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Econ-437 · economics · Economics

Dominant-currency pricing and exchange-rate pass-through

LLM status Open unverified

Statement

Atlas ID: T10; original number: 90; field: International trade. Classification: Editorial research formulation (theoretical/empirical); not a certified unsolved theorem.

Definitions and assumptions

Let exporting firm $i$ choose an invoice currency $k_i$ from a finite set $K$, a reset price, inputs and financing arrangements. Its feasible choices depend on contracts, imported-input costs and currency liabilities. A dynamic model $\theta$ specifies demand, nominal rigidities, monetary policy, exchange rates and agents’ information. An equilibrium consists of optimal feasible firm and household decisions, a Nash equilibrium of currency choices conditional on the pricing environment, market clearing and a specified selection when currency complementarities create multiplicity. Let $p_{it}^d$ be the strictly positive destination-currency price and $e_t^{d,k}$ destination-currency units per unit of currency $k$.

Formal research question

For an identified monetary-policy innovation $\varepsilon_t$ and horizon $h\le H$, estimate the equilibrium causal responses \[ B_{i,h}=\left.\frac{\partial}{\partial a} \mathbb E_\theta[\log p_{i,t+h}^{d}(\operatorname{do}(\varepsilon_t=a))] \right|_{a=0}, \] along with exchange-rate, trade-volume and invoice-switching responses. Define pass-through as a ratio to the corresponding nonzero exchange-rate response, specifying the exchange-rate pair. Identify the determinants of equilibrium $k_i$, and characterize how alternative currency configurations alter the welfare and international transmission of monetary policy. If derivatives fail because currency switching is discrete, use finite policy changes.

Interpretation and scope

A regression of prices on exchange rates does not automatically identify causal pass-through: demand, costs and policy respond jointly. Define whether prices are measured before or after a reset, and separate invoice-currency accounting from behavioral price adjustment. Changes in monetary policy may alter currency choice over longer horizons. An instrumental policy-surprise design requires an exclusion argument, especially when announcements reveal information about the economy. Currency denomination of liabilities and imported inputs can change optimal choices independently of market power. Welfare comparisons require household utility, financing and the monetary-policy rule rather than the price response alone. Fix a common initial state distribution for both policy interventions before taking their response difference.

Source audit and status

[S1]–[S3] identify benchmark currency-pricing mechanisms and evidence. Atlas link [46], identified in [S4], studies macro-announcement price discovery in FX; it does not establish an invoicing equilibrium. None of these references certifies the entire editorial identification and policy question as unresolved in 2026.

References

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  1. Gita Gopinath, Oleg Itskhoki, and Roberto Rigobon (2010). Currency Choice and Exchange Rate Pass-Through. American Economic Review 100(1), 304–336. https://doi.org/10.1257/aer.100.1.304. Locator and role: Publisher or author abstract / bibliographic record; Invoice currency and pass-through of US import prices. Provides background or a benchmark result; does not establish that the editorial question remains unresolved in 2026.

  2. Mary Amiti, Oleg Itskhoki, and Jozef Konings (2014). Importers, Exporters, and Exchange Rate Disconnect. American Economic Review 104(7), 1942–1978. https://doi.org/10.1257/aer.104.7.1942. Locator and role: Publisher or author abstract / bibliographic record; Imported inputs, variable markups and exchange-rate pass-through. Provides background or a benchmark result; does not establish that the editorial question remains unresolved in 2026.

  3. Gita Gopinath, Emine Boz, Camila Casas, Federico J. Díez, Pierre-Olivier Gourinchas, and Mikkel Plagborg-Møller (2020). Dominant Currency Paradigm. American Economic Review 110(3), 677–719. https://doi.org/10.1257/aer.20171201. Locator and role: Publisher or author abstract / bibliographic record; Dominant-currency pricing, complementarities and imported inputs. Provides background or a benchmark result; does not establish that the editorial question remains unresolved in 2026.

  4. Torben G. Andersen, Tim Bollerslev, Francis X. Diebold, and Clara Vega (2003). Micro Effects of Macro Announcements: Real-Time Price Discovery in Foreign Exchange. American Economic Review 93(1), 38–62. https://doi.org/10.1257/000282803321455151. Locator and role: Publisher or author abstract / bibliographic record; High-frequency exchange-rate reactions to macroeconomic news. This source does not identify firms’ invoice-currency equilibrium or currency-switching responses.

Common conventions: Source mathematical conventions

Unless an entry states otherwise, agent and firm sets are finite. State and action spaces are measurable, strategies and outcome maps are measurable, probability laws are specified, and expectations exist for the targets under discussion. Infinite-horizon discount factors lie in $(0,1)$ and discounted objectives are finite. Norms, tolerances and complexity input sizes must be specified for computational comparisons. Constants or primitives that appear locally are inputs, not empirical facts asserted by this catalogue.

Identification. A statistical model $m\in\mathcal M$ implies an observable law $P_m$ and target $\theta(m)$. At law $P$, its identified set is \[ \Theta(P;\mathcal M)=\{\theta(m):m\in\mathcal M,\ P_m=P\}. \] Point identification holds when this set is a singleton, or equivalently when $P_{m_1}=P_{m_2}$ implies $\theta(m_1)=\theta(m_2)$ for all compatible models. Sharp bounds mean bounds attained, or approached when the boundary is not attained, by compatible models. Writing this set is a definition, not a solution: the substantive task is to establish informative restrictions and derive or estimate the set. An unrestricted-confounding model may give only trivial bounds.

Inference. Identification, estimability and valid uncertainty quantification are separate questions. Fix $\alpha\in(0,1)$. A confidence procedure $C_n$ over a declared law class $\mathcal P$ has asymptotic uniform coverage at level $1-\alpha$ when \[ \liminf_{n\to\infty}\inf_{P\in\mathcal P}\Pr_P\{\theta(P)\in C_n\}\geq1-\alpha. \] For set-identified targets the coverage event must be defined separately, for example coverage of the full identified set. If an entry uses identification-indexed models instead of uniquely indexed laws, the same coverage convention is applied over those models. Pointwise limits do not establish uniform validity, and asymptotic validity does not guarantee finite-sample precision. Sample sizes, dependence structures and weak-identification sequences are part of each application.

Counterfactuals. $Y_i(a)$ is a potential outcome under a specified intervention, including its timing, implementation and versions. It is not $Y_i$ conditional on voluntarily choosing $a$. A full intervention vector permits interference; shorthand scalar treatment notation does not silently impose no interference. Assignment, selection, attrition, anticipation and measurement must be specified. A claim about an instrument's local effect is not automatically a population policy effect.

Economic equilibrium. A counterfactual model includes best responses, constraints, feasibility, market clearing, state transitions and expectations consistent with the stated information. When several equilibria exist, either a declared selector is an input or the target is set-valued. Comparisons across policy regimes must use the stated selection convention. Reduced-form relationships are not presumed invariant after an equilibrium-changing intervention.

Optimization and welfare. Optimization is over the stated feasible set. If attainment is not established, $\sup$ or $\inf$ and $\varepsilon$-optimal choices replace an asserted maximizer or minimizer. For example, with value $V=\sup_{a\in\mathcal A}W(a)<\infty$, an $\varepsilon$-optimal set is $\{a\in\mathcal A:W(a)\geq V-\varepsilon\}$ for $\varepsilon>0$. Benefits, costs, risk and health or environmental outcomes can be aggregated only using declared units and conversion weights. Interpersonal utility weights, the treatment of fiscal transfers and foreign profits, discounting, and the behavioral welfare criterion are explicit inputs. A comparative-static derivative additionally requires existence and appropriate differentiability of the selected counterfactual.

Sources. Local labels [S1], [S2], and so forth restart in every question. Locators identify the relevant abstract, model, section or result at the level actually checked; a bibliographic or abstract-level verification is not represented as inspection of an entire proof. Working papers are distinguished from later publications and changing versions. Source summaries are paraphrased. All URL checks and editorial formulations refer to the audit date stated above.

Statement licence: CC-BY-4.0 · Source file

Contributions 1

Econ-437-A1 · Exploration · LLM-generated · gpt 6 astra ultra ·

GPT 6 Astra Ultra attempt on Econ-437

Invoice accounting, price resets, and currency-coordination multiplicity

Problem ID: F31-433. Status: Unresolved. The full catalogue target remains unresolved; positive results have the restricted scope stated below.

Define the exchange-rate pair before taking a ratio

The canonical target is a causal response of destination-currency prices to an identified policy innovation, together with exchange rates, trade and invoice switching. Pass-through is a ratio to the response of a specified exchange-rate pair. This attempt separates mechanical invoice conversion from behavioral resetting, then solves a coordination game in which different equilibrium currencies generate different transmission. It does not supply a fully estimated international monetary equilibrium or a welfare ranking.

Let a permanent policy innovation be $a$, and suppose the logarithm of destination-currency units per invoice-currency unit responds by $b_ka$ for currency $k$. For a price fixed in that currency, destination log price therefore responds by $b_ka$. Let the desired reset destination log price instead respond by $\eta a$. Assume independent price-reset opportunities at dates $1,\ldots,h$, each with probability $\lambda\in[0,1]$. When a price resets it reaches the same desired level $\eta a$; later resets do not change the derivative. Invoice currency remains fixed in this first benchmark.

Proposition (A horizon-specific causal price response): With the initial price predetermined before the innovation, \[ B_{k,h}=(1-\lambda)^h b_k+\left(1-(1-\lambda)^h\right)\eta, \qquad h\ge0. \tag{1} \] If the response of the declared exchange-rate pair is $b_\star\ne0$, its pass-through ratio is $B_{k,h}/b_\star$.
Proof: The probability of no reset through horizon $h$ is $(1-\lambda)^h$. On that event the predetermined invoice-currency price changes in destination currency only through conversion, giving derivative $b_k$. On the complementary event it has reset to the desired destination price, giving derivative $\eta$. The hazard is assumed independent of $a$, so averaging and differentiating gives (1). The ratio is defined only for a nonzero denominator. ∎

At impact, $B_{k,0}=b_k$. When $\lambda>0$, the long-horizon limit is $\eta$. When $\lambda=0$, initial invoicing determines transmission forever in this model. For $b_k=1$, $\eta=0.2$, $\lambda=1/2$, responses at horizons zero, one and two are $1,0.6,0.4$. A dominant-currency exchange rate and an exporter-currency exchange rate can have different $b_\star$, so the same price response need not yield the same reported pass-through ratio.

This formula relies on a particular permanent innovation, a constant reset hazard and an exogenous desired-price response. With a transient shock, state-dependent adjustment or changing input costs, one must integrate responses over reset dates rather than retain the same $\eta$ for every cohort.

Currency shares and switching add another margin

Let $\pi_k(a)$ be the equilibrium share invoicing in currency $k$, with destination mean log prices $\ell_k(a)$ among the relevant fixed population. If these functions are differentiable at zero and grouping does not select different unaccounted-for firm types, the derivative of the mean is \[ \frac{d}{da}\sum_k\pi_k(a)\ell_k(a)\bigg|_0 =\sum_k\pi_k(0)B_{k,h}+\sum_k\pi'_k(0)\ell_k(0). \tag{2} \] This is the product rule, not an identification theorem. It shows the additional composition term. If all initial destination log prices coincide, the second term vanishes because $\sum_k\pi'_k=0$. That cancellation does not mean switching is economically irrelevant: changing shares can affect higher-order responses, future reset behavior and welfare.

To exhibit equilibrium multiplicity, take a unit continuum of nonatomic firms choosing currency $A$ or $B$. With share $x$ choosing $A$, their costs are \[ L_A(x)=c_A+\gamma(1-x),\qquad L_B(x)=c_B+\gamma x,\quad\gamma>0. \tag{3} \] The mismatch term captures a coordination benefit, and $c_k$ summarizes a stipulated private currency-specific cost. Firms minimize cost treating the aggregate share as given; the equilibrium selection is an additional primitive.

Proposition (Multiple currency configurations): Writing $\Delta=c_A-c_B$, all-$A$ is an equilibrium exactly when $\Delta\le\gamma$, and all-$B$ exactly when $\Delta\ge-\gamma$. Thus both exist when $|\Delta|\le\gamma$. For $|\Delta|<\gamma$, the interior share \[ x^*=\frac{1+\Delta/\gamma}{2} \] is also an equilibrium with indifferent firms.
Proof: At $x=1$, a negligible deviator faces cost $c_B+\gamma$, while staying costs $c_A$; the first condition follows. At $x=0$, the analogous condition is $c_B\le c_A+\gamma$. Interior shares require equality $c_A+\gamma(1-x)=c_B+\gamma x$, giving the displayed solution, which lies strictly between zero and one in the stated range. At equal costs any division of indifferent firms realizing that share is optimal. ∎

If $b_A\ne b_B$, the two pure equilibria have different impact responses despite identical primitives. Under a selection that chooses all-$A$ on one side of $a=0$ and all-$B$ on the other, prices normalized to agree at zero can take the form $\ell(a)=b_Aa$ for $a<0$ and $b_Ba$ for $a>0$. The derivative at zero fails when $b_A\ne b_B$. Finite policy changes remain well defined once selection is specified. Reporting a single derivative while ignoring this branch change hides a substantive equilibrium assumption.

Why price--exchange-rate regressions are insufficient

Take independent mean-zero unit-variance shocks $M$ and $U$. Let $M$ be the monetary policy innovation and $U$ a demand or cost shock. Suppose log exchange rates and prices satisfy \[ e=M+U,\qquad p=0.2M+U. \] The population regression coefficient is ${\operatorname{Cov}}(e,p)/{\operatorname{Var}}(e)=1.2/2=0.6$. The causal monetary price response divided by the monetary exchange-rate response is $0.2/1=0.2$. Both calculations are exact; their difference arises because the regression combines two shocks. An instrument isolating $M$ would recover the latter ratio only under its own relevance and exclusion conditions. An announcement surprise carrying information about $U$ need not do so.

Likewise, observing invoice currency does not identify why firms chose it. Imported-input denomination, liabilities and coordination costs can generate identical observed shares under different values of $c_k$ and $\gamma$. Those differences matter for counterfactual policy switching. Invoice conversion is an accounting identity, while estimating an equilibrium selection or pricing policy requires additional data restrictions.

The completed results are a reset-cohort response, a fully solved currency-coordination game, and a causal-regression counterexample. The remaining catalogue target requires a structural monetary environment, contract and financing data, valid policy innovations, switching observations, and household welfare with coherent ownership and budget constraints. Price pass-through alone cannot rank alternative currency regimes in welfare terms, and no such ranking is asserted here.

Completion Estimate

40%

This is a post hoc, heuristic estimate for the full catalogue target. The attempt derives horizon-specific price-reset responses, solves a currency-coordination game, and shows regression pass-through can differ from causal monetary transmission. Contract and financing determinants, invoice switching, identified policy innovations, trade responses, and household welfare under alternative currency equilibria remain unestablished.

References

  • [dcp] G. Gopinath, E. Boz, C. Casas, F. J. Díez, P.-O. Gourinchas and M. Plagborg-Møller (2020), Dominant Currency Paradigm, American Economic Review 110(3), 677--719. https://www.aeaweb.org/articles?id=10.1257/aer.20171201. The checked publisher record motivates the currency-transmission setting. The simplified reset and coordination equations above are explicitly restricted constructions, not a reproduction of the paper's full model.

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