Pricing-to-market in business cycle models

Layer 1: Overview

This paper evaluates five microfounded pricing-to-market (PTM) mechanisms and one reduced-form aggregator in a two-country DSGE model with volatile exchange rates driven by financial shocks (following Gabaix and Maggiori 2015) and real productivity shocks. The central question is whether existing open-economy theories can jointly achieve three empirically mandated targets — low exchange-rate pass-through to import prices, muted expenditure switching (low short-run trade elasticity), and plausible producer markups — when exchange rates are volatile and act as a major independent source of fluctuations. The paper’s main contribution is to show analytically and quantitatively that no existing microfounded PTM model fully escapes a structural tension among these three targets, which the authors call the parameterization trilemma.

The models evaluated are: (i) the Kimball Aggregator (KA; reduced-form, Itskhoki-Mukhin application); (ii) the Distribution Cost model (CD; Corsetti-Dedola 2005); (iii) the Price Dispersion model (PD; Alessandria 2009); (iv) the Nested CES/Cournot model (NCES; Atkeson-Burstein 2008); (v) the Deep Habits model (DH; Ravn-Schmitt-Grohe-Uribe 2007); and (vi) the Customer Capital model (CC; Drozd-Nosal 2012). The encompassing framework uses the Backus-Kehoe-Kydland (1995) two-country structure augmented with a financial sector that generates UIP deviations via a capacity-constrained arbitrageur segment and exogenous noise-trader positions. The model is estimated/calibrated to quarterly U.S. data (1981Q1–2009Q4 for prices, 1980Q1–2004Q1 for quantities), HP-filtered with lambda = 1,600.

The baseline markup target is 50%, consistent with BEA input-output tables for U.S. tradable sectors (ranging 45–50% across 2007, 2012, 2017); listed-firm SEC data imply higher values around 73–75%, which the authors treat as an upper bound. The empirical pass-through target is 0.4 (midpoint of a 0.2–0.6 range estimated by Campa-Goldberg 2005 and others; Gopinath-Itskhoki 2022 estimate 0.2–0.3). The short-run trade elasticity target is 0.7, measured using the volatility ratio of quantities to prices, which yields an upper-bound estimate. Real exchange rate volatility is targeted at 3.97 (standard deviations relative to GDP). Imports-to-GDP ratio is targeted at 12%.

The central analytic finding — the parameterization trilemma — is characterized precisely for each model. For the KA model, the demand elasticity parameter gamma(1) simultaneously pins down both the markup and the trade elasticity, so matching 50% markups implies trade elasticity of approximately 1.5 (above the desired range of less than 1) and any value below TE = 1 is simply unattainable. For the CD model, pass-through of 0.4 requires a distribution cost markup wedge of 150% above the producer’s markup, which is inconsistent with the 50% markup target. For the PD model, the structural formula links PT and markups but less severely, so the trilemma is partially mitigated. For the NCES model, the trade elasticity equals the firm-level elasticity theta, which is also the main driver of pass-through, recreating a binding version of the KA trilemma on the quantity side. For the CC model, the market-expansion friction (captured by adjustment-cost parameter psi) provides an additional degree of freedom that allows trade elasticity to be set independently of pass-through and markups; at symmetric bargaining power eta = 0.5 and 50% markups, the model delivers PT = 0.33 analytically, close to the data target.

Quantitative results confirm the analytic predictions. The KA model fails on quantity statistics because it implies trade elasticity far above target, generating counterfactually negative international comovement of consumption, investment, and employment. The CD model delivers only moderately incomplete pass-through (substantially above the 0.4 target), underperforming on price statistics, and implies a counterfactual correlation of net exports with the terms of trade. The PD model delivers pass-through of approximately 0.70 — better than CD but still above target — and performs well on quantities. The NCES model achieves pass-through of 0.63 (close to but above the 0.4 target) but at the cost of large, negative international comovement in general equilibrium, including a counterfactual positive correlation of net exports with output. The DH model generates more-than-complete pass-through in the presence of persistent exchange rates, failing on prices. The CC model delivers PT = 0.36, closest to the empirical target, achieves correct signs for international quantity comovement, and generates a positive terms-of-trade/net-exports correlation — but requires assumed productivity shock correlation of 0.75 to match measured TFP correlation of 0.3 due to endogenous marketing investment affecting measured TFP, and fails to deliver a positive correlation between terms of trade and the exchange rate.

The paper concludes that further research is needed into frictions that simultaneously dampen the price and quantity responses to volatile exchange rates without violating markup discipline. The reduced-form KA model neither nests nor outperforms the microfounded alternatives. The CC and PD search-based models perform best overall but introduce frictions that are harder to identify and measure directly.

Layer 2: Deep Dive

What is the parameterization trilemma and how is it characterized analytically?

The trilemma is the structural impossibility of jointly satisfying three empirically necessary targets: (a) plausible steady-state producer markups (calibrated at 50%), (b) low short-run trade elasticity (targeted at 0.7 or below), and (c) low exchange-rate pass-through to import prices (targeted at 0.4). The authors derive closed-form expressions for pass-through (PT), trade elasticity (TE), and markups (mu) for each model and show that satisfying any two targets forces a violation of the third. For the KA model, the key parameter gamma(1) satisfies TE = gamma(1) and mu = (gamma(1) - 1)^{-1}, so targeting 50% markups forces TE = 3 and targeting TE = 1.5 forces markups of 200%. For the CD model, PT = 0.4 requires the distribution-cost wedge xi/(theta-1) = 1.5, implying markups more than 150% above the friction-free level, incompatible with a 50% target. For the PD model the formula is PT = 1 - mu/(1+mu), which is less restrictive. For the NCES model, TE = theta (the firm-level elasticity) and theta also drives pass-through, recreating the KA-type trilemma on the quantity side. For the CC model, the friction parameter psi in marketing capital accumulation independently controls TE, providing an extra degree of freedom that lets the model partially escape the trilemma.

What is the identification strategy for pass-through and trade elasticity, and what are its main assumptions?

The theoretical pass-through coefficient (PT) is defined as the partial equilibrium, on-impact elasticity of the import price with respect to the exchange rate, computed at the steady state while holding constant marginal costs (v, v*), the stochastic discount factor, and the domestic price of the home good. This mimics what regression-based pass-through estimates do (controlling for local costs). Trade elasticity (TE) is defined analogously as the PT-scaled elasticity of the import/domestic quantity ratio with respect to the exchange rate, under a one-time shock that reverts to the steady state next period (except for the DH model, where a permanent shock is considered). A key assumption is that importers take aggregate price indices as consistent with all importers behaving the same way (a rational-expectations fixed point). General-equilibrium co-movements between exchange rates and marginal costs are abstracted from in the analytic section, consistent with the goal of isolating each model’s intrinsic PTM mechanism.

Why does the KA model fail on quantity statistics despite being able to match any degree of pass-through?

The KA model can match pass-through of 0.4 by freely choosing the curvature of the demand aggregator g’’(1) (independently of gamma(1)). However, the steady-state demand elasticity gamma(1) simultaneously determines both the markup (mu = (gamma(1)-1)^{-1}) and the trade elasticity (TE = gamma(1)). Matching 50% markups forces gamma(1) = 3 and therefore TE = 3, far above the target of 0.7. This excessive trade elasticity generates counterfactually large expenditure switching in response to exchange-rate shocks, leading to counterfactual negative international comovement of consumption, investment, and employment. A modified Kimball aggregator with a convex adjustment cost (equation 62) does not resolve the problem because the convex cost parameter also enters the steady-state markup formula, so targeting 50% markups still forces high effective trade elasticity.

Why does the Deep Habits model generate more-than-complete pass-through when exchange rates are persistent?

In the DH model, producers internalize the law of motion for habits: by lowering prices today they accumulate more customer habits, which allows them to raise prices later. When the exchange rate appreciates persistently (from the foreign exporter’s perspective), exporters expect their foreign sales and thus foreign habit stocks to fall over time. This reduces the shadow value of habit (Delta_f), so producers let prices fall by more than the exchange rate movement, generating pass-through greater than one. The authors derive analytically that, for a permanent shock, PT > 1 because dlog(gh)/dlog(x) < 0 (habit falls upon appreciation), and this dominates the direct pricing effect. For a purely transitory shock, the sign reverses (PT < 1), but since exchange rates are highly persistent in the data, the first property dominates. The quantitative section confirms this: the DH model generates PT > 1, marked as 1.00 in Table 4, disqualifying it on prices.

How does the Customer Capital (CC) model partially escape the trilemma?

The CC model introduces two key elements absent from other frameworks: (1) Nash bargaining over prices within bilateral matches, which directly ties pass-through to the sharing of exchange-rate-driven surplus rather than to demand elasticity; and (2) a convex adjustment friction on marketing capital (psi) that controls the pace of trade-share adjustment, independently setting the short-run trade elasticity. Because prices are determined by bargaining (equation 53: pf = eta*P_d + (1-eta)*v), they depend on the retail marginal value of the foreign good (P_d) and the foreign marginal cost (v), but not on quantity within the match. This decouples PT from TE. Analytically, at static steady state, PT = (1-eta)(1 + mu - (TE/gamma)(eta+mu)*omega)^{-1}; for eta = 0.5 and 50% markups and TE/gamma approaching zero, PT approaches (1-eta)/(1+mu) = 1/3. The psi parameter then tunes TE separately from markups and PT. However, a high long-run elasticity gamma (= 7.9) is required to generate sufficient retail-price responsiveness.

What does the NCES model achieve on prices and why does it fail on quantities?

The NCES (Nested CES with Cournot competition) model generates incomplete pass-through of 0.63, the second-best performance on prices after the CC model. The mechanism is that non-atomistic (Cournot) firms internalize the impact of their pricing on the sectoral price index; when the exchange rate moves, foreign exporters’ market share changes, altering the endogenous demand elasticity they face and dampening their pass-through. To calibrate the model with only one exporting firm (NX=1 out of N=5), the authors maximize the Cournot effect. However, this calibration implies TE = theta (the firm-level elasticity, set at 7.9 in calibration), far exceeding the target of 0.7. A quantity adjustment cost cannot remedy this because it would simultaneously constrain import-share movements, which are the source of the endogenous demand elasticity variation that generates incomplete pass-through. Consequently, the model implies large negative international comovement of output, consumption, employment, and investment — a worse quantity performance than most other models.

How does the paper measure markups and what data sources does it use?

The paper equates markups with gross margins under the maintained assumptions of Cobb-Douglas production and static cost minimization (Hall 1988; De Loecker et al. 2020). Under Cobb-Douglas, marginal cost v = wl/y, so markup mu = Py/(wl) - 1 = sales/(cost of goods sold) - 1. Three data sources are used, all for U.S. data 2007-2017: (1) BEA 402 Industry Input-Output Use Tables, which give gross margins of approximately 39-41% for all sectors and 45-50% for traded sectors (import share > 3%). (2) S&P 500 Compustat with BEA sector value-added adjustment, yielding approximately 73-74% for all non-FIRE/GOV/NGO firms. (3) Unadjusted Compustat, yielding 43-49%. The paper adopts 50% as the baseline calibration target, treating it as conservative given the data range, and noting that the BEA I-O measure is the broadest and likely most accurate. The paper explicitly holds that models must respect profit and margin accounting within their own structure.

How does the paper’s conclusion differ from Itskhoki and Mukhin (2021) regarding the Kimball Aggregator?

Itskhoki and Mukhin (2021) use indirect inference and treat producer margins/markups as a free parameter, implicitly allowing for a much higher markup value — substantially above 50%. Under their calibration approach, the KA model can reconcile low pass-through with better quantity performance. Drozd, Kolasa, and Nosal instead impose a markup discipline: models must match empirically observed gross margins of 50% (for tradable sectors from BEA I-O tables) in their steady state. Under this discipline, the KA model’s trilemma becomes binding, and the model fails on quantity statistics. The authors argue that higher markup assumptions change the effective structure of the model and should be treated as a separate research agenda rather than a free calibration choice.

What is the role of financial shocks in the model and how are they implemented?

Financial shocks generate exchange-rate volatility that is largely decoupled from real fundamentals — mimicking the observed ’exchange rate disconnect’ from output and consumption. They are modeled following Gabaix and Maggiori (2015): a global financial sector with short-lived arbitrageurs and noise traders. Arbitrageurs face a capacity constraint (parameterized by Gamma) that prevents them from fully exploiting UIP violations, resulting in a distorted UIP condition where the interest rate differential includes a term proportional to the arbitrageur’s position. Noise traders take exogenous positions n(t) that follow an AR(1) process (persistence rho_n = 0.97 in calibration) with standard deviations ranging from 21.2 (CC model) to 114.9 (NCES model) across calibrations. These shocks generate real exchange rate volatility of 3.97% (standard deviations relative to GDP), matching the data target. The paper notes that the precise implementation (Gabaix-Maggiori vs. Itskhoki-Mukhin) has little impact on exchange-rate properties in a linearized setting.

What robustness checks and extensions does the paper consider?

The paper considers a modified Kimball aggregator with a convex adjustment cost on the ratio of imported to domestic quantities (equation 62) as a potential fix for the KA model’s high trade elasticity. This is shown not to resolve the trilemma because the convex cost parameter also enters the steady-state markup formula, keeping the binding constraint in place. Results for this modified model are reported in the Online Appendix. The paper also notes that the DH model’s pass-through is analyzed under both permanent and transitory shocks, with the sign reversal for purely transitory shocks documented analytically. The paper abstracts from nominal rigidities throughout, justifying this by citing Gopinath-Itskhoki (2011) evidence that conditioning pass-through on price adjustments versus non-adjustments makes little difference in observed pass-through patterns, suggesting limited pass-through is largely a real phenomenon.

What are the paper’s main implications for the DSGE modeling of open economies?

The paper implies that the standard toolkit for generating incomplete exchange-rate pass-through and muted expenditure switching is inadequate when exchange rates are volatile and act as a major shock. All models face tension among the three targets; the best performers (CC and PD) do so by introducing search frictions that are intrinsically difficult to identify and measure directly. The paper does not claim to provide a solution; rather, it performs a clean diagnostic showing that more research is needed into real frictions that simultaneously insulate import prices and trade quantities from exchange-rate volatility. The finding that the Kimball reduced-form aggregator neither nests nor outperforms microfounded alternatives has implications for monetary-policy DSGE models that frequently use the KA for tractability, suggesting that researchers should be aware of the high implicit markup that is required for the KA to work well in open-economy settings with volatile exchange rates.

What moments from the data are targeted in calibration and what is the quantitative approach?

The model is calibrated quarterly and HP-filtered (lambda = 1,600). Common targets include: imports/GDP = 12%; 50% producer markups; 30% work hours relative to time endowment; investment volatility relative to GDP = 2.79; short-run trade elasticity (volatility ratio) = 0.7; cross-country TFP correlation = 0.3; TFP volatility = 0.8% and autocorrelation = 0.72; real exchange rate volatility = 3.97%. The pass-through target of 0.4 is used only as an additional degree of freedom for the KA model; for all others, pass-through is an outcome of the structural parameterization. The financial shock persistence is set arbitrarily at rho_n = 0.97 for lack of a target. When a model cannot satisfy all targets (as with KA and NCES on trade elasticity), that target is dropped in favor of best performance on prices. Pass-through is measured in the quantitative section by running regressions analogous to Campa-Goldberg (2005) on model-generated data, rather than using the analytic partial-equilibrium formula.

What is the sign of the terms-of-trade and exchange-rate correlation, and what does it imply for model evaluation?

In model-generated data (without noise), the correlation of terms of trade (tot = pf/px) with the exchange rate (x) is either -1 (when PT < 0.5) or +1 (when PT > 0.5). The empirical target from U.S. data is approximately -1. This means matching PT < 0.5 and a negative tot-x correlation are equivalent predictions. In the quantitative results, only the KA and CC models achieve PT < 0.5 and thus generate the correct negative correlation; all other models (CD, PD, NCES, DH) generate PT > 0.5 and thus positive tot-x correlation. The authors note that the strict 0.4 target may be too aggressive for aggregate data — PT slightly above 0.5 would be consistent with a positive (near zero) correlation — pointing to Gopinath et al. (2020) who find small, statistically insignificant tot-x coefficients ranging from positive to negative.

Key Concepts

Parameterization Trilemma: The structural impossibility of jointly achieving three empirically necessary targets in standard PTM models: (1) plausible producer gross margins (~50%), (2) low short-run trade elasticity (~0.7 or below), and (3) low exchange-rate pass-through to import prices (~0.4). Each PTM model can satisfy at most two of the three targets simultaneously under quantitative discipline; the third is either infeasible or inconsistent given the model’s internal constraints.

Pricing-to-Market (PTM): The practice by which internationally active firms set different prices in home and foreign markets as a function of the bilateral exchange rate, rather than uniformly passing exchange-rate changes through to import prices. In this paper, PTM is measured by the degree of incomplete pass-through (PT < 1) and is generated by specific microfounded frictions (distribution costs, search, habits, market power, customer capital) rather than by nominal rigidities.

Exchange-Rate Pass-Through (PT): The elasticity of the import price (in the importing country’s currency) with respect to the bilateral real exchange rate, computed in partial equilibrium at the steady state, controlling for local costs. Values used in calibration: empirical short-run range 0.2–0.6; paper target 0.4. Models in which PT = 1 satisfy the law of one price; models with PT < 1 exhibit pricing-to-market.

Short-Run Trade Elasticity (TE): The elasticity of import quantities relative to domestic quantities with respect to the exchange rate (equivalently, the expenditure-switching response to import price changes), measured at business-cycle frequencies. The paper measures this using the volatility ratio of trade-flow quantities to prices (an upper-bound estimate abstracting from correlations), targeting a value of 0.7. Long-run elasticity estimates based on trade liberalization episodes are much higher (typically 6 and above) and are used as the long-run elasticity parameter gamma in search-based models.

Customer Capital (CC) Model: A PTM model (Drozd-Nosal 2012) in which firms build market-specific customer relationships through costly, time-consuming investment in marketing capital, and within-match prices are set by Nash bargaining. The combination of a capacity constraint on quantities traded within each match and bargaining-determined prices decouples the short-run trade elasticity from pass-through, allowing the model to partially escape the parameterization trilemma via the adjustment-cost parameter psi.

Kimball Aggregator (KA): A reduced-form, implicitly defined demand aggregator (Kimball 1995) that generates variable demand elasticity through the curvature of the function g(·) around the steady state. In the open-economy application of Itskhoki-Mukhin (2021), two curvature parameters (g’(1) and g’’(1)) can independently control markup and pass-through — but not trade elasticity simultaneously, which is bound to the steady-state demand elasticity gamma(1) and hence to the markup. The paper shows this model neither nests nor outperforms microfounded alternatives under markup discipline.

Financial Shock: An exogenous disturbance to the position of noise traders in the international bond market (following Gabaix-Maggiori 2015), which drives deviations from Uncovered Interest Parity via the capacity constraint on arbitrageurs. These shocks generate exchange-rate volatility that is largely disconnected from real fundamentals (productivity), calibrated with persistence rho_n = 0.97 to match U.S. real exchange rate volatility of 3.97% relative to GDP.

Gross Margin / Producer Markup: In this paper, defined as (price - marginal cost) / marginal cost = (sales - cost of goods sold) / cost of goods sold, where under Cobb-Douglas production and static cost minimization, the markup equals the gross margin. The paper targets 50% for U.S. tradable-sector firms based on BEA 402 Industry I-O Use Tables (which yield 45–50% for tradable sectors across 2007–2017), treating this as a hard empirical constraint that models must satisfy in the steady state.