Individual Project: Testing the purchasing power parity (PPP) theory

Background information

An example

Billy Bull Fund specializes in investing in emerging markets. One country of interest is Turkey. Because of the high inflation in Turkey during 1960-2004, the Turkish Lira : U.S. Dollar exchange rate increases from an average of 9 lira per U.S. dollar in the late 1960s to approximately 1.65 million lira per U.S. dollar in late 2001. However, since the introduction of new lira in 2005, dropping 6 zeros from the old lira, the Turkish currency has stabilized significantly in recent years. Due to the extremely volatile Turkish exchange rates in the last century, Billy is concerned and would like to explore whether inflation is the driver of the volatile exchange rates. One theory linking inflation and exchange rate is the PPP. Billy wants to know whether PPP holds or to what extent PPP holds.

PPP Model The rate of change in (index) prices should be similar when measured in a common currency. (As long as trade frictions are unchanged).

Here is the linear relative PPP model: e_f,t = (I_DC,t - I_FC,t). We can test the relative PPP using a regression based on the relative PPP model:

e_f,t = + (I_DC,t - I_FC,t) + _t Under the relative PPP, the hypothesis to test is: H₀: =0 and =1.

1). You can specify the time & Frequency to monthly and choose your time periods for at least the last 5 to 10 years (2008 to 2018).

2). You can then click on the fourth icon above to export the data into an excel file.

3). Select the country of interest, you can then select the data for that country and post into a new spreadsheet using paste special and choose transpose. This way you can transform the data from rows into columns.

CPI for other countries can be obtained from World Bank, IMF, or other sources.

Data preparation CPI and Exchange Rates are in levels. Thus, you need to put the data into percentage changes to test relative PPP. That is, you need to create e_f,t, I_FC,t, and I_DC,t.

Here is an example of transforming data from levels to percentage changes.

Date	US CPI	Inflation US
Jan-06	101.5404
Feb-06	101.7453	0.20%	=(101.7453-101.5404)/101.5404
Mar-06	102.3085	0.55%	=(102.3085-101.7453)/101.7453
Apr-06	103.179	0.85%	=(103.179-102.3085)/102.3085

Things to Do

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1. Plot e_f,t against (I_DC,t - I_FC,t). Check if the plot forms a 45 degree line -i.e., the PPP line.

2. Determine PPP exchange rates. Graph PPP exchange rates along S_t. Based on your (visual) findings, clearly state if PPP captures the short-run and/or long-run behavior of S_t.

3. Using the whole sample, run a linear regression. Dependent variable: e_f,t. Independent variable: (I_DC,t - I_FC,t). Null hypothesis to test: =0 and =1. (Note: you can use any software of your choice to run the regression. If you want to run regressions in Excel, you can simply google and find out how to run regressions in Excel.) Clearly state if you reject or cannot reject PPP.

4. Write a brief paragraph with your views about the PPP Model. Tips: Running a Regression

Do not forget that the regression uses percentage changes. That is, before doing the regression, you need to calculate e_f, and I_DC, I_FC

Excel has a regression wizard (Analytical ToolPak), which students have found very helpful and easy to use. But, any regression package -Excel, SAS, SPSS, etc.- will estimate the coefficients and also calculate R², SSR, F-stat and t-statistics.

In Excel, on the Tools menu, click Data Analysis. (If Data Analysis is not available, load the Analysis ToolPak.) On the Data Analysis dialog box, click regression, then click OK. Input e_f as your Y variable. Input (I_DC-I_FC) as your X variable.