Misallocation Under Trade Liberalization

The paper asks how much developing countries benefit from opening to goods trade when prevalent policy and institutional distortions exist. While new trade theories suggest reallocation towards more productive firms generates gains, many developing economies exhibit firm-specific taxes/subsidies, industrial policies, and other wedges that can interact with trade. The authors posit that in such second-best environments, trade liberalization can worsen resource allocation by selecting into exporting firms that are more subsidized rather than more productive, potentially offsetting or even overturning the standard gains from trade. They build a framework to quantify these effects and assess their magnitude in China’s trade liberalization episode in the early 2000s.

The work revisits the second-best trade literature (Bhagwati and Ramaswami, 1963; Bhagwati, 1968; Johnson, 1967; Newbery and Stiglitz, 1984) noting that domestic distortions can alter welfare effects of trade. It contrasts with ACR (Arkolakis, Costinot, Rodríguez-Clare, 2012) which provides sufficient statistics in efficient environments, and with extensions showing limits under general productivity distributions (Melitz and Redding, 2015). It connects to the misallocation literature (Hsieh and Klenow, 2009; Restuccia and Rogerson, 2008; Bartelsman et al., 2009) by emphasizing wedges and selection, and to empirical work highlighting entry/exit in China’s growth (Brandt et al., 2012). The paper also situates its contribution relative to models of diffusion, adoption, and innovation as alternative sources of trade gains (e.g., Alvarez, Buera, Lucas; Perla, Tonetti, Waugh; Atkeson and Burstein), arguing these are outside scope but complementary.

Theory: A two-country Melitz model with heterogeneous firms is augmented with firm-specific wedges. Each entrant pays a sunk cost and draws productivity φ and a distortion τ that acts as an output (revenue) wedge (τ>1 tax, τ<1 subsidy). Firms face fixed and variable costs domestically; exporters additionally face iceberg trade cost τ_x and fixed exporting cost f_x. In the baseline, wedges affect domestic and foreign sales symmetrically; in an extended model, firms also draw export-specific wedges on sales (τ_ex) and on fixed costs (τ_fx). Consumers have CES demand over varieties, final producers are competitive. The government rebates tax revenues lump-sum. Equilibrium features cutoffs for domestic production and exporting that depend on τ (and τ_ex, τ_fx in the extension), and standard free-entry and labor-market clearing conditions. Welfare decomposition: Welfare W equals real consumption per capita, W=Q/L, which the authors express as −d ln P (price index effect) plus a fiscal externality term d ln(PQ/L)=d ln(1+T), where T is net tax revenue accruing from wedges. They derive sufficient-statistics expressions for small trade-cost changes. Key sufficient statistics: (i) λ, the domestic expenditure (sales) share; (ii) S, the domestic input share (share of variable labor used to serve the domestic market); (iii) extensive-margin elasticities evaluated at the domestic cutoff: γ_λ (elasticity of cumulative sales above the cutoff) and γ_s (elasticity of cumulative variable labor above the cutoff). Proposition 2 shows: d ln W = [−d ln λ + d ln M_e]/(γ_λ+σ−1) + [(γ_λ/(σ−1))/(γ_λ+σ−1)] d ln PQ, with d ln PQ summarized by gaps between S and λ and between γ_s and γ_λ. Special cases yield sufficient conditions for welfare losses. Quantitative implementation: The extended model with τ, τ_ex, τ_fx is taken to Chinese manufacturing firm data (1998–2007). The joint distribution of (φ, τ, τ_ex, τ_fx) is assumed multivariate log-normal. Parameters include fixed costs (f, f_x, f_e), trade cost τ_x, foreign economy size/productivity, and distributional moments (standard deviations and correlations). The model is estimated to match moments on TFPR (revenue-based productivity) and TFPQ (quantity-based productivity), export participation and intensity, their dispersions and correlations, and macro trade shares. Because observed wedges and productivities are affected by selection, the underlying joint distribution is estimated via simulated method of moments rather than directly inferring firm wedges. Two welfare-decomposition procedures are used: a “direct” method evaluating elasticities at the open-economy equilibrium and a “cumulative” method integrating small changes over a grid of trade costs to move from open to autarky.

Theoretical findings:

• Welfare with distortions departs from ACR due to a fiscal externality: selection changes tax revenue and thus income. Sufficient statistics beyond λ and the trade elasticity are needed: the gap between domestic input share and domestic sales share (S vs λ) and the extensive-margin elasticities (γ_s vs γ_λ).
• Negative fiscal externality arises when: (i) exporting uses a larger share of inputs than the share of export revenues (S falls more than λ, implying exporters are relatively subsidized), and/or (ii) γ_s<γ_λ so that tightening of the domestic cutoff selects relatively more subsidized firms domestically.
• Special cases: With homogeneous productivity and Pareto-distributed domestic wedges, opening to trade always reduces welfare (S<λ). With jointly log-normal (τ,φ), if στ ≥ ρσφ then S ≤ λ and γ_s ≤ γ_λ, implying opening yields a negative distortion term and ACR overestimates gains. Quantitative results for China (circa 2005):
• Estimated τ_x ≈ 2.85; the model matches import share ≈ 0.23, exporter share ≈ 30%, and firm-level dispersions and correlations of TFPR/TFPQ.
• Welfare from moving to autarky vs open: Net welfare change ≈ −3.68% (loss), despite an ACR/MR term of ≈ +11.1% to +11.23%. The distortion (fiscal externality) term ≈ −14.9% to −15.0% dominates. Decomposition of d ln PQ: about −13% due to the gap (d ln S − d ln λ), about −1% due to (γ_s−γ_λ), and ≈ +0.03% from fixed-cost wedges (τ_fx) — negligible.
• Alternative models: A hetero-trade-costs model (firm-specific iceberg and fixed costs without export wedges) fits the moments worse and yields a positive net gain ≈ +5.54% with a smaller distortion term (≈ −6.21%). This underscores that export wedges are important to replicate exporter TFPR dispersion and negative correlations with TFPR.
• Tariffs vs iceberg costs (appendix): Tariffs create a gap between input and sales shares and can partially offset exporters’ subsidies; with observed 2005 tariffs and re-estimation, the net gain can turn positive (≈ +1.82%), while iceberg-cost increases reduce gains.
• Foreign country gains are ≈ +10% and close to ACR when Foreign has no domestic distortions; Home distortions affect Foreign via import prices and relative wages but roughly offset in the baseline. Growth decomposition 1998–2005:
• China’s real GDP rose ≈ 57%. Counterfactuals attribute ≈ 55% to technology/input (mean productivity) growth, ≈ 6% to lower trade costs, and ≈ 5% to changes in the distribution of productivity/distortions. Reducing dispersion of domestic distortions alone (lower στ) would raise GDP by ≈ 68%, while reducing productivity dispersion alone (lower σφ) would lower GDP by ≈ 66%, largely offsetting each other in the observed distributional changes.

The results show that in economies with significant firm-level distortions, trade liberalization alters the composition of active and exporting firms in ways that can exacerbate misallocation. The standard selection mechanism of Melitz, which induces reallocation towards more productive firms, is undermined when wedges are sufficiently dispersed and imperfectly correlated with productivity: subsidized but less productive firms expand into exporting, while highly productive but taxed firms contract or exit. This induces a negative fiscal externality—lower net tax revenue per unit of labor—which reduces income and can overwhelm the price-index gains captured by ACR. The sufficient-statistics framework clarifies when ACR formulae overstate gains: when the domestic input share S falls more than the domestic sales share λ and when extensive-margin elasticities imply selection into more subsidized producers (γ_s<γ_λ). The quantitative exercise for China indicates that accounting for these mechanisms materially changes welfare assessments: conventional gains (~11%) are more than offset by distortion-induced losses (~15%), producing a modest net loss. Policy-wise, the findings suggest trade reforms without concurrent domestic reforms to reduce wedges may yield muted or negative welfare effects, while tariff policy can, in some configurations, counteract subsidy-driven misallocation. The growth decomposition further underscores that domestic reforms and technological progress contributed far more to China’s growth than international trade cost reductions in this period.

The paper develops a general welfare decomposition for trade liberalization in the presence of firm-level distortions within a Melitz framework, identifying sufficient statistics that extend beyond expenditure shares and trade elasticities. It shows theoretically and quantitatively that trade can reduce welfare when selection favors subsidized firms, and that ACR-based gains can be substantially overstated in distorted environments. Using Chinese firm-level data, the paper estimates the joint distribution of productivity and wedges, and finds that distortion-induced fiscal externalities largely offset conventional gains, yielding a net welfare loss from openness in the benchmark period. The results imply that to realize the full gains from trade, developing countries may need complementary domestic reforms that reduce idiosyncratic wedges. Future research directions include modeling interactions with innovation and technology diffusion, dynamic sequences of reforms and trade liberalization, and improved measurement distinguishing processing trade and within-industry technology heterogeneity.

• The analysis abstracts from other channels of gains from trade (e.g., technology diffusion, adoption, innovation, pro-competitive effects), which could alter quantitative results.
• Wedges are not directly observed; the joint distribution is inferred via a structural estimation subject to functional-form assumptions (log-normal), and selection complicates identification.
• The model is static and assumes balanced trade in the baseline; dynamic intertemporal considerations and trade imbalances are treated only in extensions.
• Exporters’ domestic vs export input allocations are not observed; processing trade cannot be cleanly separated due to data linkage and activity-mixing limitations.
• Alternative sources of exporter heterogeneity (e.g., technology differences, factor intensities within 4-digit industries) are not separately identified from wedges.
• The baseline iceberg trade cost vs tariff structure matters; while extensions discuss tariffs, the main quantitative benchmark uses iceberg costs.