Is the Purchasing Power Parity Supported by the Da

Chinese Business Review, ISSN 1537-1506

February 2011, Vol. 10, No. 2, 84-89

Is the Purchasing Power Parity Supported by the Data?

GUAN Fang

Massey University, Palmerston North Campus, Manawatu, New Zealand

This report mainly examines whether the Purchasing Power Parity (PPP) theory is supported by the data. The data

used in the report contains the exchange rate of US dollar against New Zealand dollar, Consumer Price Index (CPI)

of the US, and Consumer Price Index of New Zealand. The time period of the data is from September 30th, 1914 to

March 31st, 2010, the data were collected quarterly. Mathematical regressions and graphs are contained in the

research. In this research, the simplified form of the PPP theory is analyzed, and then there is a comparison between

the spotted exchange rates and the expected exchange rates. Finally, the observation on long-run PPP is explained.

The key conclusion of this research is that, the PPP theory is not supported by the data, however, the long-run PPP

does hold.

Keywords: the purchasing power parity theory, linear regression, inconsistent lags, real exchange rate

Introduction

The main structure of this paper is as follows: The first part will discuss the methodology used, several

equations that explain the PPP theory will be taken into discussion. In the second part, the data retrieved will be

l Rights ed, basically, the quarterly selected data contains the exchange rate of US dollar against New Zealand

dollar, Consumer Price Index (CPI) of the US, and Consumer Price Index (CPI) of New Zealand during a time

period between September 30th 1914 to March 31st 2010. The third part will focus on the analysis of the data

and the regression results, and then these results are going to be used into testing the relative PPP theory and

the real exchange rates. All the regressions in this report are using linear regression model. Finally, the

conclusion is going to be drawn based on strong evidence that the PPP theory is not supported by the data.

Methodology

The method used in the report was based on the examining through running regression on the data. First,

the formula of the relative Purchasing Power Parity must be introduced:

S1 = S0 (1 + iTerms)/(1 + iBase)

The simplified form is:

S1/S0 = iTerms-iBase

where S1 stands for spot rate at period 1, S0 stands for current spot rate, iTerms stands for the inflation of the

terms currency, and iBase stands for the inflation of the base currency (Eun & Resnick, 2009).

From the data used in the analysis, the term currency is the NZ dollar, and the case currency is the US

dollar. However, it is notable that the simplified form is easier to use but is less accurate.

In order to find out the inflation data, CPI statistics will be used into calculation, the formula is:

πt

= (CPIt+1 – CPIt)/CPIt

GUAN Fang, Business and Finance Department, Massey University, Palmerston North Campus.

84

IS THE PURCHASING POWER PARITY SUPPORTED BY THE DATA?

85where π stands for inflation (Suranovic, 2010).

After the inflation data have been worked out, the inflation differential which is the term iTerms–iBase can be

found out. Then the relationship between the change of the exchange rates and the inflation differential (=

πt+1/πt -1) can lead to a graph and a regression. Examine the regression, whether the PPP theory stands or not

can be revealed.

Data

The initial data (see Appendix A) includes only the exchange rates, the CPI in the US, and the CPI in New

Zealand. Each number was selected quarterly during a time horizon over September 30th 1914 to March 31st

2010. The reason for choosing New Zealand is because New Zealand is among the countries that have had a

relatively wide fluctuation of exchange rates during this time period, and the fluctuation is helpful in running

the regression and testing the PPP theory.

In order to satisfy the mathematical method discussed above, other important data inputs are required but

are not directly shown in the initial data. Such data inputs (see Appendix B) are inflation in the US, inflation in

New Zealand, the inflation differential, and the ratio of S1/S0.

Analysis and Results

Graphs and Regression

All the graphs are based on the data inputs, and all the tables contain regression results.

l Rights Reserved.

Figure 1. Scattered graph of inflation differential and the change in foreign exchange rate.

In Figure 1, the x axis stands for the inflation differential, and the y axis stands for the change in foreign

exchange rate. The trend line can also be seen in the graph, it is a slightly downward sloping line. If the PPP

holds, the slope should be equal to 1 which means:

S1/S0-1 = iTerms- iBase

The regression data is shown in Table 1.

From Table 1, important statistics have been highlighted.

Now set up the null hypothesis, H0: the coefficient of “inflation differential” = 1. t-stat =

|(-0.11986–1)|/0.1678 = 6.675 > 1.96 (t-test, when α = 0.05), there is enough evidence to reject H0. When α =

0.05, it means that this test is on a 95% confidence level.

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IS THE PURCHASING POWER PARITY SUPPORTED BY THE DATA?

Table 1

Regression Results for the Simplified Form

Coefficients Standard errort stat p-value

Inflation differential (NZ-US)

-0.11986

Multiple R

R Square

Standard error

0.167757

-0.7144

Lower 95% Upper 95%

Intercept 0.00536 0.003218 1.6656 0.0966 -0.00097 0.01168

0.4753 -0.44971 0.20999

Regression statistics

0.036627

0.001342

Adjusted R square -0.00129

0.062206

Observations 382

Note. R squares, coefficients, and t-stats are in bold.

Apparently, it rejects the suggestion that the PPP holds on a 95% confidence level. This condition can be

caused by a lack of consideration of lags, or inconsistent lags between inflation and changes in exchange rates

(Eun & Resnick, 2009).

After taking lags and different durations into consideration, results of regression can be shown in Table 2.

Table 2

Regression Results Combined With Lags of Different Durations

Coefficients Standard error t stat

X Variable 1

-0.20504730

-0.04372936

-0.26646332

0.186423

0.185399

0.184775

-1.09990401

-0.23586593

-1.44209545

1.0062962

p-value Lower 95% Upper 95%

Intercept 0.006031931 0.003424 1.761632281 0.078978

X Variable 2

X Variable 3

X Variable 4

-0.000701674 0.01276554

l Rights Reserved.0.272107 -0.571658571 0.16156397

0.81367 -0.408327518 0.32086879

0.150142 -0.629834081 0.09690744

0.314947 -0.169460171 0.52462852

0.177584177

0.176473

Regression statistics

Multiple R 0.108317195

R square

0.011732615

Adjusted R square 0.000782284

Standard error 0.063467461

Observations 366

Notes. R squares, coefficients, and t-stats are in bold; lag1 = 1 year, lag2 = 2 years, lag3 = 3 years, and lag4 = 4 years.

There can be more estimations and regressions from putting on more lags. However, no matter how many

lags are put into the regression, the results are not supportive to the PPP. This phenomenon can be explained by

the inconsistency within the lags themselves.

The Relative PPP and the Real Exchange Rate

As it has been stated before, the simplified form of the relative PPP is simpler but less precise. However,

some other previous researches suggest the PPP theory actually stands in the long-run (Taylor, 1988). Now take

a look at the full version of the relative PPP equation and input the data.

Here are the graphs of spotted exchange rates and expected real exchange rates estimated by the PPP:

IS THE PURCHASING POWER PARITY SUPPORTED BY THE DATA?

87

Figure 2. The spotted foreign exchange rates and the PPP implied foreign exchange rates.

As it can seen from Figure 2, their shapes are very similar to each other. Then after running regression on

the two curves, the results are shown in Table 3.

Table 3

l Rights sion Results for the Two Curves

Coefficients Standard errort stat p-value

Intercept 0.001862 0.007034058 0.264712 0.791374

USD/NZD

0.99912

0.006452431

154.8439

Lower 95% Upper 95%

-0.0119684 0.0156924

0 0.98643267 1.0118063

Regression statistics

Multiple R 0.992148

R square

0.984358

Adjusted R square 0.984317

Standard error 0.068815

Observations 383

Notes. R squares, coefficients, and t-stats are in bold.

Set the null hypothesis, H0: The slope = 1, t = (b–B)/se = (0.99912–1)/0.

=

-0.13638. α =

0.05,

t-stat

=

|-0.13638| < 1.96, therefore, there is not enough evidence to reject H0. Since the coefficient can be

“accepted” as 1, the relative PPP theory equation holds on a 95% confidence level. Although this regression has a

convincingly high R square, the regression proves nothing but that the expected spot exchange rate is on the same

level with the spotted exchange rate. However, staying on the same “level” does not explain the PPP. Foreign

exchange rates change on a very small amount, such small changes are not obvious enough, so even the spotted

rates and the expected rates are on the same level, the regression does reveal the accuracy of the PPP.

Then a more appropriate regression on the PPP implied can be tested.

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IS THE PURCHASING POWER PARITY SUPPORTED BY THE DATA?

Table 4

Regression Results for the Real Exchange Rates

Coefficients Standard error t stat p-value

X Variable 1

Regression statistics

R square

Adjusted R square

Standard error

0.004359

0.771134

0.770533

0.263225

0.000122

35.82917

Lower 95% Upper 95%

0.161313

0.004598

Intercept 0.108318 0.026953 4.018761 7.05E-05 0.055323

4.7E-124 0.00412

Multiple R 0.878142

Observations 383

Notes. R squares, coefficients, and t-stats are in bold.

This time, the regression is run on the expected rates against the time horizon. The linear trend line is

called PPP implied. From the regression, the R square is relatively large enough to prove that this regression is

convincing. Other than the reliability of the regression, the slope is also a concern. From the Table, the

coefficient is 0.004359 which is so small that it is very near to zero. It is indeed a slim amount, but it cannot be

regarded as “zero”, the test is below:

Set up a null hypothesis, H0: the slope

=

0, t = (b–B)/se

= (0.004359–0)/0.000122

=

35.82917, α =

0.05,

t-stat

= |

35.82917| > 1.96, therefore, there is enough evidence to reject H0.

Even though the slope is not perfectly equal to zero, it still offers a statistical support for the long-run PPP

theory. If the graph (see Figure 2) can be extended on an extremely wide x axis, the trend line is likely to be

l Rights to horizontal which means that the slope is almost zero.

Conclusion

According to the regression and data analysis, the Purchasing Power Parity is not supported by the data.

The reason why using the simplified form of the relative PPP equation fails to lead to a supportive result may

be caused by the lags and even the inconsistency in lags. Lags are basically the “time gap” between the

expected outcome and the real outcome over the time horizon. Sometimes lags are consistent, but under most

cases the durations of lags are different from each other, this could be an explanation of why even after running

multiple types of lags the results are still unconvincing. Although there is little statistical evidence supporting

the Purchasing Power Parity, but in the long-run, PPP is supported by the data for it fits the model very well

due to a high R square. In the long-run, real foreign exchange rates are approaching to “1”.

References

Edwards, S. (2006). The relationship between exchange rates and inflation targeting revisited. Cambridge: National Bureau of

Economic Research.

Eun, C. S., & Resnick, B. G. (2009). International financial management (5th ed.). Singapore: McGraw Hill.

Suranovic, S. (2010). The international economics. Washington: The George Washington University.

Taylor, M. (1988). An empirical examination of long-run purchasing power parity using cointegration techniques. Applied

Economics, 20(10), 1369-1381.

IS THE PURCHASING POWER PARITY SUPPORTED BY THE DATA?

Appendix A The Initial Data

89Date US Style USD/NZD CPI_NZ CPI_US

09/30/1914 0.4012 17.7453 10.2

12/31/1914 0.4122 19.0501 10.1

03/31/1915 0.4168 19.3927 9.9

12/31/2009 1.3772 1093 215.949

03/31/2010 1.4069 1097 217.631

Notes. all the data above were retrieved from the New Zealand Reserve Bank and the Federal Reserve Bank of New York. Data

have been omitted.

Appendix B The Inferred Results

Inflation_NZ (%) Inflation_US (%) Inf dif St/So

7.352932889 -0.980392157 8.333325046 1.027417747

1.798415756 -1.98019802 3.778613776 1.011159631

-0.252672397 2.02020202 -2.272874418 1.007197697

… -0.009260588 -0.173387814 0.996815287

-0.182648402

0.365965233 0.778887608 -0.412922374 1.021565495

Notes. All the data above are calculation results from Appendix A. Data have been omitted.

l Rights Reserved.