Extrapolation Bias Research Articles

Extrapolation beyond peers: An asset pricing perspective

We introduce a novel measure that captures the beta deviation of individual firms from their industry peers within China's stock market. Our analysis reveals that stocks with greater beta deviation generate significantly higher future returns. This predictive power is unaffected by established return predictors and remains robust across alternative peer identification methods, beta estimation techniques, and subsample tests. Our findings suggest a behavioral interpretation, linking positive predictability to mispricing driven by investors' extrapolation biases. Overall, our research highlights the critical role of incorporating peer firms into asset pricing, particularly in emerging markets.

Classified Mixed Model Projections

In many practical problems, there is interest in the estimation of mixed effect projections for new data that are outside the range of the training data. Examples include predicting extreme small area means for rare populations or making treatment decisions for patients who do not fit typical risk profiles. Standard methods have long been known to struggle with such problems since the training data may not provide enough information about potential model changes for these new data values (extrapolation bias). We propose a new framework called Prediction Using Random-effect Extrapolation (PURE) which involves constructing a generalized independent variable hull (gIVH) to isolate a minority training set which is “close” to the prediction space, followed by a regrouping of the minority data according to the response variable which results in a new (but misspecified) random effect distribution. This misspecification reflects “extrapolated random effects” which prove vital to capture information that is needed for accurate model projections. Projections are then made using classified mixed model prediction (CMMP) (?) with the regrouped minority data. Comprehensive simulation studies and analysis of data from the National Longitudinal Mortality Study (NLMS) demonstrate superior predictive performance in these very challenging paradigms. An asymptotic analysis reveals why PURE results in more accurate projections. Supplementary materials for this article are available online.

Simple Review of Extrapolation Bias

Extrapolation bias is a popular topic recently in economics and finance. Many researchers have become interested in this bias because it can explain many anomalies that a rational model cannot. This paper is a simple review of extrapolation bias, including its definition and bias. After reviewing past research on extrapolation, this paper selects a comprehensible definition, and three applications that can represent the recent research on extrapolation: the investor behavior model, the bubble model, and the house price model from three different top papers. After the review, it can be concluded that extrapolation bias has a wide applied range especially, in the financial market and asset pricing, and can explain many financial anomalies.

Extrapolative asset pricing

This paper studies implications of return extrapolation in a consumption-based asset pricing model. We show that return extrapolation has strong implications for the pricing kernel. The time variation in the agent's return expectations is mainly reflected in the short rate and little in return volatility and equity premium. Return extrapolation causes return volatility and equity premium to be lower than the rational counterparts. In addition to the risk premium, the equity premium can include a sentiment premium that is due to dividend expectation bias rather than return extrapolation bias. Thus, time-varying dividend (rather than return) expectation bias helps produce a volatile equity premium. These results show that return extrapolation exacerbates asset pricing puzzles and fundamental extrapolation helps resolve puzzles.

Robust optimal reinsurance strategy with correlated claims and competition

<abstract><p>This paper investigates the robust optimal reinsurance strategy, which simultaneously takes into account the ambiguity aversion, the correlated claims and the joint interests of an insurer and a reinsurer. The correlated claims mean that future claims are correlated with historical claims, which are measured by an extrapolative bias. The joint interests of the insurer and the reinsurer are reflected by the competition between them. To better reflect competition, we assume that the insurer and the reinsurer are engaged in related insurance business. The insurer is allowed to purchase proportional reinsurance or acquire a new business. Under ambiguity aversion and the criterion of maximizing the expected utility of terminal wealth, we obtain explicit solutions for the robust optimal reinsurance strategy and the corresponding value function by using the stochastic dynamic programming approach. Furthermore, we obtain the optimal reinsurance strategy under four typical cases. A series of numerical experiments were carried out to illustrate how the robust optimal reinsurance strategy varies with model parameters, and the result analyses reveal some interesting phenomena and provide useful guidance for reinsurance in reality.</p></abstract>

"The reputation premium": does hospital ranking improvement lead to a higher healthcare spending?

Global health systems have often disclosed hospital quality and performance information via hospital ranking or rating programs over the last 20years. This study aims to examine the relationship between hospital ranking and healthcare spending. Using the Basic Medical Insurance claims data from a big city in central China and the hospital ranking data from the Fudan Chinese Hospital League Table from 2016 to 2018, this study exploits the variation of hospital reputable ranking across hospitals and periods to employ the difference-in-differences (DiD) design. To alleviate the self-selection bias emerging from inpatients' selection of hospitals and the extrapolation bias emerging from the potential mis-specification of our linear model, we combine the DiD design with the 3-to-1 optimal Mahalanobis metric matching method. This study finds that ceteris paribus one hospital ascending from the Regional Famous Hospital Group to the National Famous Hospital Group significantly increases inpatients' total healthcare costs, reimbursement costs, and out-of-pocket costs by 5.9%, 6.2%, and 4.0%, respectively. Mechanism analysis reveals that it should be attributed more to physician moral hazard than patient willingness-to-pay. Leads and lags (event study) analysis validates our DiD identification framework and shows that the impact materializes slowly but significantly. In the robustness check, we transfer the outcome variables from the log value to the level value and control five digits of ICD-10 for the disease fixed-effects. The results are highly robust.

Bayesian modelling of piecewise trends and discontinuities to improve the estimation of coastal vertical land motion

One of the major sources of uncertainty affecting vertical land motion (VLM) estimations are discontinuities and trend changes. Trend changes are most commonly caused by seismic deformation, but can also stem from long-term (decadal to multidecadal) surface loading changes or from local origins. Although these issues have been extensively addressed for Global Navigation Satellite System (GNSS) data, there is limited knowledge of how such events can be directly detected and mitigated in VLM, derived from altimetry and tide-gauge differences (SATTG). In this study, we present a novel Bayesian approach to automatically and simultaneously detect such events, together with the statistics commonly estimated to characterize motion signatures. Next to GNSS time series, for the first time, we directly estimate discontinuities and trend changes in VLM data inferred from SATTG. We show that, compared to estimating a single linear trend, accounting for such variable velocities significantly increases the agreement of SATTG with GNSS values (on average by 0.36 mm/year) at 339 globally distributed station pairs. The Bayesian change point detection is applied to 606 SATTG and 381 GNSS time series. Observed VLM, which is identified as linear (i.e. where no significant trend changes are detected), has a substantially higher consistency with large-scale VLM effects of glacial isostatic adjustment (GIA) and contemporary mass redistribution (CMR). The standard deviation of SATTG (and GNSS) trend differences with respect to GIA+CMR trends is by 38% (and 48%) lower for time series with constant velocity compared to variable velocities. Given that in more than a third of the SATTG time series variable velocities are detected, the results underpin the importance to account for such features, in particular to avoid extrapolation biases of coastal VLM and its influence on relative sea-level-change determination. The Bayesian approach uncovers the potential for a better characterization of SATTG VLM changes on much longer periods and is widely applicable to other geophysical time series.

Rank extrapolation: Asymmetric forecasts of future rank after rank change

How do people forecast an actor’s future rank after observing a rank change and what are the factors that shape these forecasts? In this research, we shed new light on the attributions that people make when they observe an actor change rank and on how these attributions explain where people expect the actor to rank in the future. Specifically, in Studies 1a and 1b we document an asymmetric extrapolation bias, whereby people extrapolate upward rank trajectories more steeply into the future than downward trajectories – a pattern of results that differ in both magnitude and direction from actual rank change patterns over time. In Studies 2 and 3 we provide evidence of the different attributions that explain people’s asymmetric extrapolation through measurement and manipulation. Finally, in Study 4 we demonstrate a practical downstream consequence of this asymmetric extrapolation bias (i.e., promotion recommendation) (Study 4). Theoretical and practical implications are discussed.

Extrapolative Bias and Chinese Stocks

Extrapolative Bias and Chinese Stocks

Combining Matching and Synthetic Control to Tradeoff Biases From Extrapolation and Interpolation

The synthetic control (SC) method is widely used in comparative case studies to adjust for differences in pretreatment characteristics. SC limits extrapolation bias at the potential expense of interpolation bias, whereas traditional matching estimators have the opposite properties. This complementarity motives us to propose a matching and synthetic control (or MASC) estimator as a model averaging estimator that combines the standard SC and matching estimators. We show how to use a rolling-origin cross-validation procedure to train the MASC to resolve tradeoffs between interpolation and extrapolation bias. We use a series of empirically based placebo and Monte Carlo simulations to shed light on when the SC, matching, MASC and penalized SC estimators do (and do not) perform well. Then, we apply these estimators to examine the economic costs of conflicts in the context of Spain.

ARBITRAGEUR BEHAVIOR IN SENTIMENT-DRIVEN ASSET-PRICING

This study aims to model arbitrageur behavior in a sentiment-driven capital asset-pricing model under the premise of reflecting a more detailed decomposition of investor types in the equity markets. We explore the behavior and the impact of arbitrageur behavior, particularly, on pricing and on key financial ratios. We observe that the prevalence of the arbitrageur counteracts the effects of unsophisticated investors, resulting in a lower volatility of the price–dividend ratio, lower predictive power of changes in consumption for future price changes and lower equity premium. Thus, the results of our research allow us to conjecture that the extrapolation bias in the prices is lowered.

Synthetic control method with convex hull restrictions: a Bayesian maximum a posteriori approach

Summary Synthetic control methods have gained popularity among causal studies with observational data, particularly when estimating the impacts of the interventions implemented to a small number of large units. The synthetic control methods face two major challenges: (a) estimating weights for each donor to create a synthetic control and (b) providing statistical inferences. To overcome these challenges, we propose a Bayesian framework that implements the synthetic control method with the parallelly shiftable convex hull and provides a Bayesian inference, which is from the duality between a penalised least squares approach and a Bayesian maximum a posteriori (MAP) approach. Our approach differs from the recent Bayesian approach, which allow violating the convex hull restriction and face the potential extrapolation bias. Simulation results indicate that the proposed method leads to smaller biases compared to alternatives. We revisit Abadie and Gardeazabal (2003) by applying our proposed method.

Extrapolation Bias and Robust Dynamic Liquidity Management

We consider the optimal dynamic liquidity management of a financially constrained firm when its existing shareholders are risk neutral but ambiguity averse with respect to the firm’s future cash flows. The shareholders’ ambiguity aversion generates endogenous time-varying worst-case beliefs that overweight recent cash flow realizations, thereby providing a microeconomic foundation for extrapolation bias. Moreover, shareholders’ ambiguity aversion has different implications on firms’ liquidity management and recapitalization policies than risk. Models with risk alone imply that higher cash flow volatility increases firms’ payout and refinancing thresholds. By contrast, our model predicts that, when ambiguity-averse shareholders face a higher long-term cash flow uncertainty, they optimally reduce firms’ payout and refinancing thresholds. The implications for investment are also studied. This paper was accepted by Agostino Capponi, finance.

Extracting Extrapolative Beliefs from Market Prices: An Augmented Present-Value Approach

This paper proposes a latent-variables approach to recover biases in beliefs directly from asset prices. We focus on return extrapolation, a bias in expectations formation that has received considerable attention in recent asset pricing research. We estimate a present-value model of the price-dividend ratio of the market that embeds extrapolative beliefs alongside rational discount rates and expected dividend growth. This approach allows us to measure extrapolation bias without having to rely on survey data, and inherently guarantees that the researcher focuses on a set of beliefs that matter for price formation. We use our 70-year long time-series of extrapolative beliefs to test the key prediction of behavioral models of the stock market with return extrapolators, namely, a rise in extrapolation bias today leads to predictably lower market returns in the future. Through both in-sample and out-of-sample analysis, our results provide support for behavioral theories of asset prices in the presence of extrapolators.

Do Teams Alleviate or Exacerbate Cognitive Biases? Evidence from Extrapolation in Mutual Funds

Whether teams attenuate or exacerbate the behavioral biases which are pervasive at the individual level is an open question. To address this question, we use the mutual fund industry as a laboratory. Our focus is on how return extrapolation, a bias in investor behavior that has received considerable attention in recent work, is transmitted from individual fund managers to the team-managed funds they join. We show that teams heavily attenuate the influence of extrapolation bias on funds' trading behavior. Additional analysis reveals that this attenuation is not due to differences in investment experience, compensation contracts, workload, and investment styles between solo-managed and team-managed funds. Rather, our evidence suggests that the elicitation of team members' inner cognitive reflection can be responsible for teams' reduction in behavioral biases. Our results highlight the attenuation of the extrapolation bias as a potential benefit of team-based asset management.

Spatiotemporal Variability in Modeled Bottom Ice and Sea Surface Dimethylsulfide Concentrations and Fluxes in the Arctic During 1979–2015

Field observations suggest that oceanic emissions of dimethylsulfide (DMS) may play a dominant role in the production of Arctic aerosols and clouds and therefore modulate the surface irradiance, during spring and summer. DMS is produced not only in the water column but also in various sea ice habitats. The ongoing recession of Arctic sea ice is expected to enhance DMS emissions, but the magnitude of this increase is highly uncertain. Here we investigate the spatiotemporal variability in bottom ice and sea surface DMS concentrations and fluxes using a regional sea ice‐ocean physical‐biogeochemical model. Model results indicate that the observed accelerated decline of Arctic sea ice extent since the beginning of the 21st century is associated with upward trends in May–August pan‐Arctic‐averaged sea surface DMS concentration and sea‐to‐air DMS flux. On the other hand, strong interannual variability and statistically insignificant trends are found for bottom ice DMS concentration and ice‐to‐sea DMS flux, owing to the counteracting effects of the shrinking horizontal extent and the vertical thinning of sea ice on ice algal production. The pan‐Arctic DMS climatology products based on model simulation and satellite algorithms provide dynamically based spatial details that are absent in the in situ measurement‐based climatology due to limited spatiotemporal data coverage and inevitable extrapolation bias. Lastly, model results indicate that the bottom ice DMS and its precursor dimethylsulfoniopropionate production can be the only local source of oceanic DMS emissions into the atmosphere during May prior to pelagic blooms, suggesting that it may be a key component of the biological control on Arctic climate at that time.

Robust optimal reinsurance–investment strategy with price jumps and correlated claims

This paper considers the robust optimal reinsurance–investment strategy selection problem with price jumps and correlated claims for an ambiguity-averse insurer (AAI). The correlated claims mean that future claims are correlated with historical claims, which is measured by an extrapolative bias. In our model, the AAI transfers part of the risk due to insurance claims via reinsurance and invests the surplus in a financial market consisting of a risk-free asset and a risky asset whose price is described by a jump–diffusion model. Under the criterion of maximizing the expected utility of terminal wealth, we obtain closed-form solutions for the robust optimal reinsurance–investment strategy and the corresponding value function by using the stochastic dynamic programming approach. In order to examine the influence of investment risk on the insurer’s investment behavior, we further study the time-consistent reinsurance–investment strategy under the mean–variance framework and also obtain the explicit solution. Furthermore, we examine the relationship among the optimal reinsurance–investment strategies of the AAI under three typical cases. A series of numerical experiments are carried out to illustrate how the robust optimal reinsurance–investment strategy varies with model parameters, and result analyses reveal some interesting phenomena and provide useful guidances for reinsurance and investment in reality.

Potential Bias Associated with Modeling the Effectiveness of Healthcare Interventions in Reducing Mortality Using an Overall Hazard Ratio.

Clinical trials often report intervention efficacy in terms of the reduction in all-cause mortality between the treatment and control arms (i.e., an overall hazard ratio [oHR]) instead of the reduction in disease-specific mortality (i.e., a disease-specific hazard ratio [dsHR]). Using oHR to reduce all-cause mortality beyond the time horizon of the trial may introduce bias if the relative proportion of other-cause mortality increases with age. We sought to quantify this oHR extrapolation bias and propose a new approach to overcome this bias. We simulated a hypothetical cohort of patients with a generic disease that increased background mortality by a constant additive disease-specific rate. We quantified the bias in terms of the percentage change in life expectancy gains with the intervention under an oHR compared with a dsHR approach as a function of the cohort start age, the disease-specific mortality rate, dsHR, and the duration of the intervention's effect. We then quantified the bias in a cost-effectiveness analysis (CEA) of implantable cardioverter-defibrillators based on efficacy estimates from a clinical trial. For a cohort of 50-year-old patients with a disease-specific mortality of 0.05, a dsHR of 0.5, a calculated oHR of 0.55, and a lifetime duration of effect, the bias was 28%. We varied these key parameters over wide ranges and the resulting bias ranged between 3 and 140%. In the CEA, the use of oHR as the intervention's effectiveness overestimated quality-adjusted life expectancy by 9% and costs by 3%, biasing the incremental cost-effectiveness ratio by - 6%. The use of an oHR approach to model the intervention's effectiveness beyond the time horizon of the trial overestimates its benefits. In CEAs, this bias could decrease the cost of a QALY, overestimating interventions' cost effectiveness.

The imprints of contemporary mass redistribution on local sea level and vertical land motion observations

Abstract. Observations from permanent Global Navigation Satellite System (GNSS) stations are commonly used to correct tide-gauge observations for vertical land motion (VLM). We combine GRACE (Gravity Recovery and Climate Experiment) observations and an ensemble of glacial isostatic adjustment (GIA) predictions to assess and evaluate the impact of solid-Earth deformation (SED) due to contemporary mass redistribution and GIA on VLM trends derived from GNSS stations. This mass redistribution causes relative sea-level (RSL) and SED patterns that not only vary in space but also exhibit large interannual variability signals. We find that for many stations, including stations in coastal locations, this deformation causes VLM trends on the order of 1 mm yr−1 or higher. In multiple regions, including the Amazon Basin and large parts of Australia, the SED trend flips sign between the first half and second half of the 15-year GRACE record. GNSS records often only span a few years, and due to these interannual variations SED causes substantial biases when the linear trends in these short records are extrapolated back in time. We propose a new method to avoid this potential bias in the VLM-corrected tide-gauge record: instead of correcting tide-gauge records for the observed VLM trend, we first remove the effects from GIA and contemporary mass redistributions from the VLM observations before computing the VLM trend. This procedure reduces the extrapolation bias induced by SED, and it also avoids the bias due to sea-floor deformation: SED includes net sea-floor deformation, which is ignored in global-mean sea-level reconstructions based on VLM-corrected tide-gauge data. We apply this method to 8166 GNSS stations. With this separation, we are able to explain a large fraction of the discrepancy between observed sea-level trends at multiple long tide-gauge records and the global-mean sea-level trend from recent reconstructions.

Ecological risk assessment of combined pollution in watersheds

Water pollution in China is severe and combined pollution with multiple stressors poses a great challenge to watershed risk management. Under the conditions of combined pollution, recognizing high-risk areas of concern, identifying key toxicants from multiple stressors and comprehensively assessing their ecological risk are the urgent and difficult tasks in watershed management. Traditional ecological risk assessment mainly focuses on single pollutant, which is difficult to obtain holistic information on the risk related to combined pollution. Based on the current research progress of combined pollution assessment, this review proposes a framework for ecological risk assessment of combined pollution in watersheds, including recognition of high-risk areas, identification of key toxicants and comprehensive assessment of ecological risk of the key toxicants. Firstly, high-risk areas are identified by weight of evidence analysis, which integrates information from both laboratory and in situ exposure and effect analyses. Most of exposure and effect data so far are based on chemical analyses and bioassays in the laboratories, yet bias may exist in extrapolating information from laboratory data to the field. Alternatively, in situ analysis serves an effective approach in reducing this extrapolation bias and, at the same time, more realistically recording biological effects under some field exposure scenarios, such as pulse exposure. Passive sampling devices have been applied for in situ exposure assessment. The integration of passive sampling with in situ organism exposure chambers successfully gains both chemical and toxicological lines of evidence for ecological risk assessment. Secondly, key toxicants in the high-risk areas are identified using toxicity identification evaluation (TIE) and effect-directed analysis (EDA) techniques. Conventional TIE is of environmental relevance by using whole organism bioassays; however, it is lack of effective methods in identifying major contributors to the toxicity because it merely focuses on analyzing the contaminants in target lists. Alternatively, EDA is a powerful tool in identifying key organic toxicants with a combination of chemical fractionation and analysis of targeted and non-targeted contaminants. Nevertheless, the common use of in vitro bioassays and exhaustive extraction make EDA lack of environmental relevance. Therefore, integrating TIE and EDA would provide an environmentally relevant method to effectively determine causality of sediment toxicity by combining the merits of the two methodologies. To improve the accuracy of toxicity identification, bioavailable extraction and dosing techniques are recommended to be incorporated into the integrated method. Thirdly, probabilistic ecological risk of the key toxicants in the high-risk areas is evaluated using tiered ecological risk assessment methods. Hazard quotient method has been widely used in providing conservative risk screening information, but uncertainties could not be quantified with this method. Therefore, a probabilistic assessment method, including distributions of exposure, response and hazard quotient levels, is proposed to achieve a holistic ecological risk assessment. At the end, recent developments and challenges in ecological risk assessment of combined pollution in watersheds are prospected. Overall, integrating the understanding of joint toxicity mechanisms in combined pollution risk assessment, improving the ability in non-targeted analysis and developing bioavailability-based sediment thresholds are important to assess ecological risk of combined pollution in watersheds.