New Methodological Developments for the ICP. W. Erwin Diewert Department of Economics University of British Columbia. Introduction. The World Bank released the results for ICP 2005 in February of this year
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W. Erwin Diewert
Department of Economics
University of British Columbia
Taking logs of both sides of (1) leads to:
(2) ycnk = c + n + cnk ; c = 1,…,C; n = 1,…,N; k = 1,…,K
where ycnk ln pcnk, c ln ac, n ln bn and cnk ln ucnk.
(24) ycnkr = c + n + r + cnkr ; c = 1,…,C; n = 1,…,N;
k = 1,…,K(c,n) ; r = 1,2
where the c are the log country PPP’s, the n are the log product price effects and the r are the two log representativity effects and the cnkr are independently distributed random variables with mean zero and constant variances. In order to identify the parameters, we impose the following normalizations:
(25) 1 = 0 ; 1 = 0.
(27) prcnk ar brc cn ; r = 1,…,5; c = 1,....,C(r);
n = 1,...,N; k = K(r,c,n) ;
(28) a1 = 1;
(29) br1 =1; r = 1,…,5
where the above model pertains only to the price data for the ring countries. There are C(r) ring countries in region r = 1,2,3,4,5, the a’s are interregional PPPs and (28) means that region 1 is chosen as the numeraire region, the b’s are the country PPPs for the countries in one of the 5 regions and (29) means that country 1 in each region is chosen as the numeraire country in that region and the c’s are commodity effects that depend on the units of measurement for the products.
(33) ln prcnk ln brc = ln ar+ln cn + rcnk ; r = 1,…,5;
c = 1,....,C(r); n = 1,...,N; k = K(r,c,n).
(34) ln [prcnk/brc] = r + n + rcnk
which is a linear regression model. The r are the logs of the interregional PPPs and the n are the individual product effects for the products within the basic heading category of commodities which were price out by the ring countries.
(56)Enr pnr1c=1C(r) enrc/pnrc ; r = 1,...,5 ; n = 1,...,155.
(57)Pnr pnr ; r = 1,...,5 ; n = 1,...,155.