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