Seminar Zhao 050511

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An Accounting Method for Economic Growth

Hongchun Zhao

PhD student at University of Southern California

April 2011 Version 2.0Preliminary and Incomplete

Abstract

AsChari et al.(2007) indicate, many growth theories explaining frictionsin real economies are equivalent to a competitive economy with some ex-ogenous taxes. Using this idea, I develop an accounting method for identi-fying fundamental causes of economic growth. I use a two-sector neoclas-sical growth model with taxes as a prototype economy and show that twodetailed growth models correspond to two different wedges in the prototypeeconomy, respectively. Furthermore, the importance of wedges in explainingthe long-run growth rate, and other variables of interest, can be evaluatedthrough the prototype economy, and promising models connect to the rele-vance of their corresponding wedges. Applying this method to Hong Kong,Korea, Singapore, and Taiwan reveals that two investment wedges account

for their rapid growth, while applying to Argentina, Brazil, Chile, and Perureveals that the labor wedge helps understand their stagnant growth.

Address: 3620 Vermont Ave., KAP 300, Economics Department, University of Southern Cali-fornia, Los Angeles, CA 90089; email address: [email protected]; telephone: 323-229-0922; fax:213-740-8543. I thank Caroline Betts, Selo Imrohoroglu, Doug Joines, Michael Magill, Jeff Nugent,and Lee Ohanian for useful comments. All errors are my own.

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2 HONGCHUN ZHAO

1. Introduction

Differences in economic growth across countries have been substantial in history.

Since 1950 the industrial countries have either grown at a remarkably stable rate

or converged to the stable trend, a few developing countries have experienced

rapid growth, yet some other countries grow at only a stagnant rate. Over the

last two hundred years the industrial leaders also witness sustained economic

growth: the United Kingdom grew around 1.2% per year from 1820 to 1890; and

the United States has a 2% average annual growth rate throughout the twenti-

eth century (use data fromMaddison(2003)). What sustains growth over long

periods of time? Which country will be the industrial leader in the twenty-first

century, and what will its trend growth rate be? In this paper, I extend the Busi-ness Cycle Accounting framework ofChari et al. (2007) to provide a platform

for addressing these questions.1

The insight fromChari et al.(2007) is that a neoclassical growth (NCG) model

with taxes is a good perspective with which underlying causes of the observed

gaps in growth can be analyzed. Wedges associated with a prototype economys

equilibrium conditions can be defined as exogenous variables, and interpreted as

taxes, efficiency shifters, etc. Furthermore, specific growth models that can the-

oretically explain the observed gaps correspond to these wedges too. Compared

with the conventional growth accounting method, the whole set of equilibriumconditions, rather than only production functions, are used to decompose eco-

nomic growth; and the decomposition results can be connected to theoretical

explanations more easily. I choose a two-sector NCG model as the prototype

economy, in which the long run economic growth is endogenously driven by the

accumulation of the broadly defined human capital. The prototype economy de-

fines seven wedges, which resemble taxes, productivity shifters and government

consumption.

The reason why many specific growth models can be connected to the pro-

totype economy is because most theories in the growth literature capture certain

1Kydland and Prescott (1982) unify business cycle and growth theory by arguing that businesscycle models should be consistent with the empirical regularities of long-run growth. So growththeories can naturally take advantage of any methodology that proves to be useful in businesscycle models.

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ALTERNATIVE GROWTH ACCOUNTING 3

frictions of real economies that could prevent production from achieving opti-

mality in a neoclassical structure. For example,Lucas(1988) specifies that the ac-

cumulation 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)

andCole et al.(2005), are seen as explicit frictions in the production process.

As examples for the equivalence results that many growth theories are iso-

morphic to the prototype economy,2 I show that an international knowledge

spillover model (adapted fromKlenow and Rodriguez-Clare(2005)) and a mo-

nopolistic competition model (adapted fromRomer(1990)) correspond to a hu-man capital investment wedge and a labor wedge in the prototype economy re-

spectively. The human capital investment wedge is the wedge associated with

the Euler equation for the human capital, and the labor wedge is the wedge as-

sociated with the labor-leisure trade-off condition.

In addition, the wedges defined by equilibrium conditions of the prototype

economy can be recovered, when values of endogenous variables and parameters

are observable. Thus the relevance of potential theories in explaining economic

growth is connected to the relevance of their corresponding wedges, which are

recovered from actual data. This flexibility allows us to tackle the important

question of identifying fundamental causes of the long-term economic growth.

I collect the relevant data for four East Asian countries, four Latin American

countries, and the United States, measure various wedges for each country and

evaluate the contributions of individual wedges. The main findings confirm and

extend the results of Young(1995): country-specific features that facilitate the

accumulation of labor-augmented technology drive the growth of Hong Kong,

South Korea, and Taiwan, while the policies stimulating physical capital invest-

ment also drive the growth of Singapore and South Korea in a significant way; as

2Some endogenous growth theories are not isomorphic to the prototype economy. For ex-ample, endogenous growth models with multiple equilibria are not, because the equilibrium ofthe prototype economy is uniquely defined. Also two-sector models with a different partition ofoutput are not equivalent to each other. For example, two-sector models with a agriculture/non-agriculture partition are not equivalent to those with a consumption/capital goods partition.

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4 HONGCHUN ZHAO

for Argentina, Brazil, Chile, and Peru, the frictions that restrict competition and

impede the operation of normal market forces in product and labor markets de-

lay these countries gaining ground on the United States. 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 materi-

als, geography, preferences, and economic policies (e.g.,McGrattan and Schmitz

(1999),Cole et al.(2005),Acemoglu et al.(2001) andRodrik et al.(2004)). 3 My

paper complements this literature by organizing promising stories under a uni-fied framework. In this respect, my work provides a particular response toLucas

(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) to explore the implica-

tions 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. Section2. describes the proto-

type economy and its steady-state equilibrium. Section 3.establishes equivalence

results for two detailed models. Section 4.presents the raw data sources, the con-

struction of the broadly defined human capital and its relative price in terms of

final goods, and briefly explain the accounting procedure. Section5. shows the

experiment results, and compares them with previous level and growth account-

ing studies, both conceptually and numerically. Section6.concludes.

3Solow(1957)is an early, but modern, attempt to account for different patterns of economicdevelopment, which becomes the cornerstone of the NCG model. Lucas(1988) emphasizes theeffects of human capital accumulation; Romer(1990), among others, endogenizes technologicalchange; Klenow and Rodriguez-Clare(2005) address the interaction between open economies.McGrattan and Schmitz(1999) focus on differences in economic policies and review estimates fora wide range of policy variables;Cole et al.(2005)argue that Latin Americas failure to replicateWestern economic success is primarily due to TFP differences, and that barriers to competitionare the cause of these differences.

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2. The Prototype Economy

In this section, I specify the prototype economy as a two-sector model of endoge-

nous growth with taxes, and describe its steady-state equilibrium.

The prototype economy is a variant of Rebelos two-sector model (see Re-

belo(1991)). One sector produces final goods, which can be either consumed or

invested in physical capital; the other sector produces human capital, which en-

hances labor productivity. Both sectors use Cobb-Douglas aggregate production

functions,4

y(t) =A[v(t)k(t)][u(t)h(t)l(t)]1, (1)

xh(t) =B[(1v(t))k(t)][(1u(t))h(t)l(t)]1, (2)

wherey,l,xh,k and h are per person output of final goods, labor input, invest-

ment in human capital, physical capital stock and human capital stock respec-

tively;5 vand u represent the fractions of physical capital stock and labor devoted

to the final goods sector; represents the common capital share in both sectors;

AandB are two productivity shifters in these two sectors.6

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

y(t)(1 +1)rk(t)v(t)k(t)(1 +2)wk(t)u(t)l(t),

q(t)xh(t)rh(t)(1v(t))k(t)wh(t)(1u(t))l(t),

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 rk, wk and in the

other sectorrh,wh. Notice that factor incomes in the final goods sector are taxed

with rates1and2.

There is a representative household in the model whose size N(t)grows at

4Sturgill (2009) suggests that the inclusion of energy as a further input has a substantial impacton the estimated contribution of TFP on long-run growth. So this widely-used specification ofproduction function deserves a further consideration.

5When there is no risk of confusion, I drop time arguments, but whenever there is the slightestrisk of confusion, I will err on the side of caution and include relevant arguments.

6These production technologies are labor-augmented Y = AK(hL)1, where uppercasevariables denote total amounts. The reason why I choose the labor-augmented technology is thatany technology consistent with balanced growth can be represented by this form.

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a rate ofn. It maximizes a discounted utility over flows of consumption c(t)

and leisure 1 l(t). Let (0, 1) be its discount factor, and (0, 1) be the

consumption share in the period utility function. The households problem is,

max

t=0

t[ ln c(t) + (1)ln(1l(t))]N(t),

subject to (a) a budget constraint,

c(t) + (1 +xk)(11)xk(t) + (1 +xh)(1l)q(t)xh(t) =rk(t)v(t)k(t)

+rh(t)(1v(t))k(t) + (1l)[wk(t)u(t)l(t) +wh(t)(1u(t))l(t)] +T(t),

(b) factor prices derived from profit maximization problems,

(1 +1)rk(t) =y(t)/[v(t)k(t)],

(1 +2)wk(t) = (1)y(t)/[u(t)l(t)],

rh(t) =q(t)xh(t)/[(1v(t))k(t)],

wh(t) =q(t)(1)xh(t)/[(1u(t))l(t)],

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

7

(1 +n)k(t+ 1) = (1k)k(t) +xk(t), (3)

(1 +n)h(t+ 1) = (1h)h(t) +xh(t), (4)

with xk(t), xh(t) 0. Here xk 1, xh l, l are tax rates on physical cap-

ital investment, human capital investment, and total labor income; T is a per

person lump-sum transfer, which equals total tax revenues minus government

7If the labor-augmented human capital includes a general technology level that can be pub-licly used, population growth would not dilute the human capital stock per person. Then thelaw of motion would be h(t+ 1) = (1h)h(t) +xh(t). Both forms followBen-Porath(1967). Adifferent approach is a log-linear law of motion.Chang et al. (2002) use the log-linear approach toanalyze 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.

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consumptiong,

T =1rkkk+2wklk+ (xk1)xk+ (xhl)qxh+l[wkul+wh(1u)l]g.

And hand kdenote the depreciation rates of human capital and physical capital

respectively;xkis 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 resources balance,

c(t) +xk(t) +g(t) =y(t). (5)

The equilibrium conditions are

(1l)

c(t)

(1)q(t)xh(t)

(1u(t))l(t) =

1

1l(t) (6)

(1 +1)q(t)xh(t)v(t) =y(t)[1v(t)], (7)

(1 +2)q(t)xh(t)u(t) =y(t)[1u(t)], (8)

c(t+ 1)

c(t) (1 +xk) =[

y(t+ 1)

v(t+ 1)k(t+ 1)+ (1k)(1 +xk)] (9)

c(t+ 1)

c(t) (1 +xh) =

q(t+ 1)

q(t) [

(1)xh(t+ 1)

(1u(t+ 1))h(t+ 1)+ (1h)(1 +xh], (10)

together with production functions, laws of motion, and the resources balance.

Given the transversality condition, lim((1+)(1+)

)tc(0)y( 0) = 0, and the initial

stocks,k(0), h(0),these equations characterize competitive equilibrium paths of

the prototype economy.8

The prototype economy also has a steady-state equilibrium, whose local prop-

erties 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)).8Solving the following Bellman equation yields equilibrium conditions,

V(k, h) = max{U(c, l) +(1 +n)V(k, h)}

wherec= rkvk+ rh(1 v)k+ (1 l)[wkul+wh(1 u)l] + T (1 + xk)(1 1)[(1 + n)k (1 k)k] (1 + xh)(1 l)q[(1+n)h

(1 h)h]. Notice that equations (6), (7) and(8) are from first

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In the steady-state equilibrium, the growth rate of every variable is constant. 9

More specifically,v,u,l, andqare constants, and all other endogenous variables

grow at the 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 the ten

endogenous variables,v,u,l,q,,h/k,y/k ,c/k,xk/k, andxh/h.

For clarity, the steady-state equilibrium conditions are collected in one place

as follows,

(1l)1l

l

(1)qxh(1u)h

h

k =

1

c

k, (11)

(1 +1)vqxh

h

h

k = (1v)

y

k, (12)

(1 +2)u

qxh

h

h

k = (1u)

y

k , (13)

(1 +)(1 +xk) =[y

vk+ (1k)(1 +xk)], (14)

(1 +)(1 +xh) =[(1)xh(1u)h

+ (1h)(1 +xh)], (15)

y

k =Av(ul

h

k)1, (16)

xhh

h

k =B(1v)((1u)l

h

k)1, (17)

order conditions with respect tol,vandu,

Uc(1l)(wku+wh(1u)) +Ul= 0

rkkrhk = 0

(1l)(wklwhl) = 0.

Using canonical dynamic programming, we obtain,

c(1 +xk)(11) = c[r

k+ (1 k)(1 +xk)(11)]

c(1 +xh)(1l)q= c[(1l)(w

h)l +q(1h)(1 +xh)(1l)].

These are the Euler equations (9)and (10).9To avoid repetition, letabe the growth rate of an arbitrary variableain steady state. Equa-

tions (7) and (8) imply that u = v = 0, equation(6) implies l = 0, equation (8) impliesy = xh+q , equation (5)impliesc= xk= g =y , the law of motion for himpliesxh= h,the law of motion for k impliesxk = k, production function (1)impliesy = k+ (1)h,production function (2) impliesxh= k + (1 )h. Combining all of these results implies thatv,u,l,qare constant, and all the other variables grow at the same rate.

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xhh

=+n+h, (18)

xkk

=+n+k, (19)

c

k+

xkk

+g

k =

y

k. (20)

Altogether there are eight wedges. However, to overcome data availability

restrictions and make easy to compare with the literature, later I only experiment

with the labor wedgeL = l+21+2

, the physical capital investment wedgexk, the

human capital investment wedgeXH= xh+B1B

, the final goods efficiency wedge

A= 1 AAUS

(in additionBis similarly defined), and the government consump-

tion wedgeg/k .

3. Equivalence Results

In this section, I show that two detailed models are equivalent to the proto-

type economy with different wedges. 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. Yet

many other economic theories with policy implications can be connected to these

two wedges, and some will be discussed in section5.10

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 countrys 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 equivalentto the prototype economy with a human capital investment wedge.

10For example, McGrattan and Prescott (2007) show the relationship between development andopenness to foreign direct investment (FDI), which also corresponds to a human capital invest-ment wedge, andCole and Ohanian(1999,2004), andOhanian(2009) present theory that manytypes of cartel policies map into an optimal growth model featuring a labor wedge.

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Suppose in a country, the output is produced with a Cobb-Douglas produc-

tion function, Y = K(AL)1, where Y is total output, Kis the capital stock,

Ais a technology index, and L is the total number of workers which are grow-

ing at the rate n. Output can be used for consumptionC, investment I, or re-

search R, thusY = C+ I+ R. Capital is accumulated according to K(t+ 1) =

(1 )K(t) +I(t). The technology indexA contains effects of research efforts,

technology diffusion from abroad, and relative productivity to the world tech-

nology frontier. The growth rate of this frontier is exogenous. In particular, A

evolves according to,

A(t+ 1) = A(t) + [R(t)/L(t) +A(t)][1A(t)/A(t)], (21)

where and are positive parameters and A is the world technology frontier.

The R&D investment rate is denoted by 1s= R/Y. Let lowercase letters denote

per person values of aggregate variables. Then the production function becomes

y = kA1. Assuming that factor markets are competitive, the rental rate of

capital becomesr = k1A1, and the rate of return onA,w = (1)kA.

This model can be written succinctly as the following maximization problem:

max{c(t),i(t),(R/L)(t)}

t=0

t ln[c(t)]L(t),

subject to

c(t) +i(t) +R(t)/L(t) =r(t)k(t) +w(t)A(t),

(1 +n)k(t+ 1) = (1)k(t) +i(t),

A(t+ 1) = [1 +(1A(t)/A(t))]A(t) +[1A(t)/A(t)]R(t)/L(t),

r(t) =[k(t)]1[A(t)]1,

w(t) = (1)[k(t)][A(t)],

and initial values,k(0)andA(0).

Let a(t) = A(t)/A(t). Klenow and Rodriguez-Clare(2005) show that a is

constant in steady state. The following conditions characterize the steady-state

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Wedges Variables Parameters

Prototype (P) KRC P KRC P KRC

Ap 1 vp s p

Bp 1 up s p 0

1pl 1 hp A pk

1 +p1 1 kp k ph

(1a)(1a)

n

1 +p2 1 xph R/L

p

1 +pxk 1 xpk i n

p n

1 +p

xh

((n s

1

)(1a)+ 1s

1

)1 yp sy

gp 0 lp 1

qp 1

Table 1: Equivalence Result for Klenow and Rodriguez-Clare (2005)

equilibrium,

c+i= skA1 (22)

c+i+R/L= y, (23)

i/k= +n+ (24)

R

AL=

(1a)

(1a) (25)

1 += (r+ 1), (26)

1 += (1 +n)[(1a)w+ 1 + (1a)], (27)

wherebe the growth rate in steady state.

The following claim shows that a prototype economy replicates the interna-

tional knowledge spillover model detailed above:

Proposition 1 (Human capital investment wedge and technology spillovers):

Consider a prototype economy with a human capital investment wedge1 + pxh = ((n

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12 HONGCHUN ZHAO

s1

)(1a)+ 1s1)1, but no other wedges. Let the depreciation rate of human capital

beph = (1a)(1a)

n. Then the equilibrium allocations of both the prototype economy

and the international knowledge spillover model detailed above coincide.

Proof of Proposition1.

To prove this and other equivalence results we compare steady-state equilib-

rium conditions of the detailed model to those of the prototype economy. To save

words, all notations used in the prototype economy are with a superscriptp.

By the definition of final goods, the shares of production factors used in final

goods production are up =vp =s, and the output of final goods is yp =c + i= sy.

From the production function, capital shares in both sectors are . Let investment

in technology be xph = R/L. Then from the law of motion for technologyA insteady state, we know that hp = A, andph =

(1a)(1a)

n. 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

and human capital efficiency wedge are equal, Ap =Bp = 1. For the same reason,

the relative price of technology is one,qp = 1.

Comparing the law of motion for k in the detailed economy gives pk = ,

kp = k andxpk = i. Bear this in mind, we know pxk = 0 from the Euler equa-

tion (26). From the factor market clearing conditions, wedgesp

1 andp

2must be

zero. Since the representative household does not value leisure and supplies its

labor inelastically, the labor wedgepl is zero.

Notice that the depreciation rate of technology can be rewritten asph= (1 1

(1a)) 1

(1a)(1 a) n. As a result, the Euler equation (27) can be rewritten

as

1 += [(1 +n)(1a)w+ 1 +n+ (1a)]

=[(1 +n)(1a)w+ 1ph(1 1

(1a))((1a))]

=[(1 +n)(1a)w+ 1ph((1a)1) R

AL]

=[((ns

1)(1a)+

1s

1)w+ 1ph].

The second line is obtained by substituting ph into the Euler equation, the third

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line follows RAL = (1a)(1a)

, the fourth line uses RAL = (1s)kA, andw = (1

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

1 +pxh= ((n s1

)(1a)+ 1s1

)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 econ-

omy, and the columns labeled KRC used in the detailed economy. Substituting

the notation used in the detailed economy into the equilibrium conditions of the

prototype economy replicates the equilibrium conditions of the detailed econ-

omy.

In this simple version ofKlenow and Rodriguez-Clare(2005), the human cap-

ital investment wedge is always negative when there is a gap between the current

technology and the world technology frontier. However, positive values of thiswedge can also be microfounded. For example, in McGrattan and Prescott (2007),

which also corresponds to the human capital investment wedge, the sign of this

wedge depends on the sign of a countrys net factor payment.

3.2. The mapping between Romers model and the prototype

economy

Romer(1990) wrote a seminal paper on endogenous growth. The importance ofhis paper stems from two important features: its emphasis on the non-rival na-

ture of knowledge and ideas in order to generate sustained economic growth and

its emphasis on potential non-competitive elements. The non-rivalry of knowl-

edge microfounds endogenous growth and now becomes a widely-used speci-

fication. In particular, Romer attributes spillovers across firms to physical capi-

tal. Here I adapt his model and let the 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 edu-

cated workers and capital to produce new knowledge; a final goods sector, which

uses educated workers and capital to produce final goods; and an education sec-

tor, educating workers by using available knowledge and labor.

LetK1 andK2 be the capital devoted to producing final goods and R&D re-

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14 HONGCHUN ZHAO

spectively,A be the total number of skills currently in existence, andx1i and x2i

be the quantities of the ith 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 pro-

duction function of final goods isY = K1A0

x11i di. Letr1 be the rental rate of

K1, andp1(x1i)be the price of the ith skill. Then i [0, A],p1(x1i) = (1)K1x

1i

andr1 = K11

A0 x

11i di.

The production function of the research sector isX=K2A0 x

12i di, where

is a productivity shifter. LetpXdenote the price of investment in R&D in terms

of final goods. Similarly, we have,i [0, A], p2(x2i) = pX(1 )K2x

2i and

r2 = pXK12

A0

x12i di.

Assume that the technology available to educate workers is linear, xi = Li,whereLiis a raw labor input. Different from producers in the other two sectors,

producers in the intermediate input sector are monopolists. For the ith skill, the

profit is,i = max{p1(x1i)x1i+ p2(x2i)x2iwLi}, where the total labor supplied

equalsLi= L1i + L2i. Therefore, in equilibrium, the wage rate isw= p1(L1i)L1i +

p1(L1i) =p2(L2i)L2i +p2(L2i), and the profit is i= p

1(L1i)L

21i p

2(L2i)L

22i. Using

the demand functions for the intermediate inputs derived above, wage rates in

the final goods sector and the research sector respectively are w1 = (1)2K1L

1

andw2= pX(1)2K2L

2 , and the profit is(1)[K

1L

1 +K

2L

2 ].

Romer (1990) shows that in a symmetric equilibrium, the number of educated

workers in theith profession,xi and its raw labor supply Li are constant across

professions. Without loss of generality, let the size of the representative house-

hold be unity. Put simply, given the initial values,K(0)andA(0), the representa-

tive household maximizes,

max{C(t),L(t),I(t),X(t)}

t=0

t[ ln C(t) + (1)ln(1L(t))],

subject to,K(t+ 1) = (1k)K(t) +I(t),

A(t+ 1) = A(t) +X(t),

r1(t) =K1(t)1A(t)L1(t)

1,

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16 HONGCHUN ZHAO

Wedges Variables Parameters

Prototype Romer Prototype Romer Prototype Romer

Ap 1 vp K1/K p

Bp up L1/L pk k

1pl 1 hp A ph 0

1 +p1 1 kp K p

1 +p2 1 xph X

p

1 +pxk 1 xpk I n

p 0

1 +p

xh

1 yp Y

gp 0 lp L

qp pX

Table 2: Equivalence Result for Romer (1990)

ulation growth ben= 0. Then the equilibrium allocations of both the prototype economy

and the adapted Romer model coincide.

Proof of Proposition 2. Similar to the previous proof, I compare the equilibrium

conditions of Romers model to those of the prototype economy.

Comparing production functions ofY and X in the adapted Romer model

to those ofyp andxph in the prototype economy implies vp = K1/K, u

p = l1/l,

Ap = 1,Bp =. It is easy to verify that yp =Y,kp =K,xpk =I.

Lethp =A, andxph =X. Comparing the laws of motion forKandAimplies

pk = k,ph = 0. The marginal product of capital in the final goods sector equals

that in the research sector, and so does the wage rate. Thus 1 = 0, and2= 0.

The Euler equation of capital implies that the associated investment wedge

is zero, or pxk = 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, l = . 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

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profits equals the marginal benefit of technology A makes sure that the human

capital investment wedge is also zero, orpxh = 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 proto-

type economy will replicate the equilibrium conditions of the detailed model.

Many policies that distort incentives and reduce competition in product and

labor markets, including the monopolistic competition in the adapted Romer

(1990) model, map into a labor wedge, which is between the marginal rate of

substitution between consumption and leisure and the marginal product of la-

bor. Other policies, like government nominal wage and price fixing, increasingworker bargaining power, work in a similar way.

4. Method and Data

The accounting method consists of computing wedge values and evaluating the

fit of the model. Envisage a world consisting ofj = 1, . . . , J countries. For any

countryj, the economy experiences one eventsj , which indexes the state for that

country. This state determines country j s economic performance. Assume thatendogenous variables in the prototype economy include aggregate variables that

characterize a countrys economic performance, and that the wedges and pop-

ulation growth in the prototype economy uniquely uncover the event sj . Sub-

stituting country-specific values of endogenous variables into the steady-state

equilibrium conditions of the prototype economy gives the wedge values across

countries.

To evaluate the importance of wedges in explaining growth, I change each

wedge in the favorable direction by 50% of its observed values while keeping the

rest wedges fixed; and compare the values before and after each change.

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

first consider a comprehensive definition of human capital: all expenditures on

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18 HONGCHUN ZHAO

financial intermediation and community, social, and personal service activities

(ISIC:J-P) are regarded as investment in human capital. Later a narrow definition

only counts education as the proxy for human capital, but neglect other compo-

nents 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. As for the relative prices of the broadly defined

human capital, they are not estimated or observed directly, but derived by a few

parametric assumptions.

4.1. Estimating human capital and its relative price in terms of

final goods

Consider the following expression for human capital stock at timet,

h(t) =h(s)e(ts) e(sch(t)).

It depends on the initial stockh(s), the education stcoke(sch(t)) and a trend term.

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.11 Notice that the wage rate, by definition, is

equal to(1)GDP/l. Thus,

ln w(t) = ln(1)TFP + ln k

hl+ ln h(s) +(ts) +(sch(t))

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 w= constant +sch

11One concern is the impact of quality of years of schooling on growth. 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) andDurlauf et al. (2005)both pointed out the potential flaws of growth regressions in establishingcausalities. After adjusting the quality of schooling,Caselli(2005)finds that the quality of school-ing is not important for explaining cross-country income gaps.Pritchett(2006) summarizes someempirical results of measuring human capital stocks.

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Hall and Jones(1999) assume that()is a continuous, piecewise linear func-

tion constructed to match the rates of return on education reported in Psacharopou-

los(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. 12 Then they con-

struct human capital stocks using hHJ j =e(schj). I use theHall and Jones(1999)

specification to constructe(sch) , with the growth rate in steady state and a guess

of education stock in a base year, to construct the human capital stock.

Total GDP includes two parts: final goods output and the human capital in-

vestment in terms of final goods. The latter is the value added in all the sectorsidentified in ISIC J-P or only the education sector (ISIC:M) alternatively,13 and

corresponds toqxhin the prototype economy. The rest is the final goods output

yin the prototype. The partition between final goods and human capital invest-

ment may be arbitrary. However, they are consistent with the concepts used in

the prototype economy.14

12McGrattan and Schmitz(1999)summarize popular approaches of measuring human capitalstock, including the alternative Mincerian formula used by Klenow and Rodriguez-Clare (1997b),

hKRCj=e1sch

i

ie2experi+3exper

2

i ,

wheresch is the average schooling years in the total population over age 25 taken fromBarroand Lee (2001), exper

iis a measure of experiences for a worker in age group i and equal to

(ageis 6), and i is the fraction of the population in the ith age group. The age groups

are{25-29, 30-34, ..., 60-64}and agei {27, 32,...,62}. The coefficients are given by1 = 0.095,

2 = 0.0495, and 3 = 0.0007, which are averaged estimates of log wages on schooling andexperience.

13Kendrick(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, train-ing, health, safety, and mobility as investments in intangible human capital. Ideally humancapital should contain all tangible and intangible human capital.

14One concern about the definition of human capital investment is that GDP do not include thevalue of students time, an important component of education investment. This slippage betweenmodel and data affects estimates for xhand h. However, it will not changexh/hin steady-state.Kendrick(1976) found about half of schooling investment consists of education expenditureswhich are included in GDP.

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20 HONGCHUN ZHAO

When the human capital investment qxh is known, with the law of motion

of human capital in steady state, I construct the human capital stock in terms of

final goods as,

(qh)j = (qxh)j

j+nj+h.

Dividing this value bye(st)e(sch(t)), we have

(qh)jej(ts)e(schj(t))

=qjhj(s)e

j(ts) e(schj(t))

ej(ts)e(schj(t)) =qjhj(s)

Notice that the human capital is broadly defined and equal to the labor aug-

mented technology in the literature.Parente and Prescott(2006) argue thatmost

of the stock of productive knowledge is public information, and even propri-etary information can be accessed by a country through licensing agreements or

foreign direct investment.

This statement is, in particular, true by the end of the 20th century. Technolog-

ical innovations have improved the speed of transportation and communications

and lowered their costs. These included jet airplanes and their universal use in

transporting people and goods, the 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 per-

sonal computer, the cellular phone, the internet, and the World Wide Web thathave 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. So

around 2000, the accessible broadly defined human capital is roughly constant

across countries.

I assume that hj(2000) is constant across countries 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 countryj ,

qj = qjhj(2000)

qUShUS(2000)

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Consequently, the human capital stock for countryj is

hj(t) = (qh)US(t)e(jUS )(t2000)e(schj(t))(schUS (t))

4.2. Data and calibration

Data sources used in this analysis include the Groningen Growth and Develop-

ment Center (GGDC), the United Nations Statistics Division (UNSD), the Inter-

national Labor Organization (ILO), the World Bank, the Penn World Table 6.3 and

theBarro and Lee(2001) educational attainment dataset.15

Some variables are directly observable from data sources, such as the aver-

age growth rate for per capita GDP and population, employment-populationratio, the share of workers in the education sector, physical capital investment-

GDP ratio, consumption-GDP ratio, and schooling years. Other variables are de-

rived from these observable variables under certain assumptions. AppendixA

presents the data sources and data construction in detail.

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 equiv-

alent to that the capital input wedge 1 is always equal to zero in the prototype

economy (see equation (7)).

There are five parameters in the prototype economy: the capital share, , the

depreciation rates,k andh, the discount factor, , and the consumption share,

. Each is assumed to be constant across countries. Online appendix presents

the data used in calibration. Table3reports their calibrated values. One concern

is the heterogeneity of parameters across countries. Gollin(2002)convincingly

show that the capital shareis a number between 0.20 to 0.35 for most countries.

AppendixBchecks the robustness of the findings by changing parameter values

15The preliminary tests consider Hong Kong, Singapore, South Korea, Taiwan, Argentina,Brazil, Chile, Peru, and the United States. Later the sample extends to Argentina, Australia, Aus-tria, Belgium, Bangladesh, Bulgaria, Bahrain, Brazil, Canada, Switzerland, Chile, China, CostaRica, Germany, Denmark, Dominican Republic, Ecuador, Egypt, Spain, Ethiopia, Finland, France,United Kingdom, Greece, Guatemala, Hungary, Ireland, Iran, Iraq, Israel, Italy, Japan, Republic ofKorea, Mexico, Malaysia, the Netherlands, Norway, New Zealand, Peru, the Philippines, Poland,Portugal, Romania, Sweden, Thailand, Turkey, Uganda, Uruguay, United States, and Vietnam.

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22 HONGCHUN ZHAO

capital share 0.3333

depreciation rate of physical capital k 0.0665

depreciation rate of human capital h 0.0518

consumption share 0.3908

discount factor 0.9457

Table 3: Calibrated Values of Parameters

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 national accounts data for the US to calibrate them, by as-

suming that wedges are zero in the US economy during the 1960-2000 period.

The depreciation rate k is estimated from the perpetual inventory method

(see, for example,Kehoe and Prescott(2007), for a detailed description),

K(t+ 1) = I(t) + (1)K(t),

together with a few restrictions on the initial capital stock and the depreciationrate. The value ofk is chosen to be consistent with the average ratio of depreci-

ation 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 ratek.

The depreciation rate of human capital h comes from the same procedure,

except its value is chosen to be consistent with xhh =+n+h. By comparison,

Kendrick(1976)s estimates imply the depreciation rates of capital, k = 0.0616,

of education,e= 0.0343, of health care,hc= 0.0718and of R&D,RD = 0.0876.For the remaining two parameters, standard calibration formulae are avail-

able. The discount factorstems from the following equation,

1 +average growth rate = [ output-capital ratio

share of education in GDP+ 1k].

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The consumption share is from,

= share of consumption in GDP empl. rate

share of consumption in GDP empl. rate + (1)(1empl. rate)

.

4.3. Descriptive statistices

Table4 presents the average growth rates, physical capital-GDP ratios, human

capital-physical capital ratios, employment rates and various wedge values for

four East Asian and four Latin American countries. Apparently, four East Asian

countries experienced rapid growth after WWII, while four Latin American coun-

tries are stagnant during the same period. Look at capital-GDP ratios and hu-

man capital-physical capital ratios, Singapore accumalated much capital, whichis consistent withYoung(1995) andHsieh(2002); and physical capital accumu-

lation in Latin American countries are moderate relative to East Asian countries.

Although the employment rates are roughly the same across East Asian countries

or across Latin American countries, they are typically higher in East Asia than in

Latin America.

Not surprisingly, the labor wedges in Latin American countries are high,

given their employment rates are low. In terms of the physical capital investment

wedge, Hong Kong, Singapore, and South Korea run negative values, while Tai-

wan has a quite big positive value. However, in Latin America, values of the

physical capital investment wedges are either negligible, or large and positive.

When it comes to the human capital investment wedge, Hong Kong and Sin-

gapore have negligible values, while South Korea, Taiwan and Latin American

countries have large negative values. In addition, Latin American countries have

worse final goods efficiency wedges relative to East Asian countries. Govern-

ment consumption wedges are roughly moderate in East Asia, but in general

higher in Latin America.

5. Findings

A large number of papers study the cross-country economic performance us-

ing either growth accounting or level accounting that connects economic perfor-

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24 HONGCHUN ZHAO

Hong Kong Singapore South Korea Taiwan

Growth 4.76% 4.56% 5.67% 5.59%

Capital/GDP 2.17 3.29 2.28 1.30

Human Capital/Capital 2.01 1.36 3.63 5.59

Employment Rate 0.42 0.44 0.38 0.38

Labor Wedge 0.65 0.72 0.45 0.51

Phys. cap. inv. wedge -0.12 -0.41 -0.21 0.40Human cap. inv. wedge -0.06 0.03 -0.41 -0.41

Efficiency wedge 0.44 0.41 0.35 0.42

Government wedge 0.04 0.02 0.05 0.14

Argentina Brazil Chile Peru

Growth 1.51% 2.40% 2.36% 1.60%

Capital/GDP 1.90 1.45 2.21 2.36

Human Capital/Capital 5.70 7.94 4.86 7.35

Employment Rate 0.37 0.42 0.33 0.33

Labor Wedge 0.70 0.54 0.76 0.61

Phys. cap. inv. wedge 0.26 0.54 0.01 0.00

Human cap. inv. wedge -0.37 -0.35 -0.37 -0.44

Efficiency wedge 0.35 0.29 0.32 0.24

Government wedge 0.12 0.14 0.09 0.05

Table 4: Comparison between East Asian and Latin American Countries

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mance to inputs and the efficiency with which inputs are used.16 Despite the large

volume of work, results from many studies on a given issue frequently reach op-

posite conclusions. Moreover, a serious criticism byAcemoglu(2007) says that

at some level to say that a country is poor because it lacks physical capital, hu-

man capital and technology is like saying that a person is poor because he does

not have money. To satisfactorily understand economic growth requires, not

only the contribution of inputs and efficiency to the cross-country income vari-

ance, 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 first explore the relationship between cross-country policy

differences and observed wedges, then evaluate the importance of each wedge

in explaining growth in the above eight countries, and extend the discussion tofifty countries. As a robustness check, I replicate two previous studies using the

data I collect, and compare the concept and the consequent numerical results

derived from my method with theirs.

5.1. Wedges and their relationship with actual policies

We now discuss how the estimated wedges from the prototype economy relate

to actual policies in the eight countries.

South Korea and Taiwan. The remarkable growth of South Korea and Tai-wan is often portrayed as an example of what export-led growth can achieve in

countries that chose to open themselves to international trade. Yet,Rodrik(1994)

documents that both governments also gave investment a big push. In 1960 the

Nineteen-Point Reform Program was instituted in Taiwan. This plan contains

a wide range of tax subsidies for investment and signaled a major shift in gov-

ernment attitudes toward investment. However, by contrast, in Korea the major

form of investment subsidy was the extension of credit to large business groups

at negative real interest rates. In addition to providing subsidies, the Korean and

Taiwanese governments also played a much more direct role by organizing pri-

vate entrepreneures into investments that they may not have otherwise made.

By the early 1960s, economic growth had become a top priority for the authority

16Bosworth et al. (2003) is a comprehensive study on growth empirics, including growth ac-counting.Caselli(2005) is a state-of-the-art study using level accounting.

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26 HONGCHUN ZHAO

of the two countries. And these observations coincide with a big positive gov-

ernment wedge in Taiwan, and a negative physical capital investment wedge in

South Korea.

Singapore. The Singapore government also strongly committed to economic

growth, greatly subsidized private investment, in particular, the foreign direct

investment (FDI). Yet Singapore also introduced strict labor measures. In 1972

the National Wages Council was established, and it determined annual wage

adjustments in both public and private sectors until 1985. Thereafter, quanti-

tative restrictions were replaced by a qualitative wage restraint, which is still

effective. These policies are consistent with the large positive labor wedge and

negative physical capital investment wedge, but negligible human capital invest-

ment wedge.Hong Kong. Hong Kong is the laissez-faire economy where government

interventions are small, leading financial intermediaries, and openness to FDI.

These all witness light labor and investment wedges.

Latin American countries.Cole et al.(2005) document a number of competi-

tive barriers implemented by Latin American countries, including tariffs, quotas,

multiple exchange rate systems, and regulatory barriers to foreign and domestic

producers, inefficient financial systems, and large, subsidized state-owned enter-

prises. All these distortions witness large positive labor wedges, physical capital

investment wedges, and negative human capital investment wedges.

5.2. Contributions of individual wedges

Table5shows the difference between the growth rates when the absolute value

of an individual wedge decreases one half and the observed ones. These results

confirm that Singapore is mainly driven by the accumulation of physical capi-

tal, since the growth rate would drop very much once incentives to accumulat-

ing capital disappear. Rapid growth in Hong Kong is mainly caused by the ab-

sence of government intervention, while human capital accumulation drives the

growth in South Korea and Taiwan. Compared with East Asian countries, the

patterns across Latin American countries are quite similar. The various policies

that impede the normal market forces are the culprit.

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Effects on growth: Hong Kong Singapore South Korea Taiwan

Labor Wedge 0.64% -0.34% 2.40% 4.75%

Phys. cap. inv. wedge -1.38% -5.49% -1.49% 2.22%

Human cap. inv. wedge 4.98% 7.56% 0.17% 0.84%

Efficiency wedge -0.22% -0.04% 0.41% -0.08%

Government wedge 1.70% -1.81% -0.94% -1.81%

Argentina Brazil Chile Peru

Labor Wedge 3.06% 3.45% 4.40% 3.20%

Phys. cap. inv. wedge 1.61% 2.51% 0.11% 0.02%Human cap. inv. wedge -1.43% -0.07% -0.06% -0.51%

Efficiency wedge 0.34% 0.74% 0.57% 1.40%

Government wedge -2.43% -1.81% -2.71% -0.92%

Table 5: Effects of Wedges in East Asian and Latin American countries

One interesting observation is that the effects of the labor wedge depend onthe magnitude of the human capital investment wedge. When the human capital

investment wedges are large and negative, labor wedges impact growth signifi-

cantly; otherwise, the effects are negligible. For four slow growers in Latin Amer-

ica, the particular combination of big positive labor wedges and big negative hu-

man capital investment wedges are detrimental to growth. Another interesting

outcome is that two investment wedges seem to be substitutive, and either one

can sustain growth. Four East Asian countries verify different successful stories.

Next I extend this accounting method to fifty countries with a different def-

inition of the broadly defined human capital. Now only investments in educa-

tion are counted as human capital. Table6 summarizes the percentage change

of growth, TFP, capital intensity, and employment from their actual values for

the total sample, when a wedge changes 10% in the favorable direction. Clearly

the effects of wedges on growth scatter more evenly than those on TFP across

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28 HONGCHUN ZHAO

l 2 xk xh A B g/k

Growth 0.22 0.24 0.10 0.38 0.12 0.18 0.08

TFP 0.00 0.01 0.00 0.00 0.13 0.00 0.00

Capital-GDP 0.07 0.07 0.02 0.14 0.03 0.05 0.02

Employment 0.14 0.09 0.03 0.02 0.00 0.01 0.05

Table 6: Fractions Accounted for by Individual Wedges: Total

wedges. The human capital investment wedge is the primary factor in explain-

ing growth on average: its change can move wedges are detrimental to growth.

The labor and labor input wedges are also important, and move growth 22% and

24% respectively. As for accounting for TFP, the final goods efficiency wedge is

the dominant factor, and its change accounts for 13% of TFP while other wedges

explain almost nothing.

The equivalence results reported in section3. show that specific theories can

microfound the human capital investment wedge and the labor wedge. How-

ever, more efforts are on the human capital investment wedge, as many endoge-

nous growth theories that focus on the role of education or R&D are actually

exploiting this wedge. The role of the labor and labor input wedge, and theirassociated policy implications, on growth are not fully explored and worthy of

more attention.17

The pattern of explaining capital intensity is similar to that of explaining

growth, but with smaller magnitude. This confirms the previous observation

that growth is highly correlated with investment in physical capital. As for the

employment rate, not surprisingly, the labor and labor input wedges are two im-

portant factors. But in steady state, how efficiently a country produces goods

would not change the incentives to work much, as illustrated by the small influ-

ences of efficiency shiftersAandB.

17By comparing France and the United States,Prescott(2002) gives an example showing thatthe labor wedge is responsible for the gap in terms of relative income level between these twocountries.

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5.3. Do previous studies contradict this analysis?

Previous quantitative studies on cross-country income variance find that effi-

ciency is at least as important as inputs in explaining both growth and relativeincome differences. Does the data I collect or the alternative accounting method I

use contradict previous studies? By usingHall and Jones(1999) andBosworth et

al.(2003) as the baseline research for level accounting and growth accounting, I

redo these exercises. 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 equilib-

rium. Decomposition results suggest that the alternative method is quite close to

previous studies.

Before beginning with the detailed comparison, I would point out the differ-

ent definitions of human capital and the residual in the growth accounts used by

Klenow and Rodriguez-Clare(1997b),Hall and Jones(1999), and me. A general

form byParente and Prescott(2006) can cover these differences,

y(t) =k(t)[h(0)et edu(t)A(t)l(t)]1.

Notice that in Klenow and Rodriguez-Clare (1997b), the production function

takes the form,

y= k

1

h

2

KRC(AKRCl)

112

,

and inHall and Jones(1999) it takes the form,

y= k(AHJhHJl)1.

Notice that A is always a residual in any case. My specification followsHall

and Jones(1999), but has a slightly different measure for human capital. Table 7

illustrates definitions of human capital h and the residualA in these three cases

in terms of the notations inParente and Prescott(2006).

Hall and Jones(1999) decompose output per capita of 127 countries in 1988

into three multiplicative terms: capital intensity K/Y, education stock e(sch),

and productivity, a residual term. All terms are expressed as ratios to US val-

ues. Forty-five countries in their sample overlap the sample I collect. AsHall

and Jones(1999) do, table8 reports each terms comparable averages, standard

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30 HONGCHUN ZHAO

Human Capital Residual

This Work eduh(0)et A

Hall and Jones(1999) edu h(0)etA

Klenow and Rodriguez-Clare(1997b) edu112 h(0)et Al h(0)etA

Table 7: Different Definitions in Growth Accounts

deviations, and correlations with other terms for the overlapped forty-five coun-

tries, 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 equi-

librium, 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.

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 perpetual inventory method. However, in my study it isnot smoothed, but comes from the investment-output ratio with a linear trans-

formation.

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.

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Hall and Jones(1999) Income Capital Education Residual

Average (45) 0.481 0.957 0.695 0.678

Standard Deviation 0.283 0.194 0.165 0.278

Corrlation w/Y /L(logs) 1.000 0.658 0.700 0.812

Corrlation w/A(logs) 0.812 0.156 0.225 1.000

This Work Income Capital Human Labor Residual

Capital

Average (45) 0.437 1.001 0.665 0.895 0.683

Standard Deviation 0.284 0.205 0.179 0.179 0.262

Corrlation w/Y /L(logs) 1.000 0.788 0.771 0.394 0.785

Corrlation w/A(logs) 0.785 0.433 0.388 -0.162 1.000

Table 8: Level Accounting Comparison

Bosworth et al.(2003) Income Capital Education Residual

Industrial Countries (22) 2.2% 0.9% 0.3% 1.0%China (1) 4.8% 1.7% 0.4% 2.6%

East Asia less China (7) 3.9% 2.3% 0.5% 1.0%

Latin America (22) 1.1% 0.6% 0.4% 0.2%

This Work Income Capital Education Labor 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 9: Growth Accounting Comparison

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Table9presents 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.

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 accu-

mulates physical capital more rapidly during its miraculous growth in the past

than others; and TFP grows slowly in Latin America. My calculations also con-firm the baseline. It verifies that the data I have collected is as good (or bad) as

the data used by previous studies.

6. Conclusion

This paper presents a method to account for long-run economic growth across

countries. It also links many endogenous growth theories to a two-sector neo-

classical growth model, and sheds light on underlying mechanisms of economicgrowth. The main findings suggest that and 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 observed patterns of developing

countries.

AsKlenow 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.

Numerous studies show that the neoclassical growth model with wedges is

a useful workhorse in accounting for various macroeconomic events (Cole and

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34 HONGCHUN ZHAO

Ohanian(2004),McGrattan and Ohanian(2006) andChen et al.(2007)). These

findings suggest that the Business Cycle Accounting idea, together with neo-

classical models, is a good way to organize the increasingly available data on

various dimensions and aspects of economic growth.

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Endogenous Variable Raw Data Used Data Source

long-run growth rate per capital GDP series Maddison-GGDC

employment-pop ratio employment, population TED-GGDC

capital allocation value added by industry, UNSD

public spending on education WDI

labor allocation employment by industry ILO

investment-capital ratios population growth TED-GGDC

output-capital ratio investment share in GDP PWT 6.3

consumption-capital ratio consumption share in GDP PWT 6.3

relative price education expenditure UNSD

capital-human capital ratio educational attainments Barro-Lee 2001

Table 10: Data Sources for Endogenous Variables

A Appendix: variables in the cross-country dataset

This appendix explains how to create relevant variables for the cross-countrydataset used in the paper.

The long-run growth rates come from the per capita GDP estimates by Maddi-

son (2003). I compute the annual growth rates for each country year by year from

1951 to 2008, and assume the long-run growth rate equals the average of those

annual growth rates. Fifty-eight years are 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

from 1951 to 2008 and take the average. The Total Economy Database also has

estimates for employment in the same period. I divide employment by midyear

population and take their average as the average employment-population ratios.

As for the shares of employment in the education sector, I divide employ-

ment in education by total employment obtained from the ILO, and then take the

average. The length of these employment series varies across countries, yet the

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36 HONGCHUN ZHAO

longest one comes from 1985 to 2008. To compute the shares of education output,

I use value added of education and value added of the total economy in 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 ed-

ucation. The longest value added series comes from 1966 to 2008, and the longest

public spending share series is from 1970 to 2008.

To construct investment-capital ratios for physical capital, I use the approach

inCaselli(2005) xkk = n+ +k, together with estimates of growth rates and

population growth rates, and calibrated values of depreciation rates. Similarly,xhh

=n++hcan be constructed.

The final goods output-capital ratios are computed by the following formula,

y

k = (1

Edu VA

VA )

xkk

/ xkGDP

,

where xk/GDP is the share of investment in GDP, which is obtained from the

Penn World Table 6.3 (CI), Edu VA/VA is the share of education output in the

total economy, and(xk/k)is the investment-capital ratio for capital. The last two

variables are both known from previous calculations. Similarly, the final goodsconsumption-capital ratios can be calculated from the following formula,

c

k =

y

k[

CC

GDP

Edu VA

VA ]/[1

Edu VA

VA ],

where (CC)/(GDP) is the share of consumption (CC) in GDP from the Penn

World Table 6.3.

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 fromBarro 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 fo-

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mula,k

h=

xk(1v)GDP

xhh

k

xkq

B Appendix: robustness checks

This section is about the robustness of the findings reported in the text. I change

the value of each parameter, holding the remaining parameters fixed to their cal-

ibrated values, and see whether the pseudo goodness-of-fit of various wedges

changes very much.

B1. Capital share

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 em-

ployee 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.

Figure1plots the explanatory power of the various wedges on growth as thecapital share moves from 0.20 to 0.35. Clearly, the contribution of the human

capital investment wedgexhis quite stable with respect to alternative values of

in this range. The government spending wedge g/kis not important, and also

stable. The two labor related wedgesl and2 are always more important than

the capital investment wedgexkand two efficiency wedgesAandB.

B2. Preferences parameters

Figure2 shows the contributions of various wedges when changing between

0.90 and 1. The order of various wedges does not change much in this range of

. Thus the qualitative results in the text do not change at all.

When it comes to the values of the consumption share , different studies

report different values. McGrattan and Schmitz(1999) reports that the upper

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38 HONGCHUN ZHAO

Figure 1: Robustness check withon growth

Figure 2: Robustness check withon growth

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Figure 3: Robustness check with on growth

bound could be 0.67, and the lower bound could be 0.16. Figure3plots the con-

tributions of various wedges in explaining growth in this range. Since only

affects the labor wedge l, except for the labor wedge, the contributions 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 explana-

tory power increases sharply, and it becomes the most important factor whenis

equal or higher than 0.47. The high sensitivity oflaround the benchmark value

ofimplies that our results about the labor wedge may change non-trivially with

more precise measures of the consumption share.

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40 HONGCHUN ZHAO

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