# Evolution of topics in central bank speech communication

Magnus Hansson I would like to thank Erik Hjalmarsson, Andreas Dzemski and
Marcin Zamojski for valuable comments and suggestions, as well as participants
at the Centre for Finance Research Seminar and the PhD Student Workshop at the
University of Gothenburg.

###### Abstract

This paper studies the content of central bank speech communication from 1997
through 2020 and asks the following questions: (i) What global topics do
central banks talk about? (ii) How do these topics evolve over time? I turn to
natural language processing, and more specifically Dynamic Topic Models, to
answer these questions. The analysis consists of an aggregate study of nine
major central banks and a case study of the Federal Reserve, which allows for
region specific control variables. I show that: (i) Central banks address a
broad range of topics. (ii) The topics are well captured by Dynamic Topic
Models. (iii) The global topics exhibit strong and significant autoregressive
properties not easily explained by financial control variables.

JEL Classification: C38, C55, E52, E58
Keywords: Central bank communication, Monetary policy, Textual analysis,
Dynamic topic models, Narratives

##  1 Introduction

> I’m a weatherman, I’m a showman, and I’m an economist. I’m expected to be,
> and I am, a storyteller. I tell stories about the
> future.111https://www.bloomberg.com/news/articles/2019-09-16/wall-street-
> used-to-crunch-numbers-they-ve-moved-on-to-stories (Stefan Ingves, governor
> of the Swedish Riksbank)

Central bank communication affects financial markets [17, 15, 33] and makes
monetary policy more predictable. Traditionally, central bank communication
has had two primary functions: To reveal private information to the public,
and to affect and coordinate financial market expectations [44, 1, 11]. This
suggests that central bank communication should be focused on topics closely
related to monetary policy. Is this really the case?

In this paper, I give a descriptive analysis of speeches by the major central
banks connected to the Bank for International Settlements (BIS) and ask: (i)
What global topics do central banks talk about? (ii) How do these topics
evolve over time? In order to answer these questions I turn to natural
language processing (NLP) to estimate the content of speeches from 9 major
central banks using Dynamic Topic Models (DTM) [7].

The analysis shows that the central banks talk about a broad range of topics,
not all related to classic theory of central bank communication. The estimated
topics are persistent and exhibit a large significant autoregressive effect
which is robust to different model specifications. To control for underlying
variables, a case study using data from the Federal Reserve alone is
conducted. The case study shows that topic persistence is not easily explained
by controlling for regional financial variables related to the topics. This
suggests that the topics exhibit what one might call a narrative effect, in
which the topics are driven by economic narratives [41].222Although the
concept of narrative is new in economics, the idea has been present in other
fields, e.g., [40] pioneered Narrative Psychology. In the humanities the
theory of narrative has been researched for decades, with early works such as
[5] and [14] defining a narrative as “an account of events occurring over
time”. For an overview see [32].

The body of research relating narratives to central bank communication is
growing and there are evidence that narratives affect the economy [36, 25,
19]. These narratives could either be part of the global economy or created by
the central banks themselves. This is also consistent with the concept of
gradualism in which central banks tend to gradually change the interest rate
rather than have large jumps. For instance, from 2001 to 2003 the Fed used
gradualism to reduce the interest rate by 550 basis points over a sequence of
thirteen cuts.333This narrative was discussed by Mr Ben Bernanke, member of
the Board of Governors of the US Federal Reserve System, at his speech
Gradualism at an economics luncheon co-sponsored by the Federal Reserve Bank
of San Francisco (Seattle Branch) and the University of Washington, Seattle,
20 May 2004. Gradualism is founded on the theory of uncertainty in policy
making, in which policymakers are inclined to gradually introduce a policy
when its effect on the economy is ambiguous [13]. Similarly, central bank
communication can introduce narratives that gradually prime the public for
future policy changes, such as changes in financial market regulation or an
introduction of central bank digital currency (CBDC). At present, many of the
central banks are investigating a potential introduction of digital money and
many of them are actively communicating on the matter through speeches and
reports [4].444The ECB, Bank of Japan, Sveriges Riksbank, Swiss National Bank,
Bank of England and the Fed, are actively investigating and reporting on
CBDCs. Thus, central banks are using verbal communication to inform and
prepare the public for future structural change. This is an undocumented way
for central banks to use communication in an active manner to make sure that
monetary policy and regulatory changes are achieved as expected. This
indicates that central bank speeches might address a broader range of topics
than expected by the traditional view of central bank communication.

The two most common ways for central banks to communicate are: (i) Written
disclosures of meeting minutes and reports. (ii) Speeches. Since the 1990s
central bank communication strategies have undergone a transformation: Going
from opaque secrecy, to greater transparency, to actively using communication
as a tool for monetary policy [45, 11, 10]. One of these changes is a large
increase in the number of speeches held in the overall communication
strategies. This has led to a great growth in text data related to central
banks, which now can be analyzed by recent machine learning techniques. Text
data is multidimensional and rich in information. Using advances in
computational linguistics, it is possible to reduce the dimensionality of the
data and use it in economic analysis. The number of speeches from the central
banks affiliated with the BIS, treated in this paper, was 119 in 1997, whereas
in 2019 it was 423. Thus, the volume of the oral communication has increased
greatly. Central bank speeches, in comparison to announcements, are richer in
information, greater in number, significantly longer, and addresses a larger
variety of topics. Therefore, speeches are ideal data to analyze the content
of central bank communication.

Some research has previously been conducted analyzing central bank speeches.
[28] show that speeches from the ECB affect the volatility of the euro-dollar
exchange rate. [2] study speeches from the Swedish Riksbank and find that the
speeches affect market prices, and that the market react stronger to
communication from the head of the Riksbank. [12] show how sentiment of
central bank speeches about financial stability have a significant effect on
market returns and volatility. The two closest studies to this one, which also
rely on topic modelling, are [24] and [3]. [24] study central bank
transparency using topic modelling in an event study around 1993, the year the
Fed started to release the FOMC meeting transcripts. [3] study spillover
effects in sentiment from central bank speeches and show that cross-country
effects affect both central bank communication as well as macroeconomic
variables, where the Fed has a unique influence in creating sentiment
spillover effects.

When the interest rate is close to the efficient lower bound (ELB), central
bank communication is of increased importance, and forward guidance may be the
main policy tool [11]. At these times, the public’s expectations of the
central bank’s future policy is crucial, and indicates that central bank
communication might be weighted towards forward guidance. Yet, the results of
this paper suggest that the content of central bank communication is broad,
also at times when the interest rates are close to the ELB. This is consistent
with the research showing that the general public is either not targeted or
affected by central bank communication [29, 30, 16], and the fact that trust
in central banks is relatively low [26, 20].555According to the Eurobarometer
survey, public trust in the ECB is low [20], but increases as communication
from the ECB increases [26]. Public trust in the ECB has fluctuated during the
last decade. At its lowest in 2014 it was $31\%$, and $42\%$ at its highest in
2019 [20]. [10] predicts that “central banks will keep trying to communicate
with the general public, as they should, but for the most part, they will
fail”. Drawing from the literature of narrative economics, [23] argue that
effective communication needs to be simple, relevant, and story-based and that
central bank communication fail at all three parts, making it inaccessible for
the society in general.

This paper contributes to the literature in several ways. First, the paper
provides a comprehensive dynamic analysis, not previously conducted,
describing the evolution of the content of central bank communication. Second,
the paper introduces the application of Dynamic Topic Models to the field of
finance and economics. Third, I make inference about the autoregressive
properties of the estimated topics, and show that there is strong persistence
in the content, which is not explained by controlling for underlying financial
variables. Finally, the paper draws connections between central bank
communication, topic modelling, and narrative economics, yielding ideas for
further improvements in central bank communication strategies, and suggestions
on how topic modelling could be applied to narrative economics.

The rest of the paper is organized as follows: Section 2 describes the data;
Section 3 outlines the methodology; Section 4 presents the main findings; in
Section 5 a case study investigating the persistence of topics in speeches
from the Federal Reserve is conducted, controlling for regional financial
variables; and Section 6 concludes the paper.

##  2 Data

The central bank speech data was scraped from the BIS website.666The data was
scraped using the Request and Beautiful Soup Python libraries. 14,423 central
bank speeches were collected from 113 institutions, over the time period 1997
through 2020. The speeches consist of English sentences, meaning that the
speeches are transcribed, and when needed translated, into only content and
not including verbal sounds or utterances without meaning. This leads to a
simpler preprocessing as the text does not contain dis-fluencies, such as
fragments of words or filled pauses. [3] were first to use the BIS data
source, using a shorter time period, and to my knowledge their paper is the
only previous time the data source has been used.

The dataset was constrained to include global institutions with more than 200
speeches over the sample period. This criteria was chosen in order to select a
sufficiently homogenous global and talkative subsample. Thus, local central
bank branches, such as the Bank of Spain, were excluded from the dataset. The
final data for the analysis consist of 7,379 speeches from 9 different central
banks: Bank of Canada, Bank of England, Bank of Japan, Central Bank of Norway,
ECB, Fed (including speeches from the New York Fed), Reserve Bank of
Australia, Sweden’s Riksbank, and Swiss National Bank.

The preprocessing of the text data follows standard methodology [21]. The data
were first transformed from pdf format to text format.777The Textract Python
library was used for this task. Each document was split into lower case tokens
(words), removing punctuation, numbers and web links. Headers and footers of
the documents were removed, together with reference lists. A common list of
stop words was applied to filter out words of little importance to the topic
modelling. Through lemmatization the tokens were transformed into dictionary
form, e.g., banks becoming bank. Bigrams, i.e, sequences of two adjacent
tokens, and trigrams, i.e., sequences of three adjacent tokens, were created
of commonly followed tokens, such as central bank and real interest rate.
Extreme tokens, appearing less than 20 times in the corpus or in more than 50%
of the documents, were also filtered out to reduce dimensionality and make
interpretation simpler by avoiding topics to have the same top words in the
generating distributions.888The degree of filtering has in this paper been
determined by a grid search over topic coherence [35], using the full sample
and an LDA model. Table 1 shows the data dimensionality reduction at each step
in the preprocessing. After preprocessing, the data consist of 4,280,706
tokens and the vocabulary (alias dictionary) of 20,697 unique tokens.999A
kernel density estimation shows that the length of the speeches and the
vocabulary are smoothly distributed over the corpus, indicating that the
speeches are not clustered but continuously distributed.

| Raw text | Remove stopwords | Lemmatization | Bigrams and trigrams | Filter extremes
---|---|---|---|---|---
Total words | 22,762,644 | 11,903,054 | 11,737,316 | 9,908,456 | 4,280,706
Unique words | 66,735 | 58,478 | 53,116 | 65,282 | 20,697

Table 1: Data dimensionality reduction of each preprocessing step.

The control variables for the Fed case study were collected from the Wharton
Research Data Service (WRDS). The data include: 1 year US treasury bond
yields, US inflation, the S&P 500 Index returns, and the CBOE Volatility Index
(VIX). The S&P 500 Index data and the VIX data have been down-sampled into
quarterly observations by choosing the maximum values in each quarter. The
maximum values were chosen to preserve as much of the variance in the data as
possible.

##  3 Methodology

In order to analyze the central bank speech data, I use Dynamic Topic Models
(DTM) [7] together with Autoregressive (AR) models. DTM has not, to my
knowledge, previously been applied in the field of finance and economics. DTM
let the topics dynamically change over time, meaning that the word
distributions that define the topics are dynamic. This allows the researcher
to study the time evolution of the latent dynamic topics discovered by the
model. It also improves upon transparency when using the estimated topics in
time series modelling, since the researcher can verify homogeneity of the
topic distributions over time. One can thus identify whether a topic is about
the same subject throughout the sample period.

Latent Dirichlet Allocation (LDA) [9] has become the standard topic model in
the applied literature, building on Latent Semantic Indexing (LSI) introduced
by [18], and later extended by [37] and [27].101010The LDA algorithm has been
further developed: HDP (Hierarchical Dirichlet Process) takes an hierarchical
topic structure into account to find the number of topics [42], and CTM
(Correlated Topic Models) [8] assumes correlation between topics. These
methods have become increasingly popular in finance and economics, for an
overview of NLP in economics see [21].111111Further, efforts have been made to
write software to make natural language processing and topic modelling more
easily accessible, e.g., see [31], [6] and [38]. Like the LDA model, DTM are a
set of generative probabilistic models for discrete data, popular for text,
that introduce a time dimension to the LDA framework and let topics evolve
over time.121212Dynamic Topic Models (DTM) are also called Dynamic LDA (D-LDA)
and Sequential LDA (SLDA). The DTM are unsupervised and use a bag-of-words
structure, meaning that the order of the words do not matter. However in
contrast to the static LDA model, the order of the documents do matter. The
dynamic model addresses the static assumption of the LDA model by updating the
distributions parameters for each time slice, which in this paper is done
annually. This is done by introducing a state space model using a logistic
normal distribution. In the model, each document is generated from a mixture
of topics and each topic is generated from a mixture of words from the
vocabulary.

Given a model with $K$ topics, $D$ documents, and a vocabulary with $V$ terms,
let $\beta_{t,k}$ be a $V$-dimensional vector representing topic $k$ at time
$t$, where $t=1,\ldots,T$ and $k=1,\ldots,K$. $\beta_{t,k}$ evolves with a
Gaussian random walk,
$\beta_{k,t}|\beta_{k,t-1}\sim\mathcal{N}(\beta_{k,t-1},\sigma^{2}I)$, meaning
that the word distribution over topics change over time. Furthermore, let
$\alpha_{t}$ be a $D$-dimensional mean parameter vector of the logistic normal
distribution for the topic proportions, following a Gaussian random walk,
$\alpha_{t}|\alpha_{t-1}\sim\mathcal{N}(\alpha_{t-1},\delta^{2}I)$. A set of
topic models are sequentially chained together and the generative process for
time slice $t$ of a sequential corpus is as follows:

  1. 1.

Draw topics distributions over dictionary
$\beta_{k,t}|\beta_{k,t-1}\sim\mathcal{N}(\beta_{k,t-1},\sigma^{2}I)$.

  2. 2.

Draw mean parameters of document distributions over topics
$\alpha_{t}|\alpha_{t-1}\sim\mathcal{N}(\alpha_{t-1},\delta^{2}I)$.

  3. 3.

For each document:

    1. (a)

Draw $\eta\sim\mathcal{N}(\alpha_{t},a^{2}I)$.

    2. (b)

For each word position $n\in N_{d}$:

      1. (i)

Draw topic $Z\sim Mult(\pi(\eta))$.

      2. (ii)

Draw word $W_{t,d,n}\sim Mult(\pi(\beta_{t,z}))$.

Here
$\pi(\beta_{k,t})_{w}=\frac{\exp(\beta_{k,t,w)}}{\sum\exp(\beta_{k,t,w)}}$
maps the multinomial natural parameters to the mean parameters.131313Note that
the process is similar to that of LDA [9]. However in LDA, the topics and the
topic proportions would have been sampled from the static Dirichlet
distribution, which is the conjugate prior to the Categorical distribution,
i.e., a generalization of the Bernoulli distribution or a special case of the
Multinomial distribution (one draw instead of many), which simplifies the
estimation process, and allow for efficient use of Gibbs sampling. For a
practical overview of LDA see [22]. From a practical point of view, one does
not generate the corpus, but rather backs out the underlying latent
distributions, given a corpus, with variational Bayesian inference.141414[7]
discuss both Variational Kalman Filtering, as well as Variational Wavelet
Regression. The standard deviations of the Gaussian random walks are not
estimated but set to a fixed value given by the implementation in [7], which
is used in this paper together with a Python wrapper [38]. To not estimate
these hyperparameters is standard in the literature but nevertheless a
limitation of the methodology since it restricts to what degree the topics can
change over time.

In a practical way the model can be understood to yield two kinds of results.
First, the model outputs a set of $K$ $V$-dimensional topic distributions for
each time slice $t$. These topic distributions are functions of the vocabulary
and define the $K$ estimated topics in the model. In a topic’s probability
distribution, each word in the vocabulary at each time slice is assigned a
probability defining how likely that word is to be drawn from that topic at
time $t$. Therefore, the most probable words of a topic’s distribution
constitute the theme of that topic. The topic names are manually labelled by
these themes. By tracking the changes in a topic’s distribution across time it
is possible to study how the topic evolves. An example can be seen in Table 2
in Section 4.1 for the estimated topic about supervision and regulation.
Second, with a trained model each document in the corpus can be assigned a
static $K$-dimensional distribution of topics, where each topic is assigned a
probability. This means that each document is classified with a set of topic
probabilities describing how likely the document is to have been generated
from each of the topics. By classifying the documents and averaging the
distributions on a monthly or quarterly basis, it is possible to track the
evolution of topics discussed in the documents over time, as seen in Figure 1
in Section 4.1. Thus, by the output of the model we are able to study both the
evolution of topics discussed throughout the sample period, as well as the
terminology-evolution of the topics’ distributions.

The progression of topics discussed and the within topic change are both
functions of the underlying corpus. If certain significant global events are
happening on the financial markets we would expect a topic about financial
markets to include the contemporary relevant language and have a higher
probability of being addressed. However, the emerging literature of narrative
economics [41] suggests that there are additional variables affecting the
development and spread of topics. Narrative economics can be an explaining
theory of what is driving the unexplained persistence in the model. Narratives
in the global economy, or narratives created by the central banks themselves,
can be contributing factors to what words are likely to appear in the topics’
distributions in each time slice, as well as what topics are likely talked
about in each time slice.

Choosing the number of topics, $K$, is a non trivial and highly researched
area. In the DTM framework, the number of topics are assumed to be known, and
therefore needs to be specified beforehand.151515In contrast to DTM the
Hierarchical Dirichlet Process (HDP) [42] is a topic model built to uncover
the number of underlying topics. A common way to determine the number of
topics is to evaluate the model according to model perplexity [43] in which
the inverse of the geometric mean of the per-word likelihood is evaluated.
Another way is to evaluate the topic coherence, introduced by [35], which
addresses the issue of human interpretability of the topics. If a topic is to
make sense for humans, the top words contributing to the topic distribution
needs to be semantically close to each other. This can be measured numerically
with different coherence measures. In this paper the number of topics was
chosen by a grid search evaluating the topic coherence measure implemented by
[39] using an LDA model on the whole corpus.

Common problems in unsupervised topic modelling are residual topics without a
clear meaning and topics that are too similar to be distinguished from each
other in a meaningful way. To combat these problems some researchers choose a
large amount of topics, e.g., 100, and discard the irrelevant topics. Another
method would be to gather similar topics together and manually classify them
as one. Although these are common approaches, it can lead to overfitting and
ambiguity. In this paper I was able to preprocess the data in such a way that
meaningful and distinct topics were obtained when optimizing over the
coherence score without resorting to increasing the number of clusters in a
dramatic way, or any other human involvement.

##  4 Results

###  4.1 Central bank topics

The hyperparameter optimization subject to the coherence measure yields 29
topics in total. After the DTM estimation, the topics were categorized into 12
local and 17 global topics, depending on the themes of the most likely words
in the estimated probability distributions. The local topics are region
specific, meaning that the highest-probability words belonging to these topics
are related to the corresponding regions. For example, top tokens associated
with the topic about the Swedish Economy are Sweden, Riksbank, and Swedish,
and words relevant to the Swedish economy, such as Krona and Repo rate.
Furthermore, the probability that a local topic is mentioned in an
international setting is low, e.g., the Swedish topic is mainly talked about
by the Swedish Riksbank, hence this is another way to verify and distinguish
local from global topics.

Figure 1: Plot of the average normalized global topic probabilities of the
classified documents for each quarter.

Figure 1 shows the average normalized probability distributions for the global
topics for each quarter in the sample period, given by the classified
documents in the corpus. In each quarter all speeches are classified, their
probability distributions averaged (and normalized), and plotted. As seen in
the figure, the model captures 17 global topics that are continuously present
throughout the sample period, and thus gives an overview of what central banks
talk about. The topics are, as expected, primarily about central bank issues,
such as monetary policy. However, the analysis shows that the topics are not
mainly about coordination of financial market expectations, but addresses a
rather broad set of themes. This suggests that central bank communication is
not consistent with the traditional view that it is fundamentally used to
reveal private information to the public and to affect and coordinate
financial market expectations. Figure 1 shows that the central banks’
communication has been seemingly diverse throughout the sample period,
targeting a wide range of global topics, including payment systems, small
business communities, innovation and technology, economic modelling, and
productivity. This holds true also in times were global interest rates have
been close to the ELB. One can argue that the topics discussed are in the long
run helping the central banks to communicate monetary policy. By informing the
public regarding matters such as payment systems or innovation and technology,
central banks can build up narratives and prime the economy for future
monetary policy paradigm changes. Therefore the communication can be seen as
indirectly related to the traditional definition of central bank
communication.

Some topics have seemingly constant mass over the sample period, e.g., the
topic regarding supervision and regulation. Other topics exhibit clear trends.
After the global financial crisis in 2008, one can see a clustering in topics
associated with the financial system, financial stability, and liquidity. In
contrast, other topics exhibit steady upward trends over time. The topic about
the payment system has a positive recent trend, which is in line with
contemporary technical advancements in the area. Various countries see clear
increases in the amount of digital transactions and many central banks are
investigating possibilities for CBDCs.

An advantage of using Dynamic Topic Models, compared to static topic modelling
such as LDA, is to be able to follow the topics dynamically through the time
dimension. Table 2 shows a sample of the year-by-year evolution of the
probability distribution of the topic related to supervision and regulation.
The table shows words with the highest probability of being drawn from the
topic from years in the beginning and the end of the sample period. One can
see that the topic is apparently homogenous over time, indicating that in the
beginning of the sample, as well as in the end, the topic is about precisely
supervision and regulation. This is important in order to be able to draw more
rigid conclusions from further econometric analysis using the estimated
topics. If one concludes that there is persistence in a topic it is
appropriate to know the content of this topic through time. Furthermore, the
dynamic analysis allows for within-topic investigation of the vocabulary
distribution. Even though the topic is stable one can see that the vocabulary
has changed over time and the probability of other words have increased within
the distribution. In Table 2, the token stress test has a higher probability
in the end of the sample period. However, the token capital requirement is
present as a top word both in 1997 as well as in later years. Note that the
persistence in the word-probability distribution of topics is to some extent
built into the model. The standard deviation in the model controls the speed
at which the topics can evolve on an annually basis. The lower the standard
deviation the lower is the variation in topics over time, and with a standard
deviation of zero the model becomes static.

1997 | 1998 | 1999 | … | 2018 | 2019 | 2020
---|---|---|---|---|---|---
Supervisor (0.024) | Supervisor (0.024) | Supervisor (0.022) | … | Regulation (0.016) | Regulation (0.016) | Regulation (0.016)
Standard (0.021) | Standard (0.02) | Standard (0.017) | … | Requirement (0.009) | Stress Test (0.01) | Stress Test (0.01)
Approach (0.02) | Approach (0.018) | Approach (0.016) | … | Stress Test (0.009) | Approach (0.009) | Approach (0.01)
Supervisory (0.009) | Supervisory (0.009) | Supervisory (0.008) | … | Approach (0.008) | Requirement (0.009) | Requirement (0.009)
Internal (0.008) | Internal (0.008) | Market Discipline (0.008) | … | Capital Requirement (0.008) | Capital Requirement (0.008) | Rule (0.008)
Institution (0.008) | Institution (0.008) | Institution (0.007) | … | Rule (0.007) | Rule (0.007) | Capital Requirement (0.008)
Risk Management (0.007) | Market Discipline (0.008) | Internal (0.007) | … | Regulatory (0.007) | Regulatory (0.007) | Regulatory (0.008)
Market Discipline (0.007) | Risk Management (0.007) | Risk Management (0.007) | … | Regime (0.006) | Framework (0.007) | Framework (0.007)
Capital Requirement (0.006) | Exposure (0.006) | Exposure (0.007) | … | Standard (0.006) | Regime (0.006) | Regime (0.006)
Exposure (0.006) | Proposal (0.006) | Proposal (0.006) | … | Framework (0.005) | Stress Testing (0.006) | Stress Testing (0.006)

Table 2: Year by year evolution of the probability distribution associated
with the topic about supervision and regulation. Sorted probabilities in
parenthesis.

Figure 2 shows the probability, throughout the sample, of the tokens; Basel
II, Regulation, and Supervisor, from the topic about supervision and
regulation. One can see that there has been a shift in language from using the
word supervisor to using the word regulation, and the curves intersect around
2008. This is in line with the fact that the global financial crisis led to
new regulations in the global financial industry. Furthermore, the token Basel
II constitutes a bell shaped curve in Figure 2, with its highest probability
just after the Basel II Accord was published in June 2004. The bell shaped
pattern matches the theory of epidemiology of narratives discussed in [41]. A
narrative starts, it grows, then peaks, and finally declines. Here the
underlying narrative is easy to understand, since it depends on the
regulations and guidelines issued by the Basel Committee on Banking and
Supervision.

Figure 2: Plot of the average probabilities of the tokens; Basel II,
Supervisor, and Regulation, associated with the topic about supervision and
regulation.

[21] emphasize the value of human cross-checking when the subsequent results
of natural language processing are used beyond prediction, in descriptive or
statistical analyses. An auditing of a subsample of twenty to thirty documents
will usually give an idea if the model captures the relevant information in
the corpus. In topic modelling, it is important to validate that the topics
are doing a good job in explaining the documents they are supposedly
generating. Documents are generated from a mixture of topics. However, some
documents have likely been generated from one topic alone, and are thus
excellent candidates for manual investigation. The speech “Implementing Basel
II – choices and challenges” by Ms Susan Schmidt Bies at the Fed is the speech
in the corpus with the highest probability (99%) of being generated from the
topic about supervision and regulation. By reading the speech we can verify
this,

> In my remarks, I will focus primarily on the choices and challenges
> associated with Basel II implementation. In particular, I want to reaffirm
> the Federal Reserve’s commitment to Basel II and the need for continual
> evolution in risk measurement and management at our largest banks and then
> discuss a few key aspects of Basel II implementation in the United States.
> Given the international audience here today, I also plan to offer some
> thoughts on cross-border implementation issues associated with Basel II,
> including so-called home-host issues.  (Ms Susan Schmidt Bies, Member of the
> Board of Governors of the US Federal Reserve System, at the Global
> Association of Risk Professionals’ Basel II and Bakning Regulation Reform,
> Barcelona, 16 May 2006.)

Overall in this paper, the manual validation (of a small subset) of the
speeches suggests that the dimension reduction to topic space captures the
content of the documents well.

###  4.2 Persistence in topics

Next we construct a set of autoregressive (AR) models to investigate the
persistence in the estimated global topics. The analyses are based on
quarterly data following [3] and [36], as well as monthly data for robustness.
The following AR(1) model is estimated for each global topic,

$\theta_{k,t}=\alpha_{k}+\varphi_{k}\theta_{k,t-1}+\bm{\beta}_{k}\bm{X}_{t}+\bm{\gamma}_{k}\bm{X}_{t-1}+\epsilon_{k,t}.$
(1)

Here $\theta_{k,t}$ is the average probability for the classified documents at
time $t$ for global topic $k$, where $k=1,\dots,K$ and $t=1,\dots,T$.
$\bm{X}{t}$ is a vector of region specific control variables at time $t$, used
in the Fed case study in Section 5.

Tables LABEL:table:ar_q and LABEL:table:ar_m report the estimated coefficients
from the AR(1) model in Equation 1 without regional control variables, using
aggregated quarterly and monthly observations for each topic respectively. The
tables show strong significant autoregressive effects in the majority of the
topics.161616The results are robust to estimation in a VAR system, where the
autoregressive effects dominate the cross-sectional effects. The results
indicate large persistence in the topics, on both quarterly and monthly basis.
When central banks talk about a given global topic they tend to continue to do
so for some time. An explanation is that the underlying macroeconomic
variables that the topics reflect are themselves persistent, which we will
control for in the second part of the analysis in Section 5. Another
explanation is that narratives drive the persistence in the topics. These
narratives can either be part of the global economy or narratives set by the
central banks themselves. A few topics are not showing any autoregressive
effects. The topic about supervision and regulation does not exhibit any
significant persistence, indicating that the topic is talked about
sporadically throughout the sample, without specific trends.

##  5 FED case study

In this section, Equation 1 from Section 4.2 is estimated using the Fed speech
data alone, together with regional financial control variables. Central banks
tend to address the current economic environment in their communication.
Therefore, underlying financial and macroeconomic variables play an important
role in determining the topics of central bank communication. Central banks
display heterogeneity in the topics addressed, as well as which variables
affect their communication. The Fed is more likely to talk about topics
related to the US inflation and the US stock market than topics related to
European macroeconomic and financial conditions. By selecting speeches from
one central bank alone, in this case the Fed, it is possible to control for
the regional variables associated with that bank’s speeches.

Figure 3: Plot of average quarterly normalized probability of the topic about
the financial system, together with three normalized control variables.

Figure 3 illustrates the co-movements between the probability of the topic
about the financial system in speeches from the Fed, together with the CBOE
Volatility Index (VIX), the S&P 500 Index returns, and 1 year US treasury
returns. The figure suggests that there might be a relationship between these
variables. Thus, by controlling for the financial variables discussed in the
topic about the financial system we might be able to explain the
autoregressive feature of the topic. If the persistence is fully explained by
the controls, it would suggest that no other effects, such as global
narratives or local central bank narratives, are driving the previous observed
persistence.

Table LABEL:table:fed_q reports the AR(1) coefficients of the average topic
probabilities from 1,841 classified speeches from the Fed and the New York
Fed, from 1997 through 2020, without any control variables. Quarterly data are
used alone as there are months during the sample period in which no speeches
by the Fed were held. The speeches are classified using the DTM model in
Section 4. The model is not re-estimated but trained on the full corpus,
including speeches from the other 8 central banks analyzed in this paper.
Hence, the model is less descriptive of the Fed data, which might be a reason
why the results are weaker compared to the previous results in Table
LABEL:table:ar_q, Section 4.171717The AR(1) results are stronger when
estimating using topic probabilities from a DTM model trained on the Fed
corpus alone, see table 6 in Appendix B.

The autoregressive properties in the global topics are weakened by adding the
controls, but not fully explained, as seen in Table LABEL:table:fed_q_c.
Compared to the estimation without the control variables the results show
smaller coefficients and lower significance of the persistent topics. But,
most topics that exhibit persistence without the controls are also doing so
with the controls. Two exceptions are the topic about the financial system and
the topic about trade, where the persistence seems to be fully explained by
the control variables.

The results from the Fed case study suggest that there are factors other than
the underlying financial variables driving the topics’ persistence. Further,
the results are consistent with the theory of narrative economics and propose
that the communication on topic level is story-based. Story-based
communication is more easily spread in conversations, news and social media
[41], and coming from a central bank it is more accessible for the general
public [23].

##  6 Conclusion

The empirical findings show that central banks talk about a wide range of
global topics, not all immediately related to the traditional theory of
central bank communication. The topics are consistent with the literature
arguing that the communication is not directly targeting the general public.
However, with a broader set of topics, central banks can reveal private
information and prepare society for long term monetary policy shifts and
structural changes. Topic trends occur and vocabulary changes over time, but
most topics have significant probability mass throughout the sample period,
even at times when the interest rate is close to the ELB.

Furthermore, the topics are well captured by Dynamic Topic Models. Both in
terms of quantitative measures, such as coherence scores, as well as manual
investigation linking the topics to the representative documents. Thus, the
dimension reduction of the corpus to topic space is able to, in a meaningful
way, capture the relevant central bank communication. This encourages the use
of topic modelling, and more specifically DTM, in other social science
applications with similar data.

Topic modelling has an interesting application in estimating narratives. The
observed topic persistence is consistent with the theory of narrative
economics and proposes that the central bank communication on topic level is
story-based. The evolution of word-probabilities within the topics are also
consistent with the epidemiology models of narrative economics.

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##  Appendix A Results

Table 3 shows the full set of estimated topics. Table 4 shows the number of
speeches per central bank per year. Table LABEL:table:A_averages shows the
average topic distribution for each central bank. The average distributions
are calculated by taking the mean over the topic distributions for all
classified documents for each central bank. Table 5 shows the full set of
coefficients from the Fed caste study in Section 5, including coefficients for
the control variables.

Topics | Average $\mathrm{P}$ ($\%$) in corpus
---|---
0: Supervision | 3.17
1: Money | 1.61
2: Financial stability | 7.25
3: Payment | 2.77
4: Euro area | 2.63
5: Community | 3.3
6: Financial system | 2.56
7: Unemployment | 1.61
8: Investor | 5.33
9: Innovation | 2.63
10: Liquidity | 1.93
11: Model | 4.37
12: Fiscal | 5.51
13: Productivity | 3.88
14: Trade | 4.37
15: FOMC | 2.14
16: Deflation | 2.55
Sum global: | 57.61
17: Australia | 2.97
18: Canada | 7.02
19: ECB | 3.01
20: Euro area | 4.54
21: Federal reserve | 4.67
22: Japan economy | 1.76
23: Japan | 5.29
24: Norway | 2.12
25: Riksbank | 2.89
26: Residual | 4.08
27: SNB | 2.54
28: UK | 1.53
Sum local: | 42.39
Mean | 3.45
Sum | 100.0

Table 3: Estimated topics, both local and global, and respectively
probabilities in corpus.

| 1997 | 1998 | 1999 | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | Sum
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
CAN | 7 | 6 | 9 | 9 | 12 | 18 | 18 | 18 | 24 | 25 | 29 | 24 | 24 | 23 | 31 | 25 | 28 | 22 | 23 | 27 | 26 | 29 | 19 | 23 | 499
ENG | 13 | 15 | 12 | 22 | 21 | 14 | 7 | 10 | 12 | 17 | 17 | 21 | 28 | 38 | 34 | 25 | 36 | 37 | 47 | 38 | 37 | 44 | 48 | 32 | 625
JPN | 21 | 16 | 15 | 22 | 16 | 21 | 28 | 15 | 20 | 14 | 19 | 18 | 32 | 32 | 45 | 50 | 42 | 44 | 35 | 33 | 39 | 27 | 40 | 24 | 668
FED | 52 | 43 | 42 | 39 | 48 | 55 | 55 | 97 | 86 | 76 | 85 | 88 | 70 | 73 | 62 | 51 | 59 | 46 | 57 | 42 | 54 | 49 | 79 | 57 | 1465
NOR | 0 | 0 | 6 | 7 | 10 | 19 | 14 | 13 | 20 | 20 | 15 | 16 | 17 | 16 | 11 | 10 | 10 | 8 | 8 | 8 | 10 | 9 | 10 | 5 | 262
ECB | 0 | 8 | 46 | 45 | 36 | 40 | 31 | 56 | 51 | 58 | 88 | 149 | 130 | 121 | 139 | 103 | 152 | 130 | 136 | 120 | 169 | 135 | 143 | 99 | 2185
NYC | 5 | 7 | 5 | 7 | 2 | 4 | 3 | 8 | 10 | 12 | 9 | 4 | 11 | 23 | 22 | 18 | 29 | 26 | 34 | 32 | 29 | 26 | 28 | 22 | 376
AUS | 9 | 12 | 9 | 12 | 8 | 12 | 11 | 9 | 13 | 9 | 10 | 17 | 17 | 29 | 32 | 27 | 26 | 26 | 34 | 25 | 33 | 38 | 34 | 23 | 475
SWE | 11 | 13 | 28 | 31 | 29 | 29 | 21 | 24 | 23 | 36 | 22 | 27 | 23 | 25 | 28 | 15 | 17 | 13 | 9 | 11 | 5 | 12 | 8 | 6 | 466
CHE | 1 | 1 | 3 | 2 | 4 | 11 | 11 | 28 | 27 | 27 | 26 | 29 | 25 | 19 | 16 | 21 | 15 | 14 | 16 | 15 | 10 | 16 | 14 | 7 | 358
Sum | 119 | 121 | 175 | 196 | 186 | 223 | 199 | 278 | 286 | 294 | 320 | 393 | 377 | 399 | 420 | 345 | 414 | 366 | 399 | 351 | 412 | 385 | 423 | 298 | 7379

Table 4: Number of speeches per central bank per year.

| (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12) | (13) | (14) | (15) | (16) | (17)
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
|  Regu- lation | Money |  Financial stability | Payment |  Euro area |  Comm- unity |  Financial system |  Unemp- loyment | Investor |  Inno- vation |  Liqui- dity | Model | Fiscal |  Produ- ctivity | Trade | FOMC | Deflation
1 Lag | 0.0211 | 0.170 | 0.174 | 0.381∗∗ | 0.583∗∗∗ | 0.309 | 0.262 | 0.270∗ | 0.367∗∗∗ | 0.0928 | 0.542∗∗∗ | -0.0121 | 0.334∗ | 0.421∗∗∗ | 0.127 | 0.114 | 0.479∗∗∗
| (0.18) | (1.37) | (1.60) | (2.81) | (5.48) | (1.93) | (1.88) | (2.15) | (3.79) | (0.79) | (4.51) | (-0.10) | (2.25) | (4.06) | (0.98) | (1.31) | (3.94)
Inflation | -0.217 | 0.0326 | -0.0803 | -0.396 | -0.305 | -0.141 | 0.225 | -0.145 | -0.108 | 0.0291 | -0.416 | 0.373 | 0.518 | 0.645 | 0.165 | 0.383 | 0.114
| (-0.57) | (0.24) | (-0.13) | (-1.21) | (-1.08) | (-0.39) | (0.53) | (-0.46) | (-0.71) | (0.13) | (-1.20) | (1.31) | (1.15) | (1.41) | (0.44) | (1.37) | (0.35)
Lag Inflation | -0.165 | -0.366∗∗ | -0.125 | 0.375 | 0.0950 | -0.0224 | -0.381 | 0.350 | -0.157 | 0.204 | -0.0432 | 0.212 | 0.0725 | -0.175 | -0.0773 | -0.586 | -0.525
| (-0.49) | (-3.33) | (-0.30) | (1.09) | (0.24) | (-0.06) | (-0.84) | (1.32) | (-0.88) | (0.76) | (-0.11) | (0.69) | (0.17) | (-0.42) | (-0.26) | (-1.56) | (-1.84)
1 year bond | -0.793 | -0.0410 | -0.778 | -0.251 | -0.301 | -0.925 | -0.596 | 1.587∗∗ | 0.237 | -0.223 | -1.578∗ | -0.384 | -0.684 | -0.0599 | 2.037∗∗ | -0.259 | 0.0466
| (-1.66) | (-0.14) | (-1.10) | (-0.39) | (-0.63) | (-1.59) | (-0.70) | (2.90) | (0.84) | (-0.49) | (-2.16) | (-0.70) | (-1.24) | (-0.06) | (3.12) | (-0.42) | (0.11)
Lag 1 year bond | -0.00155 | 0.142 | -0.323 | 0.493 | -1.148∗ | -0.0752 | 1.010 | -0.161 | -0.388 | 0.384 | 0.943 | 0.549 | -0.953 | 0.611 | 0.151 | -0.336 | -1.151∗
| (-0.00) | (0.41) | (-0.45) | (0.69) | (-2.15) | (-0.11) | (1.30) | (-0.28) | (-1.44) | (0.86) | (1.32) | (1.17) | (-1.37) | (0.82) | (0.25) | (-0.57) | (-2.33)
SP500 returns | -0.244 | -0.394∗ | 1.201∗ | -0.275 | 0.424 | 0.0697 | -0.299 | 0.0832 | -0.635∗ | 0.166 | 0.313 | 1.319∗∗ | -0.0479 | 0.773 | -0.0949 | 0.158 | -0.213
| (-0.47) | (-2.04) | (1.99) | (-0.47) | (1.13) | (0.11) | (-0.48) | (0.19) | (-2.49) | (0.50) | (0.63) | (2.93) | (-0.10) | (1.35) | (-0.22) | (0.38) | (-0.59)
Lag SP500 returns | 0.331 | -0.184 | -0.176 | -0.0587 | 0.258 | -0.00507 | 0.157 | -0.0580 | 0.273 | 0.450 | -0.0878 | -0.685 | -0.327 | -0.223 | -0.258 | -0.159 | 0.186
| (0.73) | (-0.92) | (-0.37) | (-0.11) | (0.50) | (-0.01) | (0.27) | (-0.18) | (1.01) | (0.91) | (-0.17) | (-1.53) | (-0.70) | (-0.41) | (-0.62) | (-0.33) | (0.46)
VIX | 0.0000797 | 0.000707∗ | -0.000968 | 0.000413 | -0.000873 | 0.000115 | 0.000524 | -0.000402 | 0.000834∗ | -0.000293 | 0.000172 | -0.00175∗∗ | 0.000750 | -0.000922 | -0.000430 | -0.000179 | 0.000363
| (0.13) | (2.40) | (-1.40) | (0.54) | (-1.57) | (0.14) | (0.68) | (-0.73) | (2.03) | (-0.64) | (0.28) | (-2.97) | (1.11) | (-1.15) | (-0.68) | (-0.30) | (0.47)
Lag VIX | -0.000614 | -0.000143 | 0.000469 | -0.000207 | -0.000109 | 0.000461 | 0.0000854 | 0.000188 | -0.000656 | -0.000881 | 0.000762 | 0.000661 | 0.0000888 | -0.000413 | 0.000365 | -0.000162 | -0.000240
| (-1.00) | (-0.47) | (0.52) | (-0.27) | (-0.14) | (0.66) | (0.10) | (0.39) | (-1.94) | (-1.24) | (0.82) | (0.95) | (0.15) | (-0.56) | (0.59) | (-0.21) | (-0.46)
Constants | 0.0497∗∗∗ | 0.0112∗∗ | 0.0258 | 0.0191∗ | 0.0332∗ | 0.0122 | 0.0208 | 0.0192∗∗ | 0.0201∗ | 0.0401∗∗∗ | -0.0118 | 0.0572∗∗∗ | 0.0183 | 0.0405∗∗ | 0.0310∗∗ | 0.0472∗∗∗ | 0.0206
| (4.49) | (2.77) | (1.58) | (2.01) | (2.35) | (0.83) | (1.82) | (2.85) | (2.46) | (3.95) | (-0.74) | (4.37) | (1.43) | (3.36) | (3.03) | (3.60) | (1.84)
$N$ | 95 | 95 | 95 | 95 | 95 | 95 | 95 | 95 | 95 | 95 | 95 | 95 | 95 | 95 | 95 | 95 | 95
t statistics in parentheses
∗ $p<0.05$, ∗∗ $p<0.01$, ∗∗∗ $p<0.001$

Table 5: Estimated coefficients from the AR(1) models with control variables,
using quarterly data from the Fed. Each equation is represented as a column.
The t-statistics (reported in parenthesis) are based on [34] standard errors
with 1 lag.

##  Appendix B Fed robustness

Figure 4 shows the average normalized probability distributions for the topics
for each quarter, given by the classified documents using DTM trained on the
data from the Fed and the New York Fed alone. In each quarter all speeches are
classified, their probability distributions averaged, and plotted.

Compared to the main model in the paper, one can see that the topic about
supervision and regulation has split into two topics. The patterns of the
topics are familiar, and here expressed by a higher probability of the topic
related to supervision in the beginning of the corpus, and a higher
probability of the topic related to regulation in the end.

Figure 4: Plot of the average probabilities of topics over each quarter.

Table 6 reports the estimated coefficients of the AR(1) models estimated using
data from a topic model trained on data from the Fed and the New York Fed
alone.

| (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12) | (13) | (14) | (15)
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
| Labor | Forecast | Supervision | Housing | Payment |  Small business | Innovation | Regulation | Spending |  Financial markets | FED | Community | Compliance | Trade | Treasury
1 Lag | 0.672∗∗∗ | 0.171 | 0.241 | 0.797∗∗∗ | 0.0876 | 0.132 | 0.640∗∗∗ | 0.489∗∗∗ | 0.464∗∗∗ | 0.402∗∗∗ | 0.579∗∗∗ | 0.277∗ | 0.567∗∗∗ | 0.226∗ | 0.519∗∗∗
| (7.68) | (1.60) | (1.87) | (7.95) | (0.70) | (1.13) | (6.63) | (4.26) | (3.91) | (3.71) | (5.49) | (2.31) | (5.90) | (2.55) | (5.15)
Inflation | 0.882 | 1.024∗ | -0.115 | -0.588 | -0.224 | 0.0300 | 0.398 | -0.266 | 0.946 | -0.134 | -0.707 | 0.468 | -0.107 | -0.141 | -1.342∗∗
| (1.54) | (2.03) | (-0.15) | (-1.00) | (-0.45) | (0.08) | (0.67) | (-0.52) | (1.14) | (-0.23) | (-1.35) | (1.00) | (-0.28) | (-0.31) | (-2.90)
Lag Inflation | -1.284∗ | -1.517∗∗ | 1.844∗ | -0.609 | 0.0924 | -0.342 | 0.872∗ | -0.0738 | -0.545 | 1.087 | 0.298 | 0.753 | -0.0731 | -0.104 | -0.292
| (-2.45) | (-2.85) | (2.16) | (-1.61) | (0.25) | (-0.72) | (2.28) | (-0.10) | (-0.57) | (1.68) | (0.35) | (1.54) | (-0.17) | (-0.27) | (-0.71)
1 year bond | 0.404 | 0.915 | 1.204 | 1.032 | 2.253 | 1.403 | 1.162 | 0.288 | 2.605 | -1.660 | -3.243∗ | -2.436∗∗∗ | -0.0541 | -0.0578 | -1.456
| (0.45) | (0.89) | (0.72) | (1.38) | (1.76) | (1.51) | (0.88) | (0.33) | (1.24) | (-1.80) | (-2.08) | (-3.69) | (-0.08) | (-0.09) | (-1.84)
Lag 1 year bond | -2.348∗∗ | 0.341 | 2.363 | -0.295 | 2.467 | -1.662 | 1.556 | -2.346∗ | -0.589 | 0.891 | 1.720 | -0.474 | -0.527 | 1.327 | -0.119
| (-2.87) | (0.38) | (1.32) | (-0.51) | (1.79) | (-1.98) | (1.51) | (-2.04) | (-0.21) | (0.91) | (1.33) | (-0.55) | (-0.84) | (1.90) | (-0.14)
SP500 returns | -1.454∗ | 0.569 | 0.862 | 0.330 | -2.589∗∗ | -0.235 | -0.246 | -0.794 | 0.0402 | 0.303 | 1.481 | 0.693 | 0.182 | -0.0307 | 0.499
| (-2.34) | (0.61) | (0.76) | (0.55) | (-2.88) | (-0.27) | (-0.36) | (-1.10) | (0.04) | (0.49) | (1.25) | (0.99) | (0.39) | (-0.06) | (0.77)
Lag SP500 returns | 0.112 | 0.135 | -0.125 | -0.338 | 0.284 | -0.141 | 0.210 | 0.779 | 0.130 | -0.410 | -0.438 | -0.188 | -0.337 | -0.312 | 0.395
| (0.15) | (0.17) | (-0.12) | (-0.60) | (0.31) | (-0.18) | (0.27) | (0.92) | (0.08) | (-0.73) | (-0.46) | (-0.30) | (-0.61) | (-0.54) | (0.59)
VIX | 0.00232∗ | -0.00102 | -0.00154 | -0.000343 | 0.00362∗∗ | 0.000210 | -0.000281 | 0.000446 | -0.000613 | 0.000131 | -0.00170 | -0.000469 | -0.000563 | -0.000418 | -0.000140
| (2.57) | (-0.82) | (-0.97) | (-0.43) | (3.04) | (0.15) | (-0.31) | (0.45) | (-0.40) | (0.17) | (-1.28) | (-0.52) | (-0.80) | (-0.62) | (-0.18)
Lag VIX | -0.000877 | -0.00135 | 0.000293 | 0.000483 | -0.000948 | 0.000859 | -0.000203 | -0.000150 | -0.000193 | 0.000230 | 0.00127 | -0.000238 | 0.000594 | -0.000314 | 0.000576
| (-0.70) | (-1.20) | (0.18) | (0.55) | (-0.74) | (0.75) | (-0.18) | (-0.12) | (-0.10) | (0.26) | (0.67) | (-0.27) | (0.60) | (-0.39) | (0.56)
Constants | 0.0481 | 0.114∗∗∗ | 0.0385 | 0.00583 | 0.00329 | 0.0230 | 0.0153 | 0.0410∗ | 0.0528∗ | 0.0373∗ | 0.0263 | 0.0689∗∗ | 0.0277 | 0.0594∗∗∗ | 0.00835
| (1.97) | (5.30) | (1.57) | (0.48) | (0.18) | (1.24) | (1.06) | (2.44) | (2.24) | (2.08) | (0.86) | (3.30) | (1.86) | (4.00) | (0.53)
$N$ | 95 | 95 | 95 | 95 | 95 | 95 | 95 | 95 | 95 | 95 | 95 | 95 | 95 | 95 | 95
t statistics in parentheses
∗ $p<0.05$, ∗∗ $p<0.01$, ∗∗∗ $p<0.001$

Table 6: Estimated coefficients from the AR(1) models, using quarterly data
from the Fed. The documents are classified with a DTM model trained on the Fed
speeches alone. Each equation is represented as a column. The t-statistics
(reported in parenthesis) are based on [34] standard errors with 1 lag.