2.1 Congress as a political network

Congress is often conceptualized as a network in which representatives form nodes connected by edges which quantify various measurements from vote to speech agreement. Congress consists of 435 (plus 6 non-voting) House representatives and 100 senators who constitute a relatively homogeneous group of individuals. They are educated similarly, elected comparably, and perform the same set of actions over an extended time span. Likewise, they frequently mention each other, refer to the same bills, utilize similar arguments, and are subject to the same institutional pressures (Evans, Reference Evans2018; Martin, Reference Martin2001). In short, Congress presents as a network with well-defined membership in which the interactions between members are of interest, comprising a network with an exogenous boundary (Butts, Reference Butts2008).

Indeed, many studies analyze various aspects of the interactions in U.S. Congress by viewing Congress as a network. Parigi and Bergemann (Reference Parigi and Bergemann2016), for example, study how co-residency affects voting behavior in the early Congress. Minozzi and Caldeira (Reference Minozzi and Caldeira2021) find that political leaning predicts how far representatives in the early House will live apart. Focusing on offices, Rogowski and Sinclair (Reference Rogowski and Sinclair2012) find no evidence of influence based on colocated offices in the contemporary House of Representatives. Finally, Box-Steffensmeier et al. (Reference Box-Steffensmeier, Christenson and Craig2019) explore lobbying in the House and use networks of groups in “Dear Colleague” letters to predict the probability of a bill passing.

These are all very tangible attributes to analyze Congressional behavior with. Researchers have also used political networks to study more abstract phenomena such as interpersonal influence over attitudes (Baldassarri and Bearman, Reference Baldassarri and Bearman2007), party polarization (Waugh et al., Reference Waugh, Pei, Fowler, Mucha and Porter2011), ideological polarization (Mepham et al., Reference Mepham, Vörös and Stadtfeld2025) in U.S. Congress and elsewhere (Lima et al., Reference Lima, Marques, Assis, Cardoso, Mikyška, De Mulatier, Paszynski, Krzhizhanovskaya, Dongarra and Sloot2023), or membership associations in the context of the U.S. Supreme Court (Box-Steffensmeier and Christenson, Reference Box-Steffensmeier and Christenson2015). The primary difference between all of these approaches is how they conceptualize connectedness in these networks, that is, how they operationalize the links within these networks. A natural choice is vote results (Waugh et al., Reference Waugh, Pei, Fowler, Mucha and Porter2011) or shared attributes (e.g., educational attainment or party affiliation, Mepham et al., Reference Mepham, Vörös and Stadtfeld2025). In these cases, edges between nodes indicate shared attributes or votes.

Indeed, the most crucial issue to solve when conceptualizing Congress as a political network is to choose an appropriate metric to define connectedness within this network. This paper is interested in measuring issue-level polarization, that is, polarization via issues discussed by the representatives. In order to properly construct Congress as a political network, the first step therefore consists of defining what an issue is, how representatives can be connected via issues, and what polarization based on issues might look like.

2.2 Discourse and economic policy talk in U.S. Congress

Most quantitative analyses of polarization in U.S. Congress rely on vote results. However, a central complicating factor when only considering vote data is that vote behavior is heavily influenced by the congressional parties (Cox and McCubbins, Reference Cox and McCubbins2005; Evans, Reference Evans2018). This means that vote-based polarization measures cannot disentangle the institutional influence of parties on the voting behavior of representatives (Krehbiel, Reference Krehbiel1993). Speeches, on the other hand, are protected by the first amendment and thus better suited to understand ideological polarization (Fernandes et al., Reference Fernandes, Debus and Bäck2021). More specifically, representatives use their floor speeches to utter dissent, even if they vote along party lines (Erz, Reference Erz2025a). For these reasons, this paper focuses on congressional floor speeches to measure issue-level polarization.

Congressional discourse is highly formalized (Amer, Reference Amer1993). This includes the procedures for allotting floor time to speakers, how representatives discuss, and the topics they talk about (see a comprehensive summary for the House of Representatives in Davis, Reference Davis2022). Unlike discourse on, e.g., social media, it exhibits a structured appearance, even on the Senate floor, despite the larger freedom that Senators have in their speech length. This means that one can place a certain set of assumptions on the model that Congressional discourse follows. First, speeches usually focus on a single issue (Rogowski and Sinclair, Reference Rogowski and Sinclair2012). Second, in each debate, several representatives will chime in and deliver speeches and comments, and argue for various standpoints. Third, speeches form natural sites for representatives to perform position-taking in front of their peers (Abercrombie and Batista-Navarro, Reference Abercrombie and Batista-Navarro2020; Fernandes et al., Reference Fernandes, Debus and Bäck2021).

Disagreement in legislative debate is legion, and discussions feature arguments in favor or against some bill under discussion, and sometimes broader debates on what the representatives believe needs to be done (Vedres, Reference Vedres2022). Thus, Congressional discourse is a fertile space to analyze what representatives talk about, and how that may contribute to the broader polarization trends in Congress. But what exactly are the issues under discussion?

Policy issues can be as specific as a certain set of tariffs or as broad as civil rights. Representatives likely have varying views on how to address such issues. Since this paper has access to data for a long period (1873–2025), many smaller policy issues will come and go over time, i.e., will not be measurable at every time point. Only fundamental policy issues can be expected to remain relevant over the entire time span of interest. These are traditionally large issues such as the economy, social redistribution, foreign policy or social conflict (Evans et al., Reference Evans, Rueschemeyer and Skocpol1985). Since the focal issue for this paper is the economy, the paper can make use of the entire dataset to track the dynamics of issue-level polarization across the entire period.

Economic issues are debated in Congress according to the same rules as any other issue. However, there are two peculiarities to economic discussions. According to the U.S. constitution Congress has the “power of the purse,” meaning that Congress decides over the federal budget. More specifically, budget bills must originate in the House of Representatives. This means, on the one hand, that economic discussions frequently occur in the context of budget and appropriation bills. On the other hand, if economic discourse has become more polarized, this trend should be more pronounced in the House than in the Senate. In terms of this analysis, we should expect the House to feature more pronounced issue-level polarization than the Senate.

A second peculiarity of economic discourse in Congress relates to events and societal changes since the 1970s. In the 1970s, the U.S. economy was subject to a series of economic shocks, which rendered economic discussions salient (Erz, Reference Erz2025a). This is seen by some as a precursor to a fundamental paradigm shift in U.S. economic policy under U.S. president Ronald Reagan (Centeno and Cohen, Reference Centeno and Cohen2012; Fourcade and Babb, Reference Fourcade and Babb2002; Krippner, Reference Krippner2005). At the same time, research also diagnoses a change in language (Berman, Reference Berman2022) and argues that both the Democrats and Republicans adopted very similar economic policy views (Mudge, Reference Mudge2018). Much of the research of this period implies that the language with which economic issues were discussed has become more homogeneous. This could partly be the reason a lot of research has focused more on cultural issues like civil rights when analyzing differences between the two parties (Bonomi et al., Reference Bonomi, Gennaioli and Tabellini2021; Diermeier et al., Reference Diermeier, Godbout, Yu and Kaufmann2012). In short, this analysis should find a drastic change in issue-level polarization around this time.

2.3 Discursive polarization at the issue-level

Having introduced Congressional discourse and economic discussions, the next step is to understand how polarization can be measured at the issue-level. Researchers have long used Congressional speech to measure polarization. Diermeier et al. (Reference Diermeier, Godbout, Yu and Kaufmann2012), for example, use speech data from the Senate; Jensen et al. (Reference Jensen, Kaplan, Naidu and Wilse-Samson2012) use the Google Books corpus to explore partisan speech patterns across both Senate and House of Representatives. The largest-scale polarization analysis of Congress that uses speech data to date is from Gentzkow et al. (Reference Gentzkow, Kelly and Taddy2019). They use historical speeches from the inception of the Congressional Record (CREC) in 1873 (Amer, Reference Amer1993) until the 111th Congress (2009–2011) to develop an estimator similar to NOMINATE to identify the partisanship of words and phrases. They, too, are able to reproduce the findings of Poole and Rosenthal (Reference Poole and Rosenthal1984) using speech data. This paper draws on the same data to measure issue-level polarization.

Text-based analyses of polarization in U.S. politics commonly use text data as an input to scaling methods (see Carroll et al., Reference Carroll, Lewis, Lo, Poole and Rosenthal2009). This measures the partisanship in the usage of words and phrases. Diermeier et al. (Reference Diermeier, Godbout, Yu and Kaufmann2012); Jensen et al. (Reference Jensen, Kaplan, Naidu and Wilse-Samson2012), and Gentzkow et al. (Reference Gentzkow, Kelly and Taddy2019) all train machine learning classifiers or use regression models to estimate how likely it is for a Democrat or a Republican to use a word or phrase. This means that they measure the partisanship of words (how representatives talk), but not topical associations (what representatives talk about). While Diermeier et al. (Reference Diermeier, Godbout, Yu and Kaufmann2012) do find some patterns in the partisanship of words that hint towards topical associations, these are emerging from their classifier’s results (see particularly Table 5, Diermeier et al., Reference Diermeier, Godbout, Yu and Kaufmann2012, pp. 45–46). This shows that an interpretation on the issue-level—while plausible and backed by the data—is a post-hoc interpretation.

However, polarization is not limited to the mere form of speech. Polarization should also be visible in the content of the speeches. There are accounts of Congressional representatives disagreeing over issues from civil rights or abortion (Abramowitz, Reference Abramowitz2018) to the economy (Rossinow, Reference Rossinow2015; Stein, Reference Stein1988) or healthcare (Parlapiano et al., Reference Parlapiano, Andrews, Lee and Shorey2017; Pierson, Reference Pierson2007). More importantly, there are indications that, while Republicans have started to focus on taxes and “starve the beast” rhetoric, Democrats did not follow suit (Prasad, Reference Prasad2018). This indicates that there might be a deeper schism between representatives in that they no longer talk about the same issues at all. If these disagreements result in stable patterns, this can be an indication of issue-level polarization.

On the network-level, we can leverage this information to measure whether issue-level polarization occurs in economic discourse. This means that we assume polarization to be a structural feature of the resulting networks. Following the definition of Waugh et al. (Reference Waugh, Pei, Fowler, Mucha and Porter2011), a political network is polarized when stable communities emerge, which are densely interconnected, but sparsely connected to other communities. If there is polarization on the issue-level, one should find a network with identifiable communities.

A central assumption behind this analysis is therefore that discursive polarization describes a state inside a political network in which representatives form clusters based on which topics they talk about, and that topic modelling is capable of identifying the specific language used by representatives from the two parties to talk about these issues.

2.4 Research questions and hypotheses

This paper is interested in the structural and temporal dynamics of issue-level polarization at both discursive level and specifically in the economy. This involves answering three related questions:

1. 1. Is Congressional discourse polarized on the issue-level? And, if so, how does this polarization compare to polarization in voting behavior?

2. 2. Is the trajectory of polarization at both discourse (all issues) and economic issue-level comparable? Or are there significant differences, and how can they be explained?

3. 3. What contributes to Congressional issue-level polarization?

The first question validates the proposed framework against existing measures of polarization. To answer it, I measure speech similarity using what I call “speaker profiles.” A speaker profile is a vector that counts speeches by issue based on an LDA model. By calculating how similar these speaker profiles are between representatives, one can construct networks where the similarities comprise the edges connecting representatives in the resulting network. I then analyze how polarized these networks are over time using modularity scores, and compare the emerging trends with the findings of McCarty et al. (Reference McCarty, Poole and Rosenthal2006) to establish a baseline and compare the patterns of discursive polarization with the polarization visible in vote behavior. The null hypothesis for this research question is that, if Congress is polarized, there should be evidence of separate communities of speakers.

To answer the second question, I modify the speaker profiles to only include speeches on economic issues, and repeat the process. By utilizing the same model to classify speeches into topics in both instances, the results for discursive and issue-level polarization are comparable. This will show both if and how issue-level polarization happens in economic issues and allows comparing this to the discursive trend. The null hypothesis for this research question is the same as for the first in that we should see clear polarization if this is a cause for the observed discursive dynamics.

Lastly, I ask what might contribute to the patterns of discursive polarization in the networks. I test specifically for polarization along party lines to examine whether party affiliation might be a predictor of issue-level polarization. Essentially this measures whether members from the same party focus on similar issues, which is an indication of homophily (McPherson et al., Reference McPherson, Smith-Lovin and Cook2001). To assess whether homophilic trends are statistically significant, I validate these findings using Quadratic Assignment Procedure (QAP, see Krackhardt, Reference Krackhardt1987).

3.1 Measuring discursive dynamics with LDA

The goal of this analysis is to measure issues that representatives talk about, and compare individual speech profiles over time. To do so, it first needs to identify the issues representatives talk about. To this end, it uses Latent Dirichlet Allocation (LDA, Blei et al., Reference Blei, Ng and Jordan2003). The choice of LDA over more recent methods requires some justification. Egger and Yu (Reference Egger and Yu2022) provide a comprehensive comparison of four topic modeling methods: LDA, non-negative matrix factorization (NMF), Top2Vec, and BERTopic. Their results highlight that no method has clear advantages over any other (Egger and Yu, Reference Egger and Yu2022, Table 5). Instead, each method excels in certain domains, and as such, the choice of method is important.

The choice of LDA is based on three reasons. First, LDA uses only domain-specific data to arrive at a topic solution that is tailored to that data. Especially the newer methods Top2Vec and BERTopic utilize pre-trained models which have been trained on different, out-domain data. This has been shown to induce biases that are difficult to quantify (Boelaert et al., Reference Boelaert, Coavoux, Ollion, Petev and Präg2024; Garg et al., Reference Garg, Schiebinger, Jurafsky and Zou2018). For this analysis, precision is crucial to keep the resulting speech profiles comparable. This leads to the second point: explainability (Bommasani et al., Reference Bommasani, Hudson, Adeli, Altman, Arora, von Arx and Liang2022). The computational process of transformer models is still not fully understood, while LDA uses a theoretically motivated generative process with well-defined assumptions (Blei et al., Reference Blei, Ng and Jordan2003). Third, and finally, LDA has been studied extensively (see e.g., George and Doss, Reference George and Doss2018; Maier et al., Reference Maier, Niekler, Wiedemann and Stoltenberg2020). We know much about the advantages and shortcomings of the model, and as such have a large literature to draw on when implementing robustness checks (see the appendix for an array of tests and below for all considerations when implementing this model).

Even though LDA has somewhat fallen out of favor due to the improvements in computational text analysis in recent years, it remains an important tool. LDA is a Bayesian method that treats text as a bag of words and assumes that each text is generated by the speaker choosing a topic to talk about, and then using appropriate words to convey their message. By reverse-engineering this process, LDA arrives at a model that assigns probabilities to each word of being associated with specific topics, which allows turning text data into topics. The analyst then only has to interpret the resulting topic distributions. It allows us to detect what representatives in Congress talk about with minimal input from the researcher (Mohr et al., Reference Mohr, Bail, Frye, Lena, Lizardo and McDonnell2020).

While the previous sections have implied that an issue (such as “the economy”) is synonymous with a “topic,” the topics that LDA produces are not the same as what the reader understands as a topic. Since LDA simply groups words together based on co-occurrence patterns, only few LDA-topics map onto what a human researcher would intuitively understand as a “topic.” There are three cases to consider. The first two are “topic splitting” and “topic clustering” (Carlsen and Ralund, Reference Carlsen and Ralund2022). Topic splitting occurs when a human-understandable topic is spread out over multiple LDA-topics. Topic clustering occurs when multiple human-understandable topics (e.g., taxation and tariffs) are grouped into a single LDA-topic. Third, LDA also tends to group function words into their own topics. For example, speeches in Congress contain many phrases such as “I yield the floor to representative X,” and LDA tends to group those into topics.

A related issue concerns the temporal stability of LDA. Language is subject to perennial change (Lazer et al., Reference Lazer, Hargittai, Freelon, Gonzalez-Bailon, Munger, Ognyanova and Radford2021). Tone, words, grammar—all of this changes over time (Chang and DeDeo, Reference Chang and DeDeo2020). This has profound implications for the study of discourse. It is difficult to quantify the impact this has on text analysis, as text analysis methods vary in their susceptibility to linguistic change. This has led some authors to use somewhat arbitrary binning techniques and run, e.g., one model per decade (Kozlowski et al., Reference Kozlowski, Taddy and Evans2019; Stoltz and Taylor, Reference Stoltz and Taylor2021).

This paper uses a single topic model for the entire period spanning one and a half centuries, as this ensures an unchanging baseline. How problematic is this? There are again three cases to consider. First, there are words that have been used in the beginning of the dataset which fell out of fashion (such as “greenbacks”). Second, there are words that came into existence only towards the end of the dataset (such as “Watergate”). And third, the usage context of some words has changed throughout the dataset. As LDA tries to group words together which frequently co-occur, it may choose to populate some topics with words from the first case, and some with words from the second case. A common technique for LDA is to remove rarely used words to mitigate this problem (see appendix). As to the third case, it depends on how drastic the word co-occurrence patterns change, but since LDA is an admixture model (Molina and Garip, Reference Molina and Garip2019), words can contribute to multiple topics at the same time, accounting for different usage contexts.

All of this means that this analysis has to respect two constraints. First, it needs to focus on entire policy areas instead of small particular issues, as this mitigates the impact of the concerns discussed above. This reduces the measure’s resolution but makes it more robust. Second, it must consider all topics, since all will encode some part of speech similarity, mitigating the issue of topic splitting and clustering. This analysis addresses this issue by giving the topic model ample space to create clusters of words. More specifically, it uses $K = 500$ , where $K$ is the number of topics, which I have to provide to the model in advance. Using such a high number ensures (a) that the amount of mismatched speeches remains small and (b) that the topic model has the space to account for temporally limited issues which are only relevant in certain parts of the corpus.

In total, LDA requires three hyperparameters that can be only experimentally determined (Lewis and Grossetti, Reference Lewis and Grossetti2022). The parameters were set to an $\alpha$ -value of $0.5$ , a $\beta$ -value of $0.1$ and a $K$ of $500$ (see the appendix for a full description of the process and a discussion of alternative parameters). I used the final, trained models to turn every speech into a distribution of topic loadings. I recognize that there is strong evidence that speech patterns in House and Senate might differ significantly (researchers commonly only focus on a single chamber, e.g., Diermeier et al., Reference Diermeier, Godbout, Yu and Kaufmann2012; Yu, Reference Yu2014). Therefore, I train two additional models separately on speeches from Senate and House to validate the findings from the main model.

3.2 Description and interpretation of the LDA results

With the trained topic models at hand, I identified every topic which primarily captured economic speech by creating a list of all topics that contained economic terms in the top 10 words, separately for each of the three models. I then manually inspected top speeches for these topics to verify that the topic indeed contains economic policy talk. See Table 1 for a list of the economic topics from the main model (see the appendix for the lists for the two other models). Importantly, different layers of the economy—such as appropriations, debt, welfare benefits—are split up into different topics, as we would expect. This way, we can identify representatives who primarily focus on the budget, or taxation.

Table 1.

Economic topics contained in the main model. The topic number references its index in the topic-term matrix where the index starts at 0

Table 1 Long description

A table with 10 columns and 13 rows. The columns are labeled Topic, Top 10 words (stemmed), and Interpretation. The table lists economic topics identified in a main model, showing top 10 words and their interpretations. Row 1: Topic 0, Top 10 words (stemmed) omnibu; network; grossli; tent; transpir; unfound; anthrax; slot; highpai; outoft, Interpretation Discussion of appropriation bills. Row 2: Topic 11, Top 10 words (stemmed) season; trade; canada; russia; wasnt; caught; british; port; fresh; fisheri, Interpretation Fishing economy and US-Canada trade. Row 3: Topic 21, Top 10 words (stemmed) smoke; across the board; bottom; suspens; grammrudmanhol; object; consum; think; countr; lean, Interpretation Debate over the Gramm-Rudman-Hollings amendment of 1987. Row 4: Topic 32, Top 10 words (stemmed) work; employ; skill; unemploy; mechan; wage; adjust; emplo; labor; healthier, Interpretation Employment policy. Row 5: Topic 45, Top 10 words (stemmed) discretionary; unsustain; gridlock; wrongdo; object; issu; think; recog; unanim; minut, Interpretation Discretionary spending (specifically for defense contractors). Row 6: Topic 152, Top 10 words (stemmed) reveal; contradict; disclos; enlighten; spokesperson; without; respond; support; freemarket; countr, Interpretation Budgetary speeches. Row 7: Topic 164, Top 10 words (stemmed) action; rescind; inject; resciss; multitud; illicit; snake; republica; unanim; greensboro, Interpretation Appropriations, and a discussion on the Gramm-Latta budget from 1981. Row 8: Topic 183, Top 10 words (stemmed) corpor; exempt; revenu; deduct; incom; burden; fiscal; taxat; tax; deriv, Interpretation Corporate tax relief. Row 9: Topic 203, Top 10 words (stemmed) bankruptci; dream; trustee; bankrupt; generos; debt; chairwoman; creditor; resent; disrespect, Interpretation Debt and Bankruptcy. Row 10: Topic 215, Top 10 words (stemmed) benefit; retire; stuck; dropout; governmentrun; selfemplo; textbook; 1949; support; provid, Interpretation Social Security, Welfare, national disability benefits. Row 11: Topic 228, Top 10 words (stemmed) insur; 2008; societ; wipe; support; fund; particip; reunif; protect; countr, Interpretation Cutbacks in health and child care; financial crisis of 2007/2008. Row 12: Topic 297, Top 10 words (stemmed) need; badli; overnight; access; qualiti; support; capitalist; approach; million; colleague, Interpretation Economic aspect of appropriations. Row 13: Topic 380, Top 10 words (stemmed) budget; total; deficit; signific antil; clarifi; figur; decreas; head; approx; exploit, Interpretation Budget and federal deficit.

To provide qualitative insight into what the topic model has detected, Figure 1 shows a plot of the economic topics listed in Table 1 over time, highlighting the ratio of speeches per congress classified with this topic. The plot shows signs of all peculiarities of LDA discussed above. We can see some topics starting with very low salience reach high salience towards the end of the dataset, there are topics with high salience becoming less salient towards the end, and we have topics that remain stable.

Figure 1.

A plot of the 13 economic topics identified in the main topic model. The y-axis denotes how many speeches per congress have been classified with the provided topic. The topic numbers correspond to the numbers in the table of top-words.

What becomes immediately obvious is that most economic topics remain stable over time, as expected. Several topics feature spikes that correspond with phases in which the issue were salient in discourse. Most topics experience a slight increase in saliency during the end of the “progressive era” in the United States between 1910 and 1920, marked by significant economic legislation. Later, topic number 164 clearly captures a new form of discussions about appropriation bills started during the economic crises of the 1960s and remained important for the remainder of the dataset. Other topics have peaks at different time points, such as topic 380 that peaks at the height of the economic crises of the 1970s, or topic 215 that peaks after World War II. Finally, we can see that economic topics become more salient in overall discourse starting in the 1970s, indicating a qualitative change in how representatives talk about the economy.

All in all, these descriptive results indicate that economic issues have remained relatively stable, but that different parts of economic discourse are relevant at different points in time. This is corroborated, for example, by research showing that taxation has only become highly salient and a central issue for the policymaking process after the 1960s (Erz, Reference Erz2025b).

3.3 Constructing speaker profiles

To construct speaker profiles, the models classify all speeches into topics, and assume the topic with the highest loading to be the main topic of that speech. Given that LDA is an admixture model that provides values for all topics for all documents (Grimmer et al., Reference Grimmer, Roberts and Stewart2022; Molina and Garip, Reference Molina and Garip2019), this choice requires justification.

By default, LDA provides scores (often called “loadings”) for how much each topic in the model “loads” on the given document, but I chose to retain only the highest-loading topic. Since speeches in Congress primarily focus on one topic, retaining all topic loadings would be at odds with how the speaker envisioned their speech. Speakers regularly touch upon multiple issues, but only to support their main argument. Furthermore, since LDA is a Bayesian method, it tends to assign probabilities for all topics in all documents roughly uniformly (see Carlsen and Ralund, Reference Carlsen and Ralund2022, especially Figure 2). This means that retaining all topic loadings will push the similarity metric (see below) to find almost perfect similarities between all topics and speakers, and even more so when aggregated.

After having classified all speeches into their single primary topic, I construct speaker profiles by aggregating all speeches by every individual speaker for one entire congressional cycle of two years. A congressional cycle is the period between congressional elections, which are held every two years, which is further subdivided into two one-year sessions. I choose to use this two-year cycle instead of individual sessions because over the course of these two years, the make-up of the congressional network does not change significantly.Footnote 1 A speaker profile is a 500-dimensional vector in which each number denotes the frequency of speeches classified into the corresponding topic of that individual speaker within one congressional cycle. I repeat this process for all 75 congressional cycles that are part of the dataset (from the 43rd Congress to the 118th Congress). This resulted in about 40,000 vectors (ca. 535 representatives by 75 Congresses).

3.4 Measuring speech similarity

This paper measures how similar speakers address issues in their speeches, given the constraints outlined above. Cosine similarity is a popular choice to calculate speech similarity that has the right properties for this analysis (see equation). First, unlike divergence measures like Kullback-Leibler (Chang and DeDeo, Reference Chang and DeDeo2020), it is symmetric and commutative. This means that a comparison of larger or smaller distances is straight forward. Also, if representative A talks similarly to representative B, then B talks similarly to A. Since cosine similarity measures the angle $\theta$ between two vectors, the measure also accounts for different amounts of speech. Thus, similarity between representatives who talk about the same topics in the same relative frequency will be maximal. It will be minimal for those who talk about widely diverging topics in different amounts.

\begin{equation*} \cos (\theta ) = \frac {\sum _{i=1}^n \vec {A_i} \vec {B_i}}{\sqrt {\sum _{i=1}^n \vec {A_i}^2} \sqrt {\sum _{i=1}^n \vec {B_i}^2}} \end{equation*}

To demonstrate that cosine similarity accurately proxies the speech distance between various representatives in terms of what they talk about, consider the following, hypothetical example: Let us assume there are three topics, the first one denoting speeches about taxes, the second one denoting speeches about defense, and the third one denoting speeches about federal spending. Let us further assume we have four representatives; two of which are “tax hawks” one of which is a “deficit hawk” (“hawks” are representatives focusing on specific topics), and the final one is a representative who does not focus on specific topics. Table 2 demonstrates that those who focus on the same topics have the highest speech similarity, while those who focus on different topics have the lowest.

Table 2.

Hypothetical speaker profiles and corresponding cosine similarities for four exemplary ideal-typical representatives

Table 2 Long description

The table presents data on hypothetical speaker profiles and their corresponding cosine similarities for four ideal-typical representatives. It has four rows and eight columns. The columns are labeled as Rep., Tax, Defense, Spending, Tax hawk 1, Tax hawk 2, Deficit hawk, and Regular. The rows are labeled as Tax hawk 1, Tax hawk 2, Deficit hawk, and Regular. Row 1: Tax hawk 1, 12, 2, 4, 1, 0.98, 0.62, 0.88. Row 2: Tax hawk 2, 9, 3, 2, 0.98, 1, 0.53, 0.89. Row 3: Deficit hawk, 5, 1, 14, 0.62, 0.53, 1, 0.79. Row 4: Regular, 7, 5, 6, 0.88, 0.89, 0.79, 1.

The first half of Table 2 contains the absolute speech counts for each representative, while the second half denotes the cosine similarity to other representatives. The two “tax hawks” possess the highest similarity despite slightly different frequencies of speeches. The least similar speakers are those focusing on tax and the deficit, respectively. The speech similarities towards the “regular” representative are in between. What should be noted is that most similarities that should theoretically indicate a high similarity (e.g., between the two tax hawks) are above $0.9$ , while the similarities of each “specialized” representative to a regular one without a distinct speech profile are still well above $0.5$ . This is just a hypothetical example, and real data will behave differently, but this helps demonstrate how different cosine similarities can be interpreted. Cosine similarity captures the speech similarities in a way that corresponds with the research question.

Since this paper compares discursive polarization with issue-level polarization, this step needs to be repeated twice. First, I measure the speech similarity between the full speaker profiles which include all topics. In a second step, I construct a second set of matrices that measure speech similarity based only on economic topics. Since I measure similarity using the cosine between two vectors, setting any dimension in both vectors to zero effectively removes that dimension from the similarity calculation. This means that I could construct a simple mask vector, which contains ones for the economic topics, and zeros for all other topics. Multiplying a speaker profile with this mask thus yields a new speaker profile that only retains the frequency counts of economic topics. Calculating the cosine similarity between two “masked” speaker profiles therefore provides a measure of economic speech similarity. However, since both sets of matrices is constructed from the same underlying data, the results are comparable.

In total, this analysis uses about 80,000 speaker profiles (ca. 535 representatives by 75 Congresses by 2).

3.5 Community detection and modularity scores

With this measure of speech similarity, I am able to produce networks of representatives who are connected if they speak similarly. This produced 450 adjacency matrices (75 Congresses $\times$ 3 models $\times$ 2 topic subsets [economic and overall]). These matrices are weighted and symmetric, and contain between about 10,000 (Senate only) and 250,000 entries (full Congress).

To measure the amount of issue-level polarization this induces in each Congress-network, this analysis follows Waugh et al. (Reference Waugh, Pei, Fowler, Mucha and Porter2011) in their choice of using community detection algorithms. To understand what community detection algorithms measure, we need to understand the structure of the networks resulting from cosine similarity scores. By generating a Congressional network as such, one creates a weighted network in which edges connect representatives based on their speech similarity, with stronger weights being associated with higher topical similarity. Such networks will be fully connected, since even very dissimilar speakers will have a small amount of overlap. This is due to general noise that is introduced when dealing with textual data. It is unlikely for two speakers’ speech vectors to be exactly orthogonal. This raises an important question for constructing a network: dichotomization.

The Leiden community detection algorithm can work with weighted networks (Traag et al., Reference Traag, Waltman and van Eck2019). Dichotomization removes data and drastically reduces the resolution of the data. As such, the main results reported in the next section are based on the weighted, non-dichotomized networks. However, because there is a theoretical argument to be made for dichotomization, in which similarities below a certain threshold should not be considered, the appendix includes a section that reports the same results, but based on dichotomized, binary networks. Indeed, these results show the same trends as the non-dichotomized network, but more pronounced.

The aim of community detection algorithms is to find groups of nodes within a network such that the solution maximizes edges within groups while minimizing edges between groups. In our case, this means finding groups of nodes in Congress which speak similar among each other, but dissimilar to other groups. Community detection is an NP-hard problem, meaning that it requires algorithmic approximation (Bruggeman et al., Reference Bruggeman, Traag and Uitermark2012). Most algorithms choose to start with a random community assignment, measure how well the solution works, and update the assignments. This is done until no move would improve the solution. This paper relies on the Leiden algorithm (Traag et al., Reference Traag, Waltman and van Eck2019) for detecting communities (see the appendix for a comparison of Leiden with the Louvain and walktrap algorithms).

Fortunato (Reference Fortunato2010) has outlined a series of issues with community detection algorithms and their corresponding modularity score metric. Specifically, he argues that the assumption of the null-model for community detection algorithms is problematic. Community detection algorithms essentially compare the modularity of a network to one of the same amount of vertices and edges, but with randomly rewired edges (Bruggeman et al., Reference Bruggeman, Traag and Uitermark2012). If the modularity of the observed network is significantly higher than the one of the random baseline, the algorithm assumes that the network has a community structure. However, even random graphs may exhibit a community structure by chance. This means that community detection algorithms may lead to false positives or false negatives. In addition, even a community structure that we can easily observe by visual inspection of a network plot might not be properly detected by community detection algorithms. This is especially grave for sparse networks.

For dense, weighted networks, these issues may be less severe than for sparse unweighted networks (Fortunato, Reference Fortunato2010). Nevertheless, recognizing these issues with modularity scores, I handle the resulting modularity scores in the analysis with the due caution. First, I refrain from analyzing the absolute values of the modularity scores, since those can be over- or underestimates of the real community-structure of the networks. The scores will only be compared against each other to detect trends over time. Second, I compare the results with two more community detection algorithms, Louvain and walktrap. If the results from all three algorithms are comparable and stable, this indicates that the community structure is less likely a false positive by chance. But third, and most crucially, I do not expect the community structure to be neatly divided into two groups. This last point requires some elaboration.

Speech similarity does not exclusively depend on party affiliation. There are indications that political speech also depends on socio-economic variables (Canen et al., Reference Canen, Kendall and Trebbi2020), geographical origin (Ermakoff, Reference Ermakoff2008), or committee assignments (Fenno, Reference Fenno1973). For this study, which focuses on speech similarity, this means that the network community structure which the Leiden algorithm might recover will connect representatives not simply based on party affiliation, but also on various other shared attributes. This means that the analysis requires a second step to check for homophily of the resulting community structure.

3.6 Confirmatory analysis with quadratic assignment procedure

In order to verify the results from the community detection algorithm and answer the third research question, I employ QAP. QAP compares multiple networks with each other and tests whether the observed correlation between both is due to chance (Krackhardt, Reference Krackhardt1987). In this case, we can compare the observed network based on speech similarity with a synthetic network constructed based on homophily, that is, whether two nodes in the network share the same attribute (McPherson et al., Reference McPherson, Smith-Lovin and Cook2001). This method is preferable to a dyad-level OLS-regression that predicts edges based on shared attributes, because a network does not uphold the independence-assumption of OLS (Krackhardt, Reference Krackhardt1987).

By randomly permuting the synthetic network and calculating the correlations between all permutations and the observed network, QAP tests whether the observed homophily patterns are spurious. If random permutation does not produce the same amount of correlation between the attributes and the observed network significantly often (e.g., $p \lt 0.05$ ), this is an indication that the observed correlation might not be spurious. I perform one QAP analysis using $n = 1,000$ permutations.

The QAP analysis tests the third research question. It tests whether the observed networks could be caused by party homophily, that is, representatives from the same party are more frequently connected to similar peers. I do so by creating an attribute for the nodes in my network, and store the party affiliation for each node in it. Then, I create a synthetic network in which nodes are connected if they are part of the same party. By performing QAP, I check whether the speech similarity networks might be correlated to party homophily.