The Hazards of Incumbency: An Event History Analysis of Congressional Tenure

Transcription

1 The Hazards of Incumbency: An Event History Analysis of Congressional Tenure Charles J. Finocchiaro University at Buffalo Department of Political Science 520 Park Hall Buffalo, NY Phone: (716) ext. 422 Fax: (716) Tse-min Lin Department of Government University of Texas Burdine Hall 536 Austin, Texas Phone: (512) An earlier version of this paper was presented at the 58 Annual Meeting of the Midwest th Political Science Association, April 27-30, 2000, Palmer House Hilton, Chicago, Illinois. Authors are listed alphabetically. We thank Brad Jones for providing his data and Neal Beck for sharing his programs. We also thank Greg Bovitz and Jamie Carson for helpful comments.

2 Abstract Studies of leadership duration employing advanced event history techniques are quite common in comparative politics, but relatively few analyses of this type have been conducted on American congressional careers. The exceptions to this are often unsatisfactory because they presuppose hazard functions that are either constant or monotonically decreasing. In this paper, we explore the impact of congressional tenure on the hazards of electoral termination while allowing for general forms of time-dependence. Employing logistic models with indicator variables, we seek to build a more comprehensive and compelling theory of the risks associated with congressional careers. Our findings show that the likelihood of electoral defeat sharply decreases at the early stage of a member's career, with the incumbent becoming entrenched after the third term. In addition, the hazards increase slightly beyond the tenth term, suggesting constituents weariness of a long career.

3 Introduction In 1980, Rep. John Murphy, a Democrat from New York, was defeated in the general election, ending his eight-term tenure as a congressman. Two years later, Rep. Paul Findley, a Republican from Illinois, wrapped up his career at the eleventh term. While 1980 was a particularly bad year for Democrats and 1982 was equally bad for Republicans, the two congressmen had faced individual difficulties in their final reelection bids. Murphy, who had th th served as chairman of the Committee on Merchant Marine and Fisheries in the 95 and 96 Congress, was implicated in the Abscam scandal. Findley, who survived redistricting the first time he ran for reelection, had seen his electoral margin dwindle by more than 27 percentage points in 1980 because of an allegation that tied him to the Palestine Liberation Organization (PLO). These were two congressmen whose careers had reached a critical juncture. Scholars have been interested for many years in the dynamics of leadership tenure. By understanding the forces that drive the turnover of political elites, insights regarding the stability of a political system and the balance of power between multiple branch governments may be obtained. In democratic governments, the duration spent in power by elected officials has significant implications for the degree to which a government may be seen as representative and for assessing whether it is capable of fulfilling its function in a stable manner. These issues are nowhere more prominent than in the comparative politics literature on leadership and regime duration, where interest has focused on phenomena such as cabinet 1 duration in parliamentary democracies and leadership tenure more generally. One of the central 1 The burgeoning literature on cabinet duration/dissolution includes Alt and King (1994); Browne, Frendreis, and Gleiber (1986, 1988); Diermeier and Stevenson (1999); King, Alt, Burns, and Laver (1989); Lupia and Strom (1995); Strom (1985, 1988); Warwick (1992a, 1992b); and Warwick and Easton (1992). More generally, on leadership duration in the 1

4 questions in this vein has been the attempt to determine why parliamentary governments often dissolve prior to reaching the next constitutionally mandated time for an election. Recent research has centered on specifying the form of the hazard rate (or risk of termination) over time. As Alt and King (1994) note, this is a fundamental question because properly specifying the stochastic components relating to duration and their hazard rates have potentially important implications for substantive conclusions in this area (193). Surprisingly, similar research on leadership and regime duration has been quite limited in the realm of American politics. While a number of researchers have applied the methods of event history analysis to explore questions regarding individual behavior and decision-making, 2 relatively few have taken up the question of elite circulation. The earliest such work dealing with electoral forces is that of Casstevens (1989), who examines the tenure of members of the U.S. Congress. More recently, Box-Steffensmeier and Jones (1997) and Lin and Guillén (1999) employ duration analysis to explain various aspects of electoral politics in the United States. However, even these works employ models that are relatively simplistic in their specification and distributional assumptions. For instance, Casstevens (1989) models the tenure of members of the House and Senate as an exponential process, an underlying assumption of which is that the hazard rate is invariant to time. He concludes that seniority has no effect on the reelection prospects of members of Congress. In their paper expositing the uses of event history analysis, Box-Steffensmeier and Jones (1997) use a linear time framework in the context of a comparative context, see Bienen and van de Walle (1989, 1992) and Bueno de Mesquita and Siverson (1995). 2 Among those applying duration methods to other dimensions of American politics are Berry and Berry (1990); Box-Steffensmeier (1996); Box-Steffensmeier, Arnold, and Zorn (1997); and Katz and Sala (1996). 2

5 multinomial logit, in effect constraining the potential form of the influence that time may impose on electoral termination. Finally, Lin and Guillén (1999) model party turnover in American presidential elections as a Weibull process, thus allowing for only limited forms of timedependence. An example of research on leadership duration in American politics that is an exception to these restrictive approaches is Katz and Sala s (1996) study of congressional committee assignments. In this paper, we attempt to circumvent the limitations of previous work in American politics (and congressional elections in particular) by employing alternative methods of duration analysis that allow for more flexibility in modeling time dependence and enable us to include a series of relevant control variables. We do not focus solely on the empirics of elections to the U.S. Congress, however, in that our findings bear on a number of questions that have been examined at length in the literature, many of which have generated conflicting and at times quite divergent explanations. The specifics of these issues are discussed in the subsequent sections of the paper. Congressional Careers Students of Congress have extensively examined the factors purported to influence the tenure of members of the institution. Research in this area has moved in a number of different directions, all of which are relevant in obtaining a complete picture of the factors affecting the patterns of congressional careers. For instance, some analyze the decision framework within which career choices are made (see, e.g., Rohde 1979, Moore and Hibbing 1992, and Kiewiet and Zeng 1993). Others consider the issue of member behavior and its influence on incumbents electoral fortunes (see, e.g., Mayhew 1974; Cain, Ferejohn, and Fiorina 1987). Still others 3

6 examine questions dealing with the advantages of incumbency and argue both for and against the waxing and waning of its impact over time (see, e.g., Erikson 1971, Ferejohn 1977, Born 1979, Krehbiel and Wright 1983, Gelman and King 1990, and Cox and Katz 1996). What is of primary interest here is a question that is intertwined with all the above, if not transcendent of these particular areas of research. We are interested in determining the factors that lead to more or less risk of electoral termination, particularly in light of a member s tenure in office and a series of explanatory variables that are known to contribute to varying levels of electoral security. The literature on congressional career patterns, and particularly that dealing with the incumbency advantage as measured by a member s margin of victory, often focuses attention on related but distinct notions of electoral security. We hold that marginality, although a good predictor of incumbent vulnerability, is only one of a number of factors relating to a member s electoral security (or risk of defeat). A comprehensive view of electoral termination should take into account factors that relate both to individual members in specific elections and more general patterns of incumbent vulnerability over time. Arising from the literature on the incumbency advantage are a number of important insights that bear on the analysis to follow. Interestingly, a common thread in most of the research on the topic is that all or most incumbents are treated the same. Erikson (1971) notes the presence of a sophomore surge in which incumbents improve dramatically in their second electoral contest and enjoy high levels of success thereafter. Alford and Hibbing (1981) take an important step beyond this basic typology in arguing that the researcher ought to examine the entire period of service for members of Congress. They claim that the distinction between sophomore and non-sophomore status is useful as a starting point but falls short of providing the complete picture of the performance of incumbents according to tenure level (1044). They 4

7 go on to suggest that in order to obtain such a picture, it is necessary to examine the full career pattern of members. Of primary importance for the analysis presented here, Alford and Hibbing note that the incumbency advantage (as measured by electoral margins) appears to grow over members careers, although they observe diminishing marginal returns as the number of terms served increases (1046). Essentially, their findings suggest a dampening pattern of growth in electoral security, as members become increasingly insulated at a higher rate early in their careers, and less so the longer they serve. Although the rate of increase diminishes with tenure, electoral performance continues to rise even at relatively high levels of tenure (1047). Hibbing (1991) conducts a similar analysis in which he studies the variation in electoral security of members of Congress both across tenure (seniority level) and according to generational groups (broken down by decades and by class). Electoral security is measured in two ways: an incumbent s share of the vote and the percentage of incumbents reelected. Hibbing finds that, particularly in recent years, there has been little difference between the electoral success of junior and senior members of Congress. While in the early years of the post-war era there was some evidence of a life cycle effect, after a few terms modern representatives seem to be in virtually the same spots as when they were new (54). In fact, his findings in this regard lead him to pose the question What is it about the modern House that makes tenure irrelevant to variations in mean electoral performance? (55, emphasis added). His findings appear to indicate that tenure exerts little influence on a member s electoral fortunes, such that regardless of how long one has served, there will be little difference between his/her performance and that of a member at another point on the seniority spectrum. In critiquing the idea that congressional elections had grown less competitive in the 1960s (as suggested by the vanishing of marginal districts), Jacobson (1987, 2001) draws 5

8 attention to an important assumption underlying previous work. He argues that while the vote margin of incumbents expanded dramatically in the 1970s, it did not carry with it a corresponding decrease in the competitiveness of House elections. Even with the same prior margin level, Jacobson demonstrates, incumbents reelected in the 1970s could be more prone to defeat than those elected in the 1950s and 1960s. The crux of his argument is that the number of marginal districts had not changed. Instead, what has changed is the appropriate criterion for 3 marginality (1987, 129). The use of thresholds of vote margin as indicators of vulnerability can be justified only if they are stable over time. Jacobson s evidence, however, shows that they are not. While there is no question that vulnerability is influenced by prior margin level, there are other factors that a study of vulnerability must consider. These other factors may be individual specific, or they may be macro factors pertaining to the nature of the times. We suggest that an event history analysis of congressional tenure can circumvent the limitations of vote margin as a measure of vulnerability. In studying the survival pattern of congressional incumbents, the approach considers electoral defeat the event of interest as the explicit dependent variable and the probability of defeat a direct measure of vulnerability as the implicit dependent variable. As a unique feature of event history analysis, the probability of defeat is conditioned on the duration of survival, thus allowing for the possibility of tracking the dynamics of vulnerability throughout all tenure levels. The analysis is carried out at the individual level rather than in the aggregate, as is the case for much of the work on incumbency advantage. At the individual level, the probability of defeat, conditional on tenure level, is 3 While the substantive influence of Jacobson s claims has been challenged (see Bauer and Hibbing, 1989), what is important for the discussion here is that researchers must be cautious when attempting to measure incumbent vulnerability. 6

9 related via a certain functional form to a set of term-specific independent variables that can include prior margin level among individual factors as well as macro (the nature of the times) factors. An event history analysis of congressional tenure, in this sense, is a story that tracks and explains the ups and downs of an incumbent s electoral fortunes in terms of the probability of defeat at all tenure levels. In the next section, we focus on the dynamics of incumbent vulnerability and introduce event history analysis as the appropriate method to test various theoretical expectations about those dynamics. Theory, Model, and Hypotheses In Erikson s (1971) original analysis demonstrating the sophomore surge, only firstterm incumbents Erikson actually called them freshman incumbents were shown to gain more than the average vote swing of incumbents at all other tenure level, who were grouped together as veteran incumbents. Since then, the literature on congressional elections, most particularly that of Alford and Hibbing (1981) and Hibbing (1991), clearly suggests that the incumbency advantage in vote margins should be considered a function of tenure. However, concerning the exact dynamics of such a function, the only general consensus seems to be that first-term incumbents, despite the sophomore surge, are still the most vulnerable. Beginning with the second term, as the number of terms served increases, the pattern is neither clear nor fully agreed upon. Fenno (1978) noted that cultivating one s constituency is an ongoing process that often takes a number of electoral cycles to develop. As such, one might expect that congressmen only become insulated after a few terms of service. Alford and Hibbing (1981), however, cite Kurtz 7

10 (1972) as reporting a relatively abrupt leveling off of defeats rates after the second term. They also cite Cover s (1980) work on mass mailings of House members as supporting a similar career pattern. Alford and Hibbing reject these findings, presenting their own data showing increasing electoral performance as tenure increases, even at high levels of tenure, albeit with a diminishing return. More recently, Hibbing (1991), revises his opinion and argues that an incumbent s advantage in reelection is relatively flat across the span of his/her career. In another development, the literature on party incumbency at the presidential level suggests that weariness or fatigue (i.e., constituents desire for a change) can turn incumbency status into a liability (Abramowitz 1994; Fackler and Lin 1995; Fair 1996; Lin and Guillén 1999). Similarly, congressional incumbency has been seen as a handicap as a number of prominent members (among them the Speaker of the House) were defeated in their attempts at reelection in the early 1990s (Jacobson 1997). The fatigue factor suggests that veteran incumbents may exhibit increasing electoral vulnerability after serving a good number of terms. Based on such considerations, it is clear that time must be considered an essential element in the study of the incumbency advantage in U.S. congressional elections. Scholars must, as Beck, Katz, and Tucker (1998) argue, take time seriously in developing the theoretical framework and empirical models employed in studying this important dynamic of 4 American politics. We argue that the most appropriate conceptual tool for this purpose is the hazard function drawn from event history analysis. The hazard function has been used extensively in the study of government survival, but to our knowledge its application to congressional careers remains quite limited. 4 See also Bennett (1999) on duration dependence in event history analysis. 8

11 The hazard function, which is often denoted by h(t), describes the risk of some event occurring at a specific time to a particular individual. In discrete time, the hazard may be more formally defined as the conditional probability of an event occurring at time t k, given that it did not occur prior to t k, and may be written as: where t k (k = 1, 2, ) indicates the kth discrete time point since the individual became subjected to risk; is a binary random variable indicating whether the event occurs at t ; and T is a k discrete random variable indicating the time at which the event occurs. In the context of congressional elections, the event under consideration is electoral defeat that occurs to an incumbent member of Congress. Therefore, t k = k (k = 1, 2, ) are the periodic elections after the incumbent has served k terms. The random variable T represents the length of a congressional career ended by defeat: T = k when the incumbent is defeated for reelection after term k. h(t k) = h(k) is thus the conditional probability of the incumbent losing her bid for reelection, given that she has served k consecutive terms. A related concept is that of the survivor function, which is denoted by S(t). S(t) is simply the probability that the event has not occurred by time t, or that the individual has survived up to that point. In discrete time, In terms of elections to the U.S. House of Representatives, S(k) (k = 1, 2, ) is simply the probability that the incumbent member has survived (or served) k terms. The survivor function can be related to the hazard function as: 9

12 which states that S(t k) equals the joint probability that the event did not occur at t k-1, t k-2,, t 1. With the definitions of h(t ) and S(t ), it can be seen that the unconditional probability that an event occurs at time t k is k k A parametric specification of h(t k) can thus lead to a probability distribution for the random variable T that defines a discrete hazard model. For example, with t k = k (k = 1, 2, ), specifies a constant hazard function that leads to the geometric distribution for T: A more general specification of the hazard function is which is monotonically increasing ( > 1), monotonically decreasing (0 < < 1), or a constant ( = 1). In this case, T corresponds to the discrete Weibull distribution for which the geometric distribution is a degenerate case (Nakagawa and Osaki 1975). Lin and Guillén (1999) use this distribution to model the hazards of party incumbency in the American presidency. Parametric models often impose restrictive constraints on the shape of the hazard function. For example, the discrete Weibull distribution (as well as its continuous equivalent) can only rise or decline monotonically, a pattern that may not be empirically realistic. Other distributions are more flexible yet still restrictive. For example, the continuous lognormal 10

13 distribution has a non-monotonic hazard function, but it always begin at zero, rises to a maximum, and then decreases very slowly to zero (Sweet 1990). The log-logistic distribution can also attain a single maximum, or it is decreasing with an exponential tail (Cox and Oakes 1984, 21). These models do not seem to fit the theoretical expectations we developed above for the hazards of incumbency in congressional careers. The hazard function, however, does not have to be specified parametrically. There are widely used nonparametric or semiparametric event history models, such as the Cox proportional hazards model (Cox 1972), that can be used to derive hazard functions that are not as stringent as those of the parametric models. The continuous Cox model specifies a hazard function conditional on a set of covariates in a very general way: (1) where x is a vector of covariates; is a vector of coefficients associated with x; and h 0(k), the baseline hazards, is the hazard function when all covariates are set to 0. In his discrete time model, Cox replaces h and h 0 with their respective odds ratios: (2) This turns out to be mathematically identical to the logit model where k is the log odds ratio associated with the baseline hazards (Cox 1972). The advantage of the Cox proportional hazards model or the logit model is the opportunity to empirically estimate the hazard function without a priori constraints on its functional form. 11

14 Casstevens (1989) is to our knowledge the first to employ the event history framework in the analysis of congressional careers. He models the congressional career as a process in which T, the duration of tenure, is exponentially distributed. As he notes, the exponential distribution has the memoryless (Markovian) property and as such imposes the assumption that the risk of tenure termination is invariant to time. The exponential distribution, however, is not an appropriate distribution for T because it is a continuous distribution whereas T is in reality a discrete random variable. Furthermore, the exponential distribution is the continuous equivalent of the geometric distribution and likewise entails a constant hazard function. By fitting the exponential distribution without a specific alternative that carries with it a non-constant hazard function, Casstevens draws the surprising and counterintuitive conclusion that the probability of reelection does not vary with seniority (306). In more recent work, Box-Steffensmeier and Jones (1997) employ a logit framework in modeling the risk of career termination over the course of members careers. Without providing explicit theoretical expectations about the dynamics of the hazard function, Box-Steffensmeier and Jones specify the duration of tenure, measured as the number of terms in office, as one of the covariates in their model. In the logit framework, this entails that (3) where y i,k = 1 if incumbent i is defeated after serving k terms and 0 if she is reelected at that point; x is a vector of time-dependent covariates; is the coefficient vector associated with x ; i,k and is the coefficient associated with k. Note that this probability is a hazard function because the inclusion of T k in its conditionals effectively implies that electoral defeat has not occurred i,k 12

15 to the incumbent up to term k. With such a specification, it can be shown that k, as well as other covariates in x i,k, affects the log odds ratio of electoral defeat in a linear fashion: Comparing losing in the general election to winning, Box-Steffensmeier and Jones estimate for is -.09, indicating that, controlling for the covariates, the log odds ratio (which they call the log-hazard ) of losing decreases by.09 with each term served. The effect of duration on the log odds ratio is thus independent of seniority. The probability of losing, however, decreases monotonically with increasing seniority according to Equation (3) for an estimated that is negative. That is, the hazard function h(k) decreases monotonically with k, and the longer an incumbent is in office the more immune she is from general election defeat. 5 As mentioned earlier, Cox (1972) shows that the logit model is mathematically identical to his discrete-time proportional hazards model based on Equation (2). In the ordinary logit model, however, the effects of the covariates are independent of time. When time-series crosssection data are available, Brown (1975) suggests the use of indicator variables (i.e., dummy variables) for studying the time-dependence of parameters in the logit framework. If time is of the essence in studying the effect of congressional tenure on electoral termination, then it is more appropriate to use a set of indicators for each point of time rather than to include a lineartime duration term. Beck, Katz, and Tucker (hereafter BKT, 1998), without referring to Cox (1972) or Brown 5 This substantive interpretation of the estimated coefficient associated with duration is not made clear by Box-Steffensmeier and Jones, who adopt the log-hazard interpretation with a caveat that what the coefficient means substantively is not obvious (1450). 13

16 (1975), further demonstrate that the logit-dummy approach is a good approximation of a cloglog-dummy model that is mathematically identical to the Cox proportional hazards model based on Equation (1) for grouped duration data. Thus, whether one assumes the continuous Cox model (1) or the discrete Cox model (2), it is always appropriate to use dummy indicators of time in the logit framework to estimate the hazard function. Consequently, analyzing the Box- Steffensmeier and Jones (1997) data with a logit-dummy model instead of linear time is not only an important step in understanding and accounting for the impact of time, but should also produce a hazard function that is identical to the Cox method. The logit-dummy model suggested by BKT takes the form (4) where is a vector of dummy variables k such that k = 1 for time k and k = 0 otherwise, and 6 is a vector of coefficients that are associated with. Note that for a given time point k, k =, and hence among all the coefficients in, only one contributes to the evaluation of h(k x ). k Thus, when controlling for the covariates, h(k x ) varies with according to the functional form i,k in (4). In this sense, the coefficients of the dummy indicators determine the shape of the hazard function. In estimation, since there is usually high collinearity among the dummy variables, individual coefficient estimates tend to have large standard errors. While one can test the joint statistical significance of these coefficients, the estimates, and hence the hazard function thus evaluated, are likely to zigzag in time and may not be easily interpretable. BKT suggest using k k i,k 6 If the logit model is estimated with a constant, at least one time point should not be represented in to avoid perfect collinearity. 14

17 natural cubic splines to smooth out the coefficients and the hazard function based on them. In such a logit-spline approach, would be a vector of spline basis variables which are cubic polynomials of k, and would be a vector of coefficients for these variables. Since the number of spline variables needed is usually much less than the number of time dummies, statistical significance is easier to achieve. The spline approach provides flexible constraints on hazard functions that are otherwise too wild to be substantively interpretable. Compared with Cox regression, both logit-dummy and logit-spline have the advantage that it is easy to test for the time-dependence of the hazard function. We suggest and implement both logit approaches as well as Cox regression to reanalyze the Box-Steffensmeier and Jones model of congressional career termination, more specifically that of involuntary electoral termination. By doing so, we hope to present a hazard function of congressional incumbency that takes full account of the potential role of time (or incumbency) in influencing the risk of defeat and offer a substantive interpretation of the pattern. Based on the research described in the previous section, we would expect the hazard function to show the highest hazard (or risk of defeat) at term 1, at which there is nearly unanimous consent that members are most vulnerable, and to decline thereafter. We also expect the decline to be gradual, at some point perhaps reaching a level of saturation which represents the floor of incumbency entrenchment. Our framework will also allow us to determine whether, as we might expect, the hazards of incumbency rise for members serving for long periods of time. That is, we will be able to demonstrate whether some sort of constituency fatigue or inside the Beltway image contributes to higher levels of vulnerability toward the end of one s career on Capitol Hill. Formally, our hypotheses, which center on the coefficients for the logit dummies and 15

18 logit splines, are: H 0: All the coefficients in are 0. H : Not all the coefficients in are 0. A Note that accepting H A implies that the hazard function is not constant over time. The specific shape of the function, however, depends on the set of coefficients in. Analysis and Results In this section, we analyze the time-series cross-section data used by Box-Steffensmeier 7 and Jones (1997) to test our hypotheses. In their article, Box-Steffensmeier and Jones propose two competing risks models, specifically voluntary termination (retiring or running for higher office vs. running for reelection) and electoral termination (losing primary or losing general election vs. winning reelection), each of which is estimated by multinomial logit. In the following re-analysis we focus on electoral termination. For the purpose of estimating the electoral hazards of incumbency, we consider losing in the primary and losing in the general election as the same event (namely losing reelection) to be analyzed against winning reelection as a nonevent. The simplification allows us to use the binomial logit to estimate our model. We use the same set of covariates in our binomial logit analysis as do Box-Steffensmeier and Jones in their multinomial logit analysis. A brief description of these covariates is provided in Appendix A. 8 7 We thank Brad Jones for kindly providing his data, which collect full or near-full career path information covering election cycles from 1952 to 1992 on every member of the House from each freshman class from 1950 to The decision to stop at 1976 for the last freshman class included was made in order to avoid severe right-censoring problems. See Box-Steffensmeier and Jones (1997, 1447). 8 For a fuller explanation of the covariates, see Jones (1994) as well as Box-Steffensmeier and Jones (1997, ). While the covariates may not have the same effects on primary outcomes 16

19 Table 1 presents the estimates of our various models. Column I gives the results of ordinary logit. Without considering the effect of congressional tenure or survival duration, this baseline model serves as our null hypothesis that the hazards of incumbency are constant throughout the terms of a career, controlling for all the covariates included in the model. Column II differs from the baseline model in that it adds duration as a linear term among the covariates, implicitly specifying a linear effect of congressional tenure on the log odds ratio of electoral defeat. This is the approach adopted by Box-Steffensmeier and Jones (1997), although they use it in a multinomial logit setting. Column III is based on the BKT logit-dummy approach. Instead of a single length-of-tenure variable, twelve dummy variables, each 9 representing a term from term 1 through term 12, are included among the covariates. As discussed in the previous section, the approach relaxes the constraint imposed by Column II on the effect of duration, thus allowing the hazard function to be freely estimated at each term. Column IV, which is based on the BKT logit-spline approach, substitutes three spline basis variables for the twelve dummy variables in Column III in order to smooth the hazard function. Finally, Column V provides estimates of the Cox proportional hazards model. as on general election outcomes, it may be difficult to explain primary outcomes separate from general election outcomes with the pooled time-series cross-section data structure. Among the 5036 observations used in the analysis, only 69 (1.37%) are primary losses, compared with 311 (6.18%) general election losses and 4656 (92.45%) reelection successes. Primary losses are thus rare events which number dozens to thousands of times fewer than nonevents. Logit analysis can sharply underestimate the probability of rare events (King and Zeng, 1999). Following Box- Steffensmeier and Jones (1997) in their multinomial analysis of electoral termination, we drop observations registered as retiring (N=250) or running for higher office (N=226) from the estimation sample, effectively treating those incumbents careers as censored. We are able to replicate their results presented in Table 4 (1451), although we believe that their third and fourth columns of estimates should be reversed. 9 By including 12 dummy variables, the effects of terms 13 and beyond are captured by the intercept. We decide to use only 12 dummy variables because incumbents who served more terms are relatively rare. 17

20 (Table 1 about here) These results confirm the expectation that the hazards of incumbency are timedependent. As Table 1 shows, likelihood ratio tests comparing linear-time logit (II), logitdummy (III), and logit-spline (IV) against the baseline model conclude that the null hypothesis of time-independence (i.e., constant hazards) can be rejected. Specifically, the linearly specified duration variable in linear-time logit has a highly significant effect; the effects of the term dummy variables in logit-dummy are jointly significant at p =.08; and when these dummy variables are substituted by three smoothing splines to form logit-spline, the significance level improves to p = The pattern of statistical significance in individual coefficient is generally consistent across all five models: all estimates associated with substantive variables are significant with correct signs except southern Democratic status, timing of redistricting and scandal, and Watergate. A noticeable difference among the logit models, however, is the significant attenuation of the effect of the prestige position variable whether a member is in the House leadership and/or is a chair of a standing committee in the linear-time logit model. The estimated coefficient is about 15 percent smaller than in other logit models. We suspect this is an artifact of the model s inadequate specification of time-dependence. We return to this point after examining the form of time-dependence in the hazard functions. 10 The three spline basis variables correspond to knots at terms 2, 10, and 11, respectively. We choose this set of knots because it produces basis variables that have statistically significant effects individually and the lowest probability of a Type I error in rejecting the null model in likelihood ratio tests. We also experiment with four- and five-knot solutions. None of them, however, produce basis variables that are all significant, an indication that a three-knot solution is sufficient. The procedures are carried out with Stata Version 6.0. For a discussion of using splines as a smoothing device, see Hastie and Tibshirani (1990). 18

21 Based on the estimates of Table 1, we plot the typical hazard functions associated with models II-V in Figure 1. These are hazard functions estimated for an average incumbent congressperson whose values on the substantive covariates are set at their sample means or, in the case of dichotomous covariates, their sample modes. As expected, linear-time logit produces a hazard function that declines monotonically and almost linearly. Also as expected, the hazard function estimated with the logit-dummy approach varies with term rather irregularly. The pattern, however, exhibits a significant drop from the first term to the second term, as well as a tendency of increasing hazards beyond the tenth term. Such a tendency is more clear in the hazard function computed from the logit-spline estimates, which shows that electoral hazards for congressional incumbents bottom out around the eighth term before turning up. Finally, the hazard function estimated from the Cox model closely parallels that from the logit-dummy. While the Cox estimates are systematically higher than the logit-dummy estimates, we accept the parallelism as a confirmation that the logit-dummy is a good approximation to the Cox model for grouped duration data. 11 (Figure 1 about here) The fact that, when freed from the linear-time constraint, the hazard function exhibits a 11 The hazard function of the Cox model presented here is actually the baseline hazard function derived by re-estimating Column V of Table 1 with all covariates transformed to deviations from their respective mean/mode levels. Since the baseline hazards are hazards with all covariates set to zero, the transformation procedure entails that the original covariates are set to their means/modes in estimating the hazards presented. The discrepancy between the Cox hazards and the logit-dummy hazards appears to be due to the fact that the latter is only an approximation to the cloglog-dummy model that BKT establish to be identical to the continuous-time Cox model for grouped duration data (Beck, Katz, and Tucker 1998). Specifically, tied survival times, not a problem with the discrete-time logit-dummy approach, are not allowed in the continuous-time Cox model and have to be dealt with. We use the Breslow method, the default option for the Stata Cox procedure, to correct for ties. 19

22 fatigue effect at higher terms confirms the inadequacy of the way linear-time logit specifies time-dependence. If fatigue is indeed a factor, the specification of a linear duration term would unduly reduce electoral hazards at higher terms. In estimating the model, the reduced probability, specifically at the eleventh and twelfth terms and beyond, will have to be compensated in another way in some other covariates. Prestige position is a likely target because leadership is attainable only with seniority. In fact, in our sample, no member of Congress becomes a leader prior to the fifth term. The number starts from there with two leaders and rises gradually to 18, 23, and 18 leaders for the tenth, eleventh, and twelfth terms, respectively. Thus what is unduly lost with the specification of a linear duration term is gained back by the attenuation of the negative effect of prestige position. The hazard functions presented in Figure 1, while standard, are not the most realistic estimates. Recall that these are computed with all substantive covariates set to their sample means or modes while term is incremented. In fact, it is quite unreasonable to assume that the values of these time-dependent covariates can be held constant throughout all terms. For example, while members may be first elected to Congress at different ages, their ages certainly all increase by two years each term. Other covariates such as prior vote margin, and especially prestige position as discussed above, should also undergo systematic changes from term to term. Hence, a more realistic approach is to set the covariates at their within-term means or modes as term is incremented to compute the hazard functions. Figure 2 presents the hazard functions estimated from logit-dummy and logit-spline with covariates controlled at their respective termspecific means or modes. Compared with those in Figure 1, the functions feature significantly greater hazards of electoral defeat for not only first-term but also second- and third-term incumbents. To be sure, there is a reduction of about three percentage points in electoral hazards 20

23 from term one to term two in the logit-dummy hazard function. It is not until the fourth term, however, that incumbents find themselves entrenched in safe seats. From then on the hazards remain relatively stable, with the fatigue effect showing up only after the tenth term. (Figure 2 about here) The preceding figures describe the underlying risks to members of Congress under relatively normal conditions, with the relevant independent variables considered ceteris paribus. However, as is evident from Table 1, a number of important factors influence members electoral security. Thus, it is useful to consider some specific cases to demonstrate the degree to which the approach presented above captures individual members electoral hazards. Figure 3 presents the hazard plots for Rep. John Murphy and Rep. Paul Findley, whom we mentioned in the beginning of this paper. Event history analysis allows us to calculate their vulnerability their chances of an electoral defeat at each tenure level and relate it not only to macro conditions or the nature of the times but to individual, time-specific attributes, such as prior vote margin, redistricting, scandal, constituency size, prestige position, and party affiliation. On the basis of these factors, we can now tell a narrative describing the dynamics of these members electoral fortunes throughout their careers. (Figure 3 about here) Murphy (D-NY) won his first election to the House in 1962 by a slim margin of 1.5%. That would have made him vulnerable in his first reelection bid in 1964 were it not for a popular Johnson presidency (63% approval rating) and a fairly good economy (1.67% growth in real disposable income). He rode the president s coattails to a sweeping victory by a margin of 24.1%, and his congressional career progressed ever so smoothly from that point forward. In 1976, with Republican President Ford s popularity running at a lowly 45%, his electoral margin 21

24 was boosted to 45.1%. The next year, his eighth term, he became the chairman of the Committee on Merchant Marine and Fisheries. The combination of a leadership position and a formidable prior margin made him virtually hazards-free in In 1980, however, he was implicated in Abscam amidst a faltering Carter presidency (37% approval rating). With electoral hazards surging to 53.8%, his career was over. In contrast, Findley s (R-IL) event history was a story with more turns. Elected to Congress for the first time in 1960 by a margin of 11.1%, Findley had a difficult time running for reelection in 1962 against severe odds. President Kennedy enjoyed an approval rating of 62%. The economy was not booming but was adequately robust to ensure safety for the incumbent Democratic Party (.64% growth in real disposable income). Even worse, his district was redrawn in the post-census reapportionment. The combination of these factors produced a 40.1% hazard rate. Findley miraculously survived, but with only a 5.8% margin. As a result, and with presidential approval and the economy favoring the Democrats in the subsequent election, his electoral hazards remained significant (10.9%) in 1964, when he won reelection by a margin of 9.6%. From there, however, Findley s political fortunes improved quickly, and he won by 24.4% in 1966 and more than 30% in 1968, 1970, and In 1974, the economy of the post-opec oil supply shocks period exhibited a substantial negative growth (1.99% decrease in real disposable income). In the wake of President Nixon s resignation and with no advantage from President Ford s popularity (50% approval rating), Findley s electoral hazards rose to 12.5% in his seventh bid for reelection. He survived again, thanks to the cushion of his prior margin (37.5%), but saw that margin dwindle to 9.6%. He recovered, winning by 39.2% in However, his meeting with PLO Chairman Yasir Arafat that year triggered a harsh campaign against him by the pro-israeli lobby, and he encountered difficulties in both the 22

25 primary and general election in Despite President Carter s disastrous approval rating (37%) and a 39.2% prior margin, Findley won by only 12.0%. Such a cushion proved not enough to save him two years later, when a bad economy (.58% decrease in real disposable income) and a shaky level of presidential popularity at the first Regan midterm (42% approval rating) raised his hazard rate to a fatal 34.7%. He was one victim among 26 Republican incumbents (out of 168 running) who were defeated that year. Conclusion The study of congressional tenure is interesting because it helps us to understand not only the electoral process but also the circulation of elites that is so critical to the stability of democracy. As prominent an institution in American democracy as is the House of Representatives, it does not come as a surprise that members enjoy substantial incumbent advantages in sustaining the loyalty of their constituents and containing electoral competition. As a result, most members survive reelection repeatedly with relative ease. Our findings do not challenge the common understanding that most members of Congress face relatively small electoral hazards throughout their tenures. By focusing on the dynamics of the hazards, however, we hope to bring the study of congressional careers in line with what has been explored extensively in the comparative politics literature on leadership and regime duration. Based on the concepts and methods of event history analysis, our findings present evidence that the conventional understanding of the advantages enjoyed by congressional incumbents in seeking reelection is not completely justified. The effect of tenure on reelection bids is neither constant throughout all tenure levels nor characterized only by the relative vulnerability of first-term incumbents. Nor do the hazard rates decline monotonically such that 23

26 senior incumbents are virtually impossible to defeat. Instead, we find that even though first-term incumbents remain the most vulnerable, they need to survive two more terms before incumbency takes solid root. In addition, we find a slight but unmistakable upward trend in electoral hazards beyond ten terms in office. The trend suggests that constituents weariness or fatigue of a long congressional career may eventually turn into a desire for change. All these findings are attained with appropriate control of theoretically relevant and time-dependent covariates. Our findings suggest that by shifting attention away from aggregate vote margins and toward individual-level congressional career patterns, we are able to more completely understand the risk function that is associated with service in the U.S. Congress. An added benefit of this method is that we are able to assess individual members electoral risks at particular points in their careers based on a series of relevant covariates. While we have used the incumbency advantage literature as a vaulting point from which to begin our inquiry, we are not as concerned with electoral performance (as measured in terms of vote margins) as we are with understanding the pattern of electoral risk at the level of individual members of Congress. In light of this, drawing on parallel analyses in the comparative context has allowed us to more appropriately model the time dependence of the hazards of incumbency in House elections. The results we present offer an example of the usefulness of recent methods in understanding and accounting for issues that are likely to be of both substantive and theoretical interest to researchers working on a variety of questions. 24

27 Appendix A: Description of Covariates Variable Incumbent Age Description The incumbent s age (in years) at each election cycle S. Dem. Before 1970 Coded 1 if the incumbent was a southern Democrat prior to 1970 S. Dem. After 1970 Coded 1 if the incumbent was a southern Democrat after 1970 Post 1966 Cohort Prior Vote Margin Redistricting Timing of Redistricting Scandal Timing of Scandal Constituency Size Prestige Position Republican Status Same Party as President Presidential Approval Approval*Inc. Party %_RDI %_RDI*Inc. Party Watergate Election Denoted as 1 if the member was elected in the freshman class of 1966 or after, and 0 if elected prior to 1966 The incumbent s margin of victory in previous election Coded 1 if the incumbent s district was substantially redistricted Interaction of the number of terms served and Redistricting Coded 1 if the incumbent was involved in an ethical or sexual misconduct scandal or was under criminal investigation Interaction of the number of terms served and Scandal The reciprocal of the number of congressional districts in the member s state Coded 1 if the member is in the House leadership and/or is a chair of a standing House committee Coded 1 if the incumbent is a Republican Coded 1 if the incumbent s party affiliation is the same as the President s Ranges (theoretically) from 1 to 1 and reflects the Gallup Presidential Approval rating in the month prior to the election. A 0 denotes 50% approval, 1-100%, and 1-0% Interaction term between presidential approval and whether or not the incumbent is of the party of the president. Change in real disposable income from the last quarter of the year preceding the November election to the first quarter of the election year Interaction term between %_RDI and whether or not the incumbent is of the president s party Coded 1 for Republicans in the 1974 election cycle Note: Description is that of Box-Steffensmeier and Jones (1997) 25