1-INTRODUCTION
In this project, the focus will be addressed to the Purchasing Power Parity (PPP) and its applicability in the Brazilian economy from 1995 until 2009, which means after the high inflation period. Given that in these period not many works has been written. And since the theory of Purchasing Power Parity is important to contrast and evaluate the criterion of living between two or more countries taking into consideration their exchange rates and its impact in the economy.
Technique of Cointegration and unit root test will be applied in this project to inspect this hypothesis for the exchange rate market efficiency in Brazil. As said above, the spotlight period will be from 1995 because it will reflect how the economic plan applied in early 1994 at the Brazilian economy, best known as "Real Plan", has worked out. And after that ambitious economic project, we can investigate if the market exchange rates are being efficient.
It is important to bear in mind that flexible and fixed exchange rates were used at Brazilian economy in this period, though Enders (1988) reminds that cointegration can be applied to estimate the PPP relationship under fixed and flexible exchange rates.
2-LITERATURE REVIEW and THEORY
After a deep currency crisis in Brazil, where in just under 30 years (June 1965 to June 1994) an inflation of 1.142.332.741.811.851% was registered, according to General price index of the period, the most important economic project has taken place, mainly to tackle that inflation phenomenon. The plan intended to stabilize the domestic currency in nominal terms. Back in the beginning of that economic plan at July 1994, the exchange rate regime was fixed. But in January 1999 after a currency crisis in Brazil, as a result from de 1997 Asian crisis and the 1998 Russia crisis, that fixed-exchange rate regime was over given then a flexible or floating regime to vigour.
So, based on monthly data covering January 1995 to September 2009, cointegration and unit root tests of price index in Brazil and USA, and exchange rates between both countries will be conducted. USA is one of the main commercial partners of Brazil, responding for more than 20% of Brazil`s exports.
The PPP has become a very important tool nowadays in many developed countries since it analyses the long term balanced exchange rate of two or more currencies to equalize their purchasing power. And for developing countries is an important device to control and evaluate inflation. In the Brazilian case, it is not different where the exchange rate is intimately related with inflation, in addition to it the "real plan" successfully tackle inflation, turning almost 25 million people into consumers, so the PPP will be vital to compare differences in living standards between countries. For instance, according to IMF (International Monetary Fund), XXCHECARXX China is the second economy power of the world, using PPP measure, with the GDP of U$ 5.970 per capita. When using nominal terms the GDP per capita is just around U$ 3250. Thus, PPP can bring a GDP of developing countries into the same or even higher levels of developed countries` GDP.
The term PPP was first used by Gustav Cassel (1918), but history tells that the concept is linked to the University of Salamanca in the sixteen century. PPP, according to Ramirez and Khan (1999) is relatively simple and straightforward, and applies the law of one price to an equal basket of goods across countries. In other words, the same basket of goods in country X costs the same in country Y if the currencies are exchanged at that rate. On the other hand, in spite of being simple in theory, PPP is rejected in many cases in response of details such as market disequilibrium, import/export restrictions, travel costs, location, among others.
To define PPP, Rogoff K. (1996), used these words: "purchasing power parity is disarmingly simple empirical proposition that, once converted to a common currency, national price levels should be equal. The basic idea is that if goods market arbitrage enforces broad parity in prices across a sufficient range of individual goods, then there should also be a high correlation in aggregate price levels."
Knowing that PPP can be difficult to hold in some cases, two hypothesis of PPP were developed, absolute and relative. "The purchasing-power-parity (PPP) theory involves the ratio of two countries' price levels (absolute PPP) or price indices times a base period exchange rate (relative PPP) as the most important variable determining the exchange rate, but it allows both for other explanatory variables and for random influences." (Officer, L. 1976).
So, in the absolute PPP hypothesis exchange rate between the currencies of two countries is determined by the price levels of those two countries. It can be written as:
(1)
Where E will be the nominal exchange rate measured in units of currency A (Brazilian Real (BR$)) per unit of currency B (United States dollars (US$)), P will be price level in country A, and P* will be the price level in country B. It also can be written in logs equation (1) as:
(2)
On the other hand, relative PPP hypothesis states that "the ratio of the equilibrium exchange rate in a current period (t) to the equilibrium exchange rate in a base period (o) is determined by the ratio of the domestic country`s price index in period t, where both indexes are measured relative to period o." (Officer, L. 1978). This can be written, in logs as:
(3)
where it is developed the hypothesis of β = 1 for the equation above, which would imply perfect adjustment of to movements in . And the intercept is consistent with the relative version of PPP, which requires only that domestic and foreign price levels move proportionately.
A relative version of PPP will be used in the present paper, given the fact that absolute version was tested in many occasions and in its majority the theory could not hold or be accepted for its validity. And alternatively, relative PPP takes into consideration differences in the rates of inflation between two countries, bringing a more accurate analysis.
The data are monthly, as mentioned above, for the period ranging from first month 1995 to September 2009. Thus 177 observations, which could help to achieve the long-run relationship examination demanded by the theory and empirical tests of PPP. Yet, as Kugler and Lenz (1993) reminds us, despite 15 to 20 years appears to be large, in long-run analysis for the hypothesis of PPP that period is not large.
All the variables to be used in the study of the equation 3, what are price level in the US (P*) and price level in Brazil (P) are based on the Wholesale Price Index (WPI). "This is standard in the literature, which is based on the fact that the WPI gives a more accurate measure of the prices of traded goods than does the consumer price index (CPI)" (Sanchez-Fung, J. 1999). In both cases, the price indexes were taken from the International Monetary Fund`s International Financial Statistics. Just as a matter of information, in the US the WPI is better known as producer price index (PPI). The exchange rate (E) of the R$/US$ used in this analysis is the 'sell rate' for foreign exchange in Brazil, and Central Bank of Brazil (BACEN) is the source.
3 - ECONOMETRIC MODELING
As Sanchez-Fung J. (1999) reminds us once more, to apply the cointegration technique determine the degree of integration of each variable is needed as a first step, and in this present paper the equation 3 will be submitted to the test to determine the degree of integration. And the Augmented Dickey-Fuller (ADF) test is well used as a first step for this purpose, raising the order of integration among exchange rate and differential of the price levels between the those countries.
"The series , and are likely to be nonstationary, they have to be differenced once in order to become stationary." (Kugler P., Lenz C., 1993). So, after estimate a regression like (3) and obtain the residuals, the ADF test will be used on the OLS residuals. If the null hypothesis is rejected it can be said that we have cointegration. Thus, the cointegration analysis is taken at a two step approach of Engle and Granger dynamic form. Guajarati S., (2004) well states: "Economically speaking, two variables will be cointegrated if they have long term, or equilibrium, relationship between them. Economic theory is often expressed in equilibrium terms, such as PPP." He adds: "The valuable concept of unit roots, cointegration, etc. is to force us to find out if the regression residuals are stationary."
Estimating equation 3, by ………………………………….. produces the following outcome:
By the figure ….. 1….. is easy to interpreted some events, such as the devaluation of the exchange rate in beginning of 1999, when the government changed the policy from fixed to flexible exchange rate regime, which increased the country`s competitivety in the external sector. Other event, was in 2002 when a presidential running brought as a result another devaluation of the exchange rate, quickly recovered. And last but not least, the downturn of 2008 can be seen on the graph as well.
4 - CONCLUSION
5 - BIBLIOGRAFY AND REFERENCES
Enders, Walter (1988) Arima and Cointegration tests of PPP under fixed and flexible exchange rates regimes, Review of Economics and Statistics, 70(3): 504-08
Dickey, D.A. and W.A. Fuller (1979): Distribution of the Estimators for Autoregressive Time Series with a Unit Root, Journal of the American Statistical Association, 74, p. 427-431.
Gujarati, Damodar (2004) Basic Econometrics, Fourth Edition, New York, The McGraw-Hill Companies.
Kugler, Peter and Lenz, Carlos (1993) Multivariate Analysis and the long run validity of PPP, The review of Economics and Statistics, vol. 75, No. 1(feb., 1993), pp. 180-84. Pblished by: The MIT Press
Officer, Lawrence H. (1978) The relationship between absolute and relative Purchasing Power Parity, The review of economics and statistics, vol. 60, No 4 (nov., 1978), pp. 562-568 Published by: The MIT Press.
Ramirez, Miguel D., Khan, Shahryar (1999) A cointegration Analysis of Purchasing Power Parity:1973-96, International Advances in Economic Research, vol. 5, No. 3 (1999 August), pp. 369-85.
Rogoff, Kenneth (1996) The Purchasing Power Parity Puzzle, Journal of Economic Literature, vol. 34, No. 2 (jun., 1996), pp. 647-668. Published by: American Economic Association
Sanchez-Fung, Jose R. (1999) Efficiency of the black market for foreign exchange and PPP: the case of the Dominican Republic, Applied Economic Letters, 6, 173-176
