Cheat sheet · Open Economy Macro

Definitions to write verbatim

• Open economy — one that engages in international trade of goods, services and financial assets. Three items; the third is the one students drop.
• Three channels of linkage — output market (goods and services), financial market (cross-border assets), labour market (migration and outsourcing, limited by immigration law).
• Balance of payments — a summary statement of all transactions between the residents of a nation and the rest of the world over a period, usually a year.
• Autonomous transactions — undertaken for their own commercial or investment reasons, placed above the line; their net total is the surplus or deficit. Accommodating transactions — official reserve transactions that settle the gap, placed below the line.
• International investment position — a stock of assets and liabilities at a point in time, against the balance of payments which is a flow over a period. Also called the balance of international indebtedness.
• Foreign exchange market — a single electronically connected international market. Three functions: transferring purchasing power, providing credit for goods in transit and for resale, providing facilities for hedging and speculation.
• Arbitrage — the purchase of a currency in one market for immediate resale in another. No exchange risk is taken, so the profit is known before the trade.
• Hedging — the avoidance of foreign exchange risk. Speculation — the deliberate acceptance of foreign exchange risk in the hope of profit. Stabilising speculation moderates a move, destabilising speculation amplifies it.
• Currency swap — a spot sale of a currency combined with a forward repurchase, in one transaction. Most interbank forward trading takes this form.
• Foreign exchange option — the right but not the obligation to buy (call) or sell (put) a currency at a stated price by a stated date. A future carries an obligation; an option does not.

Balance of payments formulas

• BOT = goods exports - goods imports
• Current account = BOT + net invisibles (services + transfers)
• Current account + capital account + errors and omissions = change in reserves
• BoP summation (Salvatore): current account balance + capital account balance + financial account balance (less official reserve transactions, including net financial derivatives) + statistical discrepancy
• Credit or debit? Ask whether money comes in (credit) or goes out (debit). Then find the matching opposite entry: every transaction is recorded twice.
• Credits: exports, income received, transfers received, an increase in foreign-owned assets at home, a decrease in assets abroad. Debits: the mirror of each.

Exchange rate formulas

• R = units of domestic currency per unit of foreign currency R rises = DEPRECIATION R falls = APPRECIATION
• Depreciation and appreciation are market moves. Devaluation and revaluation are official acts under a fixed rate.
• Cross rate: R(A per B) = dollar value of B / dollar value of A Chained: R(Rs per EUR) = R(Rs per $) x R($ per EUR)
• Triangular arbitrage: compare the IMPLIED cross rate with the quoted third rate; the gap is the profit per unit
• Effective exchange rate = trade-weighted average of bilateral rates against the main trading partners
• Arbitrage profit: units bought = sum committed / lower quote total profit = units x (higher - lower)
• % depreciation = (R_new - R_old) / R_old x 100

Forward market and interest arbitrage

• FD or FP = ((forward - spot) / spot) x (12 / n) x 100
• Trap: the 12/n annualises the rate. Omitting it understates a three-month quote fourfold.
• Positive means a forward premium on the foreign currency; negative a forward discount.
• Covered interest arbitrage margin = interest rate differential - forward discount on the foreign currency
• Zero margin is covered interest parity, which arbitrage enforces. Uncovered arbitrage omits the forward cover and so carries exchange risk.
• Spot settles within two business days. Forward settles at a stated future date. Futures are standardised amounts on select dates on an organised market; options carry a right, not an obligation.

Price adjustment: the elasticity approach

• Marshall-Lerner: |eta_x| + |eta_m| > 1 stable, devaluation WORKS |eta_x| + |eta_m| = 1 borderline, no effect |eta_x| + |eta_m| < 1 unstable, devaluation WORSENS
• Deficit-country generalisation (Section B only): (X/M) x eta_x + eta_m > X/M.
• Stable market, case 1: supply of foreign exchange positively sloped. Stable, case 2: negatively sloped but less elastic than demand. Unstable: negatively sloped and more elastic than demand.
• In an unstable market a deficit nation must APPRECIATE, not devalue. Getting this the wrong way round widens the deficit.
• ERPT = actual % rise in domestic price / % depreciation effective response = elasticity x pass-through
• J-curve: the balance worsens first because prices move before quantities. Beachhead effect: market entry and exit costs make pass-through incomplete, especially in the short run.
• Assumptions of the trade approach: capital flows only as passive responses, correction through exchange rate change, trade flows only.

Numbers from the class problems, for checking

• Indian BoP (INTRODUCTION slide 15): goods exports 150, goods imports 240, so BOT -90; net invisibles 52, so current account -38; capital account +41.15; errors and omissions +3.15; overall balance zero.
• Devaluation case (Chapter 16 slide 4): at R = 1.00 demand for euros 12 billion, supply 8 billion, deficit 4 billion. A 20 per cent devaluation to R = 1.20 clears the market at 10 billion.
• One shock, three regimes (Chapter 14 slide 16): demand shifts from 200 to 450 million euros a day at R = 1.00. Fixed: drain 250 million a day of reserves. Flexible: R rises to 1.50, quantity 300 million, a 50 per cent depreciation. Managed float: R to 1.25, a 25 per cent depreciation, with the rest drained from reserves.
• Cross rate (Chapter 14 slide 12): dollar-euro 1.25 and dollar-pound 2.00 give 2.00 / 1.25 = 1.60 euros per pound.
• Section B Problem 1: exports and imports each 50 billion, eta_x 0.7, eta_m 0.5, 5 per cent depreciation. Sum 1.2 > 1. Exports 50 x 0.95 x 1.035 = 49.16; imports 50 x 0.975 = 48.75; balance +0.41. The improvement is entirely import compression, since eta_x < 1.
• Section B Problem 2: exports 400, imports 500, eta_x 0.6, eta_m 0.3, 10 per cent depreciation. Sum 0.9 < 1. Exports 381.6, imports 485.0, so the deficit widens from 100 to 103.4. The critical eta_m that leaves it unchanged is 0.368.
• Section B Problem 3 (J-curve): exports 40, imports 55, 10 per cent depreciation. Short run eta 0.15 and 0.20: deficit 15 to 17.36. After two years eta 1.00 and 0.70: deficit 11.55.
• Section B Problem 4 (pass-through): a 10,000 dollar machine, rupee 88.00 to 95.15, invoice Rs 9,28,000. Depreciation 8.125 per cent; full pass-through price Rs 9,51,500; actual rise 5.4545 per cent; ERPT 0.671; the exporter absorbed 32.9 per cent by cutting its dollar price to about 9,752.
• Section B Problem 5 (oil to CPI): a 150 billion dollar crude bill, rupee 88.00 to 95.15, demand elasticity about zero, exchange-rate-to-CPI pass-through 0.04. Bill rises Rs 13.20 to 14.27 lakh crore; CPI inflation +0.325 points, lifting 4.30 to about 4.63 per cent.

Traps that cost marks

• The sign of R. R rising is the currency falling. Write the definition at the top of the answer sheet before starting.
• Forgetting 12/n in the forward premium formula.
• Cross rate direction. Cancel the units instead of guessing whether to multiply or divide.
• The unstable market prescription. Test Marshall-Lerner before recommending a devaluation.
• Elasticity is not the whole answer. Effective response = elasticity x pass-through, so an elasticity of 1.0 with a pass-through of 0.6 behaves like 0.6.
• Two quarters of trade data. Never judge a devaluation on them; say J-curve.
• BoP always balances. A deficit is a statement about which items closed it, not an accounting failure. Name the accommodating item.
• Describe every diagram in words. Axes, slope of each curve with its reason, the equilibrium, then the shift. A drawing with no labels earns nothing on a pen and paper paper.

Formula cards

Definitions to write verbatim

• Income adjustment mechanism — the balance of payments is corrected by changes in the level of national income of the deficit and surplus nations. It is Keynesian; the price adjustment mechanism is classical.
• Four assumptions — the disequilibrium arises in the current account; prices, wages and interest rates are constant; the nation is on a fixed exchange rate; nations operate at less than full employment.
• Small open economy — one whose international transactions do not perceptibly affect the national income of its trade partners. That is why its exports are autonomous.
• Foreign repercussions — the feedback on a nation of the income changes its own trade induces abroad. Only a very small nation can safely ignore them.
• Absorption approach (Alexander, 1952) — integrates induced income changes into the analysis of correcting a deficit by a depreciation. A = C + I, B = X - M, Y = A + B.
• Expenditure-changing policies — fiscal and monetary tools that alter the level of aggregate expenditure. Expenditure-switching policies — devaluation or revaluation, which alter the direction of spending.
• Tinbergen's principle — a nation needs as many policy instruments as it has independent objectives. Principle of effective market classification — assign monetary policy to external balance and fiscal policy to internal balance.
• Balance of payments equilibrium (Mundell-Fleming) — a trade deficit matched by an equal net capital inflow, or a surplus by an equal net capital outflow. It does not require the trade balance to be zero.
• International monetary system — the rules, customs, instruments, facilities and organizations for effecting international payments. A good one maximises the flow of trade and investment and gives an equitable distribution of the gains.
• Adjustment — the process by which disequilibria are corrected, quickly and at low cost. Liquidity — reserve assets available to settle temporary disequilibria. Confidence — belief that the mechanism works and reserves will hold their absolute and relative values.
• Seignorage — the benefit accruing to a nation from issuing its currency, or from having its currency used as an international currency.
• Dollar overhang — large quantities of dollars held by foreigners, ready to move from one monetary centre to another in response to exchange rate fluctuations.

Income determination and the multipliers

• Closed: Y = C(Y) + I equivalently S = I Open: I + X = S + M equivalently X - M = S - I With government: I + X + G = S + M + T
• MPC + MPS = 1 MPM = dM/dY APM = M/Y income elasticity of imports = MPM/APM
• k = 1 / MPS = 4 closed k' = 1 / (MPS + MPM) = 2.5 open k = 1 / (MPS + MPM + MPT) = 2 with government
• Foreign repercussions, common denominator D = MPS1 + MPM1 + MPM2 x MPS1/MPS2 = 0.525 k'' = 1 / D = 1.90 export shock k* = (1 + MPM2/MPS2) / D = 2.86 own investment shock k** = (MPM2/MPS2) / D = 0.95 partner investment shock Check: k* = k'' + k** Ranking: k* > k' > k''
• Shortcut: Y = (autonomous injections - combined intercept) / total leakage rate
• Turning income into a trade balance: dM = MPM x dY; dS = MPS x dY; dI + dX = dS + dM solves for the missing flow; trade balance change = dX - dM

Absorption and policy arithmetic

• Y = A + B so Y - A = B At full employment (Y fixed): dB = -dA Required fall in A = the size of the deficit
• With slack: net dB = gross shift in (X - M) - MPM x dY
• Five forces that reduce absorption automatically: income redistributed from wages to profits (profit earners save more); higher prices lower real expenditure; the real balance effect; the money illusion effect; inflation pushing people into higher tax brackets.
• Sizing a policy: change in autonomous spending = income gap / k External cost: induced imports = MPM x income gap Cost ratio: k x MPM per unit of fiscal action
• BP slope = MPM / capital-flow responsiveness Deficit off the diagram = (actual Y - Y at external balance) x MPM Rate rise needed = financing gap / responsiveness
• Controls: uniform tariff t + export subsidy t = devaluation of t partial coverage: effective = t x share covered advance deposit = deposit fraction x rate x fraction of a year multiple rates: implicit tax = (luxury - essential) / essential

The diagrams, reduced to what you must draw

• Figure 17-1, closed economy. Top panel: C and I up, Y across, a 45 degree line, C(Y) from intercept 100 with slope 0.75, C + I parallel above it, crossing at Y = 1,000. Bottom panel: S and I up, I horizontal at 150, S = -100 + 0.25Y crossing it at Y = 1,000.
• Figure 17-3, open economy. Top panel: I + X horizontal at 450, S + M from intercept 50 with slope 0.40, crossing at Y = 1,000. Bottom panel: X - M sloping down (exports fixed, imports rise with income), S - I sloping up, crossing on the zero line at Y = 1,000.
• Figure 18-1, Swan diagram. R up, D across. EE external balance slopes up; YY internal balance slopes down; they cross at F. Above EE surplus, below EE deficit; above YY inflation, below YY unemployment. Zones anticlockwise from the left: I surplus and unemployment, II surplus and inflation, III deficit and inflation, IV deficit and unemployment.
• Figure 18-2, IS-LM-BP. i up, Y across. IS down (lower i, more investment, so higher Y). LM up (higher i frees money from speculative to transaction use). BP up (higher Y raises imports, so i must rise to attract financing). Left of BP surplus, right deficit. Devaluation shifts BP down.
• Figure 18-10, effective market classification. Expansionary fiscal policy across, tight monetary policy up. IB and EB both slope up, and EB is flatter because capital flows respond strongly to interest rates. Hence monetary policy to external, fiscal to internal.
• The J-curve. Time across, trade balance up. It dips below the starting level, then rises above it.

The international monetary system, by era

• Two classifications. By exchange rate mechanism: fixed, flexible, hybrids (managed float, adjustable peg, currency board, dollarisation). By reserve asset: gold standard, gold-exchange standard, fiat standard.
• Gold standard, 1880-1914. Fixed rates on gold. Mint parity = ratio of gold contents = 113.0016 / 23.22 = 4.87 dollars per pound. Gold points parity plus or minus the 3 cent shipping cost, so 4.84 and 4.90, a 1.23 per cent band. Price-specie-flow mechanism via MV = PQ. Rules: do not sterilise; deficit nations tighten credit, surplus nations loosen. Gold flows equal the size of the imbalance.
• Why it looked smooth. Economic expansion and stability; sterling the only important international currency with London as hub; greater price flexibility; nations prioritising the rate over domestic objectives. In fact adjustment came through short-term capital flows and income changes, not the price channel.
• Interwar. 1914 the classical standard ends; 1919-1924 wild fluctuations; 1925 the UK restores sterling at the prewar price, so the pound is overvalued and deflation follows. Collapse causes: no adequate adjustment mechanism, destabilising capital flows from London to New York and Paris, the Great Depression. 1931-1936 competitive devaluations, protectionism, world trade cut almost in half.
• Bretton Woods, 1947-1971. Adjustable peg on a gold-exchange standard. 1944 conference, US and UK plus 42 nations, IMF created for oversight and temporary lending. Gold at 35 dollars an ounce; bands plus or minus 1 per cent. Quota: 25 per cent gold subscription; borrow 25 per cent a year to a maximum of 125 per cent; first 25 per cent the unconditional gold tranche; net IMF position = quota minus the Fund's holdings; repayment stops at holdings of 75 per cent of quota; quotas revised every five years.
• Collapse. US deficits from 1958 (capital outflows, Vietnam, inflation). Seignorage let the US settle in its own money but it could not devalue the anchor, so it relied on fiscal policy. Operation Twist, swap arrangements, the Interest Equalization Tax, the 1961 Gold Pool, the 1968 two-tier gold market. Gold depleted, dollar overhang grew, convertibility suspended 1971. Germany and Japan refused to revalue.
• Smithsonian, December 1971. Gold 35 to 38 dollars, a dollar devaluation of 8.57 per cent; mark +17 per cent, yen +14 per cent; bands widened to plus or minus 2.25 per cent; the 10 per cent US import surcharge removed. Effectively a dollar standard. 1973: gold to 42.22, a further 11.1 per cent and 20.6 per cent in total; free floating from March.
• Present system. Managed floating from March 1973, recognised by the Jamaica Accords of 1976; IMF lending expanded by the New Arrangement to Borrow, 1997. 81 nations float; others dollarise, use currency boards, or peg. Reserves: foreign exchange, gold, SDRs, IMF reserve positions. Facilities: EFF 1974, FCL 1999, ECF/SCF/RCF 2010, PLL 2011.

Numbers from the class problems, for checking

• Closed economy. C = 100 + 0.75Y, I = 150, so S = -100 + 0.25Y and YE = 1,000. MPS = 150/600 = 0.25, k = 4. A rise of 100 in I raises Y by 400, arriving as 100, 75, 56.25, 42.19.
• Open economy. M = 150 + 0.15Y, X = 300. MPM = 150/1,000 = 0.15. I + X = 450; S + M = 50 + 0.40Y; YE = 1,000 with X = M = 300 and S = I = 150. k' = 2.5 against the closed 4. APM at Y = 1,000 is 0.30, so the income elasticity of imports is 0.5.
• Foreign repercussions. MPS1 0.25, MPM1 0.15, MPS2 0.2, MPM2 0.1, so D = 0.525. Export shock of 200: dY 380 (not 500), dM 57, net dX 152, surplus 95 (not 125). Investment shock of 200: k* 2.86, dY 571, dM 85.7, deficit 57 (not 75).
• Mundell-Fleming (Chapter 18 figures). E at i = 5.0 per cent and Y = 1,000; YF = 1,500. External balance at i = 5.0 needs Y = 700, so the deficit is (1,000 - 700) x 0.15 = 45, and external balance at Y = 1,000 needs i = 6.5 per cent. Inelastic case reaches F at i = 8 per cent, elastic case at 6.0 per cent. Perfect mobility: BP horizontal at 5 per cent, E' at 6.25 per cent, E'' at 3.75 per cent.
• Zone IV illustration. Leakages 0.50 so k = 2. A gap of 300 needs dG = 150, and induced imports of 0.15 x 300 = 45 take a deficit of 30 to 75.
• Gold standard. Parity 4.87; points 4.84 and 4.90; band 1.23 per cent. At a market rate of 4.95, settling 1,000,000 pounds costs 4,950,000 in the market against 4,870,000 plus 30,000 shipping, so gold shipping saves 50,000 dollars.
• Bretton Woods quota worked example. Quota 1,200: gold subscription 300, Fund's opening holdings 900, net position 300 which is the gold tranche. One drawing of 300 takes holdings to 1,200 and the net position to zero. Ceiling 1,500.

Traps that cost marks

• Multiplier order. MPC to MPS by the identity, MPS to k by the reciprocal. Going straight from MPC to a reciprocal is the standard error.
• Induced imports come from the change in INCOME, not from the size of the fiscal injection. dG = gap / k, then dM = MPM x gap.
• Repercussion subscripts. The extra term is MPM2 x MPS1 / MPS2: the partner's import propensity, the home saving propensity on top, the partner's saving propensity underneath. Check with k* = k'' + k**.
• Which multiplier for which shock. k'' for a shock to your exports, k* for your own investment, k** for the partner's investment.
• Absorption sign. Y - A = B, not A - Y = B. A deficit nation absorbs more than it produces.
• Zones I and III need one instrument; II and IV need two. Say which zone before prescribing anything.
• Fixed rate favours fiscal policy; flexible favours monetary. Justify it by asking what absorbs the induced capital flow: reserves or the exchange rate.
• Tinbergen is a counting rule; effective market classification is an assignment rule. They are different propositions and both get asked.
• Percentage changes compound. 8.57 then 11.1 per cent is 20.6 per cent in total, not 19.7.
• Revaluation of the quoted currency means DIVIDING. A mark revalued 17 per cent goes from 3.60 to 3.60/1.17 = 3.08 marks per dollar, not 4.21.
• A loss of currency value is not the rise in the rate. 30 to 45 is a 50 per cent rise in the rate and a 33.3 per cent loss of value. State which you mean.
• Relative price levels are ratios. 55 and 24 per cent inflation gives 155/124 = 25 per cent, not 31 per cent.

Formula cards