Research Article
Effects of Central Banks' Interference on Speculative Build-up in the Foreign Exchange Markets
CBA, Department of Finance, California State University, Sacramento, 6000 J Street, Sacramento, CA, 95819-6088, California
This study examines a question of whether central banks interventions at the FX markets act as significant determinants of the probability of experiencing extreme fluctuations in the exchange rates. The study focuses on the extreme deviations of the exchange rates from the values supported by the fundamentals and develops an application of the Cox proportional hazard test to investigate this relation. The Cox proportional hazard test, also known as the partial likelihood test, is one of the methods of the survival analysis that allows examining how different variables contribute to the probability of the event either persisting or ending. Several previous studies suggest that central banks operations can affect both the level and volatility of the exchange rates (Dominguez, 1998, 2003; Barnhart et al., 2007; Beine et al., 2006; Kim et al., 2000). However, empirical studies of the relationship to date are inconclusive due to several reasons. First, predicting the exchange rate value themselves can be impossible due to the incomplete FX markets with multiple fundamental values. Second, no single model of exchange rate equilibrium has been accepted as universal. Third, direct statistical tests of detecting the presence of a speculative deviation before it reverses do not appear feasible either due to lack of necessary data or lack of suitable statistical methodology. Due to the limitations listed above the analysis of this study focuses on the event studies of the time around extreme exchange rate deviations (i.e., +/-2 SD) away from the historical average values and the time of their convergence.
The unexpected extreme fluctuations in the exchange rates are equally risky for practitioners (investors and producers alike) and government agencies and would be avoided if they were predictable. As stated in the Federal Reserve Bank of New York in 2007 report on U.S. foreign exchange intervention: Foreign exchange rates are of particular concern to governments because changes in FX rates affect the value of products and financial instruments. As a result, unexpected or large changes can affect the health of nations markets and financial systems. Exchange rate changes also impact a nations international investment flow, as well as export and import prices. These factors, in turn, can influence inflation and economic growth. Exchange rates level and volatility are essential in determining the investment flow, overall prices, production and foreign trade dynamics. For example, a research by Sahin and Sahin (2014) shows that for exporting manufacturing firms increase in exchange rate will increase the costs and may diminish their profits on an example of Turkish economy.
The US Federal Reserve Bank describes four different reasons for its interventions in the foreign exchange markets: (1) To influence trend movements in exchange rates, (2) To calm disorderly markets, (3) To rebalance its foreign exchange reserve holdings and (4) To support fellow central banks in their exchange rate operations. Unfortunately, at the time of the intervention, US Federal Reserve Bank does not specify which one of the four reasons listed above was the intended purpose of that particular intervention.
The scope of the international foreign exchange markets is such that the average amount of intervention is dwarfed in comparison: An equivalent of about $5.3 trillion is traded daily around the world (MED., 2013). Out of this amount, it is estimated that less than 2% is motivated by merchandise trade and the majority of daily operations are carried out as arbitrage, money management and speculative activities (Baillie and Osterberg, 1997). Governments often do attempt to manipulate the value of their countrys currency but the level of daily FX transactions is greater than 30% of the US annual GNP. Consequently, even the US or any other foreign government would not intervene on the FX market to the extent of effectively shifting the supply and demand for the particular currency. It is commonly stated by the US Federal Reserve Bank that the aim of the interventions is to signal to the market participants the intended direction of the countries monetary policy. Market reactions to the announced government interventions seem to support the signaling hypothesis.
As noted by Edison (1993): Exchange market participants appear to believe that central bank intervention is important and that they therefore react to news of intervention. No commonly accepted method has been developed to estimate the effectiveness of government interventions on the FX markets (Nanto, 2007). Previous study has used time-series analysis, bi-power variation method, regression based event studies, VAR, probit and ligit, GARCH, second-moment and option pricing models. Since this question has not been settled in the finance literature, new analytical approach to look at the effects of the interventions on the exchange rates would be of interest. Hence, we have focused on new ways to examine the interconnection between government interventions and speculative build up in the FX markets by developing an application of the Cox proportional hazard rate test.
A number of past empirical studies address various aspects of the relationship between Central Banks interventions at the FX markets and the exchange rates. Studies that investigate the effects of the intervention on the level of exchange rates do not find the significant impact (Dominguez, 1998), though Barnhart et al. (2007) find stronger impact on the exchange rates from the coordinated interventions by central banks of three or more industrialized countries as opposed to single bank actions. Similarly, Beine et al. (2006) find that coordinated interventions have stronger association with exchange rate volatility than unilateral interventions. Studies that investigate the impact of the interventions on the volatility of exchange rates have reported conflicting results. Even though most studies conclude that interventions tend to increase the exchange rate volatility (Humpage, 2003; Beine et al., 2006; Dominguez, 1998, 2003; Kim et al., 2000), there exists some disagreement on whether interventions cause higher volatility or react to it. For example, Beine et al. (2006) study finds that interventions tend to create jumps in the exchange rate volatility, Dominguez (1998) study, on the other hand, finds that only secret interventions increase volatility while effects of the reported interventions on the exchange rate volatility depend on the central bank involved, the currency and the historical time period (decrease in volatility is found for the time period between Plaza Agreement and the Louvre Accord but increase is found in the post Louvre Accord period). Cai et al. (2001) results differentiate between central bank purchases and sales of the currency and finds that purchases are associated with higher volatility and sales with lower volatility. Kim (2003), on the other hand, finds evidence that interventions tend to stabilize foreign exchange rates.
In the literature review of the central banks interventions and their effects on the exchange rates, Edison (1993) concludes that existing models and the quality of the available data may not be sophisticated enough to resolve properly the questions asked. More recently in response to this shortcoming, a large body of literature has emerged that uses intraday data of foreign exchange market transactions to investigate the effects of the interventions. These studies find that foreign exchange markets do react to the interventions (Peiers, 1997; Evans, 2002; Evans and Lyons, 2002; Lyons, 1995; Dominguez, 2006).
Studies of crashes and speculative bubbles have prompted an emergence of a large body of literature, both theoretical and empirical, that tries to reconcile the exchange rates Purchasing Power Parity puzzle by concentrating on the non-linearity of the exchange rate movements (Taylor and Peel, 2000; Kilian and Taylor, 2001; Taylor et al., 2001). As noted by Taylor et al. (2001), the idea that there may be nonlinearities in real exchange rate adjustment appears in academic literature as early as 1916 with the publication by Heckscher. Studies by Kilian and Taylor (2001), Taylor and Peel (2000) and Taylor et al. (2001) have shown that linear forecast models are likely to be fundamentally miss-specified. The nonlinear models of exchange rate adjustment generally point that small deviations from the fundamentals are likely to be considered unimportant by market participants or the marginal cost of arbitrage exceeds the marginal benefit but once exchange rates move outside the threshold distance from the fundamentals, the speed of adjustment and the strength of the link between exchange rates and their fundamental values increases nonlinearly, hence the exchange rates path appears random when exchange rates are close to the fundamentals equilibrium.
The objective of this study is to develop an application of the Cox Proportional Hazard Test that might be better suited to capture the non-linear nature underlying the exchange rates adjustment processes and that is flexible to allow for the non-parametric nature of the exchange rate movements. The study strives to contribute to the understanding of the foreign exchange markets reactions to the interventions by the central banks.
The model developed in this study assumes that all agents are boundedly rational and apply the best possible strategy within their confined ability to use the limited information available to them. The idea of non-linearity of the data distribution during extreme economic events addresses by investigating the fluctuation in exchange rates with the Cox regression which allows the underlying distribution to vary for two subsets of data: For time intervals of normal vs., extreme behavior in the exchange rates. It also has been recognized in several research studies (MacDonald and Nagayasu, 1999; Osler, 2005) that exchange rates are not known to fit any parametric distribution and a statistical method that can explicitly account for the time dynamics in the exchange rates might be better suited than static one. The methodology developed by Cox (1972) utilizes a semi-parametric approach of data analysis.
Survival analysis is a class of statistical methods that originally received wide application in medicine and was aimed at determining the probability and the speed of the patients recovery based on his/her personal characteristics. The attractive statistical features of the Cox regression long have been recognized by economists and applied to numerous studies of unemployment spells, bank failures and bankruptcies (Lancaster, 1979; Kiefer, 1988; Shumway, 1999; Wheelock and Wilson, 2000; Dabos and Excudero, 2000; Dhaliwal et al., 2003). A study by Tudela (2004) has applied a duration model approach that is based on Coxs hazard test methodology to exchange rates and explaining currency crises. Developing and extending an application of the Cox hazard test methodology to the events of extreme deviations of exchange rates from their fundamentals will be an important and valuable contribution to the finance area research.
Along with other important features of the Cox methodology mentioned above, this test also allows for censored data, time-dependent covariates and both continuous-time and discrete-time data. In this study some of the data will be right-censored. The relevant data set for the exchange rates will start with the year 1973, when exchange rates became flexible, hence, there is no left censored data in this study. The data extends until the year 2000, when the Euro began circulation. Based on the available dataset, with only daily records of the exchange rates, the precise timing of changes in the exchange rates taking effect is not known. The Cox test also allows us to account for this fact as well.
An application of the Cox Proportional Hazard Test considers a problem of assessing the relation between the duration of time between the events of the extreme fluctuations in the exchange rates. Duration, T, is a random variable with some probability distribution. The hazard function describes the probability distribution of T as:
(1) |
This definition of the hazard function quantifies the probability that the event will occur during the defined time interval between t and t+Δt conditional on the probability that the event has not occurred until time t. An even will be the returning of the exchange rate to within the +/-2 standard deviation bounds. Another way to write the hazard function is:
(2) |
where, f (t) is the probability density function (p.d.f.) and F (t) is the cumulative distribution function (c.d.f.) of the distribution of times T. The F(t) is the survivor function of the form:
F(t) = pr (T≥t)
The general proportional hazard model is:
(3) |
for x1, x2, xn explanatory variables, where h (t,x) is hazard rate, λ0(t) is baseline hazard, unknown function giving the hazard function for the standard set of conditions, x is 0; β is vector of unknown parameters.
The model for the hazard for event, i, at time, t, is written as:
(4) |
Because Coxs method does not require choosing some particular probability distribution to represent the survival times, the test is referred to as semi-parametric. Coxs main interest was to explore the consequences of allowing λ0(t) to be arbitrary and instead, to concentrate on the effects of the regression explanatory variables. Because some information is lost by discarding λ0(t), the resulting β estimates are not fully efficient. The standard errors are larger than they would be with a specified base line hazard rate. In most cases the loss of efficiency is quite small and what is gained in return is robustness the estimates are consistent and asymptotically normal. They are unbiased and their sampling distribution is approximately normal.
The fact that partial likelihood test results are robust and have good properties regardless of the actual shape of the baseline hazard function is important for tests of the events in the exchange rates. This is because there is no widespread agreement in the literature on what the functional form of the distribution of these events should take. The shape of the distribution of the durations can be explicitly assumed in other types of duration models, but the resulting estimates are very sensitive to the assumed shape of the time distribution. Even if the baseline hazard is specified correctly, this type of parametric approach will usually provide only a small increase in efficiency (Meyer, 1990). The Cox regression results in estimates that are consistent, approximately unbiased and asymptotically normal. In addition, Johansen et al. (2000) and Johansen (2004) have shown that the overall distribution is modified in crash days. The Cox regression allows not only for undefined probability distribution of the duration times but also for an assumption that the two processes (normal exchange rate flows and extreme deviations) are part of the same dataset but have different underlying distributions.
Suppose there are k distinct exit times, t1<t2< < tk (time of events occurrences). For any exit time, ti, the risk set, Ri, consists of all observations for which exit time is at least ti. In this study, the risk set, Ri, consists of all the points in time for which an event of extreme fluctuation has not yet occurred. For a particular failure time, ti, the probability that the event will happen at the time period observed is defined in Eq. 5. The risk in this study is the probability of the event of extreme fluctuation in exchange rates occurring at the observed month:
(5) |
The conditioning sweeps out the baseline hazard function.
If exactly one event occurs at each distinct duration length, assuming no censored observations, the required conditional partial log-likelihood function is:
(6) |
where, k is number of distinct failure times, t1<t2< tk.
The maximum-likelihood estimator of βs is obtained by iteratively solving the L(β) by the first and second order conditions. The SAS program, PHREG procedure can be used for the Cox regression analysis.
Project design: Data analysis will be performed for the exchange rates of foreign currencies against the US dollar for daily, weekly, monthly and quarterly changes in these exchange rates over a time period 1973-2000 for Germany, Switzerland and Japan. These countries have been chosen due to data availability of their central banks and US central bank interventions in these currencies. Relevant data set for the exchange rates starts with the year 1973, when exchange rates became flexible and extends until the year 2000, when Euro began circulation. Data has been obtained from the International Financial Statistics (IFS) database, FRED database and Global Financial Database.
For the purpose of this study, we will identify an extreme fluctuation in the exchange rates as decrease or increase over a period of one day (one week, one month, three months) that is outside of the bounds of +/-2 standard deviations from the historical average.
The hazard function of the duration times from one event of extreme fluctuation until the next is calculated.
The dependent variable in our tests is duration, in days (weeks, months) between extreme events in the exchange rates. The independent variables are German, Japanese, Swiss and the US central banks interventions (dummy variable with values of 1 = there was intervention, 0 = there was no intervention), amount of currency traded by the central banks, direction of trade (dummy variable with values of +1 = purchase of currency, -1 = sale of currency and 0 = no intervention) and number of interventions over one week, one month, or three months time period.
The question that this methodology aims to answer is: What is the probability that there will be an extreme fluctuation in the exchange rates at time t dependent on the level of central banks intervention for that time period? Another way to phrase this question is: How long will it take until the next extreme fluctuation in exchange rates when we see central banks intervention at the FX market? The results of the Cox proportional hazard test will help to identify whether banks interventions (as signals of monetary policies) increase or decrease the probability of an extreme fluctuation.
• | The hypothesis tested is Ho: The coefficients of the central banks intervention variables are zero (Ho: βi = 0) |
If βi≠0, then the central banks intervention variable, i, has an association with the duration of time between extreme changes in the exchange rates. If βi = 0, then central banks intervention variable, i, does not affect the probability of experiencing extreme fluctuation in the exchange rates. The βi > 0 indicates that central banks intervention variable, i, increases the probability of occurrence of an extreme event in the exchange rate and βi<0, indicates that central banks intervention variable reduces the probability of occurrence of an extreme event, in other words, has stabilizing effect on the exchange rate.
How to interpret Cox regression results: The results of the Cox regression are summarized in Table 1-3 for Germany, Japan and Switzerland. The tests have been performed on the entire dataset for each country as well as on the subsets of data. The particular subsets of data used in a separate analysis are for the time periods of increasing vs. decreasing exchange rates (this will allow to see if the effects of the banks interventions differ at the times of depreciating or appreciating exchange rates).
Table 1-3, report β coefficients estimates and the level of significance of each coefficient, indicated in the Pr>ChiSq column. Significant coefficients appear with asterick sign. The results for Beta coefficients presented in Table 1-3 should not be interpreted in the same way as OLS regression coefficients. Pluses and minuses for the β coefficients indicate whether an increase in that variable increases or reduces the probability of experiencing extreme events in the exchange rates. The hazard rate for the probability of experiencing extreme events in the exchange rates can be calculated as eβ. The ratio 1/eβ provides an estimate of time until the next extreme event in the exchange rate after a change in the independent variable has occurred.
Table 1: | Results of the Cox regression for Germany; daily, weekly, monthly and quarterly exchange rate changes |
*Significant coefficients |
Table 2: | Results of the Cox regression for Switzerland; daily, weekly, monthly and quarterly exchange rate changes |
*Significant coefficient |
Table 3: | Results of the Cox regression for Japan; daily, weekly, monthly and quarterly exchange rate changes |
*Significant coefficient |
The following are examples of Beta coefficients interpretations in the Cox regression. From Table 1, column 1, Beta coefficient for the Daily US Bank Intervention (USD/DM, in millions) is 0.0028, significant at 0.0001 level. Hazard rate of experiencing extreme exchange rate fluctuations as a result of change in the amount of US Bank Intervention on the USD/DM FX market by 1 million USD is e0.0028 = 1.002804. This means that we can expect to experience extreme exchange rate fluctuation 1.002804 times per day when US Bank Intervention increased by 1 million USD vs., DM within that day. Another way to look at it is that we can expect to see extreme exchange rate fluctuation after US Bank Intervention increased by 1 million USD vs., DM within 1/1.002804 = 0.9972 of the day or 23.9 h. Yet another interpretation is when US Bank Intervention increased by 1 million USD vs. DM within a day, the hazard of experiencing extreme exchange rate fluctuation increases by (1.002804-1×100 = 0.2804% on that day.
If Beta coefficient has a negative sign, such as Beta coefficient for the German Bank Intervention (DM/USD, in millions) in Table 1, column 1, that is equal to -0.00074, it means that German Bank Interventions decrease the probability of occurrence of the extreme fluctuation in the DM/USD exchange rate. When German Bank Intervention is increased by 1 million DM vs., USD within a day, the hazard of experiencing extreme exchange rate fluctuation decreases by (0.99926-1)×100 = -0.074% on that day. In other words, German Bank Interventions act as stabilizing force on the DM/USD FX market.
If the variable takes only two values, i.e., dummy variables of 0 and 1, as Interest Rate Differential between Germany and US being within +/-2 standard deviations bound (coded as 0) or outside those bounds (coded as 1), the hazard ratio can be interpreted as the ratio of the estimated hazard for Group 1 to the estimated hazard for Group 0 (controlling for other covariates) or the Hazard Ratio = Group 1 Hazard/Group 0 Hazard. The coefficient for German/US interest rate differential from Table 1, column 1, one month tests, is 1.78834, significant at 0.0082 level. This means that the probability of experiencing extreme DM/USD exchange rate fluctuation in a month when German / US Interest Rate Differential is outside of +/-2 standard deviations bound is 1.78834 times higher than at the times when interest rate differential between these countries is within +/- 2 standard deviations bound.
Results for Germany: There are a number of results on the effects of central banks interventions on the exchange rates that are of interest. The results in Table 1 indicate that German Central Banks (Deutsche Bundesbank) daily, weekly, monthly and quarterly interventions act as stabilizing force at the DM/USD exchange market and decrease the probability of extreme events for DM/USD exchange rate. The US Central Banks daily and monthly intervention on the USD/DM FX market have the opposite effect, with higher number of US Bank interventions per month having higher probability of leading to an occurrence of an extreme fluctuation. The result of increased probability of extreme fluctuations in the DM/USD FX market after the intervention by the US Central Bank is in line with the studies by Barnhart et al. (2007) and Beine et al. (2006) that find evidence of increased volatility in exchange rates after central banks interventions. The stabilizing effect of the German Central Banks interventions is contrary to the two studies sited above.
From the data we can also observe that the time of DM/USD exchange rate falling coincides with Bundesbank heavy purchases of the DM and the time of DM depreciation coincides with Bundesbank heavy sales of DM (Fig. 1). This suggests that interventions at the DM/USD FX market by Bundesbank worked in the intended direction. Interventions acted as a valid signal to the market participants: Signal of the increased amount of DM at the market lead to the DM depreciation and signal of reduced amount of DM lead to its appreciation against the USD.
The effects of joint German and US interventions (i.e., interventions in the same directions, whether intentional or coincidental) worked favorably for German exports in the short term: They increase the probability of German Mark depreciation against US dollar on daily and weekly basis. On the monthly bases, on the other hand, joint interventions increase the probability of DM appreciation. This outcome is also supported by the results of the Kim et al. (2000) study that shows that purchase of the foreign currency lead to exchange rate appreciation.
Fig. 1: | German bank intervention vs. DM/$ exchange rate (scaled) |
Fig. 2: | Swiss bank intervention vs. CHF/$ exchange rate (scaled) |
Results for Switzerland: For Switzerland, US Bank interventions in CHF data were not available. The results in Table 2 indicate that Swiss National Bank intervention effects on the FX market are noticeable only when cumulative effect is considered over weekly or quarterly time periods, but not on the daily bases and similar to the Bundesbank, Swiss National Bank interventions have calming effect on the CHF/US FX market. Over the examined time period, Swiss National Bank tended to intervene more frequently with sales rather than with purchases (Fig. 2).
Fig. 3: | Japanese bank intervention vs. Yen/$ exchange rate (scaled) |
Swiss interventions, though, were more than twice less frequent than Bundesbank interventions (3.1 intervention days per month on average for the Swiss National Bank sales vs. 8.7 intervention days per month for the German Bank sales). The result is consistent with the studies by Kim et al. (2000) and Cai et al. (2001) that find higher volatility only during time periods of Central Banks purchases of the currencies rather than sales. Since Swiss National Bank intervened predominantly with sales of CHF/US currency over the investigated time period, the interventions lead to the decreased probability of the extreme fluctuations. The result is also consistent with Barnhart et al. (2007) study that finds significant impact on volatility in the FX markets only due to coordinated interventions of several central banks, that was not the case for the CHF/US exchange rate over the considered time period.
Results for Japan: Unlike the results obtained for Germany and Switzerland, Bank of Japan interventions increase the probability of occurrence of extreme changes in JPY/USD exchange rate for daily, monthly and quarterly datasets (Table 3). This is consistent with the studies by Barnhart et al. (2007), Beine et al. (2006) and Cai et al. (2001), though Cai et al. (2001) find increase in volatility only during the purchases of the JPY/USD by Bank of Japan. Bank of Japan intervened by purchasing JPY more frequently than by selling the currency (average 5.29 times per month with purchases vs. 2.46 times with sales) (Fig. 3). Similar to Bundesbank and Swiss National Bank, Bank of Japan purchased JPY at the time when local interest rates were, on average, substantially lower (1.25% for the time periods of JPY purchases, vs. 4.01% for the time periods of sales, vs. 4.47% for the time periods of no interventions).
What can account for the different results for the Bank of Japan interventions? In Japan, the official reason for interventions at the FX markets, stated in the Foreign Exchange and Foreign Trade Law, is that the Minister of Finance shall endeavor to stabilize the external value of the yen through foreign exchange trading and other measures. The Bank of Japan Law specifies that the Bank of Japan, as an agent of the Ministry, would execute foreign exchange intervention operations in accordance with the directions of the Minister of Finance. Previously, Japan has been accused by the US, including strong claims by the US automotive industry, of manipulating its currency to gain unfair competitive advantage in international trade (Such allegations of currency manipulations were also brought against China and South Korea). Some experts estimate that JPY is about 10-20% undervalued. In a special report, the (IMF., 2007), that conducts the surveillance of exchange rates of its member countries, did not find currency manipulation by Japan, but noted that compared to the United States and the Euro Area, Japan stands out for its active use of foreign exchange market intervention as a policy instrument. It should also be noted, that while most of the US, Swiss and German interventions are sterilized, Japanese interventions are not necessarily automatically sterilized by the Bank of Japan (which is the result of the 0% bid interbank rate policy).
There were no joint interventions by US Bank and Bank of Japan (i.e., intervention in the same direction on the same day).
In this study we have looked at the effects of the central banks of Germany, Japan, Switzerland and US interventions on the probability of occurrence of extreme fluctuations in the exchange rates using Cox proportional hazard test methodology. The results of our analysis suggest that German and Swiss National Banks interventions acted as stabilizing force at the DM/USD and CHF/USD exchange markets and decreased the probability of extreme events for DM/USD and CHF/USD exchange rates. Bank of Japan interventions, on the other hand, increased the probability of occurrence of extreme events at the JPY/USD FX market. The US Bank interventions at the USD/DM market also increased the probability of the extreme fluctuations.
The test methodology presented here provides a new way of examining the effectiveness of central banks interventions at the FX markets and can be utilized to investigate other aspects of the government interventions at the FX markets, such as effects of the interventions based on the announced direction of the monetary policy, based on historical time period (Plaza agreement, Louvre Accord, etc.) or based on intraday trading data.