Exchange-Rate Economics: Comprehensive Study Notes

National Income Accounting and the Balance of Payments

Core identities

• Open–economy expenditure identity: This identity shows how a country's total output (or income) is spent. $Y$ (Output/Income) is the sum of $C$ (Consumption by households), $I$ (Investment by firms), $G$ (Government spending), and $(EX - IM)$ (Net Exports, which is Exports minus Imports).
  $Y = C + I + G + (EX - IM)$

• Closed–economy benchmark: In a closed economy (no trade), Investment ( $I$ ) must equal National Saving ( $S$ ). National Saving is defined as total income minus consumption and government spending.
  $Y = C + I + G\;\Rightarrow\;S = Y - C - G = I$

• Open–economy saving–investment link: In an open economy, National Saving ( $S$ ) is used to finance domestic Investment ( $I$ ) or provide funds for the Current Account balance ( $CA$ ). A positive Current Account means a country saves more than it invests domestically, leading to lending abroad.
  $S = I + CA \quad\Rightarrow\quad I = S - CA$

Current-account interpretation

• If a nation's Exports ( $EX$ ) are greater than its Imports ( $IM$ ), then its Current Account ( $CA$ ) is positive (a surplus). This means the nation is lending to the Rest of the World (ROW).
  EX > IM \Rightarrow CA > 0

• If a nation's Exports ( $EX$ ) are less than its Imports ( $IM$ ), then its Current Account ( $CA$ ) is negative (a deficit). This means the nation is borrowing from the Rest of the World (ROW).
  EX < IM \Rightarrow CA < 0

Private vs. government saving

• Private Saving ($S<em>P$): This is the saving done by households and firms, calculated as total income minus taxes and consumption.
  $S</em>P = Y - T - C$

• Government Saving ($S<em>G$): This is the difference between government tax revenue and government spending. A positive value means a budget surplus, while a negative value means a budget deficit.
  $S</em>G = T - G$

• Combined Saving Identity: This identity shows that private saving, adjusted for government saving, contributes to domestic investment and the current account.
  $\boxed{S<em>P = I + CA - S</em>G}$

• Budget deficits (where government saving S*G < 0) reduce the amount of national saving available, which can limit or "crowd out" a country's ability to invest abroad (reduce its Current Account surplus or increase its deficit).

Balance-of-Payments (BOP) bookkeeping

• Double–entry: This principle means that every international transaction is recorded twice, once as a credit and once as a debit, ensuring the overall balance of payments always sums to zero.

• Sub‐accounts: The BOP is divided into three main accounts:

  • Current Account (CA): Records trade in goods (e.g., cars, oil), services (e.g., tourism, banking), primary income (e.g., interest, dividends on foreign investments), and secondary income (e.g., remittances, foreign aid).

  • Capital Account (KA): Records minor capital transfers, such as debt forgiveness and transfers of non-produced, non-financial assets (e.g., patents, copyrights).

  • Financial Account (FA): Records all international purchases or sales of financial assets. This includes private capital flows (e.g., direct investment, portfolio investment) and the Official Settlement Balance (changes in a country's central bank foreign reserves).

Exchange Rates and the Foreign-Exchange (FX) Market

Quotations

• Direct/American quotation: Shows the price of one unit of foreign currency in terms of the domestic currency (e.g., dollars per euro). For example, $1.10/€ means 1 euro costs 1.10 US dollars.

• Indirect/European quotation: Shows the price of one unit of domestic currency in terms of the foreign currency (e.g., euros per dollar). For example, €0.90/$ means 1 US dollar costs 0.90 euros.

Depreciation vs. appreciation

• If the exchange rate E
  {$/€} (dollars per euro) rises, for example, from $1.10$ to $1.20$, it means you need more dollars to buy one euro. In this case, the dollar has depreciated against the euro, and the euro has appreciated against the dollar.

Spot vs. forward

• Spot exchange rate: The exchange rate for immediate currency exchange, typically settled within two business days.

• Forward exchange rate: A rate agreed upon today for a currency exchange that will take place at a specified future date (e.g., 30, 90, or 180 days from now). This helps businesses hedge against future exchange rate fluctuations.

Actors & geography

• The main participants in the FX market include commercial banks, multinational firms, non-bank financial institutions (like hedge funds), and central banks. It's a 24-hour global market, with major centers in London, New York, Tokyo, Singapore, and Frankfurt. The US dollar is frequently used as an intermediary currency in transactions, known as the vehicle currency.

Asset-market (return) approach

• The Dollar return on a Euro ( €)-deposit ( R{€}^{$} ) is the total return you get in dollars if you invest in a euro-denominated asset. It combines the interest rate on the euro deposit ( $R</em>{€}$ ) with the expected capital gain or loss from converting euros back to dollars in the future.
  R{€}^{$} = R{€} + \frac{E^{e}{$/€} - E{$/€}}{E
  {$/€}}

Uncovered Interest Parity (UIP)

• UIP states that in equilibrium, the expected returns on deposits of any two currencies, measured in the same currency, should be equal. This means if you convert dollars to euros, invest, and then convert back to dollars, you should expect to earn the same return as if you had just invested in dollars. If this were not true, investors would flock to the higher-yielding currency until the rates equalized through exchange rate adjustments.
  R{\$} = R{€}^{$} \quad\Longrightarrow\quad R{\$} = R{€} + \frac{E^{e}-E}{E}

• This condition helps determine the current spot exchange rate ( $E$ ) given prevailing interest rates in both countries and the expected future exchange rate ( $E^{e}$ ).

Comparative statics

• If US interest rates ( $R*{\$}$ ) rise, the dollar appreciates ( $E$ falls). This is because higher US rates make dollar deposits more attractive, increasing demand for dollars and causing the dollar to strengthen.

• If Euro interest rates ( $R*{€}$ ) rise or the future expected exchange rate ( $E^{e}$ ) rises, the dollar depreciates ( $E$ rises). Higher euro rates make euro deposits more attractive, increasing demand for euros and causing the dollar to weaken.

Money, Interest Rates, and Exchange Rates

Money demand (individual & aggregate)

• Nominal money demand ($M^{d}$): The total amount of money people want to hold in nominal terms. It depends on the overall price level ( $P$ ), the interest rate ( $R$ ), and real income ( $Y$ ). People want to hold more money if prices are higher or if their income is higher, but less money if interest rates are higher (as holding money means foregoing interest).
  $M^{d} = P\,L(R,Y)$ where LR<0 (money demand decreases as interest rate rises) and LY>0 (money demand increases as income rises).

• Real money demand ($\frac{M^{d}}{P}$): The amount of purchasing power people want to hold in the form of money. It is solely determined by real income and interest rates.
  $\frac{M^{d}}{P}=L(R,Y)$

Money-market equilibrium

• Equilibrium in the money market occurs when the real money supply (set by the central bank) equals the real money demand. This balance determines the equilibrium interest rate.
  Given nominal money supply $M^{s}$ set by the central bank: $<br>\frac{M^{s}}{P}=L(R,Y) \;\Rightarrow\;R=f\bigl(M^{s},P,Y\bigr)$

Short-run link to FX (combining money market & UIP)

• Step 1: Money Supply Shock → Interest Rate Change: When the central bank changes the money supply ( $M^{s}$ ), it directly impacts the domestic interest rate ( $R$ ). For example, an increase in $M^{s}$ lowers $R$.

• Step 2: Interest Change → Exchange Rate Change via UIP: The change in the domestic interest rate then affects the exchange rate ( $E$ ) through the Uncovered Interest Parity (UIP) condition.

• Example: If the Federal Reserve (Fed) conducts an expansionary open-market purchase (e.g., buying government bonds), this increases the US money supply ( $M^{s}$ ). This causes US interest rates ( $R_{\$}$ ) to fall. According to UIP, lower US interest rates make dollar deposits less attractive compared to foreign deposits, leading to an immediate dollar depreciation ( $E$ rises).

Long-run neutrality (monetary approach)

• In the long run, with flexible prices, changes in the money supply are considered neutral, meaning they only affect nominal variables (like prices and exchange rates) but not real variables (like output or real interest rates). A permanent increase in the money supply will lead to a proportional increase in the price level.
  $P \propto M^{s}$

• Consequently, the exchange rate ( $E$ ) will adjust proportionally to the ratio of domestic money supply to foreign money supply. For instance, a permanent 10% increase in the US money supply ( $M^{s}<em>{US}$ ) will, in the long run, cause a 10% dollar depreciation ($E$ rises by 10%), leaving real variables untouched. $E \propto \frac{M^{s}</em>{US}}{M^{s}*{EU}}$

• This also aligns with the Fisher effect, which states that the difference in nominal interest rates between two countries reflects the expected difference in their inflation rates ($R<em>{\$}-R</em>{€}=\pi^{e}<em>{US}-\pi^{e}</em>{EU}$).

Exchange-rate overshooting

• Exchange rate overshooting occurs because goods prices are typically sticky (slow to adjust) in the short run, while financial asset prices (including exchange rates) adjust immediately to new information. When a monetary shock (like an increase in money supply) happens, the immediate jump in the exchange rate (depreciation) is larger than its eventual long-run depreciation. This "overshoot" then partially reverses as domestic goods prices gradually rise to their new long-run equilibrium.

Price Levels and the Exchange Rate in the Long Run

Law of One Price (LOOP)

• The Law of One Price states that for identical, traded goods (assuming no trade costs like tariffs or transportation fees), the price of the good should be the same across different countries when expressed in a common currency.
  For a traded good $i$: P^{US}i = E{$/€}\;P^{EU}_i

Purchasing Power Parity (PPP)

• Absolute PPP: This theory suggests that the exchange rate between two currencies should adjust so that an identical basket of goods and services costs the same in both countries when converted to a common currency.
  E*{$/€} = \dfrac{P^{US}}{P^{EU}}

• Relative PPP: This is a weaker version, stating that the rate of depreciation of the domestic currency should equal the difference between the domestic inflation rate and the foreign inflation rate. In simpler terms, if inflation is higher in one country, its currency should depreciate to maintain purchasing power parity.
  $\frac{\Delta E}{E} = \pi*{US}-\pi<br>{EU}$

Empirical issues

• In reality, the LOOP and PPP theories often do not hold perfectly. This is due to factors like:

  • Transport costs and trade barriers (e.g., tariffs).

  • The existence of non-traded goods (e.g., haircuts, real estate) whose prices are not equalized across borders.

  • Pricing-to-market by firms (where companies set different prices in different countries for the same product to maximize profits).

  • Oligopoly market structures where a few firms dominate.

  • Heterogeneous baskets of goods used to calculate price levels in different countries.

• These issues lead to sizable and persistent deviations from LOOP/PPP, sometimes referred to as the "Penn effect" (where richer countries tend to have higher price levels).

Real exchange rate

• The real exchange rate ( $q$ ) measures the relative price of a basket of goods and services in one country compared to another country, expressed in a common currency. It tells you how many foreign baskets you can buy with one domestic basket.
  $q = \frac{E\,P^{EU}}{P^{US}}$

• If q > 1, it means the foreign basket of goods is more expensive relative to the domestic basket, implying a "real appreciation" of the foreign currency (e.g., the euro becomes stronger in real terms).

• Real exchange rate movements can be caused by changes in relative demand and supply for goods, shifts in terms-of-trade (the price of exports relative to imports), and differences in productivity growth (e.g., the Balassa-Samuelson effect where higher productivity in tradables leads to higher wages and thus higher prices for non-tradables).

Output and the Exchange Rate in the Short Run (Mundell–Fleming)

Aggregate demand in an open economy

• Aggregate demand ( $D$ ) represents the total demand for goods and services in an economy. In an open economy, it includes:

  • Consumption ( $C$ ) depends on disposable income ($Y-T$).

  • Investment ( $I$ ) depends on the interest rate ( $R$ ).

  • Government spending ( $G$ ).

  • The Current Account ($CA$), which depends on the exchange rate ( $E$ ), domestic and foreign price levels ( $P, P^{<em>}$ ), and domestic and foreign income ( $Y, Y^{</em>}$ ).
    $D = C(Y-T) + I(R) + G + CA(E,P,P^{<em>},Y,Y^{</em>})$

• Disposable-income effect: When income ( $Y$ ) increases, only a portion of it is consumed (because the marginal propensity to consume is less than 1); the rest is either saved or spent on imports.

DD schedule (goods-market equilibrium)

• The DD schedule shows the combinations of the exchange rate ( $E$ ) and output ( $Y$ ) where the goods market is in equilibrium (i.e., aggregate demand equals aggregate output).

• It is downward-sloped in (E,Y) space: a depreciation of the domestic currency ( $E$ rises, meaning more domestic currency per unit of foreign currency) makes domestic goods cheaper for foreigners and foreign goods more expensive for domestic residents. This boosts net exports ($EX - IM$), which in turn increases aggregate demand and leads to a higher equilibrium output.

AA schedule (asset-market equilibrium)

• The AA schedule shows the combinations of the exchange rate ( $E$ ) and output ( $Y$ ) where the asset markets (money market and foreign exchange market) are in equilibrium, specifically satisfying the UIP condition.

• It is upward-sloped in (E,Y) space: a higher output ( $Y$ ) increases the demand for money (for transactions). To satisfy this higher money demand with a fixed money supply, the domestic interest rate ( $R*{\$}$ ) must rise. According to UIP, a higher domestic interest rate requires an appreciation of the domestic currency ( $E$ falls) to restore equilibrium in the FX market.

General short-run equilibrium

• The economy's short-run equilibrium is found at the intersection of the DD and AA schedules, where both the goods market and the asset markets are simultaneously in balance. At this point, there are no forces pushing output or the exchange rate to change, given current conditions.

Temporary policies (expected to be reversed)

• Monetary expansion: A temporary increase in the money supply (e.g., by the Fed) shifts the AA schedule to the right (or outwards). This leads to a depreciation of the domestic currency ( $E$ rises) and an increase in output ( $Y$ ) in the short run because lower interest rates and a weaker currency stimulate demand.

• Fiscal expansion: A temporary increase in government spending or a cut in taxes shifts the DD schedule to the right. This leads to an appreciation of the domestic currency ( $E$ falls) and an increase in output ( $Y$ ). The appreciation occurs because higher output increases money demand, pushing up interest rates, which attracts foreign capital and strengthens the currency.

Permanent monetary expansion

• A permanent monetary expansion has a larger impact than a temporary one because it also affects long-run expectations about the exchange rate ( $E^{e}$ ). This results in an even larger rightward shift of the AA schedule and an immediate overshooting depreciation of the currency ( $E$ rises even more than for a temporary shock).

• In the long run, as prices adjust (rise), the real money supply falls, and the DD schedule shifts back to the left. Eventually, output returns to its potential level (natural rate), but the currency remains weaker than its initial level due to the permanently higher domestic price level.

J-curve

• The J-curve effect describes the typical path of a country's trade balance (or Current Account) after a currency depreciation. Initially, right after a depreciation, the trade balance may actually worsen (fall) before it improves. This is because import and export contracts are often fixed in the short run (e.g., quantities and prices already agreed upon), so it takes time for consumers and firms to adjust their purchasing decisions based on the new, cheaper domestic goods or more expensive foreign goods. Over time, as volumes of exports increase and imports decrease, the trade balance eventually improves, forming a "J" shape on a graph.

Fixed Exchange Rates and Intervention

Mechanics

• To maintain a fixed exchange rate (peg) at a specific level (e.g., $E_0$ dollars per euro), the central bank (CB) must stand ready to buy or sell its own currency (or foreign currency reserves) at that predetermined price.

  • If there is excess demand for the domestic currency (e.g., an appreciation pressure), the CB sells its own currency (and buys foreign currency). This means its foreign reserves decrease, and the domestic money supply decreases.

  • If there is excess supply of the domestic currency (e.g., a depreciation pressure), the CB buys its own currency (and sells foreign currency from its reserves). This means its foreign reserves increase, and the domestic money supply increases.

Policy efficacy comparison

• Monetary policy ineffective: Under a fixed exchange rate, a country cannot use its independent monetary policy to influence output or interest rates. Any attempt by the central bank to change the money supply (e.g., lower interest rates) will be immediately offset, or "sterilised," by the reserve flows needed to maintain the fixed exchange rate. So, the central bank loses control over its money supply.

• Fiscal policy highly potent: In contrast, fiscal policy (changes in government spending or taxes) becomes very effective under fixed exchange rates. A fiscal expansion (e.g., increased government spending) shifts the DD curve to the right, increasing output. Any upward pressure on interest rates and appreciation pressure on the currency (which would normally dampen output in a floating regime) is counteracted by the central bank's intervention to hold the peg, which involves expanding the money supply (accumulating reserves), further supporting the expansion.

Balance-of-payments (BoP) crisis & capital flight

• A Balance-of-Payments crisis (or currency crisis) can occur when market participants expect a country to devalue its currency (i.e., abandon its fixed peg and set a new, weaker rate). This expectation causes the Uncovered Interest Parity (UIP) condition to shift, leading to a massive outflow of capital ("capital flight") as investors sell domestic assets and convert domestic currency into foreign currency to avoid expected losses. This puts immense downward pressure on the domestic currency. To defend the peg, the central bank must sell large amounts of its foreign reserves. If the central bank's reserves become insufficient to meet this demand, the peg collapses, and the currency jumps to an expected lower (more depreciated) level, often dramatically. This can be very destabilizing for the economy.

International Monetary Architecture

Open-economy trilemma

• The "impossible trinity" states that a country can only achieve two of the following three policy goals simultaneously:

  1. Fixed (or very stable) exchange rate: Providing exchange rate certainty for trade and investment.

  2. Independent monetary policy: Allowing the central bank to control interest rates and money supply for domestic stabilization (e.g., fighting inflation or recession).

  3. Free capital mobility: Allowing capital to flow freely across borders without restrictions.

• Examples:

  • Euro area (1+3): Member countries have a fixed exchange rate (the euro) and free capital mobility, but individual countries have sacrificed independent monetary policy (it's managed by the ECB for the whole bloc).

  • USA (2+3): The US has an independent monetary policy and free capital mobility, but it has a floating exchange rate with other major currencies.

  • China pre-2015 (1+2): Historically, China maintained a relatively fixed exchange rate and an independent monetary policy by imposing significant capital controls (limiting free capital mobility).

Historical regimes

• Gold Standard (1870-1914): Countries fixed their currencies' values to a specific amount of gold. This provided fixed exchange rates but limited independent monetary policy, as the money supply was tied to gold reserves.

• Inter-war chaos (1918-39): After WWI, many countries abandoned the gold standard, leading to volatile exchange rates, competitive devaluations (countries deliberately weakening their currencies to boost exports), and "beggar-thy-neighbour" policies that harmed other countries' trade.

• Bretton Woods (1946-73): Established a system of adjustable pegs where most currencies were fixed to the US dollar, and the US dollar was convertible to gold at a fixed price ($35/oz$). This system allowed for some capital controls to provide monetary policy autonomy and was overseen by international institutions like the IMF which provided support for temporary balance-of-payments difficulties.

• Post-1973: After the collapse of Bretton Woods, major currencies moved to a system of "managed float" (where central banks sometimes intervene but don't strictly peg). Many emerging market economies, however, often exhibit a "fear of floating," meaning they intervene heavily to limit exchange rate swings, even if they claim to have a floating regime.

Floating Exchange Rates – Pros & Cons

Pros (theoretical advantages)

1. Monetary policy autonomy as stabilisation tool: A floating exchange rate allows the central bank to freely adjust interest rates and money supply to address domestic economic goals like inflation control or stimulating growth.

2. Symmetry – no single anchor currency: No single country's currency needs to act as the primary reference or anchor for the global system, as all currencies' values are determined by supply and demand in the market.

3. Automatic stabiliser: A floating exchange rate can act as a shock absorber. For example, a negative demand shock that reduces output might cause the currency to automatically depreciate (a real depreciation), making exports cheaper and imports more expensive, thereby cushioning the impact on the domestic economy.

4. Facilitates external-balance adjustment: Flexible exchange rates can adjust to help correct large current account imbalances. A country with a persistent current account deficit might see its currency depreciate, making its exports more competitive and imports less attractive, thus helping to reduce the deficit.

Reality check

• Limited symmetry: In practice, many non-US central banks still heavily accumulate US dollar reserves, suggesting that the dollar continues to play a central, anchor-like role, limiting true symmetry.

• Persistent large CA imbalances: Despite floating exchange rates, major economies like the US and Japan continue to exhibit large and persistent Current Account imbalances, indicating that exchange rate adjustments alone are often insufficient to fully correct them.

• Exchange-rate volatility: While floating rates offer flexibility, the resulting volatility can create uncertainty for businesses involved in international trade and investment. However, surprisingly, the empirical evidence often shows that this volatility doesn't always fully "pass through" to import/export prices, meaning its impact on trade can sometimes be less than expected.

Optimum Currency Areas (OCA) & the Euro

OCA criteria (Mundell–McKinnon–Kenen)

• An Optimum Currency Area is a geographical region in which it makes economic sense for countries to share a common currency or to have permanently fixed exchange rates because the benefits outweigh the costs. Key criteria include:

  • Labour mobility & wage flexibility: If workers can easily move to where jobs are, or wages can adjust quickly, this helps absorb economic shocks in a currency union without needing exchange rate adjustments.

  • Fiscal transfers, integrated capital markets: The ability for richer regions to provide financial aid to poorer regions (fiscal transfers) and for capital to flow freely helps share risks and stabilize economies.

  • Similar economic shocks & structures: If countries in the union experience similar economic downturns or booms (symmetric shocks) and have similar economic structures, a single monetary policy can be suitable for all.

European Monetary Union (EMU)

• Motivation: The formation of the EMU and the introduction of the Euro were motivated by desires to eliminate intra-EU exchange rate crises, reduce currency conversion costs, and tame the dominance of the German Mark (DM) within Europe.

• Trade-off: Member countries in the Eurozone have forfeited their independent monetary policy and the ability to use exchange rate adjustment as a tool. Instead, they rely on the European Central Bank (ECB) for monetary policy and adhere to common fiscal rules. This creates tension, especially during asymmetric shocks (shocks that affect member states differently, like the Eurozone sovereign debt crisis), as a single policy may not suit all members.

• Future: The future of the Eurozone involves efforts to complete a banking union (common supervision and resolution of banks) and fiscal union (some degree of shared taxation or spending capacity) to strengthen the union and better share risks among members.

Financial Globalisation & Developing-Country Issues (outline)

• International capital markets offer significant benefits, such as increased risk-sharing (allowing investors to diversify their portfolios globally) and enhanced growth prospects (by channeling savings to productive investments worldwide). However, they also create channels for the rapid transmission of financial crises, leading to phenomena like "sudden stops" (abrupt reversals of capital inflows).

• Regulatory challenges: Global financial flows pose complex regulatory challenges, including determining who acts as the "lender-of-last-resort" during a crisis (providing emergency liquidity), managing "moral hazard" (where financial institutions take on excessive risk knowing they might be bailed out), and developing "macro-prudential tools" (policies aimed at minimizing risks to the financial system as a whole).

• Debt & reserve accumulation cycles: Developing countries often experience cycles of accumulating international debt and foreign exchange reserves. The success stories of East Asian economies (which built up large reserves) are often contrasted with the financial crises in Latin America and some Asian countries, which suffered from excessive debt or insufficient reserves. This highlights the crucial role of the IMF (International Monetary Fund) in providing financial assistance and the ongoing debate about a "new financial architecture" for managing global financial stability and crises.