Exogenous Supply-Side Instruments

• Exogenous supply-side instruments are econometric tools that leverage external supply shocks to identify causal effects and counterfactuals in complex market settings.
• They are constructed through techniques like recentering, which adjusts model-predicted responses to isolate variation uninfluenced by endogenous product characteristics.
• These instruments are vital in diverse applications, including demand estimation, shift-share designs, and macroeconomic policy analysis, offering robust performance even under weak instrument conditions.

Exogenous supply-side instruments are a broad class of empirical tools exploiting variation external to endogenous equilibrium adjustments in order to recover causal or structural elasticities, counterfactuals, or variance components. They are primarily constructed around shocks or features of the supply function—such as cost shifters, policy interventions, or regulated changes—whose assignment is as-if random with respect to unobserved components of demand or outcome equations. This approach is pivotal for circumventing the endogeneity of prices and product characteristics or for isolating exogenous variation in complex environments, particularly where traditional demand-side or characteristic-based instruments are infeasible or invalid.

1. Theoretical Foundations and Motivation

Classical econometric identification of demand and treatment effects frequently relies on observable exogenous characteristics or shifts in equilibrium quantities/prices. However, supply-side instruments specifically utilize exogenous cost shocks, regulatory interventions, exogenous input prices, or related mechanisms that perturb supply conditions, inducing variation in observed outcomes without corresponding changes in latent demand unobservables. Formally, these shocks, denoted as $g_{jm}$ or $Z$, must satisfy an exogeneity criterion such as $Z \perp \xi~|~\overline{X}$ (where $\xi$ denotes demand residuals and $\overline{X}$ product characteristics) (Borusyak et al., 29 Dec 2025).

These methods relax stringent assumptions on product entry, market characteristics, and functional-form restrictions that typically undergird demand identification. Notably, they allow for the possibility that observed product characteristics are themselves endogenous, and only require exogeneity of supply-side variation conditional on controls (Borusyak et al., 5 Apr 2025, Borusyak et al., 29 Dec 2025).

2. Construction of Supply-Side (Recentered) Instruments

Modern implementations focus on “recentered instruments,” which take model-predicted responses of endogenous variables (e.g., prices, market shares) to exogenous supply shocks and "recenter" them to orthogonalize with respect to endogenous characteristics. For a generic exogenous shock $g_{jm}$ and market-level covariates $x_m$, a typical instrument is constructed as:

$$Z_{jm} = h_{jm}(g_m, x_m, q_m) - \mathbb{E}\bigl[h_{jm}(g_m, x_m, q_m)~|~x_m, q_m\bigr]$$

where $h_{jm}(\cdot)$ is a function encoding the model-implied response (either via first-order shift-share approximation or exact predictions), and $q_m$ may include lagged shares or additional data for controls. This recentering ensures that, under exogeneity of $g$, the instrument is uncorrelated with potentially endogenous unobserved taste shocks $\xi_{jm}$ (Borusyak et al., 5 Apr 2025).

Instrument construction may follow a first-order (shift-share) logic—essentially a Taylor approach linearizing the endogenous response to supply shocks—or an "exact model" predictor that inverts the demand and pricing equations under both factual and counterfactual supply-side environments. Empirical implementation requires explicit estimation of pass-through parameters, prediction of “no-shock” counterfactual prices and shares, and rigorous demeaning or permutation-based recentering.

3. Identification, Moment Conditions, and Faithfulness

Identification from exogenous supply-side instruments is built on moment conditions leveraging recentered instruments. For flexible nonlinear or nonparametric demand models:

$$\mathbb{E}[Z_{jm}\{\mathcal{D}_j(s_m;\sigma, x_m, p_m) - \alpha p_{jm}\}] = 0$$

Here, $\mathcal{D}_j$ denotes the mean-utility inversion mapping in a mixed logit or analogous model. Under weak index restrictions and the new faithfulness condition—essentially requiring that supply-driven price variation “tests” for genuine price effects—nonparametric identification of all price counterfactuals is attained, even with endogenous characteristics (Borusyak et al., 29 Dec 2025).

Faithfulness can be ensured under finite-support, exogenous price assignment, pricing index/separability in the price-setting equation, or smooth location-scale structure on the demand index. These conditions guarantee that supply-side variation is sufficiently rich to pin down the functional relationship without contamination from omitted endogenous variation.

4. Application Domains: Demand Estimation, Shift-Share Designs, and Macro Identification

Supply-side instruments are applied in:

• Flexible differentiated-product demand models: Recentered cost-shock instruments outperform BLP-style characteristic IVs in environments with endogenous characteristics and correlated product entry, maintaining unbiasedness even as traditional IVs fail (Borusyak et al., 5 Apr 2025). Recent work establishes that only $J$ exogenous price instruments are required for $J$ products, not $2J$ as in characteristic-based approaches (Borusyak et al., 29 Dec 2025).
• Shift-share (Bartik) designs: Supply-induced variation, constructed as $Z_i = S'W_i$ (shifts times shares), is pivotal for causal identification of nonlinear and heterogeneous treatment effects in regional or sectoral policy analyses. Control-function approaches ameliorate the negative-weight pathologies of standard 2SLS, enabling flexible recovery of local average responses, average derivatives, policy effects, and average potential outcomes (Garzon et al., 29 Jul 2025).
• Macroeconomic variance decompositions and dynamic models: Exogenous instruments for supply shocks (e.g., oil, monetary, fiscal policy changes) can be applied in SVMA-IV or proxy-SVAR frameworks, providing informative bounds (and occasionally point identification) for variance shares and impulse responses, even without invertibility or with non-informative proxies (Plagborg-Møller et al., 2020, Angelini et al., 2024). Recent work exploits exogenous volatility regime changes as additional "instruments" to restore identification in the presence of invalid or weak proxies (Angelini et al., 2024).
• Trade and industrial policy: Instrumental policy tools such as tradeable import certificates (TICs) serve as supply-side interventions, endogenously modulating effective tariffs and subsidies, and linking import rights to export performance, with formally characterized welfare and efficiency implications in competitive and oligopolistic settings (Kranz, 27 Nov 2025).

5. Practical Considerations and Implementation Limitations

Successful application necessitates rigorous verification of shock exogeneity—specifically, shocks must be realized after entry decisions and be independent of demand errors conditional on observables. The rank condition (variation in exogenous supply shocks across products or clusters) is pivotal; weak or common shocks compromise identification strength.

Recentered instruments require precise modeling or credible simulation of the shock-drawing process (permutational inference or analytic demeaning in linear shift-share cases). Pass-through parameters must be estimated (though mis-specification affects only power, not validity). For macro applications, regime-detecting algorithms and stability restrictions must accommodate secular changes in volatility or transmission mechanisms.

Asymptotic inference requires sufficient independent observational units: many independent markets, shock clusters, or volatility regimes. Small-sample corrections and robustness checks against ongoing parameter estimation are advised (Borusyak et al., 5 Apr 2025, Borusyak et al., 29 Dec 2025, Angelini et al., 2024).

6. Comparative Performance and Empirical Results

Empirical studies demonstrate:

• Superiority in endogeneity scenarios: Recentered supply-side IVs remain unbiased under endogenous product characteristics, whereas characteristic-based IVs collapse under the same conditions (Borusyak et al., 5 Apr 2025).
• Robust control-function estimators: In shift-share designs, control-function methods using supply-side IVs yield reliable average and local derivatives, avoiding the misleading weighting of conventional 2SLS (Garzon et al., 29 Jul 2025).
• Variance-shares with imperfect proxies: SVMA-IV and proxy-SVARs with external supply-side instruments yield tight upper bounds or full point identification when regime shifts or additional structure are available, outperforming conventional SVAR-IV under non-invertibility and proxy contamination (Plagborg-Møller et al., 2020, Angelini et al., 2024).
• Trade policy implications: TICs as supply-side instruments ensure supply security via self-adjusting effective tariffs/subsidies, but distortions arise with market power in the certificate market (Kranz, 27 Nov 2025).

7. Policy Implications and Research Frontiers

Exogenous supply-side instruments constitute a rigorous alternative to traditional identification where product characteristics are endogenous, demand is flexibly specified, or valid demand-side instruments cannot be constructed. They enable nonparametric counterfactual analysis and support robust policy simulation.

Current research focuses on broadening sufficient conditions for the faithfulness property, leveraging high-frequency or cross-market supply shocks, and integrating supply-side instruments with machine learning and nonparametric estimation strategies. Additionally, the strategic design of instruments (e.g., combinatorial policies such as TICs) and their interaction with market structure, regulation, and endogenous entry are active areas of theoretical and applied investigation (Kranz, 27 Nov 2025, Borusyak et al., 29 Dec 2025).