Researh Project: PPP - Testing and Forecating (Due: MONDAY JUNE 26)
You will test the PPP Theory for one currency. You will forecast that exchange rate using PPP. (You are assinged a currency according to your student number. Check your assigned currency . If you do not do the assignment using your assigned currency, you'll receive zero credit.)

1. 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).

You'll use the linearized Relative PPP model:  ef,t = (IDC,t - IFC,t).

1.A PPP Model: Testing
You'll test Relative PPP using a regression based on the Relative PPP model:   ef,t = α + β (IDC,t - IFC,t) + εt

Under Relative PPP, the hypothesis to test is:   H0: α=0 and β=1.

1.B PPP-Based Model: Forecasting
You'll forecast St+1. That is, Et[St+1] = Stx(1+Et[ef,t+1])

To get Et[ef,t+1], you'll use the linearized Relative PPP based model:   Et[ef,t+1] = α + β (Et[IDC,t+1] - Et[IFC,t+1]).

To get forecasts for inflation rates -i.e., Et[IDC,t+1] - Et[IFC,t+1]-, assume the Random Walk model for inflation rates.


2. Data
You have monthly Consumer Price Indexes (CPI) and exchange rates (St) from January 1973 till now for 10 countries/exchange rates (For some countries, the starting date is later.) The countries are UK, Switzerland, Denmark, Norway, Canada, USA, Mexico, India, Japan, Korea, and Brazil. Download PPP data set (Excel format)

2.A Preliminary Work: Transform the Data
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 ef,t, IFC,t, and IDC,t.


3. Things to Do
  • Testing PPP
    (A) Visual Test
         A.1 Plot ef,t against (IDC,t - IFC,t). Check if the plot forms a 45 degree line -i.e., the PPP line.
        A.2 Determine PPP exchange rates. Graph PPP exchange rates along St.
        A.3 Determine the Real FX rate. Graph Rt along St. (Force Rt to start with St).
    (B) Formal Test
         B.1 Using the whole sample, run a linear regression. Dependent variable: ef,t. Independent variable: (IDC,t - IFC,t). Null hypothesis to test: α=0 and β=1.
        B.2 Compare PPP's MSE with a RW's MSE (MSE=Mean Square Error). Also, report the MSE for the PPP-based regression model.


  • Forecasting PPP
    Steps:
      1) Using the estimation period (a reduced sample) from start of your sample to December 2019, run a regression. Get estimated coefficients.
      2) Using the estimated coefficients and the lagged inflation rate differentials at time t+i, forecast St+i, for i=Januray 2020, End of sample.
      3) Calculate the out-of-sample MSE, and compare it with the RW's MSE.
      Estimation Period: From the start of your sample to December 2019. (The period from January 2020 till the End of your sample is your validation sample.)


    4. Writing up your Research Project
  • Show the plot of ef,t against (IDC,t - IFC,t).
  • Show the graph with PPP exchange rates, along with St. Based on your (visual) findings, clearly state if PPP captures the short-run and/or long-run behavior of St.
  • Show the graph with Rt, the Real FX rate, along with St. Based on your (visual) findings, clearly state if PPP deviations are persistent. Report the volatility of changes in Rt & St, along with the maximun & minimum PPP deviations.
  • Report the regression results for the whole sample. Report the individual t-tests and the joint F-test. Clearly state if you reject or cannot reject PPP.
  • Report the MSE for PPP and the Random Walk models. Clearly state which one is lower.
  • Report the regression results for the shorter sample, ending in Dec 2019. Using a graph, show the forecasted St, along with the actual St, for the out-of-sample period (Jan. 2020-on).
  • Report the out-of-sample MSE for the PPP-based regression model and the RW model. Which one is lower?
  • Write a brief paragraph with your views about the PPP Model. (THIS PARAGRAPH IS NOT GRADED, write your opinion based on what you have done and learned.)
  • DO NOT print the data! Your write-up should not include the data I provided.
  • I have a strong preferences for students turning in the project in class. If you are late or you cannot make it to class, you can e-mail me the project (pdf or Word files). Do not e-mail me excel files (I'm not going to open them, nor give you credit for them).


    Tips: Running a Regression
  • You need to do a regression to estimate the parameters α and β -see Examples in Lecture Notes for Chapter 8 and 9.
  • Do not forget that the regression uses percentage changes. That is, before doing the regression, you need to calculate ef, and IDC, IFC
  • Excel has a regression wizard, Data Analysis, which is installed as part of the Analytical ToolPak, which students have found very helpful and easy to use. But, any other regression package -R, SAS, SPSS, Minitab, Matlab, etc.- will estimate the coefficients and also calculate R2, SSR, F-stat and t-statistics.
  • In Excel, if you don't see Data Analysis on the DATA Tab, you need to install the Analytical ToolPak: click FILE, then Options, click Add-Ins and then, click Analysis ToolPak. Press Go; a menu will appear, check Analysis ToolPak and press OK. In the DATA Tab, you should see Data Analysis. Input ef as your Y variable. Input (IDC-IFC) as your X variable.
  • To calculate the Mean Square Error (MSE), you need to divide the sum of square errors by the number of errors you are using in the sum. The lower the Mean Square Error (MSE), the better the model.


    * Excel Worksheet Example: SEK/USD.