Modeling Behavioral and Attitudinal Drivers of Life Insurance Selection and Premiums: Polynomial Approaches to Perceived Affordability in Term and Cash Value Products

Abstract

Background: Life insurance markets are experiencing unprecedented transformation in the wake of economic disruption, evolving consumer expectations, and behavioral shifts following the COVID-19 pandemic. Traditional economic models often fail to capture the complex interplay of attitudinal, and cognitive factors that now shape insurance demand and premium selection. Methods: This study analyzes nationally representative survey data from over 3600 U.S. adults (2024 NAIC Financial Inclusion Survey). It uses a weighted full maximum likelihood Heckman selection model to identify determinants of life insurance uptake and premiums. The main innovation is modeling psychological price, a composite of perceived affordability, with higher-order polynomials. The design integrates psychometrically validated measures of financial knowledge and risk tolerance. Political ideology, race and ethnicity, and sources of financial advice serve as exclusion restrictions in the selection equation. Results: Psychological price shows an inverse-U relation with term outcomes: uptake rises at low to moderate affordability and declines at high affordability; among purchasers, term premiums rise at low to mid affordability and decline at high levels. For cash value policies, premiums decrease as psychological price increases. Financial knowledge and risk tolerance increase term uptake; financial knowledge reduces cash premiums. Education and income increase term uptake and term premiums. Compared with respondents reporting no ideology, conservative and centrist respondents have lower term uptake and higher cash uptake; using a professional advisor is associated with higher cash uptake. The selection correlation is positive for term ($\rho \approx 0.98$) and negative for cash ($\rho \approx -0.38$), indicating non-random selection in both markets. Implications: In order to reduce disparities, insurers should target the mid-affordability threshold with term offerings, streamline options for high-affordability consumers, offer pricing support and guidance for low-affordability households, increase uptake through advice channels and financial education, and address affordability barriers. Conclusions: Nonlinear affordability effects shape both market entry and pricing choices. Modeling psychological price with higher-order polynomials identifies thresholds and turning points that linear specifications miss. The results support targeted product design and outreach when perceived affordability drives insurance participation and premium choices.

1. Introduction

Life insurance is fundamental to contemporary financial management and economic growth, offering essential protection for families and serving as a crucial tool for generating long-term capital in national economies (Bhattacharya-Craven et al., 2025; Hodula et al., 2021). The global business environment is rapidly changing, characterized by heightened volatility, technological advancements, and evolving macroeconomic frameworks, hence intensifying the necessity for efficient risk management systems. Life insurance, in its various forms, aids households in mitigating the financial consequences of mortality risk while also contributing to overall financial stability and economic growth. The dual function of life insurance as both a private asset and a public stabilizer highlights the necessity for academics, practitioners, and policymakers to comprehend the factors influencing its demand (Dragoş et al., 2019; Srinivasan & Mitra, 2024; Zietz, 2003).

Although fundamental, the factors influencing life insurance adoption and coverage decisions are becoming increasingly intricate and context-specific, undermining the effectiveness of conventional actuarial and economic models. Consumer demand is influenced by a combination of factors: rational expectations concerning risk and return, current macroeconomic conditions, and various behavioral influences, including psychological perceptions of affordability, financial literacy, and cognitive biases (Kohl & Römer, 2024; Kunreuther et al., 2006; Rabin & Thaler, 2001; Srinivasan & Mitra, 2024; Tversky & Kahneman, 1992). Recent research underscores how deficiencies in financial literacy, prevailing social norms, and marketing tactics influence not only individuals’ choices between term and cash value policies but also the premiums they are prepared to pay and the extent of coverage they opt for (Bhattacharya-Craven et al., 2022; C. Chen et al., 2024; Lusardi & Mitchell, 2014; Lusardi & Tufano, 2017; Zhang, 2024). In a time of increased uncertainty and changing financial systems, innovative interdisciplinary strategies are essential to understand the interaction between economic rationality and behavioral realities, allowing insurers and policymakers to create products and interventions that overcome both financial and psychological obstacles to optimal insurance participation.

Recent research indicates that insurance datasets frequently exhibit significant selection bias for unobservable factors, resulting in analyses limited to insured individuals yielding distorted estimates of price or premium correlations. Surveys and claims studies illustrate selection and moral hazard in modern insurance markets, advocating for explicit selection corrections instead of solely predicting outcomes based on the insured subsample (Afoakwah et al., 2023; Einav & Finkelstein, 2023; Rothschild & Thistle, 2022). Many studies identify sampling and coverage heterogeneity that skew outcome regressions when the analytic sample omits nonparticipants (Dahlen & Charu, 2023). In consumer insurance, the absence of underwriting and medical risk data in non-administrative surveys results in omitted-variable bias that is associated with both purchasing behavior and observed premiums, necessitating the use of selection-corrected methodologies such as Heckman or analogous control-function techniques. Regulatory and actuarial reports reflect these data constraints and emphasize how advancing underwriting and AI-driven processes overlook significant risk indicators in conventional survey microdata. Methodological advancements in health insurance demand studies emphasize a consistent conclusion: comprehensive structural or nonparametric models effectively discern demand when extensive administrative data are accessible; however, in survey contexts, researchers depend on econometric selection corrections to prevent conditioning solely on insured individuals (Tebaldi et al., 2023).

The COVID-19 pandemic transformed insurance markets. Excess mortality during 2020–2021 heightened risk awareness and modified life expectancy trajectories, with a degree of normalization observed in 2022–2023 (National Center for Health Statistics, 2023). Consumers today anticipate enhanced protection and digital services, while regulators indicate fundamental changes in products, data utilization, and control (International Association of Insurance Supervisors, 2025). The life sector exhibited a resurgence in performance, characterized by robust premium growth in 2023–2024 and enhanced investment outcomes as markets steadied. U.S. life insurers disclose assets approximating USD 8.7–USD 9.0 trillion, underscoring market magnitude and balance sheet recuperation (OECD, 2024). Demand indicators among younger demographics intensified post-pandemic with a significant desire and intent to purchase among Gen Z and Millennials, and cost identified as the primary obstacle to acquiring coverage (Bernheim, 1991; Bhatia et al., 2021; Dhanya et al., 2023; Kohn, 2023; Life Happens, 2023). These changes render perceptions of affordability crucial for participation.

Current demand frameworks frequently presuppose monotonic price effects and evaluate premiums solely among policyholders, resulting in selection bias and minimizing perceptions (Charles et al., 2024; Domurat et al., 2021; B. Handel et al., 2015; B. R. Handel et al., 2019; Spinnewijn, 2017). This study tackles that deficiency in three phases. Initially, it characterizes psychological pricing as a cohesive affordability index that is equivalent for both insured and uninsured respondents via skip-logic assessment. Secondly, it employs higher-order polynomials to simulate psychological pricing, effectively capturing threshold and inverse-U patterns that linear forms overlook, according to best practices for flexible functional forms and threshold identification (Shampanier et al., 2007; Zyphur et al., 2016). Third, it jointly estimates uptake and premiums using a weighted Heckman maximum likelihood estimation to address selection bias related to unobservables that connect the purchase decision to observed premium choices; this is consistent with research in post-pandemic markets and the necessity to prevent insured-only inference. The design distinguishes between term and cash value products, identifies turning moments, and measures how affordability, financial literacy, and risk tolerance influence market entry and premium rates. These selections provide policy-relevant insights for bridging protection gaps and enhancing financial well-being.

Although a substantial body of work exists on life insurance demand, significant gaps remain about the psychological and behavioral factors influencing product adoption, premium payment, and policy choice. Previous studies have examined various predictors—including wealth, family structure, education, and subjective risk aversion—yielding inconsistent results regarding their predictive efficacy and significance across diverse populations and timeframes (Anderson & Nevin, 1975; Browne & Kim, 1993; Mantis & Farmer, 1968; Poterba et al., 2013; Ropponen et al., 2023; Zietz, 2003). There is increasing evidence that attitudinal factors—such as perceived affordability, risk tolerance, and financial literacy—significantly and occasionally nonlinearly influence insurance behavior (Kunreuther et al., 2006; Outreville, 2013). Although price sensitivity and affordability have traditionally been acknowledged as pivotal to insurance participation, recent research indicates that the correlation between perceived price and demand may be notably non-monotonic, necessitating more sophisticated modeling techniques to accurately represent the comprehensive range of behavioral responses (Abaluck et al., 2018; Baicker et al., 2015; Douven et al., 2020; Geruso et al., 2023; Tebaldi et al., 2023).

This study addresses important gaps in the insurance literature by analyzing a unique, nationally representative dataset collected by the National Association of Insurance Commissioners in early 2024, focusing on the shifting landscape of life insurance demand in the U.S. during the post-pandemic period. The study treats psychological price as a continuous driver of behavior and models it with higher-order polynomials inside a weighted Heckman selection framework. The variable is centered, and the model includes the linear, quadratic, and cubic terms. This structure permits non-monotonic responses and threshold effects in both uptake and premiums. The psychological price refers to the subjective expense a household attributes to acquiring or maintaining coverage, influenced by perceived affordability and the discomfort associated with payment. To capture this, we combine insured respondents’ assessments of current premium affordability with uninsured respondents’ anticipated affordability of potential coverage. While these measures reference different situations, both serve as proxies for the same underlying latent construct: the subjective financial burden or “payment pain” that shapes willingness to hold or purchase insurance. This unified scale allows us to model the psychological dimension of affordability consistently across the full sample. Recent research on behavioral pricing indicates that perceived price and payment discomfort forecast purchase frequency, expenditure, and timing (H. Chen et al., 2021; Office of Health Policy, 2025; Zhao et al., 2021). Evidence regarding payment frictions indicates that reduced payment discomfort correlates with an increased propensity to pay (Silva et al., 2023). Employing the affordability index as a continuous metric of psychological pricing corresponds with contemporary theory and market evidence, hence facilitating the estimation of nonlinear reactions in both adoption and premiums.

Polynomial modeling offers a transparent way to capture curvature and thresholds (Harrell & Levy, 2022; Lind & Mehlum, 2010; Royston & Altman, 1994; Royston & Sauerbrei, 2008; Simonsohn, 2018). This design fits cleanly with selection correction, supports clear interpretation around decision thresholds, and links directly to policy-relevant ranges of perceived affordability. This research combines prospect theory and mental accounting to elucidate the influence of psychological pricing on insurance adoption and premium selection. Prospect theory posits that individuals assess risky choices not only by expected value but also by reference-dependent perceptions of gain and loss, frequently overweighting low-probability outcomes and responding nonlinearly to changes in affordability (Kahneman & Tversky, 1979; Stapleton, 2021). Prospect theory suggests that consumers exhibit a nonlinear response to price fluctuations near reference points, resulting in demand curves that are convex initially and then concave. Recent evidence indicates that loss aversion diminishes demand for protection products, particularly near psychological thresholds (Hwang, 2016). Mental accounting, meanwhile, suggests that consumers often treat insurance premiums as a separate budget category, evaluating affordability based on psychological thresholds rather than strict actuarial cost–benefit analysis (R. Thaler, 1985). This produces fluctuations in insurance demand when consumers cross cost-sharing thresholds, with free coverage generating exceptionally high uptake rates that act as decision-making reference points (Robinson et al., 2021). Mental budgets elucidate counterintuitive behaviors such as overinsurance for minor risks and deductible avoidance, manifesting as systematic curves in willingness-to-pay (Fels, 2020). Furthermore, salience effects enhance these patterns as specific prices attract increased attention, resulting in more pronounced threshold responses (Bordalo et al., 2022). The complexity escalates as consumers concurrently determine both the decision to purchase insurance (extensive margin) and the amount of coverage to acquire (intensive margin), resulting in varying curve shapes across different product types (Geruso et al., 2023). The behavioral mechanisms produce various turning points in the price–demand relationship, thereby supporting the application of higher-order polynomial models that can effectively represent non-monotonic patterns without enforcing restrictive linearity assumptions. By integrating these insights, the study not only models affordability as a higher-order polynomial but also incorporates contemporary, psychometrically sound measures of financial knowledge (via item response theory) and risk tolerance (via combined stated and revealed preferences).

How do attitudinal and cognitive variables—especially the nonlinear effects of psychological price—influence the likelihood of life insurance uptake and the selection of premiums for term and cash value products among U.S. adults, after controlling for financial knowledge, risk tolerance, and other relevant factors? Consistent with prospect theory and the literature on attitudinal pricing, several hypotheses are advanced. First, the linear (first-order) component of psychological price is expected to be positively related to both uptake and premium paid for term insurance, while the quadratic (second-order) and cubic (third-order) components are hypothesized to be negative, supporting the idea that increases in perceived affordability initially boost demand but eventually reach a point of diminishing returns or even reversal (a behavioral “sweet spot” consistent with reference dependence and mental accounting thresholds). For cash value insurance, the first-order psychological price effect is expected to be significant for uptake but, due to greater price sensitivity and the higher entry cost, only the linear term is hypothesized to significantly predict premium choice. These relationships are anticipated to differ between term and cash value products, reflecting the distinct behavioral and psychological mechanisms—rooted in prospect theory and mental accounting—that shape how consumers evaluate affordability, risk, and product value. By rigorously modeling these interactions, this research delivers new evidence on the behavioral economics of insurance, with direct implications for policy, financial education, and insurance product design.

The research examines the attitudinal and psychological factors influencing life insurance demand in the United States during the post-pandemic era. It considers political ideology, sources of financial counsel, and race as heuristic indicators aligned with mental accounting and prospect theory (R. H. Thaler, 1999; Tversky & Kahneman, 1981; Tversky et al., 1982). These cues substitute intricate assessments with rapid determinations about trust, risk, and protective inclinations (Gigerenzer & Todd, 2000; Shah & Oppenheimer, 2008; Vis, 2019). Mental accounting divides insurance demands into budget categories influenced by ideology, adviser credibility, and cultural identification (Kahneman & Tversky, 1984; R. H. Thaler, 1999). Prospect theory suggests that reference dependency and gain-loss framing are determined by these cues (Kahneman & Tversky, 1979; Tversky & Kahneman, 1992). The model employs ideology, advisor utilization, and race as exclusion limits in the uptake equation, affecting participation through attitudes and access, while price formulae are contingent upon actuarial aspects. Evidence on post-pandemic polarization and trust substantiates this selection (Crockett & Wallendorf, 2004; Jost et al., 2009; Key & Donovan, 2017; Weyland, 2009).

2. Methodology

2.1. Data Source and Sample Design

The research analyzes the demand for life insurance and the factors influencing premium choices. It utilizes data from the 2024 Financial Inclusion Survey conducted by the Center of Insurance Policy and Research (CIPR) under the National Association of Insurance Commissioners (NAIC). The survey was administered from February to March 2024 using the Qualtrics online platform, collecting responses from 3,611 people across the United States. Prestratification weights were employed throughout the survey execution to ensure adequate representation of minority groups, leading to the oversampling of certain populations. This strategy aligns with research demonstrating that oversampling enhances the accuracy of estimates for underrepresented groups and mitigates bias (Groves, 2006; Kalton, 2009). To ensure national representativeness, poststratification weights were computed using the ANESRAKE algorithm, which adjusts sample weights to align with predetermined population totals and correct for sampling bias (Ansolabehere & Rivers, 2013; Battaglia et al., 2009; DeBell & Krosnick, 2009; Kolenikov, 2014; Pasek & Pasek, 2018). The weighting procedure incorporated six demographic dimensions—age, education level, race, income level, gender, and region—calibrated to 2024 U.S. Census Bureau population targets. The survey covered various topics related to financial inclusion, including health insurance, life insurance, retirement planning, financial literacy, and risk perception. It also collected extensive demographic data to facilitate a detailed examination of financial behaviors and attitudes across different population groups.

2.2. Main Variables

2.2.1. Dependent Variables

The study examines two primary dependent variables to assess life insurance demand and the factors affecting premium selection. The primary dependent variable is a binary indicator reflecting the existence or non-existence of life insurance coverage among respondents. This variable serves as a reliable indicator of insurance ownership, reflecting individuals’ participation in the life insurance market and highlighting the accessibility and appeal of these risk management solutions. The second dependent variable is the actual premium paid by policyholders, generally reported as a continuous monetary value. This variable is crucial for comprehending the economic trade-offs consumers encounter and the financial implications of life insurance participation. The analysis categorizes customer behavior variance by two prevalent forms of life insurance: term life insurance and cash value life insurance, encompassing whole life and universal life policies. Term life insurance offers provisional coverage for a specified duration—such as 10, 20, or 30 years—at comparatively modest premiums. It possesses neither a savings nor an investment element, and coverage terminates at the end of the term unless renewed (Heo et al., 2021; Mulholland et al., 2016; Nkouaga, 2024a; Outreville, 2013). In contrast, cash value life insurance provides continuous coverage and incorporates a savings or investment component that accrues tax-deferred cash value over time. This insurance type, albeit pricier, is frequently selected for its dual functions of providing a death benefit and facilitating wealth creation (Babbel & Merrill, 1998; Cole & Fier, 2021; Nkouaga, 2024a; Rabbani, 2020). The economic differentiation between these two policy kinds is essential: term insurance is largely regarded as risk protection, whereas cash value insurance additionally functions as a hybrid financial asset. The study facilitates a detailed assessment of how demographic, economic, and behavioral factors variably influence insurance ownership, premium selections, and coverage levels across different product categories by disaggregating the data in this manner. This dual-framework methodology offers an extensive viewpoint on life insurance demand among various consumer subgroups.

2.2.2. Independent Variables

Main Variable

Psychological price is the central independent variable in this study, capturing respondents’ perceived affordability of life insurance. The survey used skip logic: uninsured respondents rated how affordable buying coverage would be for themselves and their family, while insured respondents rated how affordable their current premium is. Both items used a six-point scale from “very unaffordable” to “very affordable,” and “no contribution required.” We code responses to a common numeric scale and combine them into a single continuous index so insured and uninsured are comparable and the uptake model avoids separation.

$$D_i\in \{0,1\}(\mathrm{insured}=1),li{5}_i\in \{1,\dots ,6\}\mathrm{if}{D}_i=1,li{6}_i\in \{1,\dots ,6\}\mathrm{if}{D}_i=0.$$

$$P_i=\left\{\begin{array}{cc}s\left(li{5}_i\right),\hfill & D_i=1(\mathrm{experienced}\mathrm{affordability}),\hfill \\ s\left(li{6}_i\right),\hfill & D_i=0(\mathrm{anticipated}\mathrm{affordability}),\hfill \\ NA,\hfill & \mathrm{if}\mathrm{both}\mathrm{are}\mathrm{missing}.\hfill \end{array}\right.$$

where i indexes respondents; $D_i$ is life insurance uptake (1 = insured, 0 = not insured); $li{5}_i$ is experienced premium affordability for insured respondents on a 1–6 scale $[1=\mathrm{very}\mathrm{unaffordable},6=\mathrm{no}\mathrm{contribution}\mathrm{required}]$; $li{6}_i$ is anticipated affordability for uninsured respondents on the same 1–6 scale; and $P_i$ is the psychological price on the common 1–6 scale, defined from the item observed for respondent i, and set to NA if neither item is observed.

Binary classification models encounter a significant estimation issue known as perfect separation, wherein predictors entirely differentiate between groups, resulting in indefinite maximum likelihood estimates and hindering convergence (Albert & Anderson, 1984; Heinze & Schemper, 2002). This separation issue arises when a uniform affordability metric is applied to all participants, as the survey design induces structural missingness: uninsured respondents ($D_i=0$) exclusively provide $li{5}_i$ responses, whereas insured respondents ($D_i=1$) solely provide $li{6}_i$ responses. Our strategy entails the development of the psychological pricing measure $P_i$ to strategically allocate each respondent their pertinent affordability evaluation, ensuring that both insured and uninsured subgroups maintain adequate variation for statistical identification. This methodology integrates effortlessly with the FIML Heckman estimation framework, wherein the correlation parameter $\rho$ connects selection and outcome processes, mitigates potential selection bias, and ensures estimation stability while retaining the polynomial specification of $P_i$ essential for identifying threshold effects (Greene, 2000; Heckman, 1979).

Behavioral theory provides the foundation for understanding how subjective costs drive purchase decisions, with mental accounting and reference dependence frameworks linking “payment pain” and budget tightness to consumers’ willingness to buy insurance. Building on this theoretical foundation, perceived affordability serves as a direct proxy for the psychological cost that becomes most relevant during the decision-making stage (Alemán & Marrugo, 2023; Ali & Anwar, 2021; Hsee & Kunreuther, 2000; Kahneman & Tversky, 1979; Prelec & Loewenstein, 1998; Soman, 2001; R. Thaler, 1985). This theoretical relationship finds strong empirical support across multiple insurance contexts, where affordability consistently emerges as a key predictor of participation. Specifically in life insurance markets, both international studies and industry research identify affordability concerns and competing financial priorities as the primary barriers to coverage purchase (OECD, 2024; Schanz, 2020). Similarly, in health insurance markets, large-scale national surveys consistently report cost as the leading reason for remaining uninsured, further reinforcing the critical affordability–uptake relationship (Tolbert et al., 2024).

Given this robust evidence base, affordability represents a strong, exogenous predictor of insurance uptake, where individuals fundamentally decide against purchasing coverage when they perceive it as financially unaffordable. Our selection model therefore assumes a clear directional relationship: affordability influences life insurance uptake (affordability → life insurance uptake). This theoretical ordering is well justified: consumers assess subjective price perceptions before making purchase decisions, and these affordability evaluations shape their decision thresholds, while insurance uptake cannot logically precede the affordability assessment in cross-sectional analysis. Supporting this directional assumption, empirical research on payment salience demonstrates that payment methods affect perceived costs primarily after enrollment occurs, representing a post-purchase channel rather than a driver of initial uptake decisions (Prelec & Loewenstein, 1998; Soman, 2001).

Due to the recognized nonlinearity of attitudinal influences on financial decision-making, psychological pricing is incorporated into the regression models utilizing a third-degree (cubic) orthogonal polynomial function. Employing polynomials for attitudinal and perceptual variables is highly advocated in the economic, psychological, and financial literature, as it facilitates the detection of non-monotonic, threshold, and “kinked” relationships that linear models may overlook (Edwards & Parry, 1993; Homburg et al., 2005; Simonsohn, 2018). This method provides a flexible and rigorous framework for modeling how changes in perceived affordability—at various locations on the psychological price spectrum—can have diverse and perhaps paradoxical effects on insurance enrollment and premium choice.

Consumer Characteristics

This research accounts for alternative explanatory variables, such as cognitive measures. The cognitive measures are financial knowledge and risk tolerance. The evaluation of financial knowledge utilized a psychometrically sound methodology based on contemporary measurement theory. This study defines financial knowledge as an individual’s capacity to comprehend, assess, and utilize fundamental financial concepts, including interest compounding, inflation, risk diversification, and the attributes of financial instruments such as stocks, bonds, and savings accounts (Delgadillo & Lee, 2021; Gladstone & Barrett, 2023; Lusardi & Mitchell, 2014; Nkouaga, 2024a, 2024b). Participants were given a set of six objective questions that have been extensively validated in global financial literacy assessments. Responses were classified as accurate or incorrect, and these binary results were examined using a two-parameter logistic (2PL) item response theory (IRT) model. The 2PL model assesses item discrimination (the effectiveness of an item in distinguishing between respondents with varying ability levels) and item difficulty (the challenge presented by an item), thus addressing discrepancies in item quality and respondent ability in measuring financial knowledge (Awopeju et al., 2017; J. T. Lin et al., 2017; Stenhaug & Domingue, 2022).

To generate a continuous, individualized financial knowledge score, the study used the expected a posteriori (EAP) method—a Bayesian empirical estimator that computes the expected value of a respondent’s latent trait (ability) given their pattern of responses and the estimated item parameters. EAP scores utilize all accessible information and exhibit reduced bias compared to conventional sum scores, particularly when items differ in difficulty or discrimination (Embretson & Reise, 2013). Subsequent to computation, the EAP scores were linearly adjusted to ensure all values were unequivocally positive, hence enhancing their interpretability and applicability in regression models.

The financial knowledge variable is constructed as a latent trait ($\theta$) using a two-parameter logistic (2PL) item response theory (IRT) model and estimated for each respondent via the expected a posteriori (EAP) method. The process proceeds as follows:

• Binary Scoring of Items: For each respondent i and question j ($j=1,\dots ,J$), define the binary response

  $$x_{ij}=\left\{\begin{array}{cc}1,\hfill & \mathrm{if}\mathrm{the}\mathrm{response}\mathrm{to}\mathrm{item}j\mathrm{is}\mathrm{correct}\hfill \\ 0,\hfill & \mathrm{otherwise}\hfill \end{array}\right.$$
• 2PL IRT Model: Each item j is characterized by a discrimination parameter $a_j$ and a difficulty parameter $b_j$. The probability of a correct response, given latent trait ${\theta }_i$, is

  $$P(x_{ij}=1\mid {\theta }_i)={\displaystyle \frac{1}{1+exp\left[-a_j({\theta }_i-b_j)\right]}}$$
• Likelihood Function: The joint likelihood of respondent i’s response vector ${\mathbf{x}}_i=(x_{i1},\dots ,x_{iJ})$ is

  $$L({\theta }_i\mid {\mathbf{x}}_i)=\prod _{j=1}^{J}P{(x_{ij}\mid {\theta }_i)}^{x_{ij}}{[1-P(x_{ij}\mid {\theta }_i)]}^{1-x_{ij}}$$
• Expected a Posteriori (EAP) Estimation: The EAP estimate of ${\theta }_i$ is given by

  $${\widehat{\theta }}_i^{\mathrm{EAP}}={\displaystyle \frac{\int \theta L(\theta \mid {\mathbf{x}}_i)p\left(\theta \right)d\theta }{\int L(\theta \mid {\mathbf{x}}_i)p\left(\theta \right)d\theta }}$$

  where $p\left(\theta \right)$ is the assumed prior (typically standard normal).
• Rescaling: To ensure all values are positive (e.g., for modeling purposes), a linear shift is applied:

  $${\widehat{\theta }}_i^{\mathrm{EAP},\mathrm{pos}}={\widehat{\theta }}_i^{\mathrm{EAP}}-\underset{i}{min}\left({\widehat{\theta }}_i^{\mathrm{EAP}}\right)+ϵ$$

  where $ϵ$ is a small positive constant (e.g., $0.01$) to ensure strictly positive values.

Risk tolerance—a central concept in expected utility theory—refers to an individual’s willingness to accept uncertainty in exchange for potential gains, shaping their choices regarding insurance, investments, and risky financial behaviors. In this study, risk tolerance is operationalized as a composite, bounded index synthesizing both stated and revealed preferences. First, respondents report the maximum amount they would pay to enter a lottery offering a 10% chance to win USD 1,000. This certainty equivalent (CE) represents the point of indifference between a sure payment and a risky prospect; higher values indicate greater tolerance for risk. The CE is capped at the lottery’s expected value (USD 100) to reflect that willingness to pay beyond this point signals risk neutrality or risk-seeking behavior, consistent with classic expected utility theory (Von Neumann & Morgenstern, 2007). Second, monthly self-reported lottery expenditure is recorded in ordinal categories and mapped to dollar midpoints, then normalized to a [0, 1] scale. The final risk tolerance index is the mean of the normalized certainty equivalent and spending fraction. This hybrid measure captures both an individual’s direct evaluation of risk and their actual behavior in risky markets, producing a continuous, interpretable, and psychometrically robust index suitable for regression modeling (Barsky et al., 1997; Bruhin et al., 2010; Dohmen et al., 2011). Because the distribution of this index is highly skewed, a natural-log transformation is applied for statistical analyses.

Let $X_i$ be respondent i’s maximum stated willingness to pay for a 10% chance at USD 1000 (certainty equivalent).

$$\begin{array}{cc}\hfill \mathrm{EV}& =0.10\times 1000=USD100\hfill \\ \hfill {\mathrm{CE}}_i& =min\{X_i,100\}\hfill \\ \hfill \mathrm{CE}\text{\_}{\mathrm{frac}}_i& ={\displaystyle \frac{{\mathrm{CE}}_i}{\mathrm{EV}}}\hfill \end{array}$$

Let $s_i$ denote respondent i’s typical monthly lottery spending, mapped from the ordinal response:

$$s_i\in \{0,2.5,10.5,23,40.5,75\}$$

The normalized spending fraction is

$$\mathrm{spend}\text{\_}{\mathrm{frac}}_i={\displaystyle \frac{s_i}{75}}$$

The composite objective risk tolerance index is then

$${\mathrm{riskTol}}_i={\displaystyle \frac{\mathrm{CE}\text{\_}{\mathrm{frac}}_i+\mathrm{spend}\text{\_}{\mathrm{frac}}_i}{2}}$$

Finally, a log transformation is applied for regression analyses to address skewness:

$${\mathrm{logRiskTol}}_i=log({\mathrm{riskTol}}_i+0.01)$$

To further strengthen the validity of the empirical research and address any confounding factors, multiple control variables are incorporated into the study, each substantiated by the existing literature. The number of dependents, ranging from none to over five, serves as a vital control, as the existence of dependents heightens the necessity for life insurance to ensure financial security for family members upon the policyholder’s demise; empirical research consistently demonstrates a positive correlation between the number of dependents and the demand for life insurance (Gropper & Kuhnen, 2025; Lewis, 1989). The level of education is also accounted for, as elevated educational attainment correlates with enhanced financial literacy, awareness of insurance products, and an increased likelihood of obtaining life insurance (Giri, 2018; Lusardi & Mitchell, 2014; Nkouaga, 2024a). A dummy variable for residing in a rural area is incorporated, as rural households frequently encounter distinct economic risks, access barriers, and financial inclusion challenges relative to urban households, influencing both the probability and nature of life insurance acquired (Giri, 2018).

Underwriting Factors

Underwriting factors denote the characteristics that insurance firms commonly utilize to evaluate risk and establish the pricing and conditions of life insurance contracts. These characteristics are used as essential controls in the empirical study to address their direct impact on both premium levels and coverage selections. Age is treated as a continuous variable for all respondents aged 18 and older, illustrating the proven correlation between advancing age and elevated mortality risk, which therefore results in increased premiums (J. R. Brown & Goolsbee, 2002; Outreville, 2013). Gender is denoted by a binary variable, with females assigned a value of 1, reflecting actuarial data indicating that women often exhibit lower death rates and may consequently benefit from more advantageous pricing (J. R. Brown & Goolsbee, 2002). Employment status is incorporated as a dummy variable (employed = 1), given that stable employment correlates with reduced risk and enhanced capacity to pay premiums. Income level is assessed using a nine-point ordinal scale, spanning from below USD 15,000 to above USD 500,000, reflecting the positive correlation between income and both the probability of acquiring life insurance and the extent of coverage secured (Outreville, 2013). Perceived physical health, rated from 1 (poor) to 5 (great), acts as an indicator of tobacco consumption and underlying medical issues, both of which are essential factors influencing insurability and premium rates in actuarial practice. Marital status is represented as a binary variable (married = 1), indicating that married persons are more inclined to acquire life insurance for the financial stability of their dependents (Y. Lin & Grace, 2007). The policy’s face value is incorporated as a control, as elevated coverage quantities generally correlate with increased premiums and may indicate variations in risk selection and financial planning requirements.

Exclusion Restriction

An exclusion restriction is a variable that influences the likelihood of inclusion in the sample but does not directly impact the outcome of interest, hence appearing solely in the selection equation of a Heckman model. This study utilizes three restrictions: political ideology (binary indicators for liberal, centrist, and conservative, with “no ideology” as the comparison group), race (Asian, Black people, Latino, Native American with White people as the comparison group), and source of financial advice (professional advisor, with personal network and book and Internet search as the reference). Each is derived from self-reported survey items and is only used in the probit model for the decision to acquire life insurance, reflecting attitudes toward risk, belief systems, and trust in expert counsel. By altering selection probabilities without incorporating the premium or coverage result equation, these instruments ascertain the Inverse Mills Ratio and guarantee consistent estimates of the conditional outcome parameters (Puhani, 2000).

Political ideology proxies beliefs and risk orientation, which influence entry into financial markets, including insurance participation, without entering actuarial rating formulas. Empirical work links ideology to risk-taking and market participation (Kaustia & Torstila, 2011). Sources of advice capture information frictions and trust in experts. Studies show advice alters participation and portfolio choices, consistent with effects on uptake rather than premiums (S. Brown et al., 2025). A weighted analysis of the 2024 Financial Inclusion Survey suggests that political ideology shapes both ownership rates and perceived importance with conservatives showing the highest values (Figure 1), and that among the source of financial advice, personal network is the main source compared to professional advisor, or book and Internet research (Figure 2). Because these factors plausibly affect only the decision to enter the insurance market and not the actuarial determination of premiums or face values once a policy is in force, they satisfy the exclusion-restriction requirement in the Heckman sample-selection model and thus identify the selection correction without biasing the outcome estimates.

Race serves as a strong and appropriate exclusion constraint for the selection equation (i.e., the decision to acquire life insurance) in the framework of U.S. life insurance regulation and empirical investigation. Historically, race significantly influenced the life insurance market in a discriminatory manner; however, current regulatory frameworks at both federal and state levels clearly forbid the use of race in deciding premiums or coverage amounts (Avraham et al., 2013; Gale et al., 2022; Lent et al., 2022). State insurance regulations, particularly those endorsed by entities like the National Association of Insurance Commissioners (NAIC), designate race as an unacceptable criterion for risk assessment, rendering its application in underwriting or pricing decisions either unlawful or heavily constrained (Center for Insurance Policy and Research (CIPR), 2020). For example, states such as Colorado and Texas explicitly prohibit insurers from rejecting coverage, limiting coverage levels, or altering premium prices based on race. In states without specific legal bans, industry practices predominantly omit race from actuarial assessments (Code, 2023; Colorado Division of Insurance, 2021). Nevertheless, race continues to be a substantial determinant of life insurance ownership owing to deep-rooted social, economic, and historical disparities. Evidence on ownership differences by race supports its relevance in selection processes while remaining excluded from pricing (Reiter & Heckman, 2017). Research consistently indicates that, when controlling for observable socioeconomic disparities, Black individuals (as confirmed in Figure 3) are generally more inclined to acquire life insurance compared to white individuals—a pattern shaped by differences in wealth, risk perceptions, trust in financial institutions, and family dynamics (Harris & Yelowitz, 2018; Kim et al., 2020). The observed patterns are not influenced by contemporary discriminatory pricing practices, but instead signify deeper systemic and historical reasons. Empirical research demonstrates a lack of current evidence supporting race-based premium setting or coverage determination, particularly in jurisdictions with stringent enforcement of anti-discrimination laws (Gale et al., 2022). Consequently, incorporating race as an exclusion constraint in the selection equation efficiently encapsulates unobservable social and behavioral determinants of insurance demand while adhering to legal norms. The exclusion from the outcome equations (premium size or coverage quantity) is warranted by legislative restrictions and empirical data indicating the lack of racial discrimination in contemporary underwriting processes. All variables used in the analysis are presented in the summary statistics (

Table 1. Descriptive summary statistics.

Label	Mean	Median	SD	Min	Max	Skew	Kurt	N
Psychological price	3.9963	4.00	1.3497	1.00	6.00	−0.587	−0.385	3211
Level of income	5.0009	5.00	2.0549	1.00	9.00	−0.576	−0.744	3211
Being married	0.4780	0.00	0.4996	0.00	1.00	0.088	−1.993	3211
Number of dependents	1.5111	1.00	0.6680	1.00	4.00	1.066	0.418	3211
Employed	0.8122	1.00	0.3906	0.00	1.00	−1.598	0.554	3211
Age	49.1548	49.00	18.1502	18.00	93.00	0.087	−1.123	3211
Female	0.5058	1.00	0.5000	0.00	1.00	−0.023	−2.000	3211
Perceived physical health	3.6185	4.00	0.9993	1.00	5.00	−0.650	−0.046	3211
Financial knowledge	1.5328	1.55	0.7882	0.01	2.55	−0.277	−1.144	3211
Risk tolerance	0.2100	0.10	0.2417	0.00	1.00	1.321	0.960	3211
Liberal	0.2401	0.00	0.4272	0.00	1.00	1.216	−0.521	3211
Centrist	0.2547	0.00	0.4358	0.00	1.00	1.125	−0.734	3211
Conservative	0.3476	0.00	0.4763	0.00	1.00	0.640	−1.591	3211
Other political ideology	0.0258	0.00	0.1587	0.00	1.00	5.973	33.690	3211
Black people	0.1345	0.00	0.3413	0.00	1.00	2.141	2.585	3211
Latino	0.1859	0.00	0.3891	0.00	1.00	1.614	0.605	3211
Native American	0.0221	0.00	0.1471	0.00	1.00	6.497	40.221	3211
Asian	0.0511	0.00	0.2202	0.00	1.00	4.076	14.622	3211
Face value (term)	3.8910	4.00	1.8134	1.00	7.00	−0.026	−0.996	2036
Premium (term)	2.4777	2.00	1.0476	1.00	6.00	0.874	1.179	381
Face value (cash)	3.9516	4.00	1.7079	1.00	7.00	0.084	−0.883	805
Premium (cash)	2.4476	2.00	1.0966	1.00	6.00	0.794	0.527	420
Level of education	4.7938	4.00	1.6238	1.00	9.00	0.393	−0.577	3211
Rural	0.1292	0.00	0.3355	0.00	1.00	2.209	2.882	3211
Professional advisor	0.3142	0.00	0.4643	0.00	1.00	0.800	−1.360	3211

).

2.3. Econometric Model

To establish strong causal inference and mitigate potential selection bias in life insurance adoption, we employ a Full-Information Maximum Likelihood Heckman selection framework with analytical weights to model the endogenous selection into life insurance. This method simultaneously estimates both uptake and premiums while correcting for outcome bias by considering correlated unobservables, yielding consistent and efficient estimates under joint normality assumptions (Bernard et al., 2023; Greene, 2000; Heckman, 1979). We evaluated multiple alternative methodologies: Control-function techniques utilize a generated regressor from the initial stage; however, they exhibit reduced efficiency and heightened sensitivity to specification concerns in the first stage. In cases of nonlinear selection, the Inverse Mills Ratio derived from Full-Information Maximum Likelihood serves as a suitable control (Puhani, 2000; Wooldridge, 2010). Bivariate probit models are applicable solely to binary outcomes, and given that premiums are continuous, this approach necessitates discretization or a switching framework, which compromises information integrity (Greene, 2000). The Full-Information Maximum Likelihood Heckman model is the most suitable baseline method for this research, given our continuous outcomes, theoretically substantiated exclusion restrictions, and robustness assessments.

The study estimates a Heckman selection model by full maximum likelihood (FIML). The selection (uptake) is modeled by a probit:

$$S_i^{*}={\mathbf{x}}_i^{\prime }\mathit{\gamma }+u_i,S_i=⊮\{S_i^{*}>0\},$$

and the outcome (premium) is observed only if insured:

$$Y_i={\mathbf{w}}_i^{\prime }\mathit{\beta }+{\epsilon }_i\mathrm{if}{S}_i=1.$$

• Distributional Assumptions

$$\left[\begin{array}{c}{u}_i\\ {\epsilon }_i\end{array}\right]\sim \mathcal{N}\left(\left[\begin{array}{c}0\\ 0\end{array}\right],\left[\begin{array}{cc}1& \rho {\sigma }_{\epsilon }\\ \rho {\sigma }_{\epsilon }& {\sigma }_{\epsilon }^2\end{array}\right]\right),$$

with the probit normalization $\mathrm{Var}\left(u_i\right)=1$.

• Weighted Log-Likelihood

Let ${\omega }_i$ denote analytic survey weights. The individual contributions are

$${\ell }_i=\left\{\begin{array}{cc}log\left[{\displaystyle \frac{1}{{\sigma }_{\epsilon }}}\varphi \left({\displaystyle \frac{Y_i-{\mathbf{w}}_i^{\prime }\mathit{\beta }}{{\sigma }_{\epsilon }}}\right)\mathsf{\Phi }\left({\displaystyle \frac{{\mathbf{x}}_i^{\prime }\mathit{\gamma }+\rho {\displaystyle \frac{Y_i-{\mathbf{w}}_i^{\prime }\mathit{\beta }}{{\sigma }_{\epsilon }}}}{\sqrt{1-{\rho }^2}}}\right)\right],\hfill & S_i=1,\hfill \\ log\left[\mathsf{\Phi }(-{\mathbf{x}}_i^{\prime }\mathit{\gamma })\right],\hfill & S_i=0,\hfill \end{array}\right.$$

and the estimator maximizes ${\sum }_i{\omega }_i{\ell }_i$.

Here,

${\mathbf{x}}_i$ is the regressor vector in the selection equation (demographics, income, health, financial literacy, risk tolerance, ideology, advice source, race/ethnicity; exclusions enter selection only). ${\mathbf{w}}_i$ is the regressor vector in the outcome equation (coverage, psychological price terms, and controls used for pricing). The prime ′ denotes transpose, so ${\mathbf{w}}_i^{\prime }\mathit{\beta }$ is a dot product. $\mathit{\gamma }$ and $\mathit{\beta }$ are parameter vectors. $u_i$ is the selection disturbance; ${\epsilon }_i$ is the outcome disturbance; ${\sigma }_{\epsilon }^2=\mathrm{Var}\left({\epsilon }_i\right)$; $\rho =\mathrm{Corr}(u_i,{\epsilon }_i)$. $\varphi (·)$ and $\mathsf{\Phi }(·)$ are the standard normal pdf and cdf. ${\omega }_i$ are analytic survey weights.

• Premium Measure and Treatment

The survey records total monthly out-of-pocket life insurance premium in six ordered bands: 0 = no contribution, 1 = $<USD100$, 2 = USD 101–USD 250, 3 = USD 251–USD 500, 4 = USD 500–USD 1000, 5 = $>USD1000$. These bands proxy an underlying continuous dollar amount. The main specification maps categories to midpoints $(0,50,175,375,750,1250)$ and treats the result as continuous. Research suggests that linear models with five to seven ordered categories provide unbiased slopes and trustworthy standard errors for continuous latent values, particularly when combined with rich covariate adjustment and robust inference (Harrell & Levy, 2022; Norman, 2010). This practice is common when bracketed monetary outcomes approximate a continuous variable (Brav et al., 2005; De Jong, 2006; Graham et al., 2013; Guiso et al., 2008; Hermansson & Jonsson, 2021; Kuzniak et al., 2015). The implementation of ordered outcome selection models using survey weights is not well supported despite the full MLE under joint normality and valid exclusions, Heckman offers a logical correction for selection and effective inference (Puhani, 2000; Vella, 1998; Wooldridge, 2010).

All outcome equations include psychological price (polynomial in centered perceived affordability), education, rural residence, underwriting-related controls, and cognitive and attitudinal measures. These variables affect premium levels conditional on purchase and do not belong in the selection equation. By restricting premium measures to the outcome stage, the model respects timing: purchase decision first, then premium–coverage choice.

Under joint normality of $(u_i,{\epsilon }_i)$ with $\mathrm{Corr}(u_i,{\epsilon }_i)=\rho$, the expected outcome conditional on purchase is

$$\mathrm{E}[Y_i\mid S_i=1]={\mathbf{w}}_i^{\prime }\mathit{\beta }+\rho \sigma {\displaystyle \frac{\varphi \left({\mathbf{x}}_i^{\prime }\mathit{\gamma }\right)}{\mathsf{\Phi }\left({\mathbf{x}}_i^{\prime }\mathit{\gamma }\right)}},$$

where $\varphi$ and $\mathsf{\Phi }$ are the standard normal density and distribution functions. The Inverse Mills Ratio ${\lambda }_i=\varphi /\mathsf{\Phi }$ corrects non-random selection. With valid exclusions, this approach yields consistent estimates of $\mathit{\beta }$ in the presence of selection on unobservables (Heckman, 1979; Wooldridge, 2010).

• Limitation in Data Collection

Despite the inclusion of core underwriting factors in this research, several important limitations must be acknowledged. First, the research does not incorporate variables routinely used in actuarial pricing and underwriting, such as detailed medical histories, family health background, occupation-specific risk, credit scores, and lifestyle factors like alcohol use or hazardous activities (J. R. Brown & Goolsbee, 2002; Y. Lin & Grace, 2007; Outreville, 2013). Second, all underwriting and behavioral variables are self-reported rather than verified with administrative or medical records, which introduces reporting bias, recall error, and social desirability effects (Y. Lin & Grace, 2007; Lusardi & Mitchell, 2014). Third, perceived physical health is used as a proxy for tobacco use and underlying conditions, which does not fully capture actuarial risk assessed through exams and laboratory tests. Fourth, the survey was fielded online without controls to prevent or detect external assistance on objective financial literacy items, including help from AI tools or web search; literacy-related estimates should be interpreted with caution. Fifth, the survey is cross-sectional and does not elicit time preferences, such as discount rates or elasticity of intertemporal substitution; the risk tolerance module measures static attitudes only, which limits interpretation of long-horizon dynamics in life insurance decisions. These limitations are consistent with broader challenges in the literature on life insurance demand and actuarial analysis (J. R. Brown & Goolsbee, 2002; Y. Lin & Grace, 2007; Lusardi & Mitchell, 2014; Outreville, 2013).

• Justification for Analytical Strategy

Psychological price captures perceived affordability. To create this variable, we map responses from both uninsured individuals (rating the affordability of buying coverage) and insured individuals (rating their current premium) onto a common numeric scale. This method preserves comparability and avoids model separation in the selection (uptake) equation. This does not treat insured and uninsured as identical. In this first stage, psychological price is included with other covariates and exclusion restrictions, which are variables that affect uptake but not premiums. The second stage estimates the premium equation using only the insured subsample. This equation includes the Inverse Mills Ratio (IMR) to correct for selection bias caused by unobserved medical or actuarial risks.

We employ the full maximum-likelihood Heckman selection model because it addresses selection on unobservables among observably similar individuals who differ in uptake. In insurance settings, important actuarial and underwriting determinants of premiums—detailed health status, family history, physician diagnoses, lab results, risk class, and insurer-specific underwriting rules—are typically missing from surveys. These unmeasured factors affect both the decision to buy coverage and the premiums chosen or offered. Ignoring them induces omitted-variable bias in premium regressions estimated only on the insured sample. Heckman’s framework estimates participation and premiums jointly and includes the Inverse Mills Ratio (IMR) as a control function in the premium equation, which absorbs the correlation between unobserved drivers of uptake and unobserved drivers of premiums under the standard joint normality assumption and valid exclusion restrictions (Heckman, 1979; Puhani, 2000; Vella, 1998; Wooldridge, 2010). IMR is a regressor, not a sampling weight. This separation of the purchase decision from the pricing outcome yields consistent and efficient estimates when latent traits—such as health risk, risk aversion, and liquidity constraints—enter both equations. This correction is well aligned with evidence on unobserved risk in insurance markets. Studies document that private information about health risk and other latent factors correlates with coverage choices and spending, creating selection on unobservables that biases naïve outcome models (Cardon & Hendel, 2001; Chiappori & Salanie, 2000; Finkelstein & McGarry, 2006). By modeling selection explicitly and adding IMR to the premium equation, the Heckman approach mitigates the resulting omitted-variable bias when underwriting data are unavailable.

3. Result

The effects of psychological price—modeled as a third-degree polynomial—emerge as both strong and highly significant predictors in all Heckman selection equations for life insurance uptake and premium outcomes (see

Table 2. Heckman selection models for term and cash insurance premiums.

	Term Insurance		Cash Insurance
	Selection (Uptake)	Outcome (Premium)	Selection (Uptake)	Outcome (Premium)
(Intercept)	−2.7912 ***	−3.0221 ***	−2.6054 ***	3.0449 ***
	(0.2677)	(0.4838)	(0.2777)	(0.5781)
Main variables
Attitudinal Variable
Psychological Price (First Order, Linear)	27.7700 ***	15.8459 **	35.1325 ***	−39.6661 ***
	(2.7393)	(5.2498)	(2.6727)	(6.9652)
Psychological Price (Second Order, Quadratic)	−13.9883 ***	−24.3731 ***	−13.5477 ***	−3.9057
	(2.5152)	(4.7325)	(2.3668)	(4.7817)
Psychological Price (Third Order, Cubic)	−12.9947 ***	−22.5624 ***	−22.7937 ***	−2.3766
	(2.5162)	(4.6772)	(2.4914)	(4.9720)
Control Variables
Consumer Characteristics
Level of Education	0.1243 ***	0.2007 ***	−0.0053	0.0305
	(0.0257)	(0.0415)	(0.0275)	(0.0374)
Living in a Rural area	0.3213 **	0.2766	0.2707 *	−0.0860
	(0.1167)	(0.1833)	(0.1203)	(0.1526)
Financial Knowledge score	0.2602 ***	0.1483	0.1608 *	−0.2756 **
	(0.0644)	(0.1084)	(0.0639)	(0.0852)
Risk Tolerance	0.8274 ***	1.1141 **	0.0189	0.3871
	(0.2333)	(0.3603)	(0.2622)	(0.3405)
Number of dependents	0.1615 *	0.1364	0.0278	−0.1393
	(0.0723)	(0.1158)	(0.0737)	(0.0873)
Underwriting Factors
Age	0.0041	0.0112 *	0.0127 ***	−0.0062 +
	(0.0027)	(0.0045)	(0.0026)	(0.0036)
Female	−0.0773	−0.2291 +	−0.0826	0.1346
	(0.0850)	(0.1361)	(0.0849)	(0.1104)
Employed	0.2679 *	0.4632 **	0.5053 ***	0.2029
	(0.1039)	(0.1646)	(0.1092)	(0.1682)
Level of Income	0.1123 ***	0.1196 **	0.0465 +	0.0813 *
	(0.0260)	(0.0422)	(0.0273)	(0.0338)
Perceived Physical Health	−0.0045	0.1123 +	0.0006	0.0590
	(0.0418)	(0.0667)	(0.0416)	(0.0542)
Being Married	0.0693	−0.0095	0.0929	0.2723 *
	(0.0985)	(0.1607)	(0.0997)	(0.1200)
Face Value		0.0375		−0.0530 +
		(0.0295)		(0.0301)
Exclusion Restriction
Source of Financial Advice (Ref. = Personal Network)
Professional Advisor	−0.0956		0.1893 *
	(0.0638)		(0.0949)
Political Ideology (Ref. = No Ideology)
Conservative	−0.2886 ***		0.2864 *
	(0.0858)		(0.1416)
Centrist	−0.2149 *		0.3407 *
	(0.0872)		(0.1474)
Liberal	−0.3652 ***		0.1781
	(0.0884)		(0.1486)
Other Ideology	−0.7414 ***		0.7065 **
	(0.1847)		(0.2315)
Race (Ref. = White People)
Latino	−0.0817		−0.2405 +
	(0.0768)		(0.1229)
Black People	0.3838 ***		0.4186 ***
	(0.0934)		(0.1246)
Native American	0.0121		0.1365
	(0.3446)		(0.4911)
Asian	0.0034		0.0629
	(0.1074)		(0.1861)
Observations	1556 (1175/381)		1595 (1175/420)
Log-Lik	−916.634		−1088.264
$\sigma$	1.5029 ***		0.9406 ***
$\rho$	0.9829 ***		−0.3774 *

Notes: Standard errors in parentheses. *** p < 0.001; ** p < 0.01; * p < 0.05; ⁺ p < 0.1. Censored/observed counts in parentheses.

). For both term and cash value insurance, the linear (first-order) term of psychological price is strongly positive for uptake (27.77 and 35.13, respectively; p < 0.001), indicating that as individuals perceive life insurance to be more affordable, their likelihood of purchase rises dramatically. However, the quadratic and cubic terms are both negative and highly significant, revealing substantial nonlinearities: increases in perceived affordability have diminishing—and eventually reversing—effects at the extremes of the psychological price spectrum. For premium outcomes, the pattern is more complex. For term insurance, the curve is non-monotonic: premiums dip slightly at low levels of affordability, rise at moderate levels, and then flatten or decline at the highest levels. This reflects the negative higher-order terms outweighing the positive linear term at the tails, consistent with the idea that consumers’ willingness to pay peaks at moderate levels of perceived affordability but tapers off when coverage feels either too cheap or too expensive. For cash value insurance, the linear effect is negative and large (−39.67; p < 0.001), with diminishing negative influence at higher-order terms, suggesting that those who perceive cash value coverage as more affordable tend to select lower-priced contracts, though this effect weakens at the extremes. Overall, these findings highlight a nonlinear, threshold-dependent relationship between perceived affordability and both the uptake and pricing of insurance products, and they show that perceptions of affordability shape not only the decision to purchase but also the type and level of premium consumers are willing to accept.

The analysis of control variables highlights several factors significantly associated with both term and cash value life insurance uptake and premium determination. Educational attainment demonstrates a strong, positive relationship with term insurance uptake (0.1243, p < 0.001) and with the premium paid (0.2007, p < 0.001), but does not significantly predict cash insurance uptake or premium, suggesting that education is particularly salient for traditional term products. Financial knowledge is robustly associated with a higher probability of both term and cash insurance uptake (0.2602, p < 0.001; 0.1608, p < 0.05, respectively), but while it predicts higher term insurance uptake, it has a negative effect on cash insurance premiums (−0.2756, p < 0.01), indicating that more financially knowledgeable individuals may opt for less costly cash value products.

Risk tolerance also strongly predicts term insurance uptake (0.8274, p < 0.001) and the premium paid (1.1141, p < 0.01), with a weaker or non-significant relationship for cash insurance. Similarly, living in a rural area is associated with higher uptake for both product types (0.3213, p < 0.01 for term; 0.2707, p < 0.05 for cash), possibly reflecting different needs or market access in rural contexts. Among traditional underwriting factors, age is a significant positive predictor for cash insurance uptake (0.0127, p < 0.001) and a weakly negative predictor for premium in the cash value model (−0.0062, p < 0.1), whereas it is only marginally significant in term insurance outcomes. Employment status and level of income are positively associated with both uptake and premiums in both models, underlining the importance of economic resources in insurance purchase decisions. Other factors, such as being married and the number of dependents, show weaker or inconsistent relationships, with statistical significance limited to certain models and outcomes.

Turning to the exclusion restrictions, several notable patterns emerge regarding the sources of financial advice, political ideology, and race. First, seeking advice from a professional advisor (such as an insurance agent or certified financial planner) is significantly associated with a higher probability of selecting cash value insurance (coefficient = 0.189, p < 0.05), but does not show a significant effect on term insurance selection. This suggests that individuals who consult with professionals may be more informed or persuaded about the potential long-term benefits of cash value products compared to those relying on informal advice networks.

Regarding political ideology, we observe a strong, nuanced relationship with life insurance selection. Compared to individuals reporting no political ideology, those who identify as conservative, centrist, liberal, or “other” are all significantly less likely to select term insurance. The negative coefficients are especially pronounced for “other” ideologies (coefficient = −0.741, p < 0.001) and for liberals (coefficient = −0.365, p < 0.001). In contrast, these same groups are more likely to select cash value insurance, with all effects significant except for the liberal category. The most substantial effect is for “other” ideologies (coefficient = 0.707, p < 0.01), with both centrists and conservatives also showing significant positive associations. These patterns point to an important role for political sophistication and value orientation in shaping insurance product preferences.

With respect to race, Black respondents have significantly higher probabilities of selecting both term (coefficient = 0.384, p < 0.001) and cash value insurance (coefficient = 0.419, p < 0.001) compared to White respondents, even after adjusting for income, education, and other covariates. The association for Latinos is negative for cash value insurance (coefficient = −0.241, p < 0.1), while there are no significant effects for Native American or Asian respondents. These findings indicate persistent disparities in product choice by race and ethnicity.

The predicted outcome plots (Figure 4) illustrate how psychological price shapes both the probability of life insurance uptake and the premium amount selected. For both term and cash value insurance, the probability of purchasing insurance follows a distinctive nonlinear pattern: extremely low for those perceiving coverage as highly unaffordable (psychological price near 1), rising sharply to near certainty (over 95%) for moderate to high affordability (psychological price between 4 and 5), and then dropping again as insurance becomes “very affordable” (psychological price near 6). This pattern is robust across all racial groups, though there are subtle differences in the predicted probabilities. For example, Black individuals exhibit a slightly higher peak uptake probability for term life insurance (approaching 99%) compared to other groups, whose peaks range from about 96% to 98%. For cash value insurance, these differences are smaller but still evident, with all groups reaching high predicted uptake rates at moderate affordability.

The analysis of predicted premiums reveals even greater heterogeneity between product types and across the psychological price spectrum. For term life insurance, the premium curve is distinctly nonlinear. At the most unaffordable end, predicted premiums are negative or close to zero (approximately −USD 2 to USD 0 in standardized units), suggesting little or no term coverage is selected among those perceiving insurance as out of reach. As psychological price increases, predicted premiums climb rapidly, peaking at approximately USD 2.6 to USD 2.8 around “somewhat affordable”. This marks the segment most willing and able to buy higher-value term insurance. However, beyond this peak, as psychological price approaches “very affordable”, the predicted premium declines dramatically, falling to about −USD 3.5 at the highest end. The total swing in predicted premium for term insurance thus spans more than USD 6 units across the psychological price scale, highlighting a substantial nonlinear and non-monotonic behavioral response to perceived affordability. This suggests that as insurance feels easier to afford, some consumers may either downsize their policy, qualify for special low-cost offers, or opt out entirely—possibly reflecting a behavioral “sweet spot” for premium maximization at moderate affordability.

It is important to emphasize that these complex, non-monotonic relationships arise not from contradictory or unstable model results, but from the intentional use of third-degree polynomial terms to capture behavioral subtleties in insurance uptake. While the table reports a strong, positive first-order coefficient for psychological price—indicating that, holding all else constant, higher perceived affordability is associated with greater premium uptake—the significant negative quadratic and cubic terms mean that this effect does not remain constant across the entire range. Specifically, at the lowest levels of psychological price, the negative influence of the higher-order terms outweighs the linear effect, resulting in a decline in predicted premium for those perceiving insurance as extremely unaffordable.

As psychological price increases past this trough, the positive linear influence becomes dominant, producing a sharp rise in premium uptake through the moderate affordability range. However, as psychological price continues to increase, the negative higher-order effects reassert themselves, causing predicted premiums to decline again among those who perceive insurance as very affordable. This dynamic captures a realistic behavioral arc: for those who find insurance completely unaffordable, uptake is negligible; for those at moderate affordability, there is an optimal “sweet spot” where there is a willingness and ability to pay converge; and for those perceiving insurance as extremely affordable, premium uptake actually falls—potentially due to opting for simpler, cheaper products or reduced coverage needs. The polynomial specification thus allows the model to flexibly represent both initial inertia and later saturation, reconciling the strong positive linear coefficient in the regression output with the observed downturns at both extremes of the plotted curve. This approach aligns with the established econometric literature on discrete choice and nonlinear price sensitivity, demonstrating how higher-order polynomials can reveal nuanced, real-world consumer decision patterns that would be obscured by simpler linear models.

In contrast, cash value life insurance displays a more monotonic relationship between psychological price and premium. At the lowest affordability (psychological price near 1), predicted premiums start at a maximum of about USD 6.3—indicating that only those who can overcome affordability barriers select high-value cash policies. As psychological price increases toward “very affordable,” predicted premiums decline smoothly and steadily, reaching close to zero at the highest end. This suggests a broader base of purchasers as insurance becomes easier to afford, but with a shift toward lower-value policies as affordability increases. Racial differences in premium selection for cash value insurance are minor, with all groups following a nearly parallel path along the psychological price spectrum. Taken together, these results demonstrate the importance of accounting for nonlinear and group-specific effects when modeling insurance decision-making: the predicted premium and uptake probability are not simply monotonic functions of affordability, but instead reflect complex, context-dependent consumer behavior that varies by product type and demographic subgroup. This reinforces the need for flexible modeling strategies—such as polynomial terms in selection models—to accurately capture real-world insurance choices.

Post-Estimation Analysis

The direction of the mean IMR ($\lambda$) in each group further clarifies the nature of selection into insurance uptake (

Table 3. Mean Inverse Mills Ratio ($\lambda$) by insurance uptake status for term and cash value models, and comparison results of the groups using Welch two-sample t-tests.

	Term Model		Cash Value Model
	No	Yes	No	Yes
Mean $\lambda$	$-0.324$	$1.089$	$-0.308$	$1.101$
t-statistic	$-94.74$		$-86.20$
p-value	$<2.2\times {10}^{-16}$		$<2.2\times {10}^{-16}$
95% CI for diff.	$[-1.44,-1.38]$		$[-1.44,-1.38]$

). For individuals who do not purchase insurance, the mean IMR is negative (e.g., $-0.324$ for the term model and $-0.308$ for the cash value model). This negative value indicates that, after accounting for observed characteristics, these individuals are less likely to select into insurance due to unobserved factors—they possess unmeasured attributes (such as risk aversion, financial constraints, or attitudes toward insurance) that systematically reduce their propensity to buy coverage. Conversely, among individuals who do purchase insurance, the mean IMR is strongly positive (e.g., $1.089$ for the term model and $1.101$ for the cash value model). This positive value implies that, conditional on observed covariates, there are unobserved influences that increase their likelihood of selecting into insurance. In other words, these purchasers may have additional, unmeasured motivations—such as heightened perceived need, prior experience, or greater financial sophistication—that lead them to opt in at a rate higher than what would be predicted by observed characteristics alone. This clear divergence in the direction of mean $\lambda$ between groups is critical. It confirms that selection on unobservables is not only present but also asymmetric: unmeasured factors act in opposite directions for purchasers and non-purchasers. From a modeling perspective, this provides direct justification for the Heckman selection approach, as it demonstrates that the error terms in the selection and outcome equations are correlated and that ignoring this would bias premium effect estimates.

The density plots of the Inverse Mills Ratio ($\widehat{\lambda }$) from the Heckman selection models (Figure 5) provide direct visual evidence of strong selection effects in both term and cash value insurance models. In each panel, the distribution of $\widehat{\lambda }$ for individuals without life insurance (labeled “No”) is tightly concentrated near zero or slightly below, whereas for those with life insurance (“Yes”), the distribution is shifted markedly to the right, with the bulk of the density around $\widehat{\lambda }>1$.

The clear separation between groups highlights the presence of substantial selection bias. Specifically, individuals who are observed to hold life insurance (term or cash value) not only differ on observable characteristics, but also possess unobserved attributes that systematically increase their likelihood of selecting into coverage—captured by higher $\widehat{\lambda }$ values. Conversely, non-insured individuals tend to have lower or even negative values of $\widehat{\lambda }$, indicating the presence of unmeasured factors that reduce their propensity for uptake. The dashed vertical lines in each panel represent the group mean $\widehat{\lambda }$ values for the insured and uninsured, with accompanying labels. The means for insured groups are well above zero, while the means for non-insured groups are negative or near zero, reinforcing the notion that the underlying selection mechanism is both strong and asymmetric. The minimal overlap between the two distributions further supports the robustness of the selection process and justifies the use of a Heckman correction. In the absence of such an approach, standard OLS estimates would fail to account for the endogeneity induced by non-random selection, leading to biased inference about determinants of insurance uptake and premium or coverage outcomes.

Table 4. Linearity check of the Inverse Mills Ratio (IMR) in Heckman outcome equations. Standard errors in parentheses. p-values in brackets. IMR is computed as $\varphi \left(z\widehat{\gamma }\right)/\mathsf{\Phi }\left(z\widehat{\gamma }\right)$.

	Term Premium Outcome		Cash Value Premium Outcome
	Linear IMR	IMR + IMR2 + IMR3	Linear IMR	IMR + IMR2 + IMR3
IMR	1.977 (0.373) [0.000]	0.081 (1.416) [0.954]	−0.784 (0.305) [0.011]	−1.039 (1.008) [0.303]
IMR2		1.645 (1.045) [0.116]		0.197 (0.662) [0.767]
IMR3		−0.420 (0.255) [0.100]		−0.043 (0.138) [0.757]
$R^2$	0.323	0.328	0.281	0.282
Adj. $R^2$	0.293	0.295	0.253	0.249
Residual SE	0.758	0.757	0.835	0.837
Observations	381	381	420	420
Wald test (IMR2 = IMR3 = 0)	F = 1.40, p = 0.247		F = 0.05, p = 0.953

substantiates that the Inverse Mills Ratio is incorporated linearly into the outcome equations, as higher-order terms lack joint significance in both market segments (term premiums F = 1.40, p = 0.25; cash value premiums F = 0.05, p = 0.95). The post-estimation Wald tests bolster the justification for the Heckman model. Heckman simultaneously estimates the discrete selection and continuous premium equations, employs exclusion limitations for identification, and provides consistent, efficient coefficients under the assumption of a bivariate normal distribution of the error terms. A basic control function incorporates residuals from a first-stage probit into the output, although it regards the second stage as exogenous, resulting in decreased efficiency compared to full maximum likelihood estimation. A recursive bivariate probit is incapable of accommodating a continuous premium, hence resulting in the loss of information. The linearity assessments indicate the absence of nonlinearity, and the Heckman specification explicitly addresses the premium decision amid endogenous selection; thus, the findings in Table 4 robustly validate that this methodology is superior to the primary alternatives.

The paired plots function as a validation measure (Figure 6). Both panels employ similar axes and illustrate an Inverse Mills ratio (IMR) approaching zero over psychological pricing, with a nearly horizontal fitted curve with a slight increase at the upper end. This corresponds with the Wald results in Table 4 and suggests the absence of residual curvature associated with psychological price. The inclusion of polynomial psychological price terms does not compromise the specification. It adeptly accommodates non-monotonic premium responses while maintaining a consistent selection correction pattern. The plots and tests collectively endorse the Heckman model, demonstrating robust estimates with quadratic and cubic psychological price implemented.

The Variance Inflation Factor (VIF) values in

Table 5. GVIF^1/(2·df) for the selection equation (uptake) and VIF for each outcome equation (premiums).

	Selection	Outcome
	Uptake	Term Premium	Cash Value Premium
Psychological Price (poly degree 3)	1.0264	1.0345	1.0387
Level of Income	1.3172	1.3581	1.4381
Being Married	1.1669	1.3433	1.2093
Number of dependents	1.1208	1.1798	1.1133
Employed	1.1112	1.0977	1.0847
Age	1.1770	1.2887	1.2257
Level of Education	1.1482	1.1177	1.2961
Female	1.0363	1.0522	1.1234
Perceived physical health	1.0663	1.0657	1.0775
Financial Knowledge	1.2209	1.3269	1.3761
Living in a Rural area	1.0312	1.0365	1.0994
Risk Tolerance	1.0760	1.0742	1.0919
Face Value		1.3494	1.0526
Professional Advisor	1.0476
Conservative	1.5077
Centrist	1.4338
Liberal	1.4420
Other ideology	1.1245
Asian	1.0299
Black People	1.0907
Latino	1.0752
Native Americans	1.0168

indicate that multicollinearity is not an issue in the models, complementing these plots. All VIF values are well below the conventional criterion of 5, predominantly ranging from 1.1 to 2.2, signifying moderate and acceptable correlation levels among predictors. Both ideology and income—the variables exhibiting the greatest VIF values—remain within an acceptable range (ideology variables slightly above 2), especially as they are theoretically substantiated and essential for modeling financial behavior. The comparatively low VIFs in the selection and outcome equations guarantee reliable coefficient estimates and enhance the robustness of the offered Heckman models.

4. Discussion

These findings expand the existing literature on the behavioral drivers of insurance demand, emphasizing the intricate ways in which consumer perceptions of affordability influence both participation and premium rates. The pronounced positive linear effects in the uptake models reflect previous research indicating that perceptions of affordability are critical predictors of insurance participation (Abaluck & Gruber, 2011; Barcellos et al., 2014; B. R. Handel, 2013). Nonetheless, the pronounced negative quadratic and cubic terms indicate that this relationship is not merely monotonic; instead, there exist regions of diminishing and even negative marginal returns, especially at the extremes of perceived affordability. This pattern aligns with theoretical and empirical research in behavioral economics, which illustrates that consumers’ propensity to buy insurance is affected not only by price but also by reference-dependent preferences, inattention, and cognitive overload (Baicker et al., 2012; B. R. Handel, 2013). Extremely low or high psychological pricing may elicit skepticism or disengagement, hence diminishing demand despite favorable objective costs.

The results for premium outcomes considerably enhance previous findings by demonstrating specific product-type variations in the relationship between perceived affordability and price sensitivity. The nonlinearities in premium response indicate complex linkages between behavioral selection and insurers’ pricing tactics, reflecting recent research that demonstrate variability in premium elasticity and benefit selection (Einav & Finkelstein, 2011; B. R. Handel & Kolstad, 2015). The significant negative linear impact of psychological price on cash value premiums indicates that viewing insurance as affordable diminishes the anticipated premium, likely indicative of a self-selection of price-sensitive, lower-risk clients. This pattern is consistent with work showing that consumers’ willingness to pay and plan choices reflect both information frictions and heterogeneity in risk and preferences, which shape elasticities across products (Einav et al., 2010; B. R. Handel & Kolstad, 2015; B. R. Handel et al., 2019). It also aligns with evidence from studies on deductible choice that reveal systematic sorting by risk attitudes and price sensitivity (Cohen & Einav, 2007). These observations underscore the necessity of employing flexible, nonlinear modeling frameworks to represent behavioral response curves in insurance markets, and they support complementary consumer education that clarifies product features and payment timing to reduce confusion and avoid unintended selection (Einav et al., 2010; B. R. Handel & Kolstad, 2015).

Uptake and premiums follow reference-dependent patterns consistent with prospect theory. Uptake rises with psychological price, peaks near the mid-range, then declines at high values. We interpret “very affordable” as a reference point that shifts the frame from loss protection to avoiding a small, certain payment. Mental accounting then lowers the salience of the benefit and raises the salience of the recurring outlay, which explains the downturn in both uptake and accepted premiums at the top of the scale (Gourville & Soman, 1998; Kahneman & Tversky, 1979; Kőszegi & Rabin, 2006, 2007; Prelec & Loewenstein, 1998; Soman, 2001; R. Thaler, 1985; R. H. Thaler, 1999). Product differences reinforce this mechanism. For cash value coverage, premiums decline as psychological price increases and higher-order terms add little added value, consistent with sorting by risk and price sensitivity and a greater willingness to choose lower-priced contracts when payments feel manageable (Cohen & Einav, 2007; Einav et al., 2010; B. R. Handel & Kolstad, 2015; B. R. Handel et al., 2019). For term coverage, premiums follow an inverted-U because the positive linear effect is offset by negative quadratic and cubic terms at the tails, which matches diminishing sensitivity around a reference point and the pain of paying at high affordability (Kahneman & Tversky, 1979; Kőszegi & Rabin, 2006, 2007; Prelec & Loewenstein, 1998; R. Thaler, 1985; R. H. Thaler, 1999). Results hold with controls for financial literacy, risk tolerance, and demographics, and after Heckman selection correction. The IMR checks support a stable selection correction, which strengthens the behavioral reading of the polynomial terms rather than a model artifact.

The analysis of control and demographic variables enhances understanding of the factors influencing consumer behavior in term and cash value life insurance markets, building on the significant effects of attitudinal variables, especially the complex, nonlinear impact of psychological price perceptions on insurance adoption and premium choice. These findings underscore the proven significance of socioeconomic and behavioral determinants in life insurance decision-making. The correlation between educational attainment and financial knowledge with insurance uptake aligns with prior studies indicating that information processing capacity and financial literacy improve consumers’ capability to comprehend intricate insurance products and diminish purchasing obstacles (Finkelstein et al., 2019; Hastings et al., 2013). The adverse impact of financial knowledge on cash value insurance premiums may suggest that informed consumers avoid over-insurance or costly features, corroborating evidence that financially astute individuals are less vulnerable to aggressive marketing tactics and more adept at aligning insurance with their requirements (C. Chen et al., 2024).

The strong predictive power of risk tolerance for term insurance—both for selection and premium payments—aligns with behavioral economics literature demonstrating that insurance choices are influenced not only by objective risk factors but by subjective perceptions and preferences (Barseghyan et al., 2011; Von Gaudecker, 2015). The positive relationship between rural residence and insurance uptake also mirrors findings in the literature that rural consumers face distinct risk exposures and may value risk pooling differently compared to their urban counterparts (Fang et al., 2008). The complex influences of age, employment, income, and family structure highlight that although traditional life-cycle and human capital models are beneficial, contemporary insurance choices are progressively influenced by economic limitations and behavioral factors, as evidenced by recent research utilizing experimental and administrative data (Barseghyan et al., 2011; B. R. Handel, 2013).

The distinct patterns identified regarding political ideology and sources of financial assistance support the hypothesis of political sophistication and its significance in intricate financial decision-making. Political sophistication, which includes both political knowledge and interest, is associated with increased engagement in public affairs and a greater tendency to process abstract or long-term information (Luskin, 1990). Individuals with defined political identities—especially liberals, centrists, conservatives, or those identifying as “other”—may demonstrate increased cognitive engagement and future orientation, rendering them more inclined to acquire complex, long-term financial products such as cash value insurance, rather than opting for simpler term policies. This aligns with research indicating that political sophistication promotes more nuanced and future-oriented economic behaviors (Carpini & Keeter, 1996; Luskin, 1990). Political ideology denotes an aspiration for wealth accumulation and intergenerational strategy, consistent with the tenets of self-reliance (Bartels, 2023; Kölln, 2018).

The role of professional financial advisors is also prominent. Previous research demonstrates that counsel from certified professionals enhances the probability of acquiring cash value or permanent insurance, as advisors frequently highlight the tax-deferred savings, estate planning, and lifetime coverage features of these products (Anagol et al., 2017; Hackethal et al., 2012; Koijen & Yogo, 2015). Conversely, informal counsel from relatives and acquaintances sometimes bolsters more cautious or budget decisions, such as term insurance. This conclusion substantiates the assertion that professional counsel not only conveys information but also contextualizes product value propositions in manners that enhance the adoption of intricate insurance contracts (Kling et al., 2012).

The robust, positive correlation between Black people and insurance acquisition—particularly for cash value products—persists even after controlling for socioeconomic position, reinforcing findings from previous studies that emphasize racial disparities in insurance coverage and product preferences (Gutter & Hatcher, 2008; Harris & Yelowitz, 2018; Wolff, 2006). These gaps may indicate both past inequities in access to conventional life insurance markets and recent efforts by brokers to target minority groups with cash value products. The somewhat adverse impact noted for Latino respondents in the cash value market indicates potential cultural or accessibility hurdles that require further examination.

The diagnostic results strongly confirm the appropriateness of the Heckman selection model for examining life insurance decisions while mitigating selection bias. The significant difference in the Inverse Mills Ratio (IMR) distributions between insured and uninsured respondents confirms the presence of non-random selection into the insurance pool, a premise frequently breached in traditional OLS models. This finding corroborates previous insurance and applied microeconometric studies, which indicate that selection into insurance is often influenced by latent characteristics such as unobserved risk aversion, health risk, or financial confidence (Bernard et al., 2023; Heckman, 1979). The consistency of this selection pattern in both term and cash value insurance types emphasizes that selection (the uptake of life insurance) is a universal behavioral phenomenon rather than being specialized to any particular product.

4.1. Policy and Managerial Implications

The results possess numerous policy ramifications. The nonlinear influence of psychological pricing highlights the necessity for insurers and regulators to acknowledge that perceptions of affordability do not correlate with straightforward, linear demand; focused communication should accentuate the value of coverage at moderate affordability levels while avoiding overselling when insurance is regarded as “very affordable.” Secondly, the significant impact of education and financial literacy indicates that consumer education programs can enhance decision-making quality; nevertheless, they must also consider the possibility that financially knowledgeable consumers may eschew or reduce their investment in cash value products, presumably stemming from mistrust over cost structures. The impact of professional advisors underscores the dual opportunity and obligation of regulated advisory channels: although advisors can promote the adoption of intricate products, enhanced disclosure and suitability standards are essential to prevent consumers from being directed towards excessively costly policies. The correlation between political ideology and product selection underscores the necessity of customizing policy and industrial tactics to various value orientations. Insurers and regulators must acknowledge that ideological beliefs can influence consumer trust in financial institutions, preferences for product intricacy, and strategies for long-term wealth management. Policy interventions that enhance openness, bolster trust in regulated advisory channels, and facilitate accessible product comparisons can protect consumers with varying ideological perspectives while promoting equitable participation across market segments.

4.2. Future Research

Future research ought to further the integration of behavioral economics with actuarial modeling by investigating dynamic consumer reactions to changing risk environments, including economic shocks and governmental reforms. Longitudinal studies that integrate administrative and survey data would facilitate a more comprehensive understanding of the evolution of psychological price perceptions, financial literacy, and risk tolerance in relation to insurance and health outcomes. Future research should investigate political ideology not merely as an attitudinal indicator but also as a potential proxy for institutional trust, preferences for intergenerational wealth transfer, and varying exposure to information networks or echo chambers. Clarifying these pathways would elucidate how ideology influences product selection and whether targeted interventions could alleviate bias or enhance customer alignment. Furthermore, empirical assessments of behavioral interventions—such as tailored communication, incentives, or financial coaching—across diverse demographic and ideological cohorts could yield practical techniques for mitigating gaps in insurance coverage and product appropriateness. Ultimately, cross-national comparisons and qualitative investigations into decision-making processes would expand the evidence base and guide the creation of more inclusive, flexible, and resilient life insurance systems in various situations.

5. Conclusions

This research enhances our comprehension of life insurance demand by focusing on attitudinal and cognitive variables, specifically the nonlinear associations with psychological price, within empirical analysis. Utilizing recent, nationally representative data and a comprehensive two-step Heckman selection model, the results indicate that consumers’ perceptions of life insurance affordability are associated with demand patterns that do not conform to simple linear relationships. Demand exhibits a complex, nonlinear trajectory: uptake and premiums are correlated with moderate levels of perceived affordability, with both variables showing declining patterns when insurance is regarded as either too costly or, paradoxically, excessively inexpensive. The concept of a “behavioral sweet spot” underscores the necessity for insurers and policymakers to reevaluate conventional approaches to pricing, marketing, and product design, transcending linear assumptions regarding consumer behavior patterns.

The results indicate that financial knowledge and risk tolerance are significantly correlated with insurance acquisition patterns, especially in the context of term insurance; however, these associations are more intricate than previously recognized. Consumers with greater financial knowledge show positive correlations with insurance purchase likelihood; however, they exhibit distinctive patterns regarding product selection and pricing preferences, frequently choosing less costly cash value policies. Risk tolerance demonstrates significant correlations with term product engagement; however, this relationship weakens for cash value coverage, highlighting the differing risk-return assessment patterns associated with various insurance types.

Political ideology, sources of financial advice, and race show significant correlations with insurance behavior patterns. Individuals identifying as conservatives, liberal, or centrist and those utilizing professional advisors demonstrate stronger associations with cash value product acquisition. Meanwhile, Black respondents show consistent correlations with both term and cash value insurance ownership, even when controlling for socioeconomic status and other variables. The findings demonstrate that sociopolitical context and trust in financial systems are significantly associated with insurance behaviors, highlighting ongoing disparities and segmentation patterns within the insurance marketplace.

The application of higher-order polynomials for attitudinal variables, along with stringent sample-selection correction, establishes a new standard in behavioral insurance modeling. The identification of significant selection bias, indicated by the Inverse Mills Ratio, underscores the necessity for advanced econometric methods in analyzing demand relationships and outcome patterns within insurance research.

Collectively, these findings have significant policy implications. To enhance life insurance participation and address ongoing coverage gaps, insurers should recognize the nonlinear characteristics associated with consumer price perceptions and customize interventions for distinct attitudinal segments. Financial education should extend beyond basic literacy to encompass product-specific knowledge and address behavioral barriers correlated with insurance decisions. Regulators must continue to monitor advisory channel functions and ensure equitable access patterns to both term and cash value products among varied populations. With the rise of economic uncertainty and consumer diversity, the significance of behavioral, psychological, and sociopolitical dimensions for the future of financial protection will continue to show stronger associations with market outcomes.