Moore and Roche (2012) showed, in a two-country complete-markets economy with Campbell–Cochrane habit persistence and a cash-in-advance monetary constraint, that the theoretical Fama regression slope is negative (the forward premium puzzle) when the conditional variance of foreign money growth is below a computable threshold and positive — as uncovered interest parity (UIP) predicts — when it is above; the sign prediction matched 55 of 56 monetary regimes across 42 countries, with model slopes correlating 0.78 with estimated slopes. The open problem is whether this monetary-volatility explanation of when UIP holds survives the assumptions most strained precisely in the economies where UIP empirically holds — complete markets and perfect international risk sharing, M1 as the proxy for transaction money (which fails for Hong Kong), and the omission of additional sources of risk — and what accounts for the substantial residual cross-regime variation in Fama slopes.

Background

Uncovered interest parity (UIP) is the textbook no-arbitrage condition of international finance: the expected change in a bilateral exchange rate equals the interest-rate differential between the two currencies, so yield advantages are exactly offset by expected depreciation. Its standard empirical test is the Fama (1984) regression, which regresses the realized change in the log spot exchange rate on the forward premium (the forward rate minus the spot rate, which by covered interest parity equals the interest differential); UIP implies a slope of +1. For developed economies the estimated slope is typically negative — the forward premium puzzle (or forward bias puzzle) — meaning high-interest-rate currencies tend to appreciate rather than depreciate, which is the basis of the carry trade (borrowing low-interest currencies to invest in high-interest ones).

A robust stylized fact is that this failure is not universal: UIP holds far better, and Fama slopes are positive, in emerging and crisis economies (Bansal and Dahlquist, 2000; Flood and Rose, 2002; Frankel and Poonawala, 2010). The carry-trade literature converged on a two-factor risk explanation in which one factor is consumption risk and the identity of the second is debated; Menkhoff, Sarno, Schmeling, and Schrimpf (2012) identify global foreign-exchange volatility as a priced second factor.

Moore and Roche (2010, 2012) give the volatility hypothesis a structural foundation. Their model is a two-country, complete-markets endowment economy with external habit persistence in the sense of Campbell and Cochrane (1999) — utility is defined over consumption relative to a slow-moving habit level, so the surplus-consumption ratio drives time-varying risk aversion — augmented with a cash-in-advance constraint (purchases require previously accumulated money balances, so money growth enters nominal pricing). Verdelhan's (2010) habit model without money generates a persistent negative Fama slope because the precautionary-saving motive dominates the intertemporal-substitution motive, so UIP would never hold; Moore and Roche show that with money in the constraint the theoretical Fama slope has a closed form whose sign flips with the conditional variance of foreign money growth, ρπ2σu2/(1−ρπ2)\rho_{\pi}^{2}\sigma_{u}^{2}/(1-\rho_{\pi}^{2}), where ρπ\rho_{\pi} is the AR(1) persistence of money growth and σu\sigma_u the standard deviation of its shocks. Under the baseline calibration (curvature γ=2\gamma = 2, surplus-consumption persistence φ=0.994\varphi = 0.994), the slope is positive — UIP holds — if and only if this conditional variance exceeds a computable cutoff of 0.5359 in the paper's monthly units. Calibrating the model to 42 countries and 56 monetary regimes (sub-periods in which the AR(1) process for money growth is stable), the sign prediction matches the empirical Fama slope in all but one regime (Hong Kong, attributed to M1 — narrow money, currency plus demand deposits — being the wrong measure of the cash-in-advance money stock), and the model-implied slopes correlate 0.78 with the estimated ones across regimes.

The paper's own conclusion identifies what remains unresolved. The complete-markets and perfect-risk-sharing assumptions are hardest to justify precisely for the least developed economies in the sample — the very economies whose volatile regimes deliver the model's distinctive positive-slope prediction — and relaxing them could change the results. M1 may not proxy the cash-in-advance money growth rate appropriately in all countries. Sensitivity of the prediction to the habit specification and calibration remains unexplored (curvature γ=0.5\gamma = 0.5 is noted to require even higher monetary volatility to produce a positive slope). And the 0.78 correlation leaves substantial residual variation in Fama slopes across regimes unexplained, indicating additional factors beyond monetary volatility and the real precautionary motive.

Problem Statement

The problem, as posed by the source's stated agenda, is to determine whether the monetary-volatility explanation of when uncovered interest parity holds survives the assumptions most strained in exactly the economies where UIP empirically holds, and to account for the variation the baseline leaves unexplained. The object of study is the volatility-threshold mechanism of the habit-based, cash-in-advance model of Moore and Roche (2012), evaluated in environments with (i) incomplete international financial markets and imperfect risk sharing rather than complete markets, (ii) monetary aggregates that appropriately measure the cash-in-advance money growth rate across countries (the baseline's M1 proxy fails for Hong Kong), and (iii) additional sources of risk. The three labeled conditions (i)–(iii) delimit the scope of environments to be examined rather than a conjunctive checklist: each is an independently admissible relaxation. The overarching objective is a friction-robust structural account of when UIP holds: whether the precautionary-savings versus intertemporal-substitution mechanism continues to separate stable from volatile monetary regimes once these frictions are admitted, how sensitive the sign threshold is to the habit specification and its calibration, and which additional factors explain the residual cross-regime variation in empirical Fama slopes (model-data correlation 0.78 in the baseline).

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