MONETARY COMMUNICATION
Research case study
Independent research · author review pendingSample through May 2026

HNB in Croatia’s
inflation debate.

Media evidence for monetary communication

How visible is the central bank when inflation dominates the news?

The Croatian National Bank (Hrvatska narodna banka, HNB) is the focus of this independent study.

The primary model associates higher inflation with lower weighted institutional visibility. Visibility also declines during April 2024–May 2026. A stable relationship with consumer expectations is not established.

Selected media corpus · associations, not causal effects

Authors Petra Palić & Luka SikićPrimary sample Jan 2021–May 2026Manuscript 17 September 2026

The evidence at a glance

Four questions. A measured answer.

Read the findings, or follow each link to the estimates and their interpretation.

01 / Explore the evidence

Start with a question.
Follow it into the evidence.

Selected measure
HICP inflationSeparate scales, aligned months

Weighted visibility relates institutional prominence and potential reach to the inflation corpus. It is not readership. Generic central-bank references can also identify the ECB or other institutions.

Full-history weighted share: 0–18%.

Weighted institutional visibility

Weighted share (%) · higher means more visible

Inflation in Croatia

HICP · year-on-year, %
HICP compares prices with the same month a year earlier. Potential reach is not observed audience exposure. The primary and common-source series each use their own numerator, denominator and historical reference.

Saved monthly aggregates · manuscript 17 September 2026.

Media context and source diagnostics · Inspection data · JSON ↓
Monthly values as a table
Primary corpus: share %, gap pp, inflation %.
MonthShare (%)Gap (pp)HICP (%)
2021-015.02-0.990.0
2021-021.882.140.7
2021-034.26-0.241.6
2021-043.990.032.1
2021-053.830.202.4
2021-065.16-1.142.2
2021-076.01-1.992.7
2021-084.64-0.623.1
2021-095.14-1.113.5
2021-104.27-0.253.9
2021-113.900.124.7
2021-124.59-0.575.2
2022-014.62-0.605.5
2022-022.261.766.3
2022-032.991.047.3
2022-043.270.759.6
2022-053.600.4310.7
2022-062.641.3812.1
2022-073.180.8512.7
2022-081.632.4012.6
2022-091.892.1312.6
2022-102.901.1312.7
2022-112.641.3913.0
2022-123.500.5212.7
2023-012.401.6212.5
2023-022.261.7711.7
2023-033.380.6510.5
2023-0414.83-10.808.9
2023-052.831.198.3
2023-063.770.258.3
2023-073.140.888.0
2023-083.600.438.4
2023-092.551.477.4
2023-102.771.266.7
2023-1110.78-6.755.5
2023-123.900.135.4
2024-042.781.254.7
2024-052.961.074.3
2024-064.75-0.723.5
2024-073.270.763.3
2024-082.231.793.0
2024-092.721.303.1
2024-101.392.633.6
2024-112.821.204.0
2024-122.321.704.5
2025-011.542.495.0
2025-023.260.774.8
2025-032.381.654.3
2025-043.021.004.0
2025-052.281.744.3
2025-062.991.044.4
2025-072.831.194.5
2025-081.462.564.6
2025-092.571.454.6
2025-102.281.754.0
2025-110.453.584.3
2025-121.652.383.8
2026-014.14-0.113.6
2026-021.522.513.9
2026-030.793.244.6
2026-040.683.345.4
2026-051.612.424.9

Inspect / compare

What is moving?
What supports the conclusion?

Inspect a measure

Hrvatski ↗

02 / Understand the measure

How media items become
weighted visibility.

The study weights institutional items by their estimated potential reach and how prominently the institution appears. It compares that total with potential reach across monitored inflation coverage. This is a constructed weighted share, not the proportion of people paying attention or a simple percentage of articles.

Relative visibility can fall even when institutional coverage stays unchanged, if the wider inflation discussion grows faster. That is a possible mechanism to investigate, not a decomposition established by the headline model.

Illustration · hypothetical values

4%Baseline share3%Current share+1 ppAttention gap

A larger gap means a smaller relative share. Zero marks a historical reference, not a communication target. The chart defaults to the share itself: up means more visibility.

How the measure is constructed ↓

Indicator overview

Relevance selects → prominence and reach weight → visibility measures.
The gap transforms visibility. Centrality and expectations answer separate questions.

Inflation relevanceInclusion rule
What is it?
Identifies institutional items about inflation.
Why use it?
Keeps the measure focused on the research question.
How is it calculated?
Apply the study’s relevance classification before weighting an item.
What can distort it?
Classification can confuse adjacent economic topics with inflation.
Where is the evidence?
Construction notes ↗
Institutional prominenceWeighting ingredient
What is it?
Describes how prominently an institution appears in an item.
Why use it?
Distinguishes a central role from a passing mention.
How is it calculated?
Salience = 0.30 × title + 0.25 × position + 0.20 × mention-frequency rank + 0.25 × agency cue.
What can distort it?
Automated cues can misread context or attribute a statement to another central bank.
Where is the evidence?
Worked scoring example ↗
Potential reachWeighting ingredient
What is it?
An estimate of an item’s potential audience.
Why use it?
Gives differently sized outlets different contributions.
How is it calculated?
Multiply each relevant institutional item’s salience by its potential reach.
What can distort it?
Potential audiences can overlap; reach does not measure reading or understanding.
Where is the evidence?
Construction notes ↗
Weighted visibilityMain constructed measure
What is it?
The institution’s weighted share of the inflation discussion.
Why use it?
Relates institutional presence to the size of the surrounding debate.
How is it calculated?
100 × sum of institutional salience × reach, divided by (sum of inflation-corpus reach + 1). Unit: percent.
What can distort it?
The denominator can grow even when institutional coverage stays constant.
Where is the evidence?
Monthly evidence ↗
Attention gapTransformation
What is it?
The same visibility information relative to a fixed historical reference.
Why use it?
Matches the manuscript’s terminology and coefficient tables.
How is it calculated?
Baseline share minus current share, in percentage points. A larger gap means lower visibility.
What can distort it?
A baseline is a reference; it is not an institutional target.
Where is the evidence?
Baseline definition ↗
Network centralitySeparate measure
What is it?
The institution’s position among actors linked through media sources.
Why use it?
Asks about network position, a different question from share of coverage.
How is it calculated?
Eigenvector centrality gives more weight to connections with well-connected actors and is normalised within each monthly network.
What can distort it?
Network composition and normalisation can change a score; centrality does not measure trust.
Where is the evidence?
Centrality estimate ↗
Consumer expectationsSeparate outcome
What is it?
A monthly survey balance describing expected price movements.
Why use it?
Examines whether media measures predict a separate household outcome.
How is it calculated?
Compare monthly projections with weekly models using linear or step assignment of the monthly survey.
What can distort it?
Assignment to weeks creates no new survey responses. The balance does not measure long-term anchoring.
Where is the evidence?
Expectations comparisons ↗

Worked example / hypothetical items and component scores

Three stories, different contributions.

All three invented items concern inflation and each has 1,000 potential-reach units. The component scores below are chosen for illustration; the weighting formula is the study’s actual rule (Appendix A2).

Title / position / frequency / agency → salience × potential reach
Illustrative itemComponent scoresInstitutional contribution
Institution in the headline and quoted1 / 0.9 / 0.8 / 10.935 × 1,000 = 935
Institution mentioned briefly0 / 0.2 / 0.1 / 00.070 × 1,000 = 70
Inflation story without an institutional referenceNo institutional contribution0; reach enters the denominator

For example, 0.30 × 1 + 0.25 × 0.9 + 0.20 × 0.8 + 0.25 × 1 = 0.935. Doubling this item’s potential reach would double its weighted institutional contribution, holding salience fixed.

3%30 weighted institutional units
÷ 1,000 denominator units × 100
1.5%The same 30 units
÷ 2,000 denominator units × 100

In this separate illustration, denominator units already include the formula’s +1. Visibility halves when the wider debate doubles while institutional coverage stays fixed. This demonstrates arithmetic, not a mechanism established by the observed results.

What “HNB” means in this dataset. The matching rules include generic central-bank terms, so some items may refer to the ECB or other institutions. The indicator describes the selected institutional corpus; it is not a verified count of HNB’s own messages or of people who read them.

Media environment / study scope

A media corpus is not an audience.

What the study observes

Recorded institutional items across these channel labels: Web, Facebook, Youtube, Forums, X / Twitter, Reddit, Comments, Instagram, Tiktok. Web items dominate this corpus. The visibility numerator uses inflation-relevant institutional items; its denominator uses the monitored inflation corpus. Dates: January 2021–May 2026.

A publisher’s website is an online source even when its brand also operates television or print. This corpus measures publication instances rather than population-wide news consumption.

Four different concepts

Potential reach
Estimated opportunity to encounter an item.
Exposure
Evidence that a person actually encountered it.
Attention
Evidence of engagement with the message.
Understanding
Evidence of what a person understood.

Reach summed across items is an additive weight, not a count of unique people. Audiences and repeated stories can overlap.

03 / Three takeaways

Three findings for
monetary communication.

Estimates matched to saved outputs of the extended draft. Research models were not re-estimated for this page.

01

Higher inflation is associated with lower visibility

−0.21

percentage points of weighted share
per +1 percentage point of inflation

The association is sensitive to time controls; it does not establish causality.

Read the estimate and interpretation

A 1 percentage-point higher HICP inflation rate is associated with a 0.21 percentage-point lower weighted share in the primary weekly model.

95% interval for the decline: 0.11 to 0.31 percentage points per +1 percentage point of inflation.

For HNB: the size of the inflation debate and the bank’s share of it answer different questions.

Section 4.2 · Table 6 · equations 8 and 9b

Inspect evidence ↗
02

Visibility declines during April 2024–May 2026

−0.076

percentage points of weighted share per month
April 2024–May 2026

This is a within-period association, not evidence that disinflation causes lower visibility.

Read the estimate and interpretation

The weighted institutional share declines by 0.076 percentage points per month after accounting for inflation and the other regressors.

95% interval for the decline: 0.035 to 0.118 percentage points per month.

For HNB: assess the coverage of monetary explanations even after the initial inflation surge has passed.

Section 4.6 · within-source trend · page 13

Inspect evidence ↗
03

A stable link to expectations is not established

No stable link

Consumer expectations · separate outcome

Some horizons are significant under other specifications. The survey balance does not measure long-term anchoring or trust.

Read the estimate and interpretation

Forward projections of consumer expectations depend on how monthly survey information is assigned to weeks and which controls are used. They do not robustly establish a persistent predictive channel.

Survey timing and model controls change the comparisons.

For HNB: read media visibility alongside survey evidence; one cannot substitute for the other.

Section 4.5 · Table 8 · Figure 5

Inspect evidence ↗

The immediate contribution is a diagnostic of media representation. Decisions about message quality, audience understanding or communication effectiveness need evidence beyond this indicator.

04 / What this means for HNB

The scale of the result.
The limits of the inference.

−1.68 percentage points

A lower weighted share when inflation moves from 2% to 10%.

This is the paper’s conditional comparison: hold the model’s other variables fixed and change only inflation. The primary weekly estimate implies a 1.68 percentage-point smaller weighted share (95% interval: 0.90 to 2.46).

That is a change in the constructed share of media coverage, not a 1.68% fall in readership. The chart shows how the estimate changes when trends or year effects are added.

Weekly models, 268 observations; all include media volume. Points show conditional differences, lines show 95% intervals. The year-effects interval includes zero. Source: Section 4.2 and Appendix A23. Download figure ↓

Separate output from relative coverage

The study distinguishes the share of relevant articles from their prominence and reach. More statements or more mentions can coexist with a smaller share of a growing debate. The results do not isolate a single cause of that change.

Paper: Section 4.3 and discussion.

Visibility and centrality are different

Visibility asks how much of the debate the institution occupies. Network centrality asks how centrally it sits among the actors linked through media sources, giving more weight to connections with well-connected actors.

Using common sources, the later monthly centrality trend is -0.0051 index units (95% interval -0.0129 to 0.0027; p = 0.187). The interval includes zero: a lasting loss of network position is not established.

Paper: Section 4.7 and Appendix B2; 25 fitted months.

Keep expectations as a separate outcome

For the article-share measure, the baseline weekly projections find no significant future horizons with linear survey interpolation, but find weeks 1–2 with step assignment. The monthly comparison finds month 12. Controls also change the results.

The paper therefore does not establish that a wider media gap causes expectations to become unanchored.

Paper: Section 4.5 and Appendix A12; corrected comparisons.

A practical investigation agenda

What to examine next

  1. Separate institutional coverage from the wider debate. Track the weighted numerator and the inflation denominator alongside the share.
  2. Validate whose voice is being counted. Check HNB-specific, ECB/Eurosystem and ambiguous institutional references separately.
  3. Pair visibility with comprehension. Use audience research to examine what people understand, alongside what they could encounter.
  4. Inspect source participation. Compare source contributions and repeated publication of the same story.
  5. Keep expectations analysis separate. Test survey-timing and model choices before interpreting any predictive relationship.

These are proposals for investigation. The findings do not establish that a particular communication campaign would improve understanding or expectations.

For the governor, the useful distinction is between what HNB publishes, how it appears in the wider debate, and what households understand. The paper measures the middle of that relationship. Its visibility indicator complements communication and survey evidence; it is not a target to maximise.

05 / For a closer look

Estimates and the choices that matter.

The inflation association

A one-percentage-point higher inflation rate, for example 4% rather than 3%, is associated with the change in the gap shown below. The identical association in weighted visibility has the opposite sign. This is not a change in the number of readers.

Associated increase in the gap

0.21 percentage points

95% confidence interval: 0.11 to 0.31 percentage points

This interval is above zero.

268 fitted weeks · January 2021–May 2026

Technical specification

Sample S1 · equation 9b · Newey–West intervals · p < 0.001

The volume control counts media items, not HNB-issued communications. Weekly inflation repeats monthly information; these are not 268 independent inflation readings. Changing the volume control is not a mediation estimate.

Do time controls change the conclusion?

Compare the primary models with additional trends or year effects. All rows below include the media-volume control and use the same gap units.

Primary
The saved model with its baseline controls and media volume.
Period trends
Tests whether the association survives additional gradual time patterns.
Year effects
Accounts for differences shared by observations in the same calendar year.

The weekly year-effect and monthly trend-control intervals include zero. A positive point estimate does not establish independence from shared time patterns. These are saved comparisons, not every possible combination of controls.

Read exact estimates as a table
Gap pp per +1 pp inflation. Additional time controls shown.
ObservationsTime controlsEstimate95% CI
MonthlyPrimary0.1750.052 to 0.298
MonthlyPeriod trends0.179-0.028 to 0.386
MonthlyYear effects0.1970.008 to 0.385
WeeklyPrimary0.2100.113 to 0.307
WeeklyPeriod trends0.2500.090 to 0.411
WeeklyYear effects0.135-0.059 to 0.329
Saved estimates · manuscript Appendix A23 ↓
The later-period trend

The controlled monthly gap trend is +0.076 percentage points per month (95% CI 0.035 to 0.118; 25 fitted months). This corresponds to a declining weighted share. Among common sources the trend is +0.056 pp per month (p = 0.045).

The comparison describes April 2024–May 2026. It does not establish that falling inflation causes lower visibility.

Why the expectations result depends on survey timing

The survey is monthly. Assigning values to weeks in different ways does not create new weekly responses. A linear assignment moves gradually between monthly values; a step assignment holds a monthly value across its weeks. Results also change with the control set.

For the article-share margin in the primary sample, the saved baseline comparisons are:

  • Weekly · linear: none of the 1–12 weeks-ahead horizons pass correction.
  • Weekly · step: horizons 1, 2 weeks ahead pass correction.
  • Monthly · original survey: horizons 12 months ahead pass correction.

The correction includes 13 horizons per family, including the contemporaneous one. These counts summarise specification sensitivity, not effect size or practical importance. The survey balance describes expected price movements, not long-term anchoring or trust. No stable predictive channel or validated forecasting tool is established.

How centrality differs from the attention gap

Centrality describes position in the network linking media sources and actors. It is normalised relative to the other actors each month, so changes in network composition can alter the score. The common-source monthly trend is -0.0051 index units per month, with a 95% interval from -0.0129 to 0.0027. The interval includes zero. This does not establish lasting structural erosion, and the score is not a measure of credibility, trust or policy influence.

Read the interpretation for HNB ↑

06 / Methods & limits

What the indicator can carry.

Return to the figure ↑

Reading the sign

Attention gap =
baseline share − current share

A positive gap means lower visibility than the baseline. A negative gap means higher visibility. Zero marks that reference, not an ideal level of communication.

The displayed monthly baseline is 4.026%: the mean weighted share in January–June 2021 after excluding baseline observations more than two standard deviations from the initial mean. Monthly and weekly baselines are calculated separately.

What enters the measure?

The numerator adds potential reach weighted by institutional salience for inflation-relevant items in the HNB corpus. The denominator adds reach across the inflation corpus, plus one. Salience combines title presence, first-mention position, mention frequency and institutional agency cues.

Formal names, acronyms and generic central-bank terms identify the institutional corpus. Generic terms can include other central banks, including ECB or Eurosystem coverage after euro adoption. The measure does not cleanly isolate every HNB message. HNB-specific, ECB/Eurosystem and ambiguous references have not been independently validated as separate categories.

Sample and institutional scope

The analysis covers January 2021–May 2026. The main regressions use 60 monthly or 268 weekly observations. This is a selected vendor corpus, not a complete census of Croatian media or a representative audience sample.

Recorded dates provide the time basis. Generic institutional terms can capture the ECB or other central banks. The indicator is distinct from HNB’s own publication output.

Three kinds of uncertainty

Estimate uncertainty: the reported 95% intervals use the saved Newey–West estimates with Bartlett weights, bandwidth floor(N1/3) and no prewhitening. They describe statistical precision conditional on the selected model.

Model sensitivity: different time controls, media-volume controls and survey assignments can change the estimates. Compare specifications in the evidence section.

Measurement uncertainty: institutional classification, potential reach and vendor sentiment are proxies. The model intervals do not quantify every possible measurement error.

The baseline models include inflation changes, euro adoption, source-reach concentration and vendor negative sentiment alongside the manuscript’s other controls. Equation 9b also includes log HNB-corpus volume. Weekly macroeconomic values are assigned from the month of the week’s start. Public estimates reproduce saved outputs; this publication does not re-estimate the models.

What the study cannot establish

Potential reach is not observed reading, exposure, trust or understanding. Vendor sentiment is not independently validated on this corpus. The gap is neither a count of HNB statements nor a score of communication quality. No threshold for policy-relevant deterioration or monetary welfare cost is established.

HANFA comparisons and instrument diagnostics do not establish an HNB-specific causal mechanism. Forward expectation results depend on interpolation and controls. Media evidence alone cannot establish anchoring of expectations or changes in individual beliefs.

The older paper’s abstract, table and recalculated initial-sample coefficients do not all agree. The extended draft reports this unresolved discrepancy; it does not claim exact legacy replication.

Dates, scope and reuse

Manuscript edition: 17 September 2026. Primary analytical sample: January 2021–May 2026. Latest included month: May 2026. Website built: 2026-09-21.

This is a static publication of one study, not a continuously updated monitoring service. The public dataset contains only the selected aggregate series and model results. Later exploratory periods and future research are outside this edition.

07 / Research & downloads

The research, at the depth you need.

Two pages / English & Croatian

The findings and their
meaning for HNB.

Two pages covering January 2021–May 2026: the full visibility and inflation timeline, the principal estimate and its uncertainty, with concise findings on trends, centrality and expectations.

English brief ↓Sažetak na hrvatskom ↓

Petra Palić & Luka Sikić

Hrvatsko katoličko sveučilište

Authors of the extended study combining media measurement, time-series analysis and specification checks. The paper documents the methods and their limits. This is an independent research presentation; no HNB partnership or endorsement is claimed.

Research status

One edition, with a traceable evidence base.

Edition & cutoff
Manuscript: 17 September 2026. Analysis through May 2026. Website revision: 19 September 2026 · presentation 2026-09-19.3.
Review
Author review is pending. The presentation and interpretation have not been signed off by the authors; no peer-review acceptance is claimed.
What this reproduces
Saved monthly observations, primary and common-source series, predefined model comparisons, centrality and expectations results. Concentration summaries are aggregated from existing scored records. Models have not been re-estimated for the website.
Earlier results
Earlier reported and recalculated coefficients do not all agree. Exact replication of the earlier paper remains unresolved.
Data & code
Aggregate CSV and JSON files and the chart code are downloadable above. The underlying media texts and the full research pipeline are not distributed in this publication.
Reuse
Cite the authors and manuscript edition. Contact the authors for permission to republish figures or aggregates. Underlying vendor media material is separate from these publication assets.
Corrections
luka.sikic@unicath.hr · include the figure or finding and selected view.
Version history

2026-09-19.3: redesigned bilingual briefs, full January 2021–May 2026 timelines, matching downloadable figures and on-site readers.

2026-09-19.2: question-based views, contextual indicator inspection, direct sensitivity comparisons, source concentration diagnostics and traceable finding records.

2026-09-19.1: evidence overview, indicator guide, worked examples, shareable selections, selected-view exports and clearer interval interpretation.

17 September 2026: extended manuscript edition underlying the saved estimates.

Citation, edition and earlier-paper discrepancy

Palić, P., & Sikić, L. (2026). Pasivno zamijenjena: cijena inflacije koju ne mjeri indeks potrošačkih cijena. Extended research draft, 17 September 2026. Hrvatsko katoličko sveučilište.

Download citation ↓

The source is the extended manuscript edition of 17 September 2026. Earlier reported and recalculated coefficients do not all agree; exact replication of the earlier paper remains unresolved. The findings here refer to saved outputs of this extended edition. No publication venue or DOI is claimed.

Traceable findings / edition 2026-09-17

A finding you can trace and cite.

Each identifier refers to a fixed research finding. The controls above change the view; they do not rewrite its reference model.

F1 Higher inflation is associated with lower weighted visibility in the primary weekly model; time-control sensitivity qualifies the association.
Reference model
Primary weekly model, equation 9b
Measure and sample
Weighted institutional visibility · S1 · January 2021–May 2026
Manuscript location
Section 4.2 · Table 6 · Appendix A23
Versions
Data: extended-2026-09-17 · Method: extended-manuscript-2026-09-17 · Presentation: 2026-09-19.3
Verification
Matched to saved outputs. Author review pending.

Palić & Sikić (2026), F1: Higher inflation is associated with lower weighted visibility in the primary weekly model; time-control sensitivity qualifies the association. Extended manuscript, 17 September 2026.

F2 Weighted visibility declines within April 2024–May 2026 in the primary and common-source monthly trend models.
Reference model
Controlled monthly trend
Measure and sample
Weighted institutional visibility · S3 · April 2024–May 2026
Manuscript location
Section 4.6 · common-source comparison
Versions
Data: extended-2026-09-17 · Method: extended-manuscript-2026-09-17 · Presentation: 2026-09-19.3
Verification
Matched to saved outputs. Author review pending.

Palić & Sikić (2026), F2: Weighted visibility declines within April 2024–May 2026 in the primary and common-source monthly trend models. Extended manuscript, 17 September 2026.

F3 A stable predictive relationship with consumer expectations is not established; survey assignment and model controls affect the results.
Reference model
Forward projections; article-share exposure; continuity controls
Measure and sample
Consumer expectations survey balance · S1 · January 2021–May 2026
Manuscript location
Section 4.5 · Table 8 · Appendix A12
Versions
Data: extended-2026-09-17 · Method: extended-manuscript-2026-09-17 · Presentation: 2026-09-19.3
Verification
Matched to saved outputs. Author review pending.

Palić & Sikić (2026), F3: A stable predictive relationship with consumer expectations is not established; survey assignment and model controls affect the results. Extended manuscript, 17 September 2026.

F4 The common-source monthly centrality interval includes zero; a lasting decline in network position is not established.
Reference model
Common-source monthly network trend
Measure and sample
Normalised eigenvector centrality · S3 · April 2024–May 2026
Manuscript location
Section 4.7 · Appendix B2
Versions
Data: extended-2026-09-17 · Method: extended-manuscript-2026-09-17 · Presentation: 2026-09-19.3
Verification
Matched to saved outputs. Author review pending.

Palić & Sikić (2026), F4: The common-source monthly centrality interval includes zero; a lasting decline in network position is not established. Extended manuscript, 17 September 2026.

Finding records and revision history · JSON ↓ · Supporting values and comparisons · JSON ↓

What changed in this release?

2026-09-19.3 · Editorial and evidence presentation. Redesigned both two-page briefs, added the full January 2021–May 2026 timeline and updated the downloadable figures and on-site readers. The published research estimates and their methods are unchanged.

How future revisions are labelled
Data correction
Identifies corrected observations and any effect on the conclusion.
Method change
Identifies changed calculations and the scope of valid comparisons.
Editorial clarification
Changes explanation or presentation while preserving the research estimates.