# Entity-Level Sentiment: More than the Sum of Its Parts

Egil Rønningstad  Department of Informatics, University of Oslo, Norway
Fundamentals of Natural Language Processing, University of Bamberg, Germany
Roman Klinger  Fundamentals of Natural Language Processing, University of
Bamberg, Germany  Lilja Øvrelid  Department of Informatics, University of
Oslo, Norway  Erik Velldal  Department of Informatics, University of Oslo,
Norway

###### Abstract

In sentiment analysis of longer texts, there may be a variety of topics
discussed, of entities mentioned, and of sentiments expressed regarding each
entity. We find a lack of studies exploring how such texts express their
sentiment towards each entity of interest, and how these sentiments can be
modelled. In order to better understand how sentiment regarding persons and
organizations (each entity in our scope) is expressed in longer texts, we have
collected a dataset of expert annotations where the overall sentiment
regarding each entity is identified, together with the sentence-level
sentiment for these entities separately. We show that the reader’s perceived
sentiment regarding an entity often differs from an arithmetic aggregation of
sentiments at the sentence level. Only 70% of the positive and 55% of the
negative entities receive a correct overall sentiment label when we aggregate
the (human-annotated) sentiment labels for the sentences where the entity is
mentioned. Our dataset reveals the complexity of entity-specific sentiment in
longer texts, and allows for more precise modelling and evaluation of such
sentiment expressions.

Entity-Level Sentiment: More than the Sum of Its Parts

##  1 Introduction

Document level annotations |
---|---
Entity |  |  Sentiment
Mick Jagger |  |  Pos-Standard
Rolling Stones |  |  Pos-Slight
Sentence-level annotations
Entity ref |  Relation |  Sentiment
Rolling Stones |  Mention |  Neg-Slight
Mick Jagger |  Mention |  Neg-Slight
(1) There is nothing pretty when Jagger and
the Rolling Stones are on stage.
Entity ref |  Relation |  Sentiment
Mick Jagger |  Mention |  Pos-Slight
(2) But Mick Jagger knows what he is doing.
Entity ref |  Relation |  Sentiment
Rolling Stones |  Coreference |  Pos-Standard
Mick Jagger |  member_of |  Pos-Standard
(3) Soon the band delivers their unique rock’n roll
aestethics that we came for.

Figure 1: Constructed example containing two entities and three sentences. The
document-level sentiment classifications on top are annotated separately from
the sentence-level annotations. Sentence (1) contains mentions of both
"Jagger" and "Rolling Stones". The mention of "Jagger" is resolved to "Mick
Jagger", the most complete mention of that entity. Sentence (2) mentions "Mick
Jagger" positively. Sentence (3) contains a sentiment regarding "the band".
This is a coreference to "Rolling Stones". The annotators also classified the
sentiment regarding "the band" to carry over to the entity "Mick Jagger" as
member of that band.

As the field of sentiment analysis progresses, sentiment analysis has
developed from providing a single positive / negative polarity label for
entire texts (e. g. Pang and Lee, 2004), into various fine-grained approaches,
such as structured sentiment analysis, where for each identified sentiment
expression in a sentence, the sentiment category is classified, and the holder
and target of the sentiment, if any, is identified (Barnes, 2023). Often
however, the end goal of sentiment analysis will be to extract more compound
information about the sentiment expressed towards each entity. Such overall
sentiment classification per entity can facilitate for better media bias
analyses and trend research where the source texts are more complex
(Steinberger et al., 2017). As we show in Section 2, we find few attempts to
classify the overall entity-specific sentiment in longer texts.

To mitigate the lack of such entity-related sentiment data, we provide a
Norwegian dataset of professionally written review texts annotated for
sentiment both at the document and sentence level regarding each person and
organization mentioned, i. e. each volitional entity in the text (Mitchell et
al., 2013). To our knowledge, our dataset is the first openly available of its
kind, in any language, providing such separate sentiment labels for each
entity, both at the sentence level and for the full document. Figure 1
exemplifies this multi-layered annotation scheme. It presents the annotation
granularity at both document- and sentence level.

Our main contributions are as follows:

  1. 1.

A novel dataset and annotation scheme for entity-wise sentiment classification
both at the sentence- and at the full-text level, consisting of 412 texts
containing 2479 entities.

  2. 2.

Analyses of the relations between sentiments expressed locally (at the
sentence level) and globally (at the full-text level) answering our research
question (RQ1): how consistently does sentiment towards each entity’s mention
agree with the entity’s document-level sentiment?

  3. 3.

Classification of sentiment-relating sentences We find that an important part
of the sentiment signal regarding an entity is found in sentences where the
entity itself is not the sentiment target. This answers our research question
(RQ2): how can we quantify the gains from including a wider set of sentences
than those containing a mention of the entity?

  4. 4.

Baseline models for predicting the global sentiment based on sequence labeling
and zero-shot LLM-prompting exemplify the complexity of the task. These are
evaluated to a F1 of 56% and 69% respectively, and are described in Section 5.

##  2 Related Work

We here present work and datasets that to various degrees support entity-
specific sentiment classification for longer texts. Similar works on
exclusively short texts are excluded, as these lack the complexity found in
our dataset.

Entities’ Sentiment Relevance Detection. Ben-Ami et al. (2015) present and
motivate the task of Entity-level Sentiment Analysis (ELSA). We apply their
task description of identifying the document-level sentiment per entity. Our
works differs in that the main focus of their paper is identifying sentiment-
relevant sentences for each entity. They create a smaller dataset for the
financial and medical domain. They do not describe the annotation process, and
we find only 10 samples from each domain available on line today. We provide
and describe a larger dataset, and the focus of our modelling is the end goal
of identifying the entity-level sentiment at the document-level.

Document-level Sentiment Inference. Choi et al. (2016) aim at inferring not
only a sentiments expressed regarding each entity in the text, but also the
holder of each sentiment conveyed in newsmedia texts. Their suggested model
for this demanding task evaluates to well below 50% F1 on all evaluations
reported. In our work, the holder is understood to be the author of the text,
and we focus on the sentiment relations between different entities and
references in the text via both coreferential and other anaphoric relations.

PerSenT. Bastan et al. (2020) annotate documents for one entity each, the main
person of interest in the text, both at the document- and the sentence-level.
Kuila and Sarkar (2024) employ this dataset in their task of determining the
overall sentiment polarity expressed towards a target entity in news texts.
The PerSenT dataset is annotated by crowd-sourcing, annotated for only one
entity per text, and the text length is limited to 16 sentences. In contrast,
our dataset annotates the texts for all volitional entities mentioned in the
text. It is annotated and curated by trained individuals, and the texts
contain on average 27.5 sentences.

NewsMTSC. This dataset by Hamborg and Donnay (2021) and the subsequent
multilingual MAD-TSC (Dufraisse et al., 2023) contain news texts with each
sentence labeled for sentiment regarding important volitional entities
mentioned by name in the sentence. The entities are given identifiers that
allow for sentiment aggregation, but an overall sentiment per entity and text
is not identified. MAD-TSC contains 4714 sentences regarding 1007 labeled
entities, with an average sentence length of 31 words.

ELSA-pilot. In Rønningstad et al. (2022), we presented a pilot study that
motivates treating the global sentiment separately from the local sentiments.
Crucially, we found that aggregation of sentence-level sentiment scores do not
sufficiently capture the entity-dependent signals regarding the overall
sentiment. We find that in the texts inspected, sentiment is related to
entities not only through name mentions and coreferences, but through
sentences with other relations as well. The findings were exploratory, and not
supported by a more complete dataset.

##  3 Data Collection

The Norwegian Review Corpus (NoReC, Velldal et al., 2018) contains 43,436
professional Norwegian newspaper reviews from a range of domains, such as
music, literature, restaurants, movies, electronics and more. The reviews
typically balance both positive and negative assessments of the entity under
review as well as various background information.

The NoReCfine (Øvrelid et al., 2020) corpus contains a subset of 412 reviews
from the NoReC corpus. These texts are annotated for fine-grained sentiment
information, including holders, polar expressions, polarity, and intensity. We
chose this dataset as our texts, and enrich the dataset with new entity-
focused sentiment annotations. More details on our dataset can be found in
Table 1.

###  3.1 Pre-processing

Since our task is to annotate texts for sentiment towards individual
volitional entities, we trained a dedicated named entity recognition (NER)
model for Norwegian on the NorNE dataset (Jørgensen et al., 2020), but
included only the PER and ORG labels (merging GPE-ORG with the ORG category).

All mentions of an entity were clustered through substring matching, to obtain
a list of entities per documents and their mentions. If an entity "John
Travolta" was mentioned in a text, the mentions "John" and "Travolta" would be
clustered together with "John Travolta". There is in Norwegian little case
inflection of proper nouns, besides genitive where the characters "’" and/or
"s" are added. Our substring matcher would therefore check if stripping of "s"
and "’" would give match. This way, "John’s" would be found to be a substring
of "John". We found few clustering errors from this approach. One exception
was that "Elisabeth I" was found to be a substring of "Elisabeth II", and the
two we therefore clustered and counted as one entity in the text.

Split | Entities | Texts | Sentences | Annotations
---|---|---|---|---
Test |  0247 |  044 |  01252 | 1057
Train | 2232 | 368 | 10083 | 8834
Sum | 2479 | 412 | 11335 | 9891
Table 1: Total counts of texts, entities, sentences and annotations for the
dataset after cleaning and postprocessing, as per its initial release.

###  3.2 The annotation task

For each volitional entity in each document, the task of the annotators is to
annotate sentiment at two different levels, as exemplified in Figure 1:

  1. Document level: Based on a reading of the entire text with the given entity in mind, label the sentiment that the full text conveys towards that entity.

  2. Sentiment-relevant references: For each sentiment-relevant sentence, identify the text span that either directly refers to the entity in question or indirectly contributes to the entity-directed sentiment through a specified semantic relation. The possible relations are, in order of priority:

    1. (a)

Name mentions, e. g. "Jagger", "Rolling Stones".

    2. (b)

Coreferences, e. g. "they", "the band".

    3. (c)

Bridging references. In addition to coreference, we annotate anaphoric
relations between entities that are not co-referent, so-called bridging
relations. The inventory of relations was motivated by the pilot study
described in Rønningstad et al. (2022) and included the relations "member_of",
"has_member" and "created_by". When other bridging relations implied sentiment
regarding a target, this was annotated under the subsequent point.

    4. (d)

Whenever a sentence was considered to imply sentiment regarding an entity in
any other way than the above mentioned, the entire sentence was labelled with
sentiment, but no text span inside the sentence was identified.

The relation categories for the bridging relations were suggested to the
annotators from our initial exploration of the data, and in annotation
meetings it was established that these categories were relevant and sufficient
for the dataset at hand. See the annotation guidelines’ list of terms in
Appendix C for further description of coreferences and bridging references.

All sentiment annotations employ a five-category scale, similar to Dufraisse
et al. (2023) and Bastan et al. (2020): "Negative–Standard",
"Negative–Slight", "Neutral", "Positive–Slight", and "Positive–Standard". For
the "Neutral" category, only name mentions are identified, since these could
be added in the pre-processing. The other references to an entity were only
annotated if they were non-neutral. Annotation was carried out using the
Inception tool (Klie et al., 2018). Figure 3 in Appendix A shows example
screenshots from the annotation process.

###  3.3 Annotation guidelines

Our annotation guidelines are derived from those of NoReCfine, which in turn
build on the work of de Kauter et al. (2015). An English translation of the
guidelines is presented in Appendix C, and we briefly present some of the most
central considerations below.

##### When factual statements express sentiment.

Our guidelines conclude that "pure" factual statements without any indication
of sentiment from the author, should be considered neutral. One should limit
the need for domain knowledge from outside the discourse, in order to conclude
whether a piece of information should be classified as conveying any sentiment
polarity. According to these rules, the sentence "The Rolling Stones album
sold over 22 million copies." contains no sentiment towards "The Rolling
Stones".

##### When sentiment towards related targets implies sentiment towards the
volitional entity.

If the annotator perceives a sentiment expression towards a movie to imply
sentiment towards the director, the annotator would, when annotating with
respect to the director, label the movie as "created by", and label the
sentiment that this related target would have. Each case requires separate
consideration by the annotators.

##### Annotate the most prominent reference.

If an entity has more than one reference in a sentence, we annotate the name
mention before coreferences, and coreferences before other anaphoric
references. In the sentence "John played for us and we all love him.", the
name mention "John" would be annotated with positive sentiment, although the
sentiment expression "love" has "him" as target, a coreferent to "John".

###  3.4 Annotation process

The dataset was annotated by five paid NLP students at the BSc level. All are
native Norwegian speakers between 20 and 35 years old. They underwent
introductory training and test annotations in preparation for the project.
During this introductory training, the annotators contributed towards refining
the annotation scheme. All annotations were curated by the first author of
this paper, as the project leader.

After manual cleaning, the pre-annotated volitional entities, 2481 documents
based on 412 texts remained for further analysis. Final counts for the dataset
are presented in Table 1. All annotators took part in the three phases of the
project:

  1. 1.

Introductory parallel annotations and discussions. Annotators were initially
provided with 75 documents, whereby 2–3 annotators would annotate the same
texts. The annotators then inspected each others’ work, the guidelines were
discussed and if neccessary adjusted.

  2. 2.

The entire training corpus annotated. The annotators subsequently annotated
the 2481 document in the dataset, according to availability, one annotator per
document. Each annotator annotated from 200 documents and upwards. The number
of documents annotated by each annotator is shown in Table 3.

  3. 3.

Parallel annotation of the test set. Finally, all annotators annotated the
test split, as pre-defined in NoReCfine, in parallel. The test data contains
44 different texts, containing a total of 247 volitional entities. Each text
contains on average 28.5 sentences.

  4. 4.

Curation The project leader reviewed all annotations in the dataset. For the
training and development splits, there was one annotator to review. The
annotations were corrected when neccessary. The amount of document-level
annotations corrected by the curator, varied among the annotators from 0.5% to
8.2%. For the test split, all annotators annotated all instances. The curator
inspected the majority vote before making the final judgement. The agreements
here are shown in Tables 2 and 3.

###  3.5 Annotator agreement

We present here the annotator agreements, both for the overall sentiment per
entity, and for the sentence-level annotations. For these analyses, we remove
the intensity levels "Slight" and "Standard", and check for agreement only in
terms of the main categories "Positive", "Neutral" and "Negative".

##### Document–entity sentiment.

We first inspect annotator agreement for the overall sentiment assigned to
each volitional entity at the document-level. Table 2 shows the agreement
towards the curated version. We find that the mean Cohen’s Kappa among
annotators compared to the curated document labels was 0.71, and standard
deviation among the five annotators is 0.11.

##### Sentence–entity sentiment.

We then turn to annotator agreement at the sentence-level, again with respect
to the labels "Positive", "Neutral" or "Negative", with Cohen’s kappa shown in
Table 3. Mean Cohen’s kappa for agreement with the curated annotation is 0.72,
and standard deviation among the annotators is 0.06.

| ann_1 | ann_2 | ann_3 | ann_4 | ann_5
---|---|---|---|---|---
curated | 0.53 | 0.81 | 0.75 | 0.67 | 0.80
ann_1 | 1.0 | 0.43 | 0.34 | 0.35 | 0.41
ann_2 |  | 1.0 | 0.65 | 0.66 | 0.79
ann_3 |  |  | 1.0 | 0.60 | 0.71
ann_4 |  |  |  | 1.0 | 0.69
# ann’d | 380 | 820 | 515 | 245 | 875
Table 2: Cohen’s kappa agreement on the documents’ sentiment polarity for each entity. Mean agreement with the curated result is 0.71. "# ann’d" indicate how many documents in the dataset each annotator had annotated before starting on the test set. | ann1 | ann2 | ann3 | ann4 | ann5
---|---|---|---|---|---
curated | 0.64 | 0.77 | 0.78 | 0.68 | 0.74
ann_1 | 1.0 | 0.54 | 0.57 | 0.52 | 0.53
ann_2 |  | 1.0 | 0.71 | 0.65 | 0.70
ann_3 |  |  | 1.0 | 0.63 | 0.77
ann_4 |  |  |  | 1.0 | 0.65
ann_5 |  |  |  |  | 1.0
# ann’d | 380 | 820 | 515 | 245 | 875
Table 3: Cohen’s kappa agreement between annotators and the curated conclusion
for sentiment polarity on the sentence level, with respect to the given
entity. Mean annotator agreement with curated is 0.72.

##### Conclusions from analyzing inter-annotator agreement.

Despite individual variations in agreement, mean Cohen’s kappa agreement at
both the document- and sentence level is above 0.70. We consider this to be a
satisfactory level of agreement, and an indication that the annotators indeed
were able to identify and classify the requested sentiment signals in the
texts. Inspecting selected disagreements indicate that one source of
disagreement lies in drawing the line for how much world knowledge to include
in a sentiment judgement. Zaenen et al. (2005) argue that world knowledge
underlies just about everything we say or write, and that this leads to
diverging readings of a text. We found in our data that annotators in deed
tended to disagree, e. g. when a person commonly considered to have been
"good" or "bad" was mentioned without a particular sentiment expressed in the
text. During curation, these cases would be judged as Neutral.

We further find it noteworthy that the two annotators with the fewest
documents annotated have the lowest agreement with the curated version. The
minimum requirement was to annotate at least 200 documents before proceeding
to annotating the test set. But in our case, annotators who annotated more
than 400 documents had noticeable higher agreement with curated, as seen in
Tables 2 and 3.

##  4 Dataset Analysis

We here present selected analyses of the main body of the dataset. The results
in this section relate to the training and development splits combined. This
collection contains 368 reviews with 2232 volitional entities and 8834
sentiment labels in total. The focus is on providing answers to RQ1 about the
relations between the individual mentions of an entity and the entity’s
document-level sentiment. We also answer RQ2 by quantifying the gain from
including more sentences than those containing a mention of the entity.

Relation category | # | %
---|---|---
Name mention | 1382 | 36.7
Coreference, anaphoric | 432 | 11.5
Bridging: created_by | 966 | 25.7
Bridging: has_member | 294 | 7.8
Bridging: is_member | 48 | 1.3
Sentence-level sentiment | 641 | 17.0
Total | 3763 | 100.0
Table 4: All non-neutral sentiment annotations in the training and development split of the dataset. We find that only 36.7% of the annotated sentiments are on sentences containing an entity’s name mention.  mentions_only | Neg-Std | Neg-Slight | Neutral | Pos-Slight | Pos-Std | Total | Neutral
---|---|---|---|---|---|---|---
Document-level |  |  |  |  |  |  | pct
Positive–Standard | 1 | 4 | 134 | 32 | 502 | 673 | 19.9
Positive–Slight | 0 | 4 | 43 | 54 | 17 | 118 | 36.4
Neutral | 2 | 2 | 1139 | 12 | 4 | 1159 | 98.3
Negative–Slight | 10 | 59 | 46 | 1 | 5 | 121 | 38.0
Negative–Standard | 97 | 9 | 48 | 5 | 2 | 161 | 29.8
Table 5: Sentiment towards entities’ name mention vs. sentiment towards the entity at the document level. Sentiments at the name mention level are aggregated by averaging the non-neutral sentiments. When inspecting the "Neutral" row, we find that 1139, or 98.3% of the Neutral entities in the documents, had neutral sentiment towards all entity mentions. For the entities with sentiments, we find that 19.9–38 pct of these had no sentiment at the name mentions, and were incorrectly aggregated to "Neutral". Aggregated entities | mentions | mentions | mentions | all sentiments | support
---|---|---|---|---|---
|  | coreferences | coreferences |  |
Document-level |  |  | bridging |  |
Positive–Standard | 83.5 | 84.9 | 89.0 | 89.5 | 673
Positive–Slight | 48.6 | 46.9 | 48.3 | 48.8 | 118
Neutral | 88.7 | 90.1 | 93.6 | 94.5 | 1159
Negative–Slight | 59.3 | 55.8 | 64.4 | 63.2 | 121
Negative–Standard | 71.6 | 73.4 | 75.4 | 77.4 | 161
Accuracy | 82.9 | 83.7 | 86.6 | 87.2 |
Weighted avg | 82.2 | 83.2 | 86.9 | 87.6 |
Table 6:  F1 scores for the five sentiment classes in the dataset, when using
increasingly more of the annotated data. For the first column, only sentiments
directed towards the entity mentions are aggregated. For the next column,
coreferences are added. Then targets with a bridging relation are added,
before all annotations at a sub-document level as aggregated per entity. All
aggregations use the strategy of averaging non-neutral sentiments. This table
is graphed in Figure 2.  Figure 2: Improvements per sentiment category and
sentence relation category. We here use a weighted average of the two
sentiment intensities in Table 6.

###  4.1 Annotations and polarity-counts

Table 4 shows the distribution of annotations in the dataset, across category
and sentiment. It shows that the sentiment-relevant coreferences beyond name
mentions are comparably few. In contrast, we find that the bridging relations
(created_by, has_member and is_member) contribute quite significantly to
entity-directed sentiment in our dataset. These relations constitute 34.8% of
the annotated sentiments, almost equally frequent to the sentiment labels that
are directly attached to an entity mention. These figures indicate that any
approach that labels only sentences for sentiment regarding an entity if that
entity is named in the sentence, appear to lose the majority of sentiment
signal, which is found in sentences with other relations to the entity.

###  4.2 Document-level vs aggregated lower level sentiment

In this work we are specifically interested in the relations between the high-
level and lower-level annotations for each entity. The availability of our
dataset enables further analysis of these correlations at the per-entity
level. In the following we will attempt to evaluate the effect of each
category of sentiment-related sentences and how the aggregation of lower
levels of sentiment classifications compare to the document-level score
independently assigned by our annotators. We start by aggregating the
sentiments for the name mentions only, before we add the remaining available
annotations. When referring to the aggregated sentiment score, we here refer
to averaging and rounding the non-neutral mentions, whereby we assign the
"Standard" sentiments the value of $\pm$2, and slight sentiments are $\pm$1.

##### Sentiment towards entity mentions only.

In the previous section, we established that the majority of sentiment signals
in our texts lay in sentences without the entity explicitly mentioned.
However, if the sentiment signals from the sentences containing an entity
mention are coherent with the sentiment signals in sentences with other
relations to the entity, these latter sentences would be redundant in order to
satisfactorily locate the document’s overall sentiment regarding the entity in
question. Table 5 shows the confusion matrix for aggregated sentiment for name
mentions, compared with the annotated document-level sentiment. The "Neutral"
column shows the distribution of entities that do not receive any sentiment
towards their name mention, over their true, document-level sentiment. We see
that 19.9% of the true "Positive–Standard" entities receive no sentiment
towards their name mention, while 38% of the true "Negative–Slight" entities
are without any sentiment towards their name mention. This gives an answer to
RQ1 through the observation that 271 out of the 1073 non-neutral entities in
the dataset (25%) are incorrectly assigned a neutral sentiment by the
sentiment-bearing sentences where their name is mentioned. To correctly
classify these entities, we need to find a sentiment signal in other parts of
the text.

##### Sentiment towards name mentions and references.

In order to further understand the sentiment contributions of the various
references to an entity, we compare the F1 scores for aggregated sentence-
level gold sentiment labels. We start with the sentences with name mentions
only, gradually adding more sentiment relation categories. This may be
considered an ablation study where we explore the impact of the various parts
of the dataset’s categories. We start with the name mention sentiments, as
described in the previous subsection. Subsequently, the coreferences are
added, then the bridging mentions, and finally the sentence-level sentiment
annotations. Table 6 and Figure 2 shows that aggregating sentiment expressed
towards both name mentions and anaphoric coreferences add just one percentage
point to the support-weighted average F1. Adding the targets with a bridging
relation to the entity, though, improves the average F1 by an additional 3.7
percentage points. From there, including also other sentences where the
annotators found a sentiment-relevant relation to the entity, only improves
weighted average F1 from 86.9% to 87.6%.
These findings indicate an answer to RQ2, that in order to find the sentiment-
relevant parts of a text with respect to an entity, looking only at sentences
with an entity’s name mention or even including any anaphoric coreference to
the entity, is not enough. Having a model that can also capture sentiment from
sentences where a target has a bridging relation to the entity, appears to be
important.

Entity |  | non- |
---|---|---|---
mentions | neutral | neutral | Total
Multiple | 231 | 566 | 797
Single | 928 | 507 | 1435
Table 7: Distribution of neutral and non-neutral entities, with one or
multiple name mentions in the text. 507 out of the 1435 entities mentioned
only once, receive a non-neutral sentiment.

###  4.3 Are single mentions in general neutral?

In our dataset, almost two thirds of the entities are mentioned only once by
their name in a given text. If we, as suggested by Dufraisse et al. (2023)
could assume that entities mentioned only once are neutral and not in focus,
that would simplify the task considerably. For our dataset, Table 7 shows that
although a majority of the entities with only one name mention are neutral,
nearly half of the entities receiving a polarity are single mention entities.
Discarding these would have meant discarding much valuable sentiment
information, and we conclude that entities with one name mention only are
worth keeping.

##  5 Baseline Modelling

We here present two approaches to using language models for predicting the
document-level sentiment regarding each entity mentioned in the text. Due to
the richness of annotations, neither of these utilize all available
annotations in the dataset. The first approach fine-tunes a model for finding
the relevant entity mentions and labeling these with sentiment polarity
"Positive", Negative" or "Neutral". The heuristics described in Section 4.2
aggregates these to the document-level prediction. The second approach prompts
a large language model with the text, the entities, and a request to return
the document-level sentiment label for each entity.

###  5.1 Predicting and aggregating mentions’ sentiments

We extract a simplified dataset containing only the entity mentions and their
sentence-level sentiments. We train a sequence labeler to identify entities
and their three-class sentiment, with evaluation results shown in Table 8. The
pretrained model applied was
NorBERT3-large111https://huggingface.co/ltg/norbert3-large (Samuel et al.,
2023). The models tested and search space for hyperparameters explored are
shown in Table 11 in Appendix B.

As discussed in Section 4, the document-level sentiment can not be fully
derived from the set of sentiments regarding each mention of an entity.
However, we aggregate the predicted sentiments, similarly to how we aggregated
the annotations for each entity mention in Section 4. This approach serves as
a naive modelling baseline and an example of the limitations of this approach.
The results from aggregating the modelled labels to the document-entity level
are presented in Table 9. Table 6 shows that 82.9% of the entities in the
training and development splits were correctly classified at the document
level when aggregating the true sentiment labels for the entities’ mentions,
and serve as an upper bound for this approach. Table 9 shows that when
aggregating the predicted labels, 70.9% of the entities in the test split were
correctly labeled with this baseline model.

| Precision | Recall | F1 | Support
---|---|---|---|---
Neg | 70.6 | 41.4 | 52.2 | 29
Neu | 73.9 | 88.3 | 80.5 | 308
Pos | 68.0 | 57.1 | 62.1 | 119
Macro avg | 70.8 | 62.3 | 64.9 | 456
W. avg | 72.2 | 77.2 | 73.9 | 456
Table 8: Sequence labelling of each individual entity name in the test split. An exact match for both the text span and sentiment label is required for the predictions to be counted as correct. At this level there is no aggregation. Aggregated sentiment labels per entity are presented in Table 9. | Precision | Recall | F1 | Support
---|---|---|---|---
Neg | 44.4 | 19.0 | 26.7 | 21
Neu | 67.4 | 95.5 | 79.0 | 132
Pos | 88.2 | 47.9 | 62.1 | 94
Accuracy | 70.9 | 70.9 | 70.9 |
Macro avg | 66.7 | 54.1 | 55.9 | 247
W. avg | 73.4 | 70.9 | 68.1 | 247
Table 9: Aggregated sequence labels from the baseline sequence labeling model,
evaluated against the entities in the test split.

###  5.2 Zero-shot LLM prompts

Recent work indicates that ChatGPT and open-source counterparts may be a
relevant resource for annotating and labeling English texts (Gilardi et al.,
2023; Alizadeh et al., 2024). We therefore constructed a zero-shot dialogue
with ChatGPT.

The prompts were what we consider clear and well-posed Norwegian questions
about which of the three sentiment categories "Positive", "Neutral" or
"Negative" is assigned to a given entity by the text. We performed the
dialogue through the web interface with a paid monthly subscription to OpenAI,
employing GPT v4 (Achiam et al., 2023).

The initial prompt was the entire text, preceded with this sentence in
Norwegian: "In the subsequent text, is the sentiment towards "Kirsten
Flagstad" Positive, Negative or Neutral?"
Where "Kirsten Flagstad" is the volitional entity in question. The prompt
would be a lengthy answer including reasoning. The next prompt would be,
translated: "Please give the answer with one word, Positive, Negative or
Neutral". Table 10 shows that this zero-shot approach yielded an accuracy of
73.3%

| Precision | Recall | F1 | Support
---|---|---|---|---
Neg | 60.0 | 57.1 | 58.5 | 21
Neu | 77.4 | 72.7 | 75.0 | 132
Pos | 70.9 | 77.7 | 74.1 | 94
accuracy | 73.3 | 73.3 | 73.3 |
macro avg | 69.4 | 69.2 | 69.2 | 247
W. avg | 73.4 | 73.3 | 73.3 | 247
Table 10:  Predicted sentiment labels per entity at the document level in the
test split, provided through ChatGPT with GPT-4.

##  6 Conclusion

We have presented a dataset annotated for entity-level sentiment analysis
based on professional review texts in Norwegian. The dataset allows for
training and evaluating models for entity-wise sentiment analysis. We have
shared insights from the dataset creation, and analyzed how sentence-level
expressions of sentiment regarding an entity relate to the entity’s overall
document-level sentiment. The dataset is available
online.222https://github.com/ltgoslo/ELSA.git

## Acknowledgements

The work documented in this publication has been carried out within the NorwAI
Centre for Research-based Innovation, funded by the Research Council of Norway
(RCN), with grant number 309834.
Baseline model training was performed on resources provided by Sigma2 – the
National Infrastructure for High-Performance Computing and Data Storage in
Norway.
We would like to thank the anonymous reviewers for their helpful comments. We
are thankful for the skilful annotation work and overall contributions from
the research assistants who annotated the dataset: Daniel Skinstad Drabitzius,
Iunia Melania Antal, Birk Søråsen, Ellen Margrethe Ulving, and Håkon Liltved
Hyrve.

##  7 Ethical Considerations

We are not aware of any misconduct or violation of rules and regulations
during the work with the presented dataset. The newspaper reviews used for our
dataset are previously published and made available for research. The
annotators were compensated with the university’s standard wages as research
assistants for all hours of involvement in the project.

The reviews in our dataset are sampled from a corpus of Norwegian reviews
published in the periode 2003–2017. Opinions and writing styles could be
considered representative for their news sources and time period.

The raw texts in our dataset have been publicly available for several years,
and have been available for llms to train on. Our annotations were not
publicly available when we prompted ChatGPT, and were not submitted as
examples during our ChatGPT experiments.

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##  Appendix A  Annotation Example

Figure 3 in the appendix shows segments from screenshots of one text being
annotated for two different entities, two members of the same band: Julian
Casablancas, the band leader and vocalist, and Nick Valensi, the guitarist in
the band. The text is machine translated from Norwegian and just briefly
corrected. Green labels are at the segment level: The sequence is annotated
for relation to the entity and for sentiment. Blue labels are the overall,
document-level sentiment towards an entity. Each document therefore, has one
such annotation. Pink labels are for sentences expressing sentiment with an
unspecified relation to the entity. We see that the annotators found some
sentiments towards the band to imply sentiment towards the band leader Julian
Casablancas. For the guitar player Nick Valensi, only sentiment regarding him
directly was recorded.

Figure 3: Annotations for two of the entities identified in the same text.
Blue labels are document-level, green labels are segment-level, red labels are
sentence-level. Sentence 19 is labeled as conveying a negative sentiment
regarding Casablancas, since he is the vocalist.

##  Appendix B Baseline Details

Table 11 shows the hyperparameters search space for the sequence labelling
model we trained for predicting an entity’s overall sentiment based on the
sentiment expressed towards each entity mention. The code employed is a copy
from the HuggingFace token classification task.

Parameter | Settings
---|---
Models | NbAiLab/nb-bert base and large
| ltg/norbert3-large
Seeds | 101, 202, 303
Batch size |  32, 64
Learning rate | 1e-05, 5e-05
Epochs (best) | 12 (6)
Table 11: Hyperparameters explored for fine-tuning a model for identifying and
labeling name mentions and their polarity. Best options in bold. The narrow
selection of models and hyperparameters is based on preliminary experiments
with the material.

##  Appendix C Annotator Guidelines

These are the guidelines used for annotating the texts of NoReCfine for
entity-level sentiment. This annotation was done as part of the ELSA project,
using INCEpTION. The original guidelines are written in Norwegian. The
following is a translation into English.

The guidelines are based on the guidelines for NoReCfine and the work that
NoReCfine refers to: Kauter, Marjan Van de et al. “The good, the bad and the
implicit: a comprehensive approach to annotating explicit and implicit
sentiment.” Language Resources and Evaluation 49 (2015): 685-720.

###  C.1 Objective

The main objective of the annotation is to create a dataset where sentiment
expressed against entities in the document is annotated. "Entities" are
limited to persons and organisations. First, the sentiment that the document
as a whole expresses towards the entity is annotated, before the sentences
that contribute to conveying sentiment towards the entity are derived. If
possible, the recipient of the expressed sentiment in the sentence should be
annotated with the sentiment and how this recipient relates to the main
entity.

##### List of terms

  * •

Sentiment: A positive or negative attitude towards something or someone.

  * •

Sentiment analysis: An inference of the sentiment expressed in a text. This
can occur both when the author conveys their sentiment directly, and when the
author conveys statements or information that can be said to convey a positive
or negative impression of the entity.

  * •

Annotate: Labelling words or phrases and entering information about these
items.

  * •

(Volitional) entity: Individual people and groupings of people who have a
proper name. This includes organisations, companies and parties. Geopolitical
organisations, such as countries or cities, are also considered volitional
entities where they function as actors with intent. Made-up characters and
organisations are also volitional entities in the given text. Examples of
volitional entities include "Elsa", "Beatles", "Jens Stoltenberg", "Black
Widow", "Norske Skog" and "Oslo City Council". In this project, entity is used
as short form for volitional entity.

  * •

(Entity) mention: Where an entity is mentioned either with all of or part of
its proper name. In the text "Jens Stoltenberg came to visit. Stoltenberg
seems tired at the moment." there are two mentions, "Jens Stoltenberg" and
"Stoltenberg", where we can interpret it as both referring to the same entity.

  * •

Coreference: Where an entity is mentioned without using the entity’s proper
name. This can be done by using nouns or pronouns such as "these", "the band",
"the prime minister" or "he".

  * •

(Sentiment) target: If a sentence expresses positivity or negativity towards
something, the target is the word or words that represent this "something"
that the sentiment is directed towards.

###  C.2 Degree of detail for the annotation

The expressed sentiment should be directly related to the main entity we are
annotating for. The annotation should take little consideration of domain
knowledge, other than that which may be found in the text. Factual information
should not be interpreted as carrying sentiment, unless a clear sentiment is
also expressed. Irony and sarcasm where a negative sentiment can be expressed
using otherwise positive words are annotated as negative sentiment. The
annotation distinguishes between 2 levels of intensity:

##### "Standard"

is used where the sentiment is clear.

##### "Slight"

is used where the sentiment is weaker in intensity. "Slight" is also used
where the sentiment appears vague or uncertain.

####  C.2.1 Document level

For each entity, you must specify the sentiment that the document as a whole
conveys towards this entity. This sentiment should be the annotator’s
impression of the document’s sentiment towards the entity after reading, which
is not necessarily an aggregate of the sentiment analysis at sentence and
entity level.

The sentiment "Neutral" is used for all entities that are only mentioned in
the text, without the text conveying any further sentiment towards the entity.

####  C.2.2 Sentence level

In cases where you find sentences that are relevant for conveying sentiment
towards the entity, without finding a target that represents the entity or is
related to the entity, the entire sentence should be annotated with the
sentiment that is conveyed.

####  C.2.3 Segment level

At segment level, we annotate sentiment targets. The sentiment must appear in
the same sentence as where the target is located. If it does not, the
sentiment-bearing sentence should be annotated at sentence level.

For each annotated sentiment, the relationship to the sentiment target must be
specified.

`-name_mention` is used where the entity is fully or partially mentioned by
name. The name corresponds to the name of the main entity in the document.

`-anaphoric` is used where the entity has an anaphoric representation in the
sentence through coreference.

`-is_member` is used where someone or something in the text is part of the
main entity.

`-has_member` is used where the main entity is part of a larger group and the
sentiment expressed towards the larger entity affects the sentiment towards
the main entity.

`-created_by` is used where some kind of product is created by the main
entity.

The word span that constitutes the sentiment target should be as short as
possible, with the exception of proper names, where each part of the name that
appears should be annotated together ("Barack Obama", not just "Barack" or
just "Obama").

Where several possible sentiment targets appear in the relevant sentence, the
following hierarchy is used to choose which relation to annotate:

  1. 1.

`name_mention`

  2. 2.

`anaphoric`

  3. 3.

`-is_member`, `has_member` or `created_by`

  4. 4.

Annotate at the sentence level

If conflicting sentiment is expressed towards the same entity in the same
sentence, the first representation of the entity (following the hierarchy
above) should be annotated with the sentiment conveyed by the sentence as a
whole.


$\delta^{b}$ | 0.074 | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$ | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$ | $5.9\times 10^{-3}$ | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$ | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$ | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$ | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$ | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$
| ( 0.037) |  |  | (0.0364) |  |  |  |  |
$\frac{\sigma^{b}}{\mu^{b}}$ | 0.409 | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$ | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$ | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$ | 0.015 | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$ | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$ | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$ | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$
| (0.172) |  |  |  | (0.156) |  |  |  |
$\mu^{\xi}$ | 0.431 | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$ | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$ | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$ | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$ | 0.271 | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$ | 0.039 | 0.04
| (0.006) |  |  |  |  | (0.019) |  | (0.022) | (0.017)
$\lambda$ | 18.838 | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$ | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$ | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$ | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$ | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$ | 4.288 | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$ | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$
| (6.795) |  |  |  |  |  | (9.293) |  |
$\Delta^{\lambda}$ | -0.0287 | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$ | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$ | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$ | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$ | 0.039 | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$ | 0.012 | $0.011$
| (0.006) |  |  |  |  | (0.022) |  | (0.01) | (0.014)
$\Delta^{\theta}$ | 0.0948 | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$ | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$ | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$ | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$ | 0.04 | $\mathchoice{\mathbin{\vbox{\hbox{{$\displaystyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\textstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptstyle\bullet$}}}}}{\mathbin{\vbox{\hbox{{$\scriptscriptstyle\bullet$}}}}}$ | $0.011$ | 0.011
| (0.019) |  |  |  |  | (0.017) |  | (0.014) | (0.017)

Note: In this table we present the estimates of mean and variance-covariance
matrix of the modal demand parameter $\Psi$ given at the modal initial
capacity $\omega_{1}^{*}$. Our modal capacity has 115 economy class seats and
14 1st-class seats. Bootstrapped standard errors are in the parentheses.

Table A.2.2: Estimated Mean Values of $\Psi$, by Capacities

Parameters${\backslash}$Capacity Index (1) (2) (3) (4) (5) (6) (7) (8) (9)
(10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) $\mu^{l}$ 411.53 431.14
455.91 511.26 298.82 455.92 405.24 354.38 429.78 411.84 427.50 436.63 354.30
330.03 444.48 478.27 504.97 422.39 498.49 438.26 $\frac{\sigma^{l}}{\mu^{l}}$
0.53 0.60 0.48 0.39 0.96 0.53 0.50 0.55 0.61 0.55 0.43 0.50 0.97 0.95 0.32
0.39 0.48 0.44 0.40 0.68 $\delta^{b}$ 0.23 0.16 0.04 0.04 0.66 0.15 0.09 0.36
0.31 0.09 0.53 0.26 0.37 0.40 0.05 0.06 0.03 0.07 0.04 0.15
$\frac{\sigma^{b}}{\mu^{b}}$ 0.12 0.16 0.53 0.51 0.16 0.29 0.29 0.45 0.14 0.34
0.59 0.14 0.56 0.40 0.56 0.40 0.55 0.55 0.48 0.33 $\mu^{\xi}$ 0.01 0.24 0.22
0.25 0.24 0.32 0.01 0.01 0.44 0.01 0.02 0.29 0.15 0.04 0.35 0.26 0.29 0.32
0.29 0.12 $\lambda$ 24.23 26.29 20.97 34.38 14.13 18.12 27.65 21.97 22.44
27.40 12.26 23.21 18.82 17.51 28.62 23.86 33.20 27.59 30.52 26.46
$\Delta^{\lambda}$ -0.08 -0.08 -0.04 -0.08 -0.05 -0.09 -0.07 -0.08 -0.09 -0.07
-0.09 -0.09 -0.09 -0.09 -0.09 -0.07 -0.08 -0.09 -0.08 -0.06 $\Delta^{\theta}$
0.07 0.07 0.09 0.05 0.08 0.07 0.08 0.09 0.05 0.08 0.06 0.08 0.07 0.08 0.06
0.09 0.07 0.08 0.06 0.10

Note: In this table we present the mean demand parameters from the conditional
distribution
$h(\Psi|\omega_{1};\widehat{\mu}_{\Psi},\widehat{\Sigma}_{\Psi})$, given the
initial-capacity $\omega_{1}$. We estimated the model for 20 different
capacities, and each capacity index corresponds to one such capacity. Table
A.2.3: Estimated Mode Values of $\Psi$, by Capacities

Parameters${\backslash}$ Capacity Index (1) (2) (3) (4) (5) (6) (7) (8) (9)
(10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) $\mu^{l}$ 100.35 433.05
128.12 444.19 119.05 224.42 381.73 107.06 114.21 106.32 287.67 476.89 101.62
308.74 258.56 381.76 615.27 210.74 376.61 587.11 $\frac{\sigma^{l}}{\mu^{l}}$
0.48 0.00 0.50 0.03 0.96 0.56 0.96 0.91 0.91 0.95 0.53 0.99 1.00 1.00 0.08
0.17 0.17 0.00 0.00 0.93 $\delta^{b}$ 0.02 0.16 0.04 0.04 0.63 0.14 0.09 0.34
0.32 0.07 0.58 0.03 0.34 0.10 0.06 0.06 0.00 0.00 0.00 0.15
$\frac{\sigma^{b}}{\mu^{b}}$ 0.01 0.17 0.53 0.06 0.18 0.20 0.84 0.27 0.17 0.90
0.44 0.14 0.63 0.24 0.52 0.38 0.32 0.60 0.26 0.22 $\mu^{\xi}$ 0.00 0.05 0.08
0.68 0.42 0.26 0.01 0.00 0.95 0.00 0.00 0.02 0.16 0.04 0.22 0.01 0.64 0.15
0.63 0.07 $\lambda$ 13.27 27.04 7.82 30.92 5.48 8.29 26.95 9.28 26.41 39.54
5.00 22.60 16.65 13.13 24.73 6.72 34.12 40.85 12.24 16.09 $\Delta^{\lambda}$
-0.10 -0.09 0.00 -0.05 -0.03 -0.10 -0.10 -0.10 -0.08 -0.09 -0.10 -0.09 -0.09
-0.10 -0.09 -0.04 -0.05 -0.08 -0.05 -0.10 $\Delta^{\theta}$ 0.07 0.02 0.12
0.12 0.12 0.03 0.06 0.11 0.11 0.09 0.00 0.06 0.07 0.10 0.10 0.12 0.12 0.11
0.12 0.05

Note: In this table we present the mode of the demand parameters from the
conditional distribution
$h(\Psi|\omega_{1};\widehat{\mu}_{\Psi},\widehat{\Sigma}_{\Psi})$, given the
initial-capacity $\omega_{1}$. We estimated the model for 20 different
capacities, and each capacity index corresponds to one such capacity.

##  A.3 Model Fit

In Figure A.3.1 we display the empirical moments and the model-implied moments
evaluated at the estimated parameters. The moments take the form of deciles of
the cumulative density functions of the data and the model predictions.242424
In practice, we match moments period by period, but here we display the
densities aggregated across periods. The deciles from our data are shown in
red and the deciles predicted by the model are shown in blue. In our
estimation step, for each initial capacity, we seek to match 620 moments to
determine weights, i.e., the conditional density $h(\Psi|\omega_{1})$ in
Equation 11 for each period.252525 We use these 20 conditional densities to
generate average welfare for our counterfactuals in Table 6.  Here, we display
the fit for the modal capacity, which is 115 economy seats and 14 first-class
seats.

Figure A.3.1: Model Fit Note: This figure displays the deciles of the
variables that we use in estimation, aggregated across all the periods. The
empirical moments are in red and include all markets in the SIAT data, and the
model implied moments are in blue. Panels (1) and (2) display the moments of
the economy fares and first-class fares, respectively; panels (3) and (4)
display the moments of the change in economy fares and first-class fares,
respectively, across two adjacent periods; panel (5) displays the moments of
the share of initial capacity sold; panel (6) displays the moments of the
change in the share of initial capacity sold across two adjacent periods;
panel (7) displays the moments of the difference in fares between first-class
and economy class; panel (8) displays the moments of business passengers’s
share; and panel (9) displays the moments of the load factor.

##  A.4 Uniqueness of the Optimal Policy

In this section we show that the optimal policy is unique under some
regularity conditions. These regularity conditions are widely used in the
literature and ensure that demand is decreasing in its own and cross price,
and that the demand for each seat class is concave. We begin by presenting
these conditions below, but for notational ease suppress the time index.

######  Assumption 1.

  1. 1.

(Downward Demand): $\left(\frac{\partial\mathbb{E}q^{e}(p^{e},p^{f})}{\partial
p^{e}}\right)\leq 0$, and
$\left(\frac{\partial\mathbb{E}q^{f}(p^{e},p^{f})}{\partial p^{f}}\right)\leq
0$.

  2. 2.

(Concave Demand): $\frac{\partial}{\partial
p^{e}}\left(\frac{\partial\mathbb{E}q^{e}(p^{e},p^{f})}{\partial
p^{e}}\right)<\frac{\partial}{\partial
p^{f}}\left(\frac{\partial\mathbb{E}q^{e}(p^{e},p^{f})}{\partial
p^{e}}\right)\leq 0$, and
$\frac{\partial}{\partial
p^{f}}\left(\frac{\partial\mathbb{E}q^{f}(p^{e},p^{f})}{\partial
p^{f}}\right)<\frac{\partial}{\partial
p^{e}}\left(\frac{\partial\mathbb{E}q^{f}(p^{e},p^{f})}{\partial
p^{f}}\right)\leq 0$.

  3. 3.

(Cross Price Curvature): $\frac{\partial}{\partial
p^{f}}\left(\frac{\partial\mathbb{E}q^{e}(p^{e},p^{f})}{\partial
p^{f}}\right)<0$, and $\frac{\partial}{\partial
p^{e}}\left(\frac{\partial\mathbb{E}q^{f}(p^{e},p^{f})}{\partial
p^{e}}\right)<0$.

The first assumption says that the demand for either of the cabins must be
weakly decreasing in its own price. The second assumption says that the demand
is concave in its own price, which ensures the revenue is well defined. It
also says that the decrease in demand of economy seat decreases more with
respect to economy fare than with respect to business fare. The third
assumption says that the change in demand for economy seats with respect to
first-class price decreases with the first-class price and vice versa.
Although these assumptions are not on the primitives of the model, we present
them in these forms because they are more intuitive, self-explanatory and thus
easier to understand than the equivalent assumptions on the primitives.

######  Lemma 1.

Under Assumption 1 there is a unique policy function
$\\{\sigma_{t}:t=,1\ldots,T\\}$.

###### Proof.

To prove this result we use induction on $T$:

  1. 1.

Suppose $T=1$ and $K^{e}$ and $K^{f}$ denote the cabin specific capacities.
There are $N:=(K^{e}+1)\times(K^{f}+1)$ possible seats combinations (state-
variables) that could be realized. We show that for each
$n\in\\{1,\ldots,N\\}$ there is a unique optimal pair
$\\{p^{e}(n),p^{f}(n)\\}$.

  2. 2.

Suppose uniqueness is true for $T=\tilde{t}$, then we show that the uniqueness
holds even when $T=\tilde{t}+1$.262626 With time we also have to keep track of
the remaining seats, we will use the short-hand notation of $n_{t}$ to mean
$n_{t}\in N$.

#### Step 1

Here, $T=1$ and for notational ease suppress the time index. The airline
solves:

$\displaystyle V(\sigma^{*})$ $\displaystyle=$
$\displaystyle\max_{p^{e},p^{f}}\left\\{\sum_{k=e,f}(p_{t}^{k}-c^{k})\int
q^{k}(p^{e},p^{f})g^{k}(q^{k}(p^{e},p^{f});p^{e},p^{f})dq^{k}\right\\}$ (A.1)
$\displaystyle=$
$\displaystyle\max_{p^{e},p^{f}}\sum_{k=e,f}(p_{t}^{k}-c^{k})\mathbb{E}q^{k}(p^{e},p^{f})$

Then the equilibrium prices $(p^{e},p^{f})$ solve the following system of
equations:

$\displaystyle\left[\begin{array}[]{c}\mathbb{E}q^{e}(p^{e},p^{f})+(p^{e}-c^{e})\frac{\partial{\mathbb{E}}q^{e}(p^{e},p^{f})}{\partial
p^{e}}+(p^{f}-c^{f})\frac{\partial{\mathbb{E}}q^{f}(p^{e},p^{f})}{\partial
p^{e}}\\\
{\mathbb{E}}q^{f}(p^{e},p^{f})+(p^{f}-c^{f})\frac{\partial\mathbb{E}q^{f}(p^{e},p^{f})}{\partial
p^{f}}+(p^{e}-c^{e})\frac{\partial{\mathbb{E}}q^{e}(p^{e},p^{f})}{\partial
p^{f}}\end{array}\right]=\left[\begin{array}[]{c}0\\\ 0\end{array}\right].$
(A.6)

The above system has a unique solution $(p^{e},p^{f})$ if the negative of the
Jacobian corresponding to the above system is a $P$-matrix (Gale and Nikaido,
1965). In other words, all principal minors of the Jacobian matrix are non-
positive, which follows from Assumption 1.

#### Step 2

Suppose we have a unique solution when $T=\tilde{t}$ and all finite pair
$\\{K^{e},K^{f}\\}$. Now we want to show that the solution is still unique if
we have one additional period, i.e., $T=\tilde{t}+1$. Consider the value
function

$\displaystyle
V(\sigma^{*\tilde{t}}):=\max_{\\{\sigma_{t}\\}_{t=0}^{\tilde{t}}}\mathbb{E}_{0}\Bigg{[}\sum_{t=0}^{\tilde{t}}\sum_{k=e,f}(p_{t}^{k}-c^{k})q_{t}^{k}(\sigma_{t})\big{|}K_{0}^{f},K_{0}^{e}\Bigg{]}$
(A.7)

where $\sigma^{*\tilde{t}}:=(\sigma_{1}^{*},\ldots,\sigma_{\tilde{t}}^{*})$ is
the unique optimal policy. Now, suppose we have $\tilde{t}+1$ periods to
consider. So the maximization problem faced by the airline becomes

$\displaystyle\max_{\\{\sigma_{t}\\}_{t=0}^{\tilde{t}+1}}\mathbb{E}_{0}\Bigg{[}\sum_{t=0}^{\tilde{t}+1}\sum_{k=e,f}(p_{t}^{k}-c^{k})q_{t}^{k}(\sigma_{t})\big{|}K_{0}^{f},K_{0}^{e}\Bigg{]}=\max_{\\{\sigma_{t}\\}_{t=0}^{\tilde{t}}}\mathbb{E}_{0}\Bigg{[}\sum_{k=e,f}(p_{t}^{k}-c^{k})q_{t}^{k}(\sigma_{t})\big{|}K_{0}^{f},K_{0}^{e}\Bigg{]}$
$\displaystyle+\max_{\sigma_{\tilde{t}+1}}\sum_{\omega_{\tilde{t}+1}\Omega_{\tilde{t}+1}}\mathbb{E}_{\tilde{t}+1}\Bigg{[}\sum_{k=e,f}(p_{t}^{k}-c^{k})q_{t}^{k}(\sigma_{t})\big{|}\omega_{\tilde{t}+1}\Bigg{]}\Pr(\omega_{\tilde{t}+1}|\sigma^{\tilde{t}})$

Consider the last period. We have shown that for any realized state space
$\omega_{\tilde{t}+1}$ there is a unique optimal policy that solves the second
term. The question is if the uniqueness is preserved when we take an
expectation with respect to the state variable $\omega_{\tilde{t}+1}$.

For the solution to be unique it is sufficient that the transition probability
$\Pr(\omega_{\tilde{t}+1}|\sigma^{t})$ is log-concave, which guarantees the
expected profit is quasi-concave, hence the solution is unique.272727 A
positive and discrete random variable $V$ is log-concave if its p.m.f.
$\Pr(V=i)$ forms a log-concave sequence. A non-negative sequence
$\\{r_{i}:i\geq 0\\}$ is log-concave if for all $i\geq
1:(r_{i})^{2}\geq(r_{i-1})\times(r_{i+1})$. Then, the fact that the uniqueness
extends from $\tilde{t}$ to $\tilde{t}+1$ follows from the usual backward
induction argument of finite-periods maximization problem. Therefore it is
enough to show that the transition probability is a (generalized) Poisson
distribution, which is log-concave (see Johnson, 2007).

For simplicity, and to provide some intuition as to why transition probability
is a (generalized) Poisson, we present the derivation of the transition
probability when there is only one cabin and without censoring. Extending the
argument to two cabins and incorporate rationing is straightforward, albeit
tedious, once we recognize that the Poisson structure is preserved under
truncation. Suppose there is only one cabin and no seat-release policy and
hence no censoring. And let $\tilde{K}_{t}=m$ is the number of seats remaining
at time $t$. Then, the probability of reaching $\tilde{K}_{t+1}=m^{\prime}$ in
$t+1$ from $m$ in period $t$ is

$\displaystyle\Pr(m^{\prime}|m,\text{Price}=p)=\Pr(Sales_{t}=\underbrace{m-m^{\prime}}_{=d}|p)=\sum_{n=0}^{\infty}\Pr(Sales_{t}=d,N_{t}=n|p)$
$\displaystyle=$
$\displaystyle\sum_{n=0}^{\infty}\Pr(Sales_{t}=d|N_{t}=n,p)\times\Pr(N_{t}=n|p)=\sum_{n=d}^{\infty}{n\choose
d}(1-\tilde{F}_{t}(p))^{d}(\tilde{F}_{t}(p))^{n-d}\frac{e^{-\lambda_{t}}\lambda_{t}^{n}}{n!}$
$\displaystyle=$ $\displaystyle
e^{-\lambda_{t}}(1-\tilde{F}_{t}(p))^{d}\lambda_{t}^{d}\sum_{n=d}^{\infty}{n\choose
d}(\tilde{F}_{t}(p))^{n-d}\frac{\lambda_{t}^{n-d}}{n!}=e^{-\lambda_{t}}\frac{[\lambda_{t}(1-\tilde{F}_{t}(p))]^{d}}{d!}\sum_{n=d}^{\infty}\frac{[\lambda_{t}\tilde{F}_{t}(p)]^{n-d}}{(n-d)!}$
$\displaystyle=$ $\displaystyle
e^{-\lambda_{t}}\frac{[\lambda_{t}(1-\tilde{F}_{t}(p))]^{d}}{d!}e^{\lambda_{t}\tilde{F}_{t}(p)}=e^{-\lambda_{t}(1-\tilde{F}_{t}(p))}\frac{[\lambda_{t}(1-\tilde{F}_{t}(p))]^{d}}{d!}$
$\displaystyle=$ $\displaystyle
e^{-\lambda_{t}(1-\tilde{F}_{t}(p))}\frac{[\lambda_{t}(1-\tilde{F}_{t}(p))]^{(m-m^{\prime})}}{(m-m^{\prime})!},$

where

$\displaystyle\tilde{F}(t)=\left\\{\begin{array}[]{cc}\int_{0}^{t}f_{t}(v)dv,&\texttt{
economy cabin}\\\
\int_{0}^{t}\int_{0}^{\infty}f_{t}(v)f_{\xi}(w/v)\frac{1}{v}dvdw,&\texttt{first-
class cabin}\end{array}\right.$

and in the fourth equality the sum starts from $n=d$ as the probability of $d$
sales when $n<d$ is zero. Therefore, the transition probability is a Poisson
with parameter $\lambda_{t}(1-\tilde{F}_{t}(p))$.

∎