A L ander-Based Forecast of the 2021 German Bundestag Election
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POLITICS SYMPOSIUM
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A Länder-Based Forecast of the 2021
German Bundestag Election
Mark A. Kayser, Hertie School, Berlin
Arndt Leininger, Chemnitz University of Technology
Anastasiia Vlasenko, Florida State University
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P
olls are poor predictors when elections are dis- provides a way to diminish the importance of one of the most
tant. Too few voters are paying attention and too difficult parts of polling: predicting who will actually vote.
much can change before Election Day. In con- Structural models also offer other advantages. Although
trast, some aspects of elections—most important, they often are less accurate than polls, especially close to an
voters’ responses to fundamentals such as the election, they can establish baseline expectations about elec-
economy and the prime minister’s time in office—are quite tion outcomes if average candidates with average campaigns
reliable (albeit incomplete) predictors of voter behavior. Struc- and average opponents were competing under the current
tural models based on such fundamentals rely on data col- conditions of the fundamentals. In multiparty elections, in
lected long before the election. They can provide informed which there are rarely single-party majority winners, figuring
forecasts of electoral outcomes long before vote-intention out the appropriate benchmark to assess which parties did well
polls become reliable predictors of election outcomes. How- or poorly is difficult. Comparing parties’ vote shares to pre-
ever, due to the limited number of postwar national elections dictions from a structural model run on data from past elec-
in most democracies, structural models tend to suffer from tions is one way to determine which parties fared better than
small samples and high uncertainty in their estimates. expected.
We present a forecast of the 2021 German Bundestag Our Länder model leverages economic and political data as
election results for individual parties designed to draw on well as state-parliament (Landtag) election results in the
the strengths of both structural models and polls while side- German states to predict party vote shares in the Länder in
stepping some of their shortcomings. We address the small- the federal election. We then use official information on the
sample problem of structural models by predicting federal- number of eligible voters and predicted turnout figures to
election vote shares in the 16 German states (i.e., Länder) in all calculate vote totals for each party in each state (Land), and
elections since 1961 as a function of Länder election outcomes then we aggregate to the national level by summing over state
and other political and economic variables before aggregating vote totals per party and dividing all by the estimated number
to the national level. Länder elections are distributed non- of votes nationwide. The staggered timing of Länder elections
synchronously over the German electoral calendar and there- between federal elections helps to pick up new events in the
fore pick up different shocks as well as actual voter prefer- data but also means that older elections, having been con-
ences. Moreover, our linear random-effects model can capture ducted in different circumstances, are less informative. To take
state-level variation in responsiveness to the covariates. Add- this concern into account, we estimate an unweighted and a
ing information on the number of eligible voters and estimates weighted version of our model—for the latter, when estimating
of state-level turnout, we turn state-level vote shares into vote the model, we weigh more heavily those states that held state
totals, which we then aggregate to generate our national-level elections closer to the upcoming national election.
forecast. In a final step, we combine the predictions from our In addition to testing how predictive Länder elections are of
structural model with polling data using a weighted average federal-election results and setting expectations for which
that increasingly favors polls as the election nears. The weight outcomes should be expected in the current conditions, this
assigned to the polls relative to the structural forecast is based article contributes in another way to the forecasting literature.
on the predictiveness of polls at different time periods in We demonstrate the value of fitting models on subnational
previous elections. units during national elections to overcome the small-sample
Vote-intention polls, of course, are more than random problems common to national-level structural models. Fore-
samples of voters. Every poll must predict which respondents cast models for Brazil (Turgeon and Rennó 2012), Turkey
will actually turn out to vote on Election Day, based on voter (Toros 2012), and Lithuania (Jastramskis 2012) used subna-
screens or likely voter models, while also confronting other tional elections to increase the number of observations.
human sources of polling errors such as desirability bias and Scholars also have created state-by-state forecasts of US presi-
changed opinions. Polls, on average, are fairly accurate shortly dential elections using state-level covariates (Enns and
before an election but combining them with structural models Lagodny 2021; Jérôme and Jérôme-Speziari 2012; Klarner
based on Länder-level elections with actual voting behavior 2012). Our contribution is unique in that it uses state elections
© The Author(s), 2021. Published by Cambridge University Press on behalf of the
doi:10.1017/S1049096521000974 American Political Science Association. PS • 2021 1...............................................................................................................................................................................................................................................
Politics Symposium: Forecasting the 2021 German Elections
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to predict federal-election outcomes in those same states, an accuracy and confirm the value of our model as a long-term
approach afforded by the fact that German state elections predictor.
provide fairly independent observations due to their staggered To forecast the 2021 election, we updated our dataset of
timing. state-level returns for all national and state elections since 1961
We, of course, are not the first to develop a forecasting by adding the results of the 2017 national election and all state
model for Germany. Several models relying on predictors from elections since then. This provides us with a panel dataset in
chancellor approval (Norpoth and Gschwend 2010) to grand- which a party’s result in a federal election in one of the
We address the small-sample problem of structural models by predicting federal-
election vote shares in the 16 German states (i.e., Länder).
coalition participation (Jérôme, Jérôme- Speziari, and Lewis- 16 German states forms the unit of analysis.3 4 This is an
Beck 2013) to economic growth relative to neighboring coun- unbalanced panel because not all parties campaigned in all
tries (Kayser and Leininger 2016) have preceded us, as elections in all states and because Eastern German states are
reviewed in part by Graefe (2015). To this list, we add elections included only since 1990. We focus on the Christian Demo-
to state legislatures as a predictor of federal-election outcomes cratic Union/Christian Social Union (CDU/CSU), the Social
in the same states. Democratic Party (SPD), the Green Party, the AfD, the Free
We have shown in the previous iteration of this forecast Democratic Party (FDP), the Left Party/Party of Democratic
(Kayser and Leininger 2017, table 3) that aggregation of sub- Socialism, and the residual category “Others.” Unlike our
national predictions reduces forecasting error. No less signifi- forecast in 2017, when we had to subsume Germany’s new
cant, this iteration allows us to test, ceteris paribus, not only populist right party AfD among the residual category Others,
how predictive state elections are of later federal elections but the AfD now has participated in sufficient elections for us to
also whether and when our model improves on polling pre- include it as a distinct party. To predict the vote shares for the
Our Länder model leverages economic and political data as well as state-parliament
(Landtag) election results in the German states to predict party vote shares in the
Länder in the federal election.
dictions. After aggregating up to the national level, we com- current set of parties, we estimate a linear random-effects
bine the predicted vote shares from our structural model with model, including random intercepts for states and parties.
polling data that are weighted more heavily over time.1 After Our model uses variables for a party’s vote share obtained
the federal election, we will be able to compare the predictive in the previous federal election, the vote share it obtained in
accuracy of simple poll aggregates to polls combined with our the preceding state election, whether the chancellor was from
model at various times. that party at the time of the election, quarterly growth in gross
Our model follows the same specification as our model for domestic product (GDP), an interaction of these two variables,
the 2017 election (Kayser and Leininger 2017).2 In 2017, our the number of years the chancellor has been in office, and an
final structural model—estimated four months before the interaction of that variable with the chancellor’s-party dummy
election—performed adequately if not entirely accurately, con- variable. The estimation equation for our model is as follows:
sidering the time to the election and the fact that the Alterna-
tive for Germany (AfD) party had not participated in sufficient votenational
p,s,t ¼ β0 þ u0p,s þ β1 votenational state
p,s,t−1 þ ðβ 2 þ u2s Þvotep,s,t þ … þ ϵ p,s,t
elections to be included as a separate category. Before the
election, several state-election results showed a surge of sup- The variable reporting a party’s vote share in the previous
port for the AfD that we could not fully pick up because we had national election allows us to form a baseline prediction. The
to include the AfD in the “Others” category. Our predictions other predictors then estimate changes from the previous vote
deviated from the final election result by an average of 3.1% share. We also include the vote share that a party obtained in
points. This compares unfavorably to the final pre-election the preceding state election. State-specific issues are of great
polls of the major German polling houses that were off by an importance in these contests, and there often are substantial
average of 1.1% points, but the polls had the advantage of being differences between a party’s national and state results. Never-
conducted shortly before the election. Polling at the time of theless, politicians and political observers consider vote shares
our final forecast in May deviated from the final results in in state elections a “thermometer” for the popularity of the
September by an average of 3.7% points. This year’s model national government and the national opposition parties. This
includes a separate category for the AfD that may improve interpretation also is shared by political scientists who
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observed that electoral politics in Western European states with weights that weigh observations representing states with
have become increasingly nationalized (Caramani and Koll- state elections closer to the federal election more heavily to
man 2017). pick up late-developing events.5 We also estimate a version of
We include a dummy variable that indicates whether the the unweighted model that omits the vote share in state
current chancellor was from the given party. Furthermore, we elections (column 2) to illustrate that including this predictor
incorporate the growth rate of GDP in the quarter preceding improves the accuracy of the model.
the election, relative to the same quarter of the previous year, All coefficients show the predicted direction of effect.
seasonally adjusted. We assume that growth, rather than Unsurprisingly, there is persistence in a party’s vote share
media reporting about growth, directly affects voter decisions. over time. Election results in the preceding elections to the
Accordingly, we use the most recent growth-data vintage, state legislature also correlate positively with results in the
which might deviate from real-time reports that are covered federal elections in each state. The coefficient on GDP growth
more frequently in the media (Kayser and Leininger 2015). We depends on the status of a party. As expected, there is no
interact the growth rate with the chancellor’s-party dummy association between economic growth and a party’s vote share
variable because responsibility for the state of the economy is if the party does not lead the national government. If it does,
attributed primarily to the head of government’s party (Duch, however, we see the expected positive relationship. Similarly,
Przepiorka, and Stevenson 2015). We also include the number time in office (i.e., how long the current chancellor at the time
of years that the chancellor has been in office, interacting it of measurement has held the chancellorship) generally is not
with the chancellor’s-party dummy variable to capture cost-of- predictive of a party’s vote share except for the present chan-
ruling effects (Thesen, Mortensen, and Green-Pedersen 2020). cellor’s party. For the chancellor’s party, it displays a negative
Table 1 reports the coefficients on our covariates in a coefficient representing the well-known cost-of-ruling effect.
multilevel random coefficients model (i.e., parties in states) The estimates differ between the unweighted and the
with parties’ vote shares serving as the dependent variable. We weighted models because the latter puts greater weight on
estimate two models, an unweighted and a weighted version observations from states that had a state election close to the
(columns 1 and 3, respectively). The latter model is estimated national election. As a consequence, in the weighted model
Table 1
The Model
Unweighted Reduced Unweighted Weighted
(1) (2) (3)
Vote Sharet−1 0.507*** 0.942*** 0.266***
(0.027) (0.010) (0.025)
Vote Share in State Election 0.393*** 0.579***
(0.024) (0.024)
Chancellor’s Party 5.313*** 2.856*** 7.191***
(0.653) (0.693) (0.606)
GDP Growth 0.004 0.021 −0.014
(0.041) (0.044) (0.035)
Chancellor’s Party GDP Growth 0.237*** 0.052 0.321***
(0.091) (0.099) (0.079)
Years in Office 0.028 0.029 0.069**
(0.032) (0.033) (0.029)
Chancellor’s Party Years in Office −0.433*** −0.462*** −0.483***
(0.072) (0.076) (0.066)
Constant 0.970*** 0.675** 1.495***
(0.353) (0.327) (0.462)
N 971 971 971
Log Likelihood −2,675.908 −3,036.203 −2,864.560
AIC 5,377.816 6,090.405 5,755.119
BIC 5,441.234 6,135.116 5,818.537
Marginal R2 0.940 0.932 0.967
Conditional R2 0.944 0.932 0.988
Notes: *** p < 0.01; ** p < 0.05; * p < 0.1. Linear random effects. Standard errors in parentheses. *p < 0.05, ** p < 0.01, *** p < 0.001. DV is vote share in Länder elections.
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(compared to the unweighted model), the importance of pre- results in recent state elections, which is why our weighted
vious national results decreases vis-à-vis state elections as model predicts a higher vote share for it. However, the Green
evidenced by a decrease in the coefficient on Vote Sharet−1 Party often has done worse in elections than in polls taken
and a larger coefficient on Vote Share in State Election. weeks—sometimes even days—before an election. Our forecast
cautions that something similar might happen again.
THE FORECAST Relative to our structural forecasts, current polling (as of
Using the coefficients from the weighted and unweighted mid-June 2021) suggests significantly more support for the
models (see table 1, columns 1 and 3) and inserting the most Green Party (24.5% on average) and less support for the
recent quarterly 2021 values for our explanatory variables into CDU/CSU (24.9%) and SPD (15%). Polls, as snapshots in time,
the equations, we obtain predicted vote shares for each party can be considerably volatile. Our structural forecasts suggest
for each of the 16 German Länder for each of the models for the that, barring unusual events, vote intention for the Green
2021 federal election. To account for differences in the size of Party should decrease and should increase for the two Volk-
Accordingly, we calculate our final prediction, which we call our hybrid forecast, as a
weighted average of our structural Länder-model forecast and the polls.
the electorates and levels of turnout between states, we translate sparteien as time progresses and the adverse events of spring
the party-state vote shares in each state into vote totals by fade (i.e., the slow COVID-19 vaccine rollout, some MPs from
multiplying the number of eligible citizens in a state with the the CDU/CSU profiteering from sales of medical masks to the
estimated vote shares and the expected turnout. The latter is health ministry, and a power struggle within the CDU/CSU for
estimated in a separate model.6 We then sum these vote totals the chancellor candidacy).
across states within parties and transform them back into To the extent that polls are driven by current events
proportions to arrive at an estimate of the national vote share unlikely to influence an election many months in the future,
for each party. To incorporate the uncertainty stemming from there are good grounds to combine them with predictions from
the estimation of the vote shares and turnout, we simulate many a structural model that are less influenced by short-run con-
predictions from both models, merge them, and aggregate over ditions. Accordingly, we calculate our final prediction, which
the simulated data to provide 95% prediction intervals. we call our hybrid forecast, as a weighted average of our
We present our predictions in table 2. In both unweighted structural Länder-model forecast and the polls (Erikson and
and weighted models, the CDU/CSU retains its plurality but Wlezien 2014). Given that polls are only weakly predictive of
comes in at only approximately 30%. The other large catchall election outcomes five months out but become more strongly
party, the SPD (Volkspartei as it is called in Germany) receives predictive as the election approaches, we model the weighting
an even lower 20%, and the Green Party receives 12.8% and parameter to match the progression of polls’ predictive power
14.4% in the two models, respectively. The AfD and the FDP over the timeline of the election (Jennings and Wlezien 2016).7
both receive approximately 9% of the vote. The biggest differ- Figure 1 illustrates how the progressively higher weight
ence in the forecasts from the two models can be seen for the accorded to the polls shifts the hybrid forecast toward the
Green Party, which at the time of this writing is polling at polling numbers as the election approaches. The figure makes
above 20%, has consistently polled above its 2017 national- the additional assumption that polling numbers will remain
election results in recent years. This also is reflected in its unchanged because we have no way of knowing how they will
Table 2
Predictions for the Six Major Parties and a Residual Category (Others) from Models
Without (Column 2) and With (Column 3) Weights
Party Forecast Forecast (Weighted Model) Polling June 2021 Hybrid Forecast
CDU/CSU 30.3 [27.2, 33.5] 29.9 [27.8, 31.7] 27.9 29.1
SPD 20.2 [18.0, 22.7] 19.7 [18.6, 20.9] 15.4 17.8
Green Party 12.7 [10.4, 14.9] 14.3 [13.3, 15.4] 20.7 16.7
AfD 12.1 [9.9, 14.4] 11.8 [10.8, 12.9] 10.3 11.2
FDP 9.5 [7.1, 11.7] 8.9 [7.8, 10] 12.1 10.8
Left Party 8.7 [6.3, 11.2] 8.4 [7.2, 9.4] 7.1 7.9
Others 6.4 [4.0, 8.7] 7.0 [5.9, 8.1] 6.4 6.4
Notes: Simulation-based 95% prediction intervals are in square brackets. Column 4 reports an average of current polling at the time of this writing (June 22, 2021).
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Figure 1
Hybrid Forecast Timeline
30
Hybrid Forecast (%)
20 Party
CDU/CSU
Bündnis 90/Die Grünen
SPD
AfD
FDP
Die Linke
Others
10
0
22 June July August September 26 September
2021
Note: Hybrid forecast values showing convergence toward the (June) polls relative to the structural forecast values as weighting increasingly favors polls as the election
nears. The election will take place on September 26, 2021.
fluctuate and trend until September. In practice, of course, the to the total of durations over all states: we now use the observed maximum
(see also footnote 4). Replication materials are available on Harvard Data-
polling numbers will be different each time we update our verse (Kayser, Leininger, and Vlasenko 2021).
forecast. However, even shortly before the election, the structural 3. Conveniently, in the German electoral system, party’s field separate party lists
component will exert some influence and potentially improve on or each Land.
pure polling. For instance, our hybrid forecast for the Green 4. In the rare cases when a state election does not occur between two federal
elections, we impute the results from a state poll conducted at least six
Party shortly before the election will be somewhat lower than months before the federal election, if these data are available.
pure polling would predict, which is plausible because the Green 5. The weight is the inverse of the time between national and state elections
Party in past elections often has fared worse than even the final divided by the maximum observed time between national and state elections
in a given year.
pre-election polls would have predicted. This provides some
6. We use a random-effects model incorporating previous turnout, state-specific
optimism that our hybrid model might still outperform pure time trends, and state fixed effects to predict state-level turnout in 2021.
polling even when the election already is very close. 7. At the time of this writing, June 22, 2021, exactly 96 days prior to the election,
the weighting on the polls component is 0.56. Taking our cue from Jennings
and Wlezien (2016), who showed that predictive power of polls increases
CONCLUSION nearly linearly as an election draws nearer, we proceed linearly as well to give
By addressing the small-sample problem common to most polls progressively more weight until the weighting of the polls attains 0.9 on
the eve of the election.
structural models, our Länder model can more precisely esti-
mate the effects of fundamentals. Not only should this set
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