## Firm-Level Innovation in Spain: Patterns, Drivers, and Policy Implications

## Source details

**Canonical URL:** [Firm-Level Innovation in Spain: Patterns, Drivers, and Policy Implications](https://www.imf.org/-/media/files/publications/selected-issues-papers/2026/english/sipea2026056.pdf)

## Other formats

- [Markdown version](/-/media/files/publications/selected-issues-papers/2026/english/sipea2026056.pdf.md)
- [Structured JSON version](/-/media/files/publications/selected-issues-papers/2026/english/sipea2026056.pdf.json)

---

### Key findings and abstract
- Paper completion date: May 4, 2026. Document: SIP/2026/056.
- Spain’s labor productivity: about 74 percent of the US level (current paper date comparison to 1990).
- Large innovation gap vis-à-vis peer high-income countries; gap especially pronounced among young firms and for higher-quality patents.
- Main frictions identified: size-dependent regulations, financial constraints, regulatory burdens, and complexity of the R&D tax credit.
- Statutory R&D tax credit design:
  - 25 percent on R&D up to the average expenditure level of the previous two years.
  - 42 percent on additional expenditure above that level.
- Actual take-up rate of R&D tax credit: around 30 percent (AIReF, 2020).
- Quantitative-model simulation headline: easing identified frictions could raise Spain’s long-term TFP growth by over 0.25 percentage points.
- Model counterfactual decomposition reported:
  - Removing the three frictions increases long-run TFP growth by 0.18 percentage points.
  - Streamlining and better targeting the R&D tax credit could increase TFP growth by a further 0.1 percentage point.
  - Combined potential gain reported in Section 1: 0.28 percentage points (“over a quarter of a percentage point”).
  - Aggregate combined impact reported in Section 2: 0.27 percentage points.

### Scope, data, and stylized facts
- Focus: empirical and model-based analysis of firm-level innovation in Spain; policy counterfactuals calibrated to micro-level patterns.
- Data sources:
  - Orbis firm-level data: sales, employment, fixed assets, industry, location.
  - PATSTAT patent data (EPO, Spanish, US, Japanese offices).
  - Matching procedure follows EUIPO (2025) and literature cleaning (Díez and others, 2021; Kalemli-Özcan and others, 2024).
- Matching rates:
  - Spain: 87 percent of patent applications by firms located in Spain assigned to harmonized Orbis firm ID.
  - France: 78 percent.
  - Sweden: 85 percent.
- Innovation measures and gaps:
  - R&D intensity in Spain has stagnated since the late 2000s; gap relative to other advanced economies persists.
  - Patents filed by residents per million population: Spain records substantially fewer patents than peer countries; patenting gap exceeds R&D spending gap.
  - Sectoral decomposition vs US:
    - Within-sector margin: about 70 percent of total patenting gap.
    - Across-sector margin: remaining 30 percent.
    - Implication: shortfall driven mainly by weaker within-industry innovative performance.

### Firm-level patenting patterns
- Patenting probabilities and quality:
  - Spanish firms are less likely to file patents than French and Swedish firms across all age groups; gap larger for younger firms and for high-quality patents (USPTO filings proxy).
  - Patent quality measured by forward citations (excluding self-citations) transformed via inverse hyperbolic sine (IHS).
  - Average patent quality:
    - Increases with firm size (proxied by employment) conditional on firm age.
    - Decreases with firm age; younger firms tend to produce higher-quality innovations.
- Polarization:
  - 0.17 percent of firms file a patent when young (age five or below).
  - Among firms that innovate when young, 36 percent also innovate at older ages.
  - Among firms that do not innovate when young, 0.3 percent file a patent later in life.
  - Interpretation: persistent heterogeneity — a small subset of startups exhibits persistent innovative activity while most are non-innovative subsistence-type firms.

### Empirical evidence on frictions and their estimated effects
- Frictions examined: size-dependent labor regulations (50-employee threshold), financial constraints (MRPK-based), regulatory burdens (region–sector–year new regulations).
- Size-dependent regulations (50-employee threshold):
  - Regression results (Table 1):
    - Any Patents: log(emp): 0.181 ***; 45≤ Emp < 50: -0.141 ***; Observations: 5,049,483; Mean dep. var.: 0.1300.
    - Patents filed in ES, EU, US: log(emp): 0.039 ***; 45≤ Emp < 50: -0.073 ***; Observations: 5,049,483; Mean dep. var.: 0.0221.
    - Average Citations: log(emp): 0.086 ***; 45≤ Emp < 50: -0.163 *; Observations: 6,496; Mean dep. var.: 1.099.
  - Interpretation: firms with employment between 45 and 49 exhibit a statistically significant decline in probability of patenting and in average citations relative to other firms at the 50-employee threshold.
- Financial constraints (MRPK):
  - MRPK definition (assuming Cobb-Douglas with output elasticity of labor α):
    - y_i = a_i l_i^α k_i^{1−α}
    - MRPK_i = (1−α) p_i y_i / k_i
  - Firms classified as financially constrained if MRPK exceeds the median within a sector–year.
  - Figure 7: negative correlation between log(MRPK) and log(firm age) conditional on firm sales and sector–year fixed effects (younger firms more likely constrained).
  - Regression results (Table 2):
    - Any Patents: log(emp): 0.180 ***; Constrained: -0.087 ***; Observations: 5,049,483; Mean dep. var.: 0.1300.
    - Patents filed in ES, EU, US: log(emp): 0.039 ***; Constrained: -0.021 ***; Observations: 5,049,483; Mean dep. var.: 0.0221.
    - Average Citations: log(emp): 0.084 ***; Constrained: -0.144 ***; Observations: 6,496; Mean dep. var.: 1.099.
  - Interpretation: financial constraints are negatively associated with probability of patenting and patent quality.
- Regulatory burdens:
  - Measured by number of newly introduced regulations at region–sector–year level.
  - Regression results (Table 3):
    - Any Patents: log(emp): 0.130 ***; ∆Log # of regulations: -0.022 ***; Observations: 4,227,020; Mean dep. var.: 0.0940.
    - Patents filed in ES, EU, US: log(emp): 0.028 ***; ∆Log # of regulations: -0.006 *; Observations: 4,227,020; Mean dep. var.: 0.016.
    - Average Citations: log(emp): 0.077 ***; ∆Log # of regulations: -0.027; Observations: 3,935; Mean dep. var.: 1.102.
  - Interpretation: increases in regulations are negatively associated with firm-level innovation activity; coefficient on average citations negative but not statistically significant.
- Magnitude and post-innovation growth:
  - High-friction firms (top decile) vs low-friction (bottom decile): combined implied probabilities suggest constraints together might account for about 88 percent of the innovation gap relative to Swedish firms at employment 45 (33 out of 37 percentage points).
  - Employment growth after patenting regressions (Table 4):
    - Column 1 (Innovation effect): Innovation: 0.344 ***; Innovation x 45≤ Emp < 50: -0.191 ***; Observations: 4,705,084.
    - Column 2 (Financial constraint interaction): Innovation: 0.352 ***; Innovation x Constrained: -0.035 **; Observations: 4,705,084.
    - Column 3 (Regulation interaction): Innovation: 0.362 ***; Innovation x Regulated: -0.046 **; Observations: 3,940,540.
  - Interpretation: conditional on innovating, firms facing larger frictions grow less; size-dependent regulation near 50 employees shows the strongest quantitative association with reduced post-innovation growth.

### Model framework, calibration, and parameter targets
- Model: continuous-time general equilibrium endogenous growth model building on Klette and Kortum (2004) with firm-level innovation, creative destruction, heterogeneous step sizes, and frictions.
- Key model features and friction implementation:
  - R&D produces Poisson arrivals with arrival rate x_i; cost C(x_i; n_i) = x_i^η n_i^{1−η} Y/α in base form.
  - Size-dependent regulations: fixed cost φ>0 when employment exceeds 50.
  - Financial frictions: additional R&D cost τ(n_i) = −τ log(n_i) (decreasing with employment).
  - R&D subsidies: effective subsidy rate (1 − s) multiplier in R&D cost.
  - Regulatory burdens: entrant fixed cost δ>0.
  - Heterogeneous innovation step size λ ∈ {λ_H, λ_L} with entrants born high-type and transition rate κ.
  - Modified R&D cost used quantitatively:
    - C(x_i; n_i) = [ (1 − s) (1 + τ(n_i)) x_i^η n_i^{(1−η)} Y ] / α
- Calibration targets and values (selected):
  - R&D / GDP (Spain) target: 1.49 percent; α calibrated: Model: 0.158; Data: 0.149.
  - TFP growth rate (2015–2025) target: 0.67 percent; λ_L calibrated: Model: 0.71; Data: 0.67; λ_H assumed twice λ_L.
  - φ (size-dependent regulation) target: marginal decline in patenting between 45 and 50 employees: target -0.44; model -0.41.
  - τ: slope of log(MRPK) over log(emp) target/model: -0.08.
  - δ (regulatory burdens) target: firm entry rate target 0.05; model 0.047.
  - κ (young vs old patent quality difference) target: 0.225; model: 0.22.
  - s (R&D subsidy rate) baseline: 10 percent = effective subsidy rate (33 percent) × take-up rate (30 percent) per AIReF (2020).
  - η (convexity of R&D cost): 2.

### Quantitative counterfactuals and growth impacts
- Friction-reduction counterfactuals:
  - Each friction’s cost parameter reduced by half, one at a time.
  - Combined reduction of all three frictions increases long-term productivity growth rate by 0.18 percentage points.
  - Size-dependent regulations alone generate relatively small gains because a small share of firms are near the threshold; cutting financial frictions and regulatory burdens yields larger gains.
- R&D tax credit counterfactuals:
  - Streamlining to increase take-up from 30 percent to 60 percent:
    - Effective R&D subsidy rate rises from 10 to 20 percent.
    - TFP growth rate increases by an additional 0.06 percentage points on top of gains from cutting the three frictions.
  - Targeting the take-up increase to firms younger than five years (keeping government spending/GDP constant):
    - Raises growth by an additional 0.03 percentage points relative to untargeted take-up increase.
    - Total incremental gain from targeting relative to baseline untargeted increase: 0.09 percentage points.
- Aggregate combined impacts (as reported in source sections):
  - Section 1 statement: Combined potential gain = 0.18 + 0.1 = 0.28 percentage points (noted as “over a quarter of a percentage point”).
  - Section 2 aggregate combined impact: All reforms together raise long-term productivity growth rate by 0.27 percentage points.

### Policy conclusions and recommendations
- Regulatory burdens:
  - Continue and amplify the “Regime 20” initiative to reduce administrative barriers across regions.
  - Complement top-down reform with bottom-up adoption of open-market laws by autonomous communities.
  - EU-level reforms (e.g., EU 28th Regime initiative) could further ease regulatory burdens.
- Financial frictions:
  - Progress toward the EU’s Savings and Investment Union would benefit financially-constrained Spanish firms.
  - The public investment fund España Crece could stimulate innovation if targeted to young and innovative firms rather than smaller, older, less innovative firms.
- Size-dependent regulations:
  - Smooth existing regulatory thresholds—particularly the 50-employee threshold that concentrates multiple regulations—to reduce discontinuities that discourage scaling.
- R&D tax credit reforms:
  - Strengthen legal certainty and simplify access to the refund option to increase take-up.
  - Improve coordination between the Ministry of Science and tax authorities to enhance the ex ante Binding Motivated Report (IMV) credibility and reduce ex post downgrades of claimed R&D expenditure.
  - Ease refund restrictions identified as constraints: 20 percent discount, one-year waiting period, and requirement to maintain number of R&D workers after refund — streamline these to increase take-up, especially among young and innovative firms.

*Source: IMF Selected Issues Paper SIP/2026/056, “Firm-Level Innovation in Spain: Patterns, Drivers, and Policy Implications,” prepared by Younghun Shim, Isabel Figueiras, and Carlo Pizzinelli (completed May 4, 2026).

### Section 1

### Firm-Level Innovation in Spain: Patterns, Drivers, and Policy Implications

### Key Findings and Abstract
- Paper completion date: May 4, 2026. Document: SIP/2026/056.
- Spain’s labor productivity was roughly comparable to that of the US in 1990; by the time of this paper Spain’s productivity is at about 74 percent of the US level.
- Spain exhibits a large innovation gap vis-à-vis peer high-income countries; the gap is especially pronounced among young firms and for higher-quality patents.
- Main frictions identified: size-dependent regulations, financial constraints, regulatory burdens, and the complexity of the R&D tax credit.
- Spain’s statutory R&D tax credit: 25 percent on R&D up to the average expenditure level of the previous two years, and 42 percent on additional expenditure above that level.
- Actual take-up rate of the R&D tax credit: around 30 percent (AIReF, 2020).
- Quantitative model simulations indicate that easing the identified frictions could raise Spain’s long-term total factor productivity (TFP) growth by over 0.25 percentage points.
- Counterfactual decomposition from model calibration:
  - Addressing all three frictions could increase long-run TFP growth by 0.18 percentage points.
  - Streamlining the R&D tax credit and better targeting it toward young firms could increase the TFP growth rate by a further 0.1 percentage point.

### Introduction and Scope
- Focus: innovation as a key driver of productivity growth; empirical and model-based analysis of firm-level innovation in Spain.
- Empirical approach: merge PATSTAT patent data with Orbis firm-level data to document patterns across firm age and size and to assess the role of frictions.
- Modeling approach: general equilibrium endogenous growth model based on Klette and Kortum (2004), extended to incorporate frictions that reduce firms’ innovation incentives and aggregate growth.
- Policy counterfactuals: calibrated to match micro-level patterns of innovation and firm size in Spain.

### R&D Tax Credit and Policy Environment
- Statutory design:
  - 25 percent tax credit up to average expenditure level of the previous two years.
  - 42 percent tax credit on additional expenditure above that level.
- Practical limitations reducing effective access:
  - Actual take-up rate: around 30 percent (AIReF, 2020).
  - Legal and regulatory uncertainty: ex-post evaluations can lead to rejection if activities are deemed not to qualify as “R&D,” raising perceived rejection risk.
  - Lack of sufficient taxable profits for small and young firms limits ability to use credit (credit cannot function as a negative tax).
  - Monetization mechanism exists but is discounted, subject to strict continuity of activity and employment requirements, and involves receipt with a lag.
  - Administrative burden from documentation, certification, and compliance is widely perceived to be large.
- Net effect: R&D tax credit is generous on paper but much less accessible in practice, particularly for small and young firms.

### Data Sources and Stylized Facts
- Data:
  - Firm-level data from Orbis: sales, employment, fixed assets, industry, location.
  - Patent data from PATSTAT (including EPO, Spanish, US, and Japanese patent offices).
  - Matching procedure follows EUIPO (2025) standardization and literature data cleaning (Díez and others, 2021; Kalemli-Özcan and others, 2024).
- Matching rates:
  - Spain: 87 percent of patent applications by firms located in Spain assigned to harmonized Orbis firm ID.
  - France: 78 percent.
  - Sweden: 85 percent.
- Input and output innovation measures:
  - R&D intensity in Spain has stagnated since the late 2000s; gap relative to other advanced economies persists.
  - Patents filed by residents per million population: Spain records substantially fewer patents than peer countries; patenting gap exceeds R&D spending gap, indicating lower innovation productivity.
- Sectoral decomposition of patenting gap with the US:
  - Within-sector margin accounts for about 70 percent of the total patenting gap between Spain and the US.
  - Across-sector (composition) margin accounts for the remaining 30 percent.
  - Implication: Spain’s innovation shortfall is mainly due to weaker innovative performance of firms within the same industries.

### Firm-Level Patenting Patterns
- Patenting probabilities:
  - Spanish firms are less likely to file patents than French and Swedish firms across all age groups.
  - The gap is larger for younger firms and is more pronounced for high-quality patents (USPTO filings used as proxy for higher-quality patents).
- Patent quality:
  - Measured via forward citations (excluding self-citations); transformation: inverse hyperbolic sine (IHS).
  - Average patent quality increases with firm size (proxied by employment) conditional on firm age.
  - Average patent quality decreases with firm age; younger firms tend to produce higher-quality innovations, suggesting importance of targeting young firms.
- Polarization in innovation:
  - Only 0.17 percent of firms file a patent when they are young (defined as age five or below).
  - Among firms that innovate when young, 36 percent also innovate at older ages.
  - Among firms that do not innovate when young, only 0.3 percent file a patent later in life.
  - Interpretation: persistent heterogeneity—small subset of startups exhibit persistent innovative activity while most startups are non-innovative subsistence-type firms.

### Empirical Analysis of Frictions
- Frictions examined: size-dependent labor regulations, financial constraints, and regulatory burdens (regional and sectoral).
- Two empirical questions:
  1. Is firm-level innovation negatively associated with the presence of the friction?
  2. Conditional on innovating, does the friction hinder firm growth following innovation?
- Estimation strategy:
  - First-stage: regress patenting indicator on friction measures to assess correlation with innovation.
  - Second-stage: regress firm employment growth on interaction between patenting indicator and friction measure to assess effect on post-innovation growth.
- Size-dependent regulations:
  - Spanish firms face significantly more stringent labor regulations once they exceed 50 employees (Almunia and others, 2024); additional threshold noted when operating revenue exceeds €6 million, but no statistically significant innovation effect associated with the €6 million threshold was found in this analysis.
  - Evidence: share of patenting Spanish firms declines near the 50-employee threshold.
  - Regression specification includes a dummy for employment in the band 45≤emp≤49 and controls for log employment, sector (4-digit NACE) and year fixed effects.
  - Dependent variables used in regressions:
    - i) Dummy for whether a firm files any patent.
    - ii) Number of patents filed at Spanish, European, and US patent offices (captures higher-quality patents via filings across multiple offices).
    - iii) IHS of average number of forward citations (indicator of patent quality).
  - Results: coefficients on the 45≤emp≤49 dummy are negative across all dependent variables, indicating firm-level innovation is negatively correlated with size-dependent regulations.

### Model-Based Quantification and Policy Counterfactuals
- Model framework: general equilibrium endogenous growth model with firm-level innovation and creative destruction (building on Klette and Kortum, 2004).
- Frictions incorporated into model reduce firms’ incentives to invest in R&D and thus aggregate growth; model is calibrated to match observed micro patterns of innovation and firm size in Spain.
- Counterfactual outcomes:
  - Removing the three frictions (size-dependent regulations, financial constraints, regulatory burdens) increases long-run TFP growth by 0.18 percentage points.
  - Streamlining the R&D tax credit to raise take-up and better targeting it toward young firms could add an additional 0.1 percentage point to TFP growth.
  - Combined potential gain = 0.18 percentage points + 0.1 percentage point = 0.28 percentage points (noted in the paper as yielding an increase “over a quarter of a percentage point”).

*Source: IMF Selected Issues Paper SIP/2026/056, “Firm-Level Innovation in Spain: Patterns, Drivers, and Policy Implications,” prepared by Younghun Shim, Isabel Figueiras, and Carlo Pizzinelli (completed May 4, 2026).*

### Section 2

### sipea2026056 - Section 2

### Empirical Evidence: Size Thresholds and Patenting
- Table 1 — Spain: 50-Employee Threshold and Innovation: Firm-Level Regression Results
  - Any Patents
    - log(emp): 0.181 ***
    - 45≤ Emp < 50: -0.141 ***
    - Observations: 5,049,483
    - Mean of dep. var.: 0.1300
  - Patents filed in ES, EU, US
    - log(emp): 0.039 ***
    - 45≤ Emp < 50: -0.073 ***
    - Observations: 5,049,483
    - Mean of dep. var.: 0.0221
  - Average Citations
    - log(emp): 0.086 ***
    - 45≤ Emp < 50: -0.163 *
    - Observations: 6,496
    - Mean of dep. var.: 1.099
  - Standard errors in parentheses. Significance: * p< 0.10, ** p< 0.05, *** p< 0.01
- Interpretation
  - Firms with employment between 45 and 49 exhibit a statistically significant decline in the probability of patenting and in average citations relative to other firms at the 50-employee threshold.

### Empirical Evidence: Financial Constraints (MRPK)
- MRPK definition (assuming Cobb-Douglas with output elasticity of labor α):
  - y_i = a_i l_i^α k_i^{1−α}
  - MRPK_i = (1−α) p_i y_i / k_i
- Classification of constrained firms
  - Firms are classified as financially constrained if their MRPK exceeds the median within a given sector–year.
- Figure 7 finding
  - Negative correlation between log(MRPK) and log(firm age), conditional on firm sales and sector–year fixed effects (younger firms more likely to be financially constrained).
- Table 2 — Spain: Innovation with Financial Frictions
  - Any Patents
    - log(emp): 0.180 ***
    - Constrained: -0.087 ***
    - Observations: 5,049,483
    - Mean of dep. var.: 0.1300
  - Patents filed in ES, EU, US
    - log(emp): 0.039 ***
    - Constrained: -0.021 ***
    - Observations: 5,049,483
    - Mean of dep. var.: 0.0221
  - Average Citations
    - log(emp): 0.084 ***
    - Constrained: -0.144 ***
    - Observations: 6,496
    - Mean of dep. var.: 1.099
  - Standard errors in parentheses. Significance: * p< 0.10, ** p< 0.05, *** p< 0.01
- Interpretation
  - Financial constraints (high MRPK) are negatively associated with probability of patenting and patent quality.

### Empirical Evidence: Regulatory Burdens
- Measurement
  - Intensity captured by the number of newly introduced regulations at the region–sector–year level (Mora-Sanguinetti and others (2022, 2024)).
  - Regression includes sector, year, and region (two-digit NUTS) fixed effects.
- Table 3 — Spain: Innovation with Regulatory Burdens
  - Any Patents
    - log(emp): 0.130 ***
    - ∆Log # of regulations: -0.022 ***
    - Observations: 4,227,020
    - Mean of dep. var.: 0.0940
  - Patents filed in ES, EU, US
    - log(emp): 0.028 ***
    - ∆Log # of regulations: -0.006 *
    - Observations: 4,227,020
    - Mean of dep. var.: 0.016
  - Average Citations
    - log(emp): 0.077 ***
    - ∆Log # of regulations: -0.027
    - Observations: 3,935
    - Mean of dep. var.: 1.102
  - Standard errors in parentheses. Significance: * p< 0.10, ** p< 0.05, *** p< 0.01
- Interpretation
  - Increases in the number of regulations are negatively associated with firm-level innovation activity; the coefficient on average citations is negative but not statistically significant.

### Magnitude of Frictions on Innovation and Post-Innovation Growth
- Figure 8 / implied probabilities
  - High-friction firms = top decile of friction measure; Low-friction firms = bottom decile.
  - For size-dependent regulations, comparison is firms with employment between 45 and 49 versus all other firms.
  - Combined implied probabilities suggest these constraints together might account for about 88 percent of the innovation gap relative to Swedish firms at employment 45 (33 out of 37 percentage points).
- Table 4 — Spain: Employment Growth after Patenting and Frictions
  - Emp growth (column 1)
    - Innovation: 0.344 ***
    - Innovation x 45≤ Emp < 50: -0.191 ***
    - Observations: 4,705,084
  - Emp growth (column 2)
    - Innovation: 0.352 ***
    - Innovation x Constrained: -0.035 **
    - Observations: 4,705,084
  - Emp growth (column 3)
    - Innovation: 0.362 ***
    - Innovation x Regulated: -0.046 **
    - Observations: 3,940,540
  - Standard errors in parentheses. Significance: * p< 0.10, ** p< 0.05, *** p< 0.01
- Interpretation
  - Conditional on innovating, firms facing larger frictions grow less; size-dependent regulation (50-employee threshold) shows the strongest quantitative association with reduced post-innovation firm growth.

### Model: Framework and Frictions
- Base model
  - Continuous-time general equilibrium model following Klette and Kortum (2004): firm dynamics driven by innovation and creative destruction; firms operate multiple product lines; R&D produces Poisson arrivals of innovations with arrival rate x_i and cost C(x_i; n_i) = x_i^η n_i^{1−η} Y/α.
- Extensions introduced
  - Size-dependent regulations: fixed cost φ>0 when employment exceeds 50.
  - Financial frictions: additional R&D cost τ(n_i) decreasing with firm-level employment; modeled as τ(n) = −τ log(n).
  - R&D subsidies: effective subsidy rate incorporated as (1 − s) multiplier in R&D cost.
  - Regulatory burdens: entry fixed cost δ>0 for entrants after successful innovation.
  - Heterogeneous innovation step size λ ∈ {λ_H, λ_L}, λ_H > λ_L; all firms start with λ_H and transition to λ_L with Poisson rate κ.
- Modified R&D cost function used in quantitative model
  - C(x_i; n_i) = [ (1 − s) (1 + τ(n_i)) x_i^η n_i^{(1−η)} Y ] / α
- Mechanism
  - Frictions reduce net returns to innovation by increasing costs or reducing private returns, thereby suppressing innovation rates and aggregate productivity growth.
  - Optimal R&D subsidy rate is higher for high-type firms because social returns rise linearly with step size while private returns rise concavely.

### Quantitative Exercise: Calibration
- Macroe calibration targets and parameter values
  - R&D / GDP (Spain): 1.49 percent targeted; α calibrated to match (model value: 0.158; data: 0.149)
  - TFP growth rate (2015–2025): 0.67 percent targeted; λ_L calibrated to match (model value: 0.71; data: 0.67); λ_H assumed twice λ_L
  - Labor supply L calibrated to match share of firms with more than 50 employees.
- Frictions calibrated to micro moments
  - φ (size-dependent regulation) calibrated to match marginal decline in patenting between 45 and 50 employees: target -0.44; model -0.41
  - τ calibrated to match slope of log(MRPK) over log(emp): target -0.08; model -0.08
  - δ (regulatory burdens) calibrated to match firm entry rate: target 0.05; model 0.047
  - κ calibrated to match young vs old patent quality difference: target 0.225; model 0.22
- R&D subsidy baseline
  - s (R&D subsidy rate) calibrated to be 10 percent = effective subsidy rate (33 percent) × take-up rate (30 percent) per AIReF (2020).
- Other
  - η (convexity of R&D cost) set to 2 following Acemoglu and others (2018).
- Table 5 — Spain: Calibration Results (selected entries)
  - L: Share of firm with emp>50.015 (Model: 0.017)
  - α: Innovation cost shifter (R&D / GDP) Model: 0.158 ; Data: 0.149
  - λ_L: Baseline step size (TFP growth rate) Model: 0.71 ; Data: 0.67
  - φ: Size-dependent regulation (Patenting decline at 45<emp<50) Model: -0.44 ; Data: -0.41
  - τ: Slope of financial friction (Slope of log(MRPK) over log(emp)) Model: -0.08 ; Data: -0.08
  - δ: Regulatory burdens (Entry rate) Model: 0.05 ; Data: 0.047
  - κ: Pr (Low type | High type) (Young vs Old patent quality difference) Model: 0.225 ; Data: 0.22
  - s: R&D subsidy rate (Effective subsidy rate x take up rate) Model: 0.10 ; Data: 0.1
  - η: Convexity of R&D cost: 2

### Quantitative Exercise: Counterfactuals and Growth Impacts
- Friction-reduction counterfactuals
  - Each friction’s cost parameter reduced by half (size-dependent regulations, financial frictions, regulatory burdens), one at a time.
  - Combined reduction of all three frictions increases long-term productivity growth rate by 0.18 percentage points.
  - Size-dependent regulations alone generate relatively small gains due to a small share of firms near the employment threshold; cutting financial frictions and regulatory burdens yields larger gains as they affect a broader set of firms.
- R&D tax credit counterfactuals
  - Streamlining R&D tax credit to increase take-up from 30 percent to 60 percent:
    - Effective R&D subsidy rate rises from 10 to 20 percent.
    - TFP growth rate increases by an additional 0.06 percentage points on top of gains from cutting the three frictions.
  - Targeting take-up increase to firms younger than five years (keeping government spending/GDP constant):
    - Raises growth by an additional 0.03 percentage points relative to untargeted take-up increase.
    - Total gain from targeting (relative to baseline untargeted increase) equals 0.09 percentage points incremental.
- Aggregate combined impact
  - All reforms considered together (cutting three frictions and streamlining plus targeting R&D subsidy) raise the long-term productivity growth rate by 0.27 percentage points.

### Policy Conclusions and Considerations
- Regulatory burdens
  - Continue and amplify the “Regime 20” initiative to reduce administrative barriers across regions.
  - Complement top-down reform with bottom-up adoption of open-market laws by autonomous communities.
  - EU-level reforms (e.g., EU 28th Regime initiative) could further ease regulatory burdens.
- Financial frictions
  - Progress toward the EU’s Savings and Investment Union would benefit financially-constrained Spanish firms.
  - The public investment fund España Crece could stimulate innovation if targeted to young and innovative firms rather than smaller, older, less innovative firms.
- Size-dependent regulations
  - Smooth existing regulatory thresholds—particularly the 50-employee threshold that concentrates multiple regulations—to reduce discontinuities that discourage scaling.
- R&D tax credit reforms
  - Strengthen legal certainty and simplify access to the refund option to increase take-up.
  - Improve coordination between the Ministry of Science and tax authorities to enhance the ex ante Binding Motivated Report (IMV) credibility and reduce ex post downgrades of claimed R&D expenditure.
  - Ease refund restrictions: 20 percent discount, one-year waiting period, and requirement to maintain number of R&D workers after refund are identified as constraints that weaken innovation and could be streamlined to increase take-up, especially among young and innovative firms.

*Source: sipea2026056 - Section 2*

### Section 3

### sipea2026056 - Section 3

### References (selected)
- Shu. (2020). “Foreign Competition and Domestic Innovation: Evidence from US Patents.” American Economic Review: Insights 2(3): 357–374.
- Bergeaud, A., G. Cette, and R. Lecat. (2016). “Productivity Trends in Advanced Countries between 1890 and 2012.” Review of Income and Wealth 62(3): 420–444.
- Choi, J., and Y. Shim. (2024). “From Adoption to Innovation: State-Dependent Technology Policy in Developing Countries.” IMF Working Papers 2024(154).
- Díez, F., J. Fan, and C. Villegas-Sanchez. (2021). “Global Declining Competition.” Journal of International Economics 132: 103492.
- European Union Intellectual Property Office and European Patent Office. (2025). Intellectual Property Rights and Firm Performance in the European Union: Firm-Level Analysis Report. January 9, 2025.
- Garicano, L., C. Lelarge, and J. Van Reenen. (2016). “Firm Size Distortions and the Productivity Distribution: Evidence from France.” American Economic Review 106(11): 3439–3479.
- Guntin, R., and F. Kochen. (2025). “The Origins of Top Firms.” Working paper.
- Hsieh, C.-T., and P. J. Klenow. (2009). “Misallocation and Manufacturing TFP in China and India.” Quarterly Journal of Economics 124(4): 1403–1448.
- Hurst, E., and B. W. Pugsley. (2011). “What Do Small Businesses Do?” Brookings Papers on Economic Activity 42(2): 73–142.
- Kalemli-Özcan, Ş., B. E. Sørensen, C. Villegas-Sanchez, V. Volosovych, and S. Yeşiltaş. (2024). “How to Construct Nationally Representative Firm-Level Data from the Orbis Global Database: New Facts on SMEs and Aggregate Implications for Industry Concentration.” American Economic Journal: Macroeconomics 16(2): 353–374.
- Klette, T. J., and S. Kortum. (2004). “Innovating Firms and Aggregate Innovation.” Journal of Political Economy 112(5): 986–1018.
- Mora-Sanguinetti, J., J. Quintana, and I. Soler. (2022). “La regulación sectorial en España. Resultados cuantitativos.” Banco de España Working Paper 2202.
- Mora-Sanguinetti, J., J. Quintana, I. Soler, and R. Spruk. (2024). “The Heterogeneous Effects of a Higher Volume of Regulation: Evidence from More than 200k Spanish Norms.” Journal of Regulatory Economics 65(1): 137–153.

### Annex I. Data — key data sources and sample construction
- Main data merge: ORBIS merged with PATSTAT.
- Main sample period: 2000 to 2019.
- ORBIS provides firm-level information on sales, employment, fixed assets, industry, and location; covers large firms and SMEs.
- Coverage statistics:
  - Spain: 82 percent of gross output in the manufacturing sector (average coverage in ORBIS, per Kalemli-Ozcan and others (2024)).
  - France: 87 percent coverage.
  - Sweden: 77 percent coverage.
- Data cleaning and matching procedures follow Kalemli-Ozcan and others (2024) and Díez and others (2021).
- PATSTAT content and use:
  - Contains patent information from multiple patent offices (including the European Patent Office, Spanish, US, and Japanese patent offices).
  - Provides assignee names, regions, citations; citation data used to construct forward citations as proxy for patent quality.
  - Reports patent family identifiers for patents registered in multiple offices.
- Merge procedure:
  - Merge PATSTAT with ORBIS using firm names following EUIPO (2025) procedure.
  - Standardize firm names in both PATSTAT and ORBIS, then conduct exact matching.
  - Merge performed at the subsidiary level (e.g., Airbus France and Airbus Spain treated as distinct firms).
- Matching rates:
  - Spanish firms: 87 percent (87 percent of all patents applied for by firms located in Spain appear in final merged sample).
  - France: 78 percent.
  - Sweden: 85 percent.
  - Comparison: Autor and others (2020) obtain a 72 percent matching rate when merging US Patent Office data with Compustat (web-based matching algorithms).

### Annex II. Model — environment, innovation, and equilibrium
- Environment
  - Time is continuous.
  - Unit continuum of products indexed by j ∈ [0,1], aggregated into a final good using a Cobb–Douglas aggregator:
    - Y = (∫ y_j dj)^{1/0} ? (expression in source: 푌= ∫ 푦_j 푑푗 1 0 .) — final good price normalized to one.
  - Representative household consumes final good and supplies labor L inelastically.
  - Each product is produced by a single producer with production function y_j = a_j l_j.
  - Firms set price equal to marginal cost of competitor, which is lower by factor λ_i.
  - Given Cobb–Douglas aggregation, each product generates revenue equal to Y.
  - Profits per product: π_i = (1−1/λ_i) Y.
  - Firms are symmetric in equilibrium; relevant firm state variable is n (number of product lines).
  - Firms receive n π_i amount of profits and hire n l labor.
  - Size-dependent regulation: deadweight cost φ Y is incurred if employment exceeds 50 workers.
    - Equivalently, firms with more than nത product lines are subject to this regulation.
- Innovation
  - Both incumbents and entrants can innovate.
  - Innovation randomly draws a product line and increases that product’s productivity; innovator becomes new incumbent on that line.
  - When average innovation rate in the economy is m, a firm with n lines loses a product at hazard rate n m.
  - Firms choose R&D expenditure to determine Poisson arrival rate x of innovation.
  - Innovation becomes easier as firms accumulate product lines (knowledge capital).
  - Flow cost of generating arrival rate x_i for firm with n_i lines:
    - C(x_i; n_i) = (1 − s) [1 + τ(n_i)] x_i^η n_i^{1−η} Y/α,  (source expression: 푪(풙풊;풏풊)= (ퟏ − 풔)൫1+휏(푛푖)൯푥푖휂푛푖1−휂푌/훼,)
    - where s is R&D subsidy rate, τ(n_i) is financial friction costs (decreases with n_i), and α is a cost shifter.
  - Entrants face same R&D cost as incumbents with one product line and additionally pay fixed entry cost δ Y.
  - Firms differ in innovation step size: λ_i ∈ {λ_H, λ_L}, with λ_H > λ_L > 1.
  - Entrants are born high-type and transition to low type at Poisson rate κ > 0 (following Acemoglu and others (2018)).
- Equilibrium — firm value functions and innovation choices
  - Incumbent value function for firm with n product lines and type q ∈ {L, H}:
    - r V(n,q) − V̇(n,q) = max_x [ x n π(q) Y − φ ⋅ 1(l ≥ 50) − C(x; n) + x( V(n+1,q) − V(n,q) ) − m( V(n−1,q) − V(n,q) ) + κ( V(n,L) − V(n,q) ) ]
  - Normalized value function v = V/Y gives:
    - r v(n,q) − v̇(n,q) = max_x [ x n π(q) − φ ⋅ 1(l ≥ 50) − c(x; n) + x( v(n+1,q) − v(n,q) ) − m( v(n−1,q) − v(n,q) ) + κ( v(n,L) − v(n,q) ) ]
    - where c(x; n) = C(x; n)/Y.
  - Incumbent innovation rate:
    - x(n,q) = [ ( v(n+1,q) − v(n,q) ) ] / ( η (1−s) [1+τ(n)] n^{η−1} )  (source expression preserved: 푥(푛,푞)=ൣ൫푣(푛+1,푞)−푣(푛,푞)൯/(휂(1−푠)൫1+휏(푛)൯൧ η−1 푛. )
    - Absent frictions, innovation scales linearly with firm size.
    - Subsidies raise innovation; financial frictions reduce it.
  - Potential entrant value function:
    - r V_E − V̇_E = max_x [ x V(1,H) − C(x;1) − δ Y ]
    - Normalized: r v_E − v̇_E = max_x [ x v(1,H) − c(x;1) − δ ]
  - Entrant innovation rate:
    - x_E = [ v(1,H) ] / ( η (1−s) [1+τ(1)] 1^{η−1} )  (source: 푥퐸=ൣ(푣(1,퐻))/ (휂(1−푠)൫1+휏(1)൯൧ 휂−1 .)
  - Aggregate growth rate given firm distribution μ(n,q):
    - g = ∫ log(λ_H) x(n,H) dμ(n,H) + ∫ log(λ_L) x(n,L) dμ(n,L) + log(λ_H) x_E.

_Italic line: Source — sipea2026056 - Section 3 (source PDF: sipea2026056 - Section 3)._

---


_Source: https://www.imf.org/-/media/files/publications/selected-issues-papers/2026/english/sipea2026056.pdf_