## Appendix 1. Making the US and the EU comparable (insea2025005-s001)

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### Matching US and EU density
- Geographic and employment totals (2021):
  - U.S.: Land Area 9,336,721 km2; Employment 158,566,825 persons; Density 17 persons/km2.
  - EU: Land Area 4,268,016 km2; Employment 203,213,250 persons; Density 47.6 persons/km2.
- Key comparisons and truncation:
  - The EU average employment density is about 2.8 times the US level (47.6 persons/km2 in EU versus 17.0 persons/km2 in the US).
  - Labor productivity–employment density relationship (2021): U-shaped in logs with a structural break around 10 employees/km2.
    - For counties with less than 10 employees/km2, labor productivity decreases with density.
    - For counties with more than 10 employees/km2, labor productivity increases with density.
    - Historical note: Michaels and others (2012) found a cut-off of 7 people/km2 for late 19th century US urbanization patterns.
  - Truncation to regions with employment density ≥ 10 persons/km2 (sample used throughout the Note unless otherwise stated):
    - U.S. dense sample: Land Area 2,222,754 km2; Employment 143,628,736 persons; Density 64.6 persons/km2.
      - Total employment decreases by 10 percent to 143 million persons; land area reduced by about 75 percent to 2.2 million km2.
    - EU dense sample: Land Area 3,152,037 km2; Employment 198,697,160 persons; Density 63.0 persons/km2.
      - Total employment of 199 million persons (2 percent less) spreads over 3.2 million km2 of land (25 percent less).
  - Appendix Figure 5 geographically maps counties and NUTS3 regions after truncation.

### Properties of EU NUTS3 regions and US counties
- Median densities:
  - Median density of US counties: 30 employees/km2.
  - Median density of EU NUTS3 regions: 58 employees/km2.
- Distributional features:
  - US employment distribution is more skewed to the right than the EU; Europe has mega-metropolitans but population is more evenly distributed.
  - The ratio of employment density of the largest city relative to the median is much larger in the US and EU than all European countries except France.
    - Illustrative ratios: New York county vs Sevier County, TN (New York ≈ 370 times Sevier); Paris vs Kassel (≈ 350).
    - Selected European country pairs: France (Paris and Vendee, 560), Greece (Athens and Pella, 315), Romania (Bucharest and Bralia, 151), Hungary (Budapest and Heves, 100).
- Region area and density interaction (truncated sample):
  - EU: 1,081 NUTS3 regions covering 3.2 million km2.
  - US: 1,353 counties across 2.2 million km2.
  - On average, an average NUTS3 region is 1.8 times larger than an average US county.
  - Elasticity of land area with respect to employment density (log-log):
    - EU: −0.77
    - US: −0.39
  - Interpretation: size of NUTS3 region decreases more rapidly as density rises in the EU than in the US; higher density pairs with lower area in the EU, reconciling similar average employment densities.

### Divergence between economic and administrative boundaries
- Administrative units do not coincide with economic boundaries; heterogeneity within regions exists (urban areas and inhabited wild areas can coexist in a single administrative unit).
  - Examples: Los Angeles County includes LA metropolitan area and Angeles National Forest; Barcelona (ES511) covers both city of Barcelona and Collserola National Park.
- Measurement implication:
  - If the true labor productivity–density elasticity is less than one (empirically relevant), less granular data tend to underestimate the true elasticity (reference: Ciccone and Hall, 1996).

### Additional empirical references within Appendix 1
- Appendix Figure 1: U-shaped relationship between labor productivity and employment density for the US.
- Appendix Figures 2–5: Employment density distributions for US and EU, by country, and geographic distribution after truncation.
- The truncated sample (regions with employment density ≥ 10 employees/km2) is the primary sample used throughout the Note.

---

### Appendix Table 2. The Effects of Local Conditions on the Elasticity of Density

### Diagnostic model of spatial misallocation (production side)
- Sectoral aggregation and technology:
  - EU output in sector h: Y_h = (Σ_{f∈F_h} y_f^{(σ−1)/σ})^{σ/(σ−1)}, σ = elasticity of substitution.
  - Firm production: y_f = z_f k_f^α l_f^{1−α}, with z_f drawn from a log normal distribution.
- Factor payments and wedges:
  - Factor payments: interest rate r and wage rate w; firm-level wedges θ_f^k and θ_f^n make total payments θ_f^k r k and θ_f^n w l.
  - Wedges may capture output distortions θ_f^y (suppressed); capital and labor wedges capture observed distortions.
  - Wedge stochastic specification: log θ_f^x = μ_{c,r} + ρ log z_f + ε_f for x ∈ {k, l}, where μ_{c,r} is country-region component, ρ captures correlation with firm productivity, ε_f is idiosyncratic log-normal shock.

### Measurement and data structure
- Geographic and sectoral aggregation:
  - Regions: NUTS1.
  - Sectors (7): (1) mining, electricity, (2) manufacturing, (3) construction, (4) trade, transportation, and food, (5) ICT, (6) professional services, (7) public services.
- Firm-level measures (following Hsieh and Klenow (2009)):
  - z_f = (p_f y_f)^{σ/(σ−1)} / (k_f^α l_f^{1−α})
  - θ_f^x = θ̄ (p_f y_f) / (k_f^α l_f^{1−α})  (θ̄ is a constant)
- Region-level scaling:
  - Average TFP in each region set to match total output (real PPP-adjusted GDP).
  - Average wedge set to match total employment.
- Data sources: Orbis (firm-level), Eurostat (region output & employment), EU Regional Trade Costs Database, European Commission Regional Innovation Scoreboard, IMF staff calculations.

### Spatial misallocation experiments (simulation design)
- Simulation details:
  - 10,000 firms per region drawn from estimated productivity and wedge distributions.
- Two counterfactual experiments:
  1. Across-country misallocation: potential gain from reallocating capital and labor across countries, holding within-country firm distributions fixed.
  2. Between-region misallocation: potential gain from reallocating capital and labor between NUTS1 regions within countries, holding within-region firm distributions fixed.
- Reporting metric:
  - Total gains reported as change in EU-level output (stocks of labor and capital fixed), reflecting changes in aggregate total factor productivity.

---

### Appendices 5–7: Model for quantifying spatial implications of EU policies and estimation methods

### Regions, preferences, firms, and wedges (model overview)
- Regions r ∈ R; total stock of workers N.
- Worker preferences and utility:
  - Period utility in region r: u_r(i) = b_r(i) c_r^γ a_r^{1−γ}, where b_r(i) ∼ Fréchet(exp(−B_r b^{−ζ})), B_r is average attractiveness, a_r is regional amenity (fixed, non-tradable).
  - Workers supply labor inelastically and are paid region wage w_r; workers in region r are assumed owners of firms in r.
- Final good and intermediate goods:
  - Final good: Y_r = (∫_{f∈F_r} y_r(f)^{(σ−1)/σ} df)^{σ/(σ−1)}.
  - Intermediate firms: y(f) = z(f) l(f).
  - Firm productivity: z_f = z̄_r N_r^κ s_f with κ>0 (agglomeration spillover) and s_f ∼ log N(0, σ_s^2).
  - Labor wedges: log θ_n(f) = ρ_r log z(f) + ε(f); ε(f) ∼ log-normal(0, σ_r^2).
  - Wedges modeled as idiosyncratic taxes transferred lump-sum to workers T_r.
  - Entry cost φ; mass of operating firms M_r determined by entry/exit.

### Equilibrium and calibration targets
- Equilibrium objects: {P_r, Y_r, c_r, a_r, N_r, X_r, M_r, w_r, q_r, T_r} and policy/behavioral functions {p_{r,r′}(z,θ_n), y_{r,r′}(z,θ_n), l_r(z,θ_n)} satisfying: (i) worker location choice maximizes utility; (ii) final good producer maximizes profits; (iii) firms set prices and labor to maximize profits; (iv) M_r by entry/exit; (v) trade balance; (vi) goods, amenities, labor markets clear.
- Common parameters calibrated:
  - β = 0.96 (implying interest rate of 4 percent).
  - γ = 0.75 (consumption share of utility).
  - ζ = 1.5 (Fréchet curvature).
  - σ = 5 (CES elasticity).
  - κ = 0.13 (agglomeration spillover elasticity).
  - φ normalized to one in each region.
- Region-level parameters calibrated/estimated: {ρ_r^n, σ_r, z̄_r, A_r, B_r} and bilateral trade costs {τ_{r,r′}}.
- Amenities A_r set proportional to region area.
- Firm-level distortions estimated from Orbis following Hsieh and Klenow (2009).

### Trade cost estimation and model fit
- Trade cost mechanics:
  - Symmetric assumption τ_{r,r′} = τ_{r′,r}.
  - τ_{r,r′} = (d_{r,r′} d_{r′,r} / (d_{r,r} d_{r′,r′}))^{1/(2σ)} following Head and Ries (2004).
  - Data: European Road Freight Transport survey (ERFT) scaled to World Input Output Database 2014 country-level trade shares.
  - Calibrated average home share: model ≈ 53 percent; data = 51 percent.
  - Distance-attributable trade cost coefficient β = 1.
  - Policy-relevant portion of trade costs: 1 − λ_{r,r′} = 1 − τ_{r,r′}^{disd} / τ_{r,r′}.
- Model fit:
  - Average correlation of log output per worker and log output between data and calibrated model ≈ 96 percent.

---

### Quantitative analysis: reform experiments and parameterization

### Four reform experiments (magnitudes and mechanics)
- Experiment definitions and parameter choices:
  1. Structural reforms to decrease misallocation:
     - Counterfactual wedge distribution: log θ_n′(f) = [(1−ξ) ρ̄ + ξ ρ_r] log z(f) + ξ ε(f)
     - ξ ∈ {0.05, 0.10}.
     - ρ̄ = min_r ρ_r.
     - ξ = 0.05 matches gains from closing half the policy gap; ξ = 0.10 matches closing full gap per Budina and others (2025).
  2. Lowering trade costs (closing intra-EU vs intra-US trade cost gap):
     - For r ∈ R_c and r′ ∉ R_c: τ_{r,r′}′ = τ_{r,r′} − ξ × (τ_{r,r′} − 1) × (1 − λ_{r,r′}).
     - For intra-country pairs τ unchanged.
     - ξ ∈ {0.25, 0.50} corresponding to closing half (ξ=0.25) and full (ξ=0.50) of the intra-EU / intra-US trade cost gap estimated in Box 2.1.
     - Empirical note: intra-US trade costs are around twice intra-EU trade costs over most sample; final year shows gap shrinking due to increased intra-US costs.
  3. Lowering mobility barriers (closing EU–US spatial employment distribution gap):
     - Measured elasticity between output per worker and employment: US ≈ 0.15; model ≈ 0.12.
     - Amenity adjustment: A_r′ = A_r (Y_r / Ȳ)^{ξ} with ξ ∈ {0.25, 0.55} to increase model elasticity by 0.015 and 0.030 respectively.
     - Interpretation: adjustment reduces mobility barriers captured in preferences B_r, applied within and between countries.
  4. Combined experiment: implements all three reforms simultaneously.
- Population adjustment:
  - In the combined reform, population increase adds a 0.5 percent increase in total employment to the combined reform scenario (reported in Appendix Figure 12 note).

### Simulated impacts by initial regional density
- Structural reforms:
  - Tend to have relatively similar impact across low-, middle-, and high-density regions.
- Trade cost reductions:
  - Larger impact in middle- and high-density regions, which are more exposed to trade and benefit from scale economies and agglomeration spillovers.
  - Low-density regions still benefit from lower trade costs.
- Mobility-friction reductions:
  - Tend to disproportionately shift economic activity toward high-density regions as workers move to higher-wage regions.
  - Higher concentration raises productivity via scale economies and agglomeration spillovers.
  - After accounting for worker losses in origin regions, output per worker increases on average across all density groups from lower mobility frictions.
- Appendix Figure 12 reports estimated long-term output (left panel) and output-per-worker (right panel) gains by initial employment-density tertile for structural reforms, lowered trade costs, lowered mobility frictions, and combined reforms.

### Aggregate results for Advanced Economies excluding CESEE and CESEE group
- CESEE countries:
  - Tend to benefit comparatively more from structural reforms and trade cost reductions (reflecting more substantial misallocation and higher trade costs).
  - Mobility reforms tend to hurt CESEE countries:
    - Mobility reforms induce a net outflow of about 7.5 percent of workers from CESEE countries, potentially accelerating unfavorable population dynamics.
- Advanced economies excluding CESEE:
  - Tend to benefit from mobility reforms (workers move to higher-productivity regions within these economies).
- Combined reforms:
  - Simulating all three reforms together allows gains from structural reforms and lower trade costs to offset losses from mobility-friction reduction, shifting CESEE outcomes toward positive net benefits.
- Timing and transition caveats:
  - Gains from structural reforms and reducing trade costs likely occur relatively quickly as firms adjust margins.
  - Worker relocations reflect long-term equilibria and are lengthier in practice.
  - Some high-impact benefits from lowering mobility barriers (e.g., access to skills) can be realized more quickly.
  - Stronger productivity growth in CESEE could counter net emigration pressures.

---

### Appendix Figure 13. Impact of simulated structural reforms on advanced and CESEE economies

### Simulated reform scenarios and definitions (recap)
- Structural reforms: lower dispersion in estimated firm-level wedges in each region.
- Trade costs: lower estimated (within EU) trade costs by half of the between EU country and US state gap for each bilateral region pair in different countries.
- Mobility frictions: lower the barriers to labor reallocation to close half of the spatial pattern of output per worker and density gap with the US.
- Combined reforms: the impact of the three reforms implemented simultaneously (structural reforms, trade cost reductions, and lower mobility frictions).
- Population increase: adds a 0.5 percent increase in total employment to the combined reform scenario.

### Key quantitative outcomes and illustrative results
- Employment increase and output:
  - Adding in an employment increase of around 0.5 percent would result in equal increase in output by both advanced economies and CESEE countries as the new population is proportionally divided across regions.
  - EU output would also increase to 9.3 percent under the scenario that adds the employment increase of around 0.5 percent to the combined reform scenario.
  - The increase in output (to 9.3 percent) is larger than the increase in employment due to scale economies and agglomeration spillovers.
- Back-of-the-envelope migration/employment calculation:
  - Migration rate: around 1.1 percent in 2024.
  - Elasticity of migration to real income: ≈1/2 from Caliendo, Dvorkin, and Parro (2019) (used in the computation as 0.043).
  - Computation: over a 10-year period, total employment could increase by around 0.5 percent (= 1.1 × 0.043×10).
- Caveats on the population/migration approximation:
  - The model does not include migration from outside the EU.
  - The assumed elasticity of migration may not directly align with the model assumptions.
  - The calculation should be taken as an approximation.

### Methodology — Barriers to Trade (Appendix 6)
- Empirical approach:
  - Gravity model following Adilbish et al. (2025) and Head and Mayer (2021), using US states in place of US country observations and allowing time-varying effects of controls.
  - Bilateral exports regressed on dummy variables p decomposing flows (EUEU, USUS, USEU, EUCHN, USCHN, EUROW, USROW) each interacted with time dummies.
  - Trade barriers inferred from β_p coefficients, identifying evolution of international trade flows relative to domestic trade flows.
- Conversion to ad-valorem equivalents:
  - Formula: (exp(β_p,t / θ) − 1) × 100, with θ = 5 following Head and Mayer (2021).
- Controls and fixed effects:
  - Controls include PTA participation and WTO membership (interacted with time), and trade cost shifters (distance in logs, border, language, legal origin) interacted with time.
  - Time-varying exporter (χ) and importer (φ) fixed effects included.
  - Country-pair fixed effects (μ) absorb time-invariant determinants of trade; identification exploits within-pair over-time variation relative to 2007.
- Alternative specification:
  - Omitting country-pair fixed effects yields upper-bound estimates for levels of trade barriers.
- Data and sample:
  - Domestic and international trade flows: OECD TiVA inter-country input-output database (2025 version).
  - Intra-US flows: Commodity Flow Surveys (CFS).
  - US state exports/imports: US Census.
  - Regressions on total manufacturing and mining trade, matched CFS and OECD TiVA sectors.
  - Sample coverage: 79 countries in OECD TiVA (without the US) and 51 US territories (50 states and DC).
  - Time periods: 2007, 2012, 2017, 2022.

### Methodology — Capital misallocation and venture capital (Appendix 7)
- Data and scope:
  - Venture capital data from PitchBook focusing on VC deals by European and US firms between 2015 and 2024.
  - For the US, analysis is conducted at the state level.
- Empirical model:
  - Gravity model estimated on bilateral VC investment flows using Poisson Pseudo-Maximum Likelihood (PPML).
  - Specification includes exporter (investor) country-time fixed effects (χ) and importer (firm) country-time fixed effects (ξ), with bilateral controls X (distance, contiguity, common legal system, language, capital taxes).
- Policy experiments and interpretation:
  - Removing withholding taxes exercise should be interpreted as an upper bound; full elimination unlikely in practice.
  - Effect of a common legal system could be a lower bound proxying effect of the 28th corporate regime, which goes beyond legal harmonization.
  - Analysis assumes perfectly elastic VC supply; if European investors are not deep-pocketed, existing VC investments may be crowded out.
  - Exercise does not account for general equilibrium feedback loops (VC inflows boosting innovation, growth, wealth, further VC supply).

*Source: Appendix 1; Appendix Table 2; Appendix Figure 13 and accompanying text, insea2025005-s001.*

### Appendix 1. Making the US and the EU comparable

### Appendix 1. Making the US and the EU comparable

### Matching US and EU density
- Geographic and employment totals (2021):
  - U.S.: Land Area 9,336,721 km2; Employment 158,566,825 persons; Density 17 persons/km2.
  - EU: Land Area 4,268,016 km2; Employment 203,213,250 persons; Density 47.6 persons/km2.
- The EU average employment density is about 2.8 times the US level (47.6 persons/km2 in EU versus 17.0 persons/km2 in the US).
- Labor productivity and employment density relationship (2021):
  - The relationship (in logs) is U-shaped with a structural break around 10 employees/km2.
  - For counties with less than 10 employees/km2, labor productivity decreases with density.
  - For counties with more than 10 employees/km2, labor productivity increases with density.
  - Historical reference: Michaels and others (2012) found a cut-off of 7 people/km2 for late 19th century US urbanization patterns.
- Truncation to regions with employment density ≥ 10 persons/km2 (sample used throughout the Note unless otherwise stated):
  - U.S. dense sample:
    - Land Area 2,222,754 km2; Employment 143,628,736 persons; Density 64.6 persons/km2.
    - Total employment decreases by 10 percent to 143 million persons; land area reduced by about 75 percent to 2.2 million km2.
  - EU dense sample:
    - Land Area 3,152,037 km2; Employment 198,697,160 persons; Density 63.0 persons/km2.
    - Total employment of 199 million persons (2 percent less) spreads over 3.2 million km2 of land (25 percent less).
- Appendix Figure 5 geographically maps counties and NUTS3 regions after truncation.

### Properties of EU NUTS3 regions and US counties
- Median densities:
  - Median density of US counties: 30 employees/km2.
  - Median density of EU NUTS3 regions: 58 employees/km2.
- Distributional features:
  - US employment distribution is more skewed to the right than the EU; Europe has mega-metropolitans but population is more evenly distributed.
  - The ratio of employment density of the largest city relative to the median is much larger in the US and EU than all European countries except France.
    - Examples cited: New York county vs Sevier County, TN (New York ≈ 370 times Sevier); Paris vs Kassel (≈ 350).
    - Ratios for selected European country pairs: France (Paris and Vendee, 560), Greece (Athens and Pella, 315), Romania (Bucharest and Bralia, 151), Hungary (Budapest and Heves, 100).
- Region area and density interaction:
  - In the truncated sample: EU has 1,081 NUTS3 regions covering 3.2 million km2; US has 1,353 counties across 2.2 million km2.
  - On average, an average NUTS3 region is 1.8 times larger than an average US county.
  - Elasticity of land area with respect to employment density (log-log):
    - EU: −0.77
    - US: −0.39
  - Interpretation: size of NUTS3 region decreases more rapidly as density rises in the EU than in the US; higher density pairs with lower area in the EU, reconciling similar average employment densities.

### Divergence between economic and administrative boundaries
- Neither US counties nor EU NUTS3 regions are defined by economic boundaries; heterogeneity within regions exists (urban areas and inhabited wild areas can coexist in a single administrative unit).
- Illustration:
  - Los Angeles County includes LA metropolitan area and Angeles National Forest.
  - Barcelona (ES511) covers both city of Barcelona and Collserola National Park.
- Measurement implication:
  - If the true labor productivity-density elasticity is less than one (empirically relevant), less granular data tend to underestimate the true elasticity (reference: Ciccone and Hall, 1996).

### Additional summary points (linked empirical material referenced)
- Appendix Figure 1 illustrates the U-shaped relationship between labor productivity and employment density for the US.
- Appendix Figures 2–5 show:
  - Employment density distributions for US and EU, by country, and geographic distribution after truncation.
  - Land area distributions and the land-area vs employment-density relationship.
- The truncated sample (regions with employment density ≥ 10 employees/km2) is the primary sample used throughout the Note.

*Source: Appendix 1. Making the US and the EU comparable (insea2025005-s001).*

### Appendix Table 2. The Effects of Local Conditions on the Elasticity of Density

### Appendix Table 2. The Effects of Local Conditions on the Elasticity of Density

### Diagnostic model of spatial misallocation (production side)
- EU output in sector h: Y_h = (Σ_{f∈F_h} y_f^{(σ−1)/σ})^{σ/(σ−1)}, where F_h are firms in sector and σ is elasticity of substitution.
- Firm production: y_f = z_f k_f^α l_f^{1−α}, with firm-specific productivity z_f drawn from a log normal distribution.
- Factor payments: interest rate r and wage rate w; firm-level wedges θ_f^k and θ_f^n make total payments θ_f^k r k and θ_f^n w l.
- Wedges may also capture output distortions θ_f^y but are suppressed; capital and labor wedges capture observed distortions.
- Wedge stochastic specification: log θ_f^x = μ_{c,r} + ρ log z_f + ε_f for x ∈ {k, l}, where μ_{c,r} is country-region component, ρ captures correlation with firm productivity, and ε_f is idiosyncratic log-normal shock.

### Measurement and data structure
- Geographic and sectoral aggregation:
  - Regions: NUTS1.
  - Sectors (7): (1) mining, electricity, (2) manufacturing, (3) construction, (4) trade, transportation, and food, (5) ICT, (6) professional services, (7) public services.
- Firm-level measures (following Hsieh and Klenow (2009)):
  - z_f = (p_f y_f)^{σ/(σ−1)} / (k_f^α l_f^{1−α})
  - θ_f^x = θ̄ (p_f y_f) / (k_f^α l_f^{1−α})  (θ̄ is a constant)
- Region-level scaling:
  - Average TFP in each region set to match total output (real PPP-adjusted GDP).
  - Average wedge set to match total employment.
- Data sources: Orbis (firm-level), Eurostat (region output & employment), EU Regional Trade Costs Database, European Commission Regional Innovation Scoreboard, IMF staff calculations.

### Spatial misallocation experiments (simulation design)
- Simulation: 10,000 firms per region drawn from estimated productivity and wedge distributions.
- Two counterfactual experiments:
  1. Across-country misallocation: potential gain from reallocating capital and labor across countries, holding within-country firm distributions fixed.
  2. Between-region misallocation: potential gain from reallocating capital and labor between NUTS1 regions within countries, holding within-region firm distributions fixed.
- Reporting: total gains reported as change in EU-level output (stocks of labor and capital fixed), reflecting changes in aggregate total factor productivity.

### Appendices 5: Model for quantifying spatial implications of EU policies (overview)
- Regions indexed r ∈ R; total stock of workers N.
- Worker preferences and utility:
  - Period utility in region r: u_r(i) = b_r(i) c_r^γ a_r^{1−γ}, where b_r(i) ∼ Fréchet(exp(−B_r b^{−ζ})), B_r is average attractiveness, a_r is regional amenity (fixed, non-tradable).
  - Workers supply labor inelastically and are paid region wage w_r; workers in region r are assumed owners of firms in r.
- Final good: Y_r = (∫_{f∈F_r} y_r(f)^{(σ−1)/σ} df)^{σ/(σ−1)}.
- Intermediate goods firms:
  - Production: y(f) = z(f) l(f).
  - Firm productivity: z_f = z̄_r N_r^κ s_f with κ>0 (agglomeration spillover) and s_f ∼ log N(0, σ_s^2).
  - Wedges on labor: firms pay θ_n(f) w_r l; log θ_n(f) = ρ_r log z(f) + ε(f) with ε(f) ∼ log-normal(0, σ_r^2).
  - Wedges modeled as idiosyncratic taxes transferred lump-sum to workers T_r.
  - Entry cost φ; mass of operating firms M_r determined by entry/exit.

### Equilibrium and calibration targets
- Equilibrium objects: {P_r, Y_r, c_r, a_r, N_r, X_r, M_r, w_r, q_r, T_r} and policy/behavioral functions {p_{r,r′}(z,θ_n), y_{r,r′}(z,θ_n), l_r(z,θ_n)} satisfying: (i) worker location choice maximizes utility; (ii) final good producer maximizes profits; (iii) firms set prices and labor to maximize profits; (iv) M_r by entry/exit; (v) trade balance; (vi) goods, amenities, labor markets clear.
- Common parameters calibrated: {β, γ, ζ, σ, κ, φ}.
  - β = 0.96 (implying interest rate of 4 percent).
  - γ = 0.75 (consumption share of utility).
  - ζ = 1.5 (Fréchet curvature).
  - σ = 5 (CES elasticity).
  - κ = 0.13 (agglomeration spillover elasticity).
  - φ normalized to one in each region.
- Region-level parameters calibrated/estimated: {ρ_r^n, σ_r, z̄_r, A_r, B_r} and bilateral trade costs {τ_{r,r′}}.
- Amenities A_r set proportional to region area.
- Firm-level distortions estimated from Orbis following Hsieh and Klenow (2009).
- Trade cost estimation:
  - Symmetric assumption τ_{r,r′} = τ_{r′,r}.
  - τ_{r,r′} = (d_{r,r′} d_{r′,r} / (d_{r,r} d_{r′,r′}))^{1/(2σ)} following Head and Ries (2004).
  - Data: European Road Freight Transport survey (ERFT) scaled to World Input Output Database 2014 country-level trade shares.
  - Calibrated average home share: model ≈ 53 percent; data = 51 percent.
  - Distance-attributable trade cost coefficient β = 1.
  - Policy-relevant portion of trade costs: 1 − λ_{r,r′} = 1 − τ_{r,r′}^{disd} / τ_{r,r′}.
- Model fit:
  - Average correlation of log output per worker and log output between data and calibrated model ≈ 96 percent.

### Quantitative analysis: reform experiments and parameterization
- Four experiments reported in main text and Figure 2.3; each has two magnitudes (partial and full) except combined:
  1. Structural reforms to decrease misallocation:
     - Counterfactual wedge distribution: log θ_n′(f) = [(1−ξ) ρ̄ + ξ ρ_r] log z(f) + ξ ε(f)
     - ξ ∈ {0.05, 0.10} adjustment scale.
     - ρ̄ = min_r ρ_r.
     - ξ = 0.05 matches gains from closing half the policy gap; ξ = 0.10 matches closing full gap per Budina and others (2025).
  2. Lowering trade costs (closing intra-EU vs intra-US trade cost gap):
     - For r ∈ R_c and r′ ∉ R_c: τ_{r,r′}′ = τ_{r,r′} − ξ × (τ_{r,r′} − 1) × (1 − λ_{r,r′}).
     - For intra-country pairs τ unchanged.
     - ξ ∈ {0.25, 0.50} corresponding to closing half (ξ=0.25) and full (ξ=0.50) of the intra-EU / intra-US trade cost gap estimated in Box 2.1.
     - Empirical note: intra-US trade costs are around twice intra-EU trade costs over most sample; final year shows gap shrinking due to increased intra-US costs.
  3. Lowering mobility barriers (closing EU–US spatial employment distribution gap):
     - Measured elasticity between output per worker and employment: US ≈ 0.15; model ≈ 0.12.
     - Amenity adjustment: A_r′ = A_r (Y_r / Ȳ)^{ξ} with ξ ∈ {0.25, 0.55} to increase model elasticity by 0.015 and 0.030 respectively.
     - Interpretation: adjustment reduces mobility barriers captured in preferences B_r, applied within and between countries.
  4. Combined experiment: implements all three reforms simultaneously.
- Population adjustment in combined reform: population increase adds a 0.5 percent increase in total employment to combined reform scenario (reported in Appendix Figure 12 note).

### Impact of reforms by initial regional density (summary of simulated outcomes)
- Structural reforms:
  - Tend to have relatively similar impact across low-, middle-, and high-density regions.
- Trade cost reductions:
  - Larger impact in middle- and high-density regions, which are more exposed to trade and benefit from scale economies and agglomeration spillovers.
  - Low-density regions still benefit from lower trade costs.
- Mobility-friction reductions:
  - Tend to disproportionately shift economic activity toward high-density regions as workers move to higher-wage regions.
  - Higher concentration raises productivity via scale economies and agglomeration spillovers.
  - After accounting for worker losses in origin regions, output per worker increases on average across all density groups from lower mobility frictions.
- Appendix Figure 12 reports estimated long-term output (left panel) and output-per-worker (right panel) gains by initial employment-density tertile for structural reforms, lowered trade costs, lowered mobility frictions, and combined reforms.

### Aggregate results for Advanced Economies excluding CESEE and CESEE group
- CESEE countries:
  - Tend to benefit comparatively more from structural reforms and trade cost reductions (reflecting more substantial misallocation and higher trade costs).
  - Mobility reforms tend to hurt CESEE countries:
    - Mobility reforms induce a net outflow of about 7.5 percent of workers from CESEE countries, potentially accelerating unfavorable population dynamics.
- Advanced economies excluding CESEE:
  - Tend to benefit from mobility reforms (workers move to higher-productivity regions within these economies).
- Combined reforms:
  - Simulating all three reforms together allows gains from structural reforms and lower trade costs to offset losses from mobility-friction reduction, shifting CESEE outcomes toward positive net benefits.
- Timing and transition caveats:
  - Gains from structural reforms and reducing trade costs likely occur relatively quickly as firms adjust margins.
  - Worker relocations reflect long-term equilibria and are lengthier in practice.
  - Some high-impact benefits from lowering mobility barriers (e.g., access to skills) can be realized more quickly.
  - Stronger productivity growth in CESEE could counter net emigration pressures.

*Sources: Eurostat; EU Regional Trade Costs Database; Orbis; European Commission Regional Innovation Scoreboard; and IMF staff calculation.*

### Appendix Figure 13. Impact of simulated structural reforms on advanced and CESEE economies

### Appendix Figure 13. Impact of simulated structural reforms on advanced and CESEE economies

### Simulated reform scenarios and definitions
- Structural reforms: lower dispersion in estimated firm-level wedges in each region.
- Trade costs: lower estimated (within EU) trade costs by half of the between EU country and US state gap for each bilateral region pair in different countries.
- Mobility frictions: lower the barriers to labor reallocation to close half of the spatial pattern of output per worker and density gap with the US.
- Combined reforms: the impact of the three reforms implemented simultaneously (structural reforms, trade cost reductions, and lower mobility frictions).
- Population increase: adds a 0.5 percent increase in total employment to the combined reform scenario.

### Key quantitative outcomes and illustrative results
- Adding in an employment increase of around 0.5 percent would result in equal increase in output by both advanced economies and CESEE countries as the new population is proportionally divided across regions.
- EU output would also increase to 9.3 percent under the scenario that adds the employment increase of around 0.5 percent to the combined reform scenario.
- The increase in output (to 9.3 percent) is larger than the increase in employment due to scale economies and agglomeration spillovers.
- Back-of-the-envelope migration/employment calculation used:
  - Migration rate: around 1.1 percent in 2024.
  - Elasticity of migration to real income: ≈1/2 from Caliendo, Dvorkin, and Parro (2019) (used in the computation as 0.043).
  - Computation: over a 10-year period, total employment could increase by around 0.5 percent (= 1.1 × 0.043×10).
- Caveats on the population/migration approximation:
  - The model does not include migration from outside the EU.
  - The assumed elasticity of migration may not directly align with the model assumptions.
  - The calculation should be taken as an approximation.

### Methodology — Barriers to Trade (Appendix 6)
- Empirical approach:
  - Gravity model following Adilbish et al. (2025) and Head and Mayer (2021), replacing country-pair observations for the US with US states and allowing time-varying effects of control variables.
  - Bilateral exports from origin i to destination l (including i = l for domestic sales) are regressed on a set Ω of dummy variables p that decompose international trade flows into cross-border flows between different sets of countries or states, each interacted with time dummies.
  - Trade flows indicators p include: EUEU (trade flows between EU-27 countries), USUS (flows between US states), USEU (EU-27 countries and US states), EUCHN (EU-27 and China), USCHN (US states and China), EUROW (EU-27 and countries other than US and China), USROW (US states and countries other than EU-27 and China).
  - Trade barriers are inferred from β_p coefficients, which identify how different types of international trade flows evolve relative to domestic trade flows.
- Conversion of estimated coefficients into ad-valorem equivalent trade costs:
  - Formula used: (exp(β_p,t / θ) − 1) × 100, where θ is the aggregate elasticity of trade with respect to trade costs.
  - Parameter choice: θ is set equal to 5 following Head and Mayer (2021).
- Controls and fixed effects:
  - Matrix T A includes participation in PTAs other than the EU and WTO membership, each interacted with time indicators.
  - Matrix τ includes trade cost shifters (distance in logs, internal and international; dummies for sharing a border, official language, origin of legal system), each interacted with time dummies; associated coefficients β_τ,t vary over time because of these interactions.
  - Time-varying exporter (χ) and importer (φ) fixed effects are included.
  - Country-pair fixed effects (μ) absorb time-invariant determinants of trade; the panel specification thus exploits variation within country pairs and over time and identifies changes in bilateral trade costs relative to 2007 (the omitted interaction year).
- Alternative specification:
  - Levels of trade barriers between EU countries and other country pairs estimated by omitting country-pair fixed effects; this approach controls for levels of time-invariant covariates and their interactions with time indicators but yields upper-bound estimates because some unobserved country-pair determinants (e.g., home bias) cannot be fully absorbed.
- Data sources and sample:
  - Domestic and international trade flows (excluding US states): OECD TiVA inter-country input-output database (2025 version).
  - Intra-US trade flows (between and within US states): Commodity Flow Surveys (CFS).
  - Exports and imports of US states: US Census.
  - Regressions estimated on total manufacturing and mining trade, including matched CFS and OECD TiVA sectors.
  - Sample coverage: 79 countries in the OECD TiVA data (without the US) and 51 US territories (50 states and the District of Columbia).
  - Time periods included (CFS availability): 2007, 2012, 2017, and 2022.

### Methodology — Capital misallocation and venture capital (Appendix 7)
- Data and scope:
  - Venture capital data from PitchBook focusing on VC deals by European and US firms between 2015 and 2024.
  - For the US, analysis is conducted at the state level.
- Empirical model:
  - Gravity model estimated on bilateral VC investment flows using Poisson Pseudo-Maximum Likelihood (PPML).
  - Equation specification includes exporter (investor) country-time fixed effects (χ) and importer (firm) country-time fixed effects (ξ), with bilateral controls X (distance, contiguity, common legal system, language, capital taxes).
- Policy experiments and interpretation:
  - Exercise on removing withholding taxes should be interpreted as an upper bound because, in practice, such taxes will not be completely eliminated; the exercise reflects potential impact of CMU proposals aimed at simplifying withholding tax procedures.
  - Results on the effect of a common legal system could be considered a lower bound to proxy the effect of the 28th corporate regime, given the proposal moves beyond legal harmonization and covers taxes and insolvency frameworks.
  - The analysis assumes a perfectly elastic VC supply (all VC demand can be met); if European investors are not deep-pocketed, existing VC investments may be crowded out.
  - The exercise does not account for general equilibrium feedback loops (increases in VC inflows boost innovation, growth, wealth, and further VC supply).

*Source: Appendix Figure 13 and accompanying text, insea2025005-s001 — Appendix Figure 13. Impact of simulated structural reforms on advanced and CESEE economies (IMF Regional Economic Outlook—Europe, November 2025).*

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_Source: https://www.imf.org/-/media/files/publications/imf-notes/2025/english/insea2025005-s001.pdf_