metadata: authors: 0: author: Herd,Richard
count: China
docna: 0: docna: Estimating Capital Formation and Capital
            Stock by Economic Sector in China : The Implications for
            Productivity Growth
docty: Policy Research Working Paper
subtopic: Urban Housing and Land Settlements,Municipal Management and Reform,Urban Housing,Urban Governance and Management,Transport Services,Investment and Investment Climate,International Trade and Trade Rules,Construction Industry
teratopic: Communities and Human Settlements,Public Sector Development,Urban Development,Transport,Macroeconomics and Economic Growth,International Economics and Trade,Industry
abstracts: cdata!: This paper aims to fill a gap in the
            literature on capital formation in China by estimating the
            capital stock in four economic sectors: business,
            infrastructure, government, and housing. Such a breakdown is
            necessary for the purpose of analysis of economic
            development in China, as the normal models of economic
            development are based on a competitive economy, which is
            clearly not the case for the country's infrastructure
            and government sectors. Moreover, the contribution of
            housing to gross domestic product in China is very poorly
            measured. Although the results of this analysis can only be
            approximate, as the required detailed information for a
            better estimate is not published, they nonetheless suggest
            that there has not been overinvestment in the Chinese
            business sector -- its capital-output ratio has risen only
            slightly over the past 40 years. Yet, there have been surges
            in the stocks of housing and infrastructure in the past
            decade. These sectors account nearly all the recent increase
            in the capital-output ratio in China.
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repnme: repnme: Estimating Capital Formation and Capital
            Stock by Economic Sector in China : The Implications for
            Productivity Growth
display_title: Estimating Capital Formation and
            Capital Stock by Economic Sector in China : The Implications
            for Productivity Growth
listing_relative_url: /research/2020/07/32239125/estimating-capital-formation-capital-stock-economic-sector-china-implications-productivity-growth
topicv3: Transport Equipment m1326014 1812,Transport m1326661 135,Trade m1326924 698,Land and Housing m1327648 817,Investment Entry m1504647 2544
publishtoextweb_dt: 2020-07-13T00:00:00Z
historic_topic: Communities and Human Settlements,Public Sector Development,Urban Development,Transport,Macroeconomics and Economic Growth,International Economics and Trade,Industry
origu: EFI-EAP-MTI-MacroFiscal-1 (EEAM1)
no_of_pages: 39
author_keys: 0: author_key: 1564458
model_extractions: Policy Research Working Paper 9317 Estimating Capital Formation and Capital Stock by Economic Sector in China The Implications for Productivity Growth _Richard Herd_ Macroeconomics, Trade and Investment Global Practice July 2020
Policy Research Working Paper 9317

# **Abstract**

This paper aims to fill a gap in the literature on capital formation in China by estimating the capital stock in four economic sectors: business, infrastructure, government, and housing. Such a breakdown is necessary for the purpose of analysis of economic development in China, as the normal models of economic development are based on a competitive economy, which is clearly not the case for the country’s infrastructure and government sectors. Moreover, the contribution of housing to gross domestic product in China is very poorly measured. Although the results of this analysis can only be approximate, as the required detailed information for a better estimate is not published, they nonetheless suggest that there has not been overinvestment in the Chinese business sector—its capital-output ratio has risen only slightly over the past 40 years. Yet, there have been surges in the stocks of housing and infrastructure in the past decade. These sectors account nearly all the recent increase in the capital-output ratio in China.

This is a background paper for the Development Research Center of the State Council and the World Bank’s 2019 report “Innovative China: New Drivers of Growth”, produced for the Macroeconomics, Trade and Investment Global Practice of the World Bank. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http:// www.worldbank.org/prwp. The author may be contacted at rherd@herdassociates.com.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **Estimating Capital Formation and Capital Stock by Economic Sector in China:**

# **The Implications for Productivity Growth**

# Richard Herd

Consultant, World Bank This paper has been produced as background for the Development Research Center of the State Council and the World Bank’s 2019 report _“Innovative China: New Drivers of Growth”_ . The dataset is available in World Bank’s Development Data Hub (https://datacatalog.worldbank.org/).

_JEL Codes: E010, E220, O110, O530._ _Keywords: China, capital stock, incremental capital-output ratio, fixed asset investment_
The official Chinese national accounts do not contain any estimate for the capital stock for the whole economy. Yet such a figure is necessary in order to determine past performance of the economy and its likely future path. This is the more so in China where the level of investment is particularly high (Figure 1). Concerns have been raised that there has been over-investment so reducing rates of return and the growth of productivity. Changes in the structure of the capital stock over time can change the average rate of return and the productivity of capital, so obscuring the underlying changes in productivity. This is particularly the case in China where the national accounts measure of the rate of sectoral return is assumed to be zero for most of the housing, infrastructure and government sectors. Thus, the question of whether there has been over-investment requires evidence both on the overall capital stock and its distribution across different sectors of the economy.

**Figure 1 Investment rate**

<!-- Start of picture text --> Current prices, % GDP<br>50<br>45<br>40<br>35<br>30<br>25<br>20<br>1981 1986 1991 1996 2001 2006 2011 2016<br>Source: NBS and author estimates<br><!-- End of picture text --> There have been many attempts to estimate the total capital stock of the economy, given the absence of official estimates. They have all been faced with similar problems. Even though investment data are available since 1952 on an internationally agreed basis, there is uncertainty about the initial value of the capital stock at that date, following a long period when the economy had been impacted by war and revolution. Moreover, in contrast to the aggregate data, the most detailed figures on investment continued to be gathered under the principles set out in the early 1950s rather than using the internationally agreed System of National Accounts (SNA). In addition, the gathering of economic data during the 1960s was sparse and sometimes was interrupted completely. Despite these problems, the Chinese authorities have made considerable efforts to produce standardized economic accounts back to 1950. However, for investment, the official macroeconomic data lack the granularity that is found in the accounts of many countries, forcing analysts to use a variety of supplementary data.

The absence of granularity for investment data is of particular concern given the high and rising level of investment. It is well-known that this rise has been driven by infrastructure and housing. Some also maintain that it has been driven by investment by state-owned enterprises, giving rise to excess capacity. This note attempts to improve the granularity of data for gross fixed capital formation in China by focusing on four sectors: housing, infrastructure, government and the business sector. By providing corresponding estimates of capital stock, a judgement can be made on the extent of overinvestment and the movement in the productivity of capital in the business sector of the economy Until recently, capital stock estimates for China have oscillated between providing estimates for the whole economy and for the non-residential sector. While earlier studies used the non-residential sector data (Chow, 1993), with the publication of aggregate official data for gross fixed capital formation, attention switched to estimates for the whole economy. Recently attention has switched back to disaggregated data. Bailliu et al. (2016) considered the non-residential capital stock. Others 2
have estimated capital stocks by province and for three types of asset (Holz and Sun, 2017). There appears to be only two studies that provide estimates of gross fixed capital formation and capital stock on a sectoral basis. (Wu, 2015) provides a breakdown into 37 sectors with two assets per sector but it is limited to the period 1980 to 2010. The Penn World Tables provide a breakdown of the capital stock into four assets but with no sectoral breakdown. The objective of this note is to provide estimated of capital formation and the capital stock for four sectors (housing, infrastructure, government and business) for the period 1952 to 2016.

# **Estimating the capital stock**

An estimate of the capital stock has been made using by cumulating gross fixed capital formation from a base year and deducting the extent to which the capital stock falls in value as time passes.

This methodology, known as the perpetual inventory method, requires the following information:

- The value of the capital stock in an initial year.

- A continuous series for the value of investment (known technically as gross fixed capital formation) broken down into sectoral detail.

- A set of price indices that can be used to convert nominal investment outlays into real outlays.

- • A measure of the extent to which different types of assets fall in value over time.

The nature of the dependence of the capital stock on investment, the growth rate of investment and the depreciation rate is shown in Box 1. The inherent nature of the perpetual inventory means that for periods of time long-removed from its starting point, the current value of the capital stock is almost independent of the initial value of the capital stock. In addition, when there have been long periods of rapid growth in capital formation, as in China, the impact of different rates of depreciation on the estimates of the current growth rate of the capital stock is very limited – though the level of the capital stock does depend on the depreciation rate to a limited extent.

# **_Initial capital stock_**

A number of authors have presented estimates of the capital stock over time. All have made an estimate for the capital stock in 1952 when investment data first became available (Table 1). Several researchers used material published in Chinese sources while others use estimates based on crosscountry comparisons or based on estimates derived from investment flows and depreciation rates. Others preferred to make an assumption based on introspection.

# _Previous estimates_

The coverage and methodology used in these studies is very variable. About half of the studies focus on the economy-wide capital stock and so include both the housing stock and government investment in assets such as offices, schools, hospitals and roads. Overall, the variation of the estimates is too large to be a guide (Table 2). Moreover, many of the estimates are based on introspection rather than original sources. In addition, only four studies provide a sectoral breakdown of capital stock in 1952 (Table 3). One book provides a compendium of economic statistics (Chen) with data on investment and capital stocks for the period 1948 to 1958. This book provides the details of the original Chinese sources which are either in the form of articles by the statistical bureau or academics or reports in official newspapers. None of the reported sources provides an estimate for the capital stock in the government sector.

3
e e c e e HHe ccee, ccooe oo cc sseeo eecce eebb e eegg cceeooe ff, cceeff ooeeoo cc ooeeffeeff c eeh eeoo e sseette ee, eehee ggooeeooeeh oocce eeoo eehee eesse ttcce ff e e e e b cce ccee sse ccss eess e ee cco eecce ff b eehee cche ccee eeoo eehee ffeeccooeecceecce oocce . HHeeooe eeoo, eehee cche ccee eeoo eehee ffeeccooeecceecce oocce ooe ee gge eeoocce ccee e ccee ffeeo eeooe ccee e eehee eesse ttcce ff e ee eeoo eehee c cce ccee sse ccss (ff) ooheecch eess gge 1 −�<sup>(1 −δδ2)</sup> � 1 −�<sup>(1 −δδ</sup> (1 + γγ)<sup>1)</sup> � ff= In the case of China, where the average compound growth rate of investment between 1952 and 2015 was 9.7%, the (1 + γγ) eventual difference (d) in the estimated level of the capital stock, with depreciation rates of 5% and 10%, will be equal to 1 −�(1 + 0.097)<sup>(1 −0.05)</sup> � 1 −�(1.097)<sup>(0.95)</sup> � = =<sup>1 −0.865998</sup> =<sup>0.134002</sup> = 0.746193 1 −�(1 + .097)<sup>(1 −0.1)</sup> � 1 −�(1.097)<sup>(0.9)</sup> � 1 −0.820419 0.179851 ff= 4
**Table 1 Studies on capital formation in China**

|**Author**|**Year of**<br>**Publication**|**Methodology**|
|---|---|---|
|Liu and Yeh|1963|Based on capital stock data for 1955 published by the State<br>Statistical Bureau in 1957, back-cast to 1952 using investment data.|
|Chow|1993|Based on data for 1952 of the original value of the fixed capital stock<br>of state-owned units published in the Statistical Yearbook.|
|Wu|2016|Partially based on the 1951 census of national assets|
|Baillu, Kruger_et al_|2016|Based on growth rate of investment and depreciation rate|
|Maddison|2007|Based on his own estimates of investment in the pre-revolutionary<br>period.|
|Perkins and Rawski|2008|Capital-output ratio set at an assumed level|
|Perkins|1998|Capital stock set a multiple of net material product in 1952|
|Wu Yarwi|2016|Assumes capital stock of zero in 1900, uses an estimated series for<br>investment between 1900 and 1952 to generate a capital stock in<br>1952.|
|Jun_et al_|2004|Based on growth rate of investment and assumed depreciation rate|
|Feenstra_et al_|2016|Based on cross-country analysis for Penn World Tables|

**Table 2 Estimates of the capital stock in 1952**

|Author|Capital Stock<br>current prices<br>1952|Capital-<br>output<br>ratio 1952|Comments|
|---|---|---|---|
|**_Studies that exclude housing_**||||
|Liu and Yeh|55.9|0.7|Excludes government|
|Chow|76.6|0.9|Excludes government|
|Wu|160.0|1.9|Includes government|
|Maddison|254.0|1.2|Based on his own GDP|
|**_Studies including housing and government_**||||
|Perkins and Rawski|82.4 or 164.8|1.0 or 2.0||
|Perkins|202.1|2.5||
|Wu Yarwi|133.8|1.6||
|Zhang_et al_|74.8|0.9||
|Feenstra_et al_|175.6|2.6|<sup>Capital stock is broken</sup><br>down into four asset types|

5
# **Table 3 Estimates of the capital stock by sector in 1952**

Billion yuan, current prices

||Chow|Liu and<br>Yeh|Chen|Feenstra<br>_et al._|Wu|
|---|---|---|---|---|---|
|**Published estimates**||||||
|Agriculture|45.0|40.9|45.0|..|48.0|
|Industry|15.9|8.7|15.8|..|12.8|
|Trade|1.2|1.0|0.2|..|..|
|Construction|0.3|0.7|..|..|..|
|Other service sectors and transport|..|..|..|..|99.2|
|Business sector|62.4|49.9|61.0|..|..|
|Transport|14.2|13.9|13.9|..|..|
|Business sector and infrastructure|76.6|63.8|74.9|..|160.0|
|**Supplementary estimates**||||..||
|Government<sup>1</sup>|13.6|13.6|13.6|..|16.5|
|Housing<sup>2</sup>|69.4|69.4|69.4|..|69.4|
|**Estimates by asset type**||||||
|Structures|..|..|..|148.6|..|
|Machinery|..|..|..|20.3|..|
|Transport equipment|..|..|..|6.8|..|
|Whole economy|159.6|146.8|157.9|175.6|281.9|
|**Calculated capital-output ratios**||||||
|Business sector|0.9|0.7|0.9|..|..|
|Infrastructure|0.2|0.2|0.2|..|..|
|Business sector plus transport|1.1|0.9|1.1|..|2.4|
|Government|0.2|0.2|0.2|..|0.2|
|Housing|1.0|1.0|1.0|..|1.0|
|Structures|..|..|..|2.2|..|
|Machinery|..|..|..|0.3|..|
|Transport equipment|..|..|..|0.1|..|
|Total|2.3|2.2|2.3|2.6|3.6|
|**Memorandum item**||||||
|GDP|67.9|67.9|67.9|67.9|67.9|

_Notes:_ 1 The capital-output ratio for government is assumed to be the same as that in India in 1975 as calculated in Arestoff and Hurlin (2006).

2 Estimate taken from Herd (2013) adjusted for revisions in data.

_Source_ : See bibliography 6
# _Choice of initial capital stock_

Three sources have been chosen as giving apparently reliable estimates of the capital stock by Chow, Liu and Leh and Chen. Two further, often quoted sources are also considered: The Penn World Tables (Feenstra _et al.)_ and those from Wu (Table 4). The estimates by Chow and Liu and Yeh are firmly based on original sources. They differ markedly in their estimates of the capital stock in the industrial sector. The reason for the difference appears to be that Chow has taken data for the original value of industrial fixed assets (see Chen, 1966, Table 3.2). In Chinese economic series, such data correspond to the concept of the gross capital stock (that is, the original cost of all assets currently in use). Such a definition ignores the impact of depreciation of the value of the asset. However, Liu and Yeh start from a 1955 official estimate of the net capital stock and work backwards to the end of 1952 by deducting net investment. Their estimate can be compared to the original value of the assets and implies a deduction for depreciation of 45%. The estimates for the business sector and infrastructure made by Liu and Yeh have been used in this paper.

These studies have to be complimented by estimates of the capital stock in the housing and government sectors. Estimates for the _residential housing stock_ are taken from Liu (1968) based on an extrapolation of estimates of the 1933 rural housing stock together with the ratio of urban to rural rents. His estimate corresponds almost exactly to an estimate of the replacement cost of urban and rural housing after allowance of an arbitrary 50% for depreciation (Herd et al, 2013). Finally, an estimate has been made of the capital stock used in the _government sector_ . It is based on estimates of the capital-output ratio for the Indian economy in 1975 (Arestoff and Hurlin). Overall, the preferred estimate for the initial capital stock is CNY 147 billion in 1952 prices, representing an overall capitaloutput ratio of 2.2.

# **_Depreciation rates_**

In the absence of published deprecation rates, it has been necessary to make assumptions about the appropriate depreciation rates for capital in China. Depreciation rates serve to measure the extent to which capital is used in a given period. Ideally, this can be measured through collecting the prices of the same type of asset as the asset ages. Here it has been assumed that assets decline in value at a constant geometric rate. In this case, the complete retirement of an asset only occurs after an infinite time period. However, given the observed rate with which price declines with age, the proportion of assets in use after a decade is small except for structures. Many studies have used accounting data to estimate the depreciation rate. This is inappropriate as such figures are a reflection of arbitrary rates set by the tax authorities.

# _Comparison with other estimates of depreciation in China_

Analyses of the performance of the Chinese economy needed to assume a depreciation rate in order to transform annual investments into a capital stock. A literature search found 36 studies (Table 4). These papers presented 42 estimates or assumptions for the national depreciation rate as some studies had different depreciation rates for different periods. Eleven of the studies were in Chinese, the remainder in English. The average depreciation in the English language studies was 5.6%.

A simple meta-regression of the results suggests that there are several trends in the reported assumptions for the depreciation rate. _First_ , there is a significant tendency for assumptions about depreciation rates to increase in papers published more recently. The estimated coefficients from the meta-regressions suggest a depreciation rate of 3.2% in 1988, rising to 7.3% for papers published in 2017. Secondly, there is a marked difference in the depreciation rate used between papers published in Chinese (including English language papers that cite Chinese papers as source for their data) and papers in English: the papers published in Chinese or using Chinese sources have an average 7
depreciation rate 3.4 percentage points higher than those in English. The estimates in Chinese papers appear too high to be reasonable. For example, Bai (2006) quotes a depreciation rate of 8% for structures and 24% for equipment, based in service lives of 38 years for buildings and 12 years for machinery (Wang and Wu, 2003).

**Table 4 Depreciation rates used to calculate capital stocks**

||**Publication**||**Time**|
|---|---|---|---|
|**Authors**|**date**|**Depreciation rate**|**period**|
|**Chinese language**||||
|Meng and Wang|2000|5.0%||
|Wang and Fan<br>|2000<br>|5.0%<br>|1952-1999|
|Wang and Wu<br>|2003<br>|10.0%<br>||
|Gong and Xie|2004|10.0%|1970-1999|
|Zhang_et al._|2004|9.6%|1952-2004|
|Bai_et al._|2007|10.0%|1952-2005|
|Shan|2008|11.0%|1952-2006|
|Lei|2009|9.7%|1952-2007|
|Ye|2010|10.0%|1952-2008|
|Fan|2012|11.3%|1952-2009|
|Bai_et al._|2016|10.0%|1998-2007|
|Zhao and Zhong|2017|11.0%|1952-2006|
|**English language**||||
|Chen_et al._|1988|3.9%|1952 -1985|
|Perkins|1988|5.0%|1953-1985|
|Hu and Khan|1997|3.6%|1952-1994|
|World Bank|1997|4.0%|1978-1995|
|Woo|1998|5.0%|1979-1993|
|Hall and Jones|1999|6.0%|1988|
|Wang and Yao|2001|5.0%|1952-1999|
|Chow and Li|2002|4.0%|1978-1992|
|Wang and Yao|2003|5.0%|1952-1999|
|Chow and Li|2003|5.4%|1993-1998|
|Young|2003|6.0%|1978-1998|
|Wu|2004|7.0%|1952-2000|
|Islam_et al._|2006|3.0%|1952-1978|
|Holz|2006|3.7%|1953-1977|
|Islam_et al._|2006|4.0%|1979-1992|
|Islam_et al._|2006|5.0%|1993-2003|
|Holz|2006|5.9%|1978-2003|
|Wu|2007|4.5%|1952-2005|
|Zhang|2008|9.6%|1952-2004|
|Perkin and Rawski|2008|7.0%/9.6%|1952-2005|
|Bulman_et al._|2011|7.0%|1952-2008|
|Cheremhukin_et al._|2015|5.0%|1953-2012|
|Wu|2015|5.2%|1952-2010|
|Wang and Zhou|2016|6.5%|1952-1999|
|<br>Ma et al.|2016|7.0%|1978-2014|
|Bailliu_et al._|2016|7.6%|1978-2014|
|Wang and Zhou|2016|10.0%|2000-2015|
|<br>Hong and Li|2017|6.0%||
|Holz and Sun|2017|7.1%|1953-2005|
|Holz and Sun|2017|8.5%|2006-2015|

_Source:_ Google search.

8
# _Approach in this study_

None of the depreciation rates in the above studies have firm empirical basis. As a result, the depreciation rates used here have been taken from figures published by the Bureau of Economic Affairs in the United States (Table 5), with the exception of housing where official Chinese depreciation rates are available. The US data distinguish three types of assets at the aggregate level:

- Structures

- Equipment

- Intellectual property

In addition, it distinguishes between the capital stock of general government and the rest of the economy.

**Table 5 Non-residential depreciation rates in the United States** Average 1990 to 2015, % per year

||Private sector|Government|
|---|---|---|
|Non-residential|8.7|4.6|
|Equipment|13.9|13.2|
|Structures|3.0|1.9|
|Intellectual property|25.1|16.7|
|Equipment and structures|6.8|3.2|

_Source_ : Bureau of Economic Affairs, https://www.bea.gov//national/FA2004/DownSS2.asp In this study it has been assumed that the depreciation rates for the Chinese business sector are the same as those for the private sector in the United States. The rates for the US government sector have been used for the government and infrastructure sectors in China, with the same depreciation rate being used for both sectors as the split of investment between structures and equipment is very similar in the two sectors. The US data, however, show intellectual property assets as a separate category, while for China such assets are included in equipment.

# _Accounting for software and intellectual property in the capital stock_

The official Chinese investment data split investment into two assets: structures and equipment. A growing share of investment in most countries has been in items such as computer software and other items of intellectual property. This type of investment has a very high deprecation rate so, if the growing importance of this type of investment is not allowed for, the depreciation rate for equipment will be understated and the capital stock over-stated.

No official estimates of investment in software and intellectual property are available for China. The authors of the Penn World Tables have estimated the investment flow in such assets by using the commodity flow methodology. Using this approach, for a given product, investment is determined as the sum of production plus net exports less consumption. The authors have also estimated a price index for this type of asset and assumed an average depreciation rate of just over 31% for these assets. On the basis of these assumptions, they find that though the share of this type of asset in the overall investment has grown rapidly, its share of the capital stock of equipment and software is nonetheless quite small (Figure 2). It is, moreover, at 4% much lower than the equivalent share in the United States, which was 34% in 2015. Thus, it would be incorrect to adopt the overall US non-residential depreciation rate for China, but it would be inappropriate to completely ignore the depreciation of the software component of the capital stock in China.

9
# **Figure 2 Share of Intellectual property in the capital stock and capital formation in investment**

Intellectual property as % of machinery, transport equipment and intellectual property <!-- Start of picture text --> 7<br>6<br>5<br>4<br>3<br>2<br>1<br>0<br>1964 1969 1974 1979 1984 1989 1994 1999 2004 2009 2014<br>Capital Investment<br><!-- End of picture text --> _Source_ : Penn World Tables version 9.0

# _Assumptions for depreciation rates_

The depreciation rate from the BEA for equipment has been modified to allow for both the share of software investment and research and development in China. It is set as a weighted average of the software depreciation rate used in the Penn World Tables, the depreciation rate for R&D estimated by Li and Hall (2017) and the BEA depreciation rate for equipment in the private sector and government sectors. The weights are the shares of software and R&D in the stock of equipment and software as estimated in the Penn World Tables plus an estimate of the stock of R&D capital (see below). To obtain the overall depreciation for each sector, the modified depreciation rate for equipment is weighted with the BEA rate for structures. The weights reflect the average shares for each type of asset for investment in each sector in urban areas in 2010 (Table 6).

**Table 6 Investment share by asset in urban areas**

||Business|Government|Infrastructure|
|---|---|---|---|
|Equipment|0.279|0.110|0.110|
|Structures|0.721|0.890|0.890|

_Source:_ CEIC In 2016, the resulting aggregate depreciation rate for the business sector is estimated at 7.8%, while the rates in the government and infrastructure sectors are estimated at 2.7% and 3.5%, respectively. The impact of including a higher deprecation rate for software and R&D outlays is minimal at around 0.3 percentage point. For the non-residential sector, combining business, government and infrastructure, these assumptions generate a depreciation rate that averaged 4.9% over the decade to 2016. Such a rate is very similar to that observed in countries that are members of the OECD: almost 60% of that group of countries had non-residential depreciation rates that were between 5.2% and 4.8% in the 10 years ending in 2016 (Figure 3).

10
# **Figure 3 Non-residential depreciation rates in OECD countries**

<!-- Start of picture text --> % per year<br>Switzerland<br>Belgium<br>New Zealand<br>Sweden<br>United States<br>Germany<br>France<br>Denmark<br>Netherlands<br>Finland<br>Hungary<br>Slovenia<br>Iceland<br>Mexico<br>Norway<br>Chile<br>Czech Republic<br>Israel<br>Slovak Republic<br>Estonia<br>Greece<br>Luxembourg<br>Poland<br>China<br>Ireland<br>Italy<br>Austria<br>Australia<br>United Kingdom<br>Canada<br>Japan<br>Spain<br>Portugal<br>Korea<br>0 1 2 3 4 5 6 7<br><!-- End of picture text --> _Source:_ OECD Economic Outlook Database, June 2017

# **_Estimates of non-residential gross fixed asset investment by sector_**

The official Chinese statistics provide estimates for the total nominal value of gross fixed capital formation from 1952 to 2016. There is not any breakdown of the total by sector or by the type of asset. It should be noted, though, that the definition of gross fixed capital formation differs from that found in the standard implementation of the System of National Accounts. In particular, expenditure on a project is counted as capital formation from the start of the project rather than as work-inprogress and being assigned to fixed capital formation when the project is completed and handed over to the final user.

# _Different measures of capital formation_

There is another statistical concept that, superficially, appears close to the concept of fixed capital formation: namely total fixed asset investment (FAI). It has the advantage of being broken down by asset and by sector since 2004 and by asset since 1981. The coverage of this concept is wider than that of capital formation. Most of the items that do not count as part of gross fixed capital formation are included under the heading “other” assets as opposed to being either a structure or equipment. According to Chao (1974), the principal elements included as investment in the category of “other” assets are:

- Cost of acquiring land leases by property developers and factory owners.

- Cost of compensating farmers and village collectives for land acquired for infrastructure.

- Cost of acquiring secondhand assets.

11
- Labor and training costs during the period between the delivery of an asset and its full entry into service.

- Costs due to the closure or relocation of a facility.

On the other hand, there are two elements of GFCF that are not included in FAI. _First_ , residential FAI is measured at the cost of the construction to the property developer. In GFCF, however, it is measured at the cost to the acquirer of the asset. The difference between these two concepts is the gross margin of the property developer (the difference between the construction cost and the selling price). The level residential investment has been corrected by adding this margin to residential FAI (Herd, 2013). _Second_ , since July 2016, research and development expenditure has been partially reclassified as a form of final capital expenditure rather than a cost element that is written off against profit in the year when the expenditure occurs. The overall result was to raise the level of GDP by 1.3% in 2016 and to increase the growth rate by 0.06 percentage point in the decade to 2015.

The NBS has not published a detailed breakdown of R&D spending by sector or type of expenditure. However, a comparison of the revisions to fixed capital formation in the 2015 and 2016 Statistical Yearbooks shows that the estimate of R&D expenditure included in GFCF was substantially lower than the estimate of R&D outlays published in the Science and Technology Yearbook. In the decade to 2014, just under 35% of outlays in the latter Yearbook were not classified as R&D. This presumably reflects a decision that a significant portion of development expenditure by companies should be regarded as a cost of production rather than an asset from which future benefits will flow.

A further measure of gross fixed investment can be derived from the data included in the Main Economic Indicators of Industrial Enterprises. This publication gives the results of a monthly census of financial data of all industrial enterprises with sales of over a threshold value that changes over time. The available series includes the balance sheet data for the depreciated historic cost of fixed assets, the cumulated depreciation of the fixed assets and the original value of the assets. The latter series is the sum of the depreciated value of the assets and the cumulative deprecation of the assets. The net value of fixed assets cannot be used as a measure of the capital stock of industrial enterprises because the assets are valued at the historic acquisition cost, though assets acquired before 1998 were revalued to 1998 prices in that year. However, the difference between the original value of the assets at the end of two adjacent years represents the gross increase in fixed capital between the two years less the amount of fixed assets that were scrapped in that year. When assets are scrapped, as opposed to being fully depreciated, the depreciated value is removed from net assets, the original cost of the asset is removed from the original value series and a deduction is made from cumulated depreciation. The scrapping rate has been estimated by Holz (2006). He suggests that if the average asset life is 40 years (which appears reasonable given a depreciation rate of around 6% in the business sector), then the scrapping rate will be 0.2% per year. This scrapping rate has been used in the calculation of investment in the industrial sector using the following identity: Gross fixed capital formationt = Original value of assetst - original value assetst-1 + scrappingt

# _Sectoral estimates prior to 2002_

The analytical problem is how to combine the various sectoral investment series in way that generates a series that corresponds to the published overall data for gross fixed capital formation. The methodology adopted here differs for the periods before and after 2003, as definitions of sectors were changed in 2003 and more data on expenditure on different assets has been published since 2003.

12
Prior to 2003, fixed asset investment (or capital construction prior to 1981) has been calculated from published data for the infrastructure, government and business sectors. A separate estimate has been made for housing GFCF (Herd _et al_ ., 2013). The sum of these four estimates has then been scaled to be equal to the published data for GFCF.

# _Sectoral estimates from 2003_

From 2003, the movements in the aggregate data for fixed asset investment are no longer a reliable guide for investment in the national accounts. To obtain sectoral estimates of GFCF, the following methodology has been adopted

- Industrial sector investment is set equal to the change in the original value of fixed assets, plus an allowance for scrapping.

- Service sector investment (excluding housing) is set equal to FAI in urban areas, excluding FAI in the asset type _other._

- Rural FAI is added to above urban estimates.

- Housing investment is taken from Herd _et al_ . (2013).

# _Comparison of estimates with official data_

The resulting estimate for aggregate investment is then scaled to be equal to the official estimate of gross fixed capital formation. Given that the estimate of GFCF includes R&D expenditure, this scaling factor incorporates an estimate of R&D expenditure not included in FAI. The reliability of the sectoral estimates can, to some extent, be judged from the overall scaling factors that have to be applied to the data (Figure 4). The scaling factor is quite large prior to the 1980s but it reflects the same error as in published data and cannot be resolved. For the period between 1980 and 2002, the sectoral estimates are close to the GFCF data. After 2002, the method used to estimate sectoral GFCF generates data that is much closer to the GFCF data than the FAI series, which by 2016 was almost double the official data for gross fixed capital formation. By contrast, the difference between the sectoral estimate of GFCF and the published data was smaller at 17% in the same year. Indeed, the cumulated sectoral estimate of GFCF from 2011 to 2016 was only 12% greater than the published estimate of GFCF, while cumulated FAI in the same period was 75% greater than GFCF. The adopted methodology has thus removed most of the discrepancy between the FAI data and that for GFCF.

**Figure 4 Scaling factor applied to estimated sector GFCF and ratio of GFCF to total fixed asset investment**

<!-- Start of picture text -->
1.8<br>1.6<br>1.4<br>Scaling factor<br>1.2<br>1.0<br>0.8<br>ratio GFCF to FAI<br>0.6<br>0.4<br>0.2<br>0.0<br>1956 1961 1966 1971 1976 1981 1986 1991 1996 2001 2006 2011 2016<br><!-- End of picture text -->

_Source_ : NBS and author estimates.

13
# **_Choosing sectoral price deflators_**

An official price deflator for sectoral gross fixed capital formation is not available for the whole of the period since 1952. Even at the aggregate level, a deflator is only available for the period 1952 to 2004. Since then the NBS has only published a deflator for the sum of fixed capital and inventory investment. On the other hand, it has published a national price index for fixed asset investment continuously since 1989. This series has sub-indices for three separate assets: construction, equipment and other assets. Given the difficultly in interpreting whether such investment should be included in GFCF, the price index for _other assets_ has been ignored.

The price trends for equipment and construction have differed markedly. Between 1995 and 2016, equipment prices fell by 1.1% annually, while construction prices rose by 2.6%. Such large differences in the movement of prices mean that a price index using the base-period expenditure shares for equipment and construction will gradually resemble an index based only on the price of construction expenditure. It will thus understate the extent of differences in the movement of prices between the four sectors of capital formation that should reflect the different shares of construction and equipment in each sector.

There are several methods available to overcome this so-called substitution bias. One method is to change the weights annually, another is to use a Törnqvist price index, which is calculated as the weighted geometric average of the price relatives using arithmetic averages of the value shares in adjacent years. Data for the share of construction and equipment in fixed asset investment exist since 1981. They show a stable trend in the share of construction in national total fixed asset investment over the period 1981 to 2007. After that date, the share of construction reflects the increase in the share of construction intensive sectors in total FAI, as the shares by sector have remained stable. It is only possible to calculate the asset structure of investment by sector in urban areas (which account for almost all FAI) since 2004.

The split the two types of asset (construction and equipment) varies considerably between the four sectors of investment. At the two extremes, construction assets account for almost all real estate investment while equipment accounts for nearly 40% of business sector investment in 2010. Moreover, the value share of different types of assets in total fixed asset investment has remained quite stable over time. Consequently, the price index for the fixed asset investment of the four sectors has been calculated by assuming the shares of different asset types in investment by sector have remained constant since 1981 at their 2010 levels (Table 7).

**Table 7 Share of type of fixed asset by economic sector**

2010

||Construction|Equipment|
|---|---|---|
|Business|0.602|0.398|
|Infrastructure|0.938|0.062|
|Government|0.873|0.127|
|Real Estate|0.981|0.019|
|Overall|0.742|0.258|

_Source_ : NBS 14
Given constant expenditure shares, the sectoral Törnqvist price index reduces to a geometrically weighted average of the construction and equipment indices using the 2010 weights. In the two decades ending in 2016, housing investment rose in price by 0.9% per year relative to all investment goods as a result of consisting almost entirely of structures (Figure 5). At the other extreme, business sector prices fell in relative terms by 0.5% per year due to the high share of expenditures on equipment. The relative prices of investment in the infrastructure and government sectors rose by 0.7% and 0.5% per year, respectively.

There is thus a substantial gain in accuracy from using sector specific price indices rather than using the same price index to deflate the investment of each sector. For the period prior to 1981 when the price indices for equipment and construction are not available, sectoral deflators have been calculated by assuming that the price of each sector follows the same trend relative to the published deflator for GFCF as did the movement of sectoral price indices relative to the overall price index of fixed asset investment in the period 1995 to 2016.

# **Figure 5 Sectoral price indices for fixed asset investment**

<!-- Start of picture text --> Estimated sectoral price relative to total price index for FAI<br>1.25<br>1.20<br>1.15<br>1.10<br>1.05<br>1.00<br>0.95<br>0.90<br>0.85<br>Housing Infrastructure Government Business<br>1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016<br><!-- End of picture text --> _Source:_ Author estimates based on NBS data.

# **Results**

# **_Investment flows_**

The estimates of sectoral investment flows quantify the marked re-orientation of the structure of capital formation in China in the past decade. There has been a shift away from investment in the business sector towards investment in housing and infrastructure (Figure 6, Panel A). A number of factors have driven this change. In the business sector, the rate of investment depends crucially on the expected growth of the economy. A fall in the expected growth rate of the economy will result in business sector investment dropping until it reaches a level that brings the growth of the capital stock to be once again in line with the lower expected growth of the economy. Indeed, in the period 2008 to 2016, economic growth slackened, from around 9.6% to about 6.7%. With growth slackening, enterprises lowered their expected need for capital and this resulted in a sharp drop in business sector investment from an estimated 20% of GDP in 2008 to 16% in 2016 (Figure 6, Panel B).

15
# **Figure 6 Share of investment in different sectors**

<!-- Start of picture text --> A. Share of total gross fixed capital formation (GFCF) B. Sectoral GFCF as share of GDP, constant prices<br> % %<br>70 25<br>60<br>20<br>50<br>40 15<br>30 10<br>20<br>5<br>10<br>0 0<br>Housing Infrastructure Government Business Housing Infrastructure Government Business<br><!-- End of picture text --> _Source:_ Author estimates However, the fall in business investment has been offset by a surge in capital formation in other sectors of the economy. Following the introduction of a private housing market at the turn of the century, private capital formation in the residential sector started to increase rapidly from 2004 onwards. By 2015, capital formation in the residential sector was greater than that in the business sector of the economy. Rising demand for new housing generates a strong demand for infrastructure outlays in urban areas as the public finance laws force the profits made by local governments from land sales to be largely invested in urban infrastructure and government-owned land has been used as security for borrowing to finance further infrastructure outlays.

# **_Capital stock_**

The estimates show an acceleration in the growth of capital starting in 2000. This acceleration was most pronounced following the investment package introduced in 2009 (Figure 7). In the five years to 2011, capital grew by 14% annually with similar increases in the business sector and the rest of the economy. As the impact of the stimulus on the economy faded, economic growth slipped and brought a marked decline in the growth rate of the capital stock in the business sector. However, in the remainder of the economy, the very rapid growth of the capital stock did not slacken. The gap between the growth of the capital stock in housing, infrastructure and government and that of GDP rose from 3.7 percentage points between 2006 and 2011 to 6.7 percentage points in the five years ending in 2016.

**Figure 7 Growth of the capital stock by economic sector**

% per year <!-- Start of picture text --> 20.0<br>18.0<br>16.0<br>14.0<br>12.0<br>10.0<br>8.0<br>6.0<br>4.0<br>2.0<br>0.0<br>1981 1986 1991 1996 2001 2006 2011 2016<br>Housing Infrastructure & Government Business Total<br><!-- End of picture text --> _Source:_ Author estimates 16
# **_Capital-output ratio_**

The consequence of these very different sectoral trends has been that the overall capital-output stock of government assets (schools, hospitals and offices _etc_ .) has only grown slightly faster than GDP, with the ratio of the capital stock to overall GDP remaining low at between 0.2 and 0.3 (Figure 8, Panel A). The increase in the overall capital-output ratio has been driven by the significant rise in the capitaloutput ratio in the infrastructure sector, predominately related to assets for transport and urban development.

The housing sector has been the other source of the rise in the overall capital-output ratio. Prior to the reform of the housing sector at the turn of the century, investment in housing had been neglected. Housing investment picked up markedly a decade ago. Given the rapid increase in GDP after the country’s entry into the WTO, the pickup in growth of housing stock did not, at first, generate an increase in the ratio of the housing stock to GDP. Housing investment rose to a new high in 2007, fueled by expectations that rapid price rises would continue. This coupled with a slackening in the growth of GDP has resulted in a steady increase in the ratio of the housing stock to GDP from 2007 onwards (Figure 8, Panel A). The business sector capital-output ratio has increased somewhat whether measured relative to total GDP (Figure 8, Panel A) or relative to GDP in the business sector (Figure 8, Panel B).

**Figure 8 Capital-output ratio by economic sector**

<!-- Start of picture text --> Constant prices<br> A. Capital stock by sector as ratio of total GDP B. Capital stock by sector as ratio of sectoral GDP<br>3.5 4.0<br>3.0 3.5<br>2.5 3.0<br>2.5<br>2.0<br>2.0<br>1.5<br>1.5<br>1.0<br>1.0<br>0.5 0.5<br>0.0 0.0<br>1980 1985 1990 1995 2000 2005 2010 2015 1991 1996 2001 2006 2011 2016<br>Government Business Infrastructure Housing Business sector Whole economy<br><!-- End of picture text --> _Source:_ Author estimates using NBS data The above estimates include an estimate for the stock of R&D capital. The stock of this type of capital is, however, quite small. Using the revisions to the estimates GFCF published in 2016 and the estimate of the average depreciation rate for R&D expenditures in the United States, which Li and Hall (2017) put at 28% per year, the stock of R&D capital can be estimated for China. Over the past two decades, the stock has risen sharply but still amounts to only slightly below 4% of GDP, accounting for about 21⁄2% of the capital stock in the business and government sectors (Figure 9).

17
# **Figure 9 R&D capital stock**

<!-- Start of picture text --> % of GDP, constant 2010 prices<br>4.5<br>4.0<br>3.5<br>3.0<br>2.5<br>2.0<br>1.5<br>1.0<br>0.5<br>0.0<br>1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015<br><!-- End of picture text --> _Source:_ NBS (2016), Statistical Yearbook 2016 and 2015, Science and Technology Yearbook The definition of infrastructure used in the above estimates attempts to exclude investment in the vehicles purchased to use transport infrastructure by enterprises in the transport sector. It assumes that the higher ratio of investment in equipment in the transport sector relative to other infrastructure sectors is due to investment in vehicles. This investment is reassigned from the infrastructure sector to the services sector.

# **_Incremental capital-output ratios_**

The rise in the overall capital-output ratio is associated with a rise in the incremental capital-output ratio (ICOR) – a measure of the productivity of capital. It is measured as the investment share divided by the growth rate. Conceptually investment should be measured net of depreciation but here it is measured on a gross basis, following a methodology used in many cross-country studies. In order to calculate sectoral ICORs, estimates have been made of sectoral GDP.

This rise in the overall ICOR has been driven by very different trends in the various sectors of the economy (Figure 10). The contrast between the ICOR in the housing, infrastructure and government sectors and the business sector is very striking both in terms of the level and the trend. The housing, infrastructure and government sectors have an ICOR that was nearly 14 times higher than in the business sector in 2016. During the recent slowdown in the economy, the incremental capital-output ratio in the business sector has risen, despite the fall in the growth rate of investment.

**Figure 10 Incremental Capital-Output ratio by sector**

<!-- Start of picture text --> Four year moving average<br>A. Infrastructure, government and housing B. Business sector ( scale changes )<br>35.0 3.5<br>30.0 3.0<br>25.0 2.5<br>20.0 2.0<br>15.0 1.5<br>10.0 1.0<br>5.0 0.5<br>0.0 0.0<br>1991 1996 2001 2006 2011 2016 1991 1996 2001 2006 2011 2016<br>Source: Author estimates<br><!-- End of picture text --> 18
# **Sensitivity of the estimates to assumptions**

# **_General sensitivity with respect to depreciation_**

There are a large number of assumptions for both the depreciation rate and the initial capital stock in the literature. For depreciation, the estimates vary between 3% and 10%. A meta-regression for the 42 identified published estimates suggests that assumptions about the depreciation rate have drifted upwards over time: from 3% in 1988 to 7.2% in 2017, with an average for English language estimates of just over 5%, consistent with the international experience and with the estimates used in this paper. If the published paper is in Chinese, or directly cites Chinese sources, then the estimate of the depreciation is 3.4 percentage points higher than the estimates in English language papers.

Given these differences, the sensitivity of the capital stock estimated in this paper to different assumptions about the initial capital stock and depreciation rates has been estimated. The estimates of the capital stock in the past two decades are almost completely unaffected by estimates of the initial capital stock given the rapid growth of investment in China since 1952 and the impact of the depreciation of the initial capital stock over time. Indeed, a doubling of the capital stock in 1952 would raise the estimated level of the capital stock in 2016 by only 0.02%.

The estimated level of the capital stock is more sensitive to the depreciation rate than to the initial value of the capital stock. The extent of the dispersion in estimates of the capital stock using the perpetual inventory method depends on the growth rate of investment over the time period for which the capital stock is estimated as well as the depreciation rates. A high growth rate of investment moderates the difference in estimated capital stocks due to assumptions about depreciation to a significant extent. For example, with a 5% depreciation rate and zero investment growth, the estimate of the capital stock will eventually converge to be half the estimate with a 10% depreciation rate. However, if the annual compound growth rate of investment is 10% (close to the 63 year average growth in Chinese capital formation), the difference in the eventual level of the capital stock will be reduced to one-quarter (see Box 1 for the derivation of this result). Moreover, the convergence to the long-run difference will be much quicker with the 10% investment growth rate than with zero growth.

With the path of sectoral investment estimated in this paper, the difference in the levels of the capital stock had converged to close to their expected long-run values by 2005 (Figure 11, Panel A). The consequence of this quick convergence of the ratio of the different estimates of the capital stock to the estimate with 5% depreciation is that over the period 1995 to 2015, there is very little difference in the growth rates of the different estimates of the capital stock contingent on different depreciation rates. From 1998 onwards, the spread between the highest and lowest estimated growth rates is rarely greater than 0.5% (Figure 11, Panel B).

**Figure 11 Sensitivity of capital stock estimates to changes in the depreciation rate**

<!-- Start of picture text --> A. Level of capital stock relative to capital stock with 5% B. Growth rate of the capital stock with different<br>depreciation depreciation rates<br>16 3.0<br>1.00 14 Different growth rates 2.5<br>2.0<br>0.95 12<br>1.5<br>0.90 10 1.0<br>8 0.5<br>0.85<br>6 0.0<br>0.80 -0.5<br>4<br>0.75 2 spread in growth rates -1.0-1.5<br>0.70 0 -2.0<br>6% 7% 8% 9% 10% 5% 6% 7% 8% 9% 10%<br>1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015<br><!-- End of picture text --> _Source:_ Author estimates using data defined above 19
# **_Results using the depreciation rate of Holtz and Sun_**

Although, the theoretical arguments above suggest a limited impact of the depreciation rate on the evolution of the aggregate estimated capital stock, there could nonetheless be more sensitivity at the sectoral level. Among recent papers, one by Holz and Sun (2017) is particularly complete both in terms of the different models of depreciation that have been used and for building national data from provincial level data. The authors use the three assets enumerated in official sources (structures, equipment and other). In their standard geometric depreciation rate model, the authors assume a depreciation rate of 5% for structures, 12.5% for equipment and 8% for the asset category “other.”<sup>1</sup> However, it is doubtful that the asset category “other” represents gross fixed capital formation (see above). Sectoral depreciation rates consistent with these asset depreciation rates have been calculated using the sectoral shares of each asset, giving a depreciation rate for housing of 5.0%, infrastructure and government of 6.2%, while that for the business sector is slightly higher at 7.3%. In aggregate, this study generates a time-varying depreciation rate that rises to an average of 4.9% in the decade to 2016.

The impact of using the Holz and Sun depreciation rates, weighted sectorally, on the estimated capital state stock is small (Figure 12). By 2016, the estimated capital stock using the alternative depreciation rates is just 9.5%. However, most of this difference emerged before 1970. Indeed, by 1995, the estimates based on alternative depreciation rates were already 11.2% below the estimates in this paper. As a result, the difference in the growth rates of these two estimates of the capital stock was only 0.08% per year in the past decade.

# **Figure 12 Impact of differing depreciation rates on estimates of capital stock in this paper**

A. Level of capital stock B. Growth of capital stock <!-- Start of picture text --> 4.0<br>18<br>3.5 16<br>3.0 14<br>2.5 12<br>10<br>2.0<br>8<br>1.5<br>6<br>1.0<br>4<br>0.5 2<br>0.0 0<br>Alternative depreciation rates This paper This paper This paper<br><!-- End of picture text --> _Sourc_ e: Author estimates, _Note:_ The alternative depreciation rates are those suggested by Holz and Sun (2017).

# **Comparison with alternative estimates of the capital stock** **_Estimates by Holz and Sun_**

The sectorally-based capital stock estimates made in this paper can be compared to the asset and province based estimates by Holz and Sun. In fact, for the 20 years ending in 2015, the estimates for the total capital stock in this paper are very similar to the overall capital stock produced by Holz and Sun (Figure 13). However, for the period 1952 to 1972, the estimates differ very sharply from those estimated in this paper due to the much lower estimate of the initial capital stock. Once this difference has been eroded due to depreciation of the initial capital stock and rapid growth of investment, the estimates of the capital stock correspond quite closely to those presented in this paper. In terms of

> 1 Holz and Sun (2017), footnote 27.

20
the capital-output ratio, by 2016, the estimates presented here are less than 1% different from those generated by H&S. Moreover, over the period 1995 to 2005, the average compound growth rate of the capital-output ratio differed by just 0.2% per year (2.9% against 2.7%).

**Figure 13 Two estimates of the capital-output ratio**

This paper and Holz and Sun <!-- Start of picture text --> 3.5 20.0<br>Level<br>3.0 15.0<br>2.5 10.0<br>2.0 5.0<br>% difference<br>1.5 0.0<br>1.0 -5.0<br>1995 2000 2005 2010 2015<br>Holz & Sun This paper<br><!-- End of picture text --> _Source_ : Holz and Sun (2017) and author estimates

# **_Estimates by Wu et al._**

While the estimates in this paper agree with those of Holz and Sun, there are substantial differences relative to the estimates published by Wu _et al._ (2016) and Bailliu _et al._ In the former case, the nonresidential capital stock is shown as growing more rapidly than the estimates in this paper (Wu _et al._ put the average annual compound growth between 1990 and 2010 at 15% against an estimate of 12% in this paper). While the estimates for the non-residential capital stock in Bailliu et al. for the period 2004 to 2014 are similar to those in this paper, their estimates for both the growth and level of the total capital stock are lower than those in this paper and grow less rapidly – indicating a difference in the estimate of the capital stock in the housing sector. By 2014, the capital stock in this paper is estimated to be 5% higher than the estimates in the Penn World Tables.

# **_International comparisons of capital-output ratios_**

The extent to which there has possibly been over-investment in China can be judged domestically by the rates of return, but cross-country comparisons of capital-output ratios can also provide evidence to judge the level of Chinese investment. The OECD publishes data on the non-residential capital stock covering 28 of its member countries for the past two decades and data for somewhat fewer countries for the previous decade. The OECD data show that the average non-residential capital-output ratio for its members was around 2.6 for the five years ending 2016. However, this estimate is based on a capital-services definition of the capital stock rather than the balance sheet estimate definition used in this paper. While the comparable capital-output ratio for China has steadily increased over the 20 years prior to 2016, as infrastructure investment rose, its level is nonetheless slightly below that in the OECD area at 2.3 (Figure 14).

21
# **Figure 14 Non-residential capital-output ratios in the OECD area and China**

<!-- Start of picture text --> 3.0<br>2.5<br>2.0<br>1.5<br>1.0<br>0.5<br>0.0<br>1986 1991 1996 2001 2006 2011 2016<br>Average OECD country China<br>Source: Author estimates and OECD Economic Outlook Database<br><!-- End of picture text -->

# **_Infrastructure and government and residential sector capital-output ratios_**

Across countries, there is much less information available that would permit a comparison of the capital stock in the government and infrastructure sectors. Information is available for investment in the general government sector but not all infrastructure is undertaken by the general government sector. Moreover, at the industry level, few countries publish detailed capital stock data that would enable an exact comparison to be made with these estimates for China. Cross-country comparisons are complicated by the differences in the classification of infrastructure investment across countries. One country, the United States, does publish estimates for the non-residential capital stock in the private sector by industry and for the total government sector. However, some of the sectors shown as infrastructure in China are in the private sector in the United States. Moreover, even in the United States, no industrial breakdown of the private sector capital stock has been published for the years after 2001.

An approximate comparison between China and the United States of the combined capital stock in the government and infrastructure sectors can be made. It requires an assumption that private infrastructure has remained a constant share of private non-residential investment since 2001. On this basis, the capital-output ratio for the infrastructure and government sector in China had reached the same level as in the United States by the beginning of this decade (Figure 15, Panel A). Since then, it has moved steadily above the level in the United States.

# **Figure 15 Capital-output ratios in the United States and China**

A. Infrastructure and government B. Housing <!-- Start of picture text -->
1.2 1.4<br>1.0 1.2<br>1.0<br>0.8<br>0.8<br>0.6<br>0.6<br>0.4<br>0.4<br>0.2 0.2<br>0.0 0.0<br>United States China United Sates China<br><!-- End of picture text -->

_Source:_ BEA Fixed Asset Database and author estimates for China 22
In the housing sector, the capital-output ratio was below that in the United States until 2010 (Figure 15, Panel B). Since then the ratio for the housing sector in China has moved above that in the United States and this development will continue unless there is an abrupt fall in housing investment in China.

# **Total factor productivity growth by sector**

The incremental capital-output ratio is one measure of the efficiency with which capital is used but it is only a partial measure of the productivity of the economy. The overall efficiency of the economy is better measured by the productivity of both labor and capital – total factor productivity. Most growth accounting studies use the total amount of employment as the labor input and add a separate variable that measures the qualifications of the overall labor force. But the overall labor force is far from being homogenous. The growth accounting analysis assumes competitive markets, so employee compensation is assumed to reflect marginal productivity.

There is a long history of not using just the numbers employed as a measure of labor input. Kendrik (1956) argued for weighting physical labor inputs by a baes-period average compensation which, as Denison (1961) pointed out, enables the contribution of structural change in the distribution of labor in the economy to productivity growth be, at least partially, eliminated. Jorgenson (1991) argued for a much fuller decomposition of labor input covering education, age and gender with each input weighted by compensation.

# **_Labor quality indicators_**

A full decomposition of labor inputs by sector would be difficult to achieve in China due to lack of underlying data and restricted publication of data from labor market surveys. However, Wu _et al_ . (2015) have published estimates of average employee compensation by industry, which can be taken as a proxy of the quality of labor input by sector. Such data permit a breakdown of employee compensation by the sectors used in the analysis of capital formation (business and government/infrastructure). However, the business sector itself is far from homogenous. In particular it contains two extreme sectors, agriculture and sectors dominated by industrial SOEs (coal mining, petroleum extraction, tobacco, petroleum refining, transport equipment and utilities). The wage levels in these two sectors differ by a factor of over five. Consequently, changes in the share of employment in agriculture will change the average level of compensation, which is being taken as measure of the quality of the labor force.

**Table 8 Employment growth absolute and weighted by sectoral employee compensation**

||Employee<br>compensation|Employment|Employment|Employment weighted<br>by average<br>compensation|
|---|---|---|---|---|
||level, CNY per<br>year, 2010|Millions, 2010|Growth pa<br>1990-2016|Growth pa<br>1990-2016|
|Business|20,031|687.3|0.6|1.2|
|Agriculture|15,383|279.3|-2.3|**--**|
|Remainder|20,650|408.0|3.5|**--**|
|Government and Infrastructure|29,871|73.7|1.1|**--**|
|Whole economy|21,523|761.1|0.7|1.2|

_Source:_ NBS and Wu (2015) for Industrial SOEs and government/infrastructure Labor input into the business sector on a weighted basis grows faster than the unweighted series as there is a move out of agriculture into the rest of the business sector (Table 8). Hence the growth in 23
business sector productivity is slightly faster when measured with a weighted labor input than when measured with an unweighted input. Similarly, in the whole economy quality adjusted labor input grows faster than the numbers employed.

In addition to the impact of changes in the industrial structure of employment, the skill level of the labor force has been steadily increasing, with the average number of years of schooling of the population aged 25 to 64 rising by 1.2% per year. International experience suggests that an additional year of education raises the level of earnings (hence productivity) by 7%.<sup>2</sup> On this basis, the years of education series has been transformed to a human capital index by exponentiating the rate of return by the number of years of education. Such a transformation halves the growth rate of human capital relative to the growth of earnings.

# **_Income shares_**

A measure of total factor productivity also requires a weighting system to combine capital and labor, usually taken to be the share of value-added coming from labor and capital. Such data are provided by the Chinese input-output table but not in enough detail to isolate the sectors used in this study. Wu et al (2015) have provided a slightly more granular IO table covering 37 industries from 1990 to 2010, with nine observations corresponding to the published IO tables. These sectors do not correspond exactly to those used in this paper for two reasons: culture, entertainment and household services are classified as one sector by the CIP data while this paper has allocated culture and entertainment to the government sector. As the bulk of value-added in the CIP sector comes from household services, this sector has been allocated to the business sector. Secondly, the housing sector is kept as part of the real estate sector in the CIP data. In this paper, the housing sector is excluded from real estate by deducting capital consumption of housing from the CIP real estate sector and its addition to the government and infrastructure sectors. The overall result is to show the compensation share to be just over half between 1990 and 2010 with a falling trend between 1997 and 2007 as reforms steadily raised efficiency and profitability (Table 9). Over the following five years there was a slight recovery in the labor share in business sector value-added.

**Table 9 Share of value added at basic prices**

Average 1990 to 2010

||Business|Government,<br>Infrastructure, housing|Whole<br>economy|
|---|---|---|---|
|Compensation of employees|0.544|0.595|0.554|
|Operating surplus|0.287|0.136|0.261|
|Capital consumption|0.169|0.269|0.185|
|Value added at basic prices|1.000|1.000|1.000|
|Production taxes|0.198|0.056|0.189|

_Source:_ Wu _et al._ (2015) CIP project and NBS.

Using these shares, the total factor input for the two sectors and the whole economy has been calculated and so the level of total factor productivity has been calculated year by year from 1990 to 2016. The resulting series can be volatile depending on the cyclical position of the economy. To view

> 2 In China, empirical estimates suggest that the average increase in earnings per year of schooling increased from around 2.5% per year in 1990 to 10% by 2004 and has remained at that level since then. On average, this time path corresponds to the average increase in earnings of 8.0% per year (Wang and Yue, 2009, quoted in ADB 2015).

24
<!-- Start of picture text --> 12.0 12.0<br>10.0 10.0<br>6.0 business sector 6.0<br>2.0 oo<br>-a ;<br>Whole economy 0.0<br>a<br>ay 2.0<br>ei 4.0<br>1991 1996 2001 2006 2011 2016 ULES UES<br><!-- End of picture text -->
The fall in the growth of total factor productivity in the whole economy has been much greater than that in the business sector. This is attributable to the poor growth of total factor productivity in the government, infrastructure and housing sectors and their increasing share of total GDP. During the 12<sup>th</sup> Plan, the growth of total factor productivity in the whole economy was barely greater than 1% per year – half of the growth rate in the 9<sup>th</sup> Plan, itself a period when the poor performance of stateowned enterprises was holding back growth (Table 10). In the business sector, productivity also fell to below the pace seen during the 9<sup>th</sup> Plan, emphasizing the need for a new boost to efficiency in the business sector.

Structural change in the economy and the education level of the population have both been powerful factors offsetting the falling growth rate of the labor force. The movement out of agriculture added nearly 0.9 percentage point to the growth rate of the business sector between the 9<sup>th</sup> Plan period and 2016. Going forward facilitating this ongoing transformation will be a key to offsetting the likely decline in the labor force. The continuing improvement in the average level of education of the labor force is likely to continue as the poorly-educated older age groups retire and are replaced by better educated young people. This process will continue even in the absence of any increase in the proportion of young people in higher education.

**Table 10 Sources of growth in the business sector and the whole economy**

||**8**<sup>**th**</sup>**Plan**|**9**<sup>**th**</sup>**Plan**|**10**<sup>**th**</sup>**Plan**|**11**<sup>**th**</sup>**Plan**|**12**<sup>**th**</sup>**Plan**||
|---|---|---|---|---|---|---|
||**1990-**<br>**1995**|**1995-**<br>**2000**|**2000-**<br>**2005**|**2005-**<br>**2010**|**2010-**<br>**2015**|**2016**|
||||Percentage p|oints peryear|||
|**_Business Sector_**|||||||
|Capital|5.08|4.49|5.27|6.23|4.62|2.63|
|Labour|0.65|0.65|0.36|0.17|-0.03|0.08|
|Structural shift|0.65|-0.10|0.00|0.60|0.35|0.77|
|Education|0.63|0.55|0.31|0.23|0.45|0.49|
|Total factor productivity|4.99|2.83|3.80|4.28|2.44|2.29|
|GDP (business)|12.47|8.63|10.00|11.90|8.00|6.40|
|**_Whole economy_**|||||||
|Capital|3.95|4.40|4.95|5.77|5.32|4.45|
|Labour|0.55|0.64|0.39|0.21|0.19|0.11|
|Structural shift|0.48|0.26|0.42|0.58|0.61|0.30|
|Education|0.65|0.58|0.30|0.19|0.49|0.49|
|Total factor productivity|6.19|2.53|3.48|4.21|1.11|1.25|
|GDP|12.26|8.63|9.80|11.31|7.87|6.70|

_Source:_ Author estimates

# **_Conclusion_**

The growth in TFP in the whole economy has followed a similar pattern to that in the business sector except that, in the past decade, its slowdown has been far more marked. This slowdown can be traced to the evolution of TFP in the economy outside the business sector, which consists of the housing, government and infrastructure sectors. As outlined in previous sections, the growth in the capital stock in these areas has been very rapid and has accelerated in the past decade. This has resulted in measured TFP ceasing to grow and even falling in some years. Most of the investment in these sectors 26
is debt financed. It is the absence of TFP growth in this sector that has generated the need for greater credit growth for the same increase in GDP. Of course, part of the decline in TFP reflects inadequate measurement of output in the sector. Capital used in housing and government-related infrastructure produces a real return but, by design, this return is not included in the official measure of GDP.

Overall, these estimates of sectoral trend growth rates combine to show a potential growth rate of the whole economy in line with government target for overall GDP growth of around 61⁄2 percent (Table 11). A noteworthy feature of these estimates is that while the level of business sector employment has been flat for the past decade, the quality-adjusted labor force has risen by nearly 7%. This reflects the continuing out movement from agriculture.

**Table 11 Estimated trend GDP growth rate by sector**

||Business<br>sector|Housing,<br>Government,<br>Infrastructure|Whole<br>economy|
|---|---|---|---|
|2012|8.2|7.1|8.1|
|2013|8.3|6.7|8.1|
|2014|7.8|6.4|7.6|
|2015|6.5|6.6|6.5|

_Source_ : Author estimates _Note_ : The whole economy trend is the result of adding the estimated level of trend GDP in the two sectors.

In the next decade, the latest UN population projections suggest a marked fall in the labor force aged 20-54. The scale of outflows from agriculture will need to increase in order to give a bigger boost to the quality of the labor force. In addition, policies designed to keep people in the labor force longer could take advantage of the increase in the 54 to 64 age-group likely in the next decade. The activity rate in this age-group is lower than the younger age-group but even so, it is likely to be sufficiently high to ensure that the quality-adjusted labor force available continues to grow in the period to 2030, with a slowdown of only a few tenths of a percentage point.

The prospects for the growth of the capital stock are more difficult to evaluate since they are clearly endogenous to the performance of the economy. The growth of the business sector capital stock was abnormally low in 2015 due to a poor performance in the industrial sector, some rebound is likely in the short-term, but in the longer-term a rebound in capital formation in the business has to be driven by an increase in total factor productivity.

27
# **Annex: Methodology used in the estimations**

# **_Definition of sectors_**

The analysis of capital formation here covers four sectors: businesses, infrastructure, government and housing. National accounts in China distinguish a government sector and a sector that covers nonfinancial enterprises. It is appealing, but incorrect to use the non-financial corporate sector as a proxy for the business sector. It is wrong because there are three sub-sets of firms in the non-financial sector, a private sector and two sets of which are controlled by the government. Of these two, there are enterprises, across all sectors of the economy, that operate commercially and often have minority shareholders from the private sector but which take into account government policies as well as returns to shareholders. In addition, there is a second group of state-owned companies that provide public services and infrastructure, some of which are known as local government financing vehicles or urban development corporations. These companies rely on subsidies from the government to continue their operations. Under the newer versions of the SNA, such companies should be classed as being part of the government sector, but in the Chinese practice they are still classified as being in the non-financial corporate sector. Moreover, businesses run by their owners are included in the household sector of the economy. As a result, the non-financial sector of the national accounts cannot be used as a proxy for the business sector. Rather, the analysis in this paper is based on an allocation of the economic sectors, as defined in the most recent Chinese Industrial Classification to sectors covering businesses, infrastructure, government and housing. Thus, the sector definition of government here is narrower than the normal definition of general government. Wholly government financed highways, for example, would be allocated to the infrastructure sector. The precise definitions are set out in Table A1.

The definition of infrastructure in this paper is narrow and focusses on services that are provided on a non-commercial basis. Thus, electricity and telecommunications are allocated to the business sector rather than to infrastructure. They are provided on a commercial basis in China, with most of the value-added being created by firms that are listed on either the Shanghai or Hong Kong SAR, China, stock exchanges. On the other hand, railways, toll highways, urban and environmental services are allocated to infrastructure. Enterprises in these are generally publicly-owned and not generally required to cover their full cost of capital. The allocation of industries to the four sectors also has to take into account that data are only available at a high level of aggregation. This leads to some sectors, such as air transport and storage, being allocated to infrastructure rather than to the business sector.

The definition of the government sector used here is also relatively wide in that it includes all scientific research, cultural activities and the activities of non-governmental organizations (NGOs). In the case of cultural and entertainment, this reflects government control of the bulk of these activities. The apparently paradoxical inclusion of NGOs in the government sector is merely a reflection of the Chinese Industrial Classification rather than a statement on the independence of NGOs.

28
# **Table A1 Definition of sectors**

## **Business sector**

Agriculture, Forestry, Animal Husbandry and Fishery Secondary sector Mining Manufacturing Production and Supply of Electricity, Heat, Gas and Water Construction Service sector Information Transmission, Software and Information Technology Wholesale and Retail Trades Hotels and Catering Services Financial Intermediation Leasing and Business Services Service to Households, Repair and Other Services Part of Real Estate **Infrastructure** Transport, Storage and Post Railway Transport Road Transport Water Transport Air Transport Transport Via Pipelines Loading, Unloading and Forwarding Agency Storage Post Management of Water Conservancy, Environment and Public Facilities Management of Water Conservancy Ecological Protection and Environmental Treatment Management of Public Facilities **Government** Education Health and Social Service Scientific Research and Technical Services Culture, Sports and Entertainment Radio, Television, Motion Picture and Video Production Cultural and Art Activities Sports Activities Entertainment Public Management, Social Security and Social Organization Organs of Communist Party of China Government Agencies People's Political Consultative Conference and Democratic Parties Social Security Non-Governmental Organizations, Social Organizations and Membership organisations Grass Roots Self-Governing Organizations **Housing** Part of Real Estate 29
# **_Estimating investment flows_**

# _Estimates for the period 2003 to the present_

For the period after 2002, the steps taken to generate sectoral series for gross fixed capital formation are as follows:

- For the industrial sector, use the industrial enterprise data to measure gross investment in fixed assets measured as the difference between the original value of fixed assets in adjacent years.

- For the service sectors in urban areas, GFCF has been estimated using the fixed asset investment data for outlays on structures and equipment.  Outlays on the asset class “other” have been excluded as they are largely outside the scope of the SNA definition of gross fixed capital formation. No data for the asset type “other” could be found for 2003 and so it was assumed that the share of “other” investment in total fixed asset investment in urban areas was the same in 2003 as in 2004 for all sectors.

- For agriculture, the national data for FAI have been used.

- For the industrial and service sectors in rural areas, the difference between the national and urban FAI data has been added to the urban series as defined above. Since 2011, the extent of this additional investment has fallen to a very low level following a change in definitions used by the NBS. No explanation is available for this change but it may be that the NBS has adopted a functional definition of urban and rural areas (as in the population data) rather than a definition based on the administrative status of the local area. Thus, most industrial investment in rural areas may have been reclassified as being in urban areas, reflecting the population density in the area where the enterprise is located.

- The business sector is estimated as the sum of the four estimates above.

- For the government and infrastructure sectors, the FAI data for urban areas have been used excluding the category “other” investment.

_Estimates for the period 1981 to 2002_ For the period prior to 2003, two different methodologies have been adopted. Between 1981 and 2002, sectoral FAI data have been used as a proxy for gross fixed capital formation without any adjustment, including for the industrial sector. Between 1952 and 1980, data for new capital construction have been used. The growth rate for this series has been used to generate a hypothetical FAI series prior to 1981, as the level of the capital construction series and that for FAI in each sector were different in 1981.

One problem with the data prior to 2003 is that the sectoral definitions used in the published data do not correspond exactly with the definitions used after 2002. Data for FAI in telecommunications are not available prior to 2003. They are included in the transport and telecommunications sector. However, the definition of infrastructure used here excludes telecom investment. A series for FAI in transport has been created by assuming that the share of telecoms in FAI is the same as in capital construction.

In the published official data for the period prior to 1981, data for the capital construction in the public administration sector (government, parties and social organizations) are amalgamated with the sector “other”. According to Chao (1974), the sector “other” refers to all of the “non-productive” investment by state-owned enterprises. Such outlays cover residential and dormitory accommodation, schools, health clinics and hospitals provided by state-owned enterprises. For the period 1959 to 1980, it has been assumed that the capital construction in the public administration sector was half the aggregate amount, based on the share in the first year for which separate data were available. For the 1950s, 30
data have been taken from Chao rather than using the data published in the Fixed Asset Yearbook. For the period 1966 to 1974, no annual data are available for capital construction in the government or infrastructure sector. The available data for plan periods have been divided equally across the years concerned.

The data for the business sector have been estimated as the difference between the non-residential FAI and the government and infrastructure FAI.

# **_Estimates of capital formation in the residential sector_**

A particular effort is needed to estimate capital formation in the housing sector due to the importance of land purchases in the cost of housing construction. The purchase of existing assets should be excluded from estimates of gross fixed capital formation, but the Chinese practice is to include land purchases in fixed asset investment. The scale of the bias introduced by these differences between FAI data and the SNA basis of estimates of gross fixed capital formation has been growing over time. In the 1980s and 1990s, there was little bias, as there was no market in real estate. The bias became more important during the decade starting in 2000 as market-based transactions dominated the housing market.

The NBS has published its methodology for overcoming this bias. The steps it takes are set out below: Gross fixed capital formation = Residential fixed asset investment _Less_ land purchases (which includes the costs of land improvement) _Plus_ difference between sales prices and construction cost multiplied by sales quantity _Plus_ investment in land improvement.

Effectively, this means that GFCF is being measured as property sales less the cost of unimproved land purchased for residential development. This definition is not quite compliant with the SNA, as the deduction for land purchases is made when the developer buys the land rather than when the land is sold to the final purchaser. Thus, if the land has increased in value between the date at which the developer made the purchase and when it is sold to a final purchaser, this increase in value will be included in GFCF. Equally, the quantity of land purchased refers to land bought in a given year rather than the quantity of land sold to the final purchaser.

# **_Adjusting sectoral estimates to agree with the published aggregate data_**

The extent of the differences between the published measures of total fixed asset investment and gross fixed capital formation varies according the time period considered. Four different periods can be identified:

|1953 to 1960|Close correspondence between fixed asset investment and gross fixed capital<br>formation.|
|---|---|
|1961 to 1984|Fixed asset investment averages three-quarters of gross fixed capital<br>formation.|
|1985 to 2002|Fixed asset investment and gross fixed capital formation are essentially equal.|
|2003 to 2015|Fixed asset investment becomes persistently and increasing larger than gross<br>fixed capital formation.|

31
The extent to which the methodology used here results in a reduction of the gap between fixed asset investment and gross fixed capital formation can be judged by comparing the ratio of the sectoral estimates of GFCF to aggregate GFCF and the ratio of total FAI to aggregate GFCF (Figure A1).

# **Figure A1 Sectoral GFCF and Total FAI as a ratio to official Gross Fixed Capital Formation, by period**

Solid line: estimated sectoral GFCF/aggregate GFCF Dotted line: Fixed asset investment/aggregate GFCF <!-- Start of picture text --> 1953 to 1980<br>2.50<br>2.00<br>1.50<br>1.00<br>0.50<br>0.00<br>1981 to 2002<br>1.80<br>1.60<br>1.40<br>1.20<br>1.00<br>0.80<br>0.60<br>0.40<br>0.20<br>0.00<br>1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001<br>2003 to 2015<br>1.40<br>1.30<br>1.20<br>1.10<br>1.00<br>0.90<br>0.80<br>0.70<br>0.60<br>0.50<br>0.40<br>2003 2005 2007 2009 2011 2013 2015<br><!-- End of picture text --> _Source:_ Author estimates using NBS data 32
Prior to 1984, the measurement errors in the FAI are essentially reproduced in the sectoral data. The only information available for a sectoral breakdown comes from the FAI data. Consequently, there is no possibility to reduce the differences between the data for fixed asset investment and that for GFCF.

Between 1985 and 2002, residential property development became increasingly important. So, using an estimate of residential GFCF rather than residential FAI results in the sectoral estimates of GFCF moving slightly closer to the aggregate GFCF data.

Between 2003 and 2015, the aggregate FAI data become essentially useless as a measure of gross fixed capital formation, but the estimated sector GFCF tracks aggregate GFCF quite well. On average, the yearly estimates of sectoral GFCF are less than 2% different from the aggregate GFCF data. Over the whole period, the cumulated sectoral GFCF is practically equal to the cumulated aggregate GFCF series – the difference being just 0.02%. However, in the two most recent years (2014 and 2015), the difference has become much larger: rising to 10% for reasons that cannot be determined. However, this difference will have little impact on the estimates of the capital stock.

Overall, between 1985 (when the reliability of investment data improved) and 2015, the annual sectoral estimates of GFCF differ from the aggregate estimate of GFCF by just 1.7%, though the standard deviation of the difference is 4.7%. Thus, the methodology for estimating sectoral GFCF gives a good basis for evaluating the development of the sectoral capital stock over the medium term but does not accurately reflect the annual year-to-year changes in GFCF and the capital stock.

In order to remove both the year-to-year differences, a uniform scaling factor has been applied to the sectoral estimates to ensure that they sum to the aggregate GFCF data.

# **_Measuring GDP by sector_**

The above estimates of investment and capital stock have to be put into the context of the valueadded that is generated by the capital stock. The sectoral classification used here does not correspond to an official breakdown published by the NBS. There are two problems: there are no estimates of the value-added of the housing sector and the breakdown of the service sector in constant price terms is inadequate to measure the value-added of the infrastructure and government sectors.

For housing, the NBS defines the gross value-added of the housing sector to be equal to the depreciation of the housing stock. The depreciation rates used are 2% per year for urban housing and 4% per year for rural housing. However, neither the stock of housing nor the value of depreciation are published by the NBS. This paper follows Herd (2013) in making an estimate of nominal and real housing depreciation, which are set equal to the value added of the housing sector.

In the Chinese national accounts, the infrastructure and government sectors are subsumed into the sector “Other” in the breakdown of the GDP in the tertiary sector, both in real and nominal terms. From 2004 onwards, more detail is available for the sub-sectors of the “Other” grouping. In particular, the data show nominal values for the following sectors:

- Information Transmission, Software and Information Technology

- Leasing and Business Services

- Service to Households, Repair and Other Services.

Once these sectors have been removed from the “Other” grouping, the remaining sectors correspond to the definition of infrastructure and government used in this paper. The coverage of the value-added in this sector extends beyond the value added created by infrastructure itself and includes the value added generated by services using this infrastructure. In particular for transport infrastructure both 33
the capital stock estimates include investment in vehicles that use transport infrastructure (aircraft, trains and trucks) and the value added of transport services.

Generating a clean series for value-added in government and services is not without problems. The aggregate estimates for the service sector “Other” in the statistical yearbook only correspond exactly to disaggregated data for the period after 2010. Prior to that date there are differences that are particularly large in 2006 and 2007. Moreover, prior to 2004 there are no official published official estimates. For this period, the sectoral GDP breakdown produced for the China Industrial Productivity (CIP) project have been used. The IT/Telecom sector corresponds exactly to the requirement for this paper. However, the other two sectors are parts of larger sectors in the CIP. In these cases, it has been assumed that the two sectors used in this paper remained a constant share of the sectors of which they are a part prior to 2004. Even then, the data in CIP for the sector cultural and household services appear to have a break in 1994. Real value-added for IT/Telecom has been estimated by deflating value-added by the gross output price for telecommunication services. Household services have been deflated by the overall service sector deflator. The two discontinuities in the data series mentioned above mean that the derived growth rates for real value added in 1994, 2006 and 2007 appear to be incorrect. The estimated growth rates for 2006 and 2007 for government and infrastructure have been averaged, while the growth rate of real value-added in the household services sector has been set at 10% per year between 1990 and 1994.

34
# **Bibliography: General**

Arestoff, Florence & Hurlin, Christophe, 2006. "Estimates of government net capital stocks for 26 developing countries, 1970-2002, _Policy Research Working Paper Series_ , No 3858, The World Bank.

- Chao, Kang (1974), _Capital Formation in Mainland China_ , University of California Press, Berkeley.

Chen, Nai- _Ruenn_ (1966), _Chinese Economic Statistics_ , Edinburgh University Press.

- Chow, Gregory C. (1993), “Capital Formation and Economic Growth in China”, _Quarterly Journal of Economics_ , Vol. 108, No 3, pp 809-842.

- Denison E.F (1961), “Measurement of Labor Input: Some Questions of Definition and the Adequacy of Data”, in _Output, Input, and Productivity Measurement,_ Conference on Research in Income and Wealth, Princeton University Press.

- Eckstein O., W. Galenson and Ta-chung Liu (1968), _Economic Trends in Communist China,_ Social Science Research council, Aldine Publishing.

- Feenstra, Robert C., Robert Inklaar and Marcel P.  Timmer (2015a), "The Next Generation of the Penn World Table", _American Economic Review_ , 105(10), 3150-3182.

- Feenstra, Robert C., Robert Inklaar and Marcel P.  Timmer (2015b), “User Guide to PWT 9.0 data files”, www.rug.nl/ggdc/docs/user_guide_to_pwt90_data_files.pdf

- Hamilton J.D. (2017), “Why You Should Never Use the Hodrick-Prescott Filter”, _Review of Economics and Statistics,_ doi: _10.1162/REST_a_00706_

- Herd, Richard, Vincent Koen, Xiao Wang and Thomas Chalaux, (2013). “Policies for Inclusive Urbanisation in China”, OECD Working Paper, Paris.

- Jorgenson D.W. (1991), “Productivity and Economic Growth”, in (eds) Berndt E. and J. E. Triplett, _Fifty Years of Economic Measurement: The Jubilee of the Conference on Research in Income and Wealth._ University of Chicago Press

- Kendrick J. (1956), “Productivity Trends: Capital and Labor”, in (ed) J. Kendrik, _Productivity Trends: Capital and Labor_ , National Bureau of Economic Research.

Liu, Ta-Chung (1968), “Quantitative Trends in the Economy” in Eckstien et al (1968).

- Liu, Ta-Chung and Kung-Chia Yeh, (1963), _The Economy of the Chinese Mainland: National Income and Economic Development_ , The Rand Corporation for the United States Air Force.

- National Bureau of Statistics (2016), “Notice of the National Bureau of Statistics on the revision of the R & D expenditure accounting method to revise the accounting data of the gross domestic product”, July 5<sup>th</sup> , Beijing.

- Perkins, Dwight H. (1988), “Reforming China’s Economic System”, _Journal of Economic Lite_ rature, June, pp. 601-645.

- Perkins, Dwight H. and Thomas G. Rawski (2008), “Forecasting China’s Economic Growth to 2025”, in ed. Brandt L. and T. G. Rawski _(2016), China’s Great Economic Transformation_ , , Cambridge University Press.

- Wu H.X., Xiniming Yue and George G. Zhang (2015), “Constructing Annual Employment and Compensation Matrices and Measuring Labor Input in China”, RIETI Discussion Paper Series 15-E-005

- Wu, Harry X. (2015), “Constructing China's Net Capital and Measuring Capital Services in China, 19802010”, _REITI Discussion paper Series 15-E-006_ , The Research Institute of Economy, Trade and Industry, Government of Japan, Tokyo.

- Zhang, Jun, Guiying Wu and Jipeng Zhang, (2004),“A Compilation of China’s Provincial Capital Stock Series using Perpetual Inventory Method, 1952 to 2000”, _Economic Research_ , October (in Chinese).

35
# **Bibliography: Depreciation rates**

- Bai C E (2009), “Factor income share in China: The story behind the statistics”, _Economic Research Journal._

- Bai C-E., & Chang-Tai Hsieh and Yingyi Qian, (2006). “The Return to Capital in China,” _Brookings Papers on Economic Activity, Economic Studies Program_ , The Brookings Institution, vol. 37(2006-2), pages 61-102.

- Bai Y., Dan Liu and Tan (2016), “Do Financial Frictions Explain Chinese Firms’ Saving and Misallocation?”, _2_<sup>_ND_</sup> _Annual Bank of Canada and University of Toronto Rotman Conference on The Chinese Economy_ .

- Bailliu J., Mark Kruger, Argyn Toktamyssov and Wheaton Welbourn (2016), “How Fast Can China Grow? The Middle Kingdom’s Prospects to 2030”. _Staff Working Paper / Document de travail du personnel 2016-15, Bank of Canada._

- Bulman, David; Kraay, Aart. 2011. “ _Growth in China 1978-2008 : Factor Accumulation, Factor Reallocation, and Improvements in Productivity”_ . Washington, DC: World Bank Group.

- Chen, K., Jefferson, G.H., Rawski, T.G., Wang, H., & Zheng, Y. (1988). “New estimates of fixed investment and capital stock for Chinese state industry”. _China Quarterly_ , 114, 243–266.

- Cheremukhin A., Mikhail Golosov, Sergei Guriev, Aleh Tsyvinski  (2015), The Economy of People’s Republic of China from 1953, NBER Working Paper No. 21397

- Chow, G.C. and Kui-Wai Li (2002), “China’s Economic Growth: 1952-2010”, _Economic Development and Cultural Change_ 51, 247-56.

- Fan, Q. (2012). “Details of perpetual inventory method and capital stock estimation of China from 1952 to 2009”. _Yunnan Caijing Daxue Xuebao_ (Journal of Yunnan University of Finance and Economics), 28(3), 42–50.

- Gong, L., & Xie, D. (2004). “Analysis of factors mobility and variation of marginal productivity in China”. _Jingji Yanjiu_ (Journal of Economic Research), 1, 45–53.

- Hall, R.E., & Jones, C.I. (1999). “Why do some countries produce so much more output per worker than others?” _Quarterly Journal of Economics,_ 114(1), 83–116

- Holz C. and Yue Sun (2017), “Physical Capital Estimates for China’s Provinces, 1952 -2015 and Beyond”, CESifo Working Paper No.6472

- Holz, C. (2006). “New capital estimates for China”. _China Economic Review_ , 17(2), 142–185.

- Hong P.and Hy Li  (2017) “Avoiding pitfalls in China's transition of its growth model”, _Journal of Policy Modeling_ , 2017

- Hu, Z. and Mohsin S. Khan (1997), “Why Is China Growing So Fast?”, _IMF Staff Papers_ 44, 103-31.

- Islam, N., E. Dai, and H. Sakamoto, (2006). “Role of TFP in China's growth”. _Asian Economic Journal_ , 20(2), 127–159.

- Lei, H. (2009). “Capital stock measurement and investment efficiency in China”. _Jingji Xuejia_ (Economist), 6, 75–83.

- Long Z., R Herrera (2016), “Building original series of physical capital stocks for China's economy methodological problems, proposals for solutions and a new database”, _China Economic Review_

- Li, Wendy C.Y. and B.H. Hall, (2017), “Depreciation of Business R&D Capital”, NBER Working paper 22473.

- Ma G., Ivan Roberts and Gerard Kelly, (2016), “Rebalancing Chinese Economy: Challenges and International Implication” in Reserve Bank of Australia (2016). _Structural Change in China: Implications for Australia and the World_ , Editors: Iris Day and John Simon

36
Maddison, A. (1998), _Chinese Economic Performance in the Long Run_ , Paris: OECD Development Centre.

Meng, L. and Xiaolu Wang (2000), “Assessment of the Reliability of China’s Economic Growth Statistics”, monograph, _National Economic Research Institute_ , Beijing.

- Perkins D.H and Thomas G. Rawski (2011), Forecasting China’s Economic Growth to 2025, in Brandt L. and T. G. Rawlski (Eds) China’s Great Economic Transformation

Perkins, D. (1988), “Reforming China’s Economic System”, _Journal of Economic Literature_ , 26, 601-45.

- Shan, H. (2008). “Re-estimating the capital stock of China: 1952–2006”. _Shuliang Jingji yu Jishu Jingji Yanjiu_ (Studies on Quantitative and Technological Economics), 10,17–31.

- Sun L. and Jao Jie, (2016), “Capital Stock Estimation of Chinese Industries Based on Endogenous Depreciation Rate”, _Journal of Beijing University of Aeronautics and Astronautics (Social Sciences Edition)_

- Wang X. and Yixiao Zhou (2016)” Forecasting China’s Economic Growth by 2020 and 2030” in _China’s New Sources of Economic Growth, Volume 1_ , ANU Press

Wang, X. and Fan, G. (2000). _Sustainability of China's economic growth_ . Beijing: Economic Science Press.

- Wang, Yan and Y.D. Yao (2001), “Sources of China’s Economic Growth 1952–1999: Incorporating Human Capital Accumulation”, _China Economic Review_ 14, 32–52.

- Wang, Yixuan, and Y. Wu, (2003).  “Preliminary Estimates for China’s Capital Stock in the State Sector,” _Statistical Research_ (in Chinese, Zhongguo Guoyou Jingji Guding Ziben Cunlia ng Chubu Cesuan), No.5, pp.40-45.

- Woo, W.T. (1998), “Chinese Economic Growth: Sources and Prospects”, in _The Chinese Economy_ edited by M. Fouquin and F. Lemoine, Economica Ltd, Paris.

- World Bank (1997), _China 2020: Development Challenges in the New Century_ , World Bank, Washington, DC.

- Wu, Y. (2004). _China's economic growth: A miracle with Chinese characteristics_ . London and New York: Routledge Curzon Press.

- Wu, Y. (2007). “Capital stock estimates for China's regional economies: Results and analyses”. _Economics Discussion Paper: UWA Business School_ , University of Western

- Wu, Y.R. (2004), _China’s Economic Growth: A Miracle with Chinese Characteristics_ , London and New York: Routledge Curzon Press Limited.

- Ye, Z. (2010). “Re-estimating the capital stock of China: 1952 – 2008”. _Tongji yu Xinxi Luntan_ (Statistics & Information Forum), 25(7), 36–41.

- Young, A. (2003), “Gold into Base Metals: Productivity Growth in the People's Republic of China during the Reform Period”, _Journal of Political Economy_ 111, 1220-61.

- Zhang, J. (2008). “Estimation of China's provincial capital stock (1952–2004) with applications”. _Journal of Chinese Economic and Business Studies,_ 6(2), 177–196.

- Zhang, J.; G. Wu, and J. Zhang, (2004), The estimation of China’s provincial capital stock: 1952–2000, Economic Research Journal 10, p35-44.

- Zhang, Jun, Guiying Wu and Jipeng Zhang (2007), “Estimation of China’s Provincial Capital Stock Series”, paper presented at _Productivity and Efficiency Workshop, Tsinghua University_ , January 13-14.

- Zhao X. and Chongwen Zhong (2017), Low Carbon Economy Performance Analysis with the Intertemporal Effect of Capital in China, _Sustainability_ .

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