## DIFFERENCES IN REGIONAL PRODUCTIVITY: WHAT IS BEHIND IT?

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### A. Introduction
- Empirical approach:
  - Employs stochastic frontier models to estimate a production frontier for Spanish regions and the distance of each region from the frontier.
  - Identifies the role of structural factors for the distance from the frontier.
  - Conducts a benchmarking exercise to demonstrate potential GDP gains from bringing regions closer to the frontier.
- Organization:
  - Section II: literature on income convergence among Spanish regions.
  - Section III: stylized facts about structural differences of Spanish regions.
  - Section IV: methodology.
  - Section V: empirical analysis.
  - Section VI: conclusions.

### B. Key background findings from the Introduction
- Spain’s productivity gap and recent productivity growth:
  - Spain’s productivity gap relative to Germany is above 10 percent.
  - Spain’s average productivity growth was negative at 0.2 percent before the Global Financial Crisis and grew by 0.5 percent per year afterwards.
- Research question: differences in productivity across Spanish regions and potential drivers (skills mismatch, technology absorption capacity, sectoral composition, regulation).

### C. Literature Review — main points
- Historical convergence patterns:
  - Strong convergence during 1950–70; slowed considerably afterwards.
  - Convergence concentrated in 1955–79; decelerated in the 1980s with persistent regional unemployment differences.
  - Rapid convergence in 1965–75; stagnation in 1975–95 due to decline in internal migration and limited absorption of labor from agriculture.
- Recent-period findings:
  - Initial differences in income per capita have persisted for the last 30 years; labor productivity contributed to convergence but divergence in unemployment rates widened regional differences; capital accumulation was main driver for convergence in labor productivity, while TFP did not play a role.
  - Regional differences in GDP per capita are primarily due to disparities in employment rather than productivity.
  - Regional disparities in income per capita are not larger than other advanced European countries; differences in employment rates across Spanish regions underlie disparities in GDP per capita.

### D. Stylized Facts — empirical observations and statistics (2016 unless otherwise stated)
- Income, labor productivity, capital, and TFP:
  - The richest region generated twice as much GDP per capita as the poorest region in 2016.
  - Employees in the most productive region produced 50 percent more output than employees in the least productive region.
  - Capital stock per employee is distributed quite evenly across regions.
  - The difference between the region with the highest and the lowest TFP was about 60 percent in 2016.
- Sectoral composition:
  - Services sector share: varies from 60 to 85 percent of GDP across regions.
  - Financial services: difference between highest and lowest shares in GDP is twofold.
  - ITC services: difference between highest and lowest shares in GDP is fivefold.
  - Community of Madrid: highest share of GDP in both financial services and ITC.
  - Manufacturing share: ranges from about 3 percent to about 25 percent of regional GDP.
  - Agriculture contribution: ranges from negligible to more than 6 percent of GDP in some regions.
  - Construction: largely similar share across regions in 2016.
- Skills, R&D, FDI, and regulatory heterogeneity:
  - Share of low skilled in labor force:
    - About 40 percent of Spain’s labor force has at most lower secondary education.
    - Regional dispersion ranges from 25–50 percent.
  - Skills mismatch:
    - Fivefold difference in the skills mismatch index between the best and the worst matched regions.
  - R&D spending and efficiency:
    - Average R&D spending = 0.98 (percent of regional GDP, average 2000-12).
    - Average R&D efficiency = 0.11 (new patents per money spent, average 2000-12).
    - Most regions spend below the country’s average (relative to the economy).
    - Top four regions are responsible for more than half of the overall R&D spending.
    - Ten out of 17 regions have R&D efficiencies below the regional average; five regions achieved above average efficiency despite spending less than the regional average.
  - Foreign direct investment (FDI):
    - Top four regions received more than 70 percent of the overall FDI attracted by the country in 2016.
  - Regulatory requirements and procedures:
    - Time required to start a business ranges between 14 to 20.5 days across regions.
    - Time to start an industrial SME ranges between 63 to 248 days across regions.
    - Divergence is similar across regions for dealing with construction permits, getting electricity, or registering property.

### E. Methodology overview
- Core empirical method: stochastic frontier analysis (Battese and Coelli (1995) panel-data specification with composite error).
- Model specification (as presented):
  - y_i,t = a + x_i,t β + ε_i,t
  - ε_i,t = v_i,t − u_i,t
  - v_i,t ~ N(0, σ_v^2)
  - u_i,t = z_i,t δ + w_i,t
- Definitions:
  - y_i,t: output of region i at time t.
  - x_i,t: vector of production inputs (capital K, human capital augmented labor LHC) and a time trend for technological change.
  - v_i,t: iid random error (measurement error/noise), independent of u_i,t.
  - u_i,t: non-negative technical inefficiency term (truncated normal with mean z_i,t δ and variance σ_u^2).
- TFP decomposition (Kumbhakar and Lovell, 2000):
  - ∆TFP = ∆T + ∆TE + (ε−1)[(ε_lhc/ε) ∆LHC + (ε_k/ε) ∆K]
  - ∆T: technological change (coefficient of time trend).
  - ∆TE: change in technical efficiency.
  - ε_lhc and ε_k: output elasticities w.r.t. human capital augmented labor and capital respectively.
  - ε = ε_lhc + ε_k represents returns to scale.
- Data and scope:
  - Sample: 17 Spanish regions over the period 2000–16.
  - Regional data sources: INE and Instituto Valenciano de Investigaciones Económicas for GDP, capital stock, employment, education attainment of the employed.
  - Structural variables for inefficiency: INE and OECD.
  - Skills mismatch index constructed following Estevão and Tsounta (2011).

### F. Empirical findings and key statistics
- Estimated production function shares:
  - Capital: 60 percent.
  - Human capital augmented labor: 40 percent.
- Technical efficiency results:
  - Twelve regions use available technologies at 81–90 percent efficiency.
  - Out of 17 regions, only three regions are close to the production frontier.
  - Many regions are far from the estimated production frontier; regions with similar capital per effective labor can have substantially different output per effective labor.
- Production frontier movement:
  - Spain’s production frontier moved inwards by about 1 percent per year on average since 2000.
  - Post-crisis: negative time-trend coefficient decreases substantially in absolute terms.
  - Interaction term: post-crisis dummy interacted with time trend is positive and statistically significant, implying a slowdown in the post-crisis inward shift of the production frontier.
- Drivers of inefficiency (examples of estimated associations):
  - Skill mismatch: positive association with inefficiency (e.g., coefficients 0.0778***, 0.0826***).
  - Foreign direct investment to GDP: negative association with inefficiency (e.g., -0.00976**, -0.00891**, -0.00882**, -0.0459***).
  - R&D spending to GDP: negative association with inefficiency (e.g., -0.0702***, -0.0600***, -0.108***).
  - Labor force with at most secondary education and share of agriculture in GDP show associations when included alone but become insignificant when controlling for skills mismatch and FDI-to-GDP ratio.
- Dynamics of technical efficiency:
  - Technical efficiency generally improved over time for most regions relative to 2000.
  - No evidence of convergence: low-efficiency regions did not converge to high-efficiency ones.
  - Regions that recorded largest gains in efficiency were already closer to the production frontier at the start of the sample.
  - Median technical efficiency improved before the crisis but deteriorated slightly afterwards; dispersion among regions widened somewhat after the crisis.

### G. Scenarios and quantitative gains
- Closing the distance to the frontier:
  - If below-average performing regions improved their efficiency up to the average, overall GDP would be 1.4 percent higher.
  - If all regions close half of their distance to the production frontier, GDP would increase by 4 percent.
- Contribution of policies to gains:
  - About 80 percent of the gains in the half-gap scenario could come from lowering the skills mismatch and increasing R&D spending.
  - Reducing skills mismatch in laggard regions to the regional average is estimated to raise GDP by 0.6 percent; closing half the distance to the best performing region yields a 1.2 percent GDP increase.
  - Raising R&D spending in below-average regions to the regional average could raise GDP by 0.5 percent; closing half the R&D gap with the best performer could create potential gains of 2.2 percent.
  - Under the assumption that below-average regions improve up to the regional average, gains from lowering skills mismatch and increasing R&D activities are similar in size. In the half-gap scenario, gains from better innovation and technology absorption are almost twice as large as gains from lower skills mismatch.

### H. Conclusion and policy recommendations
- Main findings:
  - The economy’s overall productivity frontier moved inward over time, but this trend slowed after the crisis.
  - Most regions use available technologies inefficiently; while efficiency improved for most regions, those initially closer to the frontier recorded larger gains.
  - High skills mismatch and low capacity to innovate and absorb technologies are potential factors preventing efficient use of available technologies, contributing to TFP disparities among regions.
- Policy options to lower regional disparities and raise TFP:
  - Reduce school drop-out rates to address significant skills gaps preventing employment.
  - Increase labor market relevance of tertiary education through better cooperation between private sector and universities to reduce skills mismatch at the higher education end.
  - Systematic exchanges of best practices and peer review among regions to reduce large regional differences in education outcomes.
  - Strengthen Active Labor Market Policies (ALMP) at the regional level, with a focus on well-targeted training and results-oriented funding and impact evaluation (Spanish Activation for Employment Strategy 2017-2020 referenced).
  - Improve coordination across government levels for design, implementation, and evaluation of research and innovation policies to improve R&D spending efficiency and technology absorption.
  - Improve the business environment to attract more FDI, accelerating acquisition and adoption of global innovations.

### I. Annex I — Skills Mismatch Index (summary)
- Index construction (Estevão and Tsounta, 2011 framework):
  - SSmismatch_i,t = sum_{j=1 to 3} (S_i,j,t − M_i,j,t)^2
  - j indexes skill levels: low, medium, high.
  - S_i,j,t: percentage of population with skill level j in labor force (skill supply).
  - M_i,j,t: percentage of employees with skill level j in employment (skill demand).
- Data sources and definitions:
  - Educational attainment of labor force and employment by education: National Statistics Institute.
  - Skill supply categories:
    - Low-skilled: share with less than primary, primary and lower secondary education in labor force.
    - Medium-skilled: share with upper secondary and post-secondary non-tertiary education.
    - High-skilled: share with tertiary education.
  - Skill demand approximated by corresponding shares of employees by education level.

*Source: IMF staff analysis contained in "Differences in Regional Productivity: What Is Behind It?", November 2, 2018.*

### References  ______________________________________________________________________________ 16

### DIFFERENCES IN REGIONAL PRODUCTIVITY: WHAT IS BEHIND IT?

### A. Introduction
- Recent studies suggest slow income convergence among Spanish regions since 1980, reflecting persistent regional disparities in total factor productivity (TFP).
- Empirical approach:
  - Employs stochastic frontier models to estimate a production frontier for Spanish regions and the distance of each region from the frontier.
  - Identifies the role of structural factors for the distance from the frontier.
  - Conducts a benchmarking exercise to demonstrate potential GDP gains from bringing regions closer to the frontier.
- Organization of the paper:
  - Section II: literature on income convergence among Spanish regions.
  - Section III: stylized facts about structural differences of Spanish regions.
  - Section IV: methodology.
  - Section V: empirical analysis.
  - Section VI: conclusions.

### B. Key background findings from the Introduction
- Spain’s productivity gap and recent productivity growth:
  - Spain’s productivity gap relative to Germany is above 10 percent.
  - Spain’s average productivity growth was negative at 0.2 percent before the Global Financial Crisis and grew by 0.5 percent per year afterwards.
- Research question: differences in productivity across Spanish regions and potential drivers (skills mismatch, technology absorption capacity, sectoral composition, regulation).

### C. Literature Review — main points
- Historical convergence patterns:
  - Strong convergence during 1950–70; slowed considerably afterwards.
  - Mas and others (1995): convergence concentrated in 1955–79, driven by reduction in agriculture share and narrowing infrastructure gaps; convergence decelerated in the 1980s with persistent regional unemployment differences.
  - De la Fuente (2002a, 2002b): rapid convergence in 1965–75; stagnation in 1975–95 due to decline in internal migration and limited absorption of labor from agriculture.
- Recent-period findings:
  - Puente (2017): initial differences in income per capita have persisted for the last 30 years; labor productivity contributed to convergence but divergence in unemployment rates (poorer regions with higher unemployment) widened regional differences; capital accumulation was main driver for convergence in labor productivity, while TFP did not play a role.
  - Garrido-Yserte and Mancha-Navarro (2010): regional differences in GDP per capita are primarily due to disparities in employment rather than productivity.
  - European Commission 2018 country report: regional disparities in income per capita are not larger than other advanced European countries; differences in employment rates across Spanish regions underlie disparities in GDP per capita.

### D. Stylized Facts — empirical observations and statistics
- Income, labor productivity, capital, and TFP (2016):
  - The richest region generated twice as much GDP per capita as the poorest region in 2016.
  - Employees in the most productive region produced 50 percent more output than employees in the least productive region.
  - Capital stock per employee is distributed quite evenly across regions.
  - The difference between the region with the highest and the lowest TFP was about 60 percent in 2016.
- Sectoral composition (2016):
  - Services sector dominates in all regions, varying from 60 to 85 percent of GDP across regions.
  - Variation is large for financial and information and communication (ITC) services:
    - Difference between highest and lowest shares of financial services in GDP is twofold.
    - Difference for ITC services is fivefold.
  - Community of Madrid is an outlier with the highest share of GDP in both financial services and ITC.
  - Manufacturing share ranges from about 3 percent to about 25 percent of regional GDP across regions.
  - Agriculture contribution ranges from negligible to more than 6 percent of GDP in some regions.
  - Construction had a largely similar share across regions in 2016.
- Skills, R&D, FDI, and regulatory heterogeneity:
  - Share of low skilled in labor force:
    - About 40 percent of Spain’s labor force has at most lower secondary education—one of the highest shares among Euro Area countries.
    - Regional dispersion ranges from 25–50 percent.
  - Skills mismatch:
    - Fivefold difference in the skills mismatch index between the best and the worst matched regions.
    - The skills mismatch index captures the difference between skills demand (share of workers with different level of education in employment) and skills supply (share of people with different level of education in the labor force).
  - R&D spending and efficiency:
    - Spain spends less on R&D compared with peers.
    - Most Spanish regions spend below the country’s average (relative to the economy).
    - Top four regions are responsible for more than half of the overall R&D spending.
    - R&D spending efficiency (new patents per money spent on R&D) varies widely: ten out of 17 regions have R&D efficiencies below the regional average; five regions achieved above average efficiency despite spending less than the regional average.
    - Average R&D spending = 0.98 (percent of regional GDP, average 2000-12).
    - Average R&D efficiency = 0.11 (new patents per money spent, average 2000-12).
  - Foreign direct investment (FDI):
    - Top four regions received more than 70 percent of the overall FDI attracted by the country in 2016 (foreign direct investments, 2000-16, measured as percent of regional GDP).
  - Regulatory requirements and procedures:
    - Time required to start a business ranges between 14 to 20.5 days across regions.
    - Time to start an industrial SME ranges between 63 to 248 days across regions.
    - Divergence is similar across regions for dealing with construction permits, getting electricity, or registering property.

### E. Methodology overview
- Core empirical method: stochastic frontier analysis to estimate production frontier and regional distances from the frontier.
- Empirical strategy:
  - Control for sectoral shares in GDP to capture impact of differences in sectoral productivity on aggregate TFP.
  - Use measures such as skills mismatch index, R&D spending, R&D efficiency, FDI shares, and regulatory indicators as explanatory factors for regional distances from the frontier.
- Data sources cited:
  - Fundación BBVA, INE, Instituto Valenciano de Investigaciones Económicas, IMF staff calculations, Eurostat, OECD, World Bank (Doing Business in Spain 2015).

### F. Main analytical conclusions (as reported)
- Differences in TFP across Spanish regions contribute materially to disparities in income per capita.
- Structural factors likely behind regional TFP differences include:
  - Skills mismatch and high shares of low-skilled workers.
  - Concentration and uneven efficiency of R&D spending.
  - Uneven attraction of FDI.
  - Heterogeneous regulatory requirements and procedures affecting business creation and investment.
- Policy implication illustrated by benchmarking exercise:
  - Significant potential growth benefits exist from policy measures that would bring regions closer to the production frontier.

*Source: IMF staff analysis contained in "Differences in Regional Productivity: What Is Behind It?", November 2, 2018.*

### 10.      Stochastic frontier models are used to analyze efficiency of economic agents, regions,

### 10.      Stochastic frontier models are used to analyze efficiency of economic agents, regions,

### Methodology
- Stochastic frontier panel-data model used: Battese and Coelli (1995) specification with composite error.
- Model equations (as presented):
  - 푦푦푖,푡 = 푎푎 + 푥푥푖,푡 훽 + 휀휀푖,푡  (1)
  - 휀휀푖,푡 = 푣푣푖,푡 − 푢푢푖,푡  (2)
  - 푣푣푖,푡 ~ 푁푁(0,휎휎푣2)  (3)
  - 푢푢푖,푡 = 푧푧푖,푡 훿 + 푤푤푖,푡  (4)
- Definitions and assumptions:
  - 푦푦푖,푡: output of region i at time t.
  - 푥푥푖,푡: vector of production inputs (capital K, human capital augmented labor LHC) and a time trend for technological change.
  - 푣푣푖,푡: iid random error (measurement error/noise), independent of 푢푢푖,푡.
  - 푢푢푖,푡: non-negative technical inefficiency term, obtained by truncation (at zero) of a normal distribution with mean 푧푧푖,푡 훿 and variance 휎휎푢2; 푤푤푖,푡 is the truncated normal component with point of truncation 푧푧푖,푡 훿 ensuring 푢푢푖,푡 ≥ 푧푧푖,푡 훿.
  - All parameters (including effects of structural variables on inefficiency) estimated simultaneously by maximum likelihood.
- TFP decomposition (Kumbhakar and Lovell, 2000):
  - ∆TFP = ∆T + ∆TE + (ε−1)[(ε_lhc/ε) ∆LHC + (ε_k/ε) ∆K]  (5)
  - ∆TP: technological change (coefficient of time trend in equation (1)).
  - ∆TE: change in technical efficiency.
  - ε_lhc and ε_k: output elasticities w.r.t. human capital augmented labor and capital respectively.
  - ε = ε_lhc + ε_k represents returns to scale; if ε = 1 (constant returns), factor accumulation does not impact TFP growth.

### Data and Scope
- Sample: 17 Spanish regions over the period 2000–16. (Sample constraints due to lack of structural data before 2000.)
- Regional data sources: INE and Instituto Valenciano de Investigaciones Económicas for GDP, capital stock, employment, education attainment of the employed.
- Structural variables for inefficiency: INE and OECD. World Bank Doing Business indicators not used due to single-year coverage.
- Skills mismatch index constructed following Estevão and Tsounta (2011) (see Annex I).

### Empirical findings and key statistics
- Estimated production function shares:
  - Capital: 60 percent.
  - Human capital augmented labor: 40 percent.
- Technical efficiency results:
  - Twelve regions use available technologies at 81–90 percent efficiency.
  - Out of 17 regions, only three regions are close to the production frontier.
  - Many regions are far from the estimated production frontier; regions with similar capital per effective labor can have substantially different output per effective labor, indicating inefficiency.
- Production frontier movement:
  - Spain’s production frontier moved inwards by about 1 percent per year on average since 2000 (Table 1).
  - When sample restricted to post-crisis period, the negative time-trend coefficient (technological progress) decreases substantially in absolute terms.
  - Interaction term: post-crisis dummy interacted with time trend is positive and statistically significant, implying a slowdown in the post-crisis inward shift of the production frontier.
- Drivers of inefficiency (Inefficiency component, Table 1):
  - Skill mismatch: positive association with inefficiency (coefficients reported, e.g., 0.0778***, 0.0826***).
  - Foreign direct investment to GDP: negative association with inefficiency (e.g., -0.00976**, -0.00891**, -0.00882**, -0.0459***).
  - R&D spending to GDP: negative association with inefficiency (e.g., -0.0702***, -0.0600***, -0.108***).
  - Labor force with at most secondary education and share of agriculture in GDP show associations when included alone but become insignificant when controlling for skills mismatch and FDI-to-GDP ratio.
- Dynamics of technical efficiency:
  - Technical efficiency generally improved over time for most regions relative to 2000.
  - No evidence of convergence: low-efficiency regions did not converge to high-efficiency ones.
  - Regions that recorded largest gains in efficiency were already closer to the production frontier at the start of the sample.
  - Median technical efficiency improved before the crisis but deteriorated slightly afterwards; dispersion among regions widened somewhat after the crisis.

### Scenarios and quantitative gains
- Closing the distance to the frontier:
  - If below-average performing regions improved their efficiency up to the average, overall GDP would be 1.4 percent higher.
  - In a scenario where all regions close half of their distance to the production frontier, GDP would increase by 4 percent.
  - Contribution of policies to gains:
    - About 80 percent of the gains in the half-gap scenario could come from lowering the skills mismatch and increasing R&D spending.
    - Reducing skills mismatch in laggard regions to the regional average is estimated to raise GDP by 0.6 percent; closing half the distance to the best performing region yields a 1.2 percent GDP increase.
    - Raising R&D spending in below-average regions to the regional average could raise GDP by 0.5 percent; closing half the R&D gap with the best performer could create potential gains of 2.2 percent.
  - Under the assumption that below-average regions improve up to the regional average, gains from lowering skills mismatch and increasing R&D activities are similar in size. In the half-gap scenario, gains from better innovation and technology absorption are almost twice as large as gains from lower skills mismatch.

### Conclusion and policy recommendations
- Main findings:
  - The economy’s overall productivity frontier moved inward over time, but this trend slowed after the crisis.
  - Most regions use available technologies inefficiently; while efficiency improved for most regions, those initially closer to the frontier recorded larger gains.
  - High skills mismatch and low capacity to innovate and absorb technologies are potential factors preventing efficient use of available technologies, contributing to TFP disparities among regions.
- Policy options to lower regional disparities and raise TFP:
  - Reduce school drop-out rates to address significant skills gaps preventing employment.
  - Increase labor market relevance of tertiary education through better cooperation between private sector and universities to reduce skills mismatch at the higher education end.
  - Systematic exchanges of best practices and peer review among regions to reduce large regional differences in education outcomes.
  - Strengthen Active Labor Market Policies (ALMP) at the regional level, with a focus on well-targeted training and results-oriented funding and impact evaluation (Spanish Activation for Employment Strategy 2017-2020 referenced).
  - Improve coordination across government levels for design, implementation, and evaluation of research and innovation policies to improve R&D spending efficiency and technology absorption.
  - Improve the business environment to attract more FDI, accelerating acquisition and adoption of global innovations.

### Annex I — Skills Mismatch Index (summary)
- Index construction (Estevão and Tsounta, 2011 framework):
  - Skills mismatch index for region i at time t:
    - SSmismatch_i,t = sum_{j=1 to 3} (S_i,j,t − M_i,j,t)^2
    - j indexes skill levels: low, medium, high.
    - S_i,j,t: percentage of population with skill level j in labor force (skill supply).
    - M_i,j,t: percentage of employees with skill level j in employment (skill demand).
- Data sources and definitions:
  - Educational attainment of labor force and employment by education: National Statistics Institute.
  - Skill supply categories:
    - Low-skilled: share with less than primary, primary and lower secondary education in labor force.
    - Medium-skilled: share with upper secondary and post-secondary non-tertiary education.
    - High-skilled: share with tertiary education.
  - Skill demand approximated by corresponding shares of employees by education level.

*Source: IMF staff calculations and chapter content in cr18331 (Stochastic frontier analysis of Spanish regions, sample 2000–16).*

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_Source: https://www.imf.org/-/media/files/publications/cr/2018/cr18331.pdf_