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Essays on macroeconomics and income distribution

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Content Essays on Macroeconomics and Income Distribution
by
Wenjing Chu
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulllment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(Economics)
December 2018
Copyright 2018 Wenjing Chu
To my father
ii
Acknowledgements
First of all, I would like to thank my academic advisor, Professor Vincenzo Quadrini, without
whose continuous support and encouragement I could not have done my thesis. I am very grateful
for his guidance and advice whenever I have diculties. He gave me a lot of freedom to pursue
the research that interests me, and tolerated me for my mistakes and my detours. I am amazed
by his sheer intelligence, and the way he thought about a research problem and asked inspiring
questions.
I would also like to thank my co-advisor, Professor Robert Dekle, without whom I could not
have the couragement to push my limit to be on the market. I was deeply grateful for every bit
of kindness he had shown to me. I am indebted to him for providing support and advice for my
study in the graduate school.
I want to take this opportunity to give special thanks to Professor Jerey Nugent who is also
my dissertation committee member. It was his contious support that gave me the opportunity to
spend the last six years focusing on the research work I am interested in.
I would also like to thank Dr. Mohammad Safarzadeh for whom I worked as Teaching Assistant
for ve semesters. Without his tolerance and support I could not have great work life balance
during my study. I would also like to say thank Professor Joel David, Miao Zhang and Dr. Erik
Meijer for their support in the qualifying and defense exam, respectively.
I would also like to thank my colleagues and friends at USC: Rui He, Mingming Ma, Fengyu
Wu, Junjie Xia, Dawoon Jung, Yaoyao Zhu, Urvashi Jain, Tushar Bharati, Jorge Andres Tamayo,
Qingjiao Li, and Xiaojing Xing. My thanks also extend to a number of faculties and stas at the
iii
Department of Economics. They help me in many aspects in my research and my life, and make
my PhD life much more colorful.
Finally, I would like to thank my family. My gentle, trustworthy and intelligent husband,
Yuanzhang, always believes in me. My parents always give me their generous love. My dear sons
always brighten my dark days. My in-laws always oer help whenever I need. Their love gets me
through my PhD career.
iv
Table of Contents
Acknowledgements iii
List Of Tables vii
List Of Figures viii
Abstract x
Chapter 1: Production Function and Income Distribution 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 The Stylized Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.1 Cross Section Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 The Basic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3.1 The Labor Share of Income . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3.2 The Elasticity of Subsitution between Capital and Labor . . . . . . . . . . 6
1.3.3 Micro and Macro Production Function . . . . . . . . . . . . . . . . . . . . . 9
1.4 The Empirical Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.5 The Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Chapter 2: Intangbile Capital, Corporate Savings and Labor Share of Income 24
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2 The Stylized Facts and Empirical Evidence . . . . . . . . . . . . . . . . . . . . . . 35
2.2.1 Aggregate Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.2.1.1 Time series wise: US and China aggregate . . . . . . . . . . . . . 35
2.2.1.2 Time series wise: UN and OECD countries . . . . . . . . . . . . . 36
2.2.1.3 Cross-Section wise: UN and OECD countries . . . . . . . . . . . . 36
2.2.2 The Empirical Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.3 The Baseline Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.3.1 Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.3.2 Household . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.3.3 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.4 The Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.4.1 Measured Labor Share of Income . . . . . . . . . . . . . . . . . . . . . . . . 47
2.4.2 Financial Frictions and Pledgeability of Intangible Capital . . . . . . . . . . 48
2.4.3 Accumulation of Intangible Capital . . . . . . . . . . . . . . . . . . . . . . . 49
2.5 Quantitative Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.5.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.5.2 Comparative Statics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.5.3 Accumulation of Intangible Capital . . . . . . . . . . . . . . . . . . . . . . . 52
v
2.6 Literature Revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.6.1 Koh et al., 2015 Revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.6.2 Barkai, 2017 Revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.7 The Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Bibliography 62
Appendix A
Appendix for Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
Appendix B
Appendix for Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
B.1 Details about Various Data Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
B.1.1 Country and Industry Data in Advanced Economies . . . . . . . . . . . . . 73
B.1.2 Firm Level Data in the United States . . . . . . . . . . . . . . . . . . . . . 74
B.2 Empirical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
B.3 Model Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
B.4 The Non-Stochastic Steady States . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
B.5 The Dynamic System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
B.6 The Simplied Dynamic System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
B.7 The Linear Dierence Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
vi
List Of Tables
2.1 Cross-Sectional Stylized Facts, by Quartile of Intangibles . . . . . . . . . . . . . . . 37
2.2 Parameter Values for Steady State Analysis . . . . . . . . . . . . . . . . . . . . . . 51
B.1 Parameter Values for Steady State Analysis . . . . . . . . . . . . . . . . . . . . . . 84
B.2 Denition of Intangible Assets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
B.3 Corporate Sector Accounts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
B.4 Various Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
B.5 Secular Trend of Labor Share of Income and Intangible Investment . . . . . . . . . 88
B.6 Time-Series Stylized Facts, by Decade . . . . . . . . . . . . . . . . . . . . . . . . . 89
B.7 Cross-Sectional Stylized Facts, by Quartile of Corporate Saving Share . . . . . . . 90
B.8 Summary Statisitics for Labor Share of Income in the U.S. . . . . . . . . . . . . . 91
vii
List Of Figures
1.1 US Labor Share Index of Income . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 China Labor Share of Income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 China Labor Share of Income I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 China Labor Share of Income II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5 China and US Labor Share of Income . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.6 China Labor Share of Income III . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.7 Firm Level Elasticity of Substitution between Labor and Capital . . . . . . . . . . 16
1.8 Industry Level Capital Share of Income . . . . . . . . . . . . . . . . . . . . . . . . 17
1.9 Industry Level Capital Share of Income with Total Factor Cost Weight . . . . . . . 18
1.10 Industry Level Heterogeneity Index . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.11 Industry Level Heterogeneity Index with Total Factor Cost Weight . . . . . . . . . 20
1.12 Industry Level Elasticity of Substitution between Labor and Capital . . . . . . . . 21
1.13 Economy Level Elasticity of Substitution between Labor and Capital . . . . . . . . 22
1.14 Labor Market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.15 Estimation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.1 Country Level Stylized Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2 Stylized Facts in the U.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
A.1 Economy Level Heterogeneity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
A.2 IRF with respect to output productivity . . . . . . . . . . . . . . . . . . . . . . . . 67
viii
A.3 IRF with respect to intangible productivity . . . . . . . . . . . . . . . . . . . . . . 68
A.4 IRF with respect to output productivity . . . . . . . . . . . . . . . . . . . . . . . . 69
A.5 IRF with respect to intangible productivity . . . . . . . . . . . . . . . . . . . . . . 70
A.6 IRF with respect to output productivity . . . . . . . . . . . . . . . . . . . . . . . . 71
A.7 IRF with respect to intangible productivity . . . . . . . . . . . . . . . . . . . . . . 72
B.1 US Labor Share of Income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
B.2 China Labor Share of Income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
B.3 China and US Labor Share of Income . . . . . . . . . . . . . . . . . . . . . . . . . 94
B.4 Investment in Intangibles as Share of GDP(%) 2005: EU - 27 countries(and Norway) 95
B.5 Country Level Stylized Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
B.6 Stylized Facts in the U.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
B.7 tangible share of aggregate capital . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
B.8 return to scale of nal good production . . . . . . . . . . . . . . . . . . . . . . . . 99
B.9 return to scale of intangible production . . . . . . . . . . . . . . . . . . . . . . . . 100
B.10 labor contribution in nal good production . . . . . . . . . . . . . . . . . . . . . . 101
B.11 labor contribution in intangible production . . . . . . . . . . . . . . . . . . . . . . 102
ix
Abstract
Central to income distribution is the joint distribution of labor and non-labor income, which
is determined by labor income distribution, non-labor income distribution and the depencency
between them. Constancy in the labor share of income is one of the most important Kaldor's
facts in Macroeconomics. At the same time, labor income is usually more evenly distributed cross
households than capital income in an economy if the labor share is considered to be constant. If
the income shifts more from labor to non-labor, the income is more concentrated in the top of
the distribution. My dissertation explores the reasons for the global changes in the labor share
of income and for the dierence in changes between developing and advanced economies and how
these changes are associated with those in intangibles and nancial factors in recent decades.
First, I compare the magnitude and changes in the labor share of income in developing and
advanced economies in the recent decades. Trade economists state that shifting the production
of labor-intensive goods from the developed countries to emerging economies is the main reason
for the decline in the labor share of income in the developed countries. However, data shows that
the downward trend in the labor share of income in China, one of the largest emerging economies,
is steeper than that in the United States. This chapter is trying to provide an explanation.
We use detailed rm level data in China to estimate the industry and aggregate level elasticity
of substitution between capital and labor and nd that it is below unity as economists shown
in the literature. The estimation strategy we use in this is the same as which Obereld and
Neiman (2014) proposed and used in estimating the industry level and aggregate elasticities of
substitution in the United States. Following this same strategy and comparing the results we
x
observe that heterogeneity plays an important role in determining the industry and aggregate
level elasticities of substitution between capital and labor, which suggests that to explain the
decline in the labor share of income, one needs to take a close look at rm level characteristics.
We show that misallocation induces high heterogeneity in capital to labor ratios and thus the
elasticities of substitution between capital and labor in China. Therefore, due to the reduced
missallocation and heterogeneity in capital to labor ratios in recent decades in China, facing the
same decline in relative price of investment goods, the labor share of income in China increases
in a slower rate than that in the United States.
Second, I search for the driving force behind the global decline in the labor share of income in
the recent decades. This chapter shows that the rising share of intangible capital in production is a
fundamental driver of both the decline in the labor share of income and the secular upward trend in
corporate savings. At the macro level, I provide global evidence regarding the increasing intangible
capital investments, rising corporate savings and declining labor share of income in a broad set
of economies including most EU countries, the United States and China using various sources of
country-level databases. Besides, a simple micro empirical analysis using CRSP-Compustat rm
level data shows a positive correlation between gross savings and intangible capital. I present a
standard general equilibrium model with nancial frictions to analyze how the rms' compensation
share of the value added and cash holding are aacted by the stock of intangible capital, which
links both the trend in the labor share of income to the trend in the corporate savings with the
trend in the intangible capital in an economy. The model points to the increasing importance of
intangible capital in the production from 1970s to 2000s as an explanation for the rising corporate
savings and decline labor share of income in the United States.
xi
Chapter 1
Production Function and Income Distribution
1.1 Introduction
The constant labor share of income is taken as a stylized fact in macroeconomics for a long time
and regarded as the base for modeling the aggregate production. However, since 1970s the labor
share of income started to decline globally. One popular explanation for the global phenomenon
is the decreased relative price of capital, which is based on that the elasticity of substitution
between capital and labor greater than one,, even thought the estimate of the elasticity is usually
below unity. Also, trade economists argue that the reason for the decline in the labor share of
income in developed countries is that they move the production of labor intensive goods to the
developing words. We are using detailed rm level data in China to estimate the industry and
aggregate level elasticity of substitution between capital and labor and found that it is below
unity as most literature shows. The aggregate and estimate strategy we are using is proposed by
Obereld and Neiman (2014). Since they have already use the detailed rm level data to estimate
the aggregate level elasticity of substitution between capital and labor, our estimate could be use
for comparison, which could be quite useful when modeling the production functions.
The data we use in this paper comes from the annual surveys of manufacturing enterprises
conducted by the National Bureau of Statistics of China. The database covers all state-owned
1
enterprises and non-state-owned enterprises with annual sales of at least 5 million RMB, approx-
imately US $750,000 in 2007. This database has more than one hundred variables and contains
detailed information on rm identication (company name, contact information, ownership, in-
dustry type, etc), operation (employment, inventory, gross output, export, etc), and balance sheet
(total asset, account payable, account receivable, capital stock, etc). The data is a cross-section
data, and the number of rms varies from 279,092 in 2004 to 473,487 in 2009.
The diculties in estimation of the elasticity of substitution are as follows. First, it is dicult
to identify the elasticity of substitution with biased technical change (see for example Len-Ledesma
et al. (2010)). Second, it cannot be estimated by standard linear regression techniques (see for
example Henningsen and Henningsen (2002)). The recent decline in the labor share of income in
China is steeper than that in the U.S. The reason is that the reduced heterogeneity in cost shares
in China made capital and labor more complementary. The global decline in the price of capital
increased the labor share of income in China. However, the higher degree of complementarity
made the labor share of income in China increase in a smaller magnitude, compared with that in
the developed countries.
Outline Section 2 introduces the stylized fact of the global labor share. Section 3 presents the
baseline model. Section 4 shows the empirical strategy. Section 5 illustrates the empirical results.
Section 6 concludes.
1.2 The Stylized Facts
1. The labor share of income in the US started to decline since 1970s. Figure 1.2
2. The labor share of income in China has a downward trend as well since 1980s. Figure1.2
3. The labor share of income in China has started taking a deeper trend than that in the US
since 1990s.Figure ??
2
Figure 1.1: US Labor Share Index of Income
1.2.1 Cross Section Analysis
1. The distribution of the rm level labor share of cost varies with industry in China. Figure
1.2.1
2. Within an industry the distribution of the rm level labor share of cost is fat-tailed in China.
Figure 1.2.1
3
Figure 1.2: China Labor Share of Income
1.3 The Basic Model
1.3.1 The Labor Share of Income
In general, the labor share of income refers to the national income distributed to the labor for an
economy. It is dened as follows.
s
e
L
=
wL
wL +rK
(1.1)
with w the average wage, L the labor input, r the rental rate of capital and K the capital input.
One of the questions we are interested in is how the labor share of income s
e
L
changes with the
4
Figure 1.3: China Labor Share of Income I
change in the relative price of inputs w=r. To answer this question, we have to calculate the
following partial derivative as in the Appendix, that is,
@s
e
L
@ln(w=r)
=(1s
e
L
)s
e
L
(
@ln(K=L)
@ln(w=r)
1) (1.2)
Therefore, we have to know how the choice of input ratioK=L changes with the factor price ratio.
Another question follows what the contribution of the change in the relative price of inputs is and
that of all the other changes. We decompose the change in the labor share into the change due
to the change in the relative price of inputs and that due to the other factors as follows.
ds
e
L
=
@s
e
L
@ln(w=r)
+ (ds
e
L

@s
e
L
@ln(w=r)
) (1.3)
5
Figure 1.4: China Labor Share of Income II
Following the literature we call the second term the contribution due to the biased technological
change.
1.3.2 The Elasticity of Subsitution between Capital and Labor
Based on the above derivation we know how the ratio of the aggregate capital and labor is adjusted
when their relative price changes becomes the key to answering all the questions we have. The
most important concept relevant to this question is the elasticity of substitution between capital
and labor in an economy, which is dened as
=
@ln(K=L)
@ln(MPL=MPK)
(1.4)
6
Figure 1.5: China and US Labor Share of Income
withMPK the marginal productivity of capital andMPL the marginal productivity of labor. It
measures the extent to which rms can substitute capital for labor as their relative productivity.
In general, it depends on the amount of inputs employed. We consider a special group of two-input
production functions with the constant elasticity of substitution between capital and labor, that
is, the CES production function dened as follows.
Y =F (K;L) = [(A
K
K)
1

+ (A
L
L)
1

]

1
(1.5)
whereA
K
represents capital-augmenting technological change andA
L
represents labor-augmenting
technological change. Following Barro and Sala-i-Martin (2004) it can be shown that it is a neo-
classical production function since it exhibits constant return to scale, positive diminishing returns
7
Figure 1.6: China Labor Share of Income III
to private inputs and satises Inada condition. The elasticity of substitution between capital and
labor is . If we assume that markets are competitive, then the capital and labor are paid their
marginal product. Then the elasticity of substitution can be written as
=
@ln(K=L)
@ln(w=r)
(1.6)
It implies that if = 1, @s
L
=@ln(w=r) = 0, that is, the percentage change in K=L due to the
change inw=r compensates the percentage change in r=w, which keeps the labor share of income
s
L
with s
L
= wL=(wL +rK). If > 1, the percentage change in K=L exceeds the associated
percentage change inr=w, that is,@s
L
=@ln(w=r)< 0. For example, if the rental rate of the capital
declines, the labor share of income declines as well, which is the argument of Karabarbounis and
8
Neiman(2014) for the decline in the US labor share of income since 1970s. If< 1 the percentage
change in K=L is less than the associated percentage change in r=w, that is, @s
L
=@ln(w=r)> 0.
1.3.3 Micro and Macro Production Function
Miller(2008) gives a nice literature review about the assessment of CES and Cobb-Douglas produc-
tion functions. The use of Cobb-Douglas production function as a aggregate production function
cannot be inline with the stylized facts about the labor share of income as mentioned above.
Besides, the estimate of elasticity of substitution between capital and labor is often below unity,
which challenges all the mechanism using the CES production function with elasticity of substi-
tution between capital and labor larger than one trying to explain the decline of the labor share
of income. Moreover, as many empirical results illustrate the micro elasticity of substitution be-
tween capital and labor can be very dierent from the macro one. Therefore, consistent with the
micro theory and empirical evidence we start using a CES production function with below unity
elasticity of substitution between capital and labor for a rm (called Micro production function)
to see what implication we could get about the the aggregate elasticity between capital and labor
in an economy
e
and the induced mechanism about the variance of the labor share of income
s
e
without assuming the function form of the aggregate production (called Macro production
function) following Obereld and Raval(2014). That is, in an economy, the production function
for rm i in the industry n at time t is dened as follows.
Y
i;n
t
=F (K
i;n
t
;L
i;n
t
) = [(A
i;n
K;t
K
i;n
t
)

n;n
1

+ (A
i;n
L;t
L
i;n
t
)

n;n
1

n;n
]

n;n

n;n
1
(1.7)
in this case, when ignoring the time subscript, the elasticity can be written as follows.

n;n
1 =
dlnrK
i;n
=wL
i;n
dlnw=r
=
dln(1s
i;n
L
)=s
i;n
L
dnw=r
=
1
(1s
i;n
L
)s
i;n
L
d(1s
i;n
L
)
lnw=r
(1.8)
9
Without any further assumptions, based on the denition of the elasticity of substitution for the
industry n and the economy e, we get

n
1 =
dlnrK
n
=wL
n
dlnw=r
=
dln(1s
n
L
)=s
n
L
dnw=r
=
1
(1s
n
L
)s
n
L
d(1s
n
L
)
lnw=r
(1.9)

e
1 =
dlnrK
e
=wL
e
dlnw=r
=
dln(1s
e
L
)=s
e
L
dnw=r
=
1
(1s
e
L
)s
e
L
d(1s
e
L
)
lnw=r
(1.10)
By denition,
1s
n
=
X
i2J
n
(1s
i;n
)
i;n
(1.11)
1s
e
=
X
n2N
e
(1s
n
)
n
(1.12)
where denotes rm i's factor cost share weight dened as
i;n
=
rK
i;n
+wL
i;n
rK
n
+wL
n
, while industry
n's factor cost share weight as
n
=
rK
n
+wL
n
rK
e
+wL
e
with K
n
=
P
i2J
nK
i;n
, K
e
=
P
j2N
e
P
i2J
nK
i;j
,
L
n
=
P
i2J
nL
i;n
, and L
e
=
P
j2N
e
P
i2J
nL
i;j
. To get the industry and economy elasticity of
substitution between capital and labor we can start with dierentiating equation 1.12 as follows.
d(1s
n
L
)
lnw=r
=
X
i2J
n
d(1s
i;n
)
dlnw=r

i;n
+
X
i2J
n
(1s
i;n
)
d
i;n
dlnw=r
(1.13)
The rst term of the right hand side of the above equation measures how the capital or the labor
share of the factor costs
i;n
or 1s
i;n
changes with the change in factor prices holding xed each
rm's relative size
i;n
, which is called the substitution eect. The second term gives the allocation
eect since it measures how the change in factor prices aects the rms relative size
i;n
within
the industry. Intuitively, since the rms within an industry could have dierent capital-labor ratio
K=L, the change in the relative price have dierent relative eects on dierent rms even within
the same industry. For example, when the rental rate of capital declines, the rms with relative
lower capital-labor ratio K=L have cost and price advantage. Due to the decline in the price of
10
these rms' product, their demand increases as well. Therefore, there would be reallocation of
resources among the rms within the industry. The theoretic proof is as follows.
Given the rm i's CES production function, the marginal cost denoted by MC
i
is equal
to the average cost AC
i
by the denition of CES production function. Also, the rm i's cost
minimization problem P is as follows.
min
K
i
;L
i
rK
i
+wL
i
subject to y
i
=F (K
i
;L
i
) = [(A
i
K
K
i
)
1

+ (A
i
L
L
i
)
1

]

1
Let's C
i
denote the total cost of the rm i producing y
i
and
i
is the associated Lagrange
multiplier. The necessary condition of the above minimization problem gives us the following
equation.
C
i
=
i
(
@y
i
@K
i
r +
@y
i
@L
i
w) =
i
y
i
(1.14)
The last equality is from the property of constant return to scale production function. It gives us
MC
i
=
@C
i
@y
i
=AC
i
=
i
=C
i
=y
i
(1.15)
By some rearrangement of the FOCs we get
MC
i
= [(r=A
i
)
1
+ (w=B
i
)
1
]
1
1
(1.16)
By Shephard's lemma, we know
@ln(MC
i
=r)
@lnw=r
= 1s
i
L
>0 (1.17)
It implies that
@ln(MC
i
=r)
@lnw=r
@(K=L)
=
@(1s
i
L
)
@(K=L)
<0 (1.18)
11
that is,the relative more capital intensive rms suer less from the increase in wage and or has less
cost or price advantage when the wage decreases. To determine how the demand of the product
of rm i we have to assume the structure of its demand. Here, consistent with a representative
consumer with constant elasticity of substitution across varieties within an industry and across
industries in an economy, we assume that the demand has a constant price elasticity at each level
of aggregation. That is,
y
n
= (
X
i2J
n
D
i;n
1
n
y
i;n
n1
n
)
n
n1
(1.19)
y
e
= (
X
n2N
e
D
n
1

y
n
1

)

1
(1.20)
Then the demand of variety i follows based on the cost minimization problem of each industry,
that is,
y
i;n
=D
i;n
(p
i;n
=p
n
)
n
Y
n
(1.21)
It implies that the price elasticity of demand is@lny
i;n
=@lnp
i;n
=
n
and the price index for indus-
tryn isp
n
= (
P
i2J
nD
i;n
p
i;n
1n
)
1
n1
. Assuming that rms are facing monopolistic competition
we get
p
i;n
=
n
MC
i;n
(1.22)
where
n
denotes the price markup over the marginal cost set by the rms within industry n and
solving the rms prot maximization problem gives us
n
=
n
n1
. Then we can come back to
the question how the change in relative factor price induces the reallocation of resource within an
12
industry, that is, what is
@
i;n
@lnw=r
in the equation 1.26 ? By denition,
i;n

rK
i;n
+wL
i;n
rK
n
+wL
n
, then it
follows

i;n
equ (1:15)
=
MC
i;n
y
i;n
P
i2J
nMC
i;n
y
i;n
equ (1:22)
=
(p
i;n
=
n
)y
i;n
P
i2J
n (p
i;n
=
n
)y
i;n
equ (1:21)
=
p
i;n
y
i;n
p
n
y
n
(1.23)
Besides, we also know
@p
i;n
y
i;n
@lnw=r
=
lnp
i;n
lnw=r
+
@lny
i;n
@lnp
i;n
lnp
i;n
lnw=r
(1.24)
The rst term in the nominator measures the eect of the change in the factor price on the
marginal cost or the price of the variety produced by rm i,that is,
lnp
i;n
lnw=r
=
n
(1s
i;n
L
) while
the second term in the nominator shows how the demand of the variety due to the change in its
price due to the change in the factor price,that is,
@lny
i;n
@lnp
i;n
lnp
i;n
lnw=r
=
n

n
(1s
i;n
L
). Then we get
@
i;n
@lnw=r
= (1
n
)(1s
i;n
L
) (1
n
)(1s
n
L
) (1.25)
Therefore, 1.11 becomes
d(1s
n
L
)
lnw=r
=
X
i2J
n
(1
n;n
)s
i;n
L
(1s
i;n
L
)
i;n
+
X
i2J
n
(1s
i;n
L
)(1
n
)(s
n
L
s
i;n
L
) (1.26)
where
n;n
denote the elasticity of substitution between capital and labor for all the rms i2J
n
within industryn2N
e
in an economy. Following Obereld and Raval(2014), we get the following
proposition.
Proposition: Under the following assumptions
Assumption 1. The rms production function exhibits constant elasticity of substitution between
capital and labor dened as 1.7,
13
Assumption 2. The demand has a nested structure with a constant elasticity at each level of
aggregation referring to 1.21 and 1.20, and
Assumption 3. The rms are monopolistic competitive.
we get the following elasticity of substitution at each level of aggregation, that is,
1. the elasticity of substitution between capital and labor for each industry n2 N
e
in an
economy is

n
= (1I
n
)
n;n
+I
n

n
(1.27)
with I
n

1
s
n
L
(1s
n
L
)
P
i2J
n (s
i;n
L
s
n
L
)
2

i;n
, and
2. the elasticity of substitution between capital and labor for the whole economy is

e
= (1I
e
)
n
+I
e

n
(1.28)
with I
e

1
s
e
L
(1s
e
L
)
P
n2N
e (s
n
L
s
e
L
)
2

n
It shows that the industry elasticity of substitution between capital and labor depends not only
on the elasticity of substitution between capital and labor producing the variety but also on the
elasticity of substitution between varieties within the industry. The relative importance depends
on the heterogeneity in the cost share of labor or capital, which is proportional to its cost-share-
weighted variance. That is, even if the rms from industry m and rms from industry n6= m
producing varieties with the same production function facing the same price elasticity of demand,
that is,
m;m
=
n;n
and
m
=
n
, the industry level elasticity of substitution between capital
and labor for industry m and n could be quite dierent since the heterogeneity in the cost share
of labor within the industry could play a quite role guring the industry level elasticity.
14
1.4 The Empirical Strategy
We adopt the assumptions and methodology applied in Raval (2014) to estimate the elasticity of
substitution between capital and labor using our data set. The main important assumptions are
as follows.
Assumption 4. Capital is mobile and all the rms face the same rental rate of capital r, and
Assumption 5. Labor is geographically isolated and all the rms within the same local area face
the same wage rate w
p
with p2P
e
.
The necessary conditions for the cost minimization problem P with the associated Lagrange
multiplier
i;n
in 1.3.3 are as follows.
r
i;n
=
i;n
@y
i;n
@K
i;n
; (1.29a)
w
i;n
=
i;n
@y
i;n
@L
i;n
(1.29b)
By the denition of elasticity of substitution between capital and labor we get the following
relation.
lnr
i;n
K
i;n
=w
i;n
L
i;n
= (
n;n
1)lnw
i;n
=r
i;n
Under the assumptions 4 and 5 the regression model we are using is as follows.
lnrK
i;n
=(wL)
i;n
= (
n;n
1)lnw
i
p
+
i;n
~ x
i;n
+
i;n
where r is the rental rate of capital assumed the same for all the rms in the economy, K
i;n
the capital stock measured by the xed asset of the rm i in industry n, (wL)
i;n
the labor cost
measured by the total wage payable of the rm i in industry n, w
i
p
the wage faced by the rm i
located in the province p, and
~
x
i;n
all the control variable chosen in the model.
15
1.5 The Empirical Results
Figure 1.7: Firm Level Elasticity of Substitution between Labor and Capital
The results follow.
1. The rm level elasticity of substitution between capital and labor in China is signicant ex-
cept for industry category "Electricity, production and supply" and "Oil and gas extraction"
at the signicance level of 1%. Only for the industry "Oil and gas extraction" is the elas-
ticity of substitution between capital and labor greater than unity and it is not signicant
at at the signicance level of 10%.
2. The industry with the highest labor share of cost in China is "Electricity, production and
supply" while the second highest is "Oil and gas extraction". Only 8 out of 26 industries have
16
Figure 1.8: Industry Level Capital Share of Income
the labor share of cost higher than the national average labor share of cost 0.6. However,
their share of capital holdings is quite large.
3. The relative large industries with the relative high level of heterogeneity in the labor share
of cost in China are "Computer Equipment" and "Chemicals".
4. The aggregate level of substitution between capital and labor in China is below unity.
1.6 Conclusions
The recent decline in the labor share of income in China is steeper than that in the U.S. The
reason is that the reduced heterogeneity in cost shares in China made capital and labor more
complementary. The global decline in the price of capital increased the labor share of income in
17
Figure 1.9: Industry Level Capital Share of Income with Total Factor Cost Weight
China. However, the higher degree of complementarity made the labor share of income in China
increase in a smaller magnitude, compared with that in the developed countries. In particular,
the reasoning is as follows.
1. The heterogeneity of the labor share of income plays an important role in determine the
elasticity of substitution between capital and labor, which is dierent from that in the
US. The misallocation of production factors including capital or labor could take the most
response for the heterogeneity of the cost share in China.
2. The decreased price of tangible capital good is not the reason for the decline in the labor
share of income in China since the elasticity of substitution between capital and labor is
under unity. Neither are the reasons associated with above unity elasticity.
18
Figure 1.10: Industry Level Heterogeneity Index
3. The downward trend of the labor share of income in China is steeper than that in the US.
We are not satised with the claim that the answer to the decline in the labor share of
income in the US is that more and more labor intensive goods are produced in China
19
Figure 1.11: Industry Level Heterogeneity Index with Total Factor Cost Weight
20
Figure 1.12: Industry Level Elasticity of Substitution between Labor and Capital
21
Figure 1.13: Economy Level Elasticity of Substitution between Labor and Capital
22
Figure 1.14: Labor Market
Figure 1.15: Estimation Results
23
Chapter 2
Intangbile Capital, Corporate Savings and Labor Share of
Income
2.1 Introduction
Elsby et al., 2013 and Karabarbounis and Neiman, 2014 brought our attention to the decline
in the share of GDP going to labor in the United States and many other countries in recent
years. Although the measurement of the labor share of income is suering some issues due to
the treatment of proprietor's income (Elsby et al., 2013; Gomme and Rupert, 2004), housing
(Rognlie, 2015), and intangible capital (Corrado et al., 2009; Koh et al., 2015), the decline began
in the 1980s and was particularly evident in the 2000s (Autor et al., 2017a; Grossman et al.,
2017). In the recent years many researchers have tried to explore the reasons for the decline
including Elsby et al., 2013; Karabarbounis and Neiman, 2014; Koh et al., 2015; Rognlie, 2015;
Barkai, 2017, Gonzalez and Trivin, 2016; Acemoglu and Restrepo, 2016; Grossman et al., 2017;
Abdih and Danninger, 2017; Autor et al., 2017a. Elsby et al., 2013 show that the oshoring of
the labor-intensive components of the United States manufacturing may have contributed to the
falling domestic labor share during the 1990s and 2000s. Karabarbounis and Neiman, 2014 nd
that roughly half of the worldwide fall in corporate labor share has been due to the fall of the
relative price of investment goods based on the estimate of the elasticity of substitution between
24
capital and labor greater than unity. Rognlie, 2015 suggests that the dierence between gross
and net capital shares and the increase in the cost of housing could be the reason. Barkai, 2017
distinguishes prot share from payments to capital and labor and suggests that the increasing
prot share, followed by the decreasing competition, is associated with the lower labor share of
income. Gonzalez and Trivin, 2016 provide empirical evidence that up to 57 percent of the decline
is explained by the increase in Tobin's q. Abdih and Danninger, 2017 nd that the changes in
technology that are linked to the automation of routine tasks is the reason for the deline.
1
Autor
et al., 2017a attribute the lower labor share to the rise of "superstar rms" or the concentration.
2 3
To summarize, these explanations for the decline in the labor share either focuse on those
shifting the income from labor to either capital or prots without considering the rising importance
of another factor in the production- that is, the intangible capital.
Meanwhile, the rise in the corporate savings has been documented and discussed by many
researchers, including Chen et al., 2017, Falato et al., 2013. Armenter and Hnatkovska, 2017,Bac-
chetta and Benhima, 2010, Bayoumi et al., 2010, Gruber and Kamin, 2015, and Fan and Kalemli-
Ozcan, 2016. Basically, in the United States in the 1970s and 1980s, the corporate sector was a
net debtor. However, by the 2000s, the corporate sector had switched to be a net lender.
At the same time, measured intangible capital has been argued to be an important contributor
to the economic growth. Researchers have debated the denition, the measurement and valuation
of the intangible capital, and I don't intend to wade into the debate. Instead, I will accept
the hypothesis that intangible capital plays an important role in the production and that the
1
In particular, the automation of routine task was followed by trade globalization.
2
The "superstar rms", the winners in the "winner take most" competitions, are highly protable with low
labor share and command growing market share. Autor et al., 2017b provides the evidence for the superstar rm
hypothesis: the concentration of sales among rms within industries has risen across much of the private sector;
and industries with larger increases in concentration exhibit a larger decline in labor's share.
3
Concentration is dened as the fratciton of industry sales produced by the top ten rms in the country.
25
intangible share
4
has increased in recent decades, and I will explore the implications of this
change for the trends in corporate savings and labor share of income.
The two closest papers to my work are Koh et al., 2015 and Chen et al., 2017. Koh et al.,
2015 claim that the decline in the labor share of income has been driven by Intellectual property
products(IPP) capital since the 1940s.
5
Their statement is mainly based on the national income
accounting practice assuming that the national income is either distributed to labor or to capital,
including traditional physical capital and previously ignored intangible capital, which is equivalent
to assuming that prots are zero. With this assumption they constructed a series on the return
to the intangible capital and the series of the IPP capital share of income. In other words,
they don't distinguish the income share of capital from the prot share. On the other hand,
Chen et al., 2017 relate the labor share to corporate saving empirically and theoretically, and
argue that it is important to study the labor share and corporate savings jointly; they oer a
unied explanation for their trends. In particular, they found that the variation in the labor
share is correlated with variation in components of the user cost of capital and corroborate the
importance of the relationship by jointly studying the trend in the corporate saving. I provide a
unied explanation for the upward trend in the corporate savings and downward trend in the labor
share of income in reference to the rising importance of the intangible capital in the production.
I present a standard general equilibrium model with nancial frictions to analyze how the rms'
compensation share of the value-added and savings are aacted by the stock of intangible capital,
which links the trend in the labor share of income to the trend in the corporate savings and
the trend in the intangible capital in the corporate sector. With respect to the national income
accounting practice, I distinguish the prot share from payments to physical capital, intangible
capital, and labor. On the other hand, when modeling the intangible capital I consider its special
4
The intangible share is dened as the intangible-capital ratio (intangible capital/(physical capital+intangible
capital). In this paper, the denition and measurement of the intangible capital follows Corrado et al., 2009.
Corrado et al., 2012 provide a measure of the intangible assets for 27 EU countries plus Norway and the United
States. Data details are provided in the appendices.
5
IPP capital is dened as intellectual property products capital, which includes software, R&D, and artistic
originials. In this paper, the terms "Intellectual capital" and "intangible capital" are interchangeable.
26
properties
6
and explore the implications of the rms' decisions about the resource allocations to
labor compensation, payment to the capital, and savings, which determine the functional income
distribution in the corporate sector.
When it comes to the intangible capital, its special properties have to be investigated: First,
it is dicult to measure and evaluated.(Corrado et al., 2009; Corrado et al., 2012; Corrado
et al., 2013; Corrado et al., 2016; Bacchini and Iannaccone, 2016; Jaeger, 2017; Falk, 2013; Eis-
feldt and Papanikolaou, 2013; Eisfeldt and Papanikolaou, 2014; Eisfeldt and Papanikolaou, 2017;
andHartman-Glaser et al., 2016). At the country level, Koh et al., 2015
7
gave a detailed de-
scription about the improvement in the measurement of the intangible capital in national income
accounting in the United States. Basically, the national accounts incorporate a broader deni-
tion than accounts for intangible investment, which used to be considered as expenses. On the
other hand, for the EU countries, the framework for the estimation of intangible capital also has
been improved in recent decades. Corrado et al., 2016
8
incorporated a broader denition of the
intangible assets and provided a harmonized measurement of the intangible capital in advanced
economies, which is comparable across countries. In this paper I use the newly revised and up-
dated release of the INTAN-Invest dataset to analyze the implication of the intangible capital for
the trends in the labor share and corporate savings. Second, the intangible capital is not pledge-
able (Bessen, 2008, Falato et al., 2013, Wang, 2017, et al). I follow Wang, 2017 to formulate the
6
The intangible capital is distinguished from the physical capital with respect to the measurement, the pledge-
ability and its nance. Details will be provided in the next paragraph.
7
The eleventh comprehensive revision of NIPA in 1999 recognized business and government expenditures for
software as xed investment. The most recent fourteenth comprehensive revision in 2013 treated expenditures by
business, government and nonprot institutions serving households (NPISH) for R&D, and expenditures by private
enterprises for the creation of entertainment and literary and artistic originals as investments in various forms of
durable capital and no longer, as previously done, as expenditures in intermediate nondurable goods (for the
private sector) or as nal consumption (for the government sector).These R&D and artistic originals (recognized
since 2013), combined with software (recognized since 1999), form the intangible assets in the recent national
accounts.
8
Corrado et al., 2013 expanded the xed asset boundary in national accounts, which treats as investment only a
limited range of intangible assets: R&D, mineral exploration, computer software and databases, and entertainment,
literary and artistic originals and included the overall business intangible investment, which led to the publication
of the INTAN-Invest dataset. More recently, INTAN-Invest dataset 2016 was released, which covers eighteen
European countries and the United States from 1995 to 2013.
27
limited pledgeability of the intangible capital and investigate the role of the rising intangible cap-
ital in the production in determining a rm's resource allocation. Financial frictions make these
properties especially relevant. If there were no collateral constraints, or the external funding was
costless, without other frictions, the nance of the intangible capital wouldn't be dierent from
that of the physical capital. The third property or implied property is about its nance. Hall
and Lerner, 2009 gave the literature review about the innovation nancing. In particular, it is
well documented that the intangible investment including R&D heavily relies on internal nanc-
ing( Hall, 1992, Himmelberg and Petersen, 1994, et al.). Given these properties of the intangible
investment and capital the importance of the intangible capital in the the production directly
aects the corporate sector's allocation decision about the distribution of the prots among the
savings, investment and dividends given the share of prots in value added. The investment in
the intangible capital determines the protability, which gives the labor share of costs.
ls
cost
t
=
w
t
L
t
(1 1=
y
t
)y
t
+ (1 1=
R
t
)q
R
t
H
t
(2.1)
where ls
cost
denotes the share of physical, intangible and labor income going to the labor, w
is compensation, L is labor, y is nal good, H is intangible investment, q
R
is relative price of
intangible investment,
y
is markup of the marginal product of inputs (labor, physical capital and
intangible capital) over marginal costs when producing the nal goods, and
R
is markup when
producing the intangible investment goods. In other words, ls
cost
t
measures the labor share of
costs and 1ls
cost
t
mesures the capital share of costs. The labor share of value added are dened
as follows, is lower since the markups is no less than 1 (
y
t
>= 1 and/or
R
t
>= 1).
ls
t
=
w
t
L
t
y
t
+q
R
t
H
t
(2.2)
28
On the other hand, when the intangible capital is ignored, the labor share of costs and the labor
share of value added dened as follows, respectively.
ls
cost;traditional
t
=
w
t
L
t
(1 1=
y
t
)y
t
(2.3)
ls
traditional
t
=
w
t
L
t
y
t
(2.4)
Therefore, when analyzing the labor share of income, it is necessary to clarify which denition
or measurement is used before further discussion since they determine the magnitude and the
starting date of its change. The dierence of the magnitude of the various measures comes from
the denominator, while the measurement of labor compensation is the same
9
. Since I consider the
in
uence of ntangible capital in production and distinguish prot from direct payment to inputs
(labor, physical capital and intangible capital) I mainly focus on the labor share of income dened
in equation 2.2, denoted byls
t
in the rest of the paper. In this paper, I propose a novel explanation
for its decline - that is, the rising importance of the intangible capital in the production. However,
understanding the dierences among these denitions will help us to explore the in
uence channel.
I will provide more details about the in
uence of the variation of the trend in intangible capital
on the variation of the trends in various measurements of the labor share dened above.
I start by documenting the relation between rising intangbile investment and the decline in
labor share of income and increase in the corporate savings by combining various data sources.
I have displayed and summarized the descriptive stylized facts of the trends iat the macro level.
I will show that the countries with higher intangible investment tend to have higher corporate
savings and lower labor share of income in the corporate sector. To analyze how the rms'
debt/saving choice is in
uenced by their intangible capital holding, I use CRSP-Compustat rm-
level data in the United States to do some simple empirical analysis that shows that the savings
9
The measurement of the compensation for the labor or the reported compensation for a rm, wt, according
to the data description of CRSP-Computstat, usually includes employee benet plans, other social expenditures,
pension and retirement expenses, social security contributions, sta expense not allocated to another operating
expense, wages and salaries.
29
is positively correlated with a rm's intangible capital holding. To illustrate the relationship, I
Data Source: Author's calulation, data details and construction explained in appendix
It covers 18 European countries and the United States from 1995 to 2010. The dots show the sample average of
various measures each year and the line give the tted value/time trend based on the regression of sample average
on the year.
Figure 2.1: Country Level Stylized Facts
develop a standard general equilibrium model with nancial frictions and provide a novel expla-
nation for the decline in the labor share of cost in the corporate sector. The model shows that
the intangible capital in production is critical for determining the payment share to the labor, the
prot share, and the corporate savings. I cannot resolve the dispute about why intangible capital
has become more important in the production. Instead, I draw attention to the improvement of
the measurement of intangible capital and new ndings about its implications. The Conference
Board
10
provides a series of research papers and a database to illustrate that the intangible capital
constributes much to a rm's and country's competitive edge and growth in the knowledge econ-
omy. First, with respect to the measurement of intangible capital, the new measurement exteneds
10
In particular, the Conference Board Innovation and Intangibles programm.
30
the boundary and the magnitude is much larger compared to the previously used one. Figure
B.4 shows the investment in the intangibles as share of GDP in EU-27 countries and Norway in
2005. On average, less than 20 percent of the investment in intangibles is attributable to that
in the scientic R&D, which was previously considered a critical intangible investment. On the
other hand, the proportion of the intangible investment in the other categories has increased in
recent decades. In other words, the increase in the intangible investment is mainly driven by
the increase in investment in economic competence and others. Second, the sources of growth
analysis suggest that the contribution of intangible capital account for almost half in the EU and
the United States
11
and it is associated with a lower ratio of tangible to intangible investment
in the recent decades (Corrado et al., 2016). In this paper, I will focus on the variation in the
ratio of tangible capital to intangible capital from the 1970s to the 2000s in the corporate sector
in United States and analyze its implication to the variation in the labor share of income and
the corporate savings. In particular, the average ratio of tangible capital to intangible was three
in the 1970s and one in the 2000s for the rms included in the CRSP-Compustat database
12
. I
assume that each ratio corresponds to a steady state in the model and compare the variation of
the other variables of interest. I will argue that the rising importance of intangible capital drives
a long-run decline in the labor share of income.
In what follows, I will specify the reasoning. Basically, rst, the investment in intangibles
increases the value added of a rm or an economy. With the relative constant labor compensation,
compared with the measured labor share of income, dened by equation 2.4, the real labor share
of income ls is lower. This denition is consistent with Koh et al., 2015. If the investment in
tangibles is treated in the same as the physical capital, the elasticity of substitution is a key
parameter that determines if the capital deepening accounts for the recent fall in the labor share of
income. To my best knowledge, all the papers have explained the recent decline in the labor share
11
The contribution of tangibles is 60 percent in the EU and 40 percent in the United States, respectively, while
intangibles account for a larger share (40 percent in the EU and 60 percent in the United States).
12
To calculate the ratio, rst, I take the weighted average by the value added of the ratio for the sample in each
year. Then I take the average in the 1970s and in the 2000s, respectively
31
of income either by claiming that is greater than one and that there has been capital deepening
or by claiming that is less than one and that the eective capital ratio
13
has been decreasing.
However, this paper doesn't explore the reasons from these perspectives. I still assume that the
elasticity of subsittiution between capital and labor is unity and imply that a given percentage rise
in aggregate capital-labor ratio will give rise to a same percentage fall in ratio of aggregate capital
return to wage rate and the labor share of costls
cost
orls
cost;traditional
remain constant. In other
words, my work is not con
icting with the existing works. Instead, it is complementary to the
extensive literature. Secondly, the production of the intangibles is formulated in an explicity way.
I adopt the same form of the production function for the intangibles as the traditional nal goods.
Then it becomes clear how the variations in parameters of the production function capture the
special properties of intangibles and in
uence the variations in income distribution. In particular,
the accumulation of intangibles could increase rms' prot share. Third, nancial frictions play
an important role in explaining the decline in the labor share of income and the increase in the
corporate savings jointly. To nance the increasing intangible investment needs, the rms have
to save more given their prot share since the intangible capital cannot be used as collateral
when rms apply for external nancing. In addition, the production of ntangibles provides the
rm another way to earn a higher prot share, which provides more available resources to save.
Therefore, when the importance of the intangibles increased from the 1970s to the 2000s in the
United States the labor share of income in the corporate sectore declined. With the evidence that
intangible investment has increased in a broad set of countries, the quantitative analysis provides
insights into the reasons for the global decline in the labor share of income.
This paper contributes to the literature on declining labor share of income in three ways. First,
I put togther the macro stylized facts about the rising investment in intangibles (especially those
in the non-traditional cateogories of intangible identied), the declining labor share of income
and increasing savings in the corporate sector. I mainly build on Corrado et al., 2016, and Chen
13
The eective capital-labor ratio takes the technical changes into account.
32
Data Source: Author's calulation, data details and construction explained in appendix
It covers the rms in CRSP-Compustat database in the United States from 1987 to 2013. The dots show the
sample average of various measures each year and the line give the tted value/time trend based on the regression
of sample average on the year.
Figure 2.2: Stylized Facts in the U.S.
et al., 2017 to construct a country-level database merging the information about the intangibles,
labor share of income and corporate savings. The former developed the methodology to the newly
revised, updated and released INTAN-Invest and related database about the intangibles, while
the latter provided a comparable measurement of labor share of income and corporate savings in
a broad set of countries. By merging various databases I get the following ndings about their
relationship: There is a possible relation between intangible capital and corporate savings and
a negative relation between intangible capital and labor share of income in the time-series as
well as in the cross section. In addition, in order to better understand the relationship I check it
using CRSP-Compustat rm-level data, which is complementary to the usually shown macro-level
evidence.
33
Second, this study highlights the implications of intangibles on the income distribution with
nancial frictions. This paper constributes to a large literature on the macroeconomic impor-
tance of intangible capital. The contribution of the intangibles to the economic growth based
on the growth accounting has been well documented (Corrado et al., 2016). In addition, Thum-
Thysen et al., 2017 point out that the intangible assets are vital for the rms' competence and
for economies' productivity and growth. However, compared with physical capital, intangibles
have special properties, which makes the nance more dicult. Therefore, the in
uence of an
accumulation of intangibles on income distribution is not as direct as that of physical capital. I
show that rms face the trade-o between the investment in the physical capital and intangibles
and the trade-o between investment and savings. With too much investment in physical capi-
tal rms don't have enough resources to produce the intangibles, which limits productivity and
protability. On the other hand, with too little investment in physical capital, rms cannot get
enough external funding to nance investment in intangibles. This trade-o determines the rms'
decisions about investment, which shows the dierence between the traditional measurement of
labor share and that including the production of the intangibles. Without nancial frictions, the
saving decisons is trivial. Besides, given the investment and production, the relative protability
between nal goods and intangibles aects the direction of the variation in the prot share when
the investment in intangibles increases. To the best of my knowledge, the rising importance of
intangibles in income distribution hasn't been well explored.
Third, I present a model in which the trends in the labor share of value added and corporate
savings emerge in response to the importance of intangible capital in production, which is mea-
sured by the share of intangible capital in accumulated capital, including physical and intangible
capital. The model points to the rising importance of intangible capital as an explanation for the
decline in corporate labor share and the increase in corporate saving. It is not a simple accounting
34
practice as in the related literature (Koh et al., 2015). In stead, it considers the special prop-
erties of intangibles and explicitly explores their in
uence on the rms' decisions about resource
allocation.
The paper is structured as follows: Section 2.2 summarizes the stylized facts about the intan-
gible investment, the labor share of income, and the corporate savings. It also provides empirical
evidence that rms' allocation choice is related to their intangible holding. Section 2.3 describes
the model used to quantify the relationship between the rising intangible capital and the labor
share of income. Sections 2.4 and 2.5 present the mechanism and the results, respectively. Section
2.6 revisits some of the related literature. Section 2.7 concludes.
2.2 The Stylized Facts and Empirical Evidence
2.2.1 Aggregate Level
2.2.1.1 Time series wise: US and China aggregate
Figure B.1
Figure B.2
Figure B.3
35
2.2.1.2 Time series wise: UN and OECD countries
Table B.5
Table: Secular Trend of Labor Share of Income and Intangible Investment
Data Source 1: Intangible investment from OECD
Data Source 2: Labor share of income from Karabarbounis and Neiman, 2014
Table B.6
Table: Time-Series Stylized Facts, by Decade
Data from Chen et al., 2017, country level
2.2.1.3 Cross-Section wise: UN and OECD countries
The database provided by Chen et al., 2017 gives the measurement of the labor share of income
and corporate savings of fty-nine countries for various years between 1975 and 2007. I combined
their dataset with the INTAN-Invest database that gives market sector data on intangibles assets
for twenty-seven EU countries plus Norway and the United States for 1995 to 2010 or most
recent year available
14
. Table 2.1 shows the cross-sectional stylized facts: countries with higher
intangibles tend to have lower labor share of income and lower net debt (or higher savings) in the
corporate sector.
14
The description of the data is in Appendix B.1.
36
Table 2.1: Cross-Sectional Stylized Facts, by Quartile of Intangibles
quartile labor share median net debt median
intangible capital, Q1 0.51 0.57 0.28 0.29
intangible capital, Q2 0.49 0.52 0.20 0.21
intangible capital, Q3 0.48 0.49 0.10 0.11
intangible capital, Q4 0.46 0.47 -0.07 -0.10
Summary of Stylized Facts
1. Time Series I: The decline in the labor share has occureed in a broad set of countries since
at least the 1990s. The rise in the corporate savings mirrors the decline in the labor share
of income in the corporate sector
15
.
2. Time Series II: The increasing investment in intangibles in the non-traditional categories
has accelerated the accumulation of intangible capital in recent decades.
3. Cross Section: Countries with higher intangible investment tend to have lower labor share
of income and higher corporate savings.
2.2.2 The Empirical Evidence
To understand the labor share of income in the corporate section at the aggregate level, it is
necessary to clarify the main concepts used to describe corporate-sector accounts (table B.3).
Since the secondary types of income - including transfers, teaxes and capital expenditures - are
either very small
ows, constant over time (Giovannoni, 2014), and/or not the focus of the study,
I mainly analyze the components of aggregate income, such as compensations, interest, rents,
and corporate prots as well as the debt/savings and investments. In addition, in matters of the
functional distribution of income, I follow national accounting practices and call the complement
15
Theses stylized facts have already been summarized byChen et al., 2017
37
to unity of the labor share "non-labor share" (Giovannoni, 2014) instead of "capital share" in
a stream of literature(Corrado et al., 2009, Koh et al., 2015, etc.) and then distinguish capital
share
16
from prot share, in particular,
• The labor share/compensation share is the share of wages and benets for the gross value
added in the corporate sector.
• The capital share is dened as the share of the gross value added used to rent the capital
including physical and intangible capital.
• The prot share stands for the share of prots, which is operating prots with the substrac-
tion of net interest paid.
The decline in the labor share of value added in the United States is robust to the mea-
surement. Autor et al., 2017b showed the downward trend of the labor share constructed using
the payroll, a broader measure of compensation, including non-wage labor costs(employer health
insurance contributions) and payroll normalized by sales as the numerator and value-added in
the denominator using Census data
17
. Examining Compustat data also shows a similar pattern
of results. Therefore, despite multiple caveats of Compustat data, I implemented the empirical
analysis using U.S. publicly listed rms in the Compustat database with some sample selection
rules, due to the limited access to the census data.
Formally, a linear regression equation for baseline net debtis estimated as follows:
S
ijt
=
0
+
1
Int
ijt
+
3
Control
ijt
+Ind
j
+
jt
+u
ijt
16
Karabarbounis and Neiman, 2014 states that the percentage change in the capital share is the same as the
percentage change in the ratio of investment to gross value-added and there is no decline in the capital share,
Rognlie, 2015 claims that the percentage change in the capital share is the just the percentage change in the ratio
of value of the capital stock to gross value-added and therefore there is not change in the net share.Barkai, 2017
shows the percentage change in the capital share is from the percentage change in the debt and equity costs of
capital to gross value-added and the capital share delines as well.
17
Autor et al., 2017b use rm-level data from the U.S. Economic Census for the three-decade interval of 1982-2012
for six large sectors.
38
whereS
ijt
is the net debt of rmi in industryj at timet. Int
ijt
denotes the intangibles of rmi
in industryj at timet.
1
is the parameter of interest, which measures the eect of increasing one
unit of intangibles on the net debt/savings. Control
ijt
is a vector of the rm's characteristics,
which are commonly used in the corporate nance literature. Ind
j
is the industry xed eects,
which account for time invariant heterogeneity across industries. I also include the industry-
specic time trends,
jt
to control for industry-specic deviations from the common nationwide
trend. All the variables are rescaled by the asset.
The measure of the intangible capital Int
ijt
builds on Falato et al., 2013. To the best of
my knowledge, this measure is the most comprehensive rm-level measure of intangible capital
for all non-nancial rms in Computstat between 1970 and 2016. The measurement of intangible
capital is dened as the sum of three components: the knowledge, organizational and informations
capital, which is consistent with the measurement in the macro level proposed by Corrado et al.,
2009 that I am using. The measurements of investment in each category are R&D expenditure,
SG&A expenditure and computerized information and software (IT), respectively. Following the
literature, the depreciation rate depends on the category of the intangibles.
Since the empirical analysis is not the main focus of the study, all the results with the data
construction and econometric methods are described in the appendix B.2. The OLS and FE
estimate of
1
are bothe negative, which is robust to the rm's characteristics. It gives the result
that the intangibles in a rm are positively correlated with the savings. There could be more than
one possible in
uence channel: First, if the intangibles are vital in the production and cannot be
nanced externally, the rms have to save by themselves. Second, the intangibles accumulated by
the rms give the rms opportunities to earn more prots in the production, which reduces the
labor share of value-added within a rm.
To summarize, from the aggregate-level data it is illustrated that countries with higher intan-
gible investment tend to have lower labor share of income and higher corporate savings, while
the rm-level data shows that the intangibles in a rm are relevant for the saving/debt decision,
39
which in
uences the labor share of value added. In the following section, I will explicitly model
the production of intangibles and nal goods with collateral constraints as the nancial frictions
to explain why the data show these patterns.
2.3 The Baseline Model
This section develops a dynamic model with two types of capital and nancial market frictions.
2.3.1 Firms
There is a continuum of unit mass of rms. We assume that a rm aggregates physical and in-
tangible capital and combines aggregated capital and labor inputs to produce nal goods and/or
to accumulate intangible capital. More specically, the accumulation of the two types of capital
works dierently: while the physical capital investment can be directly from the nal goods, the
intangible capital investment has to be separately produced. The technology is as follows.
Capital Aggregation
Following Koh et al., 2015, I model the aggregated capital using a CES function with the
elasticity of substitution between physical capital and intangibles
1
1+
- that is,

t
(K
t
;R
t
) = [(
K
t

)

+ (1)(
R
t
1
)

]
1=
;1<< 1
with determining the relative importance of the physical capital in the production, as in Falato
et al., 2013.
Production of Final Goods
40
As in the traditional neoclassical literature, the production of nal goods is in Cobb-Douglas
form.
y
t
=z
Y
t
[
Y
1
t
(u
n
t
L
t
)

]

; 0<< 1; 0<6 1 (2.5)
with
Y
= (u
k
k;R)), whereu
k
andu
n
denote the fraction of physical capital and labor devoted
to the production of nal goods, respectively. The process for z
Y
t
is assumed to be as follows:
ln(z
Y
t
) =
Y
ln(z
Y
t1
) +
Y
t
;
Y
t
N(0;
2
zY
)
with the Markov transition function denoted as
Y
(z
Y
t
jz
Y
t1
).
Accumulation of Intangible Capital
To illustrate the implication of the importance of intangibles to production, I model the
production of the investment in intangibles and accumulation explicitly.
R
t+1
= (1
R
)R
t
+z
R
t
[
R
11
t
((1u
n
t
)L
t
)
1
]

; 0<
1
6 1; 0<
6 1 (2.6)
with
R
= ((1u
k
)k;R) - that is, 1u
k
and 1u
n
denote the fraction of physical capital and
labor devoted to the production of intangible investment goods, respectively. The process for z
R
t
is assumed to be as follows.
ln(z
R
t
) =
R
ln(z
R
t1
) +
R
t
;
R
t
N(0;
2
zR
)
with the Markov transition function denoted as
R
(z
R
t
jz
R
t1
).
Financial Frictions
41
Individual rms need external funds to nance the investment. While external nance is
not unlimited, rms face the collateral constraints when borrowing. However, intangible capital
cannot be used as collateral. Therefore, the collateral constraint can be formed as that in Moll,
2014:
b
t
6
t
k
t
; 06< 1
That is, b
t
> 0 means that a rm borrows, while b
t
< 0 means that a rm saves.
t
measures the
tightness of the nancial constraints. In other words, the physical net worth of a rm is k
t
b
t
at time t denoted by a
t
. The collateral constraint can be formed as follows.

t
a
t
>k
t
;
t
> 1 (2.7)
The Firms' Problem
s
t
denotes a rm's state att - that is,s
t
= (z
Y
t
;z
R
t
;a
t
;R
t
). The rm maximizes its discounted
present value of dividends, subject to a set of constraints. The value function of the rm is as
follows:
V (s
t
) = max
lt;u
n
t
;kt;;u
k
t
;dt;at+1;Rt+1
d
t
+(1)E
t
U
0
(C
t+1
)
U
0
(C
t
)
V (s
t+1
)
subject to d
t
+a
t+1
=a
t
(1 +r
t
) (r
t
+
K
)k
t
W
t
l
t
+y
t
y
t
=z
Y
t
[
Y
t
1
(u
n
t
l
t
)

]

; 0<< 1; 0<6 1
R
t+1
= (1
R
)R
t
+z
R
t
[
R
t
11
((1u
n
t
)l
t
)
1
]

; 0<
1
6 1; 0<
6 1
and k
t
6
t
a
t
;
t
> 1
d
t
> 0
(2.8)
The process forz
Y
t
is assumed to be asln(z
Y
t
) =
Y
ln(z
Y
t1
)+
Y
t
;
Y
t
N(0;
2
zY
) with the Markov
transition function denoted as
Y
(z
Y
t
jz
Y
t1
). The process for z
R
t
is assumed to be as ln(z
R
t
) =
42

R
ln(z
R
t1
) +
R
t
;
R
t
N(0;
2
zR
) with the Markov transition function denoted as
R
(z
R
t
jz
R
t1
). To
consider rms' savings, the budget constraint can be rearranged as follows:
[a
t+1
(1 +r
t
)a
t
] + (r
t
+
k
)k
t
r
t
b
t
=
t
d
t
r
t
b
t
with a
t
=k
t
b
t
and b
t
> 0 rm borrows, or
[k
t+1
(1
k
)k
t
] [b
t+1
b
t
] =
t
d
t
r
t
b
t
where
t
=y
t
W
t
l
t
denotes the operating prots.
Before moving on to the household sector, it is necessary to clarify the denition and the
measurement of the items of interest in the corporate sector account shown in Table B.3. First, a
rm's value added does not include the (traditional) nal goods that can be consumed or invested
in the physical capital but does include the intangibles - that is, the value-added of a rm at the
end of time period t is y
t
+q
R
H
t
with q
R
t
as the relative price of the intangible capital goods.
The compensation of the labor is W
t
lt. The operating surplus without considering other inputs'
costs are correspondingly as follows:
y
t
+q
R
H
t
W
t
l
t
with the prots (with no taxes)
y
t
+q
R
H
t
W
t
l
t
(r
t
+
k
)k
t
after paying the interest. Therefore, given the dividend d
t
, the gross savings for the rm is
S
t
=y
t
+q
R
t
H
t
(r
t
+
k
)k
t
W
t
l
t
r
t
b
t
d
t
(2.9)
43
while the net debt is dened as the dierence between the debt and the savings. The investment
in tangible capital isk
t+1
(1
k
)k
t
, which is produced by the nal goods
18
. On the other hand,
the intangibles are produced and accumulated within a rm. The investment in the intangibles
is W
t
(1u
n
t
)L
t
+ (r
t
+
k
)(1u
k
t
)k
t
. Therefore, the net debt is as follows.
b
t+1
S
t
= (b
t+1
b
t
) (y
t
+q
R
t
H
t
(r
t
+
k
)k
t
W
t
l
t
(1 +r
t
)b
t
d
t
) (2.10)
Then the labor share, the capital share, the prot share, and the savings share of value added
corresponding to the measurement in the data are as follows.
• The labor share/compensation share is the share of wages and benets for the gross value
added in the corporate sector.
ls
t
=
W
t
l
t
y
t
+q
R
t
H
t
(2.11)
• The capital share is dened as the share of the gross value added used to rent the capital
including physical and intangible capital.
ks
t
=
(r
t
+
k
)k
t
y
t
+q
R
t
H
t
(2.12)
and
rs
t
=
(r
t
+
R
)R
t
y
t
+q
R
t
H
t
(2.13)
• The prot share stands for the share of prots, which is operating prots with the substrac-
tion of net interest paid.
ps
t
= 1ls
t
ks
t
rs
t
=
(1=
y
t
)y
t
+ (1=
R
t
)q
R
t
H
t
y
t
+q
R
t
H
t
(2.14)
18
Here it is assumed that one unit investment in physical capital is produced by one unit of nal good with no
frictions. Therefore, the relative price of the physical investment good to the nal goods is one.
44
2.3.2 Household
The representative household is innitely lived and risk neutral. The household owns the rms. In
each period, the household consumes the the consumption goods, provides the labor and physical
capital to the rm for production in return for labor compensation and rental return to capital,
receives the dividends and saves in risk-free bonds to maximize the life time utility. Therefore,
given the household states
H
t
= (K
t
;B
t
), the household faces the following maximization problem.
V (s
H
t
) = max
fCt;Lt;Kt+1;Bt+1g
u(C
t
;L
t
) +E
t
V (s
H
t
js
H
t
)
subject to C
t
+B
t+1
+K
t+1
(1
K
)K
t
=w
t
L
t
+R
K
t
K
t
+ (1 +r
t
)B
t
+d
t
(2.15)
The necessary conditions for the maximization problem are as follows:
w
t
=
u
L
(C
t
;L
t
)
u
C
(C
t
;L
t
)
1 =E
t
[
u
C
(C
t+1
;L
t+1
)
u
C
(C
t
;L
t
)
(1 +r
t+1
)]
1 =E
t
[
u
C
(C
t+1
;L
t+1
)
u
C
(C
t
;L
t
)
(1 +R
K
t+1

K
)]
where u
C
and u
L
denote the partial derivative of the one period utility function with respect
to consumption and the labor. Given the wage w
t
, the interest rate r
t
and the rental return to
physical capital R
K
t
, solving the household optimization problem gives the labor supply L
S
t
, the
physical capital supply K
S
t+1
, and the funding supply from the household B
S
t+1
. Without loss of
generality, we assume that the household has the following period utility function.
u(C
t
;L
t
) =C
t
v(L
t
)
45
In this case, we get the risk-free interest rate as r = 1= 1, and the rental return to physical
capital is R
K
=r +
K
.
2.3.3 Equilibrium
An equilibrium for this economy contains a sequence of prices and quantities such that the repre-
sentative household and rms maximize their values, and labor, nal goods and physical capital
markets clear - that is,
• Given the state of the representative household, facing the wage, the rental rate of physical
capital, and interest rate of bond, the household chooses labor supply and the savings.
• Given the state of the rms, facing the wage, the rental rate of physical capital, and interest
rate of bond and the collateral constraint, the the rms chooses the labor demand, the
physical demand, the proportion of labor and physical capital for the production of the nal
goods, the dividends, and the savings.
• All the markets are clear - that is,
L
t
=
Z
l
t
C
t
+K
t+1
(1
K
)K
t
=
Z
y
t
B
t
=
Z
b
t
46
2.4 The Mechanism
2.4.1 Measured Labor Share of Income
As shown in the previous sections, the measurement of the labor share in the data depends on the
focus. When the intangible capital is ignored, the labor share of value added is the one measured
by the national account before the data revision in 1999.
ls
traditional
t
=
w
t
L
t
y
t
After the data revision in 2013
19
the measurement corresponds to
ls
M
t
=
w
t
L
t
y
t
+q
R
t
H
t
=
w
t
L
t
[(1 1=
y
t
)y
t
+ (1 1=
R
t
)q
R
t
H
t
] + [(1=
y
t
)y
t
+ (1=
R
t
)q
R
t
H
t
]
(2.16)
where w denotes compensation, L labor, y nal good, H intangible investment, q
R
relative price
of intangible investment,
y
markup of the marginal product of inputs (labor, physical capital,
and intangible capital) over marginal costs when producing the nal goods, and
R
markup
when producing the intangible investment goods. Koh et al., 2015, the only work relating the
intangibles to the labor share of income, to the best of my knowledge, argue that the increase
in q
R
t
H
t
induces the downward trend in ls
t
. Though the conclusion of this study is consistent
with theirs, the mechanism is dierent. First, the value added, is composed of payment to the
inputs and the prots. Given the prot share of value added, the cost share of the inputs other
than labor mirrors the decline in the cost share of labor. With zero prot assumption, the decline
in the labor share osets the increase in the capital share. On the other hand, the prot share
19
The 11th comprehensive revision of NIPA in 1999 recognized business and government expenditures for soft-
ware as xed investment. The most recent 14th comprehensive revision in 2013 treated expenditures by business,
government and nonprot institutions serving households (NPISH) for R&D, and expenditures by private enter-
prises for the creation of entertainment, literary and artistic originals as investments in various forms of durable
capital and no longer, as previously done, as expenditures in intermediate nondurable goods (for the private sec-
tor) or as nal consumption (for the government sector).These R&D and artistic originals (recognized since 2013),
combined with software (recognized since 1999), form the intangible assets in the recent national accounts.
47
determines the cost share of value added, which aects the labor share of value-added as well.
The measured labor share of income ls
M
is of the following form.
ls
M
t
=
w
t
L
t
y
t
+q
R
t
H
t
=
1
1
ls
cost
t
+
pst
ls
M
t
with
ls
cost
t
=
w
t
L
t
(1 1=
y
t
)y
t
+ (1 1=
R
t
)q
R
t
H
t
where ls
cost
denotes the share of physical, intangible, and labor income going to the labor.
2.4.2 Financial Frictions and Pledgeability of Intangible Capital
External nancing is not free, and rms face collateral constraints due to the nancial frictions.
In particular, they cannot use intangible capital as collateral. Theoretically, as we illustrate
the content of intangible investment in table B.2, only investment in computerized information is
relatively easy to be measured. The investment in innovative property and economic competencies
are both dicult to verify. On the other hand, in practice, as shown by Falato et al., 2013, only
less than 3 percent of total loan value has patents or brands used as collateral.
To make the model as simple as possible, we assume there is no equity market, which is
an extreme case for equity market frictions. If there were no equity market frictions - that
is, the rms can issue equity at no cost - the debt market frictions would play no role in the
mechanism. Firms face the tradeo between the investment in the physical capital and intangibles
and the tradeo between the investment and the savings. With too much investment in the
physical capital rms don't have enough resource to produce the intangibles, which limits the
productivity and the protability. On the other hand, with too low investment in the physical
capital rms cannot get enough external funding to nance the investment in intangibles. This
tradeo determines the rms' decision about the investment, which tells the dierence between
48
the traditional measurement of labor share and that including the production of the intangibles.
Without nancial frictions the saving decison is trivial. The choice of u
n
t
and u
k
t
illustrate the
tradeo between the investment in the physical capital and the intangibles whileu
n
t
andu
k
t
denote
the fraction of labor and physical capital used for the production of the nal goods. The following
FOCs
20
equate marginal product of the labor in the production of nal goods and investment in
the intangibles and that of the physical capital.

B
t
y
t
=u
n
t
=
R
t

1
h
t
=(1u
n
t
)

B
t
(1)(y
t
=
Y
t
)(
Y
t
=u
k
t
)
1+
=
R
t

(1
1
)(h
t
=
R
t
)(
R
t
=(1u
k
t
))
1+
2.4.3 Accumulation of Intangible Capital
Since intangible capital played a more important role in the 2000s than it did in the 1970s, the
more aggressive accumulation of intangible capital requires higher corporate savings to nance the
investment. On the other hand, the accumulation of intangibles gives the rms another way to
increase the prots, which forces the decline in the labor of value-added as well. The labor share
of value-added, dened as in equation 2.16, is lower than the previously measured labor share of
value-added ls
traditional
t
since the markups is no less than 1 (
y
t
>= 1 and/or
R
t
>= 1). We
model the production of nal goods Y in the Cobb-Douglas forms, Y = (z
y

Y
1
(u
n
)

)L

with

Y
= [(
u
k
K

)

+ (1)(
R
1
)

]
1=
, respectively. Besides, with the assumption 1=1 +> 1,
intangible capital is substitute to physical capital. On the other hand, the rms accumulates the
intangibles by themselves, R
0
= (1
R
)R +z
R
t
[
R
11
((1u
n
)l)
1
]

. Therefore, including the
intangibles, the labor share of value-added is not only in
uenced by the capital share but also
20
The dynamic system is illustrated in the appendices.
49
the prot share. First, the relative protability from the production of the nal good and the
intangibles determines how the variation in the intangibles in
uence that in prot share, that is,
@ps
@(q
R
H)
= (
1

y

1

R
)
y
(y +q
R
H)
2
Second, the prot share increases in the markups. In this chanel, the increase in the prot share
mirrors the decline in the labor share, if the labor share of cost stays constant.
@ps
@
y
=
1

y2
y
y +q
R
H
@ps
@
R
=
1

R
2
q
R
H
y +q
R
H
Third, the share of physical capital in the aggregated capital aects the labor share of income
through the cost share of labor.
50
2.5 Quantitative Analysis
2.5.1 Calibration
Table 2.2: Parameter Values for Steady State Analysis
Parameter values Description Source
Financial sectors
= 1=(1 0:56) 0.56 is the fraction of physical capital as collateral Wang, 2017
Preferences
= 1:73 w
ss
= 1 and l
ss
= 1=3
= 0:5 @lnl=@lnw = 2
= 0:95 Households' annual discount factor
= 0:05 Entrepreneurs' additional discount factor
Technology
= 0:62 Labor's share in production function Hou and Johri, 2009
= 0:85 Return to scale to nal

Y
= 0:72 Annually persistence of log TFP process

zY
= 0:2 Standard deviation of log TFP
Intangible

1
= 0:68 Labor's share in production function Hou and Johri, 2009

= 0:95 Return to scale to intangible
=0:3 Elasticity of substitution of between capitals
= 0:8 Fraction of physical capital in the aggregated capital Falato et al., 2013

R
= 0:85 Annually persistence of log TFP process

zR
= 0:25 Standard deviation of log TFP
Depreciation

K
= 0:10 Annually depreciation rate of physical capital

R
= 0:10 Annually depreciation rate of intangible capital
51
2.5.2 Comparative Statics
Intangible share in the aggregate capital:
see Figure B.7 on page 98
Labor shares in production: and
1
see Figure B.10 and Figure B.11 on page 101 and 102, respectively
Markups: and
see Figure B.8 and Figure B.9 on page 99 and 100, respectively
2.5.3 Accumulation of Intangible Capital
2.6 Literature Revisited
To illustrate possible chanels which can decrease the laobr share of income it is necessary to
revisit some relevant literature. On the one hand, it shows possible discrepancy between the
52
measurements. On the other hand, it helps understand it is dicult to disentangle eects due to
the limited information avalaible.
53
2.6.1 Koh et al., 2015 Revisited
Dividends are dened as the residual of value added after investment and compensation isbpaid
within a rm or in a country - that is,
D
t
=Y
t
w
t
L
t
I
t
Under the assumption of perfect competition in both product and factor markets and constant
returns to scale in production, value-added is exhausted by payments to inputs. In a model of
two inputs, as in the traditional setting
Y
t
=R
t
K
t
+w
t
L
t
wherew andr are the competitive real wage and rental price of capital, respectively. In terms of
the income share, we get
1 =S
K
+S
L
whereS
K
andS
L
are the income share of physical capital and labor. On the other hand, without
considering other frictions, the investment is the change in capital net of depreciation
x
t
=
I
t
v
t
=K
t+1
(1
t
)K
t
where
t
i the depreciation rate. Therefore, the dividends are
D
t
=Y
t
w
t
L
t
I
t
=R
t
K
t

K
t+1
(1
t
)K
t
v
t
= (R
t
+
1
t
v
t
)K
t
K
t+1
54
That is, the dividends are only from the competitive rental market for (physical) capital. Similarly,
if we add intangible capital as another input for the production, the investment includes that in
the physical capital and the the intangible capital - that is
x
j
t
=
I
j
t
v
j
t
=K
j
t+1
(1
j
t
)K
j
t
;j2fR;Kg
where
j
t
is the depreciation rate. Therefore, the dividends are
D
t
=Y
t
w
t
L
t
I
t
=
X
j2fR;Kg
[R
j
t
K
j
t

K
j
t+1
(1
j
t
)K
j
t
v
j
t
] =
X
j2fR;Kg
[(R
j
t
+
1
j
t
v
j
t
)K
j
t
K
j
t+1
]
Clearly, this is the standard result for valuation in the perfect competition-constant returns to
scale framework including intangible capital with no adjustment costs: dividends arise from the
competitive rental market for physical and intangible capital, which is consistent with the in-
terpretation of capital including intangibles by Hall et al., 2000. Then we can get the following
propositions about the change in the labor share:
Proposition 1: In the perfect competition-constant returns to scale framework, as in Koh
et al., 2015, any decline in the labor share must be oset by an equal increase in the physical and
intangible share.
Proposition 2: In the perfect competition-constant returns to scale framework, as in Koh
et al., 2015, any decline in the labor share S
L
can be accompanied by one of the following cases:
• Case 1: increase in the physical capital share and no change in the intangible capital share
- that is, S
L
=S
K
withjS
L
j=jS
K
j
• Case 2: increase in the intangible capital share and no change in the physical capital share,
S
L
=S
R
withjS
L
j=jS
R
j
• Case 3: increase in the physical capital share and intangible share, S
L
=S
K
S
R
withjS
L
j=jS
K
j+jS
R
j
55
• Case 4: increase in the physical capital share and delince in the intangible capital share,
S
L
=S
K
S
R
withjS
L
j=jS
K
j+jS
R
j
• Case 5: increase in the intangible capital share and decline in the physical capital share,
S
L
=S
K
S
R
withjS
L
j=jS
K
jjS
R
j
Koh et al., 2015 use the optimal investment decision of a representative rm when assuming
the discount factor is
1
1+rt+1
to get the gross return of capital, or the marginal product of capital
- that is,
R
j
t+1
=
1 +r
t+1
v
j
t

1
j
t+1
v
j
t+1
.
2.6.2 Barkai, 2017 Revisited
First, we formulate the Barkai, 2017 framework in real terms. Assume there is imperfect com-
petition in the product markets. Firms with market power reward inputs with less than their
marginal products:
Y
t
=
t
(R
t
K
t
+w
t
L
t
)
where
t
is the ratio of the price of value added to marginal cost of inputs at time t. Writing the
prot share as S
P
t
= 1
1
t
, dividends are
D
t
=Y
t
w
t
L
t
I
t
= (R
t
+
1
t
v
t
)K
t
K
t+1
+S
p
t
Y
t
Dividends are now composed of two parts: one arising from the competitive rental market for
physical capital, as in the previous setting, and the other generated by an existing monopoly
franchise in output markets, which is expressed by the second term on the right-hand side of the
56
above equation. We further assume that the rms extract pure prots from downward-sloping
demand curves:

t
=

t

t
1
Then, similarly, if we add intangible capital as another input for the production, the investment
includes that in the physical capital and the the intangible capital - that is,
x
j
t
=
I
j
t
v
j
t
=K
j
t+1
(1
j
t
)K
j
t
;j2R;K
where
j
t
i the depreciation rate. Therefore, the dividends are
D
t
=Y
t
w
t
L
t
I
t
=
X
j2fR;Kg
[R
j
t
K
j
t

K
j
t+1
(1
j
t
)K
j
t
v
j
t
]+S
p
t
Y
t
=
X
j2fR;Kg
[(R
j
t
+
1
j
t
v
j
t
)K
j
t
K
j
t+1
]+S
p
t
Y
t
Under the same assumption about the monoply setting,
t
=
t
t1
gives the markup over the
marginal cost. When assuming a xed markup, that is,
t
=
t+1
= , we can get the similar
propositions.
Proposition3: In the imperfect competition-constant returns to scale framework as in Barkai,
2017, when assuming the markup is xed, any decline in the labor share must be oset by an
equal increase in the physical and intangible share.
Proposition4: In the imperfect competition-constant returns to scale framework as in Barkai,
2017, when assuming the markup is xed, any decline in the labor share S
L
can be associated
with one of the following cases:
• Case 1: increase in the physical capital share and no change in the intangible capital share
- that is, S
L
=S
K
withjS
L
j=jS
K
j
• Case 2: increase in the intangible capital share and no change in the physical capital share,
S
L
=S
R
withjS
L
j=jS
R
j
57
• Case 3: increase in the physical capital share and intangible share, S
L
=S
K
S
R
withjS
L
j=jS
K
j+jS
R
j
• Case 4: increase in the physical capital share and declince in the intangible capital share,
S
L
=S
K
S
R
withjS
L
j=jS
K
j+jS
R
j
• Case 5: increase in the intangible capital share and decline in the physical capital share,
S
L
=S
K
S
R
withjS
L
j=jS
K
jjS
R
j
On the other hand, when assuming the markup can change over time, the prot share of
income is not always xed.
Proposition 5: In the imperfect competition-constant returns to scale framework, as in
Barkai, 2017, any decline in the labor share is not necessarily to be followed by an equal increase
in the physical and intangible share.
Proposition 6: In the imperfect competition-constant returns to scale framework, as in
Barkai, 2017, any decline in the labor share S
L
can be accompanied by one of the following
cases:
• Case 1: increase in the capital share and no change in the prot share, that is, S
L
=
(S
K
+S
L
), which includes all the cases stated in Proposition 4:
Case 1.1: increase in the physical capital share and no change in the intangible capital share
- that is, S
L
=S
K
withjS
L
j=jS
K
j
Case 1.2: increase in the intangible capital share and no change in the physical capital share,
S
L
=S
R
withjS
L
j=jS
R
j
Case 1.3: increase in the physical capital share and intangible share, S
L
=S
K
S
R
withjS
L
j=jS
K
j+jS
R
j
Case 1.4: increase in the physical capital share and decline in the intangible capital share,
S
L
=S
K
+ S
R
withjS
L
j=jS
K
j+jS
R
j
58
Case 1.5: increase in the intangible capital share and decline in the physical capital share,
S
L
= S
K
S
R
withjS
L
j=jS
K
jjS
R
j
• Case 2: increase in the prot share and no change in the capital share, S
L
=S
P
with
jS
L
j=jS
P
j
Case 2.1: S
K
=S
R
with S
K
> 0
Case 2.2: S
K
=S
R
with S
R
> 0
Case 2.3: S
K
=S
R
= 0
• Case 3: increase in the capital share and prot share, S
L
=(S
K
+ S
R
) S
R
with
jS
L
j=jS
K
+ S
R
j+jS
R
j
• Case 4: increase in the capital share and delince in the intangible capital share, S
L
=
(S
K
+ S
R
) S
R
withjS
L
j=jS
K
+ S
R
j+jS
R
j
• Case 5: increase in the capital share and decline in the prot share, S
L
=(S
K
+
S
R
) S
R
withjS
L
j=jS
K
+ S
R
j+jS
R
j
To summarize, the inclusion of intangible capital doesn't necessarily increase the capital share
and decrese the prot share. First, the inclusion of the intangibles expands the measure of the
value added. The labor share of income is lower. Capital deepening due to intangibles, as claimed
in Koh et al., 2015, doesn't necessarily have an eect on the measured trends in the labor share.
They only cover the case 2 in proposition 2, which is based on the assumption that the elasticity
of substitution is greater than one. Second, Barkai, 2017 points out that only higher growth rate
of the intangibles than that of the output can generate the declining labor share, which is only
refering to proposition 6. However, a downward trend in the labor share of income, can follow by
a rising prot share generated by the accumulation of intangibles. When modeling the production
of the intangibles explicitly, with the simpliest form of the production function, Cobb-Douglas
production function with the elasticity of substitution between aggregated capital and labor of
59
unity, I can distinguish the sources of the rising prot share, either from the production of outputs
or from that of intangibles.
2.7 The Concluding Remarks
This paper studies the in
uence of the rising importance of intangible capital in rms' production
(or technological changes that lowers the tangible-to-intangible capital ratio in the production)
on the labor share of income and corporate savings. It is observed that in a broad set of countries
the declining labor share of income mirrors the rising corporate savings. At the same time, the
intangible investment increased in the recent decades. Besides, simple empirical study shows that
the intangible capital holding is positively correlated with corporate savings in the United States
using CRSP-Computstat rm leve data.
A modied neoclassical growth model with a set of general external parameters can deliver the
mechanism that the rising importance of the intangible capital (characterized by the parameter
1) is a signicant driving force for the increase in the corporate savings and the decline
in the labor share of income in the United States. The inclusion of the intangibles aects the
measured trends in the labor share of income in the following ways. First, the investment in
intangibles increases the value-added of a rm or an economy. With the relatively constant labor
compensation, compared with the measured labor share of income by the traditional national
accounting, the real labor share of income is lower. Secondly, the accumulation of the intangibles
changes the protability of the rms, depending on the markups. When the same form of the
production function for the intangibles as the traditional nal goods is adopted, it becomes clear
how the variations in parameters of the production function capturing the special properties of
the intangibles in
uence the variations in the income distribution. When the intangibles play a
more important role, the increasing markup with accumulation of the intangibles increases the
prot share of the rms, which reduces the labor share of income. Besides, the mechanisum jointly
60
explains the rising corporate savings rate and validates the chanels. At the same time, nancial
frictions play an important role. The need to nance the increasing intangible investment requires
the rms have to save more given their prot share since the intangible capital cannot be used
as collateral in applying for external nancing. In addition, the accumulation of the intangibles
provides the rm another way to earn a higher prot share, which provides more available resources
to save. To summarize, the rising importance of the intangibles in the production from 1970s to
2000s in the United States is the driving force for the declining labor share of income and the
rising corporate savings.
In addition, the evidence that intangible investment has increased in a broad set of countries,
the quantitative analysis provides insights into the reasons for the global decline in the labor share
of income. Modeling the accumulation of the intangible explicitly helps to disentangle eects of
the intangibles on the labor share of income and the savings through the changing importance of
the intangibles in the productions and the markups. However, to identify the magnitude of the
various eects needs further exploration of the data.
61
Bibliography
Abdih, Y. and S. Danninger (2017). What explains the decline of the u.s. labor share of income?
an analysis of state and industry level data. IMF Working Paper No. 17/167 .
Acemoglu, D. and P. Restrepo (2016). The race between machine and man: Implications of
technology for growth, factor shares and employment. NBER Working Paper No. 22252 .
Adrian, T., P. Colla, and H. Shin (2012). Which nancial frictions? parsing the evidence from
the nancial crisis of 2007-2009. NBER Macroeconomics Annual 27.
Armenter, R. and V. Hnatkovska (2017). The macroeconomics of rms' savings. Federal Researve
Bank of Philadelphia Working Paper No. 112-1 .
Autor, D., D. Dorn, L. F. Katz, C. Patternson, and J. V. Reenen (2017a). Concentrating the fall
of the labor share. NBER Working Paper No. 23108 .
Autor, D., D. Dorn, L. F. Katz, C. Patternson, and J. V. Reenen (2017b). The fall of the labor
share and the rise of superstar rms. Working Paper.
Bacchetta, P. and K. Benhima (2010). The demand for liquid assets, corporate saving, and global
imbalances. Universite De Lausanne Working Paper.
Bacchini, F. and R. Iannaccone (2016). Real time estimation for policy analysis. SPINTAN
Working Paper Series No. 22 .
Barkai, S. (2017). Decline labor and capital shares. Working Paper.
Bayoumi, T., H. Tong, and S.-J. Wei (2010). The chinese corporate savings puzzle: A rm-level
cross-country perspective. NBER Working Paper No. 16432 .
Bernanke, B., G. Mark, and G. Simon (1999). The nancial accelerator in a quantitate business
cycle framework. Handbook of Macroeconomics.
Bessen, J. (2008). The value of u.s. patents by owner and patent characteristics. Research
Policy 37(5), 932{945.
Carlstrom, C. and T. Fuerst (1998). Agency costs, net worth, and business
uctuations: a
computable general equilibrium analysis. American Economic Reviews 87, 893{910.
Chen, P., L. Karabarbounis, and B. Neiman (2017). The global rise of corporate saving. NBER
Working Paper No 23133 .
Chugh, S. (2013). Costly external nance and labor market dynamics. Journal of Economic
Dynamics and Control 37, 2882{2912.
Corrado, C., J. Haskel, C. Jona-Lasinio, and M. Iommi (2012). Intangible capital and growth in
advanced economies: Measurement methods and comparative results. IZA DP No. 6733 .
62
Corrado, C., J. Haskel, C. Jona-Lasinio, and M. Iommi (2013). Innovation and intangible invest-
ment in europe, japan and the united states. Oxford Review of Economic Policy 29, 261{286.
Corrado, C., C. Hulten, and D. Sichel (2009). Intangible capital and u.s. economic growth. Review
of Income and Wealth 55 (3), 661{685.
Corrado, C., K. Jaeger, and C. Jona-Lasinio (2016). Measuring intangible capital in the public
sector: A manual.
Crouzet, N. (2015). Aggregate implications of corporate debt choices. Working Paper.
Eisfeldt, A. L. and D. Papanikolaou (2013). Organization capital and the cross-section of expected
returns. The Journal of Finance 68 (4), 1365{1406.
Eisfeldt, A. L. and D. Papanikolaou (2014). The value and ownership of intangible capital.
American Economic Review 105 (5), 189{194.
Eisfeldt, A. L. and D. Papanikolaou (2017). The value and ownership of intangible capital.
American Economic Review 105 (5), 189{194.
Elsby, M. W., B. Hobijin, and A. Sahin (2013). The decline of the u.s. labor share. Brookings
Papers on Economic Activity (2), 1{63.
Faia, E. and T. Monacelli (2007). Job matching and propagation. Journal of Economic Dynamics
and Control 31, 3228{3254.
Falato, A., D. Kadyrzhanova, and J. W. Sim (2013). Rising intangible capital, shrinking debt
capacity and the us corporate savings glut. Finance and Economics Discussion Series 2013-67.
Board of Governors of the Federal Reserve System (U.S.).
Falk, M. (2013). New empirical ndings for international investment in intangible assets. Working
Paper No. 30 .
Fama, E. F. and K. R. French (1992). The cross section of expected stock returns. The Journal
of Finance 47, 427{465.
Fan, J. and S. Kalemli-Ozcan (2016). Emergence of asia: Reforms, corporate savings, and global
imbalances. NBER Working Paper No. 22334 .
Giovannoni, O. (2014). What do we know about the labour share and the prot share? partiii:
Measures and structural factors. Leavy Economics Institute of Bard College Working Paper
No. 805.
Gomes, J., A. Yaron, and L. Zhang (2003). Asset prices and business cycles with costly external
nance. Review of Economic Dynamics 6, 767{788.
Gomme, P. and P. Rupert (2004). Measuring labor's share of income. Policy Dicusson Papers,
the Research Department of the Federal Reserve Bank of Cleveland.
Gonzalez, I. and P. Trivin (2016). Finance and the global decline of the labour share.
Graeve, F. D. (2008). The external nance premium and the macroeconomy: U.s. post-wwii
evidence. Journal of Economic Dynamics and Control 32, 3415{3440.
Grossman, G. M., E. Helpman, E. Obereld, and T. Sampson (2017). The productivity slowdown
and the declining labor share: A neoclassical exploration.
63
Gruber, J. W. and S. B. Kamin (2015). The corporate saving glut in the aftermath of the global
nancial crisis. Working Paper.
Hall, B. H. (1992). Investment and research and development at the rm level: Does the source
of nancing matter. NBER Working Paper No. 4096 .
Hall, B. H., A. B.Jae, and M. Trajtenberg (2000). Market value and patent citations: A rst
look. NBER Working Paper No. 7741 .
Hall, B. H. and J. Lerner (2009). The nancing of r&d and innovation. NBER Working Paper
No. 15325.
Hartman-Glaser, B., H. Lustig, and M. X. Zhang (2016). National income accounting when rms
insure managers: Understanding rm size and compensation inequality. NBER Working Paper
No. 22651.
Henningsen, A. and G. Henningsen (2002). Econometric estimation of the constant elasticity of
substitution function in r: Package miceconces. FOI Working Paper No. 9 .
Himmelberg, C. P. and B. C. Petersen (1994). R&d and internal nance: A panel study of small
rms in high-tech industries. The Review of Economics and Statistics 76 (1), 38{51.
Hou, K. and A. Johri (2009). Intangible capital, corporate earnings and the business cycle.
McMaster University Department of Economics Working Paper Series.
Imrohoroglu, A. and S. Tuezel (2014). Firm-level productivity, risk and return. Management
Science 60, 2073{2090.
Jaeger, K. (2017). Ieu klems growth and productivity accounts 2017 release, statistical module.
The Conference Board.
Karabarbounis, L. and B. Neiman (2014). The global decline of the labor share. Quarterly Journal
of Economics 129 (1), 61{103.
Klein, P. (2000). Using the generalized schur form to solve multivariate linear rational expectations
model. Journal of Economic Dynamics and Control 24 (10), 1405{1423.
Koh, D., R. Santaeulalia-Llopis, and Y. Zheng (2015). Labor share decline and the capitalization
of intellectual property products. Working Paper.
Levin, A., F. Natalucci, and E. Zakrajsek (2004). The magnitude and cyclical behavior of nancial
market frictions. Finance and Discussion Series 70.
Len-Ledesma, M. A., P. McAdam, and A. Willman (2010). Identifying the elasticity of substitution
with biased technical change. The American Economic Review 100 (4), 1330{1357.
Merz, M. (1995). Search in the labor market and the real business cycle. Journal of Monetary
Economics 10, 327{347.
Moll, B. (2014). Productivity losses from nancial frictions: Can self-nancing undo capital
misallocation? American Economic Review 104 (10), 3186{3221.
Petrosky-Nadeau, N. (2014). Credit, vacancies and unemployment
uctuations. Review of Eco-
nomic Dynamics, 191{205.
Pissarides, C. A. (2000). Equilibrium Unemployment Theory. Cambridge, U.K.: MIT Press.
64
Rognlie, M. (2015). Deciphering the fall and rise in the net capital share. Brookings Papers on
Economics Activity 49 (1), 1{54.
Shimer, R. (2005). The cyclical behavior of equilibrium unemployment and vacancies. American
Economic Reviews 95, 25{49.
Thum-Thysen, A., P. Voigt, B. Bilbao-Osorio, C. Maier, and D. Oganyanova (2017). Unlocking
investment in intangible assets. European Commission Discussion Paper 047 .
Wang, Y. (2017). Debt market friction, rm-specic knowledge capital accumulation and macroe-
conomic implicationsl. Review of Economic Dynamics.
65
Appendix A
Appendix for Chapter 1
Figure A.1: Economy Level Heterogeneity
66
Figure A.2: IRF with respect to output productivity
67
Figure A.3: IRF with respect to intangible productivity
68
Figure A.4: IRF with respect to output productivity
69
Figure A.5: IRF with respect to intangible productivity
70
Figure A.6: IRF with respect to output productivity
71
Figure A.7: IRF with respect to intangible productivity
72
Appendix B
Appendix for Chapter 2
B.1 Details about Various Data Sources
B.1.1 Country and Industry Data in Advanced Economies
• INTAN-Invest database, which gives market sector data on intangible assets for 27 EU coun-
tries plus Norway and the United States Corrado et al., 2012 describes the methods and
sources used to bulid the estimates. "A brief description of the data is as follows: The coun-
tries are, where available, EU countries (Austria, Belgium, Bulgaria, Cyprus, Czech Repub-
lic, Denmark, Estonia, Finland, France, Germany (including ex-GDR from 1991), Greece,
Hungary, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Poland, Por-
tugal, Romania, Slovakia, Slovenia, Spain, Sweden, and United Kingdom) and Norway,
USA. INTAN-Invest market sector data cover NACE sectors A through K (excluding real
estate) plus sector O. Data are for 1995-2010 or most recent year available. The intangible
assets are computerised information (software and databases), innovative property (R&D,
design, product development in nancial services, mineral exploration and spending on the
production of artistic originals), and economic competencies (market research, advertising,
training and organisational capital). Data use harmonized software de
ators, that is, soft-
ware de
ators calculated consistently across countries."
• EU KLEMS database, which gives the basic output, input and productivity data for 34
industries and 8 aggreagets according to the ISIC Rev. 4(NACE Rev. 2) industry classi-
cation. Jaeger, 2017 decscribes the methods and sources used to construct the database.
"A brief description of the data is as follows: The countries are, where available, EU coun-
tries (Austria, Belgium, Bulgaria, Cyprus, Czech Republic, Denmark, Estonia, Finland,
France, Germany (including ex-GDR from 1991), Greece, Hungary, Ireland, Italy, Latvia,
Lithuania, Luxembourg, Malta, Netherlands, Poland, Portugal, Romania, Slovakia, Slove-
nia, Spain, Sweden, United Kingdom ,and Croatia). Data are from 1995-2016 for most
countries and industries. The data on output, value added and employment is nearly fully
consistent with Eurostat at the corresponding industry levels. The data on gross xed capital
formation, prices, and capital stocks is nearly fully consistent with Eurostat at the corre-
sponding industry levels. The asset types were modied and extended according to the ESA
2010 requirements. For labour services use has been made of the micro-data underlying the
European Labour Force Survey (LFS) and the Structure of Earning Survey (SES) for recent
years.
• WORLD KLEMS database, which includes a broad set of countries around the world.
WORLD KLEMS website describes the various sources of KLEMS-type databases. A brief
description of the data is as follows: it extends the EU KlEMS database to that includes the
data of the United States to 2017, Japan to 2013, Canada to 2012, Russia to 2017, China to
73
2015, Korea to 2014 and Argentina to 2012. The data in these databases is structured and
built up in the same way as the data in the EU KLEMS database to increase comparability
across a larger set of countries. This harmonisation process includes input denitions, price
concepts, aggregation procedures and comparable measures of inputs and productivity.
• SPINTAN database, which gives the intangibles estimates in the Public sector (1995-2012)
and Real Time data (2013-2015). Corrado et al., 2016 describes the methods and sources
used to construct the database. Bacchini and Iannaccone, 2016 decribes the methodology
for constructing the real time data A brief description of the data is as follows: The database
includes data on public intangible investment and capital services for 22 European countries
and other additional countries, over the period 1995-2012. The data is cross-country har-
monized and consistent with the National Accounts (NA) principles. This implies that it is
coherent with other NA aggregates (output, tangible gross xed capital formation, intermedi-
ate costs) and with the business sector estimates of intangibles developed by INTAN-Invest.
• Chen et al., 2017
B.1.2 Firm Level Data in the United States
• Compustat. The sample includes all United States rm in CRSP-Compustat merge le from
1962-2016. I include rms with December as the scal year ending month (fyr=12) and use
the following variables: Book Value of Gross Physical Capital (Items 7), Book Value of Total
Assets (Item 6), R&D Investment (Item 46), Employment (item 29), Gross Debt (Item 9+
Item 34), Cash and Equivalents (Item 1), operating income before depreciation (Item 13).
These denitions are commonly used in empirical corporate nance.
• AWI: AWI refers to Average Wage Index given by the social security administration(https://www.ssa.gov/oact/cola/awidevelop.html).
The average wage is an average per worker, not an average per job.
The main data is from Compustat data. Following Fama and French, 1992, I use the sample
from 1962 since Compustat data for earlier years have a serious selction bias. I include rms with
non-missing SIC codes and I use additional sample selction rules. I use the following variables from
CRSP/Compustat Merged - Fundamentals Annual. To compute the value added of output y
it
of
a rm I use [Sale - Materials]. Sales is net sales, sale (Item 12), following Imrohoroglu and Tuezel,
2014 without considering the intangible capital. Materials is mesured as [Total expenses - Labor
expenses], where Total expenses is approximated as [Sale-Operating Income Before Depreciation
and Amortization]. Operating Income Before Depreciation and Amortization is oibdp (Item 13)
and Labor expense is xlr (Item 42)
74
B.2 Empirical Analysis
Formally, a linear regression equation for baseline net debtis estimated as follows:
S
ijt
=
0
+
1
Int
ijt
+
3
Control
ijt
+Ind
j
+
jt
+u
ijt
whereS
ijt
is the net debt of rmi in industryj at timet. nt
ijt
denotes the intangible investment
of rm i in industry j at time t.
1
is the parameter of interest which measures the eect of
increasing 1 unit of intangible investment on the net detb/savings. Control
ijt
is a vector of
the rm's characteristics, which are commonly used in the corporate nance literature. Ind
j
is
the industry xed eects which account for time invariant heterogeneity across industries. I also
include the industry-specic time trends,gamma
jt
to control for industry-specic deviations from
the common nationwide trend.
75
B.3 Model Solution
s
t
denotes a rm's state at t, that is, s
t
= (z
Y
t
;z
R
t
;a
t
;R
t
). The rm maximizes its discounted
present value of dividends, subject to a set of constraints. The value function of the rm is as
follows.
V (s
t
) = max
lt;u
n
t
;kt;u
k
t
;dt;at+1;Rt+1
d
t
+(1)E
t
U
C
(C
t+1
)
U
C
(C
t
)
V (s
t+1
)
subject to d
t
+a
t+1
=a
t
(1 +r
t
) (r
t
+
K
)k
t
W
t
l
t
+y
t
y
t
=z
Y
t
[
Y
t
1
(u
n
t
l
t
)

]

; 0<< 1; 0<6 1
R
t+1
= (1
R
)R
t
+z
R
t
[
R
t
11
((1u
n
t
)l
t
)
1
]

; 0<
1
6 1; 0<
6 1
and k
t
6
t
a
t
;
t
> 1
d
t
> 0
The Lagrangian function follows.
L(s;) =d +(1)E
U
C
(C
0
)
U
C
(C)
V (s
0
)
+
B
(da
0
+a(1 +r) (r +
K
)kWl +z
Y
[
Y
1
(u
n
l)

]

)
+
R
(R
0
+ (1
R
)R +z
R
[
R
11
((1u
n
)l)
1
]

)
+
a
(ak)
+
d
d
The necessary conditions contain
[l]
B
(Wy=l) =
R

1
h=l (B.3.1)
[u
n
]
B
y=u
n
=
R

1
h=(1u
n
) (B.3.2)
[k]
B
[(r +
K
)(1)(y=
Y
)
@
Y
@k
] =
R
[
(1
1
)(h=
R
)
@
R
@k
]
a
(B.3.3)
[u
k
]
B
@y
@
Y
@
Y
@u
k
=
R
@h
@
R
@
R
@u
k
(B.3.4)
[a
0
] (1)E
@V
0
@a
0
=
B
(B.3.5)
[R
0
] (1)E
@V
0
@R
0
=
R
(B.3.6)
[d] 1
B
+
d
= 0 (B.3.7)
The envelope condition gives
@V
@a
=
B
(1 +r) +
a
(B.3.8)
@V
@R
=
B
@y
@R
+
R
@h
@R
(B.3.9)
76
B.4 The Non-Stochastic Steady States
The steady states of all the variables are characterized as follows. In steady states, there is no
uncertainty, that is, z
R
=z
R
= 1. For the rms,assume that
d
= 0, that is, d> 0 never binds,
we get

B
= 1
from the equation B.3.7. The equation B.3.5 and B.3.8 give
(
B
(1 +r) +
a
)(1) = 1
then we get

a
= (1 +r)

1
1

> 0
that is, the collateral constraint binds. B.3.1 gives

R
=
Wly

1
R
B.3.2 gives

R
=
y=u
n

1
h=(1u
n
)
or then we get
ls
m

wl
y
=
y
u
n
that is the measured labor share of income. h B.3.3 gives
(r +
K
)(1)
y

Y
@
Y
@k
=
y=u
n

1
h=(1u
n
)

(1
1
)
h

R
@
R
@k
(1 +r)

1
1

(B.4.1)
together with
R = (1)R + (
R
11
((1u
n
)l)
1
)

(B.4.2)
and
y
u
n
=wl (B.4.3)
Also, B.3.4 gives
@y
@
Y
@
Y
@u
k
=
y=u
n

1
h=(1u
n
)
@h
@
R
@
R
@u
k
(B.4.4)
with

Y
= (u
k
k;R))

R
= ((1u
k
)k;R)
@y
@
Y
@
Y
@u
k
=(1)(Y=
Y
)(
Y
=u
k
k)
1+
k
@h
@
R
@
R
@u
k
=
(1
1
)(h=
R
)(
R
=(1u
k
)k)
1+
k
@y
@
Y
@
Y
@k
=(1)(Y=
Y
)(
Y
=u
k
k)
1+
u
k
@h
@
R
@
R
@k
=
(1
1
)(h=
R
)(
R
=(1u
k
)k)
1+
(1u
k
)
77
@y
@
Y
@
Y
@R
=(1)(Y=
Y
)((1)
Y
=R)
1+
@h
@
R
@
R
@R
=
(1
1
)(h=
R
)((1)
R
=R)
1+
78
B.5 The Dynamic System
The dynamic system is characterized by the following equations.

B
t
(w
t
y
t
=l
t
) =
R
t

1
h
t
=l
t
(B.5.1)

B
t
y
t
=u
n
t
=
R
t

1
h
t
=(1u
n
t
) (B.5.2)

B
t
[(r
t
+
K
)(1)(y
t
=
Y
t
)
@
Y
t
@k
t
] =
R
t
[
(1
1
)(h
t
=
R
t
)
@
R
t
@k
t
]
a
t
(B.5.3)

B
t
(1)(y
t
=
Y
t
)(
Y
t
=u
k
t
)
1+
=
R
t

(1
1
)(h
t
=
R
t
)(
R
t
=(1u
k
t
))
1+
(B.5.4)
(1)E
t
[
B
t+1
(1 +r
t+1
) +
a
t+1

t+1
] =
B
t
(B.5.5)
(1)E[
B
t+1
@y
t+1
@R
t+1
+
R
t+1
@h
t+1
@R
t+1
] =
R
t
(B.5.6)
1
B
t
+
d
t
= 0 (B.5.7)
w
t
=
u
L
(C
t
;L
t
)
u
C
(C
t
;L
t
)
(B.5.8)
1 =E
t
[
u
C
(C
t+1
;L
t+1
)
u
C
(C
t
;L
t
)
(1 +r
t+1
)] (B.5.9)
1 =E
t
[
u
C
(C
t+1
;L
t+1
)
u
C
(C
t
;L
t
)
(1 +R
K
t+1

K
)] (B.5.10)
c
t
+k
t+1
(1
K
)k
t
=y
t
(B.5.11)

Y
t
= [(
u
k
t
K
t

)

+ (1)(
R
t
1
)

]
1=
(B.5.12)

R
t
= [(
(1u
k
t
)K
t

)

+ (1)(
R
t
1
)

]
1=
(B.5.13)
y
t
=z
Y
t
[
Y
1
t
(u
n
t
L
t
)

]

; 0<< 1; 0<6 1 (B.5.14)
ln(z
Y
t
) =
Y
ln(z
Y
t1
) +
Y
t
;
Y
t
N(0;
2
zY
) (B.5.15)
R
t+1
= (1
R
)R
t
+z
R
t
[
R
11
t
((1u
n
t
)L
t
)
1
]

; 0<
1
6 1; 0<
6 1 (B.5.16)
ln(z
R
t
) =
R
ln(z
R
t1
) +
R
t
;
R
t
N(0;
2
zR
) (B.5.17)
The exogenous states contain z
Y
t
and z
R
t
. The endogenous states are a
t
and R
t
. The other
endogenous variables are l
t
, k
t
, u
n
t
, u
k
t
, c
t
, y
t
,
Y
t
,
R
t
, b
t
,
B
t
,
R
t
,
a
t
. Since we assume that the
rms are uniform distributed facing the same productivity, the uppercase and lowercase letters
are inter-changeable in the notations.
79
B.6 The Simplied Dynamic System
To make the system as simple as possible we are making the following assumptions.
• u(C
t
;L
t
) =C
t
v(L
t
), risk-neutral household.
•
d
t
= 0, the non-negative dividends constraint never binds.
The dynamic system is simplied as follows.
w
t
l
t
=
y
t
u
n
t
(B.6.1)
r +
K

@y
t
@
Y
t
@
Y
t
@k
t
=
R
t
@h
t
@
R
t
@
R
t
@k
t

a
t
(B.6.2)
@y
t
@
Y
t
@
Y
t
@k
t
=(1)(Y
t
=
Y
t
)(
Y
t
=u
k
t
k
t
)
1+
u
k
t
(B.6.3)
@h
t
@
R
t
@
R
t
@k
t
=
(1
1
)(h
t
=
R
t
)(
R
t
=(1u
k
t
)k
t
)
1+
(1u
k
t
) (B.6.4)
(1)(y
t
=
Y
t
)(
Y
t
=u
k
t
)
1+
w
t
y
t
=l
t
=

(1
1
)(h
t
=
R
t
)(
R
t
=(1u
k
t
))
1+

1
h
t
=l
t
(B.6.5)
E
t

a
t+1
=

(1)
(B.6.6)
(1)E[
@y
t+1
@R
t+1
+
R
t+1
@h
t+1
@R
t+1
] =
R
t
(B.6.7)

R
t
=
y
t
=u
n
t

1
h
t
=(1u
n
t
)
(B.6.8)
@y
t
@
Y
t
@
Y
t
@R
t
=(1)(Y
t
=
Y
t
)((1)
Y
t
=R
t
)
1+
(B.6.9)
@h
t
@
R
t
@
R
t
@R
t
=
(1
1
)(h
t
=
R
t
)((1)
R
t
=R
t
)
1+
(B.6.10)
w
t
=l

t
(B.6.11)
c
t
+k
t+1
(1
K
)k
t
=y
t
(B.6.12)

Y
t
= [(
u
k
t
K
t

)

+ (1)(
R
t
1
)

]
1=
(B.6.13)

R
t
= [(
(1u
k
t
)K
t

)

+ (1)(
R
t
1
)

]
1=
(B.6.14)
y
t
=z
Y
t
[
Y
1
t
(u
n
t
L
t
)

]

; 0<< 1; 0<6 1 (B.6.15)
h
t
=z
R
t
[
R
t
11
((1u
n
t
)l
t
)
1
]

; 0<
6 1 (B.6.16)
R
t+1
= (1
R
)R
t
+h
t
; 0<
1
6 1 (B.6.17)
k
t
= a
t
(B.6.18)
ln(z
R
t
) =
R
ln(z
R
t1
) +
R
t
;
R
t
N(0;
2
zR
) (B.6.19)
ln(z
Y
t
) =
Y
ln(z
Y
t1
) +
Y
t
;
Y
t
N(0;
2
zY
) (B.6.20)
80
The exogenous states contain z
Y
t
and z
R
t
. The endogenous states include a
t
and R
t
. The other
endogenous variables are l
t
, k
t
, u
n
t
, u
k
t
, w
t
, c
t
, y
t
, h
t
,
Y
t
,
R
t
, yk
t
=
@y
@
Y
@
Y
@k
, hk
t
=
@h
@
R
@
R
@k
,
yR
t
=
@y
@
Y
@
Y
@R
, hR
t
=
@h
@
R
@
R
@R
,
R
t
, and
a
t
. Since we assume that the rms are uniform
distributed facing the same productivity, the uppercase and lowercase letters are inter-changeable
in the notations.
81
B.7 The Linear Dierence Equations
Dene the deviation from the deterministic state state for a variable
^
d =ln(d)ln(d
ss
) =
dd
ss
d
s
s
where d
ss
denote the steady state of the variable d. Collect the deviation of all the variables in
the model in x
t
, that is,
x
t
=f
^
z
Y
t
;
^
z
R
t
; ^ a
t
;
^
R
t
;
^
l
t
;
^
k
t
;
^
u
n
t
;
^
u
k
t
; ^ w
t
; ^ c
t
; ^ y
t
;
^
h
t
;
^

Y
t
;
^

R
t
;
^
yk
t
;
^
hk
t
;
^
yR
t
;
^
hR
t
;
^

R
t
;
^

a
t
g
Using log-linearization around the steady state, the dynamic system is transformed to a linear
system dierence equations, that is,
AE
t
x
t+1
=Bx
t
It includes 2 exogenous variables and 18 endogenous variables.
0 = ^ y
t

^
l
t
^ w
t

^
u
n
t
(B.7.1)
0 =
f
yk
^
yk
t
+
R
f
hk
^

R
t
+
R
f
hk
^
hk
t

a
^

a
t
(B.7.2)
0 =
^
yk
t
+ ^ y
t
+
^

Y
t

^
u
k
t
(1 +)
^
k
t
(B.7.3)
0 =
^
hk
t
+
^
h
t
+
^

R
t
(1 +)
^
k
t
+
u
k
1u
k
^
u
k
t
(B.7.4)
0 = ^ y
t
+
^

Y
t
(1 +)
1
1u
k
^
u
k
t

^

R
t

w
wy=l
^ w
t
+
y=l
wy=l
^ y
t

w
wy=l
^
l
t
(B.7.5)
E
t
^

a
t+1
= 0 (B.7.6)
E
t
[
f
yR
^
yR
t+1
+
R
f
hR
^
hR
t+1
+
R
f
hR
^

R
t+1
] =
(1)

R
^

R
t
(B.7.7)
0 =
^

R
t
+ ^ y
t

^
h
t

1
1u
n
^
u
n
t
(B.7.8)
0 =
^
yR
t
+ ^ y
t
+
^

Y
t
(1 +)
^
R
t
(B.7.9)
0 =
^
hR
t
+
^
h
t
+
^

R
t
(1 +)
^
R
t
(B.7.10)
0 = ^ w
t
+
^
l
t
(B.7.11)
k
^
k
t+1
=c^ c
t
+ (1
K
)k
^
k
t
+y^ y
t
(B.7.12)
0 =
^

Y
t
+ (
Y
)

(
u
k
k

)
^
u
k
t
+ (
Y
)

(
u
k
k

)

^
k
t
+ (
Y
)

(1)(
R
1
)

^
R
t
(B.7.13)
0 =
^

R
t
(
R
)

(
(1u
k
)k

)

u
k
1u
k
^
u
k
t
+(
R
)

(
(1u
k
)k

)

^
k
t
+(
R
)

(1)(
R
1
)

^
R
t
(B.7.14)
0 =^ y
t
+
^
z
Y
+(1)
^

Y
t
+
^
u
n
t
+
^
l
t
(B.7.15)
0 =
^
h
t
+
^
z
R
+
(1
1
)
^

R
t
+
1
^
l
t

1
u
n
1u
n
^
u
n
t
(B.7.16)
RR
t+1
= (1
R
)R
^
R
t
+h
^
h
t
(B.7.17)
0 =
^
k
t
+ ^ a
t
(B.7.18)
82
E
t
^
z
R
t+1
=
R ^
z
R
t
(B.7.19)
E
t
^
z
Y
t+1
=
Y ^
z
Y
t
(B.7.20)
The Schur decomposition algorithm proposed by Klein, 2000 is used to solve the linear expectation
system. The solution is characterized by a rst-order-accurate decision rules, that is,
kk
t+1
=PPkk
t
+
t+1
uu
t
=FFkk
t
while s
t
characterizes the law of motion for the states, while g
t
decribes the decision rules. The
driving system has the form:
x
t
=Q
t

t+1
=%
t
+G
t
where x(t) is the vector of exogenous variables and delta(t) is the vector of exogenous state
variablesfz
Y
t
;z
R
t
g.
83
Tables
Table B.1: Parameter Values for Steady State Analysis
Parameter values Description Source
Financial sectors
= 1=(1 0:56) 0.56 is the fraction of physical capital as collateral Wang, 2017
Preferences
= 1:73 w
ss
= 1 and l
ss
= 1=3
= 0:5 @lnl=@lnw = 2
= 0:95 Households' annual discount factor
= 0:05 Entrepreneurs' additional discount factor
Technology
= 0:62 Labor's share in production function Hou and Johri, 2009
= 0:85 Return to scale to nal

Y
= 0:72 Annually persistence of log TFP process

zY
= 0:2 Standard deviation of log TFP
Intangible

1
= 0:68 Labor's share in production function Hou and Johri, 2009

= 0:95 Return to scale to intangible
=0:3 Elasticity of substitution of between capitals
= 0:8 Fraction of physical capital in the aggregated capital Falato et al., 2013

R
= 0:85 Annually persistence of log TFP process

zR
= 0:25 Standard deviation of log TFP
Depreciation

K
= 0:10 Annually depreciation rate of physical capital

R
= 0:10 Annually depreciation rate of intangible capital
84
Table B.2: Denition of Intangible Assets
national Accounts OECD(1998) CHS(2012)
computerized
information
software software
software
computerized database
innovative
property
R&D expenditure
patents
scientic R&D
new architectural&
engineering designs
new product development costs
in the nancial industry
entertainment,
literary or
artistic originals
entertainment,
literary or
artistic originals
mineral
exploration&
evaluation
mineral
exploration
economic
competencies
economic
competencies
market research,
advertising expenditure
employee training exmployee training
organisational capital
85
Table B.3: Corporate Sector Accounts
Gross value added
{ redCompensation of employees
{ Taxes less subsidies on production
= Gross operating surplus = Operating prots
{ Net interest paid
+ Net other current transfers received = Prots before tax
{ Direct taxes paid = Prots after taxes
{ Dividends paid
= Gross saving = Undistributed prots+redFixed capital consumption
+ Net capital transfer received
{ Gross xed capital formation
{ Other capital expenditure
= Net lending
86
Table B.4: Various Models
labor capital prots intangible intangible Note
no intangible & no prots 70.4 29.6 0 0 0 NA
1
no intangible & prots 70.4 20.6 9 0 0
intangible & no prots 60 25 0 15 17
intangible & prots 60 17.7 7 15.3 17
87
Table B.5: Secular Trend of Labor Share of Income and Intangible Investment
(1) (2)
VARIABLES Labor share of income Intangible Investment
year = 1996 0.00411 0.287
(0.00901) (0.205)
year = 1997 -0.0101 0.583***
(0.00901) (0.205)
year = 1998 -0.00876 0.969***
(0.00901) (0.201)
year = 1999 -0.0171* 1.269***
(0.00901) (0.201)
year = 2000 -0.0228** 1.458***
(0.00886) (0.200)
year = 2001 -0.0183** 1.581***
(0.00886) (0.200)
year = 2002 -0.0226** 1.469***
(0.00880) (0.198)
year = 2003 -0.0265*** 1.358***
(0.00880) (0.198)
year = 2004 -0.0350*** 1.488***
(0.00880) (0.198)
year = 2005 -0.0332*** 1.677***
(0.00880) (0.198)
Constant 0.587*** 4.800***
(0.00639) (0.146)
Observations 270 279
R-squared 0.146 0.391
Number of country 27 27
Standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
Data Source 1: Intangible investment from OECD
Data Source 2: Labor share of income from Karabarbounis and Neiman, 2014
88
Table B.6: Time-Series Stylized Facts, by Decade
group labor share median saving share median dividend share median
1960s 0.699034 0.700374 0.31982 0.269849
1970s 0.663022 0.658162 0.215542 0.167055
1980s 0.62327 0.634181 0.221971 0.196745
1990s 0.548571 0.571114 0.228912 0.221264 0.118931 0.10077
2000s 0.489046 0.504877 0.270905 0.245199 0.139455 0.117538
2010s 0.485547 0.494723 0.943092 0.243771 0.134155 0.115556
Data from Chen et al., 2017, country level
89
Table B.7: Cross-Sectional Stylized Facts, by Quartile of Corporate Saving Share
quartile labor share median dividend share median
Saving share, Q1 0.530045 0.558409 0.196852 0.210315
Saving share, Q2 0.555544 0.601057 0.157698 0.148616
Saving share, Q3 0.518583 0.530397 0.108383 0.100298
Saving share, Q4 0.443883 0.46694 0.091894 0.101098
Data from Chen et al., 2017, country level
90
Table B.8: Summary Statisitics for Labor Share of Income in the U.S.
year sample size average standard deviation 1st quantile 3rd quantile
1987 2865 0.618475 0.205357 0.485384 0.770012
1988 2684 0.610208 0.207087 0.475012 0.759682
1989 2633 0.605543 0.209769 0.472593 0.764355
1990 2639 0.605468 0.210492 0.477978 0.762134
1991 2700 0.615312 0.20754 0.48156 0.768228
1992 2933 0.608659 0.208548 0.476832 0.767322
1993 3119 0.598374 0.209503 0.460469 0.756116
1994 3288 0.587175 0.212114 0.446395 0.745539
1995 3369 0.584406 0.218102 0.434406 0.753219
1996 3526 0.582633 0.215826 0.437737 0.74693
1997 3469 0.582408 0.216664 0.441052 0.745457
1998 3276 0.590075 0.209245 0.451184 0.742857
1999 3000 0.594706 0.217534 0.452621 0.760455
2000 2758 0.587016 0.225516 0.438939 0.756767
2001 2548 0.600683 0.222794 0.450552 0.771793
2002 2553 0.59366 0.220151 0.444007 0.764094
2003 2609 0.582214 0.228506 0.428596 0.75695
2004 2638 0.567741 0.226743 0.415061 0.742495
2005 2539 0.557015 0.230312 0.395569 0.736562
2006 2463 0.549678 0.234917 0.379529 0.732101
2007 2295 0.545982 0.236814 0.375722 0.732079
2008 2156 0.552335 0.239061 0.384816 0.740633
2009 2101 0.557837 0.235169 0.38523 0.751003
2010 2152 0.526136 0.237808 0.353073 0.709065
2011 2071 0.526571 0.244161 0.349547 0.714557
91
Figure B.1: US Labor Share of Income
92
Figure B.2: China Labor Share of Income
93
Figure B.3: China and US Labor Share of Income
94
Figure B.4: Investment in Intangibles as Share of GDP(%) 2005: EU - 27 countries(and Norway)
Data from INNODRIVE National Intangibles Database, which provides time series of the Gross Fixed Capital
Formation for dierent intangible capital components for the EU-27 countries and Norway. Capital stocks and
modied National Accounts series (consistent with New Intangible GFCF) are available only for a subgroup of
countries. Current release (May 2011) of the National Intangibles Database covers years from 1995 to 2005. For
an overview of the methodology and main data sources used in the construction of the INNODRIVE National
Intangibles Database, refer to: Jona-Lasinio C., Iommi M. and Roth F. (2011), "National Measures of Intangible
Capital in EU27 and Norway", in H. Piekkola (ed), "Intangible Capital Driver of Growth in Europe".
95
Figure B.5: Country Level Stylized Facts
96
Figure B.6: Stylized Facts in the U.S.
97
Figure B.7: tangible share of aggregate capital
98
Figure B.8: return to scale of nal good production
99
Figure B.9: return to scale of intangible production
100
Figure B.10: labor contribution in nal good production
101
Figure B.11: labor contribution in intangible production
102

Abstract (if available)

Abstract Central to income distribution is the joint distribution of labor and non-labor income, which is determined by labor income distribution, non-labor income distribution and the dependency between them. Constancy in the labor share of income is one of the most important Kaldor’s facts in Macroeconomics. At the same time, labor income is usually more evenly distributed cross households than capital income in an economy if the labor share is considered to be constant. If the income shifts more from labor to non-labor, the income is more concentrated in the top of the distribution. My dissertation explores the reasons for the global changes in the labor share of income and for the difference in changes between developing and advanced economies and how these changes are associated with those in intangibles and financial factors in recent decades. ❧ First, I compare the magnitude and changes in the labor share of income in developing and advanced economies in the recent decades. Trade economists state that shifting the production of labor-intensive goods from the developed countries to emerging economies is the main reason for the decline in the labor share of income in the developed countries. However, data shows that the downward trend in the labor share of income in China, one of the largest emerging economies, is steeper than that in the United States. This chapter is trying to provide an explanation. We use detailed firm level data in China to estimate the industry and aggregate level elasticity of substitution between capital and labor and find that it is below unity as economists shown in the literature. The estimation strategy we use in this is the same as which Oberfield and Neiman (2014) proposed and used in estimating the industry level and aggregate elasticities of substitution in the United States. Following this same strategy and comparing the results we observe that heterogeneity plays an important role in determining the industry and aggregate level elasticities of substitution between capital and labor, which suggests that to explain the decline in the labor share of income, one needs to take a close look at firm level characteristics. We show that misallocation induces high heterogeneity in capital to labor ratios and thus the elasticities of substitution between capital and labor in China. Therefore, due to the reduced misallocation and heterogeneity in capital to labor ratios in recent decades in China, facing the same decline in relative price of investment goods, the labor share of income in China increases in a slower rate than that in the United States. ❧ Second, I search for the driving force behind the global decline in the labor share of income in the recent decades. This chapter shows that the rising share of intangible capital in production is a fundamental driver of both the decline in the labor share of income and the secular upward trend in corporate savings. At the macro level, I provide global evidence regarding the increasing intangible capital investments, rising corporate savings and declining labor share of income in a broad set of economies including most EU countries, the United States and China using various sources of country-level databases. Besides, a simple micro empirical analysis using CRSP-Compustat firm level data shows a positive correlation between gross savings and intangible capital. I present a standard general equilibrium model with financial frictions to analyze how the firms’ compensation share of the value added and cash holding are effected by the stock of intangible capital, which links both the trend in the labor share of income to the trend in the corporate savings with the trend in the intangible capital in an economy. The model points to the increasing importance of intangible capital in the production from 1970s to 2000s as an explanation for the rising corporate savings and decline labor share of income in the United States.

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Asset Metadata

Creator Chu, Wenjing (author)

Core Title Essays on macroeconomics and income distribution

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Economics

Publication Date 11/19/2020

Defense Date 06/18/2018

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag aggregate factor income distribution,Chinese economy,income inequality,intangible investment,OAI-PMH Harvest

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Dekle, Robert (committee chair), Quadrini, Vincenzo (committee chair), Nugent, Jeffrey (committee member)

Creator Email wchu.pku@gmail.com,wenjingc@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-108562

Unique identifier UC11675912

Identifier etd-ChuWenjing-6975.pdf (filename),usctheses-c89-108562 (legacy record id)

Legacy Identifier etd-ChuWenjing-6975.pdf

Dmrecord 108562

Document Type Dissertation

Format application/pdf (imt)

Rights Chu, Wenjing

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

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