Labor Supply with Social Interactions: Econometric Estimates and Their Tax Policy Implications

Transcription

1 DISCUSSION PAPER SERIES IZA DP No Labor Supply wit Social Interactions: Econometric Estimates and Teir Tax Policy Implications Andrew Grodner Tomas J. Kniesner September 2007 Forscungsinstitut zur Zukunft der Arbeit Institute for te Study of Labor

2 Labor Supply wit Social Interactions: Econometric Estimates and Teir Tax Policy Implications Andrew Grodner East Carolina University Tomas J. Kniesner Syracuse University and IZA Discussion Paper No September 2007 IZA P.O. Box Bonn Germany Pone: Fax: Any opinions expressed ere are tose of te autor(s) and not tose of te institute. Researc disseminated by IZA may include views on policy, but te institute itself takes no institutional policy positions. Te Institute for te Study of Labor (IZA) in Bonn is a local and virtual international researc center and a place of communication between science, politics and business. IZA is an independent nonprofit company supported by Deutsce Post World Net. Te center is associated wit te University of Bonn and offers a stimulating researc environment troug its researc networks, researc support, and visitors and doctoral programs. IZA engages in (i) original and internationally competitive researc in all fields of labor economics, (ii) development of policy concepts, and (iii) dissemination of researc results and concepts to te interested public. IZA Discussion Papers often represent preliminary work and are circulated to encourage discussion. Citation of suc a paper sould account for its provisional caracter. A revised version may be available directly from te autor.

3 IZA Discussion Paper No September 2007 ABSTRACT Labor Supply wit Social Interactions: Econometric Estimates and Teir Tax Policy Implications * Our econometric researc allows for a possible response of a person's ours worked to ours typically worked by members of a multidimensional labor market reference group tat considers demograpics and geograpic location. Instrumental variables estimates of te canonical labor supply model expanded to permit social interactions pass a battery of specification cecks and indicate positive and economically important spillovers for adult men. Ignoring or incorrectly considering social interactions in male labor supply can misestimate te response to tax reform by as muc as 60 percent. JEL Classification: J22, Z13 Keywords: labor supply, social interactions, reference group, instrumental variables, social multiplier, PSID Corresponding autor: Tomas J. Kniesner Department of Economics Syracuse University 426 Eggers Hall Syracuse, NY USA tkniesne@maxwell.syr.edu * We are grateful for financial support from te MacArtur Researc Network on Social Interactions and Economic Inequality and tank Gerald Auten, Badi Baltagi, Dan Black, Gary Engelardt, Bo Honore, Bill Horrace, Jeff Kubik, Anil Kumar, Lung-fei Lee, Josep Marscand, Cristian Megea, and Jan Ondric for teir elpful comments.

4 2 1. Introduction Social interactions, te situation were individuals respond to te actions of people wit wom tey interact, may ave a biological basis or stem from information gatering. Social interactions are a potentially important aspect of economic beavior because interdependencies can affect ow people react to te expected and unexpected canges in teir environment, including ones caused by public policy. We investigate te econometric nuances and empirical importance of social interactions in labor supply wit taxes were te interdependence is a response of te individual to te ours worked by te members of a reference group. We find evidence of a positive spillover effect in ours worked tat is important for tax policy and demonstrate ow ignoring or misinterpreting labor supply social interactions effects can lead to substantial under or overestimates of te labor supply effects of tax reforms. Te presence of social interactions in labor supply means tat individuals respond to oters ours worked by a non-negligible amount. A social interactions effect is important because policy affecting te wages or anoter independent variable of a subgroup will not only affect te individual but also affect oters in te individual s reference group. We terefore focus on te consequences of interdependence for te estimated effect of wages on labor supply, wic economists use widely in welfare effect simulations of tax reform proposals. Our researc contribution is to implement a tractable labor supply model wit spillover effects and ten demonstrate te value of econometric estimates of te importance of social interactions in labor supply for tax policy. Teoretical solutions to optimal static or dynamic taxation in te presence of social interactions externalities use te parameters of te utility and attendant

5 3 consumption and labor supply functions (Kooreman and Scoonbeek 2004, Abel 2005). To fles out briefly te enriced policy implications of a labor supply model wit social interactions consider a basic proportional tax reduction applied to married men in a case were one need be careful wit potential social interactions effects. Suppose te proportional tax rate cange applied only to families wit disabled cildren. Te subpopulation affected would be relatively small and scattered geograpically; reference group effects could be ignored safely. Alternatively, suppose we were examining te effect of a proportional state income tax cange on te igest earners in a state suc as California, were many would live in te same area. Now feedback effects would be present. Te labor supply elasticity to consider would ten include non-negligible social interactions effects. Put simply, te benefits of empirical social interactions researc are tat after identifying any interdependencies te economist can perform a more complete welfare analysis. Identification of social interactions is econometrically complex (Soetevent 2006, Lee 2007a,b). Te primary callenge a researcer must confront is wat is te correct reference group (Durlauf 2004). Tere is a wide-ranging belief tat people in close proximity can ave a significant effect on te individual's labor supply decisions (Weinberg et al. 2004). Similarly, tere is labor supply researc were reference points come from oters wo are demograpically similar but need not live near eac oter (Woittiez and Kapteyn 1998). Here we syntesize te two possibilities wereby our econometric model allows te data to reveal reference groups tat are multidimensional in demograpic and geograpic closeness wit te weigts left as free parameters to be estimated.

6 4 In summary, we address many of te practical issues related to identifying te effect of endogenous social interactions on an individual's actions. We create a flexible measure of te economic distance approximating te level at wic individuals interact among one anoter. We define te economic distance between individuals as a combination of personal caracteristics and pysical distance. Our measure reflects te varying costs of interaction as iger economic distance implies iger cost of interaction, wic implies a lower level of interaction. We ten define te reference groups, eac of wic consists of persons wo are in a close economic proximity, and compute ours worked for eac person in te reference group (endogenous social interactions). We create and verify te econometric validity of an instrument from te mean of ours worked for persons wo are in te adjacent reference group for te purpose of instrumenting endogenous social interactions. Te specification lets us examine te core issue of weter te ours supplied by persons in close economic proximity are related. To frame te importance of social interactions we purposely use cross-section data from 1976 so as to ancor our researc to te seminal and oft cited cross-section studies of male labor supply by Hausman (1981) and MaCurdy et al. (1990). Our econometric results suggest positive and non-negligible social interactions in ours worked. Focal results are tat U.S. male labor supply data (1) reject a model ignoring social interactions against one wit spillovers and (2) reject a model wit spillovers treated as exogenous against one wit spillovers treated as endogenous. A regression model tat ignores spillovers in labor supply underestimates te wage elasticity of labor supply by about 40 percent; if one uses a social interactions model but ignores

7 5 endogenous interactions one underestimates te wage elasticity by over 60 percent. We conclude wit a demonstration of ow improperly accounting for social interactions can lead to substantial under or over estimation of te labor supply effects of tax reform. 2. Teory Teories of social interactions ave a long istory in te economic literature. Teoretical exercises since Becker (1974) sare te common feature tat te utility of te individual is someow affected by eiter utility or coices made by members of a reference group, wo are people wit wom te individual interacts. Especially interesting is te recent researc into ow information and species survival considerations may be te source of equilibrium social interactions in utility (Samuelson 2004; Rayo and Becker 2007a,b). In our teoretical framework we follow Brock and Durlauf (2001, 2002) and Grodner and Kniesner (2006) wo introduce interactions into a baseline model wit additive total utility consisting of individual utility and social utility. We assume tat te economy is in an equilibrium developed neigborood structure (Durlauf 1996). In wat follows we use te terms membersip group, neigborood, and community as equivalent and meaning persons wo are part of te individual's reference group. Consider now a general utility function tat includes a negative spillover effect for oters ours worked: V ig ( c, ; b ( μ )) = u ( c, T ) b ( μ ) s( ) ig ig g st. c ig ig ig w ig g, ig g g ig (1) were V () represents total utility of person i wo belongs to te reference group g, ig u () represents a private utility over consumption (c) and leisure (T ), were T is total

8 6 available time, is ours worked/labor supplied, and bg ( μ) s( ig) is total social disutility of working. Unlike te canonical utility function, total disutility of ours worked depends on te level of b ( ) g, wic represents te importance of social disutility. For te individual i in reference group g, b ( ) is increasing in average ours g worked in te reference group, μ g, excluding te i t worker (so g ( i) g μ = ), wit b ( 0 ) = 0, ( ) g b, and 0 g b >. Total social disutility also depends on ( ) g s, wic is te social disutility of individual ours worked (disutility of te individual from ow oters judge is or er work level) wit s( 0) = s0 > 0, ( ) 0 s, s < 0, and s > 0 ; s 0 is autonomous social disutility, wic is equal across individuals and reference groups. Finally, w g is a wage rate in te reference group g. Social disutility of individual's ours worked s ( ) is always non-zero wit a maximum value of s 0 at zero ours worked. 1 Social disutility of one s ours worked seems most likely to be decreasing ( s < 0) at a decreasing rate ( s > 0). Te decrease in te social disutility means tat as individuals work more ours tey believe oters judge tem less arsly. A decrease of social disutility at a decreasing rate means tat as individuals work more ours te gain of appearing better in te eyes of peers is getting smaller. Te worker may also view certain levels of ours worked as satisfactory and care less and less about opinions of oters as long as te worker reaces some accepted levels of ours worked according to is or er personal belief system. 2 A typical maintained ypotesis is tat te importance of te social utility term, b g, is increasing in te average ours worked in te individual's reference group ( b g < 0).

9 7 So, wen workers see an environment filled wit oter ard-working people tey expect to be judged more if tey stick out more relative to te labor market performance of oters. Te individual may feel more negatively perceived if furter down te ranking of work effort. After setting up te Lagrangian, taking te total differential of te first-order conditions of (1), and performing comparative statics based on te properties of social interactions in labor supply just described, te result emerging is tat + ( ) ( ) d b s = > dμ bs wu u w u 0 2 ( ) + 2 c cc ( + ) ( + ) (2) wit te partial derivatives of private utility, u cc < 0 and u < 0. In equation (2) an increase in average ours worked in te reference group increases te individual s ours worked. Te intuition is tat wen te average labor supply increases te parameter b increases, social disutility increases, and total utility decreases. To find a new maximum total utility te worker increases ours worked; altoug utility decreases because ours worked are a bad ( u < 0 ), an increase in te labor supply reduces social disutility because s < 0. Overall, an increase in ours worked increases total utility because te decrease in social disutility is iger tan te decrease in individual utility. Te model suggests tat workers wo are in an environment wit relatively many ard working people are induced to work more ours tan wen tere is no social interactions effect. Te utility function u ( c, ; μ ) = [( b) / β]exp [1 + β( c + s ) /( b )], were b = α / β, ig ig ig g ig ig ig 2 s = ( s/ β ( α / β ), α and β are parameters, and s is a linear

10 8 combination of reference group variables ( μ ), is te utility function derived by g Hausman (1980, 1981) amended to include social interactions. We will use te resulting linear labor supply function in order to ancor our results to Hausman s and MaCurdy s influential researc, wic facilitates judging te economic importance of adding social interactions to labor supply. In te empirical work to follow we regress individuals ours worked on average ours worked in teir reference groups, ceteris paribus. A positive coefficient on labor supplied by te reference group indicates te presence of a positive spillover effect in ours worked (Woittiez and Kapteyn 1998, Aronsson et al 1999). We now fles out te econometric details involved wit examining possible exogenous and endogenous social interactions in individual labor supply. 3. Econometric Model estimate is Te canonical linear labor supply model wit social interactions added tat we = θ + αω + βυ + γ x+ δ + δ x + ε, (3) 1 ( i) g 2 ( i) g were ω is te after-tax real wage, υ is after-tax virtual income, x is a vector of individual control covariates, ( i) g is reference group average labor supplied, x( i) gis te vector of control covariate averages for te reference group, ε is te error term, and [θ, α, β, γ, ρ, δ 1, δ 2 ] are parameters to estimate. 3.1 Independent Variables Te net wage rate (ω ) uses a marginal tax rate τ provided by te PSID, and is ω = (1 τ )w. Virtual income (υ ) also uses te marginal tax rate from te PSID. 3 To

11 9 control for possible endogeneity wen estimating (3) we instrument bot te after tax wage and virtual income using last year's gross wage and non-labor income (Ziliak and Kniesner 1999). Te control covariates in labor supply include number of cildren less tan six years old, family size, an indicator if te person is more tan 45 years old, te equity te family as in teir ouse, and an indicator of a pysical or nervous condition tat limits te amount of work, wic are standard exogenous explanatory variables in labor supply studies. Finally, in some specifications x includes ours worked in te previous year ( 1 ) to allow for te possibility noted by Rayo and Becker (2007a,b) tat te reference point in utility may depend not only on reference group outcomes but also on te individual s abits. 3.2 Social Interactions Variables Te mean for ours worked in te reference group is te sample average of ours worked for oter people wo are close in economic distance to te worker. In te computing te average we exclude te individual for wom we are computing a reference group mean outcome. Te estimated value of te parameter δ 1 represents te effect of endogenous social interactions in ours worked. Computing te mean of covariates takes multiple steps. First, we create a proxy variable summarizing te information in te exogenous covariates. We ten use factor analysis and take te first factor as a proxy variable for exogenous information. Te new variable does not ave a direct interpretation because it is standardized to ave zero mean and unit variance, owever it is igly correlated wit all te exogenous variables as well as te individual s ours worked. Te mean in te reference group for te created proxy

12 10 variable uses te same range of te economic distance variables as used for computing mean ours worked, again excluding te person for wom we are computing te reference group mean. Te proxy variable controls for te common caracteristics of te reference group, and te estimated coefficient δ 2 indicates any presence of exogenous social interactions. 3.3 Identifying Social Interactions Te form of te labor supply equation in (3) can identify te presence of bot endogenous (in te dependent variable) and exogenous (in te independent variables) social interactions. Identification requires some additional structure, toug (Manski 1993, Moffitt 2001). If te reference groups are completely separable ten a randomly distributed sock tat affects ours worked for some individuals and not oters can elp identify endogenous social interactions (Moffitt 2001). Wen reference groups overlap tere are a variety of empirical approaces including repeated samples (Aronsson et al. 1999), structural models (Brock and Durlauf 2002, Kapteyn et al. 1997, Kraut 2006), aggregated data (Glaeser et al. 2002), witin versus between variation (Graam and Han 2005), or spatial econometric tecniques (Kelejian and Pruca 1998, Lee 2007a,b). Alternatively, suppose tere are workers wo belong to more tan one reference group, and we use tem to compute te (endogenous) mean for reference group ours worked. Hours worked by people in te adjacent reference group can now be an instrument; tis is similar to using past values of te dependent variable in a dynamic panel data model (Arellano and Bond 1991). Here we use as an instrument te mean for workers in te adjacent reference groups, wic are defined by a social grid wit two

13 11 social coordinates from factor analysis. Te instrument is correlated wit mean ours worked in te individual s reference group (endogenous social interactions) because people in te specific reference group and te adjacent reference group belong to te same economic neigborood. Te instrument sould also be uncorrelated wit unobservables affecting individual labor supply because te particular individual does not belong to te adjacent reference group. 4 In any event, te IV approac tat we use will be cecked in te usual ways for weak instruments and tat te overidentifying restrictions are satisfied and if te cecks are passed ten we are no less comfortable wit our approac just like any oter IV application. Figure 1 illustrates our particular identification strategy. We present te ypotetical two-dimensional social coordinate space wit two reference groups: g 1 and g 2. Suppose now tat individual 0 g 1 belongs to te reference group g 1 and responds to te outcomes of te members of te reference group, represented by te observations labeled as 1 g 1 and (empty and gray-filled circles). If we use te mean of all 2 g1g2 1 g 1 and observations (referred furter as 2 g1g2 ( 0) g 1 ) as an independent variable in te regression (3) to try to identify endogenous social interaction in because observations 1 g 1 and are also affected by te outcome 2 g1g2 0 g 1 te coefficient will be biased 0 g 1, wic causes endogeneity in te. However, if tere are observations in te reference group g 1 tat ( 0 ) g 1 also belong to te neigboring reference group g 2, ten part of ( 0) g 1 attributed to te outcomes can be instrumented by te outcomes of te members of te reference 2 g1g2 group g 2, denoted by 3 g 2. If te usual diagnostic cecks are passed plus an additional one developed in Lee (2007b) tat reference group size varies ten we can reasonably use

14 12 instrumental variables (IV) estimation because 3 g 2 are correlated wit all observations because tey belong to te same reference group, and wit te error terms associated wit eiter 0 g 1 or belong to te same reference group. Observations outcomes 0 g 1 and 2 g1g2 3 g 2 are not correlated 1 g 1 observations because tey do not 3 g 2 are transitorily correlated wit te 1 g 1 only troug te deterministic part of observations. 2 g1g2 In practice, if we instrument observations wit outcomes 2 g1g2 3 g 2 tere may still be observations 1 g 1 tat are not instrumented and tus will make a part of te endogenous, wic is te case presented in Figure 1. Instead of using just one reference ( 0) g 1 group we can imagine using a full set of observations in te adjacent reference groups tat form te ring around te particular reference group (represented by te dotted circle). 4. Data We use data from te University of Micigan's Panel Study of Income Dynamics (PSID) collected in years 1975 and 1976 (PSID Wave IX). One reason for using te PSID is tat it is te most frequently used data to study U.S. labor supply (Blundell and MaCurdy 1999, Ziliak and Kniesner 1999). We purposely coose te 1976 cross-section of te PSID data because we seek to understand te possible importance of social interactions in labor supply by ancoring our estimates to te influential researc of Hausman (1980, 1981) and MaCurdy et al. (1990) wo use te same data to examine ow taxes affect labor supply witout modeling social interactions. 4.1 Sample We follow te sample selection process described in Eklöf and Sacklén (2000)

15 13 wo compare te studies by Hausman (1981) and MaCurdy et al. (1990) to wic we ancor our researc. Bot studies estimate an almost identical linear labor supply model wit income taxation. We select observations according to te following criteria: married males years old wit positive ours worked in 1974 and 1975 (but no iger tan 5096 annual ours), wo are eads of ouseolds in te cross-sectional random subsample; tere were no canges in te family composition of te ead or wife (oters can cange) in years ; te ead is not retired, permanently disabled, ousewife, student, or oter; te ouseold resides in te United States; and te ead is not selfemployed or a farmer. Using our exclusion criteria for te 1976 PSID we obtain 1077 observations, wic is close to te Hausman sample of 1084 and te MaCurdy sample of 1018 as reported by Eklöf and Sacklén (2000) Individual Regression Variables Te wage rate comes from a direct question in te PSID, including an imputed value for workers wo are not paid by te our. We also estimate a wage equation to impute ourly wages for observations wit unobserved or truncated wages. In particular, we use observations tat ave positive and not top-coded wage rates (839 observations) to estimate a Tobit regression tat uses as te dependent variable observed (un)truncated wages on a constant term, age, age squared, years of scooling, years of scooling squared, college degree, and family size. We ten use te estimated wage equation to produce a fitted value for all wages. Te procedure is similar to tat in Hausman (1981), and so our mean ourly wage is $6.17, wic nearly identical to te $6.18 reported by Hausman. Hours worked, te dependent variable, also comes from a directly asked question

16 14 in te PSID. Non-labor income is a constructed variable tat is te difference between total 1975 taxable income of te usband and wife and total 1975 labor earnings of te usband. Te ours worked and te non-labor income measures we use are also tose of MaCurdy et al. (1990). Oter independent variables include number of cildren less tan six years old (KIDSU6), family size (FAMSIZ), an indicator variable for individuals more tan 45 years old (AGE45), te amount of equity te family ad in its ouse (HOUSEQ), and an indicator of a pysical or nervous condition tat limited te amount of work te respondent could do (BHLTH). Appendix A presents descriptive statistics for all regression variables. 4.3 Reference Group and Economic Distance Specifying te composition of te individual's reference group is te researcer s central decision in any study of interdependence (Manski 1993, 2000). Implementing te reference group concept means acknowledging tat people wo are in relative economic proximity to eac oter may interact wit one anoter because te cost of interactions is low. We use te concept of economic distance among individuals as an indicator of te potential significance and magnitude of workers interdependencies (Conley 1999). We take people wo are in close economic distance as belonging to te same reference group. Economic distance is a combination of weter te workers are similar demograpically and live in close pysical proximity. We use a combination of personal and family caracteristics to define demograpically similar persons and use te distance between centers of counties in wic people reside for teir relative geograpic locations. Tere are multiple difficulties involved wit selecting from a large variety of caracteristics to measure economic distance. Acknowledging tat eac caracteristic

17 15 measure as a difference scale, and determining te relative importance of eac input variable on economic distance, we use a statistical model of factor analysis (Woittiez and Kapteyn 1998). Te factor analytic model deals naturally wit caracteristics aving different measurement scales; te procedure standardizes individual variables ten fits a linear model to find common latent variables called factors (Bai and Ng 2002, Bai 2003). Te intuition is tat tere are unobservable variables (factors) tat are ortogonal to one anoter and tat are strongly correlated wit observed variables. We use te factors as social coordinates to establis reference groups. Because te typical variables explaining labor supply can affect weter workers interact wit eac oter by being related to economic distance, our factor analysis inputs all independent variables from te econometric labor supply model (3). We also use pysical coordinates indicating te location by te center of te county were te person resides. We use two factors to summarize demograpic and pysical coordinates because tere is usually a muc better fit wit multiple factors tan wit only one factor, but using too many factors tends to be uninformative. 6 By using two factors we ave te convenient feature tat te computed latent variables serve as two social coordinates (SocCoord1, SocCoord2) for were individuals are located on a social interactions grid wit economic distance measured by Euclidean distance between two points. 5. Econometric Results: Labor Supply wit Social Interactions Because in our study tere is no clearly defined reference group we first select persons likely to ave interdependent labor supplies by using te two social coordinates to define overlapping neigboroods. Te reference group now defined, we ten estimate te labor supply model in (3) using instrumental variables for identification. If te

18 16 appropriate econometric specification cecks are satisfied, we ten interpret te social interactions effects in terms of endogenous versus exogenous wage effects. 5.1 Selecting te Reference Group Because we do not ave direct information on wo belongs to te reference group for a particular person we use a statistical procedure to infer it from te location and caracteristics of te group s members. We believe tat our observations are representative for working married men in terms of teir individual caracteristics and spatial distribution. We can tink of te reference group as a ring of certain radius centered around te individual in two-dimensional social coordinate space (Figure 1). Te problem is ten to select te radius best representing te borders of te reference group. Te borders selection problem is key because we use sample observations to compute te caracteristics of close-by individuals. Eac observation establises possible multiple reference groups so tat careful selection of borders is critical ere for identification. To find borders for te membersip groups we use a result from spatial econometrics tat as te reference group size expands te coefficient on endogenous social interactions tends to minus infinity (Kelejian and Pruca 2002). 7 In our application endogenous social interactions are represented by te mean of ours worked by oters in te worker's reference group, AnnHSRG_0_R, were R indicates te radius dimension of te reference group s circle. If tere are social interactions present at a certain size of te reference group, ten te upward bias because of reference group labor supply endogeneity will overcome te statistical tendency for ˆ δ 1 in (3) to become negative as te neigborood size increases, (Anselin 2001). Te reference group wit te most positive

19 17 ˆ δ 1 in exploratory estimates of (3) ten reveals te size of te worker s reference group. In Table 1 we present results from baseline labor supply regressions wit a social interactions variable, AnnHSRG_0_R. Estimation starts wit R = 1, wic means tat te average of ours worked uses nearby workers in te social space witin te distance of 0.1 or less. Wen te indicator R = 1 te reference group as around 13 workers. As te size of te reference group increases in te social space (te radius indicator R increases), te number of persons wo are considered to be economically close to a worker increases from 44 to about 271 in Table 1. As expected a priori, te coefficient on average ours worked by neigboring persons is increasingly negative across te columns of Table 1, going from about 0.2 to 1.5 as te reference group size increases. Suc a tendency will be observed for any estimator including te IV regressions of Table 1 (Kelejian and Pruca, 2002). Critical to our researc is tat te reference group labor supply coefficient becomes positive at te size of te reference group were radius indicator R = 2. Te importance of Table 1 is tat te pattern of regressions reveals te group size wit te largest upward bias due to endogeneity of te AnnHSRG variable. Te endogeneity caused by labor supply interdependencies is most positive for te range (0,0.2), so we pick 0.2 as te radius most closely capturing te true size of te reference group. Results from a Moran I test (Anselin 2001, p. 323) confirm te presence of social interactions in ours worked and tat te radius we adopt to define te reference group based on te preliminary regression in Table 1 also maximizes te Moran I statistic measure of association. Te practical consequence of our specification searc is it indicates tat te average reference group contains about 44 persons ( 44), wic

20 18 means tat it is small enoug to guarantee sufficient outcome variation across groups but large enoug so tat te computed average ours worked are meaningful and ave relatively small error due to aggregation. Our results also satisfy te identification condition for general spatial econometric models establised in Lee (2007b) tat groups vary in size ( 38, (max) = 139). 5.2 Social interactions Effects Te focus of our researc is on examining interdependence in ours worked using te canonical model of labor supply applied to cross-section data. Tis ancors our results for purposes of interpretation to te influential labor supply researc of Hausman (1980, 1981) and MaCurdy et al. (1990). We first confirm tat our estimates for te uncompensated wage and income elasticities are similar to te results of Hausman and MaCurdy et al. Te first column of Table 2 presents IV regression wage and income coefficients for teir canonical models of labor supply. Te uncompensated wage elasticity at te means is 0.14 and te income elasticity at te means is.008; bot values are typical estimates in te standard econometric labor supply literature tat serves as our starting point for judging te importance of social interactions. Our focal regression results are presented in te second column of Table 2, were we include bot abits and social interactions. We also use as a regressor te average of te proxy variable for te exogenous variables constructed via factor analysis (IndVORG_2_6). Te estimated social interactions effect is tat a 10 ours increase in te reference group labor supplied would increase individual's ours worked by about 6 ours. Comparing columns two and tree of Table 2 yields te important result tat te

21 19 estimated social interaction effect is significant statistically and economically reasonable in magnitude only wen abits in labor supply are part of te specification. 8 It is important to re-empasize tat te estimated social interactions effect, ˆ δ 1, wic is te impact of average ours worked by persons in te worker's reference group (AnnHSRG_0_2), as te expected sign and magnitude only after te interdependence as been instrumented, wic we do in Table 2. Te results in Table 1 are inconsistent because tey suggest te presence of endogenous social interactions (Durbin-Wu- Hausman test rejects exogeneity at te 5 percent level). Because of te difference between te results in Tables 1 and 2 we need to empasize te metod we use to construct te instrument for social interactions in labor supply. As noted, tere are no obvious variables to provide exogenous variation wit wic to instrument reference group work effort, so we use te structure of te data to construct an instrument for te reference group s labor supplied. Taking reference groups as overlapping wit boundaries as fixed, average ours worked by persons in te adjacent reference groups can be instruments. Te outer boundary of te persons for te instrument group will be exactly twice te size of te radius for eac neigborood because tere may be workers wo are located exactly on te boundary for bot te reference group of interest and te adjacent reference group. 9 We construct ours worked by individuals in te outside ring in Figure 1, (0.2, 0.6], wic as an average of 226 observations for eac instrument group. First-stage goodness of fit and Sargan test results for te regressions in Table 2 confirm tat our instruments (for all tree rigt-and side endogenous regressors) are valid in terms of passing te standard cecks for weak instruments and tat te overidentifying restrictions are satisfied. Equivalently, te

22 20 strengt of our identifying instruments ere means tat te potential bias of te IV estimator of te social interactions effect in Table 2 is relatively tiny: less tan 4% of te potential bias of OLS (Han and Hausman 2003; Stock and Yogo 2005). 5.3 Additional Econometric Validity Cecks of te Reference Group In is instructive to examine ow our results may or may not be robust to te sizes of te reference group or adjacent groups comprising te instrument set. How migt our results cange by (1) srinking te outer circle boundary in Figure 1, wic leaves te reference group size te same but decreases te number of observations viewed as nearest neigbors for te reference group, or cange by (2) srinking te inner reference group circle boundary in Figure 1, wic makes te reference group smaller? In te first sensitivity experiment, as te instrument group srinks te IV estimated social interactions effect is similar wile becoming statistically less precisely estimated. Our interpretation is tat te instrument loses power as te size of te instrument set srinks. In te second sensitivity experiment, we find tat wen te reference group size srinks te estimated social interactions effect is again basically uncanged altoug statistical efficiency of te estimate again decreases. We interpret te result of te second sensitivity experiment as indicating tat te range for te reference group is well cosen because witin te group tere sould be a similar level of interactions, and we are just coosing a progressively smaller and small subgroup wo still interact. Having discussed te sensitivity of our results instrument construction we now turn our attention to te economic interpretation and policy implications of our estimated social interactions effects in male labor supply.

23 Interpreting te Importance of te Estimated Social Interactions Effect Te presence of social interactions in labor supply means tat individuals respond to oters ours worked by a non-negligible amount. A social interactions effect is important because policy affecting te wages or anoter independent variable of a subgroup will not only affect te individual but also affect oters in te reference group. We terefore focus on te direct versus te indirect effect of interdependence. In particular, we study te consequences of interdependence for te estimated effect of wages on labor supply, wic economists use widely in welfare effect simulations of tax reform proposals. Taking te mean values in equation (3) and focusing on ours worked and wages, 1 = αω+ δ1 = α ω, (4) 1 δ were te quantity 1/ ( 1 δ 1 ) is known as te global social multiplier because it represents te effect of social interactions at te igest level of aggregation (Glaeser et al. 2003). Te total effect of a wage cange can be decomposed into 1 α αδ1 / ω = = α +, (5) 1 δ 1 δ 1 1 were α is te exogenous effect, and ( αδ ) /1 ( δ ) 1 1 is te endogenous effect. Notice tat te endogenous effect depends on bot te magnitude of te initial exogenous cange and te social multiplier. Multiplying equation (5) by ω / te uncompensated elasticity is were η, αω/ w exogenous η = η + η, (6) w, total w, exogenous w, endogenous = and η αδω/1 ( δ ) =. For δ 1 < 0.5 te exogenous w, endogenous 1 1

24 22 effect is larger tan te endogenous effect, but for δ 1 > 0.5 te endogenous effect is larger. As we will later empasize, te decomposition in (6) underscores ow ignoring labor supply interdependencies may ave serious consequences for te elasticity estimates of interest. Using te values from te second column of Table 2, te total uncompensated wage elasticity of labor supply at te means is 0.22, wit an exogenous part of 0.08, and a endogenous part of In comparison, te baseline model results from column one of Table 2 are an uncompensated net wage elasticity of Wen we purposely ignore social interactions te estimated exogenous wage effect is about 60 percent too ig; te positive bias in te canonical model appens because te single (wage) coefficient estimate also imbeds te effect of labor supply interdependencies. Te twin findings tat (1) te wage elasticity as two unequal and sizeable parts in te social interactions model and tat (2) te wage coefficient of te traditional model as sizeable omitted variable bias ave important consequences for evaluating tax policy. 5.5 Implications for Tax Policy Calculations We ave noted tat numerical solutions to optimal income taxation need appropriate econometric estimates. Furter our core results are tat for U.S. male labor supply a regression model tat ignores spillovers in labor supply underestimates te wage elasticity of labor supply by about 40 percent; if one uses a social interactions model but ignores endogenous interactions one underestimates te wage elasticity by over 60 percent. It is less obvious ow we sould apply estimates tat let te policy-maker apportion te total wage elasticity into segments wit and witout social interactions.

25 23 Some back-of-te-envelope calculations for te proportional tax rate case are instructive. Te preferred model in Table 2, column 2 implies tat a 10 percent compreensive tax rate cut would raise male labor supply by as muc as 2.2 percent wen social interactions are considered; ignoring social interactions would lead to about a 60 percent underestimate of te labor supply effect of te tax cut (0.8 percent). Less well establised is ow to use in policy calculations our decomposition of te total wage elasticity into its exogenous component (+0.08) and its endogenous social interactions component (+0.14). To empasize te enriced implications of a labor supply model wit social interactions let us again note a case were one need be careful wit potential social interactions effects. Suppose tere is a proportional tax rate cange applied only to families wit disabled cildren. Te subpopulation affected would be relatively small and scattered geograpically; te reference group effects could be ignored safely, and te appropriate elasticity to use would be closer to 0.08 tan to Alternatively, suppose we were discussing te effect of a proportional state income tax cange on te igest earners in a state suc as California, were many would live in te same area. Now feedback effects would be present. Te elasticity to use would ten include nonnegligible social interactions effects and would probably be closer to 0.22 tan to Te importance of gauging wat is te correct elasticity in terms of te exogenous and endogenous parts is only useful if we can define weter or not a particular group will be affected by interactions. If te persons wo are affected do not belong to te same reference group ten most likely we would only observe te exogenous effect, and te elasticity would overestimated if we used an elasticity tat contained bot exogenous and endogenous components, wic was te first example in te previous paragrap. If te

26 24 tax reform applied to members of a reference group, toug, ten tere would be a fullblown feedback effect and te elasticity tat used only an exogenous component would underestimate te total labor supply effect, wic was te second example above. 6. Conclusion Our researc uses te canonical (linear in means) model of labor supply tat adds possible social interactions in ours worked. We fles out te econometric nuances of testing weter an increase in ours worked by te members of te reference group increases ours worked for te individual (endogenous social effect). Te reference group ere contains persons in close economic distance to eac oter. Our measure of economic distance uses factor analysis, wic allows mapping neigborood variables into a twodimensional social space. Our identification strategy builds on te likeliood tat some persons belong to more tan one reference group so tat teir ours worked may be used to instrument for endogenous labor supply of individuals in te worker s reference group. As in any oter IV exercise we are careful to apply cecks of instrument strengt and tat te overidentifying restrictions are satisfied. In our regression model of married men s labor supply if social interactions are treated as exogenous tere is no estimated effect of te reference group beavior on te individual worker's beavior. Wen we instrument mean ours worked of te reference group and include individual abits in labor supplied we find a social interactions effect tat is reasonable bot statistically and economically. Te estimated total wage elasticity of labor is 0.22, were about one-tird is due to te exogenous wage cange and twotirds is due to social interactions effects. Te policy implications are tat if one is to understand fully te labor supply and

27 25 welfare effects of income taxes, wic may be conditioned on demograpic and location information, a model including social interactions is best. Equally important is a proper interpretation of te social interactions model results. We demonstrate ow a misspecified model or a properly specified model tat is mis-interpreted can easily lead to mis-estimates of te labor supply effects of tax reform by as muc as 60 percent.

28 26 Endnotes 1. Te baseline level of social disutility, s 0, is exogenous, and we begin by assuming tat it is constant for all individuals across all groups. Homogeneity is important because if s 0 varies eiter across individuals due to eterogeneity or across te groups due to reference-group specific caracteristics, ten it is impossible to discuss te effect of social utility b ( ) versus te effect of autonomous social utility s Te overall result ere would not cange if s < υ = [NLI + (τ (TT/(TI NLI)) (TI NLI))], were NLI is non-labor income, TT are total taxes, and TI is taxable income (Ziliak and Kniesner 1999). 4. A strategy similar to ours just described is in Case and Katz (1992), wo instrument for te endogenous effect using te average levels of adjacent neigbors caracteristics tat are supposedly exogenous. Similarly, Evans et al. (1992) instrument scool composition wit city-wide variables for te unemployment rate. 5. Te difference between te number of observations used by MaCurdy et al. (1990) and our study comes from te fact tat we dropped two observations because te ead s age was missing and tat we did not exclude persons wo were self-employed and farmers in 1975 but not in 1976 (canged employment status). Due to restricting te sample to individuals wo also reported ours worked for year 1974, we ave a final sample of 910 men. 6. Te first factor loads primarily on demograpics and explains about 75 percent of

29 27 te total variation in te variables. Te second (rotated) factor loads primarily on location and ten explains about 15 percent of te information. 7. Te intuition beind te result is tat as te size of te group used to produce te average grows it approaces a similar value for everyone and become increasingly collinear wit te regression constant term. 8. Te coefficient on te ours worked for te reference group needs to be less tan 1.0 ere. Oterwise, a one our increase in te mean ours worked for te reference group would induce a worker to increase is labor supply by more tan one our, wic in turn would increase te ours worked for oter men in te individual's reference group even furter. Te labor market equilibrium would be explosive, and a small positive sock to ours worked for any individual in te reference group would cause a domino effect were in te limit all workers coose te maximum feasible ours. 9. Te result stems from symmetric boundaries around eac member. We tank Dan Black for tat observation.

30 Table 1. Selection of te Reference Group Using IV Regression 28 (1) (2) (3) (4) (5) (6) AnnualHours AnnualHours AnnualHours AnnualHours AnnualHours AnnualHours AfterTaxWage * ** ** * * ( ) ( ) ( ) ( ) ( ) ( ) VirtualInc (0.0059) (0.0058) (0.0058) (0.0057) (0.0057) (0.0057) AnnHSRG_0_ ** (0.0867) AnnHSRG_0_ (0.1432) AnnHSRG_0_ (0.2411) AnnHSRG_0_ (0.3231) AnnHSRG_0_ *** (0.3566) AnnHSRG_0_ *** (0.4709) Observations Average obs in ref group Identifying WageRate75, WageRate75, WageRate75, Instruments NLIncome75 NLIncome75 NLIncome75 Standard errors in parenteses Endogenous variables coefficients in bold. Weak instrument ceck statistics appear in Table 2. Additional Control Variables: KIDSU6, FAMSIZ, AGE45, HOUSEQ, BHLTH, Constant * significant at 10%; ** significant at 5%; *** significant at 1% WageRate75, NLIncome75 WageRate75, NLIncome75 WageRate75, NLIncome75

31 29 Table 2. IV Regressions wit Social Interactions Dependent Var: (1) (2) (3) (4) Annual Hours Worked Baseline Social interactions Only abits Only social interactions and abits AfterTaxWage * ** ( ) ( ) ( ) ( ) VirtualInc (0.0058) (0.0047) (0.0045) (0.0061) IndVRG_0_ ( ) ( ) ( ) ( ) AnnHSRG_0_ ** *** (0.2689) (0.3532) Observations Sargan test P-value Identifying Instruments WageRate75 NLIncome75 WageRate75 NLIncome75 AnnHSORG_2_6 IndVORG_2_6 WageRate75 NLIncome75 WageRate75 NLIncome75 AnnHSORG_2_6 IndVORG_2_6 Standard errors in parenteses Endogenous variables coefficients in bold. F(Sea partial R 2 ) = 53.0(0.189), 368.1(0.621), 51.9(0.188) Additional control variables in all equation: KIDSU6, FAMSIZ, AGE45, HOUSEQ, BHLTH, Constant Additional control variable in (2) and (3): AnnualHours75 * significant at 10%; ** significant at 5%; *** significant at 1%

32 30 Figure 1. Demonstration of te Identification Strategy for te Endogenous Social Interactions. Social Coordinate 2 Boundary for reference group g 2 Boundary for reference group g 1 0 g1 1 g1 3 g2 2 g1g2 Inner Boundary for instrument group Outer b oundary for instrument group Social Coordinate 1

33 31 Appendix A. Descriptive Statistics Variable Observations Mean Standard Minimum Maximum Deviation AnnualHours AnnualHour AfterTaxWage WageRate WageRate VirtualInc NLIncome NLIncome AnnHSRG_0_ AnnHSORG_2_ IndVORG_2_ IndVRG_0_ KIDSU FAMSIZ AGE HOUSEQ BHLTH

34 32 References Abel, Andrew B Optimal Taxation Wen Consumers Have Endogenous Bencmark Levels of Consumption. Review of Economic Studies 72(1) (January): Anselin, Luc Spatial Econometrics. In A Companion to Teoretical Econometrics. Badi H. Baltagi (ed.), Malden, MA, Blackwell Publisers, Inc., pp Arellano, Manuel, and Stepen Bond Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations. Review of Economic Studies. 58(2) (April): Aronsson, Tomas, Sören Blomquist, and Hans Sacklén Identifying Interdependent Beaviour in An Empirical Model of Labour Supply. Journal of Applied Econometrics 14(6): Bai, Jusan Inferential Teory for Factor Models of Large Dimensions. Econometrica 71(1): Bai, Jusan and Serena Ng Determining te Number of Factors in Approximate Factor Models. Econometrica 70(1): Becker, Gary S A Teory of Social Interactions. Journal of Political Economy 82(6) ( November-December): Blundell, Ricard, and Tomas MaCurdy Labor Supply: A Review of Alternative Approaces. In Handbook of Labor Economics. Volume 3A, Asenfelter, Orley; Card, David (eds.), Amsterdam, Elsevier Science, Nort-Holland, pp Brock, William A., and Steven N. Durlauf Interactions-based Models, (SSRI).