Social Interactions and Social Preferences in Social Networks∗ Chih-Sheng Hsiehy Xu Linz Department of Economics Department of Economics National Taiwan University Virginia Tech September 26, 2019 Abstract We extend the utility specification in Ballester et al.(2006) to study social interactions when individuals hold altruistic preferences in social networks. We show that rich network features can be captured in the best response function derived by maximizing the extended utility which incorporates altruism, thereby providing microfoundation for studies on how network features mediate peer effects or other important features in social interactions. We demonstrate that the often ignored altruism is another serious confounding factor of peer effects. Our results show that the estimates of peer affects are approximately 36% smaller un- der social preferences. Furthermore, we could separately identify two different types of effects caused by peers' outcomes: the (usually positive) spillover effects and the direct (negative or positive) externality effects, which is impossible in a conventional social interactions model based on the self-interest hypothesis. JEL Classification: I10 I20 C31 Keywords: altruism, social preferences, externality, friendship networks, social interac- tions, spatial autoregressive model. ∗The authors are grateful to Lung-fei Lee, Jarom´ırKov´aˇr´ık,Joseph Tao-yi Wang, Kim Sau Chung, Melody Pei-yu Lo, Eleonora Patacchini, and the seminar participants at Chinese University of Hong Kong, University of Kentucky, Virginia Tech, National Taiwan University, the XI conference of Spatial Econometrics Association, and the annual meeting of the Midwest Econometrics Group for their helpful comments. We also greatly thank Nieyan Chen for her research assistance. All error are our own. yDepartment of Economics, National Taiwan University, Taipei 10617, Taiwan. Email: [email protected]. zDepartment of Economics, Virginia Tech, 3016 Pamplin Hall, 880 West Campus Drive, Blacksburg, VA 24061. Email: [email protected]. 1 1 Introduction An overwhelming amount of evidence from experimental and field works indicates that, in- stead of self-interest as assumed in classical economic theory, many people are altruistic and concerned about the welfare of others.1 Many economists, including Arrow(1981), Becker (1974), Samuelson(1993), Smith(1759), and Sen(1995), pointed out that when making deci- sions in many situations, such as among family members and friends, and within organizations, altruism plays an important role in forming an individual's utility function. The literature on social preferences has been firmly established theoretically and empirically. Recently, the literature on social preferences has started to uncover the connection between peer effects and social preferences. A few studies have shown that the extent to which people are willing to sacrifice their self-interest is sensitive to social influences; among these research are Falk et al.(2013), Fischbacher and Gachter(2010), Krupka and Weber(2009), and Mittone and Ploner(2011). Through a novel gift-exchange experiment, Th¨oniand G¨achter(2015) provide strong evidence for peer effects in pro-social behaviors. Other studies on conditional cooperation, including Chen et al.(2010), Croson and Shang(2008), Frey and Meier(2004), and Rustagi et al.(2010), show that the observed results in their studies are consistent with peer influences and social preferences. These studies have indicated that situations in which social preferences matter are often suitable settings for peer effects. Surprisingly, the literature on social interactions has mainly focused on the influences of peers on individual behaviors and decisions, rarely considering the possible formation of social preferences among peers. Many of these studies have applied the Spatial Autoregres- sive (SAR) model to study social interactions on various outcomes, such as academic perfor- mance, club participation, smoking, obesity, sports, and screen activities (see Boucher et al., 2014; Bramoull´eet al., 2009; Calv´o-Armengolet al., 2009; Christakis and Fowler, 2007; Hsieh and Lee, 2016; Lee et al., 2010; Lin, 2010; Liu et al., 2014).2 Similar to most conventional economic models, the SAR model is based on the standard self-interest hypothesis, assum- ing that individuals act exclusively on their own self-interest. Ballester et al.(2006) and Calv´o-Armengolet al.(2009) provide game-theoretical microfoundation for the SAR model 1See e.g., Andreoni, 1995; Andreoni and Miller, 2002; Anderson et al., 1998; Brandts and Schram, 2001; Croson, 2007; Fischbacher et al., 2001; G¨uth et al., 1982; Keser and Van Winden, 2000; Sonnemans et al., 1999; Sugden, 1984. 2The advantage of the SAR model over the conventional linear-in-means model in studying social inter- actions is that the SAR model on network data can solve the “reflection problem" inherited in the linear- in-means model (Manski, 1993). The spatial weights matrix of the SAR model can be used to represent the friendship (network) links of individuals in a group. As friendship links are specific to each individual and could be nontransitive, i.e., my friend's friend may not be my friend, the SAR model introduces necessary individual heterogeneity to distinguish between endogenous peer effects and contextual effects. 2 by considering a conventional non-cooperative game in which rational and self-interest indi- viduals maximize their own utilities. The resulting SAR model captures the pure strategy played by individuals in a unique interior Nash equilibrium. As social interactions occur on a regular basis and within small groups, altruism is expected to play an important role since people may intrinsically care about the well-being of their social contacts and take into account their preferences when making decisions. As shown in a number of studies, including those by Bourl`eset al.(2017), Goeree et al.(2010), Jones and Rachlin (2006), Leider et al.(2009), and Yamagishi and Mifune(2008), frequent interactions with peers may have important impact on the formation of individuals' preferences. Hence, relaxing the assumption of individual selfishness under the social interaction framework becomes necessary. It would be interesting to see how an openness to the altruistic preferences leads to new perspectives on modeling social interactions. In this paper, we provide the first analysis on social interactions and social preferences in social networks, building a bridge between the two strands of rapidly growing yet unrelated literature. We investigate the model specification issues that emerge after we extend the stan- dard assumption of self-interest to a more evolutionary foundation in which individuals can be altruistic. In particular, we specify individual utility function by combining a general altruistic utility with the specific quadratic specification of Ballester et al.(2006) in order to capture the complementary effect from peers' behaviors.3 We show that the extended utility frame- work has important implications for social interactions model specification.4 Several papers on social interactions have extended the econometric model derived from the classical utility maximization of rational and selfish individuals to - arbitrarily, in a sense - include some addi- tional terms for studying how network features mediate peer effects or other important features in social interactions. For instance, Ballester et al.(2006) examine how network centrality and individual position in the network affect social interactions and equilibrium outcomes. Battaglini et al.(2017) investigate the direct externality generated by peers in the self-control of students. Lin and Weinberg(2014) extend the standard SAR model to capture the peer effects generated by reciprocated, unreciprocated, and unchosen friends on adolescents' be- haviors and outcomes. These studies have provided interesting and important insights into social interactions, but they do not have a clear microfoundation based on classical theory. We demonstrate that the interesting features investigated by these papers, such as the in-degree of the network, can be well captured in the best response function derived by maximizing 3We also extend the model to incorporate more structured forms of altruistic preferences, such as those specified in Leider et al.(2009) and Levine(1998). 4Blume et al.(2015) illustrate that different specifications of the utility function may give rise to different econometric models used for empirical studies. 3 the extended utility that incorporates altruism, thereby providing microfoundations for these studies.5 Another important contribution of this paper is that it shows that, although often ignored, altruism is another serious confounding factor of peer effects. Intuitively, peer effects imply that people respond to others' behaviors because they are - often unconsciously - influenced by others; while altruism means that people might adapt their behavior towards others - con- sciously - to either help or not hurt them. Therefore, the estimation of peer affects is even more challenging than previously thought because ignoring altruistic preferences in social networks will cause bias in peer effect estimation. In our analysis of the National Longitudinal Study of Adolescent to Adult Health (Add Health) data, we find that significant peer effects exist on students' academic achievement, smoking behavior, and extracurricular activities, even after controlling for altruistic preferences and endogenous network formation. We also find