Political Analysis

Political Analysis Advance Access originally published online on June 5, 2006
Political Analysis 2006 14(4):421-438; doi:10.1093/pan/mpj014

This Article Abstract FREE Full Text (PDF) Supplementary Data All Versions of this Article: 14/4/421    most recent mpj014v1 Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Add to My Personal Archive Download to citation manager Request Permissions Google Scholar Articles by Boehmke, F. J. Search for Related Content Social Bookmarking          What's this?

© The Author 2006. Published by Oxford University Press on behalf of the Society for Political Methodology. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

The Influence of Unobserved Factors on Position Timing and Content in the NAFTA Vote

Frederick J. Boehmke

Department of Political Science, University of Iowa, 341 Schaeffer Hall, Iowa City, IA 52242, and Department of Health Management and Policy, University of Michigan, 109 Observatory, Ann Arbor, MI 48109

e-mail: boehmke{at}umich.edu

A variety of factors have been shown to influence position timing and the content of positions taken by legislators on important issues. In addition to these observed factors, I argue that unobserved factors such as behind-the-scenes lobbying and party loyalty may also influence position timing and position content. Although hypotheses about observed factors can be tested using traditional methods, hypotheses about unobserved factors cannot. To test for systematic effects of unobserved factors on position timing and content, I develop a seemingly unrelated discrete-choice duration estimator and apply it to data from the vote for the North American Free Trade Agreement. The results indicate that even after controlling for observed factors, there is still evidence that unobserved factors such as Presidential lobbying and/or party loyalty influence both choices.

	1. Introduction

Top 1. Introduction 2. Linking Position Timing... 3. An SUDCD Estimator 4. The Role of... 5. SUDCD Estimates of... 6. Conclusion Notes References

 
When deciding what position to adopt on an issue or a specific bill, legislators may be influenced by a variety of factors, including personal policy preferences, constituents' interests, lobbying by organized interests, and the positions of other legislators or the President. Many of these factors may also influence the timing of position taking—public announcements of policy positions or vote intentions—which may occur well before the final vote on an issue. Legislators who announce a position early on before a vote may do so in hopes of influencing the course of the debate and, ultimately, the final vote tally. In addition, they may wish to signal support to constituents and organized interests or to put themselves at the center of future negotiations over the final legislative product. Alternatively, members who are uncertain may delay revealing their preferences because they are waiting for more information to come along or are subject to cross-pressures from constituents and organized interests.

Previous studies have argued and provided support for the notion that many observed factors influence both position timing and position content (e.g., Box-Steffensmeier, Arnold, and Zorn 1997; Caldeira and Zorn 2004). Yet these two choices are estimated as independent processes: although they may be influenced by the same factors, there is no interplay between the two. Based on the motivations behind the timing of position announcement, however, we should expect these two processes to be inextricably linked. For example, legislators may intentionally delay announcing their position, particularly when the upcoming vote is expected to be close, in the hope that key players may offer them incentives to vote a certain way. This implies a relationship not only based on observed factors but also due to unobserved factors in the position timing and content decisions.

In this paper I attempt to theoretically and statistically link the effect of unobserved factors on the timing and content of legislators' position announcements. First, I develop two arguments about the effects of party loyalty and horse-trading by party elites on vote choice. Legislators who are not sure how to vote may delay announcing their position in order to determine how close the vote will be. This provides an opportunity both to weigh the consequences of voting against the party and to see if side payments are offered. Second, in order to test whether these unobserved factors have a systematic influence on position timing and position content, I develop estimators akin to a seemingly unrelated regression model. These estimators link a duration equation with a discrete outcome equation by estimating the correlation between the unobserved factors in the two equations; versions are derived for both Weibull and log-normal durations.

To test for this strategic behavior I analyze the 1994 vote on the North American Free Trade Agreement (NAFTA) in the House of Representatives. The NAFTA vote provides an excellent opportunity to study the relationship between the timing of position taking and position content because it was a highly visible debate and vote, the outcome of which was uncertain. In addition, the timing of position taking on the NAFTA vote has been discussed and analyzed by Box-Steffensmeier, Arnold, and Zorn (1997), who did extensive research to determine the timing of position taking over the year prior to the NAFTA vote. My empirical results extend their analysis by linking the influence of unobserved factors. The estimates indicate that the content of legislators' positions was influenced by factors consistent with strategic delay: unobserved factors that caused legislators to hold out longer than expected (i.e., given their observed characteristics) also made them more likely to vote for NAFTA.

	2. Linking Position Timing and Position Content

Top 1. Introduction 2. Linking Position Timing... 3. An SUDCD Estimator 4. The Role of... 5. SUDCD Estimates of... 6. Conclusion Notes References

 
Given the choice of when to announce their position on an important issue or an upcoming vote, legislators should choose the moment that maximizes their effectiveness by weighing the benefits and costs of staking out their position at each point in time. Early and late announcements offer different advantages on different dimensions, often in conflict with each other. Reasons to announce early on include staking out a clear position in support of constituent interests, establishing oneself as a potential policy entrepreneur in an area to increase the opportunity to shape final legislation, and sending signals to other legislators (Mathews and Stimson 1975; Lohmann 1993, 1994b; Box-Steffensmeier, Arnold, and Zorn 1997); delaying position announcement may be beneficial since it provides the opportunity to become more informed about policy and constituent opinion (Caldeira and Zorn 2004) and it may increase the value of a single vote if others' announcements presage a narrow margin.¹

Existing studies have considered the effect of a variety of observed factors on both phenomena.² Here, I wish to focus on the influence that unobserved factors may have once observed factors are controlled for. To delineate the two components, then, I refer to the portion of position timing determined by observed factors as the expected timing; deviations from expected timing are based on unobserved factors and are referred to as unexpected or unanticipated. If unobserved factors systematically influence both position timing and content, then information about delay by a given legislator will reveal information about the content of the position ultimately taken.

Two potentially unobserved factors that may influence both position timing and content, particularly when the vote is expected to be close, are pressure to vote the party position and side payments. Consider the former. A legislator whose expected vote may be inconsistent with her party's position may prefer to delay announcing her position until she knows whether the vote will be close. If it is, then she may feel pressured to vote against her own position in order to help further the party's platform. Thus, legislators experiencing cross-pressures from constituent and party influences may wait longer than expected in order to determine whether their votes are crucial for party success. If it is, then their observed votes may reflect party pressure and differ from their expected votes. This would lead legislators who unexpectedly delay their announcement to also be unusually likely to vote for or against the bill. The study of Glazer, Griffin, Grofman, and Wattenberg (1995) of the timing of roll-call votes on veto overrides provides evidence consistent with this type of behavior: members of the President's party who voted during the last minute of the 15-min roll-call period are often significantly more likely to vote against the President than those who voted earlier, particularly when the margin is large.

Alternatively, legislators may delay precisely in the hope that the vote will be close and other political actors may offer them inducements to vote a certain way. These inducements may come in the form of vote trading, sweeteners added to the current proposal, promises for future recompense, or transfer of campaign funds or public endorsements. The NAFTA vote involved many of these types of trades, including promises from Clinton that he would campaign for legislators if they supported NAFTA and negotiated pork projects that would benefit specific members and their districts. This strategy may be particularly appealing for legislators who are already indifferent and whose constituents will not punish them whichever way they vote.³ Since many of these inducements may be unobserved, then legislators who delay announcing their positions will vote differently than expected if their ploy is successful.⁴ The direction of the effect depends on the balance of political favors doled out by the opposing sides.

Both these processes—conflict between party and constituent preferences and behind-the-scenes vote trading—are based on frequently unobserved factors. Further, depending on the forces at work, they may operate in opposite directions, depending on which side is doing more vote buying or which party members have greater cross-pressures. In some circumstances, then, although one may be able to state the expected direction of their effects, it may be difficult to sort them out empirically. The important consequence for the moment is that they both predict a relationship between unobserved factors in the two models. This dictates the use of an empirical model that permits the testing of hypotheses about observed and unobserved factors. Existing methods only allow us to account for the role of observed factors on position timing and position content but leave open the question of how unobserved factors influence both. In the next section, then, I develop the seemingly unrelated discrete-choice duration (SUDCD) estimator that allows me to test hypotheses about observed and unobserved factors.⁵

	3. An SUDCD Estimator

Top 1. Introduction 2. Linking Position Timing... 3. An SUDCD Estimator 4. The Role of... 5. SUDCD Estimates of... 6. Conclusion Notes References

 
In this section, I develop two SUDCD estimators that link the position content and position-timing equations by estimating the correlation between the unobserved factors. Building an empirical model that links duration and discrete outcome processes can be accomplished with a bivariate distribution that allows for nonzero correlation between the error terms in the two equations. This rules out estimating the semiparametric Cox duration model, for example, since it does not make a parametric assumption about the distribution of the error terms.

One of the important concerns encountered when estimating a duration model for time until failure is how to control for duration dependence, which allows the baseline hazard rate to change over time. Duration dependence occurs when the rate of failure changes over time, holding observed variables constant. Ignoring or incorrectly specifying the form of duration dependence is a big concern in duration analyses since biased coefficients may result (see, e.g., Bennett 1999; Box-Steffensmeier and Jones 2004). A variety of parametric models are available for this task; I develop SUDCD estimators for two of them: the Weibull and the log-normal. The Weibull model is probably the most common parametric duration model and is therefore a logical choice. Linking it to a discrete-choice model can be accomplished through the bivariate exponential distribution, which necessitates developing an exponential discrete-choice model. To allow for a different form of duration dependence and because a discrete exponential model may imply different behavioral assumptions than a logit or probit model, I also develop a log-normal SUDCD estimator that links a probit discrete-choice equation with a log-normal duration equation. Whereas the Weibull model only allows for monotonic changes in the hazard rate (the instantaneous chance of failure), the log-normal allows for nonmonotonic changes.

Before developing the SUDCD estimators it is useful to observe that alternate methods that may be useful for analyzing duration data in general are inappropriate for testing my hypotheses about unobserved behavior. A competing risks approach, for example, would model the two distinct forms of failure (announcing pro- and anti-NAFTA positions) with separate equations and errors. Yet my hypotheses suggest that unusually late announcements affect the probability of support, which requires estimating the relationship between the unobserved components of position timing and content. A competing risks model combines these two outcomes; even if the unobserved components were correlated (e.g., Gordon 2002), one would only be able to determine whether legislators who announce favorable positions unusually late would also announce opposition positions unusually late or early. I wish to test whether delaying position announcement influences position content, so the two must be kept separate.

Next, note that my hypotheses do not have implications for the form of duration dependence exhibited by the position-timing model. Whereas duration dependence helps determine the expected timing of position announcement, my hypotheses are about the consequences of deviations from this expected timing. Although one could parameterize the duration dependence parameter (Zorn 2000) as a function of party membership or position taken to see whether supporters exhibit different forms of duration dependence than opponents, this does not provide information about the effect of deviations from expected position timing on position content.⁶

3.1 Deriving the SUDCD Estimator
Construction of the model involves combining the duration equation with the discrete outcome equation. Thus, an observation for individual i is of the form (D_i, V_i), where D_i is the timing of position announcement and V_i is the decision whether to support or oppose NAFTA. The important difference between observations for the purpose of constructing the likelihood function is that some have V_i = 1 and others have V_i = 0. So the likelihood of the data is determined by dividing it into these two types of observations for each individual i. Since the duration equation is the same for both types of individuals, I write the likelihood using the marginal density of the duration and the conditional probabilities of support.

(1)

(2)

These densities and probabilities are then calculated according to the appropriate distributions. Note that when there is no correlation between the two error terms the two conditional choice probabilities are the same as the marginal probabilities and the likelihood is merely the product of the likelihoods of the two independent models.

3.2 The Weibull SUDCD Estimator
For the Weibull SUDCD estimator, the joint density and conditional probabilities are calculated using the bivariate exponential distribution—I use a bivariate exponential distribution proposed by Gumbel (1960; Johnson and Kotz 1972). The exponential is a common distribution for duration models and is easily adapted to allow for Weibull duration dependence, though it requires developing a discrete-choice model in which the errors follow an exponential distribution. The cumulative and probability density functions for this distribution take the following form:

(3)

(4)

The correlation between x and y is given by = /4. Since –1 1, it follows that –0.25 0.25. Although this restriction is somewhat limiting, this is the most flexible version of the bivariate exponential since it allows both positive and negative correlations. Furthermore, it includes = 0 as a special case and allows an explicit test for whether the error terms are correlated.

The first component of the estimator is a standard exponential duration equation, which generates data according to the following process: d_i = exp(x_iß)_i, where x_i is a vector of explanatory variables and _i follows an exponential distribution. Employing the more general Weibull distribution is straightforward since a variable u_i follows a Weibull distribution with shape parameter p if follows an exponential distribution (Johnson and Kotz 1970).⁷ The marginal density of observing a duration d_i, controlling for independent variables x_i, is thus given by

(5)

where _2i = exp(–x_iß).

The second component of the estimator is the exponential discrete-choice equation. As with a probit or logit I model, I assume that there is an underlying continuous variable that leads to a binary outcome variable that indicates whether the continuous variable exceeds some threshold. Because the exponential distribution is defined only for positive numbers, I set the threshold at one rather than at zero. Thus,

(6)

_i is assumed to follow an exponential distribution.⁸ The marginal probability that V_i is zero is then:

(7)

(8)

where _1i = exp(–w_i).

Given these two pieces I can now return to the likelihood function and explicitly write out the probabilities using the duration and discrete-choice models described above.

(9)

(10)

where is the conditional probability that V_i is one.⁹

The final step is to extend the model to deal with the consequences of right censoring.¹⁰ For these observations all we know is that they survived until the censoring point—they may have announced their positions at some point if the vote had been delayed.¹¹ Their contribution to the overall likelihood is the joint probability of surviving until right censoring occurs and the probability of the observed discrete-choice outcome. These are calculated for censoring point as follows:

(11)

(12)

3.3 The Log-Normal SUDCD Estimator
In this section, I briefly outline the derivation of the SUDCD estimator that uses the bivariate normal distribution to combine a probit model for the discrete-choice equation and a log-normal model for the duration equation. Developing this alternate model is useful because it allows for a different form of duration dependence and because it relies on the more commonly used probit model for the binary outcome equation.

The only difference in the derivation involves substituting the appropriate distributions in equation (2). As readers are probably more familiar with the bivariate normal distribution and because the derivation parallels the one for the exponential, I just outline the two equations and the appropriate steps following equation (2). For the discrete-choice portion, the data are generated according to the following model:

(13)

When _i N(0, 1), this is a standard probit model. For the duration equation, the data are generated according to a log-normal duration model:

(14)

(15)

Note that since _i follows a log-normal duration model with shape parameter , ln(_i) has a normal distribution with variance ². In addition, I assume that _i and ln(_i) have correlation . Following standard results, the conditional probability of a one in the discrete outcome equation is then:

(16)

Right censoring is allowed with the following two cumulative normal probabilities, denoted by F_N, which exploit the symmetry of the bivariate normal density:

(17)

(18)

These pieces are assembled into a log-likelihood function as in equation (10).

	4. The Role of Unobserved Influences in the NAFTA Vote

Top 1. Introduction 2. Linking Position Timing... 3. An SUDCD Estimator 4. The Role of... 5. SUDCD Estimates of... 6. Conclusion Notes References

 
Many of the processes discussed in Section 2 appear to have been at work in the case of NAFTA, making it an excellent opportunity to test whether deviations from expected position timing are related to deviations from a legislators' expected vote. Particularly prominent, unobserved factors in this case were the efforts of President Clinton to secure a winning margin and conflict between party leaders, especially among Democrats, about whether to support NAFTA. In addition, the close margin of victory provides an excellent opportunity to study the effects of these factors on vote choice. So although the NAFTA debate and vote is not randomly selected, it does provide a suitable environment for a first test of my predictions. If they are confirmed in this case, future work may be warranted to understand the circumstances under which they hold.

My two hypotheses concern how unobserved factors shape legislators' responses to a potentially close margin of victory. In the case of NAFTA, the final outcome was up in the air until the last minute and President Clinton had strong incentives to attempt to sway undecided voters.¹² He adopted two strategies to secure final passage. First, in concert with his work with USA-NAFTA, Clinton attempted to provide cover for pro-NAFTA votes by providing arguments about why it was good for America (Wink, Livingston, and Garand 1996; Uslaner 1998). Second, the importance of the issue to Clinton made it likely that he would expend considerable political capital to ensure its success. For members who held out until the last month or so, this proved to be the case: using data on contact with members of Congress after August 13, Uslaner (1998) shows that President Clinton was most likely to contact undecideds, then supporters, and lastly the opposition.¹³ Related studies find that at least 90 members, 71 of which were Democrats, were contacted extensively (Palazollo and Swinford 1994) and that as the date of the vote approached he doled out plenty of political favors, including concessions to Florida citrus growers; promises of campaign visits to vulnerable Democrats in California, Ohio, and Maryland; a promise to build a plutonium laboratory in Texas; and dozens of phone calls and face-to-face meetings at White House dinners and the Kennedy Center (Kollman 1998).

Because of the President's extensive lobbying efforts and the amount of capital he had to expend on the issue, there appears to be a clear prediction generated from the vote-trading process: legislators who held out longer than expected may have received payments from the President and, upon receiving them, should have been more likely to vote for NAFTA than similar representatives who announced their positions earlier. In the words of Uslaner (1998), these legislators were strategically "playing coy."¹⁴ In fact, many members signaled to Clinton that they would like to vote for the agreement but needed something to offset the perceived costs among their constituents (Palazollo and Swinford 1994). Since the fruits of this strategy are unknown, this means that the unobserved factors in the two equations are positively correlated.

The second margin-related factor is the potential conflict among legislators between voting their own preferences and supporting their party's agenda. Because of the split among the Democratic leadership over the issue, this pressure may have been particularly acute for Democrats. Many of them may have wanted to vote against NAFTA due to constituent concerns but felt pressure not to undermine the President and hurt the party's fortunes. Although there may have been Republicans who faced the same tension, the split was not as great for their party, which was generally in favor of free trade. Thus, the party-pressure forces lead me to predict that members who held out to see if their vote would hurt their party should be more likely to vote for NAFTA—Republicans because NAFTA fit their agenda and Democrats because they did not want to hurt the President. Thus, both of the unobserved forces in this particular case should work in the same direction, leading me again to predict a positive correlation between the unobserved factors in the position-timing and position content equations.¹⁵ Because the effect of Clinton probably intensified these effects for Democrats, I estimate additional models that allow the estimate of the correlation to be different for members of the two parties. Although this does not allow me to fully separate the two predictions in the empirical test, it does allow me to test whether the effect is greater for those individuals for whom the pressure is most intense.

	5. SUDCD Estimates of the NAFTA Vote

Top 1. Introduction 2. Linking Position Timing... 3. An SUDCD Estimator 4. The Role of... 5. SUDCD Estimates of... 6. Conclusion Notes References

 
I use the SUDCD estimators constructed in Section 3 to test whether unobserved factors have consistent effects on position timing and content in the NAFTA debate and vote. The first step, then, is to determine the factors that determine expected timing and vote choice in order to isolate the influence of unobserved factors above and beyond observed ones. My approach here is to use the analysis of Box-Steffensmeier, Arnold, and Zorn (1997) as a starting point and then to make a few small modifications.

A number of variables are included to control for constituency factors. Legislators closer to the Mexican border are expected to be in favor of NAFTA and should stake out their position clearly by announcing early on. Corporate influence in a representative's district should have a similar influence. Box-Steffensmeier, Arnold, and Zorn measure this with a variable for a district's household income. Legislators representing districts with large union memberships, on the other hand, should be more likely to oppose NAFTA and should come out early in opposition to it. Yet the effect of these two variables will be different if they conflict with a legislator's ideological predisposition: Republicans representing districts with large union memberships and Democrats from wealthier districts may experience cross-pressures that push them to delay their announcements and that may mute the effects of constituent characteristics on vote choice. These two variables are therefore interacted with a legislator's ideology as measured by a Chamber of Commerce conservative indicator.

In addition to constituent preferences, lobbying activity on the part of labor and business coalitions is expected to influence both the timing and content of positions taken. Although labor groups came out early and strongly opposed to NAFTA, business interests' lobbying efforts were lackadaisical at first. In the end, though, the pro-NAFTA lobby, led by USA-NAFTA and spurred by Clinton, ultimately spent $8 million and sent approximately half a million correspondences to Congress in the last months before the vote (Kollman 1998).¹⁶ Contributions are controlled for by including corporate political action committee (PAC) contributions and labor PAC contributions, where both are expressed as a proportion of total contributions received by a member.¹⁷ Both are expected to have clear and opposite effects on vote choice; in order to increase parsimony, I include net labor contributions in the vote choice equation and note that I was unable to reject the hypothesis that the two coefficients sum to zero. In terms of the timing of positions, one would expect that greater receipts should lead to early position announcements. Yet because the contribution variables do not vary over time and because many legislators were left waiting to see if business would gin up their lobbying campaign, in this case greater corporate lobbying may be associated with later position taking. Thus, I include these two variables separately in the position-timing equation.

In addition to these variables, I also follow the lead of Box-Steffensmeier, Arnold, and Zorn by including measures of a legislator's institutional position. First, I include variables for legislators that held positions in the Democratic leadership or the Republican leadership. Although leaders should, in general, stake out early positions, conflict among Democrats may have led them to delay; therefore, the leadership variable is included separately for both parties. Finally, I control for whether a legislator is on a committee that had jurisdiction over NAFTA issues. In particular, three different committees—Ways and Means, Banking, and Energy and Commerce—had some jurisdiction. I expect the NAFTA committee indicator to lead to quicker position taking but to have no effect on position content; it is excluded from the latter equation.

Beyond these variables included from the Box-Steffensmeier, Arnold, and Zorn study, I include one additional variable to test whether observed signals from legislators actually influence the positions of legislators. If signals reveal private information, then they may have an effect on subsequent decisions by other legislators.¹⁸ Both game-theoretic models (e.g., Lohmann 1993, 1994a, 1994b) as well as models of information cascades (e.g., Bikhchandani, Hershleifer, and Welch 1992; Gomez 2000) predict that as observed net support for a decision increases, decision makers should become more likely to favor that decision. I therefore construct a variable, net endorsements, by taking the difference between the number of favorable positions and the number of opposing positions observed before the time a legislator announces her position. When the balance of observed signals is positive, legislators should be more likely to vote for NAFTA; when the balance is negative, they should be less likely.¹⁹ Since we know the date of a legislator's position announcement, it is straightforward to determine the net balance of observed signals at that moment.²⁰ Summary statistics for variables used in the analysis are contained in Table 1.

View this table: [in this window] [in a new window]   Table 1 Summary of variables

 
Having controlled for a variety of observed factors, I use the SUDCD estimator to test whether unobserved factors have a systematic influence on position timing and content. As discussed in the previous section, the particular forces at work in the NAFTA case lead me to expect that representatives who announce their positions later than expected, given their observed characteristics, are more likely than expected to be in favor of NAFTA, implying a positive correlation between the error terms in the two equations.²¹ Furthermore, I expect this relationship to be particularly strong for Democrats.

For comparison, I estimate a total of six models. First, I estimate independent models of vote choice and position timing that replicate the approach of Box-Steffensmeier, Arnold, and Zorn (1997), subject to slight differences based on the use of the Weibull rather than the Cox model.²² I then estimate two versions each of the Weibull and log-normal SUDCD estimators; the first assumes a constant correlation parameter, whereas the second allows the correlation to be different for Democrats, thereby providing a better test of the possible influence of unobserved factors. Note that the coefficient estimates should not change; the only differences are the estimate of the correlation parameter and possible efficiency gains.

The results for these models are presented in Table 2. The top half presents the results for the vote model, and the bottom half presents the results for the timing model. The two independent models in the first column of results produce results essentially the same as those in Box-Steffensmeier, Arnold, and Zorn (1997), though the significance levels of the two PAC contribution variables drop a little in the timing results: labor contributions are significant at the .05 level and corporate contributions barely miss significance at the 0.10 level (p = .13).²³ Note, however, that there are some notable differences between the Weibull and log-normal duration models, with three variables changing significance levels and labor contributions, though insignificant, switching signs.²⁴ Further, the results are quite similar for the probit and exponential discrete-choice equations.²⁵ In fact, the exponential discrete-choice components of the SUDCD results are preferred in terms of predictive power, with a proportional reduction in error of 44.5% compared to 44.1% for the probit model.

View this table: [in this window] [in a new window]   Table 2 Separate and SUDCD models of position taking and position timing on the NAFTA

 
Overall, the observed factors performed as expected. In the vote choice equation, legislators receiving greater net support from labor PACs and those with greater union membership in their districts are less likely to vote for NAFTA, whereas those with wealthier districts are more likely to vote for it. Signaling also plays an important role: legislators who announce their position when the net balance of signals is positive are more likely to vote for NAFTA and those who announce when the balance is negative are less likely to declare in favor.

In the duration equation, I find that relatively few variables matter and that the results are slightly different for the log-normal and Weibull SUDCD models. The two consistent findings are that increased corporate PAC contributions increase and representing a Mexican border district decreases the time to position announcement. Republican leadership also has a negative effect, though it misses significance in the log-normal model. Whether the Chamber of Commerce scores a representative as conservative increases duration, but only in the log-normal models. Finally, there is evidence of the delaying effect of cross-pressures in the Weibull models: liberal representatives from union districts announce early but not conservative ones from similar districts.

The main difference between the results of the independent models and the unified models is the ability to estimate the correlation between the two stochastic components. Although neither the Weibull model nor the log-normal model that assumes constant error correlation—parameterized in the log-likelihood function by Z ^–1()—produce a significant finding, the p value for the Weibull model approaches weak significance levels (p = .11).²⁶

I argued earlier, however, that the theoretical implications combined with circumstances surrounding the NAFTA vote imply that the effect of unobserved factors should be greatest for Democrats. The second pair of SUDCD models therefore allows the correlation to be different for Democrats than for Republicans by parameterizing it as If my prediction is correct, then the effect for Democrats should be positive and significantly greater than the effect for Republicans. The empirical results generally confirm this prediction. The baseline correlation, which captures the effect of unobserved factors on Republicans, is near zero and insignificant in both models. The effect for Democrats, however, is significantly greater than zero in the Weibull model. The estimated parameter is 0.55 (=0.48 + 0.07) with a value of 2.88 (p = .09); for the log-normal the effect is 0.13 Further, when legislators who announce on the final day are not treated as right-censored, the results are unchanged for the Weibull models and become weakly significant for Democrats (p = .08) and nearly so for all legislators (p = .13) for the log-normal models. Overall, then, the estimates provide evidence consistent with my predictions by indicating a positive correlation between the error terms in the vote and timing equations precisely among legislators for whom the pressure was almost surely greatest. Translating these results into the correlation between the error terms results in estimated correlations of for Democrats.²⁷

Estimating the SUDCD models thus provides additional information about the relationship between the timing of position announcement and the actual position taken: members of Congress, particularly Democrats, who waited longer than expected (given their observed characteristics) to take a position were more likely to vote for NAFTA than similar representatives who announced "on time" and members who announced earlier than expected were less likely to vote for NAFTA. This result suggests that delaying the timing of position announcement significantly altered the probability of supporting NAFTA. In order to obtain a better understanding of how unanticipated delay influences vote choice, I performed a series of simulations using the Weibull SUDCD estimates. The simulations estimate the probability of voting for NAFTA while varying the deviation of a legislator's announcement from its expected day. In order to obtain a sense of the substantive magnitude of this effect, I also plot how changes in observed signals—the only other variable that change over time—alter the probability of voting for NAFTA. The results are displayed in Fig. 1 and indicate how (1) changes in only unobserved factors influence Democrats, (2) changes in unobserved and observed factors (legislative signals) affect Democrats, and (3) changes in observed factors only influence Republicans (since unobserved characteristics are not found to matter for Republicans). Changes in the probability of a pro-NAFTA vote in the figure are caused solely by these factors—if there was no relationship, the curve would be a horizontal line.

View larger version (21K): [in this window] [in a new window]   Fig. 1 Effect of legislative signals and correlation in unobserved factors on predicted probability of yes vote for NAFTA. Graph depicts the effect of observed and unobserved factors on a hypothetical member's predicted probability of voting for NAFTA. Predictions based on Weibull estimates. Observed factors are the public positions known at each point in time; unobserved factors are determined by the deviation from the expected timing of position announcement. The vertical line indicates the expected time the representative Democrat would announce a position. The baseline probabilities of voting for NAFTA are calculated for a representative member of each party.

 
I generated the predicted probabilities by starting with a hypothetical, representative member of each party.²⁸ Such members have an expected position announcement timing of 403 days for Democrats and 413 for Republicans and have a predicted probability of voting yes equal to 39% and 77%, ignoring the effect of legislative signals and unobserved factors.²⁹ I then calculate how these probabilities vary over time when unobserved factors and changes in the balance of legislative signals are taken into account. Start with the effect of unobserved factors. If the hypothetical Democrat deviates from the expected announcement time (indicated by the vertical line in Fig. 1), this deviation must have been caused by some unobserved factor. Individuals who announce to the right of the vertical line wait longer than their characteristics predict; individuals to the left of the line wait less than expected. Since these deviations from expected timing are positively correlated with deviations in the expected vote, knowing that an individual announced later or earlier than expected informs us that they are more or less likely to vote for NAFTA than expected, respectively.

The relationship between unobserved deviations in timing and the probability of a yes vote are given by the plotted curve in Fig. 1.³⁰ Because the estimated correlation between the residuals is positive, the curve increases as the observed position announcement increases. The probability of voting yes starts at 32% when our hypothetical Democratic legislator announces at least 130 days too early (i.e., within the first 290 days) and increases to 46% when the same individual announces on the day of the vote (i.e., 33 days later than expected). This is a reasonably large effect given that the difference is based solely on changes in the expected value of the residual and that the vote equation does a respectable job of predicting the votes in the first place.³¹

For comparison, the second step in the simulations accounts for both the unobserved factors and the net endorsements to see how variation in publicly available information over time changes the probability of a yes vote. The effect of observed signals is calculated by first determining the net endorsements available at each point in time and then calculating the probability that the representative Democrat and Republican would vote yes if they announced at each point of time. Because I employ the actual public signals from NAFTA, which jump around over time if many individuals announce on the same day, the predicted probabilities do not change smoothly. It is clear from the estimates that the effect of unobserved factors remains strong in comparison to observed factors like publicly observed signals. For Democrats, public signals alone increase the probability anywhere from –0.09 to 0.12; for Republicans, the effect of observed signals ranges from –0.04 to 0.07. In fact, the average absolute deviation from the probability at the mean for Democrats based solely on unobserved factors is slightly greater than the mean absolute deviation for Republicans based solely on observed signals. Together, these results demonstrate that the role of both observed and unobserved factors over time is substantively large.

	6. Conclusion

Top 1. Introduction 2. Linking Position Timing... 3. An SUDCD Estimator 4. The Role of... 5. SUDCD Estimates of... 6. Conclusion Notes References

 
This paper extends our understanding of the link between position timing and position content by explicitly incorporating information revealed through premature or delayed position announcements into the chance that a legislator will announce a favorable position. The empirical results are consistent with my expectations for the case of NAFTA and demonstrate that legislators who hold out longer than expected are unusually likely to vote for NAFTA. I interpret these results as indicative of strategic delay on the part of legislators who are waiting either to see if their vote may hurt their party leadership or whether they may be offered inducements to vote a certain way.

The SUDCD estimator derived in this paper may be used to further disentangle the potentially competing effects of observed and unobserved factors on position timing and position content. The effect of public signaling is dependent on the existence of uncertainty and private information among legislators whereas the effects of party loyalty and vote buying should be greatest when the vote margin is expected to be small. The NAFTA vote provides one constellation of forces, but other votes may allow the isolation of one or more effects. Other policy areas that might feature many of the same dynamics include health care, declarations of war, the Clinton impeachment vote (Caldeira and Zorn 2004), the vote on the Medicare Part D prescription drug benefit under President George W. Bush, and Supreme Court nominations—the Bork nomination shares many features of the NAFTA vote, including widespread interest group lobbying, a small vote margin, but involving a President who exerted less effort to influence the final outcome (Wright 1996).

The estimator may also be used in other areas where testing theoretical predictions about the effect of unobserved factors has proven thorny. For example, theories of international conflict suggest that many factors that influence the timing of crises may also influence crisis escalation and outcomes. Some of these factors, such as resolve, may be unobserved or unobservable (Schultz 2001). As Fearon (1994) argues, countries may signal their resolve in a crisis through delay, ultimately reaching a point where neither country will back down and escalation is inevitable. This suggests a positive correlation between unobserved factors, like resolve, that lead crises that are longer than expected to also be more likely to end in conflict than expected (see Lai and Boehmke 2004).

Finally, the SUDCD estimator can be further developed in at least three ways. First, the model can be adapted to allow for time-varying covariates, which would make it applicable to a wider variety of phenomena. Second, other bivariate distributions may be employed to allow for different forms of duration dependence and alternate discrete-choice models. Third, one could discard the bivariate distribution approach used here and link a variety of different distributions together using copula (Smith 2003) or by allowing for correlated random effects.

	Notes

Top 1. Introduction 2. Linking Position Timing... 3. An SUDCD Estimator 4. The Role of... 5. SUDCD Estimates of... 6. Conclusion Notes References

 
Author's note: I thank Doug Dion and Chuck Shipan for helpful comments and discussion. Previous versions of this paper were presented at the University of Iowa's Political Science Faculty Workshop and the University of California at Santa Barbara's Political Science Seminar Series. Financial support from the Robert Wood Johnson Foundation is gratefully acknowledged. Any errors or lapses in judgment are solely the author's responsibility. Replication materials are available on the Political Analysis Web site.

¹ A related issue is how often representatives engage in public position taking. Certainly they do so on many issues, particularly highly visible ones. And these may be the issues of greatest concern to the public, suggesting that it is not merely the raw frequency of position taking that is important but also the relative importance of the issues for which it does occur. Empirical studies of position taking, while focusing on any public position (including votes), provide estimates that Senators intentionally avoid taking positions on less than 5% of all bills (Thomas 1991; Jones 2003).

² In addition to the studies mentioned above on position timing and content, see also Kingdon (1989) for a discussion of how different factors influence position content, specifically in the context of voting decisions. Many of these factors, which include constituent interests, organized interests, other legislators, the administration, staff, the media, etc., may be observed or unobserved, depending on the particular circumstances involved.

³ Several legislators may be able to successfully pull off this strategy due to uncertainty about the final vote outcome but also due to incentives that may lead elites to want to establish a supermajority in favor of their position (Groseclose and Snyder 1996).

⁴ Further, even if these favors are observed, it may be impossible to link them to behavior. If strategic delay is based on the anticipation of future payoffs, then payoffs will only be targeted to those individuals who have declared themselves "in play" by not taking a position. Measures of attempts to sway them will therefore appear to influence position content by definition: the only condition under which the payoffs are made is when the recipient has essentially indicated that the payoffs will work.

⁵ Although the ability to estimate the correlation parameter is my primary motivation for developing the SUDCD estimator, it may also have the added benefit of improved efficiency relative to estimating two independent models.

⁶ I did test for different hazards for each party and although these results indicated greater duration dependence parameters for Democrats, they also continued to indicate significant correlation between the unobserved factors in the two equations.

⁷ Note that the estimated correlation is between and the discrete-choice error rather than between u_i and the other error term.

⁸ See Boehmke, Morey, and Shannon (2006) for additional information on the discrete exponential model. I use the standard exponential distribution to derive this model, which derives from the exponential distribution: f_e() = ^–1 exp(–( – )^–1) with = 0 and = 1. Note that this model implies different assumptions about individual behavior than a logit or probit model. In particular, the distribution is skewed and the marginal change in probabilities is greatest at the minimum value of zero. One could relax this assumption by relaxing the restriction that = 1, but as with the probit model, the resulting estimator would not be identified. If 1, however, the estimate of the constant term is biased by an amount equal to –ln(). Assuming follows a Weibull distribution also results in identification problems.

⁹ The cumulative conditional exponential distribution can be derived straightforwardly from the joint marginal and conditional exponential distributions given above; it is discussed in more detail in Johnson and Kotz (1972).

¹⁰ Observations are considered right censored if some other event occurs that precludes future occurrence or observation of the timing of failure. In the case of NAFTA, a member of Congress who chooses not to announce a position before the vote forfeited the opportunity to influence other members' votes; one could interpret this as right censoring since the occurrence of the actual vote eliminated the possibility of them taking a public position. Since these legislators do take a position when they vote, and since the theory predicts that delay until the last minute is related to their vote, it makes sense to include these individuals in both equations but treat their positions as right censored.

¹¹ See King, Alt, Burns, and Laver (1990) for a duration likelihood function that accounts for observable, fixed right-censoring points in the context of cabinet duration. Because of greater incentives for waiting until the censoring point, my approach seems more appropriate for these circumstances.

¹² In part due to the unions' early lobbying efforts as well as conflicting positions taken by the Democratic leadership, the pro-NAFTA side appeared to be several votes short in early October (Kollman 1998).

¹³ This relationship holds up overall for Democrats, though the last two categories are reversed for Republicans. Uslaner (1998) does not report whether the differences between these categories are significant.

¹⁴ And it appears to have paid off—Uslaner's (1998) study shows that legislators who were contacted by the President were more likely to vote for NAFTA than other legislators.

¹⁵ If they worked in the opposite direction it would be difficult to make a prediction regarding the direction of the net effect, but the model would still make it possible to sort it out.

¹⁶ A related phenomenon was the efforts of Ross Perot to parlay his showing in the 1992 presidential election into grassroots efforts to defeat NAFTA (Holian, Krebs, and Walsh 1997). Although support for Perot may have been associated with opposition to NAFTA, his poor showing in a debate with Vice President Gore a week before the final vote was seen as a victory for the pro-NAFTA forces and may have freed up hesitant legislators to support NAFTA in much the same way as business' late lobbying efforts, though representatives denied that this affected their votes (Palazollo and Swinford 1994). Ultimately, the Perot vote was not found to influence position timing or content or the other results and was omitted from the final model.

¹⁷ Campaign contributions may be intended to obtain access to key legislators (Wright 1990), to directly buy votes—either at the floor stage (Grenzke 1989; Austen-Smith and Wright 1994) or at the committee stage (Wright 1990)—or to induce legislators to spend time on legislation or intralegislative lobbying (Hall and Wayman 1990) on the group's behalf. See Baumgartner and Leech (1998) for an overview of these literatures. Admittedly, contributions are a very coarse measure of interest group lobbying as it excludes certain types of lobbying and includes campaign contributions that may have been motivated by interest on other issues during the same time period.

¹⁸ See Mathews and Stimson (1975) for an extended discussion of the roles of cue taking and cue giving in legislators' voting decisions, Krehbiel (1991, 66–77, especially) for an overview of signaling models of legislative behavior, and Banks (1991) for a more general and technical overview of signaling models in political science.

¹⁹ One shortcoming with these data is that the Box-Steffensmeier, Arnold, and Zorn (1997) study only includes the actual NAFTA vote rather than the announced position. Although 92% of the legislators voted their announced position, this may introduce some errors into the net endorsements variable. The fact that I use net endorsements means that some of these errors may cancel each other out, reducing the actual error.

²⁰ The data and variables used in this study are based on those in Box-Steffensmeier, Arnold, and Zorn (1997), which are available for download at the publication-related archive at the Inter-university Consortium for Political and Social Research under the original authors' names or as study #1126. Other studies that examine the vote choice include Keech and Pak (1995); Wink, Livingston, and Garand (1996); Holian, Krebs, and Walsh (1997); Uslaner (1998); and Gomez (2000).

²¹ By extension, it must also be the case that those that announced earlier than expected are less likely to vote for NAFTA.

²² I also estimated a Cox model and obtained the same results as in Box-Steffensmeier, Arnold, and Zorn (1997), who also reported similar results for the two models. One potential difference between the Cox and the Weibull models is that the Cox model does not have an intercept, which Box-Steffensmeier, Arnold, and Zorn (1997) claim precludes the inclusion of the ideology indicator variable. The Weibull does not have this restriction, however, so I include it in my reported results since it is included in interactions with union membership and household income, though the resulting coefficient is zero.

²³ Note that the Weibull results are adjusted from the Stata hazard interpretation estimates to ease comparability. Stata reports whereas the SUDCD model I constructed reports Values of can be obtained in Stata by specifying the time option (for an accelerated failure time interpretation) during estimation.

²⁴ Because the models are not nested, one cannot say which is correct, though given that the Weibull results are similar to the Cox model, they are probably preferred.

²⁵ The main difference arise in comparing the constants, which are expected to be different given the nonzero mean and asymmetry of the exponential distribution. The results are also substantively the same as those reported by Box-Steffensmeier, Arnold, and Zorn (1997).

²⁶ Since the correlation must lie between –1 and 1, I use the inverse of Fisher's Z transformation, such that = Z(^*) = (exp(2^*) – 1)/(exp(2^*) + 1). The model reports Z^–1() = ^*; the corresponding correlation parameter is = /4 for the Weibull model and = for the log-normal model. Standard errors are obtained using the delta method.

²⁷ These results also make it less likely that the findings are caused by other omitted variables that belong to both equations, since the evidence indicates that those omitted variables must be irrelevant for Republicans but important for Democrats.

²⁸ This member has the average values for all continuous variables and the modal value for all dichotomous variables among members of that party. Interactions are regenerated using the representative values for the interacted variables.

²⁹ The expected duration for the Weibull is (1 + 1/p)exp(x_iß).

³⁰ The conditional probability of a yes vote for an individual with timing characteristics vote characteristics and observed announcement time d is calculated for the Weibull SUDCD estimator using the following formula:

³¹ Of course, these wide deviations require extremely small or large errors. Within a more reasonable range of 30 days of the expected announcement time, each 10-day deviation in timing changes the predicted probability of a pro-NAFTA vote by about 0.8%.

	References

Top 1. Introduction 2. Linking Position Timing... 3. An SUDCD Estimator 4. The Role of... 5. SUDCD Estimates of... 6. Conclusion Notes References

 

Austen-Smith David and Wright John R. (1994) Counteractive lobbying. American Journal of Political Science 38:25–44.

Banks Jeffrey S. (1991) Signaling games in political science (Harwood Academic Publishers, Chur, Switzerland).

Baumgartner Frank R and Leech Beth L. (1998) Basic interest: The importance of groups in politics and political science (Princeton University Press, Princeton, NJ).

Bennett D Scott. (1999) Parametric models, duration dependence, and time-varying data revisited. American Journal of Political Science 43:256–70.

Bikhchandani Sushil, Hershleifer David, Welch Ivo. (1992) A theory of fads, fashion, custom, and cultural change as informational cascades. Journal of Political Economy 100:992–1026.[CrossRef][Web of Science]

Boehmke Frederick J, Morey Daniel, Shannon Megan. (2006) Selection bias and continuous-time duration models: Consequences and a proposed solution. American Journal of Political Science 50:192–207.

Box-Steffensmeier Janet M, Arnold Laura W, Zorn Christopher JW. (1997) The strategic timing of position taking in Congress: A study of the North American Free Trade Agreement. American Political Science Review 91:324–38.[CrossRef][Web of Science]

Box-Steffensmeier Janet M and Jones Bradford D. (2004) Event history modeling: A guide for social sciences (Cambridge University Press, Cambridge).

Caldeira Gregory A and Zorn Christopher. (2004) Strategic timing, position-taking, and impeachment in the House of Representative. Political Research Quarterly 57:517–28.

Fearon James D. (1994) Domestic political audiences and the escalation of international disputes. American Political Science Review 88:577–92.[CrossRef][Web of Science]

Glazer Amihai, Griffin Robert, Grofman Bernard, Wattenberg Martin. (1995) Strategic vote delay in the U.S. House of Representatives. Legislative Studies Quarterly 20:37–45.

Gomez Brad T. (2000) The dynamics of information exchange: Reevaluating the strategic timing of position taking in Congress. Paper presented at the 2000 annual meeting of the Midwest Political Science Association.

Gordon Sanford C. (2002) Stochastic dependence in competing risks. American Journal of Political Science 46:17.[Medline]

Grenzke Janet M. (1989) PACs and the congressional supermarket: The currency is complex. American Journal of Political Science 33:1–24.[CrossRef][Web of Science]

Groseclose Tim and Snyder James M Jr. (1996) Buying supermajorities. American Political Science Review 90:303–15.[CrossRef][Web of Science]

Gumbel EJ. (1960) Bivariate exponential distributions. Journal of the American Statistical Association 55:698–707.[CrossRef]

Hall Richard L and Wayman Frank W. (1990) Buying time: Moneyed interest and the mobilization of bias in congressional committees. American Political Science Review 84:797–820.[CrossRef][Web of Science]

Holian David B, Krebs Timothy B, Walsh Michael H. (1997) Constituency opinion, Ross Perot, and roll-call behavior in the U.S. House: The case of the NAFTA. Legislative Studies Quarterly 22:369–92.[CrossRef]

Johnson Norman L and Kotz Samuel. (1970) Distributions in statistics: Continuous univariate distributions (Houghton Mifflin Company, Boston) Vol. 1:.

———. (1972) Distributions in statistics: Continuous multivariate distributions (Wiley, New York).

Jones David R. (2003) Position taking and position avoidance in the U.S. Senate. Journal of Politics 65:851–63.

Keech William R and Pak Kyoungsan. (1995) Partisanship, institutions, and change in American trade politics. Journal of Politics 57:1130–42.[CrossRef]

King Gary, Alt James, Burns Nancy, Laver Michael. (1990) A unified model of cabinet duration in parliamentary democracies. American Journal of Political Science 34:846–71.

Kingdon John W. (1989) Congressmen's voting decisions (University of Michigan Press, Ann Arbor).

Kollman Ken. (1998) Outside lobbying: Public opinion and interest group strategies (Princeton University Press, Princeton, NJ).

Krehbiel Keith. (1991) Information and legislative organization (University of Michigan Press, Ann Arbor).

Lai Brian and Boehmke Frederick J. (2004) Empirically modeling strategic behavior with a unified model of crisis outcome and duration. Paper presented at the 2004 annual meeting of the American Political Science Association.

Lohmann Susanne. (1993) A signaling model of informative and manipulative political action. American Political Science Review 87:319–33.[CrossRef][Web of Science]

———. (1994a) The dynamics of informational cascades: The Monday demonstrations in Leipzig, East Germany, 1989–91. World Politics 47:142–101.[CrossRef]

———. (1994b) Information aggregation through costly political action. American Economic Review 84:518–30.

Mathews Donald R and Stimson James A. (1975) Yeas and nays: Normal decision making in the U.S. House of Representatives (Wiley, New York).

Palazollo Daniel J and Swinford Bill. (1994) Remember in November: Ross Perot, presidential power, and the NAFTA. Paper presented at the 1994 annual meeting of the American Political Science Association.

Schultz Kenneth A. (2001) Looking for audience costs. Journal of Conflict Resolution 45:32–60.[Abstract/Free Full Text]

Smith Murray D. (2003) Modeling sample selection using Archimedean copulas. Econometrics Journal 6:99–123.

Thomas Martin. (1991) Issue avoidance: Evidence from the Senate. Political Behavior 13:1–20.

Uslaner Eric M. (1998) Let the chits fall where they may? Executive and constituency influences on congressional voting on NAFTA. Legislative Studies Quarterly 23:347–71.

Wink Kenneth A, Livingston C Don, Garand James C. (1996) Dispositions, constituencies, and cross-pressures: Modeling roll-call voting on the North American Free Trade Agreement in the U.S. House. Political Research Quarterly 49:749–70.

Wright John R. (1990) Contributions, lobbying, and committee voting in the U.S. House of Representatives. American Political Science Review 84:417–38.[CrossRef][Web of Science]

———. (1996) Interest groups and Congress (Allyn and Bacon, Boston).

Zorn Christopher JW. (2000) Modeling duration dependence. Political Analysis 8:367–80.

CiteULike    Connotea    Del.icio.us    What's this?

This Article Abstract FREE Full Text (PDF) Supplementary Data All Versions of this Article: 14/4/421    most recent mpj014v1 Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Add to My Personal Archive Download to citation manager Request Permissions Google Scholar Articles by Boehmke, F. J. Search for Related Content Social Bookmarking          What's this?

Online ISSN 1476-4989 - Print ISSN 1047-1987

Copyright © 2009 Political Methodology Section of the American Political Science Association

Oxford Journals Oxford University Press

• Site Map
• Privacy Policy
• Frequently Asked Questions

Other Oxford University Press sites: Oxford University Press Oxford Journals China Oxford Journals Japan American National Biography Booksellers' Information Service Children's Fiction and Poetry Children's Reference Corporate & Special Sales Dictionaries Dictionary of National Biography Digital Reference English Language Teaching Higher Education Textbooks Humanities International Education Unit Law Medicine Music Online Products Oxford English Dictionary Reference Rights and Permissions Science School Books Social Sciences Very Short Introductions World's Classics