Polls are poor predictors when elections are distant. Too few voters are paying attention and too much can change before Election Day. In contrast, some aspects of elections—most important, voters’ responses to fundamentals such as the economy and the prime minister’s time in office—are quite reliable (albeit incomplete) predictors of voter behavior. Structural models based on such fundamentals rely on data collected long before the election. They can provide informed forecasts of electoral outcomes long before vote-intention polls become reliable predictors of election outcomes. However, due to the limited number of postwar national elections in most democracies, structural models tend to suffer from small samples and high uncertainty in their estimates.

We present a forecast of the 2021 German Bundestag election results for individual parties designed to draw on the strengths of both structural models and polls while sidestepping some of their shortcomings. We address the small-sample problem of structural models by predicting federal-election vote shares in the 16 German states (i.e., Länder) in all elections since 1961 as a function of Länder election outcomes and other political and economic variables before aggregating to the national level. Länder elections are distributed non-synchronously over the German electoral calendar and therefore pick up different shocks as well as actual voter preferences. Moreover, our linear random-effects model can capture state-level variation in responsiveness to the covariates. Adding information on the number of eligible voters and estimates of state-level turnout, we turn state-level vote shares into vote totals, which we then aggregate to generate our national-level forecast. In a final step, we combine the predictions from our structural model with polling data using a weighted average that increasingly favors polls as the election nears. The weight assigned to the polls relative to the structural forecast is based on the predictiveness of polls at different time periods in previous elections.

Vote-intention polls, of course, are more than random samples of voters. Every poll must predict which respondents will actually turn out to vote on Election Day, based on voter screens or likely voter models, while also confronting other human sources of polling errors such as desirability bias and changed opinions. Polls, on average, are fairly accurate shortly before an election but combining them with structural models based on Länder-level elections with actual voting behavior provides a way to diminish the importance of one of the most difficult parts of polling: predicting who will actually vote.

Structural models also offer other advantages. Although they often are less accurate than polls, especially close to an election, they can establish baseline expectations about election outcomes if average candidates with average campaigns and average opponents were competing under the current conditions of the fundamentals. In multiparty elections, in which there are rarely single-party majority winners, figuring out the appropriate benchmark to assess which parties did well or poorly is difficult. Comparing parties’ vote shares to predictions from a structural model run on data from past elections is one way to determine which parties fared better than expected.

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. We then use official information on the number of eligible voters and predicted turnout figures to calculate vote totals for each party in each state (Land), and then we aggregate to the national level by summing over state vote totals per party and dividing all by the estimated number of votes nationwide. The staggered timing of Länder elections between federal elections helps to pick up new events in the data but also means that older elections, having been conducted in different circumstances, are less informative. To take this concern into account, we estimate an unweighted and a weighted version of our model—for the latter, when estimating the model, we weigh more heavily those states that held state elections closer to the upcoming national election.

In addition to testing how predictive Länder elections are of federal-election results and setting expectations for which outcomes should be expected in the current conditions, this article contributes in another way to the forecasting literature. We demonstrate the value of fitting models on subnational units during national elections to overcome the small-sample problems common to national-level structural models. Forecast models for Brazil (Turgeon and Rennó Reference Turgeon and Rennó2012), Turkey (Toros Reference Toros2012), and Lithuania (Jastramskis Reference Jastramskis2012) used subnational elections to increase the number of observations. Scholars also have created state-by-state forecasts of US presidential elections using state-level covariates (Enns and Lagodny Reference Enns and Lagodny2021; Jérôme and Jérôme-Speziari Reference Jérôme and Jérôme-Speziari2012; Klarner Reference Klarner2012). Our contribution is unique in that it uses state elections to predict federal-election outcomes in those same states, an approach afforded by the fact that German state elections provide fairly independent observations due to their staggered timing.

We, of course, are not the first to develop a forecasting model for Germany. Several models relying on predictors from chancellor approval (Norpoth and Gschwend Reference Norpoth and Gschwend2010) to grand-coalition participation (Jérôme, Jérôme- Speziari, and Lewis-Beck Reference Jérôme, Jérôme-Speziari and Lewis-Beck2013) to economic growth relative to neighboring countries (Kayser and Leininger Reference Kayser and Leininger2016) have preceded us, as reviewed in part by Graefe (Reference Graefe2015). To this list, we add elections to state legislatures as a predictor of federal-election outcomes in the same states.

We have shown in the previous iteration of this forecast (Kayser and Leininger Reference Kayser and Leininger2017, table 3) that aggregation of subnational predictions reduces forecasting error. No less significant, this iteration allows us to test, ceteris paribus, not only how predictive state elections are of later federal elections but also whether and when our model improves on polling predictions. After aggregating up to the national level, we combine the predicted vote shares from our structural model with polling data that are weighted more heavily over time.Footnote ¹ After the federal election, we will be able to compare the predictive accuracy of simple poll aggregates to polls combined with our model at various times.

Our model follows the same specification as our model for the 2017 election (Kayser and Leininger Reference Kayser and Leininger2017).Footnote ² In 2017, our final structural model—estimated four months before the election—performed adequately if not entirely accurately, considering the time to the election and the fact that the Alternative for Germany (AfD) party had not participated in sufficient elections to be included as a separate category. Before the election, several state-election results showed a surge of support for the AfD that we could not fully pick up because we had to include the AfD in the “Others” category. Our predictions deviated from the final election result by an average of 3.1% points. This compares unfavorably to the final pre-election polls of the major German polling houses that were off by an average of 1.1% points, but the polls had the advantage of being conducted shortly before the election. Polling at the time of our final forecast in May deviated from the final results in September by an average of 3.7% points. This year’s model includes a separate category for the AfD that may improve accuracy and confirm the value of our model as a long-term predictor.

To forecast the 2021 election, we updated our dataset of state-level returns for all national and state elections since 1961 by adding the results of the 2017 national election and all state elections since then. This provides us with a panel dataset in which a party’s result in a federal election in one of the 16 German states forms the unit of analysis.Footnote ³ Footnote ⁴ This is an unbalanced panel because not all parties campaigned in all elections in all states and because Eastern German states are included only since 1990. We focus on the Christian Democratic Union/Christian Social Union (CDU/CSU), the Social Democratic Party (SPD), the Green Party, the AfD, the Free Democratic Party (FDP), the Left Party/Party of Democratic Socialism, and the residual category “Others.” Unlike our forecast in 2017, when we had to subsume Germany’s new populist right party AfD among the residual category Others, the AfD now has participated in sufficient elections for us to include it as a distinct party. To predict the vote shares for the current set of parties, we estimate a linear random-effects model, including random intercepts for states and parties.

Our model uses variables for a party’s vote share obtained in the previous federal election, the vote share it obtained in the preceding state election, whether the chancellor was from that party at the time of the election, quarterly growth in gross domestic product (GDP), an interaction of these two variables, the number of years the chancellor has been in office, and an interaction of that variable with the chancellor’s-party dummy variable. The estimation equation for our model is as follows:

$$ {vote}_{p,s,t}^{national}=\left({\beta}_0+{u}_{0p,s}\right)+{\beta}_1{vote}_{p,s,t-1}^{national}+\left({\beta}_2+{u}_{2s}\right){vote}_{p,s,t}^{state}+\dots +{\epsilon}_{p,s,t} $$

The variable reporting a party’s vote share in the previous national election allows us to form a baseline prediction. The other predictors then estimate changes from the previous vote share. We also include the vote share that a party obtained in the preceding state election. State-specific issues are of great importance in these contests, and there often are substantial differences between a party’s national and state results. Nevertheless, politicians and political observers consider vote shares in state elections a “thermometer” for the popularity of the national government and the national opposition parties. This interpretation also is shared by political scientists who observed that electoral politics in Western European states have become increasingly nationalized (Caramani and Kollman Reference Caramani and Kollman2017).

We include a dummy variable that indicates whether the current chancellor was from the given party. Furthermore, we incorporate the growth rate of GDP in the quarter preceding the election, relative to the same quarter of the previous year, seasonally adjusted. We assume that growth, rather than media reporting about growth, directly affects voter decisions. Accordingly, we use the most recent growth-data vintage, which might deviate from real-time reports that are covered more frequently in the media (Kayser and Leininger Reference Kayser and Leininger2015). We interact the growth rate with the chancellor’s-party dummy variable because responsibility for the state of the economy is attributed primarily to the head of government’s party (Duch, Przepiorka, and Stevenson Reference Duch, Przepiorka and Stevenson2015). We also include the number of years that the chancellor has been in office, interacting it with the chancellor’s-party dummy variable to capture cost-of-ruling effects (Thesen, Mortensen, and Green-Pedersen Reference Thesen, Mortensen and Green-Pedersen2020).

Table 1 reports the coefficients on our covariates in a multilevel random coefficients model (i.e., parties in states) with parties’ vote shares serving as the dependent variable. We estimate two models, an unweighted and a weighted version (columns 1 and 3, respectively). The latter model is estimated with weights that weigh observations representing states with state elections closer to the federal election more heavily to pick up late-developing events.Footnote ⁵ We also estimate a version of the unweighted model that omits the vote share in state elections (column 2) to illustrate that including this predictor improves the accuracy of the model.

Table 1 The Model

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.

All coefficients show the predicted direction of effect. Unsurprisingly, there is persistence in a party’s vote share over time. Election results in the preceding elections to the state legislature also correlate positively with results in the federal elections in each state. The coefficient on GDP growth depends on the status of a party. As expected, there is no association between economic growth and a party’s vote share if the party does not lead the national government. If it does, however, we see the expected positive relationship. Similarly, time in office (i.e., how long the current chancellor at the time of measurement has held the chancellorship) generally is not predictive of a party’s vote share except for the present chancellor’s party. For the chancellor’s party, it displays a negative coefficient representing the well-known cost-of-ruling effect.

The estimates differ between the unweighted and the weighted models because the latter puts greater weight on observations from states that had a state election close to the national election. As a consequence, in the weighted model (compared to the unweighted model), the importance of previous national results decreases vis-à-vis state elections as evidenced by a decrease in the coefficient on Vote Share _t−1 and a larger coefficient on Vote Share in State Election.

THE FORECAST

Using the coefficients from the weighted and unweighted models (see table 1, columns 1 and 3) and inserting the most recent quarterly 2021 values for our explanatory variables into the equations, we obtain predicted vote shares for each party for each of the 16 German Länder for each of the models for the 2021 federal election. To account for differences in the size of the electorates and levels of turnout between states, we translate the party-state vote shares in each state into vote totals by multiplying the number of eligible citizens in a state with the estimated vote shares and the expected turnout. The latter is estimated in a separate model.Footnote ⁶ We then sum these vote totals across states within parties and transform them back into proportions to arrive at an estimate of the national vote share for each party. To incorporate the uncertainty stemming from the estimation of the vote shares and turnout, we simulate many predictions from both models, merge them, and aggregate over the simulated data to provide 95% prediction intervals.

We present our predictions in table 2. In both unweighted and weighted models, the CDU/CSU retains its plurality but comes in at only approximately 30%. The other large catchall party, the SPD (Volkspartei as it is called in Germany) receives an even lower 20%, and the Green Party receives 12.8% and 14.4% in the two models, respectively. The AfD and the FDP both receive approximately 9% of the vote. The biggest difference in the forecasts from the two models can be seen for the Green Party, which at the time of this writing is polling at above 20%, has consistently polled above its 2017 national-election results in recent years. This also is reflected in its results in recent state elections, which is why our weighted model predicts a higher vote share for it. However, the Green Party often has done worse in elections than in polls taken weeks—sometimes even days—before an election. Our forecast cautions that something similar might happen again.

Table 2 Predictions for the Six Major Parties and a Residual Category (Others) from Models Without (Column 2) and With (Column 3) Weights

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).

Relative to our structural forecasts, current polling (as of mid-June 2021) suggests significantly more support for the Green Party (24.5% on average) and less support for the CDU/CSU (24.9%) and SPD (15%). Polls, as snapshots in time, can be considerably volatile. Our structural forecasts suggest that, barring unusual events, vote intention for the Green Party should decrease and should increase for the two Volksparteien as time progresses and the adverse events of spring fade (i.e., the slow COVID-19 vaccine rollout, some MPs from the CDU/CSU profiteering from sales of medical masks to the health ministry, and a power struggle within the CDU/CSU for the chancellor candidacy).

To the extent that polls are driven by current events unlikely to influence an election many months in the future, there are good grounds to combine them with predictions from a structural model that are less influenced by short-run conditions. 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 (Erikson and Wlezien Reference Erikson and Wlezien2014). Given that polls are only weakly predictive of election outcomes five months out but become more strongly predictive as the election approaches, we model the weighting parameter to match the progression of polls’ predictive power over the timeline of the election (Jennings and Wlezien Reference Jennings and Wlezien2016).Footnote ⁷

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.

Figure 1 illustrates how the progressively higher weight accorded to the polls shifts the hybrid forecast toward the polling numbers as the election approaches. The figure makes the additional assumption that polling numbers will remain unchanged because we have no way of knowing how they will fluctuate and trend until September. In practice, of course, the polling numbers will be different each time we update our forecast. However, even shortly before the election, the structural component will exert some influence and potentially improve on pure polling. For instance, our hybrid forecast for the Green Party shortly before the election will be somewhat lower than pure polling would predict, which is plausible because the Green Party in past elections often has fared worse than even the final pre-election polls would have predicted. This provides some optimism that our hybrid model might still outperform pure polling even when the election already is very close.

Figure 1 Hybrid Forecast Timeline

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.