Silviase/jgov_v1.4_full_ann huggingface dataset:
### 1. Introduction

Exchange rate management is one of the central issues of macroeconomic policies. Since the postwar period, a lengthy debate has simmered over the merits of fixed versus floating exchange rates. The debate, which is typically framed in terms of the trade-off between credibility and flexibility, has gone through several swings of the pendulum (Frankel 1999, Frankel et al. 2000).

Recently, the debates on exchange rate regimes have become focused on whether the intermediate regimes that “soft peg” their currencies, by tactics such as target zones, crawling, and basket pegs, are vanishing. In other words, the question is whether exchange rate regimes are moving toward a corner solution with the “hard peg” approach or the “free float” one. The corner solutions hypothesis claims that, under the principle of the “impossible trinity,” countries will be increasingly forced toward more purely floating or more purely fixed regimes as capital market integration increases (Fischer 2001, Summers 1999). As a counter-argument against the corner solutions hypothesis, the “fear of floating” hypothesis justifies an intermediate exchange rate regime mainly from the viewpoint of establishing credibility in the financial markets so that the local currency will not lose value against foreign currencies, particularly among emerging market economies (Calvo and Reinhart 2000, Williamson 2000, Kawai 2002). So far, no clear consensus has been reached.

The 1997-98 Asian financial crisis has refocused attention on exchange rate management within the East Asian countries. Most views expressed criticize the pre-crisis US-dollar-pegged rate regime as one cause of the crisis. It is said that this regime induced short-term external over-borrowing and caused the appreciation of real exchange rates with the loss of competitiveness (Ito 2001, etc.). The question also arises as to whether, after the crisis, the East Asian countries are simply returning to the pre-crisis US dollar standard (McKinnon 2001), or whether they have learned a lesson from the crisis and are finding another path to follow (Kawai 2002, etc.).

The recent debates over the exchange rate regimes take it a step further, arguing that there must be coordination in selecting an exchange rate regime among countries in the region with similar trading structures and with high intra-regional trading shares (Ogawa and Ito 2000). The possibility of an optimal currency area in East Asia has also been discussed on an empirical basis (Bayoumi, Eichengreen, and Mauro 2000).

Among the literature on exchange rate regimes mentioned above, this paper examines exchange rate regimes from the viewpoint of the validity of purchasing power parity (PPP). The main questions are these: under which exchange rate regimes has PPP
held? And, if some regimes allow PPP to hold, which adjustments of exchange rate or relative price have been effective in keeping PPP?

In the following sections we will first review previous studies and clarify this paper’s position (Section 2). We will then present our own empirical study (Section 3), and end with some concluding remarks (Section 4).

### 2. Previous Studies, Our Position

There is now a vast body of literature on the validity of purchasing power parity (PPP). Within this immense body of work, professional opinion on both the short and long run appears to have shifted several times in the post-war period. Taylor (2003) provides a selective and critical review of the literature, with special reference to the literature of the past two decades. As Dornbusch and Krugman (1976) wrote: "Under the skin of any international economist lies a deep-seated belief in some variant of the PPP theory of exchange rate."

Subsequently, the flurry of empirical studies employing unit-root tests on real exchange rate data for verifying the validity of the PPP—which emerged toward the end of the 1980s—were unanimous in their failure to reject the unit-root hypothesis (e.g., Enders 1998, Taylor 1988, Mark 1990). Then, Frankel (1986, 1990) pointed out that the tests typically employed to examine the long-run stability of the real exchange rate—if based on data covering just 15 years or so—may have very limited power to reject the null hypothesis. A logical next phase of the analysis of long-run real exchange rates involved testing for mean reversion using long spans of data to increase the power of the tests. Using annual data from 1869 to 1984 for the dollar-sterling real exchange rate, Frankel (1986) estimated an AR(1) process for the real rate and was able to reject the random-walk hypothesis. An alternative approach to increase the power of the tests involved using a panel of data; i.e., data on more than one real exchange rate. Abuaf and Jorion (1990) examined a system of ten first-order autoregressive regressions for real dollar exchange rates over the period 1973–87 and indicated a rejection of the null hypothesis of joint non-mean reversion as evidence in favor of long-run PPP.

In the course of the literature above for verifying the validity of PPP, this paper can be classified into an empirical study that employs unit-root tests on a panel of real exchange rate data. The main contribution of this paper lies in the point where it conducts the panel unit-root tests on real exchange rates according to exchange rate regimes such as hard peg, soft peg, managed float, and free float, i.e. the empirical link between exchange rate regimes and behavior of real exchange rates using a large panel
of countries in the world.

We find few studies in which the behavior of real exchange rate arrangement is examined under various exchange rate arrangements in a world-wide level, although these kinds of studies are often found on specific countries and areas. Among them, Parsley and Popper (2001) found important differences in real exchange rate behaviors across various official designations of exchange rate arrangement on a world-wide level, and showed notably that real exchange rate mean reversion is fastest when nominal exchange rates are officially pegged, and that nominal exchange rates, rather than prices, do most of the adjusting.

The new contributions of this study, which are different from Parsley and Popper (2001), are as follows. First, this study uses de facto exchange rate arrangements estimated by Reinhart and Ilzetzki (2009), while Parsley and Popper (2001) use the one reported in the International Monetary Fund (IMF). Second, the estimations in this study are based on monthly data of the International Financial Statistics of the IMF and monthly estimates of exchange rate arrangements by Reinhart and Ilzetzki (2009), while Parsley and Popper (2001) estimate on annual base. Third, a large panel of countries in the world is divided between industrial countries and developed ones in this study's estimation, although not in Parsley and Popper (2001). Fourth, this study adopts various types of the panel unit root tests with both common unit root process and individual unit root processes, while Parsley and Popper (2001) adopts only the tests with individual unit root processes of Im, Pesaran, and Shin (2003) and Maddala and Wu (1999).

### 3. Empirical Studies

We will now proceed to the empirical analysis, which we’ll take in two steps. First, we will conduct the panel unit-root tests to examine the stationarity of the real exchange rate according to exchange rate arrangements during the post-Bretton Woods period on the member-countries of the International Monetary Fund. Second, we will use an error correction framework to examine separately the adjustment of the nominal exchange rate and of relative prices, in case the stationarity of the real exchange rate is identified under some of exchange rate arrangements. Before conducting this two-step analysis, we clarify the following three issues: the relationship between real exchange rates and purchasing power parity, the specification of the real exchange rate, and the classification of exchange rate arrangements.

### 3.1 Relationship between real exchange rates and purchasing power parity
We first refer to the relationship between real exchange rates and the purchasing power parity (PPP). The real exchange rate is an indicator of a country's international price competitiveness, specifically of a country's prices relative to those of other countries. It can also be expressed as the nominal exchange rate adjusted for relative national price level differences. We may formulate the real exchange rate, $ y_{t} $ , in logarithmic form as:

$$ y_{t}=s_{t}-\left(p^{*}{}_{t}-p_{t}\right)\ (1) $$

where $ s_{t} $ is the nominal exchange rate, $ p_{t} $ is the domestic price level, and $ p^{*}_{t} $ is the foreign price level. On the other hand, the PPP exchange rate is the exchange rate between two currencies that would equate the two relevant national price levels if expressed in a common currency at that rate, so that the purchasing power of a unit of one currency would be the same in both economies. It may be formulated as:

$$ s_{t}=p^{*}{}_{t}-p_{t} $$

Comparing (1) and (2), we can see that, if the logarithm of the real exchange rate is identically equal to zero, PPP should hold. Thus, movements in the real exchange rate are tantamount to deviations from PPP. Further, an examination of the time-series properties of the real exchange rate may lead to the issue of whether the nominal exchange rate and relative national prices all settle down together at a level consistent with PPP over the long run. For the real exchange rate to settle down at any level whatsoever, it must display reversion toward its own mean. Hence, if the real exchange rate is mean-reverting, a necessary condition for long-run PPP to hold is satisfied. Generally, investigations into this issue have tested the null hypothesis of non-mean reversion (a unit root) against the alternative of mean reversion, in the process driving the real exchange rate.

### 3.2 Specification of the real exchange rate

We next discuss the issue of how to specify the real exchange rate defined above so as to calculate it. The real exchange rate is usually shown as a bilateral rate, like the nominal exchange rate. In general, the U.S. dollar is selected as the partner’s currency. Then, Equation (1) may be rewritten as:
$$ y_{t(US\ dollar/Local\ currency)}=s_{t(US\ dollar/Local\ currency)}-\left(p_{t\ US}-\ p_{t}\right) $$

Since a country has many trade partners and competitors in the world, the bilateral real exchange rates have to be unified to obtain a single indicator of a country’s international price competitiveness. The real effective exchange rate (REER) is such an indicator. We can express the REER as the weighted average of the bilateral real exchange rates, as follows:

$$ REER_{t}=W_{us}*y_{t(US dollar/Local currency)}+W_{JP}*y_{t(Japanese yen/Local currency)}+\ldots,(4) $$

where $ W_{us}, W_{JP}, \ldots $ are the weights attached to each bilateral real exchange rate.

The International Monetary Fund has had its own Information Notice System since 1983, under which real and nominal effective exchange rate series are computed for almost all Fund members and published in the International Financial Statistics (IFS). The weighting scheme is based on trade data for manufactured goods, primary goods, and, where significant, tourism services, with the weights reflecting both the relative importance of a country’s trading partners in its direct bilateral trade relations and that resulting from competition in third markets. $ ^{1} $

We will thus take the data from IFS for REER of the IMF member-countries during the post-Bretton Woods period: the monthly data from March 1973 $ ^{2} $ to December 2007. There are two kinds of REER: the one based on unit labor costs and the other based on consumer price indices. Since the former are computed only for 18 industrial countries and the euro area, we use the latter, which are computed for almost all Fund members. $ ^{3} $

### 3.3 Classification of exchange rate arrangements

The IMF represents exchange rate arrangements of the Fund members. However, its classification is often criticized as the one that does not necessarily reflect actual
exchange rate arrangements, since it is based on the Fund member’s formally announced regime. Many economists, therefore, have often showed their own analysis of the de facto exchange rate regimes. One famous estimate on exchange rate arrangements is the chronologies of the exchange rate arrangements represented by Reinhart and Ilzetzki (2009), which reclassified exchange rate regimes by employing newly complied monthly data sets on market-determined exchange rates.

From their estimates, we will adopt four categories of “monthly coarse classification,” which is composed of six categories of exchange rate arrangements. The first category consists of “no separate legal tender,” “pre-announced peg or currency board arrangement,” “pre-announced horizontal band that is narrower than or equal to $ \pm2\% $ ,” and “de facto peg,” which we will call “hard peg.” The second one is “pre-announced crawling peg,” “pre-announced crawling band that is narrower than or equal to $ \pm2\% $ ,” “de facto crawling peg,” and “de facto crawling band that is narrower than or equal to $ \pm2\% $ ,” which we will call “soft peg.” The third one is “pre-announced crawling band that is wider than or equal to $ \pm2\% $ ,” “de facto crawling band that is narrower than or equal to $ \pm5\% $ ,” “moving band that is narrower than or equal to $ \pm2\% $ (i.e., allows for both appreciation and depreciation over time),” and “managed floating,” all of which we will call “managed floating.” The fourth one we will call “freely floating.” We will take the data during the post-Bretton Woods period: the monthly data from March 1973 to December 2007. It is prudent, however, to draw strong conclusions by using the classification of Reinhart and Ilzetzki (2009), since the classification might not be always the best estimate, and since the test results in following sections might be subject to the selection of the classifications.

### 3.4 Panel unit root tests on the real exchange rate

We step into the panel unit root tests on the real exchange rate under various classifications of exchange rate arrangements during the post-Bretton Woods period from March 1973 to December 2007 on the Fund members, which we divide into industrial countries and developing countries in the analysis. We first clarify the procedures of panel unit root tests and then discuss the test results.

#### 3.4.1 Procedures of the panel unit root tests

Recent literature suggests that panel-based unit root tests have higher power than unit root tests do, based on individual time series. We will adopt the following five types
of panel unit root tests on the real exchange rate shown in the EViews 6 User’s Guide: Levin, Lin and Chu (2002), Breitung (2000), Im, Pesaran and Shin (2003), and Fisher-type tests using ADF and PP tests (Maddala and Wu (1999) and Choi (2001)). $ ^{4} $

We begin by classifying our panel unit root tests on the basis of whether there are restrictions on the autoregressive process across cross-sections or series. Consider a following AR(1) process for panel data:

$$ y_{it}=\rho_{i}y_{it-1}+X_{it}\delta_{i}+\varepsilon_{it} $$

where $ i = 1, 2, \ldots, N $ are cross-section units or series, that are observed over periods $ t = 1, 2, \ldots, T_{j} $ . The $ X_{it} $ represents the exogenous variables in the model, including any fixed effects or individual trends, $ \rho_{i} $ are the autoregressive coefficients, and the errors $ \varepsilon_{it} $ are assumed to be mutually independent idiosyncratic disturbance. If $ |\rho_{i}| < 1 $ , $ y_{i} $ is said to be stationary. On the other hand, if $ |\rho_{i}| = 1 $ then $ y_{i} $ contains a unit root. For purposes of testing, there are two natural assumptions that we can make about the $ \rho_{i} $ . First, one can assume that the persistence parameters are common across cross-sections so that $ \rho_{i} = \rho $ for all i. The Levin, Lin, and Chu (LLC), and Breitung tests all employ this assumption. Alternatively, one can allow $ \rho_{i} $ to vary freely across cross-sections. The Im, Pesaran, and Shin, and Fisher-ADF and Fisher-PP tests are of this form.

## Tests with common unit root process

LLC and Breitung both consider the following basic ADF specification:

$$ \Delta\mathrm{y}_{\mathrm{i t}}=\mathbf{\alpha}y_{i t-1}+\sum_{j=1}^{p i}\beta_{i j}\varDelta y_{i t-j}+X^{\prime}{}_{i t}\delta_{i}+\varepsilon_{i t} $$

where we assume a common $ \alpha = \rho - I $ , but allow the lag order for the difference terms, $ p_{i} $ , to vary across cross-sections. The null and alternative hypotheses for the tests may be written as:

$$ \begin{aligned}&H_{0}\colon\alpha=0\\&H_{1}\colon\alpha<0\qquad(7)\end{aligned} $$
Under the null hypothesis, there is a unit root, while under the alternative, there is no unit root. The LLC and Breitung method elect to include individual constant terms (fixed effects), or to employ individual constants and trends.

## Tests with individual unit root processes

The Im, Pesaran, and Shin, and the Fisher-ADF and PP tests all allow for individual unit root processes so that many vary across cross-sections. The tests are all characterized by the combining of individual unit root tests to derive a panel-specific result. The tests begin by specifying a separate ADF regression for each cross section. The specification is shown as the same equation as (6). The null hypothesis may be written as,

$$ \mathrm{H}_{0}\colon\alpha_{\mathrm{i}}=0,\mathrm{f o r}i $$

while the alternative hypothesis is given by:

$$ \begin{aligned}H1:\left\{\begin{array}{ll}\alpha_{i}=0&for i=1,2,\ldots,N_{1}\\\alpha_{i}<0&for i=N+1,N+2,\ldots,N\end{array}\right.\end{aligned} $$

which may be interpreted as a non-zero fraction of the individual processes is stationary. This means that the null hypothesis is joint non-mean reversion of all of the real exchange rates considered. Hence, the null hypothesis will be violated even if only one of the real exchange rates exhibits mean-reverting behavior. Taylor (2003) criticizes the panel unit root tests with the null hypothesis of joint non-mean reversion in such a way that “if univariate unit-root tests applied to a set of real exchange rates lead to rejection of the null hypothesis of non-mean reversion for one or more of the rates, then the results of a panel unit-root test applied to the same group of exchange rates is completely uninformative.” In this sense, it might be not appropriate if we depended only on the results of the tests with individual unit root processes. We therefore adopt both the tests with common unit root process and the ones with individual unit root processes. The method can choose to include individual constants, or to include individual constant and trend terms.

To sum up, we will conduct the five types of panel unit root tests of the LLC; Breitung; Im, Pesaran and Shin; and Fisher-type tests using ADF and PP tests, on the
real effective exchange rate based on consumer price indices taken from the IFS, under the various kinds of the exchange rate arrangements represented by Reinhart and Ilzetzki (2009), in industrial and developing countries of the Fund members, during the post-Bretton Woods period.

#### 3.4.2 Discussion of the test results

Table 1 shows the test results in the cases of full sample countries, industrial countries and developing countries. In the case of full samples, “hard peg” reveals the rejection of the null hypothesis of a unit root on REER in five types of tests with either intercept or trend and intercept at the significance level of one, to five and ten percent. “Free float” does it in four tests, whereas “soft peg” and “managed float” do it in only one test. These test results appear to be ambiguous in full samples because the corner arrangements of “hard peg” and “free float” show more definitely the REER stationarity than the intermediate arrangements of “soft peg” and “managed float.” We, therefore, divide full samples into industrial countries and developing countries.

In the case of industrial countries, “free float” gets the support of the REER stationarity from three tests, while the other arrangements get it from zero or only one test. In contrast, the case of developing countries shows that “hard peg” gets the support of the REER stationarity from all the tests, whereas the other arrangements get it from only one test.

We may interpret the results above in the following way. There seems to be some contrast in the real exchange rate behavior under the corner arrangements between industrial countries and developing countries: industrial countries may possibly keep the REER stability by rendering exchange rate sensitive to relative prices under “free float.” The test results, however, show weak support for this speculation because the REER stationarity is identified in the panel unit root test not with a common unit root process but with individual ones and also at the significance level of not a one percent level but a five and ten percent level. On the other hand, developing countries definitely present the REER stability under “hard peg,” getting full support from five types of tests. The results seem to be consistent with the previous study of Parsley and Popper (2001), which showed that real exchange rate mean reversion is fastest when nominal exchange rates are officially pegged. The REER stability under “hard peg” may tempt us to speculate that price adjustments have worked under the condition that the nominal exchange rate is rigidly pegged. However, there may also be the possibility that countries have often revised their pegs. We will then examine which adjustments of