Abstract
We study the Purchasing Power Parity (PPP) hypothesis and the PPP puzzle for a sample of seventeen OECD economies when real exchange rates (RERs) are subject to multiple structural breaks. Applying recent panel econometric methods, we first show that RERs are found to be I(1) non-stationary processes when the analysis neglects structural breaks, while they are characterized as I(0) stationary stochastic processes when structural breaks are accommodated. This indicates that ignoring structural breaks can lead to model misspecification, which can bias (upward) shocks’ persistence measures. After controlling for structural breaks, our half-life point estimates appear below one year for both idiosyncratic and common measures of persistence of deviation from the changing mean.
- 1
See Perron (1989).
- 2
See e.g., Rossi (2005).
- 3
The specification of the null hypothesis of unit root implies that the theory is false, which is contrary to the notion of PPP.
- 4
Note that the sequential approach in Bai and Perron (1998) can be used here since under the null hypothesis we have that the units are I(0). Consequently, the consistency on the specification of the number and position of the structural breaks is warranted. Furthermore, the test remains consistent against the alternative hypothesis of I(1) as shown, for instance, in Lee, Huang and Shin (1997), Kurozumi (2002) and Carrion-i-Silvestre (2003).
- 5
We are thankful to Takashi Yamagata for making the data available to us. We include the observations for 1973 in our analysis, while Pesaran (2007) starts at 1974.
- 6
We thank Natalia Bailey for providing us the GAUSS code that has helped us to implement the proposal in Bailey, Kapetanios and Pesaran (2012).
- 7
Following Maddala and Wu (1999), we have computed the bootstrap empirical distribution of the statistics using 20,000 replications – we offer the percentiles of interest in Table 1. Further details are given in the Appendix.
- 8
The number of common factors (r) has been estimated using the panel BIC information criterion in Bai and Ng (2002) with up to six common factors.
- 9
The AR regression equation in which the statistic is based uses the t-sig criterion in Ng and Perron (1995) to select the order of the autoregressive correction with up to ten lags.
- 10
Our results are qualitatively different from Harris, Leybourne and McCabe (2005) who are unable to find favorable support for the PPP hypothesis when applying panel stationary test with cross-sectional dependence and structural breaks. One possible reason for the discrepancy of research conclusions is the constrained framework imposed in Papell (2002) and maintained in Harris, Leybourne and McCabe (2005). As mentioned, our results are based on an unconstrained set-up that does not restrict the RERs to return to the levels previous to the structural change.
- 11
See Taylor and Taylor (2004) for discussion related to the PPP puzzle.
- 12
As above, the selection of the order of the autoregressive model is done using the t-sig information criterion in Ng and Perron (1995) with up to ten lags.
- 13
Empirical estimates of the half-life of shocks to the RER may also be biased upward due to (i) temporal aggregation in the data and (ii) nonlinear adjustment of RERs. However, the possibility of nonlinear adjustment could arise due to the presence of structural breaks, which has been cogently addressed in our work. Whereas, the time aggregation problem emphasized by Taylor (2001) is difficult to deal with since one would require long-spans of high frequency data, which may not always be available in panels. Another source of aggregation bias, that might induces a positive bias in persistence estimates, may result from aggregating across different sectors of the economy (Imbs et al. 2005). Recently, Pesaran and Chudik (2012) addressed the problem of aggregation in the context of large linear dynamic panels that allow for a general pattern of cross-section dependence across the individual units. They derived an ‘optimal aggregate function’ that is shown to recover the distributional features of individual (micro) parameters from the aggregate model. Further, the empirical illustration in their paper suggests that in addition to the dynamic heterogeneity of individual units (as emphasized by Imbs et al. 2005), the unobserved common factor persistence is also needed to understand the slow response of aggregate variables to macro shock.
- 14
As the presence of structural breaks gives rise to nonlinear adjustment in real exchange rates, our results are also relevant to a strand of literature that uses nonlinear models to analyze mean-reversion of real exchange rates – see e.g., Sarno and Taylor (2002: pp. 68–73) for a list of related papers. These models support the view that real exchange rates are driven by an arbitrage process, such that the speed of reversion to PPP is an increasing function of the scale of the shock and hence of the divergence from equilibrium. Applying different classes of nonlinear models both Taylor, Peel and Sarno (2001) and Peltonen, Popescu and Sager (2011) observe a substantial reduction in half-life persistence, compared to what was found using linear PPP models.
- 1)
We thank an anonymous referee for constructive comments and the participants at the “Factors Structure for Panels and Multivariate Time Series Data” conference held at the Maastricht University in 2008 for helpful comments. Carrion-i-Silvestre acknowledges financial support for this research under the Spanish Ministerio de Ciencia y Tecnologa grant ECO2011-30260-C03-03. The views expressed here are those of the authors and do not necessarily reflect the official view of the Qatar Central Bank. The errors that remain are solely ours.
Appendix
The paper computes the bootstrap distribution of the panel stationarity test statistics in order to control for cross-section dependence. The approach that has been followed is the one described in Maddala and Wu (1999) considering that our null hypothesis is that the times series in the panel data are I(0). This approach has also been used in other existing papers in the panel data literature – see, for instance, Smith et al. (2004) and Westerlund (2006, 2008). To be specific, we have proceeded in the following steps:
Estimate (1) using the procedure described in Section 2, which allows us to get a consistent estimate of ɛi,t and

Specify an AR(pi) model to control the dynamics of
where the parameters are estimated using OLS method – the order of the AR(pi) is approximated using the t-sig criterion in Ng and Perron (1995) with the maximum order given by pmax=5 lags. As a result, we obtain
where
denotes the estimated autoregressive polinomial. Note that here we assume that we are under the null hypothesis of I(0), and that each time series has its own dynamics.Obtain
by randomly resampling the rows of the fitted (T×N) matrix of residuals
Note that resampling the rows of the matrix of estimated residuals preserve the cross-correlation structure of the error term that exist among the units of the panel – see Maddala and Wu (1999: pp. 646). Then, define the centered resampled residuals
where TBOOT denotes the sample size used in the resampling. Finally, construct the first set of bootstrap samples
recursively usinggiven the initial values
for t=0,…,1–pi, t=1,…,TBOOT – in the paper we define TBOOT = T+30. This step amounts to the usual sieve bootstrap for
i=1,…,N, t=31,…,TBOOT – note that the first 30 observations are discarded to attenuate the effect of the initial conditions.Generate the first bootstrap samples for
fromwhere
are the estimated parameters that have been obtained in the first step, and compute the statistics of interest using the panel data given by the (T×N) matrix
applying the procedures described in the previous sections.Replicate the steps 3 and 4 a large number of times (20,000 times in our case) to obtain the empirical distribution of the panel data statistics.
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Articles in the same Issue
- Masthead
- Masthead
- Advances
- How have global shocks impacted the real effective exchange rates of individual euro area countries since the euro’s creation?
- Employment by age, education, and economic growth: effects of fiscal policy composition in general equilibrium
- Overeducation and skill-biased technical change
- Strategic wage bargaining, labor market volatility, and persistence
- Households’ uncertainty about Medicare policy
- Contributions
- Deconstructing shocks and persistence in OECD real exchange rates1)
- A contribution to the empirics of welfare growth
- Development accounting with wedges: the experience of six European countries
- Implementation cycles, growth and the labor market
- International technology adoption, R&D, and productivity growth
- Bequest taxes, donations, and house prices
- Business cycle accounting of the BRIC economies
- Privately optimal severance pay
- Small business loan guarantees as insurance against aggregate risks
- Output growth and unexpected government expenditures
- International business cycles and remittance flows
- Effects of productivity shocks on hours worked: UK evidence
- A prior predictive analysis of the effects of Loss Aversion/Narrow Framing in a macroeconomic model for asset pricing
- Exchange rate pass-through and fiscal multipliers
- Credit demand, credit supply, and economic activity
- Distortions, structural transformation and the Europe-US income gap
- Monetary policy shocks and real commodity prices
- Topics
- News-driven international business cycles
- Business cycle dynamics across the US states
- Required reserves as a credit policy tool
- The macroeconomic effects of the 35-h workweek regulation in France
- Productivity and resource misallocation in Latin America1)
- Information and communication technologies over the business cycle
- In search of lost time: the neoclassical synthesis
- Divorce laws and divorce rate in the US
- Is the “Great Recession” really so different from the past?
- Monetary business cycle accounting for Sweden
Articles in the same Issue
- Masthead
- Masthead
- Advances
- How have global shocks impacted the real effective exchange rates of individual euro area countries since the euro’s creation?
- Employment by age, education, and economic growth: effects of fiscal policy composition in general equilibrium
- Overeducation and skill-biased technical change
- Strategic wage bargaining, labor market volatility, and persistence
- Households’ uncertainty about Medicare policy
- Contributions
- Deconstructing shocks and persistence in OECD real exchange rates1)
- A contribution to the empirics of welfare growth
- Development accounting with wedges: the experience of six European countries
- Implementation cycles, growth and the labor market
- International technology adoption, R&D, and productivity growth
- Bequest taxes, donations, and house prices
- Business cycle accounting of the BRIC economies
- Privately optimal severance pay
- Small business loan guarantees as insurance against aggregate risks
- Output growth and unexpected government expenditures
- International business cycles and remittance flows
- Effects of productivity shocks on hours worked: UK evidence
- A prior predictive analysis of the effects of Loss Aversion/Narrow Framing in a macroeconomic model for asset pricing
- Exchange rate pass-through and fiscal multipliers
- Credit demand, credit supply, and economic activity
- Distortions, structural transformation and the Europe-US income gap
- Monetary policy shocks and real commodity prices
- Topics
- News-driven international business cycles
- Business cycle dynamics across the US states
- Required reserves as a credit policy tool
- The macroeconomic effects of the 35-h workweek regulation in France
- Productivity and resource misallocation in Latin America1)
- Information and communication technologies over the business cycle
- In search of lost time: the neoclassical synthesis
- Divorce laws and divorce rate in the US
- Is the “Great Recession” really so different from the past?
- Monetary business cycle accounting for Sweden