Estimates of Capital Input Index by Industries of China, 1981-2005

• Sun Linlin , Beihang University

• Ren Ruoen ， Beihang University

Capital Input Index

• Cross-classified the capital of each sector by 3 types of assets: structure, equipment, and auto.

• Estimate the capital stock under the PIM.

• Estimate the capital rental price with the help of the capital compensation from the input-output series.

• Aggregation of capital service over different asset types with the weights of capital rental price.

Perpetual Inventory Method

• PIM can be expressed by the following equation:

Capital stock estimation need data: 1)a capital stock benchmark,

2) the investment series in current prices

3) Investment deflator

4) Depreciation rate is chosen.

0t tdA I

Investment Data

• From 1996, there are investment data with disaggregated into structure and equipment by sector.

• We use 1996 composition for each industry to disaggregate investment before 1996 by sector into structure and equipment.

• We use the annual domestic revenue of auto plus the net import value of auto , minus auto consumption by household as auto investment data.

• With the application of auto investment ratio for the economy into every sector, we estimate the annual auto investment by sector.

Adjust the investment data to capital formation

• Investment in fixed assets excludes the small-scale investment, but includes the purchase of second-hand capital goods , gross fixed capital formation is a better investment data for PIM.

• Capital formation= investment data – land purchase fee – secondhand capital investment + investment below 500,000 Yuan(50,000 before 1997) + appreciation of commercial house.

Adjust the investment data to capital formation

• Assume the investment below 500,000 is 0.2% of total investment in all years (according to the NBS method ).

• We compare the sector gross value proportion with sector investment proportion, find some sector need to be upward adjustment. These sectors include ： textile mill products furniture, rubber ,leather, stone clay ,glass.

• We will decomposition the 0.2% total investment to these sectors.

Adjust the investment data to capital formation

• Obtain the aggregate second-hand capital investment from the fixed asset investment yearbook for 2003-2005.

• We assume the secondhand capital investment is 1% of total investment for years before 2003 according to the available three years data.

• These aggregate secondhand capital investment are divided into sector with sector investment proportion.

Adjust the investment data to capital formation

• appreciation of commercial house– land purchase fee= Capital formation -investment data+ secondhand capital investment- investment below 500,000 Yuan(50,000 before 1997)

• From the fixed asset investment yearbook, the building investment by sector is available for 2003-2005. We average the 3 years proportions, then apply the proportion to all years.

• The value “ appreciation of commercial house– land purchase fee” is divided with building investment sector ratio.

Investment Deflator

• A deflator for investment in fixed asset is only available since 1992.

• The structure investment deflator for 1980-1991 was construction ex-factory price index, which is from the IO time series price index.

• The auto investment deflator for 1980-2005 was the ex-factory price index from the IO time series price index.

• the equipment investment deflator for 1980-1991 was from the NBS.

Depreciation Rate

• We assumed an asset life of 16 years for equipment, and 10 years for auto, 40 years for structure.

• Under geometrically relative efficiency pattern, with our assumption of assets life, the depreciation rate of equipment is 17%, and structure is 8%, the auto is 26%.

Capital Stock Benchmark

• We estimated the structure and equipment benchmark based on the PIM.

• Under the assumption that the gross value of fixed asset ratio is the same with the capital stock ratio, we estimated the auto capital stock benchmark.

• Net valued of fixed assets in 1980 for sectors were used to distribute the aggregate capital stock for state owned firms over sectors in 1980.

Land Capital Stock

• We can obtain the agriculture land quantity data from “China statistical yearbook”, we must estimate the land price ourselves.

• We adopt the profit discount method, which denotes the price of land as: P=a/r

• a refers to the annual profit, r refers to the annual discount rate.

• From “china agriculture statistical yearbook”, we find the data of profit and cost for land.

Capital Rental Price

• The capital rental price include rates of return, depreciation, and capital gain for each of asset.

• Data on asset prices and rates of depreciation for all assets are required for the PIM .

1 , 1 1(1 ) ( )

tt t t D t t t t tr rp q q p q q q q

Rate of return

we can solve for the rate of return, given data on capital compensation for the sector:

1

1

{ ( )}tt t t

tt

property compensationr

q q q Aq A

Tax Structure

• The capital rental price can be modified to incorporate China tax structure:

• u: the corporate income tax rate, is the property tax rate; h: is the value-added tax rate; z: the present discounted value of depreciation allowances of 1 Yuan investment.

1 1[ ( )](1 (1 ) )

1

ttt t t t

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r h u h z

u

q q q qq

Sector Property Compensation

• Our data source of sector property compensation is the input-output table time series. We subtract the labor compensation from sector value-added to obtain the capital property compensation.

• From farm proceeds per unit area, we estimated agriculture capital and labor input compensation ratios for every year.

Self-employed compensation

• Estimate the number of self employed workers (other than agriculture). (data from professor Yue)

• Estimate the capital stock owned by these companies for the whole economy.

• Allocate the total capital to sector using the sector self employed workers proportion.

• The sector self-employed capital compensation =sector capital rental price* sector capital stock.

• Final capital compensation=capital compensation (IO)+ self-employed capital compensation

Measurement of Capital Input Index

• The capital input index is a Translog quantity index of individual capital inputs :

• where weights are given by the average shares of each component in the value of property compensation.

1 1 2ln ln (ln ln )

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Industry Capital Input Index Results

• Wide range of industry capital input growth rates, service had a high capital accumulation speed. varies from 1.02%(machinery) to 15.91%

(communication)

We compare two sub-period, 1982-1994,1994-2005.

Most manufacturing experience higher capital input. (apparel, lumber, furniture, paper, instrument, etc).

Only few industries experience lower capital input.

(metal and nonmetallic mining, oil and gas extraction, finance insurance and real estate, other private services).

Industry Capital Input Index (%)1981-2005

Note: Industries sorted by growth, in percentage points. Annex Table A3 in text.

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Thank You!