This document summarizes an econometric model that estimates purchasing power parity (PPP) levels for gross domestic product (GDP) and its components (C, I, G) across countries and over time. The model extends previous work by integrating PPP benchmarks from international comparison programs with national GDP deflator time series in a state space framework. Estimation is done using a Kalman filter algorithm. Results are presented graphically for China and India, comparing constrained and unconstrained models. Dropping constraints from the 2005 and 2011 rounds has little and more noticeable impacts, respectively, on estimated price level indexes.

1. Econometric Estimation and Aggregation of
PPP Panels for Components of GDP
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
A. N. Rambaldi, L. T. Huynh, D. S. P. Rao, University of Queensland
Discussant: Kim Zieschang, IMF
International Association for Income and Wealth, Rotterdam, 2014
The views expressed are the author’s and should not be attributed to the IMF, IMF staff ,or Executive Board

2. Real Sector Division
IMF Statistics Department
Overview
 Extends earlier work by Rao, Rambaldi, and Doran
(RRD)(RIW 2010) on integrating PPP benchmarks with
national GDP deflator time series
• Includes GDP components C, I, G as well as total GDP in the
same system
• Continues RRD features such as
 Full information, integrated estimation of time series and cross
sectional (PPP) GDP (and now component) price developments
 Estimates of precision of parameters and the implied price levels
 Feasible Kalman filter estimation algorithm

3. Real Sector Division
IMF Statistics Department
Very brief sketch of RRD [1]
 State space signal extraction model, mapping from PPPs
observed with some error to a vector of “true” but
unobserved PPPs
 Countries placed in one of three groups:
• ICP benchmark year: Reference country, non-ICP (non-reference)
participating countries, ICP (non-reference)
participating countries
• Non-ICP benchmark year: Reference country, all others

4. Real Sector Division
IMF Statistics Department
Very brief sketch of RRD [2]
yt  Zt pt  t
Benchmark year mapping of observations y (log
transformed PPPs) on selection matrix Z with random error
term
   S
  
     
   
      %         
1 0 0
ˆ ; ; ; t t t np t np t
y p Z S S
 
p S S

t p p t
PPP extrapolation
ln it it it it p%  PPP  p 
where i t t
 
,[ 1, ]
, 1
1,[ 1, ]
it i t it it it
t t
GDPDef
p p c c
GDPDef


   

5. Real Sector Division
IMF Statistics Department
Very brief sketch of RRD [3]
 For nonparticipating countries in PPP benchmark years,
and for all countries in non-benchmark years, RRD poses
an econometric prediction equation for GDP (and C, I, G
in the more elaborate model). The RHS of this equation is
a set of predetermined variables; for example, for PPP-GDP,
this model sets the “price level index” (PPP over the
exchange rate) as a function of explanatory variables
used in, e.g., Kravis and Lipsey (1983), and others.
 The model can be straightforwardly constrained not to
touch the estimate of the evolution of national deflators
through setting the variance of the error term in the log
PPP update equation to zero.

6. Real Sector Division
IMF Statistics Department
Very brief sketch of RRD [3]
 For nonparticipating countries in PPP benchmark years,
and for all countries in non-benchmark years, RRD poses
an econometric prediction equation for GDP (and C, I, G
in the more elaborate model). The RHS of this equation is
a set of predetermined variables; for example, for PPP-GDP,
this model sets the “price level index” (PPP over the
exchange rate) as a function of explanatory variables
used in, e.g., Kravis and Lipsey (1983), and others.
 The model can be straightforwardly constrained not to
touch the estimate of the evolution of national deflators
through setting the variance of the error term in the log
PPP update equation to zero.

7. Real Sector Division
IMF Statistics Department
Comments and questions on RRD [2]
 By reference, e.g., to the Oulton paper, this session, this
model seems to be enforcing homotheticity on the
results stochastically, unless you set the variance on the
update equation to zero, in which case it does this with
certainty. Could you comment?
 If so, would you need to include a systematic component
to explicitly allow nonhomothetic “extrapolation drift?”
 From Deaton and Aten (2014), there are likely problems
with the regional links computed in the 2005 ICP round;
could the model be constrained to adjust only the
between ICP region parities in 2005 but retain within
region “fixity” of PPPs as a way of incorporating ICP
history to correct or shed light on the approximate size of
this issue?

8. Real Sector Division
IMF Statistics Department
Comments and questions on RRD [3]
 Comment: It appears that constraining the model not to
touch national GDP deflators (other than level) would
have consequences for the “fixity” of previous PPP
benchmarks (because this constraint generates revisions
to previous benchmarks); users of these will need to
accommodate to this, as have users of revisable series
elsewhere that may have administrative uses have had to
do.

9. Real Sector Division
IMF Statistics Department
Results [China]

10. Real Sector Division
IMF Statistics Department
Results [India]

11. Real Sector Division
IMF Statistics Department
Observations on results
 Dropping the 2005 ICP round as a constraint
(Ignore2005) seems to have very mild impacts on the
time profile of the price level indexes (PLIs) of GDP for,
e.g., China and India
 Dropping the 2011 ICP round as a constraint
(Predict2011), on the other hand, predicts a higher PLI
than the 2011 benchmark for both; the estimate lies
outside the upper 2 SE confidence band around the PLI
estimate that is constrained (stochastically) to the 2011
benchmark results.
 Interpretation?