon, the term limit law became effective in 1998, but the Oregon Supreme Court struck down the law in 2002. Nevada was excluded from this categorization because its term limits became effective in 2010.

^{17}

California’s limits were extended from 6 years in the assembly and 8 years in the senate to 12 years in both chambers after 2012.

^{18}

The website is found at http://www.ncsl.org/Default.aspx?TabId=14844.

^{19}

This includes three subcases: (i)

^{20}

Here, we assume that

^{21}

To be precise, denote