Comparing the Wealth of Nations: Reference Prices and Multilateral Real Income Indexes

This paper considers the problem of comparing real incomes across countries. The available methods are reviewed and their performance is compared using the raw data underlying the Penn World Table. We propose and implement a test of the "Gerschenkron Effect": the downward bias in a country's measured real income when its own prices are used as weights. The test confirms that this Effect obtains with fixed-weight indexes but not with true bilateral indexes based on empirical demand parameters. We also demonstrate the feasibility of estimating the G A I A ("Geary-Allen International Accounts") System which yields true multilateral real income indexes. I I N T R O D U C T I O N I t i s w e l l k n o w n t h a t i n t e r n a t i o n a l c o m p a r i s o n s o f r e a l i n c o m e a r e s e n s i t i v e t o t h e re fe rence p r i ces used . O n e h y p o t h e s i s c o n c e r n i n g t h e n a t u r e o f t h e s e n s i t i v i t y i n v o l v e d i s t h e so-ca l led " G e r s c h e n k r o n Effec t" : a c o u n t r y ' s m e a s u r e d r e a l i n c o m e i s h i g h e r t h e m o r e t h e reference p r ices d i f f e r Paper presented at the Eleventh Annual Conference of the Irish Economic Association. *This research has been supported by the Social Science Research Council of the Royal Ir i sh Academy and forms part of the International Economic Performance Programme of the Centre for Economic Performance at the London School of Economics. We are very grateful to Bettina Aten at the University of Illinois for making the data available to us; to Gavan Conlon and Dave Madden for providing the econometric estimates used in Section I V ; and to Patrick Honohan, Colm McCarthy, an anonymous referee and participants at a seminar in University College Dublin and at the 1997 Irish Economic Association Annual Conference for helpful comments. f r o m i t s o w n pr ices . T h i s effect is u s u a l l y t h o u g h t to re f lec t t h e b ias a r i s i n g f r o m t h e l a c k o f s u b s t i t u t a b i l i t y a s s u m e d i n s t a n d a r d r e a l i n c o m e indexes . Less w i d e l y a p p r e c i a t e d i s t h e fac t t h a t even " t r u e " indexes , w h i c h are based o n u t i l i t y t h e o r y a n d so a l l o w for s u b s t i t u t i o n , are i n g e n e r a l s ens i t ive t o t h e re ference p r i c e vec to r used. I n t h i s paper w e set o u t to t e s t t h e i m p o r t a n c e o f these s e n s i t i v i t i e s , u s i n g t h e r a w d a t a w h i c h u n d e r l i e t h e P e n n W o r l d Tab le . T h e o t h e r i s sue w e address i n t h e pape r i s t h e choice o f i n d e x n u m b e r fo r use i n m u l t i l a t e r a l c o m p a r i s o n s o f r e a l i n c o m e s b e t w e e n c o u n t r i e s . S u c h c o m p a r i s o n s h a v e become i n c r e a s i n g l y c o m m o n i n r ecen t years , r e f l e c t i n g t h e g r e a t e r a v a i l a b i l i t y o f c o m p a r a t i v e da t a , o f w h i c h t h e m o s t ex tens ive source is t h e P e n n W o r l d T a b l e w h i c h d r a w s o n t h e U n i t e d N a t i o n s s p o n s o r e d I n t e r n a t i o n a l C o m p a r i s o n s Pro jec t ( I C P ) . 1 T w o p r i n c i p a l m e t h o d s a re used i n p r a c t i c e i n s u c h c o m p a r i s o n s . T h e I C P a n d P e n n W o r l d T a b l e use a m e t h o d o r i g i n a t e d b y G e a r y (1958) , w h i c h ca lcu la tes w o r l d pr ices a n d exchange r a t e s t h a t c o r r e c t fo r d e v i a t i o n s f r o m p u r c h a s i n g p o w e r p a r i t y . H o w e v e r , i t has b e e n e x t e n s i v e l y c r i t i c i s e d fo r i t s l a c k o f t h e o r e t i c a l f o u n d a t i o n s , n o t a b l y b y S a m u e l s o n a n d S w a m y (1974) a n d D i e w e r t ( 1 9 8 1 a n d 1987) . D i e w e r t i n p a r t i c u l a r h a s a r g u e d i n s t e a d i n f a v o u r o f v e r s i o n s o f t h e so-ca l led E K S m e t h o d , d u e t o E l t e t o a n d Kbves (1964) a n d Szulc (1964) , w h i c h is u s e d b y t h e O E C D a n d b y E u r o s t a t . Recen t w o r k b y N e a r y (1996a , 1996b) a rgues t h a t t h e c l a i m s m a d e for t h e t h e o r e t i c a l s u p e r i o r i t y o f t h e E K S a n d r e l a t e d indexes do n o t h o l d u p i f tas tes a r e n o t n o m o t h e t i c . M o r e o v e r , i n t h a t case, i t is necessary to select f r o m a n i n f i n i t y o f " t r u e " indexes t o use as a n i d e a l o r b e n c h m a r k . N e a r y proposes for s u c h a b e n c h m a r k t h e "GALA." or " G e a r y A l l e n I n t e r n a t i o n a l A c c o u n t s " S y s t e m , w h i c h h a s t h e ease o f i n t e r p r e t a t i o n o f t h e G e a r y s y s t e m b u t is c o n s i s t e n t w i t h u t i l i t y t h e o r y i n t h e c o n t e x t o f m u l t i l a t e r a l c o m p a r i s o n s . H o w e v e r , t h e ease o f c o m p u t a t i o n o f such G A I A indexes a n d t h e i r r e l a t i o n ­ s h i p i n p r a c t i c e w i t h t h e G e a r y a n d E K S indexes r e m a i n o p e n q u e s t i o n s . These issues are addressed be low. F i r s t , w e p resen t a b r i e f o v e r v i e w o f some r e l e v a n t r e s u l t s f r o m t h e t h e o r y o f i n d e x n u m b e r s . I I I N D E X N U M B E R T H E O R Y 2 2.1 Fixed-Weight Bilateral Comparisons and the Gerschenkron Effect F i g u r e 1 i l l u s t r a t e s t h e p r o b l e m s w h i c h a r i s e i n m a k i n g b i l a t e r a l com­ p a r i s o n s o f r e a l i n c o m e s across c o u n t r i e s . P o i n t s J a n d K r e p r e s e n t t h e q u a n t i t i e s c o n s u m e d o f goods 1 a n d 2 w h i l e t h e slopes o f t h e l i n e s t h r o u g h t hose p o i n t s r e p r e s e n t t h e domes t i c r e l a t i v e pr ices o f good 1 i n each o f t w o 1. See Krav i s (1984) and Summers and Heston (1991) for overviews of the I C P and the Penn World Table respectively. 2. See Diewert (1981, 1987), Pollak (1971) and Neary (1996a) for more detailed accounts.