EFFECTIVE EXCHANGE RATES AND BIG MAC INDEXES: A COMPARISON OF CURRENCY MISVALUATION ESTIMATES

Transcription

1 EFFECTIVE EXCHANGE RATES AND BIG MAC INDEXES: A COMPARISON OF CURRENCY MISVALUATION ESTIMATES Thomas J. O Brien* Santiago Ruiz de Vargas** December 2016 ABSTRACT For each of The Economist s two Big Mac methods of intrinsic currency valuation (raw and adjusted), this study compares estimates of currency misvaluation versus different effective exchange rate (EER) baskets: (1) weighted equally, (2) by GDP, (3) by equity market capitalization, and (4) by financial wealth. All of these EER basket types imply a consistency between two currencies EER misvaluation and the bilateral misvaluation of the two currencies versus each other. For the adjusted Big Mac method, the EER misvaluation estimates are fairly consistent with each other across the different basket types. *Department of Finance, University of Connecticut, School of Business, 2100 Hillside Road, Storrs, CT ; thomas.obrien@uconn.edu ** Advisory Services, NOERR AG, Wirtschaftsprüfungsgesellschaft Steuerberatungsgesellschaft, Brienner Str. 28, Munich; santiago.ruizdevargas@noerr.com Keywords: Effective exchange rates; misvaluation; Big Mac index; currency indexes Comments invited. A prior version of this paper was presented at the 2016 European Financial Management Association conference (Basel). For helpful suggestions and discussions, we thank Kenneth Clements, Assaf Eisdorfer (especially), Lok Sang Ho, and Jiawei Si.

2 EFFECTIVE EXCHANGE RATES AND BIG MAC INDEXES: A COMPARISON OF CURRENCY MISVALUATION ESTIMATES The term effective exchange rate (EER) refers to an exchange rate between a given currency and a basket of currencies. That is, an EER is essentially a currency index from the perspective of the given currency. An EER is deemed to be a more effective way to measure a given currency s value than a bilateral exchange rate between the given currency and another individual currency (Chinn, 2006). With an EER and a standard of intrinsic foreign exchange (FX) value, like purchasing power parity (PPP) for example, one can estimate a given currency s misvaluation versus other currencies in general. As Chinn (2006) explains, researchers have typically weighted the currencies in EER baskets by relative trade levels--a trade-weighted currency index. For example, Cline and Williamson (2008) summarize various Chinese yuan EER misvaluation estimates based on tradeweighted currency baskets. However, trade weights are economy-specific; therefore, two currencies EER misvaluations will generally be inconsistent with the bilateral misvaluation of two currencies with each other. That is, a Chinese yuan EER misvaluation versus a currency index based on China s trade weights, and a US dollar EER misvaluation versus an index based on U.S. trade weights, would not necessarily be consistent with the bilateral misvaluation of the yuan versus the US dollar. 1

3 Overview of the Study This study compares currency misvaluation estimates across several EER basket weighting methods. None of the methods are economy-specific, and all use simple portfolio weighting rather than the geometric weighting often used in trade-weighted currency indexes (Chinn, 2006). Therefore, all the methods imply that two currencies EER misvaluations are consistent with the bilateral misvaluation of the currencies versus each other. We compare the EER misvaluation estimates for the several basket types using each of The Economist s two standards of intrinsic FX value: (1) the original Big Mac index, which applies the PPP condition and is now usually called the raw Big Mac index; and (2) the adjusted Big Mac method, which takes into account per capita GDP differences across economies using a regression equation that links Big Mac prices and per capita GDPs. The Economist introduced the adjusted Big Mac approach in July 2011 as a better way to measure intrinsic bilateral FX values than the original (raw) Big Mac index. Consistent with this intent, O Brien and Ruiz de Vargas (2016) found that adjusted Big Mac s bilateral misvaluation estimates forecasted subsequent exchange rate changes better than raw Big Mac estimates in 73.7 percent of 179 observations. O Brien and Ruiz de Vargas (2016) also clarified that in the adjusted Big Mac method, a given currency s regression residual is an estimate of the currency s percentage overall misvaluation versus the regression line basket of all currencies in the analysis, including itself and the reference currency. The researchers moreover showed that a given currency s misvaluation estimate versus an equally-weighted basket of the currencies is approximately equal to the regression residual. With equal weighting, the basket s currency positions convert to the same amount of the given currency using the bilateral intrinsic exchange rates versus the currency. The 2

4 basket s percentage misvaluation versus the given currency is the simple average of the basket currencies bilateral misvaluation percentages versus the currency. This study compares currency misvaluation estimates for equally-weighted EER baskets with three, more meaningful EER basket types: (1) GDP-weighted; (2) equity market capitalization-weighted; and (3) financial wealth-weighted. With GDP weighting, the currency positions in the EER basket are weighted by the economies nominal GDP estimates. This approach is based on Ho s (2012) argument that weighting the currency positions in an EER basket by global economic significance is more meaningful in a globalized economy than weighting by trade with specific trading partners. The equity market cap method is based on a similar rationale to Ho s, but from the perspective of international financial investment rather than trade. Internationally diversified investors, like those who would hold the world market portfolio in the International CAPM (Solnik, 1974, 1997, Sercu, 1980, Adler and Dumas, 1983, and Stulz, 1995), would find relevant the misvaluation of their home currency versus an EER basket weighted by the economies equity market capitalizations. (3) The financial wealth weighting method yields an EER basket that overlaps with the wealth-weighted currency risk hedging index in the International CAPM version introduced by Ross and Walsh (1983). 1 Each EER basket type is useful, depending on the specific purpose. So the research question is not whether one EER basket type is better than the others, but how much dufference the EER basket type makes in EER misvaluation estimates, particularly for the improved intrinsic FX value method, the adjusted Big Mac approach. 1 Ross and Walsh (1983) simplify the well-known Solnik (1974) Sercu (1980) special case of the international CAPM by aggregating individual currency risks into a currency index, based on the assumption that the representative investor of each economy has the same average degree of relative risk aversion. This approach was also applied by O Brien and Dolde (2000). 3

5 For each semiannual date that The Economist has published the adjusted Big Mac index, the study estimates bilateral misvaluations for 37 currencies, which belong to economies representing between 95 and 97 percent of world financial wealth, depending on the estimation year. The EER misvaluation estimates are then determined by the bilateral misvaluation estimates and the weighting method for the EER basket type. The GDP weights are based on International Monetary Fund (IMF) nominal GDP estimates, using current prices and market FX rates to convert from local currency to US dollars. The equity market cap weight estimates are from Bloomberg. The wealth weight estimates are from the Global Wealth Data Book, published by the Credit Suisse Research Institute. 2 The report features the EER misvaluation estimates for three currencies of economies with relatively high GDP, equity market cap, and wealth: the US dollar, the euro, and the Chinese yuan. The results show that for the adjusted Big Mac method, the EER misvaluation estimates are fairly consistent with each other across the different basket types, given the inevitable noise in the estimation process. Also, (1) the US dollar has recently been less effectively overvalued for the adjusted Big Mac index than for the raw Big Mac index; and (2) the yuan has been less effectively undervalued for the adjusted Big Mac index than for the raw Big Mac index, and was slightly above intrinsic effective value for the adjusted Big Mac index in January We use the IMF 2010 GDP estimates for July 2011 and January 2012, the IMF 2011 estimates for July 2012 and January 2013, and so forth. The only exception is the Eurozone GDP, which is not provided by the IMF, and for which we use World Bank estimates. We use the 2010 market cap weight and wealth weight estimates for July 2011 and January 2012, and so forth. 4

6 Measuring Effective Currency Misvaluation A difference between actual and intrinsic FX rates indicates a currency misvaluation. The percentage misvaluation of currency F versus currency R is denoted /, and is equal to / / 1, where (in direct terms of currency R) / is the actual FX rate and / is the intrinsic FX rate. The percentage misvaluation of currency R versus currency F is / / / 1. It is straightforward to show the relationship between / and / in equation (1): 1 / 1 / 1 1 For example, if the euro s misvaluation versus the US dollar is 15.4%, it follows from equation (1) that the US dollar s misvaluation versus the euro is 18.2% (using numbers in Table 1). Applying the misvaluation concept to a currency basket (B) results in the percentage EER misvaluation of the basket versus currency R, / / / 1, and the percentage EER misvaluation of currency R versus the basket, / / / 1. We next need to distinguish between (1) currency R s overall EER misvaluation, denoted /, which is versus an overall basket that includes currency R, and (2) currency R s multilateral EER misvaluation, denoted /, which is versus a multilateral basket that excludes currency R. We are really interested currency R s multilateral EER misvaluation, but because the study s overall EER baskets have the same weights from the perspective of any currency, the useful consistency relationship in equation (2) holds for each of the study s overall EER baskets: 1 / 1 / 1 / 2 5

7 In words, equation (2) says that the percentage bilateral misvaluation of currency F versus currency R must be consistent with the percentage overall EER misvaluations of currency F and currency R. The logic for equation (2) is as follows: Given that currency F is misvalued by 6.8% versus the overall EER basket, and currency R is misvalued by 26.2% versus the (same) overall EER basket, it follows that currency F s bilateral misvaluation versus currency R is , or 15.4%. (This logic may be easier to see if we substitute the British pound for the basket. That is, if currency F is overvalued by 6.8% versus the British pound, and currency R is overvalued by 26.2% versus the British pound, it is intuitive and easy to show that currency F would be undervalued versus currency R by 15.4%.) Because a currency s bilateral misvaluation with itself is zero, the multilateral EER basket s misvaluation versus currency R, /, depends on the overall EER basket s misvaluation versus currency R, /, and currency R s overall EER basket weight,, per equation (3): / / 1 3 For equally-weighted EER baskets of a large number of currencies, the difference between overall and multilateral EER misvaluation is small. But for EER weighting by GDP, market cap, or wealth, the overall and multilateral EER misvaluations may be substantially different for currencies with large weights, which is the case for the currencies featured in the study (the US dollar, the euro, and the yuan). 3 3 The estimate of the U.S. share of the total GDP (market cap, financial wealth) of the 37 countries in the study was 24.7% (29.8%, 27.4%) for July 2011, and was 24.4% (38.1%, 35.4%) for July The estimate of the Eurozone share of total GDP (market cap, financial wealth) was 20.9% (11.0%, 24.2%) for July 2011, and was 18.8% (10.1%, 19.8%) for July The estimate of China s share of total GDP (market cap, financial wealth) was 9.8% (6.3%, 8.4%) for July 2011, and was 14.6% (7.8%, 9.4%) for July

8 For example, let currency R be the US dollar with an overall EER weight of 24.4%. Assume the US dollar is misvalued versus the overall EER basket by 26.2%, implying an overall EER basket misvaluation of 20.8% versus the US dollar (equation (1)). Using equation (2), the multilateral EER basket s misvaluation is 20.8% % versus the US dollar. Using equation (1), the multilateral misvaluation of the US dollar is 37.9%. Thus, the US dollar s overall EER misvaluation is 26.2%, versus an EER basket that includes the US dollar with a weight of 24.4%, whereas the US dollar s multilateral misvaluation is 37.9%, versus a basket that includes only currencies other than the US dollar. Note that / 1 /. Although often an acceptable approximation, the inequality implies that an exact relation between /, /, and / is cumbersome, but a more practical consistency relation, between /, /, and /, is as shown in equation (4): 4 1 / 1 1 / 1 1 / 4 Going forward, we use subscripts to specify the EER basket type and the intrinsic FX valuation method. For the type of basket: E = equal weighting; G = GDP weighting; M = market cap weighting; W = wealth weighting; and R = regression. For the intrinsic FX valuation method, represents the raw Big Mac method, and represents the adjusted Big Mac method. So, /$ for example, represents the percentage multilateral misvaluation of the US dollar using GDP weighting for the EER basket and the raw Big Mac method of intrinsic FX valuation. We are mainly interested in the misvaluation estimates for the adjusted Big Mac index than for the raw Big Mac index, but the presentation flows better if the raw Big Mac estimates are presented first. 4 To get equation (4), use equation (1) to rewrite equation (2) as 1 / 1 / 1 /, and then apply equation (3) for both / and /. 7

9 The Raw Big Mac Index The Economist s original Big Mac index, published semiannually since 1986, views a Big Mac as a composite of traded and nontraded goods. Despite limitations and warnings by The Economist to take it with a grain of salt, the Big Mac index has appealing simplicity and overcomes the problem that CPI baskets are usually different across countries. As a result, the Big Mac index has a history of popularity with practitioners, instructors, and researchers. 5 The original raw Big Mac index uses domestic and foreign local Big Mac prices to estimate traditional (absolute) PPP intrinsic FX rates. Let be the domestic Big Mac price in the reference currency and * be the foreign Big Mac price in the foreign currency; the raw Big Mac intrinsic FX rate (in direct terms of the reference currency) is: = / * (5) The percentage misvaluation of the foreign currency versus the reference currency in the raw Big Mac approach is = / 1, where X is the actual FX rate in direct terms of the reference currency. 6 Equivalently, using equation (1), = * / 1, where P* is the actual foreign Big Mac price expressed in the reference currency. The euro s bilateral misvaluation versus the US dollar is thus equal to the ratio of the Eurozone Big Mac price stated in US dollars to the local U.S. Big Mac price. For example, letting 5 Clements, Lan, and Seah (2010, 2012) and Clements (2013) provide reviews of the Big Mac literature. For examples of research, see Annaert and De Ceuster (1997), Clements and Lan (2010), Click (1996), Pakko and Pollard (1996, 2003), Cumby (1997), The Economist (2006, 2011), Landry (2008), Ong (1997, 2003), Lutz (2002), Parsley and Wei (2007), Rogoff (1996), Taylor and Taylor (2004), and Yang (2004). 6 / is also known as the real exchange rate. A deviation from 1 is a PPP misvaluation. 8

10 and denote the Eurozone and U.S. Big Mac prices, in US dollars, the euro s percentage misvaluation versus the US dollar in the raw Big Mac approach is shown in equation (6): $/ = / 1 (6) For example, with the U.S. and Eurozone Big Mac prices of $4.79 and 3.70 in July 2015, the intrinsic FX rate (in US dollars per euro) was $4.79/ 3.70 = $/. The actual FX rate, $/, implied that = $ Using equation (6), the euro s misvaluation versus the US dollar was thus $4.054/$ = 0.154, or 15.4%, as shown in Table 1. Table 1 shows the bilateral misvaluation estimates for 37 currencies versus the US dollar, the euro, and the yuan (including a zero bilateral misvaluation for each currency versus itself), as reported by The Economist in July

11 Table 1: Misvaluation of Currencies vs the US Dollar, Euro, and Yuan Raw Big Mac Method (July 2015) ECONOMY (%) (%) (%) GDP MKT CAP WEALTH Argentina Australia Brazil Britain Canada Chile China Colombia Czech Republic Denmark Egypt Eurozone Hong Kong Hungary India Indonesia Israel Japan Malaysia Mexico New Zealand Norway Pakistan Peru Philippines Poland Russia Saudi Arabia Singapore South Africa Korea Sweden Switzerland Taiwan Thailand Turkey United States / / / / (%) Total 100 Total 100 Total 100 (%) (%) (%) Table 1 shows bilateral misvaluation percentages for the raw Big Mac method versus the US dollar, the euro, and the Chinese yuan. $/, /, and / denote currency C s percentage bilateral misvaluation versus the US dollar, the euro, and the yuan, respectively. /, / / /, and denote the overall misvaluation estimates versus currency C for the equal-, GDP-, market cap-, and wealth-weighted EER baskets, respectively. Data sources: The Economist s downloadable data spreadsheet, International Monetary Fund (IMF) for GDP, Bloomberg for market cap, and Credit Suisse Research Institute for wealth. 10

12 Effective Exchange Rate Misvaluations and the Raw Big Mac Method Estimates of bilateral misvaluation between individual currencies are useful, but do not show a currency s effective misvaluation versus a basket of other currencies in general. For the raw Big Mac index, this section summarizes effective multilateral misvaluation estimates over time for the US dollar, the euro, and the Chinese yuan versus EER baskets of 36 other currencies. The GDP, market cap, and wealth weights for July 2015 are shown in the last three columns of Table 1. Table 1 s last four rows show the percentage misvaluation estimates of the overall EER baskets (equal-, GDP-, market cap-, and wealth-weighted, in that order) versus the US dollar, the euro, and the yuan. It is worth noting again here that all of the overall EER misvaluation estimates are consistent with the bilateral misvaluation estimates. The EER basket misvaluation estimates are converted from overall to multilateral estimates using equation (3), and then converted from the multilateral basket misvaluation versus a given currency to the currency s misvaluation versus the multilateral basket using equation (1). The three featured currencies multilateral misvaluation estimates for July 2015 are shaded in Table 2. Table 2 shows the multilateral misvaluation results for July 2011 through January Each currency showed the lowest valuation (least overvaluation or most undervaluation) for the wealth-weighted basket and the highest valuation for the equal-weighted basket, with the sole exception of the euro in July The results also indicate that: (1) The US dollar was effectively overvalued and became more so over time versus all four multilateral EER basket types. (2) The euro was effectively overvalued, and tended to become effectively less overvalued over time for all but the equal-weighted multilateral EER basket. (3) The yuan was effectively undervalued throughout the period versus all four EER basket types and became gradually less undervalued. 11

13 Table 2: Effective Multilateral Misvaluation Estimates: Raw Big Mac US Dollar, Euro, and Yuan: (July 2011 January 2016) PANEL A: DATE PANEL B: /$ /$ (%) US DOLLAR /$ (%) /$ (%) Jul Jan Jul Jan Jul Jan Jul Jan Jul Jan DATE PANEL C: EURO / (%) / (%) / (%) / (%) Jul Jan Jul Jan Jul Jan Jul Jan Jul Jan DATE YUAN / (%) / (%) / (%) / (%) Jul Jan Jul Jan Jul Jan Jul Jan Jul Jan Table 2 shows multilateral misvaluation estimates for the raw Big Mac method for the US dollar, the euro, and the yuan versus equally-weighted, GDP-weighted, market cap-weighted, and wealth-weighted EER baskets of 36 currencies. /, / / /, and denote currency C s multilateral misvaluation estimate versus each of the four EER basket types, respectively. Data sources: The Economist s downloadable data spreadsheet, International Monetary Fund (IMF), Bloomberg, and Credit Suisse Research Institute. (%) 12

14 The Adjusted Big Mac Method The Economist s adjusted Big Mac method involves estimating a cross-sectional line of best fit between Big Mac prices and per capita GDP estimates, measured in a reference currency: 7 = α + β (7) where is the predicted Big Mac price, expressed in the reference currency, α is the intercept, and β is the slope coefficient of the regression line. The adjusted Big Mac method is an offshoot of the Penn effect, which refers to the positive cross-sectional empirical association between traditional PPP deviations and per capita GDPs, and is frequently used in FX valuation by research economists like Rogoff (1996), Frankel (2006), Xu (2009), Zhang (2012), and Cheung and Fujii (2014). 8 The Balassa-Samuelson effect (Balassa, 1964; Samuelson, 1964) is the most prominent theoretical explanation (and an often-used synonym) for the Penn effect. The Balassa-Samuelson effect is the tendency for a high income economy to have higher nontraded goods prices, relative to traded goods prices, than a low income economy. Therefore, the traditional PPP condition does not hold using composite price indexes that include both traded and nontraded goods, even if FX rates align with traded goods prices according to the international law of one price. Relative to 7 We use the term "line of best fit" to be consistent with The Economist's language; for all purposes it refers to a simple OLS regression. 8 Typically, Penn effect research uses logarithms, whereas the adjusted Big Mac method does not, which we presume is because The Economist wants the adjusted Big Mac method to be digestible. When we estimated a respecified equation (7) in terms of logarithms, the r-squared was surprisingly much lower. The name Penn effect is credited to Samuelson (1994) and refers to the research home of pioneering empirical studies of price level and GDP, the University of Pennsylvania. See Kravis and Lipsey (1983, 1987), Kravis, Heston, and Summers (1978), and Summers and Heston (1991). 13

15 traditional PPP intrinsic FX value, the currency of a high (low) income economy tends to be overvalued (undervalued). However, economists have been unable to derive a theoretical relationship between PPP deviations and per capita GDP (Asea and Corden, 1994; Asea and Mendoza, 1994). Therefore, by assuming that currencies are correctly valued on average per the estimated line, the estimated Penn effect line often serves as a model of intrinsic FX valuation. Of course the estimated line varies over time, because of changes in prices, FX rates, and GDP estimates. The Economist estimates a line of best fit with data for 49 economies, including 12 individual Eurozone countries and the Eurozone aggregate. However, we exclude the individual Eurozone countries in our adjusted Big Mac analysis, and thus use only 37 economies/currencies to estimate a line-of-best-fit. Figure 1 shows the estimated 37-currency line-of-best-fit for July 2015 for the US dollar as the reference currency. 9 9 The intercept, 2.493, and slope coefficient, (with in 000s of US dollars), are only slightly different from those of The Economist s estimated line-of-best-fit using 49 economies. The r-squared with 37 currencies is is even a bit higher than with 49 economies. The adjusted Big Mac regressions use The Economist s per capita GDP estimates for July 2015 and January The estimates for these two dates are practically the same, with the July 2015 estimates being identical to the 2014 International Monetary Fund (IMF) estimates. Because of this relationship, and because The Economist s earlier per capita GDP estimates are unavailable, we use the IMF 2010 estimates for July 2011 and January 2012, the IMF 2011 estimates for July 2012 and January 2013, and so forth. The only exception is the Eurozone GDP, which is not provided by the IMF, and for which we use World Bank estimates. (The Economist s Eurozone GDP estimate seems to be constructed from the individual estimates of Eurozone countries.) We also investigated averaging the most recent two years IMF estimates for the January dates; the results are not materially affected. Note also: we use only 36 currencies for January 2012, because the data for Peru are missing in The Economist s downloadable data spreadsheet. 14

16 Figure 1: Adjusted Big Mac Method Line of Best Fit for 37 Currencies (July 2015) Figure 1 shows the scatter plot for Big Mac prices and GDP per capita (both in US dollars) and the estimated line of best fit for the July 2015 adjusted Big Mac method based on 37 currencies (instead of 49 economies used by the The Economist). Data source: The Economist s downloadable data spreadsheet. 15

17 A currency s residual is the actual Big Mac price minus the predicted Big Mac price (in the reference currency,. The relative residual is the residual divided by the predicted Big Mac price, ( /. For example, the euro s relative residual is given by equation (8): / = / / 1 (8) A currency s relative residual measures the currency s percentage misvaluation relative to / the line of best fit. The notation thus indicates that the euro s relative residual is the misvaluation versus an overall EER basket with weights implicitly determined by the regression. Unfortunately, The Economist does not report these effective overall misvaluation estimates. The relative residual estimates of overall misvaluation versus the 37-currency line-ofbest-fit basket for July 2015 are shown in the first data column of Table 3. For example, the Eurozone s estimated (in US dollars) was $40,028, so the predicted Eurozone Big Mac price (in US dollars),, was $3.93. Given the price of a Eurozone Big Mac in US dollars in July 2015, $4.054, the euro s relative residual, /, was $4.054/$ = 0.032, or a 3.2% effective overall overvaluation versus the regression line, as highlighted in Table 3. The adjusted Big Mac method also finds a residual for the reference currency. For example, the US dollar s relative residual is / / 1, where is based on equation (7) and the U.S.. Given the US dollar as the reference currency, the actual U.S. Big Mac price of $4.79, and the predicted U.S. Big Mac price of $4.45 (determined by equation (7) using the US ), the US dollar s July 2015 relative residual, /$, was $4.79/$ = 0.076, or a 7.6% effective overall overvaluation versus the regression basket, as highlighted in Table Note that a currency s residual misvaluation estimate in the adjusted Big Mac method is the same from the perspective of any reference currency, including itself. 16

18 The adjusted Big Mac method calculates the estimated bilateral misvaluation between two currencies using equation (2) and the relative regression residuals of both currencies. For example, in July 2015, the adjusted Big Mac estimate of the euro s bilateral misvaluation versus the US $/ dollar was 1 1 / /$ 1 = 1.032/ = 0.041, or 4.1% (as highlighted in Table 3), which is substantially different from the raw Big Mac estimate of 15.4%. In addition to the relative residual estimates of effective overall misvaluation in the first data column, Table 3 shows the percentage bilateral misvaluation estimates versus the US dollar, the euro, and the yuan (including a zero misvaluation for each currency versus itself). The last column of Table 3 shows the per capita GDP estimates used in the adjusted Big Mac analysis. Table 3 s last four rows show the misvaluation estimates of the four overall EER baskets versus each of the three featured currencies, found as (weighted) averages of the bilateral misvaluations. For example, the overall misvaluation estimate for the equally-weighted EER basket versus the US dollar, $/, is 7.1%. Using equation (1), this estimate implies the US dollar s estimated overall misvaluation versus the equally-weighted basket, /$, is approximately equal to the US dollar s overall misvaluation versus the regression basket, /$, 7.6% (rounded). The EER basket misvaluation estimates are converted from overall to multilateral estimates using equation (3), and then converted from the multilateral basket misvaluation versus a given currency to the currency s misvaluation versus the multilateral basket using equation (1). The three featured currencies multilateral misvaluation estimates for July 2015 are shaded in Table 4. 17

19 Table 3: Regression Residuals and Bilateral Misvaluation Estimates versus the US Dollar, Euro, and Yuan: Adjusted Big Mac Method (July 2015) ECONOMY / $/ (%) / (%) / (%) (%) ($) Argentina ,873 Australia ,219 Brazil ,604 Britain ,653 Canada ,398 Chile ,477 China ,589 Colombia ,076 Czech Republic ,563 Denmark ,564 Egypt ,304 Eurozone ,028 Hong Kong ,871 Hungary ,881 India ,627 Indonesia ,534 Israel ,991 Japan ,332 Malaysia ,804 Mexico ,715 New Zealand ,837 Norway ,013 Pakistan ,343 Peru ,458 Philippines ,865 Poland ,379 Russia ,926 Saudi Arabia ,454 Singapore ,319 South Africa ,483 Korea ,101 Sweden ,491 Switzerland ,475 Taiwan ,598 Thailand ,445 Turkey ,482 United States ,597 / (%) / (%) / / (%) (%) Table 3 shows currency C s residual misvaluation percentage, / versus the US dollar, the euro, and the Chinese yuan, $/, and estimated bilateral misvaluation percentage, / /, and, for 37 currencies for the July 2015 adjusted Big Mac approach. ($) denotes estimated per capita GDP in US dollars; /, / /, and / denote the overall misvaluation estimate versus currency C for the equal-, GDP-, market cap-, and wealthweighted EER baskets, respectively. Data sources: The Economist s downloadable data spreadsheet, International Monetary Fund (IMF) for GDP, Bloomberg for market cap, and Credit Suisse Research Institute for wealth. 18

20 The Adjusted Big Mac Method and Multilateral Effective Exchange Rates Table 4 summarizes the effective multilateral misvaluation estimates for the three featured currencies for the five EER basket types, based on the semiannual 37-currency adjusted Big Mac analyses from July 2011 to January When converting from overall misvaluation to multilateral misvaluation, per equation (3), the adjustment for the equally-weighted basket is small, because the weight for each currency in the overall basket is the reciprocal of the number of currencies in the basket. The same small adjustment applies for the regression basket, because all 37 currencies are used to estimate the line-of-best-fit, as in The Economist s methodology. The adjustments for the GDP-, market cap- and wealth-weighted baskets are more substantial for the three featured currencies because of their economies relatively high GDP, market cap, and wealth. Throughout Table 4, one can see that the EER basket with market cap weights tended to give the highest estimate of each currency s multilateral valuation. The equally-weighted basket tended to give the lowest valuation. (These patterns change slightly in the most recent periods.) These patterns are in contrast to the raw Big Mac results where the equally-weighted basket tended to yield the highest valuations and the wealth-weighted basket tended to yield the lowest. One can also see the close approximation of the multilateral misvaluation estimates for the regression and equally-weighted baskets. Given this close approximation, the study s research question is to whether the multilateral misvaluation estimates for the GDP-, market cap-, and wealth-weighted EER baskets are substantially different from the estimates for the equallyweighted basket. Given the inevitable noise in the estimation process, the Table 4 results indicate relatively small differences between the multilateral EER misvaluation estimates among the different basket types. The average difference between the highest and lowest misvaluation estimates across the basket types is about 6.6%. For the raw Big Mac estimates in Table 2, the 19

21 average between the highest and lowest misvaluation estimates across the basket types is about 9.8%. The misvaluation estimation differences among the basket types tend to be smaller for the adjusted Big Mac method, because the method is designed to take some of the variation out of the bilateral misvaluation estimates relative to the raw Big Mac index. Table 4 s adjusted Big Mac estimates of effective multilateral misvaluation indicate the following trends: (1) The US dollar was effectively undervalued versus the EER baskets until January 2015 and was overvalued after that time. By comparison the US dollar was effectively overvalued throughout the sample period for the raw Big Mac index. (2) The euro was effectively overvalued throughout the entire sample period, reaching a maximum overvaluation between January 2013 and January However, the euro s overvaluation estimates are not as high as with the raw Big Mac index. (3) The yuan was less effectively undervalued for the adjusted Big Mac index than for the raw Big Mac index, and the undervaluation gradually diminished until becoming a slight overvaluation in January

22 Table 2: Effective Multilateral Misvaluation Estimates: Adjusted Big Mac US Dollar, Euro, and Yuan: (July 2011 January 2016) PANEL A: DATE PANEL B: DATE PANEL C: DATE /$ /$ (%) US DOLLAR /$ (%) /$ (%) /$ (%) 11-Jul Jan Jul Jan Jul Jan Jul Jan Jul Jan EURO / / / / (%) (%) (%) / (%) 11-Jul Jan Jul Jan Jul Jan Jul Jan Jul Jan / YUAN / / (%) (%) / (%) / (%) 11-Jul Jan Jul Jan Jul Jan Jul Jan Jul Jan Table 4 shows percentage effective multilateral misvaluation estimates for the US dollar, the euro, and the yuan, given the adjusted Big Mac method, versus: (1) the regression residual EER basket. / ; (2) the equally-weighted EER basket / ; (3) the GDP-weighted EER basket, / ; (4) the market cap-weighted EER basket, / ; and (5) the wealth-weighted EER basket, /. Data sources: The Economist s downloadable data spreadsheet, the International Monetary Fund (IMF), and Credit Suisse Research Institute. (%) (%) (%) 21

23 Conclusion This study compares currency misvaluation estimates versus effective exchange rate (EER) baskets using The Economist s two Big Mac approaches to intrinsic currency value: (1) The original (raw) Big Mac method is based on traditional purchasing power parity (PPP). (2) The adjusted Big Mac method tries to control for the tendency of relatively rich (poor) economies to have overvalued (undervalued) currencies, versus PPP intrinsic FX rates, by a regression equation that links Big Mac prices and per capita GDPs. The analysis includes EER baskets where the currency positions are (1) weighted equally; (2) weighted by GDP; (3) weighted by equity market capitalization; and (4) weighted by financial wealth. The adjusted Big Mac method provides a fifth EER basket represented by the line-ofbest-fit. All of the EER basket types imply a consistency between two currencies EER misvaluation and the bilateral misvaluation of the two currencies versus each other. The study distinguishes a currency s overall EER misvaluation, versus a basket that includes the currency, from the currency s multilateral EER misvaluation, versus a basket that excludes the currency. The study finds that a given currency s effective multilateral misvaluation estimates are relatively consistent across the various EER basket compositions for the adjusted Big Mac method but not as much so for the raw Big Mac method. The findings pertain for any given currency, but the report highlights the effective multilateral misvaluation estimates for the US dollar, the euro, and the Chinese yuan. From July 2011 until January 2016, for example, the yuan s multilateral undervaluation was effectively much smaller for the adjusted Big Mac method than for the raw Big Mac method, and the yuan s multilateral undervaluation for the adjusted Big Mac method gradually diminished until becoming a slight overvaluation by January

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