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

Gift giving is a prevalent social custom, particularly in Chinese society. Since people do not act independently of social norms, they are also motivated by the views of others when giving gifts. However, there is no existing literature on this important topic for China. To fill this gap, based on the law of diminishing marginal utility, this study investigates the effects of social conformity on gift giving in China. A relative index is constructed to capture the following behaviours in gift giving. The likelihood of following behaviours is measured by a statistical model derived from utility functions. Panel and dynamic ordinal discrete regressions are employed for empirical analysis. A case study in China employing a nationally representative longitudinal dataset with 37,147 individuals over three periods is applied. The results show that overall, more than half of the population in China tends to follow others in regard to gift expenses. However, from 2014 to 2018, this tendency declined sharply. Men are more likely to follow their peers in gift expenditure than are women. Older people have a lower preference to follow others than young people. More specifically, the assumption of diminishing marginal utility in gift giving is fully supported by the empirical findings in this study.

Introduction E veryone has been involved at some point in some type of gift exchange (Komter, 1996). The practice is so normal that gift giving has become a prevalent social custom in most countries. This custom has been widely investigated from the perspectives of politics and economics. Givi and Galak (2021) stressed the importance of signalling care and meeting expectations in gift giving in the United States. Galak et al. (2016) reviewed several studies conducted across many countries, summarized a variety of potential errors in gift giving, and proposed a model to understand them. Minowa and Belk (2018) addressed the role of gifts among consumers who attempt to express and construct romantic relationships by introducing a number of critical studies that have been conducted around the world.  argued that gifts are more likely to be considered a bribe in China if they have a high economic value. Li and Peng (2021) found that gift giving is popular in live streaming and that many users in China irrationally send virtual gifts to their favourite live streamers.
Gift giving plays an important role in Chinese social relations (Steidlmeier, 1999). Several studies have highlighted the predominant role of gift giving in Chinese social relationships in all areas of life (Chan et al., 2003;Yeung and Tung, 1996). A range of studies have emphasized the reciprocity of gift giving at the individual level in Chinese social interactions (Steidlmeier, 1999;Chen, 1995). An alternative expression of gift giving in China is renqing, which actually extends the inherent to include both material gifts and currency. According to Hwang (1987), renqing represents a resource that one person gives to another as a gift in any form in the social exchange process and acts as a set of social norms in China. Wang (2007) proposed that renqing can be understood in terms of two elements, namely, reciprocity and empathy. The above-mentioned literature has shown that gift giving in the Chinese social relationship system can be interpreted by both reciprocity and social norms. Hwang (1987) clearly underlined that one can give a gift to another person just to get along well with others. Other studies have proposed that some sort of gift giving is socially obligated, as reciprocity is a foundational pillar of social intercourse in China (Steidlmeier, 1999;de Mente, 1994).
A number of studies have claimed that gift giving is central to traditional Chinese business concerns (Steidlmeier, 1999;de Bary, 1991). In the context of business interactions, gift giving has a rational motivation in establishing trust between sellers and buyers. As an important means of expressing respect and honour for the other person in traditional Chinese relationships (Steidlmeier, 1999), gift giving creates an atmosphere of trust in business transactions. Thus, renqing would facilitate beneficial business relationships in China. To date, a number of studies have examined renqing in China from the perspective of business and cultural traditions. Zhang et al. (2022) discovered a positive relationship between renqing and purchase intentions in the Chinese business-to-business context. Ren et al. (2021) examined the mediating role of renqing perceptions in the effects of twoway congruences and incongruences in paternalistic leadership. Ren et al. (2020) found that both renqing perception and rule perception in China are two-dimensional constructs. Here, rule perception is defined as the extent to which employees perceive that the actions in their organizations follow the formal rules of the workplace (Ren et al., 2020). Although the formal rules may contradict the renqing norm, Ren et al. (2020) argued that the Chinese always strive to achieve a balance between renqing and rules. Yen et al. (2017) found that renqing has significant effects on reducing emotional conflict in Chinese-American business relationships. Chen et al. (2018) examined the role of leaders' renqing orientation as a moderating factor in the domains of knowledge management.
Although a large number of existing studies in the field of experimental economics adopt a narrow definition for the motivation of gift giving as material payoff or positive reciprocity, others show that gift giving in the system of social interaction is not solely determined by this mechanism (Camerer, 2003;Stanca et al., 2009). A large body of evidence has shown that people often do not act independently of social norms (Francisco et al., 2008). Most people are motivated by the views of others (Kuran, 1995). However, empirical evidence and clear findings on the motivation mechanism of gift-giving behaviour are still scarce, particularly in China. Most of the available literature quantitatively examines the relationship between perceived intention and reciprocity through laboratory experiments (Francisco et al., 2008). Although experiments have the advantage of controlling influences, they also have obvious drawbacks, particularly when generalising findings outside the laboratory environment (Levitt and List, 2007). Thus, more solid evidence from field investigations and the real world with better representativeness is necessary to complement existing theories.
For China, there is no existing literature that examines gift giving at the national level using a large representative sample. Both laboratory evidence and field investigations in mainland China are scarce. This paper, employing a large and representative panel dataset, investigates the significance of gift giving and other influential covariates on people's utility by panel ordered-outcomes regressions and thus fills in the missing pieces of knowledge. Another attractive point is related to the dataset, which is a representative and large sample drawn randomly from the population. Therefore, the results are more generalizable than those from experiments, although most of the existing studies analyse the effect of conformity based on laboratory or field experiments with a relatively small sample size (Francisco et al., 2008;Fischbacher et al., 2001;Frey and Meier, 2004). Thus, this study sheds new light on the investigation of following behaviour in gift giving.
Furthermore, although the material payoff is widely recognized as the core of success in social interactions, a general sense of belonging to and identification with a specific group are also important motivations that drive gift-giving behaviour (Attila and Matjaz, 2015). A widespread behaviour for success in social interactions is conforming to the actions of others. This paper concurs with the key view behind most of the existing studies. i.e., people tend to comply with others' actions for belonging and identification. Thus, a person acquires hints from others and accordingly updates his or her behaviours to follow them. This following behaviour is prominent in accounting for the conformity (also called relative effects in this study) of gift giving.
Regarding the conformity of gift giving, the main purpose of this study is to examine the relative effects of gift giving in the Chinese system of social relationships. The likelihood of following behaviours in the population is measured by an econometric model. This statistical model provides an estimated relative frequency of followers in the population with respect to gift giving, which has never been examined before. According to the law of large numbers, the relative frequency converges on the probability of the event as the number of observations increases. Thus, the estimated relative frequency can also be used as a proxy for the expected probability of following behaviours given a large sample size. To measure following behaviour, the significance of conformity is examined through the peer effects of gift expenditure using continuous regressions. Then, a relative index of gift giving is constructed to capture following behaviour in gift-giving expenditures. The relative index is obtained by dividing the individual gift-giving expenditure by the leave-out average of peers' gift-giving expenditure. A statistical model to predict the frequency of following behaviour in the population is derived from the utility function. A merit of the approach utilized in this study is that it estimates the effect of conformity by solely measuring the frequency of following behaviour.

Statistical models
In this study, a i designates the expenditure of gift giving for an individual i in the past 12 months. a i * represents the average giftgiving expenditure for the individuals in the same age group and the same community excluding the target individual i. It is defined to capture the social norms and social attitudes. A similar definition for calculating peer effects in populations has been widely used (Angrist, 2014;Loh and Li, 2013;Nie et al., 2015). The equation to calculate a i * is alternately expressed as follows: where N designates the number of individuals of the same age and community. a indicates the average expenditure on gift giving over the same age within the same community in the same period. To account for the individual's behaviour compared with the peer group, I define a function a i = R(a i *, x i ), where x i is a vector of explanatory covariates. According to most of the literature (Angrist, 2014;Loh and Li, 2013;Nie et al., 2015), a regression can be conducted between a i and a i *, while considering other controlling covariates and potential endogeneity: For the sake of using panel data in this study, subscript t is added in the function to represent different periods. β 0 is constant. β 1 is the coefficient of a it *. γ is a series of coefficients for explanatory variables x it . c i represents the individual effect for each i. ε it is the idiosyncratic error term for each observation. β 1 is the coefficient of interest. It can be easily estimated to examine whether the average peer significantly and positively influences an individual's absolute value. If it does, then conformity is significantly effective in the system of social interaction. Particularly, if a it * is significantly and positively associated with a it , then people may follow their peer groups. Otherwise, on average, the people tend to act either independently or oppositely. Endogeneity may be exerted by a it * in function (2) since it creates reciprocal reactions between individuals. This problem can be addressed by employing Lewbel's instruments (Lewbel, 2012) or lagged internal instruments (Arellano and Bover, 1995). However, the above method only provides an estimation of the association between a it and a it * at the sample level instead of the individual level. Thus, it cannot provide a clear mechanism to predict the relative frequency of personal preference to follow others. One of the main contributions of this study is to examine the preference of people to follow the social norms and the behaviours of peers. To achieve this purpose, a person's tendency to follow others can be captured by the comparative static derivative function da it /da it *. This index (also called the relative index) is employed in this study to measure relative effects with respect to peer groups. If one follows the peer group, then da it /da it * will be positive. If one does not, it will be negative or zero. Therefore, to depict the effect of conformity or following behaviour on gift giving, the sign of da it /da it * for each individual should be estimated. The basic statistical model similar to the idea proposed by Clark and Oswald (1998) and Blanchflower et al. (2009) is outlined and particularly adapted to the case of gift giving in the system of social interaction. As widely used, the utility function is employed to describe the network of gift giving, peer effects, influential covariates, and utility at the individual level. Define f (a it , a it *) to be the utility function. Here, the following behaviour or conformity effect can be captured through comparative static analysis. To search for the sign of da it /da it *, the assumption of utility maximization is applied. The first-order condition for a maximum with respect to a it is f a (a it , a it *) = 0. Then, according to the comparative static analysis, if the value of a it * changes, the following equation must be satisfied: Here, people are assumed to obey the law of diminishing marginal utility. According to this law, f (a it , a it *) is necessarily concave in a it . Lemma 1. Because f is concave in the argument a it , f aa (a it , a it *) is negative. Thus, the sign of da it /da it * depends only on the sign of f aa* (a it , a it *).
Specifically, according to Clark and Oswald (1998), the utility function of f (a it , a it *) with a ratio relative index is given by the following: In the above function, the utility that an individual i in period t gains from gift giving is separated into two parts; u(a it ) describes the direct effects of gift giving on utility, and v (a it /a it *) depicts the relative effects of gift giving on utility, where a it /a it * is the relative index capturing the ratio of absolute value and peer for a specific individual. The relative index is calculated by dividing a it by a it *, where a it * is the mean expenditure of gift giving in the same age group within the same community during the same period while leaving out a it (using function (1)). c(a it ) measures the marginal cost for utility, including some important controlling covariates. One merit of such specification of the utility function is that it allows the sign of a it /a it * to be either positive or negative. In the real world, people may act in a dispersed manner. This model also allows the tendency for deviant or independent behaviour. In the above function, the indirect relative effect is determined by the ratio of a it to a it *. As the value of gift-giving expenditure and its leave-out average are positive, the ratio of a it to a it * must be positive, whereas da it /da it * can be either positive or negative depending on the direction of deviation. Generally, the change in a it affects utility through direct effects, as well as relative and peer effects. Obviously, the relative and peer effects indicate the influence of conformity.
Specifically, the hypothesis that expenditures on gift giving and the relative index are significantly correlated with utility may be postulated. The hypothesis can be simply tested by regressions. If this hypothesis is supported, then both the direct effects and relative effects with respect to gift giving will be significantly correlated with utility. More essentially, according to Lemma 1, the sign of da it /da it * depends only on the sign of f aa* (a it , a it *). If the sign of da it /da it * can be simulated for each individual, the overall percentage of the following preference for all observations will be obtained. Here, individuals are assumed to seek to obtain the highest level of satisfaction from their decisions (also called utility maximization). To gain the sign of f aa* (a it , a it *), the first-order condition for the maximization of function (4) with respect to a it has to be solved. Then, the cross-partial derivative of a it with respect to a it * based on the first-order condition function is derived as follows: Finally, the sign of da it /da it * can be retrieved from the following: The above model describes the theoretical idea of obtaining an individual's personal preference for following a peer group. In the empirical analysis, function (4) must be specified in an estimable form. Thus, the elasticity of marginal utility with respect to the relative index can be estimated and then utilized to simulate the sign of da it /da it * for each observation.
As widely used in empirical studies, life satisfaction is used as a proxy for utility in function (4). It is an ordered 5-outcome discrete variable that ranges from "1" to "5". In this case, the empirical utility function has to be estimated by ordinal outcomes (also called ordered responses) regressions.
To specify a panel model for ordered responses, let y it be an ordered response taking on the values {1, 2, 3, 4, 5} representing utility. The ordered responses or outcomes of y conditional on explanatory variables can be retrieved from a latent variable regression. For panel data, a latent variable y it * is determined by the following: and where observed ordinal responses y it are generated from the latent continuous responses y it * with the cut-points κ labeled from 1 to 4. Again, i represents individual and t indicates period, x it is a vector of explanatory variables of individual i at period t, c i designates the individual effect for each i, and ε it is the error term for each observation. β 1 , β 2 , β 3 , and β 4 are the coefficients of a it , a it 2 , a it /a it *, and (a it /a it *) 2 , respectively. Certainly, γ is a series of coefficients for explanatory variables. It should be noted that due to the nature of panel data, the endogenous problem is not severe in this study. In addition, as 21 explanatory variables are included in the regression, the risk of endogeneity generated from omitted variables is mitigated.
For the panel ordinal-responses models, five different regressions with distinct underlying hypotheses are employed. Fixedeffects ordered logit regression can yield consistent estimations for function (7) without the assumption that individual effects are uncorrelated with idiosyncratic errors. This regression was recently developed and now can be easily conducted in Stata (Chris, 2017;Gregori et al., 2020Gregori et al., , 2015. Random-effects ordered logit regression conditional on the assumption that c i is uncorrelated with idiosyncratic errors is also estimated for robust checks. The Hausman test can be carried out for comparison. Considering potential endogeneity from omitted variables, the correlated random-effects ordered probit regression (Papke and Wooldridge, 2008) using Lewbel's instruments (Lewbel, 2012) is employed and then adapted. Accounting for the potential simultaneous and dynamic endogeneity and serial correlation, dynamic random-effects ordered probit regression proposed by Wooldridge (2010Wooldridge ( , 2005 and Greene and Hensher (2008) is utilized. Finally, traditional random-effects ordered probit regression is used for sensitivity analysis. Considering the dynamic random-effects ordered probit regression, function (7) must be modified as follows: As y i,t takes on values ranging from 1 to 5, it can be decoded into 5 lagged indicators. The ordinal responses in the initial period can also be decoded into 5 indicators. Thus, y i,t−1 signifies the vector of indicators representing ordinal responses in the lagged period for the same individual i, and ρ is a series of coefficients for them. y i,0 signifies the vector of indicators designating ordinal responses in the initial period for the individual i, and η is a series of coefficients for them. z i is a vector of covariates for the entire history of all explanatory variables, and ξ is a series of coefficients for them. All the others are the same as those used in function (7). The latent function for instrumental panel ordered probit regressions can be easily obtained by dropping the lagged indicators and initial indicators and adding Lewbel's instruments in function (8). Based on function (6) and function (7) or (8), to finally determine the sign of da it /da it *, the partial effect for each individual is estimated. As the above functions contain nonlinear terms of variables, with respect to function (7) (for example), v' (da it /da it *) would be specified as follows: and v" (da it /da it *) would be as follows: Incorporating functions (9) and (10) into function (6) finally gives the sign of da it /da it * for each individual. j in functions (9) and (10) designates a person's response for life satisfaction (j = 1,…., 5). It should be noted here that according to Papke and Wooldridge (2008) and Wooldridge (2005Wooldridge ( , 2010, the coefficients need to be divided by 1/(1 + σ c 2 ) 1/2 when estimating the marginal effects for instrumental ordered probit and dynamic ordered probit when using panel data. σ c 2 is the variance of estimated individual effects c i .
After obtaining the sign of da it /da it * for each individual, an indicator variable w is generated by Then, the relative frequency of followers across both the time and the cross section is calculated by the following: the relative frequency of followers for each period can also be achieved easily by the following: where N represents the number of observations over individuals and periods. N t designates the number of individuals in period t.

Empirical estimations and robustness checks
In this study, heterogeneity, endogeneity, and serial correlation are fully considered in the empirical regressions. From Table 1, it can be discovered that, due to the wide dispersion of data for some variables (e.g., income and savings), heterogeneity may exist. To address this potential problem, robust estimation is employed for the regression using gift-giving expenditure as a continuous dependent variable, while heterogeneous ordered logit can be used for the regression using utility as an ordered discrete dependent variable. According to Huber (1973) and Yohai (1987), a robust estimation can be used to account for potential outliers and heteroskedasticity while yielding consistent and robust estimations.
In addition to heterogeneity, endogeneity should be considered. The covariates may be correlated with random errors. The potential endogeneity of target variables (relative gift-giving expenditure) can be corrected by employing Lewbel's method of instruments. Lewbel (2012) constructs an internal instrument based on the heteroscedasticity of data. This method is argued to be particularly useful when considering the exclusion restriction. For function (2), fixedeffects two-stage least squares (fixed-effects TSLS) based on ARTICLE HUMANITIES AND SOCIAL SCIENCES COMMUNICATIONS | https://doi.org/10.1057/s41599-022-01214-4 Lewbel's instruments is employed in the regression using gift-giving expenditure as a continuous dependent variable. For the panel discrete regression using utility as a dependent variable, we adapt Lewbel's instruments (Lewbel, 2012) and Papke's panel instrumental method for ordered response variables (Papke and Wooldridge, 2008) to address the potential endogeneity.
Due to the longitudinal characteristics of the panel data utilized in this study, serial correlation over different periods may be available. For robustness checks, the Arellano-Bond (Arellano and Bond, 1991) test for the lagged period is applied after ordinary least squares (OLS). The Arellano-Bond (1991) test is specifically developed for autocorrelation in panel data. The estimated z statistic for AR(1) (autoregressive process) is 48.35, which shows the existence of serial correlation over periods. In this case, dynamic panel regression is utilized for function (2) as it has a continuous dependent variable. Thus, the two-step method developed by Arellano and Bover (1995) and Blundell and Bond (1998) is employed to estimate the dynamic panel regression for function (2). The Arellano-Bond test for functions (7) and (8) is also executed. If serial correlation also exists, then a dynamic ordered discrete model should be employed for robustness checks. In this case, the Arellano-Bond test for AR(1) after OLS provides a z statistic at 30.41, which indicates the existence of potential serial correlation in panel data for utility functions. Thus, the dynamic random-effects ordered probit regression (Wooldridge, 2010(Wooldridge, , 2005 using function (8) is employed to account for arbitrary serial correlation.
In addition to heterogeneity, endogeneity, and serial correlation of regressions, asymptotic inference for the estimator of the following percentage is also considered by the bootstrap technique. The bootstrapping process can provide the standard error and the confidence interval for the estimated following percentage. Both the spatial structure and panel structure are considered in the bootstrap process. Spatial structure is kept by drawing bootstrap samples for each individual subsample identified by the peer group. The panel structure is kept by drawing bootstrap samples taking random draws of clusters identified by the individuals. Each cluster is composed of one individual's observations across all periods. Thus, in the bootstrapping process, the cluster is embedded in the spatial subsample. Variable selection. The dependent variable "utility" (or wellbeing) is measured by self-reported life satisfaction. It can be used as a proxy for well-being (Diener, 1984). The ordinal utility ranges from 1 to 5, representing different levels of life satisfaction. A value of 1 indicates strong dissatisfaction, whereas a value of 5 represents strong satisfaction. In this study, life satisfaction is assessed with one item. A number of studies from different countries have pointed out that this method is a reliable measurement of life satisfaction (Buijs et al., 2016;Cheung and Lucas, 2014;Liu et al., 2022;Lucas, 2012;Woo and Kim, 2018). Furthermore, one-item measures of life satisfaction and happiness from the CFPS have also been employed in a series of previous studies Liu et al., 2022). Except for the absolute value of renqing expenditure, relative renqing expenditure, and the leave-out average of renqing expenditure (which have been fully described and discussed in the previous section), there are 21 variables employed as controlling covariates in the regressions (x it in functions (2), (7), and (8)). These control covariates take account of a variety of influential factors potentially relating to utility and thus reduce the possibility of endogeneity.
Some important social and demographic factors (age, gender, marital status, location in rural or urban areas, education, social status, and family size) are treated as control variables in the regressions. These variables have been widely used in prior studies with respect to well-being (Liu et al., 2022;Steele and Lynch, 2013;Van Hoorn, 2007). For example, except for age, gender, marital status, and education, Liu et al. (2022) proposed that family size and rural/urban area are two important independent variables when investigating life satisfaction's influential factors in China. As a number of studies have found a significant relationship between medical factors and well-being (e.g., Steele and Lynch, 2013;Liu et al., 2022), the variable of total expenses on medical treatment is included in the regressions. Moreover, it has been proposed that income is an important factor influencing well-being (Lee and Zhao, 2017;Liu et al., 2022;Steele and Lynch, 2013). However, it has been further argued that only using income as a proxy for economic well-being is a narrow measurement of the factors potentially influencing overall well-being (Ng and Diener, 2014;Burland, 2019). Wealth is a better indication of lifetime financial status (Burland, 2019). Thus, to fully consider the impact of wealth status on well-being, in addition to income, a wide range of variables (real estate value, savings, debt for real estate, and several expenditures) are also contained in the regressions.
Data description. Descriptive statistics for 20 variables are depicted in Table 1. The utility (life satisfaction) is averaged at 3.83, which suggests that most respondents are satisfied with their lives. The absolute values of renqing expenditure range from 0 to 350,000, with a mean of 4355, which shows a wide dispersion of renqing expenditure. Relative renqing expenditure ranges from 0 to 87.38, with a mean of 1.16, which shows that the renqing expenditures of most individuals are close to the local average. The average renqing expenditure per year ranged from 265 to 6975, with a mean of 3990. The other variables are all assumed to be exogenous. They are used to represent the individual characteristics or the expenditure-related behaviours that potentially influence utility. Some variables have standard deviations larger than the means, which demonstrates the possible existence of heteroskedasticity. The percentage distributions of the four dummy variables are listed in Table 2.
Results Table 3 depicts the estimated results from five regressions using function (2) with renqing expenditure as the dependent variable. A Hausman test comparing the fixed effects model and random effects model yields a chi-square (χ 2 ) statistic of 134.06 and thus significantly rejects the null hypothesis. This outcome shows that the random-effects model may not be consistent and that the result from the fixed-effects model is more asymptotically reliable. The estimated coefficients of the average renqing expenditure from the five regressions are all statistically significant and positive, which shows the obvious existence of peer effects with respect to renqing expenditure. The coefficients of age and squared age are only significant for the robust regression and the random-effects model. An inverted U-shaped curve is discovered for renqing expenditure and age. The estimated coefficients of marriage are insignificant for four regressions. The dynamic panel regression yields a positive and significant coefficient, which shows that residents in urban areas have more renqing expenditures than those in rural areas. The estimated coefficients for gender are significantly negative for the dynamic, random-effects, and robust regressions. For educational level, only the robust regression gives a positive and significant coefficient, which indicates that a higher level of education may lead to higher level of spending on renqing. The coefficients of family size from the fixed-effects model, random-effects model, and two-stage least squares (TSLS) using Lewbel's instruments are significant, which suggests a positive correlation between family size and renqing expenditure. The dummy variable for participating in agricultural work has insignificant coefficients for all five regressions. Four regressions show that people with higher incomes tend to spend more on renqing. Social status is significant for the random-effects, robust, and dynamic panel regressions and has been shown to be positively correlated with renqing expenditure. Expenditure on medical treatment is positively and significantly correlated with renqing expenditure. People who have more real-estate properties tend to spend more on renqing. The coefficients of savings are significant and positive for three regressions. Debt for real estate, food expenditure, donation expenditure, and transportation expenditure have positive and significant correlations with renqing for all four regressions except the dynamic panel ordered probit. Entertainment and training expenditures are only significant for the robust regression. Travel expenditure is positive and significant for the random-effects and robust regressions but not for the other three. Spending on health supplements is insignificant for all five regressions. Cosmetology expenditure is the only spending behaviour highly significant and positive for all five regressions, which suggests that people who spend more on cosmetology also have higher renqing expenditure. In addition, F statistics for four regressions and likelihood-ratio (LR) chi-square statistics for the random-effects model are all highly significant, which indicates the significance of all jointly included covariates in the regressions. The Arellano-Bond test for AR(1) in the first differences for the dynamic panel regression yields a z statistic of −3.82, which is significant at the 1% level. The Hansen statistic of the overidentification test for dynamic panel regression is 16.86 with a p value of 0.97, which indicates that the null hypothesis of valid instruments cannot be rejected. In addition, for fixed-effects TSLS using Lewbel's instruments, the underidentification test, the weak identification test, and the overidentification test all justify the validity of the instruments. Table 4 provides estimated results using functions (7) and (8) with utility as the dependent variable. A Hausman test comparing fixed-effects ordered logit and random-effects ordered logit yields a chi-square statistic of 333.52, which suggests a significant difference between the two regressions. Since the fixed-effects model is considered to be consistent, whereas the random-effects model is not, this outcome shows that the estimation from the fixedeffects ordered logit model may be asymptotically more reliable. The chi-square statistic for Lewbel's instruments is 12.61, indicating a high level of significance. Wald tests for all five regressions show that all included covariates are jointly significant at a 1% level. For the dynamic ordered probit, the estimated  Table 3 Regression results with renqing expenditure as dependent variable using Function (2).

Random-effects regression
Robust regression

Dynamic panel regression using Arellano-Bond estimation
Coeff.

t-val.
Average renqing expenditure leaving oneself out (Yuan) coefficients for lagged utility are significant for ordinal outcome 5. Except for outcome 2, the initial utility is highly significant for 3, 4, and 5, implying a substantial correlation between the unobserved heterogeneity and the initial condition. Moreover, the estimated coefficients on the initial utility are all larger than the coefficients on the lagged outcomes. According to Table 4, the estimated coefficients of renqing expenditure are positive and statistically significant for all five regressions. The estimated coefficients of relative renqing expenditure are also positive and significant for all five regressions. Both renqing expenditure and relative renqing expenditure are shown to have a significantly concave relationship with utility.
Age and squared age are significantly correlated with utility, indicating a convex relationship between the variables. The estimated coefficients of marital status are all positively and significantly correlated with utility, showing that married people have a higher utility than that of single persons in China. Except for the fixed effects ordered logit, the other four regressions give significant coefficients for residential location. The gender Table 4 Regression results with utility as dependent variable using Functions (7) and (8) Wellbeing 2 for lagged 1 period 0.037 0.52 Wellbeing 3 for lagged 1 period 0.044 0.62 Wellbeing 4 for lagged 1 period 0.121 1.5 Wellbeing 5 for lagged 1 period 0.308 *** 3.28 Wellbeing 2 for initial period 0.108 1.29 Wellbeing 3 for initial period 0.349 *** 4.25 Wellbeing 4 for initial period 0.546 *** 6.11 Wellbeing 5 for initial period 0.808 *** 7.99 Wald chi-square test for all included covariates 1128.7 *** 2239.7 *** 2299.0 *** 7443.5 *** 1347.7 *** * , ** , and *** give the coefficients' significance indicated by estimated standard errors at 10%, 5% and 1% level individually. The estimates of cut points are not reported. The coefficients of averaged covariates over periods in function (8) are not reported either. LR test of random-effects ordered probit vs. oprobit model has chi-square statistic at 706.22 with p-value at 0.0000. LR test of randomeffects ordered logit vs. ologit model has chi-square statistic at 719.25 with p-value at 0.0000. Chi-square statistic for testing the Lewbel's instruments is 12.61 with p-value at 0.002. Due to potential reverse causality and multicollinearity, the lagged renqing expenditure and squared renqing expenditure are used in the regressions.
dummy variable is negatively associated with utility, although only three regressions yield significant estimators. This outcome shows that women have relatively higher levels of utility than men. Three regressions yield significantly negative coefficients for family size, which indicates that a person in a large family has a lower level of utility. Educational level is significantly negative for three regressions. The dummy designating whether a person participates in agricultural work is statistically insignificant for all five regressions, showing that there is no clear relationship between agricultural work and utility. Income is positively and significantly correlated with utility according to all five regressions. The estimated coefficients of self-reported social status are positive and highly significant for all five regressions. Except for the fixed effects ordered logit, the other four regressions yield significantly negative coefficients for spending on medical treatment. Except for the fixed effects ordered logit, the other four regressions show that real estate value and savings are significantly and positively correlated with utility. The estimators of food expenditure are insignificant for four regressions except for the dynamic ordered probit. The coefficients of debt for real estate are significantly negative for three regressions but insignificant for the fixed-effects ordered logit and dynamic ordered probit. The associations between expenditures on entertainment, travel, health supplements, donation and utility are all insignificant for the five regressions. Expenditures on transportation and training are only statistically significant for random-effects ordered probit and fixed-effects ordered logit. Apart from the fixed-effects ordered logit, the other four regressions yield significantly positive coefficients for cosmetology expenditure. Table 5 depicts the estimated relative frequencies of followers from 5 ordinal discrete regressions. In Table 5, the first row provides the estimated percentages of followers over all periods and individuals. The second to fourth rows give the estimated percentages of followers from 2014 to 2018. For the dynamic panel ordered probit, the estimated following percentage for 2014 is dropped due to the lagged variables. It can be found that the following percentage in 2014 is the highest of the three examined periods.
All estimators from the five regressions range from approximately 49% to 60%, showing that nearly or more than half of people are followers with respect to renqing expenditure in China. All five regressions show that a decreasing trend in the relative frequency of followers is clearly visible from 2014 to 2018. Men are more likely to follow peers than women with respect to renqing expenditure. The groups of following percentages divided by age span are also reported in Table 5. The following percentages of the people with ages lower than or equal to 22 range from 54% to approximately 64%. Except for the fixed effects ordered logit, the other four regressions yield the highest following percentages for people aged from 22 to 30 among all age spans. The fixed effects ordered probit gives the highest possibility of following others for people aged from 30 to 40 among all age spans. After this age group, the estimated relative frequencies for followers decrease gradually. Thus, people aged higher than 70 have the lowest tendency to follow others with regard to such expenditures. Therefore, it can be summarized that the people with a higher likelihood of exhibiting following behaviour in renqing expenditure are mainly clustered in the age range from 22 to 40. An older person has a lower tendency to follow others with respect to renqing expenditure. Table 6 describes the bootstrapped estimates for the following percentages over all periods and individuals. The bootstrapping process is applied with 400 repetitions. Bootstrapped standard errors, z statistics, and confidence intervals for estimators from five regressions are provided. The outcome clearly shows that all estimated percentages are highly significant. According to Table 6, the estimated percentages from the random-effects ordered probit and logit and the dynamic panel ordered probit are all around 49%, and they have nearly overlapped confidence intervals ranging from 0.46 to 0.51. The random-effects ordered probit using Lewbel's instruments provides estimates and confidence intervals larger than those from the former three regressions. It gives a relative frequency of 55.59% and a confidence interval ranging from 0.54 to 0.58. It shows that the upper limit of the CI from the random-effects ordered probit using Lewbel's instruments overlaps with the lower limit of the CI from the fixed-effects ordered logit. It yields a significant relative frequency of 60.52% and a confidence interval ranging from 0.57 to 0.64. In summary, it can be concluded that more than half of the people in China are followers in regard to renqing expenditures.

Discussion
According to the estimated results in Table 3, the significantly positive coefficients of the leave-out average of renqing expenditures show the existence of peer effects. Thus, people have the potential to follow others regarding renqing expenditures. However, the estimated coefficients from the five regressions are all lower than 1 (ranging from 0.09 to 0.65), showing that this peer effect is diminishing. Although this is the first study to explore peer effects regarding Chinese renqing expenditure, a similar phenomenon was discovered in the prevalence of obesity in China (Nie et al., 2015). Such phenomena can be explained by cultural mindsponge theory (Vuong and Napier, 2015), as people can adopt new values and adapt their behaviours to the dynamic environment. In terms of knowledge management theory (Vuong et al., 2022), gift giving can be viewed as a "practical solution" to adopt or adapt cultural values (i.e., Confucianism), which enables people to have better opportunities later on. Similar cultures exist in other Asian countries, such as Vietnam.
Based on the results of the robust regression and random-effects model, an inverted U-shaped association is found between renqing expenditure and age in China. The turning points of the estimates from the robust and random-effects regressions are 45.26 and 46.52, respectively, which shows that people's renqing expenditure increases before the age of 45 (or 46) and decreases thereafter. Adults aged approximately 45 years may have the heaviest burden of renqing expenditure in China. The outcome also shows that women have higher renqing expenditures than men. This is consistent with the argument that women in rural areas are more affected by renqing ethics than men (Yan, 1996). The significantly positive coefficient for urban areas shows that urban residents are prone to spending more on renqing expenditures than are rural residents. Another coefficient shows that a higher education level leads to higher spending on renqing. This result can also be explained by cultural mindsponge theory (Vuong and Napier, 2015;Vuong et al., 2022). A person's mindset can be improved by education (Vuong and Napier, 2015). Therefore, it is easier for a person with a higher level of education in an urban area to adapt to the renqing norm in the workplace. The variables of income and several living expenditures all show a significantly positive correlation with renqing. This implies that a wealthier person tends to spend more on renqing. This is coincident with the findings of the study by Ren et al. (2020). In particular, the significantly positive coefficients of cosmetology expenditure show that a person who spends more on cosmetology also has a higher renqing expenditure. In the traditional social norms of China, the characteristic of dignity or being 'more nice than wise' could be an interpretation of the above phenomenon.
According to Table 4, the significantly positive coefficients show that an increase in renqing expenditure improves a person's utility. An inverted U-shaped (concave) association is found between renqing expenditures and utility. In addition, relative renqing expenditure has a significantly concave relationship with utility. This result is consistent with the assumption that people obey the law of diminishing marginal utility with respect to renqing expenditure. Thus, Lemma 1 and function (6) are supported by the empirical evidence in this study.
A U-shaped (convex) relationship between age and utility is also discovered. A number of studies have discovered a similar relationship between these variables (e.g., Van Hoorn, 2007). Utility is higher in young people, decreases in middle age, and increases again in old-aged people (Steele and Lynch, 2013). A married person has a higher utility than a single person. Women are correlated with a higher level of utility. Both of these findings are consistent with prior literature (Steele and Lynch, 2013). The positive estimators show that urban residents have higher utility than rural residents. Income is positively and significantly correlated with utility. This is also consistent with most existing studies (Steele and Lynch, 2013), although some debated relationships have been found in some developed countries. For example, Easterlin (1995) discovered that income growth does not increase happiness levels in Japan. However, generally, a positive association exists between well-being and income (Steele and Lynch, 2013). A person who highly rates his or her social status has a higher level of subjective utility. The significantly negative coefficients for spending on medical treatment show that a person who spends more on medical treatment has lower level of utility. Again, this is consistent with previous literature in that better health is correlated with a higher level of utility (Steele and Lynch, 2013). The significantly positive coefficients for cosmetology expenditure suggest that a person who spends more on cosmetology also has a higher level of utility. A person with a higher level of self-perceived appearance also has a higher level of utility.
According to the estimated results in Table 5, more than half of the surveyed Chinese individuals follow others regarding renqing expenditures. An interesting phenomenon emerges when considering the following percentages for different periods. From 2014 to 2018, people's tendency to follow others in renqing expenditures decreased. The decreasing likelihood of following behaviour with respect to renqing expenditures may be due to more rigorous regulations of the Chinese central government during this period. Another possible interpretation stems from cultural mindsponge (Vuong and Napier, 2015;Vuong et al., 2022) and cultural additivity (Vuong et al., 2018) theories. The mindsponge theory offers proper ways to explain how individual mindsets absorb new values and expel existing values from them (Vuong and Napier, 2015). Cultural additivity allows the possibility of the addition of values from different value systems (Vuong et al., 2018). With the transition to a market economy, although both collectivistic and individualistic factors are still important predictors of individual well-being in China, Chinese people are increasingly prioritizing individualistic factors (Steele and Lynch, 2013). In this process, people may integrate new values into their mindsets and become more individualistic. Thus, in these periods, a declining tendency to follow others in renqing expenditure is displayed in China. Analogical phenomena may be found in similar culture countries in Asia with respect to cultural interaction (e.g., Vietnam). Moreover, from Table 5, men are shown to have a higher tendency to follow peers in renqing expenditure than are women. Older people, particularly those aged more than 70 years, have a decreased preference for following others. Both of these phenomena can be interpreted by the renqing norm in the workplace (Ren et al., 2020). In the traditional cultural values of China, men may have a higher motivation to follow the renqing norm in the workplace in order to better pursue their career goals. However, older people have retired from their formal jobs and thus are more individualistic regarding relative renqing expenditure. Table 6 provides the results of bootstrap tests for the following percentages across all periods and individuals. The results show that all estimated following percentages are highly significant. Subsequently, the estimates in this study are asymptotically robust.
Despite the fact that a nationally representative longitudinal dataset is employed in this study, the data were collected only from China. Although the study attempts to compare the research findings to the other Asian countries with similar cultures, the use of a dataset from only one country prevents us from rigorously comparing analyses in depth. Therefore, new populations with similar cultures should be fully investigated in the future.

Conclusions
Gift giving or renqing is a prevalent social custom in China. Since there is ample evidence that people do not act independently of social norms, they might also be motivated by the views of others. This study examines the effects of conformity on renqing in Chinese social relationships. A person conforms to others for belonging or identification and acquires hints from others. Thus, a person may update his or her individual behaviours to follow others. Accordingly, following behaviour can be used to account for conformity or relative effects. In this study, based on the leave-out average of renqing expenditure, a relative index is constructed to capture following behaviours in relation to renqing expenditure. The likelihood of engaging in following behaviour is measured by a statistical model based on ordinal discrete regressions and utility functions.
According to five regressions for the continuous dependent variable, the estimated coefficients of the leave-out average of renqing expenditures on the absolute value of the renqing expenditure are all significantly positive. This result represents the obvious existence of a peer effect. People may follow others in regard to renqing expenditures, although this effect diminishes. Five discrete ordinal regressions are employed to estimate the utility functions. The significantly positive coefficients show that an increase in renqing spending can improve a person's utility. The coefficients of relative renqing expenditure are positive and significant in all regressions, which suggests that a higher relative renqing expenditure improves one's personal utility. Considering the squared relative renqing expenditure, a significant concave relationship between relative renqing expenditure and utility is found. Since relative renqing expenditure has a concave relationship with utility, the assumption of the law of diminishing marginal utility is fully supported. Thus, the statistical model in this study is justified by the empirical evidence.
Based on the estimated results, the percentage of those who follow others in regard to renqing expenditure can be calculated by a specified statistical model. It is found that more than half of the surveyed Chinese individuals generally tend to follow others with respect to renqing expenditures. However, from 2014 to 2018, the tendency to follow others in regard to renqing expenditure decreased. Men have a higher tendency to follow peers than women. Older people, particularly those over 70, are less inclined to follow others. Finally, the bootstrapped algorithms are conducted for the following percentages for all five regressions. The bootstrap results show that all the estimated following percentages are highly significant.
The estimated results could be easily generalized to the entire population of China because they are based on a nationally representative dataset. The validated approach in this study would allow greater generalization to other studies. This approach can be easily extended to investigate other countries and populations.