VECM estimations of the PPP reversion rate revisited: the conventional role of relative price adjustment restored

Cheung et al. (2004) use a vector error correction model (VECM) for the current float nominal exchange rate and the relative price data and claim that the sluggish Purchasing Power Parity (PPP) reversion is primarily driven by the nominal exchange rate, not by relative price adjustment, which is at odds with the conventional sticky-price models. Our major findings are as follows. First, we suggest cases where VECMs are of limited usefulness even when all the variables in the system are not weakly exogenous. Second, using century-long exchange rates, we find that the relative price plays an important role for PPP reversion when real shocks occur. Third, protracted hump-shaped responses of real exchange rates are frequently observed when there is a relative price shock, leading to sluggish adjustments toward PPP. Nominal exchange rate shocks generate humped dynamics much less frequently.Purchasing Power Parity; Convergence Rate; Half-Life; Up-Life; Quarter-Life; Hump-Shaped Response; Variance Decomposition

VECM estimations of the PPP reversion rate revisited: the conventional role of relative price adjustment restored

Cheung et al. (2004) use a vector error correction model (VECM) for the current float nominal exchange rate and the relative price data and claim that the sluggish Purchasing Power Parity (PPP) reversion is primarily driven by the nominal exchange rate, not by relative price adjustment, which is at odds with the conventional sticky-price models. Our major findings are as follows. First, we suggest cases where VECMs are of limited usefulness even when all the variables in the system are not weakly exogenous. Second, using century-long exchange rates, we find that the relative price plays an important role for PPP reversion when real shocks occur. Third, protracted hump-shaped responses of real exchange rates are frequently observed when there is a relative price shock, leading to sluggish adjustments toward PPP. Nominal exchange rate shocks generate humped dynamics much less frequently

Country-specific shocks and optimal monetary policy

This paper studies optimal monetary policy responses to country-specific shocks in a simple two-country new open macroeconomic model that features sticky-price and local-currency pricing. Technology shocks in the home country are allowed to diffuse to the foreign country with a one-period lag, and vice versa. We find, even in the presence of price-stickiness and local-currency pricing, real shocks may generate market overreaction, to which central banks respond by implementing contractionary monetary policy. This is exactly opposite to the Devereux and Engel's (2003) prediction and many other''s. However, it may be consistent with empirical evidence of rising nominal interest rates during economic boom.

A Century of Purchasing Power Parity Confirmed: The Role of Nonlinearity

Taylor (2002) claims that Purchasing Power Parity (PPP) has held over the 20th century based on strong evidence of stationarity for century-long real exchange rates for 20 countries. Lopez et al. (2005), however, found much weaker evidence of PPP with alternative lag selection methods. We reevaluate Taylor’s claim by implementing a recently developed nonlinear unit root test by Park and Shintani (2005). We find strong evidence of nonlinear mean-reversion in real exchange rates that confirms Taylor’s claim. We also find a possible misspecification problem in using the ESTAR model that may not be detected with Taylor-approximation based tests.Purchasing Power Parity; Transition Autoregressive Process; inf-t Unit Root Test

Bias Correction and Out-of-Sample Forecast Accuracy

The least squares (LS) estimator suffers from signicant downward bias in autoregressive models that include an intercept. By construction, the LS estimator yields the best in-sample fit among a class of linear estimators notwithstanding its bias. Then, why do we need to correct for the bias? To answer this question, we evaluate the usefulness of the two popular bias correction methods, proposed by Hansen (1999) and So and Shin (1999), by comparing their out-of-sample forecast performances with that of the LS estimator. We find that bias-corrected estimators overall outperform the LS estimator. Especially, Hansen's grid bootstrap estimator combined with a rolling window method performs the best.Small-Sample Bias; Grid Bootstrap; Recursive Mean Adjustment; Out-of-Sample Forecast; Diebold-Mariano Test

Purchasing Power Parity and the Taylor Rule

In the Kehoe and Midrigan (2007) model, the persistence parameter of the real exchange rate is closely related to the measure of price stickiness in the Calvo-pricing model. When we employ this view, Rogo's (1996) 3 to 5 year consensus half-life implies that rms update their prices every 18 to 30 quarters on average. This is at odds with most estimates from U.S. aggregate data when single equation methods are applied to the New Keynesian Phillips Curve (NKPC), or when system methods are applied to Dynamic Stochastic General Equilibrium (DSGE) models that include the NKPC. It is well known, however, that there is a large degree of uncertainty around the consensus half-life of the real exchange rate. To obtain a more efficient estimator, this paper develops a system method that combines the Taylor rule and a standard exchange rate model to estimate half-lives. We use a median unbiased estimator for the system method with nonparametric bootstrap confidence intervals, and compare the results with those from the single equation method typically used in the literature. Applying the method to the real exchange rates of 18 developed countries against the U.S. dollar, we nd that most of the half-life estimates from the single equation method fall in the range of 3 to 5 years with wide confidence intervals that extend to positive infinity. In contrast, the system method yields median-unbiased estimates that are typically shorter than one year with much sharper 95% confidence intervals, most of which range from 3 quarters to 5 years. These median unbiased estimates and the lower bound of the confidence intervals for the half-lives of real exchange rates are consistent with most estimates of price stickiness using aggregate U.S. data for the NKPC and DSGE models.Purchasing Power Parity, Calvo Pricing, Taylor Rule, Half-Life of PPP Deviations, Median Unbiased Estimator, Grid-t Confidence Interval

On the Importance of Span of the Data in Univariate Estimation of the Persistence in Real Exchange Rates

This paper revisits the empirical evidence on real exchange rates' convergence to their purchasing power parity (PPP) levels. In their recent empirical study, Murray and Papell (2002) claim that the univariate approach provides no useful information on the size of the half-lives of real exchange rate deviations from PPP. However, we obtain finite confidence intervals for the half-life for a maximum of 8 out of 16 countries by applying the nonparametric grid bootstrap technique of Hansen (1999) to over a century of real exchange rates data for 16 developed countries relative to the US dollar. Our finding sharply contrasts to that of Murray and Papell (2002) with the post Bretton Woods real exchange rates. Our finding suggests that span of the data, not the estimation methods, matters more for obtaining useful information on long-run propositions such as PPP.Median Unbiased Estimator

Examining the Evidence of Purchasing Power Parity by Recursive Mean Adjustment

This paper revisits the empirical evidence of purchasing power parity under the current float by the recursive mean adjustment (RMA) method (So and Shin, 1999). We first demonstrate superior finite sample performance of the RMA-based unit root test over the augmented Dickey-Fuller test via Monte Carlo experiments for 18 linear and nonlinear autoregressive data generating processes. The RMA-based unit root test rejects the null hypothesis of unit root for 16 out of 20 current float real exchange rates relative to the US dollar.We also find that the computationally simple RMA-based asymptotic confidence interval can provide useful information regarding the half-life of the real exchange rate.Recursive Mean Adjustment; Finite Sample Performance; Purchasing Power Parity; Half-Life

Nonlinear Mean Reversion across National Stock Markets: Evidence from Emerging Asian Markets

This paper seeks empirical evidence of nonlinear mean-reversion in relative national stock price indices for Emerging Asian countries. It is well known that conventional linear unit root tests suffer from low power against the stationary nonlinear alternative. Implementing the nonlinear unit root tests proposed by Kapetanios, et al. (2003) and Cerrato, et al. (2009) for the relative stock prices of Emerging Asian markets, we find strong evidence of nonlinear mean reversion, whereas linear tests fail to reject the unit root null for most cases. We also report some evidence that stock markets in China and Taiwan are highly localized.Linear Unit Root Test; Nonlinear Unit Root Test; Nonlinear Panel Unit Root Test; International Relative Stock Prices

Generalized Impulse Response Analysis: General or Extreme?

This note discusses a pitfall of using the generalized impulse response function (GIRF) in vector autoregressive (VAR) models (Pesaran and Shin, 1998). The GIRF is general because it is invariant to the ordering of the variables in the VAR. The GIRF, in fact, is extreme because it yields a set of response functions that are based on extreme identifying assumptions that contradict each other, unless the covariance matrix is diagonal. With an empirical example, the present note demonstrates that the GIRF may yield quite misleading economic inferences