THe HUNT FOR PARTY DISCIPLINE IN CONGRESS
Introduction
The
past several years have seen renewed scholarly investigation of how political
parties and their leaders influence legislative institutions and behavior (see
Aldrich 1995, Cox and McCubbins 1993, Rohde 1991, and Sinclair 1995). Much of this contemporary research
investigates how parties solve the collective action problems that are inherent
in the legislative and electoral processes.
Cox and McCubbins, who conceptualize political parties as “cartels” that
direct legislative activity to enhance the collective electoral fortunes of
their members, provide a typical variant on this theme, but by no means the
only one. The primary function of a
cartel is to build a collective reputation for its members to run under. They argue, however, that without strong
leadership members have individual incentives to engage in legislative
activities (such as pork) that diminish the collective reputation.
This
focus on the problems of collective action has generated much interest in the
cohesiveness of parties as floor coalitions.[1] The principal prediction is that a party
produces more cohesive coalitions of its members than would be possible if the
members were to act on the basis of their individual preferences. Rohde (1991) uses evidence of the increase
in party cohesion since 1975 to demonstrate an increasing role of party in the
post-reform House. Aldrich, Berger, and
Rohde (1999) also use party voting as the main dependent variable to test the
predictions of “conditional party government,” and Cox and McCubbins (1993) use
member support on leadership votes to test for the role of leaders in creating
voting coalitions. Furthermore, some
scholars, including Rohde (1991), see a reassertion of party strength behind
the increased cohesiveness and polarization of congressional parties since the
mid-1970s (for alternative explanations, see Poole and Rosenthal 1984; McCarty,
Poole, and Rosenthal 1997; and King 1998).
As
Krehbiel (1993, 1998) points out, however, these empirical studies of party
voting suffer from the problem that the patterns of behavior that have been
uncovered are consistent with both theories of strong, influential parties and non-partisan models where member
preferences are sorted along party lines.
This dilemma is exacerbated by the problem of measuring legislative
preferences. Ideally, one would like
some exogenous measure of these preferences to test party theories. Voting behavior under the null hypothesis of
no party influence could then be compared with actual voting behavior. The problem is that our usual measures of
legislative preferences are derived from the voting behavior itself.
In
this paper, we attempt to untie this Gordian knot. We begin by reviewing the evidence from work that analyzes
congressional roll call votes under the maintained hypothesis of sincere
spatial voting. We discuss how the
evidence from this work in fact suggests the presence of some party discipline. We next develop the party discipline model
of Snyder and Groseclose (2000). We
argue that their estimation method both seriously biases the estimate of ideal
points for ideological moderates and overestimates the extent of party
discipline. In the text, we provide a
compelling theoretical illustration of the bias. We detail our case further in Appendix B.
To
assess party discipline (a.k.a. pressure) properly, we propose an alternative
approach. The basic idea is very simple.
We start with Krehbiel’s (1993, 1998) proposal that the spatial model of
purely preference-based voting is the appropriate benchmark for evaluation of
models that incorporate party effects.
In one-dimension, the spatial model asserts that, on each roll call,
“Yea” and “Nay” voters are separated by a cutpoint on the liberal-conservative
continuum. Now assume that the
Republicans apply “pressure” to their membership. This will cause some moderate Republicans to the left of the
“sincere” cutpoint to vote with the conservative wing of the party. Republicans will have a cutpoint to the left
of the sincere cutpoint. Similarly, if
the Democrats apply pressure, the cutpoint for Democrats will be to
the right of the sincere cutpoint. That
is, when one or both parties apply pressure, the voting patterns should look as
if there were separate cutpoints for each party, with the Democrat cutpoint
being to the right of the Republican
cutpoint. Consequently, if pressure is
important, we should find a better fit to the data when we estimate two
cutpoints than when we estimate a single cutpoint.
To
keep the analysis as simple as possible, we use non-parametric optimal
classification analysis where legislator ideal points and roll call cutpoints
are jointly rank ordered to maximize predictive success on roll call votes
(Poole, 2000). By classifying the
voting of each party independently and then comparing the results to
classifying both parties together, we can evaluate the maximum possible
improvement in correct classification attributable to party discipline. An
advantage of the cutpoint approach is that it does not require any assumptions
about which specific roll calls are subject to party pressure. A particular advantage of the non-parametric
approach is that it assumes only that the amount of pressure applied to
individual members does not change the order of their induced ideal
points. It does not require making
parametric assumptions about how pressure varies with the ideal point of the
individual member, such as equal pressure being applied to all. On the basis of our optimal classification
analysis, we conclude that allowing for party discipline affords only a very
marginal improvement over the sincere spatial model, particularly in recent
Congresses.
Where,
then, is party discipline? We argue
that the main influence of party discipline is not on the votes on specific
roll calls but on the choice of ideal point made by the representative. The smoking gun is provided by the great
changes in ideological position demonstrated by those few legislators who have
switched parties. Wayne Morse and Strom
Thurmond are two well-known examples in the post-war Senate. The Democrats who defected to the
Republicans after the 1994 election made equally dramatic shifts. Our finding that parties shape ideal points
ends our hunt for party discipline in roll call voting.
Independent Voting on the
Floor: The Evidence from the Spatial Model
The
well-known standard spatial model provides a benchmark approach to independent floor voting. Poole and Rosenthal (1991, 1997)
demonstrated that the spatial model is quite successful in accounting for floor
decisions. With two dimensions, one can
correctly predict roughly 85% of the individual decisions -- even on close roll
calls -- for the period 1789-1985.
McCarty, Poole, and Rosenthal (1997, p. 7) report additional results for
the period 1947-1995.[2] In recent Congresses, a one-dimensional
model classifies nearly 90% of the individual decisions (see figure 5).
The
spatial estimates present a strong suggestion that party influence underpins
much of this remarkable classification success:[3]
n In
Congresses where voting is largely one-dimensional, party-line votes are along
the main dimension. The distribution of
ideal points is strongly bimodal. The
two parties appear as two very distinct “clouds”. The clouds, particularly in recent years, barely overlap. [As an
illustration, see McCarty, Poole, and Rosenthal (1997, p. 11).] The presence of a “channel” between the
clouds suggests that party affiliation may discipline the roll call voting
behavior of members. The main dimension
of political conflict clearly appears to reflect partisan conflict. Parties perhaps also influence their
members’ votes on specific roll calls.
n In
Congresses where voting is two-dimensional, there are also two distinct clouds
separated by a channel. Party-line
votes are no longer on the main dimension, but a blend of the first and second
dimensions. [See Poole and Rosenthal,
1991, p. 233 or 1997, p. 44 for an example.]
An interpretation of such plots is that ideal points projected onto roughly
a 45° line represent
the ideological (liberal-conservative) dimension. The orthogonal projection, roughly at –45°, represents a
party loyalty or valence dimension.
Most votes occur along the main, 0°
dimension. On these votes, the
legislator’s decision depends both on ideology and on party loyalty.
Although this evidence shows that
the structure of voting coalitions in Congress coincides strongly with party
affiliation, it does not prove that party per
se has any influence on voting behavior.
Party-line voting is, of course, consistent with both strong party
models and ideological models where preferences are sorted by parties. In the sections that follow, we review a
recent attempt to separate partisan effects from preferences and propose a method
of our own.
The Snyder-Groseclose Model of Party Discipline
One
of the inherent problems in identifying the effects of party is that we observe
only behavior, which is presumably a mix of individual preferences and party
influence. This problem is particularly
acute with congressional voting data.
If party discipline is exercised on floor votes, the ideal points
estimated on the assumption of independent spatial voting might be very biased
estimates of legislator preferences. If
party influences these estimates, it is inappropriate to use them as controls
for preferences when testing for a party effect. Snyder and Groseclose (2000) noted this potential for bias. They proposed both a method for first
estimating unbiased ideal points and then for using the unbiased ideal points
to estimate the effect of party discipline.[4]
The basics of the
one-dimensional Snyder-Groseclose model are as follows:
n On
roll call j, a legislator i, if a Republican, has induced ideal
point xij = xi
n On
roll call j, a legislator i, if a Democrat, has induced ideal
point xij = xi + gj
In
other words, the true ideal points of the Democrats, the xi, are displaced by the amount of party pressure given
by gj.[5] It turns out that only the relative amount
of party pressure matters in the model, so the ideal points of the Republicans
can just be given by their true values.
For the difference in pressure to be consistent with discipline, we
would expect that pressure must move Democrats in a liberal direction relative
to Republicans. Thus, pressure works to
increase the separation of the parties.
If preferences are scales such that left is liberal and right is
conservative, then we would expect g
to have a negative sign
Snyder
and Groseclose argue that, because there would be little need to apply party
discipline on votes not expected to be close, ideological position-taking could
occur on lopsided votes. These votes,
for example, those with margins over 65-35, could be used to estimate the true
ideal points. On these votes, the gj
would be zero. The true ideal points
could then be used to estimate the gj
on close votes, say those with margins less than 65-35.
In brief, their
procedure is:
Stage 1. Use votes with margins greater than 65-35 to
estimate the ideal points, xi.
Stage
2. On the
remaining votes, for each roll call j,
estimate the following OLS (ordinary least squares) model:
(1)
where Di = 1, if legislator i is a Democrat, = 0 if Republican; and Yij = 1, if i votes Yea, = 0 if i votes Nay. In the
Appendix A, we show that if the underlying spatial utility is quadratic, then
. (2)
As
we noted above, the party pressure model predicts a negative estimate for g when
preferences are scaled with Democrats on the left (as we assume they are). Consequently, the two estimated b’s
should be of opposite sign.
Why the Method Overestimates Party
Discipline
This method is
likely to generate the inference that party pressure is substantial even when
all voting is preference based.
Consider, for example, a six-member legislature with the party
affiliations and spatial preferences given in figure 1. If all
voting in this legislature is spatial without error, there are only 12 possible
voting configurations, which are given in figure 2.
Stage
1 of the Snyder-Groseclose method estimates a preference score using only
voting patterns 1-10. But, since voters
3 and 4 cast identical votes in each of these patterns, any scaling procedure
will estimate voters 3 and 4 as having the same position. Thus
stage 1 provides biased estimates of the preferences of moderates. There is not enough information in the
lopsided votes to discriminate “left” moderates from “right” moderates. The preference ordering that maximizes
the classification of votes is shown in figure 3.
In stage 2, the preferences in figure 3 and
party affiliation are used to explain vote patterns 11 and 12. The votes of legislators 1, 2, 5, and 6 are
correctly classified on the basis of the preference estimates, but the votes of
legislators 3 and 4 cannot be. However,
since 3 and 4 are members of different parties, adding party to the model
increases its explanatory power even
though voting is purely preference driven.
Our example extends naturally to larger
legislatures. In general with perfect
spatial voting, a first stage based only on lopsided votes will produce identical
preference estimates of all members in the interval between the 35th
and 65th percentiles. The
second stage will therefore produce a spurious party effect so long as party
and ideology are correlated within this interval. Given the assumptions of no voting error and no overlap of
preferences between the parties, this example is somewhat special. However, in Appendix B, we present Monte
Carlo evidence that shows how this result extends to large legislatures where,
as in the Snyder and Groseclose approach, there is some error in voting and the
distributions of preferences of each party overlaps. We now present an alternative procedure that maintains the
essential features of their model of discipline.
A Non-Parametric Model
All
specifications of a spatial model of voting have two critical elements: ideal
points for the legislators and cutpoints (or separating hyperplanes) for the
roll calls. The Snyder-Groseclose
model, with a discipline parameter to each roll call, is isomorphic with one
where each party has its own cutting line.
(See Appendix A.) That is, moving the ideal points for all Democrats to
the left by a magnitude gj is equivalent to
moving the cutpoint for Democrats to the right by the same amount. Party discipline generally involves getting moderates to
vote with extremists.[6] Consequently, if there is party discipline,
the cutpoint for the Democrats should be to the right of the cutpoint for
Republicans.[7]
Consider
a one-dimensional spatial configuration.
If the cutpoint is constrained to be the same for both parties, this
produces the standard spatial model.
For example, in figure 4, with a common cutpoint, there are three
classification errors, legislators 3, 11, and 15. When each party can have its own cutpoint, this produces a model
that allows for party discipline.
Moderate Democrats to the right of some Republicans can vote with the
majority of their party. Moderate
Republicans to the left of some Democrats can vote with the majority of their
party. The best cutpoint for the
Republicans in figure 4 remains the common cutpoint. Legislator 15 is the only R classification error. But the best cutpoint for the Democrats is
to the right of the common cutpoint.
The D cutpoint leaves only legislator 3 as a classification error for
this party. Rather than estimate either
the one-cutpoint model or the two-point model via a metric technique, such as
Poole and Rosenthal's (1991) NOMINATE or Heckman and Snyder's (1997) method,
one can simply find the joint rank order of legislators and cutpoints that
minimizes classification error. Poole
(2000) presents an efficient algorithm that very closely approximates the
global maximum in correct classification.[8] Note that this method, in contrast to
equation (1), does not require a uniform adjustment in the ideal points of all
members of a party. Only moderates
would need to be disciplined. All that
is required is a displacement of the cutpoint.
We
now turn to our empirical analysis.
This analysis involves both the testing of implications of our
methodological critique of Snyder and Groseclose as well as testing the
implications of their model of party discipline utilizing our two cutpoint
model. We begin by presenting evidence
on three methodological predictions. In
each case, these predictions are
consistent with the mismeasurement of preferences in the
Snyder-Groseclose framework under the hypothesis of purely spatial voting. In only one of the cases is the prediction
also consistent with their theoretical model.
Therefore, verification of these relationships illustrates the inability
of Snyder-Groseclose to distinguish party pressure from mismeasurement of
preferences. The three methodological
predictions are as follows:
M1.
Estimate the rank order of ideal points
by one-dimensional optimal classification first using all roll call votes and
then using only lopsided votes. The
correlation of the all votes rank orders and the lopsided votes rank orders
will be greater for extremists (the first and last thirds of the all votes
distribution) than for moderates (the middle third). While this prediction is consistent with the Snyder-Groseclose
assertion that party pressure primarily affects moderates, it also follows from
our claim that, if there is preference-based voting, ideal points of moderates
will be inaccurately recovered if only lopsided votes are used to estimate
ideal points.
M2.
Similarly, when the rank order is
estimated first on all roll call votes and second on only close votes, the
correlation of the all votes ranks and the close ranks will be greater for
moderates than for extremists. The
motivation for this prediction is similar to that of the first. If there is preference-based voting, the
ideal points of extremists will be inaccurately recovered if only close votes
are used to estimate ideal points. This
prediction is inconsistent with Snyder and Groseclose as they implicitly assume
that extremists will have similar preference estimates on pressured votes as
they do on unpressured votes.
M3.
The close-all correlations for moderates will
be high if there is preference-based voting, lower if there is party
discipline. The reason is that, if
there is discipline only on close votes as claimed by Snyder and Groseclose,
all votes estimates will mix preference-based lopsided votes and disciplined
close votes. The close votes estimates
will have more distortion of the true ideal points.
After
these tests concerning the effects of Snyder and Groseclose’s procedure on
ideal point estimates, we turn to testing hypotheses from the party discipline
model. In all cases, the null model of
preference-based voting predicts no difference.
H1.
Classification should be substantially
higher with a two-point model than with a one-point model. Note that classification cannot be lower
with the two-point model.
H2.
The improvements in classification should
be greater on close votes. Since
Snyder-Groseclose predict that rational parties will whip close votes, the
incremental predictive power of the two-cutpoint model should be accordingly
higher on those votes.
H3.
The rank order of the legislators should
disclose more separation of the parties in the one-point model than in the
two-point model. The reason is that the
one-point model ignores party discipline.
Moving Democrats to the left and Republicans to the right should pick up
some of the effects of party pressure.
In contrast, in the two-point model, each legislator's ideal point can
take on its true rank order position, because the cutpoints can pick up the
effects of party discipline.
H4.
The separation of the cutpoints should be
greater on close votes. The identifying
assumption of the Snyder-Groseclose model is that party pressures are more
likely on close votes. Therefore, under
their assumptions, the distance between the Democratic and the Republican
cutpoint should be greatest on those votes.
H5.
The estimated cutpoint for the Democrats
should be to the right of the estimated cutpoint for the Republicans.
A Caveat
Some
instances of party pressure may be masked.
Consider a legislature with no party overlap. All Democrats are to the left of all Republicans. Suppose that, were there no pressure, a
Republican Party bill would be rejected by a majority composed of all Democrats
and some moderate Republican defectors.
If the Republicans then apply “pressure” to the defectors, resulting in
a party-line vote, the vote will still appear to be a vote consistent with
preference-based voting. Thus when
ideal points are estimated correctly, the true explanatory power of party may
be masked. In fact, when there is no
overlap in the distribution of party ideal points and there is errorless
spatial voting, it is impossible to identify party pressure effects.
This
masking of party pressure is inherent to spatial analysis. It would confound a correct
Snyder-Groseclose analysis as well as our optimal classification method. Albeit important, the question we can ask is
limited to “Can allowing for party discipline improve on the classification of
a purely preference-based model?”[9]
With
our optimal classification method, it is possible to calculate an upper bound
for the amount that party pressure can increase vote classification, roughly as
a function of the overlap between the two parties. This upper-bound represents the classification on a strict party
line vote of a two-cutpoint model (perfect classification) minus the
classification of a strict party line vote using a single cutpoint.[10] When there is no overlap between the
parties, a single cutpoint correctly classifies a party line vote so as noted
above their can be no classification gain for the two cutpoint model. However, the greater the party overlap, the
worse a one-cutpoint model does in explaining a strict party-line vote. Thus, the maximum classification gain
increases in the overlap. If we use the
configurations of preferences that emerge from optimal one-cutpoint
classification to measure overlap, the maximum classification gain from
party-pressure consistent cutpoints (i.e. D>R) ranges from 0 in the 80th
House (where there is zero overlap) to 16% in the 92nd House. The average upper bound over all of the
congresses we analyze is 5%. However,
it is important to remember that these upper bounds are simply for roll calls
consistent with party pressure (i.e. Democratic cutpoint to the right of the
Republican cutpoint). Perfect
classification is the upper bound if we allow other cutpoint configurations
(e.g the Republican cutpoint on the right).
Secondly, as we discuss below, optimal classification with a single
cutpoint will underestimate party overlap which would lead to the
underestimation of these upper-bounds.
Tests Using the
Non-Parametric Model
One Dimensional
Classification
We
begin with the three predictions concerning correlations of ideal points. In order to show that the pattern of
estimates we expected would arise in actual data, we first performed optimal
one-point classification using all
the roll call votes in each House from the 80th through the 105th. If the basic spatial model is correct, this
procedure should produce a rank order of legislator ideal points that is very
close to the true order. Next, we did
optimal classification using only lopsided
votes, those with greater than 65-35 margins.
Finally, we did optimal classification using only close votes, those with margins of 65-35 or less.
We
then computed Spearman rank order correlations between the lopsided vote rank orders and the all votes rank orders for left-wingers, the one-third of the
legislators furthest to the left in the all
votes classification; moderates, the middle one-third; and right-wingers, the
one-third furthest to the right. We
would expect these correlations to be high for the left-wingers and
right-wingers but low for the moderates because the lopsided votes provide little information about the ideal points of
moderates (M1). Conversely, when
correlations are made between close votes rank orders and all votes rank orders, we expect the correlations to be high for
moderates but low for left-wingers and right-wingers.[11]
Insert Table 1 about here
The
hypothesized patterns occur, as shown in Table 1. Indeed, for the lopsided-all
comparison, in every post-war House but one, the middle one-third
correlation is lower than both that for the left-wingers and that for the
right-wingers.[12] Table 1 indicates that the middle correlation
is particularly low in the period preceding the passage of the major civil
rights bills of the 1960s. In this
period, there was an important second dimension (Poole and Rosenthal, 1997)
that confounds the recovery of moderate positions on the first dimension. When the second dimension vanishes, even the
middle correlations are reasonably high because the “errors” in voting provide
some information about moderates. That
is, for example, a relatively liberal moderate is still less likely to vote with
the right-wingers than is a relatively conservative moderate, even on lopsided
votes. Nonetheless, as predicted by M2,
correlations for moderates are lower than for extremists.[13]
As
predicted, these results reverse for the close-all
comparison. The moderates always
produce a correlation above 0.9. The
left-winger and right-winger correlations are always below 0.9, usually much
below, and in one case, the correlation is negative.
The
close-all correlations for moderates
are strikingly high, predicted by preference-based voting but not by voting
subject to party discipline (M3). If
the party discipline effect were important, we would expect lower rank order
correlations, particularly for Houses before 1980, when there was still
considerable overlap in the ideal point distributions of the two parties.
Classification with
Two Cutpoints
In this section, we assess the ability of a party discipline model to
improve on a preference-based model.
Our criterion is percentage of votes correctly classified.
To find the highest classification possible for a party discipline model,
there is a simple solution: just classify each party separately. This allows the cutpoint on each roll call
to adjust to pressures internal to the party.
Because the cutpoints can adjust, one
will find the true intra-party rank order of the ideal points. The classification from this model can be
compared to a single cutpoint model.
The results of this exercise appear in figure 5, which shows results for
one-, two-, and six-dimensional models.
We used a six-dimensional model to parallel the high dimensionality used
by Snyder and Groseclose in their empirical work. With multiple dimensions, the cutpoint is replaced with a
separating hyper-plane.
In one dimension, it is
apparent that a two-party model adds little, particularly in recent Congresses.
The improvement in
the earlier Houses is at the level that results when a two-dimensional model
with one cutting line is used. In one
dimension, the two cutpoints allow for Southern Democrats to vote with Northern
Democrats on some issues, but they also allow for votes where a coalition of
conservative Republicans and Southern Democrats opposes liberal Republicans and
Northern Democrats. Since the Democrats
were the majority party in the conservative coalition era, these votes
demonstrate breakdowns of party discipline that would be exactly opposite to
the basic assumption of the Snyder-Groseclose model.
In two or six dimensions, allowing for
two (as against one) separating hyperplanes results in even less improvement
than in the one-dimensional case. In
fact, the improvement is almost always less than 1% for all post-war
Houses. The smaller improvement occurs
because, in one dimension, “party” was picking up some effects than can be
accounted for just as well by a higher-dimensional preference-based voting
model. The
strength of the results in figure 5 is further emphasized by two
observations. First, some of the
increase in fit is simply noise-fitting due to the extra degrees of
freedom. Second, classifying each party
separately allowed for “both ends against the middle” voting where liberal
Democrats and conservative Republicans vote together. This last problem and other considerations lead us to adopt a
slightly different approach.
The remainder of the analysis in this section uses a two-stage
procedure:
1.
Using optimal classification, we
estimate a one-dimensional spatial model that has a single cutpoint, common to
both parties.
2.
Holding the rank order positions of the legislators constant at the positions produced by step 1, we then estimate separate cutpoints for the two
parties. The two cutpoints must be
placed to maintain polarity. That is, unlike in the separate scalings
reported in figure 5, we did not consider improving classification by allowing
moderates to be opposed by extremists at both ends of the spectrum. Bob Barr and Maxine Waters can’t vote
together against Connie Morella. This
constraint is fully consistent with the Snyder-Groseclose approach that calls
for an order-preserving shift in a party's ideal point distribution but not for
a flip-flop.
The motivation for this two-step approach is that it is not
possible to estimate jointly a single order for the legislators and two
cutpoints for each roll call. The
reason is that the rank order of the legislators within each party is pinned
down only by the cutpoints for that party.
Consequently, it is impossible to rank order either the legislators of a
party or the cutpoints for that party with those for the other party. In contrast, once we fix the rank order of
the legislators, we can estimate separate cutpoints and test theoretical
predictions about these cutpoints. We
cannot directly test H3, however,
that preferences will show less party overlap in a one-point model than in a
two-point model. That hypothesis could
be tested only indirectly, by our test of M3.
To
justify holding the legislators constant, we computed within-party Spearman
rank order correlations between the rankings of the single cutpoint model and
the rankings when optimal classification is applied to the party
separately. Recall that this separate
classification is consistent with a party pressure model—there is a true
underlying order of ideal points but cutpoints are adjusted to reflect party
pressure. As table 2 shows, these
correlations are remarkably high. For
both parties, the correlations are above 0.95 since the mid-1960s. [Previously, some correlations were lower as
a consequence of the presence of an important second dimension.] Consequently, the single cutpoint ratings,
particularly for the past 30 years, are likely to provide accurate rankings of
the “true” ideal points within each party.
Insert Table 2 about here
Note that the analysis
presented in table 2 informs us that the relative order of legislators within
each of the two parties is insensitive to whether we just assume pure
preference-based voting or explicitly account for party pressure. The result does not rule out party pressure;
it just tells us, consistent with equation (1), that party pressure is unlikely
to change the relative order of induced ideal points. The result does not rule out party pressures polarizing one party
relative to the other. The lack of
overlap we observe in the 1990s might, for example, be the result of party
pressure. We return to this point
presently.
The two-point model creates only minor gains in classification of roll
call votes. As the second dimension has
diminished in importance, these gains, as shown in figure 6, have declined to
under 0.5% in the last 8 Congresses.
In other words, adding a second cutpoint typically
allows correct classification of only an additional 2 of the 435
representatives (assuming full turnout).
Note that (1) the classification must get better with a second cutpoint,
(2) the second cutpoint can just fit noise in the data (see Poole and
Rosenthal, 1997, p. 156), and (3) much of the improvement in classification
occurs from using two cutpoints that have the Democratic cutpoint
counter-hypothesis to, that is left
of, the Republican cutpoint (see table 3).
Thus, the improvements of under 1 percent are truly small potatoes. [14] H1 is not supported.
Figure 7 shows the results for close and lopsided roll calls and contains
a wee bit of good news for advocates of party pressure theories. The classification gain is greater on close
roll calls than on all roll calls, but only since the mid-1960s. The evidence for the earlier Congresses
reinforces our contention that the larger improvements in classification for
these Congresses shown in figures 5 and 6 are the work of a second
dimension. If discipline were producing
the gain, the gain should not occur on lopsided roll calls. There is a systematic difference in the gain
on close and lopsided roll calls in later Congresses. However, some of the gain on close roll calls must result from
non-discipline factors—such as noise fitting—that affect lopsided as well as
close votes. The difference between the
gain on close and lopsided votes is roughly one percent. The gap of only one percent suggests that
party pressures are changing not more than about 4 votes per roll call on the
close votes. At best, H2 is weakly supported.
The fourth hypothesis derived from the party pressure model is also
weakly supported. To test H4
we computed the average of the difference between the rank of the Democratic
cutpoint and the rank of the Republican cutpoint and then divided by the number
of legislators serving in the House.
This procedure normalized the difference in the rank orders to a –1 to
+1 scale so that the Houses could be more easily compared. We used the difference rather than the distance (absolute difference) between
the ranks because the pressure model predicts that the Democratic cutpoint
should be greater than the Republican cutpoint (D > R).
We classified
all roll calls into three types. Our
first type includes roll calls where, in line with the fifth hypothesis, the
Democrat cutpoint was greater than the Republican cutpoint (D>R). Note that whenever there is some overlap in
the ideal point ranks of the two parties, straight party-line votes are counted
as D>R. Our second type is clearly
counter-hypothesis roll calls with R> D that satisfied this condition. Finally, for many roll calls (see table 3),
the relative locations of the two party cutpoints were ambiguous. We term this third type “Undecided”. Note that cutpoints which are interior to
the legislators of a party can be identified for only a subset of roll
calls. A portion of our analysis will
be restricted to such roll calls. [15]
When the ideal
point distributions of the two parties have no overlap, as happened in the 80th
House (1947-48), we cannot identify any roll calls as D>R so the average
difference must be less than
zero. In contrast, when there is
substantial party overlap, as in the 1970s, the party pressure model predicts that the average difference for close votes
should be greater than zero and be greater than the average difference for
lopsided roll calls. The average difference for lopsided roll
calls should be close to zero. The
results, computed for all roll calls with interior cutpoints in both parties,
appear in figure 8.
The average difference for the close roll calls is indeed above zero for
19 of the 26 Houses. Since the 91st
House, however, the average difference is very
close to zero – hovering around .02 or an average difference of about 8 to 9
ranks. In only three Houses, all in the
two-dimensional 1950s and 1960s, does it exceed 0.1 or 10% of the House
membership. To benchmark this difference, the normalized difference or overlap
between the third rightmost Democrat and the third leftmost Republican averages
46% of the House membership for the 26 Houses we analyze; it exceeds 32% in all
but the 80th, 84th, and 100th to 105th
Houses. Moreover, note that this
average difference is highly biased in favor of the party pressure model in
that it does not include “Undecided” roll calls. These include, for example, all roll calls on which the
Republicans are unanimous but the Democrat cutpoint is to the left of the
leftmost Republican. Such roll calls
are most likely ones where party discipline broke down among the Democrats so
that D<R.
The average difference for the lopsided roll calls is negative for all 26
Houses. That the difference is negative
probably reflects instances of “both ends against the middle” voting. If the six most liberal Democrats and the
six most conservative Republicans cast protest votes on final passage and they
are the only negative votes, with fixed polarity, one of the party cutpoints
will be near an end of the dimension while the other party cutpoint will be
near the middle of the dimension.
Consequently, the difference in ranks will be negative and large in
magnitude. The negative differences can
reflect a few conservative Republicans and a few liberal Democrats voting
against a lopsided majority.
Finally, H5's prediction that the Democrat cutpoint would be to the right of
the Republican cutpoint is not supported, as shown in table 3. The pattern, except for the no overlap or
low overlap Congresses 80 and 103-105, is quite stable, so we present results
in tabular form. Recall that in low
overlap Congresses, there are very few or no roll calls with D>R. But even in Congresses with overlap, the
pattern runs counter to the Snyder-Groseclose model, with R>D roll calls
outnumbering the “pressure” D>R roll calls by more than 3 to 2.
Insert
Table 3 about here
Table 3 is much less favorable to the party pressure model than figure 8
because for many of the Houses a handful of Southern Democrats were in the
midst of the Republicans and a handful of liberal Republicans were in the midst
of the Democrats. Consequently, on
party-line or near party-line votes, D>R and the difference in ranks was
quite large. The differences in ranks
are smaller in magnitude on counter-hypothesis R>D votes, but such votes are
typically a majority of the roll calls.[16]
Some of the
counter-hypothesis R>D votes almost certainly indicate a true breakdown of
party discipline. A breakdown of party
discipline can occur, for example, when the majority is subject to a few
defections of its own moderates but offers bills or makes promises that buy the
support of moderates of the opposite party.
The seduction of minority moderates is a scenario that seems to fit the
two Gingrich Houses, where, in the single cutpoint analysis, the modal cutpoint
fell interior to the Democratic Party (see McCarty, Poole, and Rosenthal, 1997,
12). [The two Gingrich Houses are the
last two points in every plot.]
These results about cutpoints
are, however, subject to the warning that the single cutpoint estimation of
ideal point ranks might possibly show too much separation of the parties. We therefore calculated how far the ideal
points of Republicans would have to shift leftward until the average difference
for lopsided roll calls was zero. Once
each House has been shifted, a new version of figure 8 would have a flat line
through zero for lopsided votes. That
is, the shift forces the average pattern for lopsided votes to match the theoretical
level in the Snyder-Groseclose model.[17]
The results of this exercise
are shown in figure 9. When the
lopsided vote difference is just slightly negative, as in the late sixties,
very few ranks need to be shifted. In
these cases the close vote difference is near zero and R>D roll calls
outnumber D>R, so the Snyder-Groseclose model is not supported. Where the lopsided vote difference is
sharply negative (see figure 8), in the late forties and in the nineties, many
ranks have to be shifted to force the lopsided votes to show a zero
average. In the most recent Congresses
in our time series, the order of change is of 100 ranks, or about half the
Democratic membership. Nevertheless,
placing the “true” ideal points of the most moderate Republicans in the middle
of the Democratic Party is seriously lacking in face validity. The amount of overlap in the ideal point
distribution is just too great to make a party pressure model credible. In fact, the amount of shifting needed
matches the decrease in party polarization in the post-war period and its
increase since the late 1960s (McCarty, Poole and Rosenthal, 1997) as measured
via NOMINATE scores. The increasing
separation of the parties one sees is, in our view, much more likely to reflect
fundamental political changes, such as a large increase in southern Republican
representatives, than an increase in party discipline within Congress.
Since our initial ideal point
distribution has greater face validity than the shifted distribution, we use
the initial distribution to ask a final question in this section. Does discipline make a difference in
outcomes? We assess this in two ways:
A.
We assume the true cutpoint is the
minority cutpoint. Pressured voters are
those majority party voters with ideal points between the minority and majority
cutpoints. This reflects a benchmark
where all pressure is exerted by the majority party. Would the outcome have changed were their votes reversed?
B.
We assume that the true cutpoint is
the average of the two party cutpoints, reflecting a scenario in which both
parties exert equal pressure. Pressured
voters are those voters with ideal points between their party cutpoint and the
average. Would the outcome have changed
were their votes reversed?
The results vary
substantially from one Congress to the next, in part a function of the
separation of party ideal points. We
find that, averaged across Congresses, discipline makes a difference, for
assumption A, on 16.97% of close roll calls (Std. Dev. 9.17) and, for
assumption B, 11.07% (Std. Dev. 8.03%).
While these numbers are substantial, they are well below the proportion
of significant t-statistics reported by Snyder and Groseclose. Moreover, they are almost certainly
overestimates. One qualification is
that assumption A is extreme, since it assumes only the majority party exerts
pressure. Another is that some of the
pressured voters may not have changed their votes were “pressure” removed. This is because under the null hypothesis of
a single cutpoint, errors in voting will result in there being legislators on
the yea side of the cutpoint who vote nay, and vice versa. Similarly, under the alternative hypothesis
of two cutpoints there will be two types of legislators between the cutpoints –
those who are pressured and those who voted with their party for idiosyncratic
reasons. Scenario A mistakenly counts
both types of legislators as pressured.
This section, in summary, has established that:
n Allowing for party discipline does not make an important
contribution to classification.
n
Those improvements in classification
that do occur are, more frequently than not, the result of using cutpoints that
are inconsistent with the party pressure model.
Ideal
Point Changes in Party Switchers
If
there is little evidence that many ideal points are displaced on individual
votes, there is very substantial evidence that party affiliation has a strong
influence on ideal points. To see this,
we used the procedure of Poole (2000) to obtain rank orders of the ideal points
in separate estimations for the House and Senate using all roll calls from 1947
to 1998.[18] Each member was constrained to have a
constant ideological position in his or her career, except that party switchers
were allowed to have two positions, one before and one after the switch. There were 472 senators and 2,326
representatives (counting the party switchers as two individuals). The orderings were normalized to 0-1 by
dividing the raw ranks by 472 for the Senate and 2,326 for the House.
When
legislators switch from R to D, they should have a lower rank. The reverse should hold for D to R
switchers. There were 19 legislators
who both switched parties and remained in the same house in the period of our
analysis. They are listed in table
4. In 18 of 19 cases the rank changed
as expected. The only exception is
Strom Thurmond. His slightly more
moderate position as a Republican is a reflection of his more moderate views on
race relations in the past 20 years. A
simple sign test is overwhelmingly significant. Induced ideal points respond to party affiliation.[19]
We
have shown that party switchers generally move in the theoretically expected
direction. Did they move very
much? The average rank movement was
0.28; thus a switch induced a jump over more than one-fourth of all legislators
serving in the period. To benchmark
this movement, we reran the analysis for the House allowing two positions not
only for the party switchers but also for some legislators who never changed
party. Specifically, we picked in the
legislator file every 500th legislator among moderates — that is
those with ideal points between -0.3 and +0.3 — who served in at least 2
Houses.[20] There were 15 such representatives, matching
the number of actual switchers in the House.
For each group of 15 we computed the average partisan switch. That is, for Democrats the switch was just
the change in the coordinate, as Democrat switchers are expected to increase
their ranks. But for Republicans, we
used the negative of the change. Actual
switchers moved substantially, a change in normalized rank of 0.281. On average, non-switchers barely budged,
moving only 0.026 in ranks. The
(one-tail) t-statistic for the differences in the means indicate a high level
of statistical significance.
Insert
Table 4 about here
This
evidence is consistent with a party effect, but a couple of caveats are in
order. First, it is silent on the
mechanism that generates this effect.
Therefore, the source may not be internal to the legislature. Switchers after all have to adapt to a new
set of primary constituents and contributors as well as legislative
leaders. Second, party switchers are
obviously not a random sample of all legislators. In the 104th House, southern Democrats switched to the
Republican Party for a reason -- they wanted to reflect the increasingly
conservative temperament of their districts.[21] Therefore, selection bias precludes us from
suggesting that the shift in ideal points is an unbiased estimate of party
pressure. But even if the selection
bias were severe, it is telling that changing party labels was deemed necessary
to reflect changing district sentiment.[22] Third,
the estimates based on party switchers are almost certainly an upwardly biased
measure of the average amount of discipline.
Those members who do not switch probably have more congruence between
their personal/constituency position and the party's desires.[23] In particular, those representatives close
to the party median are likely to vote “correctly” without any discipline.
Conclusion
In the past decade, theorizing
about the influence of parties and leaders on legislative behavior has
outstripped progress in solving difficult methodological and measurement
problems necessary to test these theories.
In this paper, we have addressed the problems associated with
distinguishing party effects from a null hypothesis of individual
preference-driven behavior. We began by
demonstrating the unattractiveness of regression-based procedures such as that
of Snyder and Groseclose. We find that
these methods of estimating the effects of party discipline on individual roll
call votes are biased toward exaggerating the effect of party discipline. To remedy these statistical problems, we
incorporate the theoretical insight of Snyder and Groseclose into the spatial
model of voting, which we estimated non-parametrically. We find that empirically, a party discipline
approach makes, at best, a marginal improvement over the standard spatial
model.
We do not conclude, however, that
party is irrelevant. Voting behavior
changes fairly dramatically when members change parties. Party discipline, we conclude, is manifest
in the location of the legislator’s ideal point in the standard spatial
model. It is not a strategic variable
manipulated by party whips, but a part of a legislator’s overall environment
that forms her induced preferences. The
legislator, in choosing a spatial location, may be responding as much to the
external pressures of campaign donors and primary races as to the internal
pressures of the party.
On the other hand, the evidence we
presented does not suggest that a resurgence of party or party-induced
institutional changes is responsible for the greater voting cohesiveness of
parties and the emergence of polarized politics in Congress. Having distinct cutting lines (or separating
hyperplanes) for the Democrats and Republicans never adds substantially to the
classification success of the spatial model in the post World War II
period. Indeed the additions have
fallen throughout this period, both during the period of declining polarization
(1947-circa 1975) and during the more recent surge in polarization.[24]
Appendices
Appendix A: Shifts
in Ideal Points
Let
zyj and znj be the “yea” and “nay”
outcomes of roll call j. In
both the Heckman-Snyder and NOMINATE methods for estimating the spatial model,
the non-random portion of the utility a legislator i has for roll call
outcome 
, can be expressed as:
(A1)
where
f
is a negative monotonic function and dijz denotes the Euclidean distance from xi, i’s ideal point, to zj.
Now
let the “party-pressured” ideological coordinates for Democrats equal xi + gj. We obtain:
(A2)
But this
expression for distance is identical to the expression we would have if the
ideal point were unchanged but the yea roll call outcome were changed to zyj - gj. The distance to znj would also be unaffected if it were also changed to
znj - gj . Shifting both roll call outcomes by gj also shifts the
midpoint 
by gj. So, for example, a leftward shift in the
ideal points for all Democrats is equivalent to a rightward shift in the
outcome locations and midpoint for Democrats.
The argument extends readily to multi-dimensional shifts. Since for every ideal point shift there is
an equivalent outcome shift, neither Heckman-Snyder nor NOMINATE can
discriminate between a model where a party alters ideal points on a roll call
and one where each party has its own midpoint or separating hyperplane on each
roll call.
Now
consider the more general situation where the amount of pressure is not equal
for all members but where the pressured ideal points maintain the same order as
the original members and the magnitude of the pressure, for Democrats, is
increasing in spatial position.
Moderates are pressured more than liberals are. Since the pressure is not uniform, the shift
in ideal points can no longer be captured by a simple shift in outcome
locations. Nonetheless, in the map from
the pressured ideal points back to the original ideal points, there will
continue to be a point where a party member is indifferent between voting Yea
and Nay. Let this point be the
pressured midpoint for the party on the roll call. Optimal classification should be reasonably robust in identifying
the pressured midpoint as long as the form of pressure does not depart too strongly
from uniform pressure.
Appendix B: Monte Carlo Analysis of the Snyder-Groseclose Approach
To
demonstrate that the Snyder-Groseclose method is likely to reject the null
hypothesis of preference-based voting when it is true, we conduct a number of
Monte Carlo experiments. The Monte Carlo
data are generated by one-dimensional spatial voting with error. Snyder and Groseclose use the scaling method
of Heckman and Snyder (1997). Our
specification of the underlying random-utility model is therefore identical to
that assumed by Heckman and Snyder.
Legislator i votes Yea rather than Nay if and only if
(A3)
where xi
is the ideal point of legislator i, zyj and znj are the positions of the Yea and Nay voting
alternatives, and the e
are random shocks. Let zMj = (zyj + znj)/2
be the midpoint of the roll call and dj
= (zyj - znj)/2 be half the (directional) distance
between the yea and nay outcomes. To
simulate realistic values for the yea and nay positions, we assume that zMj is distributed on [-1,1]
according to the density f(z) = 1-|z| which produces a modal voting margin of 50%-50%. Further we assume that dj is distributed uniformly on [-1,-.05]È[.05,1]. The “gap” from -.05 to .05 prevents votes in
which the yea and nay outcomes are too similar so that voting is purely random.
We divide the 435 members of our House of
Representatives into 218 Democrats and 217 Republicans. The ideal points of the Democrats are
distributed uniformly across the interval [-1,r] and those of the Republicans are distributed across [-r,1].
(See columns (a), (b) of table A1.) The variable r controls the extent of overlap in the ideal points of members of
the two parties. If r
= 0, then the parties are perfectly spatially separated. If r
= 1, the parties are drawn independently from the same distribution. In general, in expectation, a fraction 2r/(1+r)
of each party overlaps with the other party.
In our experiments, we let r Î {0.1, 0.2,
0.3} so that the corresponding correlations between party and preferences take
on the values of -0.82, -0.76, and -0.68.
These are consistent with measures of party overlap and correlation in
the post-war House of Representatives.
Also
following Heckman and Snyder, we assume that
hij
º eijy - eijn
(A4)
is drawn from U[-m,m]. We let mÎ {0.2, 0.4,
0.6}. (See column (c) of table A1.) These
values are chosen to be consistent with the range of goodness-of-fit measures
such as classification success reported in Heckman and Snyder (1997). In the experiments that follow, the correct
classification of voting decisions following Heckman-Snyder estimation of the
ideal points ranged from 81% to 92%. Finally, the experiments are conducted
with 1000 roll calls.[25] This is roughly the number of actual roll
calls in recent Houses.[26]
For each set of experiments, we produced two
sets of estimates for ideal points using the Heckman-Snyder scaling method:
1. The
Snyder-Groseclose estimates using only roll calls with margins greater than
65-35.
2. “Naïve”
estimates using all the votes.[27]
Note
that the Heckman-Snyder method should estimate ideal points very close to the
true ideal points when the naïve model is used, because the Monte Carlo
experiments generate the artificial data from a preference-based voting model.
Each specification was run ten times, so
that 10,000 second-stage regressions were performed for each. In table A1, we present the percentage of
times the null hypothesis of no party voting [that is, b2=0
in equation (1)] was rejected at the 1% level (one-tail) using White’s heteroscedasticity-consistent standard
errors. Snyder and Groseclose also used
the 1% criterion and White’s standard errors, but whether the tests were
one-tailed or two-tailed is unclear.
That is, because preference-based voting generated the data, we expect
to find a “significant” b2
in only 1% of the simulated roll call votes.
The actual results are strikingly different.
The
extent of over-rejection for close roll
calls (column (d)) is enormous. Under the most favorable conditions, shown in the last three rows
of table A1 — large party overlap — the
Snyder-Groseclose model rejects the null at approximately the expected 1%
rate. However, in the least favorable
conditions[28] — less overlap and precise voting — shown in
the first row, the over-rejection rate is 73.1%.
The example
shown in figure 2 indicates that the naïve method should lead to lower levels
of rejection than the Snyder-Groseclose method because the better estimation of
ideal points using all votes will leave less room for the party dummy to act as
a proxy for the ideal points. This
intuition is borne out. In all of the 9
matches of cells in table A1, the rejection rate for close roll calls (column (f)) is lower using the naïve method than using the Snyder-Groseclose
method.[29] In the intermediate cases of rows 4-6 where
Snyder-Groseclose rejects over 5 times the expected rate, the naïve method
rejects at just about the expected rate.
One explanation
for the Snyder-Groseclose bias on close roll calls is that the ideal points are
recovered incorrectly as we argued with figure 2. Figure 2 was based on voting without errors. Errors in voting are not sufficient, even
with large numbers of roll calls, to permit accurate recovery of legislator
positions. Compare columns (i) and (j) of table A1. The
correlations for the middle sixth of the legislature are systematically less
using only close votes to estimate the ideal points than using all votes. That is, the effect we illustrated with
figure 2 occurs even when both error is present and the number of roll calls is
very large.
In many of our
simulations the Heckman-Snyder estimates contradict the assumption of the
underlying linear probability model. In
particular, many of the voting probabilities lie outside the [0,1]
interval. We indicate the percentage of
these probabilities in column (h) of
Table A.1. While it is true that the
over-rejection rate is increasing in the number of improper probabilities, the
variation in these proportions is too small to generate the large variation in
the over-rejection rates. Furthermore,
the percentage of extreme probabilities is approximately what one finds in
applications of the Snyder-Groseclose method to actual roll calls from the
House of Representatives.
At this point, the reader may have
noticed an apparent anomaly. Under the naïve model, we should expect to get
about 1% of the coefficients significant at the 1% level. The results are not too far off both for
lopsided votes (column (g)) and for
close votes (column (f)) where there
is considerable party overlap. On the
other hand, there are far too many significant coefficients for other close
votes, particularly those in the first rows of the tables, where there is
little overlap and only a small amount of randomness in voting.
There is an additional anomaly in our
Monte Carlo experiments. For lopsided
votes, both the näive and Snyder-Groseclose methods produce a large number of
statistically significant coefficients at the one-tailed 1% level, but with the
wrong sign.[30] Table A2 presents the percentage of “wrong”
coefficients for the experiments on 1000 vote legislatures. Note that the problem is worst for the naïve
model with little party overlap and lopsided votes.
Both of these anomalies arise because the
Snyder-Groseclose second stage provides biased estimates of the party effect, even when the ideal points have been
correctly estimated in the first stage.
The intuition for both anomalies is provided by considering the case of
a uniform distribution of ideal points on [-1,+1] with r = 0, no overlap.
Moreover, assume, errorless voting, that is, m = 0. (And continue to
assume no party pressure.)
Consider midpoints c in the interval [-1,+1]. A straightforward calculation shows that the
coefficient on the party dummy is given by b2
= -1 + 4|c| -3c2. Thus, b2
is -1 for c = 0, the quintessential
close 50-50 vote opposing Ds and Rs.
From equation (2), the estimate of the extent of party discipline is g = -1/0 = -¥. On the other hand we get a wrong sign with b2
= 1/4 for c = 1/2, that is, for a
lopsided 75-25 split. More generally,
the party coefficient is of the wrong sign for party-pressure voting when 1
> |c| > 1/3. Although the coefficient should always be
zero for preference-based voting, the coefficient is 0 only when the magnitude
of c is exactly 1/3. When the magnitude
of c is 1/3, we would get a 67-33
split. Like Snyder and Groseclose, we
chose 65-35, very close to 67-33, to differentiate lopsided from close
votes. The results in the tables,
“correct” signs for close votes when the true coefficient should be zero and
“wrong” signs for lopsided votes, conform to this theoretical analysis.
The theoretical example can be extended to
allow for both overlap in party ideal points and for errors in voting. We focus on c=0, or predicted 50-50 splits, since this is the situation where
Snyder and Groseclose expect the greatest party pressure. We begin by showing that allowing for overlap
does not eliminate bias.
Introduce
overlap in the party positions as follows.
Let the left-most 25% of the legislature, those with ideal points in
[–1, –½) be Democrats, the next 25% in [–½,0) be Republicans, then another 25%,
in [0, ½), be Democrats and the rightmost 25%, in [½,1] be Republicans. On average, the Democrats are still the
left, with a mean position of –¼ and the Republicans are at ¼. This is more overlap than appears in any
Congress in the last two decades.
For
this overlap case, the coefficient on the dummy is +6/13, showing an incorrect
sign when voting is purely preference based.
In
the no overlap example, the coefficient on the dummy was –1, indicating strong
party pressure when there was none.
Obviously, as the overlap increases the coefficient on the party dummy
increases. There is some amount of
overlap that will make the coefficient on the dummy 0, but this would be
knife-edge.
Does
error save the day? Yes and No. To see this, let the probability of voting
Yes be linear in the ideal point between –w,
+w, with
Prob(Yes vote|x£-w)
= 0
Prob(Yes
vote|-w<x<w) = .5+ x/(2w)
Prob(Yes vote|x³w) = 1.
Again
assume a uniform distribution of (or equally spaced) ideal points and a
legislature that is 50% D.
After
calculating the appropriate variances and covariances and then plugging into
the standard formula for the regression coefficient with two independent
variables, we can compute values for the coefficient in both the overlap and no
overlap cases. The results appear in
Table A3.
In
the no overlap case, we have a “correct” sign when the coefficient should be
zero. In the overlap case, we have a
“wrong” sign. The bias falls as the
amount of error increases. For w of 0.8
or 0.9, which correspond to the error levels likely to occur with actual data,
the bias is quite small. However, since
the expected value is not zero, there still should be a disproportionate number
of “significant” coefficients in reasonably large samples—such as the US House.
The
no overlap case is more disturbing, since the bias does not fall as fast. With w
of 0.8, the coefficient is -.04, which corresponds, in the example, to 2% of
the legislators being switched by non-existent pressures. Thus, for no overlap or very low levels of
overlap, one is quite likely to incorrectly conclude that there is some
pressure when none exists.
More
generally, the expected value of the party dummy coefficient, for a fixed
non-random distribution of true ideal points and party affiliations, is a
linear combination of the expected value of two covariances
The
linear coefficients depend on the variances of the ideal points and the party
dummy and their covariance. The
expected covariances depend on the error process, the distributions of the
dummy and the ideal points, and the true cutting line for the roll call. Therefore, the sign and magnitude of the
party dummy will depend in a complex way on both the distribution of ideal
points and the distribution of errors.
Only in special cases will the coefficient on the dummy have an
expectation of zero when voting is based solely on spatial preferences and
stochastic errors.
To illustrate how the patterns uncovered
in the Monte Carlo experiments reappear in actual voting data, we replicate the
analysis of Snyder and Groseclose for a number of Congresses.[31] Table A4 contains those results. In addition to the reported percentages of
significant party coefficients, we also report the percentage of “wrong signs”. Note that the pattern of the Monte Carlo
experiments is echoed in the actual data.
The number of “correct” significant coefficients is consistently higher
for the Snyder-Groseclose model than the naïve model, and the number of “wrong”
coefficients is higher for the naïve model.
The differences are most striking with respect to correct signs on close
votes. Parallel to the Monte Carlo
work, the Snyder-Groseclose method produces many more significant instances of
party discipline than does the naïve method.
In conclusion, our results demonstrate
that the Snyder-Groseclose technique is heavily biased toward rejecting the
null hypothesis of preference-based voting.
Even if Snyder and Groseclose were able to estimate ideal points
correctly in the first stage, they would get too many “significant”
coefficients with the correct sign in the second stage on close votes and too
many with the wrong sign on lopsided votes.
The bias arises because they use OLS in the second stage. The bias is attenuated and becomes
unimportant when there is a high degree of party overlap. Even when there is substantial party
overlap, however, the Snyder-Groseclose method is biased toward finding too
many “significant” coefficients because the first stage provides biased
estimates of ideal points.
Appendix C: Procedure for Computing the Difference in Cutpoint Ranks
We used the following procedure for
determining roll call cutpoints, classifying roll calls into the three
categories, and computing the differences in ranks:
1. Optimally
classify all legislators using a single cutpoint. Rank order the legislators from 1 to N, starting at the
left.
2. Estimate
the two cutpoint model for roll calls using the rank order of legislators from
step “1”. (Note that the estimation
must “maintain polarity”:
Classification is optimal subject to making the same prediction for Ds
and Rs to the left of their party’s cutpoint.)
3. Every
interior Democrat cutpoint must be between two Democratic legislators. Let their ranks be i and j. The rank of the roll call cutpoint is then
given as cD = (i+j)/2.
When the cutpoint is to the right of the rightmost Democrat, denote the
cutpoint by cD=dR=rank
of rightmost Democrat. When the
cutpoint is to the left of the leftmost Democrat, denote the cutpoint by
1. The Republicans are treated
similarly; when the cutpoints is to the left of the leftmost Republican, denote
the cutpoint by cR=rL=rank
of leftmost Republican, to the right of the rightmost Republican, denote the
cutpoint by N.
4. Score
the roll calls as follows:
a. If
cD=1 and cR>rL or if 1<cD<dR and cR>rL and cD < cR, score
the roll call D<R.
b. If
1<cD and cR<N and cD>cR, score
the roll call D>R.
c. Otherwise,
the roll call is “undecided”.
5. For
roll calls with interior cutpoints in both parties, the difference in ranks is cD-cR. Roll calls with one or more party cutpoints exterior
are excluded from the difference in ranks computations (figure 8). (Thus, more roll calls are included in the
ordinal comparisons under “4” above.)
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