Transcript What is Happening to U.S. Productivity Growth

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:

d
A 
I

t
0
t 
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.
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 smallscale 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 investmentinvestment 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.
p
t
 (1  r )q  q 
t 1
t
p
D ,t
 r q   t q  (q  q )
t 1
t
t
• Data on asset prices and rates of
depreciation for all assets are required for
the PIM .
t 1
Rate of return
we can solve for the rate of return, given data
on capital compensation for the sector:
r
propertycompensation  { q  (q  q )} At
t
q A
t 1
t
t
t 1
Tax Structure
• The capital rental price can be modified to
incorporate China tax structure:
[r q   q  (q  q )](1  h  u (1  h) z )
t 1
t
t
t 1
1 u
 q
t
t
l
• 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.
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 :
ln k  ln k
t
t 1
  v Kk (ln Ak  ln Ak )
t 1
t 2
k
• where weights are given by the average shares of each
component in the value of property compensation.
1 t
t 1
t
v k  2 (v k  v k )v Kk 
t
t
K
Kk
t
k p
k p
t
K
Kk
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, 1982-1994,19942005.
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).

Note: Industries sorted by growth, in percentage points. Annex Table A3 in text.
17.00
16.00
15.00
14.00
13.00
12.00
11.00
10.00
9.00
8.00
7.00
6.00
5.00
4.00
3.00
2.00
1.00
0.00
finance insurance and real estate
gas
other private services
public services
communication
elc. Machinery
electrical
mot. Veh
oil and gas extraction
transportation
stone clay ,glass
foods and kindred products
appral
construction
misc mfg
paper
petroleum and coal products
lumber
chemical
metal and nonmetallic mining
printing
fab. ,metal
prim. Metal
furniture
leather
textile mill products
trade
trasp. Equip and ordnance
rubber and misc plastics
instrument
coal mining
agriculture
machinery
Industry Capital Input Index (%)
1981-2005
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