CSSS/POLS 512:
Time Series and Panel Data
for the Social Sciences
Problem Set 3
Professor: Chris Adolph, Political Science and CSSS
Spring Quarter 2020
Due in class on Tuesday 26 May 2020
General instructions for homeworks: Homework can be handwritten or typed. For any
exercises done with R or other statistical packages, you should attach all code you have
written and all (interesting) output. Materials should be stapled together in order by
problem. The most readable and elegant format for homework answers incorporates
student comments, code, output, and graphics into a seamless narrative, as one would
see in a textbook. Working in groups on R code is allowed, but (1) each member of the
group must provide his or her own writeup and (2) you must list all members of your
group.
Problem 1: Analyzing partisan seat shares in US state legislatures
[100 points total.] In the last homework, we examined the dynamic relationship between
the number of seats held by Democrats in the US House of Representatives and
a set of political and economic variables testing the effect of election cycles, presidential
coattails, and judgment of the president’s economic performance on the size of the
Democratic majority. If we turn to American state legislatures, we can test similar
questions but with much more data.
1
We will restrict our scope in several ways to make the problem more manageable (a
more complete analysis might avoid these restrictions, but would require a more flexible
panel data model). First, we look only at legislatures elected in 1978 or later, up
through the 2016 elections. Second, we exclude South Carolina (for which some data
are missing), Nebraska (which has non-partisan legislative elections) as well as Alaska
and Hawaii. Third, we restrict our attention to the lower house of each state’s legislature
(typically known as the “House”). Fourth, we include only states that elect house
members to two-year terms, which excludes Alabama, Louisiana, Maryland, Mississippi,
and North Dakota. Finally, states vary in the year they hold gubernatorial elections,
but most hold them only in the sequence of years that runs 2010, 2014, 2018. . ..
We include only these states (note this means we also exclude New Hampshire and Vermont,
which hold gubernatorial elections in every even year). As a result, our scope
includes 28 states each observed for 20 lower house election cycles.
Because each state has a varying number of total house seats, in this analysis, we will
focus on the share of seats held by the Democrats. Following on our analysis in the last
homework, we consider three kinds of explanations for shifts in Democratic control.
Economic performance. When a state’s unemployment rate is higher than the long-term
national average on election day, it may hurt the electoral prospects legislators belonging
to the party in government – but for state legislative elections, which party is that?
The party of the governor or the party of the president?
Spillovers from votes for president, congress, or governor. Few voters pay close attention
to state legislative elections, so partisan swings in the state house may reflect spillovers
from votes on the presidential, congressional, or gubernatorial races. This could involve
presidential coattails – where a new party sweeps into the presidency and lower
offices at the same time. It could also take the form of “gubernatorial coattails” within
a state, whereby a new governor brings in a larger seat share for his party. Finally, just
as voters use congressional races to vote against the president during midterms, they
could use state house races in the same fashion.
Trends. American politics passed through a major re-alignment in the late twentieth
century as white voters in the South switched from solid support of the Democratic
Party to solid support of Republicans. This proceeded at different rates in different
states. Possibly in reaction to this and other socioeconomic trends, other regions may
be shifting in partisanship as well.
2
Variable Description
State Two letter state abbreviation
Statename Full state name
FIPS Unique numeric code for each state (non-consecutive)
Year Start year of the legislative session; duplicated as trend
GovCycle 1 indicates states that last held gubernatorial elections in 2014,
2 indicates 2015, 3 indicates 2016, 4 indicates 2017
HouseTerm The length in years of elected house terms
DemHouseShare Proportion of lower house seats held by Democrats [0, 1]
PartisanMidterm 1 for legislatures elected in midterms in which the Democrats
held the presidency, −1 for legislatures elected in midterms in
which there was a Republican president, and 0 for legislatures
elected in other years
PresUnem equal to the difference between this state’s election-year unemployment
and the national 1978–2016 average (5.97%) for legislatures
elected when a Democrat was president, and to −1× this
quantity for legislatures elected under Republican presidents
GovUnem equal to the difference between this state’s election-year unemployment
and the national 1978–2016 average (5.97%) for legislatures
elected when a Democrat was governor, and to −1× this
quantity for legislatures elected under Republican governors
PresCoattails 1 if the presidency shifted to the Democrats when this legislature
was elected, −1 if the presidency shifted to the Republicans, and
0 if the party of the president was unchanged
GovCoattails 1 if the governorship shifted to the Democrats when this legislature
was elected, −1 if the governorship shifted to the
Republicans, and 0 if the party of the governor was unchanged
Midwest Region dummy for the Midwest, broadly defined
West Region dummy for the West, broadly defined
Northeast Region dummy for the Northeast, broadly defined
South Region dummy for the South, broadly defined
Table 1. Codebook for State House Seats data. Data are in statehouse.csv, and are
taken from the Bureau of Labor Statistics (unemployment), the Book of States (legislative shares)
and Wikipedia (governors and cycles), or constructed from these data by your instructor & TA.
3
Throughout the homework, we will consider two basic specifications. In the first
specification, called M1, we control for midterm effects, presidential and gubernatorial
unemployment effects, and presidential and gubernatorial coattails.1
In the second
specification, called M2, we control for all these variables and region specific trends.2
In the file statehouse.csv, you will find the variables described in Table 1. Examine
the data file and note well the behavior of these variables over time. Then work through
the following exercises. This is potentially a long assignment with several tricky steps, so start
now, work in groups, and email the class and instructors often for advice. It’s okay to share as much
code as you like in seeking help – we’re all working together on this one!
a. [5 points.] Preprocess the data to remove unwanted states. Specifically, you
should create a new dataframe that removes all states that have a GovCycle other
than 1 or a HouseTerm other than 2. Confirm that you now have 28 states and 20
election cycles left in your dataset. Then, create the first four lags of the outcome
variable using lagpanel() in the simcf library.3
b. [15 points.] For each state left in the analysis, plot the time series DemHouseShare
and plot its ACF and PACF (there is no need to show these plots; please offer general
impressions). Perform augmented Dickey-Fuller and Phillips-Peron tests for
unit roots for each time series and examine their distribution using histograms.
Finally, conduct two Im-Pesaran-Shin panel unit root tests of DemHouseShare, assuming
fixed intercepts and trends, respectively. Sample code for the first test is
given by:
ts <- with(statehouse,
data.frame(split(DemHouseShare, as.character(State))))
purtest(ts, pmax = 4, exo = "intercept", test = "ips")
Describe your findings, being sure to describe what kind(s) of time series process
may be at work.
1 The specific variables to be control are thus PartisanMidterm, PresUnem, GovUnem, PresCoattails,
and GovCoattails.
2 To add region specific trends, you could include the following terms in a model specification:
trend:South, trend:Midwest, trend:Northeast, and trend:West. Note that in a model without
state fixed effects, you should also control for the regions themselves (why can’t you do this in
a fixed effect model?).
3 I recommend naming these lags DemHouseShareL1, DemHouseShareL2, etc.
4
c. [10 points.] Fit M1 using a model that treats the intercept as a state random
effect. To deal with the dynamic nature of the outcome, consider and estimate
a variety of ARMA(p,q) specifications.4 Using the insights gleaned from part b.
and goodness of fit tests, select the best model of the time series and call this the
“best RE model for M1.”
d. [10 points.] Fit M2 using a model that treats the intercept as a state random
effect. To deal with the dynamic nature of the outcome, consider and estimate
a variety of ARMA(p,q) specifications. Using the insights gleaned from part b.
and goodness of fit tests, select the best model of the time series and call this the
“best RE model for M2.”
e. [10 points.] Fit M1 using a model that treats the intercept as a state fixed effect.
To deal with the dynamic nature of the outcome, consider controlling for one
or more lags of the outcome variable.5 Using the insights gleaned from part b.,
goodness of fit tests, , and tests of serial correlation, select the best model of the
time series and call this the “best FE model for M1.”
f. [10 points.] Fit M2 using a model that treats the intercept as a state fixed effect.
To deal with the dynamic nature of the outcome, consider controlling for one
or more lags of the outcome variable. Using the insights gleaned from part b.,
goodness of fit tests, and tests of serial correlation, select the best model of the
time series and call this the “best FE model for M2.”
g. [30 points.] Using each of four “best” models, forecast what will happen to
the size of the Democratic majority in the average state in the 2019 and 2021
sessions for the following single scenario. Assume the Democrats resume this
state’s governorship in 2019 and the presidency in 2021, and compute appropriate
counterfactual values of PartisanMidterm, PresCoattails, GovCoattails. Assume
unemployment falls to 3.6% for both elections and construct PresUnem and
GovUnem accordingly. Set all trend variables at the average value they will take
across regions in 2019 and 2021, respectively. Make appropriate assumptions for
the prior value(s) of the outcome variable (e.g., the average Democratic House
share in 2017).
4 For this problem and the next, I recommend you use lme in the nlme package for estimation.
5 For this problem and the next, I recommend you use plm in the plm package for estimation and
the lags premade using lagpanel as controls.
5
For each model, report or graph the predicted Democratic majority and its 95%
confidence (or predictive) interval for the 2019 and 2021 sessions. Describe the
substantive impact of your forecast results in as much detail as you feel comfortable,
as well as how much confidence we should have in the forecasts. Be sure to
consider the scale of the outcome variable in assessing what counts as a substantively
large or small change.
NB: As a check on your work, report the table of counterfactual covariate values
you used to make your forecasts. Be very careful when constructing these values
to capture to logic of the covariates; each one is tricky in its own way. To carry
out the forecasts, use the simcf library’s ldvsimev(), pay close attention to the
example code, and think through all modifications you need to make.
h. [10 points.] Using everything you have learned in this assignment and in the
course, which of the four best models should we use to write-up our results,
and why? (You may argue for multiple models if you think that’s appropriate.)
What are your final substantive conclusions? Substantively, does it make much
difference which model we choose? How does this affect the way you would
write this analysis up in a paper?
There’s a lot we’ve left out to make this analysis managable: panel-corrected standard errors, crossvalidation
tests of fit, efficient presentation of the full model results through simulation, and so on.
Projects using panel data are oftencomplex, with many modelingchoices and opportunities to exploit
the model to answer substantive and statistical questions. This assignment is just a start. . .