Research " GENERAL HUMAN CAPITAL AND SPECIALIZATION IN ACADEMIA " docx

First, if general skill is substitutable complementary for specialized knowledge in the production of specialized output, then the more able workers tend to generalize specialize more be

THE UNIVERSITY OF CHICAGO

GENERAL HUMAN CAPITAL AND SPECIALIZATION IN ACADEMIA

A DISSERTATION SUBMITTED TO THE FACULTY OF THE DIVISION OF THE SOCIAL SCIENCES

IN CANDIDACY FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

®

UMI

UMI Microform 3088752 Copyright 2003 by ProQuest Information and Learning Company

All rights reserved This microform edition is protected against unauthorized copying under Title 17, United States Code

ProQuest Information and Learning Company

300 North Zeeb Road P.O Box 1346

Ann Arbor, MI 48106-1346

All rights reserved

SMS cố e V

SG) 71-0 “3 vi

ACKNOWLEDGEMENTS :.cccccccccessetececessseeeceseneseseceecsneeeesesesaueeeeseseneaaaeess vill 1 THEORETICAL FORMULATION HS TT TH nghe 1 1.1 Hbx09009510 8000188 .ố.Ố - 1

In Review of Literature ố 3

HH n0 6

2 AN EMPIRICAL APPLICATION TO ECONOMIC RESEARCH 30

PS ` Nào ccc 30

2.2 Measures of General Human CapIfaÌL cà St St irrrsrskrreree 32 2.3 Measures of Author Specla]izafiOn óc St vn HS HH gx cey 35 2.4 — Data Set Description nh 36

2.5 Regresslon Results .eececceccescessesessessceeeeeeeaeeeceseeceeseeaeseesnecsseessceeeesseaesesseaseasens 40 2.6 Individual Authors Ranked by Generality .ccccccsescesessessessscessesesecseeseeseseens 59 3 SPECIALIZATION AND SALARIES .:cccccceccssessececessessseseeessessseesecsessaeees 62 “5n ốc on 62

KPAXN s80 63

3.3 Spcclalization and Wages among Academic Economisfs - 65

3.4 l1 Ha 75

4 GENERAL JOURNALS VERSUS SPECIALIZED JOURNALS 77 4.1 InfrOduCfiOT - - - Ăn S93 11211 1 1 ng TH TH TH TH TH To TH TH gu nàn 77

BIBLIOGRAPHY

FIGURE 1.1 A World with Only Two TaSĂkS Q9 te 13

FIGURE 1.2 A World with Three ÏasksS -à Sàn HH kg 15

FIGURE 2.1 Distributions of JEL Letter Codes in Sample and at “Top Five”

Department 0N 40

FIGURE 2.2 Average Number of JEL Letter Codes Listed per Publication 41

LIST OF TABLES

TABLE 2.1 Top Fifty Economics Departments, by NRC Faculty Teaching Rankings 34

TABLE 2.2 JEL Classification Leff€TS - SG cv 11 1111111181141 121 111 1x krxek 37

TABLE 2.3 Top Fifty Economics Departments, by NRC Faculty Research Rankings 38

TABLE 2.5 Codes Used Per Publication, Linear Regression -s-ccs 25552 44

TABLE 2.6 Codes Used Per Publication, Poisson Regression - - 5-55- 46

TABLE 2.7 Self-Citedness Rate oo ccccceccsssssssssessesesssesesscseessesecsecsesseseeeseecaesscenseneees 47

TABLE 2.8 8-Journal Concentration Ratio ccccsseesessssesscscssssesscsesscasescsesesseeseseaes 49

TABLE 2.10 Generality of Education Provided by Top 20 Institutions 52

TABLE 2.11 Codes Used Per Publication, Including “Variance” Measure of Education

TABLE 2.12 Codes Used Per Publication, Including “HHI” Measure of Education

TABLE 2.13 Different Letter Codes Used, Linear Regression . 55-5- 56

TABLE 2.14 Different Letter Codes Used, Poisson Regression - -‹- 58

TABLE 2.15 Does the Substitutability of Co-authors Differ at Different Graduating

TABLE 2.16 Top Twenty Economists in Sample, By Two Measures of Generality 61

TABLE 3.1 Summary Statistics, Tenured and Untenured -c <s<sscsscxc<zs 67

TABLE 3.2 Do Authors from Better Ranked Graduate Schools List Different Numbers

Of JEL Codes? wo ccccceecccccccscssscecssesessscecescscsccececscacenucecseacecesensuececusucseausevsnaceesenasess 68

TABLE 3.3 Do Better Paid Authors List Different Numbers of JEL Codes? 69

TABLE 3.4 Do Better Paid Authors Publish in More General Journals? 71

TABLE 3.5 Do Authors from Better Ranked Graduate Schools Publish More Different JEL Codes Throughout Their Careers? .ccccecccccsesscssssesscssesscsessecsesseeeesssaesaeseesees 73

TABLE 3.6 Do Better Paid Authors Publish More Different JEL Codes Throughout

I iá9 1 74

TABLE 4.1 Journals Ranked by Self-Citedness Rate 25 ccccSsscsserrres 80

TABLE 4.2 Journals Ranked by 4-Journal Citation Concentration Ratio 86

TABLE 4.3 Journals Ranked by 8-Journal Citation Concentration Ratio 91

TABLE 4.4 Journals Ranked by Citations HHH 2S scvsssresrresrrrrsresee 96

ACKNOWLEDGEMENTS

I would like to thank my dissertation committee: Gary S Becker, Casey B

Mulligan, and Allen R Sanderson Steven D Levitt was also extremely helpful in

advising me on this project

In addition to my academic advisors, others without whom this dissertation would never have been completed include Jamie Foltz, Chris and Maria Freeman, Rosemary Krieger, Joan Smutny, Sandra Wesolowski, and most importantly, my parents, Susan and

David Kendall

Theoretical Formulation

11 Introduction

Casual empiricism indicates that, at any given time, in any particular place, some

individuals specialize far more than others One man “is a hunter, a fisherman, a

shepherd, or a critical critic, and must remain so if he does not want to lose his means of

livelihood”, while another is a modern-day diVinci, who may “hunt in the morning, fish

in the afternoon, rear cattle in the evening, criticize after dinner ”

Both Isaac Newton and G.W Leibnitz made fundamental contributions to the discovery of calculus In addition, Newton also formulated a system of mechanics Some physicians are heart surgeons, while others are pediatricians or general

practitioners Professional baseball teams usually include many players who specialize at particular positions, as well as a few “utility” players who are able to play several

positions Some economists write many articles on a particular topic, while others write one article on each of many topics

It would be easy to list many other industries in which individuals specialize to different degrees This phenomena has been included as an “input” into models in other

' Marx and Engel’s (1939/1881) description of the proletariat lot under capitalism and

communism, respectively.

understand the conditions under which these choices are made

Three conditions affecting specialization will be specifically modeled here: the degree to which specialized skill is substitutable with generalized skill, the degree of monopoly power which specialists hold over their specialties, and whether different specialized skills are complements in production

First, if general skill is substitutable (complementary) for specialized knowledge

in the production of specialized output, then the more able workers tend to generalize (specialize) more because specialized knowledge in a particular task is marginally less (more) useful to them

Second, any “monopoly” power workers hold over their specializations generates the result that higher general human capital is correlated with less specialization, even in the absence of substitutability between general and specialized human capital, since for those with higher general human capital not to apply themselves in more different tasks would imply prices for their outputs that are “too low” from a monopolist’s perspective

Third, when the various outputs of specialized production are complements in production, then the division of labor among workers in a firm may require more able workers to generalize more so as not to over-produce any particular specialized output relative to the production of less able co-workers’ outputs

Section 1.2 presents a brief review of the literature on specialization and the division of labor and places the present research in context Section 1.3 develops a model

of the specialization choices of a cross-section of workers of different general skill levels

This chapter fits into two strands of previous literature It adds to the theoretical literature on specialization, division of labor, and matching within firms, and presents empirical evidence on the economics of research and development, particularly within universities I focus here on describing the chapter’s place in the theoretical literature on specialization, and leave to later sections its relation to the job matching literature and to previous empirical work on academic research

Specialization and division of labor are central to many, if not most, economic problems Hence, there is a very large literature Only a brief summary of the papers most relevant to the current study is attempted here.’

Economists have described two basic causes for the division of labor The

“comparative advantage” or “Ricardian*” theory suggests that the division of labor sprouts from heterogeneity in specific knowledge, skill and opportunity across workers People who are relatively better at a particular task, or who have access to resources relatively more fit for that task, specialize in it Rosen (1978) shows in a modern

treatment how workers are assigned to tasks intensive in skills in which they have

comparative advantage

There are some obvious cases in which inborn or early-socialized physical or mental qualities play a part in an individual’s choice of specialization, such as a very tall person becoming a basketball player However, such cases are relatively rare Typically,

* Yang and Ng’s (1998) survey is more complete

3 Ricardo, of course, was primarily concerned with understanding patterns of international trade,

as his famous example of Portugal’s production of wine and England’s production of cloth makes clear; thus, it is not quite fair to make him the whipping boy for the difficulties associated with applications of his model to labor markets Eponymy aside, there is some debate about whether Ricardo (who published his theory in 1817) was familiar with the previous work on comparative advantage by Torrens in 1815.

one is not “born” to be an accountant, a lawyer, a construction worker, an economist, or

most any other profession

Based on this critique, the “increasing returns” theory considers ex ante identical individuals who can increase their consumption through the division of labor because of economies of specialization.* Adam Smith (1776), who first placed the division of labor

at the center of economic-social study, emphasized the relative importance of increasing returns over comparative advantage in understanding the division of labor in a modern society.” Smith identified three factors underlying increasing returns to specialization: improvements in dexterity from repetition of specialized tasks, less time spent moving from task to task, and increased ability to invent time-saving machines in specialized tasks Rosen (1983) emphasized increasing returns to specialization based on the fact that investments in specialized human capital do not depreciate more when employed more intensively, providing a “fixed cost” element to specialized human capital

investment Becker (1991, Ch 2 and Supplement) uses an increasing returns model to understand specialization within the family, and finds that some family members will specialize more than others; however, without comparative advantage, it is indeterminate which family members will specialize more Becker and Murphy (1992) and Yang and Borland (1991) have used increasing returns theory to explore how specialization has changed over time and in response to macroeconomic variables such as the size of the market and the predominating economic system While these two studies have

investigated how the general level of specialization in society is determined, they do not attempt to explain the simultaneous appearance of generalists and specialists

advantages in some tasks, but not do not allow for differences in ability

The model presented in this chapter agrees generally with the increasing returns approach, and so assigns no ex ante comparative advantages to workers However, in contrast to this approach, it does allow workers to differ in their general ability or early- socialized general human capital Thus, there is no comparative advantage, though there are differences in ability Since it seems obvious that individuals do differ from each other, differences in general human capital seem an appropriate factor to consider if differences in comparative advantage are off the table

Section 1.3 below shows that even in a situation with no comparative advantage

across workers, when one worker is abler in all tasks than another worker, the two may

not choose the same degree of specialization — one may specialize more than the other If

a “job” is defined at least partly by the number of different tasks associated with

employment, then this model can help to explain workers’ employment choices

The model used in this chapter is one of specialization and the division of labor; however, it closely resembles the “span-of-control” literature, which considers the

relationship between entrepreneurial characteristics and firm size In particular, Rosen (1982) shows that complementarity between managers’ skill and workers’ skill implies that higher skill managers have greater spans of control Similarly, one of the models below uses complementarity conditions to understand the relationship between general skill and the “span” of different specialized skills workers choose A related work is Garicano (1998), which develops a concept of firms as “knowledge-based hierarchies” where managers invest in general problem-solving skills, while the workers they

supervise hold specialized production skills In the model below, however, there is no explicit division between managers and workers — the focus is on differences between workers at the same level in the hierarchy

In sub-section 1.3.1 below, the outputs of specialized tasks may be marketed by individual workers independently of the production of other tasks and other workers This will be referred to as a “simple” production process.° Two factors affecting the correlation between general human capital and specialization will be considered in the simple process: complementarity or substitutability between general and specialized human capital, and the degree of price-setting power workers hold in their specialties

In sub-section 1.3.2, specialized tasks are complementary in the production of a single marketable product This situation will be introduced under the rubric of a “complex” production process, and a third factor will be considered: complementarity across tasks produced by different workers within the same firm

1.3.1 Simple Production Process

Suppose there is a set of tasks that each produce specific outputs In order to produce a particular task’s output, a worker must spend time investing in the specific human capital associated with that task, as well as spend time actually performing the

Š [ borrow the terms “simple” and “complex” from Taussig (1915) who delineates them as

follows:

The division of labor may be analyzed under two heads On the one hand there is the

simpler form, under which a workman carries through the whole of one of the stages in

production The tailor, the cobbler, the carpenter, ply their several trades On the other

hand there is the more complex form, under which there is a splitting up of several

operations all belonging to one stage of production (pg 30)

Like Taussig, one must admit that outside the theoretical constructs of a model, “‘a hard-and-fast line cannot

be drawn between these two aspects of the division of labor.” Nevertheless, as in his textbook, clarity of

exposition demands it here.

specific human capital they will invest in; the total amount of time they will spend on each task; and the division of time on each task between investing in specific human capital and producing

All tasks are equivalent, in the sense that none are more difficult than others Assume that all workers are endowed exogenously with some characteristic 4, higher values of which improve productivity in all tasks For the discussion that follows, h will

be assumed to be some form of general skill, IQ, or general human capital, though some other inborn or early-socialized qualities could be analyzed similarly Thus, / identifies a worker’s absolute ability in production

Let the universe of possible tasks be called Z A worker’s output on any task zéZ per unit time is a function of his general human capital and the amount of time he has spent investing in the specialized human capital associated with task z As a general form, productivity per unit time in task z will be denoted

HỊ #“=#ữứ.r)

where /,ˆ is time spent investing in the specialized human capital needed to perform task

z Since by assumption, all tasks are equivalent, the function £ is not superscripted with

z The function E is assumed to be increasing and concave in both of its arguments.’

A worker’s total output in a task z may then be denoted

[2] Y=E%¿/

7 All hours of work have the same productivity E’ This assumption can be relaxed to allow marginal productivity to decrease in 4,’ without changing the results Baumgartner (1988) develops a model in which workers have some market power, and thus face declining demand curves for task-specific outputs; this type of model will be considered explicitly later in the chapter.

Let the total amount of time spent investing and producing in task z be

[3] £#=/, +:

One may think of the worker’s problem as being solved in two stages First, the worker chooses ¢,” and ¢,,’, taking ¢’ as given Then, he chooses ¢’ for each ze Z, with t’ = 0 for tasks in which the worker chooses not to specialize

The set of maximization problems associated with the first stage are (for each z):

[4] max E(h,t,’)t,’ subject to equation [3]

Substituting equations [5] and [3] into equation [2] indicates that output on task z may be written as a function of f alone:

] YfŒ,z)= Eứ,£ - /Œ)/0)

Theorem 1.1 There are increasing returns to specialization

Proof This follows from the fact that Y* is increasing and convex in t* Note that Y,=E,f(—f,)+ Ef, > 0 due to the bounds on f, given in equation [6] Then note that

Consider now the second stage of a worker’s choice, that of determining the optimal ¢* for each z Assume that workers each have the same total amount of time T

outside of leisure, and thus that

If there were no costs to specialization, Theorem 1.1 implies that workers would specialize completely, i.e., = 7 for some z

However, there are costs to specialization in most instances Knight (1967)

enumerates three: increased interdependence upon other workers, costs of coordinating task outputs and output transfers, and boredom.’ In addition to these costs of

specialization, Murphy (1986) and Carrington (1990) identify uncertainty about the future prices of specialized outputs as an incentive to generalize Kim (1989) theorizes that search costs of employment increase with specialization

One intuitive specification of the costs of specialization is simply an increasing function of the number of specialties in which ¢ > 0 In this case, however, workers would tend to specialize almost completely, i.e., set f ~ T for one z, and f = ¢ for all other z, where ¢ is some very small positive number near zero Thus, they would

minimize costs while retaining the returns from specialization Alternatively, if the costs

of specialization were simply increasing in some measure of inequality between the r’’s, such as the Herfindahl Index or the Gini coefficient, workers would either specialize

completely or generalize completely, depending on the relative convexity of the cost function and Y

Since we do observe some choices between perfect specialization and perfect generality in the market, these function forms seem inadequate However, specialization costs that depend on both the number of tasks, and the amount of inequality in the f’s can give an interior solution to the problem, while remaining intuitively appealing Thus, let the costs of specialization take the following form:

Z Z

where 1 is an indicator function taking the value 1 if the expression that forms its

argument is true and 0 otherwise Note that the first argument is the Hirfendahl Index and the second argument is the number of tasks the worker performs.’°

Hence, specialization costs decrease continuously with relative equality of the 7’s, and discretely with the number of tasks chosen This reflects an assumption that the costs

of specialization decrease with generality, but that there is a discrete cost of knowing absolutely nothing about any particular subject.'!

Then the maximization problem associated with the second stage is given by

[10] mex [E0 - /0)/0)|-cQWQ02?WAΠ> oD subject to equation [8]

'° Alternatives to the Hirfendahl Index could be substituted without loss of generality

"! For instance, knowing just the names of car parts can allow one to appear informed when conversing with auto mechanics and significantly reduce the likelihood of fraud.

The objective function is simply the sum of equation [7] for each task, minus the costs of specialization given in equation [9] The first order condition associated with equation [10] is

ay E,/q- ƒ)- Eƒ,~2C„„# =ồ >0

E,/q- #)- Eƒ,— Cy(HHI,N)<õ =0

where 5 is a constant Lagrangian multiplier

Lemma 1.1 Workers split their time equally between all tasks that they perform in

positive amounts

Proof From equation [11] one can observe that if t? >0 and t” >0 for some z; and z2, then t* =t* =t* This follows directly from the fact that all tasks are assumed equivalent, and hence the function E is independent of z

Lemma 1.1 does not show that there will be a solution other than perfect

generality or complete specialization To see that such a solution may exist, first observe Figure 1.1 The upper panel in Figure 1.1 represents a situation where there are only two tasks in the universe, Z, and the choice of the worker is merely to split his time between the tasks Points A and B represent the output (not including costs) from specializing completely in tasks 1 or 2, respectively The convex line connecting points A and B represents the output from splitting the worker’s time T between the two tasks in various combinations Since there are increasing returns to specialization, any non-complete specialization produces less output than points A or B The output line is symmetric because tasks are equivalent

t

Het,

Figure 1.1 A World with Only Two Tasks

The convex line below the output line represents the costs of specialization, given that the worker has chosen positive values for both ¢’ and 7’ The convexity of this line represents the fact that costs decrease with increasing generality (i.e., decreasing HHI) The points labeled C(1,1) represent the costs from specializing completely, so that HHI =

1 and N= 1 Note the discrete jump in cost at the point where N falls from 2 to 1 In this figure, the optimum point is perfect generality, where f = = T-

The lower panel in Figure 1.1 shows the case in which near-complete

specialization dominates generality in this two-task world The distance between A (or B) and C(1,1) is greater than that between the output and cost functions at perfect

generality In this case, workers would choose 7 = T- ¢ and ’ = « (or equivalently, 7 = T-

e and / =e),

With these facts in mind, now consider a universe of three tasks, as pictured in Figure 1.2 The shaded surface is the output function given the values of ¢’, 7, and Points 1, 2, and 3 represent the output from perfect specialization in any of the three tasks The two points marked as C(1,1) are the costs from perfect specialization in any of the three tasks.’

The set of three convex lines marked as C(HHI, 2) are the costs from specializing

in two tasks, for any division of time between the two tasks, assigning zero time to the third task The surface traced by the dashed lines is the cost of specialization when some quantity of time is allocated to all three tasks Consider first the workers choice between complete specialization and two tasks Without loss of generality, compare complete specialization in either task 1 or task 2 versus generality between the two tasks, so that

" For readability, the equivalent point on the far axis not labeled

t'= T/2 and ¢ = T/2 If the length BB’ is greater than the distance between point 1 and C(1,1), then generality between the two tasks is preferred to complete specialization

This is the same as the top panel in Figure 1.1, i.e., the case where C(HHI, 2) is more convex than the output function Now compare equal division of time between tasks 1 and 2 with an equal division of time between tasks 1, 2 and 3 (i.e., perfect

generality) If the length BB’ is greater than the length AA’, then the worker prefers to perform only tasks 1 and 2, and to not perform task 3.'? This can be the case if the

C(HHI, 2) line is more convex than the C(HHI, 3) surface

More precisely, the optimal selection in this case is actually B°B*’, as marked in Figure 1.2 This is because the worker can eliminate the discrete cost of being

completely ignorant of task 3 by moving slightly off of BB’ So in this model, workers are always “generalists” in the sense that they choose positive values of f for all z

However, they will generally set f = ¢ for some of the z For the purposes of the analysis below, assume that ¢ can be made close enough to zero that it can be ignored If so, then the number of different tasks chosen by a worker can be denoted

Theorem 1.2 Workers with more general human capital specialize more if general and specialized human capital are complements If general and specialized human capital are significantly substitutable, then workers with more general human capital specialize less

Proof The first order condition for the maximization problem in equation [13] is

EF + FESS, -D-FE, = Cu - Cun T

From this, we can derive Nụ by taking the derivative oƒ the first order condition with respect to h Doing so gives the solution:

N, _ E,( ;wWT/)—y E„/(Œ,

SOC

where SOC is the second order condition from the maximization problem Hence, Np is

negative if and only if

EAS) -F Ent TS, -)> 0

Using the facts that f is convex, and f, is between zero and one, a sufficient condition is that Ey, is positive, i.e., that general and specialized human capital are complementary in production However, if Ey is sufficiently negative, then N; will be positive This

corresponds with the case where general and specialized human capital are

substitutable QED

Whether general and specialized human capital are substitutes or complements

may vary across fields of endeavor Moreover, general and specialized knowledge might

be complementary for low levels of specialized knowledge (investment), but then grow more substitutable at higher levels of specialized knowledge For instance, a good

economist can sometimes deliver several interesting testable hypotheses about a new

issue simply by applying his general knowledge of economic theory, but he must at least

be given the basic information about the issue first His understanding of price theory may then be somewhat substitutable for a thorough mastery of previous and related literature on the issue

Empirical evidence suggesting that abler workers tend to invest more in on-the- job training (Altonji and Spletzer, 1991) suggests that general and specialized knowledge are often complementary In other instances, they may be substitutes Thomas Edison was, by any measure, an extraordinarily gifted engineer and a creative inventor who holds patents for more than 100 inventions, including the light bulb Yet, he did not spend his entire career creating higher and higher quality light bulbs Instead, he

developed a bulb quite rudimentary from a modern perspective, then switched his

research efforts to the home phonograph, storage battery, and other inventions, allowing less-famous engineers to refine higher wattage and longer-lasting light bulbs

So far, it has been assumed that workers are price-takers with respect to the

outputs of the tasks they perform, and this is the typical assumption in the labor literature However, it may be violated in some special cases, or in broader considerations for

entrepreneurs and others who develop fairly unique outputs Hence, assume now that there are declining demand curves for production in each specialty This may be the case, for instance, with academic research if specialties are defined narrowly enough such that additional knowledge provides fewer changes in policy implications than the original research As an example of such a phenomenon, Kendall (2001) provides some evidence

on declining demand for research in the “real business cycle” economics literature

As before, productivity per unit time in task z will be denoted

E* = E(h,t,’)

where ¢,” is time spent investing in the specialized human capital needed to perform task

z, and the function E is assumed to be increasing and concave in both of its arguments

A worker’s total output in a task z may then be denoted

Hence, according to Theorem 1.1, there are still increasing returns to

specialization However, now assume that there exist prices for output in each task, and that the price of output in any particular task is a decreasing function of output in that

task:

[14] pe =p”)

For simplification, p has no z superscript, implying that tasks are equivalent from the worker’s perspective Using the cost function defined in equation [9], the

maximization problem analogous to equation [10], associated with a worker’s decision to

divide his time across tasks, is

[15] man PCE ~#0))Z0)|E@,# - /Œ))/02)]- COMFY AE > op}

subject to equation [8]

Equation [15] is equivalent to equation [10], except that prices are included

Since all tasks have equivalent demand curves, a corrollary of Lemma 1.1 applies, and workers split their time equally between all tasks that they perform in positive amounts Hence, define again

Proof For simplicity, denote the derivative of p with respect to N as py Then the FOC Jor the maximization problem in equation [16] is

PyNEf + PRES + FESS, -D- FB = Cy - Can +

Note that the terms inside the LHS brackets correspond to the LHS terms in the FOC for the maximization problem in equation [10]

Taking the derivative of the FOC with respect to h gives the solution:

N = PEA AAS) ~ Ent SG, ~D} - Dy NES

where SOC is the second order condition from the maximization problem From

Theorem 1.2, the terms inside the brackets in the numerator are positive when general and specialized human capital are complements If the second term in the numerator,

PNnNEbf, is negative, then N,, is necessarily negative Hence, to prove the theorem, one

must show that pyNEpf, is positive

To see this, write out the explicit derivation of the derivative py:

1.3.2 Complex Production Process

The previous section considered a “simple” production process, in which the specialized task-outputs can be sold as separate products on the market It was shown that in this circumstance, the question of which workers specialize more depends upon

the substitutability or complementarity between general and specialized human capital as production inputs

Now we consider what is in some ways the more typical case, in which the salable product is composed of the outputs of various complementary tasks, and thus, some co- ordination between tasks is necessary.'* In some cases, this co-ordination may be

accomplished through market-clearing price schedules that give individuals incentives to produce task outputs in optimal proportions In other cases, individual workers may be directly coordinated within a firm and paid to undertake a certain number of tasks, as in Matsui and Postelwaite (2000) and MacDonald and Marx (2001)

An intuitive example motivates the theory below Consider a shoe factory with two workers One produces right shoes and the other left shoes If they specialize in this way, the right shoe worker produces 15 shoes an hour and the left shoe worker produces

20 shoes an hour It is easy to see how it might be better for the left shoe worker to

make, say, 17 left shoes and then produce two right shoes to go along with the right shoe workers’ 15 Hence, the abler worker “generalizes” to two tasks

To see more concretely how workers of different general skill behave when their outputs are complements in the production of a single product, consider a case in which firms consist of teams of workers producing the product through a set of tasks Let the output of a specific task be again given by equation [7] As a general case, let the firm’s output be of a general functional form:

[7] 4= G(jy›fz)› Tay; gay )»- )

'* Garicano and Hubbard (2002) analyze some factors that predict whether an industry will

conform more closely to the simple or complex production process.

where 7(7) is an function assigning task i to a worker named /(i) employed by the firm The arguments of G correspond to the outputs of the various tasks performed by workers

firms to hire sets of employees homogeneous in / (Becker, 1973) Even in this case,

however, there are other factors which may keep firms from matching workers perfectly

For instance, Shimer and Smith (2000) and Chen (2002) discuss matching problems

when search is costly In these models, workers seek firms with similar quality

employees until the marginal benefit from finding a better match falls below the cost of

continuing to search If search costs are significant, this point may sometimes occur

before the homogeneous match is found Alternatively, if workers’ types are not

completely observable and firing is costly (perhaps because of labor market regulation or

because of the presence of firm-specific human capital investments), or if the optimal

firm size is greater than the number of workers of a particular type available in the

economy,’’ these are other avenues for imperfect matching to occur, even when an

'S Since the labor market equilibrium that assigns workers to firms has not been presented

formally, it is not obvious that every task will be performed by only one worker Indeed, if the number of

tasks is less than the number of workers in the firm, it will certainly not be so However, Theorem 1.1 implies that assigning only one worker to a task is more efficient than any other situation For simplicity,

and to focus on the firm’s assignment problem, the assumption is made that the equilibrium allows for this However, this assumption is not necessary to the results below

'® More generally, supermodularity of G is a sufficient condition for the existence of a

homogeneous equilibrium

'’ Kendall (2002a) provides an example of a production function with complementarities in which the optimal firm size is always the same as the number of available workers of each type.

equilibrium with homogeneous firms is Pareto-optimal from a costless search

perspective

Workers of different skill levels may also choose to match together in firms if the costs of specialization enter into the firm’s objective function in particular ways For example, suppose that specialization costs relate to the costs of coordinating various task- outputs within the firm, and the existence of some “coordinator” workers can ameliorate these costs In this case, homogeneous firms may have “too much” specialization and incur large coordination costs, where heterogeneous firms have some workers

specializing more than others, who can naturally perform coordination as they generalize

To see more specifically how this mechanism may operate, suppose there are no labor market frictions like those in Shimer and Smith (2000) Consider the special case

in which firms consist of two workers only, and each firm produces an output composed

of two complementary tasks In particular, assume these tasks are perfect complements

in production, such that

q = mm{Y(h,í,) + VÚ;,T — f„), Y(h,T — f,) + Y(u,,t,)}

where h; is worker i’s general human capital level, and 7; is worker i’s time spent on one

of the tasks, again assuming that workers have total time endowment T

The labor force consists of four workers, named by their general human capital

levels: H, H, h, and h, where H > h Thus, there are two “high” general human capital

workers, and two “low” general human capital workers in the labor force

First consider the case with no specialization costs If the two high human capital workers form a homogeneous firm together, they maximize g by each specializing

completely, so that t; = t2 = 1 Thus, the output of such a firm is

4(H,H}) =Y(HJ1)> 1

Similarly, the output of a firm composed of the two low human capital workers is

q(t, h}) = ¥ Al)

A heterogeneous firm composed of one H worker and one h worker maximizes q

by letting the h worker specialize completely in one task, while the H worker does two tasks.'* Because of the Leontief nature of the production function, optimality implies that the outputs of the two tasks must be equal:

!8 To see this, note the firm solves the following program:

max{Y(H,t,)+Y(A,1-1,)} st Y(H,f„)+ Y(h,L— t,)= Y(H,1— t„) + Y(h,t„))

Theorem 1.4 The optimal sorting of workers in this economy is perfect homogeneous matching

Proof We need to show that qQH ,H » + q({h, h}) > 2q({H AS) Note that equation [18] implies:

Y(H,1) + Y(A,t,,)-Y(A,1-t,) = Y(A,D+ Y(AD

Now because Y is convex in t,

So without any costs of specialization, workers sort homogeneously, and there is

no relationship between general human capital and specialization — all workers specialize completely

Now suppose that specialization is costly in the sense that it makes coordination

of the task-outputs difficult If, however, a firm has a “coordinating” worker, or a

“manager”, who is significantly involved in both tasks, it can avoid this cost As a simple example, assume the firm incurs the cost

Ce {0 ift, >t’ for alli

0 otherwise

That is, if both workers are “too” specialized, the firm pays a cost, M Whether

homogeneous or heterogeneous firms are optimal in this situation depends on the values

of t, M, H, and h; however, a numerical example shows it to be possible for

heterogeneous firms to be optimal

Let H = 2, h= 1, M be positive and very large, and ` = ø Let the task output

function be

Y(h,t) = hr’

Equation [18] implies that ty = 2/3 Then homogeneous firms set t; = t) = t, and

their outputs are

This equilibrium results because heterogeneous firms have a worker who

generalizes, and this worker can also do the coordinating Homogeneous firms do “too much” specializing

Note that in these heterogeneous firms, the H worker performs two tasks, while the h worker performs only | task Thus, the higher general human capital worker

“generalizes” This will turn out to be a more general property of firm behavior when there is complementarity across tasks, as Theorem 1.5 below will show

Thus consider a specific form for the production function in equation [17]; for simplicity of exposition, allow G to be the Leontief function:

4 = MiIN{Y (Ajay st jay), Y Ajaystiay)

Further assume that because of search costs or specialization costs, that there is some

heterogeneity in firms, i.e., there exist workers named x and y, where h, > hy

Theorem 1.5 The worker with more general human capital, x will specialize less than worker with less general human capital, y

Proof Optimality requires that the firm set the outputs of each specialized task equal In particular, for any two tasks performed by x and y respectively,

Y(A,,t,) = Y(A,,t,)

Since Y is increasing in both arguments, h, > hy implies t, < ty Lemma 1.1 implies that a worker splits his time equally across all the tasks that he does Thus, x does n,=T/t,

tasks, while y does ny=T/ty By this definition, n> ny QED

Note that this result applies to workers coordinated in the same production

process Two workers employed at different firms, for instance, may choose different degrees of specialization even if they have the same h

To summarize the theory provided in these two subsections, abler workers tend to specialize less (more) when:

a.) general ability and specialized skill are substitutable (complementary) in production; or when

b.) different specialized skills are complements (substitutes) in production and firms are heterogeneous in workers’ general human capital levels

One general caveat is in order Recall the assumption made throughout that all tasks are equivalent in their production process, i.c., E7 = E for all z However, if some tasks are more “difficult”, so that output per hour in those tasks is less at every level of h than some other “easy” tasks, then the 7’’s will not necessarily be the same for all the tasks a worker chooses In this case, a worker with higher / can simply switch his production to more “difficult” tasks instead of performing more tasks Some preliminary evidence on whether this phenomena is important is explored in the empirical work in the next

chapter

An Empirical Application to Economic Research

This chapter seeks to apply the analysis of Chapter 1 to an actual market situation, that of the specialization choices of professional academic economists

It is often claimed that general and specialized knowledge are substitutable to

some degree in economic research An economist who is well trained in price theory or

mathematics may address a problem using general theorems in combination with

relatively little knowledge about the specifics of the problem This I believe is consistent

with Gary Becker’s commonly quoted statement from his Nobel address (1993): “ I

believe that what most distinguishes economics as a discipline from other disciplines in the social sciences is not its subject matter but its approach I contend that the economic approach is uniquely powerful because it can integrate a wide range of human behavior.” Many of the articles considered to be important in economics admit to being simply applications of some long-understood idea to a novel situation.!

It is also commonly observed that there may be complementarities between the outputs of specialties across the field of economics Macroeconomists calibrate models

' Sherwin Rosen told his first-year Ph.D classes that “there are only six important ideas in economics,” and that all modern literature is simply new applications of these ideas He refused to reveal exactly what the six ideas were

30

using parameters estimated by labor economists Asset pricing models make use of models of preferences and budget constraints developed by microeconomic theorists and

behavioral economists

There may also be complementarities between research interests within a single

university because of teaching commitments Because undergraduate and graduate

students typically begin schooling without a definite knowledge of their future

specialization choices, universities prefer to have equal quality faculty researchers in many specialties In this way, students do not have to switch universities if they decide to

specialize in particular fields While some cases may be cited of economics departments that focus substantially on one or two fields, the vast majority of departments attempt to cover most or all specialties roughly equally (Tschirhart, 1989)

If general and specialized knowledge are substitutable in economic research, or if there are research or teaching-based complementarities across the outputs of particular fields, then the model of the previous chapter implies that higher ability researchers should specialize less relative to lower ability researchers, at least within the same

specialization used in the study