Bang-bang control and the exchange rate
IN OPTIMAL control theory, there is the bangbang solution among other solutions. It is still optimal control theory, but bang-bang is a bit peculiar. The bang-bang solution is non-linear and it involves path-dependence –hysteresis. It is an ‘either or’ solution. The control switch goes between the two extremes and if the bang-bang gap is large there is visible hysteresis. It is conducive to ideas like “the nominal exchange rate never forgets the level it has reached before, i.e. it will depreciate up to that point again”. The typical example is a thermostat that regulates heat. It cuts off the heat when the room temperature reaches say 25 °C and it re-runs the system when it falls to say 20 °C. In principle one could go between zero and X Celsius degrees if there is an automatic double switch that sets the lower and the upper bounds. You get an average obviously but the average isn’t a middle-of-the road solution: it is the average of two extremes. First, high temperature disturbs you, and second, if the lower bound is set to zero you freeze to death. This is what bang-bang is. Another example could be an automatic gearbox that allows your car to hit 100 km/ hour in just 4 seconds and then brakes off with equal power so you stop suddenly. Admittedly, it wouldn’t be an easy drive.
OVERSHOOTING
The overshooting hypothesis of Rudi Dornbusch is probably his most memorable contribution. In order to become stationary around equilibrium, the exchange rate jumps first and surpasses the equilibrium value by a wide margin, i.e. overshoots. Only after that does it recede and stabilizes. The contribution lies in the conjecture that volatility isn’t there just because there is incomplete information or because financial markets aren’t efficient. It plays a more fundamental role in the process of equilibration.
Otherwise, volatility would always be nil assuming markets are efficient. The fundamental idea is something like this. In international and domestic markets bonds are perfect substitutes. If they are substitutes and if capital knows no boundaries an interest rate differential between the two bonds, say US T-bills and British bonds, can only persist if economic actors expect high volatility, a volatility high enough to compensate for the differential. Otherwise, arbitrage will make sure the two rates of interest are always the same. Dornbusch assumes perfect foresight. High interest rate increases the opportunity cost of holding cash balances and money demand falls. However, money demand for production purposes, i.e. working capital, increases and money demand is proportional to the general price level.
Where does overshooting come to the forefront? The general price level can’t instantaneously adapt to the change in money supply and if there is a surprise money supply increase adaptation takes a lot of time. Production is exogenous, and doesn’t immediately respond to changes in the money supply. Money is neutral in the long-run, which means an increase in the money base causes increases in the exchange rate and prices at the same rate.
If this scenario holds, the loss of value of the currency, i.e. depreciation, should be so high in the first phase as to cause the exchange rate to jump and fall back to equilibrium after a period of over-depreciation. So, if prices and production aren’t elastic money supply isn’t neutral and the exchange rate overshoots. This is an old but beautiful idea that dates back to 1973.
THE VASICEK MODEL
The Vasicek model is technically different, but the model of Dornbusch and the Vasicek model share a similar idea. The model delineates the dynamics of the rate of interest as a function of market risk, the equilibrium interest rate and of course volatility. Accordingly, the market interest rate reverts back to a short-run historic mean. Mean-reversion is the property both the Vasicek interest rate and the Dornbusch exchange rate models share. The Vasicek model is also used to predict oil prices. The model is based on the idea that actual oil prices will revert back to a couple of historic oil price average levels that serve as equilibrium values. If the model is realistic and the estimation is correct, oil prices would go up and down, but in the end they would be attracted to those means. This can in general be true for exchange rates as well but not for the USD/TL rate. There is no historic mean towards which the USD/TL exchange rate would be attracted. The exchange rate has gone up from 3.77 on January 1, 2018 to 19.02 on March 23, 2023. The CAGR is 31%. Furthermore, the exchange rate jumped from plateau to plateau and fell back. It fluctuated as (if ) the switch is on or off.
BANG̞-BANG
So, bang-bang is neither overshooting nor Vasicek.
TURKEY IN THE EARLY 2000S
In 2000, the nominal anchor Turkey made use of was the exchange rate. The last of the
infamous IMF Tablita stabilizations failed miserably in February 2001. The exchange rate initially overshot, but starting from January 2002 the Lira began to appreciate. It appreciated to such an extent that it became overvalued by all metrics by 2005. In a sense directly targeting the exchange rate didn’t work although over-appreciation after the initial depreciation wasn’t necessarily caused by the post-2001 Derviş-IMF programme dynamics. There was a global ‘savings glut’ and ample dollars journeying all over the world was the main culprit. In 2004 and 2005 Bovespa and the İstanbul Stock Exchange moved in tandem although Brazil and Turkey were quite dissimilar in economic terms. Eurodollars and loose Fed policy were the common factor that explained why the same pattern in stock prices was observed in many countries. If a repetition of 2002-2007 can be re-staged, that is if there is a sound macro framework and if the economic management team can build reputation and credibility in international markets, inflation will fall and the exchange rate will move away from the bang-bang zone quickly.
Implied volatility, July 2022-March 2023: volatility is no more –At what price?
WHAT NEXT?
The bang-bang solution I mentioned above should be eliminated after the elections. Should the opposition win, there will be a return to normalcy in every respect. Monetary policy will be rendered rational and more effective. It will be conducted in accordance with the received economic wisdom and be concomitant with economic theory. In order to make sure the exchange rate doesn’t jumpstart the policy rate will be raised. This much is clear but what we don’t know is the speed of change or reversal in monetary policy after the elections. The observation that the Turkish banking sector as a whole won’t be hit hard as interest rates increase is correct.
Banks aren’t exposed to interest rate risk to the same extent SVP was. Banks have credit risk, but the securities they are holding are either indexed or floating and they aren’t overwhelmingly booked as held to maturity (HTM). Less than 8% of bank assets are HTM. Total securities are only 16.8%. Except public banks that are constantly being re-capitalized commercial banks have enough capital. They can’t suddenly lose their equities as SVP did. There is ample buffer to protect their equity. However, they are subject to credit risk and FX risk. Left alone private commercial banks –most of them are owned by other foreign banks and corporates- could easily manage their risks but they have to be in good terms with Ankara. The risk is the interference risk. Once this episode is over, banks can reposition themselves and with relatively strong capital bases they will be ready to operate healthily.
Even so I wouldn’t recommend a drastic rate hike. I don’t think this will happen either. The opposition has enough experience and technical staff abound. They know what to do. Most importantly, they know that raising or cutting policy rates is only a minor item in the general economic policy make-over. We have long forgotten that. Economic policy isn’t just about cutting rates or raising them. Economic policy must be whole from money to public finance, from industrial strategy to microeconomic restructuring.