Time-Varying Risk of Realignment in the European Rate Mechanism: A Comparison of Linear and Nonlinear Estimation Techniques
Liga E. Bauer - University of California, Santa Cruz
In the economic literature on exchange rate target zones, Krugman (1991)
argues that currency bands are perfectly credible, such that no [central
parity] zone exchange rates in the Exchange Rate Mechanism (ERM) of the
European Union (EU). Svensson, in his 1993 European Economic Review paper,
"Assessing Target Zone Credibility", argues that interest rate differentials
are a "naive" measurement of devaluation expectations for a currency with an
exchange rate realignments are expected. As a result, a negative
deterministic relationship should exist between interest rate differentials
and exchange rates in target zones. However, actual data do not accord with
this view. Svensson (1992, 1993) proposes the existence of "time-varying
[central parity] realignment expectations" to explain why observed
correlations between interest rate differentials and exchange rates are
often positive or zero. Accurate estimation and measurement of time-varying
risk of realignment is important, because it would allow for possibility of
coordinated central bank (CB) intervention to mitigate against currency
crises and speculative attacks, thereby increasing the credibility of each
country's commitment to "targetband". As such, Svensson develops two
methodologies, both of which adjust interest rate differentials for the
expected rate of depreciation within the band. Resulting expected rates of
devaluation are estimated under maintained asssumptions of uncovered
interest rate parity, rational expectations, and a negligible risk premium.
By using this interest rate adjustment mechanism, Svensson is able to
considerably improve measurements of devaluation expectations for a currency
with an exchange rate band over a 3- and 12-month time horizon.
At the end of 1992, the United Kingdom (UK) and Italy exited the European Exchange Rate Mechanism (ERM). Both the British and Italian central banks, in response to growing devaluation pressures and resulting speculative sales of the pound and the lira, opted to no longer defend their currency exchange rates within established ERM target bands (Mishkin, 1994). However, Svensson's 1993 paper, measuring devaluation expectations for a currency within an exchange rate band, does not include the UK in its database. In building upon Svensson's original work, this research incorporates both the UK and Italian currencies into Svensson's original database, to assess how well his "simplest" and "drift-adjustment" tests are able to accurately predict the actual devaluation of the pound sterling ex-post. Additionally, under the maintained hypothesis that this model of expected rates of devaluation is correct, these tests can be seen as tests of how well market agents were able to predict the actual devaluation of the pound and the lira in 1992.
More importantly, this paper introduces three innovations, which build on previous research by Svensson (1992, 1993) and by Chen and Giovannini(1993). First, Svensson's original data set is extended to include Italy and the UK, both of whose currencies came under speculative attack during the ERM crises in 1992 and 1993. It was the speculative attacks on these currencies, following the Maastricht Treaty, which eventually led to a widening of ERM exchange rate bands. Second, Svensson's original data set is extended through 1995, three years beyond the speculative attack period. As a result, credibility of the European target zone measured by the expected rate of change in realignment after the bands were widened in 1992 can begin to be measured. Third, and most importantly, Svensson's Ordinary Least Squares (OLS) linear estimation of time-varying risk of exchange rate band realignment for each of the given European currencies will be augmented by estimating this same risk of realignment via a neural network (nonlinear) model.
This third innovation incorporates a new on-line, exponentiated gradient EG( ) learning algorithm, motivated by the Minimum Relative Entropy Principle of Kullback and recently-developed by Helmbold, Kivinen and Warmuth (1996) to assess the time-varying risk of exchange rate band realignment in the ERM. Whereas Svensson's linear OLS regression minimizes a Squared Euclidean distance function to estimate linear weights over each period ("regime") between exchange-rate realignments, the key notion here is a Relative Entropy distance (or Kullback-Leibler divergence) function. At each trial, if the loss of the EG( ) algorithm is an exogenously given learning rate is much larger than that of the current weight vector (w), then the algorithm updates its current weight vector so that it gets closer to w. It works particularly well in avoiding "local minima", when the best weight-vector may be "sparse".
Data
This research exercise relies on the same daily Bank of International Settlements (BIS) database for seven initial ERM currencies over the period March 13, 1979 through April 9, 1992, as did the Svensson (1993) paper, with the addition of the UK pound. Spot exchange rates are ecu-rates, recorded at a central bank telephone conference at 2:30 pm Swiss time. The BIS ecu-rates are recorded simultaneously for the relevant currencies, whereas "official fixing" dollar rates of each central bank are not. Spot ecu-rates are "smoother". (Svensson, 1993) Interest rates are annualized bid rates of 3- and 12-month Euro-market deposits recorded at 10a.m. Swiss time. Additionally, Svensson's original data base has been extended through 1995 for eight ERM currencies. The following ERM currencies are included: Belgian/Luxembourg franc,(BF), the Deutsche mark (DM), the French franc (FF), the Italian lira (IL), the Netherlands guilder (NG), the Danish krone (DK), the Irish punt (IP) and the British pound (BP).
Methodology
The data is divided into two sets a training set and a test set. Parameter estimates using Least squares regression and a two-layer neural net are conducted on the training set. The test set is then used to assess how the parameter estimates perform on the test data ex-ante. The closer the output estimation are to the actual test output, the better the parameter estimates. Two sets of tests are conducted. First, a Least Squares regression is performed on the original Svensson data, 1973-1992 without inclusion of Italy and the UK to reproduce Svensson's benchmark (1993) results. Then this same data set is "piped" through a feed-forward, two-layer neural network. Importantly, during the back propagation learning phase, the two-layer net implements a recently-developed, exponentiated gradient EG( )-update algorithm (Warmuth, 1996) to learn those parameters determining the time- varying expected rate of realignment and thereby assess the probability of central parity realignment maintaining or switching out of the given target zone. Resulting estimates of the expected rate of realignment using both Least Squares and a two-layer neural network on the original Svensson (1993) data are then compared and assessed.
The second set of tests again estimates the expected risk of realignment or the credibility of the target zones using a rolling Least Squares regression and the feed-forward, two-layer network given earlier. However, this second set of tests adds the British pound to the seven country currencies given above. As already mentioned, the inclusion of this currency is significant in that speculative attacks on British pound (and the Italian lira) in November 1992, resulted in subsequent realignment and widening of ERM target zones for all EU currencies.
A third set of tests again estimates the time-varying, expected risk of realignment using Least Squares regression and feed-forward networks as above; however, the data set is extended through 1995 for all eight currencies, inclusive of the British pound. The time-varying expected rate of central parity realignment using both methodologies is again estimated.
Scheduled for Session 4.1 Times Series Analysis Of Asset Pricing