An Event History Analysis of the
Supreme Court’s Work in the 1948-2010 Terms
(version 3.7)
Mintao Nie
Eric N. Waltenburg
William P. McLauchlan
Purdue University
Abstract: What explains the variation in the amount of time it takes the U.S. Supreme Court to
process (i.e., terminate) a case appealed to it? We hypothesize that the Court’s processing time is
a function of case characteristics and institutional features, Using event history analysis to model
the hazard rate of all paid petitions made to the Court between 1948 and 2010 in six different
issues areas, we find case complexity, case salience, and docket size affect processing time in
theoretically consistent ways. However, we find no evidence of the effect of ideological
heterogeneity among the justices on the Court’s processing time.
Paper prepared for presentation at the 2014 annual meetings of the Western Political Science
Association, Seattle, WA.
An Event History Analysis of the
Supreme Court’s Work in the 1946-2010 Terms
The Supreme Court’s work has attracted the attention of scholars for some time. To a
substantial degree, the focus of this attention has been the substantive decisions the Court
reaches. Some attention, however, has also been paid to the amount of work the Court handles
and the time involved in completing that work – i.e., screening the 1000s of appeals and petitions
made to it each term and then rendering substantive decisions on those few cases the Court
decides to decide (for example, Frankfurter and Landis 1928; McLauchlan and Waltenburg
Forthcoming). Some of these latter analyses, while documenting the Court’s workload, are
largely prescriptive in nature.
The research we report here explores and explains the time it takes for the Court to process
its workload. Now, understanding this aspect of the Supreme Court’s work is of no small
consequence. To the Court, possessing neither the purse nor the sword, its legitimacy is of
profound importance; and two pillars of an institution’s legitimacy are procedural fairness and
efficiency (Weatherford 1992). Thus, how the Court processes its workload affects its precious
store of institutional credibility. To begin, potential litigants might be discouraged from seeking
resolution in the Court if the perception takes root that it is unable to dispose of their cases in a
timely manner, and this may disproportionately affect certain types of litigants. After all, some
litigants (e.g., most individuals) are less able to wait (more or less patiently) for the Court to
process its business. As a result, these litigants may be especially discouraged from locating their
efforts in the Court, and the Court, therefore, effectively becomes closed to them as a venue in
which to pursue their policy goals. Procedural fairness requires that “access to decisional arenas
is open and equal” (Weatherford 1992, 150); but according to these potential litigants’
perceptions, the Court, as a decisional arena, is not equally open to them.
Second and relatedly, if the Court is perceived as inefficient and incapable of performing its
job – i.e., of processing its workload in a timely manner – it will likely see its institutional
credibility erode. This “keeping the trains running on time” aspect of political legitimacy taps
evaluations of an institution’s policy outputs. Inefficient institutions produce less satisfactory
policy outputs, outputs that the mass public is less likely to accept or tolerate. And since the
Court is a reactive institution, efficient, timely outputs may be even more consequential to it.
2
Indeed, although it is well worn, the expression justice delayed is justice denied is not
threadbare. Untoward delays can have a deleterious effect. Simply put, if delays become so
common that they are expected, the Court’s capacity to persuade individuals to accept or tolerate
unpopular policies may well be degraded. After all, if the Court’s decision on a controversial
policy is so removed in time from the policy’s initial implementation that the mass public has
accommodated itself to the policy, the Court’s decision is all but irrelevant. It is a bit like
shutting the barn door after the horse has bolted.
What, then, affects the Court’s processing time? Theoretically, we expect that the amount of
time it takes for the Court to process its workload is a function of inputs and institutional
features. We test this expectation by examining the amount of time it takes for the Court to fully
process any paid appeal (i.e., the number of days elapsed between the filing for a writ of
certiorari and that appeal’s final disposition) filed with it between 1948 and 2010 in six different
issue areas (n = 7314). Using event history analysis, we find evidence that supports our
expectations. Both case and institutional characteristics affect the Court’s processing time in a
manner consistent with our theory.
We present and discuss these results in section 3, which follows a description of our data and
methodology (section 2). We conclude in section 4 by taking stock of our findings and offering
suggestions for future research. But first we turn to the identification of forces we expect are
related to the amount of time it takes for the Court to screen cases and then render final judgment
on those very few it deems worthy of its full attention.
I. Toward an Explanation of Supreme Court Processing Time
The Court disposes of its work in a two-stage process. First it screens cases, deciding which
cases warrant its full attention (ds). The vast bulk of cases that come to the Court do not clear
this first stage. The Court rejects between 85 and 99 percent of the fillings presented to it for
decision.1 Those very few cases that are accepted for review are then decided on the merits.
These cases will have additional periods of time in the system. There is the period between the
screening decision and the conduct of oral argument (dp). Finally there is a period of time after
1
The difference in the proportion accepted for decision on the merits is based on whether the cases include the in
forma pauperis petitions or just the paid filings. The Court accepts a much higher proportion of the paid cases than
the unpaid cases. This study examines only the paid filings.
3
oral argument while the members of the Court prepare (majority, concurring, or dissenting)
opinions in the cases after the Court reaches its decision on the merits (do).
As a result of these phased steps in the process, the total time a case is before the Court (Dt)
is represented by this simple function:
𝐷𝑡 = 𝑑𝑠 + 𝑑𝑝 + 𝑑𝑜
Each of these components is a period of time rather than a point in time. So each component can
be analyzed separately or in total. In the analysis that follows, we examine separately the
screening time (ds) and the amount of time between oral argument and the Court’s
announcement of its merits decision (do).2
Although there is a large body of literature on the Court’s decisional processes at these two
stages, there is very little existing research on the amount of time it takes for the Supreme Court
to arrive at these decisions (ds) and (do). There are several studies, however, that examine the
efficiencies and processing time at other levels of courts in the United States (see, for example,
Heise 2000; Christensen and Szmer 2011; Szmer, Christensen, and Kuershen 2012; Goelzhauser
2012; Cauthen and Latzer 2008). This research suggests that case and institutional characteristics
will affect the amount of time it will take for the Supreme Court to dispose of an appeal.
Among the key features of a case are its legal complexity, whether it is salient, and the nature
of the litigants. Complex cases involve multiple legal issues and questions. They permit the
justices greater freedom to pursue their policy preferences because these cases do not have clear
legal provisions that guide their resolution (Baum 1997, 66). Complex cases, thus, might present
just the type of legal controversies the Supreme Court is predisposed to hear. Thus, they may
effectively be “fast tracked” onto the Court’s docket. We hypothesize, therefore, that complex
cases will spend less time at the screening stage (ds). Complexity, however, might have just the
opposite effect at the merits stage. There is a greater likelihood of disagreement among the
justices on complex cases, which would extend the amount of time it takes for the Court to arrive
2
Thus, the analysis of the cases decided on the merits does not include the dp period. The reason for that is that this
period of time is determined by the scheduling of due dates for briefs and oral argument. The Court does not
consider a case during this period at all, since the materials have not been filed or are being considered individually
by the justices in preparation for oral argument on each case. As a result, the analysis of these cases will be based
on: 𝐷𝑡 = 𝑑𝑠 + 𝑑𝑜
4
at a decision and dispose of them (do). Accordingly, we expect that complex cases would take
longer for the Court to process and reach its final decision on the merits.
We expect that the effect of case salience on processing time will be similar at both stages of
the Court’s decisional process. Bartels (2011), for example, has shown that the justices are more
apt to engage in ideological voting in salient, high visibility cases (see also Christensen and
Szmer 2011). Like complexity, then, salience engenders disagreement among the justices.
Accommodation of different legal positions in written opinions and cobbling together or
maintaining a majority coalition takes time. Thus, we hypothesize that salient cases take longer
to process at the merits stage (do).
Salient cases, however, might be more rapidly screened (and docketed). Caldeira and Wright
(1988) have demonstrated that the Court seeks to decide cases with broad social, economic, or
political consequence – i.e., salient cases. When a case attracts broad public attention and/or is
expected to have substantial impact is appealed to the Court, it seems unlikely that the Court will
find itself spending much time deciding to decide that case. We hypothesize, therefore, that
salient cases are screened more rapidly (ds).
If the United States is a party to the appeal, the amount of time it takes for the Court to
process the case might be affected at either stage. At the screening stage, the U.S. as a party is
strong indication of the case’s consequence. We know from the docketing literature that when
the federal government is the petitioning party, the Court is significantly more likely to grant the
appeal (see, for example, Tanenhaus et al. 1963; Caldeira and Wright 1988). Thus, we expect
that screening time will be shortened when the U.S. is present on the appeal (ds).
By the same token, the federal government is unlikely to be a party to a legally “simple”
case. It is more likely that complexity is a common characteristic to these cases, and we
hypothesize that the United States as a party will increase the amount of time it takes for the
Court to reach a merits decision (do).
Along with the inputs of the cases and their characteristics giving shape to the Court’s
workload, we expect that the Court’s own institutional features affect its capacity to process this
workload as well. First, the size of the Court’s docket, particularly the incidence of cases carried
over from previous terms should affect the Court’s processing time (see Christensen and Szmer
2011; Szmer et al. 2012; Cauthen and Latzer 2008). Cases awaiting resolution require resources
5
and time that might be spent on processing new cases. We hypothesize, therefore, that the greater
the number of cases carried over from previous terms, the longer it will take the Court to process
cases at both the screening and merits stages (ds) and (do).
There were two events that relate to Supreme Court processing cases. These might affect the
time it takes the Court to screen or decide cases. First, in 1972, the Court established the Cert
Pool. This involves rotating several law clerks through the process of reading and preparing Pool
Memos on all the case filings for a period of time (O'Brien 2014). These memos are distributed
to the members of the pool as a shorthand method for each of the justice’s chambers to assess
whether to explore the petition more closely. This replaced the prior practice of each justice’s
chambers processing all the Cert Petitions by whatever procedure each justice established. The
intended effect of this change was to reduce the amount of time it takes the Court to screen cases
(ds). So this event, even though all nine justices did not participate in the pool, provides a
demarcation that might be reflected in shortened screening time.
A second event was the enactment of the Supreme Court Case Selections Act in 1988 (102
Stat. 662; codified in 28 U.S.C. § 1257.) This statute removed the Court’s appellate jurisdiction
as a matter of right. This made the discretionary Writ of Certiorari the only avenue of appeal to
the Court. The purpose of this statute was to reduce the waiting time between screening and oral
argument, and thus to speed up the entire decisional process for those cases that the Court
decided to review on the merits. As a result we might expect that the processing time for
Supreme Court cases, decided on the merits, to be decided more quickly than before the
enactment of the statute. Thus, after the start of the 1988 Term the cases decided on the merits
might take less time than before this event (do). This assumes that the Court’s screening of the
entire set of paid cases using Certiorari will take less time than if the paid cases are divided into
two sets, those with mandatory review (Appeal) and those governing by Court decisions
(Certiorari). This assumption may not be correct. So we cannot predict (hypothesize) whether the
change in jurisdiction will speed up, slow down, or have no effect on screening time.
Finally, the diversity of the Court, its ideological heterogeneity, may affect the amount of
time it takes to process a case. Diverse Courts are more likely to have difficulty arriving at
collective decisions (Christensen and Szmer 2011; Szmer et al. 2012; Cauthen and Latzer 2008).
6
This should extend the amount of time it takes for the Court to arrive at a majority opinion (do),
but the effect of diversity also might be felt at the screening stage (ds).
II. Data and Methodology
The Data
We put these hypotheses to the test by examining the Court’s processing time with respect to
the paid appeals in six categories of cases – abortion, antitrust, apportionment, environmental
law, preemption, and eminent domain/takings. As we discuss in greater detail below, some of
these hypotheses will be tested on the universe of paid filings between the 1948 and 2010 terms
of the Court in these categories (n = 7314). Because of data limitations, however, other
hypotheses will only be tested on the subset of appeals for which the Court granted review on the
merits. The decision to concentrate on the processing time associated with cases involving these
particular issue areas ensures that we have measures of the amount of time it takes for the Court
to process its workload on cases that exhibit certain archetypical features with respect to
doctrinal development, the demand for adjudication, and broader societal or political
controversy.
Abortion and apportionment first appeared on the Court’s docket during the 63 terms
analyzed here. Thus, they represent the emergence and development of new doctrines. They also
concern highly politicized issue domains. The politics of abortion, for example, are never far
below the surface of national elections, and the constitutional foundation of abortion has become
a constant in the drama surrounding Court nominations and confirmations,3 with politicians and
interest groups alike using the confirmation battles as opportunities to propagandize for resources
and support. Apportionment cases touch politics at perhaps its most basic level – partisan
electoral advantage. Of additional analytical value, the apportionment cases would demand the
Court’s attention in a predictable, cyclical pattern, as the reapportionment following each
decennial census would trigger legal challenges.
While abortion and apportionment concern new and developing business for the Court,
antitrust and eminent domain cases represent well-developed fields of the law. Certainly by the
3
Indeed, John Paul Stevens was the last justice to be confirmed to the Supreme Court (1975) without being queried
about abortion.
7
mid-twentieth century there could be a nearly constant flow of work brought to the Court
involving these issues. Fluctuations in these filings might occur because of changes in Supreme
Court doctrine on either issue. Some variation might well occur because of external factors such
as presidential administration changes in anti-trust policy objectives.
Environmental cases represent another feature of the Court’s workload. A wave of new,
complicated statutes enacted largely between the 1960s and 1990s created a demand for
adjudication as the Court was asked to construe and clarify these statutes and their operation.
These cases, which also begin partway through the period explored here, are prompted by the
enactment of statutes rather than the development of Supreme Court doctrine, as was the case
with abortion and apportionment cases.
Finally, the preemption cases do not fall into a single substantive category. Rather, they
represent a large range of different types of cases, each varying with the specific federal statute
raising the question of federal preemption. Early preemption cases related to whether federal
labor relations statutes preempted state employment statutes. However, later the doctrines that
presented preemption cases expanded a great dal to a widely diverse set of substantive issues that
generated a preemption question for the Court. It might well be that this category of issue
generates the most diverse and varied set of petitions to the Court.
Operationalizations
One set of key covariates related to case features in this study includes case complexity, case
salience, and the United States as a party to the appeal. The other set of covariates concerning
institutional features of the Court includes the heterogeneity of the Court’s membership, the size
of the Court’s docket, the proportion of carried over cases, and two dummies for the year of 1972
when the Court established the Cert Pool and for the year of 1988 when the Supreme Court Case
Selections Act was enacted.
For the case complexity score, we conducted a principal factor analysis on the number of
issues, the number of legal provisions, and the number of opinions present for each case and then
generated a factor score to index the complexity score for each case (McLauchlan and
Waltenburg Forthcoming, n. 13; Wahlbeck, Spriggs II, and Maltman 1998). Larger factor scores
indicate higher degrees of case complexity. We used the Epstein and Segal (2000) New York
Times measure to operationalize case salience. Cases that were reported on the front page of the
8
New York Times take the value of 1. Finally, we measure the presence of the United States as a
party to the case with a simple a dummy variable, equaling 1 for yes, 0 otherwise.
Our measure of the Court’s heterogeneity is the standard deviation of the Judicial Common
Space Score for each term of the Court between 1948 and 2010 (Epstein et al. 2007). Larger
heterogeneity scores for a given term indicate greater diversity among the justices’ ideology for
that term. The docket size measures the amount of paid appeals for a given term. Finally,
proportion of carried over cases is simply the percentage of cases carried over for each term of
the Court from 1948 to 2010. Table 1 reports descriptive statistics for the covariates used in the
models estimated below.
[Insert Table 1 about here]
Figure 1 displays the Kaplan-Meier survival curves for two subsets of the data relative to
each of the six types of case. Each graph in the figure shows the survival rates for those cases
that were screened out at the certiorari stage and those that were chosen for decisions on the
merits. For abortion, antitrust, and preemption cases, both the log-rank test statistics and the
Wilcoxon test statistics show a significant difference in survival functions between screened-in
cases and screened-out cases (Cleves et al. 2010; Manjtel and Haenszel 1959; Breslow 1970;
Gehan 1965). However, for apportionment, environment, and eminent domain cases, there is
little difference between the time for screening those selected for decision and those denied
certiorari. Moreover, it might be relevant to note that the time at which the survival curves
intersect the 0.5 line in these figures is the point when half the cases have been screened. This is
indicated by the median screening time displayed in Table 1.
[Insert Figure 1 about here.]
Table 2 reports descriptive statistics for screening time (ds) and merits decision time (do).
The median duration of screening days for all cases as well as the subset of docketed cases is
about three months. So is the median duration of merits decisions for docketed cases. Among the
six types of cases, there are discrepancies in terms of the Court’s processing time at the screening
stage and the merits stage. When examining the median duration of screening in the full sample,
Table 1 shows it takes the Court a couple of weeks longer to screen environmental and
apportionment cases than the average duration. The median duration of screening for eminent
domain cases, however, is about a week shorter than the average duration. We observe similar
phenomena in the subset of docketed cases. For the median duration of merits decision, it takes
9
the Court a substantially longer time, 160 days, to render a final decision on abortion cases. For
other categories of cases, the amount of days from oral argument to the Court’s decision on the
merits varies from 77 days to 99 days.
[Insert Table 2 about here.]
Model Specification: Event History Analysis
In this study, we analyze the dynamics underlying the duration of the Court’s processing
time with respect to docketing decision and merits decision. We use event history analysis to
study how case attributes and institutional attributes of the Court affect the duration of screening
(ds) and the duration of merits decision (do) (Box-Steffensmeier and Jones 2004, 1997). Event
history analysis models the hazard rate or the transition rate at which observations change their
state, or experience a critical event by t, given that the observation under study has not changed
its state before t (Box-Steffensmeier and Jones 2004, 12-15; Blossfeld, Golsch, and Rohwer
2007, 31-34). At the screening stage, the Court considers all paid appeals and makes the decision
to review a case on its merits or not. Hence, all paid appeals experience a change in their state at
the stage of screening; that is, a case is either screened-in or screened-out. Screened-in, or
docketed cases subsequently move along to the merits decision state. Docketed cases no longer
stay in the Court system after the Court renders a final decision.
As to statistical modeling, we employ the Cox proportional hazard model, a semiparametric method, to estimate the effects of hypothesized covariates on the Court’s processing
time of paid appeals (Cox 1972). Although there are parametric alternatives to the Cox model,
one advantage of the Cox model is that it leaves the distribution of the baseline hazard function
unspecified (Box-Steffensmeier and Jones 2004, 88). In spite of that, the Cox model assumes
that the effect of a covariate is constant over time. Grambsch and Therneau’s global proportional
hazards test statistic and Harrell’s rho statistic are appropriate tests of the proportional hazards
assumption. If the proportional hazards assumption is violated, interaction terms of the covariates
with a measure of time should be added into the model to account for the nonproportional effects
on the hazard rate (Box-Steffensmeier and Zorn 2001, 979; Box-Steffensmeier and Jones 2004,
131-37; Grambsch and Therneau 1994; Harrell 1986).
In addition to the proportional hazards assumption underlying the Cox proportional
model, another important feature of the data set that requires attention when it comes to
10
statistical modeling is the non-random selection of cases filed with the Court. Specifically, the
data set under analysis is a cluster sample in which cases falling into our pre-defined six
categories were selected. As we have discussed above, we believe that the cases we collected
optimally represent the population of all the cases filed with the Court, but we are uncertain that
the characteristics of the cases in our data set identically mirror population characteristics.
Though we take into consideration two attributes at the case-type level, we believe that there are
still some unobserved or unknown characteristics for which we have not accounted. Failing to
account for clustering or heterogeneity in the observed failure times at the level of the type of
case will produce incorrect estimates of covariate effects (Hanagal 2011, 73-76).
In event history analysis, the shared frailty model is often used to model unobserved
variability in the failure times at the group level (Hanagal 2011, 73-76; Gutierrez 2002; Clayton
1978; Vaupel, Manton, and Stallard 1979). “Shared frailty” is a term used to represent an
unobservable random effect that “describes excess risk or frailty” shared by distinct groups of
observations (Hanagal 2011, 71-74; Gutierrez 2002, 23). That being said, we assume that cases
in the same type are more similar than cases in other types. For semi-parametric modeling of
event history, the Cox shared frailty model is used to account for within-group correlations
(Cleves et al. 2010, 156-61). Different from the standard Cox proportional hazard model, the
Cox shared frailty model estimates the effects of covariates conditional on the frailty at the group
level. The latter also uses a penalized likelihood approach to test unobserved frailty shared across
groups of observations, that is, to test whether the variance component θ is statistically different
from zero.
Here, we use the following stepwise approach to build multivariate models regarding the
Court’s screening time (ds) and merits decision time (do) of paid appeals. We first specify a
standard Cox model. We then test the proportional hazard assumption by examining the
Grambsch and Therneau’s global test statistic and the Harrell’s rho statistic. If the proportional
hazard assumption is not satisfied, we interact relevant covariates with log-analysis time – i.e.,
ln(t). The advantage of choosing ln(t) over t is that the effects of time-varying variables have a
natural interpretation as those of time-constant variables (Box-Steffensmeier and Zorn 2001,
983).
Building on the standard Cox model that accommodates possible time-varying effects of
covariates, we add a shared frailty component to account for intra-case-type correlation. If there
11
is no unobserved heterogeneity across case types, the Cox shared frailty model reduces to the
standard Cox model. The Cox shared frailty model can be written as:
hij(t)=h0(t)wiexp(βxij)
where i indicates case type (i=1,…, 6)
j indicates individual paid appeals (j=1,…, ni).
h0(t) is the baseline hazard function.
x is a vector of covariates that are hypothesized to affect the duration of screening (ds)
and the duration of merits decision (do).
β is a vector of regression coefficients corresponding to the set of covariates.
wi is the case type-level frailty terms.
The frailty terms are assumed to have a gamma distribution with mean 1 and variance θ. If there
is strong evidence showing that θ significantly deviates from zero, we conclude that substantial,
unobserved heterogeneity exists across case types.
Because our research interest concerns two time intervals of the Court’s processing time,
we fit both the standard Cox model and the Cox shared frailty models for both outcome
variables. Specifically, Model 1 takes into consideration both screened-in and screened-out cases
and estimates the effects of docket size, the proportion of carried over cases, the heterogeneity of
the Court’s membership, and both year dummies on the duration of screening (ds). To examine
the effects of case features on the duration of screening (ds), in Model 2, we restrict our analysis
to the subset of docketed cases. For Model 2, we add case complexity, case salience, and the
U.S. government as a party variables to the covariates included in Model 1. In Model 3, the
outcome variable is the duration of merits decision (do). In this model, we analyze the effects of
case attributes including case complexity, case salience, and the U.S. government as a party as
well as the Court attributes of docket size, the proportion of carried over cases, the Court’s
heterogeneity, and the 1988 dummy variable. We also include an interaction term of the Court’s
heterogeneity and case complexity. Finally, in all three models, covariates whose effects vary
across time are interacted with log-duration. We use Stata 13 to conduct all the statistical
analyses and to plot quantities of interests.
12
III. Empirical Results
As we have discussed in the last section, before we include time-varying covariates, we
use the Grambsch and Therneau’s test to examine the proportional hazard assumption. We
interact covariates with potential, nonproportional effects with log-duration and add these
interaction terms when fitting the Cox models. Table 3 presents Harrell’s rho statistics and the
Grambsch and Therneau’s statistics for the proportional hazard tests. ρ, the Harrell’s rho statistic,
reports “the estimated correlation between the scaled residuals and log-duration for each
independent variables while χ2 and p-values indicate the confidence with which we can reject the
null hypothesis that the hazard ratios for different values of that covariate are constant over time”
(Box-Steffensmeier and Zorn 2001, 980).
[Insert Table 3 about here.]
For Model 1, we find evidence of nonproportionality for the year 1972 dummy variable
at the conventional .05 level. The global test statistic (χ2 = 112.66, p < .001) also confirms that
the proportional hazard assumption is violated. We therefore interact the 1972 year dummy with
ln(t). We do not find any evidence showing the proportional hazard assumption is violated in
Model 2. For Model 3, test results show that the effects of case complexity, docket size, and the
year 1988 dummy are not constant as their values change. Thus, we interact these three
covariates with ln(t) in the Cox models we estimate below.
Because we suspect that there is unobserved heterogeneity across different types of cases,
we estimate shared frailty models, adding a shared frailty term based on the standard Cox model
to account for intra-case type correlation. Table 4 reports the regression coefficients of the Cox
shared frailty model as well as the standard Cox model. The interpretation of the regression
coefficients in the standard Cox model is straightforward. Positive coefficients indicate an
increased hazard rate or a shorter duration of processing time, while negative coefficients imply
a decreased hazard rate or a longer duration of processing time.
[Insert Table 4 about here.]
To facilitate the interpretation of the effect of covariates, we will also discuss hazard
ratios. Hazard ratios are exponentiated values of estimated regression coefficients. Hazard ratios
that are greater than one indicate an increased hazard rate or shorter duration of processing time,
while hazard ratios that are smaller than one imply a decreased hazard rate or longer duration of
processing time. In the Cox shared frailty model, the interpretation of the size of covariate effects
13
is the same as that in the standard Cox model except that the effects of covariates in the former
are conditional on the frailty. That being said, the effects of covariates in the Cox shared frailty
model are estimated controlling for intra-case type correlation.
The interpretation of the effect of a covariate with time-varying effect is less
straightforward because its effect on the hazard rate depends on both the time-constant
component and the time-varying component. To estimate the time-varying effect of a covariate
x, Golub (2007; Golub and Steunenberg 2007; Licht 2011) constructs the following equation of
hazard ratio in which observations i and j differ in values of x:
hi
( x -x )( b̂ +b̂ ln(t ))
=e i j 1 2
hj
When discussing the effect of a covariate with time-varying effect, if its time-varying component
is statistically significant, we can conclude that its main effect either increases or decreases over
the time interval under analysis. More precisely, a positive direction of the time-varying
component indicates an increasing rate of the time-constant effect over time, while a negative
direction of the time-varying component implies a waning rate of the time-constant effect over
time.
For Model 1, we choose the Cox shared frailty model over the standard Cox model
because we find evidence of unobserved heterogeneity across types of cases; we reject the null
hypothesis that θ = 0 at the .05 level (θ = .010, p < .001). The regression results of the Cox
shared frailty model estimation show that in the full sample docket size positively affects the
duration of screening (ds) (coefficient = -.452, p < .001). With a one-unit increase in docket size,
the conditional hazard rate decreases by 36% (hazard ratio = exp(-.452) = .64; 1 - .64 = .36). In
other words, as the Court’s docket size increases by one unit from term to term, paid appeals that
have not been screened are 36% less likely to be decided the next day. To put it simply, it takes
the Court a longer time to make a decision at the screening stage when the size of its docket is
larger.
The establishment of the Cert Pool is positively associated with the duration of screening
(ds) at the initial screening stage (coefficient = -3.272, p < .001). The conditional hazard rate of
the post-1971 cases is about 96% smaller than that of pre-1971 cases at the initial screening stage
(hazard ratio = exp(-3.272) = .04; 1 - .04 = .96). However, as Figure 2 displays, this negative
effect gradually increases and becomes positive at a later period in our analysis (coefficient =
14
.746, p < .001). Substantively, the establishment of the Cert Pool lengthens the screening time at
the beginning of the screening stage, but it eventually generates the desired effect. This finding
implies that it took some time for the Court to implement and accommodate itself to that change
in its procedures and therefore for the altered procedure to have the intended effect.
[Insert Figure 2 about here]
The enactment of the Supreme Court Case Selections Act in 1988 is negatively associated
with the duration of screening (ds) (coefficient = .317, p < .001). The conditional hazard rate of
the post-1987 cases is about 37% higher than that of the pre-1987 cases (hazard ratio = exp(.317)
= 1.37; 1.37 - 1 = .37). In other words, the enactment of the Act shortens the Court’s screening
time by 37% (ds). It is not exactly clear what the expected result of this change would be either
in screening time or in decisional time. There might be explanations for either result, but it
appears that after the enactment of the statute, the Court screened cases at a more rapid rate than
it did when it had mandatory (Appeal) jurisdiction over some of its appeals.
The variance component of the frailty term embedded in the Cox shared frailty model is
statistically different from zero (θ =.010, p < .05), indicating the existence of unobserved, casetype level risk factors that increase the hazard rate. Figure 3 displays the predicted frailties (viz.,
log frailties) or random effects for each type of case. Types of cases with positive frailties are
more likely to experience a shorter duration of processing time, whereas those with negative
frailties are more likely to experience a longer duration of processing time (Box-Steffensmeier,
De Boef, and Joyce 2007, 252). In terms of the amount of days it takes for the Court to make a
decision at the screening stage, apportionment cases are the least frail and eminent domain cases
are the most frail (see Figure 3). In other words, ceteris paribus, it takes the Court more days to
make a certiorari decision on apportionment cases than on other types of cases in our data. But
when it comes to eminent domain cases, the Court is much quicker. Indeed, the Court screens
these cases faster than any other type of case in our data set. Similar to apportionment cases, the
Court spends more time screening preemption, environment, and abortion cases. Antitrust cases,
however, have a positive frailty, and thus, the Court spends less time screening them.
[Insert Figure 3 about here]
For Model 2, we find that the proportional hazard assumption is satisfied in the standard
Cox model. In this instance, the shared frailty Cox model reduces to the standard Cox model, and
the estimates of the shared frailty Cox model are the same as the standard Cox model estimates.
15
In Model 2, only docket size has a statistically significant effect on the duration of screening
(ds). Specifically, a one-unit increase in docket size results in a 52% drop in the conditional
hazard rate (hazard ratio = exp(-.725) = .48 ; 1- .48 = .52). Simply put, a larger docket size for a
given term increases the Court’s processing time at the screening stage.
The effect of the U.S. government as a party to the appeal is positively associated with
the hazard rate at the screening stage (coefficient = .202, p < .05). Cases with the U.S.
government as a party are 22% more likely to be acted on from one day to the next at the
screening stage (hazard ratio = exp(.202) = 1.22; 1.22 – 1 = .22). This result is consistent with
our hypothesis that the U.S. government’s involvement in a case speeds up the screening time
because the U.S. government as a party to the appeal strongly indicates the cases’ consequence.
The two event covariates, that is, the establishment of the Cert Pool and the enactment of the
Supreme Court Case Selections Act, no longer have statistically significant effects on the
duration of screening (ds).
As to modeling the effects of case and Court attributes on the duration of the merits
decision, we use the Cox shared frailty model because the frailty term is statistically different
from zero (θ =.033, p < .001). In Model 3, we find evidence for significant, effects of case
complexity, case salience, and docket size on the number of days it takes for the Court to decide
on the merits after oral argument. Specifically, case complexity has a strong negative effect on
the conditional hazard rate of being decided on the merits at the initial stage (coefficient = 2.626, p < .001). Controlling for other covariates, a one-unit increase in case complexity results
in about a 93% decrease in the hazard rate at the initial stage (hazard ratio=exp(-2.626) = .07; 1.07 = .93). To put is concretely, more complex cases prolong the duration required for the Court
to reach a merits decision. The time-varying coefficient of case complexity is positive
(coefficient = .425, p < .001), suggesting that the effect of case complexity on the conditional
hazard rate increases across the time interval (see Figure 4). The effect of case complexity,
however, becomes insignificant after about four months.
[Insert Figure 4 here]
For salient cases, the hazard rate of the merits decision, given a level of frailty,
decreases by 21% (coefficient = -.232, p < .001; hazard ratio=exp(-.232) = .79, 1-.79=.21). This
indicates that salient cases are 21% less likely to be granted a final decision at a certain point
16
across the time interval. In other words, on average, the days spent by the Court at the stage of
merits decision for salient cases are 21% more than those for non-salient cases.
The negative effect of docket size on the conditional hazard rate of being decided on the
merits is surprisingly high (coefficient = -6.187, p < .001). Controlling for other covariates, a
one-unit increase in docket size reduces the conditional hazard rate of the merits decision by
99.8% at the initial stage (hazard ratio = exp(-6.187) = .002, 1-.002 = .998). In other words, at
the initial stage of the merits decision, it takes the Court a much longer time to render a final
decision when it faces a large bulk of paid appeals for a given term. Moreover, the time-varying
coefficient of docket size is positive and statistically significant (coefficient = 1.288, p < .001),
suggesting that the effect of docket size on the duration of merits decision decreases over time.
Unlike case complexity, case salience, and docket size, the enactment of the Supreme
Court Case Selections Act is positively associated with the hazard rate of the merits decision
(coefficient = 2.731, p < .001). This suggests after the passage of the Act, the Court renders a
final decision more quickly at the initial stage. If we pool all the docketed cases together, the
post-1987 cases that have not been rendered a final decision by the Court have fifteen times the
chance of being decided on the merits the next day at the initial stage compared to the pre-1988
cases (hazard ratio = exp(2.731) = 15.35). However, the main effect of the enactment of the Act
wanes as time goes by and becomes insignificant after 91 days following the date of oral
argument (see Figure 5).
[Insert Figure 5 here]
The 1988 change in Court jurisdiction has a momentary but statistically significant effect
on the Court’s decision time (do). The intended effect of the statute, however, was focused on the
earlier stages in the Court’s process (ds and dp). The effect of this change on ds is reported in
Model 1 (Table 4), and that effect was salutary. The duration time for screening after the
enactment was lower than before. At the time of the statute’s adoption, it was also expected to
have a positive impact on the time from screening to oral argument (dp). The effect of the statute
on this feature of processing time is beyond the scope of this research but that is worth some
future exploration.
Concerning the random effects of case types when we analyze the determinants of the
duration of merits decision, we find evidence of case type-level heterogeneity (θ = .033, p <
.001). With respect to the number of days from oral argument to merits decision, all other things
17
being equal, abortion cases are the least frail and preemption cases are the most frail (see Figure
3). It takes for the Court more days to reach a final decision regarding abortion and
apportionment cases but fewer days regarding cases of preemption, antitrust, environment and
eminent domain.
[Insert Figure 6 here]
IV. Conclusions
What affects the amount of time it takes for the U.S. Supreme Court to process (i.e.,
terminate) a petition that has arrived at its doors? We hypothesized that a combination of case
and Court characteristics affect the speed with which a petition moves through the Court’s
workload process. By and large, our hypotheses were supported in the event history model we
estimated. Case characteristics such as complexity and salience and institutional features dealing
with the processing demands placed on the Court and mechanisms it has adopted to meet those
demands were shown to have their anticipated effects.
At the screening stage, a busier Court is a slower Court, all other things being equal.
When case characteristics measuring complexity, salience, and the U.S. government as a party
were not included in the model, we also found that that Cert Pool and the Case Selections Act
affected screening time duration. The desired effect of the Cert Pool (speeding up the screening
process), however, was not immediate. Indeed, it took some time before this procedure began to
reduce the screening time duration, suggesting there was an “institutional” learning curve
involved. When we added case characteristics to the screening model, only the Court’s crush of
business maintained statistical traction, We found that the U.S. government as a party to the
petition also affected screening time, significantly reducing the amount of time it takes for the
Court to screen the petition. At the merits stage, we again found – not surprisingly, to be sure –
that a busier Court takes longer to render a decision. We also found that complex and salient
cases take longer for the Court to process.
Perhaps the most surprising result is the insignificant effect of Court heterogeneity. An
ideologically divided Court does not appear to increase the amount of time necessary to reach a
decision on the merits. (Court heterogeneity also had an insignificant effect at the screening
stage.) This suggests the justices effectively are acting as “nine little law firms” (O'Brien 2014).
They talk about the case in conference, vote, and retire to their respective chambers to write
18
various opinions. Apparently, little time is invested among the justices in an effort to build a
larger majority. An ostensible advantage of a collegial Court and a decision process requiring
majorities is that the extreme edges in an opinion would be sanded off during the majoritybuilding process, but our results suggest that kind of carpentry work is not going on.
Finally, we should point out what this analysis does not address. We do not report on
whether the Court is processing its workload too slowly or too fast. Nor do we have a benchmark
to determine whether the Court has become more or less efficient across the sixty-odd terms
under analysis. We do have indications of what forces affect the Court’s processing time and
how they affect it. Consequently, interested actors could try to adjust these forces in an effort to
address the Court’s ability to process its work if it were determined there was a problem in need
of resolution. At the same time, however, there is probably little that could be done regarding
these forces. Salience and complexity are two of the most consequential, but by its nature, the
Court is expected to hear and decide complex and salient cases. Controlling the processing
demands made on the Court (i.e., the incidence of petitions made to it) is probably impracticable
as well. As we noted earlier, a crucial aspect of an institution’s legitimacy is access to it
(Weatherford 1992). To narrow access to the Court, therefore, would degrade its institutional
legitimacy. But with neither the purse nor the sword, the Court’s reservoir of diffuse support is
its one essential resource.
19
Table and Figures
Table 1. Descriptive Statistics
Duration of Screening, All Cases
N
7314
7314
7314
7314
7314
7314
Mean
100.15
8.43
.18
2.23
.80
.46
S.D.
71.20
.47
.04
.32
.40
.50
Min
1
7.07
.10
1.17
0
0
Max
937
9.09
.28
3.10
1
1
Duration of Screening, Docketed Cases
N
Screening days
985
Case complexity
985
Case salience
985
U.S. government
985
Size of Docket
985
Proportion of carried over cases
985
Heterogeneity
985
Year 1972
985
Year 1988
985
Mean
111.55
.03
.19
.16
8.22
.19
2.21
.67
.28
S.D.
77.64
.85
.39
.37
.52
.04
.36
.47
.45
Min
1
-1.56
0
0
7.07
.10
1.17
0
0
Max
574
4.57
1
1
9.09
.28
3.10
1
1
Screening days
Size of Docket
Proportion of carried over cases
Heterogeneity
Year 1972
Year 1988
Duration of Merits Decision, Docketed Cases
N
Mean
S.D.
Min
Max
Merits decision days
1007
92.62
50.72
2
477
Case complexity
1007
.02
.84
-1.56
4.57
Case salience
1007
.19
.39
0
1
U.S. government
1007
.16
.37
0
1
Size of Docket
1007
8.22
.53
7.07
9.09
Proportion of carried over cases
1007
.18
.04
.10
.28
Heterogeneity
1007
2.20
.36
1.17
3.10
Year 1988
1007
.29
.45
0
1
Notes: The score for the size of docket is the logarithm value of the amount of paid appeals for a
given term. Descriptive statistics for covariates are limited to those observations without missing
values on the covariates that we include in the corresponding models.
20
Table 2. Durations of Screening and Merits Decision
Screening Days, All Cases
All
Abortion
Cases
N
7314
269
Mean
100.1
102.8
Median
81
84
IQR
55
61
Apportionment
AntiTrust
2399
95.7
76
53
Environmental
Preemption
1187
105.1
96
54
1761
108.5
83
61
Screening Days, Docketed Cases
All
Abortion Apportionment
Cases
N
985
43
92
Mean
111.6
118.5
119.8
Median
88
89
96
IQR
73
75
83.5
AntiTrust
317
106.5
80
62
Environmental
Preemption
150
110.4
97
64
278
120.2
95
92
Screening Days, Screened Out Cases
All
Abortion Apportionment
Cases
N
6288
220
166
Mean
98.2
97.9
115.6
Median
80
83
87
IQR
51
57
78
AntiTrust
2064
93.8
75
49
Environmental
Preemption
1035
104.7
95
53
1471
105.8
82
55
259
116.1
90
80
Eminent
Domain
1439
90.0
75
48
Eminent
Domain
105
95.5
76
37
Eminent
Domain
1332
89.4
75
48.5
Merits Decision Days, Docketed Cases
All
Abortion Apportionment
AntiEnvironmental
Preemption
Eminent
Cases
Trust
Domain
N
1007
43
94
333
151
279
107
Mean
92.6
138.2
114.4
85.3
98.8
85.7
87.2
Median
83
160
98.5
77
96
78
76
IQR
58
113
70
53
53
51
51
Note: Descriptive statistics for durations of screening and merits decision are limited to those
observations without missing values on covariates that we include in corresponding models.
21
Table 3. Test Results of Proportional Hazard Assumption
ρ
Case complexity
Case salience
U.S. government
Size of docket
Proportion of
carried over cases
Heterogeneity
Year 1972
Year 1988
Model 1
χ2
p-value
ρ
Model 2
χ2
.016
.004
1.85
.12
.174
.731
-.013
.044
.031
.047
-.031
.14
1.92
.99
2.08
.94
pvalue
.706
.166
.320
.149
.333
.010
.045
.007
.77
14.56
.36
.381
.000
.551
-.009
.014
-.034
.08
.19
1.08
.773
.664
.300
ρ
Model 3
χ2
p-value
.093
.035
.045
.211
-.040
10.95
1.27
2.08
42.61
1.67
.001
.260
.150
.000
.197
-.003
-.115
.01
12.20
.938
.001
Global Test
112.66
.000
14.62
.067
80.71
.000
Note: Test statistics for individual variables are generated from the Harrell (1986) correlation test.
Global test statistics are generated from the Grambsch and Therneau’s (1994) global test.
22
Table 4. Estimated Coefficients By the Standard Cox Model (SCM) and the Cox Shared
Frailty Model (CSFM)
Model 1:
Duration of Screening, All
Cases
SCM
CSFM
Time-Constant Covariates
Case Attributes
Case complexity
Case salience
Party Characteristic
U.S. Government
Court Attributes
Size of Docket
Proportion of Carried-Over Cases
Heterogeneity
Year 1972
Year 1988
-.479***
(.064)
.497
(.518)
-.007
(.048)
-3.314***
(.258)
.304***
(.055)
-.452***
(.064)
.594
(.520)
-.008
(.048)
-3.272***
(.259)
.317***
(.055)
Model 2:
Duration of Screening,
Docketed Cases
SCM
CSFM
-.014
(.036)
-.058
(.084)
-.014
(.036)
-.058
(.084)
-2.544***
(.539)
-.341***
(.085)
-2.626***
(.538)
-.232**
(.088)
.202**
(.088)
.202**
(.088)
.051
(.086)
.054
(.089)
-.725***
(.181)
1.065
(1.384)
-.128
(.137)
.030
(.132)
.240
(.156)
-.725***
(.181)
1.065
(1.384)
-.128
(.137)
.030
(.132)
.240
(.156)
-6.249***
(.712)
.601
(1.398)
-.180
(.137)
-6.187***
(.711)
.664
(1.418)
-.155
(.139)
2.959***
(.873)
2.731**
(.875)
.225
(.152)
.228
(.152)
.403***
(.093)
1.298***
(.162)
.425***
(.093)
1.288***
(.162)
-.597**
(.193)
-.545**
(.194)
Interaction Term
Case complexity x Heterogeneity
Time-Varying Covariates
Case complexity x ln(t)
Size of Docket x ln(t)
Year 1972 x ln(t)
.751***
(.058)
.746***
(.058)
Year 1988 x ln(t)
Random Effect
θ (Shared frailty Parameter)
Model 3:
Duration of Merits
Decision
SCM
CSFM
.010***
(.007)
.000
(.000)
.033**
(.027)
Number of observations
7314
7314
985
985
1007
1007
Number of failures
7314
7314
985
985
1007
1007
Log-Likelihood
-57677.85
-57653.92
-5768.30
-5768.30
-5876.20
-5871.80
Notes: Positive coefficients indicate shorter duration of processing time while negative coefficients indicate longer duration of processing
time.
Standard errors are in parentheses.
*p < .10, ** p < .05, *** p < .001
23
Figure 1. Kaplan-Meir Survival Estimates, Duration of Screening for Six Case types.
Note: The log-rank test (Manjtel and Haenszel 1959) and the Wilcoxon test (Breslow 1970;
Gehan 1965) show a significant difference in survival functions between screened-in and
screened-out cases for the abortion, antitrust, and preemption case types. However, no statistical
evidence shows this difference for the apportionment, environment, and eminent domain case
types.
24
Figure 2. Effect of the Establishment of the Cert Pool on the Duration of Screening, Model
1
Note: Thick line depicts the combined coefficient with respect to the establishment of the Cert
Pool on the duration of screening. Thin lines represent 95% confidence intervals.
25
Figure 3. Frailty Effects, Duration of Screening, Model 1
26
Figure 4. Effect of Case Complexity, Model 3
Note: Thick lines depict the combined coefficients of case salience scores at the 25%, 50%, and
75% percentiles as compared to the minimum value of case complexity score. Thin lines
represent 95% confidence intervals.
27
Figure 5. Effect of the Enactment of the Supreme Court Case Selections Act, Model 3
Note: Thick line depicts the combined coefficient of the effect of the Enactment of the Supreme
Court Case Selections Act. Thin lines represent 95% confidence intervals.
28
Figure 6. Random Effect, Duration of Merits Decision, Model 3
29
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