Page 331 - Contributed Paper Session (CPS) - Volume 7

CPS2118 Yang Wang
1. domestic real price contribution factor
2. terms of trade contribution factor
3. real output growth
Diewert (2008) further pointed out that if we use GDFE as deflator to calculate
real income, the first component can be eliminated from the decomposition.
3.4 PPPs for output-side
Following Inklaar and Diewert (2016), the aggregate price of real value
added in country k in period t relative to the aggregate price of real value
added in country j in period s can be measured by Törnqvist–Theil output price
index:

 1 i 

i
i
P  exp   (s  s )ln( p i p js  ) ,i  , X M (7)
D
,
kt / js js kt kt
 i 2 
where the value-added output shares s defined as:
i
kt

s  i v i kt , i  , X M where v  v D +v  X v (8)
M
,
D
kt v kt kt kt kt
kt
To get a base invariant PPPs, we follow the CCD strategy to get the transitive
PPPs:
1
 K T  KT
P kt *   P kt / js  (9)
j 1 s 1 
By rearrangement, we can get a much simple form:
ln P  ln P  
kt * kt **
1 1 1
lnP kt **  (s  s kt D )ln(p D p ..D ) (s  s kt X )ln(p X kt p ..X ) (s ..M  s M )ln(p kt M p ..M
)
kt
kt
..X
..D
2 2 2
(10)
Set first country and period 1 as base:
P  kt P kt * P  11* P kt ** P (11)
11**
3.5 PPPs for expenditure-side
The aggregate price of domestic absorption in country k in period t relative to
the aggregate price of domestic absorption in country j in period s can be
measured by the following price index:
p D
P D  kt (12)
/ kt js
p D js

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