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Are Integration and Comparison Between CPIs and PPPs Feasible? Read chapter Read first chapter

2010 | OriginalPaper | Chapter

Modelling Spatially Correlated Error Structures in the Time-Space Extrapolation of Purchasing Power Parities

Authors : Alicia N. Rambaldi, D.S. Prasada Rao, K. Renuka Ganegodage

Published in: Price Indexes in Time and Space

Publisher: Physica-Verlag HD

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Abstract

The paper examines the role and significance of modeling spatially correlated disturbances in the extrapolation of purchasing power parities and real incomes. Alternative specifications for the spatial weighting matrix are experimented within the general econometric framework developed by Rao et al for the purpose of constructing a consistent time-space tableau of PPPs based on the PPPs for benchmarks constructed as a part of the International Comparison Program (ICP) and temporal movements in national price levels. The paper presents a comparative analysis of the effect of alternative specifications of the spatial weights matrix on the PPP extrapolations. A method based on the principal components approach is suggested when several spatial weights matrices are available. The paper presents empirical findings from the application of the methodology to ICP data available including the recently completed 2005 ICP Benchmark comparisons available from the World Bank. The results clearly indicate the need to model and use a spatially correlated error structure especially when the benchmark data are incomplete. The results are very similar when the spatial weights are based on trade data or on principal component weights.

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previous chapter Harmonized Cross Region and Cross Country CPI Time-Space Integration in the Euro-Zone
next chapter Price Indexes across Space and Time and the Stochastic Properties of Prices
Appendix
Available only for authorised users
Footnotes
1
For example, the Human Development Index is computed and published on an annual basis. Similarly, the World Development Indicators publication provides PPP converted real per capita incomes for all the countries in the world for every year.
 
2
We define “national growth rates” in the next section.
 
3
This follows because \(\phi\) is strictly bounded by the inverse of the eigenvalues of \(\textbf{\textit{W}}_{t}\).
 
4
The form of this covariance follows from the definition of PPP. The interested reader is referred to Rao et al. (2009) for details.
 
5
In the empirical implementation we model \(\sigma_{it}^{2}\) as inversely related to \(GDP_{it}\) per capita measured in $US (exchange rates adjusted). It is well known that exchange rates adjustments accentuate the difference between developed and developing countries and thus provide a suitable measurement of the desired effect.
 
6
The PPPs between currencies of two countries are invariant to the choice of the base country, which in turn requires the predictions of the reference country to be zero with variance zero in all time periods, \(p_{US,t} = 0\). See Rao et al. (2008) for a proof that the method is invariant to the choice of the reference currency.
 
7
However, if the distribution of the disturbances in the state-space from are symmetric, it is median-unbiased. We thank an anonymous referee for making this point.
 
8
The standard errors are computed under the assumption of the lognormality of the predictions.
 
9
We are indebted to Ms Francette Koechlin (OECD) for providing ICP benchmark data for these years. PPPs for those countries which joined in the Euro zone, the pre-Euro domestic currencies were converted using the 1999 Irrevocable Conversion Rates (Source:http://​www.​ecb.​int/​press/​date/​1998/​html/​pr981231_​2.​en.​html). The irrevocable conversion rate of the drachma vis a vis the euro was set at GRD 340.750 Source: http://​www.​bankofgreece.​gr/​en/​euro.
 
10
This was brought to our attention by Steve Dowrick who attended a seminar on the topic presented at the Australian National University in October 2007.
 
11
We are conscious of the fact that serious multicollinearity issues may be present here as the variables are potentially correlated. As the main purpose of inclusion of these variables is to improve the quality of the predictions, we decided to leave the variables in the model with the view that the model results in better predictions.
 
12
We make use of exchange rate converted per capita incomes to overcome the problem of possible endogeneity arising out of the use of PPP converted exchange rates. These data are drawn from the UN sources. Given the systematic nature of the exchange rate deviation index (ratio of PPP to ER), use of exchange rate converted per capita GDP is likely to magnify differences in per capita incomes.
 
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Metadata
Title
Modelling Spatially Correlated Error Structures in the Time-Space Extrapolation of Purchasing Power Parities
Authors
Alicia N. Rambaldi
D.S. Prasada Rao
K. Renuka Ganegodage
Copyright Year
2010
Publisher
Physica-Verlag HD
Book
Price Indexes in Time and Space

Print ISBN: 978-3-7908-2139-0

Electronic ISBN: 978-3-7908-2140-6

Copyright Year: 2010

DOI
https://doi.org/10.1007/978-3-7908-2140-6_4