Parallel session IARIW 2014

1. Role of Capital in India’s Economic Growth:
Capital Stock versus Capital Services
Reproductions of this material, or any parts of it, should refer to the IMF Statistics Department as the source.
Real Sector Division
IMF Statistics Department
Abdul Erumbian and Deb Das
Discussant: Kim Zieschang
International Association for Research in Income and Wealth, Rotterdam, August 29, 2014
The views expressed are the author’s and should not be attributed to the IMF staff or its
Executive Board

2. Real Sector Division
IMF Statistics Department
Overview
 Improving accuracy of the capital measure for India by
disaggregating capital assets by type and activity of use
(104 cells)
• 5 types of capital assets
 Buildings and constructions
 Transport equipment
 Non-ICT machinery
 Hardware and software
 Communication equipment
• 26 industries spanning the Indian economy
• Land is available but was not used in the interest of
compatibility with KLEMS, and because it hasn’t made much
quantitative difference in studies that have included it.

3. Real Sector Division
IMF Statistics Department
Preliminaries [1]
 Total capital rental for each of 26 industries/activities
 
R p K
t k 
5 types k,t k,t
 One capital asset bin per industry has been used in India
prior to this paper
 
p S
  5 types , ,
   
R p K S
t t k 5 types k ,
t
t k k t k t
 S

 k 5 types
k







)
)
 Besides under use of data on industry detail, the capital
price p has been an asset acquisition rather than rental
value
 For each industry/activity the authors break total capital
rental into 5 capital component bins and decompose each
activity’s capital rental into price and volume factors

4. Real Sector Division
IMF Statistics Department
Preliminaries [2]
The log change in total capital rental R for activity j
(suppressing j subscript) is
1 1, 1, ln ln ln ln t t t t t t R R P K      % 
where the log capital service volume index is
  

K v v S S
ln   ln 
ln
t t k k t k t jk t jk t
   
1, 5 types of capital asset 2 , 1 , , , 1
 
1
S S I p
1 
/ [Perpetual inventory]
, , 1 , ,
 
p S
, ,
,
, ,

, , , , , 1
[User cost of ca
I
k t k t k k t k t
k t k t
k t
k k t k t
K I I I I
k t k t t k k t k t k t
v
p S
p p i 
p p p


  

   
  1, 1 1,
pital]
ln ln ln ln [Implicit service price index] t t t t t t P R R K    %   

5. Real Sector Division
IMF Statistics Department
Results [1]
 Capital service volume indexes reveal significant
differences in capital stock growth rates, and importantly
for this paper, significant composition biases in simple
sum aggregates, variable across the 26 industries, driven
importantly by different capital service shares for
equipment

6. Real Sector Division
IMF Statistics Department
Results [2] – Differential capital growth
across activities
Figure 2: Indices of Capital Services, Aggregate Economy and broad sectors, 1980-
2011(1980=100)
Note: Capital service growth rates are calculated using equation (1) and indexed to 1980. All the aggregates are
obtained using a Tornqvist aggregation procedure. Source: India KLEMS database

7. Real Sector Division
IMF Statistics Department
Results [3] – Composition bias of simple
sum capital aggregate
Note: capital composition effect is measures as capital service growth rate minus capital
stock growth rate, where the aggregate capital services in each broad sector and total
economy are obtained by aggregating sectoral capital service growth rates using Tornqvist
aggregation.
Source: India KLEMS database

8. Real Sector Division
IMF Statistics Department
Comments (minor)
 The authors mention exploring replacement of the
“external” financing cost rate i sourced from the central
bank by an “internal” cost of capital calculation; this
would be worth doing
 Is “non-Equipment” Fixed capital?
 On excluding land, does it have a small rental share in
total capital, and thus limited influence? Rental cost itself
might be significant—high implicit financing cost, low
depreciation, but possible significant appreciation offset.
 A lot of work; nicely done.