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Working Paper Series

Transition Dynamics in the Neoclassical
Growth Model: The Case of South Korea

WP 11-04R

Yongsung Chang
University of Rochester and Yonsei
University
Andreas Hornstein
Federal Reserve Bank of Richmond

This paper can be downloaded without charge from:
http://www.richmondfed.org/publications/

Transition Dynamics in the Neoclassical Growth
Model: The Case of South Korea
Yongsung Changy and Andreas Hornsteinz
August 26, 2013
Federal Reserve Bank of Richmond Working Paper No. 11-04R

Abstract
Many successful examples of economic development, such as South Korea, exhibit
long periods of sustained capital accumulation. This process is characterized by a
gradually rising investment rate along with a moderate rate of return to capital, both
of which are strongly at odds with the standard neoclassical growth model that predicts
an initially high and then declining investment rate with an extremely high return to
capital. We show that minor modi…cations of the neoclassical model go a long way
toward accounting for the capital accumulation path of the South Korean economy.
Our modi…cations recognize that (i) agriculture (which makes up a large share of the
aggregate economy in the early stage of development) does not rely much on capital
and (ii) the relative price of capital declined substantially during the transition period.
Keywords: Neoclassical Growth Model, Transition Dynamics, Industrialization, Price
of Capital, South Korea
JEL: E13, E22, O11, O13, O14, O16, O4, O53
We would like to thank discussants and participants at various conferences and seminars, in particular, Francesco Caselli, Jang-Ok Cho, Seijik Kim, Yongjin Kim, Kyoungmook Lim, Jong-Wha Lee, Jaewoo
Lee, Diego Restuccia, and Kei-Mu Yi. Kangwoo Park has provided excellent research assistance. Any opinions expressed are those of the authors and do not necessarily re‡ect those of the Federal Reserve Bank
of Richmond or the Federal Reserve System. Our e-mail addresses are yongsung.chang@gmail.com and
andreas.hornstein@rich.frb.org.
y
University of Rochester and Yonsei University
z
Federal Reserve Bank of Richmond

1. Introduction
The neoclassical growth model is a fundamental building block of modern macroeconomics,
yet the economic development (i.e., transition dynamics) predicted by the neoclassical model
is strongly at odds with the experience of many growth miracles such as South Korea or
Taiwan. These countries started out with low initial capital stocks, which according to the
standard growth model would imply high initial rates of return to capital and correspondingly
high initial investment rates. Yet, as Figure 1 shows, most Asian economies that made a
successful transition started out with low initial investment rates that gradually increased
over time.

[Figure 1. Investment Rates of Asian Growth Miracles]

For the case of the South Korean economy, we argue that with two minor modi…cations a
calibrated version of the neoclassical model can account for most of the capital accumulation
pattern observed in the data since 1960. Our approach builds on recent insights in the
economic growth literature that emphasize the role of a large agricultural sector (Gollin,
Parente, and Rogerson, 2007) and a high relative price of capital during the early stages of
development (Caselli and Feyrer, 2007). An analysis of Korea’s development process is of
interest for two reasons. First, it has been studied extensively as a successful case of economic
development. Second, we have reliable data on the two newly added features: the transition
from an agricultural to an industrialized economy and the declining price of capital. Table 1
summarizes these features for the Korean economy. First, in 1963 agriculture accounted for
two-thirds of aggregate employment and one-third of GDP. Since agriculture does not rely
heavily on physical capital, a low aggregate capital-output ratio (or investment-GDP ratio)
therefore does not necessarily imply a high rate of return to capital. Second, in 1963 capital
goods were more than twice as expensive as they were in 2005. This initial high relative price
of capital also lowers the implied rate of return on capital in the early stages of development.
These observations on the development process of Korea are consistent with those of
Caselli and Feyrer (2007) based on a broader cross-section of countries. They show that
the size of the agricultural sector and the relative price of capital are negatively correlated
1

with the level of development, measured as aggregate per capita output. Caselli and Feyrer
(2007) then calculate rates of return on capital in the non-agricultural sector, accounting for
di¤erences in the relative price of capital, and …nd that this correction substantially reduces
the variation of estimated returns to capital in the cross-section of countries.
Based on detailed data for the Korean economy, we quantitatively evaluate the transition
dynamics of the neoclassical model augmented for the industrialization process. We use the
framework of Gollin et al. (2007), who study the equilibrium transition from a labor-intensive
agricultural economy to a capital-intensive industrial economy. Whereas Gollin et al. (2007)
are interested in the determinants of the allocation of labor between the agricultural and
non-agricultural sectors during this transition, we take this allocation as given and study
its implications for the economy’s capital accumulation path. We assess the role of the
expanding industrial sector and the declining relative price of capital by calibrating the
model to the Korean development experience from 1960 to 2005. Accounting for these two
features substantially reduces the implied rate of return to capital relative to the standard
one-sector neoclassical growth model during the early phase of development. In particular,
the model-implied real interest rate in 1960 decreases from a high 90 percent to a more
reasonable 13 percent.
Next, following Chari, Kehoe, and McGrattan (2007), we introduce three “wedges”into
the model so that the model’s equilibrium outcome exactly matches the observed transition
dynamics of the Korean economy. The wedges we introduce to …ll the gap between the model
and the data are measured total factor productivity (TFP) to account for the production of
non-agricultural goods, “…nancial frictions”to satisfy the intertemporal optimality condition
for consumption, and autonomous demand for non-agricultural output to satisfy the resource
constraint for non-agricultural goods. We then evaluate the quantitative importance of all
exogenous drivers for the transition dynamics of the Korean economy from 1960 to 2005 and
…nd that four drivers account for 90 percent of capital and output growth over this period,
and the standard neoclassical transition dynamics account for the remaining 10 percent of
capital accumulation during this time period. First, the two newly introduced features—
employment growth in the non-agricultural sector and the declining relative price of capital—
account for close to 60 percent of the growth in capital and output, with the capital price
decline contributing relatively more to capital growth and the increase in non-agricultural
2

employment contributing relatively more to output growth. Second, the non-agricultural
TFP and …nancial frictions wedges account for close to 30 percent of capital and output
growth, with declining …nancial frictions contributing relatively more to capital growth and
increasing TFP contributing more to output growth. Although the quantitative contribution
of …nancial frictions remains modest for the overall transition path of capital and output,
the decline of …nancial frictions plays an important role for the hump-shaped path of the
investment rate.
Our work complements earlier quantitative research on the growth contribution of capital
accumulation, such as King and Rebelo (1993) and references therein for a comprehensive
analysis of the transition dynamics in the standard growth model. As Mankiw, Romer, and
Weil (1992) and Barro and Sala-i-Martin (1995) show, for a neoclassical growth model to
generate a prolonged process of capital accumulation requires either a capital share that is
much larger than measured in the data and/or low values of the intertemporal elasticity of
substitution for consumption.1 A more recent literature studies how declining capital goods
prices (e.g., Hsieh and Klenow (2007), Caselli and Feyrer (2007), Restuccia and Urrutia
(2001)) and the transition from agriculture to industry (e.g., Gollin et al. (2007), Duarte
and Restuccia (2010)) a¤ect development. We follow this literature but take the sectoral
allocation of labor as given and study its implications, together with the declining relative
price of capital, for capital accumulation in the non-agricultural sector.2 The closest paper
to our approach is Lu (2012), who also adopts a “wedge” approach to identify the relative
importance of the di¤erent forces that drive growth in four Asian economies: Hong Kong,
1

There is also a large literature that focuses on the properties of investment during this transition.
Young (1994, 1995) documents increasing investment rates and the important contribution of factor input
accumulation to growth in the Asian ‘growth miracles.’ Hayashi (1986) documents the hump-shaped savings
rate for Japan in the 1950s and 1960s. Christiano (1989) shows that a time-varying intertemporal elasticity
of substitution due to subsistence consumption may explain a low savings rate during the early phase of the
growth transition. Chen, I·mrohoro¼
glu, and I·mrohoro¼
glu (2006) show that if economic agents perfectly foresee
the relatively high Japanese TFP growth rates of the early 1970s, then their optimal response will exhibit
a hump-shaped savings rate. Gilchrist and Williams (2004) show that the putty-clay model of production
and investment can generate a rising rate of investment and moderate rates of return to capital that are
consistent with the transition period in Japan and Germany. For a model with two unspeci…ed types of
capital, Rappaport (2006) shows that high adjustment costs in one sector can lead to transition dynamics
with increasing investment rates even if the sector is small. Papageorgiou and Perez-Sebastian (2006) discuss
the possibility of hump-shaped investment rates in an endogenous growth model with embodied technology
where the lack of human capital delays an adoption of new technology.
2
Ngai (2004) includes the relative price of capital in a model like Gollin et al. (2007) and studies its
implications for transition dynamics.

3

Singapore, South Korea, and Taiwan. Unlike Lu’s analysis, which is explicitly limited to
the standard one-sector growth model, we emphasize the declining relative price of capital
and the sectoral transformation away from agriculture. Jones and Sahu (2009) also adopt
the wedge approach for a multi-sector analysis (agriculture, manufacturing, and services) of
the Indian economy. They focus on the role of relative distortions for the allocation of labor
and capital across sectors, and not so much on the role of capital accumulation during the
transition. In particular, they do not allow for changes in the relative price of capital. Finally,
Buera and Shin (2013) explicitly model the …nancial frictions wedge and the TFP wedge and
argue that …nancial frictions contribute to the prolonged capital accumulation process. In
their model, collateral constraints act as …nancial frictions, and the TFP wedge re‡ects the
ine¢ cient allocation of resources due to tax distortions. In Buera and Shin (2013), removing
the tax distortions generates a delayed transition to the long-run equilibrium, relative to the
standard transition dynamics of the neoclassical growth model, only if there are …nancial
frictions.
This paper is organized as follows. Section 2 presents a modi…ed growth model that distinguishes between a labor-intensive agricultural sector and a capital-using non-agricultural
sector. In Section 3 we describe the data for Korea and how they are used in a way that
is consistent with our model. Then, the model parameters are calibrated to the Korean
economy for the period 1960-2005. In Section 4 we show that, once we take into account
the transition to an industrialized economy and the declining price of capital, the model
can reproduce the development process of the Korean economy. In Section 5 we compute
counterfactual transition paths to evaluate the quantitative contribution of various drivers
of economic development. Section 6 concludes.

2. Model Economy
Our model of the Korean economy is a modest extension of the standard neoclassical growth
model. To capture the transition from a traditional agricultural economy to an industrialized
economy, we adopt a simpli…ed version of Gollin et al. (2007).
There is a representative household with constant intertemporal elasticity of substitution
preferences for per capita consumption of a manufactured good, ct , and an agricultural

4

good, at , and utility is proportional to population size, nt . For simplicity we assume that
the household consumes a …xed per capita amount a of the agricultural good.
1
X
t=0

with 0 <

< 1 and

t

nt

c1t
1

1

+a ;

(2.1)

> 0.3 In the following, all variables are expressed in per capita terms.

Household labor supply, et , is exogenous and labor is allocated between the production
of agricultural goods, eat , and manufactured goods, eyt ,
(2.2)

eat + eyt = et :
The agricultural good is produced using labor as the only input,

(2.3)

at = Aat eat ;

and Aat is labor productivity in the agricultural sector. The manufactured (or non-agricultural)
good, yt , is produced with a Cobb-Douglas production technology using labor and (reproducible) capital, kt , as inputs:
yt = kt (Ayt eyt )1

;

(2.4)

and Ayt is labor-augmenting technical change in the non-agricultural sector. Abstracting
from reproducible capital as an input in the Korean agricultural sector is a justi…able approximation. During the initial phase of development from 1960 to 1980 when the agricultural
sector is still large, land represents most of the capital input in Korea’s agricultural sector;
see Kim and Park (1985). Furthermore, in 1960 almost all of the reproducible capital stock,
85 percent of all equipment and 98 percent of all structures, was used in the non-agricultural
sector; see Pyo (1998).
The non-agricultural good is used for private consumption and investment in capital
3

Gollin et al. (2007) consider a slightly more general version where the household’s utility function is
linear in the consumption of the agricultural good if consumption is less than a, and of the form (2.1) when
consumption of the agricultural good is a a. We simply assume that the agricultural sector is productive
enough such that in equilibrium the sector provides the …xed per capita consumption amount a.

5

goods, xt ,
(2.5)

yt = ct + qt xt + gt :

The autonomous demand for goods, gt , includes public consumption and net exports. The
price of investment goods in terms of consumption goods is denoted by qt .4 Investment
augments the capital stock,
kt+1 =

nt
[(1
nt+1

(2.6)

) kt + xt ] ;

and capital depreciates at rate .
We assume that markets are competitive. Wages, wt , and the capital rental rate, ut , are
equal to their marginal products. Aggregate GDP is de…ned as the value of agricultural and
non-agricultural production in units of the non-agricultural good,5
(2.7)

Yt = yt + wt ea;t :
Income is taxed at rate

t,

and we assume that the government budget is balanced through

some additional lump-sum tax.
Under perfect foresight, the rate of return on capital is
RtK =

(1

t+1 )

ut+1
+ [1
qt+1

(1

t+1 )

]

qt+1
:
qt

(2.8)

The after-tax rate of return for the household consistent with intertemporal utility maximization is de…ned by the Euler equation
RtH =

1

ct+1
ct

:

(2.9)

We allow for a divergence between the rate of return on capital and the rate of return faced
by the household,
RtH = (1

ft ) RtK :

4

(2.10)

For a two-sector interpretation of this technology, see Greenwood, Hercowitz, and Krusell (1997).
In the following we take the allocation of labor to the two sectors, agriculture and manufacturing, as
given. With free mobility of labor between the two sectors this is equivalent to productivity in the agricultural
sector satisfying a = Aa ea and the price of the agricultural goods satisfying pa = w=Aa .
5

6

We interpret the “wedge,”ft , as representing …nancial frictions: a fraction ft of the returns
on capital is diverted by the …nancial intermediation sector. Thus, we have introduced three
wedges (TFP in the non-agricultural sector, Ayt , the …nancial frictions, ft , and autonomous
spending, gt ) to …ll the gap between the model and the actual data. In Section 4, the wedges
are constructed as residuals so that the observed time series of the (calibrated) Korean
economy represents a perfect foresight competitive equilibrium.
Our analysis of the Korean capital accumulation process below will proceed in two steps.
First, in Section 4 we will show that accounting for the structural transformation toward a
non-agricultural economy and the declining relative price of capital helps us to interpret the
economic development process of Korea from a neoclassical perspective. Second, in Section
5 we conduct the counterfactual experiments to evaluate the contributions of all exogenous
drivers to the transitional paths of output and capital.
To compute the transition dynamics of the model, we …rst need to specify the steady
state. We assume that the Korean economy converges to an asymptotic balanced growth
path (BGP) where the following variables grows at constant rates. Population grows at
rate

n,

productivity in the agricultural and non-agricultural sector grow at

respectively, and the relative price of capital declines at rate

q.

a

and

y,

The income tax rate is

constant at rate , …nancial frictions are constant at f , and the aggregate employment rate
remains constant at e. Together with positive productivity growth in agriculture, the latter
implies that the employment share of agriculture asymptotically goes to zero in our long-run
equilibrium.
There exists a limiting BGP where non-agricultural output, expenditure components,
and capital grow at constant rates, and all employment is in the non-agricultural sector.
For a given time path of non-agricultural productivity, Ayt , the relative price of capital, qt ,
and the non-agricultural employment rate, eyt , we have a stationary transformation for the
model. For this transformation, output and consumption are scaled by zyt and investment
and the capital stock are scaled by zkt ,
k~t
y~t

kt
and zkt
zkt
yt
and zyt
zyt

7

Ayt eyt qt

1=(1

)

Ayt eyt qt

=(1

)

:
;

(2.11)
(2.12)

For the stationary economy, the expressions for the resource constraint, production, capital
accumulation, and intertemporal optimality are rewritten as
y~t = c~t + x~t + g~t = k~t ;
zk;t+1
zk;t
zy;t+1
zy;t

~

= (1

c~t+1
c~t

= (1

n;t+1 kt+1

(2.13)

) k~t + x~t ;
ft )

qt+1
qt

(1

(2.14)
t+1 )

y~t+1
+ [1
k~t+1

(1

t+1 )

] :(2.15)

These equations, together with a transversality condition, characterize the transition dynamics of the perfect foresight equilibrium in the growth model.

3. Data and Calibration
As we evaluate the quantitative implications of the declining capital price and sectoral transformation, it is crucial to carefully calibrate the model to the observed data for the Korean
economy. In this section we provide a detailed explanation of our data sources and calibration procedure. For the model calibration, we assume that by 2005 the Korean economy
has essentially completed its transformation from an agriculture-dominant economy to an
industrialized one— i.e., it is close to its balanced growth path.
Most of our National Income Account (NIA) data are from the Bank of Korea (BoK). In
addition, we use the data on aggregate employment, sectoral employment, and gross product
originating (GPO) from the Groningen Growth and Development Center (GGDC). Since we
are mainly interested in the long-run transition dynamics of the Korean economy, we remove
short-run ‡uctuations using the Hodrick-Prescott …lter with a smoothing parameter of 100,
a conventional value for annual data.
Annual data from 1953 to 2005 for GDP and its expenditure components (private and
public consumption, investment in equipment and structures) are available in both current
and constant (base year 2000) prices from the BoK. Structures include both residential and
non-residential structures. Real total investment is de…ned as the sum of real investment in
equipment and structures. The price index of total investment is the ratio between nominal
and real total investment. Finally, we construct the relative price of investment goods in
terms of consumption goods as the ratio of the price index of total investment and the price
8

index of private consumption.
Aggregate employment from 1960 to 2005 is the number of employees based on the Total
Economy Data Base (Conference Board (2009)). We use sectoral data (agricultural and
non-agricultural) on persons employed and value-added from 1963 to 2005 from the GGDC
10-Sector Data Base (Timmer and de Vries (2007)).6 Per capita values are expressed relative
to the working age population. Data on the working age population (15 years and older)
from 1953-2005 are from the Penn World Table 6.2v1.
We interpret the actual path of the Korean economy as the perfect foresight equilibrium
of the model. Thus, aggregate time series variables have to satisfy all resource constraints
and optimality conditions; see Equations (2.4), (2.5), (2.6), (2.8), (2.9), and (2.10). This has
several implications in terms of measurement. First, the measure of real output consistent
with our theory is GDP in terms of consumption goods, not the standard measure of real GDP
from the NIAs. Second, since we have separated the agricultural sector from the rest of the
economy and we assume that this sector produces a separate consumption good, the natural
interpretation of the agricultural sector’s output is that of food production. We therefore
exclude the consumption of food and alcohol from our de…nition of consumption produced by
the non-agricultural sector.7 Third, we de…ne autonomous spending as the residual from the
NIA expenditure identity for non-agricultural GPO after accounting for private consumption
and investment, using Equation (2.5). Thus, our measure of autonomous spending combines
government spending and net exports. Fourth, we construct the capital stock using the
perpetual inventory approach with the Hodrick-Prescott trend values of investment as an
input to the capital accumulation equation (2.6).
We assume that capital, both equipment and structures, depreciates at the rate

=

0:053.8 Following the convention in the literature, we construct the initial value of the
capital stock as the steady-state capital stock associated with investment in 1953 and the
6

We extrapolate sectoral employment and value-added data to the three years prior to 1963 assuming
constant 1963 employment and value-added shares.
7
In most industrialized economies, distribution accounts for the largest share of food consumption. Thus
our correction understates the contribution of the non-agricultural sector to consumption, at least towards
the end of the sample. None of our results depend crucially on this correction.
8
This represents a weighted average of standard depreciation rates assumed for equipment, e = 0:10,
and structures, s = 0:03 per year; for example, see Timmer and van Ark (2002).

9

average growth rate of real investment during the …rst 10 years of available data.9 While this
is a crude approximation, it does not have a signi…cant impact on the transition dynamics
from 1960 onward. The size of the initial capital stock is very small and any approximation
error almost disappears by 1960, the beginning year of our analysis.
In addition to the initial capital stock that is far below its steady-state value, we have
a number of time-varying drivers of the Korean economic transition from 1960 to 2005.
We have direct observations on four of these drivers: the relative price of capital (qt ), the
non-agricultural employment rate (eyt ), the capital income tax rate ( t ), and the population
growth rate (

n;t ).

The three remaining drivers are constructed as wedges from the model:

…nancial frictions (ft ), measured TFP of the non-agricultural sector (Ayt ), and autonomous
spending (gt ).
We have already mentioned the declining relative price of capital and the increasing nonagricultural employment rate (Table 1). The autonomous spending share increased almost
monotonically from close to zero in 1960 to about 25 percent in 2005. This monotone increase
re‡ects the combination of a slight increase in the government spending share and a switch
from a current account de…cit in the 1960s to a current account surplus in the mid-1980s.
Our measure of the capital income tax rate, the e¤ective marginal income tax rate from
Hyun, Won, and Yoo (2000) for the period 1960 to 1998, does not show a clear trend. It
declines from about 20 percent in 1960 to less than 5 percent in 1980 and then rebounds to
about 20 percent in 1998. Finally, the population growth rate declines steadily from a high
of 3 percent in the early 1970s to close to 1 percent in 2005.
Per capita output growth on the BGP is determined by the growth rate of laboraugmenting technical change and the growth rate of the relative price of capital. Since
the gross rate at which the relative price of capital declines seems to be converging to one,
we set

q

= 1 for the steady state. We take the United States as a reference point for

long-run growth, and since average U.S. per capita output growth has been about 2 percent,
we set

Ay

= 1:02. Based on the evidence for the e¤ective marginal income tax rate, we

…x the capital income tax rate at

= 0:2 after 2000. The population growth rate declines

steadily from a high of 3 percent in the early 1970s to close to 1 percent in 2005. Given
9

K1953 =

I1953
+ I;0 1

where

I;0

is the gross growth rate of investment for the …rst 10 years.

10

the observations on Korean population growth, we set population growth on the BGP at
n

= 1:01.
Toward the end of our sample the capital-output ratio of the Korean economy (based on

our corrected GDP measure) is close to 3. Given that the relative price of capital is close
to one at that time, we set the nominal capital-output ratio on the BGP at qk=y = 3:0.10
According to Bernanke and Gürkaynak (2001), the Korean capital income share is relatively
stable over time, and the average capital income share for Korea is

= 0:35. Given the

assumptions on depreciation, the capital income share, the nominal capital-output ratio,
and the capital income tax rate, we get the implied rate of return on capital on the BGP,
RK = 1:05.
We assume logarithmic preferences,

= 1, which are consistent with standard parame-

terizations of preferences in business cycle applications of the growth model. Everything else
equal, a lower intertemporal elasticity of substitution, higher , would make it easier to obtain an increasing investment rate on a transition path, according to Barro and Sala-i-Martin
(1995). Using the preference parameter together with the BGP values for the consumption
growth rate, the rate of return on capital, and assuming that there are no …nancial frictions
on the BGP, f = 0, the household Euler equation determines the time preference parameter,
= 0:97.
We calibrate the BGP value of the autonomous spending share in a roundabout way, using
the transition dynamics to the BGP starting with initial conditions for the endogenous and
exogenous state variables in 2005. The endogenous state is simply the observed capital stock
in 2005. For the exogenous state variables, we assume that starting in 2005 all exogenous
variables converge to their BGP values according to an AR(1) process with persistence
parameter

= 0:9. Conditional on the BGP value for the autonomous spending share,

we can construct the log-linear approximation of the growth model. We then choose the
autonomous spending share such that in 2005 the log-linear approximation generates the
consumption observed for the Korean economy in 2005.
10

For comparison, based on the net capital-stock data from the BEA, the nominal capital-output ratio for
the U.S. has been ‡uctuating between 2 and 2.5 since the 1950s. Thus, our assumption on the BGP value
of the Korean capital-output ratio slightly exceeds the observed long-run value for the U.S.

11

4. Equilibrium Transition
Accounting for the measured decline in the relative price of capital and the transformation
toward an industrialized economy from agriculture provides a di¤erent perspective on Korea’s
transition dynamics. As we emphasized in the introduction, between 1963 and 2005, the
relative price of capital declined by a factor of 2.3, and employment in the non-agricultural
sector increased from 31 percent to 92 percent.11 We now discuss how these two newly added
features a¤ect the transition dynamics.
One of the salient features of the neoclassical model in accounting for the economic
transition is the rate of return to capital. This rate of return is often measured by the
inverse capital-output ratio. Capital-deepening is then associated with a declining rate of
return to capital. In an economy with a changing price of capital, the relevant measure of
capital deepening is not the real capital-output ratio but the nominal capital-output ratio,
that is, the ratio of nominal capital to nominal output. The same holds for the investmentoutput ratio. Furthermore, if capital is mainly used in the non-agricultural sector, then the
denominator of the capital-output ratio has to be adjusted accordingly. In Figure 2.A we
plot both the real and nominal capital-output ratio when output is aggregate GDP (solid and
dashed lines), and the nominal capital-output ratio when output is non-agricultural GDP
(dash-dot line). For the period from 1960 to 2005 the ratio of real capital to real aggregate
output increases by a factor of eight, whereas the ratio of nominal capital to nominal nonagricultural output increases only by a factor of three. Thus, after taking into account the
declining relative price of capital and the small initial share of non-agricultural output, the
relevant capital-output ratio for the Korean economy in 1960 was substantially higher than
the usual measure. Similarly, Figure 2.B shows that the nominal non-agricultural investment
rate appears to be more stable than the real aggregate investment rate. However, it clearly
still shows that the non-agricultural investment rate increased over time from about 20
percent in the 1960s to 35 percent in late 1970s.

[Figure 2. Capital Accumulation in Korea, 1960-2005]

11

The overall employment rate increased by only 10 percent from 48 percent during the same period.

12

Turning to the rate of return on capital, Figure 3 shows the time path for various measures
of the rate of return implied by our calibrated model, Equation (2.8). All measures use the
same time series for the capital stock, but they di¤er with respect to the de…nition of output
and the treatment of the relative price of capital and capital income taxes. The top line
represents the rate of return on capital when we use the standard measure of real aggregate
GDP (along with a constant relative price of capital, q = 1, and no adjustment for taxes,
= 0). Based on this measure, used in most cross-country growth accounting exercises,
we would conclude that the return to capital in Korea in 1960 was almost 90 percent. The
next line depicts the rate of return using real non-agricultural output. Correcting for the
appropriate output measure reduces the initial rate of return by a third, but it still remains at
a high rate of 62 percent. Accounting for changes in the relative price of capital (qt ) further
reduces the initial return to capital to 18 percent. Finally, accounting for capital income tax
rates ( t ) further reduces the initial return to capital to 13 percent. To summarize, after one
accounts for the relevant measures of capital’s marginal product, relative price, and taxes,
the model-implied rate of return to capital in Korea in 1960 is high, but not extraordinarily
high.

[Figure 3. Implied Rates of Return on Capital in Korea, 1960-2005]

The household rate of return is implied by the consumption Euler equation (2.9), the
bottom line in Figure 3. At the beginning of the sample, that rate of return is about
8 percent. Comparing the model-consistent rate of return on capital with the household
interest rate suggests that in the early 1960s …nancial frictions might have implied a loss of 5
percent for households. While this is a signi…cant wedge, it is substantially smaller than the
80 percent wedge if one does not consider the decline in the relative price of capital and the
transformation toward an industrialized economy. Furthermore, the model no longer requires
a …nancial wedge by the mid-1980s in order to match the interest rates in the data.12
12

Note that toward the end of the sample, the household rate of return actually exceeds the rate of return
on capital. This negative …nancial friction results from our calibration of the household’s time preference
parameter. We assume that there are no …nancial frictions on the BGP, so that the interest rate is equal
to the return on capital, and the latter is implied by our assumption on the capital-output ratio on the
BGP. Given the assumption on household consumption growth and intertemporal elasticity of substitution,

13

Using “correct” measures of output and employment also a¤ects the measured TFP for
the Korean economy. In Figure 4, we plot measured TFP implied by di¤erent measures of
output and employment. All measures use the same capital stock series. The …rst measure
is standard TFP based on aggregate GDP and employment, the solid line. This standard
measure indicates that TFP increased by 90 percent from 1960 to 2005. The second measure
is non-agricultural TFP (dashed line). The non-agricultural TFP increased by only 10
percent from 1960 to 2005. In fact, according to this measure, non-agricultural TFP declined
from 1960 to 1980 before rebounding, which is somewhat unusual. From the perspective
of the model, however, the relevant measure of non-agricultural output is non-agricultural
output in terms of consumption goods, that is, nominal non-agricultural output de‡ated
by the consumption goods price index. This model-consistent measure of TFP shows a
reasonable monotonic increase from 1960 to 2005, but half as much as the conventional
measure of TFP based on aggregate output and employment.

[Figure 4. Total Factor Productivity in Korea, 1960-2005]

5. Counterfactuals
We now evaluate the quantitative contributions of the di¤erent drivers— newly introduced
features that are directly measured (non-agricultural employment and the relative price of
capital) and model-implied wedges— to the transition dynamics of Korea. For this purpose
we calculate the “marginal” contribution of each driver by constructing a counterfactual
equilibrium growth path where we keep the driver constant at its initial value. From this
exercise we conclude that over the long run, the most important drivers of Korean growth
have been increased non-agricultural employment and a reduced relative price of capital,
followed by higher TFP and reduced …nancial frictions. These four drivers account for close
we then obtain the time preference parameter. There are two alternative calibrations that avoid negative
…nancial frictions on the sample path. First, we can choose the time preference parameter such that the
…nancial frictions wedge never exceeds one. This procedure implies a capital-output ratio of 4:3 on the
balanced growth path, which is substantially higher than the already high capital-output ratio in the current
calibration. Second, we can increase the intertemporal elasticity of substitution. Both procedures will
increase the impact of …nancial frictions in the early sample period, but not in any dramatic way. We
therefore decided to stay with our more conventional calibration.

14

to 90 percent of capital and output growth from 1960 to 2005. Even though the endogenous
transition from a low initial capital stock to a higher BGP capital stock makes a substantial
contribution to capital accumulation during the …rst 20 years of development, the long-run
contribution of the transitional dynamics is limited to 10 percent.
Our growth accounting scheme uses counterfactuals to decompose the cumulative change
in capital and output into components that are attributable to changes in the di¤erent
exogenous drivers and the divergence of the initial capital stock from its BGP value. To be
precise, let

ln kt = ln kt

ln k1960 denote the cumulative log di¤erence between the capital

stock in year t and the initial year 1960. We decompose the change in the capital stock as
follows
ln kt =

X

ln kt

ln ktCF;i +

i

+ ln k

CF;0

(

ln kt

ln ktCF;0

X
i

;

ln kt

ln ktCF;i

)

(5.1)

where k CF;i denotes the counterfactual capital stock obtained when we …x the i-th exogenous
variable at its initial value and set all other exogenous variables at their actual values, and
k CF;0 denotes the counterfactual capital stock obtained when we …x all exogenous variables
at their initial base period values. The …rst term in this expression can be interpreted as
the sum of the marginal contributions coming from the changes in the di¤erent exogenous
variables, and the second term captures potential non-linear interactions between the different exogenous variables. The third term captures the standard transition e¤ect due to
an initial capital stock being di¤erent from its BGP value (implied by the initial values of
exogenous variables). Table 2 displays the decomposition of the marginal contributions of
various drivers based on equation (5.1).

[Table 2. Sources of Korean Growth]

For the discussion of marginal contributions, it is useful to distinguish between nonagricultural employment, the relative price of capital, and TFP on the one hand, and the
remaining exogenous drivers on the other hand. We single out these three factors because
they determine the scale of the economy in the long run, as can be seen from the stationary
15

transformation of capital and output in the growth model, equations (2.11) and (2.12). Over
the long run— that is, the time period from 1960 to 2005— the three scale factors account
for more than 60 percent of growth in the capital stock and 80 percent of growth in nonagricultural output, with most of it coming from an increase in non-agricultural employment
and a decline in the relative price of capital. This feature is consistent with the three
variables determining the scale of the economy. Over the medium term, however, the overall
contributions of these variables to growth are smaller than their direct scale e¤ect would
suggest. For example, for the period 1960 to 1970 the contribution of non-agricultural
employment growth to capital accumulation was only 16 percent, even though this was the
period when employment was growing the fastest.
The smaller medium-term contribution to growth of the scale factors can be attributed
to the countervailing transition e¤ects that the changes in the scale factors induce. The
endogenous transition dynamics are characterized by the system of normalized variables,
(2.13), (2.14), and (2.15). From the normalized Euler equation (2.15) it is apparent that most
of the exogenous variables will a¤ect the transition dynamics through their impact on the
e¤ective discount rate or the return to capital. In the case of non-agricultural employment,
rapid growth means a high growth rate of the output scale factor, which in turn implies a
smaller e¤ective discount factor. The representative household being e¤ectively less patient
requires a higher rate of return to capital and cuts back on capital accumulation. This
endogenous response to fast employment growth counteracts the direct scale e¤ect, and the
net contribution of employment growth to capital accumulation over the medium term is
below its long-run contribution. Over the long run, these transitional e¤ects are, however,
quite small, and the contributions of the scale factors are remarkably close to the direct
contributions associated with their impact on the scale factors for capital and output.
The second group of exogenous variables— …nancial frictions, autonomous spending shares,
income tax rates, and population growth rates— a¤ect only the transition dynamics of per
capita capital and output; they have no direct scale e¤ects. Among this group, reduced …nancial frictions have the biggest impact in the long run, accounting for 20 percent of capital
accumulation and 10 percent of output growth from 1960 to 2005. Note that even though
most of the decline in …nancial frictions took place by 1970, the growth contributions of
…nancial frictions are actually increasing over time and are biggest after 1980. The other
16

non-scale variables make no appreciable long-run contributions to capital or output growth.
For the period 1960 to 2005 the combined contributions of these variables is less than 1
percent. Signi…cant contributions to growth from reductions in the income tax rate and autonomous spending are limited to the period from 1960 to 1970, and even in this period, the
combined contribution to output growth stays around 10 percent.
So far we have studied the marginal e¤ect one exogenous variable at a time. If we
add up all these marginal e¤ects and compare them with the e¤ect of …xing all exogenous
variables at their initial 1960 values, we can obtain a measure of how much the changes in the
exogenous variables interact with each other. As we can see from Table 2, Column (10), the
interaction e¤ects from the simultaneous change in all exogenous variables are quantitatively
quite limited, at most about 6 percent.
Finally, …xing all exogenous variables at their initial 1960 values also yields the typical
transition dynamics for capital in the neoclassical growth model (King and Rebelo (1993)).
Starting out with a capital stock that is below its BGP value, the capital stock converges
rapidly within 10 years toward its BGP value. During the early phase of development in
the 1960s and 1970s, this transition makes a signi…cant contribution to capital and output
growth: close to 40 percent of capital growth and 20 percent of output growth. The magnitude of the contribution coming from the capital transition declines over time, but it remains
over 10 percent even for the full period from 1960 to 2005.
The rapid convergence of the capital stock for the counterfactual capital-only transition
is accompanied by the typical neoclassical transition dynamics for the investment rate path,
which starts out high and then declines toward its BGP value. In Figure 5, we plot the time
path of the actual nominal investment rate in the Korean economy, as well as the investment
rate paths for each of the counterfactuals we just described. As is typical for most of the
East Asian growth miracles, the actual Korean investment rate, the solid black line, is humpshaped, increasing …rst and then declining, unlike the counterfactual capital-only transition
path of the investment rate, the dashed black line. According to the counterfactuals, …xing
any one of the exogenous variables at its 1960 value does not change the basic hump-shaped
path of the investment rate. This suggests that the dynamics of the Korean investment rate
are the joint product of the dynamics of all exogenous variables. It is, however, true that
…nancial frictions have the biggest impact on the investment rate path. Keeping …nancial
17

frictions at their initial value (solid pink line) persistently lowers the investment rate. Not
only does the investment rate not increase as much as observed from the 1960s to the early
1970s, the investment rate then also declines much earlier and faster in the late 1970s. But
recall that even though …nancial frictions have, according to our counterfactuals, the biggest
impact on the investment rate, their impact on overall capital accumulation remains limited.
Thus, capital and output accumulation are not necessarily closely tied to the investment
rate.13

[Figure 5. Sources of Variation in the Investment Rate]

We have shown that a sustained increase in employment in the non-agricultural sector
and a sustained decline in the relative price of capital are important for understanding the
prolonged process of capital accumulation of Korea. We have not provided a reason why
employment in the non-agricultural sector increased only gradually and why capital was so
expensive in Korea in the 1960s. A study of these two topics is beyond the scope of this
paper, but we want to comment brie‡y on them.
First, why was labor not reallocated from the agricultural sector to the non-agricultural
sector at a faster rate? In our model we assume that prices and wages in the agricultural
sector adjust such that the returns to labor are the same in both sectors. Thus, we do not
assume any barriers that prevent a faster reallocation of labor toward the non-agricultural
sector. For the Korean economy, it is reasonable to assume that the net return of moving
out of agriculture for older workers in rural areas would have been quite limited. First,
investment in nonfarm human capital would have generated a relatively low rate of return
for older workers. Second, the Korean government regulated the ownership of farm land,
which likely generated some rents for older rural farmers. These factors should have limited
the ‡ow of older workers out of the agricultural sector. In fact, according to Kim and
13
As our discussion indicates, allowing for the shift of employment toward the non-agricultural sector and
a declining relative price of capital a¤ects the interpretation of the transition dynamics. In Lu’s (2012) onesector interpretation of the South Korean growth path, a substantial part of output growth in the period
prior to 1985 is attributed to …nancial frictions, and in the period after 1985 to TFP growth. In our setup
increasing non-agricultural employment and a declining relative price of capital make bigger contributions
than either TFP growth or declining …nancial frictions (Table 2).

18

Topel (1995), there is little evidence that labor migration out of agriculture was a major
source of increasing employment in Korean manufacturing. Virtually all of manufacturing’s
employment growth was achieved by hiring ever-larger numbers of new entrants to the labor
force, and there was no net hiring of workers older than age 25. Thus, it appears that
employment in the Korean non-agricultural sector was growing about as rapidly as one
could have expected.
Second, why was capital so expensive in Korea at the early stage of development? On
this aspect Korea has not been an exception. Rather it is well known that the relative price
of capital and income levels are negatively correlated across countries; see, for example,
Restuccia and Urrutia (2001) or Caselli and Feyrer (2007). Hsieh and Klenow (2007), as
well as Barro (1991), argue that in many low-income countries a high relative price of capital
is largely driven by cheap consumption goods. Eaton and Kortum (2001), in turn, argue that
poor countries tend to specialize in the production of consumption goods and import capital
goods. Trade barriers that are highly correlated with income then contribute to higher prices
of capital goods in poor countries.

6. Conclusion
Capital deepening played an important role during the transition of the Korean economy
from an agricultural economy to a modern industrialized economy. While capital accumulation is a core element of the neoclassical growth model, the model-implied dynamics are
strongly at odds with the actual pattern of investment rates in many countries. Using various
detailed data from the Korean economy, we show that this apparent failure of the model is
mainly due to using the “wrong”data to evaluate the model. First, the neoclassical growth
model with its emphasis on capital accumulation applies to the capital-intensive modern
industrialized sector of the economy and not to the more labor-intensive agricultural sector
of the economy. Second, in the early stage of economic development, the relative price of
capital is high. Accounting for both features dramatically lowers the model-implied rates
of return to capital during early stages of development and contributes signi…cantly to the
relatively low investment rate. The quantitative analysis based on the calibrated model suggests that the two most important sources of long-run capital accumulation in the Korean

19

economy have been increasing employment in the non-agricultural sector and a declining relative price of capital, accounting for about 55 percent of capital growth from 1960 to 2005.
Increased TFP and reduced …nancial frictions contributed an additional 30 percent to capital
growth, whereas the contribution coming from the endogenous transition of the capital stock
toward its long-run BGP value accounts for only 10 percent of capital accumulation over the
long run. These standard transition dynamics were, however, more important during the
…rst 20 years of development from 1960 to 1980, accounting for 20 to 40 percent of capital
accumulation.
While our model successfully accounts for a prolonged path of capital accumulation, it
abstracts from some important features of the transition of the Korean economy. Similar
to many other developing economies, at the onset of the transition path, structures, in
particular, residential structures, made up most of the aggregate capital stock. As a result,
the capital-output ratio for equipment was much lower than that for structures. Thus, the
implied rates of return and …nancial frictions for the two types of capital are potentially quite
di¤erent. In the context of a disaggregated model of the capital stock, the interaction between
human and physical capital (e.g., capital-skill complementarity as in Krusell, Ohanian, RiosRull and Violante (2000)) might have been important for the sluggish accumulation of capital,
as the supply of skilled labor is limited in the early stage of economic development. Finally,
our model does not consider international trade, which has been recognized as an important
factor for economic growth among East Asian countries. For example, Connolly and Yi
(2009) argue that a large set of institutional and trade policy reforms have contributed to
the economic growth of Korea.

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23

Table 1. Transformation of the Korean Economy

1963 2005
Size of Agricultural Sector
(in percent)
Employment Share

69

8

Value-Added Share

34

2

2.3

1.0

Relative Price of Capital

Notes: See Section 3 for a detailed explanation of the data.

24

Table 2. Sources of Growth in the Korean Economy
(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

A. Sources of Capital Accumulation
Year t ln kt

Marginal Contributions (in percent)

ln k1960
ey

q

Ay

f

g

n

res.

k0

k

1970

1.01

16.2

7.2

-0.4

8.1

14.3

8.5

3.8

4.3

38.1

1980

2.24

24.9

18.0

6.3

14.4

4.7

6.1

0.2

4.6

21.0

1990

3.19

27.1

23.8

6.6

19.9

-0.6

2.2

-0.7

6.4

15.3

2005

4.22

27.9 26.8

8.5

19.3

0.8

-0.3 -0.3

5.5

11.7

B. Sources of Output Growth
Year t

ln yt

Marginal Contributions (in percent)

ln y1960
ey

q

Ay

f

g

n

res.

k0

k

1970

0.79

51.8

3.2

10.6

3.6

6.4

3.8

1.7

1.9

17.0

1980

1.49

51.4

9.4

12.6

7.5

2.4

3.2

0.1

2.4

11.0

1990

2.12

49.5

12.5

15.7

10.5

-0.3

1.1

-0.4

3.4

8.1

2005

2.66

47.3 14.9 17.4 10.7

0.5

-0.2 -0.2

3.1

6.5

Notes: Column (2) denotes the log di¤erence between year t and the initial year 1960. The
decomposition of marginal contribution is based on equation (5.1) in Section 5. Numbers in
Columns (3) through (9) denote the contribution of non-farm employment (ey ), the relative
price of capital (q), TFP (Ay ), …nancial frictions (f ), autonomous spending (g), income tax
rates ( ), and population growth (n). Column (10), "res." captures the residual term from
possible non-linear interactions among variables, respectively. Column (11), k0 k , captures
the transition from the initial capital stock being below its BGP value.

25

Figure 1. Investment Rates for Asian Growth Miracles

0 .5

← Singapore
0 .4 5

0 .4

0 .3 5

Investment/GDP

Japan →
0 .3

← Hong Kong

0 .2 5

← Korea
0 .2

← Thailand

← Taiwan

0 .1 5

← Indonesia
0 .1

0 .0 5
1950

1955

1960

1965

1970

1975

1980

1985

1990

1995

Year

Notes: Data are based on the Penn World Table v6.2.

26

2000

Figure 2. Capital Accumulation in Korea, 1960-2005
A. Capital-Output Ratio

B. Investment-Output Ratio

3

0.4

0.35
2.5

0.3

2
0.25

1.5

0.2

0.15
1

0.1

0.5
0.05
Real
Nominal
Nominal non-agri GDP

Real
Nominal
Nominal non-agri GDP

0
1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

0
1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Notes: The capital-output and investment-output ratios are calculated as described in Section 4 for “Real” and “Nominal” values of capital, investment, and aggregate GDP. For
the ratio “Nominal non-agri GDP” we use nominal non-agricultural GDP as a measure of
output.

27

Figure 3. Rates of Return on Capital in Korea, 1960-2005

100
Aggregate GDP
Non-agri GDP
Non-agri GDP and q
Non-agri GDP, q and
Euler Equation

90

80

τ

70

Percent

60

50

40

30

20

10

0
1960

1965

1970

1975

1980

1985

1990

1995

2000

2005

Notes: The implied rate of return to capital is calculated as described in Section 4 using
data on aggregate GDP; non-agricultural GDP, “Non-agri GDP”; non-agricultural GDP and
the relative price of capital, “Non-agri GDP and q”; and non-agricultural GDP, the relative
price of capital, and the tax rate on capital income, “Non-agri GDP, q, and :”The implied
rate of return for the household is labeled “Euler Equation.”

28

Figure 4. Total Factor Productivity in Korea, 1960-2005

0.8
Aggregate GDP
Non-agri GDP
Non-agri GDP in cons units

Log Level, 1960=0

0.6

0.4

0.2

0

-0.2
1960

1965

1970

1975

1980

1985

1990

1995

2000

2005

Notes: TFP is calculated as described in Section 4 using data on aggregate GDP; nonagricultural GDP, “Non-agri GDP”; and non-agricultural GDP in units of consumption
goods, “Non-agri GDP in cons units.”

29

0.4
Data
ey
q
Ay
f
τ
n
k0

0.35

Fraction

0.3
0.25
0.2
0.15
0.1
0.05
0
1960

1970

1980

1990

2000

2010

2020

2030

Figure 5. Investment Rate under Each Counterfactual Scenario
Notes: ‘Data’ denotes the actual normalized capital stock. The other lines represent the
investment rate under each counterfactual scenario where each variable is …xed at its initial
1960 value (and all other variables are set to actual values). For example, ‘ey ’ denotes
the investment rate when non-agricultural employment remains at its 1960 level; all other
exogenous drivers are as in the data. ‘k0 ’ denotes the traditional neoclassical transition
dynamics — i.e., all exogenous drivers remain at their 1960 values.

30