Uncertainty in currency mispricing

ABSTRACT

Declaring a currency to be mispriced is fraught with uncertainties. In this article, these uncertainties are explicitly recognized in a model of pricing a homogeneous commodity around the world. This allows for a common driver of prices, due to a base-currency effect, and country-specific factors that lead to departures from absolute PPP on account of income differences, local taxes and charges, etc. This approach leads to estimates of currency mispricing whose significance can be tested in the usual way. Using Big Mac prices, we show that the approach has advantages over the popular Big Mac Index to currency valuation.

KEYWORDS:

• Currency mispricing
• PPP
• stochastic index numbers
• equilibrium exchange rates

JEL CLASSIFICATION:

• F31
• C43

Acknowledgements

We thank Haiyan Liu for excellent research assistance. For helpful comments, we would like to thank an anonymous referee. This research was financed in part by the ARC and BHP. All errors are our own.

Disclosure statement

No potential conflict of interest was reported by the authors.

Supplementary material

The supplementary material for this article can be accessed here.

Notes

¹ In addition to PPP, other approaches to equilibrium exchange rates (EERs) include the Fundamental EER (FEER) of Wren-Lewis (1992) and Williamson (1994), the Behavioural EER (BEER) by Edwards (1989), the Natural Real Exchange Rate (NATREX) by Stein (1995a), Stein (1995b)), the new open economy macroeconomic (NOEM) approach by Obstfeld and Rogoff (1995), the Permanent EER (PEER) by Clark and MacDonald (2004), etc. The International Monetary Fund employs related concepts (see, e.g. Lee et al. 2008). These models have their own advantages and disadvantages and differ in the formulation of the EER, time frame and the way exchange rate dynamics are modelled. For recent reviews, see Rogoff (2009) and Manzur (2017).

² Empirical evidence on the validity of PPP has been controversial (see, e.g. Taylor and Taylor 2004; Manzur 2008). Research on PPP has been voluminous, with recent studies including Arize, Malindretos, and Ghosh (2015), Bahmani-Oskooee and Ranjbar (2016), Chortareas and Kapetanios (2009), Dong and Nam (2013), Hall et al. (2013), Jiang, Bahmani-Oskooee, and Chang (2015), Sarno and Valente (2006), Taylor (2013) and Zhou and Kutan (2011).

³ The data derived from surveys conducted by the International Comparison Program (ICP) are widely used in PPP-based studies. For example, Frankel (2006), Cheung, Chinn, and Fujii (2007; 2010) and Coudert and Couharde (2007), among others, use these data to measure the undervaluation of the Chinese Renminbi. For details of the most recent rendition of the ICP data, see World Bank (2015). Cheung and Fujii (2014) find that ICP data revisions can lead to substantial changes in the estimates of exchange rate misalignment.

⁴ For example, as shown below, on the basis of the BMI, the Australian dollar was undervalued for at least 15 consecutive years up to 2010.

⁵ Since 2012, The Economist has published an ‘adjusted’ BMI to take into consideration income differences between countries. This is an attempt to deal with the issue of systematic departures from parity. As far as we are aware, no studies have evaluated the performance of the adjusted index, possibly because of its short life.

⁶ For details of the stochastic approach, see, for example, Clements, Izan, and Selvanathan (2006), Diewert (2005) and Selvanathan and Rao (1994).

⁷ Earlier research has also considered that PPP is a time-dependent equilibrium. See, e.g. Manzur and Ariff (1995) who carry out PPP tests based on Divisia indices calculated from deviations of the exchange rate and prices from their respective time effects, and Westerlund and Blomquist (2013) who incorporate a time-specific common factor in panel PPP tests.

⁸ Our EBMI is different from the ‘adjusted’ index published by The Economist since 2012, as mentioned earlier. The ‘adjusted’ index takes account of criticisms that Big Macs are cheaper in poorer countries where the labour costs are lower and vice versa. The underlying model is $P_i/S_i=\delta +\lambda \mathrm{G}\mathrm{D}{\mathrm{P}}_i+e_i$, where $P_i,$ $S_i$ and $\mathrm{G}\mathrm{D}{\mathrm{P}}_i$ are the Big Mac price, the exchange rate and GDP per capita in country i. The Economist calculates the adjusted Big Mac index as $\left({\hat{P}}^{\ast }/{\hat{P}}_i\right)\left(P_i/P^{\ast }\right)-1$, where ${\hat{P}}_{ }^{\ast }=\hat{\delta }+\hat{\lambda }\mathrm{G}\mathrm{D}{\mathrm{P}}^{\ast }$ and ${\hat{P}}_i^{ }=S_i\left(\hat{\delta }+\hat{\lambda }\mathrm{G}\mathrm{D}{\mathrm{P}}_i\right)$ are the fitted prices in the US and country i, with $\hat{\delta }$ and $\hat{\lambda }$ being the estimated intercept and slope.

⁹ The data are from The Economist (2015).

¹⁰ Total trade is the sum of current-price exports and imports of goods in US dollars, from the IMF (2015). For details of the data, see Appendix A2 of the online supplementary material.

¹¹ Interestingly, these three are commodity exporters. There is a similar pattern for Brazil, also a commodity exporter.

¹² We have carried out some sensitivity analysis by using two other sets of weights, those based on GDP with (i) market exchange rates used to convert to US dollars, and (ii) PPP exchange rates from the World Economic Outlook published by the International Monetary Fund. Although there are changes, in the main, the results are not overly sensitive to the choice of weights. When trade weights are used (the case reported earlier), the overvaluation of the dollar lies between that from the other two other cases. For details, see Appendix A2 of the online supplementary material.

¹³ The rank correlation is −0.25.

¹⁴ The difference between the two indices is approximately the sum of the estimated year and country effects, ${\hat{a}}_t+{\hat{b}}_i.$ Hence, in Figure 6 the two almost coincide in 2010, when ${\hat{a}}_{2010}$ almost offsets ${\hat{b}}_{AU}.$ For comparisons of the two indices for each of the 24 currencies, see Appendix A3 of the online supplementary material.

¹⁵ For analyses along similar lines, see Cumby (1996) and Clements, Lan, and Seah (2012).

¹⁶ Cumby (1996) and Clements, Lan, and Seah (2012) also make a similar conclusion along this line. Though not mentioned in these papers, simple algebra shows that if sampling implications are ignored, the regression slope coefficient over the h-year horizon (h > 1) is approximately h times that of the 1-year horizon regression.

¹⁷ We also experimented with separate intercepts for each year. Qualitatively, the results for the slope are almost the same.

¹⁸ Note that if the disturbances in model (4), ${\epsilon }_{it},$ are serially uncorrelated, then the h-year differences in Equation (8), ${\epsilon }_{i,t+h}-{\epsilon }_{it},$will not be. While this is ignored, any serial correlation declines as the horizon increases, that is, as PPP becomes more likely to hold.

Additional information

Funding

This work was supported by the Australian Research Council;BHP Billiton.