Unit Outline econ2210

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Figure 2

Percentage Deviations from Big Mac Parity

Figure 3

Percentage Deviations from Big Mac Parity

(Means, 1994 – 2008)

Figure 4

Predicting Future Currency Movements

2. Under purchasing power parity, the spot exchange rate, S, is equal to the ratio of prices at home to those abroad, P/P*. Accordingly, the difference between S and P/P* can be used to determine the extent to which the currency is over or under valued.

Each year The Economist magazine does this by using the price of a Big Mac hamburger in one country relative to that in the US as a measure of the relative price The deviation from parity is known as the “Big Mac Index” (BMI). For a recent example, see The Economist (2009). What is the justification for using hamburger prices to identify currency mispricing?

Figure 5

Evidence on BMI Predictions

(24 countries, 1994 – 2008)

A. 1-year horizon

B. 2-year horizon

C. 10-year horizon

D. 14-year horizon

Note: To facilitate the presentation, observations with changes greater than 40% in absolute value have been omitted from this figure. The straight lines are the least squares regression lines and the corresponding equations are given in the boxes. The standard errors are given in the parentheses.3. Figure 2 plots the BMI against time for Australia. This reveals that the average deviation from parity is about -30 percent, so the $A is undervalued, relative to the $US, by this amount. This -30 percent value is plotted in Figure 3 for Australia, together with similar averages for a number of other countries. What do you conclude from these two graphs? Is the BMI useless?

4. Let be the value of the BMI in year t, so that if, for example, then the currency is overvalued by 20 percent.1 If there are T years in which the BMI is available, then we have , which can be summarised by their average

From Figure 2 above, for the Australian dollar Interpreting as the “permanent” deviation from parity, the “true” extent of mispricing in any year is then the deviation of the BMI from , that is, If, for example, the BMI declares that the $A is undervalued by 10 percent in some year, while it is permanently undervalued by 30 percent, then its true mispricing is In this case, the currency is in fact overvalued by 20 percent.

If the approach has content, the mispricing should be eliminated in the future by the currency subsequently depreciating. That is, overvalued currencies subsequently depreciate and undervalued ones appreciate, as indicated by Figure 4. This graph refers to the subsequent change in the exchange from now, year t, to h years in the future, year t+h; the period h can be called the “forecast horizon”. Why is there a minus sign on the right-hand side of the equation at the top of the figure? How, exactly, does Figure 4 work?

5. Figure 5 presents some evidence on the above approach for 24 currencies over the period 1994- 2008, so that T=15. Panel A of this figure refers to a forecast horizon of h=1 year, so the total number of observations is The other panels contain the results for horizons of 2, 10 and 14 years.

What do you conclude from this figure? Is there any money to be made from this approach to forecasting currency values? (Disclaimer: The University of Western Australia, and its staff, will not be liable for any losses incurred!)

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1 Technical note for those who read Clements et al. (forthcoming):That paper uses a logarithmic formulation, so that is defined as the log of the ratio of the relative price to the spot exchange rate When multiplied by 100, this is approximately equal to the percentage deviation, that is

Thus, the wording of this question uses this approximation. This footnote can be safely ignored by those who choose not to read Clements et al. (forthcoming).

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