Introduction Social skills are important for success in many activities and market participants often, but not always, select team members with those

Transcription

1 Becker meets Ricardo Multisector matching with social and cognitive skills Robert J. McCann, Xianwen Shi, Aloysius Siow & Ronald Woltho University of Toronto October, 2012

2 Introduction Social skills are important for success in many activities and market participants often, but not always, select team members with those skills.

3 Introduction Social skills are important for success in many activities and market participants often, but not always, select team members with those skills. Social intelligence shows itself abundantly in the nursery, on the playground, in barracks and factories and salesroom (sic), but it eludes the formal standardized conditions of the testing laboratory. Thorndike (1920).

4 Introduction Social skills are important for success in many activities and market participants often, but not always, select team members with those skills. Social intelligence shows itself abundantly in the nursery, on the playground, in barracks and factories and salesroom (sic), but it eludes the formal standardized conditions of the testing laboratory. Thorndike (1920). Social intelligence has proved di cult for psychometricians to operationalize. Kihlstrom and Cantor (2000).

5 Why are social skills hard to measure? We need a model of social skills.

6 Why are social skills hard to measure? We need a model of social skills. Personality traits are the relatively enduring patterns of thoughts, feelings, and behaviors that re ect the tendency to respond in certain ways under certain circumstances. Roberts (2009).

7 Why are social skills hard to measure? We need a model of social skills. Personality traits are the relatively enduring patterns of thoughts, feelings, and behaviors that re ect the tendency to respond in certain ways under certain circumstances. Roberts (2009). Personality is the system of relationships that map traits and other determinants of behavior into measured actions. Almlund, Duckworth, Heckman & Kautz (2011).

8 Why are social skills hard to measure? We need a model of social skills. Personality traits are the relatively enduring patterns of thoughts, feelings, and behaviors that re ect the tendency to respond in certain ways under certain circumstances. Roberts (2009). Personality is the system of relationships that map traits and other determinants of behavior into measured actions. Almlund, Duckworth, Heckman & Kautz (2011). 1 A model of social skills is one of social interactions in multiple contexts where individuals have heterogenous social skills.

9 Why are social skills hard to measure? We need a model of social skills. Personality traits are the relatively enduring patterns of thoughts, feelings, and behaviors that re ect the tendency to respond in certain ways under certain circumstances. Roberts (2009). Personality is the system of relationships that map traits and other determinants of behavior into measured actions. Almlund, Duckworth, Heckman & Kautz (2011). 1 A model of social skills is one of social interactions in multiple contexts where individuals have heterogenous social skills. 2 The model should di erentiate cognitive skills from social skills.

10 This Paper Builds a theory of matching in school, work and marriage where individuals have social and cognitive skills. In each sector, we assume frictionless matching, team production and transferable utility or pro t maximization.

11 This Paper Builds a theory of matching in school, work and marriage where individuals have social and cognitive skills. In each sector, we assume frictionless matching, team production and transferable utility or pro t maximization. 1 The problem of modelling social and cognitive skill interaction becomes: In each sector, how does cognitive and social skills a ect team output?

12 This Paper Builds a theory of matching in school, work and marriage where individuals have social and cognitive skills. In each sector, we assume frictionless matching, team production and transferable utility or pro t maximization. 1 The problem of modelling social and cognitive skill interaction becomes: In each sector, how does cognitive and social skills a ect team output? 2 Given e cient team prduction, the problem of matching within and across sectors is a linear programming problem. This is great for simulation and estimation.

13 This Paper Builds a theory of matching in school, work and marriage where individuals have social and cognitive skills. In each sector, we assume frictionless matching, team production and transferable utility or pro t maximization. 1 The problem of modelling social and cognitive skill interaction becomes: In each sector, how does cognitive and social skills a ect team output? 2 Given e cient team prduction, the problem of matching within and across sectors is a linear programming problem. This is great for simulation and estimation. A rst pass model of social and cognitive skills.

14 Cognitive and social skills in team production Cognitive skills are complementary in team production: Becker

15 Cognitive and social skills in team production Cognitive skills are complementary in team production: Becker Team production is due to gains from specialization: Smith

16 Cognitive and social skills in team production Cognitive skills are complementary in team production: Becker Team production is due to gains from specialization: Smith Specialization incurs communication costs which takes time away from completing tasks (E.g. Becker and Murphy 1992; Dessein and Santos 2006; Garicano 2000)

17 Cognitive and social skills in team production Cognitive skills are complementary in team production: Becker Team production is due to gains from specialization: Smith Specialization incurs communication costs which takes time away from completing tasks (E.g. Becker and Murphy 1992; Dessein and Santos 2006; Garicano 2000) Individuals have di erent communication costs (social skills)

18 Cognitive and social skills in team production Cognitive skills are complementary in team production: Becker Team production is due to gains from specialization: Smith Specialization incurs communication costs which takes time away from completing tasks (E.g. Becker and Murphy 1992; Dessein and Santos 2006; Garicano 2000) Individuals have di erent communication costs (social skills) Optimal tasks assignments, based on comparative advantage (Ricardo), assign team members with more social skills to tasks with higher communication costs.

19 Results Overview Full tasks specialization in labor and education, but partial specialization in marriage. Who matches with whom di er by sectors: Labor market: (i) Many-to-one matching in teams in the labor market, a commonly observed organizational form. (ii) Individuals with high social and cognitive skills become managers and teachers. (iii) Managers and workers sort by cognitive skills. Education market: Students with di erent social skills and initial cognitive abilities match with teachers of the same cognitive skill. Marriage market: Spouses match on both cognitive and social skills. Educational attainment is not a continuous function of a student s social skill and initial cognitive ability.

20 Predecessors Garicano, Garicano and Rossi Hansberg study how communication costs a ect organization design, time use, occupation choice, team matching & human capital investments at work where individuals di er by cognitive skills. Using a di erent production technology, we extend them by: Add another dimension of individual heterogeneity: communication costs. Studying multisector (school, work and marriage) matching.

21 Model Setup Risk-neutral individuals live for two periods. Enter education market as students, and then work and marry as adults. One unit of time endowment for each sector. Free entry of rms and schools. Individuals are heterogenous in two dimensions: h i ( xed) gross social skill η, with η 2 η, η initial cognitive ability a, with a 2 [a, a] education transforms a into adult cognitive skill k, with k 2 k, k Individuals net payo : wage (ω) + marriage payo (h) Individual decision: who to match with in each sector. tuition (τ)

22 Single Agent Production in each Sector Output is produced by completion of two tasks, I and C : θ I i, θc i : times i spent on task I and C respectively time constraint in each sector: θ I i + θ C i 1 Single agent production: βk i min n θ I i, γθ C i o, β < 1; γ > 1 (Single) no need for coordination: gross social skill η i does not enter production.

23 Team versus Single Agent Production Single Agent Production Team Production βk i min n θ I i, γθ C i o, β < 1; γ > 1 Consider a two-person team with (η i, k i ) and (η j, k j ). θ I i, θc j : times i and j spend on task I and task C respectively Specialization needs coordination. Individual on task C bears (one-sided) coordination cost Team output: p ki k j min n θ I i, γη j θ C j o, η j < 1 (Team) Assume team production is always superior to working alone.

24 Specialization in the Labor Market Let social skill n: n γη. Team output: p n k i k j min θi I, n j θj C ω(n l, k l ) is total earnings of type l employee with skills (n l, k l ). Let a rm hires i and j to produce δ p k i k j units of output where δ is small. Need to allocate δ units of e ective time to tasks I and C. Let θi I and (δ θi I ) be times i and j allocate to task I respectively. Then θj C = θi I n j 1 and θi C = (δ θi I )n i 1 are times j and i allocate to task C respectively. o

25 Firm pays for time used. Leftover time sold elsewhere. The expenditure of the rm s allocations is: ω(n i, k i )(θ I i + (δ θi i ) n i ) + ω(n j, k j )(δ θ I i + θi i n j ) The rm chooses θ I i to minimize above. Proposition. Full task specialization is optimal, i.e., an individual is assigned to task I or C. Corollary.(Ricardo): Specialization is by comparative advantage. Let i do I if ω(n i, k i ) ω(n j, k j ) 1 n j 1 1 n 1 i

26 Many-to-one matching in teams: one member (manager) on task C and several members (workers) on task I. Manager social skill: span of control or leadership. Workers social skills have no value for team production. So ω(n i, k i ) = w(k i ). Proposition.There is a cuto bn (k) such that a type-(n, k) individual does task C if and only if n bn (k). Managers are individuals with better social skills. Occupation choice is based on cognitive and social skills.

27 PAM in the Labor Market Consider a type-(n m, k m ) manager who chooses n m workers of type (n i, k i ) at wage ω(k i ) to maximize n m max (k 1,...,k nm ) i=1 h p km k i ω(k i )i In optimum, workers have the same k w. Can be rewritten as φ (k m ) = max kw p km k w ω(k w ) De ne equilibrium matching µ (k m ) 2 arg max kw p km k w ω(k w ) Proposition.(Becker) Equilibrium exhibits positive assortative matching (PAM) along cognitive skills: µ 0 (k) > 0

28 Equilibrium Wages in the Labor Market Due to free entry of rms, a type-(n, k) manager earns nφ (k) with hp i φ (k) = max kk 0 ω(k 0 ) k 0 First-order condition dω (k 0 ) dk 0 j k 0 =µ(k) = 1 r k dω (k) 2 k 0, = 1 r µ 1 (k) dk 2 k Envelope condition dφ (k) dk = 1 2 r µ (k) k

29 Time Allocation in the Marriage Market Monogamy between i and j means they spend all their time with each other (cannot sell time to outside market) Assuming that it is not e cient to each produce alone, choose θi I (θi C = 1 θi I ) and θi j (θj C = 1 θj I ) to maximize marital output o o qk i k j min nθi I, n j (1 θj I ) + min nθj I, n i (1 θi I ) Optimal solution Optimal marital output θi I = n i n j n j n i n j 1, and θi j = n i n j n i n i n j 1. p ki k j 2n i n j n j n i n i n j 1.

30 Partial Specialization and PAM in the Marriage Market Proposition. Full specialization is not optimal; equilibrium exhibits PAM along both n and k. Monogamy limits specialization. Equilibrium sorts in two dimensions: individuals marry their own type. Equilibrium total marital output for a (n, k, n, k) marriage: 2n n + 1 k

31 Education Market Task assignment is exogenous: teachers do task C students do task I Team production function: p a i k t min θ I i, n t θ C t in equilibrium, a type-(n t, k t ) teacher can manage n t students input: student s initial cognitive skill a i output: student s adult cognitive skill k i Tuition and teacher s wages tuition τ (k t ) depends on school quality teacher s cognitive skill k t teacher s wages: n t τ (k t )

32 Equilibrium Education Choice Education choices maximize future net payo n max n s φ( p a s k t ), ω( p a s k t ), n s τ( p o a s k t ) + n s p as k t τ (k t ) k t n s + 1 Conditional on occupation choice: equilibrium exhibits PAM future managers/teachers choose higher k t if a s and n s are larger: endogenous positive correlation between social and cognitive skills. future workers choose more k t if a s is larger. Proposition. There is an educational gap: a student who has marginally more a s or n s and switches from being a worker to being a teacher/manager will discretely increase his or her schooling investment.

33 General Equilibrium All markets clear labor market clears: equilibrium wages for workers, managers, and teachers equal demand with supply for each type of adult. marriage market clears: trivial with a sex ratio of one. education market clears: school tuitions are set such that available slots in schools equal the total supply for each type of student. Equilibrium equivalent to a utilitarian social planner solving a linear programming problem.

34 Linear Programming Social planner chooses number (measure) of (n m, k m, n w, k w ) rms and number of (n t, k t, n s, a s ) schools to maximize: rm types # rm type (n m, k m, n w, k w ) p n m km k w + # marriage type (n, k, n, k) marriage types subject to, for each adult type (n, k), demand by rms + schools supply of adults and for each student type (n, a), school slots for students supply of students 2n n + 1 k wages and student payo s: multipliers attached to the constraints. in nite dimensional, dual program.

35 Related Literature (Partial List) Importance of non-cognitive (including social) skills: Almlund, Duckworth, Heckman and Kautz (2011), Heckman (2011)... Tradeo between specialization and communication cost: Becker and Murphy (1992), Dessein and Santos (2006). Frictionless transferable utility model of marriage: one factor: Becker (1973,1974)... two factors: Anderson (2003), Chiappori, Ore ce and Quintana-Domeque (2010) Task assignments and hierarchies: Roy (1951), Sattinger (1975)... Lucas (1978), Rosen (1978, 1982), Eeckhout and Kircher (2011) Communication costs, organization design, time use, occupational choice, human capital investment, one factor labor market matching: Garicano (2000), Garicano and Rossi Hansberg (2004,2006) Linear programming models of frictionless matching models: Labor market: Prescott and Townsend (2005) Marriage market: Chiappori, McCann and Nesheim (2010)

36 Two sided communication costs Let i and j spend θi I on task I and θj C on task C respectively. Team output: p n o ki k j min η i θi I, γη j θj C N wm is a set of workers managed by manager m where N wm η w = γη m Then the manager solves: Some results: φ(k m ) = max N wm N wm η w p km k w ω(η w, k w ) ω(η w, k w ) = η w w(k w ) ω(η m, k m ) = η m φ(k m ) No matching between social skills of manager and her workers. Future workers will also make schooling investments based on their social and cognitive abilities.

37 Conclusion We present a tractable framework for multisector matching. All three sectors share qualitatively the same team production function. Team production function incorporates specialization and task assignment. Specify an explicit role for social skills in production. A rst pass theory of social and cognitive skills. many possible extensions

38 Numerical Simulation: Education Choice

39 Numerical Simulation: Equilibrium Wage

40 Numerical Simulation: Wage Distribution