Finance research over 40 years: What can we learn from machine learning?

3.1 Textual data cleaning

This section describes the process of cleaning textual data and determining the parameters of the models in a general way.

4.1 LDA

A collection of M abstracts is denoted by $$D=\{{w}_{1},{w}_{2},{\rm{\ldots }},{w}_{M}\}$$, and each abstract d with $${N}_{d}$$ words is denoted by $${w}_{d}=\{{w}_{d,1},{w}_{d,2},{\rm{\ldots }},{w}_{d,{N}_{d}}\}$$. The model assumes that text is generated by unobserved variables $$\beta $$ and $$\theta $$ that are to be estimated. Let V denote the number of unique words across all abstracts, and K denote the number of topics. $${\beta }_{k}$$ is a V-dimension vector over V words for topic k. $${\beta }_{k,v}$$, the vth element in $${\beta }_{k}$$, represents the appearing probability of word v given topic k. $${\theta }_{d}$$ is a K-dimension vector of probabilities over K topics for abstract d. $${\theta }_{d,k}$$, the kth element in $${\theta }_{d}$$, represents the percentage distribution of topic k in abstract d.

For $${w}_{1}$$, $${N}_{1}=3$$, and $$\{{w}_{1,1},{w}_{1,2},{w}_{1,3}\}=\{\mathrm{bank},\mathrm{crucial},\mathrm{entrepreneurship}\}$$. For $$\{{w}_{2,1},{w}_{1,2},{w}_{1,3}\}=\{\mathrm{bank},\mathrm{crucial},\mathrm{invest}\}$$ now assign our parameters' numerical values. We assign $$\beta $$'s value matrix as follows:

The value $${\beta }_{k,v}$$, or $${\beta }_{{topic},{word}}$$, is the probability of the word conditional on the topic. Here we set the number of topics to be 3, so $$K$$ is 3; we have a dictionary of 4 unique words, so $$V$$ is 4. The topic names are not the direct output of LDA. When we implement the machine learning strategy, the algorithm only returns the key word list for each topic. We assign topic names to facilitate the readability. For example, under the condition that the topic is 1 (banking), the word “bank” appears with probability 0.7, and “crucial” appears with probability 0.3. We could also arrange the matrix into a different representation

where each topic is associated with a list of words and their probabilities. We then proceed to assume $$\theta $$ as

The value $${\theta }_{d,k}$$, or $${\theta }_{{abstract},{topic}}$$, is the percentage distribution of the topic in the abstract. We could see that abstract 1 bank crucial entrepreneurship consists of 0.6 of topic 1 (banking) and 0.4 of topic (entrepreneurship), and abstract 2 bank crucial invest consists of 0.7 of topic 1 (banking) and 0.3 of topic 2 (investment).

By adjusting the values of $$\theta $$ and $$\beta $$, we would obtain different probability values. The goal of topic modeling and LDA is to find an optimized set of $$\theta $$ and $$\beta $$ so that the computed probability is maximized.

With the conjugation property between Dirichlet distribution and categorical distribution, this optimization of the probability of a corpus becomes tractable, and we are able to estimate the latent variables by maximum likelihood/minimum perplexity methods. $$\alpha $$ and $$\eta $$ are hyperparameters of this model, and they can be tuned for different model behaviors. For example, abstracts contain fewer topics with lower $$\alpha $$ and they contain more topics with higher $$\alpha $$. Following Griffiths and Steyvers (2004) and Steyvers and Griffiths (2007), we choose $$\alpha =50/K$$, and $$\eta =0.025$$ in our analysis.

Various properties of LDA are worth noting. LDA is a bag-of-words language model, where each abstract is modeled as the occurrence frequency of each word inside the abstract. This approach ignores word order and simplifies the computation complexity. Hansen et al. (2018) argue that the resulting information loss has little impact on our goal of determining the topic coverage. In addition, LDA is an “unsupervised” machine learning algorithm. This means that the algorithm requires no pre-assigned labels—it is enough to simply feed the textual data into the algorithm. This unsupervised property significantly reduces workload when processing big data.

4.2 DTM

In our experiment, we set t as the publishing year of an abstract. Therefore, each year we obtain a different $${\beta }_{t,k}$$, the probability of each word that appears in each topic. Then we can observe the evolution of word usage of every topic.

Apart from the discrete time DTM described above, continuous time DTM is proposed by Wang et al. (2012). Rather than being discrete, t can take on any point on a continuous timeline. While continuous time DTM is useful for high-frequency textual data, such as tweets from Twitter, it is hardly applicable in our project that mainly uses yearly data.

5.1 Appropriate number of topics

To determine the appropriate number of topics, we run LDA and maximize the log-likelihood and minimize the perplexity of the data from the models trained for different numbers of topics. We use Gibbs sampling to estimate the model parameters under a different number of topics, and we choose the model with the highest log-likelihood/lowest perplexity as our model in this paper. We compute the probability of a set of abstracts unseen to the estimated model at the end of the machine learning process to avoid the caveat of overfitting. The optimal number of topics should be accompanied by the highest computed probability. Figure 1 reports the log-likelihood of the data from the trained model of different numbers of topics. The number of topics with the highest likelihood is approximately 40. In implementing this approach, we find that there are topics that represent general sentences and do not indicate specific research interest. For example, a topic with keywords “relat,” “posit,” “neg,” “associ,” and “evid” may simply represent an often used general sentence “we provide evidence on a positive/negative relation/association.” Therefore, we finally choose 50 topics when implementing LDA and exclude 12 general sentence topics from them. A full list of general sentence topics is presented in Table A2.

5.2 Naming the topics

Table 2 presents each topic's top 10 keywords generated by LDA, that is, the 10 words with the highest appearing probability in each topic. We name each topic by reading the keywords and the articles that belong to it. For example, if we observe that “bank,” “loan,” “borrow,” “lend,” “commerce,” and “deposit” appear in one topic, after reading the articles belonging to this topic, we name it as “Commercial Banking”; if we observe that “ceo,” “manag,” “board,” “compens,” “incent,” “director” appear in one topic, we name it as “CEO, Board, Director.” The abstracts are categorized into 38 research topics and 12 general sentence topics.

As we explained in the previous example of Laeven and Levine (2009), each abstract has a quantitative distribution on different topics. We define that an abstract focuses on a topic if it has over 10% distribution on it. An abstract with a higher distribution of a certain topic tends to have more keywords for that topic. An abstract may have two or more topic focuses. For example, Laeven and Levine (2009) is 12.7% on “Systematic Risk and Risk Premium,” 11% on “Shareholder Right, Ownership Structure,” 10.3% on “Commercial Banking,” and 10.1% on “Financial Regulation.” Therefore, Laeven and Levine (2009) focus on the four topics “Systematic Risk and Risk Premium,” “Shareholder Right, Ownership Structure,” “Commercial Banking,” and “Financial Regulation” by our definition.

“Option Pricing” is the topic with the most publications that focus on it, followed by “Commercial Banking,” “CEO, Board, Director,” “Market Microstructure,” “Central Bank, Monetary Policy,” and “Mergers and Acquisitions.”

Table 3 lists the most cited articles on each topic. The citation numbers were collected on February 25th, 2016. The year of publication is in the parenthesis. The number of citation is behind the comma. We present the Web of Science citation behind the author-years. In unreported table, we present the most cited articles in each topic by Google Scholar citation and find the results similar to our results using the Web of Science data.

5.3 Historical trend of topics

We observe that the research interest in “Financial System, Banking Crisis” often spiked around or after the financial crises, such as the savings and loan crisis in the late 1980s and early 1990s. It grew even faster after the 2008 financial crisis. The research interest of “CEO, Board, Director” has been growing stably in the past 40 years. Other topics that attracted more attention include “Behavioral Finance,” “Central Bank, Monetary Policy,” “Commercial Banking,” “Corporate Cash Holding,” “Hedge Fund, Mutual Fund,” “International Capital Markets,” “Social Network and Cultural Effect,” “Venture Capital, Entrepreneurship,” and “Volatility.” The research interest in topics like “Bond Term Structure” and “Optimal Choice Model” has been shrinking.

For topics that have garnered increased attention, the reasons for their rise can be classified into two categories. The first category is heightened interest in traditional research questions. For example, during and after the financial crisis, researchers focused more on the impact of the crisis. Therefore, the popularity of “Financial System, Banking Crisis” often spiked around events such as the savings and loan crisis in the late 1980s and early 1990s, and the 2008 financial crisis.

The second category is the emergence of new research questions. For instance, by the 1980s and 1990s, CEOs began to face tough decisions such as shuttering operations, relocating manufacturing overseas, and orchestrating key mergers. Additionally, the rise of cable news required CEOs to communicate directly with investors and customers. This evolution in the CEO's role led to a growing research interest in “CEO, Board, Director.” Similarly, mutual funds gained significant investor attention in the 1980s and 1990s, and the number of hedge funds surged during the 1990s, driven by the new wealth created by the unprecedented bull run in the equity markets. Thus, research interest in “Hedge Fund, Mutual Fund” increased in the 1980s and grew substantially in the 1990s.

It is worth noting that high fluctuation of values exists in the 1970s and 1980s for most of the topics. Figure A1 plots the number of active journals and articles every year. In the 1970s and 1980s, there were fewer journals and articles, resulting in more volatile values. Figure A2 plots the yearly publication numbers in JF, JFE, and RFS. Zivney and Bertin (1992) explain that the output has become constant since the 1980s, following rapid growth in the number of journals and articles published in the 1960s and 1970s. Our results show continuous growth in the number of journals and articles after the 1990s.

5.3.1 Topics with fastest growth and contraction

Figure 3A plots three fastest-growing and three fastest-shrinking topics in 17 journals. The topics are identified by LDA. The horizontal axis represents the year of publication. The vertical axis represents the popularity of the given topic, calculated as the average percentage of each article's percentage distribution on that topic. “Financial System, Banking Crisis,” “Hedge Fund, Mutual Fund,” and “Social Network and Cultural Effect” grew fastest from 2006 to 2015. “Market Microstructure,” “IPO,” and “Option Pricing” experienced the greatest contraction during the same period.

Figure 3B plots the topics with fastest popularity increase and a decrease in JF, JFE, and RFS. “Social Network and Cultural Effect,” “Default and CDS,” and “CEO, Board, Director” grew fastest from 2006 to 2015. “IPO,” “News, Analyst Report, Earnings Announcement,” and “Determinants of Stock Return” experienced the most contraction during the same period.

5.3.2 Working papers

For many articles, there is a time lag between its first circulation and final publication. Sometimes the lag can be several years. Therefore, the trend of the published articles that we show in Figure 3 may not reflect the most recent dynamics of finance research. To address this concern, we apply the LDA model trained from published articles on 130,547 working paper abstracts that we obtained from the SSRN Financial Economics Network. We do not use working papers uploaded to IDEAS because IDEAS does not distinguish working papers in finance from those in economics.

We present three fastest-growing and three fastest-shrinking topics among working papers in Figure 4, which is similar to Figure 3. Figure 4 reports the rise and fall of each topic's popularity from 2006 to 2015. The horizontal axis represents the year of publication. The vertical axis represents the popularity of the given topic, calculated as the average percentage of an article's distribution on that topic.

Working papers on “Social Network and Cultural Effect,” “News, Analyst Report, Earnings Announcement,” and “International Capital Markets” grew fastest from 2006 to 2015. “Market Microstructure,” “Macro Finance,” and “Statistical Estimation Methodology” experienced the greatest contraction during the same period.

5.3.5 The trend of cross-topic research

In this section, we study whether there was more cross-topic research over the years. To put it another way, we examine whether research articles become broader or narrower in terms of research topic coverage. To measure how broad an article is, we calculate the Herfindahl Index of each abstract:

$$$H=\sum _{i=1}^{38}{s}_{i}^{2},$$$()

where $${s}_{i}$$ represents the percentage distribution of the abstract on topic $$i$$.

Figure 5 presents the trend of published articles' research interest concentration. The solid line represents the average Herfindahl Index of abstracts in 17 journals; the dashed line represents the average Herfindahl Index of abstracts in JF, JFE, and RFS. The average Herfindahl Index dropped sharply from 1976 to 1982, perhaps because many topics' pioneering works started to emerge during the early period and therefore cross-topic research were more common. The two lines went up between 1982 and 2000, indicating that on average research becomes narrower. One possible explanation is that many topics matured and the literature was established after two decades' development, and researchers made a more incremental contribution. The average Herfindahl Index of abstracts in 17 journals continued to increase after 2000 while that in the three top journals tended to remain at a constant level and even declined after 2010, indicating that the three top journals still publish more broad and cross-topic articles.

5.4 Citation network between topics

To understand how topics relate to each other and the “distance” between the topics, we use the cross-reference data of each article to construct a citation network between topics. In Figure 6, there are 38 nodes, and each of them represents a topic. A node's size is proportional to the number of articles that focus on the topic that the node represents. Topics with more articles have larger nodes.

The nodes are connected through edges. An edge represents the cross-reference between the two topics. An edge is thicker if there is more cross-reference. For example, if topic A has $$N$$ articles, in total the $$N$$ articles cite articles in topic B for $${\sum }_{i=1}^{N}{R}_{i}^{B}$$ times, where $${R}_{i}^{B}$$ is the number of times that article $$i$$ cites articles in topic B. Similarly, if topic B has $$M$$ articles, in total the $$M$$ articles cite articles in topic A for $${\sum }_{j=1}^{M}{R}_{j}^{A}$$ times, where $${R}_{j}^{A}$$ is the number of times that article $$j$$ cites articles in topic A. Then the total number of cross-reference is $${\sum }_{i=1}^{N}{R}_{i}^{B}+{\sum }_{j=1}^{M}{R}_{j}^{A}$$ and is proportional to the thickness of the edge between A and B.

Each node is positioned by a force-directed gravity algorithm called “Force Atlas 2,” and the node is in a position when the forces from each edge's direction are balanced (Jacomy et al., 2014). Intuitively speaking, the algorithm assumes a force to push every node outward from the centre; the algorithm also allows every node to exert gravity on its connected nodes and drive them inward. Each node is connected with other nodes via edges. A thicker edge represents greater gravity. If a topic (node A) has a small cross-reference (thin edge) with another topic (node B) and a large cross-reference (thick edge) with the third topic (node C), then node A will exert larger gravity on node C. Therefore, the topics with more cross-reference will be “attracted” closer by their connected edges. The network structure dynamically evolves and eventually reach an equilibrium where the topics with more cross-reference cluster. Therefore, the relative position of the nodes is determined by the algorithm, not chosen by ourselves. The distance between two nodes approximately represents how close the two topics are related in terms of cross-reference.

We conduct modularity analysis to categorize the topics into clusters based on the computation of the distance and attraction between the nodes. The number of clusters is determined by the modularity analysis algorithm, and 38 topics are compartmentalized into five clusters, or “territories”: asset pricing, corporate finance, market microstructure, banking, and macro finance, and “mixed areas.” Each node's color reflects the territory it belongs to.

The left side18 of Figure 6 is clustered with corporate finance topics, including large topics such as “CEO, Board, Director,” “Mergers and Acquisitions,” “Shareholder Right, Ownership Structure,” and “IPO.” The bottom side is clustered with banking and macrofinance topics, including large topics such as “Commercial Banking,” “Central Bank, Monetary Policy,” “Financial System, Banking Crisis,” and “Financial Regulation.” The right side is clustered with asset pricing topics, including large topics such as “Option Pricing,” “Volatility,” “Return Distribution and Value-at-Risk (VaR),” and “Bond Term Structure.” The central side is clustered with market microstructure topics, including large topics such as “Market Microstructure,” “Trader Behavior,” and “Information Asymmetry, Disclosure, Insider Trading.” The upper side is clustered with “mixed areas,” including large topics such as “Hedge Fund, Mutual Fund,” “News, Analyst Report, Earnings Announcement,” “Behavioral Finance,” and “Statistical Estimation Methodology.”

This figure may be too obvious to senior finance researchers, but perhaps useful to junior researchers, PhD students, researchers of other economics areas, and the general public who are interested in this profession.

5.5 Bibliometric regularity

Figure 7 presents a bibliometric regularity: the number of researchers covering n topics is around twice the number of researchers covering n + 1 topics. A researcher covers a topic if she publishes at least one article with over 10% distribution on that topic. The horizontal axis of Figure 7 represents the number of topics, and the vertical axis represents the number of researchers.

The solid line is generated from our data, which is downward sloping because fewer researchers are able to cover more topics. The value of each point on the line indicates how many researchers cover exactly how many topics. For example, the first point on the solid line is (1, 6830), meaning that 6830 researchers publish articles that focus on just one topic. The second point is (2, 3507), meaning that 3507 researchers publish articles that focus on just two topics. We use the dashed line $$y=13215/{2}^{n}$$ to fit the solid line, where y is the number of researchers covering n topics. When $$n=1$$, $$y=6625.5$$; when $$n=2$$, $$y=3312.75$$. The R² value of the fitting is 0.998.

Our findings suggest a specific regularity in the way researchers allocate their focus across different topics, reminiscent of power law (PL)—a number of regularities observed in various domains of economics and finance. A PL represents a relationship of the form $$Y=k{X}^{\alpha }$$, where Y and X are variables of interest, $$\alpha $$ is the PL exponent, and k is typically a constant. Gabaix (2009) illustrates how PLs manifest in a myriad of economic and financial metrics, from city sizes to income distribution, and stock market fluctuations. Moreover, the pattern we identified follows the relation of $$Y=k{\alpha }^{X}$$, where Y and X are variables of interest, and k is typically a constant. This resemblance suggests that we have discovered a new form of PL. It not only aligns our observations with well-established economic principles but also provides a deeper theoretical framework that enhances the robustness of the patterns observed in our analysis, enriching our comprehension of research dynamics.