|
At a lunchtime meeting on 29 January, Paul de Grauwe reported the findings of preliminary research incorporating concepts from `chaos' theory into models of exchange rate behaviour. De Grauwe is a Research Fellow in the Centre's International Macroeconomics programme. His talk was based on CEPR Discussion Paper No. 370, with Kris Vansanten, `Deterministic Chaos in the Foreign Exchange Market'. Financial support for the meeting was provided by the Ford and Alfred P Sloan Foundations, as part of their support for the Centre's International Macroeconomics programme.Since the early 1970s, exchange rate theories have been dominated by linear models in which exchange rate changes are driven by stochastic disturbances, or `news'. Since news is by definition unpredictable, so are exchange rate changes. Though these models have provided important insights, they leave many puzzles unexplained. Quite often exchange rates are subject to relatively large changes even if no significant `news' can be identified. This approach has also failed convincingly to explain such phenomena as the strong rise in the dollar during 1980-5 and its subsequent decline. In some interpretations, both are attributed to the same news: the US budget deficit. Model-based forecasts for future spot rates on the basis of current forward rates also perform very badly, producing larger errors than predictions which assume exchange rates follow a `random walk'. Renewed interest in `chaos' models initially developed in the natural sciences, where the near-random properties of turbulent fluid flows have been successfully described by systems of non-linear, deterministic differential equations, apparently capable of displaying `chaotic' dynamic behaviour. These models have been analysed in economics, but with relatively little success despite strong prima facie evidence for the occurrence of non-linear, chaotic phenomena. Some research, for example, has indicated the existence of non-linearities in the foreign exchange markets, suggesting that their behaviour could be determined if a model could be developed that generated sufficiently complex dynamics. De Grauwe's research had used a widely accepted model of the exchange rate consisting of equations explaining international capital flows, imports, exports and exchange rate expectations. The two non-linearities introduced into the model were both justified by economic theory. First, a `J-curve' effect captured the tendency for an exchange rate depreciation initially to produce a negative effect on the balance of trade, as the terms of trade move adversely before import and export volumes have time to adjust. Second, in modelling expectations formation, agents' forecasts were assumed to take into account not only economic `fundamentals' but also the exchange rate's own past values. This was designed to represent the `chartist' element of forecasts, in which dealers base their expectations on recurring patterns of prices. In Discussion Paper No. 341, Mark Taylor discovered that a large majority of dealers in the London foreign exchange market took some account of chartist considerations when making their forecasts. Even speculators who do not themselves subscribe to the chartist approach account for it in others. The inclusion of chartist behaviour produced a model capable of generating complex exchange rate dynamics of the sort seen in reality, de Grauwe reported, and which met the two requirements of `chaotic' motion. First, the exchange rate time series were aperiodic, i.e. starting from an initial value, they did not follow any recurrent patterns, or if they did, the patterns faded away in time and so were not true cycles. The second requirement of chaotic behaviour is for small changes in the model's initial conditions or parameter values to produce unrecognizably different time series. A 5% variation in the exchange rate led, after only a few periods, to a path that diverged completely from the original series. The two seemed to have completely different histories, although only the initial conditions were different, and this only in a small way. Similarly, a 1% adjustment to the parameter representing the weight given to `chartist' considerations in exchange rate forecasts also yielded time paths that looked as if they were generated by completely different models or by completely different disturbances. These results are only preliminary, and the model should be extended to account properly for the influences of goods and other financial markets. More rigorous empirical testing is also required, but if the preliminary results are supported, de Grauwe noted, they have important implications. First, though they do not mean exogenous news is unimportant, they do warn against a tendency to look for `news' behind every exchange rate movement that we find difficult to explain. Second, the research strongly suggests that it is actually impossible to use exchange rate models to make predictions about future exchange rate movements. The extreme sensitivity of the model to small changes in its initial conditions and parameters means reliable forecasts can only be produced if we have an exact knowledge of the model's underlying structure. Despite the overall unpredictability of the model, it was possible to identify which changes in its structure tended to increase or reduce exchange rate volatility. De Grauwe simulated two kinds of intervention policies conducted by monetary authorities. A non-sterilized intervention policy, in which the authorities raised interest rates or tightened the money supply in order to dampen a depreciation of the exchange rate, had a stabilizing effect on exchange rate volatility in the model, so long as interventions were based on up-to-the-minute information. If the information was delayed, these interventions were not necessarily stabilizing. Similar effects were produced in response to sterilized interventions, when the authorities responded to a depreciation by buying foreign exchange, but leaving the domestic money stock unchanged. This contradicts the conventional view, that sterilized intervention is ineffective for exchange rate stabilization. The reason why previous models have failed to establish the stabilizing properties of sterilized intervention, de Grauwe suggested, is that they have failed to account for chartist influences. Interventions to dampen exchange rate fluctuations mean that extrapolations from previous patterns of price movements have less effect on forecasts. Hence intervention sterilized or not has stabilizing effects. |