Saturday, September 21, 2019
Purchasing Power Parity; Does It Exist Essay Example for Free
Purchasing Power Parity; Does It Exist Essay Introduction            The Purchasing Power Parity doctrine is perhaps one of the most controversial financial theories. Over the years, it has had its ebbs and flows, with proponents expositing several mathematical and statistical formula to strengthen the theory, while critics have severally condemned the utility of the theory; however, according to Belassa1 the doctrine has managed to survive nevertheless. Belassa argues that, though in somewhat ambiguous terms, the doctrine has been invoked as early as during the Napoleonic wars, the christening and explanation of the doctrine came from Prof. Gustav Cassel during the First World War and was popularized after the Second World War. The author further posits that interests in the theory tend to be invoked when existing exchanges rates were thought to be unrealistic and there was, therefore, a search for what is considered equilibrium rates2.            Perhaps one of the controversies that have built up around the Purchasing Power Parity starts with the issue of definition. Different authors tend to come up with their own definition (version) of the theory, and as a result, the theory has come to mean different things to different authors3. Before looking at some of the conceptualizations of the theory that has generated over time, it is pertinent, to first examine the theory as was professed by its author Prof. Gustav Cassel.            Bunting4  presents the first exposition of the theory in Cassels’s Money and Foreign Exchange after 1914, which he said was one of the earliest and best explanation of the theory by the author. Bunting explains that the concept of purchasing power parity was borne out of the need to establish what determined exchange rates in Europe after the era of gold standard was gone, that is, when national currencies were on inconvertible basis. On this basis, Cassel explains that considering the fact that the primary reason a country’s currency is in demand in a foreign country is the need to purchase goods produced in that country. Thus, when normal, unrestricted trade between [two] countries have been established over time, the exchange rates become fixed relative to the purchasing power of each currency domestically, and as long as this domestic purchasing power of the currencies do not change, nothing will happen to the exch ange rates5. Further, the theory states that when the currencies of these countries undergo inflation, the â€Å"the normal rate of exchange will be equal to the old rate multiplied by the quotient of the degree of inflation in the one country and in the other†6. While this explanation describes the basic skeleton of the theory, there have been several adjustments and modifications of the meanings and concept of the theory as several authors tend to strengthen or criticize it. Some of these adjustments to the meaning of the theory will suffice to buttress this point.            Everett and his colleagues7 attempting to measure currency strengths and weakness with the purchasing power parity concept, posited that as long as there is unrestricted trades, exchange rates of currencies tend to obey the purchasing power of the currencies. In this regard, they succinctly conceive the theory to mean thus regardless of how currencies are denominated, when adjusted for units; all currencies tend to command the same basket of goods8. This definition is similar to that adopted by Klein et al.9, who likened the purchasing power parity doctrine to the law of One Price with the explanation that an identical good (or service) would command the same price, measured in a given numeraire system, all over the trading world10.            Belassa, however, gave a more elaborate explanation of the purchasing power doctrine, differentiating between the relative and absolute interpretations of the theory. According to him, the absolute version of purchasing power parity theory argues that when purchasing power parities are calculated as a ratio of consumer goods prices for any pair of countries, the result reflects the equilibrium rates of exchange. On the other hand, the relative version of the theory asserts that, when compared to a period when equilibrium rates prevailed, changes in the relative prices of goods would indicate the necessary adjustments in exchange rates11. In a sense, one can infer from these definitions that the absolute version of the theory seeks to establish ‘equilibrium’ exchanges rates between any pair of countries based on purchasing power of their currencies, while the relative version intends to measure the over and undervaluation of currencies at any period in time12.            Despite the controversies surrounding the validity and utility of this theory, recently, authors have sought to clothe the doctrine in â€Å"the garments of respectability†and in this regard, several statistical materials have been presented that more accurately reflects the relationship between power of currencies and exchange rates, as conceived in the theory 13. The purpose of this paper is, therefore, to examine some of the literatures regarding the theory and perhaps to infer from these, the implications and future research possibilities of the theory. Literature Review  Balassa, Bela (1964). The Purchasing-Power Parity Doctrine: A Reappraisal.            Belassa14 apparently belongs to the group of authors that intend to strengthen the validity and utility of the purchasing power parity doctrine. He begins by first differentiating between absolute and relative versions of the theory, as explained above. He, however, asserted that the doctrine as postulated by Cassel tends towards the absolute version when he states that the rate of exchange between two countries will be determined by the quotient between the general levels of prices in the two countries15. Further, he explains that theory as invoked by another author indicates that the German mark was undervalued against the dollar, while the mark too was overvalued, and the Austrian shilling, Danish crown and Dutch guilder all undervalued, by extending the theory to the currencies of less developed countries, their currencies appears to be undervalued against the dollar. The author contends that the deviation from the calculated exchanges were too much to be caused by errors.            In the bid to correct the perceived weakness in the theory, Belassa created a new model for the theory by introducing non-traded goods (services) into the traditional two-country, two-commodity model of the theory. This model of the theory is strengthened by the following assumptions; that there is only one limiting factor – labor, and constant input coefficient. Also, under the assumption of constant marginal rates of transformation, countries with relative higher productivity levels will experience higher relative price of non-traded commodity compared to another. From these propositions, the author posit that income levels play a significant level in the calculation of purchase powers and that purchasing power parities will be more closely related to exchange rates when prices are expressed in terms of wage units.            From this equation, the author posit that if we were to assume production of traded goods relative to non-traded goods constitutes the major difference in international productivity, currencies of country with higher productivity will appear to be overvalued using purchasing power parity calculations. However, if per capita income was to be used as a representative of levels of productivity, the ratio of purchasing power parity to exchange rate will be an increasing reflection of income levels            In providing empirical confirmation the proposed relationship between purchasing power parity, exchange rates and income levels, the author argues thus: â€Å"if differences in tastes do not counterbalance differences in productive endowments, there will be a tendency in each country to consume commodities with lower relative prices in larger quantities†16 . The result is that the purchasing power of country II’s currency will be undervalued if country I’s consumption pattern is used as weights and overestimated if country II’s consumption is used. This is shown in the tables below.            The second table above shows the comparison of the cost of household services in the United States and Italy for 1950. The author argue that after conversion at exchange rates, domestic services in Italy seem to cost about one-fifth of their United states’ price, barber and beauty shops cost one-fourth, laundry and dry cleaning the same cost. In the same vein, purchasing power equivalents for household services was 391 lira at US weights and 165lira at Italian weights. These figures confirm, the author argues, that services (non-traded goods) cost more, relatively, in countries with higher income levels. Thus, it buttresses the relationship between purchasing power parity, exchange rates and income levels. Bunting, H. Frederick (1939). The Purchasing Power Parity Theory Reexamined.            Bunting18, while conceding that the purchase power parity doctrine has been severally criticized, further adds his criticism by, according to him, submitting the theory to an improved statistical test. The basis of the argument set forth in this paper is that though the author of the doctrine of purchasing power parity discussed some likely exceptions to the theory, which could account for the differences observed between actual exchanges rates and parity calculated rates, several other exceptions that render the theory impracticable exists.            The author proffered an elaborate definition (explanation) of the theory, as conceived by Cassel and the proposed relationship between purchasing power of currencies and their exchange rates. Further, he went on to summarize the major exceptions to the general rule into seven main points, as discussed by Cassel in his book; Money and Foreign Exchange After 1914. Accordingly, he explained that exchange rates are expected to deviate from the calculated rates if, domestic prices fluctuate in relation to one another, due to any series of factors; tariffs and/or shipping costs change in relation to those prevalent in the base year used for the calculation; obstructions to trade other tariffs and shipping costs becomes operational during the year under consideration; sudden devaluation of currency occurs during the transition period; the activities of speculators affect exchange rates; governments are in need of foreign exchange, for example to pay international debts; and the base year or general price index is not properly selected, as defects in the price index used or the base year could cause predictive error in calculated rates. In sum, Bunting posits that though these exceptions are many and powerful, they do not fully subsume factors/reasons responsible for differences in actual rates and calculated rates.            In this regard, the author asserts that the critique of the theory can be simplified by considering problems of price levels and direction of change. On the issue of price level, he argues that, problems with choice of base year and the commodities that should make up the price indices to be used in the calculation shows ambiguity in the theory. First, with base year determination, the author argues that Cassel’s contention that it is only if we know the exchange rate which represents a certain equilibrium that we can calculate the rate which represents the same equilibrium at an altered value of the monetary units of the two countries19 i.e. we can only calculate the equilibrium rate now if we know the rate at a particular ‘base’ year; is faulty because there is no such thing in international trades. He argues that the fact that international economic conditions do not persist for long means that a given base year can only be reasonably used to measure relative price changes for only a short period of time.            On the commodity prices to be included in the price index, Bunting also faults Cassel’s insistence that ‘general’ price index should be used, arguing that not all goods are traded internationally. Thus changes in commodities not traded internationally can, therefore, have no effect on foreign country’s evaluation of a country’s currency. Further, on the direction of change, the author argues that Cassel’s contention that â€Å"when currencies are not on a convertible specie standard it is parities which determine exchange rates†20  tend to overlook the possibility that the direction of change could be the reverse i.e. price levels may be caused by changes in exchange rates. Thus, while Cassel concedes that the actions of speculators could cause changes in exchange rates without necessary price changes; there are several other factors that are capable of inducing change in exchange rates. Bunting mentions the following factors; Government monetary policies – alterations of central bank rates, stabilization funds, international government loans; Private international loans and special considerations such as large corporations transferring their capital holdings from one country to the other to protect their profits, or tourist expenditures and immigration remittances, which both involve the purchase of foreign currencies with no regard for the purchasing power of the currencies involved.            Subjecting the purchasing power parity theory to statistical tests, the author presents his result in the graphical form shown below. In the charts below, Franco-American exchange rates were compared for 1920s and 1930s. The solid line represents calculated rates while the broken line labeled no lag represents actual rates. The differences exhibited between the actual and calculated rates for the statistical test constitute discrepancy in the theory. The 1month, 2months and 3months lag periods were allowed in the assumption that time should be allowed for changes in purchasing power parities to effect a change in exchange rate, thus the 1-3months lag should show more correlation with the actual rates, however, this was not the case. The author concludes that proponents of the theory should simply recognize the fact that the theory as it stand is defective and needs to be refined. The authors of this paper proffered answers to criticisms of the validity and utility of the purchasing power parity theory, and especially to the claims that though the theory worked relatively in the 1920s, it failed in the 1970s by some other authors. Davutyan and John21 contend that possible reasons for the apparent failure of the purchasing power theory to predict exchange rates accurately when figures from the 1970s are used could include the fact that relatively to 1920; monetary policies were more coordinated in the 1970s. They therefore, assert that it is the coordination of monetary policies, not the failure of the purchasing power parity theory that causes conventional statistical tests to reject the validity of purchasing power parity for the 1970s. Providing evidence to support their claims, the authors posit that if we are to assume that there are no obstructions to trade, i.e. all goods are tradable and effective arbitrage refers to the relative version of the purchasing power theory, as explained by Bellassa22 above. In consolidating their argument, the authors contend that purchasing power parity tend to fail under two instances: when arbitragers fail to respond to profitable opportunities or when transaction costs and other impediments inhibit trades. However, they contend that the first factor might not be feasible, so the latter appears to be more important. Elucidating on the second factor, Davutyan and John  posit that under the assumption of zero transaction costs all goods are tradable, when this assumption is listed, goods could be divided into two categories, tradables with zero transaction costs and non-tradables with high transaction costs. Thus, in the absence of transaction costs, arbitrage keeps relative prices of tradable goods across countries equal, but this is not the case between non-tradables as well as between tradables and non-tradables. Therefore, when there are economic shocks, the equation above holds tradables but not for non-tradables. Furthermore, the authors contend that even with tradables, while the zero transaction costs is convenient in theory, it is not always so in reality. The fact is that relative transaction cost differs between countries and this too, tends to introduce errors into the purchasing power parity calculation, as with the non-tradables. Another source of error in purchasing power calculation, according to the authors, is unequal weights used for calculation. They argue that in the second equation above, the weights in the price index are the same for both countries; however, using CPI or wholesale price index or GNP deflators would violate the requirement for similar weights and could introduce error into the measurement. To support their claims, the authors present the data in the table below, where R2 and estimate of the regression coefficient supports the argument that purchasing power parity works.            Everett24 and his colleagues presented a practical and working model of the purchasing power parity theory and argued that by using this model of the theory to calculate exchange rates, currency strengths and weakness can be measured. Defining purchasing power parity, the authors contend that the primary concept of the theory is that when the forces of price mechanism are unrestricted, exchange rates tend to conform to the purchasing power of currencies. Thus, instead of price levels adjusting to exchange rates, the reverse is the case. In this regard, the authors assert that while this general idea of the theory applies to a world of floating exchange rates, their model of the purchasing power theory can be adapted to a variety of exchange rate regimes, such as managed floats, crawling pegs and fixed exchange rates.            In explaining this model of the purchasing power parity, the authors refer to what they called the parity chart. As shown below, the chart is derived thus: the horizontal axis measures time from a chosen time of origin – the base year; while the vertical axis measures two things, one, the difference in the percentage of the purchasing power of currencies and two, the percentage change in the actual exchange rate from the base year. While the dotted line represents the actual/observed exchange rates, the parity (solid) line represents parity (calculated) exchange rates over time.            Using the two country model to explain the ‘parity chart’, the authors explain that if we assume that there are no restrictions to trade, and the perfect base time, under this scenario, if the change in the purchasing power of country A’s currency differs from that of country B, the parity line in the chart above will have a positive or negative slope, depending on the sign of the difference between the purchasing power of the currencies under consideration. Further, if actual exchange rates were to be plotted on the same chart, the slope should conform closely to that of the parity line. What can be inferred from this explanation is that the parity line in the chart closely reflects the expected change in exchange rates that should follow changes in the purchasing power of country currencies.            To support their claims that the parity chart can be used to measure changes in exchange rates under any type of exchange rate regime, the authors presented empirical results of several currencies with different exchange rate regimes, these included the German mark-a more or less freely floating exchange rate; Spanish peseta-a strictly managed exchange rate; Colombian peso-a crawling peg currency; and South African rand-a fixed exchange rate25. The result for the German mark is presented below:            The authors explain that the vertical axis measures the percentage deviation from the calculated rate. While the line representing the inflation factor shows a fairly steady rise, in line with the well known fact of relatively lower rates of increases in the West German price level compared with most other countries, the line representing the exchange rate, on the other hand, shows no apparent trend, reflecting the fact that the exchange rates of West Germanys trading partners vis-à -vis the dollar on a trade-weighted basis may have moved in opposite directions. These two factors when compounded, yields the parity line.            After presenting empirical results for all the four representative countries listed above, the authors concluded that an indepth examination of the parity chart and line indicates that the parity line provides an effective and informed judgment about future currency movements. Further, that if â€Å"the parity rate diverges from the actual rate, this indicates that the currency is presently either over- or undervalued, and will therefore have to adjust, the longer the persistence of such a divergence, the more likely that an adjustment will occur soon†26.            This is another study that attempted to strengthen the validity and utility of the purchasing power parity doctrine. These authors, in this study, posited that purchasing power parity could be used to derive a more effective simulation or projection of world economy. Admitting that the theory has come to mean different thing to different writers, the authors adopted the law of ‘one price’ definition of the theory, which explains that an â€Å"identical good or service would command the same price, measured in a given numeraire system, all over the trading world†27.            The authors further state that though there are several controversial issues about the theory, such as what category of goods should be included in the calculation or what time should be used as origin/base in the calculation, they assert that any detailed exchange rate modeling system should obey the purchasing power parity rule, in the long run. Statistically estimating the movement of exchange rates in relation to the purchasing power parity principle for the 1970s, the authors presented the following formula:            According to the authors, this formula states that the â€Å"U.S. dollar terms, should have a common rate of change across all countries, namely, the U.S. rate of change of export prices†28. Thus, if the exchange rates during this time, had moved in accordance with the principle of purchasing power parity, then the estimates of: would be consistent with the hypothesis of purchasing power parity. Where a =O; b = -1.0; c = +1.0; eit =additive random error. Scatter diagrams of the data points of the two equations above are shown below. Conclusively, the authors assert that judging by these statistics, all the regression estimates in the charts above passed significance tests. Thus, it could be deduced that the relationship between purchasing power of currencies and the actual exchange rates was tightest for members of the EMS, but slightly less tight when the UK is included. Based on this evidence, the authors believe that their contention that, on average, purchasing power parity movements approximately reflects actual exchange rates in the 1970s has been adequately justified, and as a result, it could be generalized that calculations of purchasing power parity could be used in predicting movements of exchange rates.            John29 proffered answers to criticisms concerning the predictive errors observed with exchange rates calculated from purchasing power parity. They observed that studies carried out by several authors indicate that for several countries, the predictive error of purchasing power parity during the 1970s followed what they referred to as ‘random walk’ i.e. whatever the deviation between the parity rate and actual rates observed this month, next month it is likely to increase as decrease.            In this regard, the author argued that the basic idea behind the purchasing power parity doctrine is that in the long run, the differences between the parity rates and the actual exchange rates tend to disappear and the tow rates are equated. They argue that, though economic shocks, in whatever guise, could, in the short term, drive the actual rate from the parity rates, but in the absence of new shocks, the price mechanism tend to equate the tow rates, in the long run. Based on this argument, the author contend that predictive errors for purchasing power parity should not perform a random walk, instead there should be a gradual decline or increase towards the actual rate.            Supporting their claims that predictive errors in purchasing power parity does not perform random walk in the long run; the authors presented the results of empirical studies of several countries using data for over seventy years.            Following the same path with paper reviewed above, Yeager30 also sought to strengthen the validity and utility of the purchasing power parity theory. He started off his argument with the basic assumption that people primarily value currencies for what could be bought with it, based on this assumption, he argues, it is safe to presume that in an unrestricted market, people will tend to exchange such currencies for their relative purchasing powers. The author admits that the theory, in its basic form, as stated above, is loose and ambiguous, he posits, however, that the theory performs tow main functions. First, the theory gives an expression of what the equilibrium exchange rates should be for currencies, however crude this rate appears. And two, the theory act like a stabilizing force for exchange rates. Explaining this second function, he assert that when for any reason, actual exchange rates deviate from the equilibrium rates, the theory describes pressures at work tending to check and reverse this random departures from the range of equilibrium rates.            The author provides this example to buttress the point made above about the stabilizing powers of the parity theory:            Let us suppose, for example, that prevailing exchange rates unmistakably           undervalue the British pound in relation to the purchasing powers of the pound    and of foreign currencies. Foreigners -say Americans- will offer dollars for      pounds to buy British goods at bargain prices. Britons will offer relatively few pounds for dollars to buy, American goods at their apparently high prices.           Unmatched attempts to sell dollars and buy pounds will bid the exchange rate toward the equilibrium level.            In the same light, the author evaluates some of the numerous objections raised about the theory and posits that in most of these objections, the stabilizing pressures aspect of the theory has been mostly ignored. In sum, the author concludes that most of the discrepancies observed in purchasing power parity rates are due to â€Å"inappropriate base periods; disequilibrium exchange rates (including base-period rates), often imposed by official pegging; tariffs, quotas, and other interferences with trade, payments, and exchange rates.31†           Wyman32  extends the utility of the purchasing power parity further, by applying the concept of the doctrine to calculating gains or losses incurred by holding foreign items, such as foreign currencies or goods. Relating purchasing power parity to currency changes, the author explain that purchasing power is related to the exchange rates of currencies, in that, differential rates of inflation between, say the United States and a foreign country, influences the exchange rates between the monetary units if each country. Putting this definition into an equation, he states that the calculation of the purchasing power parity can be illustrated thus: If the exchange rate between the United States and a foreign country is 20FC = $1 where FC denotes a unit of ‘foreign currency’, if during the year, the US price level index changed from 100 to 110 and that of the foreign country changed from 100 to 120, the purchasing power parity rate can be calculated by determining an adjustment factor that would be applied to the exchange rate. The adjustment factor is calculated as:  Èt à · Øt = the adjustment factor for period t or (120,100t 110,100) = 1.0909 where Èt =  the price-level ratio in the United States defined as the general price-level index at            the end of period t divided by the general price-level index at the beginning of         period t Øt = the price-level ratio in the foreign country defined as the general price-level index at         the end of period t divided by the general price-level index at the beginning of         period t            Explaining this formula, the author assert that when the adjustment factor is applied to the exchange rate, for the example above, result is FC 20x 1.0909 = FC 21.8182=$1. So, if the actual exchange rate at the end of the time t is at the calculated rate of FC 21.8182 to $1, investors in either country will maintain their purchasing power relative to each other, however, if for example, the exchange rate was to be at FC 22 to $1, FC would have depreciated more than is necessary to maintain the purchasing power parity, and so US investors in need of the foreign currency would have exchanged the currency at a loss. The author went on to establish a multiequation system that can be employed in analyzing potential gains and losses in foreign exchange, based on the purchasing power parity concept. Ruble, L. William (1961). A Comparison of the Parity Ratio with Agricultural Net Income Measures: 1910-1958. Journal of Farm Economics, 43(1):101-112. And Stine O. C. (1946). Parity Prices. Journal of Farm Economics, 28(1):301-305.            These two works covered a slight different aspect of purchasing power parity. They were focused on the purchasing power of farmers, comparing prices changes in farm and non-farm products, and thus, what farmers are paid for their farm products and what they have to pay to buy non-farm products. Stine33  explains that in the years after the first World War, when the purchasing power parity concept was birthed and first applied as measurement in of changes in purchasing power, marked changes in general price levels was observed, as expected, however, it was also observed that farm products declined more rapidly and farther compared to non farm products. As a result, what farmers had to pay for products they buy was considerably different from what they earn from the sells of farm products.            Ruble34  supporting this line of argument, argues that since the prices received by farmers and prices paid by farmers affect the livelihood and wellbeing of the farming family, the parity ratio provides a good indicator of the standard of living of farmers. Further, contends that the level of the parity ratio is expected to give good indication of the following methods of estimating the standard of living of farmers: Net money income per capita, per farm, or per worker. Net real income per capita, per farm, or per worker. Income of farmers compared to income of non-farmers on a per      capita or per worker basis (the parity income concept)      However, data and result of empirical studies was presented to measure the relation between the parity ratio and the well being of farmers suggests that the parity ratio might not indeed properly reflects the general well being of farmers, if the well-being of farmers in general is expressed by the per capita, per farm, or per worker net income, real or money. In arriving at the figures in the table, the parity ratio was correlated separately with the per capita net agricultural income of the farm population, the net income of farm operators from farming per farm, and the net income of farm workers from farming per worker, income from all sources, and deflated by the index of prices paid by farmers for family-living items (1917-19 = 100) Summary            There is no denying the fact that the Purchasing Power Parity doctrine is an important theory in the financial world. It is true that a lot of controversies have been generated about its validity and utility, but it is also true that several authors have been able to categorically prove its validity, and more importantly, utility, in an array of fields. Just as the theory has come to mean different thing to different authors, it has also carved for itself, different functions, depending on the perspective one adopts. It is not surprising, therefore, that authors have been able to apply the doctrine to a number of endeavors, as seen in the reviews above.      In its most basic form, the concept argues that people primarily need currencies of other countries for the purpose of buying goods/commodities of that country. Therefore, people will only be prepared to exchange currencies for its relative worth. Here lies the relationship between purchasing power parity and the exchange rates of currencies i.e. when it is suspected that a currency is under or over valued, market forces will tend to force the rate back to the equilibrium level. Equilibrium here describes the rate achieved after trades have occurred between two countries, uninterrupted, for a certain period of time and a common exchange rate has been established, as a result.      From this very basic understanding of the theory, as proposed by the author Prof. Gustav Cassel, several modifications, adjustments, and extension of the theory have been proposed and proved. For example, Bellasa fine tuned the predictive value of the theory by modifying the basic two-country, two-commodity model, to include considerations for non-traded goods (services) and the per capita income of each country, which, he argues, play crucial role in the purchasing power of currencies. Klein and his colleagues  modified the theory and employed it in simulating/projecting changes in world economy; Everett and others , also modified the theory and proved it to be useful in appraising strengths and weaknesses of countries’ currencies; while John  showed that the predictive errors in rates calculated with the purchasing power parity concept could be as a result of         faults inherent in the calculation methods and data.      From the foregoing, one can only infer that purchasing power parity is still an important financial concept. Although, further academic and research efforts should be geared towards resolving some of the objections raised against the theory. It is obvious that criticism of the theory will further help to strengthen it, in the future, as we have seen it done in the past. Most of the objections raised have been somehow addressed, even if not completely resolved. One can, thus conveniently conclude that with time, the theory might be better fine tuned and become more effective at explaining and predicting exchange rates of currencies. Endnotes Balassa, Bela (1964). The Purchasing-Power Parity Doctrine: A Reappraisal. Ibid p.584 Klein, R. Lawrence, Shahrokh Fardoust and Victor Filatov (1981). Purchasing Power Parity in Medium Term Simulation of the World Economy; Balassa, Bela (1964) Bunting, H. Frederick (1939). The Purchasing Power Parity Theory Reexamined Bunting (1939) provided almost a word-for-word definition and explanation of the theory as postulated by Cassell. The author gives a better idea of the original theory Ibid p.283 Everett, M. Robert, Abraham M. George and Aryeh Blumberg (1980). Appraising Currency Strengths and Weaknesses: An Operational Model for Calculating Parity Exchange Rates. Ibid p.80 Klein et al., 1981 Ibid p.486 Belassa, 1964 p.584-585 This is personal opinion based on the definition of the absolute and relative PPP proffered by Bellasa, 1964 Ibid Ibid Belassa, 1964 p.585 quoting Cassel in his book Money and Foreign Exchange After 1914. Ibid  Ibid p.587 Bunting, H. Frederick (1939). The Purchasing Power Parity Theory Reexamined. Bunting, 1939 p.285 quoting Cassel in his book Money and Foreign Exchange After 1914. Bunting, 1939 p.288 Davutyan, Nurhan and John Pippenger (1985). Purchasing Power Parity Did Not Collapse During the 1970s Balassa, 1964 Davutyan and John, 1985 p.1151 Everett, M. Robert, Abraham M. George and Aryeh Blumberg (1980). Appraising Currency Strengths and Weaknesses: An Operational Model for Calculating Parity Exchange Rates. Ibid p.84 Ibid p.90 Klein, R. Lawrence, Shahrokh Fardoust and Victor Filatov (1981). Purchasing Power Parity in Medium Term Simulation of the World Economy. p.486 Ibid p.487 John, Pippenger (1982). Purchasing Power Parity: An Analysis of Predictive Error Yeager, B. Leland (1958). A Rehabilitation of Purchasing-Power Parity Ibid p.529 Wyman E. Harold (1976). Analysis of Gains or Losses from Foreign Monetary Items: An Application of Purchasing Power Parity Concepts. Stine O. C. (1946). Parity Prices Ruble, L. William (1961). A Comparison of the Parity Ratio with Agricultural Net Income Measures Bibliography Balassa, Bela (1964). The Purchasing-Power Parity Doctrine: A Reappraisal. The Journal         of Political Economy, Vol. 72:6 pp. 584-596. Bunting, H. Frederick (1939). The Purchasing Power Parity Theory Reexamined.         Southern Economic Journal, Vol. 5:3. pp. 282-301. Davutyan, Nurhan and John Pippenger (1985). Purchasing Power Parity Did Not           Collapse During the 1970s. The American Economic Review, Vol. 75:5.          pp.1151-1158. Everett, M. Robert, Abraham M. George and Aryeh Blumberg (1980). Appraising         Currency Strengths and Weaknesses: An Operational Model for Calculating    Parity Exchange Rates. Journal of International Business Studies, Vol. 11:2. pp.       80-91. John, Pippenger (1982). Purchasing Power Parity: An Analysis of Predictive Error. The Canadian Journal of Economics, Vol. 15:2, pp. 335-346. Klein, R. Lawrence, Shahrokh Fardoust and Victor Filatov (1981). Purchasing Power    Parity in Medium Term Simulation of the World Economy. The Scandinavian         Journal of Economics, Vol. 83: 4 pp. 479-496. Ruble, L. William (1961). A Comparison of the Parity Ratio with Agricultural Net        Income Measures: 1910-1958. Journal of Farm Economics, Vol. 43:1. pp. 101-         112. Stine O. C. (1946). Parity Prices. Journal of Farm Economics, Vol.28:1. pp.301-305. Wyman E. Harold (1976). Analysis of Gains or Losses from Foreign Monetary Items: An         Application of Purchasing Power Parity Concepts. The Accounting Review, Vol.           51: 3. pp. 545-558. Yeager, B. Leland (1958). A Rehabilitation of Purchasing-Power Parity. The Journal of           Political Economy, Vol. 66:6, pp. 516-530.
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