A measurement to analyze the relative change in the Absolute Parity of Power Purchase: An application to the European Union

In the present paper an index to measure the changes in the Absolute Purchasing Power Parity. in the short term of a group of territories that conform an unique market, using the information of the Harmonized Index of Consumer Prices and the Exchange Rates. This measurement is utilized to study the change in relative prices of the countries of the European Union for the period 1991-2002, and the fulfillment of the theory of the Relative Purchasing Power Parity, taking as a reference the Absolute Purchasing Power Parity in the reference time of the Price Index. The difficulties found to do these comparisons have given rise to multitude of jobs that can be classified in two large groups. In the first group are the efforts focused to find the best instrument to do comparable the figures of the distinct economies. In this line, it is emphasized the use and the advances in the index numbers theory [for a historic revision applied to price index see Diewert, W. (1993), for a theoretical revision see Balk, B. (1995) and Hill, T. (1988)] and the jobs carried out in the International Program of Comparison (ICP), program belonging to the statistical division of United Nations with near 35 years of life, and whose objective is to produce estimations of the National Gross Product and its components, that can be comparable among countries in real terms. It utilizes the concept of Purchasing Power Parity (PPP), [UN (1992)]. In the same line, the European Program of Comparison is developed by Eurostat and the OCDE since 1980. In the second group the investigations based in the unit price law and the theory of of the PPP to explain the behavior of the rate of change among two or more countries. In this case, the objective is focused in the analysis of the economic implications of its fulfillment or not, and how being able to test its fulfillment [Cheung, AND W., Lai, K. (2000), Engel, C. (2000), Reads, M. (1976), Taylor, A. (2001)] This job is inside of the first group of investigations. An index is defined to reflect changes in the Relative Purchasing Power Parity among a group of countries that do not share a common currency. This measurement can be obtained from Harmonized Index of Consumer Prices (HICP), and from the Exchange Rates among the currencies of the distinct countries. The results show the strong distorting effect that exchange rate has upon the Purchasing Power Parity among countries. The evolution of the internal prices of each country is a residual factor to explain the changes in the Purchasing Power Parity. In this sense, the apparition of euro contributes to a clear stability for the consumers whose countries have adopted the euro than those that have not adopted yet. However, in the euro zone systematic behaviours in some of the countries are detected that indicate that, their Purchasing Power Parity is changing in a systematic way, with regard to the average Purchasing Power Parity of the Monetary Union.

Formulas for Consumer Price Index at the elementary aggregate - A new proposal from the economic point of view

The price level in the aggregate economy and, more concretely, controlling its changes, has become one of the high-priority objectives within the framework of the regional macroeconomic analysis. Its different evolution could modify the interregional capital and commercial flows, being able to cause strong shocks, and of asymmetric nature, in each economy. The first step to reach this objective is obtaining a trustworthy and comparable measurement of the inflation in the different regions to be compared. The Index Number Theory is then used to calculate Consumer Price Indexes (CPI) the regional level. The calculation of CPI is made, at least, in two phases. In the first one, Elementary Price Index is considered (EPI). In the second and later phases, these EPI are combined, along with weighting information based on household’s expenditure, to obtain CPI for different aggregation levels to the country level. As previous step to the calculation of the IPE and CPI, the set of goods and services has to be defined based on households’ consumption behaviour. These sets are grouped in layers, named elementary aggregates, based on their homogeneity of satisfying consumer’s necessities. The COICOP (Classification Of Individual Consumption by Purpose) has important implications at the time of analyzing the behaviour of the consumer within each elementary aggregate, because of a high possibility of substitution between products. Nevertheless, this possibility diminishes and can get to be null when the goods and services satisfy necessities with very different nature. Whether what is wanted it is to calculate an EPI that correctly reflects the consumer behaviour, the described homogenous character cannot be forgotten, especially if, in addition, we take into account that National Statistics Agencies have no expenditure information available for weighting purposes, only data of prices to calculate EPI. This paper is focussed on analysis of the formula used to obtain the IPE, with the limitations of available information just commented. The election of the formula for the IPE has not been widely studied in the economic literature, being the proposal by Carli in 1764 and Dutot in 1738 [ extracted Reference of OIT (2003), chapter 20, pages 12-13 ] the most often used for practical purposes. Nevertheless, Fisher (1922) had already recommended not using the Carli’s formula because of the bias to the rise that it introduces [Fisher (1922), pages 29-30]. Throughout the 20th century different authors has continued looking for the ideal formula extending possible approaches to the subject: the approach of Divisia, the stochastic approach, the economic approach and the axiomatic approach. The final summary of these studies can be synthesized in "Toward to Dwells Accurate Measure of The Cost of Living” by the Advisory Commission To The Study The Consumer Price Index presented in 1996. This report, also known as Boskin’s Report, suggests the use of geometric mean price indices at the elementary aggregate for the EPI, this formula is attributed to Jevons in 1983 [OIT (2003), chapter 20, pages 12-13 ]. In the present paper, we demonstrate that all usually formulas for the calculation of the IPE are incoherent with the theory of consumer behaviour, in an aggregate characterized by the high level of substitution caused by homogeneity in the consumption purpose. In addition, the formula proposed by Rodriguez, González and Rodriguez (2004), is not only superior from the axiomatic point of view, but also from the economic approach, is the only one that is able to reflect the expected consumer behaviour.

Markov Chain approach to Purchasing Power Convergence in the 15 European Union

In the present paper we study the degree of convergence in the European Union from the Purchasing Power Parity (PPP) point of view. The price of the shopping basket can be the cause of disparities in a global market in construction that, like the European Union, is formed by different countries with different consumption habits. In addition, in this construction process twelve out of fifteen countries of the EU have left its national currency to adopt the Euro like common currency. Therefore, it is necessary for the stability of the Union process in the long run that, among others, purchasing power of the different state members tends towards a same common value. Moreover, the question is whether that process of convergence within the European Union is taking place or not. In order to solve this question, the series of the Absolute Purchasing Power Parity (APPP) are estimated through the suggestion of Rodriguez et al (2004). These authors use the Harmonized Consumer Price Index in the European Union and the nominal exchange rates of the different currencies with euro. Monthly estimates of the APPP series for the 1995-2002 period are obtained for each of the fifteen countries. These figures show, for each country, their relative position to the average value of the European Union. Using these series we applied the Markov Chain methodology to study the time evolution of the distribution of APPP in the European Union. This methodology has been very used by its facility of calculation and interpretation of the results. Nevertheless, with the purpose of obtaining good estimations it is necessary to solve the discretization problem of a continuous variable. This is, to use a finite set, and relatively small number of states, for a variable with infinite values. In the present work different approaches are used to solve the problem. We test for structural change on the estimated probabilities using adapted test to Markov Chains. This allows us to study if an effect exists on the Purchasing Power Parity with the entrance of the Euro. Markov Chains are estimated by Maximum likelihood, and allow us to do different analyses. In the first place, we can study the mobility of the distribution, measured through the probabilities of permanence or not in the same state, and in the degree of diagonal structure of the resulting matrix. This objective can obtained by direct observation, calculating Mobility Index, or using expected time of first passage. Secondly, we can obtain the ergodic or long term distribution. This one shows the temporary evolution in the long run of the distribution, under the hypothesis of maintenance of the present conditions. This distribution would show the possible convergence or not of the whole distribution. We also estimate elasticities of ergodic probabilities, to analyze the effect of each probability in the Markov chain in the long run distribution. Results show differences with the Euro Entry, mobility towards convergence within the distribution is slow, with high elasticities of the ergodic distribution to changes in the transition probabilities.

Formulas for Consumer Price Index at the elementary aggregate - A new proposal from the economic point of view

The price level in the aggregate economy and, more concretely, controlling its changes, has become one of the high-priority objectives within the framework of the regional macroeconomic analysis. Its different evolution could modify the interregional capital and commercial flows, being able to cause strong shocks, and of asymmetric nature, in each economy. The first step to reach this objective is obtaining a trustworthy and comparable measurement of the inflation in the different regions to be compared. The Index Number Theory is then used to calculate Consumer Price Indexes (CPI) the regional level. The calculation of CPI is made, at least, in two phases. In the first one, Elementary Price Index is considered (EPI). In the second and later phases, these EPI are combined, along with weighting information based on household's expenditure, to obtain CPI for different aggregation levels to the country level. As previous step to the calculation of the IPE and CPI, the set of goods and services has to be defined based on households' consumption behaviour. These sets are grouped in layers, named elementary aggregates, based on their homogeneity of satisfying consumer's necessities. The COICOP (Classification Of Individual Consumption by Purpose) has important implications at the time of analyzing the behaviour of the consumer within each elementary aggregate, because of a high possibility of substitution between products. Nevertheless, this possibility diminishes and can get to be null when the goods and services satisfy necessities with very different nature. Whether what is wanted it is to calculate an EPI that correctly reflects the consumer behaviour, the described homogenous character cannot be forgotten, especially if, in addition, we take into account that National Statistics Agencies have no expenditure information available for weighting purposes, only data of prices to calculate EPI. This paper is focussed on analysis of the formula used to obtain the IPE, with the limitations of available information just commented. The election of the formula for the IPE has not been widely studied in the economic literature, being the proposal by Carli in 1764 and Dutot in 1738 [ extracted Reference of OIT (2003), chapter 20, pages 12-13 ] the most often used for practical purposes. Nevertheless, Fisher (1922) had already recommended not using the Carli's formula because of the bias to the rise that it introduces [Fisher (1922), pages 29-30]. Throughout the 20th century different authors has continued looking for the ideal formula extending possible approaches to the subject: the approach of Divisia, the stochastic approach, the economic approach and the axiomatic approach. The final summary of these studies can be synthesized in "Toward to Dwells Accurate Measure of The Cost of Living” by the Advisory Commission To The Study The Consumer Price Index presented in 1996. This report, also known as Boskin's Report, suggests the use of geometric mean price indices at the elementary aggregate for the EPI, this formula is attributed to Jevons in 1983 [OIT (2003), chapter 20, pages 12-13 ]. In the present paper, we demonstrate that all usually formulas for the calculation of the IPE are incoherent with the theory of consumer behaviour, in an aggregate characterized by the high level of substitution caused by homogeneity in the consumption purpose. In addition, the formula proposed by Rodriguez, González and Rodriguez (2004), is not only superior from the axiomatic point of view, but also from the economic approach, is the only one that is able to reflect the expected consumer behaviour

A measurement to analyze the relative change in the Absolute Parity of Power Purchase: An application to the European Union

In the present paper an index to measure the changes in the Absolute Purchasing Power Parity. in the short term of a group of territories that conform an unique market, using the information of the Harmonized Index of Consumer Prices and the Exchange Rates. This measurement is utilized to study the change in relative prices of the countries of the European Union for the period 1991-2002, and the fulfillment of the theory of the Relative Purchasing Power Parity, taking as a reference the Absolute Purchasing Power Parity in the reference time of the Price Index. The difficulties found to do these comparisons have given rise to multitude of jobs that can be classified in two large groups. In the first group are the efforts focused to find the best instrument to do comparable the figures of the distinct economies. In this line, it is emphasized the use and the advances in the index numbers theory [for a historic revision applied to price index see Diewert, W. (1993), for a theoretical revision see Balk, B. (1995) and Hill, T. (1988)] and the jobs carried out in the International Program of Comparison (ICP), program belonging to the statistical division of United Nations with near 35 years of life, and whose objective is to produce estimations of the National Gross Product and its components, that can be comparable among countries in real terms. It utilizes the concept of Purchasing Power Parity (PPP), [UN (1992)]. In the same line, the European Program of Comparison is developed by Eurostat and the OCDE since 1980. In the second group the investigations based in the unit price law and the theory of of the PPP to explain the behavior of the rate of change among two or more countries. In this case, the objective is focused in the analysis of the economic implications of its fulfillment or not, and how being able to test its fulfillment [Cheung, AND W., Lai, K. (2000), Engel, C. (2000), Reads, M. (1976), Taylor, A. (2001)] This job is inside of the first group of investigations. An index is defined to reflect changes in the Relative Purchasing Power Parity among a group of countries that do not share a common currency. This measurement can be obtained from Harmonized Index of Consumer Prices (HICP), and from the Exchange Rates among the currencies of the distinct countries. The results show the strong distorting effect that exchange rate has upon the Purchasing Power Parity among countries. The evolution of the internal prices of each country is a residual factor to explain the changes in the Purchasing Power Parity. In this sense, the apparition of euro contributes to a clear stability for the consumers whose countries have adopted the euro than those that have not adopted yet. However, in the euro zone systematic behaviours in some of the countries are detected that indicate that, their Purchasing Power Parity is changing in a systematic way, with regard to the average Purchasing Power Parity of the Monetary Union

An Empirical Study of the Purchasing Power Parity in the European Union

This paper studies the convergence in the European Union on Purchasing Power Parity. Firstly, we develop a method for the estimation of PPP series and then, we put it into practice and estimate the monthly Purchasing Power Parity for the period January 1995 to July 2003. Secondly, convergence is studied using distribution dynamics from the continuous and discrete approximations. Results show some slow convergence in the European Union. Keywords: Purchasing Power Parity, Convergence, Distribution Dynamics, Markov Chain

Markov Chain approach to Purchasing Power Convergence in the 15 European Union

In the present paper we study the degree of convergence in the European Union from the Purchasing Power Parity (PPP) point of view. The price of the shopping basket can be the cause of disparities in a global market in construction that, like the European Union, is formed by different countries with different consumption habits. In addition, in this construction process twelve out of fifteen countries of the EU have left its national currency to adopt the Euro like common currency. Therefore, it is necessary for the stability of the Union process in the long run that, among others, purchasing power of the different state members tends towards a same common value. Moreover, the question is whether that process of convergence within the European Union is taking place or not. In order to solve this question, the series of the Absolute Purchasing Power Parity (APPP) are estimated through the suggestion of Rodriguez et al (2004). These authors use the Harmonized Consumer Price Index in the European Union and the nominal exchange rates of the different currencies with euro. Monthly estimates of the APPP series for the 1995-2002 period are obtained for each of the fifteen countries. These figures show, for each country, their relative position to the average value of the European Union. Using these series we applied the Markov Chain methodology to study the time evolution of the distribution of APPP in the European Union. This methodology has been very used by its facility of calculation and interpretation of the results. Nevertheless, with the purpose of obtaining good estimations it is necessary to solve the discretization problem of a continuous variable. This is, to use a finite set, and relatively small number of states, for a variable with infinite values. In the present work different approaches are used to solve the problem. We test for structural change on the estimated probabilities using adapted test to Markov Chains. This allows us to study if an effect exists on the Purchasing Power Parity with the entrance of the Euro. Markov Chains are estimated by Maximum likelihood, and allow us to do different analyses. In the first place, we can study the mobility of the distribution, measured through the probabilities of permanence or not in the same state, and in the degree of diagonal structure of the resulting matrix. This objective can obtained by direct observation, calculating Mobility Index, or using expected time of first passage. Secondly, we can obtain the ergodic or long term distribution. This one shows the temporary evolution in the long run of the distribution, under the hypothesis of maintenance of the present conditions. This distribution would show the possible convergence or not of the whole distribution. We also estimate elasticities of ergodic probabilities, to analyze the effect of each probability in the Markov chain in the long run distribution. Results show differences with the Euro Entry, mobility towards convergence within the distribution is slow, with high elasticities of the ergodic distribution to changes in the transition probabilities