PURCHASING POWER PARITY
PURCHASING POWER PARITY
Introduction
This assignment will help you to become familiar with important issues in applied time series modelling, such as testing for stationarity, cointegration, error correction models and so on. Please remember to attach a header sheet.
You must answer all questions. You should prepare a word-processed report as your answer. Give details of results obtained and any inferences which have been drawn from them. You must also include short excerpts of output to justify your answers.
The data set for this project is provided on Moodle. What follows is a description of the problem and
the tasks required to perform.
The data
The data set contains information about 9 variables: 5 columns of time series on Consumer Price Indices for, respectively, Belgium, Canada, France, Japan and United States; followed by 4 columns of data on the nominal exchange rates of the first 4 of these countries in terms of US dollars. The frequency of the data is monthly, ending December 2009.
The basic task for this project is to assess the evidence for and against the presence of unit roots in the nominal exchange rate and relative price data. Also, to assess the evidence for and against the presence of cointegration in the exchange rate data and the support, or otherwise, that this lends to the PPP hypothesis.
The main reference for this assignment is Patterson (2000, An Introduction to Applied Econometrics: A Time Series Approach, Palgrave, Chapter 13).
Part 1
The first part is intended to give you the opportunity to apply the various tests for unit roots to some exchange rate and relative price level data to access the order of integration of these series. The tasks required are:
1. Briefly outline some of the main economic features of the theory of Purchasing Power Parity (PPP) and provide a short account of the doctrines of absolute PPP (APPP) and relative PPP (RPPP). Useful reading for this part is Rogoff, K. (1996), The Purchasing Power Parity Puzzle, Journal of Economic Literature, XXXIV, 647-668.
2. Graph the (log) relative price indices and the (log) nominal exchange rates. What features of the data are likely to be important in the analysis?
3. Calculate the (augmented) Dickey-Fuller tests for a unit root for the log relative price indices and for the log nominal exchange rates. In each case consider the need to allow for the presence of a constant and time trend for the Dickey-Fuller tests. Do the residuals from the test regressions appear to be white noise (i.e. serially uncorrelated)?
4. Use KPSS tests to test the null hypothesis that the various exchange rates and relative price indices are stationary against the alternative that they have unit roots. Comment on the extent to which the two approaches to unit root inference lead to different conclusions.
5. What do you conclude about the likelihood of the exchange rates and relative prices being stationary in your data?
Part 2
The second part of this empirical work is intended to build on the work of the first part and test for PPP. The tasks required are:
6. Given the results of the first part, calculate the real exchange rates and test for a unit root using the (augmented) Dickey-Fuller test approach. (There are four exercises to be conducted here, considering USA to be the “domestic” country.) Discuss the implications of your results for RPPP.
7. Test RPPP using a weaker version of the theory, which imposes a cointegrating regression of (1,-β). How do your results compare with your earlier results?
8. Now extend your analysis for each pair of currencies to the three variables: nominal exchange rate and each of the two price indices (in other words, remove the restriction that the coefficients on the two (log) price variables are equal and opposite in sign). Employ the same residual-based (Dickey-Fuller style) techniques. How do your results compare with your earlier results?
9. Provide a summary of your evidence for and against PPP. Suggest any limitations of your work and provide suggestions for future research.
