Inter-temporal allocation of human capital and economic performance

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INTER‐TEMPORAL ALLOCATION OF HUMAN CAPITAL AND ECONOMIC PERFORMANCE

by

Hongchun Zhao

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ECONOMICS)

August 2011

Copyright 2011 Hongchun Zhao

ii

Acknowledgements
I would like to thank the Economics Department at USC. Without its support, this
dissertation would never have been finished. Additional thanks are due to my advisers: Jeff
Nugent, Selo Imrohoroglu, Lee Ohanian, Michael Magill, Caroline Betts, and Doug Joines, for
their assistance, advice, and constant encouragement. My parents, Zhao Zhongzhen and
Mao Fuxiu, have given me their unconditional love and support. Without them, I would
have quit long ago. Finally, I cannot express the level of gratitude and love that I have for my
passed‐away grandfather, Zhao Pei‐Qi. His encouragement, support and understanding are
so appreciated that I would exchange anything for his coming back, if I could.

iii

Table of Contents
Acknowledgements ii
List of Tables iv
List of Figures v
Abstract vi
Introduction 1
Chapter One: An Accounting Method for Economic Growth
Introduction 5
The Prototype Economy 9
Equivalence results 15
The Accounting Method 28
Chapter Two: Estimating Human Capital and Accounting for Economic Performance
Introduction 32
Estimating Human Capital Stocks and Relative Price of Human Capital in
terms of Final Goods 33
Estimating Other Variables and Calibration 38
Decomposition Results 41
Do Previous Studies Contradict Ours? 53
Chapter Three: An Alternative Empirical Test for Growth Models
Introduction 61
Equivalence Results 64
Data and Results 72
Conclusion 76
References 78
Appendices
Appendix A: Variables in the Cross‐country Dataset 81
Appendix B: Data for Calibrating Parameters 84

iv

List of Tables
Table 1: Equivalence Result for Klenow and Rodriguez‐Clare (2005) 21
Table 2: Equivalence Result for Romer (2005) 27
Table 3: Calibrated Values of Parameters 40
Table 4: Average Importance of Wedges on Growth Rate 43
Table 5: Average Importance of Wedges on the level of TFP 44
Table 6: Average Importance of Wedges on the Capital‐Output Ratio 46
Table 7: Average Importance of Wedges on Employment Rate 47
Table 8: Different Definitions of Human Capital and the Technology
in Growth Accounts 54
Table 9: Level Accounting Comparisons 56
Table 10: Growth Accounting Comparisons 60
Table 11: Test Results for McGrattan and Prescott (2007) and Klenow
and Rodriguez‐Clare(2005) 74

v

List of Figures
Figure 1: Robustness Check with α on Growth 48
Figure 2: Robustness Check with α on TFP 49
Figure 3: Robustness Check with   on Growth 50
Figure 4: Robustness Check with   on TFP 51
Figure 5: Robustness Check with   on Growth 52
Figure 6: Robustness Check with   on TFP 53

vi

Abstract
Differences in economic growth across countries have been substantial in
history. Industrial countries have grown at a remarkably stable rate since 1870, but the
growth rates of other countries have varied considerably. Why countries grow at
divergent rates over time? Which countries will become industrial leaders in the twenty‐
first century, and what will their long term trends look like? I extend the “Business Cycle
Accounting” framework of Chari, Kehoe and McGrattan (2007) to provide a platform for
addressing these questions.
Using the “Business Cycle Accounting” idea of Chari, Kehoe, and McGrattan
(2007), I develop an accounting method that decomposes economic growth, and other
endogenous variables of interest, into effects of exogenous wedges in a prototype
economy. Furthermore, a number of endogenous growth theories can be shown to be
equivalent to the prototype economy, with specific implications on wedges. Thus,
potential theoretical explanations connect to the relevance of the various wedges,
whose values are recoverable from available data. By using data for fifty countries, our
results show that the wedge associated with the inter‐temporal allocation of the
broadly defined human capital, or the human capital investment wedge, is important in
explaining growth.
Based on this accounting method, an empirical testing procedure that fully
explores a theory’s implications is applied to the US data. I choose two endogenous

vii

growth models which both are equivalent to the human capital investment wedge in the
prototype economy, but imply different functional forms and determinants of the
human capital wedge. One is a model on the openness to foreign direct investment by
McGrattan and Prescott (2010), and the other is an international knowledge spillover
model by Klenow and Rodriguez‐Clare (2005). Results suggest that McGrattan and
Prescott’s model is more consistent with data.

1

Introduction
My dissertation is about an alternative growth accounting, its implications on
underlying causes of growth, and its application for empirically testing endogenous
growth theories. It is widely known that cross‐country differences in the long run
growth rates are enormous. The conventional growth accounting uses data on output
and inputs for a particular country over time to assess the relative contribution of
growth rates of production factors, and growth rates in the efficiency with which those
factors are used, to these vast differences in long run economic growth. Typically, the
conventional growth accounting utilizes a parametric form of the production function,
,,
Compared with the conventional growth accounting, the alternative growth
accounting imposes further restrictions on the observed differences in output and
production factors. An optimal growth model with taxes, in which growth is
endogenously driven, and technology, preferences, and other exogenous structures
fulfill the neoclassical assumptions, is fully specified. As a result, the comprehensive set
of equilibrium conditions, rather than only production functions are utilized to
decompose the long run growth rate into effects of exogenous taxes, efficiency shifters,
and so on. In the paper, the optimal growth model is called the prototype economy, and
these relevant exogenous items wedges.

2

In addition, many detailed endogenous growth theories share a common
structure as the prototype economy’s structure, but have different implications on the
corresponding wedges. Since wedges are recoverable from data, when the values of
endogenous variables and parameters in the prototype economy are known, the
importance of wedges in explaining growth can be evaluated through the prototype
economy. Thus the potential theories in explaining economic growth are connected to
the relevance of the corresponding wedges.
The consensus view in the conventional growth accounting is that the total
factor productivity (TFP) or the labor‐augmented technology plays a very large role.
Differences in TFP account for at least one third of differences in long run economic
growth. Like the conventional growth accounting, the alternative growth accounting is
useful for identifying underlying causes of growth. If one found that one particular
wedge is able to account for a large share of the differences in growth, TFP or some
input intensity, then development economics could focus on exploring corresponding
theories to that wedge. Chapter one explains these above theoretical relationships.
Operationally, the key steps in the alternative growth accounting also include:
(1) choosing a specification for the prototype economy, (2) accurately measuring
endogenous variables, and (3) evaluate the relative importance of each wedge in
explaining economic growth. Wedges are backed out as a residual, like TFP in the
conventional growth accounting.

3

Since the definition and, as a result, the measurement of the broadly defined
human capital I use is related to, but also different from those in previous studies on
gauging the human capital stock, the construction of the broadly defined human capital
and its relative prices in terms of final goods are particularly discussed and compared
with previous studies. In chapter two, I discuss the feasibility of the accounting method.
The identification of underlying determinants of growth has long been a primary
topic in the field of growth and development. One popular approach to estimate the
effects of policy variables on growth is to run cross‐sectional regressions of growth rates
on initial income levels, and economic policy and political variables. However, as chapter
one has shown, many growth theories are compatible with each other, and the number
of theoretical specifications to be tested increases exponentially with the number of
mutually compatible theories. If using the conventional econometric approach, even
testing one theory would require a large number of regressions and make the
econometrical approach infeasible. Using the same fact that many growth theories are
compatible with one another, the quantitative approach embodied in the alternative
accounting method circumvents this difficulty and provide a different testing approach,
which is more straightforward to understand and easier to implement.
In chapter three, I explore this empirical approach by testing two endogenous
growth models that correspond to the same wedge in the prototype economy, but have
different implications on the functional form and determinants of the wedge.

4

Before plunging into the data and the calculations, it is worthwhile to stress the
limits of the alternative growth accounting. The specification assumes that the values of
parameters in the prototype economy are constant across countries, and does not
incorporate cross‐country heterogeneity in technology, preferences, and institutions
into the structural explanation. Furthermore, the measurement of endogenous variables
does not consider the quality, the detailed components, and the possible measurement
errors of the various endogenous variables very much. Despite these limits, this work is
an attempt to incorporate fundamental causes of economic growth into an accounting
framework.

5

Chapter One: An Accounting Method for Economic Growth
1.1 Introduction
Differences in economic performance across countries are as substantial today
as they have been in history. For example, in 1900, GDP per person in the United States
was about $4000. In contrast, GDP per person in the same year was much lower in many
other countries: about $1300 in Mexico, $500 in China, $600 in India. Whereas in 2000,
GDP per person was $28400 in the US, it is $7200 in Mexico, $3400 in China and $1900
in India (all these figures are in purchasing power parity (PPP) 1990 prices, and are taken
from Maddison (2003)). Another remarkable comparison is that the fastest growing
countries now grow at nine percent per year, whereas one hundred years ago the
highest rates of growth were around two percent per year (McGrattan and Schmitz
(1999)). In order to explain these large observed gaps of cross‐country economic
performance, I extend the “Business Cycle Accounting” framework of Chari et al. (2007)
by explicitly allowing for investment in human capital in a neoclassical growth (NCG)
model.
The insight from Chari et al. (2007) is that a NCG model with taxes is a good
perspective with which underlying causes of the observed gaps in growth can be
analyzed. The residuals associated with a prototype economy’s equilibrium conditions
can be defined as exogenous variables, and interpreted as taxes, efficiency shifters, etc.
Furthermore, specific growth models that theoretically explain the observed gaps

6

correspond to these wedges too. Compared with the conventional growth accounting
method, the whole set of equilibrium conditions, rather than only production functions
are used to decompose economic growth; and the decomposition results can be
connected to theoretical explanations more easily. The authors call the NCG model the
prototype economy, and these residuals the wedges. I choose a two‐sector NCG model
as the prototype economy, in which economic growth in the long run is endogenously
driven by the accumulation of broadly defined human capital. The prototype economy
defines seven wedges, which resemble taxes, productivity shifters and government
consumption.
The reason why many specific growth models can be connected to the prototype
economy is that most theories in the growth literature capture certain frictions of real
economies that could prevent production from achieving optimality in a neoclassical
structure. For example, Lucas (1988) specifies that the accumulation of human capital is
not subject to diminishing returns; Romer (1990) incorporates both monopolistic
competition and knowledge externalities into a neoclassical framework; and Klenow and
Rodriguez‐Clare (2005) explicitly claim that their models incorporate externalities.
Additionally, economic policies and competitive barriers, which are emphasized by
McGrattan and Schmitz (1999) and Cole et al. (2005), are seen as explicit frictions in the
production process. In addition, the wedges defined by equilibrium conditions of the
prototype economy can be recovered, when endogenous variables are observable.

7

As examples for the equivalence results that many growth theories are
isomorphic to the prototype economy,
1
I show that an international knowledge spillover
model (adapted from Klenow and Rodriguez‐Clare (2005)) and a monopolistic
competition model (adapted from Romer (1990)) correspond to a human capital
investment wedge and a labor wedge in the prototype economy respectively. The
human capital investment wedge is the residual associated with the Euler equation for
the human capital, and the labor wedge is the residual associated with the labor‐leisure
trade‐off condition.
The flexibility of this method allows us to tackle a number of important
questions. For example, it can evaluate the importance of each wedge in explaining
economic growth, and other variables of interest. I collect the relevant data for fifty
countries, measure each of the different wedges and decompose endogenous variables
into the effects of wedges around their observed values. These decomposition results
reveal some interesting observations about the large gaps mentioned in the
introduction of this section. In accounting for growth rates across countries, on average,
the wedges with the production function of human capital and with Euler equation for
human capital are of primary importance. The wedges associated with the labor‐leisure
trade‐off condition, and with the condition of the allocation of labor across sectors are

1
Some endogenous growth theories are not isomorphic to the prototype economy. For example,
endogenous growth models with multiple equilibria are not, because the equilibrium of the prototype
economy is uniquely defined. Also two‐sector models with a different partition of output are not
equivalent to each other. For example, two‐sector models with agriculture/non‐agriculture partition are
not equivalent to those with a consumption/capital goods partition.

8

also important, though their effects are smaller. As for TFP across countries, the wedge
with production function of final goods almost completely explains it. Moreover, these
patterns are robust across the sub‐samples of countries in and out of the Organization
for Economic Co‐operation and Development (OECD). These results will help researchers
develop quantitative models of economic growth.
This paper relates to a large literature that studies the determinants of the large
gaps of economic performance. Some studies deal with proximate causes, such as
physical and human capital, or technology changes and adoption (e.g., Lucas (1988),
Romer (1990) and Klenow and Rodriguez‐Clare (2005)). Others pay more attention to
fundamental causes, such as differences in luck, raw materials, geography, preferences,
and economic policies (e.g., McGrattan and Schmitz (1999), Cole et al. (2005), Acemoglu
et al. (2001) and Rodrik et al. (2004)).
2
My paper complements this literature by
organizing promising stories under a unified framework. In this respect, my work
provides a particular response to Lucas (1988), where the author recommended
economists: (1) to develop quantitative theories that describe the observed differences
across countries and over time, in both levels and growth rates of income per person;

2
Solow (1957) is an early, but modern, attempt to account for different patterns of economic
development, which becomes the cornerstone of the NCG model. Lucas (1988) emphasizes the effects of
human capital accumulation; Romer (1990), among others, endogenizes technological change; Klenow
and Rodriguez‐Clare (2005) address the interaction between open economies. McGrattan and Schmitz
(1999) focus on differences in economic policies and review estimates for a wide range of policy variables;
Cole et al. (2005) argue that Latin America’s failure to replicate Western economic success is primarily due
to TFP differences, and that barriers to competition are the cause of these differences.

9

(2) to explore the implications of competing theories with respect to observable data;
and (3) to test these implications against observation.
The rest of the paper is organized as follows. Section 2 describes the prototype
economy and its steady‐state equilibrium. Section 3 establishes equivalence results for
two detailed models. Section 4 presents the accounting procedure and describes the
experiments carried out. Section 5 displays parameter calibration, the dataset, the
experiment results, with an emphasis on how to construct relative prices of human
capital across countries. Section 6 concludes.
1.2 The Prototype Economy
In this section, I specify the prototype economy as a two‐sector model of
endogenous growth with taxes, and describe its steady‐state equilibrium.
The prototype economy is a variant of Rebelo’s two‐sector model (see Rebelo
(1991)). One sector produces final goods, which can be either consumed or invested in
physical capital; the other sector produces human capital, which enhances labor
productivity. Both sectors use Cobb‐Douglas aggregate production functions,
3

(1.1)

3
Sturgill (2009) suggests that the inclusion of energy as a further input has a substantial impact on the
estimated contribution of TFP on long‐run growth. So this widely‐used specification of production
function deserves a further consideration.

10

1 1

(1.2)
where , , ,   and   are per person output of final goods, labor input, investment in
human capital, physical capital stock and human capital stock respectively;
4
  and
represent the fractions of physical capital stock and labor devoted to the final goods
sector;   represents the common capital share in both sectors;   and   are two
productivity shifters in these two sectors.
5

Output and factor markets are competitive, and firms maximize their profits,
1
1

1
1
given the relative price of human capital in terms of final goods q, and factor prices of
physical capital and labor in the final goods sector r
, w
and in the other sector r
, w
.
Notice that factor incomes in the final goods sector are taxed with rates   and .
There is a representative household in the model whose size   grows at a
rate of . It maximizes a discounted utility over flows of consumption   and leisure
1 . Let 0,1 be its discount factor, and 0,1 be the consumption share
in each period’s utility function. The household’s problem is,

4
When there is no risk of confusion, I drop time arguments, but whenever there is the slightest risk of
confusion, I will err on the side of caution and include relevant arguments.

5
These production technologies are labor‐augmented YAK
hL
, where uppercase variables
denote total amounts. The reason why I choose the labor‐augmented technology is that any technology
consistent with balanced growth can be represented by this form.

11

max ln c t 1 ln1
subject to (a) a budget constraint,
1

1
1

1

1 1

1
(b) factor prices derived from profit maximization problems,
1
/
1
1/

/1
1/1
(c) the law of motion for physical capital and human capital,
6

11 1

(1.3)

11 1

(1.4)

6
If labor‐augmented human capital were to include a general technology level that can be “publicly”
used, population growth would not dilute the human capital stock per person. Then the law of motion
would be h t11δ
h t x
t . Both forms follow Ben‐Porath (1967). A different approach is
a log‐linear law of motion. Chang et al. (2002) use the log‐linear approach to analyze learning by doing,
Hansen and Imrohoroglu (2009) extend it to study on‐the‐job training. Both approaches are
approximately isomorphic to each other around steady state.

12

with ,
0 . Here

,

,   are tax rates on physical capital
investment, human capital investment, and total labor income;   is a per person lump‐
sum transfer, which equals total tax revenues minus government consumption ,

1
And   and   denote the depreciation rates of human capital and physical capital
respectively;   is per person physical capital investment.
The competitive equilibrium of the prototype economy is a set of prices and
allocations such that they are solutions to firms’ and consumers’ problems, and satisfy
the resource balance,

(1.5)
The equilibrium conditions are:

1
1 1 1
1
(1.6)

1
1 (1.7)

1
1 (1.8)

1 1
1

111 1

(1.9)

13

1
1 1
1

11 111 1

(1.10)
together with production functions, laws of motion, and the resources balance. Given
the transversality condition, lim 0
0 0 , and the initial stocks, 0 ,
0 , these equations characterize competitive equilibrium paths of the prototype
economy.
7

The prototype economy also has a steady‐state equilibrium, whose local
properties are now well understood: a unique steady‐state equilibrium exists, and it is
saddle‐path stable (e.g., Mulligan and Sala‐i‐Martin (1993), Bond et al. (1996)). In the
steady‐state equilibrium, the growth rate of every variable is constant.
8
More
specifically, , , , and   are constants, and all other endogenous variables grow at the

7
Solving the following Bellman equation yields equilibrium conditions,
V k, h maxU c, l β1 nVk
,h
where cr
vk r
1v k 1τ
w
ul w
1u l T 1τ

1 τ
1n k
1δkk1τxh1τlq1nh1δhh . Notice that equations (1.6), (1.7) and (1.8) are from first order
conditions with respect to l, v and u,
U
1τ
w
u w
1u U
0
r
kr
k0
1τ
w
l w
l 0
Using canonical dynamic programming, we obtain,
1

1
1

1

1 1

These are the Euler equations (1.9) and (1.10).

8
To avoid repetition, let   be the growth rate of an arbitrary variable   in steady state. Equations (1.7)
and (1.8) imply that
0 , equation (1.6) implies 0 , equation (1.8) implies

,
equation (1.5) implies

, the law of motion for   implies

, the law of motion for
implies

, production function (1.1) implies 1 , production function (1.2)
implies
1 . Combining all of these results implies that , , ,   are constant, and all
the other variables grow at the same rate.

14

same rate, . As a result, solutions to the steady‐state equilibrium are only ratios or rates.
There are ten equations that can be used to solve for ten endogenous variables, , , ,
, , / , / , / , / , and / .
For clarity, the steady‐state equilibrium conditions are collected in one place as
follows,

1
1 1
1 1

(1.11)

1

1
(1.12)

1

1
(1.13)

1
1

1

(1.14)

1 1 1
1 1

(1.15)

(1.16)

1 1

(1.17)

(1.18)

15

(1.19)

(1.20)
I call   the labor wedge,   the capital input wedge,   the labor input wedge,

the capital investment wedge,
the human capital investment wedge,   the final
goods efficiency wedge,   the human capital efficiency wedge, and / the
government consumption wedge.
1.3 Equivalence Results
In this section, I show that two detailed models are equivalent to the prototype
economy with different wedges.
9
In particular international knowledge spillovers accord
with a human capital investment wedge, while monopolistic competition in the
intermediate inputs market corresponds to a labor wedge. In general, many theories
that capture certain economic features are isomorphic to the prototype economy.
However, since a class of models can be consistent with one wedge, to identify a
particular model one needs to do more than to identify the wedge to which it
corresponds.


9
Second best allocations in development economics also match the prototype economy, if the detailed
model also has a neoclassical structure. Whatever the underlying cause for a second best result is, it
distorts some equilibrium condition and will appear as a wedge.

16

1.3.1 The mapping between an international knowledge spillover model and the
prototype economy
Klenow and Rodriguez‐Clare (2005) present a growth model with international
knowledge spillovers. In its simplest version, the production of knowledge of a certain
country is affected by the country’s productivity relative to an exogenous world
technology frontier and technology diffusion from abroad that does not depend on
domestic research efforts. Here I show that this version is equivalent to the prototype
economy with a human capital investment wedge.
10

Suppose for a particular country, the output is produced with a Cobb‐Douglas
production function,
, where   is total output,   is the capital stock,
is a technology index, and   is the total number of workers which are growing at the
rate . Output can be used for consumption , investment , or research , thus
. Capital is accumulated according to 1 1 .
The technology index   contains effects of research efforts, technology diffusion from
abroad, and relative productivity to the world technology frontier. The growth rate of
this frontier is exogenous. In particular,   evolves according to,

1 1/
(1.21)

10
Klenow and Rodriguez‐Clare (2005) studied a continuous‐time model. Here, to maintain consistency, I
consider their model in discrete time.

17

where   and   are positive parameters and   is the world technology frontier. The R&D
investment rate is denoted by 1 . Let lowercase letters denote per person values
of aggregate variables. Then the production function becomes
. Assuming
that factor markets are competitive, the rental rate of capital becomes
,
and the rate of return on , 1
.
This model can be written succinctly as the following maximization problem:
max ln
subject to

11 1
1 1/

1

and initial values, 0 and 0 .

18

Let . Klenow and Rodriguez‐Clare (2005) show that   is constant
in steady state. The following conditions characterize the steady‐state equilibrium,

(1.22)

(1.23)

(1.24)

1 1
(1.25)

1 1 (1.26)

1 1 1 11
(1.27)

where   be the growth rate in steady state.
The following claim shows that a prototype economy replicates the international
knowledge spillover model detailed above:
Proposition 1 (Human capital investment wedge and technology spillovers):
Consider a prototype economy with a human capital investment wedge 1

1

, but no other wedges. Let the depreciation rate of

19

human capital be . Then the equilibrium allocations of both
prototype economy and the international knowledge spillover model detailed above
coincide.
Proof of Proposition 1: To prove this and other equivalence results we compare
steady state equilibrium conditions of the detailed model to those of the prototype
economy. To save words, all notations used in the prototype economy are with a
superscript .
By the definition of final goods, the shares of production factors used in final
goods production are
, and the output of final goods is .
From the production function, capital shares in both sectors are . Let investment in
technology be / . Then from the law of motion for technology   in steady state,
we know that , and . Notice that the production functions
for consumption plus investment and for the investment in technology in the detailed
model are the same. Thus the final goods efficiency wedge and the human capital
efficiency wedge are equal,
1 . For the same reason, the relative price of
technology is one, 1 .
Comparing the law of motion for   in the detailed economy gives ,
and . Bear this in mind, we know
0 from the Euler equation (1.26).
From the factor market clearing conditions, wedges   and   must be zero. Since the

20

representative household does not value leisure and supplies its labor inelastically, the
labor wedge   is zero.
Notice that the depreciation rate of technology can be rewritten as 1 1 . As a result, the Euler equation (1.27) can be
rewritten as
1 1 1 1 1 1 1 1
1
1
1 1 1 1 1
11
1
1
1
1
1
The second line is obtained by substituting   into the Euler equation, the third
line follows

, the fourth line uses

1
, and
1
, and collects like terms. Finally, the human capital investment wedge is
1

1

. QED.
The mapping between these two economies is shown in table 1, where the
columns labeled “Prototype” or “P” contain notation used in the prototype economy,
and the columns labeled “KRC” used in the detailed economy. Substituting the notation

21

used in the detailed economy into the equilibrium conditions of the prototype economy
replicates the equilibrium conditions of the detailed economy.
Wedges Variables Parameters
Prototype (P) KRC P KRC P KRC
1
1 0
1
1
1
1
1
1 /
1

1
1

1
1
1 1

0 1

1 1
1
Table 1: Equivalence Result for Klenow and Rodriguez‐Clare (2005)
1.3.2 The mapping between Romer’s model and the prototype economy
Romer (1990) wrote a seminal paper on endogenous growth. The importance of
his paper stems from two important features: its emphasis on the non‐rival nature of
knowledge and ideas in order to generate sustained economic growth and its emphasis
on potential non‐competitive elements. The non‐rivalry of knowledge microfounds
endogenous growth and now becomes a widely‐used specification. In particular, Romer
attributes spillovers across firms to physical capital. Here I adapt his model and let the

22

spillovers work through human capital. Monopolistic competition in the intermediate
inputs sector is a distinguishing feature of this model, turning out to be a labor wedge.
In this model there are three sectors: a research sector, in which firms use
educated workers and capital to produce new knowledge; a final goods sector, which
uses educated workers and capital to produce final goods; and an education sector,
educating workers by using available knowledge and labor.
Let   and   be the capital devoted to producing final goods and R&D
respectively,   be the total number of skills currently in existence, and
and
be
the quantities of the th skill from educated workers in the final goods sector and
research sectors, respectively. All producers are profit maximizers.
As usual, final goods can be either consumed or invested in capital. The
production function of final goods is

. Let   be the rental rate of ,
and _1
be the price of the th skill. Then 0, ,
1

and

.
The production function of the research sector is XδK
x

di
A
, where δ is
a productivity shifter. Let   denote the price of investment in R&D in terms of final
goods. Similarly, we have, 0, ,

1

and

.

23

Assume that the technology available to educate workers is linear,
,
where   is a raw labor input. Different from producers in the other two sectors,
producers in the intermediate input sector are monopolists. For the th skill, the profit
is, max

, where the total labor supplied equals

. Therefore, in equilibrium, the wage rate is

, and the profit is

. Using the
demand functions for the intermediate inputs derived above, wage rates in the final
goods sector and the research sector respectively are 1
and

1
, and the profit is 1

.
Romer (1990) shows that in a symmetric equilibrium, the number of educated
workers in the th profession,   and its raw labor supply   are constant across
professions. Without loss of generality, let the size of the representative household be
unity. Put simply, given the initial values, 0 and 0 , the representative household
maximizes,
max ln 1 ln1
subject to

24

1 1

1

1

1

where
is the total capital stock,   is its depreciation rate, and the total
labor supply is
.
Let   be the growth rate of endogenous variables in steady state. Then the
steady‐state equilibrium is characterized by the following conditions,
1 1 1
(1.28)
(1.29)
(1.30)

(1.31)

(1.32)

(1.33)

(1.34)

25

1
1
(1.35)
1 1 1 (1.36)
(1.37)
The following claim shows that a prototype economy with a labor wedge
replicates Romer’s model detailed above.
Proposition 2 (labor wedge and monopolistic competition in an education
sector): Consider a prototype economy with a human capital efficiency wedge ,
and a labor wedge . Let the depreciation rate of human capital be 0 , and
the population growth be 0 . Then the equilibrium allocations in both the prototype
economy and the adapted Romer model coincide.
Proof of Proposition 2: Similar to the proof for the previous proposition, I
compare the equilibrium conditions of Romer’s model to those of the prototype
economy.
Comparing production functions of   and   in the adapted Romer model to
those of   and   in the prototype economy implies , , 1 , .
It is easy to verify that , , .

26

Let , and . Comparing the laws of motion for   and   implies

, 0 . The marginal product of capital in the final goods sector equals that in
the research sector, and so does the wage rate. Thus 0 and 0 .
The Euler equation of capital implies that the associated investment wedge is
zero, or
0 . Notice that the wage rate is 1 times of the marginal product of
labor due to the monopoly in the education sector. This implies a labor wedge, .
Although there is a labor wedge, which plays the role as the human capital investment
wedge, the fact that the sum of labor income and profits equals the marginal benefit of
technology A makes sure that the human capital investment wedge is also zero, or

0 . QED.
The mapping between these two economies is shown in table 2, where the
columns labeled “Prototype” contain notation used in the prototype economy, and the
columns labeled “Romer” used in the detailed economy. Substituting the notation used
in the detailed model into the equilibrium conditions of the prototype economy will
replicate the equilibrium conditions of the detailed model.
In summary, in the simple version of Klenow and Rodriguez‐Clare (2005), that
technology level depends on both the efforts on R&D and the gap between current
technology and the world technology frontier shows up as a human capital investment
wedge. In the adapted Romer (1990) model, the monopolistic competition in the

27

intermediate inputs market becomes a labor wedge. There is a correspondence
between particular economic features and the wedges in the prototype economy.
Wedges Variables Parameters
Prototype Romer Prototype Romer Prototype Romer
1 /
/
1
1
1
1 0
1
1
1

1 0
1

1
0

Table 2: Equivalence Result for Romer (1990)
In addition to the examples shown above, many other models bear the same
structure as the prototype economy, and possess distinct implications to wedges in the
prototype economy. Identifying and evaluating the significance of wedges from real
data can indicate the importance of potential models embedded in the related wedges,
as will be demonstrated in the following section.

28

1.4 The accounting Method
In this section, I describe how to measure wedges from real data, and evaluate
the importance of wedges in explaining the long‐run growth rate, TFP, and other
endogenous variables.
Envisage a world consisting of 1,…, countries. For any country , the
economy experiences one event , which indexes the state for that country. This state
determines country ’s economic performance. Assume that endogenous variables in
the prototype economy include aggregate variables that characterize a country’s
economic performance, and that the wedges and population growth in the prototype
economy uniquely uncover the event .
Such a mapping is understandable. When exogenous variables in the prototype
economy, including wedges, are known, values of endogenous variables are
determined. Remember that each equilibrium condition defines only one wedge. Hence,
once observable aggregate variables are fed into the prototype economy, wedges are
uniquely determined. Thus there is a one‐to‐one mapping between wedges and
aggregate variables. Recall that each aggregate variable of country   is a function of its
experienced state . Naturally wedges of a country   implied by the prototype economy
can uncover its state.

29

Despite resembling tax rates, efficiency levels or government consumption in the
prototype economy, wedges are clearly not formal tax rates, measures of technological
efficiency, or observed government consumption. Rather wedges are the results of
policies and institutions that make economic activities more costly or reduce their
associated returns. In particular, every wedge in the prototype economy is a measure of
overall frictions in the particular market with which it is associated. For example,
measures the frictions in the labor market;
measures the frictions in the financial
market that allocates physical capital over time, and so on.
Suppose we observe the endogenous variables across countries and substitute
them into the steady‐state equilibrium conditions of the prototype economy. This
allows us to compute values of wedges across countries. In addition to measuring
wedges from real data, the accounting method also evaluates the importance of wedges
in explaining different aspects of economic performance, such as the long‐run growth
rate and TFP.
11
Particularly, I decompose them into the effects of wedges.
Since any differentiable function can be linearly approximated around a value of
its independent variables, I decompose an endogenous variable, for example, country
’s long‐run growth rate , as follows,

11
The importance of long‐run growth rate and TFP cannot be over‐emphasized. As many studies suggest,
the choices that determine better long‐run, supply‐side policies dwarf all other economic policy concerns
(see Lucas (2003)), and large differences in output per person between rich and poor countries are due to
differences in TFP (see Klenow and Rodriguez‐Clare (1997b), Hall and Jones (1999), and Caselli (2005)).

30

/

For country , each variable with the superscript   is its value observed from the data;
is the computed value of growth rate when all wedges are slightly different from their
observed values; and

is the difference between the observed value and the
computed value of the growth rate when only one wedge   is slightly different from its
observed value, but all other wedges are kept at their observed values. It imitates the
marginal effect of wedge   on growth rate . Thus the left‐hand side of this expression
is the comprehensive marginal effect on growth rate ; the right‐hand side is the sum of
individual marginal effects. Dividing the marginal effect of a wedge by the
comprehensive effect displays how important this wedge is in explaining the observed
value of .
Decomposing TFP is different because TFP is a compound variable, which means
it consists of other aggregate variables, as well as wedges,

1 1

31

As we can see, TFP consists of the effects of resource allocation ( and ), the relative
price of human capital ( ), as well as efficiency wedges ( and ). Wedges   and   will
affect TFP directly and indirectly, while other wedges affect TFP only indirectly through
, , and .
To decompose TFP, first change a wedge a little, and calculate the values of , ,
and   after perturbation. Then using the definition of TFP, I calculate the value of TFP
after perturbation. And similarly, the marginal effect of this wedge on TFP is the
difference between values of TFP before and after perturbation. Calculating the
marginal effect for each wedge and adding them together gives the comprehensive
marginal effect on TFP. The importance of each wedge in explaining TFP in country j is
the fraction of its individual marginal effect over the comprehensive marginal effect.
The procedure works for other simple variables and compound variables as well.
In practice, I make a 0.1% change in each wedge in the favorable direction,
compute the absolute values of partial change for each endogenous variable, and divide
each partial effect by the sum of all individual partial effects as normalization, for all
wedges and all endogenous variables.

32

Chapter Two: Estimate Human Capital and Accounting for
Economic Performance
2.1 Introduction
In this section, I (1) present the construction of the necessary dataset from
public sources, (2) discuss how to construct the broadly defined human capital
investment and stocks which is consistent with the aforementioned prototype economy;
(3) calibrate the parameters in the prototype economy; and show some decomposition
results for the long‐run growth rate, TFP, the output‐capital ratio and the employment
rate across countries in comparison with previous studies.
Two points are worth noticing when preparing the dataset: How to divide GDP
into final goods and the broadly defined human capital investment and how to measure
the relative prices of human capital in terms of final goods. I count education as the
proxy for the broadly defined human capital, but neglect other components including
experience, health, R&D, and any other factors that may change the production
efficiency. The expenditures on these components, if accounted, are in the final goods
output in my calculation. One reason to focus on education is because the schooling
years is more accurately measured and more available than others; another is that the
relationship between schooling years and labor income is a much studied topic in labor
economics. As for the relative prices of the broadly defined human capital, they are not

33

estimated or observed directly, but derived by a few parametric assumptions for its
evolution.
2.2 Estimating Human Capital Stocks and Relative Price of Human
Capital in Terms of Final Goods
The investment in education is assumed to be an adequate proxy for the broadly
defined human capital investment

. Naturally, the education stock grows
around a steady state in the long run, and the relative price of education in terms of
final goods is also .
12

After optimization, the expenditure on education is a convex cost function of
schooling years and salaries paid for teaching,

1
· ·
where   is a function of schooling years. As an economy grows in steady state,
salary also grows at the same rate. Thus,

1
·

0 ·
·


12
Soares (2005) reports a high correlation between average schooling years and life expectancy at 5 for
two cross sections. This evidence supports that education is a good proxy for human capital.

34

By the restriction imposed by the steady state, education stock also accumulates
exponentially,
· ·

or
· ·

If the initial stock of education, steady state growth rate, schooling years and the
function form of · are known, then an estimate for the broadly defined human
capital stock is available.
13
Notice that the wage rate, by definition, is equal to
1 / . Thus
ln ln1·ln
ln
The average wage rate depends on a constant term, a trend term, and schooling years.
Labor economists estimate the following Mincerian regression (see Mincer (1974)),
which is informative to construct · ,
ln ·

13
One concern is the quality of education, reflected by the relative price in the model. Hanushek and
Kimko (2000) support the quality of schooling is a major factor for an explanation of long‐run growth by
using growth regressions. From different perspectives, McGrattan and Schmitz (1999) and Durlauf et al.
(2005) both pointed out the potential flaws of growth regressions in establishing causalities. After
adjusting the quality of schooling, Caselli (2005) finds that the quality of schooling is not important for
explaining cross‐country income gaps. Pritchett (2006) summarizes some empirical results of measuring
human capital stocks.

35

Hall and Jones (1999) assume that · is a continuous, piecewise linear function
constructed to match the rates of return on education reported in Psacharopoulos
(1993). For schooling years between 0 and 4, the return to schooling   is assumed
to be 13.4 percent which is an average for sub‐Saharan Africa. For schooling years
between 4 and 8, the return to schooling is assumed to be 10.1 percent, which is the
world average. With 8 or more years, the return is assumed to be 6.8 percent, which is
the average for the OECD countries.
14
Then they construct human capital stocks using

. I use the Hall and Jones (1999) specification to construct , with
the growth rate in steady state and a guess of education stock in any year, to construct
the human capital stock.
Total GDP includes two parts: final goods output and the education investment
in terms of final goods. The latter is the sum of the value added in the private education
sector and the public expenditure on education,
15
and corresponds to
in the model.

14
McGrattan and Schmitz (1999) summarize popular approaches of measuring human capital stock,
including the alternative Mincerian formula used by Klenow and Rodriguez‐Clare (1997b),

^

where   is the average schooling years in the total population over age 25 taken from Barro and Lee
(2001),   is a measure of experiences for a worker in age group i and equal to ( 6 ), and
is the fraction of the population in the th age group. The age groups are {25‐29, 30‐34, ..., 60‐64} and
{27, 32,…, 62}. The coefficients are given by =0:095, =0:0495, and =‐0.0007, which are
averaged estimates of log wages on schooling and experience.

15
Kendrick (1976) discussed a broad class of capital stocks, including tangible and intangible, human and
non‐human capital. He categorized physical capital as “tangible non‐human capital”, child rearing costs as
investments in “tangible human capital”, research and development (R&D) expenditures as investments
in “intangible non‐human capital”, and outlays of education, training, health, safety, and mobility as
investments in “intangible human capital”. Ideally human capital should contain all tangible and intangible
human capital. In this paper I only consider education.

36

The rest is the final goods output,   in the model. This partition between final goods and
human capital investment may be arbitrary; however, it is consistent with the concepts
used in the prototype economy.
16

Using the law of motion of human capital in steady state, I construct the human
capital stock in terms of final goods as,

Dividing this value by , we have

· ·

Notice that the human capital is broadly defined and equal to the labor‐
augmented technology in the literature. Parente and Prescott (2006) argue that “most
of the stock of productive knowledge is public information, and even proprietary
information can be accessed by a country through licensing agreements or foreign direct
investment”.
This statement has become generally true by the end of the 20
th
century.
Technological innovations have improved the speed of transportation and

16
One concern about the definition of human capital investment is that GDP do not include the value of
students’ time, an important component of education investment. This slippage between model and data
affects estimates for x
and h. However, it will not change xh=h in steady‐state. Kendrick (1976) found
about half of schooling investment consists of education expenditures which are included in GDP.

37

communications and lowered their costs. These included jet airplanes and their
universal use in transporting people and goods, the large containers used in
international shipping, the improved road infrastructure that enabled a large share of
trade to be carried by freight trucks in Western Europe and North America, and
importantly, the personal computer, the cellular phone, the internet, and the World
Wide Web that have contributed to profound socio‐political and economic
transformations.
In addition, changes in production methods, the political developments in 1990s,
economic policies towards deregulation, multilateral efforts to liberalize international
trade, and to stabilize macroeconomic environment have helped all countries in the
world access the most advanced available knowledge.
For example, after the Marshall plan in Europe, China’s economic reform, the fall
of the Berlin Wall and the collapse of the Soviet Union, the major political impediments
to economic integration have ended. Industrial countries power their economies from
coal to oil and gas, and oil producers in the Middle East joined the global economy.
Currencies have become increasingly convertible and balance‐of‐payments restrictions
relaxed. The Eurodollar market emerged to increase the international liquidity and
promote cross‐border transactions in Western Europe. Beginning in the 1970s, many
governments deregulated transport and telecommunications industries. GATT
negotiations and the consequent establishment of the WTO, as well as bilateral trade

38

agreements and unilateral trade reforms have liberalized international trade
significantly. The US Federal Reserve successfully ended the US and thereby global
inflation and the Louvre Accord stabilized major exchange rates in 1980s. Institutionally,
the IMF, the World Bank and the GATT assure that the process of globalization would
not be reversed. So around 2000, the accessible broadly defined human capital is
roughly constant across countries.
I assume that 2000 and rescale the relative price of the broadly
defined human capital across countries by assuming that relative price is one in the US.
So for any country ,
2000

2000

Consequently, the education stock for country   is

·

2.3 Estimating Other Variables and Calibration
Data sources used in this analysis include the Groningen Growth and
Development Center (GGDC), the United Nations Statistics Division (UNSD), the
International Labor Organization (ILO), the World Bank, the Penn World Table 6.3 and
the Barro and Lee (2001) educational attainment dataset. Appendix A presents the data
sources and data construction in detail.

39

Some variables are directly observable from data sources, such as the average
growth rate for per capita GDP and population, employment‐population ratio, the share
of workers in the education sector, physical capital investment‐GDP ratio, consumption‐
GDP ratio, and schooling years. Other variables are derived from these observable
variables under certain assumptions.
I use the approach in Caselli (2005) to construct the physical and human capital
stocks. This approach is a variant of the perpetual inventory method, and arises from
the law of motion for any capital stock in steady state,

Since no much information of capital used in education across countries is available, I
assume that the share of education expenditure in GDP is equal to the share of capital
used in the education . Notice that this assumption is equivalent to that the capital
input wedge   is always equal to zero in the prototype economy (see equation (1.7)).
Since I distinguish education investment from consumption, the final goods
consumption is consumption less educational expenditures. And relevant data are the
consumption share in GDP (CC in PWT 6.3) and the share of education expenditure in
GDP .

40

In addition, there are five parameters in the prototype economy: the capital
share, , the depreciation rates,   and , the discount factor, , and the consumption
share, . Each is assumed to be constant across countries. Appendix B presents the data
used in calibration. Table 3 reports their calibrated values. One concern is the
heterogeneity of parameters across countries. Gollin (2002) convincingly show that the
capital share   is a number between 0.20 and 0.35 for most countries. The next section
checks the robustness of the observed patterns by changing parameter values in
reasonable ranges for the full sample.
Following the literature, I assume that the capital share is 0.3333. For other
parameters, I use the US national accounts data to calibrate them, by assuming that
wedges are zero in the US economy during the 1960‐2000 period.
Capital share α 0.3333
Depreciation rate of physical capital δ
0.0665
Depreciation rate of human capital δ
0.0518
Consumption share θ 0.3908
Discount factor β 0.9457
Table 3: Calibrated Values of Parameters
The depreciation rate   is estimated from the perpetual inventory method (see,
for example, Kehoe and Prescott (2007), for a detailed description),
1 1

41

together with a few restrictions on the initial capital stock and the depreciation rate.
The value of   is chosen to be consistent with the average ratio of depreciation to GDP
observed in the data from 1980 to 2004. The initial stock of capital is chosen so that the
initial capital‐output ratio in 1959 should match the average capital‐output ratio over
the 1960‐1970 period. Using this rule gives the estimate for the depreciation rate .
The depreciation rate of human capital   comes from the same procedure,
except its value is chosen to be consistent with

. By comparison,
Kendrick (1976)’s estimates imply the depreciation rates of capital, =0.0616, of
education,
= 0.0343, of health care,
= 0.0718 and of R&D,
=0.0876.
For the remaining two parameters, standard calibration formulae are available.
The discount factor   stems from the following,
1

1

The consumption share   is from,

.
. 1 1.
2.4 Decomposition Results
There has been an explosion of quantitative research on cross‐country economic
performance. Influential growth accounting exercises include Young (1995), Hsieh

42

(2002), Bosworth and Collins (2003), and Kehoe and Prescott (2007), among others;
influential level accounting exercises include Mankiw, Romer, and Weil(1992), Klenow
and Rodriguez‐Clare (1997), Hall and Jones (1999), McGrattan and Schmitz (1999),
Caselli (2004), Cole, Ohanian, Riascos, and Schmitz (2005), and Hsieh and Klenow (2010).
Despite the large volume of work, results from many studies on a given issue frequently
reach opposite conclusions. Moreover, a serious criticism by Acemoglu (2007) says that
“at some level to say that a country is poor because it lacks physical capital, human
capital and technology is like saying that a person is poor because he does not have
money”. To satisfactorily understand of economic growth requires, not only the
contribution of inputs and efficiency to the cross‐country income variance, but also an
analysis of the reasons making some countries more abundant in physical capital,
human capital and technology than others.
In this section, I use the method proposed in the previous chapter to decompose
the growth rate, TFP, the capital‐output ratio and the employment rate into wedges
that can be connected to fundamental causes of economic growth. In the next section, I
replicate two previous studies using the data collected, and compare the concept and
the consequent computational results derived from my method with theirs. In the next
chapter, I would focus on one important wedge in explaining economic growth, the
human capital investment wedge, and test two promising endogenous growth models
using their respective implications from this wedge.

43

2.4.1 Basic Findings
Basic findings of the artificial experiments performed are: (1) when explaining
long‐run growth rate, the human capital efficiency and human capital investment
wedges play primary roles, while the labor and labor input wedges play secondary roles;
(2) in explaining TFP, the effect of the final goods efficiency wedge is dominant; and (3)
these patterns are robust across OECD/non‐OECD sub‐samples. But also bear in mind that
these results are under the assumption that parameter values are identical across countries.
Sub‐sample Total OECD Non‐OECD Above
median
Below
median
Obs 50 26 24 25 25
τ
15.7% 14.2% 17.2% 12.9% 18.4%
τ
16.5% 16.4% 16.7% 15.1% 18.0%
τ

6.0% 6.4% 5.5% 6.8% 5.2%
τ

21.9% 22.3% 21.6% 23.3% 20.5%
A 11.9% 12.2% 11.6% 12.7% 11.2%
B 23.8% 24.4% 23.2% 25.3% 22.4%
g/k 4.2% 4.1% 4.3% 3.9% 4.4%
Table 4: Average Importance of Wedges on Growth Rate
Tables 4 and 5 summarize the average importance of each wedge in explaining
the long‐run growth rate and TFP for the full sample and across different sub‐samples.
Note that the median in table 4 refers to the median growth rate of the total sample,
while the median in table 5 is the median TFP. Clearly the effects of wedges on the long‐

44

run growth rate scatter more evenly than those on TFP across wedges. The human
capital efficiency wedge and the human capital investment wedge explain 23.83% and
21.93% of the long‐run growth rate on average. However, the final goods efficiency
wedge alone accounts for 88.86% of TFP.
Sub‐sample Total OECD Non‐OECD Above
median
Below
median
Obs 50 26 24 25 25
τ
0.6% 0.8% 0.5% 0.7% 0.5%
τ
6.3% 6.1% 6.5% 5.7% 6.9%
τ

0.2% 0.3% 0.1% 0.2% 0.2%
τ

3.1% 3.4% 2.7% 3.3% 2.8%
A 88.9% 88.1% 89.7% 88.9% 88.9%
B 0.8% 1.1% 0.5% 1.0% 0.6%
g/k 0.1% 0.2% 0.1% 0.2% 0.1%
Table 5: Average Importance of Wedges on the level of TFP
This result does not contradict previous studies that TFP growth is as important
as capital accumulation in explaining growth across countries. In the conventional
growth accounting, economic growth is decomposed into the growth of capital
accumulation and technological progress. If the steady state equilibrium conditions
imposed on my calculation were imposed on the growth accounting exercise, then the
growth rate of capital would be equal to the growth rate of per capita GDP, and the
share explained by capital accumulation would be exactly the value of capital share, 1/3.

45

That is not interesting. The decomposition I develop connects economic growth to the
fundamental causes of economic growth, rather than to changes in proximate causes.
Another interesting observation is that the labor and labor input wedges also
play a role in accounting for long‐run growth rate. By comparing France and the United
States, Prescott (2002) gives an example showing that the large difference in labor
supply can explain why the GDP per person of one industrial country could be depressed
by about 30% relative to that in another industrial country; and that policies that result
in a labor wedge are responsible for such difference. As a result, the implications of the
labor market frictions on long‐run economic growth are worthy of more attention.
Tables 6 and 7 report the decomposition results for two other important
endogenous variables: the capital‐output ratio and the employment rate. A few striking
observations for the decomposition of capital‐output ratio are: (1) that the relative
importance of the various wedges on capital‐output ratios is similar to those on growth
rates; (2) that the human capital efficiency wedge is more important than the final
goods efficiency wedge, even if the human capital efficiency wedge plays a tiny role in
determining TFP; (3) that the human capital investment wedge explains more than the
physical capital investment wedge. The fact that other wedges than the final goods
efficiency wedge explain a majority of the capital‐output variations suggests that the
correlation between TFP and capital intensity is weak. Many channels that are known to
affect the incentives to accumulate capital may not affect TFP very much.

46

Sub‐sample Total OECD Non‐OECD Above
median
Below
median
Obs 50 26 24 25 25
τ
14.9% 13.7% 16.2% 16.2% 13.5%
τ
16.0% 16.0% 16.1% 17.5% 14.6%
τ

4.2% 3.3% 5.1% 4.5% 3.9%
τ

21.2% 21.7% 20.8% 20.5% 22.0%
A 17.6% 18.8% 16.4% 16.5% 18.8%
B 22.0% 22.7% 21.3% 21.1% 22.3%
g/k 4.0% 3.9% 4.1% 3.8% 4.2%
Table 6: Average Importance of Wedges on Capital‐Output Ratio
As for the employment rate, not surprisingly, the labor wedge and the labor
input wedge are two important factors. But in steady state, how efficiently a country
produces goods would not change the incentives to work much, as illustrated by the
small influences of efficiency shifters   and . Surprisingly, the government
consumption wedge is noticeable in explaining the employment rate, though it is not a
major factor in determining other variables. Taxes, even lump sum taxes, are
detrimental to working hard.
17

Notice that the aforementioned patterns for the full sample do not change much
across sub‐samples of countries in and out of the OECD; below and above the median
values of respective variables. One possible limitation is that countries in the dataset are

17
Although a higher government consumption used to distort labor supply, any effect through the margin
with the labor‐leisure condition is captured the labor wedge, and government consumption wedge works
through the lump sum tax.

47

mostly rich and middle‐income countries, whereas extremely poor countries may have
different patterns. Another possibility is that the illustrated local effects of wedges on
endogenous variables could depend more on the NCG structure than the magnitude of
country‐specific biases.
Sub‐sample Total OECD Non‐OECD Above
median
Below
median
Obs 50 26 24 25 25
τ
40.4% 37.3% 43.8% 31.8% 49.0%
τ
28.7% 29.3% 28.1% 34.0% 23.4%
τ

8.5% 10.0% 6.9% 10.0% 7.1%
τ

5.5% 6.9% 4.0% 6.2% 4.9%
A 1.6% 1.4% 1.8% 1.4% 1.8%
B 3.1% 2.7% 3.5% 2.7% 3.5%
g/k 12.1% 12.4% 11.9% 14.0% 10.3%
Table 7: Average Importance of Wedges on Employment Rate
Before closing this section, a few words about the role of the two efficiency
wedges are in order. Compared with the other wedges, two efficiency wedges can
hardly be supported by models with micro‐foundation. These wedges seem to reflect
everything except for the mechanism suggested by the detailed model. If this is true,
then, even after decomposing TFP into the effects of seven wedges, it is still mostly a
black box, because the final goods efficiency wedge alone takes up nearly 90% of it. As
Prescott (1998) points out, a theory of TFP differences is still needed.

48

2.4.2 Robustness Check
In this sub‐section I check the robustness of the findings reported above. In
particular, I look at three parameters of the prototype economy: the capital share in the
production function , the discount factor   and the consumption share in the utility
function . I change the value of one parameter, holding the remaining parameters
fixed to their calibrated values, and see whether the explanatory power of various
wedges changes very much.

Figure 1: Robustness Check with   on Growth
The capital share in the US has been rather stable. When it comes to cross‐
country comparisons, a traditional measure of the capital income is the residual after

49

employee compensation has been taken out from national income. These estimates are
generally higher in poor countries than in rich countries. After adjusting the labor
income in self‐employed and small firms, and some other differences, Gollin (2002) has
convincingly shown that for most countries the capital share is in the range of 0.20 to
0.35.

Figure 2: Robustness Check with   on TFP
Figure 1 plots the explanatory power of the various wedges on growth as the
capital share   moves from 0.20 to 0.35. Clearly, the importance of the human capital
investment wedge
and the human capital efficiency wedge   is quite stable with
respect to alternative values of   in this range. The government spending wedge
is not
important, and also stable. Other wedges are more sensitive. But the two labor related

50

wedges   and   are always more important than the capital investment wedge
and
the final goods efficiency wedge .
The pattern for TFP is quite simple: in the plausible range, all wedges are
insensitive, thus the final goods efficiency wedge   is always dominant (see figure 2).

Figure 3: Robustness Check with alternative values of   on Growth
Figure 3 and figure 4 show the decomposition results for growth and TFP when
changing   between 0.90 and 0.99. The order of importance of various wedges in
explaining growth does not change in this range of . Thus the qualitative results in the
text do not change at all. As   moves, the change of the power of
is mainly due to a

51

reverse change in the power of
. In the case of explaining TFP, when   changes, the
change of the importance of the various wedges is not appreciable.

Figure 4: Robustness Check with   on TFP
When it comes to the values of the consumption share , different studies
report different values. McGrattan and Schmitz (1999) shows that the upper bound
could be 0.67, and the lower bound could be 0.16. Figure 5 plots the explanatory power
of various wedges in explaining growth in this range. Except for the labor wedge, the
order of the relative importance of all other wedges does not change. The labor wedge,
however, is quite sensitive to changes in . When   is around 0.23, the labor wedge
reaches its bottom, and could be the least important factor in accounting for growth.
But its explanatory power increases sharply, and it becomes the most important factor

52

when   is equal or higher than 0.47. The high sensitivity of   around the benchmark
value of   implies that our results about the labor wedge may change non‐trivially with
more precise measures of the consumption share.

Figure 5: Robustness Check with   on Growth
As for explaining TFP, the pattern is still dull: the final goods efficiency wedge is
the primary component (see figure 6).

53

Figure 6: Robustness Check with   on TFP
2.5 Do Previous Studies Contradict Ours?
Previous quantitative studies on cross‐country income variance find that
efficiency is at least as important as inputs in explaining both growth and relative
income differences. Does the data I collect or the accounting method I develop
contradict previous studies? By using Hall and Jones (1999) and Bosworth et al. (2003)
as the baseline research for level accounting and growth accounting, I replicate these
studies. In the growth accounting case, I use my data set; in the level accounting case, I
further impose a constant growth rate by steady state equilibrium. Decomposition
results suggest that the alternative method is quite close to previous studies.

54

Human capital Residual
Mine edu · h 0 e

A
HJ (1999) edu A·h 0 e

KRC (1997)
edu

·h 0 e

·Al
A·h 0 e

Table 8: Different Definitions of Human Capital and the Technology in Growth Accounts
Before beginning with the detailed comparison, I would point out the different
definitions of human capital and the residual in the growth accounting used by Klenow
and Rodriguez‐Clare (1997b), Hall and Jones (1999), and me. A general form by Parente
and Prescott (2006) can cover these differences,
0
· ·

Notice that in Klenow and Rodriguez‐Clare (1997b), the production function
takes the form:

in Hall and Jones (1999) it takes the form:

My specification follows Hall and Jones (1999), but has a slightly different measure for
human capital. Table 8 illustrates definitions of human capital   and the residual in
these three cases in terms of the notations in Parente and Prescott (2006).

55

2.5.1 Level Accounting
Mankiw, Romer, and Weil(1992) write an influential level accounting paper
which has led to many follow‐ups. They argue that differences in inputs can account for
a large fraction of the disparity in per capita income whereas Klenow and Rodriguez‐
Clare (1997) and Hall and Jones (1999) argue that it accounts for much less. By analyzing
Latin American countries, Cole, Ohanian, Riascos, and Schmitz (2005) verify that slow
TFP growth, but not slow accumulation of inputs, is the reason of virtual stagnation
growth in Latin America. Caselli (2005) concludes that efficiency is at least as important
as (physical and human) capital in explaining income differences. This answer is robust
to different measures of human capital by allowing for differences in the quality of
schooling and in health status of the population; to the age composition of the capital
stock; to sectorial disaggregation of output, and to several other robustness checks.
Hsieh and Klenow (2010) argue that TFP also exerts indirect effect on inputs, and
misallocation of inputs across firms and industries is a key determinant. In this
subsection, I choose Hall and Jones (1999) as a reference, and do a comparable level
accounting using the data I collected.
Hall and Jones (1999) decompose output per capita of 127 countries in 1988 into
three multiplicative terms: capital intensity
, education stock , and productivity,
a residual term. All terms are expressed as ratios to US values. Forty‐five countries in
their sample overlap the sample I collect. As Hall and Jones (1999) do, table 9 reports

56

each term’s comparable averages, standard deviations, and correlations with other
terms for the overlapped forty‐five countries, from their work and this analysis. Bear in
mind that the human capital in my level accounting includes a growth trend imposed by
the steady state equilibrium, plus the education stock which is the same as the “human
capital” in the baseline study. As a result, the residual in their exercise is different from
mine. I also exclude the effect of relative labor participation from the residual term,
since this information is available in my dataset.
Income Capital Education Residual
Average (45) 0.481 0.957 0.695 0.678
Standard Dev. 0.283 0.194 0.165 0.278
Corr. with Y/L (ln) 1.000 0.658 0.700 0.812
Corr. with A (ln) 0.812 0.156 0.225 1.000
Income Capital Human
capital
Labor Residual
Average (45) 0.437 1.001 0.665 0.859 0.683
Standard Dev. 0.284 0205 0.179 0.179 0.262
Corr. with Y/L 1.000 0.788 0.771 0.394 0.785
Corr. with A 0.785 0.433 0.388 ‐0.162 1.000
Table 9:   Level Accounting Comparisons
The comparable characteristics for relative income and capital intensity are quite
close to each other, as shown in the second and third column. The capital intensity in
my accounting is more correlated with both per capita output and the residual than the
baseline study. This is because, in the baseline study, capital is smoothed using the

57

perpetual inventory method. However, in my study it is not smoothed, but comes from
the investment‐output ratio with a linear transformation.
The education stock in the baseline study and the human capital stock in this
work are related, but not identical concepts. Remember that I choose 2000 as the base
year, and use the average growth rate to infer human capital stock. If all countries
would share the same average growth rates, then the relative human capital would be
identical to the education stock in the baseline study. And if a country grows faster than
the US, its derived relative human capital would be smaller than its relative education
stock. The observation that the average human capital stock is slightly smaller than the
education stock confirms that countries in the sample grow slightly faster than the US,
on average. It seems that the steady‐state equilibrium is not too restrictive to examine
cross‐country differences in economic performance, at least for countries in this sample.
The labor participation says that, on average, other countries in this sample work
less than the US. The residual in the alternative study, not surprisingly, looks similar to
the baseline study; given that the human capital stock differs little from the education
stock.
2.5.2 Growth Accounting
Young (1995) and Hsieh (2002) are two influential growth accounting studies on
the new industrialized countries of East Asia. Klenow and Rodriguez‐Clare (1997) do

58

growth accounting for a large number of countries using a different decomposition
approach. Bosworth and Collins (2003) do a comprehensive empirical study on growth,
including growth accounting.
These different growth accounting studies use two different approaches to
decompose growth and to evaluate contributions of efficiency and capital. Klenow and
Rodriguez‐Clare (1997) use the following formula to decompose growth
Δln Δln 1

Δln 1
Δln

where the sum of inputs’ contribution can be expressed as Δln . They also use co‐
variances to measure the contribution of each term to growth,
Δln ,Δln Δln
Δln ,Δln Δln
1
Bosworth et al. (2003) use a production function and a definition of human capital that
is similar to Hall and Jones (1999), but they use a more conventional decomposition
growth,
Δln ΔlnΔln 1 Δln

59

with averages to measure the contribution of each term,
18

1
Δln Δln 1
αΔ ln Δln 1
1 αΔ ln Δln 1
Notice that if the steady‐state equilibrium were imposed, Klenow and Rodriguez‐Clare
(1997) would attribute growth entirely to technological progress and not at all to capital
accumulation; and Bosworth et al. (2003) would attribute   of growth to capital
accumulation. Growth accounting would not be interesting. So I use Bosworth et al.
(2003) as the baseline to account for growth without imposing further restrictions.
Table 10 presents the results from the baseline study in the upper panel and
from my calculations in the lower panel. Decompositions are made for four regions:
industrial countries, China, East Asia less China, and Latin America. Notice that mostly,
there are fewer countries in my sample. For example, twenty‐two Latin American
countries are in the baseline, but only nine are in my sample. Another point worth
noticing is that the effect of labor participation is excluded from the residual in my
calculation, while not in the baseline study.
19


18
Co‐variances are actually weighted averages, with higher weights for representing larger deviations
from the average.
19
Actually, Klenow and Rodriguez‐Clare (1997) find that, under different specifications at least 85% of
economic growth is due to technology growth, verifying that most countries in their sample are close to
their steady states.

60

Baseline GDP Capital Education Residual
Industrial
Countries (22)
2.2 0.9 0.3 (14%) 1.0 (45%)
China (1) 4.8 1.7 0.4 (8.3%) 2.6 (54.2%)
East Asia less
China (7)
3.9 2.3 0.5 (13%) 1.0 (26%)
Latin America (22) 1.1 0.6 0.4 (33%) 0.2 (17%)

My Calculations GDP Capital Education Labor
Participation
Residual
Industrial Countries (20)
2.1 0.9 0.4 0.2 0.6
China (1) 4.3 2.4 0.7 0.4 0.9
East Asia less China (4)
3.5 1.9 0.8 0.4 0.4
Latin America (9) 1.8 1.1 0.5 0.3 ‐0.1
Table 10: Growth Accounting Comparison
Bosworth et al. (2003) confirms widely accepted observations across regions: in
general, TFP contributes as much as physical capital accumulation and the increase of
education explains a relatively small part; East Asia less China accumulates physical
capital more rapidly during its miraculous growth in the past than others; and TFP grows
slowly in Latin America. My calculations also confirm the baseline. It seems that the data
I have collected is as good (or bad) as the data used by previous studies.

61

Chapter Three: Openness or Efforts: An Alternative Empirical
Test for Underlying Driving Forces of Growth
3.1 Introduction
The identification of underlying determinants of growth has been a primary topic
in the field of growth and development. One popular approach to estimate the effects
of policy variables on growth is to run cross‐sectional regressions of growth rates on
initial income levels, and economic policy and political variables. However, as Durlauf,
Johnson and Temple (2005) point out, many growth theories are compatible with each
other, and the number of theoretical specifications to be tested increases exponentially
with the number of mutually compatible theories.
20
Therefore, if using the conventional
econometric approach, even if testing one theory would require a large number of
regressions and make the econometrical approach infeasible. Using the same fact that
many growth theories are compatible with one another, a quantitative approach can
circumvent this difficulty and provide an alternative testing approach which is both
more straightforward to understand and easier to implement.
The idea originates from Chari, Kehoe and McGrattan (2007). This insight shows
that an optimal growth model is equivalent to various macroeconomic models. Detailed
models correspond to different residuals of equilibrium conditions in the prototype

20
If there is a set of K potential growth theories, all of which are logically compatible with each other,
there exist 2
K
1 potential theoretical specifications, each one of which corresponds to a particular
combination of theories.

62

optimal growth model. And when endogenous variables are observable, substituting
data into the prototype economy can deduce these residuals. Since residuals are
exogenous variables in the prototype economy, using these deduced values and the
prototype economy, the authors make inferences on the explanatory power of a few
detailed models to answer an important macroeconomic question.
In this analysis, I further explore the potential of the aforementioned insight by
testing two endogenous growth models that correspond to the same residual in the
prototype economy, but have different implications on the observable characteristics of
this residual.
These two models examine the underlying causes of cross‐country differences in
growth performances. McGrattan and Prescott (2007) argue that openness to foreign
direct investment (FDI) and technology adoption can explain many growth experiences
(thereafter MP). However, Klenow and Rodriguez‐Clare (2005) write a model
emphasizing the importance of international knowledge spillover in driving growth in
developing countries (thereafter KRC). Both models are isomorphic to a simpler
neoclassical growth (NCG) model with a human capital investment wedge, which is a
friction associated with the inter‐temporal allocation of human capital. But the MP
model implies that the human capital investment wedge is a function of the ratio of
Gross National Product (GNP) to Gross Domestic Product (GDP). However, the KRC
model implies that the human capital investment wedge is proportional to the gap

63

between a country’s own total factor productivity (TFP) and the world technology
frontier. Since both the GNP‐GDP ratios and TFP gaps are observable and the human
capital investment wedge can be derived from the prototype economy, comparing the
imputed values of the human capital investment wedge with the values implied by a
detailed model suggests a test for that model.
Using data for the US economy from 1968 to 1978, I calculate the GNP‐GDP
ratios, the TFP gaps, and the imputed values of the human capital investment wedge. I
compare the imputed values of the human capital investment wedge on the implied
variables by each theory. The MP model has a better explanatory power than the KRC
model.
Although the mapping between a detailed macroeconomic model and the
residual to which it corresponds, is not one‐to‐one, or when more than one detailed
model corresponds to the same residual, the mapping between detailed models and
implied function forms of the residual is not one‐to‐one, this approach eliminates those
explanations that are not consistent with observations, and limits the range of the
search. If it rejects a particular residual, or a particular form of that residual, it rejects all
respective models. In contrast, the estimation approach considers a comprehensive
econometric model, which mixes many potential explanations and many possibilities for
combining their effects, and consequently complicates the testing.

64

The paper is organized as follows. Section 2 describes the equivalence results
between two detailed models and the prototype economy. Section 3 describes the data
used in the paper and reports the results.
3.2 The Equivalence Results
In this section, I consider two models explaining the driving forces of economic
growth. One is by McGrattan and Prescott (2007), which emphasizes that openness to
FDI and technology adoption is important for relatively poor countries to catch up with
rich countries. This model is equivalent to a simper neoclassical growth model with a
human capital investment wedge, and furthermore, it implies the relevant wedge is a
function of the GNP‐GDP ratio. The other model is by Klenow and Rodriguez‐Clare
(2005), which describes how external effects across countries in research and
development can explain the growth experiences. This model is also equivalent to a
simpler NCG model with a human capital investment wedge, but this time, the relevant
wedge is proportional to the gap of a country’s own technology level and the world
technology frontier.
These connections between different theoretical efforts to explain growth can
shed light on empirically testing of their consistency with observable data. In the
prototype economy, all residuals associated with equilibrium conditions can be
imputed, once values of endogenous variables and parameters are known. At the same

65

time, the GNP‐GDP ratio is also observable and the technology gap can be constructed
from available data. Comparing the imputed human capital investment wedge and the
same wedge implied by a detailed model is a straightforward way to see if the detailed
model is consistent with observations.
3.2.1 Openness to FDI and the GNP‐GDP ratio
The first example is the openness to FDI mechanism explored by McGrattan and
Prescott (2007). Consider its stripped‐down version, in which there are only two
countries in the world, countries 1 and 2. Each country owns a representative firm,
which is also a multinational company, company 1 or 2. The model satisfies the first
welfare theorem. Thus the optimal allocation is also the competitive allocation. And a
simpler planning problem is sufficient to determine the competitive equilibrium.
The technologies available to the planner are:

(3.1)

(3.2)

(3.3)

66

(3.4)
where , 1,2 is technological capital owned by multinational company ; ,
1,2 are the population in country , and the aggregate output in country   is the sum
of what is produced by the domestic and the foreign multinational company,

, 1,2 . The social planner maximizes the following comprehensive utility with
utility weight ,
maxln

ln1

1 ln

ln 1

subject to the global resources constraint and the laws of motion for capital and
technology,

,
,

, 1

,
, 1

,
1

1

67

as well as initial stocks
, 1,2 , and , 1,2 . Note that the aggregate capital
stocks and labor inputs in country   are distributed between domestic and foreign
companies,

  and

.
The following first‐order conditions characterize the competitive equilibrium of
the above model, for country j,

1 1

(3.5)

, , 1 , , 1 (3.6)

, ,
,
, 1
(3.7)

(3.8)

(3.9)

68

,

(3.10)
Consider a simple closed‐economy optimal growth model as a prototype
economy to the above detailed model. Assume that the production function is Cobb‐
Douglas, y
k
h
A
l

, where   is per capita output,   is an efficiency shifter,
and   are per capita physical capital and human capital broadly defined respectively,
and   is per capita market hours. Assume that both the final goods and factor markets
are competitive. Firms maximize profits given the rental rate for physical capital,
, for
human capital
, and the wage rate, :
k
h
A
l

r

k
r

h
w
l

Consumers maximize utility over per capita consumption and non‐market hours,

1

subject to the budget constraint,

1

where there is a tax levied on investment in human capital; and the laws of motion for
physical and human capital are,

69

1 1

11

where x

and
denote per capita investment in physical capital and human
capital,
is a tax rate on human capital investment, the discount factor,   the
depreciation rate on both capital stocks, and   is per capita lump‐sum transfers (or tax).
The equilibrium conditions of the prototype economy include

1
1 1 (3.11)

1 (3.12)

1

1 (3.13)
and the resources balance,

(3.14)

,

70

and the production function. Notice that the tax on human capital investment shows up
as a wedge in the Euler equation for broadly defined human capital. I call it the human
capital investment wedge.
Notice that in the detailed model, for any country ,

, and

. So the equation (3.5) is identical to (3.11), and equation (3.6) is identical
to (3.12). In the detailed model, the production function in country   is,

/

Comparing the Euler equation in the detailed model (3.7) with the Euler
equation in the prototype economy (3.12) suggests that,
1
,
, ,

/
1
,
, , 1

Remember that the net factor payment (NFP) from country   to country   equals
,
and the net factor revenue (NFR) from country   to   equals
. By definition, the
difference between NFP and NFR equals the difference between GDP and GNP. As a
result, the human capital investment wedge is a function of the GNP‐GDP ratio.
1 1

1

71

3.2.2 The international knowledge spillover and the TFP gap
Klenow and Rodriguez‐Clare (2005) present a growth model with international
knowledge spillovers. In its simplest version, the production of knowledge of a certain
country is affected by the country’s productivity relative to an exogenous world
technology frontier and technology diffusion from abroad that does not depend on
domestic research efforts. Here I show that this version is equivalent to the prototype
economy with a human capital investment wedge.
Suppose that in a country, the output is produced with a Cobb‐Douglas
production function,
, where   is a technology index. Output can be
consumed, invested in capital, or in research, thus . Capital is
accumulated according to 1
. Technology evolves according to,

1
where   and   are positive parameters and   is the world technology frontier. Assume
that factor markets are competitive. Let lowercase letters denote per person values of
aggregate variables. This model can be written succinctly as the following maximization
problem,
β
ln c
L

72

subject to

the laws of motion for capital and technology, factor prices, and initial values,   and
.
Let , and refer to the proposition 1.2, the Euler equation for technology is
the only equilibrium condition that suggests a wedge, with a changing depreciation rate
for human capital,

1 1 1 (3.15)
This implies that the human capital investment wedge in the prototype economy
1
1 , or the wedge is proportional to the labor‐augmented TFP gap.
3.3 Data and Results
The data used in this paper are from the Current Population Survey (CPS), the
NIPA of the US, and the total economy database. The two endogenous variables in the
prototype economy are the growth rates of real consumption and the output‐human
capital ratios. The growth rates of consumption are obtained from the NIPA of the UN
directly. The approach of estimating the nominal human capital stock is borrowed from

73

Christian (2010). This approach uses the present discounted value of the lifetime
earnings from market work as an estimate for nominal human capital stock. For the US,
the CPS and Life Tables are sufficient. The nominal investment in human capital comes
from,
1

Total output is the sum of GDP and investment in human capital. In addition, the
GNP‐GDP ratios are easy to obtain from the NIPA. And the ratio of GDP per worker is
obtained from the total economy database.
To test the openness to FDI mechanism, I run the following regression,
1
. 1

To test the international knowledge spillover effects, I assume that the capital
per worker is roughly constant over time, so that the GDP per worker equals TFP.
Furthermore, I assume that the world technology frontier grows at the same rate as the
TFP of the US in the long term, thus the regression equation becomes,
1
1,1,

where   is an efficiency shifter at time t, and g is the long‐term growth rate for both the
US TFP and the world frontier. To recover , I regress the logarithm of ,
on the year

74

variable, with a constant, and use the associated residuals as an estimate of the
efficiency shifter. It suggests a long‐term growth rate around 1.62% per year. Next I run
the following regression with a constant term,
1
.
Table 1 shows the test results for the above two models. The coefficient
estimate for McGrattan and Prescott (2007) has the expected positive sign, as theory
predicts, while the sign of the coefficient estimate for Klenow and Rodriguez‐Clare
(2005) is not the expected one, as the theory predicts a negative sign, though neither
estimate is statistically significant. The point estimate for MP suggests that the share of
technology capital is around 3.2% (1/31.14), which is not far away from what the
authors use in their original work, 7%.
21
The goodness‐of‐fit of MP is also better than
that of KRC. Statistically, the GNP‐GDP ratio accounts for around 23% of the observed
variation of the human capital investment wedge.
Theory to be tested Openness to FDI (MP) Knowledge externalities
(KRC)
GNP/GDP 31.14 [19.00]
Predicted values for TFP 14.72 [17.60]
Goodness of fit 22.98% 8.04%
Table 11: Test Results for McGrattan and Prescott (2007) and Klenow and Rodriguez‐Clare
(2005)

21
  is selected to match a technology capital to output ratio of 0.5 for a country that is totally closed in
McGrattan and Prescott (2007).

75

The estimates of the impact of policy variables in conventional cross‐country
regressions are under debate. First of all, the number of growth regressors approaches
the number of countries available in even the broadest samples. And the estimated
coefficients on variables designated as policy variables have been shown to be sensitive
to which variables are included in the regression.

76

Conclusion
This paper presents a method to account for differences in aggregate variables, such as
long‐run growth rate and TFP, across countries. The method also links many endogenous growth
theories to a two‐sector neoclassical growth model, and sheds light on the mechanisms lying
behind economic growth. The main findings suggest that building up a theory of TFP is still the
most needed task and in addition, endogenous growth theories that are equivalent to the
prototype economy with a human capital investment wedge and/or a labor wedge are more
consistent with the data than other theories.
Development or growth accounting has helped us learn a great deal about the
proximate determinants of income differences. But they do not uncover the ultimate causes
why some countries are much richer than others. They also have nothing to say on the causes of
low factor accumulation, or low levels of efficiency. Indeed, the most likely scenario is that the
same ultimate causes explain both. Furthermore, it has nothing to say on the way factor
accumulation and efficiency influence each other, as they most probably do. The alternative
growth accounting is a powerful tool to getting started thinking about the fundamental causes
of long run economic growth differences across countries.
As Klenow and Rodriguez‐Clare (1997a) said, more work should be done to empirically
distinguish between theories of endogenous growth; to accomplish this, a quantitative approach
avoids misspecification in empirical work and fully exploits the quantitative implications of
candidate models. Banerjee and Duflo (2005), moreover, show that even a series of convincing
micro‐empirical studies is not enough to give an overall explanation for aggregate growth, and
that a promising alternative is to build macroeconomic models.

77

Numerous studies show that the neoclassical growth model with wedges is a useful
workhorse in accounting for various macroeconomic events Cole and Ohanian (2004),
McGrattan and Ohanian (2006) and Chen et al. (2007)). These findings suggest that the
“Business Cycle Accounting” idea, together with neoclassical models, is a good way to organize
the increasingly available data on various dimensions and aspects of economic growth.

78

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Appendix A: Variables in the Cross‐country Dataset
This appendix explains how to create relevant variables for the cross‐country dataset
used in the paper.
22

The long‐run growth rates come from the per capita GDP estimates by Maddison (2003).
I compute the annual growth rates for each country year by year, and assume the long‐run
growth rate equals the average of those annual growth rates. The sample sizes are quite large.
The longest series have 188 years, and include those for Australia, Chile, Denmark, France, the
Netherlands, and Sweden. The countries with the shortest series have 58 years, most of which
are countries that became independent after the Second World War. And usually this length can
be regarded as long enough for a country to converge.
The long‐run population growth rates are from the midyear population estimates of the
Total Economy Database. Similarly, I compute the annual growth rates over time and take the
average. The length of the series of each country is 58. The Total Economy Database also has
estimates for employment over time. To obtain a measure of employment‐population ratios, I
divide employment by midyear population and take their average.
As for the shares of employment in education, I divide employment in education by
total employment obtained from the ILO, and then take their average. To compute the shares of
education output, I use value added of education and value added of the total economy in

22
The dataset includes Argentina, Australia, Austria, Belgium, Bangladesh, Bulgaria, Bahrain, Brazil,
Canada, Switzerland, Chile, China, Costa Rica, Germany, Denmark, Dominican Republic, Ecuador, Egypt,
Spain, Ethiopia, Finland, France, United Kingdom, Greece, Guatemala, Hungary, Ireland, Iran, Iraq, Israel,
Italy, Japan, Republic of Korea, Mexico, Malaysia, the Netherlands, Norway, New Zealand, Peru, the
Philippines, Poland, Portugal, Romania, Sweden, Thailand, Turkey, Uganda, Uruguay, United States, and
Vietnam.

82

constant prices obtained from the National Accounts Official Country Data (Table 2.2) by the
United Nations Statistics Division, and the public spending on education as a percentage of GDP
is obtained from the World Development Indicators (WDI). I divide value added of education by
value added of the total economy, take the average of them, and add it to the average
percentage of public spending on education.
To construct investment‐capital ratios for physical capital, I use the assumed condition

, together with estimates of growth rates and population growth rates, and
calibrated values of depreciation rates. Similarly,
can be constructed.
The final goods output‐capital ratios are computed by the following formula,
1

where

is the share of investment in GDP, which is obtained from the Penn World Table 6.3
(CI),

is the share of education output in the total economy, and
is the investment‐
capital ratio for capital. The last two variables are both known from previous calculations.
Similarly, the final goods consumption‐capital ratios can be calculated from the following
formula,

1

where

is the share of consumption (CC) in GDP from the Penn World Table 6.3.

83

Variables Raw variables from sources Data sources
Long‐run growth rate Per capita GDP Maddison‐GGDC
Employment‐population Employment, population TED‐GGDC
Capital allocation Value added by industry UNSD
Public spending on
education
WDI
Labor allocation Employment by industry ILO
Investment‐capital (derived) Population growth TED‐GGDC
Final goods output‐capital
(derived)
Investment share in GDP PWT 6.3
Final goods consumption‐capital
(derived)
Consumption share in GDP PWT 6.3
Relative price of human capital
(derived)
Education expenditure UNSD
Physical capital‐human capital
(derived)
Schooling years Barro‐Lee 2001
Table A1: Data Sources
The method of estimating human capital and its relative price in terms of final goods is
detailed in the text. The data on schooling years are from Barro and Lee (2001). In particular, I
use the average schooling years in the total population over age 25.
The physical capital‐human capital ratio is derived using the following formula,
1

84

Appendix B: Data for Calibrating Parameters
The method of calibrating the parameters in the model is detailed in the text. Here I
explain how to construct the necessary data using the US national income and product accounts
(NIPA), with the detailed formula for each variable.
 Output per person ( )
Real GDP without the software investment
‐ Real value added in private education industry
‐ Real value added in private health care industry
‐ Real government expenditures on education
‐ Real government expenditures on health
‐ Real total R&D output
+ Real business sector R&D output
+ Real R&D output of FFRDC administered by business sector
‐ Sales tax deflated by the PCE deflator
+ Services from consumer durables deflated by the PCE durable deflator
+ Depreciation from consumer durables deflated by the PCE durable deflator
All divided by non‐institutional population, 16‐64.
From the above formula, the products of both private and public education and health
care activities are removed from GDP. Since R&D outlays in the business sector are counted as

85

expenses but not products and, thus, are excluded from GDP,
23
only R&D outputs of the
households and institutions sector and the general government sector are removed from GDP.
Since NIPA records investments in capital very well, I follow the standard procedure in
Chari et al. (2007) to generate it.
 Investment in capital per person ( )
Real gross private domestic investment
+ Real government gross investment
+ Real personal consumption expenditures on durables
‐ Sales tax deflated by the PCE deflator _ share of durables in PCE
All divided by non‐institutional population, 16‐64.
As for government consumption, NIPA estimates include government expenditures on
R&D, education and health care, so the part counted as government consumption of these
items should be removed to make consistent measures. Total government expenditures of these
items are known, but not the portions of counted as government consumption. I assume that
they have the same portion as the total government expenditure.
 Government consumption per person ( )
Real government consumption
+ Real net exports of goods and services

23
Federal funded R&D centers (FFRDC) are administered by either business sector or public universities
and colleges. Outputs of those administered by business sector are recorded like business R&D outputs,
so they are not included in the conventional GDP estimates.

86

‐ Real government expenditures on education _ consumption share
‐ Real Government expenditures on health _ consumption share
‐ Real Federal R&D output _ consumption share
‐ Real State and local government R&D output _ consumption share
All divided by non‐institutional population, 16‐64.
Investment in labor‐augmented technology is counted in terms of final goods. Three
categories of spending are included: education, health care, and R&D.
 Gross investment in education per person ( )
Real value added of private education industry (SIC: M)
+ Real government expenditures on education
All divided by non‐institutional population, 16‐64.
 Gross investment in health care per person ( )
Real value added of private health care (SIC: N) and social assistance industry (O)
+ Real government expenditures on health
All divided by non‐institutional population, 16‐64.
Investment in and depreciation of R&D are available in table 2.4, 1959‐2004 R&D data,
BEA. The investment of labor‐augmented technology h is the sum of investment series of
education, health care, and R&D.
24


24
A common concern is the double‐counting of the intersection of R&D investments and education or
health investments. Since only R&D investments by government and household sectors are accounted in

87

To calculate share of capital stock devoted to producing final goods , we need to know
capital stock used in the technology sector first. Here are a few places worth noticing: (1) Capital
stock consists of fixed assets, consumption durables, and inventories. Since fixed assets are
majority, I only count fixed assets used in technology sector. (2) Fixed assets mainly include
equipment and structures. There are estimates of government structures in education and
health care, but estimates of government equipment are not available in national accounts.
Thus when computing government fixed assets used in education and health care, the ratio of
government structures in education and health over total government structures is assumed to
be close to the corresponding ratio of government fixed assets. (3) The capital expenditure on
R&D for the U.S. is not publicly accessible. I use an OECD data to estimate shares of capital
expenditure in total R&D expenditure,
25
and assume this is a good approximate for the U.S. The
OECD collects capital expenditures on R&D for 36 countries.20 The data reveals capital
expenditure shares from 1981 to 2004. For those before 1981, instead I use its simple average,
13%.
When both R&D expenditure and shares of capital expenditure in R&D expenditure are
available, I form a series of capital investment in R&D. Following Caselli (2005), its initial stock
0 is set to 0 , where 0 is the initial investment, and   is its average growth
rate. Thus the share   can be inferred once   is known.
 Capital stock in technology sector (1

NIPA, and compared with business R&D investments, their magnitude is small, I did not make further
assumptions to separate them out.
25
Dougherty et al. (2007) report an estimate of 9%, which is lower than our estimates. Their estimate
seems based on data of France, Germany, Japan, the Netherlands, and the United Kingdom.

88

Real gross stock of fixed assets in private education and health industries
+ Real gross stock of government fixed assets
share of gross stock of government structures in education and health
+ Real gross stock of capital used in R&D activities
Forming share of labor devoted to producing final goods   is similar. One thing worth
noticing is that the number of employees in education and health care hired by government is
unknown. Assuming that the cost structures of education and health care are similar in both
private and public sectors, ratios of government expenditure over private output are close to
employment ratios. The number of government employees in education and health care is
inferred by this assumption.
 Number of workers in the technology sector (1
Number of mathematicians and scientists
+ Full‐time equivalent employees in private education and health industries
(1+ ratio of government expenditure over private output)
Since non‐institutional population, 16‐64, is observable, its growth rate n can be
computed directly. Per person consumption is gauged by the following formula, and is its
average growth rate.
 Consumption per person ( )
GDP‐ Constructed investment in capital‐ Constructed government consumption
All divided by non‐institutional population, 16‐64.

Asset Metadata

Creator Zhao, Hongchun (author)

Core Title Inter-temporal allocation of human capital and economic performance

Contributor Electronically uploaded by the author (provenance)

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Economics

Publication Date 05/27/2011

Defense Date 04/05/2011

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

Tag growth accounting,human capital,macroeconomic model testing,oai:digitallibrary.usc.edu:usctheses,OAI-PMH Harvest,prototype economy

Language English

Advisor Nugent, Jeffrey B. (committee chair), Betts, Caroline M. (committee member), Imrohoroglu, Selahattin (committee member), Joines, Doug (committee member), Ohanian, Lee (committee member)

Creator Email hongchuz@usc.edu,zhcpku@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c127-613486

Unique identifier UC1409937

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Legacy Identifier etd-ZhaoHongch-8-0.pdf

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Document Type Dissertation

Rights Zhao, Hongchun

Type texts

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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...

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Abstract (if available)

Abstract Differences in economic growth across countries have been substantial in history. Industrial countries have grown at a remarkably stable rate since 1870, but the growth rates of other countries have varied considerably. Why countries grow at divergent rates over time? Which countries will become industrial leaders in the twenty-first century, and what will their long term trends look like? I extend the “Business Cycle Accounting” framework of Chari, Kehoe and McGrattan (2007) to provide a platform for addressing these questions.

Using the “Business Cycle Accounting” idea of Chari, Kehoe, and McGrattan (2007), I develop an accounting method that decomposes economic growth, and other endogenous variables of interest, into effects of exogenous wedges in a prototype economy. Furthermore, a number of endogenous growth theories can be shown to be equivalent to the prototype economy, with specific implications on wedges. Thus, potential theoretical explanations connect to the relevance of the various wedges, whose values are recoverable from available data. By using data for fifty countries, our results show that the wedge associated with the inter-temporal allocation of the broadly defined human capital, or the human capital investment wedge, is important in explaining growth.

Based on this accounting method, an empirical testing procedure that fully explores a theory’s implications is applied to the US data. I choose two endogenous growth models which both are equivalent to the human capital investment wedge in the prototype economy, but imply different functional forms and determinants of the human capital wedge. One is a model on the openness to foreign direct investment by McGrattan and Prescott (2010), and the other is an international knowledge spillover model by Klenow and Rodriguez-Clare (2005). Results suggest that McGrattan and Prescott’s model is more consistent with data.