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Applying a New Approach to Estimate the Net Capital Stock of Transport Infrastructure by Region in South Korea

Author & Article History

*Professor, KDI School of Public Policy and Management (e-mail: jongyearn@gmail.com; jonlee@kdischool. ac.kr).

Manuscript received 16 March 2018; revision received 19 March 2018; accepted 29 May 2018.


Regional Capital Stock, Transport Infrastructure, Modified Benchmark Year Method

JEL Code

H54, R53, R42, R58

I. Introduction

Estimating the size of capital stock by region is an important task that serves as the foundation of related research such as that on the growth of the national economy and the allocation of budgetary funding and resources in social overhead capital (SOC) investments for balanced regional growth. Due to the lack of basic data in South Korea, however, no official time-series statistics of regional capital stock is secured and estimation methods are very limited.

Methods of estimating the capital stock can be divided into direct survey methods for estimating stocks through investigations by telephone and/or field surveys and indirect estimation methods using available statistical data. Representative indirect estimation methods include the perpetual inventory method (PIM), the benchmark year method (BYM), and the polynomial BYM (for a detailed description of each, see Kim and Kwon, 2002, pp.16-22).

Types of capital stock are divided into gross capital stock and net capital stock. Gross capital stock refers to an estimate of the cost of repurchasing all fixed assets still in use at current prices, irrespective of the age of the assets. Net capital stock, on the other hand, is the market value of the fixed assets of the economy at some point in time. It represents the gross capital stock minus the consumption of fixed capital accumulated up to some point in time (Pyo, Jung and Cho, 2007, p. 143).

Gross capital stock using the PIM is the total investment in assets within the useful life period, and net capital stock can be estimated as gross capital stock excluding depreciation. Therefore, in order to apply the PIM, it is necessary to provide not only a long-term investment time-series but also information about the economic useful life of the asset and the disposal distribution. However, without credible data available in South Korea, it is impossible to use the PIM as used by most OECD member countries. For this reason, international comparisons are not possible.

As an alternative, the BYM uses the initial capital stock at the base year obtained through a direct survey method and the time-series of the investment over the estimation period. This method has the advantage of reducing the estimation error because the estimated results can be verified with survey data from the base year. Unfortunately, it also has the disadvantage of upward bias as it moves away from the base year because it cannot reflect the sudden disappearance of the capital or discoloration of the value (Kim, 2011, p. 195).

Finally, the polynomial BYM estimates capital stock between baselines using capital stock data for two base years and the investment time-series during that period. Therefore, it cannot be used in the absence of capital stock data for multiple base years (for more detailed comparisons of estimation methods in the context of South Korea, see Seo, 2000).

In South Korea, the National Wealth Survey (NWS) using the direct survey method was conducted once every ten years in 1968, 1977, 1987 and 1997. Since 1998, the indirect estimation method based on the 1997 survey results has been adopted because the direct investigation approach was deemed to be too expensive. Subsequently, the National Asset Statistics (NAS) as a replacement of the NWS has been released.

In order to replace the NAS, the Bank of Korea (BOK) and Statistics Korea provisionally announced in 2014 the results of the joint development of the National Balance Sheet (NBS) for the nation’s net assets up to 2012 and announced the preliminary results of the national balance sheet up to 2013 in May of 2015. The NBS was intended to comply with the United Nations’ new national accounts system (System of National Accounts 2008), which included non-financial assets, financial assets and financial liabilities, as opposed to how the existing NAS compiled non-financial assets only (Statistics Korea and Bank of Korea, 2015, p.22). However, it is also impossible to estimate the capital stock of each region using the SOC data with both the NAS and the NBS.

Given such a limitation, this study proposes a means of estimating regional capital stock by modifying the BYM and applies it to estimate the regional net capital stock by sector in transport infrastructure, specifically roads, railroads and ports. Estimations by this method are done in three stages. First, the method estimates the time-varying sectoral depreciation rates using the sectoral net capital stock and the investment amount for each period. Second, it estimates the net capital stock of each period using the net capital stock in the base year and the investment amount in each period. Third, in order to ensure that the sum of net capital stocks by region is equal to the nationwide estimate, the national estimates are allocated to each region according to the proportion of the values derived from the previous stage.

The proposed method can alleviate some well-known problems of conventional BYMs. First, it is possible to realize the improvement of eliminating the upward bias of conventional BYMs, by which the sum of regional estimated values exceeds the national estimated value as the distance from the base year is increased. Second, it is possible to enhance the reliability of the estimation results by allowing time-varying depreciation rates for each sector instead of fixing these rates arbitrarily as some conventional BYMs do.

The rest of this paper is structured as follows. Section II examines previous studies attempting to estimate capital stock in South Korea. Section III explains the estimation method proposed by this study and Section IV discusses the results of estimating the regional net capital stock of the transport infrastructure in South Korea using this estimation method. Section V compares the results of this study with those of similar previous studies and discusses ways to use them in future policy-making efforts. Finally, Section VI presents the concluding remarks.

II. Related Literature

As shown in Table 1, previous studies which estimate the capital stock of South Korea given the limitations of the above-mentioned data cannot use the PIM completely, instead using the BYM, the polynomial BYM or the PIM in part. Only Kim and Cho (2006) have estimated the SOC using the modified PIM, but they targeted only ports in their study. Moreover, one can confirm that related studies commonly used estimation methods involving annual investment amounts in conjunction with the NWS. For a more detailed explanation of these previous studies, the reader can refer to Moon (2014) and Gong (2015).




Note: 1) GCS=Gross Capital Stock and NCS=Net Capital Stock. 2) Y##=National wealth statistics at year ##. 3) NA=National Account, NIA=National Income Account, iMOCT=internal data of the Ministry of Construction and Transport, iBOK=internal data of the Bank of Korea, CIS=Construction Industry Survey, GFCF=gross fixed capital formation table (supplementary table of the Bank of Korea’s input-output table), NCTP=national comprehensive territorial plan (actual value) and VS=various sources. 4) BY=benchmark year method, PBY=polynomial benchmark year method, PI=perpetual inventory method, MPI=modified perpetual inventory method and RA=regional allocation.

Previous studies also used a variety of data to estimate capital stock investment by year. Early studies, such as those by Kim (1996) and Pyo (1998), used the gross fixed capital formation values from the National Accounts and from National Income Accounts. However, this is limited in that with these approaches, SOC stock cannot be divided according to different sectors. Later, Ha and Cho (2000) and Hyun and Kwon (2002) used internal data of the Ministry of Construction and Transportation and the BOK as annual investment levels. In these cases, the credibility of investment data is weak due to inconsistencies over time and large variations across datasets (for a more detailed explanation, see Kim, 2010, pp.74-76). In order to overcome these limitations, Kim (2002) proposed a method which used investment data from the Construction Industry Survey (CIS) of Statistics Korea (formerly the Construction Industry Statistics Survey (before 2007)). This method became a typical way in the context of South Korea to which it is difficult to apply the PIM.

In addition, when estimating capital stock by region, it can be seen that certain data limits restrict the subject to SOC. At the nascent stage of the related research, the capital stock of the nation was allocated according to the capacity of the infrastructure, such as extensions of roads and railways, and the sizes of the facilities of ports and airports (Park, Jun and Park, 1996; Byeon, 2000; Ha and Cho, 2001). This method, however, incurs a major disadvantage in that accurate local allocations of stocks estimated according to monetary units cannot be performed. To overcome this challenge, Kim (2010) adopts a method which allocates regions using the progress payments of investments in CIS via the method of Kim (2002). In so doing, the procedure searches for the “progress payment of public construction in SOC by region” such that each yearly progress payment amount for domestic construction in SOC divided by region is multiplied by the proportion of the public construction amount from among the total progress payments in SOC for each year. This method has been established as a typical method with regard to the distribution of capital stock by region.

On the other hand, several studies have attempted to examine the effects of local capital stocks on local economies after estimating them. Park, Jun and Park (1996) showed that the influence of SOC is approximately 60% of that of private capital according to regional production function estimations. In particular, it has been shown that the transport sector contributes significantly to the increase in production compared to non-transport sectors. Byeon (2000) also estimated regional production and employment functions. As a result of estimating the regional production function, the effect of SOC and private capital on the gross domestic product (GDP) was found to be similar, and traffic and communication facilities have a greater impact on regional development than do other facilities. As the economy grows, the effects of SOC on regional development decline. Moreover, the regional employment function estimation shows that SOC affects local employment in the order of regional utilization facilities, transport and communication facilities, total SOC, and other facilities.

Ahn and Kim (2006) examined the relationship between the regional allocation policy for transport infrastructure and the growth of the regional economy. First, they concluded through a cointegration analysis that road investments are not the cause of the gaps in regional economic growth. Second, as a result of a causality test, it was found that investments in growing regions expanded regional gaps before 1998, whereas the gaps between regions were reduced after 1999, as investments in the transport infrastructure affected regional economic growth in a limited manner and the growing regions did not drive investment demand. Third, they concluded that the interregional allocation of investments in infrastructure gradually shifted with concerns over efficiency. The rigor of their analysis, however, is limited given the fact that their conclusion stemmed from the finding that the marginal productivity of the transport infrastructure is similar to that of private capital.

Gong and Kim (2016) estimated the spatial lag model (SAM) using the SOC net capital stock estimated by Gong (2015). They show that the building of transport infrastructure can lead to growth in the affected region and in neighboring areas but that the effect of non-transport infrastructure is reversed. They judged that investments in non-infrastructure areas reflect equity concerns and the public interest.

III. A New Approach to Estimate Capital Stock by Region

As discussed above, because capital stocks in the transport sector are not broken down into regional and sectoral data in South Korea, it is necessary to use estimations. In this paper, we propose a modified BYM to obtain more reasonable estimates. Unlike previous research, we use the method of the regional allocation of quarterly net stock data by sector provided by the BOK. In other words, we regard the time-series data of secured sectoral capital stock as the national amount for each sector. This is done to compensate for the shortcomings of the conventional BYM, which does not reflect the sudden disappearance of capital or the discontinuance of value, as mentioned above, and which tends to show upward bias as the outcomes move away from the base year.

Moreover, with the proposed method, the depreciation rates for each segment are allowed to have different values over time. With this flexibility, the depreciation rate in this study can be accurately calculated for each sector and period using survey data. This generality stands in contrast to a recent study by Gong (2015), which is most similar to this study. That study applies the depreciation rate according to SOC assets as of 2011 from the NBS, which are assumed to be identical to the depreciation rate according to the SOC throughout the period.

However, a “negative” depreciation rate is still likely to be obtained due to the difference between the stock deflator and the flow deflator and the differences in the valuation methods of the assets according to the dataset used (Kim, 2011, p.197). The negative depreciation rate problem has been consistently raised in stock-estimating studies, but there remains no clear solution without a significant improvement in the data. Moreover, if the estimate is revised, it will negate the numerical value of the NWS (Kim, 2004, p.91). At present, therefore, we accept the limitations of the data and proceed with the estimation.

A. Background and Assumption

In this study, we assume that the most recent available data on the regional and sectoral capital stock provided in NWS 1997 is the stock of the base year. Similar to Kim (2010; 2011) and Gong (2015), we use publicly funded progress payment amounts of regional investment in SOC from the CIS as the investment amount. Table 2 shows the type of construction involved. In order to obtain quarterly data, the investment amount is assumed to be identical quarterly, and the actual investment amount in each case is based on the quarterly value of the GDP deflator in the construction sector.


Note: The numbers in parentheses are the work type classification codes in the CIS.

Source: Adopted from Statistics Korea (2015), pp.72-73, and arranged.

The targeted transport infrastructure is limited to roads, railways and ports. This is done fundamentally because the BOK’s quarterly net capital stock data show that the transport infrastructure is divided into roads, airports, railways and ports. Airports included in the road category here pertain to runways. In Gong (2015), the type of construction at airport facilities is also considered to be runways when calculating the investment amount. In that there are no available time-series of quarterly net capital stock data and considering that the stock of airports is estimated to reach at most one to two percent of that of roads in previous studies (Kim, 2011; Gong, 2015), airports (runways) were included in the road category.

In addition, the BOK’s quarterly net capital stock data is divided into the government and private sectors according to the current NAS sector classification. The capital stock of the transport infrastructure in this study adopts these sums for the following reasons. First, the function of the facility is a more important consideration than the identity of the client of the transport infrastructure capital stock. In other words, unlike other sectors, transport infrastructure is used not only for private investment but also for providing public services such as government investments.


Note: A quasi-corporate enterprise means a private company that is large enough to report a balance sheet or income statement to the National Tax Service, and private companies not falling into this category are included as households and non-profit organizations.

Source: Rearranged from Table II-2 in Bank of Korea (2014), p.25.

Third, investments in transport infrastructure are made not only by public corporations but by private investments, typically in significant amounts. Figure 1 shows the trend of private investment compared to fiscal investment in the SOC sector. In particular, since the mid-2000s, private investment has accounted for seven to seventeen percent of the total investment for each year. Table 5 compares the self-investment amounts by public corporations and private capital investments with a governmental budget for SOC. It can be confirmed once again that the shares of public corporations and the private sector are significant.


Source: Rearranged from Table 3 in Cho and Park (2013), p.4 and internal data of the Ministry of Strategy and Finance.


Source: Internal data of the Ministry of Strategy and Finance.


Note: 1) Figures in parentheses represent the proportion of the total investment. 2) * Private investment accounts for nationally managed businesses, with the amount in 2015 preliminary.

Source: Rearranged from Table 1-3 in the Working Group of the SOC Field in the National Finance Operation Plan (2015), p.6.

Finally, the regional unit was set to seven metropolitan cities and nine provinces in South Korea. Although it is not possible to classify by city or county in more detail due to data limitations, it is possible to classify all metropolitan cities and provinces, excluding the Sejong Special Self-Governing City, with the NWS 1997 data as the base year. Sejong Special Self-Governing City, which was launched in 2012, was included in Chungcheongnam-do (do = province), to which it previously belonged to.

B. Estimation Strategy

To estimate the transport infrastructure stock by region, this study uses the modified BYM divided into three stages. In the first stage, the time-variable depreciation rates are calculated by sector. Let δjt be the depreciation rate of sector j at time t (quarterly spaced from 1998 to 2014 in the data); hence, we can use the formula

to obtain each period’s depreciation rate δjt sequentially. Here, jep-40-2-23-e002.jpg and jep-40-2-23-e003.jpg represent the sectoral net capital stock and investment (progress payment by construction type), respectively, and their time-series {jep-40-2-23-e002.jpg} and {jep-40-2-23-e003.jpg} are obtained from data from the BOK and the CIS, respectively.

Meanwhile, it can be assumed that the depreciation rate of capital stock by sector may change depending on the region more flexibly, but it is considered that there are no large differences between regions of specific sectors in South Korea in a given epoch and that it is impossible to acquire suitable data. Therefore, depreciation is assumed to be different for each sector but not for different regions. In the second stage, the ratio of the interregional distribution of capital stock by region and sector is obtained. Substituting the depreciation rates of capital stocks by sector as obtained above, δjt into the equation

the “preliminary” time-series of regional and sectoral capital stock, {jep-40-2-23-e005.jpg}, can be obtained for each region i and sector j at time t . In so doing, using the capital stock value of each region and sector of NWS 1997 (fourth quarter) corresponding to the base year, jep-40-2-23-e006.jpg, and the time-series of investment by region and sector of the CIS, {jep-40-2-23-e007.jpg}, the values in the time-series {jep-40-2-23-e005.jpg} can be obtained sequentially for all time points.

The above-mentioned time-series of capital stock by region and sector, {jep-40-2-23-e005.jpg}, is called the “preliminary” value because the estimated regional capital stock using the conventional BYM may show a large difference from the actual value after a long period of time from the base year (In fact, the total of these regional estimates, jep-40-2-23-e008.jpg, revealed a significant overestimation compared to the national level data of the BOK, jep-40-2-23-e002.jpg).

In the third stage, the capital stock by sector at the national level is allocated by region. Rather than taking the level of the time-series obtained in the previous step as the capital stock for each region and sector, it would be more appropriate to take the ratio between them only and allocate more accurate capital stock estimates to the corresponding ratio. Finally, it is possible to establish the regional and sectoral capital stock time-series, { Cijt }, the entire procedure of the estimation strategy is illustrated in Figure 2.


IV. Estimation Results

Figures 3, 4 and 5 show the regional transport infrastructure capital stock estimated through the above-mentioned method for roads, railroads and ports, respectively. All cases are the real net capital stocks of transport infrastructure chained at 2010, and the unit is billion Korean won (KRW).

First, for roads, as shown in Figure 3, the stock increase is more prominent in provinces than the metropolitan cities. This suggests that more roads for inter-regional traffic are replenished than for intra-regional traffic. From the data in CIS, in fact, during the period from 2000 to 2014, the actual investment amount by the central and local governments in metropolitan cities and provinces was 23.2 trillion KRW and 175.9 trillion KRW, respectively, showing a considerable discrepancy.




Among metropolitan cities, stocks in Seoul were significantly higher than those in Incheon and Busan. However, after the rapid increase of stocks in Incheon in the early 2000s, this data tended toward a constant gap. Subsequently, Daegu followed with a weak increase. On the other hand, the stock of Gwangju was estimated to be the lowest, but it did not show much of a difference from Ulsan and Daejeon, which showed lower levels among the comparison group.

For provinces, the stock of Gyeonggi-do is highest, as expected from its unrivaled high level of urbanization. Next, Gyeongsangbuk-do and Gyeongsangnam-do are close to each other, and the stocks of Gangwon-do and Jeollanam-do are shown to converge at a similar level more recently. It can be seen that the amounts for Gangwon-do and Jeollanam-do grew relatively high in the early 2000s and in the late 2000s, respectively. Also, Chungcheongnam-do, Jeollabuk-do and Chungcheongbuk-do show similar trends, most likely due to some similarities caused by the proximity of their locations.

In the case of the railroads, shown in Figure 4, Seoul, Busan and Daegu metropolitan cities consistently occupied the top slots. They have a common point of being base regions for a wide area railways and relatively developed cities in a railway area. Subways began operating in 1974 in Seoul, 1985 in Busan and 1997 in Daegu. The remaining metropolitan cities showed low levels at the beginning of the estimation period, but the increase in the stocks of Daejeon, whose city railway opened in 2006, in the early 2000s and Incheon in late 2000s showed a marked increase.




Unlike the metropolitan cities, however, the stocks of railroads in provinces at the end of the 1990s were not very large. This is due to the fact that the proportion of road investment out of South Korea’s total transport infrastructure is high, though the relative share of railways was reduced in the 1980s to 1990s (Ahn and Kim, 2006, pp.37-38). Nevertheless, during the era of the expansion of infrastructure investment in the 1990s, the stock of Gyeonggi-do grew steadily, followed by Gyeongsangbuk-do with a large gap. In addition, Gyeongsangnam-do during the late 2000s and Jeollabuk-do in the early 2010s showed relatively large increases in stocks. The construction of high-speed railways in each region can be regarded as the main driver of the stock growth. Other provinces showed no significant differences, only showing moderate growth.

Finally, the ports shown in Figure 5 were excluded from Seoul, Gwangju and Daejeon metropolitan cities, and Chungcheongbuk-do, which have very low stocks due to their inland geographical characteristics. With regard to metropolitan cities, stock levels were in the order of Busan, Incheon, and Ulsan over most of the estimation period. However, the increase in the stock in Incheon Metropolitan City is noticeable in the early part of the estimation period, as are the recent reversals of Incheon and Busan.




Among the provinces, the stock of Jeollanam-do grew steadily, followed by Gyeongsangnam-do with recent rapid growth in the middle and late 2000s. Other provinces showed gradual growth, and the recent growth of Chungcheongnam-do is remarkable.

The following are some of the distinguishing features of each sector of transport infrastructure. First, in the case of roads, the concentration on specific regions tended to be relatively small compared to other sectors, although Seoul is more concentrated among metropolitan cities. This can be deduced from the fact that transport infrastructure investment in South Korea concentrates on roads. In other words, as a result of steadily expanding roads based on traffic demand, for instance, various types of roads, specifically highways, national roads, national subsidy roads and local roads, were relatively uniformly constructed in each area.

Second, railroads are concentrated heavily in Gyeonggi-do when compared to other provinces, and the concentration in Seoul among metropolitan cities is relatively low compared to roads. In addition, for railroads, regional reversal phenomena, by which relatively low (high) regions tend to become relatively higher (lower) over time, occur more frequently than in other sectors. These results are inferred from the analogy of the characteristics of roads above and from the fact that the proportion of relative investments in railroads is low, which may result in the concentration on a specific region being prominent. For example, the construction of city railways in various metropolitan cities has the effect of reducing the gaps between them. In contrast, the gap between Gyeonggi-do, where city railways were constructed, and other provinces is widening. Furthermore, given that investments in railways are relatively low compared to those for roads, the number of individual projects is small. Accordingly, the scope of the region in which the project is conducted also becomes smaller, resulting in the investment being concentrated in a specific region. Regional reversal can also occur between areas where railway projects are promoted and areas where they are not.

Third, ports have recently grown more than the other two sectors. This stems from the fact that investments in ports in the late 2000s increased greatly.

The estimates of the transport infrastructure stocks that comprise all three sectors are shown in Figure 6.




In addition, as discussed above, the depreciation rates may vary over time when using the modified BYM proposed in this study. The average quarterly depreciation rates for the road, railway and port divisions were 0.231%, 0.342% and 1.88%, respectively. It should be noted again that negative depreciation rates may occur due to data limitations. As a result of the estimation, negative depreciation rates account for 33.8%, 21.1% and 9.86% for roads, railroads and ports, respectively.

V. Discussions and Policy Implications

A. Comparison with Previous Studies

We can now compare the transport infrastructure stocks estimated in this study with those in previous studies. In so doing, it becomes possible to compare the results obtained from the studies by Kim (2011) and Gong (2015), of which the targets and estimation periods are similar to those in this study. Both studies estimated the net capital stock of transport infrastructure, as was done here, and the results are compared in Figure 7. For the sake of an equal comparison with this study, roads and airports in the previous studies were combined into the road category. Note that the result of this study shown in Figure 7 is identical to the sectoral capital stock estimated by the BOK, which can be considered most reliable for its dominance in accessibility to basic data among all three given the limitations of the data.


The differences between Kim (2011) and Gong (2015) are based on differences between the estimation methods, the method of avoiding negative depreciation rates, and whether private capital is included, as discussed in Gong (2015, pp.64-67). As shown in Table 1, Kim (2011) adopted the polynomial BYM using the net capital stock in 2007 as the basis; this was arbitrarily estimated based on the NWSs of 1977, 1987 and 1997, while for Gong (2015), the estimation was done using the BYM with NWS 1997. Moreover, the fact that Kim (2011) considers both the public and private sectors while Gong (2015) estimates only for public capital when estimating the SOC capital stock will also factor into the difference in the results (Gong, 2015, p.66).

The results of these studies by sector are compared as follows. First, for roads (including airport runways), the result in Kim (2011) showed a tendency to increase significantly over time, while that in Gong (2015) indicated a trend similar to that here. Compared to this study, Kim (2011) and Gong (2015) tend to overestimate by 79.0% and 8.6% on average, respectively.

Second, railroads and ports in their studies were estimated to be smaller than the sectoral capital stocks adopted in this study. Kim (2011) and Gong (2015) showed a tendency toward underestimation by approximately 18.0% and 27.5% for railroads and 55.5% and 28.8%, respectively, for ports. Recalling that both Kim (2011) and this study included both the public and private sectors while Gong (2015) took into account only the public sector, and given that the share of private sector is higher for railroads and ports than it is for roads, it can be seen that the estimation results of Gong (2015) are closer to the sectoral capital stock data of the BOK than those of Kim (2011), especially in the railroad and port sectors.

Let us now compare the interregional allocation results of the transport infrastructure capital stock estimated in this study with those from the earlier studies. In this case, it is more appropriate to compare the share of each region because the amount of national capital stock in this study differs from that in the previous studies, as shown in Figure 7. In addition, we excluded regions with very low stocks in the sector, such as railroads in Jeju-do and ports in Chungcheongbuk-do. For a comparison with Kim (2011), the regions in this study are reorganized; i.e., some metropolitan cities and provinces are amalgamated, as structured in Kim (2011, p.205, Table 1).

Table 6 summarizes the results of such a comparison. First, the results of Kim (2011) differed from the results of this study by less than one percent on average in all sectors. However, the range of the difference was lowest in the case of roads, while those for railroads and ports were relatively large. This appears to be due to the fact that the stock of roads is much larger than those of other sectors. On the other hand, when the results of Gong (2015) are compared with those of this study, a similar tendency is shown, but the difference is considerable.


Note: *** indicates that the p-value is less than 0.001.

To determine if the difference between the pair of estimates follows a symmetric distribution around zero, we conducted Wilcoxon signed-rank tests for the percentages of the differences. As a result, the above null hypothesis was rejected only for roads and railroads in Gong (2015). Consequently, the interregional allocation of the transport infrastructure capital stocks in this study can be interpreted as similar to that in Kim (2011) rather than Gong (2015).

B. Applicability to Policy Making

Although the scope of this study is limited to estimating the capital stock of transport infrastructure by region using available data, the results of this study can be used for future research and policy formulation purposes. Some possible uses are discussed below.

First, it is possible to look at the immediate trends in the estimates, as listed in the Appendix. For example, it is clear how the regional disparity has been changing with changes in the capital stock amount itself and its rate of growth in formulating policies to attain balanced regional growth. It is also possible to make cross-regional comparisons using other indices, such as regional net capital stock versus gross regional domestic product (GRDP) or regional net capital stock per employed person.

Second, the results of this study can be used for an in-depth analysis to derive policy implications, similar to some of the previous studies introduced in Section II. For example, how much transportation infrastructure influenced economic growth, whether allocations were made according to regional demand, or whether there was any political influence on the distribution of transport infrastructure by region can be studied, to name a few.

Third, the results here can be used when discussing the optimal level of transport infrastructure stock. As an example, Ryu (2006) presents an immediate application using regional SOC stock among others in estimations using an endogenous growth model.

Fourth, the results can be used for a closer examination of the appropriateness of the inter-sectoral allocation of transport infrastructure. We noted above that transport infrastructure investments in South Korea are centered on roads. Considering that roads play a pivotal role as the basis of all forms of transport infrastructure, road-based investments may be inevitable. Nonetheless, it would be worthwhile to examine whether the relative share of investment in South Korea is excessive based on the inter-sectoral distribution of regional capital stocks. To the best of the author’s knowledge, however, no such study exists. Alternatively, Figure 8 compares the proportion of road investments relative to railroads among OECD member countries. South Korea is located close to the OECD average, except for a few years when the country marked relatively low levels. The shaded domain in Figure 8 represents the range between the minimum and the maximum values of the proportion of road investment relative to that for railroads by country for each year; particularly, the dark shaded region represents the interquartile range (IQR). South Korea is located within the IQR of all available years (2001~2013), suggesting that the proportion of road investment relative to that for railroads by the country does not deviate significantly from the average for OECD member countries. However, such a comparison is intended to skim the extent to which South Korea has invested heavily in roads, and it should be avoided when interpreting this result as over- or under-investment in transport infrastructure. Such a conclusion should be made after carrying out a more rigorous analysis taking into account regional stock amounts by sector in transport infrastructure.


Note: 1) Only data from the year after joining the OECD were included, and in some years, data from some countries are missing. (14% of the total) 2) The light shading indicates the range of the minimum and maximum values, and the dark shading indicates the IQR of each year.

Source: OECD Infrastructure investment indicator. (doi: 10.1787/b06ce3ad-en, accessed on March 15, 2018)

Although examining the above domains with rigorous analyses of sectoral and regional investment allocations and accumulated capital stocks is beyond the scope of this study, we can highlight several stylized facts as a basis for future research and policy making from the times-series of investment in transport infrastructure published in CIS and the capital stock amounts estimated in this study.

Figure 9 illustrates the trends of nationwide sectoral investment in transport infrastructure, where Figure 9 (a) shows the investment amount by sector and Figure 9 (b) represents the ratio of investment to capital stock. Both are in real values. In both figures, the decline in investment is noticeable, except for gentle increases in investments in railroads and ports in the late 2000s. In terms of investments, roads, railroads, and ports remain in that order during the entire analysis period. On the other hand, the ratio of investment to stocks indicates that ports have high amounts during most of the period. Recently, the values for railroads and ports are higher than those for roads.


Source: Construction Industry Survey, Statistics Korea.

Moreover, similar exercises can be performed by region to obtain the results shown in Figure 10. In this case, the investment amount and the ratio of investment to stocks are calculated for each metropolitan city and province, except for regions where the amounts are miniscule for railroads and ports. Looking at the amount of investment, it can be seen from the lightly shaded areas that the regional disparities in all three sectors were large in the late 2000s. Excluding abnormalities, IQR shows that the regional disparities in investments in roads and ports have declined since the mid-2000s, while that for railroads was maintained for the same period. On the other hand, if we look at the ratio of investment to stocks, the gap between regions tends to decrease, at least recently. In particular, this tendency appears throughout the analysis period for roads, which is larger in scale than the other sectors.


Note: The dotted line represents the average, the light shading indicates the range of the minimum and maximum values, and the dark shading is the IQR for all metropolitan cities and provinces.

Source: Construction Industry Survey, Statistics Korea.

The results presented in both Figure 9 and Figure 10 reflect the fact that the budget for SOC has been reduced in recent years. As a result of examining the amount of investment relative to stocks, a trend of declining disparity between regions along with a nationwide declining trend can be observed. Consequently, it will be an interesting future research topic to explore how efficiency and equity are considered when allocating transportation infrastructure investments in South Korea using the results of this study.

VI. Concluding Remarks

Although estimations using the PIM are logical and accurate for the time-series of capital stocks, using this method is impossible in South Korea because basic data such as the disposal function and the economic useful lifetimes of facilities are not provided in the country. Given these limitations, this paper proposed a new method by which to estimate the net capital stock, which is the market value of fixed total assets at a certain point in time by region, through improvements in the BYM. The proposed method is applied to three sectors of transport infrastructure: roads, railroads and ports. The method consists of the following three steps.

First, it substitutes the sectoral capital stocks in two consecutive periods and the sectoral investment amount into the capital accumulation equation to obtain the sectoral depreciation rate for each period. Second, the ratio of the capital stock for each region and the sector for each period is calculated sequentially using the capital stock and investment amount of each region and sector provided by the NWS for the base year (1997) and CIS data for each period, respectively. Third, capital stock by sector is allocated to each region using the above ratio.

There are two advantages of this method over the conventional BYM. First, by making the sum of regional estimates coincide with national estimates, it is possible to eliminate upwards bias (a phenomenon by which the sum of regional estimates is larger than that in national estimates), which is common in existing BYMs. Second, it is possible to increase the reliability of the estimation results by allowing the depreciation rates for each sector to vary over time for each period instead of fixing them arbitrarily.

Nevertheless, the method proposed in this study also has limitations. The most serious is that negative depreciation rates cannot be prevented during the estimation process. This is a common drawback of a methodology based on BYM. In addition, the method is restricted to cases when time-series data of capital stock by sector can be secured. Therefore, at least credible estimates of sectoral capital stock should be kept and made public so that one can estimate the persistent sectoral capital stock by region. This will be a very important reference when establishing a national agenda, such as balanced regional growth.




Note: Prices are chained at 2010.


Note: Prices are chained at 2010.


Note: Prices are chained at 2010.


[†] Supported by

This paper is based upon Lee, Jongyearn, “Regional Allocation of Public Investment with Respect to Efficiency and Equity” in Roles and Challenges of Public Investment to Improve the Productivity of the Korean Economy, edited by Jaejoon Lee and Kangsoo Kim, Research Monograph, KDI, 2016 (in Korean). I am grateful to Jinkyeong Kim for outstanding research assistance. All errors are my own.



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