Fixed Capital Stock Depreciation in Developing Countries:
Some Evidence from Firm Level Data
Yisheng Bu1
Liberty Mutual Group
175 Berkeley Street, S3B
Boston, MA 02116
USA
This Version: December 2004
1
Mailing address: Liberty Mutual Group, 175 Berkeley Street, S3B, Boston, MA 02116, USA. Tel: +1617-894-4713. Email address: yisheng.bu@libertymutual.com. The author is indebted to George von
Furstenberg and two anonymous referees for their review, very valuable comments and suggestions. The
author is solely responsible for any remaining errors and omissions.
Fixed Capital Stock Depreciation in Developing Countries:
Some Evidence from Firm Level Data
Previous growth accounting studies suggest severe capital underutilization and
mismeasurement of the stocks of capital in some developing countries. Using the firm
level data sets from the World Bank surveys, this paper estimates the economic
depreciation rates of fixed capital stocks in the manufacturing industries of seven
developing countries. The findings indicate that the stocks of fixed capital may
depreciate at higher rates in these countries, as compared with the normal rates usually
assumed for advanced industrial countries. This study also discusses the economic and
social forces that may influence the incentive to maintain capital appropriately and the
implications of high depreciation for the total factor productivity [TFP] growth estimates
and volatility of capital accumulation.
JEL Classification: E22, O10
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The theoretical foundation for the measurement of economic depreciation rates and stocks of
fixed capital has been well established in a series of papers by Hulten and Wykoff [1981],
Jorgenson [1989, 1996] and Hulten [1990]. The empirical application of this measurement theory
and methodology is still limited to the United States. Other advanced industrial countries have
well developed methods for calculating gross stocks of capital but derive their net stock estimates
by imposing certain strong assumptions about the capital depreciation patterns [OECD 1993,
2001]. Moreover, the methodologies for developed countries may not be appropriate for the
measurement of stocks of fixed capital in developing countries, on account of either
unavailability of relevant data (such as used asset prices in resale markets) or various
inefficiency-related factors, such as excessive costs of capital creation and low productivity of
capital expected even ex ante.
All the international capital stock data sets that are currently available, which include the
Penn World Table [PWT 5.6], and the ones used in Easterly and Rebelo [1993] and Nehru and
Dhareshwar [1993], are constructed by applying a single common depreciation rate1 to aggregate
or disaggregated investment series uniformly for all countries. However, as noted in PWT 5.6,
the assumption of common depreciation rates across countries may be wrong because of country
differences in the costs of capital maintenance and of new capital investment. By assuming equal
depreciation rates across countries nonetheless, the conventional growth accounting studies have
yielded misleading results and suggested severe capital underutilization and mismeasurement of
the stocks of capital in some developing countries [Pritchett 1997, 1999]. By exploring available
evidence on the resale value of fixed assets in selected developing countries, this paper intends to
show that the economic depreciation rate in certain developing countries may well exceed the
standard rate assumed in the growth studies.
This paper uses the firm level survey data, collected by the World Bank in the 1990s, on
total fixed assets, land and buildings, machinery and equipment in a group of selected countries in
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Africa, East Asia and Southeast Asia. It obtains the implied rates of economic depreciation
through the capital accumulation equation both for the individual firms and for all firms in the
sample combined. The findings in this paper indicate that some developing countries, including
the ones studied in this paper (Cote d’Ivoire, Ghana, Kenya, Zimbabwe, Indonesia, Philippines
and South Korea), may depreciate their stocks of capital much faster than the U.S. economy and
other OECD economies. High depreciation in the process of capital accumulation may then
diminish the growth-promoting effect of high saving and investment rates in those countries as
well as the effect of foreign aid.
Abnormal depreciation rates observed for developing countries may be due to
undermaintenance leading to premature discarding of capital. This is implied from the
comparison with the depreciation rates calculated by directly using depreciation expenses
recorded on the corporate financial account. High depreciation may be due to many economic
and social forces. Government-provided investment incentives and capital underutilization may
increase the marginal cost of capital maintenance or decrease its marginal benefit, both relative to
the respective values of new capital investment, thus leading to faster capital depreciation. Other
cases in which high depreciation results include corruption in capital goods procurement lowering
the effectiveness of converting new investment into capital stock, or incompatible infrastructure
facilities and technical services negatively affecting the rate of capital utilization.
The findings in this paper on capital depreciation anomalies in certain developing
countries have important implications for the total factor productivity [TFP] growth estimates
obtained in previous growth accounting studies. Different capital depreciation profiles imply
different rates of capital accumulation, and hence accounting for the higher rates of depreciation
in constructing capital stock series would necessarily lead to comparatively higher estimates of
TFP growth. This provides a possible explanation for the negative TFP growth rates reported for
some developing countries in Pritchett [1997, 1999]. Another implication of higher depreciation
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rates is higher volatility of capital stock growth. In the presence of much faster depreciation of
existing capital, the stock of fixed capital becomes more vulnerable to the volatility of fixed
investment and hence other macroeconomic variables in the economy.
The structure of this paper is organized as follows. The next section presents and
assesses the results from previous growth accounting studies and more importantly, stresses their
implications for measuring the depreciation rate in developing countries. Sections 2 and 3
describe data sources and measurement methodology, respectively, and section 4 reports the
empirical estimates of the economic depreciation rate for selected less developed countries in
Africa, East Asia and Southeast Asia. Possible causes for capital undermaintenance in
developing countries are discussed in section 5. Using conventional growth accounting
regressions, section 6 investigates the implications of high depreciation for the estimates of TFP
growth and the volatility of capital accumulation. Concluding remarks are given in section 7.
1. Capital Stock and Depreciation Rate Estimates for Developing Countries
There are many authors who, through growth accounting studies or econometric
regressions, find little contribution to economic growth of massive capital accumulation in most
developing countries [Hulten 1996, Pritchett 1997, 1999, Easterly 1999, Devarajan et al. 2003].
For example, using the aggregate capital stock data2, Pritchett [1999: 28] finds that ‘over the last
30 years, 55 per cent of developing countries have measured TFP growth less than zero, with
more than a quarter showing TFP as low as negative one per cent per annum.’ Negative TFP
growth in an economy implies that the same amount of capital per unit of labour has been
yielding progressively less output during the relevant period. It could be a direct indication of
productivity decline, such as knowledge or skill loss, or destruction of institutional structures in
developing countries, but one would view it as the outcome of many other factors to be discussed
next.
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Negative TFP growth observed for most developing countries may be explained by the
mismeasurement of the stocks of capital by way of Cumulated, Depreciated, Investment Effort
[CUDIE] in those countries. The concept of CUDIE, which is introduced in Pritchett [1997],
refers to the accumulated investment spending less the accumulated capital depreciation
calculated with standard depreciation rates. By imposing the assumption of zero minimum
growth rate in TFP and solving for the growth of capital as the residual factor in growth
accounting, Pritchett finds a much smaller growth in the effective stock of capital (which he calls
the ‘implied’ rate of capital accumulation) than the CUDIE growth. Specifically, he finds that the
regional average ratio of the ‘implied’ rate of capital accumulation to the CUDIE growth is 45.8%
for the Middle East and North Africa, 48.8% for the Sub-Saharan Africa, 54% for South Asia,
72.2% for the Latin America and Caribbean, 94.5% for the fast growing Asian economies and
97.8% for OECD countries, respectively – see Table 5 in Pritchett [1997]. Even though these
numbers cannot, in any way, accurately reflect the actual growth rates of the stocks of capital in
the developing countries, they do indicate the mismeasurement of capital and its misleading
implications for TFP growth.
The mismeasurement of the stocks of capital for the developing countries may in turn be
due either to excessive costs of capital creation3 or to high capital depreciation, both of which are
being ignored in the CUDIE measure of the capital stock. The efficiency with which real capital
is created from investment does differ greatly across countries, especially for capital creation in
the public sector in countries with corrupt public agencies. For example, the cost (in 1985$) of
constructing a kilometre of similar road ranges, across countries, from $771,068 in Honduras to
$65, 277 in Sri Lanka, with a sample average of $287,359 [Canning and Fay 1995, and
mentioned in Pritchett 1997]. Unusually high expenditure in creating a unit of capital may
include the commission surcharge, in the forms of kickback, political contributions, or
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nonpecuniary benefits demanded by public officials from private and public contractors for the
project.
Another cause for mismeasurement may relate to high rates of fixed capital stock
depreciation in both public and private sectors. High depreciation of capital stock can result from
lack of appropriate maintenance and premature discard. For privately used capital, the relative
price of investing in new capital and maintaining existing capital may be distorted by favourable
government policies toward investment, lack of competent maintenance and operational staff,
unavailability of qualified repair parts, and so on. For publicly provided capital, high
depreciation is even more pronounced on account of the accounting and budgetary treatment of
depreciation4 in the government and various corruption-related factors.
Declining TFP can also result if capital has been underutilized over a long period of time.
The intensity with which the capital is utilized depends not only on the nature of the capital itself
but also on many other complementary factors, such as technology, necessary following-up
spending (for example, operating staff’s salaries and training), and supporting public services
applied to the quasi-fixed capital. Moreover, capital underutilization could also lead to lowerthan-efficient level of capital maintenance and thus higher-than-normal capital depreciation, just
as low maintenance expenditures may be responsible for extended downtime in a vicious cycle.
The following sections intend to present empirical evidence supporting that the economic
depreciation rates in certain developing countries are much higher, as compared to the standard
rates assumed in the growth literature.
2. Data Sources and Description
To empirically measure the economic depreciation rate for developing countries, I use the
firm level data sets published by the World Bank on its website. The data sets cover a selected
group of developing countries in Africa, East Asia and Southeast Asia. Numerous studies have
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made use of these firm level data sets; however, no prior studies have ever used the asset prices in
the data sets to measure capital depreciation rates in these developing countries. In this paper, the
economic depreciation rate is estimated for four African countries (Cote d’Ivoire, Ghana, Kenya
and Zimbabwe), one East Asian country (South Korea), and two Southeast Asian countries
(Indonesia and Philippines). Table 1 gives details of data availability for measuring the economic
depreciation rate for each type of assets in each country. For each type of assets (buildings,
machinery and equipment, and total fixed assets), firms that have missing values for the relevant
variables are dropped, while the remaining firms form new samples for which the economic
depreciation rates are to be measured. For the African countries, Table 1 also reports the number
of firms in the corresponding new samples that sold their fixed assets during the measurement
period.
{Insert Table 1 about Here}
The firm level data sets came from questionnaire surveys conducted by the World Bank
in the 1990s through interviews with firms. Similar sampling procedures and techniques were
used in the survey across all sample countries, so that the data sets are comparable. For each
country, firms were randomly selected from the industrial sectors that reflect the general
composition of each country’s manufacturing sector and represent the largest sectors within each
country’s manufacturing industries in terms of valued added, export and employment. In
addition, firms of different size, age, location, ownership structure, and production orientation,
and firms with foreign ownership (either in the form of joint venture or subsidiary of a foreign
parent) were included in the sample for each country. For the Asian countries, the survey was
conducted between October 1998 and March 1999. For the four African countries, the data sets
were collected over three rounds of firm level interviews in successive years between 1992 and
1996, and the same sample of firms were intended to be included in all three surveys. Firms that
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had dropped out of the previous sample for some reasons have been replaced with firms of the
same size, from the same sector, and in the same region.
The data sets on the African countries provide current market value of fixed assets, the
selling price of assets that were sold, and the (nominal) value of new investment, for the time
periods of up to six years. For some of the countries, the data sets also report the disaggregated
market values of land and buildings, machinery and equipment. The current replacement values
of total fixed assets and its disaggregated components are also available for Ghana, Kenya and
Zimbabwe. Cote d'Ivoire is the only country for which the data set spans six years (1990-1995),
while the time span of the data set is relatively short for the other three African countries: three
years for Zimbabwe (1993-1995) and two years for both Ghana (1992-1993) and Kenya (19931994). For the Asian countries, the resale value of each type of asset is not available from the
survey, and the net book values5 are used in the estimation as approximates. The data are
available for the period 1996-1998 for South Korea and Philippines, and only for the period 19971998 for Indonesia. A summary of the variables used in the measurement of depreciation is
provided in Table 2.
{Insert Table 2 about Here}
3. Estimation Methodology
The estimation methodology employed in this paper uses the direct estimates by firm
managers of the current market values of land and buildings, machinery and equipment and of
total fixed assets. Hence, the estimates of economic depreciation rates thus obtained measure
how the value of capital assets changes over time for individual firms, instead of for individual
classes of assets as studied in the traditional depreciation estimation. The traditional
methodologies for measuring economic depreciation rates use market transaction data on asset
resale or rental prices. A large number of studies [Hulten and Wykoff 1981, Oliner 1996,
Fraumeni 1997], which were based on vintage asset prices, estimated the economic depreciation
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rates for various classes of assets in different U.S. and Canadian industries. However, these
approaches require the existence of thick resale or rental markets, which is lacking for most
developing countries. Should these data become available, the traditional methodologies ought to
be used to estimate the depreciation rates of capital assets in developing countries and validate the
findings of high capital stock depreciation in some of these countries.
For each country and wherever it is possible, I calculate the economic depreciation rate
for total fixed assets in each firm, and also separately, for buildings, machinery and
equipment. By the perpetual inventory method, the depreciation rate, which is assumed to be
constant, can be implied from the investment series and the firm's estimates for the sale values of
fixed assets at the beginning and end of the period that the investment series spans. In other
words, the depreciation rate can be solved for from the following capital accumulation equation:
K ti ⋅ (1 − δ ) T +
T −1
∑ {( I
i
t + s ,t
− DI ti+ s ,t ) ⋅ (1 − δ ) T − s −1 } = K ti+T ,t ,
s =0
where K ti is the market value of fixed assets at the beginning of period t, I ti is the amount of new
investment during period t, and DI ti is the selling price of assets sold during period t, all
measured at the prices prevailing in period t , with the superscript i denoting firm i 6. The series
K ti+ s ,t , I ti+ s ,t and DI ti+ s ,t are measured in constant (period t ) local currencies to exclude the
effect of asset inflation on the asset value. Here, notice that the resale of fixed assets is
considered as disinvestments. The major reason for firms to sell part of existing machinery and
equipment, as reported in the survey, is normal replacement of old assets with new assets, and as
a result, the selling price of old assets largely reflects their salvage values. Besides, firms have
also sold their existing assets because of excess capacity, liquidity needs and no demand for
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products. For the three Asian countries that are lacking in the data on the resale of fixed assets,
the depreciation rate may be overestimated. Also in the measurement, the net book value of fixed
assets recorded on the company account is used to approximate the value of K ti for the Asian
countries. Table 2 summarizes the variables used in the measurement and their corresponding
data series in the data sets.
For the sample countries, all the investment series and sale values of fixed assets are
recorded in current prices. The investment goods deflator is used and calculated from each
country's nominal and constant domestic investment in capital goods, both in local currencies.
The relevant data are obtained from the African Development Indicators [World Bank 2000a] and
the World Development Indicators [World Bank 2000b].
For Ghana, Kenya and Zimbabwe, for which the data sets contain the current replacement
values of fixed assets, an alternative aggregate investment goods deflator is constructed through
the following two steps:
i.
For each individual firm in each country, a deflator is calculated as the changes in the
replacement value of fixed assets between successive years. Mathematically, the realized
asset inflation rate ( π ti ) can be obtained from (1 + π ti ) = (
∑I
v ≤t −1
∑I
i
v ,t +1
i
v ,t +1 ) /(
∑I
i
v ,t )
, where
v ≤t −1
is the replacement value at the beginning of period t + 1 of fixed assets that
v ≤ t −1
have been purchased and put in place at or before the beginning of period t . Further,
∑I
v ≤ t −1
i
v ,t +1
can be written as (
∑I
i
v ,t +1 )
− I ti,t +1 , where in the estimation,
∑I
i
v ,t +1
is
v ≤t
v ≤t
approximated by the replacement value of fixed assets at the beginning of period t + 1 .
This approximation may bias downward the estimates of the economic depreciation rate,
as some assets that may have exited from production during the previous period are still
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assumed to be included in the stock of assets at the beginning of the current period and
the asset price deflator is thus underestimated.
ii.
The aggregate investment goods deflator, denoted by (1 + π ta ) , is then obtained as the
weighted sum of the deflators of individual firms by using each firm's current
replacement value of fixed assets as weights to average out any firm-specific factor7 that
may influence asset prices.
In the capital accumulation equation, I ti+T ,t = I ti+T /
T
∏ (1 + π
a
t + s −1 ), and
s =1
K ti+T ,t = K ti+T /
T
∏ (1 + π
a
t + s −1 ) ,
for T ≥ 1 , where (1 + π ta ) is the aggregate investment goods
s =1
deflator that is obtained through the method just described. Here, to deflate the stock of capital at
current prices to constant prices (that is, from K ti+T to K ti+T ,t ) requires the assumption that in
i
i
i
each period the asset inflation rate is constant across asset vintages, or ( p t +1,v − p t ,v ) / pt ,v = π ti ,
∀v .
{Insert Table 3 about Here}
It deserves noting that the asset inflation rate, calculated as the rate of change in the
replacement cost of the same cohort of assets, may be inaccurate and biased, given that most
developing countries imports most of their capital equipment, and that exchange rate fluctuations
may significantly modify the market value of capital. Table 3 presents the investment goods
deflators calculated from using the replacement values of fixed assets between successive years
(called the ‘weighted’ deflator and presented in Panel A) and those implied from each country’s
national accounts (called the ‘SNA’ deflator and presented in Panel B). For Ghana, Kenya and
Zimbabwe for which the weighted deflators are constructed, the ‘weighted’ deflator is generally
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larger than the ‘SNA’ deflator, except that for Zimbabwe, the former is smaller than the latter for
the year 1995. As an illustrative example, Table 4 describes the data and calculation formulas
used in estimating the depreciation rate of fixed assets in a South Korean firm.
{Insert Table 4 about Here}
4. Estimation Results
Using the managers’ valuation of firms’ capital assets, I calculate the implied
depreciation rates for each individual firm. The selected percentiles (10th, 25th, 50th, 75th, and
90th) along with the means and standard errors are presented in Table 5. The depreciation rates in
Panel A of Table 5 are calculated using the investment goods deflators obtained from the
countries’ system of national accounts. For Ghana, Kenya and Zimbabwe, alternative sets of
deflators are calculated from the replacement costs of capital assets, and the resulting depreciation
rates are shown in Panel B of the table. The depreciation rates in Table 5 are for machinery and
equipment in Ghana and Kenya, and for fixed assets (including nonresidential structures,
machinery and equipment) in the other sample countries.
{Insert Table 5 about Here}
As observed from Table 5, except for Indonesia, over 10% of the firms in the sample
countries have negative depreciation rates. Other than reporting and measurement errors, this
may come from the following sources. First, provided that the countries import most of their
capital equipment from advanced industrial countries, currency depreciation (relative to the
capital exporting countries’ currency) can cause the values of capital assets to rise and thus
possibly lead to negative depreciation rates. The changes in the valuation of capital assets due to
foreign exchange fluctuations could not be fully captured in either of the investment goods
deflators calculated here. Second, the asset prices have been deflated to a common base using a
common investment goods deflator for all firms in each country. Some firms with industryspecific assets may have had experienced much higher (than average) asset inflation.
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Consequently, the market value of the same vintage of assets may not be on the same level as
before even after being adjusted for general asset inflation8.
The other extreme result from the estimation is that some estimates of the depreciation
rate exceed 1, the maximum value allowed in theory. This implies that the economic value of
capital goods declines immediately after they are installed; in other words, the investment
spending occurring during the current period is less than the corresponding increase in the stock
of capital at the end of the period. This corresponds to the concept proposed in Pritchett [1997]
that the actual cost of investment is not equal to the value of capital created.
Table 5 shows that for the four African countries, a large proportion of the firms have
experienced much more rapid value decline in capital assets (machinery and equipments for
Ghana and Kenya), at the rates much larger than the corresponding normal values. For instance,
for over 75% of the firms in Cote d’Ivoire, the depreciation rate of total fixed assets exceeds 0.1,
as compared to the rate of 0.07 usually assumed for the U.S. economy [Easterly and Rebelo
1993]. For machinery and equipment in Ghana, the depreciation rate exceeds 0.5 for half of the
firms, as compared to the standard rate of 0.15 for machinery and 0.24 for transport equipment
[PWT 5.6]. For Zimbabwe, while both the mean and the median are much higher than 0.07, the
sample mean would be greater than 0.07 for more than 80% of the time if using the SNA
deflators and for nearly 100% of the time if using the weighted deflators. The depreciation rates
of capital in the sample of Kenyan firms are so dispersed that the sample could not give
meaningful implications for population characteristics.
High depreciation rates are also observed for the Asian countries. In Indonesia, the
economic depreciation rates of fixed assets are over 0.4 in more than 90% of the firms. Similarly
but to a much lesser extent, Philippines has about 75% of the firms having depreciation rates
larger than 0.07 and about 50% larger than 0.17. In contrast, South Korea is the only Asian
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country in the sample in which most of the firms have depreciation rates close to the standard
value.
{Insert Tables 6 and 7 about Here}
As the percentile summary of individual firms’ depreciation rates treats firms of disparate
sizes equally, I also calculate the sample average of depreciation rates for all firms combined for
each country using the aggregated capital stock and investment series. Consistent with the
findings at the individual firm level, Table 6 shows that at the aggregate level, the depreciation
rates of fixed assets in the selected firms in the four African countries are much higher than the
rates usually assumed in growth literature, while such high depreciation has been least severe in
Kenya. For Ghana, the sample average rate of economic depreciation of machinery and
equipment is 0.448 if the SNA deflators are used, exceeding the standard rate for machinery and
equipment by at least 0.2. As compared, machinery and equipment in the Kenyan firms are
estimated to depreciate at 0.158, which is within the normal range. The same situation holds for
Cote d’Ivoire for the same type of assets. However, business constructions in Cote d’Ivoire
depreciate, by estimation, at about 0.10, higher than the usually assumed rate of 0.035 for
constructions [PWT 5.6]. This brings the overall depreciation rate of fixed assets in the country to
an estimated value of 0.148. Also shown in the table, machinery and equipment and overall fixed
assets in the Zimbabwean firms have higher depreciation rates, with the depreciation rate of fixed
assets estimated to be at least 0.12 higher than the normal rate. For all sample countries, using
the weighted deflators, which are lower in value than the corresponding SNA deflators, yield
even higher depreciation rates.
The Southeast Asian countries are also found to have anomalous capital depreciation
rates at the aggregate level. While both Indonesia and Philippines have much larger depreciation
rates for all sample firms combined, high depreciation has been far more severe in the former
than in the latter countries. By contrast, for machinery and equipment in the manufacturing
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industries of South Korea, the sample average rate of depreciation for the period 1996-1998 is
0.174, comparable to the standard values. High depreciation observed in the two Southeast Asian
countries might be, by conjecture, partly due to the large amount of resale of fixed assets by a
large proportion of firms in the sample during the measurement period9; however, the data on the
resale of assets in the Asian countries are not available from the surveys.
It should be pointed out that for both Philippines and South Korea, the economic
depreciation rate is much smaller in the second measurement period 1997-1998 when the
financial crisis hit the region. Such differences in depreciation rates between different time
periods may be caused by the same factor having caused negative depreciation rates. Domestic
currency devaluation, which occurred during the financial crisis, makes capital assets imported
from advanced industrial countries or incorporating lots of imported parts appreciate in value, and
consequently lowers the estimates of their rates of economic depreciation.
{Insert Table 8 about Here}
For comparison purposes, the depreciation rate is also directly calculated as the ratio of
the depreciation expenses recorded in the company account to the value of total fixed assets at the
beginning of the period for each country. The results are summarized and presented in Table 8.
The results show that using the recorded depreciation expenses can yield ‘normal’ depreciation
rate estimates for all the sample countries. In this sense, it provides additional evidence for
Pritchett’s statement that the stock of capital obtained by way of CUDIE deviates from or exceeds
the market value of capital assets in place in certain developing countries.
5. Possible Causes of High Depreciation in Developing Countries
The results in the previous section suggest that larger-than-standard rates of physical
capital depreciation may commonly exist in some developing countries. The same type of capital
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may have a much larger depreciation rate in some countries than in others, because of
undermainteance10 and extraordinary discard, the reasons for which are discussed below.
Various related literatures have suggested many economic forces that may influence the
level of capital maintenance. Tanzi and Davoodi [1997], using cross country data and regression
analysis, find that the countries with widespread corruption are associated with higher public
investment but lower expenditures on maintenance and operation. With the presence of
noncompetitive and nontransparent bidding and contracting procedures, the corruption ‘premium’
may be much higher on capital-intensive expenditures, and as a consequence, labour-intensive
activities, such as maintaining existing capital, are unattractive to the public officials.
The low level of capital maintenance may be related to the expected future utilization
rates of existing capital. As argued in Bitros [1976], the rational decision will ensure that the
discounted value of expected returns from maintaining old equipment or structures must be at
least equalized with maintenance expenditures thus incurred. Given that the profitability of
capital maintenance must be increasing in the intensity of future capital utilization, the lower the
expected rates of future capital utilization, the less is the expenditure on capital maintenance and
hence the larger is the capital discard rate. Winston [1984] conducted a survey of capital
utilization rates in selected industries for a sample of developing countries and found that capital
was generally underutilized in those countries. If, however, capital underutilization and high
costs of new capital goods relative to maintenance and repair costs exist simultaneously, as is
often the case in the developing countries, it would be difficult to predict how the expenditures on
maintenance, and thus the depreciation rates, would change on balance.
The time preference rate used by the firms in developing countries may also be relevant
to the country differences in depreciation rates. The theoretical findings in Becker and Mulligan
[1997], supported with empirical evidence in their paper, suggest that a low level of wealth and
uncertainty induce impatience or high time preference rate. An increase in the time preference
17
rate would result in a reduction in asset market value, which in turn implies a higher economic
depreciation rate. It remains to be further explored how the investment behaviour and
depreciation rate of each individual firm may depend on its discount rate.
{Insert Table 9 about Here}
Using the data collected from the World Bank surveys, Table 9 shows that high capital
depreciation observed in the manufacturing industries of some developing countries may be a
consequence of distortions due to government financing policies, such as special tax credits to
corporate investment, or subsidies to investment loans. Table 9 reports and compares the
depreciation rates between firms with government investment incentives and those without such
incentives for Indonesia and South Korea, the only two countries for which the surveys collect
relevant data on government-provided incentives. The depreciation rates are presented by
industry sector. Within the same industry in South Korea, the firms receiving government
incentives have higher depreciation rates than those without incentives. The overall depreciation
rate is 0.195 for all the government-supported firms combined, as compared with the rate of 0.07
for the firms with no support. The incentive-induced differences in depreciation rate also vary by
industry. For instance, for the automobile parts industry, the difference is as large as nearly 0.3,
but much smaller for the chemicals and garments and textiles industries. Government incentives
are likely to raise the relative cost of maintaining existing capital by causing the costs of new
investment to decline, and hence result in the substitution of new capital for appropriate
maintenance on old capital.
As shown in Panel B of Table 9, for the electronics sector in Indonesia, investment
incentives from the government causes a much higher depreciation rate (0.817 as compared to
0.343), whereas the rate differences for the other three industry sectors (food, chemicals,
garments and textiles) are much less significant. The overall depreciation rate for all firms with
support is 0.775, as compared to 0.712 for the firms with no support.
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6. Implications of High Depreciation for TFP Growth Estimates and Capital Growth
In this section, I use the Nehru and Dhareshwar [1993] data set on physical capital stock
covering the period 1950-1990 to examine how the estimates of TFP growth should be revised for
the developing countries in which high capital depreciation prevails. Before subsequent analysis,
the Nehru and Dhareshwar capital stock series are reproduced for all the sample countries, using
the depreciation rate of 0.04 assumed in that paper. Gross domestic fixed investment in the data
set includes investment in equipment (including machinery and transportation equipment) and
structures (including both residential and nonresidential construction). As a result, the
depreciation rates of fixed assets in Tables 6 and 7 are weighted with the depreciation rate of
residential structure, which is assumed to be 0.035 as in PWT 5.6, to obtain the aggregate
depreciation rate of physical capital stock for each country. The respective weights for business
fixed capital assets and residential structure are obtained from PWT 5.6, which reports on capital
stock compositions. For the African countries, the SNA deflators are used to obtain the implied
depreciation rates, which are more conservative as compared to those using the weighted
deflators. The resulting estimates are presented in Table 10.
{Insert Table 10 and Figures 1 about Here}
The estimates of physical capital depreciation rates given in Table 10 are used to
construct a new capital stock series for each of the seven countries. The time series of physical
capital-output ratios, computed using the new capital stock series and the series constructed with
the assumed rate of 0.04, are plotted and compared in Figure 1. Except for Kenya and
Zimbabwe, the old ratios have apparent positive trends for the sample countries during the period
1950-1990. However, the ratios of the new capital stock series to output have much less or no
significant trends for the countries with much higher implied depreciation rates. A higher
19
physical capital depreciation rate may lead to a lower growth rate of capital, which in turn will
revise the TFP growth estimates obtained in previous studies.
{Insert Table 11 about Here}
The TFP growth rate is estimated for each of the seven countries using the two sets of
capital stock series. In the estimation, a Cobb-Douglas production function is assumed, so that
the TFP growth rate is estimated as the residual between output growth and the weighted sum of
labour and capital growth. In Table 11, the TFP growth estimates in columns (7) and (9) are
obtained by treating raw labour and human capital as one explanatory variable and separately as
two variables, respectively. The growth rates in columns (4), (5), (6) and (8) are the trend
estimates by fitting exponential curves to the time series of output, physical capital, labour and
human capital, respectively, where human capital is measured by the average number of years of
education also taken from the Nehru and Dhareshwar data set. In the calculations for column (9),
the factor shares of physical capital, raw labour and human capital are assumed to be 0.4, 0.3 and
0.3, respectively, while for column (8) the share of labour is 0.6. Here, the values of the factor
shares are chosen to be consistent with the choices in Pritchett [1997, 2000].
Except for Indonesia, the new capital stock series had been accumulating at lower rates,
as compared to the old series. As a result, the resulting TFP growth estimates should be higher to
various degrees for these countries. For instance, in the case of Ghana, when the depreciation
rate changes from 0.04 to 0.17, the TFP growth estimates is revised from –0.0118 to –0.0017 if
human capital is combined with raw labour, or from –0.0189 to –0.0087 if human capital is
treated separately. With human capital and raw labour combined, a zero growth rate of TFP
would require a depreciation rate of close to 0.25 for Ghana (not shown in Table 11). In this
respect, some factors other than high depreciation (for example, capital underutilization and low
capital productivity) should also contribute to the negative estimates of TFP growth observed in
Pritchett [1997].
20
{Insert Figure 2 about Here}
One issue is worthy of further comments. As shown in the case of Indonesia, a higher
depreciation rate does not necessarily imply a lower growth rate of capital. As a time-invariant
depreciation rate is assumed and used throughout the paper to depreciate the value of capital
investment geometrically, faster depreciation of fixed capital assets may be associated with
higher volatility of capital stock growth. Figure 2 plots out the R-squares obtained in the
exponential fit of capital stock series against the depreciation rate. In the figure, as the
depreciation rate increases, the goodness of fit for all the countries decreases. This implies that
the growth rate of physical capital stock is more volatile when capital depreciates at a higher rate.
The relationship between capital depreciation rates and capital growth volatility also varies across
countries. The goodness of exponential fit for the three Asian countries is relatively stable in
response to the changes in the rate of capital depreciation, as compared with those for the four
African countries. It can be simulated how capital accumulates under different assumptions of
depreciation rate and investment series, a topic that is beyond the scope of this paper but should
be explored in further studies of capital accumulation in developing countries. Using Ghana as
an example, and for the depreciation rates of 0.04 and 0.172, Figure 2 also graphs the evolutions
of capital stock against time and the associated exponential fits.
7. Concluding Remarks
Using the firm level data sets on the resale values of capital assets and investment series
in a group of countries in Africa, East Asia and Southeast Asia, this paper estimates the economic
depreciation rates of physical capital stock for each individual firm as well as for all sample firms
combined. In the estimation, all capital assets, including business buildings and machinery and
equipment, have been deflated to a common basis, and where data are available, appropriate
adjustments made for the resale of assets during the measurement periods. The results indicate
21
that capital may have been depreciating at comparatively higher rates in the developing countries,
whereas the extent of high depreciation varies by country. This paper then reviews relevant
literatures on the possible causes of capital undermaintenance in developing countries, and shows
with empirical evidence that government-provided investment incentives induce high capital
depreciation in South Korea, and in some of the manufacturing industries in Indonesia. This
paper further calculates the TFP growth rates for all the sample countries, using the newly
estimated depreciation rates and capital stock series. The revisions to the growth rate of capital
stock necessarily lead to corresponding changes in the TFP growth estimates. Besides its growth
effect, lowering the high depreciation rates of fixed capital stock can also significantly stabilize
the process of capital accumulation and thus indirectly promote capital and output growth.
To understand the underlying causes for high depreciation in developing countries,
further research may fully develop a conceptual framework to explore the economic implications
of various political-economy factors for capital accumulation. Relevant inquiries may include
whether corruption, government and international financing policies may reduce the incentive to
well maintain existing assets and thus result in faster depreciation. Besides, an independent and
comprehensive industrial survey of capital stocks in developing countries is also needed for
systematically validating and measuring the depreciation rates in the developing countries.
NOTES:
1. Easterly and Rebelo [1993] use the depreciation rate of 7% uniformly for all countries and all periods, as
compared to 0.04 in Nehru and Dhareshwar [1993]. Penn World Table 5.6 uses 15% for machinery, 24%
for transport equipment, and 3.5% for constructions including both residential and nonresidential structures.
2. The aggregate capital stock data sets currently available for economic research are constructed by using
the perpetual inventory method and the standard assumptions about the capital depreciation rates.
3. In the presence of inefficiency, as argued in Pritchett [1997], the accounting cost incurred during creating
new capital may well exceed the economic cost, which is defined as, by Pritchett, the minimum cost of
creating the same amount of capital given the optimal (or undistorted) market prices of investment goods.
4. As Leonard [1985] points out, there is no systematic financial account in the government to keep track of
the accumulated depreciation on infrastructure capital. Also even though capital maintenance is
investment-type expenditure in the sense that it yields returns over a much longer run than most ‘current’
expenditures, maintenance expenditure has long been treated as a current operating cost of the government.
22
5. Net book value, as defined in the survey, is the initial value or acquisition cost of fixed assets less
accumulated depreciation charges. Here, it is considered as an approximate for the asset market value.
6. The capital depreciation rate estimates obtained through the above equation are de facto the assetsweighted averages of the depreciation rates during the time period under study. However, the capital
depreciation rates, especially at the firm level, should vary in response to various factors such as corporate
tax policies, and reallocation of physical capital assets across firms and sectors.
7. Such factors may include the corruption surcharge in corporate procurement of assets, which may differ
across firms.
8. However, if firm-specific investment goods deflators are used for each individual firm, such deflators,
which are calculated from the replacement values for the firm’s fixed assets and investment, could be
heavily biased due to measurement errors and reporting errors.
9. Using the equipment level data from aerospace industry auctions, Ramey and Shapiro [2001] show that
capital is sector-specific, and reallocation of sector-specific capital, combined with thinness of asset resale
markets, results in substantial decline in market value.
10. Undermaintenance on public capital in particular is commonly observed for many developing countries
[World Bank 1994].
23
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Journal of Political Economy, 84(5), 917-936.
Becker, G.S. and Mulligan, C.B., 1997, The Endogenous Determination of Time Preference.
Quarterly Journal of Economics, 112(3), 729-753.
Devarajan, S., Easterly, W. and Pack, H., 2003, Low Investment is not the Constraint on African
Development. Economic Development and Cultural Change, 51(3), 547-571.
Easterly, W., 1999, The Ghost of Financing Gap: Testing the Growth Model Used in the
International Financial Institutions. Journal of Development Economics, 60(2), 423-438.
Easterly, W. and Rebelo, S., 1993, Fiscal Policy and Economic Growth. Journal of Monetary
Economics, 32(3), 417-458.
Fraumeni, B.M., 1997, The Measurement of Depreciation in the U.S. National Income and
Product Accounts. Survey of Current Business, 7-23.
Hulten, C.R., 1990, The Measurement of Capital, in: E.R. Berndt and J.E. Triplett (eds) Fifty
Years of Economic Measurement, Studies in Income and Wealth, (Chicago: Chicago University
Press for the National Bureau of Economic Research), pp. 119-152.
24
Hulten, C.R., 1996, Infrastructure Capital and Economic Growth: How Well You Use It May Be
More Important Than How Much You Have. NBER Working Paper, No. 5847.
Hutlen, C.R. and Wykoff, F.C., 1981, The Estimation of Economic Depreciation Using Vintage
Asset Prices. Journal of Econometrics, 15(3), 367-396.
Jorgenson, D.W., 1989, Capital as Factor of Production, in: D.W. Jorgenson and R. Laudau (eds)
Technology and Capital Formation, (Cambridge, Massachusetts: MIT Press), pp. 1-35.
Jorgenson, D.W., 1996, Empirical Studies of Depreciation. Economic Inquiry, 34(1), 24-42.
Leonard, H.B., 1985, Checks Unbalanced: The Quiet Side of Public Spending (New York: Basic
Books).
Nehru, V. and Dhareshwar, A., 1993, A New Database on Physical Capital Stock: Sources,
Methodology and Results. Revista de Analisis Economico, 8(1), 37-59.
OECD, 1993, Methods Used by OECD Countries to Measure Stocks of Fixed Capital, National
Accounts: Sources and Methods No.2 (Paris: Organisation for Economic Co-Operation and
Development).
OECD, 2001, Measuring Capital: OECE Manual: Measurement of Capital Stocks, Consumption
of Fixed Capital and Capital Services (Paris: Organisation for Economic Co-Operation and
Development).
25
Oliner, S.D., 1996, New Evidence on the Retirement and Depreciation of Machine Tools.
Economic Inquiry, 34, 57-77.
Penn World Table (Mark 5.6), Centre for International Comparisons, University of Pennsylvania
(available at: http://pwt.econ.upenn.edu/home.html).
Pritchett, L., 1997, Mind Your P's and Q's: the Cost of Public Investment in Not the Value of
Public Capital. World Bank Working Paper, No. 1660.
Pritchett, L., 2000, The Tyranny of Concepts: CUDIE (Cumulated, Depreciated, Investment
Effort) is Not Capital. Journal of Economic Growth, 5(4), 361-384.
Ramey, V.A. and Shapiro, M.D., 2001, Displaced Capital: A Study of Aerospace Plant Closings.
Journal of Political Economy, 109(5), 958-992.
Tanzi, V. and Davoodi, H., 1997, Corruption, Public Investment, and Growth. IMF Working
Paper, No. 97/139.
Winston, G., 1984, The Utilization of Capital in Developing Countries: A Survey of Empirical
Estimates. Prepared for Global and Conceptual Studies Branch, Division for Industrial Studies,
United Nations Industrial Development Organization.
World Bank, 1994, World Development Report 1994: Infrastructure for Development
(Washington D.C.: Oxford University Press).
26
World Bank, 2000a, African Development Indicators CD-ROM (Washington D.C.: World Bank).
World Bank, 2000b, World Development Indicators CD-ROM (Washington D.C.: World Bank).
27
Table 1. Data Description
[1]
[2]
Country
Cote d'Ivoire
Ghana
Kenya
Zimbabwe
Indonesia
Philippines
South Korea
Period
1991-95
1992-93
1993-94
1993-95
1997-98
1996-98
1996-98
[3]
[4]
[5]
[6]
Total
229
212
215
213
562
541
863
Fixed
Assets
61
.
.
79
401
162
485
Buildings
47
.
.
.
389
170
434
ME
59
115
71
102
406
203
473
[7]
Resale of
Fixed
Assets
18
.
.
25
.
.
.
[8]
[9]
Resale of
Buildings
2
.
.
.
.
.
.
Resale
of ME
15
4
3
29
.
.
.
Column 3 is the number of firms in the data set, or the number of firms that responded to the World Bank surveys. Columns 4
through 6 are the numbers of the firms for which the data needed for measuring economic depreciation are available for the type of
asset. Columns 7 through 9 are the number of firms that have sold assets during the measurement period.
Table 2. Summary of Variables
Country
Kt
Cote d’Ivoire
Current market value
Ghana
Current market value
Kenya
Current market value
Zimbabwe
Current market value
Indonesia
Net book value
South Korea
Net book value
Philippines
Net book value
It
Nominal
investment
Nominal
investment
Nominal
investment
Nominal
investment
Nominal
investment
Nominal
investment
Nominal
investment
∑I
v ,t +1
v ≤t
.
Current replacement
value
Current replacement
value
Current replacement
value
DIt
Resale price
Resale price
Resale price
Resale price
.
.
.
.
.
.
Table 3. Investment Goods Deflators
Panel A. Deflators Calculated from System of National Accounts
Cote d'Ivoire
Ghana
Kenya
Zimbabwe
1.000
.
.
.
1990
0.983
.
.
.
1991
1.018
1.000
.
.
1992
0.900
2.316
1.000
1.000
1993
1.734
.
1.180
1.210
1994
1.041
.
.
1.293
1995
1996
1997
1998
Indonesia
.
1.000
2.042
Philippines
1.000
1.045
1.119
South Korea
1.000
1.057
1.114
Panel B. Deflators Calculated from Assets Replacement Costs
Ghana
Kenya
Zimbabwe
Fixed
ME
ME
ME
Assets
1.000
.
.
.
1992
3.006
1.000
1.000
1.000
1993
.
1.751
1.473
1.777
1994
.
.
1.183
1.173
1995
30
Table 4. Calculating the Implied Depreciation Rate of Fixed Assets for a
South Korean Firm: An Illustration
596
Firm ID
(in million won)
Given:
Investment
[1]
[2]
1996
1997
100
100
[3]
1998
20
[4]
1996
3600
Fixed Assets
[5]
1997
3400
[6]
1998
2939
Investment Goods Deflator
[7]
[8]
[9]
1996
1997
1998
1.000
1.057
1.114
Calculated:
Investment - Deflated Value
[1]'
[2]'
[3]'
1996
1997
1998
100
95
18
Fixed Assets - Deflated Value
[4]'
[5]'
[6]'
1996
1997
1998
3600
3218
2637
Implied Rate of Depreciation
[10]
[11]
[12]
1996-98
1996-97
1997-98
0.160
0.133
0.186
(a) The formulas used in calculations:
[i]'=[i]/[7], for i = 1, 4; [i]'=[i]/[8], for i = 2, 5; [i]'=[i]/[9], for i = 3, 6;
[10] = 1 - {[[2]'^2-4*[4]'*([3]'-[6]')]^0.5-[2]'}/(2*[4]'), which is the solution to
the equation [6]'=(1-[10])^2*[4]'+(1-[10])*[2]'+[3]';
[11] is solved from the equation (1-[11])*[4]'+[2]'=[5]'; and
[12] is the solution to (1-[12])*[5]'+ [3]'= [6]'.
(b) 'Investment' occurs during the period indicated, while 'Fixed Assets' refers to
the end-of-the-period value.
31
Table 5. Percentile Summary for the Depreciation Rates of Fixed Assets:
Panel A. Use Deflators implied from SNA
Cote d'Ivoire
Ghana
1991-95
1992-93
0.2723
0.3437
Mean
0.0420
0.0507
Standard Error
-0.0438
-0.3185
10th
0.1265
0.0624
25th
0.2594
0.5079
Median
0.3897
0.6680
75th
0.4578
0.8867
90th
Kenya
1993-94
-0.1495
0.1492
-1.4568
-0.4236
0.1661
0.5256
0.8727
Zimbabwe
1993-95
0.1118
0.0482
-0.4377
-0.0548
0.2109
0.3826
0.5856
Panel B. Use Weighted Deflators
Ghana
Kenya
Zimbabwe
1992-93
1993-94
1993-95
0.4943
0.2250
0.2221
Mean
0.0391
0.1006
0.0418
Standard Error
-0.0159
-0.6565
-0.2501
10th
0.2775
0.0401
0.0704
25th
0.6208
0.4377
0.3141
Median
0.7442
0.6801
0.4595
75th
0.9127
0.9141
0.6166
90th
For Ghana and Kenya, the depreciation rates are for machinery and equipment.
Indonesia
1997-98
0.8408
0.0644
0.4278
0.5234
0.6142
0.9515
1.2044
Philippines
1996-98
0.2585
0.0383
-0.0161
0.0711
0.1659
0.3300
0.9587
South Korea
1996-98
0.0927
0.0201
-0.0628
0.0527
0.1186
0.2010
0.3452
Table 6. Depreciation Rates for the African Countries: Sample Weighted Averages
Fixed Assets
Buildings
ME
SNA
Weighted
SNA
Weighted
SNA
Weighted
Country
Period
Deflator
Deflator
Deflator
Deflator
Deflator
Deflator
1991-95
0.148
.
0.100
.
0.183
.
Cote d'Ivoire
1992-93
0.249
0.303
.
.
0.448
0.575
Ghana
1993-94
0.123
0.236
.
.
0.158
0.432
Kenya
1993-95
0.183
0.286
.
.
0.266
0.300
Zimbabwe
(a) The depreciation rates under 'SNA Deflator' are calculated by using the deflators implied from the country's
national accounts, while those under 'Weighted Deflator' are calculated by using the deflators obtained from the
replacement values of fixed assets between successive years.
(b) In calculating the depreciation rates of fixed assets in Ghana and Kenya, the depreciation rate of buildings in
Cote d'Ivoire is weighted with their respective rates for machinery and equipment. The relative market values of land
And buildings and machinery and equipment (in the year of 1993 for Ghana and 1994 for Kenya) are used as weights
in the calculation.
33
Table 7. Depreciation Rates for the Asian Countries: Sample Weighted Averages
Fixed Assets
Buildings
Country
1996-98
1996-97
1997-98
1996-98
1996-97
.
.
0.772
.
.
Indonesia
0.286
0.302
0.276
0.229
0.258
Philippines
0.116
0.217
0.024
0.062
0.144
South Korea
34
1997-98
0.755
0.210
-0.020
Machinery and Equipment
1996-98
1996-97 1997-98
.
.
0.778
0.363
0.362
0.363
0.174
0.294
0.072
Table 8. Depreciation Rates: Sample Weighted Averages Using
Depreciation Expenses Recorded on the Company Account
Aggregate
Depreciation Rate
Country
Period
Assets
.
.
.
Cote d'Ivoire
1992-93
ME
0.076
Ghana
1993-94
ME
0.066
Kenya
1993-94
Fixed Assets
0.063
Zimbabwe
1994-95
Fixed Assets
0.050
1996-97
Fixed Assets
0.020
Indonesia
1997-98
Fixed Assets
0.010
1996-97
Fixed Assets
0.070
Philippines
1997-98
Fixed Assets
0.010
1996-97
Fixed Assets
0.100
South Korea
1997-98
Fixed Assets
0.090
Table 9. Capital Depreciation Rate and Government Incentives
by Industry Sector:
Panel A. South Korea (1996-98)
Sector
Electronics
Auto Parts
Chemicals
Machinery
Garments and Textiles
Overall
Financial
Support
No Financial
Support
Overall
0.284
(42)
0.204
(24)
0.135
(48)
0.107
(25)
0.154
(33)
0.195
(172)
0.111
(22)
-0.095
(30)
0.091
(76)
-0.046
(39)
0.129
(65)
0.07
(232)
0.195
(72)
0.021
(64)
0.115
(138)
0.012
(74)
0.133
(105)
0.118
(453)
Panel B. Indonesia (1997-98)
Incentives for
No
Investment
Incentives
Sector
Overall
0.817
0.343
0.75
Electronics
(22)
(26)
(48)
0.636
0.712
0.685
Food
(28)
(102)
(130)
0.851
0.776
0.8307
Chemicals
(39)
(77)
(116)
0.639
0.748
0.656
Garments and Textiles
(21)
(76)
(97)
0.775
0.712
0.753
Overall
(110)
(281)
(391)
(a) The numbers in the parentheses are the number of firms.
(b) 'Financial Support' and 'Incentives for Investment' are the words used in the
surveys for South Korea and Indonesia, respectively.
Table 10. Implied Depreciation Rates for Aggregate Physical Stock of Capital
Country
Period
SNA Deflator
Weighted Deflator
1991-95
0.102
.
Cote d'Ivoire
1992-93
0.172
0.207
Ghana
1993-94
0.092
0.164
Kenya
1993-95
0.168
0.259
Zimbabwe
1997-98
0.607
.
Indonesia
1996-99
0.230
.
Philippines
1996-98
0.099
.
South Korea
(a) The depreciation rate of aggregate physical stock of capital is calculated as the weighted
average of the depreciation rates of fixed assets reported in Tables 6 and 7 and that of
residential construction. The weights are obtained from the Summer-Heston Penn World Table
5.6, and residential construction is assumed to depreciate at 0.035 for all sample countries;
(b) For Ghana, I use Kenya's capital stock composition as weights, and for Indonesia, use
Philippines' capital stock composition as weights, as the Penn World Table 5.6 does not report
capital stock composition for Ghana and Indonesia.
37
Table 11. Estimates of TFP Growth Rates
[1]
[2]
[3]
Country
Cote d'Ivoire
Period
1960-90
Ghana
1951-90
Kenya
1951-90
Zimbabwe
1955-90
Indonesia
1951-90
Philippines
1951-90
South Korea
1954-90
Physical
Capital
Depreciation
Rate
0.0400
0.1016
0.0400
0.1722
0.0400
0.0917
0.0400
0.1676
0.0400
0.6072
0.0400
0.2300
0.0400
0.0987
[4]
[5]
[6]
Output
Growth
Rate
0.0537
0.0537
0.0178
0.0178
0.0518
0.0518
0.0434
0.0434
0.0593
0.0593
0.0472
0.0472
0.0803
0.0803
Physical
Capital
Growth
Rate
0.0781
0.0625
0.0381
0.0127
0.0335
0.0226
0.0359
0.0145
0.0710
0.0721
0.0655
0.0500
0.1184
0.1142
Labor
Growth
Rate
0.0374
0.0374
0.0240
0.0240
0.0339
0.0339
0.0341
0.0341
0.0240
0.0240
0.0302
0.0302
0.0229
0.0229
[7]
TFP
Growth
Rate w/o
human
capital
0.0000
0.0063
-0.0118
-0.0017
0.0181
0.0224
0.0086
0.0171
0.0165
0.0161
0.0029
0.0091
0.0192
0.0209
[8]
Human
Capital
Growth
Rate
0.0968
0.0968
0.0475
0.0475
0.0405
0.0405
0.0247
0.0247
0.0376
0.0376
0.0165
0.0165
0.0377
0.0377
[9]
TFP
Growth
Rate w/
human
capital
-0.0178
-0.0116
-0.0189
-0.0087
0.0161
0.0204
0.0114
0.0200
0.0124
0.0120
0.0070
0.0132
0.0148
0.0164
(a) The physical capital depreciation rate of 0.04 is used in Nehru and Dhareshwar [1993] in constructing physical capital stock series. The
implied depreciation rates are taken from Table 10.
(b) The calculations of the 'TFP growth rate w/o human capital' assume the output share of physical capital to be equal to 0.4, and the output
share of labor 0.6, while the calculations of the 'TFP growth rate w/ human capital' assume 0.3 for the output share of human capital and
0.3 for raw labor.
Figure 1. Capital-Output Ratios
Gh a n a 19 5 1- 9 0
C o t e d ' I v o i r e 19 6 1- 9 0
K/ Y
K/ Y
3. 00
3. 00
2. 50
2. 50
0.040
2. 00
0.040
2. 00
1. 50
1. 50
0.102
1. 00
0.172
1. 00
0. 50
0. 50
0. 00
0. 00
1951 1955 1959 1963 1967 1971 1975 1979 1983 1987
1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990
K e n y a 19 5 1- 9 0
Z i m b a b we 19 5 5 - 9 0
K/ Y
K/ Y
5. 00
8. 00
7. 00
4. 00
0.040
6. 00
5. 00
0.040
4. 00
3. 00
3. 00
2. 00
0.092
2. 00
0.168
1. 00
1. 00
0. 00
0. 00
1950 1954 1958 1962 1966
1970 1974 1978 1982 1986 1990
1954
1958
1962
1966
1970
1974
1978
1982
1986
1990
P h i l i p p i n e s 19 5 1- 9 0
I n d o n e si a 19 5 1- 9 0
K/ Y
K/ Y
2. 50
3. 50
3. 00
2. 00
2. 50
1. 50
0.040
2. 00
0.040
1. 50
1. 00
0.607
0. 50
1. 00
0.23
0. 50
0. 00
0. 00
1950 1954 1958 1962 1966 1970 1974 1978 1982 1986 1990
S o u t h K o r e a 19 5 4 - 9 0
K/ Y
2. 50
2. 00
0.040
1. 50
1. 00
0.099
0. 50
0. 00
1953
1957
1961
1965
1969
1973
1977
1981
1985
1989
1950 1954 1958 1962 1966 1970 1974 1978 1982 1986 1990
Figure 2. Depreciation Rate and Capital Stock Growth Volatility
R - Squa r e f r om
E x pone nt i a l Fi t
D ep r eciat io n R at e and Exp o nent i al F i t
o f C ap it al St o ck Ser ies
C a pi t a l S t oc k
C ap it al St o ck Evo lut io n and Exp o nent ial F it
Ghana 19 50 - 19 9 0
1.20
1.00
Expon. R2 =0.8882
Korea
Philippines
0.80
Indonesia
0.04
0.60
Cot e d'Ivoir e
0.40
0.20
Kenya
Zimbabwe
Ghana
0.00
P hy s i c a l C a pi t a l D e pr e c i a t i on R a t e
0.172
Expon. R2 =0.3568