What determines the exchange rate — the price of one currency in terms of another? It is one of the most-studied and least-successfully-predicted prices in economics. This module covers the main theories, each capturing part of the truth, and the humbling empirical fact that none of them reliably beats a coin flip in the short run.
Purchasing power parity
PPP and the law of one price
Purchasing power parity (PPP) builds on the law of one price: identical goods should cost the same everywhere once converted to a common currency (otherwise arbitrage — buy where cheap, sell where dear — would erase the gap). Absolute PPP says the exchange rate should equate the price of a common basket of goods across countries; relative PPP says the exchange rate should move to offset inflation differentials (a country with higher inflation sees its currency depreciate). The Big Mac index is PPP made vivid — comparing the local-currency price of a Big Mac across countries to spot 'overvalued' and 'undervalued' currencies. The reality: PPP fails badly in the short run (exchange rates deviate from PPP for years) and holds only loosely over the long run (a tendency, not a tight relationship). The reasons it fails — non-traded goods (a haircut isn't arbitraged across borders), transport costs and trade barriers, and the Balassa-Samuelson effect (richer countries have higher price levels because high productivity in traded goods raises wages and hence non-traded prices) — are the 'PPP puzzle' Rogoff highlighted: deviations are both large and persistent. So PPP is a useful long-run anchor and a way to spot gross misalignment, but useless for short-run prediction.
Uncovered interest parity
UIP and the carry-trade puzzle
Uncovered interest parity (UIP) is the financial-side condition: if capital is mobile, the expected return on assets across currencies should be equal, so the interest-rate differential should equal the expected depreciation: i_domestic − i_foreign = expected depreciation of the domestic currency Intuition: if a country's interest rate is higher, its currency should be expected to depreciate by the difference, otherwise investors would pile into the high-yield currency. The reality: UIP fails systematically — the 'forward-premium puzzle'. High-interest-rate currencies do NOT, on average, depreciate as UIP predicts; they often appreciate or hold, so borrowing in low-rate currencies to invest in high-rate ones (the carry trade) is profitable on average — until it isn't, because the carry trade periodically crashes (the high-yield currency suddenly collapses, wiping out the accumulated gains). UIP's failure and the carry trade's 'picking up pennies in front of a steamroller' character are central to understanding capital flows into high-yield emerging markets — including African frontier markets, which attract carry-trade inflows that can reverse violently.
Structural models
Beyond the parity conditions, structural models try to pin down the rate. The monetary model derives the exchange rate from relative money supplies and demands (more domestic money, weaker currency) — clean in theory, weak in fit. The portfolio-balance model treats domestic and foreign bonds as imperfect substitutes, so the exchange rate depends on the relative SUPPLY of assets and on risk premia (the channel through which sterilised intervention, from the Monetary Policy course, can work). These models capture real forces but, like PPP and UIP, fit the data poorly in the short run.
The Meese-Rogoff puzzle
Nothing beats a random walk
The most famous and humbling result in exchange-rate economics: Meese and Rogoff (1983) showed that, at short horizons, NONE of the structural exchange-rate models — monetary, portfolio-balance, or any combination — could out-predict a naive random walk (the forecast that tomorrow's rate equals today's). Decades of subsequent research have barely overturned this: short-run exchange-rate movements are essentially unpredictable, dominated by news and shifts in expectations that no model captures in advance. The implications are profound and practical: be deeply sceptical of anyone confidently forecasting short-run exchange rates; the fundamentals (PPP, interest differentials, current accounts) matter for long-run levels and for spotting gross misalignment, but not for next month's rate; and the unpredictability is itself a fact policymakers must live with (it is why fear of floating and intervention are so tempting — the rate's movements are erratic and disconnected from fundamentals in the short run). Humility about exchange-rate prediction is not a confession of ignorance; it is the state of the art.
Exercise
A frontier-market currency offers a 12% local-currency T-bill yield while dollar rates are 4%. Foreign investors pour in to capture the 8% carry. An analyst claims, 'By uncovered interest parity, this currency should depreciate about 8% a year, so the carry is an illusion.' (1) Explain the analyst's UIP reasoning. (2) Explain why UIP fails empirically and what that means for the carry trade. (3) Explain the danger lurking in the carry inflows despite their profitability. (4) The finance ministry asks you to forecast the exchange rate in three months to plan debt issuance — what do you tell them, citing Meese-Rogoff?