Hardening Soft Information: Evidence on Analyst Integration Costs

Analysts communicate their subjective expectations for firms’ future using natural language rather than numerical forecasts, and this linguistic expression predicts errors in those numerical forecasts. This finding suggests that useful information is often vaguely known and only communicated through language, which has significant implications for how financial analysts form and revise their expectations.

Theoretical Framework of Vague Knowledge

The study incorporates vague knowledge into models of subjective expectations by relaxing standard information structures, arguing that people often observe and understand the state of the world in vague ways. This is summarized in Proposition 1: A well-defined boundary is not a necessary condition for an information set to be informative. Standard economic theory assumes all observed signals are precise (crisp sets), but real-world knowledge often involves vagueness, where objects cannot be definitely classified as belonging to an information set or not, leading to borderline cases. This distinction is reflected in the physical world: natural language is vague, while numbers are precise.

Mechanism of Linguistic Communication

The paper proposes that people convey their vague knowledge through natural language. Proposition 2 states that A rough set cannot be faithfully represented by any crisp set (e.g., numbers), but it can be faithfully represented by another rough set (e.g., text). Linguistic expressions are advantageous because they:

1. Allow analysts to describe information for which a relevant precise measure is unavailable, such as concepts like management ability, innovation, brand names, governance, and synergy.

2. Convey imprecision truthfully when the underlying information base is too limited to warrant mathematical modeling and precise predictions, avoiding numerical estimates that may lend false clarity.

3. Reduce production costs and enable prompt communication within analysts’ processing capacity because quantification incurs additional processing costs.

Empirical Predictions on Forecast Errors

The theory leads to several empirical hypotheses concerning the relationship between textual tone and forecast errors:

1. H1 predicts a systematical negative relation between errors in numerical forecasts and textual opinions in the same report. This is tested by finding that the tone is significantly and negatively related to the forecast error of the same report, suggesting that analysts’ numerical forecasts are too low (high) when they include more optimistic statements in natural language.

2. H2 predicts that vague expectation in earlier reports, though expressed in natural language, precedes numerical forecasts. This is supported by finding that the positive (negative) textual tone in the earlier analyst reports to be predictive of subsequent upward (downward) revisions in the analysts’ numerical research outputs.

3. H3 predicts that linguistic expressions convey a vague expectation that is too costly to be incorporated into numerical forecasts, and this effect is stronger when analysts are constrained by time or processing capacity.

Moderating Effects of Uncertainty and Constraints

The predictive power of linguistic expressions is not constant; it varies with external factors:

1. The relation between errors in numerical forecasts and textual opinions is stronger when the report exhibits a higher degree of vagueness. Specifically, the interaction term between textual tone and the indicator variable for vagueness shows a significant negative coefficient.

2. The positive relation between current textual opinions and future revisions is stronger when the analyst faces a higher degree of uncertainty in forecasting tasks, such as longer forecast horizons, high macroeconomic/market volatility (VIX), or poor information environments (small firm size, low analyst coverage).

3. The effect of linguistic expressions on subsequent revisions is also moderated by processing capacity: the positive relation between current textual opinions and future revisions is stronger when the analyst's processing capacity is more constrained.

Alternative Explanations and Conclusion

The study tests alternative explanations for the observed effects:

1. Optimistic bias in numerical forecasts (using percentages of positive/negative sentences) was shown not to fully explain the results, as both good news and bad news conveyed linguistically can predict errors in respective directions.

2. Offering clients an information advantage (delaying quantification of precise signals) was ruled out by testing subsamples where analysts were less likely to have such incentives (e.g., firms with low institutional ownership).

The overall conclusion is that some useful information is vaguely known and only communicated through language, and this finding has implications for accounting systems, suggesting that intangibles such as breakthrough and disruptive innovation, customer relations, and corporate culture are not reflected in financial reports but are instead communicated linguistically. Analysts make rational choices between soft (linguistic) and hard (numerical) communication formats based on the precision of underlying knowledge.

Key Empirical Findings Summary

**: The overall textual tone is significantly and negatively related to the forecast error, meaning optimistic language leads to forecasts that are too low relative to actual earnings. **

**: The relationship between current textual opinions and future revisions is positive, indicating that analysts wait for new evidence before quantifying vague expectations. **

**The predictive power of linguistic expressions increases when reports are vaguer, when uncertainty is higher, and when analysts are busier.

As a fastidious and diligent researcher, I have analyzed the core theoretical contributions and empirical findings of this paper, Vague Knowledge: Evidence from Analyst Reports. The central insight is that analysts communicate useful information about future states not through precise numerical forecasts (hard information), but through vague natural language (soft information), which predicts errors in those numerical forecasts.

Here are specific improvements to AI systems based on this research, and what the improved AI system can achieve:

) 1. Implementation of Vague Expectation Modeling for Uncertainty Quantification:

The paper develops a formal decomposition of future states into precise expectations (based on numbers), vague expectations (based on language/rough sets), and unpredictable residual, leading to Equation (3):

Forecast Error = - [Vague Expectation] + Bias(Precise) + Noise.

Improvement: AI models used for financial forecasting should incorporate a mechanism to explicitly separate hard quantifiable signals from soft linguistic signals. The system must be able to estimate the Vague Expectation term—the portion of the forecast error attributable to unquantifiable, vague knowledge expressed in textual reports.

Improved System Capability: An AI financial model would not only output a numerical forecast but would also provide a confidence interval for that forecast, explicitly quantifying the uncertainty arising from qualitative analyst commentary. This allows downstream risk management systems to distinguish between risks driven by quantifiable market volatility and risks driven by ambiguous, unmeasurable sentiment expressed in reports (e.g., predicting earnings revisions based on the tone of language).

) 2. Linguistic Signal Extraction and Tone-Based Error Prediction:

The study uses FinBERT to quantify textual tone (positive, negative, neutral) and empirically finds a significant negative relationship between this tone and forecast errors (Prediction 1). Furthermore, it tests how the degree of vagueness (measured by the percentage of non-numerical sentences or hedging words) modulates this predictive power (Prediction 2).

Improvement: AI systems designed to process analyst reports must move beyond simple sentiment analysis. They need a layered linguistic processing pipeline that extracts not just what is said but how it is said. This involves fine-tuning large language models (like FinBERT) specifically for financial text and developing classifiers sensitive to linguistic vagueness (identifying hedging words, approximators, and qualitative descriptors).

Improved System Capability: An AI research assistant could ingest thousands of analyst reports and automatically flag reports where the vague expectation is likely to cause forecast errors. If a report uses high levels of vague language or hedging (high vagueness indicator), the system should assign a higher weight to its textual signal when predicting subsequent numerical revisions, effectively predicting which qualitative statements will lead to future quantitative forecast adjustments.

) 3. Uncertainty-Dependent Information Prioritization:

The research shows that analysts wait for new evidence when uncertainty is high (H2), and that the predictive power of linguistic expressions increases with the degree of forecasting uncertainty (Prediction 4).

Improvement: The AI's information-gathering module should dynamically adjust its reliance on different data types based on perceived future uncertainty. If a forecast horizon is long or macroeconomic volatility is high, the system must prioritize analyzing qualitative textual signals over refining precise numerical parameters until new, more precise evidence becomes available.

Improved System Capability: A predictive AI for long-term investment strategy would use linguistic cues (e.g., shifts in tone toward caution) as leading indicators that a period of vague knowledge is prevalent, prompting the system to reduce reliance on short-term numerical models and instead focus on scenario planning or qualitative risk assessment until the uncertainty resolves.

) 4. Processing Capacity and Cost-Benefit Analysis for Communication:

The paper suggests that linguistic expressions are economically feasible because they have lower production costs than quantification when dealing with vague knowledge (H3, Prediction 5).

Improvement: AI systems tasked with generating analyst reports or summarizing complex data should incorporate a cost-benefit layer. When presenting information, the system should weigh the precision gained from numerical output against the processing cost of producing that precision. If the underlying knowledge is inherently vague (as identified by linguistic features), the system should favor lower-cost, linguistically expressed summaries over high-precision numerical ones.

Improved System Capability: An automated reporting tool could generate a summary for a client, choosing between two outputs: (A) A highly precise numerical projection with associated high computational cost, or (B) A linguistically nuanced summary that conveys the expected vague expectation with lower processing overhead, thereby optimizing the communication of imperfect knowledge.

We examine how the cost of transforming qualitative information into precise numerical estimates--a form of integration cost--creates a structural friction in expectations formation. To isolate this integration cost from the costs of information awareness and acquisition, we exploit sell-side analyst reports, in which the same forecaster simultaneously produces textual narratives and numerical forecasts. Because the information underlying the text has already been acquired, any systematic gap between the two outputs can be attributed to integration costs. We document systematic quantification inefficiency: an analyst's textual tone negatively predicts her contemporaneous forecast errors and positively predicts her subsequent numerical revisions, revealing that analysts leave part of their qualitative insights unquantified until further evidence arrives. Consistent with this integration-friction explanation, this inefficiency intensifies when reports are linguistically vaguer, environmental uncertainty is higher, or analysts' processing capacity is more constrained, and it persists where strategic and behavioral explanations are weaker. Our findings provide direct, large-sample evidence that integration costs constitute a distinct economic friction, explaining why soft information carries value-relevant content beyond contemporaneous hard numbers.