Tsukuba Economics Working Papers
No. 2014-001

Entry Costs, Task Variety, and Skill Flexibility: A Simple Theory of (Top) Income
Skewnessby
Manoj Atolia and Yoshinori Kurokawa
February 2014
This version: July 2018

UNIVERSITY OF TSUKUBA
Department of Economics
1-1-1 Tennodai
Tsukuba, Ibaraki 305-8571
JAPANEntry Costs, Task Variety, and Skill Flexibility: A Simple
Theory of (Top) Income Skewness
Yoshinori Kurokawa
University of Tsukubaz

Manoj Atolia
Florida State Universityy

July 17, 2018

Abstract
This paper develops a simple model that provides a uni…ed explanation for both anincrease in below-top skewness and a much larger increase in within-top skewness ofwage income distribution. It relies on a single mechanism based on the …xed costs ofentry, linking a decrease in entry costs to an increase in both types of skewness under theassumption that higher-skilled workers are more ‡exible in handling a variety of tasks.
Di¤erences in ‡exibility are modeled as di¤erences in the …xed setup costs required tohandle a given number of tasks. Our numerical experiments in a calibrated model show
that, by increasing task variety, a decrease in entry costs— entry deregulation— can be aquantitatively important source of both the increase in below-top skewness and the muchlarger increase in within-top skewness observed in the U.S. Moreover, the experiments
imply that the observed di¤erences in entry deregulation can cause signi…cant di¤erencesin the top skewness across countries that have similar technological change. This canprovide an answer to Piketty and Saez’s (2006) question: Why have top wages surged
in English speaking countries in recent decades but not in continental Europe or Japan,
which have gone through similar technological change?
Keywords: Entry costs, Task variety, Skill ‡exibility, Within-top skewness, Below-top
skewness, Entry deregulation, Technological change
JEL Classi…cations: D31, D33, D63, J31, F12, L51
We are very grateful to Timothy Kehoe for his suggestions and advice and to Jim Anderson, Henrique
Basso, Luca Bossi, Serguey Braguinsky, Daphne Chen, Hiroshi Fujiki, Ippei Fujiwara, Rahul Giri, Nobuyuki
Hanaki, Naohisa Hirakata, Hiro Ishise, Mitsuru Katagiri, Munechika Katayama, Sagiri Kitao, Keiichiro
Kobayashi, Takushi Kurozumi, Ben Li, Noriaki Matsushima, Matthew Mitchell, Hiroaki Miyamoto, Robert
Murphy, Ryo Nakajima, Masao Ogaki, Akira Ohtani, Hideo Owan, Ariell Reshef, Roberto Samaniego,
Felipe Schwartzman, Carol Scotese, Yoshimasa Shirai, Juliana Yu Sun, Pin Sun, Robert Tamura, RongshengTang, Takayuki Tsuruga, Mike Veall, Daniel Westbrook, Tomoo Yoshida, and participants in seminars andconferences at Boston College, the Bank of Japan, Kyoto (IER), Osaka (ISER), Keio, the Midwest Macro
Meetings, the JEA Meeting, the WEAI Biennial Paci…c Rim Conference, the NASM of the EconometricSociety, and the AMES for their comments and help. The previous titles of this paper were “Task Variety
and Skill Flexibility: A Simple Uni…ed Theory of Between- and Within-group Inequality”and “Fixed Costs,
Task Variety, and Skill Flexibility: A Simple Uni…ed Theory of Below- and Within-top Inequality.”y
Department of Economics, Florida State University, Tallahassee, FL 32306, USA. Tel.: +1-850-644-7088.
Email: matolia@fsu.edu.
zCorresponding author. Faculty of Humanities and Social Sciences, University of Tsukuba, Tsukuba,
Ibaraki 305-8571, Japan. Tel.: +81-29-853-7426. Email: kurokawa.yoshi.fw@u.tsukuba.ac.jp.

11Introduction

This paper attempts to provide a uni…ed explanation for both an increase in below-top
skewness and a much larger increase in within-top skewness of wage income distribution. It
relies on a single mechanism based on the …xed costs of entry, linking a decrease in entry
costs to an increase in both types of skewness under the assumption that higher-skilledworkers are more ‡exible in handling a variety of tasks. In this paper, we call skewness
below the top 10 percent of the income distribution as “below-top skewness” and skewness
within the top 10 percent as “within-top skewness.”1
One of the most well-known facts relating to income skewness in the U.S. is the increase in below-top skewness: the upper-tail inequality in the bottom 90 percent of income
distribution, such as the ratio of the 90th to the 50th percentile, has risen rapidly but thelower-tail inequality, such as the ratio of the 50th to the 10th percentile, has barely changed
since the late 1960s. Based on Internal Revenue Service (IRS) micro data …les, Dew-Becker
and Gordon (2005)2 recon…rm this fact for the U.S. over 1966–2001.3
Dew-Becker and Gordon (2005), however, go further and …nd a new fact that the skewness within the top 10 percent of the U.S. income distribution has increased substantiallyover the same period and, in fact, it has increased more than the below-top skewness. They
could do so because the IRS micro data …les allow a microscopic view of incomes within the
top 10 percent that the more frequently used Current Population Survey data cannot.4
Dew-Becker and Gordon (2005) then do some simple calculations and show that without
this increased skewness within the top, the increased below-top skewness by itself cannot(1) cause 46 percent (almost half) of the real income gains to go to the top 10 percent5 or(2) cause the mean real income to increase more than the median to the extent implied by
the U.S. data over the same period. Thus, to comprehensively explain the observed changes
relating to U.S. income skewness, models should be able to explain not only below-top
skewness but also within-top skewness. This is a challenge to theorists developing models.
The past studies have provided a separate explanation for each type of skewness. DewBecker and Gordon (2005), for example, argue that while skill-biased technological change
1

It was brought to our attention that in the labor economics literature, authors often discuss betweenand within-group inequality but groups are de…ned by characteristics other than income, such as educationlevel or occupation. For example, in a recent work by Scotese (2012), “between-group inequality” and“within-group inequality” refer to inequality between and within occupations, respectively.
2
See also Dew-Becker and Gordon (2008), which is based on Dew-Becker and Gordon (2005), for a surveyof several aspects of the rising inequality that are usually discussed separately.
3
Dew-Becker and Gordon (2005) calculate real income using the Personal Consumption Expendituresindex. Data on median and mean income are also shown in Table 1 in Gordon (2009).
4
A number of other studies corroborate the new …ndings by Dew-Becker and Gordon (2005) by analyzing
income distribution (1) in a country other than the U.S., such as Germany or Sweden (e.g., Bach et al.,2007; Roine and Waldenström, 2008; Dustmann et al., 2009), (2) across countries (e.g., Piketty and Saez,
2006; Roine and Waldenström, 2011), or (3) during a di¤erent period (e.g., Levy and Temin, 2007; Willis
and Wroblewski, 2007; Kaplan and Rauh, 2010; Thompson and Smeeding, 2010).
5
For example, the bottom 20 percent also gained, but their share of the gains was only 1.7 percent(Dew-Becker and Gordon, 2005).

2

(the bene…ts of which are widespread) plays some role in explaining the observed rise in
below-top skewness, it fails to explain the much larger rise in within-top skewness. They
argue that the “economics of superstars”(Rosen, 1981) and escalating CEO pay premia areneeded to explain the large increase in within-top skewness, particularly skewness within
the top 1 percent.6
This paper, however, attempts to provide a uni…ed, alternative explanation for bothtypes of skewness.7 To do so, we draw attention to the observation that the increase in
the skewness of income distribution was accompanied by the decrease in entry costs inmany developed countries. As shown in Figure 1, there is a positive relationship (solid line)
between the entry cost reduction and income growth of the top 10 percent in 13 countries
over the period 1978–1998.8 The data for the entry cost reduction are from Nicoletti etal. (2001), and the data for the income growth of the top 10 percent are from Atkinson
et al. (2011).9 Here, we want to emphasize that this positive relationship remains even
if the entry cost reduction data are replaced with the 1978–1997 data from Ebell and
Haefke (2009) as in Figure 2 (solid line).10 While this positive relationship is initially notstatistically signi…cant, removing Portugal (which is a distinct outlier in both cases) makes
it both more positive (dashed lines) and statistically signi…cant in both cases.11 Motivatedby this observation, in this paper, we provide a mechanism that links the decrease in entry
costs to an increase in the skewness of income distribution.
The structure of the model is as follows: There are a variety of goods that are di¤erentiated by the …rms that produce them. There are also many types of workers. The productionof each variety is subject to …xed costs of entry and requires combining all varieties of goods
and a speci…c type of labor with a nested CES function. As handling each variety during the
production process and combining it with all other varieties of goods constitutes a di¤erent
6
Dew-Becker and Gordon (2008) broaden this distinction to a three-way distinction between superstars,
highly-paid lawyers and investment bankers, and CEOs. Dew-Becker (2008) focuses on CEO pay in particular.
7This paper focuses on the distribution of labor/wage income. Most of Dew-Becker and Gordon’s (2005)
analysis focuses on labor income but they analyze non-labor income distribution as well. Their results showthat the dominant share of real income gains at the top is as large for labor income as it is for total income,which contradicts economists who believe that the growing inequality is entirely a matter of the dominant
share of non-labor income at the top.
8
The 13 countries are Australia, Finland, France, Germany, Ireland, Italy, Japan, Netherlands, Portugal,
Spain, Sweden, the U.K., and the U.S. We concentrate on developed countries for two reasons. First, entry
cost data are available only for these countries. Second, the mechanism underlying the rise in inequality
may be di¤erent for developing economies with di¤erent structural characteristics.
9
Nicoletti et al. (2001) measure entry costs based on barriers to entry, public ownership, vertical integration, market structure, and price controls. Atkinson et al. (2011) use income tax data (e.g., the IRS data
for the U.S.). Due to the data limitation, the top 5 percent income growth is used for Japan.
10Ebell and Haefke (2009) measure entry costs using the data on entry fee, entry delay, etc.
11
As mentioned in Carrington and de Lima (1996), a number of Portuguese colonies became independent
in the early 1970s, which led to a large scale return of the retornados from former colonies. They alsomention that Portugal did widespread nationalization as it started charting a more socialist path during the1970s and 1980s. These might be possible factors making Portugal an outlier: the increase in top skewness
was large despite low deregulation.

3

task. As a result, we can interchangeably refer to varieties of goods and varieties of tasks.12
Types of labor di¤er with respect to ‡exibility, i.e., their ability to handle the diversityof tasks. Flexibility is measured in terms of the …xed setup costs incurred by a …rm toenable workers to handle diversity of tasks, as described in Mitchell (2005). A worker withgreater ‡exibility is able to handle a given number of varieties of tasks used in production
at lower setup costs.13 A representative consumer with homothetic preferences consumes
all varieties of goods.
We calibrate the key parameters of the model, the labor setup costs and the productivity
parameter, to the wage data for 1979 provided by Dew-Becker and Gordon (2005) and thedata on the cost share of intermediate goods in gross output provided by Jorgenson et al.
(1987), respectively. The reason for calibrating the model to the 1979 data is that the dataon entry costs that we use for our numerical experiments allow us to see the change in entry
costs from 1978 to 1998 and the closest year to 1978 with the wage data is 1979. We alsochoose the values of other parameters based on the evidence.
In our benchmark numerical experiment in the calibrated model, we change entry costs
as in the data. In addition, we change productivity parameter, which measures technologicalchange, to match the change in GDP in the data. We then examine the ability of the model
to match the change in the skewness of the U.S. income distribution. This experiment
allows us to assess the overall impact of two channels— entry deregulation that is our maininterest and technological change that is the central hypothesis in the literature explaining
the increase in U.S. income inequality— on the change in the U.S. income distribution. In
particular, we show how our calibrated model is able to qualitatively and quantitatively
capture the empirical facts regarding changes in both below- and within-top skewness andalso reproduce the related facts on the changes in the mean versus the median and on theshare of the top 10 percent in the income gains. Overall, the results of this benchmark
numerical experiment show a good performance both qualitatively and quantitatively.
In order to separate the contributions of changes in entry costs and technological change
to the overall quantitative performance of the model, we conduct two counterfactual experiments where we allow for: (1) only technological change and (2) only entry deregulation.
The …rst counterfactual experiment indicates that technological change does not have quantitatively important impact on the skewness of wage distribution. The second counterfactual
experiment, on the other hand, indicates that entry deregulation and the resulting change
in entry costs can result in a quantitatively important increase in income skewness that is
12This is similar to the task-based-model literature in which a variety of goods used in production are
construed as a variety of tasks. For examples of this interpretation, see Mitchell (2005), Grossman andRossi-Hansberg (2008), and Blanchard and Willmann (2016).
13
While we consider worker ‡exilibity, Campbell and Fisher (2004), for example, consider producer ‡exibility. In their model, increasing idiosyncratic risk induces a producer to substitute workers away fromstructured jobs that are costly to create and destroy and towards unstructured jobs that are costless. This
substitution leaves the producer’s employment more responsive to both idiosyncratic and aggregate disturbances.

4

consistent with the empirical facts mentioned above.
The key mechanism driving the results for entry deregulation is very simple. The reduction in entry costs increases the number of varieties produced, which directly increases
the marginal products of labor of all types but the increase in the marginal products ofthe more-‡exible labor with lower setup costs is disproportionately large. This is because
a given decrease in entry costs corresponds to a larger decrease in total …xed costs— entry
costs plus labor setup costs— for …rms employing more-‡exible workers with lower setup
costs. Thus the relative demand and wages of the more-‡exible labor increase, which makes
the wage distribution more unequal.
It is worth emphasizing that our main mechanism is also consistent with available evidence. We link a decrease in entry costs to an increase in top skewness under the assumptionthat higher-skilled workers are more ‡exible in handling a variety of tasks. First, this link
between entry costs and top skewness is compatible with the data shown in Figures 1 and2. The countries with a greater reduction in entry costs have witnessed a larger growth in
the income share of the top 10 percent. Second, the assumption about ‡exibility is also
compatible with the data on Stanford business school alumni and Denmark’s registry data.
Using data on Stanford business school alumni, Lazear (2005, 2012) empirically con…rmedthat leaders, top income earners such as CEOs, are ‘generalists’who are competent in manyskills, i.e., are highly ‡exible.14 Using Denmark’s registry data, Frederiksen and Kato (2017)
extended Lazear’s analysis to the population of Danish workers and empirically con…rmedthat becoming a generalist is advantageous for career success.
Of course, there are a number of recent studies that strive to explain the causes andunderstand the e¤ects of the observed changes in the skewness of wage income distribution.
For example, one set of studies attempts to provide job-polarization-based explanations forthe increase in below-top skewness (upper-tail inequality in the bottom 90 percent of income
distribution has risen rapidly but lower-tail inequality has barely changed).15 Here, “jobpolarization” refers to employment shifts into high- and low-wage jobs at the expense of
middle-wage jobs (Goos and Manning, 2007). For example, Autor et al. (2006) and Goldin
and Katz (2007) both argue that computers strongly complement the non-routine tasks ofhigh-wage jobs, directly substitute for the routine tasks found in many traditional middlewage jobs, and may have little impact on the non-routine manual tasks of many low-wage
jobs. Furthermore, they note that this pattern of demand shifts appears to be reinforced
by international outsourcing and o¤shoring. In fact, Blanchard and Willmann (2016) builda model in which trade can cause job polarization, and they derive policy implications
regarding the potential di¤erential impacts of strengthening educational institutions versus
trade protection. Furusawa and Konishi (2013) also link trade to wage polarization.
Another set of studies attempts to analyze the e¤ects of increased income skewness
14
15

1/3 of the top 1 percent incomes go to CEOs in the U.S. (Bakija et al., 2012).
By comparison, Palley (2007) argues that …nancialization is a factor of the increased income inequality.

5

on phenomena such as equity returns and …nancial crises. For example, Walentin (2010)
develops a model to study the e¤ects of increased labor income skewness on equity prices
through an increase in stockholders’ share of aggregate labor income. Fitoussi and Saraceno (2010) and Hein (2011) both argue that increased income skewness can contribute to…nancial crises.
Our paper makes the following contributions to this line of studies. First, previous
studies have paid signi…cant attention to below-top skewness but little attention to withintop skewness due to the limitations of data. Although Dew-Becker and Gordon (2005)
look at both below- and within-top skewness, as mentioned above they suggest a separate
explanation for each, i.e., a di¤erent mechanism for each. They argue that while skill-biased
technological change (the bene…ts of which are widespread) plays some role in explaining
the observed rise in below-top skewness, the economics of superstars and escalating CEOpay premia are needed to explain the large increase in within-top skewness.16 However,
our paper provides a uni…ed explanation for both types of skewness. That is, it uses asingle mecanism based on entry costs, demonstrating that through a change in task variety,a decrease in entry costs due to entry deregulation can cause an increase in below-top
skewness as well as a much larger increase in within-top skewness. Thus, while Dew-Becker
and Gordon (2005) view below- and within-top skewness arising for di¤erent reasons, theseare just two variations of the same phenomenon in our model, that is, both below- andwithin-top skewness are results of the di¤erences in ‡exibility among workers.17
Second, our benchmark and counterfactual numerical experiments imply that di¤erencesin entry deregulation can cause signi…cant di¤erences in the top skewness between countries
that have similar technological change. Thus, our paper provides an answer to the question
posed by Piketty and Saez (2006): Why have top wages surged in English speaking countries
in recent decades but not in continental Europe or Japan, which have gone through similar
technological change? In fact, as Figures 1 and 2 indicate, entry deregulation has been
more pronounced in English speaking countries. Jones and Kim (2018) also answer thesame question. They argue that top skewness is determined by the interaction between two
mechanisms. The one is that existing entrepreneurs expend e¤ort to increase the pro…ts
from their existing ideas, which increases top skewness. The other is that outside innovators
seek new ideas to replace incumbents in a process of creative destruction, which decreases
top skewness. Economic forces, such as globalization, that a¤ect these two mechanisms
may explain di¤erences in the top skewness between countries. Thus they provide a twomechanism-based answer, whereas our paper provides a single-mechanism-based one.
The rest of this paper is organized as follows: We develop our simple model in Section
16

As mentioned in Dew-Becker and Gordon (2005, 2008), the increased superstar premia can also beinterpreted as a result of a particular type of skill-biased technological change (e.g., the development of CDs,
downloaded internet music, cable television, and other forms of “audience magni…cation”). They, however,still distinguish a cause of the increased CEO pay premia from that of the increased superstar premia. They
argue that the CEO premia could depend on stock market valuations.
17
Gabaix and Landier (2008) attribute the income di¤erence within the top workers to …rm size.

6

2. Section 3 explains our calibration. In Section 4, we conduct our numerical experiments
and also derive an important implication on Piketty and Saez’s (2006) question. Section 5
concludes.

2

Model

Consider a country in which there are a variety of goods that are di¤erentiated by the …rms
that produce them. Those goods produced are used both for consumption as …nal goods andfor production as intermediate goods. There are also I types of workers i = 1; 2; ::; I:18 The
production of each variety requires the combination of all varieties of goods and a speci…ctype of labor. The country has a given endowment of each type of labor equal to Li .
Handling each variety of good during the production constitutes a di¤erent task. Typesof labor di¤er in their ‡exibility to handle the diversity of tasks, which is measured by …xed
setup costs ai , as it is in Mitchell (2005). Higher i re‡ects a greater ‡exibility/ability tohandle task diversity, which translates into lower setup costs ai so that a1 > a2 > ::: > aI :Therefore, higher i corresponds to higher skill in our model. As we will show later, more‡exible workers have higher wages, and particularly, the most ‡exible workers have top
wages. This is consistent with the evidence that top income workers such as CEOs are‘generalists’(Lazear, 2005, 2012) who are competent in many skills, i.e., are highly ‡exible.
A representative consumer solves the problem of maximizingu = C;(1)subject to19
PI

i=1 wi Li ;

qC
C

(2)

0:

Here, C is the CES consumption aggregator for the consumer and q is its price. wi is thewage for labor i. The CES aggregator C of di¤erent varieties is given by
C=

Z

1

(Cz ) dz

;

(3)

D

where parameter ;< 1; governs the elasticity of substitution, 1= (1), between any

two di¤erentiated varieties in the interval D = [0; n] of the varieties of goods.
The technology for producing goods exhibits increasing returns to scale because of the18

As will be shown later, the assumption that there are I types of workers allows us to analyze changes ininequality, such as the top/bottom ratio, the medium/bottom ratio, and the increased skewness within thetop, in a simple manner.
19
As will be shown later, we allow free entry of …rms, which makes the pro…t of each …rm zero. Thus there
is no pro…t in the consumer’s budget.

7presence of …xed costs. Speci…cally, every …rm z 2 Di , i = 1; 2; ::; I, has the production
functionyz;i = max

8 "
Z
<1
:A

D

xz 0 ;z dz0"=+ (li;z

ai )"

#1="

9
=
F; 0 ;;

z 2 Di ;(4)0where A > 0 is a productivity parameter and xz 0 ;z and li;z refer to variety z and worker
i, respectively, used in the production of variety z. Thus, production requires varieties andworkers with a nested CES function.20 Here, …rms face …xed costs of entry F > 0 in termsof output, which are common across all …rms. As mentioned above, …rms also face …xed
setup costs for labor ai , which are di¤erent across types of …rms but the same across …rms
using labor type i. One might think of ai as training costs that depend on labor type i.
We note that due to ai this production function is non-homothetic. Thus, total …xed costs
consist of entry costs F in terms of output and setup costs ai . For the results of this paper,
the critical distinction between the two components of total …xed costs is that F does notdepend on the type of labor employed whereas setup costs do. The manner in which thesedi¤erent components of …xed costs are modeled is not critical to the results.
It is important to note that although all …rms create this composite good in-house,
we assume that the same CES aggregator is used by all …rms (and consumers) to convert
varieties into a composite good. We assume it only to simplify aggregate demand functions
for the varieties.
Let c~z (q; wi ; yz;i +F; ai ) be the solution to the cost minimization problem for …rm z 2 Di :Given that each …rm produces output using a nested CES function with workers and acomposite input made from varieties as inputs, the cost function can be written in terms of
the sub-cost functions as follows:c~z (q; wi ; yz;i + F; ai ) = wi ai + cz (q; wi ) (yz;i + F );where
cz (q; wi ) = A q

"
1 "

+ wi

"
1 "

1 "
"

:

(5)

(6)

Thus, we can write c~z (:) as a linear function of yz;i + F :c~z (q; wi ; yz;i + F; ai ) = G1;i + G2;i (yz;i + F ) ;z 2 Di ;(7)

where G1;i and G2;i are independent of a …rm’s choices.
The …rms are monopolistic competitors facing a downward sloping demand curve, and20
The …rms in the model use one type of labor. This can be rationalized by interpreting them as real-world,
within-…rm units that employ workers with similar skills. In any case, in our numerical computations, …rms
in the model never …nd it optimal to combine labor of di¤erent types.

8…rm z 2 Di sets its price qz;i to maximize pro…ts:maxz;i = qz;i yz;iG1;iG2;i (yz;i + F ) ;(8)taking all other prices as given.
Let us derive the demand for each variety z 2 Di ; yz;i . The demand by the consumer

for variety z 2 Di is:

1

qz;i
q

Cz;i =

1PI

i=1 wi Li

q

;

(9)

where q can be written as an exact consumption-based price index of the prices of individual
varieties as follows:
q=

Z

1

(qz )

dz

1

;

(10)

D

where D is the set of all varieties, as de…ned earlier. Hence, we can write the consumption
demand for variety z 2 Di faced by the …rm as
1

Cz;i = Eqz;i1
where
E=

PI

;

i=1 wi Li

q

(11)

:

(12)

1

Thus, the consumption demand varies with price qz;i with elasticity

1= (1

).

We can also write the demand for input by each …rm for variety z 2 Di as1xz;z 0 = Ti qz;i1
where
Ti = Aascz (q; wi )
Aq

;

(13)

1
1 "

(yz;i + F )

1
q

1
1

:

(14)

Thus, the total consumption and input demand for variety z 2 Di ; yz;i ; can be expressed
1yz;i = T qz;i1
where
T =E+

;

z 2 Di ;(15)PI

i=1 ni Ti ;(16)which is again independent of a …rm’s choices.

Hence, given the number of varieties, the pro…t of …rm z 2 Di can be rewritten as11z;i = qz;i T qz;i

1G2;i T qz;i1

9

G1;i

G2;i F:(17)

The …rst order condition for pro…t maximization with respect to qz;i then gives
qz;i =

G2;i;z 2 Di :(18)

Further, we allow free entry. Then, by the zero pro…t condition for this qz;i ,
z;i =

G2;i

yz;i

G2;i (yz;i + F )we obtainyz;i =

F+

1

G1;i
G2;i

;

G1;i = 0;(19)

z 2 Di :(20)

De…nition 1 An equilibrium is a vector of prices fqz;i ; wi gIi=1 and quantities fC z;i ; yz;i ; li;z gIi=1 ;xz 0 ;z ; (z 0 ; z) 2 D

D and an interval D = [0; n] such that:

1. Given the prices, the consumption plans Cz;i solve the utility maximization problemof the consumer;
2. Given factor prices, price qz;i and production plans (including the factor demands) of
the …rm z maximize pro…ts and minimize costs;
3. Every …rm z 2 D earns zero pro…ts;
4. The markets for goods clear
Cz;i +

ZD

xz;z 0 dz 0 = yz;i ;z 2 Di ;(21)

5. The factor markets clear
ni li;z = Li ;i = 1; 2; ::; I;(22)

where ni is the measure of Di ;6. The number of varieties available for consumption is the number of varieties produced,
D = [Ii=1 Di = [0; n]:3

Calibration

In this section, we describe the calibration of the model. Table 1 shows the values of theparameters calibrated or chosen based on empirical evidence.
10

We begin by choosing the values of some of the parameters based on the available
evidence. We choose= 5=6, which implies a 20 percent markup for the monopolisticallycompetitive …rms. This 20 percent markup is in accordance with the evidence relating to
manufacturing industries in OECD countries presented by Martins et al. (1996). We alsochoose " = 1=6 so that the elasticity of substitution between inputs and labor, 1=(1"),

is 1.2. This is compatible with Rotemberg and Woodford’s (1992) estimate. Basu (1995)
notes that this elasticity (1.2) looks relatively large but is not surprising if service inputs areincluded. In fact, in our model, there is no distinction between varieties of manufactured
or service inputs.
We next normalize the values of the …xed cost of entry, F , and the price index, q, to 1
and turn to calibrating the key parameters: the …xed setup costs, ai , and the productivity
parameter, A. We calibrate the setup costs so that the wage distribution generated by themodel reproduces some of the major characteristics of the wage data for 1979 provided by
Dew-Becker and Gordon (2005).21 The decision to use 1979 data is guided by the fact that
we have data on the change in entry costs from 1978 to 1998 which we use in our numericalexperiments in the next section and 1979 is the closest year to 1978 for which wage data
is available. As we use the pro…le of wage distribution to calibrate setup costs, without
loss of generality, we can divide the pool of workers into multiple types of equal measure.
In particular, we set I = 20, so that there are 20 types of workers, each corresponding
to a ventile. All types have the same measure with Li = 5 for i = 1; 2; :::; 20. Twenty is
the minimum number of types needed to calibrate and analyze skewness within the top 10
percent. Types 19 and 20 constitute the top 10 percent, and thus type 19 versus type 20
is skewness within the top 10 percent. The average of workers of types 10 and 11 is themedian. With the normalization of the setup costs for the most ‡exible worker a20 = 0, we
calibrate values of a1

a19 . Then, as shown in Figure 3, the wage distribution generated by

the model exactly captures the wages for the 20th , 50th , 80th , 90th , 95th , and 99th percentiles
in the data. As also evident from Figure 3, the wage distribution curve has been generated
through a smooth inter/extrapolation of the wages of 20 di¤erent types of workers that are
generated by the model.
Lastly, we calibrate the productivity parameter, A. This parameter a¤ects the cost shareof labor in gross output. We, therefore, calibrate the value of A so that the cost share oflabor in gross output is 0.5 and so is the cost share of intermediate goods. This is compatible
with the evidence provided by Jorgenson et al. (1987) that the share of intermediate inputs
in total manufacturing output is 50 percent or more over the period 1947–1979.
21

For the 1979 wage data, see the top panel “Real and Adjusted Wage and Salary Percentiles in Year 2000
Dollars, Selected Years, 1966-2001” in Table 8 in Dew-Becker and Gordon (2005).

11

4

Numerical Experiments

In this section, we assess the ability of the model to reproduce the changes in the U.S. wage
income distribution over 1979–1999. In our benchmark experiment, we do so by accounting
for both entry deregulation that is our main interest and technological change that is thecentral hypothesis in the literature explaining the increase in U.S. income inequality. Next,
we also conduct two counterfactual experiments allowing for: (1) only technological changeand (2) only entry deregulation. In each experiment, we see how our calibrated model canqualitatively and quantitatively capture the facts on both below- and within-top skewness
and also reproduce the related facts on the mean versus median and on the share of the top
in the gains.

4.1

Entry Deregulation, Technological Change, and Skewness of Income
Distribution

We begin with the bechmark experiment. To capture entry deregulation, we decrease the…xed costs of entry, F , by 65 percent. This is in accordance with the evidence (see Figure 1)
for the U.S. over 1978–1998 provided by Nicoletti et al. (2001). This decrease corresponds
to a 20.354 percent reduction in total …xed costs. Technological change is not directly
observable. We account for it indirectly by decreasing (inverse) productivity parameter,
A, by 4.92 percent to allow for gross output to increase by 41.2 percent over 1979–1999.
This is in accordance with the evidence for the U.S. productivity growth presented by DewBecker and Gordon (2005). According to them, the average productivity of the nonfarm
private business (NFPB) sector in the U.S. grew at the rate of 1.74 percent over 35 years(1966–2001) implying a productivity growth of 41.2 percent over 20 years.22,23
We, then, examine the ability of the model to match the change in the skewness of the
U.S. income distribution. This experiment allows us to assess the overall impact of twochannels— entry deregulation and technological change— on the change in the U.S. income
distribution.
The resulting change in wage distribution is shown in Figure 4, which shows that themodel is able to generate a substantial increase in skewness, especially within the top.
Ironically, it generates too much within-top skewness relative to the data. More detailed
quantitative performance based on measures used in the literature (see Table 2) can besummarized as follows:
1. Change in below-top skewness: In the data, from 1979 to 1999 the ratio of the 50th
to the 20th percentile decreased by 0.52 percent, and the ratio of the 90th to the50th percentile increased by 19.23 percent with a di¤erence between the two of 19.75
22

According to Dew-Becker and Gordon (2005), the average productivity growth over the same 1966-2001
period for the entire economy is 1.57 percent.
23
In our model, productivity growth and output growth are equivalent.

12percentage points.24 In this experiment, these ratios respectively decrease by 1.62
percent and increase by 7.93 percent, which implies a di¤erence of 9.55 percentage
points.
2. Change in within-top skewness: In the data, from 1979 to 1999 the ratio of the 99th
to the 90th percentile increased by 32.74 percent. In this experiment, it increases by
79.85 percent.25
3. Change in mean versus median: In the data, from 1979 to 1999 the mean increasedby 45.71 percent while the median increased by 3.43 percent with the di¤erence being
42.28 percentage points.26 In this experiment, the mean rises by 37.41 percent while
the median rises by 19.12 percent, which implies a di¤erence of 18.29 percentage
points.
4. Share of the top 10 percent in total real wage gains: In the data, 54.61 percent of total
real wage gains over 1979–1999 went to the top 10 percent.27 In this experiment, it
was 57.75 percent.
It is worth mentioning that, in this experiment, the top 6.7 percent of workers experience
above-average wage growth. In the data, this number is 10 percent.
Overall, the results of this experiment show a good performance both qualitatively andquantitatively. The performance of the model vis-a-vis facts 1 and 3 above is a bit inferior.
It may be pointed out that this is mainly driven by a much larger increase in the medianin the model. In the next subsections, we separate the contributions of entry deregulationand technological change to the overall quantitative performance of the model.

4.2

Counterfactual Experiment 1: Only Technological Change

In order to assess the role of technological change in the above change in wage income
distribution, we now only change the productivity parameter, A. Speci…cally, keeping the…xed costs of entry, F , unchanged at the initial value 1, we decrease the (inverse) productivity parameter, A, by 4.92 percent as in the benchmark experiment. The resulting change
in wage distribution shown in Figure 5 seems to suggest that technological change does areasonable job of capturing changes in the below-top part of the wage income distribution,
while it clearly fails to generate enough within-top skewness. More detailed quantitative
performance based on measures used in the literature (see Table 2) can be summarized asfollows:
24

See Dew-Becker and Gordon’s (2005) Table 8. For the ratios for 1999, we take a geometric average ofthe data for 1997 and 2001.
25
See footnote 24.
26
The mean is calculated from the data in Dew-Becker and Gordon’s (2005) Table 2. The median for 1999
is a geometric average of that for 1997 and 2001 in Dew-Becker and Gordon’s (2005) Table 8.
27
See Dew-Becker and Gordon’s (2005) Table 7. For calculating the level of real wage of the top 10 percent
for 1999, we take an arithmetic average of that for 1997 and 2001.

13

1. Change in below-top skewness: In the data, from 1979 to 1999 the ratio of the 50th
to the 20th percentile decreased by 0.52 percent, and the ratio of the 90th to the 50th
percentile increased by 19.23 percent with a di¤erence between the two of 19.75 percentage points. In this experiment, these ratios respectively decrease by 0.86 percent
and increase by 1.86 percent, which implies a di¤erence of 2.72 percentage points.
2. Change in within-top skewness: In the data, from 1979 to 1999 the ratio of the 99th
to the 90th percentile increased by 32.74 percent. In this experiment, it increases by
5.96 percent.
3. Change in mean versus median: In the data, from 1979 to 1999 the mean increasedby 45.71 percent while the median increased by 3.43 percent with the di¤erence being
42.28 percentage points. In this experiment, the mean rises by 13.92 percent while themedian rises by 11.95 percent, which implies a di¤erence of 1.97 percentage points.
4. Share of the top 10 percent in total real wage gains: In the data, 54.61 percent of total
real wage gains over 1979–1999 went to the top 10 percent. In this experiment, it was
34.91 percent.
In this experiment, the percent of workers with the above-average wage growth is the
top 10.77 percent, while it is the top 10 percent in the data.
As can be seen, this technological change is skill biased since this productivity growthincreases the relative demand for more-‡exible labor. Because higher skill corresponds togreater ‡exibility in our model, this technological change shows a positive skill bias. However, comparing the results of this counterfactual experiment with those of the benchmark
experiment indicates that the skill bias of technological change does not have quantitatively
important impact on the skewness of wage distribution. While visually its performance in
explaining changes in below-top part of income distribution seems reasonable, quantitative
assessment vis-a-vis facts 1 to 4 suggests otherwise.

4.3

Counterfactual Experiment 2: Only Entry Deregulation

In this counterfactual experiment, we assess the role of entry deregulation in generating
the increase in skewness of wage income distribution in the benchmark experiment. We
do so by only changing the …xed costs of entry, F . Speci…cally, we keep the productivity
parameter, A, unchanged at the initial level, and decrease entry costs, F , by 65 percent as
in the benchmark experiment. The resulting change in wage distribution is shown in Figure
6, which clearly shows the ability of entry deregulation to explain changes in within-top
skewness. More detailed quantitative performance based on measures used in the literature(see Table 2) can be summarized as follows:
1. Change in below-top skewness: In the data, from 1979 to 1999 the ratio of the 50th
to the 20th percentile decreased by 0.52 percent, and the ratio of the 90th to the 50th14

percentile increased by 19.23 percent with a di¤erence between the two of 19.75 percentage points. In this experiment, these ratios respectively decrease by 0.76 percent
and increase by 6.64 percent, which implies a di¤erence of 7.4 percentage points.
2. Change in within-top skewness: In the data, from 1979 to 1999 the ratio of the 99th
to the 90th percentile increased by 32.74 percent. In this experiment, it increases by
66.37 percent.
3. Change in mean versus median: In the data, from 1979 to 1999 the mean increasedby 45.71 percent while the median increased by 3.43 percent with the di¤erence being
42.28 percentage points. In this experiment, the mean rises by 19.46 percent while themedian rises by 6.01 percent, which implies a di¤erence of 13.45 percentage points.
4. Share of the top 10 percent in total real wage gains: In the data, 54.61 percent of total
real wage gains over 1979–1999 went to the top 10 percent. In this experiment, it was
70.15 percent.
In this experiment, the percent of workers with the above-average wage growth is the
top 6.77 percent, while it is the top 10 percent in the data.
The primary implication of this counterfactual experiment is that entry deregulation
can result in a quantitatively important increase in the skewness of wage distribution thatis consistent with the empirical facts outlined above. Comparing the results of this counterfactual experiment 2 with those of counterfactual experiment 1 reveals that the impact
of entry deregulation is quantitatively much more important than that of the technologicalchange.
The key mechanism driving the results of this experiment is actually very simple. The
reduction in entry costs, F , results in a signi…cant proliferation of the number of varieties
produced. The number of varieties that are produced using type i labor, ni , increases for
all i. The overall number of varieties n (= n1 + ::: + n20 ) increases by about 180 percent(177.21 percent). This rise in n directly increases the marginal products of labor of all types
but the increase in the marginal products of the more-‡exible labor with lower …xed setup
costs, ai , is disproportionately large. This is because a given decrease in F corresponds to alarger decrease in total …xed costs— entry costs plus labor setup costs— for …rms employing
more-‡exible workers with lower setup costs. For example, the ratio of the total …xed costsof …rms employing the most ‡exible workers to those employing the least ‡exible workers
falls by about 59 percent. As a result, the relative demand and wages of the more-‡exible
labor rise, which causes the wage distribution to become more unequal, as shown in Figure
6. Note that as the more-‡exible sectors (like every sector) use the composite intermediate
input produced using all intermediate varieties, there is an indirect increase in the demand
for the less-‡exible labor as well. Overall, therefore, wages rise for all types of labor, but
wages of the more-‡exible labor increase more. For example, in this experiment, w1 rises
by 5.07 percent whereas w20 rises by 63.40 percent.
15

To understand the mechanism in more detail, note that the reduction in F increases thenumber of varieties produced by all labor types. However, the proportionally large decreasein F results in a disproportionately larger increase in the number of varieties produced by
the more-‡exible labor. This can be seen from looking at the distribution of varieties for thecase of only entry deregulation in Figure 7 (left panel). Speci…cally, n1 rises by only 0.32
percent while n20 rises by 301.81 percent! This relative increase in the number of varieties
produced by more-‡exible labor translates into an increase in these varieties’share in GDP,as shown in Figure 7 (right panel). In contrast, these two e¤ects are very weak for the caseof only technological change as a look at the distribution of varieties and GDP share forthat case reveals.
As the amount of each type of labor, Li , is …xed, an increase in ni implies that the size ofeach type of …rm i, measured by the size of employment, decreases. Then the employment
size of …rms using the more-‡exible workers shows a larger decrease. This is because while
Li is …xed, ni shows a larger increase for …rms using the more-‡exible labor as has shownin Figure 7. The average size of …rms, measured by output, also decreases from 22.12 to
8.65.28 This implication of the model is consistent with the evidence documented by, e.g.,
Davis and Haltiwanger (1991) and Mitchell (2005). Both of these studies show that the sizeof U.S. manufacturing plants declined during the second half of the 20th century.
Though we do not report the results here, as an alternative experiment we also decrease
entry costs, F , by 88.45 percent. This is in accordance with the evidence for the U.S. over
1978–1997 provided by Ebell and Haefke (2009), which has been shown in Figure 2. As
expected, this can result in a more quantitatively important increase in the skewness ofwage distribution.

4.4

An Answer to Piketty and Saez’s (2006) Question

Our numerical experiments suggest an answer to the following question posed by Piketty andSaez (2006): Why have top wages surged in English speaking countries in recent decades
but not in continental Europe or Japan, which have gone through similar technologicalchanges? In fact, as shown in Figures 1 and 2, the increase in top incomes in the U.S. since
the late 1970s was much greater than in continental Europe and Japan (see also Dew-Becker
and Gordon, 2008).
A comparison of our benchmark and counterfactual numerical experiments readily showsthat technological change is not that important a source of increased skewness of the wage
income distribution. On the other hand, entry policy possibly is. This, in turn, implies thatdi¤erences in entry deregulation can cause signi…cant di¤erences in the top skewness between
countries that have similar technological change. Thus, our paper suggests di¤erences inentry policy changes as one explanation for these di¤erences in the experience of English
speaking countries versus continental Europe or Japan.
28

The average size of …rms, measured by the value of output, also decreases from 27.10 to 11.84.

16

To be more explicit, consider our benchmark experiment and counterfactual experiment
1. In both experiments, technlogical change is the same, but the former also has entry
deregulation. Their results together show that entry deregulation is a very powerful driver to(top) income skewness. Thus, countries with similar technological change but with di¤erent
experiences vis-a-vis entry deregulation can have signi…cant di¤erences in the evolution of(top) income skewness, which can provide an answer to Piketty and Saez’s (2006) question.
Consider, for example, the U.S. and Japan. According to Nicoletti et al. (2001) (seeFigure 1), over 1978–1998 the entry costs decreased by 44 percent in Japan and by 65
percent in the U.S. Thus Japan showed a lesser decrease in entry costs than the U.S.
This might be a factor responsible for a lesser increase in top income skewness in Japan
compared to the U.S. It is worth mentioning other factors that might also be weakening
the top skewness in Japan. As Ito (1992), for example, documents, one characteristic of
the Japanese labor market is rotation, pursuant to which workers rotate through di¤erent
tasks requiring various skills early in their careers. “It is sometimes said that in Japan ageneralist is valued more than a specialist”(Ito, 1992, p. 214). It is thus possible that, due
to rotation, the share of ‡exible workers is larger in Japan and the top skewness is therefore
smaller in Japan than in the U.S.

5

Conclusion

The main purpose of this paper was to develop a simple model that provides a uni…ed
explanation of the facts on both below- and within-top skewness. It linked a decrease in
the …xed costs of entry to an increase in top income skewness under the assumption thathigher-skilled workers are more ‡exible in handling a variety of tasks. Using a calibrated
model, our numerical experiments showed that by increasing task variety, a decrease inentry costs due to entry deregulation can be a quantitatively important source of such wage
income changes. Moreover, the numerical experiments implied that the observed di¤erencesin entry deregulation signi…cantly cause di¤erences in the top skewness between countries
that have similar technological changes, which can provide an answer to Piketty and Saez’s(2006) question.
This paper focused on entry deregulation and technological change as factors a¤ecting
wage income skewness. As Dew-Becker and Gordon (2005, 2008) argue, however, unions,immigration, and trade could be also possible factors.29 We leave the assessment of contributions of these factors to income skewness to future research.
29

Dew-Becker and Gordon (2005, 2008) also discuss unions, immigration, and trade as other factorsa¤ecting the below-top inequality. Dew-Becker and Gordon (2008) go beyond these three factors to also
discuss the real minimum wage and the progressivity of taxation.

17

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21

Parameter values= 5=6" = 1=6

Targets
20 percent markup
Elasticity of substitution of 1.2
between intermediate inputs
and laborai
U.S. real wage data for 1979
A = 26:92
50 percent share of intermediate
goods in output
Normalizations: F = q = 1; I = 20; Li = 5:

Based onMartins et al. (1996)
Rotemberg and Woodford (1992)

Dew-Becker and Gordon (2005)
Jorgenson et al. (1987)

Table 1: The parameterization of the model

P50/P20
P90/P50
P99/P90
Mean
MedianTop 10%’s share in gains

Data(1979–1999)–0.52%+19.23%+32.74%+45.71%+3.43%
54.61%

Both–1.62%+7.93%+79.85%+37.41%+19.12%57.75%

Only
technologicalchange–0.86%+1.86%+5.96%+13.92%+11.95%34.91%

Only
entry
deregulation–0.76%+6.64%+66.37%+19.46%+6.01%
70.15%

Table 2: The data and the results for numerical experiments

22Portugal

Top 10% income share growth (%)
0
10
20
30

40

UK

US
Ireland

Australia
Italy
FinlandGermanyJapan

SwedenSpain
Netherlands

France20

40
Entry cost reduction (%)

60

80

Figure 1: Nicoletti et al. (2001) and Atkinson et al. (2011), 1978-1998
Portugal

30

US
Ireland20

Australia
Italy

10

Germany
FinlandJapan

SwedenSpain

Netherlands
France0

Top 10% income share growth (%)

40

UK

20

40
60
Entry cost reduction (%)

80

100

Figure 2: Ebell and Haefke (2009) and Atkinson et al. (2011), 1978-1997

23

wage
99 th

5

4

w 19 95 th

3

Wages w i
w 15

Initial Data

2

w 13

w 17

90 th

80 th

w 11
1
w1

w5

w3
20

w9

w7

50 th

th

Percentile

20

40

60

80

100

Figure 3: Calibrated wage distribution
wage

10

Initial8

FinalInitial Data

6

Final Data

4

2

Percentile
20

40

60

80

100

Figure 4: Benchmark experiment
wage

10

InitialOnly Technological Change

8

Final with Both
6

Initial Data
Final Data

4

2

Percentile
20

40

60

80

100

Figure 5: Counterfactual experiment 1 with only technological change

24

wage

10

InitialOnly Entry Deregulation

8

Final with Both
6

Initial Data
Final Data

4

2

Percentile
20

40

60

80

100

Figure 6: Counterfactual experiment 2 with only entry deregulation

Varieties
20
15
10

GDP Share
30

Initial25

Only Technological Change

20

Only Entry Deregulation

15

Final with Both

10

5

InitialOnly Technological Change
Only Entry Deregulation
Final with Both

5

5

10

15

20

Type of Labor , i

510Figure 7: Distributions of varieties and GDP share

25

15

20

Type of Labor , i