《武汉工程大学学报》 2013年11
69-76
出版日期：2013-11-30
ISSN:1674-2869
CN:42-1779/TQ
巴拉萨\|萨缪尔森效应下购买力平价模型在中美汇率应用中的评估
0引言 经济中的实际汇率可以用两种手段获得：通过理论模型估算获得［1\|2］；由名义汇率计算获得.考虑到现有文献中对人民币汇率高估与否以及高估比例的讨论众说纷纭［3\|5］，评估巴拉萨\|萨缪尔森效应下购买力平价模型（简称为“修正购买力平价模型”）在人民币与美元汇率案例中的适用程度是有必要的.1模型的推导及对实际均衡汇率的估算根据购买力平价理论的基本观点，实际汇率被定义为名义利率与两国价格水平之比的乘积，利用巴拉萨\|萨缪尔森效应的五条假设，推导出了计算实际汇率（RER）的计算公式：RER=(ACN-TACN-N)α(AUS-TAUS-N)β式中：A代表劳动生产率，α、β分别为中美两国非贸易品在所有商品中的所占份额［6\|7］，ACN、AUS分别表示中国和美国的劳动生产率，T、N分别描述贸易品和非贸易品. 通过分析从StatAPEC等权威网站获取的相关数据，笔者对巴拉萨\|萨缪尔森效应的基本假设进行验证，且证实了效应里的条件均成立.将相关数据代入公式后，笔者得到了实际汇率的估算值如图1所示.图11997年至2010年实际汇率估算值Fig.1Estimated RER from 1997 to 2010从图1可以看出实际汇率估算值与真实值之间有比较大的差别，说明巴拉萨\|萨缪尔森效应下的购买力平价模型在人民币与美元汇率案例应用中可能存在一些问题.2修正购买力平价模型的检验 笔者把实际汇率的估算值与真实值进行简单线性回归并得到下列结果（见表1）.表1拟合值及检验统计量Table 1Fitted values and test statistics拟合纵截距拟合斜率R2R2adjp值80.866 00.221 00.160 40.090 450.155 9从表1可以看出实际汇率的估算值与真实值拟合程度很低，回归非常不显著，并且拟合值与预期的理论值相差甚远.为了进一步证实这一判断，笔者对中美之间购买力平价数据及名义汇率数据进行比较（见图2），并利用简单线性回归对估算结果进行分析，发现一价定律在中美货币汇率的案例中并不完全适用.图2中美之间购买力平价数据及名义汇率数据比较Fig.2PPP and NER from 1997 to 20103结语 通过分析比较，巴拉萨\|萨缪尔森效应下的购买力平价模型在人民币与美元汇率案例中可能主要有下述四点缺陷：贸易品与非贸易品之间没有明确界限；汇率与价格水平之间的影响关系不确定［8］；假设条件忽略了政府在市场中的干涉；中美人民购买的商品品种不具可比性.0Introduction In finance, real exchange rate between two specific currencies can be calculated by the nominal exchange rate, and latter is influenced by foreign exchange and the price levels. Also, real exchange rate can be theoretically estimated by mathematical models, namely the four mainstream exchange rate models［1\|2］. There will be discrepancies between the actual data and estimated data because models are normally based on simplified assumptions. But there should be one model, whether it is found or not, that is superior to all the others in a specified context. Among all mainstream models, the purchasing power parity model revised for Balassa\|Samuelson effect (revised PPP) is extensively employed to evaluate real exchange rates, especially the rates between Chinese currency, Yuan, and U.S.dollar. But results in papers show enormous disagreements. Most of the research carried out by academia reported an undervaluation of China Yuan. But there exist dissensions in the degree to which CNY is undervalued. In［3］, CNY is undervalued by 43%\|50%, which deviates from the result of 65% in［4］. But it is argued that there is little statistical evidence that CNY is undervalued in［5］. Actually, whether China Yuan is undervalued is significant, but the reassessment of the applicability of the model is more inspiring. As few scholars have taken this issue into consideration, we decide to investigate the applicability of the model in this paper. Meanwhile, the data used in this paper are collected from 1997 to 2010.1Derivation of the Model and Estimation of RERTo begin modeling, it is important to look at the definitions of variables. Two core variables are real exchange rate (RER) and nominal exchange rate (E). Also we take labor productivity (A), wage rate and price level (P) into consideration. Using subscripts CN (for China), US (for the U.S.), T (for traded sector) and N (for non\|traded sector), we distinguish variables considering traded and non\|traded variables. We also consider the overall price level in China and the overall price level in the U.S.. Under the revised purchasing power parity model, goods produced in a country can be divided into two separate parts:traded goods and non\|traded goods. Traded goods are the goods that can be exported and imported freely. Non\|traded commodities are mostly services that cannot be transported between countries. According to purchasing power parity theory, real exchange rate is the product of nominal exchange rate and the ratio of price levels.RER=E·PCNPUS（1） There are five basic assumptions according to Balassa\|Samuelson effect:①wage rates in both traded and non\|traded good sectors are the same; ②differences of labor productivity exist between sectors, and differences in traded sectors are greater than in non\|traded sectors; ③the Law of One Price holds in traded sector;④perfect competition exists in each sector in each country; ⑤price levels are defined as weighted geometric averages of prices in both sectors, and the geometric weights［6\|7］ are the expenditure shares on non\|traded goods . Based on above assumptions, after complex and careful computation and derivation, we obtain a simplified RER formula:RER=(ACN-TACN-N)α(AUS-TAUS-N)β（2） This formula tells Balassa\|Samuelson effect. It shows that if the ratio of traded goods productivity to non\|traded goods productivity is growing faster in China than in the U.S., China should experience an appreciation of the real exchange rate. Commodities are classified into either traded good sector or non\|traded good sector based on their physical forms. According to this classification, we roughly estimate the productivity by calculating real GDP per capita using the data from StatAPEC. We also find that all the assumptions in Balassa\|Samuelson effect hold, which means that the conditions for applying this method are well satisfied.第11期舒荆阳，等：巴拉萨\|萨缪尔森效应下购买力平价模型在中美汇率应用中的评估武汉工程大学学报第35卷Having had the data from StatAPEC and the World Bank, using the simplified RER formula, the estimated real exchange rate from the revised purchasing power parity model is easily achieved. Here we take a base year of 2005 and set the Estimated RER to be 100 numerically and go on computing the numbers for both the previous and ensuing years. Then the diagram of estimated RER associated with REER is given (Figure 1).Fig.1Estimated RER from 1997 to 2010From Figure 1, our preliminary diagnostic is that the purchasing power parity model adjusted for Balassa\|Samuelson effects doesn’t work well, since the two lines don’t match closely. There are significant differences in both the early years from 1997 and recent years since 2007.2Assessment of Revised PPP Model The final step is to assess the feasibility of the model mathematically. Conducting a simple linear regression of Estimated RER on REER can give an easier depiction of the result. Regression coefficients and test statistics are shown in Table 1.Table 1Fitted values and test statisticsFitted InterceptFitted SlopeR2R2adjp\|value80.866 00.221 00.160 40.090 450.155 9From the test statistics in Table 1, we conclude that the regression is not significant due to a high p\|value. Furthermore, great difference between fitted intercept and the expected intercept (which is zero) and the significant disparity between fitted slope and the expected slope (which is one) indicate a bad fitted line. Based on further investigation, it is found that the annual comparative price level data between China and the U.S. associated with average nominal exchange rate, and then we depict the two lines of the purchasing power parity and the nominal exchange rate trends in the same graph (Figure 2).Fig.2PPP and NER from 1997 to 2010According to the Law of One Price, purchasing power parity should be equal to nominal exchange rate in ideal conditions. However, as shown in Figure 2, purchasing power parity is always lower than the nominal exchange rate. While the nominal exchange rate landed after 2005 as a consequence of the exchange rate regime reform by the People’s Bank of China, purchasing power parity showed bare variation. So the purchasing power parity theory is not feasible in this CNY\|USD case. By the same regression approach for NER on PPP, we find a fitted intercept of 4.356, which largely deviates from the expected slope (which is zero).3Conclusion We combine the results from real equilibrium exchange rate and nominal exchange rate, and therefore conclude that the revised purchasing power parity model does not at all hold for the CNY\|USD case. The estimation cannot work well in the revised PPP framework. To complete our conclusion, some disadvantages of this model that may affect our result must be pointed out:Drawback 1:There is no clear definition for traded goods and non\|traded goods. Although both traded goods and non\|traded goods have already been defined, there exist a great number of disputes in research field. However, no matter how this classification criterion is set, trade barriers, travel costs, capital movement, tariff speculation, and other factors can never be neglected. In the real world, these factors violate the free flow of goods. The high transportation costs between China and the U.S. and the high tariff of China custom can be considered as crucial factors that influence the applicability of the model.Drawback 2:The effects of changes in foreign exchange rate are ignored. The purchasing power parity theory asserts that changes in price level induce changes in the foreign exchange rates, but it ignores the fact that the mechanisms may act reversely, i.e. changes in foreign exchange rate also influence the price level, as is illustrated in［8］. People will not be able to make clear of which factor moves ahead of the other and becomes dominant or determining.Drawback 3:The intervention of governments isn’t considered. The purchasing power parity theory only holds in free capital markets, in which the prices of commodities are only determined by supply and demand. However, in the real condition, government will surely exert price control policies to some specific goods, which breaks the auto regulating function of the market.Drawback 4:The bundles of goods that Chinese people buy and Americans buy are not the same. The mostly extensively consumed goods and services in both countries are not comparable due to the existence of cultural gaps and differences among religions. One example is that Chinese have much stronger preference for the consumption of luxuries while the U.S. citizens spend a greater portion of dispensable income on daily necessities. So it’s impossibly hard to choose the bundle of goods that is representative and fair given the different preferences. In the model that we discuss, assumptions are so idealized that under no circumstance can they be satisfied in the real world, especially in this Sino\|American case. So it makes sense that the purchasing power parity model adjusted for Balassa\|Samuelson effects doesn’t work for the CNY\|USD case in the paper.AcknowledgementsWe would like to express the deepest appreciation to our sponsor Professor Bagher Modjtahedi in Department of Economics, University of California, Davis. He gave us the most support and encouragement in the research process. He also kindly instructed us with his insightful understanding of economics. The product of this paper would not be possible without him.References：［1］ISARD P.Equilibrium exchange rates: assessment methodologies,IMF working paper,WP/07/296\[R\]. Washington,DC USA:International Monetary Fund ,2007.［2］BALASSA B. The purchasing\|power parity doctrine: A reappraisal\[J\]. Journal of Political Economy, 1964,72（6）：584\|596.［3］COUDERT V, COUHARDE C.Real equilibrium exchange rate in China,CEPII working paper,2005\|1\[R\].Paris:Centre d’tude Prospectives et d’Informations Internationale,2005.［4］SATO K, SHIMIZU J, SHRESTHA N, et al. New estimates of the equilibrium exchange rate: the case for the Chinese renminbi\[J\]. The World Economy ,2012,35 (4): 419\|443.［5］CHEUNG Yin\|Wong, CHINN M D,FUJII E.The overvaluation of Renminbi undervaluation\[J\]. Journal of International Money and Finance, 2007 (26)：762\|785.［6］FARIA J R, LEN\|LEDESMA M. Testing the Balassa\|Samuelson effect: Implications for growth and the PPP\[J\]. Journal of Macroeconomics, 2003 25(2): 241\|253.［7］FISHER E, PARK J Y. Testing purchasing power parity under the null hypothesis of co\|integration\[J\].The Economic Journal, 1991,101 (409): 1476\|1484.［8］DORNBUSCH R. Exchange rates and prices\[J\]. The American Economic Review ,1987,77（1）：93\|106.Appendix A: Derivation of FormulaeThere are five basic underlying assumptions considering the definition:1. Wage rate in both traded and non\|traded goods sectors are the same:WCN -T=WCN-N=WCN,WUS-T=WUS-N=WUS2. Difference of labor productivity exists between sectors:AUS-T>ACN-T,AUS-N>ACN-N and difference between traded sector is greater than non\|traded sector:AUS-TACN-T>AUS-NACN-N3. The Law of One Price holds in traded sector:E=PUS-TPCN-T4. Perfect Competition, i.e., wage rate equals the multiplication of labor productivity and price in each sector in each country:WCN=ACN-T·PCN-T=ACN-N·PCN-NWUS=AUS-T·PUS-T=AUS-N·PUS-N5. Price levels are defined as weighted geometric averages of prices in both sectors:PCN=［PCN-T］1-α·［PCN-N］αPUS=［PUS-T］1-β·［PUS-N｝βwhere parameters α and β (geometric weights) are the expenditure share on non\|traded goods in China and the U.S., respectively.Thus we derive formula (2) from formula (1) as follows:RER=E·PCNPUSRER=E·［PCN-T ］1-α·［PCN-N］α［PUS-T］1-β·［PUS-N］βRER=E·WCNACN-T·（ACN-TACN-N)αWUSAUS-T·(AUS-TAUS-N)βRER=WUSAUS-TWCNACN-T·WCNACN-T·(ACU-TACN-N)αWUSAUS-T·（AUS-TAUS-N)βRER=(ACN-TACN-N)α(AUS-TAUS-N)βAppendix B:Basic Indicators in ChinaIndicator1997199819992000200120022003Total Population (in thousands)1 230 0751 241 9351 252 7351 262 6451 271 8501 280 4001 288 400Population, Ages 0\|14 of total population/%26.79526.451 2826.016 8525.483 1324.838 4824.097 6123.311 06GDP, Current USD (in millions)952 652.71 019 4591 083 2781 198 4751 324 8071 453 8281 640 959Labor Force Participation Rate, Total of total population ages 15+/%78.004 9477.646 5577.309 1176.993 2176.622 8376.269 2675.918 14Unemployment Rate, Total of total labor force/%3.13.13.13.13.644.3Value Added, Agriculture of GDP/%18.287 1417.555 9816.470 2215.063 0114.391 7513.742 7312.797 34Value Added, Industry of GDP/%47.539 0346.212 1845.757 5545.916 6545.152 4544.789 8245.968 95Value Added, Services of GDP/%34.173 8336.231 8437.772 2339.020 3440.455 7941.467 4441.23 371Employment, Agriculture of total employment/%49.949.850.150505049.1Employment, Industry of total employment/%23.723.52322.522.321.421.6Employment, Services of total employment/%26.426.726.927.527.728.629.3Indicator2004200520062007200820092010Total Population (in thousands)1 296 0751 303 7201 311 0201 317 8851 324 6551 331 3801 337 825Population, Ages 0\|14 of total population/%22.547 2521.855 7421.254 1820.731 6120.273 5819.854 3219.455 12GDP, Current USD (in millions)1 931 6442 256 9032 712 9513 494 0564 521 8274 991 2565 930 529Labor Force Participation Rate, Total of total population ages 15+/%75.559 975.292 1475.081 8874.916 174.546 6974.367 3774.195 23Unemployment Rate, Total of total labor force/%4.24.24.144.02*4.44*4.1*Value Added, Agriculture of GDP%13.393 1212.123 0211.113 4510.769 7110.731 5710.333 1510.095 32Value Added, Industry of GDP%46.225 3447.366 3647.948 4947.338 847.446 4646.241 5446.669 3Value Added, Services of GDP%40.381 5440.510 6240.938 0641.891 4941.821 9743.425 343.235 38Employment, Agriculture of total employment/%46.944.842.640.839.638.1*36.7*Employment, Industry of total employment/%22.523.925.226.827.227.8*28.7*Employment, Services of total employment/%30.631.332.232.433.234.1*34.6*Note 1: statistical data above comes from StatsAPEC: http://statistics.apec.org/Note 2: datum with an asterisk comes from China Statistical Yearbook, 2012: http://www.stats.gov.cn/tjsj/ndsj/2012/indexeh.htmAppendix C: Basic Indicators in the U.S.Indicator1997199819992000200120022003Total Population (in thousands)272 657275 854279 040282 162.4284 969287 625.2290 107.9Population, Ages 0\|14 of total population/%21.771 6221.659 9221.524 921.373 3821.205 8821.024 7120.840 56GDP, Current USD (in millions)8 256 5008 741 0009 301 0009 898 80010 233 90010 590 20011 089 300Labor Force Participation Rate, Total of total population ages 15+/%66.184 366.240 7866.300 9166.324 1365.984 6965.673 3265.333 1Unemployment Rate, Total of total labor force/%4.94.54.244.75.86Value Added,Agriculture of GDP/%1.685 7591.300 091.219 9341.190 9791.181 4031.009 2411.197 298Value Added, Industry of GDP/%25.365 7924.099 5824.04723.440 6322.295 0621.797 9921.568 78Value Added, Services of GDP/%72.948 4574.600 3374.733 0775.368 3976.523 5477.192 7777.233 92Employment, Agriculture of total employment/%2.72.72.62.62.42.51.7Employment, Industry of total employment/%24.223.823.223.122.621.920.8Employment, Services of total employment/%73.173.574.274.37575.677.5Indicator2004200520062007200820092010Total Population (in thousands)292 805.3295 516.6298 379.9301 231.2304 094306 771.5309 349.7Population, Ages 0\|14 of total population/%20.666 6420.512 6620.380 7620.269 8620.181 8320.117 7620.077 08GDP, Current USD (in millions)11 797 80012 564 30013 314 50013 961 80014 219 30013 863 60014 447 100Labor Force Participation Rate, Total of total population ages 15+/%65.098 8465.145 3465.279 1265.105 1965.073 1264.398 9663.665 15Unemployment Rate, Total of total labor force/%5.55.14.64.65.89.39.6Value Added, Agriculture of GDP/%1.345 0751.212 4841.042 8951.130 171.220 3781.103 4141.180 634Value Added, Industry of GDP/%22.039 3822.185 5522.240 8921.986 7321.132 5719.614 2719.995 69Value Added, Services of GDP/%76.615 5576.601 9776.716 2176.883 177.647 0579.282 3278.823 68Employment, Agriculture of total employment/%1.61.61.51.41.51.51.6Employment, Industry of total employment/%20.820.620.820.619.917.617.2Employment, Services of total employment/%77.677.87878.680.981.2Note: Statistical data above comes from StatsAPEC: http://statistics.apec.org/