# _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