Page 332 - Contributed Paper Session (CPS) - Volume 7

CPS2118 Yang Wang
To get a base invariant PPPs, we follow the CCD strategy to get the transitive
PPPs:
1
 K T  KT
P kt D *   P kt D / js  (13)
j 1 s 1 

By rearrangement, we can get a much simple form:
ln P  kt D * ln P  kt D * ln P (14)
..D
Set the first country and period 1 as base:
P  P D P (15)
D
D
kt kt * 11*
3.6 Terms of trade contribution factor
Diewert (2008) show that terms of trade contribution factor can be defined
as follows:
 1 p X p D 1 p M p D 
X
M
M
X
P kt XM  exp  (s  s )ln( kt X kt D )  (s  s )ln( kt M kt D )  (16)
js
kt
js
kt
/ js
 2 p js p js 2 p js p js   
To get a base invariant PPPs, we follow the CCD strategy to get the transitive
PPPs:
1
 K T  KT
/ js 
P XM   P XM (17)
kt * kt
j 1 s 1 
By rearrangement, we can get a much simple form:
ln P kt XM  ln P kt XM  
**
*
ln P kt XM     1 (s ..X  s kt X )ln( p kt X p ..X )  1 (s ..X  s kt X )ln( p kt D p ..D  )  
**
2
2
 1 1  (18)
   2 (s ..M  s M )ln( p M p ..M )  2 (s ..M  s M )ln( p D kt p ..D  ) 
kt
kt
kt
Set the first country and period 1 as base, we have P XM  P XM P XM  P XM P XM .
kt kt * 11 * 11 ** 11 **
We can show that the following equation holds: P  P kt D * P kt XM .
kt
v
Real GDP on output-side is Y  kt , while Real GDP on expenditure-side is
kt P
kt
v
Z  kt .
kt
P D
kt
Using P  P kt D * P kt XM , we can get Z  Y kt *P kt XM .
kt
kt
So we can get the year-on-year decomposition:

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