exchange rate economics with free floats

Exchange Rate Economics
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Exchange Rate Economics
Introduction
Overview of Exchange Rates
Exchange rates are simply an expression of a countries’ national currency in respect foreign currencies. Therefore, exchange rates are ratios, multipliers, or conversion factors with regard to direction of currency conversion. Exchange rates are dependent on economic aspects such as balance of payment equilibrium, economic growth, interest rates, and relative inflation rates among other factors. The relative change in these factors determine the value of each nation’s currency against other currencies in the international market. A change in one of these economic variables can lead to either depreciation or appreciation of currency.
• Depreciation of currency is the decrease in a currency’ s value relative to the value of another currency. If the domestic currency falls in value relative to foreign currency, it buys a smaller quantity of the foreign currency. For example, if £1 used to be equivalent to $2 and now £1 is equal to $1.75. In this scenario, purchasing goods from USA becomes costly therefore reducing American exports to UK and increasing UK exports to America leading to cost push and demand pull inflation in the UK. In summary, A currency depreciation in exchange rates increases the price of imports while exports become increasingly competitive in the international market.
• Appreciation of currency is the increase in a currency’s value relative to the value of another currency.

In the case of US dollar ($) versus Pounds (£), if the value of pounds appreciate in the forex market, US imports will be cheaper for consumers in the UK market while UK exports to US will be more expensive. An appreciation of currency is likely to lower the rates of inflation because import prices will be lower, aggregate demand will fall, and firms will have more incentives to reduce costs (MacDonald, 2007).
Exchange Rate Regimes
• Free floating exchange rate- this is a flexible system of exchange rate dependent solely on the demand and supply of either domestic or foreign currency in the forex market. In this exchange regime, government intervention does not exist rather the rates are based on free market or laissez-faire economics. A free floating exchange rate regime allows nations to retain their monetary autonomy, giving them a chance to focus on internal economic aspects and control unemployment and inflation without being worry of the external elements. External shocks like capital flights or oil price rises can make it difficult if not impossible to maintain a clean floating system of exchange rates.
• Fixed Exchanged Rate- this is where the government interferes with the natural law of demand and supply using monetary policies to sustain a currencies’ value at a particular level on other currencies (Cavallo et.al, 2005).
Exchange rate quotations
• Nominal exchange rate- It is the price at which a country’s currency can be exchanged for foreign currency. It is simply the value of currency A that can be bought with a single unit of currency B. From country A’s perspective, this method of currency expression is identified as a direct method of quoting exchange rates. An indirect method of quoting exchange rate from country A’s perspective would present this exchange rate regarding the total value of currency B required to be able to buy one unit of A.
• Effective nominal exchange rate- This is an average of a country’s bilateral rates of exchange. The index weight is often provided by trade shares.
• Spot rate- This refers to currency exchange rates for immediate delivery.
• Forward Rates- These are exchange rates negotiated by two present parties for exchanging currency at a specific date in the future going as far as 360 days in the future (Isaac, n.d.).
Overshooting of Exchange Rates
The rapid depreciation of currency depicts an episode of overshooting of exchange rates. Historically, exchange rate overshooting occurs during times of macroeconomic crisis or turbulence. Exchange rate overshooting is a phenomenon where the short-run rate of depreciation is bigger than the long-run rate of depreciation. Alternatively, the exchange rate after the macroeconomic crisis tends to be below the highest level in the short run. Several factors can be linked with short-run overshooting of exchange rates. Currency supply and demand is the major determinant of exchange rates in a floating exchange rate regime. Economic downturns like a decline in tourism, exports, or similar activities that lower local currency demand leads to a depreciation in its value (Krugman & Obstfeld, 2000). Economic crises, when publicized, leads to a financial crisis which is a key driver of overshooting of exchange rates. The decline of economic outlook leads into people converting assets denominated in local currency to a more stable currency. With the downturn of macroeconomic outlook, creditors may be swayed to withhold their credits if other lenders are also avoiding lending to the borrower. A herding behaviour erupts where every individual may opt to emulate the behaviour of others even though their information directs them to act otherwise (N a k n o i, 2003).
One of the main response policies to exchange rate overshooting by the central bank in the aftermath of an economic crisis is through monetary policies. This is meant to increase the margin on interest rate and foresee an influx in capital inflow, and therefore a rise in the rates of interest is linked to appreciation in value of the currency. Historical evidence depicts currency depreciation in the occurrence of a macroeconomic crisis. However, the currency appreciates as investors recuperate from financial panic and policy measures are enacted to ensure the stability of the local currency (MacDonald, 2007).
Exchange rate overshooting model
Concerning real exchange rate definition,
1. Q = P / Π P*
Where Q represents real exchange rate, Π depicts nominal rate of exchange described as domestic currency price tag on foreign currency, and P* and P represents the foreign and domestic price levels. In the formula above, it shows that real and nominal exchange rates will move opposite one another when foreign and domestic price levels remain constant. The price of foreign currency on domestic currency will rise, meaning foreign goods will be more expensive and devaluation of domestic currency in nominal terms when the corresponding price of local goods on foreign goods drop. The nominal and real values of local currency, therefore, shift towards a similar direction even if real and nominal exchange rates move towards opposite directions.
Equation 1 can similarly be expressed to shift the nominal exchange rate towards the left side and yield;
2. Π = P / Q P*
The nominal rate of exchange is the product of: real exchange rate reciprocal 1/Q and domestic to foreign price ratio P/P*. If real exchange rate remains constant and the local price levels increase, Π will increase proportionately. Domestic currency’s value externally will drop in proportion to its value internally. If Q drops, and devalues, at constant price levels, the nominal rates of exchange will devalue, i.e. Π will increase in the same ratio.
Suppose that full-employment real rate of exchange is constant over time and presume that money supply is increased by the domestic authorities. For this to occur, the nominal rate must be determined by market forces of demand and supply. The effect of increasing money supply on income and output and level of prices is depicted in figure 1 below.

The IS curve constitutes market equilibrium equation of real goods.
3. Y = (ΦBT + DSB − ΦS-I )/(s + m) − μ/(s + m) r + m*/(s + m) Y* − σ/(s + m) Q
ΦS-I depicts exogenous factors changing savings with respect to investment at every level of local income Y. s and m are the local domestic tendency to import and save, r* represents domestic rates of interest, which is dependent on the prevailing conditions in the world currency market. Y* is foreign income and output, m* represents the foreign marginal tendency to import; DSB stands for the debt service balance, and ΦBT stands for exogenous elements changing the balance of trade domestically (“Topic 4. Exchange Rate Overshooting”, n.d.). The LM curve shows the asset market parity equation;
4. r* = − (1/θ)( M/P − ΦM ) − τ + (ε/θ) Y
Where M represents the local nominal stock of money, ΦM is a money demand change aspect, and τ stands for the expected domestic rate of inflation. The ZZ line shows the real interest rate domestically determined by prevailing economic conditions in the world market.
Under floating exchange rates symmetry is determined by the point of intersection between ZZ and LM with the nominal rate of exchange consistently adjusting to push IS through the intersection between LM and ZZ. An increase in the supply of money moves LM towards the right to LM’, as a result, residents re-adjust their portfolios by buying assets abroad. The local currency falls in value and Π increases, lowering the real exchange rate, changing global demand onto local goods and increasing output level in the short run when the level of prices are not flexible. IS curve moves to IS’. The domestic rates of unemployment drops below the usual (full-employment) level, the pressure on labor market ultimately causes prices and nominal wages to rise (“Topic 4. Exchange Rate Overshooting”, n.d.).
The progressive increase in prices leads to a decline in the real money stock, moving LM back to its initial position. This increase in the level of price also lowers the real exchange rate to the initial level; repositioning IS to its initial position. When full employment is regained, the nominal rate of exchange and level of prices will have increased with respect to increasing the supply of money and the quantity of real exchange rates and real output will have repositioned. The increase in money supply, therefore, has a temporary downward impact on the real rates of exchange and an upward impact on real income and an irreversible upward effect on the nominal rate of exchange and local price levels. This analysis presumes that the short-term adjustment of employment and output is instant while the price level adjustment takes a while. Output adjustment is also not immediate, as it takes time for the devaluation of nominal and real exchange rates to direct world demand towards domestic goods and an extended period of the rise in demand to increase local output. This has significant implications for the whole process of adjusting exchange rates.
Consider the equilibrium equation, reorganized to place real money stock on the equation’s left side, with both sides of the equation multiplied by P
5. M = P [ ΦM − θ (r* + τ ) + ε Y ]
If M increases the left side of the equation increases promptly, however, it will take some time for the occurrence of an event that increases the right side of the equation. During this span of time, domestic residents will be holding excess money and trying to replace them with international asset market. Even though output adjustment will take time, exchange of money for assets and the pressure on exchange rates due to these transactions will occur immediately. We should, therefore, compute the real money stock using the price index of commodities purchased by home country, residents. These goods have both the non-traded and traded components. The price of the traded components and non-traded components of output in local currency can be expressed as PT and PN respectively. The price unit to be used in Equation 4 is, therefore;
6. P’ = w PN + (1 – w) PT = w PN + (1 – w) Π PT*
Where w represents the proportion of non-traded components in total domestic consumption and (1-w) is the proportion of traded components. The stock or asset equilibrium equation can now be expressed;
7. M = P’ [ ΦM − θ (r* + τ ) + ε Y ] = [ w PN + (1 – w) Π PT*] [ ΦM − θ (r* + τ ) + ε Y ]
A rise in the nominal rate of exchange will directly increase the well-defined level of price locally in expression 7 in the proportion (1-w). The increase in P’ will be lower than the increase in Π because (1-w) < 1. Because P’ must increase in proportion to the increase in M and realign asset equilibrium nothing else has time to adjust, an increase in Π above the increase in M and excess of the long-term equilibrium increase in Π must happen in the short-run. Overshooting of exchange rate occurs- the exchange rate overshoots it current long-term equilibrium in the in the short-term through the steps of achieving the long-run asymmetry.

As illustrated in figure 2 above, when all aspects including the changes immediately, P, M and Π will all move up by the amount a b at period t0 and maintain their new limits indefinitely. And Y and Q will be constant. When income and prices cannot adjust immediately, Π will rise all the way up to c and then gradually drop to its long-term equilibrium level. The real rate of exchange Q will drop down to d and then slowly resume its original level. The price of non-traded output PN will increase gradually as depicted by the dotted line in the diagram, to the long-run equilibrium position which equals long-term equilibrium level of Π PT* and PT. And Y will increase temporarily in proportion to its long-term level as the prices are still adjusting. When t1 is reached, everything will resume in the long-run equilibrium (“Topic 4. Exchange Rate Overshooting”, n.d.).
Conclusion
Economists can explain with an assurance that the adjustment will be of the type explained above and portrayed in figure 2, but cannot precisely predict in real-world scenarios the accurate magnitude of exchange rate overshooting or the period required for long-run symmetry to be achieved. If the public knows that the government is increasing M, they will adjust prices and wages promptly unless they are tied to long-term contracts. Nobody can willingly take less than the optimal; price or wage. Thus t0 and t1 will happen simultaneously. If it takes a while for people to know that M has shifted or when contracts temporarily tie prices and wages, there will be a significant distance between t0 and t1. The adjustment period is likely to be different in every situation in the real world depending on the situations.
References
Cavallo, M., Kisselev, K., Perry, F., & Roubini, N. (2005). Exchange rate overshooting and the costs of floating (1st ed.). Retrieved from http://www.frbsf.org/economic-research/files/wp05-07bk.pdf
Isaac, A. Exchange Rate Overshooting (1st ed.). Retrieved from https://subversion.american.edu/aisaac/notes/stickyp.pdf
Krugman, P. & Obstfeld, M. (2000). International economics. Reading Mass.: Addison-Wesley.
MacDonald, R. (2007). Exchange rate economics. London: Routledge.
N a k n o i, K. (2003). Exchange rate overshooting. Retrieved 6 October 2016, from http://willmann.com/~gerald/econ165-I03/section-ho7.pdf
Topic 4. Exchange Rate Overshooting. Retrieved 6 October 2016, from https://www.economics.utoronto.ca/jfloyd/modules/xrov.html