Economic analysis about The Big Mac Index

~ ) Pergamon J o u n t a l q f l n t e r n a t i o n a l Monca' a n d Finance Vol. 16. No. 6, pp. 865 878, 1997 © 19t~7 Elsevier Science Ltd. All rights rcservcd Printed in G r e a t Britain

P I I : S0261-5606(97)00032-6 0 2 6 1 - 5 6 0 6 / 9 7 $17.00 + 0.00

Burgernomics: the economics of the Big Mac standard*

L I L I A N O N G +

Department of Accounting and Finance, The University of Western Australia, Nedlands, WA 6907, Australia

In the course of PPP research, much o f the debate over the validity has been over the choice o f an a p p r o p r i a t e ' b a s k e t ' for making purchasing power comparisons. The different compositions of goods and services in these baskets across countries have resulted in arguments against their usefulness for PPP purposes. This problem is a u g m e n t e d by the existence o f productivity differentials in t r a d e d and non-traded goods across coun- tries. T h e r e f o r e we consider the use o f the Big Mac as the international monetary s t a n d a r d as being a more palatable alternative: It is p r o d u c e d locally in over 80 countries a r o u n d the world, with only minor changes in recipe and thus has the flavour of ' t h e perfect universal commodity'. O u r results indicate that the Big Mac Index is surprisingly accurate in tracking exchange rates over the long-term, which is consistent with previous PPP research findings. W e subsequently enhance our PPP comparisons by taking into account the productivity differentials between countries and excluding n o n - t r a d e d goods from the Big Mac Index to derive the No-Frills Index. ( J E L F31). © 1997 Elsevier Science Ltd. All rights reserved.

'Suppose a man climbs five f e e t up a sea wall, then climbs down 12 feet. Whether he drowns o r not depends u p o n how high above sea-level he was when he started. T h e same p r o b l e m arises in deciding whether currencies are under- or o v e r - v a l u e d . . . ' The Economist, 26 August 1995 (p. 70)

The purchasing power parity (PPP) doctrine is perhaps o n e o f the oldest and most widely researched areas in international finance. The origins o f PPP theory can be traced back to Spanish scholars o f the sixteenth century, although the intellectual origins o f the doctrine are credited to Wheatley's and

*This p a p e r is a revised version o f a section o f my PhD thesis at the University o f W e s t e r n Australia, jointly supervised by Professor H. Y. Izan and Professor K. W. Clements. I ' d also like to thank G e o f f Kingston, P e t e r Forsyth, M a r d i Dungey, James R. Lothian, the participants at the 1995 PhD Conference in Economics and Business and an anonymous referee for their helpful comments; and the Australian Agency for I n t e r n a t i o n a l D e v e l o p - ment ( A u s A I D ) , and the D e p a r t m e n t of Accounting and Finance, The University o f Western Australia for their financial support. All remaining errors in this p a p e r are mine. *Corresponding author. Tel.: + 6 1 08 93803625; fax: +61 08 93801047; e-mail: long@ecel.uwa.edu.au

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Burgemomics: the economics of the Big Mac standard: Li Lian Ong

Ricardo's w o r k in the n i n e t e e n t h century. ~ PPP t h e o r y as we know it today, however, is attributed to Gustav Cassel's writings during the 1920s. This interest has intensified over the last two decades with t h e collapse o f t h e B r e t t o n W o o d s system and the reintroduction o f flexible exchange rates in t h e early 1970s. 2 T h e controversial findings during this time have resulted in some researchers rejecting the merits of PPP in explaining exchange rate move- ments, while others c o n t e n d that PPP does i n d e e d provide a strong basis for exchange rate determination, with useful policy implications.

In t h e course o f PPP research, m u c h o f the debate over its validity has b e e n over t h e choice o f an appropriate 'basket' for making PPP comparisons. T h e different compositions of goods and services in these baskets across countries and the extent to which these items affect the exchange rates have resulted in arguments against their usefulness for PPP purposes. F r o o t and R o g o f f (1994) observe that most empirical tests do not a t t e m p t to c o m p a r e identical baskets, but instead use different countries' c o n s u m e r and wholesale price indices which consist o f different weights and mixes o f goods across countries. This m e a n s that even if PPP holds, it m a y not necessarily show up in the results unless the two countries in question have identical baskets. Similarly, B e t t o n e t al. (1995) argue that w h e n consumption bundles are not identical, price indices based on local consumption patterns m a y behave differently even though the law o f one price holds for each commodity, resulting in biased outcomes o f PPP tests. 3

A n o t h e r major limitation in PPP research has b e e n t h e productivity bias hypothesis (PBH), which is probably considered the most serious criticism o f the absolute PPP t h e o r y today. This hypothesis, first introduced by H a r r o d (1939) and subsequently formalised by Balassa (1964) and Samuelson (1964), is based on the premise that productivity growth in the tradeable goods sector is faster t h a n that in the non-tradeable goods sector. 4 T h e result is that if t h e real exchange rate b e t w e e n two countries is c o m p u t e d using price deflators that include both tradeable and non-tradeable goods, t h e n the currency o f t h e country with faster productivity growth in the t r a d e d sector than in the n o n - t r a d e d sector will be systematically overvalued relative to its PPP level. 5

T h e U n i t e d Nations International Comparisons Project (ICP) m e t h o d o f accounting for PPP, which has received wide attention recently, is also based on the premise o f productivity differentials b e t w e e n countries. 6 According to Kravis (1986), this system o f international income and purchasing p o w e r comparisons improves t h e m e a s u r e m e n t o f countries' average incomes and t h e differences b e t w e e n them. Moreover, the ICP m e t h o d also enables t h e compar- ison o f price levels b e t w e e n countries and n o t just the relative changes in t h e m ] Using t h e ICP data, O h (1996) finds that PPP holds in the long-run f o r G-6 and O E C D countries u n d e r flexible exchange rates.

Given t h e prevailing index-number and productivity bias problems, we have d e c i d e d to use the Big Mac as the international m o n e t a r y standard in this test o f PPP, in place o f the traditional basket o f goods and services. O u r decision is based on the Big Mac being 'the perfect universal commodity'. 8 F u r t h e r m o r e , since t h e Big Mac comprises both t r a d e d and n o n - t r a d e d goods, we are able to incorporate the productivity bias concept into o u r research. Pakko and Pollard

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Burgernomics: the economics o f the Big Mac standard: Li Lian Ong

(1996) provide an i n d e p e n d e n t analysis o f Big M a c PPP. In that paper, the authors investigate t h e p e r f o r m a n c e o f absolute and relative Big M a c PPP. T h e y also provide a discussion on why PPP fails. While we also p e r f o r m tests o f absolute and relative PPP similar to Pakko and Pollard's, we extend the analysis by (i) examining the productivity bias problem in g r e a t e r detail using the Big M a c h a m b u r g e r ; and (ii) improving on the Big Mac Index by introduc- ing the No-Frills Index, which takes into account the productivity differentials b e t w e e n countries.

T h e data used in this study consist of the prices o f M c D o n a l d ' s Big M a c hamburgers in 34 countries and the corresponding exchange rates over t h e 1986-1994 period. These are published annually in The Economist magazine. O u r results indicate that the Big Mac Index performs just as well as, if n o t b e t t e r than, most indices used in tests of PPP. Like Pakko and Pollard (1996), we find that the Index is surprisingly accurate in tracking exchange rates over the long-term (i.e. t h e 9 years o f o u r sample period) which is consistent with previous PPP research findings. Even though individual currencies m a y deviate f r o m Big M a c PPP on a country-by-country basis, there is a distinct t e n d e n c y for deviations to offset o n e a n o t h e r so that the world currencies, in aggregate, are at parity for any 1 particular year. Moreover, geographic influences a p p e a r to play an important role in currency valuation. We show that PPP compar- isons can be e n h a n c e d by taking into account the productivity differentials b e t w e e n countries and excluding n o n - t r a d e d goods from the Big Mac Index to derive the No-Frills Index.

This p a p e r is organised as follows. Section I examines t h e valuation o f currencies relative to their Big Mac PPP. This is followed by f u r t h e r tests o f PPP using regression analysis in Section II. In Sections III and IV, the Big Mac is d e c o m p o s e d into its t r a d e d and n o n - t r a d e d c o m p o n e n t s in o r d e r to e n h a n c e PPP comparisons. W e conclude with a s u m m a r y o f o u r findings in Section V.

I. T h e v a l u a t i o n o f c u r r e n c i e s

In this section, we investigate the valuation of currencies relative to their Big Mac PPP. Let Pc, be t h e domestic currency price o f a Big Mac in c o u n t r y c in y e a r t; P,* be the price in US dollars o f a Big Mac in the US; and Sct be the spot exchange rate, defined as the domestic currency cost o f US$1. Accord- ingly, P, JPt* is the Big M a c PPP. Expressed in logarithmic form, we have

(1) log Pct/Pt* Pet rct==- ( Set ) = log~-t. - log Sct,

such that a currency is said to be overvalued if rot is g r e a t e r t h a n zero, undervalued if r,., is less than zero and at parity if r , equals zero. T h e p e r c e n t a g e deviation f r o m parity is approximately rct X 100. Figure 1 shows the country averages o f t h e o v e r / u n d e r - v a l u a t i o n s , rc., w h e r e t h e 'o' notation indicates averages over time. Broadly speaking, it appears that t h e high-growth, developing economies in the A S E A N - O c e a n i a and E a s t e r n E u r o p e a n regions are generally u n d e r v a l u e d against the US, while the currencies o f d e v e l o p e d

867

Burgernomics: the economics o f the Big Mac standard: Li Lian Ong

rt. x 100

60

40

> 20 ©

-20

-40 >

60

-80

i l t I L l l i i i O i l l l O i O i O l O i O i O i l l i O i l l i O i O i ~ i i i i i i ,

I I I

n o,o

Grand Average

O , , ,, ,, ,, I

I The Americas Western and Central Europe Eastern Europe East Asia ASEAN-

Oceania

FIGURE 1. Over/under-valuation of currencies: regional groups, 1986-1994 averages.

r., x 100

35

30

25

o= "~ 20

i ,5 o

10

0 .=

"~ -5 .g

-10

Grand Average

] ] ~ ' I I ' [ ] . . . . . [ 1986 1987 119881 1989 1990 1991 1992 1993 1994

I I FIGURE 2. Over/under-valuation of currencies: annual cross-country averages, 1986-1994.

countries in Western and Central Europe, along with t h o s e o f the highly industrialised East A s i a n countries o f Taiwan, Japan and S o u t h Korea, are overvalued. 9 Figure 2 plots the annual averages o f the deviations from parity across countries, to,, where the ' . ' n o t a t i o n indicates averages across countries. A s can be seen, the U S dollar appears overvalued in 1988 and 1994, a l th o u g h n o t by much in the latter year. The dollar appears undervalued in all o t h e r ye ars. 10

868

Burgernomics: the economics of the Big Mac standard." Li Lian Ong

II. F u r t h e r tests o f Big M a c P P P

In Section I, we look at the valuation o f currencies relative to their Big Mac PPP and find that geographic influences play an important role in currency valuation. Furthermore, it appears that the U S dollar is generally at parity on a year-by-year basis. Using both time-series and averaged data, we now conduct regression-based tests to corroborate our results. Consider the following rela- tionship between the actual exchange rate in country c and year t (Set) and the corresponding price ratio Pet -= P c t / P t * :

( 2 ) log S a = o~ + / 3 log p ~ ,

where the PPP hypothesis implies a zero intercept term and a unit slope coefficient (o~= 0, / 3 = 1). The regression results are presented in Table 1. II Overall, Eq. ( 2 ) appears to model short-term PPP very well. 12 We subse-

TABLE 1. Regression results: exchange rates and prices (standard errors in parentheses)

Year PPP M o d e l N u m b e r o f Intercept Slope A d j u s t e d S.E. observations R 2

I. Cross-country 1986 A b s o l u t e 14 0.124 (0.118) 0.915 (0.046) 0.968 0.318 1985/1986 Relative . . . . . . . 1987 A b s o l u t e 8 - 0 . 2 2 5 (0.087) 0.953 (0.026) 0.995 0.183 1986/1987 Relative 7 - 0 . 0 5 2 (0.012) 0.167 (0.080) 0.358 0.031 1988 A b s o l u t e 16 0.180 (0.116) 0.958 (0.035) 0.980 0.353 1987/1988 Relative 7 - 0 . 3 7 6 (0.207) - 0 . 6 5 3 (0.557) 0.058 0.044 1989 A b s o l u t e 17 - 0 . 0 1 0 (0.145) 0.991 (0.037) 0.978 0.427 1988/1989 Relative 16 - 0 . 2 6 3 (0.033) 1.635 (0.088) 0.958 0.093 1990 A b s o l u t e 18 - 0 . 0 1 4 (0.135) 0.953 (0.041) 0.969 0.422 1989/1990 Relative 17 0.002 (0.033) 1.075 (0.022) 0.993 0.132 1991 A b s o l u t e 19 - 0 . 0 6 3 (0.128) 0.964 (0.039) 0.972 0.388 1990/1991 Relative 18 - 0 . 0 4 8 (0.033) 0.879 (0.115) 0.771 0.127 1992 A b s o l u t e 22 - 0 . 0 7 3 (0.154) 0.990 (0.042) 0.964 0.485 1991/1992 Relative 18 - 0 . 1 9 1 (0.083) 2.155 (0.184) 0.889 0.317 1993 A b s o l u t e 24 - 0 . 0 4 8 (0.112) 0.987 (0.029) 0.981 0.392 1992/1993 Relative 20 0.036 (0.026) 0.798 (0.030) 0.974 0.112 1994 A b s o l u t e 31 - 0 . 0 2 8 (0.103) 1.010 (0.025) 0.982 0.360 1993/1994 Relative 23 0.053 (0.022) 0.850 (0.025) 0.981 0.103

II. C r o s s - c o u n t r y / t i m e - s e r i e s 1986-1994 A b s o l u t e 169 - 0 . 0 1 7 (0.042) 0.981 (0.012) 0.977 0.388

Relative 126 0.002 (0.024) 1.000 (0.031) 0.896 0.272

III. Average over time 1986-1994 A b s o l u t e 34 - 0 . 0 1 8 (0.094) 1.001 (0.024) 0.982 0.347

Relative 26 0.003 (0.014) 1.127 (0.032) 0.980 0.073

869

Burgernomics: the economics o f the Big Mac standard: Li Lian Ong

quently run the regression using country data averaged over time, such that log So° = o~ + / 3 log Pc.. T h e results suggest that P P P holds as a long-run proposi- tion. ~3

Previously, we e m p l o y e d P P P in terms of levels which is also known as absolute P P P . W e now e m p l o y the relative version of P P P which is in first differences, i.e. Alog Set = a ' + / 3 'Alog Pc,, w h e r e Pc~ = P ~ J P * , as before. The use o f first differences accounts for the proven I(1) p r o p e r t y o f exchange rates. ~4 As with the absolute P P P regressions, we estimate the relative P P P m o d e l for each year's d a t a as well as for the p o o l e d data. W e also consider the use o f averaged data. ~ O u r results from using p o o l e d data s u p p o r t the use o f Big M a c prices for making P P P comparisons. Thus, o u r findings once again show that Big M a c P P P holds over the long-term.

O u r findings to this point indicate that Big M a c P P P generally holds for o u r sample countries, b o t h on a year-by-year basis and averaged over 9 years. However, these results are not without exception. In certain cases, exchange rates have b e e n f o u n d to deviate significantly from parity. W e will now briefly discuss the different possibilities as to h o w these deviations could o c c u r in the context of o u r research.

P P P theory assumes that there are no barriers to trade. It has long b e e n recognised that such barriers prevent arbitrage from taking place and lead to d e p a r t u r e s from parity. 16 In the case of a Big Mac, for instance, the cost o f i m p o r t e d b e e f in J a p a n (which accounts for nearly 80% o f the ingredients in a Big Mac) includes a 50% tariff. 17 Big Mac prices could also b e distorted by high taxes in countries such as D e n m a r k and Sweden and inflated p r o p e r t y costs in H o n g Kong, J a p a n and Singapore, which could exaggerate the degree o f d e p a r t u r e f r o m parity for these currencies. It has also o f t e n b e e n held that the failure o f the law o f one price is due, in large part, to systematic attempts by firms operating in international markets to stabilise destination m a r k e t prices, when nominal exchange rates change, in o r d e r to p r o t e c t m a r k e t share. ~s A n o t h e r reason for observed d e p a r t u r e s from Big M a c P P P is the 'status symbol' argument, which suggests that in certain countries, fast-food chains in general (and the M c D o n a l d ' s franchise in particular) are rarities and are thus able to c o m m a n d a m o n o p o l y p r e m i u m over o t h e r commodities. This is n o t the case in the U S w h e r e intense competition from o t h e r fast-food chains w o u l d serve to k e e p margins slim. A further i m p o r t a n t reason for deviations from P P P is the existence o f productivity differences b e t w e e n countries, m e n t i o n e d earlier. This will b e investigated in the next two sections.

III. Is the Big M a c all tradeable?

H a r r o d (1939) argues that P P P holds true for t r a d e d goods ( T ) only, as the prices o f these goods are purcly thc effect of exchange rate movements. Accordingly, these prices should not vary outside the limits sct by transporta- tion costs and tariffs. T h e r e f o r e P P P should no longer hold o n c c n o n - t r a d e d goods ( N ) are taken into account, sincc they are not expected to have the same prices in different countries except u n d e r spccial circumstances. Balassa (1964) subsequently formalises H a r r o d ' s exposition by looking at deviations f r o m P P P

870

Bu~ernomics: the economics of the Big Mac standard: Li Lian Ong

in the context o f productivity biases. H e finds that m a r k e d productivity differ- entials in T b e t w e e n 'rich' and ' p o o r ' countries, along with wage equalisation within each economy, cause the prices o f T in terms of N to b e c h e a p e r in the richer economies. W e will use this a p p r o a c h as a basis for slicing the Big M a c into its T and N components.

Clements and Frenkel (1980) take the price level to b e a linear h o m o g e n e o u s ( C o b b - D o u g l a s ) function of the prices of n o n - t r a d e d goods, P!v, and t r a d e d goods, PT, with weight ~ given to N:

( 3 ) e - ". 1 - . - P , ~ PT ,

w h e r e 0 < ce < 1 Thus, if P P P applies to T only, then S = P r / P ~ and it follows that

(45 P r = S . P ~ .

By rewriting Eq. ( 3 ) for the foreign country and rearranging b o t h versions o f the equation, we are then able to substitute P r and P.~ in Eq. (4) to obtain

( 5 ) S = ( P r / P N ) " . P--- ( p . ~ / p ~ ) " " p * •

Looking at Eq. ( 5 ) , we can see that the ( P T / P N ) a t e r m b e c o m e s smaller, on the basis o f a simple P P P calculation, as T b e c o m e s relatively c h e a p e r to N in the rich country, as explained by the P B H . In o t h e r words, since N e n t e r into the calculation o f PPP, via the overall price level, b u t do not directly affect exchange rates, the currency of the richer country will a p p e a r to b e 'overval- ued'.

C o n s i d e r also the Clements and S e m u d r a m (1983) relationship b e t w e e n relative prices and G D P p e r capita: 1~

( 6 ) log ~ = A + 0 5 1 o g G D P .

W e rewrite Eq. ( 6 ) for the foreign e c o n o m y and substitute b o t h versions o f the equation into the logarithmic form o f Eq. ( 5 ) to obtain

( 7 ) log S = 3 , + / 3 log G D P - / 3 * log G D P * + log ~ ,

w h e r e 3/= c~A - c~*A*, /3 = c~05 and /3* = a'05". Assuming for expository pur- p o s e s that ~ = ~* and 05= 05*, /3 would then b e equal to /3*. W e also i n c o r p o r a t e the definition in Eq. ( 1 ) so that Eq. ( 7 ) b e c o m e s

, ( G D P ~ ( 8 ) r = y ' + / 3 l o g i c ) ,

w h e r e 7 ' = - ~ and /3' = - / 3 . 2o As the coefficient /3 = o~05, with 0 < a < 1 and 05 < 0, we expect 13 < 0 and /3' > 0. The estimates of Eq. ( 8 ) are given in Table 2 . 21

The estimate o f /3' in Table 2 indicates that, on average, a 10% growth in G D P causes a 2 % appreciation o f the currency in real terms. Recall that o n e of the structural p a r a m e t e r s o f this m o d e l is o~, the share o f non-tradeables in

871

Burgemomics: the economics o f the Big Mac standard." Li Lian Ong

TABLE 2. Regression results: currency valuation and G D P c r o s s - c o u n t r y / t i m e - s e r i e s , 1986-1994 (standard errors in parentheses)

, [ G D P

I n t e r c e p t coefficient y ' Coefficient of relative G D P / 3 ' A d j u s t e d R 2 S t a n d a r d error of estimate

0.259 (0.026) 0.240 (0.023) 0.415 0.266

total costs. As the coefficient /3' = - a4,, we can obtain an estimate o f a given estimates o f /3' and ~b. We use the Clements a n d S e m u d r a m (1983) estimate (h = - 0.256 to derive ~ = 0.937. Thus, the n o n - t r a d e d c o m p o n e n t in a Big Mac accounts for approximately 94% o f its price. This figure appears reasonable given the p r o m i n e n c e o f wages, rent, o t h e r overheads, etc. in the cost o f a Big Mac.

IV. Improving the Big Mac Index: the No-Frills Index

As previously discussed, PPP t h e o r y needs to bc extended to take account o f n o n - t r a d e d goods. O u r calculations in t h e previous section indicate that, on average, non-tradcablcs account for approximately 94% o f the h a m b u r g e r prices. Since these goods play only a very small part in determining exchange rates, they should be excluded in a m o r e sophisticated PPP calculation. We pursue this idea in this section by introducing the No-Frills Index (NFI) in which the non-tradeables arc excluded from t h e Big M a c Index (BMI).

We rewrite Eq. (4) in logarithmic form to r e p r e s e n t t h e PPP condition:

(9) log S = log PT -- log P~

= f ( l o g P , log GDP) - f * (log P * , log GDP*)

g ( l o g ~ - . , ' G D P , =

In the above, the second line reflects Eqs. (3) a n d ( 6 ) and their foreign-coun- try counterparts. The third line invokes (i) a h o m o g e n e i t y assumption that prices at h o m e relative to those abroad affect the exchange rate; and (ii) an assumption that the relevant p a r a m e t e r values are identical in the two coun- tries (o~ = a * and ~h = ~b*, in the notation o f Section III).

Once we have an estimate o f the p a r a m e t e r s o f t h e function g (-, .) in Eq. (9), we can estimate the NFI as log S = ~ (log P/P*, log GDP/GDP*). It can be shown that the N F I is c o m p u t e d as log S -- log S - k, w h e r e S is the actual exchange rate and k is the residual from regression (8). 22 A n o t h e r way o f visualising the N F I is that it incorporates the systematic relationship b e t w e e n departures from parity according to t h e B M I and GDP; this relationship is t h e productivity bias Eq. (8). F o r illustration purposes, Table 3 presents t h e N F I

872

Burgernomics: the economics o f the Big Mac standard: Li Lian Ong

TABLE 3. A c t u a l e x c h a n g e r a t e s , t h e Big M a c I n d e x a n d t h e N o - F r i l l s I n d e x

C o u n t r y

L o g a r i t h m i c

A c t u a l

e x c h a n g e r a t e

(1)

L o g a r i t h m i c d i f f e r e n c e s x 100

Big M a c N o - F r i l l s A c t u a l E R - A c t u a l E R - B M I -

I n d e x I n d e x B M I N F I N F I

(2) (3) (4) = (1) - (2) (5) = (1) - (3) (6) = (2) - (3)

1994

A r g e n t i n a 0.00 0.45 0.47 - 4 5 . 1 1 - 4 7 . 3 0 - 2 . 2 0

A u s t r a l i a 0.35 0.07 - 0.09 28.30 44.18 15.88

A u s t r i a 2.48 2.69 2.47 - 20.97 1.96 22.94

B r i t a i n - 0.38 - 0.24 - 0.39 - 13.94 0.81 14.75

C a n a d a 0.33 0.22 0.04 11.42 28.47 17.05

C h i l e 6.03 6.02 6.23 0.48 - 20.38 - 20.87

C h i n a 2.16 1.36 2.10 79.98 6.16 - 7 3 . 8 2

D e n m a r k 1.90 2.42 2.16 - 5 1 . 5 3 - 2 5 . 5 2 26.01

F r a n c e 1.76 2.08 1.87 - 32.14 - 10.89 21.25

G e r m a n y 0.54 0.69 0.49 - 15.67 5.03 20.69

G r e e c e 5.53 5.60 5.60 - 7.30 - 7.75 - 0.45

H o l l a n d 0.65 0.86 0.66 - 21.58 - 1.66 19.92

H u n g a r y 4.63 4.30 4.49 33.77 14.93 - 18.85

I t a l y 7.40 7.59 7.43 - 18.68 - 2.82 15.86

J a p a n 4.64 5.14 4.80 - 49.14 - 15.88 33.26

M a l a y s i a 0.99 0.49 0.72 49.48 26.79 - 22.70

M e x i c o 1.21 1.26 1.45 - 4 . 6 5 - 2 3 . 7 6 - 19.11

P o l a n d 10.02 9.51 9.82 50.95 19.48 - 31.47

P o r t u g a l 5.16 5.25 5.28 - 9.32 - 12.27 - 2.95

R u s s i a 7.48 7.14 7.47 34.19 1.64 - 32.54

S i n g a p o r e 0.45 0.26 0.04 18.87 41.20 22.33

S o u t h K o r e a 6.70 6.91 6.92 - 21.07 - 22.53 - 1.46

S p a i n 4.93 5.01 4.94 - 8.34 - 1.62 6.72

S w e d e n 2.08 2.41 2.20 - 33.13 - 12.01 21.12

S w i t z e r l a n d 0.36 0.91 0.58 - 54.36 - 21.88 32.48

T h a i l a n d 3.23 3.04 3.36 19.25 - 12.58 - 31.83

M e a n - 3.09 - 1.85 1.23

S t a n d a r d e r r o r o f m e a n 6.76 4.21 5.08

t - s t a t i s t i c - 0.46 - 0.44 0.24

for 1994, as well as the test statistics for that year. N o t e that for China, one o f the poorest countries in the sample, the deviation o f the BMI from the actual exchange rate is approx. 80%; when the NFI is used, the deviation falls to approx. 6%.

We find that, on average, the excess o f the BMI over its No-Frills counter- part is approx. 10%, over the 1986-1994 period. 23 In other words, the BMI undervalues currencies by 10%, on average. Consequently, if The Economist magazine wishes to make some rough adjustments to its BMI to allow for productivity bias, a simple approach would be to add 10% to its estimates o f currency values, especially for the poorer countries.

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V. Summary and conclusion

The Economist magazine is considered the most influential and prestigious financial n e w s p a p e r in the world. In view o f its well-known breezy style which has b e e n described as 'simplify and then exaggerate', one suspects that w h e n the editor first i n t r o d u c e d the Big Mac Index in 1986, it was a s o m e w h a t tongue-in-cheek contribution to what is perhaps the m o s t widely-researched and d e b a t e d doctrine in international finance. M a n y years later, the Big M a c Index is still going strong and is now widely cited and u s e d by academics and practitioners alike. Given the competitive nature o f publishing, one would assume that the survival o f the index would have to be b a s e d on s o m e intrinsic merit and usefulness o f the m e a s u r e in judging the long-term value o f curren- cies.

O u r test results d e m o n s t r a t e that the Big M a c Index is surprisingly accurate in tracking exchange rates o v e r the longer-term, which is consistent with previous findings. The regression tests indicate that purchasing p o w e r parity holds with the Big M a c Index over a 9-year horizon. H o w e v e r , this is n o t to say that the currencies o f all individual countries for all years are at parity. G e o g r a p h i c influences a p p e a r to play a part in those instances w h e r e devia- tions from parity occur. F o r example, the currencies o f developing Asian and East E u r o p e a n countries are consistently undervalued, while the currencies o f the industrialised e c o n o m i e s are overvalued, on average.

The versatility o f the Big M a c Index notwithstanding, we are still able to improve on it by taking into account the existence o f productivity bias b e t w e e n countries. As it is well known, services are relatively c h e a p e r in p o o r e r countries and because these goods have little, if any, role in determining exchange rates, standard P P P calculations which include services tend to show that the currencies o f these countries are systematically undervalued. In o t h e r words, these deviations from parity are related to income. W e confirm the existence o f this productivity bias in the Big Mac Index and subsequently introduce the new No-Frills Index to solve the problem. T h e n e w index excludes the n o n - t r a d e d c o m p o n e n t o f Big Mac h a m b u r g e r s in computing parity. Interestingly, we estimate that this c o m p o n e n t accounts for as much as 94% o f the cost o f a Big Mac. O u r new results indicate that the No-Frills Index p e r f o r m s even b e t t e r than the Big Mac Index, especially for the p o o r e r countries and could b e o f use to practitioners and policy-makers.

Notes

1. The origins of PPP theory are analyzed in detail by Frenkel (1976) and Officer (1982). 2. Studies by A d l e r and Lehmann (1983), Huizinga (1987) and Meese and Rogof~ (1988)

are unable to reject the hypothesis that real exchange rates follow a r a n d o m walk under the floating exchange rate regime. However, recent studies by A b u a f and Jorion (1990), D i e b o l d et al. (1991) and Lothian (1990) find evidence o f mean-reverting behavior in real exchange rates using long-term time series data. O t h e r research into real exchange rate behavior during the float include Dornbusch (1987), F r a n k e l and M e e s e (1987), M e e s e (1990) and Officer (1976). Recent surveys o f the literature are provided by Lothian (1997), R o g o f f (1996) and Taylor (1995).

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3. F r o o t and R o g o f f (1994) and Officer (1982) provide comprehensive reviews o f the l i t e r a t u r e in this area.

4. As an example, consider a two-country, two-good (traded and non-traded, T and N ) world, where one country is rich and the o t h e r poor. Let the rich country be m o r e productive in the production of both T and N. Although this country has an absolute advantage in both goods, it is plausible to postulate that it is relatively m o r e productive in T. The reason lies in the nature of N which have large service c o m p o n e n t s and are labor-intensive. Thus, productivity improvements are m o r e difficult in these areas. Consequently, the relatively higher productivity o f T in the rich country means that their relative prices will be c h e a p e r in the rich country (in terms of N).

5. The mechanics of this concept are discussed in further detail in Section III. O t h e r research into the PBH include Bartolini (1995) and Clemcnts and S e m u d r a m (1983).

6. See Summers and H e s t o n (1991) for a description of the data. 7. T h e r e have been strong criticisms o f the reliability of the ICP method, however. They

include the fact that (i) world average prices are used to value the G D P c o m p o n e n t s , which means that since world average prices are d o m i n a t e d by the larger weights o f rich countries, price weights that are not reflective of the low-income countries t e n d to push up their relative quantity indices (Isenman, 1980); (ii) the ICP prices ' c o m p a r i s o n resistant' services, which have no identifiable unit of output which could be easily priced (Maddison, 1983); and (iii) ICP d a t a are only g a t h e r e d at 5-year intervals (beginning in 1970) and country coverage is limited, which means that data from n o n - b e n c h m a r k years and countries must be o b t a i n e d by extrapolation; moreover, there is also a long time lag between collection of the d a t a and their availability (Rogoff, 1996).

8. The Big Mac hamburger is p r o d u c e d locally in more than 80 countries a r o u n d the world, with only minor changes in recipe. It is 95 mm in diameter, weighs 205 g and generally uses the same ingredients everywhere - - two b e e f patties, a special sauce, lettuce, cheese, pickles and a sesame-seed bun ( L o o k Japan, June 1994). As well as being a ' s t a n d a r d product', this means that its local prices are less likely to be d i s t o r t e d by international t r a n s p o r t a t i o n and distribution costs.

9. t-test results indicate that the majority of the W e s t e r n and Central E u r o p e a n currencies a p p e a r to deviate significantly from parity at the 0.1% level. Only I r e l a n d is at parity with the US. In the A m e r i c a s group, parity with the US is achieved by Mexico and Brazil, while Canada, surprisingly, deviates from its North A m e r i c a n neighbour at the 5% level. This result could perhaps be explained by Engel and Rogers' (1995) finding that crossing the US C a n a d i a n b o r d e r is equivalent to adding 7182 miles between two cities in the same country, in the context o f price differences between locations. Meanwhile, all the A S E A N - O c e a n i a currencies are significantly undervalued. Results of t-tests for parity by region indicate that except for Western and Central E u r o p e which is significantly overvalued, all o t h e r regions are, on average, either undervalued or at parity with the US. The currencies o f A S E A N - O c e a n i a and Eastern E u r o p e are significantly undervalued by approx. 28%, while the null hypothesis of PPP holds for the A m e r i c a s and East Asia. These findings are explained to some extent by F r a n k e l and W e i ' s (1995) research into the existence o f currency blocs. Finally, the t-statistic for the entire sample indicates that the currencies, averaged over time and countries, deviate significantly from parity at the 5% level.

10. Results of t-tests seem to imply that the over- or under-valuation of each currency, with respect to the US dollar, t e n d to offset one another on an annual basis. W i t h the exception o f 1987, when the US dollar is significantly undervalued at the 1% level, it a p p e a r s that the US dollar is m o r e or less at parity in each year. Cumby (1996) finds that deviations from Big Mac PPP are useful for forecasting exchange rates. A f t e r account- ing for currency-specific constants, a 10% undervaluation in 1 year, according to the Big Mac Index, is associated with a 3.5% appreciation over the following year.

11. Initially, we estimate Eq. ( 2 ) for each year, using cross-country data; the results are given in the first part o f Table 1. The adjusted R 2 figures indicate a very significant relationship between the implied and actual exchange rates on a year-by-year basis. The hypotheses of a zero intercept, a unit slope coefficient and the joint hypothesis o f a z e r o

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Burgernornics: the economics of the Big Mac standard." Li Lian Ong

intercept and unit slope coefficient cannot be rejected for any 1 year, except for 1986 and 1987. Next, we pool the data over time and across countries; the results are p r e s e n t e d in the second part o f Table 1. In this case, both the null hypotheses, when taken separately, cannot be rejected. However, the joint hypothesis is rejected at the 5% level o f significance.

12. F r a n k e l and R o s e (1995), H a k k i o (1984) and Oh (1996) show that the higher variability in cross-sectional data, relative to time-series data, allows for m o r e precise p a r a m e t e r estimates in tests of PPP. Similarly, Cumby (1996) d e m o n s t r a t e s that a larger cross-sec- tion yields enough power to detect substantial mean-reversion in his tests of Big Mac PPP. H e finds little persistence in deviations from Big Mac PPP, with only 30% o f deviations persisting into the following year

13. As can be seen in the third part of Table 1, the adjusted R 2 remains very high at 98%. The intercept and slope coefficient are not significantly different from zero and unity, respectively, while the joint hypothesis for the slope and intercept also cannot be rejected. This finding of long-run PPP is consistent with the results o f A b u a f and Jorion (1990), D i e b o l d et al. (1991), Frenkel (1981), Lothian (1990) and Officer (1976). M a n z u r (1990) shows that the long-run in PPP terms is 5 years.

14. See Blundell-Wignall et al. (1993), Edison and Pauls (1993) and F r o o t and Rogoff (1994). Note that as our d a t a observations are both across countries and over time, non-stationarity may not be such a problem as c o m p a r e d with the situation with pure time-series data.

15. The results o f the relative parity regressions o f annual data are given in the first part o f Table 1. With the exception of 1986/1987 and 1987/1988, we find the adjusted R - to be very high for each year. However, the joint hypothesis o f a zero intercept and unit slope is rejected for all years except 1990/1991. The j o i n t hypothesis is also rejected when averaged d a t a are used. W h e n the d a t a are pooled across countries and over time, the adjusted R 2 is approx. 90%. In this instance, both the null hypotheses of a zero i n t e r c e p t / u n i t slope coefficient as well as the joint hypothesis cannot be rejected.

16. See H a r r o d (1939). 17. Look Japan, June 1994. 18. Firms are said to ' p r i c e to m a r k e t ' when they charge different local prices across export

markets to reflect the particular local competitive situation; any exchange rate move- ment is a b s o r b e d by altering the home currency export price (Ghosh and Wolf, 1994). Cumby (1996) finds that relative local currency prices a p p e a r to adjust to reduce deviations from Big Mac PPP.

19. Using the price of haircuts in 24 countries to measure the price of N, they find a strong positive association between the price of a haircut and the GDP. They estimate the income elasticity o f the relative price of T, as r e p r e s e n t e d by the regression coefficient ~/, in Eq. ( 6 ) , as being equal to - 0 . 2 5 6 , with s t a n d a r d e r r o r 0.061. Their finding that N become relatively more expensive with increasing income is consistent with the PBH.

20. Note that the negative o f r, as defined in Eq. (1), is the conventional definition of the real exchange rate.

21. To estimate Eq. ( 8 ) , we use the d a t a on r, calculated in Section I, and G D P figures o b t a i n e d from the International Financial Statistics of the International M o n e t a r y F u n d (1996). Observations are omitted in instances where G D P d a t a are unavailable.

22. See Ong (1995). 23. Not shown in Table 3; see Ong (1995) for calculation details.

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