FraNK: Fragmentation in the NK Model

Moro and Nispi Landi develop FraNK, a multi-country New Keynesian model designed to study geoeconomic fragmentation — defined, following Aiyar et al. (2023), as a policy-driven reversal of economic integration guided by strategic considerations. The model extends Gali and Monacelli (2005) along three dimensions: it is multi-country rather than small-open-economy; it assumes incomplete international financial markets, relaxing perfect risk sharing; and it incorporates commodities as intermediate inputs in production, capturing both domestic and imported commodity sourcing. A fragmentation shock is modeled as a simultaneous increase in three tax rates imposed on rival countries: a tax on imports of final goods, a tax on imports of commodities, and a tax on the purchase of foreign bonds (capital controls).

The paper proceeds in two stages. First, under a symmetric two-bloc calibration, closed-form analytical results establish the distinct macroeconomic channels of each tax. The good import tax operates through both demand (households reduce consumption of foreign goods) and supply (firms face higher real marginal costs), with the demand channel dominating: output falls unambiguously and PPI inflation decreases, though CPI inflation rises on impact due to the direct pass-through of import prices. The commodity import tax operates exclusively through supply — raising intermediate input costs — so both output and PPI inflation move in the same direction: output falls and PPI inflation rises. The bond tax is neutral under symmetric calibration: because each country’s net foreign asset position is unchanged (each country reduces its holdings of rival-bloc bonds by exactly as much as it reduces its own issuance), output and inflation are unaffected.

Second, the model is calibrated to four asymmetric regions: the United States (US), US-allied countries including the European Union (WE), the China-Russia-aligned bloc (CR), and a neutral rest of the world (NE). Bloc assignment follows Den Besten et al. (2023), using a political alignment index combining sanctions data, military imports, Belt and Road Initiative participation, and UNGA voting on Russia’s invasion of Ukraine. The US and WE impose all three taxes on CR, and vice versa; NE neither imposes nor receives taxes.

Five main findings emerge from the asymmetric simulation. First, fragmentation predominantly affects CR and WE: both experience substantial declines in consumption and production across all three tax scenarios, with CR most affected when goods or asset taxes are applied. Second, the US is largely insulated: its lower trade and financial exposure to the rival bloc relative to WE limits the pass-through of fragmentation. Third, spillovers to neutral NE are nearly negligible: the expenditure-switching channel (which raises demand for untaxed NE goods) and the global income channel (which reduces demand for all goods as the world becomes poorer) roughly cancel each other out. Fourth, fragmentation is not necessarily inflationary: whether PPI inflation rises or falls depends on the relative weight of commodities in production and the mix of taxes applied — a goods tax lowers PPI inflation, while a commodity tax raises it. Fifth, the bilateral exchange rates most affected are those of the CR bloc, which appreciate under goods and asset taxes and depreciate under commodity taxes.

Sensitivity analyses confirm robustness across higher elasticity of substitution between domestic and foreign goods (eta raised from 1.5 to 5), lower elasticity of substitution between labor and commodities (xi lowered from 0.4 to 0.1), tighter financial market integration (bond transaction costs multiplied by 5), and permanent shocks (persistence rho raised to 1). Under permanent shocks, the goods-tax effect on PPI inflation approaches zero — consistent with the closed-form result — while commodity-tax effects on production become larger and more persistent.

Q: What is the core research question of FraNK? A: The paper asks how geoeconomic fragmentation — modeled as policy-driven increases in taxes on rival countries’ goods, commodities, and bonds — affects output, inflation, exchange rates, and capital flows at both the global and country level. It also asks whether different sources of fragmentation (real versus financial) have distinct macroeconomic implications, and whether neutral countries experience meaningful spillovers.

Q: How does the model depart from the Gali-Monacelli (2005) benchmark? A: Three departures are made. The model is multi-country (N countries) rather than a single small open economy facing the rest of the world. Financial markets are incomplete, so international risk sharing is imperfect — a realistic assumption in a fragmented world. And intermediate-good production uses a CES bundle of labor and a commodity bundle that includes both domestic and imported commodities, which is essential for capturing commodity market disruptions such as those following Russia’s invasion of Ukraine.

Q: What are the three tax instruments and what does each represent? A: The goods import tax (tau_ijt) is a tariff on final goods imports, representing trade barriers. The commodity import tax (tau_O_ijt) is a tariff on imported commodity inputs, representing sanctions or restrictions on energy and raw material trade. The bond tax (theta_ijt) is a capital control discouraging purchases of bonds issued by rival countries, representing financial fragmentation or sanctions on financial assets.

Q: What does the closed-form symmetric-calibration result establish about output? A: Under the symmetric calibration, both the goods import tax and the commodity import tax reduce output unambiguously (Proposition 3.3). The bond tax is neutral for output under symmetry because each country’s net foreign asset position is unchanged — any reduction in holdings of rival-bloc bonds is exactly matched by a reduction in own-bond issuance, leaving net positions and aggregate demand unaffected (Proposition 3.4).

Q: Why does the goods import tax reduce PPI inflation while the commodity import tax raises it? A: The goods import tax operates through two opposing channels: a demand channel (households substitute away from foreign goods, reducing aggregate demand) and a supply channel (import taxes raise firms’ real marginal costs). The closed-form solution establishes that the demand channel dominates, so PPI inflation falls. The commodity import tax operates only through the supply channel — raising the cost of intermediate inputs directly — so PPI inflation rises unambiguously. CPI inflation rises on impact under the goods tax because import prices are directly included in the CPI even as PPI falls.

Q: Under what condition does simultaneous fragmentation (goods and commodity taxes together) produce PPI inflation? A: When both taxes are imposed simultaneously, the net effect on PPI inflation is ambiguous. The paper shows analytically that PPI inflation rises if and only if omega * gamma_O_tilde > gamma_tilde * (phi/sigma), where omega is the commodity weight in production, gamma_O_tilde captures commodity import weights, and gamma_tilde captures goods import weights. That is, fragmentation tends to be stagflationary the larger the weight of commodities in the production function, consistent with the empirical finding in Caldara et al. (2024) of stagflationary effects from elevated geopolitical risk.

Q: Why is the US more shielded from fragmentation than its WE allies? A: The US has relatively lower trade and financial exposure to the CR bloc compared to WE. Because the trade and financial weights calibrated from UN Comtrade, IMF CPIS, BIS LBS, and IMF CDIS data place WE in closer economic relationships with CR countries, a tax on CR imports or assets falls more heavily on WE than on the US. This asymmetry is a direct consequence of the calibration: no structural or strategic advantage of the US is assumed beyond its actual pattern of trade and financial linkages.

Q: What happens to the CR bloc’s exchange rate under each tax scenario? A: Under the goods import tax, the CR exchange rate appreciates: CR’s own tax reduces demand for US/WE goods, increasing domestic demand relative to the rest of the world, and the reduced demand for CR bonds from abroad raises CR interest rates, further attracting capital. Under the commodity import tax, the CR exchange rate depreciates: lower commodity demand reduces CR commodity prices and production, shifting labor toward goods, increasing goods supply, and lowering the CR price level relative to trading partners. Under the bond tax, the CR exchange rate also appreciates, as reduced CR demand for US/WE bonds is interpreted by markets as a shift in capital flows favoring CR assets.

Q: What explains the near-zero spillovers to neutral countries? A: Two forces operate on NE in opposite directions. The expenditure-switching channel raises demand for NE goods and commodities, as taxing countries divert purchases away from taxed rival goods toward untaxed NE products — a positive demand shock for NE. The global income channel reduces demand for all goods, including NE’s, as the taxing and taxed regions become poorer and reduce imports from everywhere. In the calibration these two forces approximately cancel, leaving NE macroeconomic variables nearly unchanged.

Q: How is the commodity sector modeled, and why does this matter for the commodity tax result? A: Each country has a representative commodity firm using a linear production function (Y_iOt = A_iO * H_iOt), where A_iO is interpretable as a per-capita endowment of natural resources. Intermediate-good firms use a CES bundle of labor and commodities (domestic and imported) with elasticity xi=0.4 between the two. When the commodity import tax is imposed, firms face higher commodity input costs, raising real marginal costs and PPI inflation while depressing production. The asymmetry between commodity exporters (CR, NE) and importers (WE) under this tax is the main source of differential regional effects.

Q: How are financial openness differences across country pairs captured, and what effect do they have? A: Bond transaction costs psi_ijF differ across pairs: psi_12F = psi_21F = 0.01 for the US-WE pair (reflecting high financial integration), while all other pairs have psi_ijF = 1 — one hundred times higher — reflecting limited cross-bloc financial integration. The sensitivity analysis multiplies all psi_ijF by 5 (less open financial markets) and finds that bond position volatility falls but qualitative results are unchanged, confirming that the financial openness calibration does not drive the main results.

Q: What are the main caveats acknowledged by the authors? A: The model omits capital accumulation, so investment dynamics are absent. Cross-country production networks (global value chains) are not modeled, which the authors acknowledge limits the richness of the production structure relative to Baqaee-Farhi (2024) style models. Domestic financial markets are assumed frictionless. The model has no role for dollar dominance in the global economy, which may matter for exchange rate and capital flow dynamics in reality. These are flagged as directions for future research.

Q: What is the key result for permanent (rho=1) versus temporary (rho=0.9) fragmentation shocks? A: Under permanent shocks, output reductions become permanent rather than transitory. For the goods import tax, the effect on PPI inflation approaches zero in the permanent case, consistent with the closed-form prediction that the demand channel effect on PPI vanishes when the tax persists indefinitely (households no longer have an intertemporal substitution motive). The commodity tax permanent shock induces a larger and more persistent fall (rise) in production for commodity importers (exporters). Bond tax permanent shock has larger magnitude effects but is otherwise qualitatively similar to the temporary case.

Q: How does FraNK relate to the existing DSGE literature on sanctions and trade wars? A: The paper positions FraNK as providing a unified framework covering all three forms of fragmentation (goods, commodity, and financial) simultaneously, with nominal rigidities allowing for inflation analysis, closed-form analytical results for transparency, and a multi-country setup rather than small-open-economy. Ghironi et al. (2024) study sanctions in a three-country model but without nominal rigidities. Itskhoki and Mukhin (2022) analyze sanctions on Russia but in a small-open-economy. Attinasi et al. (2023) and Conteduca et al. (2024b) use richer production networks (Baqaee-Farhi) but are static and exclude financial fragmentation. FraNK trades production network richness for dynamics, nominal rigidities, financial fragmentation, and analytical tractability.

Geoeconomic fragmentation: A policy-driven reversal of economic integration, often guided by strategic or geopolitical considerations, operationalized in FraNK as simultaneous increases in taxes on rival countries’ goods imports, commodity imports, and bond purchases.

Fragmentation shock: A simultaneous increase in three tax rates — goods import tax (tau), commodity import tax (tau_O), and bond tax (theta) — applied by each bloc against the other, representing the policy instruments through which integration is reversed.

Demand channel (goods tax): The mechanism by which a goods import tax reduces aggregate demand, as households substitute away from now-more-expensive foreign goods, reducing output and — because this channel dominates the supply channel — lowering PPI inflation.

Supply channel (commodity tax): The mechanism by which a commodity import tax raises intermediate input costs for firms, increasing real marginal costs and PPI inflation while reducing output — a purely cost-push effect with no offsetting demand-side force.

Bond tax neutrality: Under symmetric calibration, capital controls on rival-bloc bonds are macroeconomically neutral because each country’s net foreign asset position is unchanged: the reduction in holdings of rival bonds is exactly matched by a reduction in own-bond issuance, leaving the IS curve and Phillips curve unaffected.

Expenditure-switching channel: The force by which fragmentation between two blocs diverts import demand toward untaxed third-country (neutral) goods, generating a positive demand spillover for NE countries that roughly offsets the global income channel.

Global income channel: The negative spillover to neutral countries arising from the reduction in world income caused by fragmentation between the taxing blocs, which reduces demand for all goods including those of neutral producers, approximately canceling the expenditure-switching channel.