Investment intensity of currencies and the random walk hypothesis: Cross-currency evidence

Journal of Banking & Finance 35 (2011) 372–387

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Investment intensity of currencies and the random walk hypothesis: Cross-currency evidence q Tuugi Chuluun a, Cheol S. Eun b, Rehim Kiliç c,⇑ a

Department of Finance, Sellinger School of Business, Loyola University Maryland, Baltimore, MD 21210, United States The College of Management, Georgia Institute of Technology, Atlanta, GA 30332, United States c Department of Economics, Koç University, Istanbul 34450, Turkey b

a r t i c l e

i n f o

Article history: Received 3 June 2009 Accepted 16 August 2010 Available online 20 August 2010 JEL classification: F31 G15 Keywords: Exchange rate Random walk Investment intensity Variance ratio

a b s t r a c t This paper studies the cross-currency and temporal variations in the random walk behavior in exchange rates. We characterize currencies with relatively large investment flows as investment intensive and conjecture that the more investment intensive a currency is, the closer its exchange rate adheres to random walk. Using 29 floating bilateral USD exchange rates, we find that the higher the investment intensity, the less likely it is to reject random walk and the smaller the deviation from random walk is. However, the effect of investment intensity is non-monotonic. Application of threshold models shows that after investment intensity reaches the estimated thresholds, the level of investment intensity has no further effect on the deviation from random walk. These findings help reconcile the previous conflicting results on the random walk in exchange rates by focusing on the effect of cross-currency and temporal variations in investment intensity. Ó 2010 Elsevier B.V. All rights reserved.

1. Introduction Understanding the behavior of exchange rates has been one of the challenging issues in international finance since the beginning of the modern floating exchange rate era in the early 1970s. Specifically, a central question in international finance is whether the exchange rate follows random walk. Samuelson posed this question as early as in 1965, but it is the seminal work of Meese and Rogoff (1983) that brought it to the center of academic attention. Since then, an extensive literature has focused on investigating the random walk behavior in exchange rates, as the resultant findings may provide insights into the efficiency of the foreign exchange markets. Also, understanding the behavior of exchange rates would be useful to investors and policy makers such as central bankers. However, the results of the previous studies that explicitly test for random walk in daily and weekly exchange rates vary. For example, Baillie and Bollerslev (1989) report a unit root component in several exchange rate series, while Klaassen (2005) rejects the random walk hypotheq

We would like to thank to seminar participants at Georgia Institute of Technology, participants at the 79th Annual Meeting of Southern Economic Association at San Antonio, TX, and Richard T. Baillie, Menzie Chinn, Tanya Molodtsova, an anonymous referee and the editor for their helpful comments on the previous versions of this paper. The usual disclaimer applies. ⇑ Corresponding author. Tel.: +90 01 212 338 1877. E-mail addresses: [email protected] (T. Chuluun), [email protected] (C.S. Eun), [email protected] (R. Kiliç). 0378-4266/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jbankfin.2010.08.013

sis. On the other hand, Chang (2004), Belaire-Franch and Opong (2005), Yang et al. (2008), and Rossi (2006) obtain mixed results.1 The objective of this study is to examine the variation in the random walk behavior of exchange rates. Rather than simply testing for random walk or comparing the predictive power of various models based on economic fundamentals in explaining the movements of exchange rates, we take a different approach from the previous literature and investigate the cross-currency and temporal variations in the random walk behavior of exchange rates. We examine a conjecture that different exchange rates may adhere to the random walk behavior to different degrees, due to the cross-currency variation in investment intensity. We define investment intensity of a currency as the extent to which the currency’s transactions in foreign exchange markets are motivated by investment related activities, such as speculation and arbitrage involving various assets, relative to the extent of the transactions motivated by international trade of goods and services. 1 A related extant literature investigates the predictability of exchange rates using monetary and non-monetary fundamentals. Following the work of Meese and Rogoff (1983), a number of studies have found that random walk predicts exchange rates better than the macroeconomic models in the short run. However, a growing number of studies (e.g., Chortareas and Kapetanios, 2009) have reported results that suggest the predictability of exchange rates in the short-run by employing panel forecast methods, innovative estimation procedures, more powerful out-of-sample test statistics, and new structural models (see Rogoff and Stavrakeva (2008) for a critique and discussion of the recent literature).

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International trade has experienced an enormous growth during the recent decades, but the surge in investment flow has been even more dramatic. Consequently, the relative importance of investment and trade flows has changed. If an exchange rate is increasingly driven by investment flows, rather than trade flows, it may exhibit more random walk like behavior. This is partly because as investment intensity increases, currencies are more frequently traded for investment and speculative purposes and hence become an asset of their own class. Therefore, we expect exchange rates to become less predictable, as they are increasingly characterized by their own speculative markets rather than by trade of goods and services, which tends to be much less volatile. Moreover, the relationship between the investment intensity and the degree of deviation from the random walk may have threshold type nonlinearities similar to those documented in other areas of international finance. Intuitively speaking, once the investment intensity of a currency increases and exceeds a threshold level, then, its effect on the random walk behavior may diminish, as a currency with large enough investment intensity is expected to be heavily characterized by the factors of its own speculative market and already closely adhere to random walk. Thus, we explore the impact of various measures of investment intensity on the likelihood of rejecting the random walk hypothesis and the degree of deviation from random walk, by using an extensive data set on 29 floating bilateral US dollar (USD) exchange rates. The variance ratio is used to measure the random walk behavior. We use linear regressions and probit model, as well as recent nonlinear threshold models, in our analysis. The findings from our study show that the higher the investment intensity, the less likely it is to reject random walk in weekly exchange rates. After financial openness reaches a high level and investment flow becomes dominant over trade flow, random walk is no longer rejected. We also focus on the degree of adherence to random walk. Our results show that exchange rates adhere more closely to random walk and the deviations from random walk are smaller when the level of investment intensity is higher. We use various proxy measures for investment intensity, such as a measure of financial openness (KAOPEN), investment-to-trade flow (ITF) and currency turnover-to-trade (CTT) ratios. We also investigate if the relationship between our measures of investment intensity and the deviation from random walk has some threshold effects by using recent econometric threshold estimation methods. Our findings indicate that for KAOPEN, ITF and CTT values higher than certain critical levels, the investment intensity has no further effect on the deviation from the random walk behavior, and various robustness checks uphold our results. Although we are not testing any specific model in this paper, our findings are generally consistent with the basic asset pricing model formalized by Samuelson (1965) and some present value models (e.g., Engel and West, 2005), which imply that under certain plausible conditions, the behavior of exchange rates should be ‘‘near” random walk as expectations increasingly become more important in characterizing the short-term dynamics of exchange rates. Moreover, the findings of variations in random walk behavior across currencies and the diminishing deviation from random walk over time suggest that as global financial integration increases, currencies tend to show asset characteristics and hence, their behavior is increasingly driven by expectations. In the context of efficient market hypothesis, these findings may also suggest linkages between the weak form market efficiency and the investment intensity of a currency and hence variation in the efficiency of foreign exchange markets both temporally and across currencies. Our work differs from the previous studies on random walk along two critical dimensions. First, unlike prior works, we do not restrict our focus to the bivariate outcome of either rejecting

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or failing to reject random walk. Instead, we examine a conjecture, which states that the cross-currency degree of adherence to random walk depends on the investment intensity of currencies. Second, we use 29 USD bilateral exchange rates, a much broader set than those used in prior studies. The novel approach of this study leads to two main contributions. First, our findings have the potential to reconcile the conflicting empirical findings of the previous studies on random walk. The cross-currency and temporal variations in the random walk behavior of exchange rates could explain why findings from the previous studies varied vastly across different currencies and sample periods. Our empirical results indicate that the rejection or non-rejection of random walk may not be universal across exchange rates, but rather depends on the investment intensity of the currency at the time. Second, we introduce measures of investment intensity such as investment-to-trade flow ratio and currency turnover-totrade ratio. The rest of the paper is organized as follows. In Section 2, we elaborate our conjecture and provide further motivation for the study. Section 3 introduces the data. Section 4 discusses the variance-ratio test in detail. The analysis and the results are presented in Section 5, and the various robustness tests are reviewed in Section 6. Finally, Section 7 concludes.

2. Investment intensity of currencies and random walk in exchange rates The conjecture that the extent of the random walk behavior of exchange rates is related to the degree of investment intensity is based on the empirical observation of the cross-country differences in investment and trade flows. As an example, we plot investment and trade flows between six different countries and the US in Fig. 1. Investment flow refers to the total transactions in long-term domestic and foreign securities between the residents of the US and a foreign country during a calendar year. Trade flow refers to the sum of exports and imports between the US and a foreign country during the same calendar year. Over the past several decades, capital markets around the world have opened up, leading to increased investment flows. As a result, the relative magnitudes of investment and trade flows have dramatically changed. As Panel A of Fig. 1 shows, the investment flow between Canada and the US has surpassed the trade flow between the two countries since around 1990. As of 2005, the investment flow is about 3.5 times as large as the trade flow. A similar pattern of investment flow dominance can be observed in the cases of Japan and United Kingdom (UK) since the mid-1980s. Moreover, the sheer size of investment flow is impressive. For instance, the size of investment flow between the UK and the US is about 172 times as large as the trade flow in 2005. This number is largely driven by the fact that the UK is a major world financial center with tremendous amount of investment that does not necessarily originate in the UK. Among developing countries, we observe more variability in the pattern of investment and trade flows. The investment flow between Korea and the US is about 2.25 times as large as the trade flow in 2005,2 whereas the magnitudes of investment and trade flows are relatively similar (with a ratio of about 1.06 as of 2005) in the case of India. From Fig. 1, we can clearly see that investment flow is relatively volatile, while trade flow is considerably persistent and predictable. The dramatic surge in investment flow between Brazil and

2 The size of investment flow between Korea and the US starts to dominate that of the trade flow in 1999. This coincides with Korea further opening its capital market and letting Korean won freely float following the Asian crisis of 1997.

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Panel D

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the US in the mid-1990s,3 as well as between Japan and the US in the late 1980s, illustrates this point. In fact, the sample standard deviation of annual percentage change in trade flow is 14% versus 467% in investment flow during the period of 1974–2005.4 After simple linear detrending, the estimated autocorrelation in annual trade flows is statistically significant at 0.53, while the autocorrelation in investment flows is insignificant. Motivated by the evidence reported above, we point to variations in trade and investment flow across time and countries as a possible factor that characterizes the random walk behavior. If trade flow mainly affects the exchange rate behavior, the exchange rate may follow a predictable pattern since trade flow between countries is not random. Trade patterns do not display substantial changes from year to year, as gross domestic product (GDP) and consumption patterns are stable in the short run. On the other hand, if investment flow has a significant impact on the exchange rate, we expect to see a behavior similar to random walk since investment flow is much more random and volatile than trade

3 The surge in investment flow in the mid-1990s was fueled by the renewed interest in Brazilian markets as inflation rate fell to single digit annual figures. At its peak in 1996, the investment flow was about 11 times as large as the trade flow. 4 The mean percentage annual change in trade flow is 6% versus 72% in investment flow. The median percentage annual changes are 7% and 17%, respectively.

flow. Investment decisions are largely based on rapidly flowing news, and investors can quickly adjust their portfolios in today’s technologically advanced markets. The geographical boundaries are no longer significant barriers to investment flows. An example of volatile investment flow is the case of Brazil: Brazil experienced an increase of 289% in its investment flow with the US in 1996 from the previous year followed by a 56% decline in 1999. We simply do not observe such dramatic changes in trade flow. One way to think about the conjecture is to imagine two extreme characterizations of the currency markets: (1) a world in which capital movements across countries are limited and therefore, the movements in goods flow largely characterize the behavior of currencies, and (2) a world in which movements in capital flows are free and hence, exchange rates are largely characterized by their own speculative market. The first characterization is similar to the goods market approach of the pre-1970s. According to this approach, demand and supply of currencies come primarily from purchases and sales of goods, that is, exports and imports. In this framework, trade flow drives exchange rate movements, and thus, the currency market is, in some sense, a derivative market, as flow of goods across countries leads to changes in the supply and demand of currencies. One extension of the goods market approach suggests that the purchasing power parity (PPP) will hold approximately, because large relative price differences may lead

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to movements in goods, which, in turn, would lead to changes in currency supply and demand. Therefore, under the first approach, it is plausible that exchange rates are consistent with PPP and hence less random in terms of their behavior. Under the second approach, currency demand and supply may not only come from the purchases and sales of goods, but also from the purchases and sales of currencies for investment and speculative purposes. As controls on capital movements are removed, investment activities in stocks, government and private bonds increase across countries. These increased investment activities obviously lead to increases in the movement of deposits in various currencies across countries. In other words, purchases and sales of assets increase trade in currencies. Therefore, in this paper, we define investment intensity of a currency as the degree to which the currency’s transactions in foreign exchange markets are motivated by investment related activities rather than international trade of goods and services. Thus, if a country is in the early (final) stage of capital account liberalization with restricted (free) crossborder capital flow, its currency is likely to have a low (high) level of investment intensity. According to the Bank for International Settlements’ (BIS) (April 2007) survey, on average 3.2 trillion US dollars are traded each day on the global foreign exchange markets, representing a 70% increase from 2004 and a 290% increase from 1992. Of this daily trading volume, only a small fraction – less than 5% – is due to export and import activities. This points to the increasing relevance of the second approach discussed above, which emphasizes the currency trading motivated by investment and speculative activities. Moreover, the effect of investment intensity on the exchange rate may not be linear. When countries are in the early stages of capital account liberalization with limited cross-border investment flows, increases in investment flows may have much greater impact on the exchange rate behavior compared to the impact of increases of the same magnitude when the countries already have high levels of investment flows. Therefore, it is possible that beyond certain levels of investment intensity, further increases in investment intensity may no longer affect exchange rate behavior. Such a threshold effect has been documented in other areas of international finance. For example, Chinn and Ito (2006) find that a higher level of financial openness promotes financial development only if a threshold level of legal development is present. As discussed in the previous paragraphs, the first view of currency markets is consistent with the goods market approach, while the second is in line with assets as well as market microstructure approaches. However, we should stress that we do not test any of the exchange rate determination models or approaches in this paper. Our discussion above suggests that in the cross-section of multiple currencies, the variation in the behavior of exchange rates can be consistent with a spectrum of models ranging from one extreme to the other or a hybrid of models. This may explain why the verdict on random walk varies across exchange rates even within the same study in the previous literature. For example, BelaireFranch and Opong (2005) examine the behavior of 10 bilateral euro exchange rates and obtain mixed results: random walk is rejected for the Canadian and Singaporean dollar exchange rates, but not for the others. Yang et al. (2008) also find that the martingale behavior cannot be rejected for euro exchange rates with major currencies, but there is nonlinear predictability in the euro exchange rates with several smaller currencies. Similarly, using tests robust to parameter instability, Rossi (2006) reports mixed results for five USD monthly exchange rates. The results on random walk in the exchange rate may vary across sample periods as well. Newbold et al. (1998) find very little departure from the random walk pattern in USD/ECU exchange rate, but the results are inconsistent between the full sample period and the sub-periods. Lastly, Chang (2004) shows that from 1989 onwards the random walk hypothe-

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sis cannot be rejected for four out of five exchange rates in his sample. Yet, prior to 1989 there is some evidence of random walk rejection in those currencies. Therefore, examining the cross-sectional and time series behavior of exchange rates taking into consideration the investment intensity of currencies may shed light on the random walk behavior of exchange rates.

3. Data Our sample period starts in 1974 after the collapse of the Bretton Woods fixed exchange rate system in March 1973. For the purpose of this study, we focus only on the currencies that are identified as having managed or independently floating exchange rate regime according to the classification of exchange rate arrangements and monetary policy frameworks conducted by International Monetary Fund (IMF) on June 30, 2006. Since countries rarely go back to fixed exchange rate regime once they adopt the floating rate regime, this criterion provides us with an accurate identification of currencies with floating exchange rate regimes. From the countries with these two categories of exchange rate regime, managed or independently floating, we exclude small economies that have negligible trade and investment flows such as Cambodia, Guyana, Jamaica, Mauritius, and Slovenia. This leaves us with 29 countries including Euro zone. We further research the history of each currency to identify when the countries switched to floating exchange rate regime from either fixed rate or intermediate regime. Some countries (e.g., Indonesia) first switched to managed floating exchange rate regime and after some time to independently floating exchange rate regime, while others (e.g., Australia) directly moved onto independently floating regime after abandoning fixed exchange rate system. Appendix A provides the detailed list of all 29 currencies as well as their sample inclusion date and brief history, including the date of any regime switch if such a switch occurred. For example, India is included in our sample from March 1, 1993 because that is when India has officially switched to managed floating exchange rate regime from an intermediate regime, under which the exchange rate moved within a band linked to a basket of currencies. Prior to that, Indian rupee was pegged to the pound sterling from 1947 to 1975. To measure the deviation from random walk across exchange rates, we employ the commonly used random walk measure of variance ratio developed by Lo and MacKinlay (1988) and its modifications by Wright (2000). We discuss this measure in detail in the following section. We obtain weekly bilateral USD exchange rates from Datastream for all the currencies. Each exchange rate series has a specific start date as specified in Appendix A. For the purpose of our analysis, measures of investment intensity of currencies are needed. A promising starting point is a measure of financial openness. Although financial openness is not the only determinant of investment flow, an open capital market is essential for substantial investment flow. Thus, we use financial openness as a broad and encompassing measure of investment intensity. We use the KAOPEN index developed and updated by Chinn and Ito (2002, 2006) that is designed to measure the extent of financial openness using IMF’s Annual Report on Exchange Arrangements and Exchange Restrictions (AREAER). This index is the first principal component of the four binary variables reported in AREAER: presence of multiple exchange rates, restrictions on current account transactions, restrictions on capital account transactions, and requirement of the surrender of export proceeds. By construction, the index has an annual cross-country mean of zero, and a higher index value indicates a more open market. The major advantages of this index are its emphasis on the intensity of capital controls and wide coverage (more than 100 countries over 1970– 2007). However, it should be noted that the financial openness

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index of a country does not necessarily change from year to year and after some time many of the countries achieve high levels of openness and maintain those levels. Alternative measures that we use as a robustness check are the capital liberalization indices developed by Quinn (1997) and Quinn and Toyoda (2008).5 These indices are also created from AREAER, but Quinn’s openness measure, CAPITAL, ranges on the scale of 0–100. In order to measure investment intensity more directly, we propose an alternative proxy using bilateral investment and trade flow data. Specifically, we compute investment-to-trade flow (ITF) ratio, which measures the size of the investment flow relative to the trade flow between a foreign country and the US Investment flow is computed as the sum of total transactions in long-term domestic and foreign securities between the residents of a foreign country and the US during a calendar year as reported by the Treasury International Capital (TIC) Reporting System.6 Trade flow refers to the sum of exports and imports between a foreign country and the US during a calendar year as reported by Foreign Trade Division of the US Census Bureau. The ratio between investment and trade flow is a bilateral measure, and it is our second proxy for investment intensity, in addition to the financial openness measures. Since no measure may be perfect, we propose a third measure of investment intensity that is based on foreign exchange turnover. As we know, foreign exchange turnover data are hard to obtain and produced rather infrequently. However, BIS has conducted triennial central bank surveys on foreign exchange markets every third April since 1989. BIS surveys report foreign exchange turnover data for major currencies against all other currencies in USD. The survey also reports turnover data by country. Based on these turnover measures, we compute the currency turnover-to-trade (CTT) ratio, which refers to the annualized foreign exchange turnover of a currency divided by the sum of total exports and imports of the corresponding country. We also create a slight variation of this ratio: country turnover-to-trade ratio, which is the annualized foreign exchange turnover of a country divided by the sum of total exports and imports of that country. For countries that do not have well developed financial sector, these two turnover-to-trade ratios produce close estimates. Since the foreign exchange turnover of a currency is measured against all other currencies, these proxies are multilateral, unlike the bilateral ITF ratio. Moreover, only a small number of observations are available because the survey is conducted every 3 years. Additionally, central bank intervention can be a factor affecting the exchange rate behavior (e.g., Beine et al., 2009). But since our sample is comprised of those currencies with floating exchange rate regimes, central bank intervention is not likely to have a major impact on the exchange rate behavior. Nevertheless, to control for the possible impact of central bank intervention, we create proxies for central bank intervention activities using foreign reserve data. Note that there exists no comprehensive data for central bank intervention activities.7 Thus, we first obtain monthly total reserve data from International Financial Statistics (IFS) maintained by IMF and compute the absolute percentage change in monthly foreign reserve levels.8 We expect to see relatively small changes in the 5 We are grateful to Prof. Quinn for kindly providing us with these capital liberalization indices. 6 Every quarter since 1945, the US government has published TIC bulletins that contain data on capital movements. Bulletins from 1996 are available online at http:// www.treas.gov/tic. 7 A few central banks such as Swedish central bank (Riksbank) report their past activities, but this is rather uncommon. Researchers have also attempted to identify intervention operations using news reports. 8 As an alternative measure of central bank intervention activity, we also compute the annual standard deviation of percentage changes in monthly reserve levels. However, we only use the percentage change measure in our analysis because these two variables, percentage change in reserve level and its annual standard deviation, are highly correlated with each other.

foreign reserve level if a central bank does not actively engage in intervention operations.

4. Variance-ratio test of random walk in the exchange rate To measure the random walk behavior in the exchange rate, we employ the commonly used random walk measure of variance ratio developed by Lo and MacKinlay (1988) and its recent modifications suggested by Wright (2000). The intuition behind the variance ratio is that the variance of the increments in random walk is linear to the sampling interval. For example, if a series follows random walk, the variance of 8-week interval should be eight times the variance of weekly interval. Thus, the ratio of sample interval variance to base interval variance divided by the length of the interval should be close to one: random walk has a variance ratio of one. This simple, straightforward test of random walk is used widely in various studies. For instance, Liu and He (1991) use 2-, 4-, 8-, and 16-week interval heteroskedastic robust variance ratios to detect random walk in exchange rates. Chang (2004) conducts similar tests using bootstrapped variance ratios. To investigate the efficiency of the US art market, Erdõs and Ormos (2010) apply variance-ratio tests to art price indices. Lo and MacKinlay (1988) originally apply the variance-ratio test to stock return data, and they propose test statistic denoted by M1 and its heteroscedasticity robust version M2 based on the variance ratios. Wright (2000), on the other hand, proposes new variance-ratio tests that are based on ranks and signs, denoted by R1, R2, and S1, where the first two statistics are based on the ranks of the time series and its normal inverse transformation and the latter on the sign. The details of these test statistics are provided in Appendix B. In line with previous research, we use the logs of the nominal exchange rates of Wednesdays to compute the heteroskedasticity-robust variance ratios for 2-, 4-, 8-, and 16-week intervals (k = 2, 4, 8, and 16) with 1 week base period. We utilize the moving window approach and compute the variance ratios over rolling 5year periods moving forward a year at a time. In total, there are 29 rolling 5-year periods between January of 1974 and December of 2006. The variance ratios estimated with less than 200 weekly exchange rate observations are excluded from the sample. Much of the following analysis employs the variance ratios computed with 8-week interval (k = 8), but variance ratios estimated over other intervals are used in robustness tests. Since currencies are included in the sample only when they are under the floating exchange rate regime, our data are unbalanced panel dataset. As a result, for instance, we have variance ratios reported for Argentine peso only for the last couple of periods, since this currency is included in our sample only from January 11, 2002. In the case of Japanese yen, on the other hand, we have the variance ratios computed for all the periods. Although not reported to conserve space, we plot the distribution of the computed variance ratios from various tests. The plots show considerable variations in the variance ratios, despite some clustering around unity. The plots also show that when the variance ratios deviate from unity, they are more likely to be greater than one, which suggests that exchange rates tend to exhibit positive rather than negative autocorrelations. To gain further insight into the rejection/non-rejection of random walk by various tests, Table 1 presents the descriptive statistics on the frequency of random walk rejection by various tests at the 5% significance level. The frequency of rejection in Table 1 shows that Wright’s (2000) rank- and sign-based variance-ratio tests tend to reject the random walk null more often than the conventional Lo and MacKinlay (1988) variance-ratio tests. This is consistent with the Monte Carlo evidence reported in Wright (2000) that the variance-ratio tests using ranks and signs have more

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T. Chuluun et al. / Journal of Banking & Finance 35 (2011) 372–387 Table 1 Summary results from the variance-ratio tests. The following table displays the frequency of random walk rejection based on each variance-ratio test statistic. M1 and M2 are the conventional variance-ratio test statistics developed by Lo and MacKinlay (1988), where M2 is the heteroscedasticity robust version. R1, R2, and S1 are the recent modifications proposed by Wright (2000) that are based on ranks and signs. R1 and R2 are the variance-ratio test statistics based on the ranks of the time series and its normal inverse transformation, and S1 is based on the signs. Test

Number of VR tests

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Standard deviation

M1 M2 R1 R2 S1

441 441 441 441 441

0.128 0.109 0.223 0.194 0.205

0.335 0.312 0.417 0.396 0.405

power than the conventional tests. These results hold true for various other k’s. To better understand the temporal variation in the variance-ratio test statistics, we display the average of the variance-ratio test statistics of different currencies that have observations during each 5-year sub-period in Fig. 2. Although the values of five variance ratio statistics are not directly comparable with each other, the crosscurrency averages of five statistics tend to move together across the sample period. The group of Lo–MacKinlay test statistics (M1 and M2) tends to behave similarly, while Wright test statistics, especially R1 and R2, exhibit similar behavior. In addition, the averages of Wright (2000) test statistics show more variation than the Lo–MacKinlay statistics, which is consistent with the results in Table 1. Since the variance-ratio test statistics should have a mean value of zero under the random walk null, the plots suggest that on average, the variance-ratio test statistics tended to be far from zero during the 1970s and hence, on average exchange rates were far from random walk. Fig. 2 shows that on average, the varianceratio test statistics exhibited convergence towards zero during the first half of the 1980s and then deviated from zero during the second half of the 1980s. Subsequently, the test statistics were, on average, relatively close to zero during the early 1990s, but from the late 1990s they deviated more from zero.9 Inspection of the plots in Fig. 2 shows that the average of each variance-ratio test statistics has a negative trend over our sampling period. Table 2 presents the results of time-trend regressions, in which each variance-ratio test statistic is regressed on a constant and a time trend. The results from the simple time-trend regressions show statistically significant negative time trend coefficients, concurring with the results from the plots in Fig. 2.10 In the following section, we investigate the relationship between various measures of investment intensity and the random walk behavior of currencies by focusing on the rejection of random walk by the variance-ratio tests as well as the deviation from random walk. In the remainder of the paper, we only report results under M2 and R2 to conserve space. We report results for M2, as it is robust to the presence of heteroscedasticity (indeed findings are very similar to M1), and R2, since the findings from other Wright (2000) tests are very similar to those from R2.11 9 We plot the variance-ratio test statistics in Fig. 2 to provide some insights into average values of various test statistics over time. Note that since plots in Fig. 2 display the cross-currency averages of variance-ratio test statistics in each sub-period without confidence intervals, deviation from zero for a given test statistic does not necessarily imply a rejection of random walk. We do not display confidence intervals as it is not clear how to interpret the confidence intervals for averages in the current context. 10 We have also estimated simple trend regressions on average deviations from random walk, where deviations are defined as the absolute distance of a variance ratio from unity under all five tests. Results and plots of deviations show very similar temporal behavior to the variance-ratio tests discussed here. 11 We point out similarities and differences in findings from M2 and R2 test statistics throughout the paper. Our overall findings are similar across all the tests. Complete results from all the tests can be obtained upon request.

Fig. 2. Cross-currency average variance-ratio test statistics over time. The graph displays the cross-currency averages of the variance-ratio test statistics, M1, M2, R1, R2 and S1, over rolling 5-year periods. M1 and M2 are the conventional variance-ratio test statistics developed by Lo and MacKinlay (1988), where M2 is the heteroscedasticity robust version. R1, R2, and S1 are the recent modifications proposed by Wright (2000) that are based on ranks and signs. R1 and R2 are the variance-ratio test statistics based on the ranks of the time series and its normal inverse transformation, and S1 is based on the signs. The variance-ratio tests are computed with 1 week base observation interval and 8-week testing interval (k = 8) over rolling 5-year periods. The dates in the figure refer to the middle year of the rolling 5-year estimation periods.

Table 2 Time trend regression analysis of variance-ratio test statistics. This table presents the results of time-trend regressions, in which each variance-ratio test statistic is regressed on a constant and a time trend. M1 and M2 are the conventional varianceratio test statistics developed by Lo and MacKinlay (1988), where M2 is the heteroscedasticity robust version. R1, R2, and S1 are the recent modifications proposed by Wright (2000) that are based on ranks and signs. R1 and R2 are the variance-ratio test statistics based on the ranks of the time series and its normal inverse transformation, and S1 is based on the signs. The heteroscedasticity robust standard errors are given in parentheses.

Intercept Time trend R2

M1

M2

R1

R2

S1

1.172 (0.00) 0.044 (0.00)

1.024 (0.00) 0.039 (0.00)

2.192 (0.00) 0.069 (0.01)

1.796 (0.00) 0.061 (0.01)

2.440 (0.00) 0.067 (0.00)

0.379

0.403

0.334

0.324

0.504

5. Effect of investment intensity on the exchange rate behavior: Regression results 5.1. Explanatory variables As a preliminary analysis, we plot the time series of two main explanatory variables in Fig. 3. In Panel A, we observe a strong upward trend in the average KAOPEN of all the countries in our sample,12 especially in the late 1970s and early 1990s with some stagnation afterwards around the Asian crisis of 1997. The average ITF ratio of our sample currencies is presented in Panel B of Fig. 3. An upward trend over the years starting from the mid-1980s, that is especially strong in the late 1990s and early 2000s, is apparent. Although we do not present the figure of the central bank intervention proxy measure here, we find that the change in international reserve levels has decreased somewhat over time. This is consistent with less frequent intervention in the foreign exchange market by central banks. 12 Please note that, for illustrative purposes, KAOPEN indices and ITF ratios of all the countries in our sample for all the years are included in the computation of the average, regardless of when the indices and ratios are actually used in our regression analysis.

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Panel A: Average KAOPEN over time 1.2 1.0

KAOPEN

0.8 0.6 0.4 0.2 0.0 -0.2 2003

2001

1999

1997

1995

1993

1991

1987

1989

1983

1985

1981

1979

1977

1975

1973

-0.4

Panel B: Average investment-to-trade flow (ITF) ratio over time 18 16 14

ITF ratio

12 10 8 6 4 2

2005

2003

2001

1999

1997

1995

1993

1991

1989

1987

1985

1983

1981

1979

1977

1975

1973

0

Fig. 3. Time series behavior of the explanatory variables. Panel A: Average KAOPEN over time. The following figure shows the average of KAOPEN indices of all the countries across all the sample years, regardless of when the countries are actually included in the regression analysis. KAOPEN is a financial openness index developed and updated by Chinn and Ito (2002, 2006). KAOPEN for Euro zone is computed as the GDP-weighted average of the KAOPEN indices of the 12 member countries between 1999 and 2005, with Greece added from 2001. Higher values of the index represent more financially open economies. Panel B: Average investment-to-trade flow (ITF) ratio over time. The following figure depicts the average of ITF ratios of all the countries across all the sample years, regardless of when the countries are actually included in the regression analysis. ITF ratio measures the size of the investment flow between a foreign country and the US relative to that of the trade flow. Investment flow is computed as the sum of total transactions in long-term domestic and foreign securities between the residents of the US and a foreign country during a calendar year as reported by the Treasury International Capital (TIC) Reporting System. Trade flow refers to the sum of exports and imports between a foreign country and the US during a calendar year as reported by Foreign Trade Division of the US Census Bureau. ITF ratio for Euro zone is computed as the GDP-weighted average of the ITF ratios of the twelve member countries between 1999 and 2005, with Greece added from 2001.

but there are only 52 observations since this measure is based on triennial BIS surveys. Mean annual absolute percentage change in monthly reserve levels, which proxies for foreign exchange market intervention, is about 8.37%. The descriptive statistics of the variables that are used in the robustness tests – country turnover-totrade ratio and CAPITAL liberalization index – are also provided in Panel A. Panel B of Table 3 presents the mean of the various variables by country. It is apparent that the developed countries such as Japan, the UK, Canada, and Switzerland have high KAOPEN indices, while many developing countries, such as India and South Africa, still have lower index values. The countries with the highest mean ITF ratios with the US are the UK and Norway followed by Uruguay, Czech Republic, and Euro zone. The variables for Euro zone are computed as the GDP-weighted average of the variables of the individual 11 member countries from 1999 to 2005. Greece is added from 2001. Countries with the lowest mean ITF ratios are Mexico, Philippines, and Malaysia. Investment intensity variables based on foreign exchange turnover are not reported for all the countries because BIS surveys report data for only selected currencies and countries. Lastly, the correlation coefficients among the explanatory variables are presented in Table 4. As expected of a financial openness measure, KAOPEN has significant correlation with each of the other explanatory variables. However, the correlation coefficient between KAOPEN and ITF ratio is only 0.250, which suggests that the proxies based on exchange controls and capital flow capture different aspects. The correlation between KAOPEN and CAPITAL indices is 0.493, which implies that these two indices are constructed differently and capture somewhat different aspects of financial openness. The correlation coefficient between investment intensity measures based on currency and country turnovers are 0.565. This correlation shows the discrepancy between turnover measures based on locality versus currency. We expect the currency turnover measure to be more suitable for our analysis, as we focus on the behavior of bilateral exchange rate. The negative correlation between KAOPEN and the intervention proxy suggests that countries in our sample intervene less in the foreign exchange market as their capital markets become more open. ITF ratio also has a negative correlation with the intervention proxy measure. These summary statistics suggest that the explanatory variables we use are non-redundant. 5.2. Probability of rejecting random walk

The descriptive statistics of all the variables are presented in Table 3. The dependent variable is the deviation from random walk, which is measured by the absolute difference between the computed variance ratio and the value of one. We use the variance ratios estimated over rolling 5-year periods with k = 8 and at least 200 weekly exchange rate observations. We use the middle year of the 5-year period as the corresponding year for the variance ratio and match it with the explanatory variables of that year. Panel A shows the summary statistics of the full sample. The mean and median deviations from random walk are 0.21 and 0.16, respectively. The financial openness measure, KAOPEN, ranges from 1.75 to 2.62, with a mean of 1.66 and a median of 2.62. The computed ITF ratios have a mean of 10.04 and a median of 3.46, which means that the median long-term investment flow between a foreign country and the US is about three and half times as large as the median trade flow between that country and the US. This ratio has a wide variation as evidenced by the 25th and 75th percentile values of 0.96 and 8.64. The high mean ITF ratio of 10.04 is driven by positive outliers, where some countries, such as the UK, have mean ITF ratio as large as 51. The third measure of investment intensity, currency turnover-to-trade ratio, has a mean of 1.64,

Returning to the spirit of the previous studies that focus on the rejection or non-rejection of random walk in the exchange rate, we start our regression analysis by estimating the likelihood of rejecting random walk. By using the variance-ratio tests, we create a binary dependent variable that is equal to one if the null of random walk is rejected by a given test statistic at the 5% significance level. Using these binary dependent variables and various measures of investment intensity and several control variables, we estimate the linear probability and probit models to explore the likelihood of rejecting the random walk. Specifically in Table 5, we report the estimation results from probit model, where the dependent variable equals to one if the random walk in the exchange rate is rejected at the 5% significance level based on M2 and R2.13 As the significant and negative coefficients of 0.225 and 0.402 on KAOPEN in Model 1 in Panels A and B indicate, it is less likely to reject random walk in the exchange rate when financial 13 The results from the Linear Probability Model (LPM) and probit model that use other variance ratios are not reported to conserve space, but can be obtained upon request. Findings from both models with different binary dependent variables are qualitatively similar to the results reported in Table 5.

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Table 3 Descriptive statistics of the regression variables. The following table in Panel A presents the descriptive statistics of the variables used in our analysis. Panel B displays the mean values of the variables by country. Please, note that not all the countries have explanatory variables available for all the years. Deviation from random walk is measured as the absolute difference between the value of one and the computed variance ratio. Variance ratios are estimated over rolling 5-year periods with a base observation interval of one week and testing interval of 8 weeks (k = 8). KAOPEN index is a measure of financial openness developed and updated by Chinn and Ito (2002, 2006). The KAOPEN data is obtained from Menzie Chinn’s website. Investment-to-trade flow (ITF) ratio measures the size of the investment flow between a foreign country and the US relative to that of the trade flow. Investment flow is computed as the sum of total transactions in long-term domestic and foreign securities between the residents of a foreign country and the US during a calendar year as reported by the Treasury International Capital (TIC) Reporting System. Trade flow refers to the sum of exports and imports between a foreign country and the US during a calendar year as reported by Foreign Trade Division of the US Census Bureau. Investment intensity measures based on foreign exchange turnover are computed using the triennial central bank surveys of foreign exchange and derivatives market activity conducted by the Bank for International Settlements (BIS). Currency turnover-to-trade (CTT) ratio refers to the annualized foreign exchange turnover of a currency divided by the sum of total exports and imports of the corresponding country. Country turnover-to-trade ratio is the annualized foreign exchange turnover in a country divided by the sum of total exports and imports of that country. The total exports and imports data are obtained from International Financial Statistics (IFS) maintained by International Monetary Fund (IMF). Absolute percentage change in reserve level is computed as the annual mean of monthly absolute percentage changes in foreign reserve levels. Reserve levels of countries are obtained from IFS. CAPITAL liberalization index is designed by Quinn (1997) and Quinn and Toyoda (2008) to measure capital account liberalization. Prof. Quinn has kindly provided us with the data. Explanatory variables for Euro zone are computed as the GDP-weighted average of the corresponding variables of the 12 member countries between 1999 and 2005 with Greece added from 2001.

Panel A: Full sample Deviation from random walk KAOPEN index Investment-to-trade flow ratio Currency turnover-to-trade ratio Absolute percentage change in reserve level Country turnover-to-trade ratio CAPITAL liberalization index Country

Deviation from random walk

Panel B: Country subsamples Argentina 0.16 Australia 0.09 Brazil 0.07 Canada 0.14 Chile 0.52 Colombia 0.40 Czech Republic 0.09 Euro zone 0.20 Germany 0.15 India 0.31 Indonesia 0.29 Japan 0.35 Korea 0.24 Malaysia 0.23 Mexico 0.15 New Zealand 0.13 Norway 0.14 Peru 0.26 Philippines 0.18 Poland 0.07 Russia 0.38 Singapore 0.18 South Africa 0.22 Sweden 0.16 Switzerland 0.14 Thailand 0.50 Turkey 0.34 UK 0.24 Uruguay 0.03

Mean

Median

25th percentile

75th percentile

Std. dev.

N

0.21 1.66 10.04 1.64 8.37 2.02 87.20

0.16 2.62 3.46 1.18 6.40 1.01 100.00

0.07 1.24 0.96 0.33 3.77 0.33 75.00

0.29 2.62 8.64 2.84 10.23 3.30 100.00

0.18 1.33 22.07 1.55 7.55 2.23 15.83

341 321 330 52 341 85 168

KAOPEN

ITF ratio

Currency turnoverto-trade ratio

Country turnoverto-trade ratio

Absolute % change in reserve

CAPITAL

0.05 2.06 0.31 2.62 0.51 1.09 1.50 2.58 2.62 0.99 1.89 2.34 0.40 1.19 1.01 2.61 1.99 2.31 0.15 0.20 0.73 2.51 1.09 2.39 2.62 0.05 1.09 2.18 2.62

3.25 7.19 4.19 1.93 4.18 2.51 14.92 13.66 2.31 0.90 1.14 6.30 2.26 0.78 0.52 1.11 35.81 0.92 0.57 7.93 6.45 7.65 1.07 7.72 10.73 1.26 3.74 51.77 19.43

n.a. 3.64 0.36 1.18 n.a. n.a. 0.27 n.a. 0.31 0.26 0.10 3.86 0.39 n.a. 0.46 3.01 1.69 n.a. 0.09 0.43 0.36 0.48 1.73 1.80 4.29 0.17 0.12 2.46 n.a.

0.01 3.60 0.31 0.83 0.53 0.20 0.24 n.a. 0.06 0.29 0.25 2.13 0.37 n.a. 0.36 1.96 0.94 0.15 0.13 0.39 0.84 5.00 1.45 1.28 3.92 0.16 0.21 7.60 n.a.

2.59 9.08 6.64 10.85 2.29 3.43 6.61 2.30 3.28 8.77 5.26 8.05 9.65 1.98 8.18 9.15 8.21 7.26 16.56 4.12 23.74 4.98 12.84 7.70 8.81 3.71 8.59 8.99 5.64

n.a. 75.00 n.a. 89.06 50.00 n.a. 75.00 n.a. 98.30 50.00 75.00 64.58 62.50 62.50 62.50 91.35 100.00 100.00 50.00 n.a. n.a. 100.00 50.00 87.50 98.44 37.50 n.a. 94.79 n.a.

Table 4 Correlations among the explanatory variables. The following table presents the Pearson correlation coefficients among the explanatory variables. For variable description, please refer to Table 3. p-Values are reported in parentheses.

KAOPEN ITF ratio Currency turnover-to-trade ratio Country turnover-to-trade ratio Absolute % change in reserve

ITF ratio

Currency turnover-to-trade ratio

Country turnover-to-trade ratio

Absolute % change in reserve

CAPITAL

0.250 (0.00)

0.450 (0.00) 0.249 (0.07)

0.430 (0.00) 0.675 (0.00) 0.565 (0.00)

0.289 (0.00) 0.119 (0.03) 0.055 (0.70) 0.089 (0.42)

0.493 (0.00) 0.252 (0.00) 0.451 (0.12) 0.107 (0.58) 0.330 (0.00)

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Table 5 Regression analysis of the probability of random walk rejection. This table presents the estimation results from probit model, where the dependent variable equals to one if the random walk in the exchange rate is rejected at the five percent significance level based on M2 and R2, and zero otherwise. M2 is the heteroscedasticity robust, conventional variance-ratio test statistic developed by Lo and MacKinlay (1988), and R2 is the recent modification based on ranks proposed by Wright (2000). The descriptions of the explanatory variables are provided in Table 3. The regressions allow for clustering among observations of the same country, and p-values are reported in parentheses. (1) Panel A: Random walk rejection based on M2 Intercept 0.917 (0.00) KAOPEN 0.225 (0.00) ITF ratio Independently floating dummy

(2)

(3)

(4)

(5)

(6)

(7)

(8)

0.886 (0.00)

0.936 (0.00)

1.287 (0.00)

0.803 (0.00) 0.188 (0.01)

0.783 (0.00) 0.193 (0.01)

0.722 (0.00)

0.738 (0.00)

0.069 (0.01) 0.309 (0.11)

0.068 (0.01)

0.075 (0.01) 0.471 (0.01)

Absolute % change in reserve N Max-rescaled R2

321 0.071

Panel B: Random walk rejection based on R2 Intercept 0.288 (0.01) KAOPEN 0.402 (0.00) ITF ratio Independently floating dummy

321 0.149

0.265 (0.21)

0.307 (0.12) 0.002 (0.87)

0.002 (0.87)

330 0.088

341 0.037

341 0.002

321 0.081

321 0.081

330 0.102

330 0.102

0.365 (0.00)

0.253 (0.07)

1.074 (0.00)

0.100 (0.52) 0.357 (0.00)

0.038 (0.84) 0.324 (0.00)

0.146 (0.38)

0.068 (0.72)

0.115 (0.00) 0.898 (0.00)

0.108 (0.00)

0.114 (0.00) 0.904 (0.00)

Absolute % change in reserve N Max-rescaled R2

0.270 (0.20) 0.006 (0.59)

330 0.112

341 0.085

0.687 (0.00) 0.023 (0.02)

0.765 (0.00)

341 0.018

321 0.192

0.793 (0.00) 0.017 (0.15) 321 0.198

0.028 (0.01) 330 0.172

330 0.194

openness is high. The same is true for ITF ratio in Model 2: the probability of rejecting random walk is lower when investment intensity is higher. The negative coefficients on the independently floating dummy variable in Model 3 in both panels suggest that it is less likely to reject random walk in exchange rates with independently floating exchange rate regime.14 The absolute percentage change in foreign reserve level in Model 4 has the expected positive sign and is significant in Panel B, where we base the decision of rejection/non-rejection of random walk on Wright (2000) test. The difference between the findings in Panels A and B is attributable to the differences in the proportion of rejections and variations in the rejections between Lo and MacKinlay (1988) and Wright (2000) tests. Models 5–8 in both panels of Table 5 present the multivariate regression results of the probability of rejecting random walk. KAOPEN remains significant when we control for other variables in Models 5 and 6 in both panels. Whether a currency is under independently floating exchange rate regime or not has no additional impact on the probability of rejecting random walk once KAOPEN is controlled for when we use Lo and MacKinlay (1988) test, but it stays significant under Wright (2000) test. As for the effect of investment intensity, the estimated coefficients on ITF ratio are all significant and negative in Models 7 and 8 in both panels. Similarly, the independently floating dummy variable stays significant under R2. Moreover, generally speaking, the coefficients on all investment intensity variables and other control variables are larger (in absolute terms) and more significant under Wright (2000) tests than Lo and MacKinlay (1988) tests. Consistent with this, the max-rescaled R2 measure of model fitness is considerably higher with Wright (2000) tests in Panel B than Lo and MacKinlay

(1988) tests in Panel A.15 In unreported regressions, we estimate the probability of rejecting random walk using CTT ratio and find that the coefficients are negative, but insignificant. Overall, the results in Table 5 support our hypothesis that the probability of random walk rejection depends on the degree of investment intensity of currencies. The higher the financial openness and investment intensity, the less likely it is to reject random walk in the exchange rate. However, we are interested not only in random walk rejection, but also the extent of deviation from random walk, which is the focus of the subsequent analysis.

14 In a few cases, we adjust the independently floating rate regime dummy to create a more accurate de facto classification. A country with independently floating regime is reclassified as having managed floating exchange rate regime if the country has an IMF-supported or other monetary program as indicated in the notes of the IMF classification.

15 The estimates from the LPM and probit models for all five binary variables that are generated by using various variance-ratio tests tell a consistent story. Although the magnitudes of the coefficient estimates between LPM and probit models are not directly comparable, they have the same signs and are statistically significant at the five percent level across all regressions.

5.3. Deviation from random walk 5.3.1. KAOPEN In this section, we investigate the link between investment intensity and the deviation from random walk using a broad proxy for investment intensity, KAOPEN index. The dependent variable, deviation from random walk, is measured as the absolute difference between the value of one and the computed variance ratio with a base interval of 1 week and testing interval of 8 weeks (k = 8) using Lo and MacKinlay (1988) and Wright (2000) tests. Table 6 presents the results of OLS regressions of random walk deviation estimated on the pooled panel data under M2 and R2. All the regressions allow for clustering among observations of the same country. All the coefficients have the expected signs in the univariate Models 1–3 in both panels of Table 6. The estimated coefficients on KAOPEN in Model 1 are 0.036 and 0.064 and statistically significant in Panels A and B, respectively. These significant negative coefficients indicate an association of a higher financial openness

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Table 6 Regression analysis of the deviations from random walk: the effect of KAOPEN. The table presents the estimated coefficients of regressions of random walk deviations. Deviation from random walk is measured as the absolute difference between the value of one and the computed variance ratio with k = 8 under M2 in Panel A and R2 in Panel B. M2 is the heteroscedasticity robust, conventional variance-ratio test statistic developed by Lo and MacKinlay (1988), and R2 is the recent modification based on ranks proposed by Wright (2000). The descriptions of the explanatory variables are provided in Table 3. The regressions allow for clustering among observations of the same country. p-Values are reported in parentheses. (1) Panel A: Absolute deviations from random walk with M2 Intercept 0.270 (0.00) KAOPEN 0.036 (0.00) Independently floating dummy

(2)

(3)

(4)

(5)

(6)

0.268 (0.00)

0.198 (0.00)

0.294 (0.00) 0.028 (0.01) 0.054 (0.19)

0.275 (0.00) 0.037 (0.00)

0.001 (0.74)

0.296 (0.00) 0.029 (0.00) 0.054 (0.18) 0.000 (0.88)

0.088 (0.03)

Absolute % change in reserve

0.001 (0.55)

N 321 R2 0.073 Panel B: Absolute deviations from random walk with R2 Intercept 0.295 (0.00) KAOPEN 0.064 (0.00) Independently floating dummy

341 0.052

341 0.002

321 0.090

321 0.074

321 0.090

0.261 (0.00)

0.138 (0.00)

0.325 (0.00) 0.059 (0.00) 0.052 (0.03)

0.264 (0.00) 0.059 (0.00)

0.004 (0.07)

0.293 (0.00) 0.052 (0.00) 0.066 (0.00) 0.004 (0.02)

321 0.216

321 0.237

0.101 (0.00)

Absolute % change in reserve N R2

0.006 (0.00) 321 0.205

341 0.057

with a smaller deviation from random walk, which is consistent with our hypothesis. Countries with independently floating exchange rate regime also display a smaller deviation from random walk as evidenced by the significant negative coefficients of Model 2. This makes intuitive sense as currencies under free-floating exchange rate system cannot be used as a policy instrument and hence should be characterized by ‘‘free” interaction of market participants and their own speculative market. It is also known that these countries do not extensively engage in intervention operations in the foreign exchange market. For example, New Zealand has abstained from official intervention since it adopted the independently floating exchange rate regime in 1985. The intervention proxy that we computed using the foreign reserve level data, i.e., the absolute change in the reserve level, is significant in Panel B with the expected positive sign. We expect a higher level of intervention to distort the exchange rate behavior more and lead to larger deviations from random walk. In the multivariate regressions in Models 4–6, KAOPEN remains significant and negative with coefficients ranging from 0.028 to 0.037 in Panel A and from 0.052 to 0.059 in Panel B. Once we control for KAOPEN, whether the country has independently floating regime or not does not have an additional impact as evidenced by the insignificant coefficients in Panel A. However, the independently floating dummy stays significant under Wright (2000) tests. The R2 of the multivariate regressions ranges from 0.074 to 0.090 in Panel A and from 0.216 to 0.237 in Panel B. This is consistent with the findings from Table 5 that using Wright (2000) tests tends to provide stronger results and greater explanatory power. The results of the regressions in both panels of Table 6 clearly suggest that exchange rates adhere more closely to random walk when the level of financial openness is high. This is consistent with the hypothesis that capital openness is associated with increased capital flow and consequently, with more random walk like behavior in the exchange rate. 5.3.2. ITF ratio We shift our focus to the investment-to-trade flow (ITF) ratio that is specifically designed to measure investment intensity. ITF

341 0.053

321 0.219

ratio measures the size of investment flow between a foreign country and the US relative to that of trade flow. The results of the estimated OLS regressions of random walk deviation on ITF ratio are presented in Table 7. As Model 1 shows, the ITF ratio has statistically significant and negative coefficient estimates under both measures of deviation from random walk. The negative sign of the coefficient is consistent with our conjecture that a higher

Table 7 Regression analysis of the deviations from random walk: the effect of ITF ratio. The table presents the estimated coefficients of regressions of random walk deviations. Deviation from random walk is measured as the absolute difference between the value of one and the computed variance ratio with k = 8 under M2 in Panel A and R2 in Panel B. M2 is the heteroscedasticity robust, conventional variance-ratio test statistic developed by Lo and MacKinlay (1988), and R2 is the recent modification based on ranks proposed by Wright (2000). The descriptions of the explanatory variables are provided in Table 3. The regressions allow for clustering among observations of the same country. p-Values are reported in parentheses. (1) Panel A: Absolute deviations from random walk Intercept 0.220 (0.00) ITF ratio 0.001 (0.02) Independently floating dummy

(2) with M2 0.271 (0.00) 0.001 (0.14) 0.078 (0.06)

(3)

(4)

0.212 (0.00) 0.001 (0.04)

Absolute % change in reserve

0.001 (0.60)

0.263 (0.00) 0.001 (0.18) 0.078 (0.06) 0.001 (0.58)

N 330 330 R2 0.014 0.054 Panel B: Absolute deviation from random walk with R2 Intercept 0.205 0.266 (0.00) (0.00) ITF ratio 0.002 0.001 (0.00) (0.00) Independently floating dummy 0.087 (0.00) Absolute % change in reserve

330 0.016

330 0.056

0.157 (0.00) 0.001 (0.00)

0.005 (0.00)

0.223 (0.00) 0.001 (0.00) 0.104 (0.00) 0.006 (0.00)

N R2

330 0.083

330 0.140

330 0.035

330 0.076

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Table 8 Regression analysis of the deviations from random walk: the effect of CTT ratio. The table presents the estimated coefficients of regressions of random walk deviations. Deviation from random walk is measured as the absolute difference between the value of one and the computed variance ratio with k = 8 under M2 in Panel A and R2 in Panel B. M2 is the heteroscedasticity robust, conventional variance-ratio test statistic developed by Lo and MacKinlay (1988), and R2 is the recent modification based on ranks proposed by Wright (2000). The descriptions of the explanatory variables are provided in Table 3. The regressions allow for clustering among observations of the same country. p-Values are reported in parentheses. (1) Panel A: Absolute deviations from random walk Intercept 0.237 (0.00) CTT ratio 0.036 (0.01) Independently floating dummy

(2) with M2 0.272 (0.00) 0.025 (0.06) 0.073 (0.27)

Absolute % change in reserve N R2

52 0.132

Panel B: Absolute deviations from random walk Intercept 0.222 (0.00) CTT ratio 0.045 (0.00) Independently floating dummy

52 0.164 with R2 0.286 (0.00) 0.028 (0.00) 0.119 (0.09)

Absolute % change in reserve N R2

52 0.207

52 0.292

(3)

(4)

0.234 (0.00) 0.036 (0.01)

0.001 (0.84)

0.271 (0.00) 0.025 (0.05) 0.073 (0.28) 0.000 (0.97)

52 0.133

52 0.164

0.187 (0.00) 0.046 (0.00)

0.006 (0.29)

0.251 (0.00) 0.030 (0.01) 0.109 (0.11) 0.005 (0.31)

52 0.256

52 0.326

investment intensity leads to a smaller deviation from random walk. However, the significance of the estimated coefficient disappears when we control for the independently floating exchange regime dummy in Models 2 and 4 in Panel A while it stays statistically significant in Panel B. The intervention proxy is positive and insignificant in Panel A, while it is statistically significant in Panel B. Again, Wright (2000) test tends to provide much stronger results both in terms of precision of estimates as well as the magnitude of coefficients. Consistent with this, R2 values are higher when we use Wright (2000) test. Overall, the results in Table 7 indicate that when the size of investment flow relative to trade flow is larger, the exchange rate adheres to random walk more closely. 5.3.3. CTT ratio Using the alternative measure of investment intensity that is based on foreign exchange turnover data, we re-investigate the impact of investment intensity on the deviation from random walk in Table 8. Currency turnover-to-trade (CTT) ratio refers to the annualized foreign exchange turnover of a currency divided by the sum of total exports and imports of the corresponding country. As the regression results of Table 8 indicate, CTT ratio has significant negative coefficients that range from 0.025 to 0.036 in Panel A and from 0.028 to 0.046 in Panel B. Thus, the higher the level of investment intensity, the more closely the exchange rate follows random walk. These regressions that use the multilateral measure of investment intensity produce much stronger results than those based on bilateral measures. All the other variables are insignificant at the 5% level, although they display the expected coefficient signs. However, it should be noted that we use a much smaller number of observations in these regressions than those in the previous analysis because foreign exchange turnover data are obtained from the BIS surveys that have been conducted only triennially since 1989.

Table 9 Regression analysis of threshold effects. The estimated model is, yi ¼ b0 þ b1 xi;1 Iðqi 6 cÞ þ b1 xi;1 Iðqi > cÞ þ h x2 þ ui , where x1 = {KAOPEN, ITF, CTT}, I() is the indicator function, c the threshold parameter, and x2 a vector of control variables including a dummy variable for the floating exchange rate regime and absolute percentage change in reserve level, and q is the threshold variable. The dependent variable is the absolute deviation of variance ratio from one, where the variance ratios are computed with R2. R2 is the recent modification to the conventional variance ratios based on ranks proposed by Wright (2000). In Panel A, LM1 and LM2 are the Lagrange multiplier tests for the presence of one and two thresholds according to Hansen (2000), respectively. The p-values are reported in parentheses. In Panel B, values in parentheses underneath the coefficient estimates are the bootstrapped standard errors while the values in square brackets are the bootstrapped 95% confidence intervals. R21 and R22 are the R2s for the regimes below and above the estimated thresholds, respectively. Similarly, n1 and n2 are the sample sizes in each regime. See Table 3 for variable definitions. Threshold variable

ITF

CTT

Panel A: Tests for threshold effects Test for a single 15.644 threshold, LM1 (0.01) Test for double 5.352 thresholds, LM2 (0.31)

15.201 (0.01) 5.662 (0.31)

9.957 (0.14) 6.269 (0.44)

Panel B: Threshold regression results ^1 0.065 b (0.032) [0.13, 0.01] ^ 0.031 b 1 (0.025) [0.08, 0.07] ^c 1.243 [1.02, 1.73]

0.022 (0.007) [0.004, 0.006] 0.000 (0.000) [0.001, 0.000] 12.338 [6.42, 19.93]

2.607 (0.438) [3.66, 0.91] 0.007 (0.015) [0.02, 0.04] 0.325 [0.27, 0.35]

(281, 49) (0.13, 0.17)

(13, 39) (0.61, 0.17)

(n1, n2) ðR21 ; R22 Þ

KAOPEN

(105, 216) (0.20, 0.12)

5.3.4. Threshold effect in deviation from random walk As previously mentioned, the effect of investment intensity on the exchange rate may not be linear. Thus, we study threshold effects in the relation between investment intensity and the deviation from random walk in this subsection. In other words, we investigate whether there is a level of investment intensity below which the relation between our measures of investment intensity and the deviation from random walk is more pronounced than it is above such a threshold. It seems plausible that investment intensity matters more at some levels than others since the characteristics of a currency may change as its investment intensity changes. In order to study threshold effects, we utilize the threshold regression (TR) model proposed by Hansen (2000), which is discussed in Appendix B. Panel A of Table 9 reports the test results for a single and double threshold effects in the deviations from random walk using R2.16 Bootstrap p-values suggest the presence of a single threshold effect when KAOPEN and ITF are used as the threshold variable. On the other hand, the results suggest no threshold effects when CTT is used as the threshold variable. One issue with respect to CTT is that we only have 52 observations and thus, tests may fail to detect any threshold effect due to the small sample size. Nevertheless, we report the estimated TR model results for CTT in Panel B for completeness. In Panel B of Table 9, we report the estimated results from the threshold models. When KAOPEN is used as the threshold variable, the results show that there is a statistically significant threshold effect: whenever KAOPEN falls below the estimated threshold level of 1.243, the effect of investment intensity is significantly greater (with the 95% interval estimate that ranges between 0.13 and 0.01) than when KAOPEN exceeds the estimated threshold level. In fact, the effect of KAOPEN on the deviation from random walk 16 Findings from the estimated threshold models using M2 are very similar to those reported in Table 9 and can be obtained upon request.

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becomes insignificant above the estimated threshold level as the 95% confidence interval contains zero. As for the ITF tests, the estimation results suggest the presence of a threshold effect as well. The estimated threshold value is 12.338. The results show that the impact of changes in ITF is pronounced and significant when the ITF ratio is below the estimated threshold, whereas it is insignificant when the ITF ratio is above the threshold. Although the tests for threshold effects in Panel A do not show any evidence of threshold effects for CTT, the reported findings in Panel B show that the estimated slope coefficient below the threshold level of 0.325 is negative and statistically different from zero (i.e., 2.607), while it is insignificant above the threshold level for CTT (i.e., 0.007).

Table 11 Logistic smooth transition threshold regression results. This table presents the summary of estimation and diagnostic tests for Logistic Smooth Transition Regression (LSTR) model. The estimated LSTR model is, yi ¼ b0 þ b1 xi;1 ð1  Fðqi ; c; cÞÞþ b1 xi;1 Fðqi ; c; cÞ þ h x2 þ ui , where Fðqi ; c; cÞ ¼ ð1=ð1 þ expðcðqi  cÞÞÞÞ is the logistic transition function, q is the transition variable, c > 0 is a slope parameter (or the transition parameter) that characterizes the speed of transition across regimes, and c is a location parameter (or the threshold parameter). p_RNL and p_C are the p-values for testing remaining nonlinearity of logistic form in the residuals of the estimated models and for testing parameter constancy, see Teräsvirta (2004). SSRL/SSRSTR is the ratios of residual sum of squares from the linear regression and the LSTR models. The values in parentheses underneath the coefficient estimates are the heteroscedasticity robust standard errors. The values in squared brackets are the 95% confidence intervals. Transition variable

KAOPEN

ITF

CTT

^1 b

0.090 (0.034) [0.17, 0.02] 0.021 (0.014) [0.05, 0.06] 6.081 (3.096) 1.190 (0.405)

0.022 (0.006) [0.03, 0.01] 0.001 (0.000) [0.002, 0.000] 2.802 (10.665) 10.447 (0.691)

2.613 (0.758) [4.09, 1.13] 0.074 (0.024) [0.18, 0.01] 1.193 (0.581) 0.146 (0.118)

0.144 0.240 0.905

0.939 0.198 0.917

0.998 0.523 0.733

6. Robustness tests Since KAOPEN is one proxy for financial openness, we repeat the regression analysis with an alternative proxy for financial openness, CAPITAL, developed by Quinn (1997) and Quinn and Toyoda (2008) as a robustness check in Panels A and B of Table 10. The latter proxy attempts to measure capital account openness and ranges from 0 to 100. As the results in Table 10 show, the CAPITAL index has significant and negative estimated coefficients as KAOPEN, in both Panels A and B. All the other variables including the independently floating regime dummy are insignificant. The results are qualitatively similar to those of KAOPEN. Hence, the financial openness results remain robust to alternative proxy. In unreported regressions, we repeat the previous regressions using the variance ratios computed over rolling four-year periods and also with different testing intervals (k) such as 2-, 4- and 16weeks. We also re-estimate the regressions using the logs of the absolute deviations. Furthermore, we repeat the regression analysis with ‘country’ turnover-to-trade ratio. Lagged explanatory variables instead of contemporaneous ones are used in the regression

Table 10 Regression analysis of the deviations from random walk: the effect of CAPITAL. The table presents the estimated coefficients of regressions on random walk deviations. Deviation from random walk is measured as the absolute difference between the value of one and the computed variance ratio with k = 8 under M2 in Panel A and under R2 in Panel B. M2 is the heteroscedasticity robust, conventional variance-ratio test statistic developed by Lo and MacKinlay (1988), and R2 is the recent modification based on ranks proposed by Wright (2000). The descriptions of the explanatory variables are provided in Table 3. The regressions allow for clustering among observations of the same country. p-Values are reported in parentheses. (1) Panel A: Absolute deviations from random walk Intercept 0.588 (0.00) CAPITAL 0.005 (0.03) Independently floating dummy

(2) with M2 0.538 (0.00) 0.005 (0.02) 0.064 (0.50)

Absolute % change in reserve N R2

168 0.198

Panel B: Absolute deviations from random walk Intercept 0.693 (0.00) CAPITAL 0.006 (0.00) Independently floating dummy

168 0.204 with R2 0.708 (0.00) 0.006 (0.00) 0.016 (0.82)

Absolute % change in reserve N R2

168 0.301

168 0.302

(3)

(4)

0.614 (0.00) 0.005 (0.03)

0.001 (0.53)

0.564 (0.00) 0.005 (0.02) 0.066 (0.48) 0.001 (0.50)

168 0.200

168 0.207

0.663 (0.00) 0.006 (0.00)

0.001 (0.55)

0.682 (0.00) 0.006 (0.00) 0.021 (0.77) 0.001 (0.53)

168 0.304

168 0.305

^ b 1

c^1 ^c p_RNL p_C SSRL/SSRSTR

analysis as an alternative. We also compute the moving averages of the explanatory variables over rolling 5-year periods and repeat the analysis with these variables. Finally, all the regressions of the deviations from random walk are re-estimated using only the deviations that are statistically significantly different from zero. We find that all the results remain qualitatively the same with the implementation of these alternative specifications described above. As a result, we conclude that the rejection of random walk and the deviations from random walk in the exchange rate depend on the investment intensity of currencies. Ideally, it would be useful to take into account the cross-country heterogeneity across 29 countries that we have in our sample. An appropriate tool for this purpose would be the Panel Smooth Transition Regression (PSTR) model suggested by Gonzalez et al. (2005) or the Panel Transition Regression Model (PTR) model suggested by Hansen (1999). As pointed out in Hansen (1999), PTR model is developed for balanced panel data. Similarly, the PSTR model needs balanced panel data. However, our data are unbalanced, as we include currencies in our sample only when they are under the floating exchange rate regime. Given the limitation of the data, we adopt the Smooth Transition Autoregressive (STAR) model and estimate a Logistic Smooth Transition Regression (LSTR). The LSTR model is based on the STAR model of Granger and Teräsvirta (1993) and the PSTR model of Gonzalez et al. (2005). A detailed description of the LSTR model is provided in Appendix B.17 Summary of estimation and diagnostic test results for the LSTR model is reported in Table 11. The estimated transition parameters (c) are statistically significant. Note, however, that strictly speaking, t-statistic is not valid, since under the null hypothesis of c = 0, b1 ; b1 and c are not identified. The estimates of the transition function indicate some variations in the speed of transition between extreme regimes, as the estimate for KAOPEN is much larger than those for ITF and CTT. This suggests that the speed at which investment intensity affects the deviations from random 17 To the best of our knowledge, this is the first paper that estimates a smooth transition regression model (STAR) in a pooled sample of cross-sectional data. Most of the applications of smooth transition models are primarily in time series context. Note also that the LSTR model is very similar to PSTR model with a single time period.

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walk may vary, depending on the transition variable used. The estimated threshold parameters for KAOPEN, ITF, and CTT are statistically significant and considerably close to the estimates from the single threshold model reported in Panel B of Table 9. The results also suggest that whenever KAOPEN, ITF and CTT fall below the estimated threshold values, the relation between the investment intensity and the deviations from random walk becomes more pronounced. As the investment intensity exceeds the estimated threshold levels, the effect of a currency’s investment intensity on the random walk behavior tends to be weaker in all the estimated models.18

Yearbooks and IMF’s Annual Reports on Exchange Arrangement and Exchange Restrictions (AREAER). Currency

Start date

Notes

Argentine peso

01/11/2002

Until 2002 – pegged exchange rate system From 01/11/2002 – managed floating exchange rate

Australian dollar

12/12/1983

1945–1973 – fixed exchange rate system 1974–1976 – exchange rate pegged to trade-weighted index 1976–1983 – crawling peg system linked to a basket of about 20 currencies From 12/12/1983 – independently floating exchange rate

Brazilian real 02/01/1999

1967–1990 – crawling peg system 1990–1995 – floating exchange rate system 1990–1993 – Cruzeiro is used as legal currency 1993–1994 – Cruzeiro Real is used as legal currency From 1994 – Real is used as legal currency 1995–1999 – quasi fixed system with a band From 02/01/1999 – independently floating exchange rate

Canadian dollar

01/01/1974

Independently floating exchange rate

Chilean peso 01/24/1997

Until 1985 – pegged exchange rate system 1985–1997 – exchange rate within a band, which was widened over time 01/24/1997 to 09/02/1999 – managed floating exchange rate From 09/02/1999 – independently floating exchange rate

Colombian peso

09/25/1999

1967–1994 – crawling peg system 1994–1999 – crawling peg with a fairly large band From 09/02/1999 – managed floating exchange rate

Czech koruna 05/26/1997

02/08/1993 – separate Czech and Slovak currencies were introduced 1991–1997 – exchange rate within a band against a basket of currencies From 05/26/1997 – independently floating exchange rate

7. Conclusions This paper examines the cross-currency and temporal variations in the random walk behavior in exchange rates. In particular, we investigate the effects of the investment intensity of currencies on the probability of rejecting random walk and the extent of the deviations from random walk, using 29 floating bilateral USD exchange rates. We hypothesize that the more investment intensive a currency is, the closer its exchange rate adheres to random walk and the smaller the deviation from random walk is. The variance ratio is used to measure the random walk behavior. Our findings show that the rejection of random walk and the deviations from random walk in the exchange rate depend on the investment intensity of currencies. We use financial openness index (KAOPEN), investment-to-trade flow ratio (ITF), and currency turnover-to-trade ratio (CTT) to proxy for the investment intensity of currencies. The results show that the higher the investment intensity, the less likely it is to reject random walk. Our results also show that exchange rates adhere more closely to random walk when the level of investment intensity is high. However, this effect is non-monotonic. Using threshold regression models, we uncovered the presence of threshold effects in the relation between the deviations from random walk and the investment intensity. For KAOPEN, ITF and to some extent, CTT values that are higher than the threshold levels, the investment intensity has little or no effect on the deviations from random walk. These results are robust to alternative specifications and measurements. Overall, the contributions of our paper are twofold. First, our findings help reconcile the conflicting empirical findings of the previous studies on random walk. Previous works mainly focus on the bivariate outcome of rejection or non-rejection of random walk. We document the cross-currency and temporal variations in the random walk behavior in the exchange rate and relate the variations to the different levels of investment intensity among currencies. Second, we introduce various measures of investment intensity, such as investment-to-trade flow ratio and currency turnover-to-trade ratio to examine the exchange rate behavior. An important implication that emerges from our findings is that exchange rates would follow random walk more closely in the future, as more countries open their capital markets leading to increased investment flows.

Appendix A. Sample currencies The following table presents the list of all currencies used in our analysis. A currency is included in our sample only when it is under the floating exchange rate regime. Start date refers to the date when the country switched to the floating exchange rate regime, either managed or independent, as defined in the World Currency 18 We have estimated the LSTR model using M2. Findings are qualitatively similar to those reported in Table 11.

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Appendix A (continued)

Appendix A (continued)

Currency

Start date

Notes

Currency

Start date

Notes

Euro

01/01/1999

Peruvian nuevo sol

07/01/1991

Deutsche mark

06/06/1979 to 12/31/ 1998

Independently floating exchange rate Independently floating exchange rate

Until 1989 – fixed exchange rate 1989–1990 – crawling peg 08/08/1990 to present – managed floating exchange rate From 07/01/1991 – Sol replaced Inti as the legal currency

Philippine peso

10/10/1984

10/10/1984 to 03/15/1998 – managed floating exchange rate From 03/15/1998 – independently floating exchange rate

Polish zloty

04/12/2000

1991–2000 – crawling peg From 04/12/2000 – independently floating exchange rate

Indian rupee 03/01/1993

Indonesian rupiah

03/31/1989

1947–1975 – pegged to UK pound 1975–1993 – exchange rate within a band linked to a basket of currencies From 03/01/1993 – managed floating exchange rate 03/31/1989 to 08/14/1997 – managed floating exchange rate From 08/14/1997 – independently floating exchange rate

Japanese yen 01/01/1974

Independently floating exchange rate

Korean won

1964–1980 – exchange rate pegged to USD 1980–1997 – crawling peg system linked to a basket of currencies 1989–1997 – exchange rate was allowed to fluctuate within a narrow band that widened over time From 12/16/1997 – independently floating exchange rate

Malaysian ringgit

Mexican peso

12/16/1997

04/01/1993 to 09/02/ 1998

1975–1993 – pegged exchange rate 04/01/1993 to 09/02/1998 – managed floating regime 09/02/1998 to 07/21/2005 – pegged exchange rate From 07/21/2005 – managed floating exchange rate

12/22/1994

1976–1993 – crawling peg system From 12/22/1994 – independently floating exchange rate

New Zealand 03/04/1985 dollar

1973–1985 – exchange rate linked to a basket of currencies From 03/04/1985 – independently floating exchange rate

Norwegian krone

Until 1990 – pegged to a basket of currencies 10/22/1990 to 12/1/1992 – pegged to ECU From 12/10/1992 – independently floating exchange rate

10/22/1990

Russian 09/09/1998 Federation rouble

1995–1999 – corridor system 01/01/1998 – currency redenomination (1 new = 1000 old) From 09/09/1998 – managed floating exchange rate

Singaporean 01/01/1985 dollar

1973–1985 – pegged exchange rate system From 1985 – managed floating exchange rate

South African 03/02/1995 rand

03/02/1995 – two exchange rates were unified Independently floating exchange rate

Swedish krona

05/17/1991

1977–1991 – pegged to a basket of currencies 05/17/1991 to 11/19/1992 – pegged to ECU From 11/19/1992 – independently floating exchange rate

Swiss franc

01/01/1974

Independently floating exchange rate

Thai baht

07/02/1997

1978–1997 – pegged to a basket of currencies From 07/02/1997 – managed floating exchange rate

Turkish lira

02/22/2001

Until 2001 – crawling peg against a basket of currencies From 02/22/2001 – independently floating exchange rate

UK sterling pound

01/01/1974

Independently floating exchange rate

Uruguayan peso

06/19/2002

Until 2002 – exchange rate within an adjustable band From 06/19/2002 – independently floating exchange rate

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Appendix B. Variance-ratio tests and threshold models B.1. Variance-ratio tests Suppose yt is a time series of asset returns with a sample size T. PT 1 ^ Þ2 ðyt þyt1 þþytk kl (where Defining the variance ratio as VR ¼ Tk t¼kþ11PT 2

l^ ¼ 1T

T

PT

t¼1

^Þ ðyt l

t¼1 yt and k is a factor of asset holding period), Lo and MacK 12 is inlay (1988) show that the statistic, M 1 ¼ ðVR  1Þ 2ð2k1Þðk1Þ 3kT

asymptotically standard normal under the null of random walk. Furthermore, if yt exhibits conditional heteroscedasticity, the ro 12 Pk1 h2ðkjÞi2 bust test statistic, M 1 ¼ ðVR  1Þ d , where j j¼1 k P T 1 ^ Þ2 ðyt l , is also asymptotically standard normal under dj ¼ Tk1Pt¼kþ1 T 2 T

t¼1

^Þ ðyt l

the null. Based on Lo and MacKinlay (1988), Wright (2000) proposed three alternative variance-ratio tests using ranks and signs. Letting rt(yt) be the rank of yt among the time series, and defining   rðyt ÞTþ1 tÞ 2 ffi , with U being the standard norand r 2t ¼ U1 rðy r1t ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffi Tþ1 ðT1ÞðTþ1Þ 12

mal cumulative distribution, Wright’s (2000) rank-based tests substitute r1t and r2t in place of yt in the definitions of R1 and R2 test statistics above. The rank-based variance-ratio test statistics denoted by R1 and R2 are defined as

R1 ¼

1 Tk

PT

t¼kþ1 ðr 1t

þ r 1t1 þ    þ r1tk Þ2 PT 2 1 t¼1 r 1t T

! 1 2ð2k  1Þðk  1Þ 2 ; 3kT

þ r 2t1 þ    þ r2tk Þ2 PT 2 1 t¼1 r 2t T

! 1 2ð2k  1Þðk  1Þ 2 : 3kT

and

R2 ¼

1 Tk

PT

t¼kþ1 ðr 2t

If we let s1t = 2u(yt, 0), with the function u(yt, q) = 1(xt > q)  0.5, the sign-based variance ratio statistic using st is defined as

S1 ¼

1 Tk

PT

t¼kþ1 ðs1t

þ s1t1 þ    þ s1tk Þ2 PT 2 1 t¼1 s1t T

! 1 2ð2k  1Þðk  1Þ 2 : 3kT

Under the random walk null, Wright (2000) shows that the exact sampling distributions of R1, R2, and S1, can be simulated to an arbitrary degree of accuracy for different choices of T and k. Monte Carlo experiments performed by Wright (2000) shows that rank-based tests, R1, and R2, are generally more powerful than the conventional Lo and MacKinlay variance-ratio tests, M1, and M2. B.2. Threshold regression model and Logistic Smooth Transition Regression model Given the observed sample of size n, fyi ; xi ; qi gni¼1 , where y and q are real-valued scalars and x is a k-vector, the threshold model we estimate in this paper takes the form,

yi ¼ b0 þ b1 xi;1 Iðqi 6 cÞ þ b1 xi;1 Iðqi > cÞ þ h0 x2 þ ui ;

there). Since under the null of no threshold effects (i.e., b1 ¼ b1 ), the threshold parameters are not identified, the asymptotic critical values for the LM test are not valid. Therefore, we compute p-values for the LM tests by a bootstrap method discussed in Hansen (2000). We use 1000 bootstrap replications in computing the p-values. We estimate the threshold models by using the (concentrated) least squares method discussed in Hansen (2000), where the optimization of the objective function is done over a grid search for the threshold parameter and the quintiles of the threshold variable are used in constructing the grid search. The Logistic Smooth Transition Regression (LSTR) model we estimate in this paper takes the form,

yi ¼ b0 þ b1 xi;1 ð1  Fðqi ; c; cÞÞ þ b1 xi;1 Fðqi ; c; cÞ þ h0 x2 þ ui ;

ðB:2Þ

where F(qi; c, c) = (1/(1 + exp(c(qi  c)))) is the logistic transition function, c a slope parameter (or the transition parameter) that characterizes the speed of transition across regimes, and c a location parameter (or the threshold parameter). The parameter restriction c > 0 is an identifying restriction. The transition function 0 6 F(qi; c, c) 6 1 is bounded between 0 and 1 by construction. The threshold variable, q, is called the transition variable. The transition variable, q, characterizes the transition and hence, the relationship between investment intensity of a currency and its deviation from random walk. Note that in the Smooth Transition Autoregressive (STAR) models (Granger and Teräsvirta, 1993), a time series process smoothly evolves or adjusts to an equilibrium relationship in a nonlinear fashion, where the nature of the nonlinear dynamics is governed by the past values of a predetermined (endogenous) variable called the transition variable. Indeed, the adjustment process in the STAR model (and the LSTP model we consider in this paper) occurs for each value of the transition variable and the speed of adjustment is governed by the values of a transition variable and the transition parameter, which measures the speed of transition across various regimes. The logistic function is bounded between 0 and 1. The logistic transition function approaches to zero for very large negative values of transition variable, i.e., as qi ! 1; FðÞ ! 0 and as qi ! þ1; FðÞ ! 1 and whenever the transition variable is in the neighborhood of the threshold parameter c, it takes on the value of 0.5. Note also that when c ! 1, the logistic transition function becomes a step function (the indicator function given in Eq. (B.1) above, i.e., I()), such that the LSTR model becomes effectively a threshold model. Therefore, the LSTR model nests a two-regime threshold model given in Eq. (B.1). Since we have only one candidate variable for a transition variable and function in this application, we follow Teräsvirta (2004) and estimate LSTR model and use diagnostic tests for remaining nonlinearity and parameter constancy in the estimated models by using the tests discussed in Teräsvirta (2004). We use nonlinear least squares estimation in estimating the parameters of the model in Eq. (B.2). References

ðB:1Þ

where x1 = {KAOPEN, ITF, CTT}, I() is the indicator function, c is the threshold parameter, and x2 is a vector of control variables including a dummy variable for the floating exchange rate regime and absolute percentage change in reserve level. For the threshold variable, q, we use x1 = {KAOPEN, ITF, CTT}. This model allows the effect of investment intensity on the deviations from random walk to differ depending on the value of the threshold variable q. We follow Hansen (2000) in specifying and estimating the threshold models. First, we test for threshold effects by using Lagrange multiplier (LM) tests (see Hansen (2000) and the references

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