Small-open-economy NK Model

The Small Open Economy New Keynesian (SOE-NK) model extends the closed-economy NK core with exchange rates, external demand, and imported goods pricing. The canonical treatment is Gali and Monacelli (2005), which embedded a small open economy into a world of identical economies, each featuring Calvo-style price stickiness. Monacelli (2005) enriched the framework with incomplete exchange rate pass-through by introducing local-currency pricing for imports. Earlier open-economy DSGE work by Obstfeld and Rogoff (1995, Redux model) and Corsetti and Pesenti (2001) set the stage, but these were flexible-price or one-period models. Schmitt-Grohe and Uribe (2003) contributed the SOE-RBC benchmark and techniques for inducing stationarity in small open economy models - a technical prerequisite that Gali-Monacelli inherited.

The mechanism layer adds three channels absent from the closed-economy NK model. First, exchange rate pass-through: a depreciation of the nominal exchange rate raises the domestic-currency price of imports, pushing up CPI inflation even when domestic inflation is stable. The pass-through can be complete (producer-currency pricing) or incomplete (local-currency pricing), with large empirical consequences. Second, the terms of trade channel: changes in the relative price of home goods versus foreign goods shift demand between domestic and foreign production, creating an expenditure-switching effect that links monetary policy to net exports. Third, the uncovered interest parity (UIP) condition ties the expected depreciation of the exchange rate to the interest rate differential between home and abroad, so domestic monetary tightening appreciates the currency, compressing import prices and amplifying the contractionary effect through the trade channel.

Small open economy central banks - the Riksbank, Bank of Canada, Reserve Bank of New Zealand, Reserve Bank of Australia, Norges Bank, and most emerging-market inflation targeters - use SOE-NK models as their core forecasting and policy analysis tools. The Bank of Canada's ToTEM, the Riksbank's Ramses, and the Reserve Bank of New Zealand's KITT are all medium-scale descendants of the Gali-Monacelli structure. These institutions need models that capture how global commodity price shifts, foreign demand fluctuations, and capital flow reversals interact with domestic monetary policy - questions the closed-economy NK model cannot address.

Key extensions include Corsetti, Dedola, and Leduc (2010), who studied optimal monetary policy under incomplete markets and deviations from the law of one price; Justiniano and Preston (2010), who performed Bayesian estimation of the SOE-NK model for Canada and Australia and found that foreign shocks account for a large fraction of output variance; and De Paoli (2009), who showed that the optimal policy in the open economy departs from strict inflation targeting because the central bank can improve welfare by partially stabilizing the real exchange rate.

The SOE-NK model has five equation blocks and five to six endogenous variables beyond the closed-economy triple. The domestic demand block is an open-economy IS curve derived from the household Euler equation, augmented with a terms-of-trade gap that captures how changes in relative prices shift demand between home and foreign goods. The domestic supply block is a New Keynesian Phillips curve for domestically produced goods, structurally identical to the closed-economy NKPC but with real marginal cost now depending on the terms of trade (because imported inputs or consumption baskets affect firms' costs). A CPI inflation identity links overall inflation to domestic inflation and imported inflation, weighted by the openness parameter alpha. The external block contains the UIP condition (linking interest differentials to expected depreciation), a terms-of-trade evolution equation, and a specification for foreign demand and foreign interest rates (treated as exogenous for the small open economy).

Inputs to the system include: the openness parameter alpha (import share in the CPI basket), the exchange rate pass-through coefficient (complete under producer-currency pricing, partial under local-currency pricing), the intratemporal elasticity of substitution between home and foreign goods (eta), the intertemporal elasticity of substitution (1/sigma), the Calvo price stickiness parameter (theta), and Taylor rule coefficients. Foreign variables - foreign output, foreign inflation, foreign interest rate - enter as exogenous driving processes. A risk premium shock can be added to the UIP condition to generate exchange rate movements not explained by interest differentials.

The structural constraints parallel the closed-economy case but with open-economy twists. The Taylor principle still governs determinacy, but the threshold depends on the openness parameter and whether the central bank targets CPI or domestic inflation. Complete markets across countries (the standard Gali-Monacelli assumption) tie the real exchange rate to relative consumption via a risk-sharing condition, but this can be relaxed. The law of one price for traded goods pins down the relationship between the nominal exchange rate, foreign prices, and domestic import prices under producer-currency pricing - deviations from LOOP under local-currency pricing require an additional equation for import price dynamics.

The Reserve Bank of New Zealand's KITT model, the Bank of Canada's ToTEM II, and the Riksbank's Ramses II are all medium-scale SOE-NK models used for quarterly forecasting and policy scenario analysis. These institutions face questions the closed-economy NK model cannot answer: how does a terms-of-trade shock from commodity prices propagate to CPI? How does a foreign demand collapse affect domestic output through the trade channel versus the financial channel? Should the central bank lean against exchange rate movements or focus on domestic inflation?

The SOE-NK framework is the standard tool for evaluating exchange rate regime choices. Gali and Monacelli (2005) compared domestic inflation targeting (DIT), CPI inflation targeting (CIIT), and an exchange rate peg within the model, showing that DIT replicates the flexible-price allocation when pass-through is complete. This result breaks under incomplete pass-through (Monacelli 2005), where CIIT or managed float rules can dominate. The IMF's Article IV consultations for small open economies routinely invoke SOE-NK logic when assessing exchange rate policy.

The model breaks down for economies with significant foreign-currency debt (original sin), where exchange rate depreciation triggers balance sheet crises that the standard SOE-NK model with complete markets cannot capture. It also fails for large open economies where the small-economy assumption is violated. And it struggles with commodity exporters whose terms of trade are driven by global supply factors rather than relative demand - the standard model needs commodity-specific extensions (Medina and Soto 2007 for Chile). For dollarized or euroized economies, the exchange rate channel disappears entirely.

Emerging-market central banks (Brazil, Mexico, India, South Africa) increasingly use SOE-NK models calibrated to their specific trade structures and pass-through coefficients. Justiniano and Preston (2010) showed that the SOE-NK model with foreign shocks can match Canadian and Australian business cycle dynamics well, particularly the large contribution of external shocks to domestic output fluctuations - a feature invisible in closed-economy models.