Measuring following behaviour in gift giving by utility function: statistical model and empirical evidence from China

The study examines whether and to what extent social conformity influences gift-giving (renqing) expenditures in China. It addresses a gap in the literature by using nationally representative data rather than laboratory experiments to quantify following behaviour and peer effects in gift giving. Motivated by the idea that individuals are influenced by social norms and peers, the paper constructs a relative index comparing individual gift spending to peer averages and develops a utility-based statistical model to estimate the likelihood (relative frequency) that individuals follow others in their gift expenditures. The purpose is to measure conformity in gift giving, assess its impact on subjective well-being, and test the law of diminishing marginal utility in this context. The study is important as gift giving plays a central role in Chinese social relations and business, yet national-level quantitative evidence on conformity in gift spending has been lacking.

Prior research highlights gift giving’s roles in signaling care, reciprocity, and social norms across cultures (e.g., Givi and Galak, 2021; Galak et al., 2016). In China, renqing encompasses gifts in material or monetary forms and is embedded in reciprocity and social norms (Hwang, 1987; Steidlmeier, 1999; Wang, 2007). Renqing also influences business trust and relationships (de Bary, 1991; de Mente, 1994; Chan et al., 2003), with contemporary studies linking renqing to purchase intentions and workplace perceptions (Zhang et al., 2022; Ren et al., 2020, 2021; Yen et al., 2017; Chen et al., 2018). While experimental economics often models gift giving via material payoff or reciprocity (Camerer, 2003; Stanca et al., 2009), broader evidence shows individuals conform to social norms and peer behaviour (Kuran, 1995; Francisco et al., 2008). Yet, empirical, nationally representative evidence on conformity in gift giving in China has been scarce, with many prior works relying on small samples or experimental settings that may not generalize well (Levitt and List, 2007). This study extends the literature by quantifying conformity in renqing using a large, representative Chinese panel.

Design and measures: The study uses a utility-based framework to model conformity in gift giving. Individual annual gift expenditure is denoted a_it, and the peer benchmark a_it* is the leave-out mean of gift spending among individuals in the same age group and community: a_it* = (N·ā − a_it)/(N − 1). A relative index of conformity is defined as a_it / a_it*. Panel regressions of a_it on a_it* and controls assess peer effects: a_it = β0 + β1 a_it* + γ x_it + c_i + ε_it, addressing endogeneity via Lewbel instruments and dynamic GMM. To estimate the share of followers at the individual level, a utility function f(a_it, a_it*) = u(a_it) + v(a_it / a_it*) − c(a_it) is specified. Under utility maximization and diminishing marginal utility (concavity in a_it), the sign of ∂a_it/∂a_it* (following behaviour) depends on the cross-partial, yielding sign(∂a_it/∂a_it*) = sign[−v''(a_it/a_it*) / (a_it*)^2]. Empirically, life satisfaction (ordered 1–5) proxies utility. The latent model is: y_it* = β1 + β2 a_it + β3 (a_it/a_it*) + β4 (a_it/a_it*)^2 + γ x_it + c_i + ε_it, with observed y_it mapped via cut-points. A dynamic specification augments with lagged outcomes and initial conditions: y_it* = β1 + β2 a_it + β3 (a_it/a_it*) + β4 (a_it/a_it*)^2 + γ x_it + ρ y_it−1 + η y_i0 + ξ z_it + c_i + ε_it. The marginal effects from ordered models are used to compute v′ and v′′ and thus the sign of ∂a_it/∂a_it* per individual. The indicator w_it = 1[sign(∂a_it/∂a_it*) > 0] identifies followers; relative frequencies are Pr(followers) = Σ_i Σ_t w_it / N and by-period analogs. Estimation strategy: - Continuous outcome (a_it): fixed-effects, random-effects, robust regression; fixed-effects two-stage least squares with Lewbel’s instruments; and dynamic panel regression using system GMM (Arellano–Bover/Blundell–Bond). OLS residual Arellano–Bond tests confirm serial correlation (z ≈ 48.35), motivating dynamics; instrument validity checked via Hansen and identification tests. - Ordered outcomes (utility): five panel ordered models: fixed-effects ordered logit (consistent under correlated effects), random-effects ordered logit/probit, correlated random-effects ordered probit with Lewbel instruments, and dynamic random-effects ordered probit (Wooldridge approach) with lagged and initial condition indicators; Hausman tests favor fixed-effects over random-effects for consistency. Marginal effects are adjusted by 1/√(1+σ²) for instrumental and dynamic ordered probit per Papke and Wooldridge. Data: China Family Panel Studies (CFPS) 2014, 2016, 2018, covering 31 provinces, 580 counties, 1,787 communities. Sample: 37,147 individuals; 21,685 balanced across three waves. Utility is self-reported life satisfaction (1–5). Key variables: a_it, a_it*, relative index (a_it/a_it*), and 21 controls: demographics (age, age², gender, marital status, rural/urban, education, family size, agricultural work), socioeconomic status (income, social status, real estate value, savings, debt for real estate), and expenditures (medical treatment, food, entertainment, travel, transportation, training, health supplements, cosmetology, charity). Robustness and inference: Heterogeneity addressed via robust estimation and heterogeneous ordered logit; endogeneity via Lewbel instruments; serial correlation via dynamic models; bootstrapping (400 reps) with clustering preserving spatial (peer group) and panel structures provides standard errors and confidence intervals for follower percentages.

- Peer effects in gift spending: Across five regressions with a_it as dependent variable, the coefficient on leave-out average a_it* is positive and significant (approx. 0.09 to 0.65), indicating meaningful but diminishing peer effects. - Utility effects: In five ordered models, coefficients on renqing expenditure and on the relative index (a_it/a_it*) are positive and significant, with significant negative squared terms, showing concave relationships. This supports the law of diminishing marginal utility for both absolute and relative gift spending. - Following behaviour prevalence: Estimated overall follower shares (all periods) from five ordered models range from about 48.5% to 60.5%: 55.59% (correlated panel ordered probit with Lewbel instruments), 48.62% (RE oprobit), 49.22% (RE ologit), 60.52% (FE ologit), 48.51% (dynamic RE oprobit). Bootstrapped 95% CIs confirm significance (e.g., FE ologit 0.568–0.642; Lewbel panel oprobit 0.536–0.576). - Time trend: Following percentages decline from 2014 to 2018 (e.g., FE ologit: 62.84% in 2014, 59.89% in 2016, 58.75% in 2018; other models show similar downward trends). - Gender: Men have higher following propensity than women (e.g., FE ologit: 61.11% men vs. 59.95% women; similar gaps across models). - Age pattern: Highest following among ages roughly 22–40; probabilities decline with age thereafter. For instance, FE ologit shows elevated following for 30–40; other models show peaks at 22–30. Lowest following among those >70 (e.g., correlated panel oprobit: 46.24%; RE oprobit: 35.00%). - Determinants of gift spending levels (a_it): Evidence of an inverted U-shaped relationship with age (turning points ~45–47 years) in robust and random-effects models; higher spending associated with urban residence (dynamic panel), larger family size (several models), higher income, social status, real estate value, savings, and multiple spending categories (e.g., cosmetology strongly positive across all five models). - Determinants of utility: Utility exhibits a U-shaped relationship with age; marriage is positively associated; women report higher utility (negative gender coefficients); urban residence positive in most models; income and social status positive; medical expenditures negative; real estate and savings positive in most models; cosmetology expenditure positive in most models. - Serial correlation and instruments: Arellano–Bond tests indicate AR(1) serial correlation; dynamic specifications address it. Instrument validity supported (e.g., Hansen p=0.97 for dynamic panel; Lewbel instrument tests significant; Hausman tests favor FE ordered logit for consistency).

The findings directly address the research question by demonstrating statistically significant peer effects in gift spending and quantifying the prevalence of following behaviour in a large, representative Chinese sample. The concave relationships between gift expenditures (absolute and relative) and utility empirically support the assumption of diminishing marginal utility in the utility-based model, validating the approach to infer following behaviour via comparative statics. The documented decline in following propensity from 2014 to 2018 may reflect changing norms driven by stricter government regulations and broader cultural shifts toward individualism, as interpreted through cultural mindsponge and cultural additivity theories. Gender and age patterns align with renqing norms in workplace and social contexts—men’s higher conformity possibly tied to career-related social expectations, while older individuals (particularly retirees) display more individualistic tendencies. Overall, the results underscore the importance of social norms and peer comparisons in shaping gift-giving behaviour and subjective well-being in China.

This study develops and validates a utility-based, ordinal panel modeling approach to measure following behaviour (conformity) in gift giving using a relative index constructed from leave-out peer averages. Using CFPS 2014–2018 panel data, it finds robust peer effects in renqing expenditures and shows that more than half of Chinese individuals tend to follow others in gift spending, with this tendency declining from 2014 to 2018. The positive but concave associations of both absolute and relative spending with utility confirm the law of diminishing marginal utility in this context. Men are more likely to follow peers than women, and following propensity concentrates among ages 22–40, declining in older ages. The approach generalizes to other populations and behaviours driven by social comparison. Future research could apply the framework to other countries with similar cultural contexts, incorporate richer network definitions of peers, and explore policy or institutional drivers behind temporal shifts in conformity.

Although the data are nationally representative within China, the study draws on a single-country dataset, limiting rigorous cross-country comparisons. The peer group is defined by age and community averages and may not capture all relevant social networks. Despite employing instrumental and dynamic methods, residual endogeneity or measurement error may persist. The utility proxy relies on single-item life satisfaction measures, which, while validated, may not encompass all aspects of well-being.