Republic of South Africa Systematic Country Diagnostic An Incomplete Transition: Overcoming the Legacy of Exclusion in South Africa Background note Exchange Rate Misalignment and its Relationship to Output Growth in South Africa Ha Nguyen Real Exchange Rate Misalignment and its Relationship to Output Growth in South Africa Ha Nguyen1 Abstract This paper establishes a simple theory-based real exchange rate (RER) Misalignment Index for countries around the world from 1950-2014, and shows that South Africa’s RER has been undervalued over the last decade. For the most recent year of 2014, depending on the proxy for productivity, it is undervalued from about 15% to 18%. We find that terms of trade fluctuations explain a large part of the undervaluation. Introduction and motivation A country’s real exchange rate (RER) is formally defined as the relative price of a domestic consumption basket (which includes a domestic non-tradable good and the tradable good) in terms of a foreign consumption basket (which includes a foreign non-tradable good and the tradable good). A depreciated RER generally means that the country’s non-tradable goods are cheap compared to the tradable goods. When a country increases its exports, it effectively reduces the domestic supply of tradable goods and hence raises their relative price in terms of non-tradable goods (i.e. undervalued RER) and stimulates the production of tradable goods. An undervalued RER is also argued to boost growth via other indirect channels. The first one is productivity improvement. The earliest theory to explain the productivity channel is based on the seminal paper of Lewis (Lewis, 1954). As the export sector -- mostly manufacturing -- expands due to a low RER, it attracts labor from the agricultural sector. Since labor moves from agriculture or services - relatively less productive sectors- to manufacturing- a relatively more productive sector, the economy’s aggregate productivity rises, and so does output. More recently, Rodrik (2008) theorizes that, an undervalued exchange rate, or equivalently, an increase in the relative price of tradables, acts as a second- best mechanism to alleviate distortions that disproportionately hurts the tradable sector.2 The distortions, he argues, come from the institutional weakness and contracting incompleteness that characterize low- income environments. Korinek and Serven (2016) present a theory based on learning-by-investing externality: the expansion of investment in the export sector increases the sector’s productivity. The export - driven productivity improvement increases output over and above the direct impact that export brings about. In this paper, we base our calculation of RER misalignment on the work of Rodrik (2008). He has a simple theory-based approach to measure RER misalignment. In his work, he has shown that undervalued real exchange rates are associated with higher output growth. He does not discuss export growth however. In the section below, we will slightly modify his approach to measure RER misalignment and will present evidence about the relationship between undervaluation and a series of economic outcomes: exports, imports, manufacturing production, TFP and output. South Africa’s RER has been undervalued in the last decade. In the most recent year of 2014 when the data are available, the RER misalignment for South Africa equals 0.15-0.18, which means that South Africa’s RER was about 15-18% undervalued. In addition, on average, across all countries and all time, a 10% RER undervaluation boosts growth in real export by 1%, in real value added by 0.38%, in TFP by 0.23% and in real GDP per capita by 0.29%. However, with South Africa data, we do not see the effects. Of course, this 1 World Bank 2 Weak institutions reduce the ability of private investors to appropriate the returns on their investment through a variety of mechanisms: contractual incompleteness, hold-up problems, corruption, lack of property rights, and poor contract enforcement. Rodrik argues that this problem is more severe in tradables than in nontradables because production systems tend to be more complex and roundabout in tradables. When the institutions that foster these relationships are weak, the result is to impose a higher “tax� on tradables—especially modern tradables. finding comes with the caveat of small sample size in the within-country regression. In section 5, we provide some hypotheses for the insignificant effects. The Real Exchange Rate Definition of the Real Exchange Rate The Real Exchange Rate (RER) measures the relative purchasing power of the two currencies. The RER of the Rand versus the U.S. dollar is the purchasing power of the rand versus the dollar. It is calculated as the dollar price of the rand (the nominal exchange rate) times the dollar price of one unit of the consumption basket in the U.S. divided by the rand price of one unit of the consumption basket in South Africa. �𝑟𝑖�𝑒 𝑅𝐸𝑅�,𝑈𝑆 = 𝑛𝑒𝑟�,𝑈𝑆 �𝑟𝑖�𝑒 𝑈𝑆𝐷 (1) 𝑅𝑎𝑛𝑑 For developing countries, the RER is usually greater than 1 because the prices in the U.S. is usually more expensive. Hence the ratio is greater than 1. This is also true for South Africa’s RER. Figure 2.1 below shows the evolution of RER of the South Africa’s Rand versus the U.S. dollar since 1990. Data are from the Penn World Table 9.0. The detailed Rand’s RER versus the U.S. dollar are in Appendix A1. Figure 2.1: South Africa’s RER versus the U.S. 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 1992 2003 2014 1990 1991 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 Why are the RER for developing countries is usually greater than 1? In other words, why prices in developing countries are generally cheaper than prices in the U.S. and other developed countries? One explanation is the Balassa-Samuelson effect. The Balassa-Samuelson effect captures the effect of an economy’s productivity on its non-tradable goods’ prices. In details, this can be explained as follows: We usually observe that the prices of services (like a haircut) are higher in developed countries than in developing countries, because wages are higher in developed countries. But why wages are higher in developed countries? It is because the tradable sector of developed countries has higher productivity than that in developing countries. Given the law of one price on tradable goods, this implies that wages paid to tradable-sector workers in developed countries must be higher to commensurate their high productivity. In other words, low productivity explains a large part why prices are cheaper in developing countries. On Purchasing Power Parities (PPP) conversion rate We find that the PPP conversion rate is consistent with the nominal exchange rate and the real exchange rate. From the OECD, “Purchasing power parities (PPPs) are the rates of currency conversion that equalize the purchasing power of different currencies by eliminating the differences in price levels between countries �. In other words, it is the rate of currency conversion between the rand the U.S dollars so that 𝑅𝐸𝑅�,𝑈𝑆 = 1 (i.e. the purchasing power of the Rand and the U.S. dollar are equalized). �𝑟𝑖�𝑒 𝑃𝑃𝑃�,𝑈𝑆 �𝑟𝑖�𝑒 𝑈𝑆𝐷 = 1 (2) 𝑅𝑎𝑛𝑑 From (1) and (2), it should be: 𝑛𝑒𝑟�,𝑈𝑆 = 𝑅𝐸𝑅�,𝑈𝑆 𝑃𝑃𝑃�,𝑈𝑆 Figure 2.2: South Africa’s RER and NER/PPP ratio. 4.500 4.000 3.500 3.000 2.500 2.000 1.500 1.000 0.500 0.000 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 NER/PPP RER 𝑛𝑒𝑟 Figure 2.2 presents 𝑃𝑃𝑃�,𝑈𝑆 and 𝑅𝐸𝑅�,𝑈𝑆 where 𝑛𝑒𝑟�,𝑈𝑆 is the Rand’s nominal exchange rate versus the US �,𝑈𝑆 dollar (data from the Penn World Table), 𝑃𝑃𝑃�,𝑈𝑆 is the purchasing power parities (PPPs) conversion rate (data from the OECD), and 𝑅𝐸𝑅�,𝑈𝑆 is the real exchange rate versus the U.S. (data from the Penn World Table). The detailed data are in Appendix A2. NER/PPP and RER series are similar and move in the same direction. In other words, PPP currency conversion rate provided by the OECD is consistent with the nominal and real exchange rate data by the Penn World Table. Data Our main data sources are Penn World Table 9.0 and World Development Indicators 2017. The Penn World Table 9.0 covers 182 countries between 1950 and 2014. The World Development Indicators cover 217 countries between 1960 and 2016. The following variables are from the Penn World Table 9.0: Real Exchange Rates: A real exchange rate to the U.S. dollar is calculated as the inverse of the price level of consumption. In the PWT data, the variable name for the price level of consumption is pl_con. Rodrik (2008) also uses this approach to calculate the Real Exchange Rate. Nominal exchange rates. Population (in millions) Employment (in millions) The following variables are from the World Development Indicators Nominal GDP per capital in current $US Terms of trade. We use net barter terms of trade index. Net barter terms of trade index is calculated as the percentage ratio of the export unit value indexes to the import unit value indexes, measured relative to the base year 2000 (the index is normalized to 100 in 2000). On South Africa’s RER misalignment We should start by stating that it is difficult to determine if a country’s exchange rate is undervalued and if so, how much it is. Currently, the most popular approach is to regress a country’s real exchange rate against a large set of country’s fundamentals to establish a real exchange rate norm. The gap between a country’s actual real exchange rate and its norm (i.e. the residual in the regression) is considered the “misaligned� part. The most well-known research using this approach is from the IMF (Lee et al, 2006; and subsequently IMF, 2013). The study forms the basis for the IMF’s work on assessing countries’ RER misalignment in its Article IV papers. The basic problem with this approach is that this is a “comprehensive� approach: researchers put many fundamental variables to the right-hand side of the regression, sometimes without a rigorous theory behind them. The approach answers the following questions: what is the “typical� exchange rate of a country as a function of its fundamentals? It does not address the question of what a country's real exchange rate should be, or what is its frictionless benchmark. In other words, the methods calibrate the “typical" rather than “normative" or �frictionless" exchange rates. There are two problems with this. First, the residual may include neglected fundamentals affecting the real exchange rate. It is impossible to come up with an exhaustive list of factors affecting productivity and consumption and saving decisions. The identification of the real exchange rate misalignment as a regression residual is likely to be very noisy, as the residual includes other things as well. Second, many variables considered “fundamentals" might contain elements that distort the real exchange rate. For example, in Lee et al (2006), government spending is considered a “fundamental". 3 However, there are several reasons why government consumption could be directly affected by an incentive to lower the real exchange rate. Government consumption may be incorrectly counted as a “fundamental" thereby concealing a real exchange rate misalignment. Eden and Nguyen (2012) offer more detailed criticisms of the current approaches. Balassa-Samuelson effect In this part, we base our calculation of RER misalignment on the work of Rodrik (2008). He has a simple theory-based approach to measure RER misalignment. In his work, he has shown that undervalued real exchange rates are associated with higher output growth. He did not discuss export growth however. In the section below, we will slightly modify his approach to measure RER misalignment and will present evidence about the relationship between RER undervaluation on other economic outcomes, namely, growth in exports, imports, manufacturing and labor productivity. We are aware that the approach is simplistic and might not capture other true fundamentals. 3 In IMF (2013), government spending was tried but ultimately not used because the estimated coefficient is not significant or has an opposite sign to theoretical priors. In the first step, we measure an RER misalignment index after controlling for the Balassa-Samuelson effect. The Balassa-Samuelson effect captures the effect of an economy’s productivity on its non-tradable goods’ prices. Intuitively, this can be explained as follows: We usually observe that the prices of services (like a haircut) are higher in developed countries than in developing countries. This is because wages are higher in developed countries. But why wages are higher in developed countries? It is because the tradable sector in developed countries has higher productivity than that in developing countries. Given the law of one price of tradable goods, this implies that wages paid to tradable-sector workers in developed countries must be higher to commensurate their higher productivity. In other words, low productivity explains a large part why tradable /non-tradable good price ratio (i.e. the real exchange rate) in developing countries is larger than that in developed countries. After the Balassa-Samuelson effect is captured, the remaining residual is considered the misaligned part. We capture the Balassa-Samuelson effect with four different variations of the Rodrik regression. 𝑙𝑛𝑅𝐸𝑅𝑖,𝑈𝑆,𝑡 = 𝛽0 + 𝛽lny𝑖,𝑡 + 𝑓𝑒𝑡 + 𝑢1𝑖,𝑡 (1) 2 𝑙𝑛𝑅𝐸𝑅𝑖,𝑈𝑆,𝑡 = 𝛽0 + 𝛽(lny𝑖,𝑡 − lny𝑈𝑆,𝑡 ) + 𝑓𝑒𝑡 + 𝑢𝑖,𝑡 (2) In the first two variations, a country’s productivity is proxied by its nominal output per capita. Equation (1) is the original Rodrik regression, where 𝑙𝑛𝑅𝐸𝑅𝑖,𝑈𝑆,𝑡 is the log of real exchange rate of country i relative to the US; lny𝑖,𝑡 is log of country i’s nominal output per capita in US$ at time t and 𝑓𝑒𝑡 is a time fixed effect. Note that we do not use country fixed effects. Coefficient 𝛽 captures the Balassa-Samuelson effect with an expected negative sign. The idea is that per Balassa-Samuelson effect, a country RER, at any given time, is larger if its output per capita (a proxy for productivity) is smaller. 𝑢1 𝑖,𝑡 will be our RER misalignment � variable of country i where 𝑢 𝑖,𝑡 is the residual of the regression. A positive 𝒖𝒊,𝒕 implies an undervalued ̂ RER. That is, the RER is larger (more depreciated) beyond the explanation of the Balassa-Samuelson effect. In equation (2), rather than log output per capita, productivity is proxied by the difference in country i’s log output per capita and the U.S.’ (lny𝑈𝑆,𝑡 is the U.S.’s nominal output per capita at time t). Since RER is a relative concept, we add the U.S. output per capita to the right-hand side of the equation to generate output differential, which is a relative concept as well. 4 𝑙𝑛𝑅𝐸𝑅𝑖,𝑈𝑆,𝑡 = 𝛽0 + 𝛽 ln 𝑙�𝑟𝑜𝑖,𝑡 + 𝑓𝑒𝑡 + 𝑢𝑖,𝑡 (3) 5 𝑙𝑛𝑅𝐸𝑅𝑖,𝑈𝑆,𝑡 = 𝛽0 + 𝛽(ln 𝑙�𝑟𝑜𝑖,𝑡 − ln 𝑙�𝑟𝑜𝑈𝑆,𝑡 ) + 𝑓𝑒𝑡 + 𝑢𝑖,𝑡 (4) Equations (3) and (4) are similar to (1) and (2). The only difference is instead of using log output per capita as a proxy for productivity, we use nominal labor productivity in US$. 𝑙�𝑟𝑜𝑖,𝑡 is calculated as total nominal output divided by total employment. Equation (4) will be the baseline results of this paper because labor productivity is closer to the concept of productivity (compared to GDP per capita). This is the first key difference to Rodrik. The second difference is our use of annual data, as opposed to the 5-year average data as in Rodrik (2008). We argue that unlike the slow-moving impacts of other traditional explanations for growth (such as education or institutions), the impact of RER misalignments on export growth is faster. Hence, annual data are probably more suitable than 5-year average data. The third difference is the use of nominal GDP. While Rodrik (2008) uses PPP GDP per capita, we argue that market-value GDP per capita is more precise to proxy for the tradable productivity. Appendix A4 presents a model to show exactly why that is the case. Intuitively, the difference between the PPP GDP and market-value GDP rests with the non-tradable sector: while market-value GDP takes different prices of non-tradable goods in different countries, PPP GDP equates the prices of non-tradable goods to international PPP prices. Since the non-tradable price gap reflects the tradable productivity gap, market- value GDP is more precise. Table 3.1 presents the result of the regression with Penn World Table 9.0 data. The coefficient of the GDP gap is negative and highly significant, suggesting that Balassa-Samuelson effect is in effect. The coefficient of -0.16 implies that if the labor productivity gap with the U.S. improves by 1%, the real exchange rate with 4 the $US on average goes down by 0.21%. The residuals of this regression, 𝑢𝑖,𝑡 , are considered the RER misalignments for countries. They are a component of the real exchange rate not explained by the Balassa- Samuelson effect. Table 3.1: On the Balassa-Samuelson effect (1) VARIABLES Real exchange rate Log(labor productivity) -0.214*** [0.003] Constant 1.848*** [0.035] Year fixed effects Y Observations 6,954 R-squared 0.746 Robust standard errors in brackets *** p<0.01, ** p<0.05, * p<0.1 On South Africa’s RER misalignment 4 Figure 3.2 plots the residuals 𝑢𝑖,𝑡 for South Africa since 1960 until 2014. This is South Africa’s RER misalignment. As shown in Figure 3.2, South Africa’s RER was mostly undervalued but the trend is going down, suggesting prices are getting more expensive. The magnitude of RER undervaluation is quite consistent across specifications. With the baseline results from equation (4), as of 2014, the level of undervaluation is about 15%. See Appendix A3 for the country’s detailed misalignment values from 1950 until 2014. Figure 4.2: South Africa’s RER misalignment 0.700 0.600 0.500 0.400 0.300 0.200 0.100 0.000 1972 1976 1980 1984 1960 1962 1964 1966 1968 1970 1974 1978 1982 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 -0.100 u1 u2 u3 u4 Note: u1,u2 represent RER misalignment derived from equations (1) (2); u4, u5 and u6/s represent RER misalignment derived from equations (4), (5) and (6); u8 and u9/s represent RER misalignment derived from equations (8) and (9). u9/s is our benchmark series. A positive u implies RER undervaluation. Explaining South Africa misalignment The most important candidate is South Africa’s terms of trade. Regression result indicates that terms of trade explain 26% the variation of South Africa’s RER misalignment (see table 5.1) Log terms of trade and RER misalignment is strongly negatively correlated as shown in the scatter plot below. Net barter terms of trade index is calculated as the percentage ratio of the export unit value indexes to the import unit value indexes, measured relative to the base year 2000. What this means is higher terms of trade are associated with episodes where RER misalignment is low (i.e. appreciating RER). They are the for example the years of 2010, 2011, 2012. In other words, an improvement of terms of trade causes RER to appreciate, above and beyond the effect of productivity. 4 4 One could also include terms of trade as an additional explanatory variable in addition to productivity (see equations 1,2,3,4). However, given the limit of terms of trade data, we could not do so. The reason is that terms of trade in all available sources are normalized to 100 for year 2000 for all countries. In other words, countries’ terms of trade are normalized to have the same value of 100 in 2000, which prev ents us from including it as an explanatory variable in a cross-country regression. 1985 1986 .6 1984 1989 2002 1988 1987 1982 1980 .4 1981 2001 1983 2008 1990 1998 1999 1996 2000 2003 1991 1997 .2 2007 2009 1993 1994 1992 1995 2014 2006 2004 2013 2005 2010 2012 0 2011 4.6 4.7 4.8 4.9 5 Log(terms of trade) Recently, the role of terms of trade is larger. Since 1990s, terms of trade explain 39% of the variation in South Africa’s RER misalignment (table 5.1). This reflects the increasing trade integration of South Africa to the world economy. As can be seen in Figure 5.1, terms of trade have strong predictive power in 2010s. Table 5.1: Terms of trade and RER Misalignment 1980-2014 1990-2014 VARIABLES RER Misalignment logtot -0.731*** -0.538*** [0.146] [0.116] Constant 3.735*** 2.749*** [0.699] [0.556] Observations 35 24 R-squared 0.260 0.398 Robust standard errors in brackets *** p<0.01, ** p<0.05, * p<0.1 Conclusion The goal of this short paper is three-fold. First, it provides intuition why the PPP conversion rate provided by the OECD is consistent with the nominal and real exchange rate data by the Penn World Table. Second, it establishes the level of RER misalignment for South Africa, based on the method by Rodrik (2008). It finds that South Africa’s RER is consistently undervalued during the last few years. In 2014, the value of RER undervaluation is about 15-18%. The magnitude is robust across specifications. Finally, the paper examines terms of trade as a factor that drives RER misalignment. References Aizenman, J. and Lee, J. (2010). The real exchange rate, mercantilism, and thelearning-by-doing externality. Pacific Economic Review, 15(3):324-335. Barro, Robert J. & Lee, Jong-Wha, (1993) "International comparisons of educational attainment," Journal of Monetary Economics, Elsevier, vol. 32(3), pages 363-394, December. Easterly, William & Kremer, Michael & Pritchett, Lant & Summers, Lawrence H., (1993) "Good policy or good luck?: Country growth performance and temporary shocks," Journal of Monetary Economics, , vol. 32(3), pages 459-483 IMF (2013) “External balance assessment (EBA) Methodology: technical background� Dooley, M. P., Folkerts-Landau, D., and Garber, P. M. (2003). An essay on the revived Bretton Woods system. NBER Working Paper, w9971 Eden Maya and Ha Nguyen (2012), “Correcting Real Exchange Rate Misalignment: Conceptual and Practical Issues�, World Bank Policy Research Working Paper No. 6405 Korinek Anton and Luis Serven (2016), “Undervaluation through Foreign Reserve Accumulation: Static Losses, Dynamic Gains�, Journal of International Money and Finance, (64) pp 104-136 Lee, Jaewoo, Gian Maria Milesi-Ferretti, Jonathan Ostry, Alessandro Prati, andLuca Antonio Ricci.(2006) “Exchange rate assessments: CGER methodologies�,.IMF Occasional Paper 261 Rodrik, Dani (2008) “The Real Exchange Rate and Economic Growth�, Brookings Papers on Economic Activity, Fall 2008 Viegi, Nicola (2017) Appendix A1: Rand’s Real exchange rate since 1990 Sources: Penn World Table 9.0 South Africa 1990 2.96217 South Africa 1991 2.714271 South Africa 1992 2.426224 South Africa 1993 2.519301 South Africa 1994 2.492247 South Africa 1995 2.378418 South Africa 1996 2.646778 South Africa 1997 2.586339 South Africa 1998 2.881728 South Africa 1999 2.956967 South Africa 2000 3.08014 South Africa 2001 3.589817 South Africa 2002 4.015152 South Africa 2003 2.720636 South Africa 2004 2.163257 South Africa 2005 2.061976 South Africa 2006 2.074863 South Africa 2007 1.976473 South Africa 2008 2.115962 South Africa 2009 1.969394 South Africa 2010 1.606678 South Africa 2011 1.490731 South Africa 2012 1.588317 South Africa 2013 1.771206 South Africa 2014 1.885916 Appendix A2: Comparing NER/PPP and RER Nominal PPP exchange rate (NER) NER/PPP RER 2000 2.733 6.940 2.539 3.080 2001 2.877 8.609 2.992 3.590 2002 3.179 10.541 3.316 4.015 2003 3.297 7.565 2.294 2.721 2004 3.419 6.460 1.889 2.163 2005 3.493 6.359 1.821 2.062 2006 3.601 6.772 1.880 2.075 2007 3.818 7.045 1.845 1.976 2008 4.075 8.261 2.027 2.116 2009 4.348 8.474 1.949 1.969 2010 4.569 7.321 1.602 1.607 2011 4.774 7.261 1.521 1.491 2012 4.946 8.210 1.660 1.588 2013 5.158 9.655 1.872 1.771 2014 5.369 10.853 2.021 1.886 Appendix A3: South Africa’s RER misalignment 1959 u1 u2 u3 u4 1960 0.372 0.372 0.333 0.333 1961 0.396 0.396 0.339 0.339 1962 0.400 0.400 0.353 0.353 1963 0.404 0.404 0.367 0.367 1964 0.403 0.403 0.368 0.368 1965 0.401 0.401 0.376 0.376 1966 0.396 0.396 0.371 0.371 1967 0.389 0.389 0.372 0.372 1968 0.367 0.367 0.355 0.355 1969 0.344 0.344 0.341 0.341 1970 0.280 0.280 0.264 0.264 1971 0.265 0.265 0.250 0.250 1972 0.335 0.335 0.321 0.321 1973 0.328 0.328 0.317 0.317 1974 0.337 0.337 0.326 0.326 1975 0.370 0.370 0.357 0.357 1976 0.420 0.420 0.435 0.435 1977 0.394 0.394 0.424 0.424 1978 0.404 0.404 0.444 0.444 1979 0.382 0.382 0.420 0.420 1980 0.361 0.361 0.411 0.411 1981 0.348 0.348 0.398 0.398 1982 0.394 0.394 0.448 0.448 1983 0.305 0.305 0.361 0.361 1984 0.446 0.446 0.499 0.499 1985 0.601 0.601 0.650 0.650 1986 0.555 0.555 0.618 0.618 1987 0.402 0.402 0.460 0.460 1988 0.430 0.430 0.484 0.484 1989 0.440 0.440 0.492 0.492 1990 0.229 0.229 0.279 0.279 1991 0.172 0.172 0.221 0.221 1992 0.120 0.120 0.170 0.170 1993 0.140 0.140 0.189 0.189 1994 0.134 0.134 0.184 0.184 1995 0.124 0.124 0.175 0.175 1996 0.207 0.207 0.258 0.258 1997 0.165 0.165 0.215 0.215 1998 0.225 0.225 0.275 0.275 1999 0.218 0.218 0.267 0.267 2000 0.200 0.200 0.248 0.248 2001 0.319 0.319 0.377 0.377 2002 0.425 0.425 0.475 0.475 2003 0.192 0.192 0.252 0.252 2004 0.063 0.063 0.126 0.126 2005 0.056 0.056 0.115 0.115 2006 0.110 0.110 0.160 0.160 2007 0.136 0.136 0.194 0.194 2008 0.257 0.257 0.306 0.306 2009 0.148 0.148 0.201 0.201 2010 -0.021 -0.021 0.039 0.039 2011 -0.055 -0.055 -0.003 -0.003 2012 -0.020 -0.020 0.025 0.025 2013 0.090 0.090 0.127 0.127 2014 0.141 0.141 0.176 0.176 This appendix presents the RER misalignment indices based on equations (1) to (4). The first two columns show the RER misalignment indices using nominal GDP per capita as the proxy for productivity. The last two columns show the indices using nominal labor productivity as the proxy for productivity. The last column (column 4) is our benchmark result. Appendix A4: Model