Fluctuating Market Conditions and Currency Values
A new study published by the Federal Reserve Bank of San Francisco provides direct empirical support for the mechanism linking imperfect risk sharing and exchange rates, offering an explanation for the Backus-Smith puzzle. The paper, titled "Incomplete Markets and Exchange Rates," was authored by Marin and Singh in 2025.
The Backus-Smith puzzle refers to the empirical observation where exchange rates exhibit a counterintuitive aggregate relationship with relative consumption growth across countries. This puzzle challenges standard international macro-finance models that assume perfect risk sharing.
The study proposes that imperfect risk-sharing within countries can generate scenarios where exchange rates are sufficiently risky with respect to idiosyncratic consumption shocks at the household or individual level. This riskiness is crucial for reconciling the observed exchange rate cyclicality because:
- Even if aggregate consumption in a country grows, idiosyncratic risk remains elevated, meaning that not all agents in the economy share risks perfectly. This partial sharing means individual consumption and discount factors vary more than aggregate consumption suggests.
- As a result, exchange rate dynamics reflect not only aggregate shocks but also these unshared idiosyncratic risks. Exchange rates become more sensitive to these heterogeneous consumption risks, which helps explain their cyclical behavior relative to consumption that standard models miss.
The role of market incompleteness differs within versus across countries: incomplete markets inside countries limit risk sharing among agents, while cross-country market incompleteness influences international risk-sharing patterns. Both dimensions are necessary to match observed exchange rate moments and the Backus-Smith puzzle.
The study analyses household-level data to measure discount factor wedges, which capture the effects of imperfect risk-sharing. These measurements provide direct evidence for how within-country risk-sharing imperfections affect exchange rates and their relation to consumption growth.
In summary, imperfect risk-sharing within countries coupled with risky exchange rates linked to idiosyncratic states creates the conditions where the Backus-Smith puzzle arises and is reconciled. This complexity arises from the incomplete markets both domestically and internationally, leading to risk premia embedded in exchange rates that standard complete-market models fail to capture.
The paper, "Incomplete Markets and Exchange Rates," can be accessed through its DOI: 10.24148/wp2025-11.
[1] Marin, M., & Singh, A. (2025). Incomplete Markets and Exchange Rates. Federal Reserve Bank of San Francisco Working Paper 2025-11.
- The paper "Incomplete Markets and Exchange Rates," authored by Marin and Singh in 2025, offers a solution to the Backus-Smith puzzle by explaining how imperfect risk-sharing within countries can make exchange rates sensitive to idiosyncratic risks, which is crucial for reconciling observed exchange rate cyclicality.
- In the business of finance, the study published by the Federal Reserve Bank of San Francisco in 2025 suggests that incomplete markets, both domestically and internationally, lead to risk premia embedded in exchange rates, a complex phenomenon that standard complete-market models fail to capture.
