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Purchasing Power Parity Between the UK and Germany: The Euro Era

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Abstract

We use the Johansen cointegration approach to assess the empirical validity of the purchasing power parity (PPP) between the UK and Germany since the introduction of the euro. We conduct the empirical analysis in the context of the global financial crisis that began in 2007 and find that it directly affects the cointegration space. We fail to validate the Johansen and Juselius (1992) original hypothesis that nonstationarity of PPP associates with the nonstationarity of interest rate differentials to produce a stationary relation. On the other hand, we do not reject PPP. We find that PPP cointegrates with inflation differentials. We also find, contrary to conventional wisdom, that (i) equilibrium adjustment occurs between the German and UK inflation rates, while weak exogeneity exists for the German and UK interest rates and the PPP condition, and (ii) three common trends associated with the German interest rate the UK interest rate, and the PPP condition “push” the system with the German interest rate and the PPP condition playing dominant roles in affecting inflation in both Germany and the UK. These results cast serious doubt on the presumed independence of the UK monetary policy.

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Notes

  1. Germany and the UK form a most important trade relationship. In 2011, only the US surpassed Germany in UK exports and Germany did hold the position as the top trading partner for imports, accounting for 11.06 % and 12.87 % of the UK’s primary exports and imports, respectively. In comparison, the US accounted for 14.71 % and 9.74 %, respectively.

  2. Mazumder and Pahl (2013) construct counterfactual exercises designed to compute the unemployment and output in the UK, if they had joined the euro in 1999. Their overall results indicate that the UK made the correct decision not to join the euro back in 1999. The recent sovereign debt crisis that substantially affected some of the countries of the Euro area, most notably Greece, Ireland, Italy, Portugal and Spain, makes it even more unlikely that the UK will join the common European currency in the near future. Germany and the UK appear to have withstood the disruptive macroeconomic shocks of the crisis. Arghyroua and Kontonikas (2012) provide a detailed empirical investigation of the crisis.

  3. Few empirical studies (Alquist and Chinn 2002; Gadea et al. 2004; Lopez and Papell 2007; Hall et al. 2013) examine PPP within the Euro area. Alquist and Chinn (2002) find a nonstationary real exchange rate, suggesting that PPP does not hold in the Euro area. Gadea et al. (2004) find some support for PPP within the Euro area after incorporating two structural breaks. Also, scant evidence exists of PPP validity between the Euro area and other major economies. Lopez and Papell (2007) study the convergence to PPP in the Euro area from 1973 to 2001 and find that PPP holds better within the Euro area than between the Euro area and other European countries. Alquist and Chinn (2002), using data on the “synthetic” euro-dollar exchange rate for 1985 to 2001, rejects PPP, but documents a stable long-run relationship between the real euro-dollar rate, productivity differentials, and the real price of oil. Koedijk et al. (2004), in addition to examining the validity of PPP within the Euro area, also use “synthetic” euro data to study PPP validity between the Euro area and other major economies. They find that with the exception of Switzerland, PPP does not hold. Manzur and Chan (2010), using data through April 2007, construct a measure of “pooled” inflation among the 12 Euro countries and use this measure to test, in a simple regression framework, relative PPP for the euro against the currencies of Japan, the UK, and the US. Their results provide weak support for relative PPP in the case of dollar-euro and pound-euro exchange rates, and rejects relative PPP for the yen-euro. Hall et al. (2013) apply a time-varying-coefficient technique to investigate the homogeneity condition underlying the PPP for nine euro area countries (Austria, Belgium, France, Germany, Greece, Italy, Netherlands, Portugal, and Spain) as well as for the euro area as a whole, using data from January 1999 to March 2011. Using the US as the foreign country, Hall et al. (2013) find strong support for long-run homogeneity, thus providing strong support for PPP.

  4. International finance theory typically argues that financial flows and interest rate parity dominate exchange rate determination in the short run while goods and service flows and purchasing power parity dominate in the long run. This suggests that we will more likely uncover evidence supporting UIP rather than PPP. But, UIP suffers from the evidence on the success of carry trade, whereby investors sell currencies in markets with low interest rates to buy currencies in markets with high interest rates, which runs counter to UIP. See Hansen and Hodrick (1983).

  5. We use not seasonally adjusted harmonized indices of consumer prices (HCPI), 2005 = 100. We compute the rates of inflation as the logarithmic first difference of consumer prices. Data on exchange rate and price indices come from the statistical database of the European Central Bank (sdw.ecb.europa.eu), while data on bond yields come from the OECD Main Economic Indicators database (stats.oecd.org). We convert annual interest rates to monthly rates and divide by 100 to make the estimates comparable with logarithmic monthly inflation rates.

  6. A longer version posted at http://ideas.repec.org/p/uct/uconnp/2012-46.html provides extensive discussion of tests reported in Section 3 as well as additional tests..

  7. The multivariate versions of the Akaike information criterion (AIC), the Bayesian information criterion (BIC), and the Hannan-Quinn (H-Q) criterion suggest a lag length of 2, given a maximum lag order of 4. We cannot justify the VAR(2) specification, however, as diagnostic tests suggest residual serial correlation. Consequently, we specify a VAR(3) model, using a number of specification tests. This implies 2 lags of the first differences of the variables in the VEC model of the data. Following Johansen (1995), we specify the model to include a restricted constant, since the variables do not show growth. Thus, the constant term should appear in the cointegrating space, implying that some equilibrium means in the cointegration space can differ from zero. We do not include a linear deterministic trend, since a trend is inconsistent with PPP (Papell and Theodoridis 1998; Amara and Papell 2006). Excluding a linear deterministic trend also proves consistent with the unit-root analysis. We include three different types of dummy variables. First, following Johansen (1995), we introduce centered seasonal dummy variables to account for seasonality in the data. Second, we use a shift dummy variable to account for the developments of the global economic crisis. We assume that the break occurs in 2007:10 based on the visual inspection and institutional consideration about the beginning of the global financial crisis and sub-prime lending crisis in the housing markets. The dummy variable equals 0 before October 2007 and 1 from October 2007 onward. Finally, we include an intervention dummy variable in December 2008 to account for a residual exceeding in absolute value 3σ ε .

  8. A longer version of this paper reports the test statistics referred to in this and the next three paragraphs. See http://ideas.repec.org/p/uct/uconnp/2012-46.html.

  9. Graphs appear in longer version posted at http://ideas.repec.org/p/uct/uconnp/2012-46.html.

  10. The unknown sampling distribution of the eigenvalues, which precludes testing whether eigenvalues significantly differ from one, makes this a tentative conclusion.

  11. We note that rejecting the hypothesis that r = 1 runs counter to the frequent use of single equation models in the exchange rate determination literature. That is, a single equation model implies just one long-run cointegrating relationship between the relevant variables, whereas concluding that r = 2 means that existing data require a more complex model.

  12. If we impose r = 3 when the appropriate rank is r = 2, then the third root comes closer to unity, and we should reduce r from 3 to 2. When r = 2, we observe the lowest first root beyond the unit root is 0.562. See Juselius (2006).

  13. By fixing the estimates of the short-run parameters, we reduce the variance of the long-run parameters, which is the primary interest of cointegration analysis (Hansen and Johansen 1999). This motivates the R1(t)-form.

  14. We fix the base period, January 1999 to December 2002, at about 35 percent of the sample, following the suggestion of Brüggemann et al. (2003).

  15. Graphs of the discussions in this and the next paragraph appear in the longer version of the paper posted at http://ideas.repec.org/p/uct/uconnp/2012-46.html

  16. See http://ideas.repec.org/p/uct/uconnp/2012-46.html for graphs of these tests.

  17. During the transition period, which lasts from January 1999 to December 2001, transactions in the countries of the Euro area could use both the euro and national currencies. During this transition period, the euro only serves an accounting unit, and euro notes and coins only start circulating in January 2002, when countries withdraw their national currencies from circulation.

  18. See http://ideas.repec.org/p/uct/uconnp/2012-46.html for graphs of the tests in this paragraph.

  19. Whereas likelihood ratio testing for cointegrating rank leads to a nonstandard inference situation, conditional likelihood ratio testing, for a given cointegrating rank, produces standard asymptotically chi-squared test statistics.

  20. We can justify this result, however, by appealing to the “imperfect knowledge economics” approach developed by Frydman and Goldberg (2003, 2006). Under imperfect information expectations, exchange rates fluctuations do not represent movements toward a fundamental purchasing power equilibrium, but movements generated by traders’ behavior in the foreign exchange market (Juselius and MacDonald 2004).

  21. The hypotheses conform to β = (Hφ,ψ), where H is the design matrix, φ contains the restricted parameters, and ψ is a vector of freely estimated parameters. For details, see Juselius (2006).

  22. Since the rank equals two (r = 2), we can only test for cointegration, where theoretical relations restrict at least two of the parameters. The degrees of freedom of the χ 2(υ) distribution, where υ = k – (r – 1) and k is the number of restrictions (Juselius 2006), impose this requirement.

  23. This result questions the stationarity of the inflation rate differential (H 2). That is, if the inflation rate differential is really I(0), then it cannot cointegrate with ppp t , which is I(1).

  24. For completeness, we also test, following Pedersen (2002b), for cointegration between ppp t and the rate of inflation of Germany or the UK separately, which implies that the adjustment costs fall unilaterally on only one country. In each case, we reject the hypotheses that ppp t forms a stationary relation with either the German inflation (χ 2(2) =11.739 p ‐ value = 0.003) or the UK inflation (χ 2(2) = 5.264 p ‐ value = 0.072) rate alone at the 5-percent level.

  25. The unrestricted estimates of the α matrix, obtained without imposing the weak exogeneity restriction, do not significantly differ from zero.

  26. Ball (2012) observes that a central question for monetary policy is how to respond to shocks that affect exchange rates. Our findings indicate that monetary policies that stabilize output will not keep inflation under control.

  27. This argument is also made by Manzur and Chan (2010).

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The authors gratefully acknowledge the helpful comments of a referee and the editor.

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  1. University of Nevada, Las Vegas, Las Vegas, NV, 89154-6005, USA

    Giorgio Canarella & Stephen M. Miller

  2. Trident University International, Cypress, CA, 90630, USA

    Stephen K. Pollard

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  1. Giorgio Canarella
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Canarella, G., Miller, S.M. & Pollard, S.K. Purchasing Power Parity Between the UK and Germany: The Euro Era. Open Econ Rev 25, 677–699 (2014). https://doi.org/10.1007/s11079-014-9309-9

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