13 - Heterogeneous Risk Tolerance and Time Preference

What do happiness and health satisfaction data tell us about relative risk aversion?

We consider the economy in which an agent faces, in addition to market risk, an additive independent background risk in consumption. In contrast to the Lucas (Econometrica 46:1429–1445, 1978) complete consumption insurance model, under plausible assumptions about the unconditional mean and variance of the agent’s subjective distribution of background risk the model with the additive independent background risk fits the historical average excess return on the US stock market with the coefficient of relative risk aversion (RRA) below five for the subsets of households designated as assetholders. The greater the size and/or the lower the expected value of background risk, the lower (compared to the Lucas (Econometrica 46:1429–1445, 1978) model) the value of the RRA coefficient needed for the model with background risk to match the historical average equity premium. Allowing for an extremely unlike large decrease in the agent’s consumption considerably decreases the required coefficient of RRA. It is concluded that the presence of the additive independent background risk in the consumption of assetholders can account for nearly 60 % of the historical average equity premium, hence rationalizing the equity premium puzzle of Mehra and Prescott (J Monet Econ 15:145–162, 1985). With RRA below five, the model with background risk is consistent with the historical average real interest rate if the agent has the subjective time discount factor lower than, but close to, 1. The findings are robust to the assumed type of background risk, the proxy for the market portfolio, and the threshold value in the definition of assetholders.

BackgroundEarlier research has documented an association between depressive symptomatology and heightened stroke risk. However, prior work largely assessed depressive manifestations at isolated time points and failed to differentiate symptom subtypes. This investigation seeks to characterize the longitudinal progression of depressive symptoms via repeated measurement and explore their link to stroke risk by considering total depressive symptoms alongside cognitive-affective and somatic dimensions.MethodsThis prospective cohort study included individuals aged ≥ 45 years from the Health and Retirement Study (HRS) in the United States and the English Longitudinal Study of Ageing (ELSA) in the United Kingdom, excluding those with a history of stroke during the exposure period. Depressive symptoms were measured using the 8-item Center for Epidemiologic Studies Depression Scale (CES-D) across four biennial assessments. Individuals were categorized into five distinct depressive symptom trajectories: consistently low, decreasing, fluctuating, increasing, and consistently high, based on assessment scores. Over a subsequent decade of follow-up, incident strokes were identified through self-reported physician diagnoses. The analyses incorporated adjustments for demographic factors (sex, age, etc.), health-related behaviors (smoking, drinking, etc.), and health status covariates (hypertension, diabetes, etc.). Cox proportional hazards regression models generated hazard ratios (HRs) and 95% confidence intervals (CIs) to evaluate links between trajectories of total depressive symptoms, cognitive-affective and somatic subtypes, and stroke occurrence.ResultsThe final cohort included 10,011 participants (63.3% female; mean age 60.2 years). During the 10-year follow-up, 720 incident strokes were recorded. Analyses demonstrated that, after adjusting for the aforementioned demographic and health-related confounders, relative to the consistently low trajectory, participants with fluctuating (HR = 1.24, 95% CI: 1.01–1.52), increasing (HR = 1.31, 95% CI: 1.03–1.67), and consistently high (HR = 1.42, 95% CI: 1.03–1.97) total depressive symptom trajectories exhibited significantly elevated stroke risk. Conversely, the decreasing trajectory (HR = 1.11, 95% CI: 0.85–1.45) did not significantly impact stroke risk. Furthermore, an increasing trajectory of cognitive-affective depressive symptoms (HR = 1.43, 95% CI: 1.13–1.82), alongside fluctuating (HR = 1.27, 95% CI: 1.03–1.55) and consistently high (HR = 1.97, 95% CI: 1.42–2.74) somatic depressive symptom trajectories, were each significantly associated with heightened stroke risk. Critically, the consistently high somatic trajectory demonstrated the most robust association with stroke.ConclusionTrajectories of total depressive symptoms marked by escalation, instability, or sustained elevation exhibited significantly elevated stroke risk. In contrast, individuals displaying decreasing depressive symptoms exhibit stroke risk comparable to those maintaining consistently low levels. Specifically, an ascending trajectory of cognitive-affective symptoms, alongside unstable and persistently elevated trajectories of somatic symptoms, are linked to increased stroke risk. These findings emphasize the clinical importance of monitoring dynamic changes in depressive symptoms and their subtypes for stroke prevention. Future investigations should elucidate underlying mechanisms to refine identification and intervention strategies for high-risk populations.

Harmonizing late‐life cognitive performance data across two population‐based cohort studies: The Health and Retirement Study and National Health and Aging Trends Study

Optimal Diversification in the Presence of Parameter Uncertainty for a Risk Averse Investor

In this paper, expected utility, defined by a Taylor series expansion around expected wealth, is maximized. The coefficient of relative risk aversion (CRRA) that is commensurate with a 100% investment in the risky asset is simulated. The following parameters are varied: the riskless return, the market standard deviation, the market stock premium, and the skewness and the kurtosis of the risky return. Both the high extremes and the low extremes are considered. With these figures, the upper bound of the market CRRA is 3.021 and the lower bound is 0.466. Log utility, which corresponds to a CRRA of 1, is not excluded.

PurposeThis paper seeks to reconsider the Euler equation of the Consumption Capital Asset Pricing Model (CCAPM), to derive a regression‐based model to test it, and to present evidence that the model is consistent with reasonable values for the coefficient of relative risk aversion (CRRA). This runs contrary to the findings of the literature on the equity premium puzzle, but is in agreement with the literature that estimates the CRRA for the purpose of computing the social discount rate, and is in line with the research on labor supply. Tests based on General Method of Moments (GMM) for the same sample produce results that are extremely disparate and unstable. The paper aims to check and find support for the robustness of the regression‐based tests. Habit formation models are also to be evaluated with regression‐based and GMM tests. However, the validity of the regression‐based models depends critically on their functional forms.Design/methodology/approachThe paper presents empirical evidence that the conventional use of GMM fails because of four pathological features of GMM that are referred to under the general caption of “weak identification”. In addition to GMM, the paper employs linear regression analysis to test the CCAPM, and it is found that the regression residuals follow well‐behaved distributional properties, making valid all statistical inferences, while GMM estimates are highly unstable.FindingsFour unexpected findings are reported. The first is that the regression‐based models are consistent with reasonable values for the CRRA, i.e. estimates that are below 4. The second is that the regression‐based tests are robust, while the GMM‐based tests are not. The third is that regression‐based tests with habit formation depend crucially on the specification of the model. The fourth is that there is evidence that market stock returns are sensitive to both consumption and dividends. The author calls the latter “extra sensitivity of market stock returns”, and it is described as a new puzzle.Originality/valueThe regression‐based models of the CCAPM Euler equation are novel. The comparison between GMM and regression‐based models for the same sample is original. The regression‐based models with habit formation are new. The equity premium puzzle disappears because the estimates of the CRRA are reasonable. But another puzzle is documented, which is the “extra sensitivity of market stock returns” to consumption and dividends together.

Optimal retirement consumption with a stochastic force of mortality

Can VAR Models Capture Regime Shifts in Asset Returns? A Long-Horizon Strategic Asset Allocation Perspective

Harmonization of Cross-National Studies of Aging to the Health and Retirement Study - User Guide

The Health and Retirement Study (HRS), a principal source for American public health research, has numerous global sister studies. Harmonization efforts seeking to establish measurement equivalence amongst these various datasets, is a critical prerequisite to cross-cultural research. Given well-known cultural variability in depressive symptom endorsement, the purpose of this study was to assess measurement invariance in a brief mood measure used in the HRS and the Mexican Health and Aging Study (MHAS). Total sample size using both groups was 15,319 participants (10,931 HRS; 4,388 MHAS) who were 65 and older from Waves 6 to 13 in the HRS and Waves 1 to 4 in the MHAS. MPlus Version 8.4 was used to conduct CFA analyses of measurement invariance. A contemporary approach with categorical data calls for examining threshold invariance first while establishing configural invariance, before examining invariance tests of thresholds, loadings, and intercepts in a second step. Results were that measurement invariance was not supported in this series of two steps with four out of six indices showing model fit in the first model and none of the indices showing model fit in the second model. These findings implied that there were differences in ways of responding to the brief mood measure between HRS and MHAS participants at the conceptual level. Thus, comparisons based on these measures may result in misleading findings and should be interpreted very conservatively. This study adds to the growing body of literature guiding harmonization efforts from the Program on Global Aging, Health and Policy.

Consumption and portfolio choice with time-inconsistent preferences

ObjectiveChronic pain and depression are common in older adults, yet pain is dynamic and may follow distinct longitudinal courses. This study examined whether chronic pain trajectories are associated with incident depressive symptoms among adults aged 50 years and older.MethodsAnalyzed were two prospective cohorts of community-dwelling adults: the English Longitudinal Study of Ageing (ELSA) and the US Health and Retirement Study (HRS). Biennial self-reported pain (yes/no) across four waves was used to classify five mutually exclusive pain trajectories: no pain, decreasing pain, fluctuating pain, increasing pain, and consistent pain. Participants with depressive symptoms at baseline were excluded. Incident depressive symptoms were defined as a Center for Epidemiologic Studies Depression scale (CESD-8) score ≥3. Cox proportional hazards models estimated hazard ratios (HRs) adjusted for sociodemographic characteristics, health behaviors, and chronic conditions.ResultsThe analytic samples included 2476 participants in ELSA and 6238 in HRS, with a mean follow-up of 6.3 years and 6.1 years, respectively; incident depressive symptoms occurred in 19.7% and 18.3%, respectively. Compared with the no-pain trajectory, fluctuating, increasing, and consistent pain were associated with higher risk of depressive symptoms in ELSA (HRs, 1.70 [95% CI, 1.37-2.10], 1.76 [95% CI, 1.27-2.45], and 2.60 [95% CI, 1.98-3.43], respectively) and HRS (HRs, 1.48 [95% CI, 1.29-1.71], 1.84 [95% CI, 1.47-2.29], and 2.15 [95% CI, 1.78-2.59], respectively). Decreasing pain was not significantly associated with risk in either cohort.ConclusionsPersistent or worsening pain trajectories were consistently predicted subsequent depressive symptoms in older adults, whereas improving pain was not. Longitudinal pain monitoring may help identify high-risk individuals through earlier depression screening, along with integrated pain-mental health care.

BackgroundAlthough social position plays a pivotal role in cognitive aging, most dementia prevention strategies and risk prediction models continue to emphasize biomedical and genetic factors (particularly APOE status). This disconnect raises critical questions about how social environments may shape the effect of genetic risk on dementia. We examined how APOE alleles interact with social adversity to determine dementia risk.MethodsWe conducted an observational analysis using two large cohort studies—the Health and Retirement Study (HRS) and the English Longitudinal Study of Ageing (ELSA)—including individuals aged 55 years or older without dementia at baseline. A social adversity index was constructed based on the five domains of social determinants of health outlined in the Healthy People 2030 framework: education access, economic stability, healthcare quality, neighborhood environment, and social context. Participants were classified as having low (APOE-ε2), intermediate (APOE-ε3/ε3), or high (APOE-ε4) genetic risk of dementia. Dementia was ascertained via clinical diagnosis, cognitive testing, or validated caregiver report. Cox proportional hazards models were used in each cohort, and estimates were pooled using random-effects adjusting for covariates.ResultsA total of 9,849 participants (HRS = 5,797; ELSA = 4,052) were followed for up to 12 years. Genetic effects were most pronounced among individuals with social advantage (reference: APOE-ε3/ε3 with social advantage; APOE-ε2 HR = 0.67, 95%CI = 0.48–0.93; APOE-ε4 HR = 1.68, 95%CI = 1.37–2.06). In contrast, those experiencing high social adversity had elevated dementia risk regardless of genotype (reference: APOE-ε3/ε3 with social advantage; APOE-ε2 HR = 3.26, 95%CI = 2.06–5.16; APOE-ε3/ε3 HR = 3.12, 95%CI = 2.47–3.95; APOE-ε4 HR = 3.21, 95%CI = 2.34–4.41). Notably, individuals with high genetic risk but social advantage had a lower dementia risk than those with low genetic risk but high social adversity.ConclusionsThe influence of genetic risk on dementia appears shaped by social position. Addressing social adversity may reduce dementia risk across genotypes and enhance equity in dementia prevention strategies.

ObjectivesPrevious studies suggested protective associations of vegetables and fruits (VF) intake with cognitive function, but evidence on specific types of VF was insufficient. MethodsThe current study included 4066 participants from 1997 to 2006 in the China Health and Nutrition Survey (CHNS) and 6170 participants from 2013 to 2020 in the Health and Retirement Study (HRS). Dietary intake (using 3-day 24-h dietary recalls in CHNS and food frequency questionnaire in HRS) and cognitive function (using the Telephone Interview for Cognitive Status-Modified, TICS-m) were measured. Linear mixed-effects models were used to estimate the beta coefficients (β) and the 95% confidence intervals (CI) to evaluate the association of VF with cognitive function (z-score) and its decline. ResultsHighest intake of total VF was associated with better cognitive function and slower cognitive decline. Differences in cognitive function z-score between the highest and lowest tertiles of VF consumption were 0.039 (95% CI: 0.002, 0.076) for CHNS and 0.063 (95% CI: 0.026, 0.100) for HRS. The corresponding differences in annual cognitive decline were 0.011 (95% CI: 0.002, 0.021) and 0.012 (95% CI: 0.003, 0.020) units respectively. Vegetables and fruits showed independent associations with cognitive function and its decline. In specific VF subgroups, when comparing the highest to the lowest tertile intake, cruciferous vegetables (β = 0.058, 95% CI: 0.017, 0.100 in CHNS and β = 0.067, 95% CI: 0.032, 0.101 in HRS) and green leafy vegetables (β = 0.036, 95% CI: −0.001, 0.073 in CHNS and β = 0.082, 95% CI: 0.046, 0.117 in HRS) was associated with better cognitive function in both cohorts. Similarly, higher intake of dark-colored vegetables (β = 0.019, 95% CI: 0.008, 0.030 for red/yellow vegetables in CHNS and β = 0.004, 95% CI: 0.001, 0.007 for green leafy vegetables in HRS) were associated with slower cognitive decline in subsequent years. Moreover, rigorous sensitivity analyses confirmed the stability of the results. ConclusionsOur findings support the potential beneficial roles of VF, especially cruciferous vegetables, green leafy vegetables, and red/yellow vegetables, in maintaining cognitive function and slowing cognitive decline in middle-aged and older adults.