## What is Needed for Convergence? The Role of Capital and Finance

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---

### Research question and scope
- Examines drivers of convergence across countries and industries, focusing on the role of physical capital, human capital, and financial development.
- Empirical focus: labor productivity in manufacturing industries at the cross-country level and links to macro-level per capita GDP convergence.
- Industry-level sample: 2-digit manufacturing industries (ISIC Rev. 3, 15-36) in 99 developing, emerging market, and advanced economies over 1980-2022.
- Data transformation: four 10-year non-overlapping periods to relate beginning-of-period industry labor productivity to average growth over the subsequent decade (1981-1990, 1991-2000, 2001-2010, 2011-2022; last period has 12 years).

### Key empirical approach
- Follows Rodrik (2013) framework for unconditional convergence in labor productivity across countries and industries.
- Uses Rajan and Zingales (1998)-style identification exploiting within-country cross-industry variation in reliance on human and physical capital.
- Benchmark industry-level measures of human and physical capital intensity based on US data to capture technology/production-process differences.
- Definitions:
  - Human capital intensity (HCI): share of workers in each industry with at least a high school degree (Erman and Kaat 2019).
  - Physical capital intensity (PCI): ratio of total real capital stock to value added in each industry (NBER manufacturing database, 1980).

### Major industry-level empirical findings
- Unconditional convergence in labor productivity across countries and 2-digit manufacturing industries is documented (consistent with Rodrik 2013).
- Estimated convergence magnitude:
  - An industry at the 25th percentile of the labor productivity distribution sees a boost in labor productivity growth of about 3 percentage points annually, on average over the subsequent decade, relative to its peer at the 75th percentile.
  - The sample average annual growth of labor productivity is 4 percent.
- Human capital matters:
  - Convergence is faster for industries that rely more intensively on human capital.
  - Example convergence rates by HCI percentile:
    - Industry at the 25th percentile of HCI (wood products): converges at 1.1 percent.
    - Industry at the 75th percentile of HCI (machinery): converges at 1.6 percent.
  - Convergence-driven growth implications:
    - Machinery industry initially at the 25th percentile of industry labor productivity: an additional 2.7 percentage points growth per annum from convergence (1.6×ln (5.5)).
    - Wood industry analogous boost: 1.9 percentage points (1.1×ln (5.5)).
    - Differential convergence boost between these industries: 0.8 percentage points.
- Physical capital:
  - PCI alone does not correlate with the pace of convergence in a statistically significant way.
- Finance interacts with PCI:
  - Industries with greater dependence on physical capital converge only when financial development exceeds thresholds; otherwise they can diverge (see thresholds under “Role of financial development”).

### Data — industry- and country-level measures
- Industry-level sources and variables:
  - UNIDO: number of employees, value added, output for 2-digit manufacturing industries.
  - Baseline nominal labor productivity = value added (in USD) / number of employees; alternative: output / number of employees.
  - Labor productivity growth = log difference of these ratios each year; winsorized at the 1st and 99th percentiles.
  - HCI baseline: US March supplement of the 1980 Current Population Survey (share with at least high school).
  - PCI baseline: total real capital stock / value added from NBER manufacturing database in 1980.
  - Correlation between HCI and PCI = 0.12.
- Country-level variables:
  - Financial development: IMF composite index of financial development (range 0–1; higher = greater financial development; Svirydzenka 2016).
  - Bank credit to private sector (share of GDP) from World Bank WDI.
  - Sectoral value added shares (percent of GDP): Agriculture, Industry, Services (WDI).
  - Exchange rates, CPI, GDP (constant 2015 USD), GDP per capita (constant 2015 USD), producer price index (Ha et al. 2023).

### Sample composition and aggregation
- Industry-level sample:
  - 22 manufacturing industries (ISIC 15–36), 99 countries (38 advanced economies), 1980–2022.
  - Annual data collapsed into four non-overlapping 10-year periods (last period 2011–2022 has 12 years).
  - Two sample restrictions: drop country-industry pairs with only one period observation; drop countries with less than 20 country-industry-period observations.
- Country-level sample:
  - Global sample with all available data over 1980–2022; annual data also examined as robustness.
  - Average annual growth rates computed within each 10-year period as log changes (percent).

### Methodology — empirical specifications
- Industry-level baseline (Rodrik 2013 style):
  - Δlog(LP)_{c,i,p} = β1 log(LP)_{c,i,t} + θ_i + θ_p + θ_{i,p} + ε_{c,i,p}
    - β1 < 0 implies β-convergence (faster growth where initial LP is lower).
    - Fixed effects: industry, period, industry-period; standard errors clustered at country level.
- Extended industry specification including HCI and PCI:
  - Δlog(LP) = β1 log(LP) + β2 log(LP)×HCI_i + β3 log(LP)×PCI_i + fixed effects.
  - Convergence parameter for industry i: λ_i = β1 + β2 HCI_i + β3 PCI_i.
    - β2 < 0 ⇒ higher HCI_i → faster convergence.
    - β3 < 0 ⇒ higher PCI_i → faster convergence.
- Role of finance (industry-level extension):
  - Full interaction specification includes FD_{c,t} and triple interactions: log(LP)×HCI×FD and log(LP)×PCI×FD, plus controls HCI×FD and PCI×FD.
  - β7 and β8 (triple interactions) test whether FD conditions the effects of HCI and PCI on convergence.
- Country-level baseline and linkage to sectoral structure:
  - Δlog(GDP per capita)_{c,p} = β1 log(GDP per capita)_{c,t} + θ_p + ε_{c,p}; β1 < 0 indicates convergence.
  - Add interactions with beginning-of-period sectoral shares: Agriculture_{c,t}, Industry_{c,t}, Services_{c,t} to test how sectoral composition conditions convergence.
  - Financial development test at country level: include log(GDP per capita)×FD_{c,t} interactions and FD_{c,t} level.

### Stylized methodological diagnostics (select figures)
- Overall sample association between initial LP and subsequent growth: -0.26.
- Industry-specific correlations: mean -0.29, standard deviation 0.08.
- Range across industries: largest -0.52 (ISIC 35), smallest -0.14 (ISIC 16).
- Correlation of industry-specific convergence with HCI: -0.25 (preliminary); later industry-specific analysis reports correlation -0.49.
- Average annual growth rate of LP (net of fixed effects) is -1.23 (1.23) percent for industries with initial LP above (below) the sample median.

### Industry-specific convergence results (selected)
- Labor productivity in all 2-digit manufacturing industries converges to its own global frontier.
- Mean value of industry-specific convergence coefficient estimates: -1.96
- Standard deviation of coefficients: 0.77
- Correlations:
  - Industry convergence coefficients with HCI: -0.49
  - Industry convergence coefficients with PCI: 0.12
- Selected industry-specific β1 estimates (ISIC, β1, Std. error, Observations, R-squared):
  - ISIC 15: -1.662*** (0.164) — 317 obs — R-squared 0.186
  - ISIC 16: -0.828*** (0.290) — 214 obs — R-squared 0.057
  - ISIC 17: -1.785*** (0.394) — 315 obs — R-squared 0.135
  - ISIC 19: -2.023*** (0.560) — 132 obs — R-squared 0.202
  - ISIC 23: -2.394*** (0.421) — 225 obs — R-squared 0.149
  - ISIC 30: -2.574*** (0.626) — 100 obs — R-squared 0.169
  - ISIC 32: -4.147*** (1.235) — 24 obs — R-squared 0.208
  - ISIC 35: -3.729*** (0.764) — 110 obs — R-squared 0.473
  - ISIC 36: -1.461*** (0.251) — 312 obs — R-squared 0.122

### Role of financial development — industry-level
- Main patterns:
  - HCI: industries with higher HCI converge regardless of financial development levels (negative and significant log(LP)×HCI interaction).
  - PCI: industries with higher PCI tend to diverge at low FD and converge only when FD exceeds thresholds.
- FD index thresholds (FD index range 0–1):
  - Industries with higher PCI diverge when FD index < 0.17 (≈ 26 percent of observations).
  - Industries with higher PCI start to converge when FD index > 0.61 (≈ 17 percent of observations).
  - When FD index ∈ [0.17, 0.61], PCI does not play a detectable role in convergence.
- Selected coefficients (FD index column, standard errors in parentheses):
  - log(LP)×HCI: -3.015** (1.159)
  - log(LP)×PCI: 0.400** (0.161)
  - PCI×FD: 12.440** (6.155)
  - log(LP)×PCI×FD: -1.316** (0.565)
- Robustness: results persist using FD index residual (FD net of log real GDP per capita and fixed effects) and Credit to private sector (share of GDP) as alternative FD proxies.

### Robustness checks (industry and country composition, alternative measures)
- HCI alternative measures and results (Table 3):
  - Dummy high/low HCI (median split): log(LP)×HCI = -0.499*** (0.159).
  - HCI as average years of schooling: log(LP)×HCI = -0.187*** (0.070).
  - HCI from European industries: log(LP)×HCI = -2.312** (1.141).
  - HCI from broader WBES sample: log(LP)×HCI = -7.082*** (2.122) — note mean 0.93, std. dev. 0.03 for this HCI measure.
- Alternative LP measures and corrections:
  - LP based on output: log(LP)×HCI = -1.938*** (0.740).
  - Deflating LP growth by real exchange rate appreciation: log(LP)×HCI = -2.283** (1.111).
  - Relative to US industry levels (dropping US): log(LP)×HCI = -1.781*** (0.648).
- Industry-size controls:
  - Weighted regressions by beginning-of-period value added: log(LP)×HCI = -2.524*** (0.687).
  - Controlling for beginning-of-period value added share: V A share coefficient = -0.006 (0.019); log(LP)×HCI = -2.017*** (0.638).
- Sample composition robustness:
  - Results hold when dropping extreme industries, trimming outliers in growth or levels, excluding ISIC 32, restricting to complete panel, and extending sample to include one-period pairs (see Table A3).
  - Country-sample robustness: results hold when dropping the US, excluding G7, trimming richer/poorer or smaller/larger countries, and extending to countries with few observations (see Table A4).
  - Excluding Covid-19 period (1980–2019) yields similar estimates: log(LP) = -1.718*** (0.221); log(LP)×HCI = -2.066*** (0.665); log(LP)×PCI = -0.085 (0.101) — Observations 5,560, R-squared 0.157.

### Country-level (macro) findings: structural transformation and finance
- Structural composition and convergence:
  - Per capita GDP convergence across countries is faster when the economy has a higher share of activities that need more human capital (industry and services) rather than agriculture.
  - Poorer countries with initially higher shares of agriculture tend to shift toward non-agricultural activities faster, supporting per capita GDP convergence.
- Selected country-level coefficients (Table 6, Table 7; standard errors in parentheses):
  - log(GDP per capita)×Industry: -0.033** (0.015)
  - log(GDP per capita)×Services: -0.025* (0.013)
  - Industry (level): 0.234* (0.140)
  - log(GDP per capita): -0.193** (0.098) [Table 7, column (1)]
  - log(GDP per capita)×FD: -2.196*** (0.457) [Table 7, column (2)]
  - FD (level): 25.963*** (4.891) [Table 7, column (2)]
- Convergence rate examples:
  - Industry share percentiles:
    - 25th percentile industry share = 20.2 percent → convergence rate 0.67 percent.
    - 75th percentile industry share = 33.3 percent → convergence rate 1.10 percent.
    - Convergence boost in per capita GDP growth for a high-industry-share country (33.3 percent) vs low (20.2 percent): 2.3 percentage points per annum (1.1×ln(8.4) vs 0.67×ln(8.4)).
  - Financial development percentiles:
    - 75th percentile FD index ≈ 0.34 → convergence rate 1.01 percent; implies convergence boost 2.3 percentage points per annum for a country at 25th percentile of per capita GDP relative to 75th percentile (1.01×ln(9.5)).
    - 25th percentile FD index ≈ 0.10 → convergence rate 0.49 percent; implies boost about 1.1 percentage points per annum (0.49×ln(9.5)).

### Conclusions and policy implications
- Core conclusions:
  - The composition of the economy matters for convergence and for which factors accelerate it.
  - Within manufacturing, labor productivity converges faster across countries and industries when there is a high reliance on human capital.
  - Physical-capital-intensive industries require sufficiently high financial development to converge; otherwise they may diverge.
  - At the aggregate level, higher shares of non-agricultural, more human capital-intensive sectors (industry and services) predict faster per capita GDP convergence.
  - Poorer countries are shifting from agriculture toward industry and services faster, which supports aggregate convergence.
  - Financial development, human capital accumulation, and fostering high-HCI industries are key to helping developing countries converge faster to advanced-economy peers.
- Policy priorities implied:
  - Invest in human capital accumulation (e.g., schooling) and policies that promote industries intensive in human capital.
  - Implement structural and macroeconomic policies that enable reallocation of resources toward sectors that benefit from convergence.
  - Deepen domestic financial markets to allow PCI-dependent industries to converge (raise financial development beyond identified thresholds).
  - Facilitate the shift from agriculture to industry and services, especially in poorer economies.

*Source: wpiea2025112-print-pdf (IMF Working Paper — What is Needed for Convergence? The Role of Capital and Finance).*

### 1. Introduction ........................................................................................................

### 1. Introduction

### Research question and scope
- Examines what drives convergence across countries and industries, focusing on the role of physical capital, human capital, and financial development.
- Empirical focus on labor productivity in manufacturing industries at the cross-country level and links to macro-level per capita GDP convergence.
- Industry-level sample: 2-digit manufacturing industries (ISIC Rev. 3, 15-36) in 99 developing, emerging market, and advanced economies over the period 1980-2022.
- Data transformation: four 10-year non-overlapping periods to relate beginning-of-period industry labor productivity to average growth over the subsequent decade.

### Key empirical approach
- Follows Rodrik (2013) framework for unconditional convergence in labor productivity across countries and industries.
- Uses Rajan and Zingales (1998)-style strategy exploiting within-country cross-industry variation in reliance on human and physical capital.
- Benchmark industry-level measures of human and physical capital intensity using a developed economy (US) to capture technology/production-process differences rather than country-specific frictions.
- Definitions (from Erman and Kaat 2019, as used in the paper):
  - Human capital intensity (HCI): share of workers in each industry with at least a high school degree.
  - Physical capital intensity (PCI): ratio of total real capital stock to value added in each industry.

### Major empirical findings (industry-level)
- Unconditional convergence in labor productivity across countries and manufacturing industries is documented, consistent with Rodrik (2013).
- Estimated convergence magnitude:
  - An industry at the 25th percentile of the labor productivity distribution sees a boost in labor productivity growth of about 3 percentage points annually, on average over the subsequent decade, relative to its peer at the 75th percentile.
  - The sample average annual growth of labor productivity is 4 percent.
- Human capital matters:
  - Convergence is faster for industries that rely more intensively on human capital.
  - Example convergence rates by HCI percentile:
    - Industry at the 25th percentile of HCI (wood products): converges at 1.1 percent.
    - Industry at the 75th percentile of HCI (machinery): converges at 1.6 percent.
  - Implications in growth rates:
    - A machinery industry initially at the 25th percentile of industry labor productivity exhibits a 2.7 percentage points additional growth per annum (on average, during the subsequent decade) coming from convergence relative to a machinery industry initially at the 75th percentile.
    - A similarly estimated convergence boost remains 1.9 percentage points in an industry with low HCI (i.e., wood).
    - Differential convergence boost based on HCI differences across these two industries is 0.8 percentage points.
- Physical capital does not correlate with the pace of convergence on its own.
- Finance interacts with PCI:
  - Industries with greater dependence on physical capital start to converge only when the level of financial development exceeds a threshold, consistent with Aghion et al. (2005).

### Macro-level linkage and findings
- Structural composition and convergence:
  - Per capita GDP convergence across countries over time is faster when the economy has a higher share of activities that need more human capital (industrial production and services) rather than agriculture.
  - Poorer countries with initially higher shares of agriculture tend to shift toward non-agricultural activities faster, which likely supports per capita GDP convergence.
- Role of finance at the macro-level:
  - Greater financial development is linked to faster per capita GDP convergence across countries over time.
- Implication: Faster shifts by poorer countries toward non-agricultural, more human capital-intensive activities and improvements in financial development are suggestive of continued convergence moving forward.

### Contributions to the literature
- Confirms and extends literature on manufacturing convergence (Rodrik 2013; Klein and Crafts 2023; Bénétrix et al. 2015) by:
  - Showing the type of capital used in an industry matters: human capital-intensive industries drive convergence.
  - Documenting where finance matters: financial development contributes to convergence in industries where physical capital is more important, highlighting how financial constraints can prevent convergence in such industries.
- Connects to literature on technological diffusion and structural transformation by showing faster convergence in industries that typically use more human capital, consistent with easier technological absorption in those industries.
- Relates to growth and finance literature emphasizing financial development and human capital accumulation as drivers of productivity and long-run growth.

*IMF WORKING PAPERS What is Needed for Convergence? The Role of Capital and Finance — Introduction.*

### 2. Data

### 2. Data

### 2.1. Industry-level variables
- Data sources and baseline measures:
  - Number of employees, value added and output for 2-digit (ISIC Rev. 3, 15-36) manufacturing industries from the UNIDO database.
  - Baseline nominal labor productivity = value added (in USD) / number of employees.
  - Robustness alternative: output / number of employees.
  - Labor productivity growth = log difference of these ratios each year; winsorized at the 1st and 99th percentiles.
  - Industry value added share in each country’s manufacturing sector calculated for robustness controls.
  - Table A1 in the Appendix provides data sources and summary statistics for industry-level variables.

- Identification strategy for industry heterogeneity:
  - Aim: test whether industries exhibit different degrees of convergence based on innate differences in the use of human and physical capital.
  - Approach follows Rajan and Zingales (1998): compute proxies for industries’ dependence on human and physical capital using benchmark-country data (the US).
  - Rationale: detailed historical industry-level human and physical capital measures are not available for most sample countries; using US avoids endogeneity from country-specific capital allocation driven by local frictions.
  - Assumptions:
    - Relative differences across US industries are representative of those in other sample countries (ordering preserved).
    - Ordering of human and physical capital intensity across industries does not change much over time.

- Definitions and data used for proxies:
  - Human capital intensity (HCI): share of workers in each industry with at least a high school degree; calculated using the March supplement of the 1980 Current Population Survey (employees’ schooling).
  - Physical capital intensity (PCI): ratio of total real capital stock to value added in each industry based on the NBER manufacturing database in 1980.
  - Measures adopted from Erman and Kaat (2019).
  - Correlation between HCI and PCI = 0.12.

- Industry patterns (qualitative summary from Table 1):
  - Lowest HCI industries: Textiles, tobacco and apparel products.
  - Highest HCI industries: Refined petroleum, chemicals and communication equipment products.
  - Smallest PCI industries: Wearing apparel, leather and computing machinery products.
  - Largest PCI industries: Basic metals, minerals and refined petroleum industries.

- Robustness checks and alternative HCI measures:
  - Four alternative approaches to proxy HCI:
    1. Use dummy variables categorizing industries as high/low HCI and PCI based on median values (see Table A1).
    2. Average years of schooling for workers in each industry from the US in 1980 (adopted from Ciccone and Papaioannou 2009).
    3. HCI computed from European data: industry-level employment share of high-skilled workers in 1988 in seven European countries (Belgium, Denmark, France, Germany, Netherlands, Spain, UK) from Erman and Kaat (2019). Correlation with US baseline HCI = 0.85.
    4. HCI from a broader sample using World Bank Enterprise Surveys (WBES) estimates from 21 countries (first half of 2000s) adopted from Shikher (2014). HCI defined as ratio of value added by workers with secondary and tertiary education to total labor value added. Correlation with US baseline HCI = 0.81.
  - Note: a possible caveat for HCI is variation in education quality across countries, which is not captured.

- Table 1: Industry human and physical capital intensity (adopted from Erman and Kaat (2019))
  - Food and beverages 15 — Human capital intensity (HCI) 0.63 — Physical capital intensity (PCI) 1.81
  - Tobacco products 16 — HCI 0.52 — PCI 0.86
  - Textiles 17 — HCI 0.51 — PCI 1.95
  - Wearing apparel, fur 18 — HCI 0.52 — PCI 0.49
  - Leather, leather products, footwear 19 — HCI 0.54 — PCI 0.61
  - Wood products (excl. furniture) 20 — HCI 0.55 — PCI 2.08
  - Paper and paper products 21 — HCI 0.74 — PCI 2.23
  - Printing and publishing 22 — HCI 0.61 — PCI 1.00
  - Coke, refined petroleum, nuclear fuel 23 — HCI 0.86 — PCI 2.42
  - Chemicals and chemical products 24 — HCI 0.81 — PCI 2.31
  - Rubber and plastics products 25 — HCI 0.69 — PCI 2.14
  - Non-metallic mineral products 26 — HCI 0.64 — PCI 2.63
  - Basic metals 27 — HCI 0.63 — PCI 3.35
  - Fabricated metal products 28 — HCI 0.68 — PCI 1.36
  - Machinery and equipment n.e.c. 29 — HCI 0.78 — PCI 1.39
  - Office, accounting, computing machinery 30 — HCI 0.79 — PCI 0.62
  - Electrical machinery and apparatus 31 — HCI 0.78 — PCI 1.04
  - Radio, TV, communication equipment 32 — HCI 0.81 — PCI 1.01
  - Medical, precision, optical instruments 33 — HCI 0.78 — PCI 0.69
  - Motor vehicles, trailers, semi-trailers 34 — HCI 0.74 — PCI 2.28
  - Other transport equipment 35 — HCI 0.74 — PCI 0.81
  - Furniture; manufacturing n.e.c. 36 — HCI 0.55 — PCI 0.97
  - Notes: Human capital intensity (HCI) is the share of employees with at least high school degree. Physical capital intensity (PCI) is the total real capital stock as share of value added.

### 2.2. Country-level variables
- Financial development measures:
  - IMF’s composite index of financial development (accounts for depth, access, efficiency across financial markets and institutions); constructed via principal component analysis of underlying series (Svirydzenka 2016); range between 0 and 1 (higher = greater financial development).
  - Bank credit to the private sector by banks (as share of GDP) from World Bank WDI.

- Other country-level controls:
  - Value added shares (percent of GDP) of sectors from WDI:
    - Agriculture (including agriculture, forestry, and fishing).
    - Industry (including mining, manufacturing, construction, electricity, water, and gas).
    - Services (including wholesale and retail trade, hotels and restaurants, transport, and government, financial, professional, and personal services such as education, health care, and real estate services).
  - Nominal exchange rate (local currency vis-a-vis USD), consumer price inflation (CPI), GDP (constant in 2015 USD), and GDP per capita (constant in 2015 USD) from WDI.
  - Producer price index from the World Bank (pulled from Ha et al. 2023).
  - Real exchange rate used in a robustness check is calculated based on nominal exchange rate vis-à-vis USD and inflation based on producer prices in the US and based on consumer prices elsewhere.

### 2.3. Sample
- Industry-level sample:
  - 22 manufacturing industries (2-digit ISIC, listed in Table 1).
  - 99 countries (38 advanced economies) over 1980-2022.
  - Annual data transformed into four non-overlapping 10-year periods to calculate growth rates of labor productivity:
    - 1981-1990
    - 1991-2000
    - 2001-2010
    - 2011-2022 (last period has 12 years)
  - Average annual growth rate of labor productivity in each 2-digit industry calculated within each period (in percent).
  - Two sample restrictions:
    - Drop country-industry pairs with only one (10-year) period observation to maintain within-industry variation.
    - Drop countries with less than 20 country-industry-period observations to ensure within-country variation.
  - Authors report these steps do not change results.
  - List of countries in the industry sample is in the Appendix.

- Country-level (per capita GDP) sample:
  - Focus on country-level convergence using per capita GDP.
  - Annual data transformed into non-overlapping 10-year periods.
  - Average annual growth rate of real per capita GDP calculated within each period (as log change and in percent).
  - Global sample with all available data over 1980-2022, dropping countries with only one (10-year) period observation to maintain within-country variation.
  - Note: annual-data results are also presented as robustness.

*IMF Working Paper — 2. Data (extracted content from the provided chapter).*

### 3. Methodology

### 3. Methodology

### 3.1. Convergence at the industry-level
- Objective:
  - Examine heterogeneity in the unconditional convergence of manufacturing labor productivity (LP) across countries and 2-digit manufacturing industries.
  - Test whether (i) industries with initially lower LP exhibit higher LP growth (β-convergence), and (ii) industries’ reliance on human and physical capital, and the role of finance, affect this convergence.

- Data aggregation and frequency:
  - Main analysis collapses annual data into four non-overlapping 10-year periods.
  - Rationale: (i) maintain within-country-industry variation while smoothing annual noise; (ii) capture medium-run dynamics.
  - Annual-frequency results are also examined as a robustness check.

- Baseline industry-level specification (Rodrik 2013 framework):
  - Δlog(LP)_{c,i,p} = β1 log(LP)_{c,i,t} + θ_i + θ_p + θ_{i,p} + ε_{c,i,p}
    - c = country, i = 2-digit manufacturing industry, t = year, p = 10-year period with initial year t.
    - Δlog(LP)_{c,i,p} is the average annual change in LP over a 10-year period p (average of annual growth rates over years t+1,...,t+10).
    - log(LP)_{c,i,t} is the initial log LP at year t.
    - Standard errors are clustered at the country-level.
    - Fixed effects: industry (θ_i), period (θ_p), and industry-period (θ_{i,p}).
      - Industry-period fixed effects isolate global USD inflation effects, common annual shocks, global demand, and industry-specific global trends.

- Interpretation of β1:
  - β1 < 0: convergence (LP grows faster where initially lower).
  - β1 ≈ 0: no narrowing of LP differences.
  - β1 > 0: divergence (widening LP gaps).
  - Main focus: unconditional convergence (no country fixed effects), following Rodrik (2013). Conditional convergence results (with country fixed effects) are presented separately.

- Industry-specific convergence analysis:
  - Run equation (1) for each industry i to estimate industry-specific β1_i.
  - Goals:
    - Assess within-industry convergence across countries (industry convergence to its global frontier).
    - Confirm cross-country cross-industry results are not driven by a few industries.
    - Compare β1_i with measures of HCI and PCI to infer whether human- or physical-capital-intensive industries converge faster.

- Extended specification to test role of human and physical capital intensities:
  - Δlog(LP)_{c,i,p} = β1 log(LP)_{c,i,t} + β2 log(LP)_{c,i,t}×HCI_i + β3 log(LP)_{c,i,t}×PCI_i + θ_i + θ_p + θ_{i,p} + ε_{c,i,p}
    - HCI_i and PCI_i are industry-level human and physical capital intensity measures.
  - Convergence parameter for industry i: λ_i = β1 + β2 HCI_i + β3 PCI_i.
    - If β1 is negative:
      - β2 < 0 implies higher HCI_i links to faster convergence.
      - β3 < 0 implies higher PCI_i links to faster convergence.
      - Positive β2 or β3 implies reliance on the respective capital hinders convergence.

- Identification assumptions (following Rajan and Zingales 1998 approach):
  - Some industries inherently and persistently rely more on human or physical capital due to production processes/technologies.
  - These inherent differences are consistent across countries, so industry-level HCI and PCI computed using US data are reasonable proxies for global industry dependence on those capital types.

- Caveat:
  - Nickell (1981) bias may be a potential issue because industry fixed effects are included; robustness checks at annual frequency suggest similar results and a longer panel may alleviate this concern.

### Role of finance in industry-level convergence (extension)
- Full specification incorporating financial development (FD):
  - Δlog(LP)_{c,i,p} = β1 log(LP)_{c,i,t} + β2 log(LP)_{c,i,t}×HCI_i + β3 log(LP)_{c,i,t}×PCI_i
    + β4 log(LP)_{c,i,t}×FD_{c,t} + β5 HCI_i×FD_{c,t} + β6 PCI_i×FD_{c,t}
    + β7 log(LP)_{c,i,t}×HCI_i×FD_{c,t} + β8 log(LP)_{c,i,t}×PCI_i×FD_{c,t}
    + β9 FD_{c,t} + θ_i + θ_p + θ_{i,p} + ε_{c,i,p}
    - FD_{c,t} is a proxy for financial development taken from the initial year t for each period p.
- Interpretation:
  - β4 captures average role of FD in convergence.
  - β7 and β8 test whether FD’s role in convergence depends on industries’ HCI and PCI.
  - β9 captures FD’s role in LP growth on average.
  - β5 and β6 control for FD’s interaction with HCI and PCI to avoid omitted variable bias.

### 3.2. Convergence at the country-level
- Baseline country-level unconditional convergence test:
  - Δlog(GDP per capita)_{c,p} = β1 log(GDP per capita)_{c,t} + θ_p + ε_{c,p}
    - c = country, t = year, p = 10-year period with initial year t.
    - Δlog(GDP per capita)_{c,p} is average annual change in log real GDP per capita over a 10-year period p (average of annual growth rates over years t+1,...,t+10).
    - log(GDP per capita)_{c,t} is the beginning-of-period level at year t.
    - Period fixed effects θ_p control for global common shocks.
    - Standard errors clustered at the country-level.
  - Interpretation: β1 < 0 indicates β-convergence of per capita GDP.

- Linking industry results to country outcomes via sectoral structure:
  - Motivation: structural transformation (shifting from agriculture to other sectors) commonly requires more human capital; test whether countries’ reliance on human-capital-intensive sectors predicts different convergence dynamics.
  - Specification:
    - Δlog(GDP per capita)_{c,p} = β1 log(GDP per capita)_{c,t}
      + β2 log(GDP per capita)_{c,t}×Agriculture_{c,t}
      + β3 log(GDP per capita)_{c,t}×Industry_{c,t}
      + β4 log(GDP per capita)_{c,t}×Services_{c,t}
      + β5 Agriculture_{c,t} + β6 Industry_{c,t} + β7 Services_{c,t} + θ_p + ε_{c,p}
    - Agriculture_{c,t}, Industry_{c,t}, Services_{c,t} are beginning-of-period value-added shares in GDP for agriculture, industry, and services (including manufacturing).
    - Double-interaction coefficients (β2, β3, β4) gauge how sectoral shares affect convergence.
      - Example: β4 < 0 implies countries with higher share of services in GDP converge faster.
    - Services and Industry shares (apart from agriculture) are interpreted as proxies for reliance on human capital.

- Financial development and country convergence:
  - Specification:
    - Δlog(GDP per capita)_{c,p} = β1 log(GDP per capita)_{c,t} + β2 log(GDP per capita)_{c,t}×FD_{c,t} + β3 FD_{c,t} + θ_p + ε_{c,p}
    - FD_{c,t} is a measure of financial development.
    - Expectation: β2 < 0 if higher FD fosters convergence.

### Notes on empirical diagnostics and preliminary stylized facts (methodological implications)
- Industry-level preliminary correlation exercise:
  - For each industry calculate correlation between initial industry LP and its growth rate (net of industry, period, and industry-period fixed effects), averaged over the subsequent 10-year period.
  - Negative correlation implies β-convergence within industry across countries.
- Reported summary from stylized facts (methodological relevance):
  - Overall sample association between initial LP and subsequent growth: -0.26.
  - Industry-specific correlations: mean -0.29, standard deviation 0.08.
  - Range across industries: largest in size -0.52 (other transportation equipment, ISIC 35), lowest -0.14 (tobacco products, ISIC 16).
  - Correlation of industry-specific convergence with HCI: -0.25.
  - Correlation of industry-specific convergence with PCI: 0.04.
  - Note in footnote: average annual growth rate of LP (net of fixed effects) is -1.23 (1.23) percent for industries with initial LP above (below) the sample median.

_Italic: Source — wpiea2025112-print-pdf, section 3. Methodology (and related methodological notes in sections 4–5 as provided)_.

### 2.05 percent, and it is statistically significant at the 1 percent level. This suggests that an industry at the

### What is Needed for Convergence? The Role of Capital and Finance

### Main findings on convergence and human capital intensity (HCI) and physical capital intensity (PCI)
- The interaction coefficient implies differential convergence rates by HCI: an industry at the 25th percentile of HCI (wood) converges with a rate of 1.1 percent, whereas an industry at the 75th percentile of HCI (machinery) converges with a rate of 1.6 percent.
- This difference implies an additional convergence-driven growth:
  - Machinery (high HCI) in a country at the 25th percentile of the labor productivity distribution exhibits a 2.7 percentage points additional growth per annum coming from convergence (1.6×ln (5.5)).
  - Wood (low HCI) yields a similarly estimated convergence boost of 1.9 percentage points (1.1×ln (5.5)).
- PCI does not show a statistically significant link with the rate of convergence.
- Industries with higher HCI (above the median) have a 4.1 percent higher labor productivity level on average, compared to peers with relatively low HCI.
  - This pattern, if anything, would weaken convergence for high HCI industries because they start from a somewhat higher level of labor productivity.
- Industries with higher PCI (based on the median value) have 3.1 percent higher labor productivity compared to their peers with low PCI, on average.
- Conditional convergence results (joint evaluation of 훽1 and 훽2) show a similar pattern:
  - Convergence rate is 2.8 percent for machinery (75th percentile of HCI).
  - Convergence rate is 2.5 percent for wood (25th percentile of HCI).
  - Convergence boosts become 4.8 and 4.2 percentage points per annum for machinery and wood industries, respectively.
- Results are similar when using annual frequency instead of 10-year non-overlapping periods (see Appendix Table A2).
- Statistical significance reported in Table 2 (selected coefficients):
  - 푙표푔(퐿푃): -1.753*** (0.231) in column (1)
  - 푙표푔(퐿푃)×퐻퐶퐼: -2.054*** (0.645) in column (2)
  - In conditional specifications, 푙표푔(퐿푃): -2.861*** (0.791) in column (3) and -1.830** (0.765) in column (4)
  - 푙표푔(퐿푃)×퐻퐶퐼: -1.249** (0.585) in column (4)
- Table 2 sample and fit statistics:
  - Observations: 5,560 (all columns)
  - R-squared: 0.151, 0.152, 0.286, 0.287 for columns (1)–(4), respectively.
- Notes: LP, HCI and PCI are labor productivity, human capital intensity and physical capital intensity, respectively. Standard errors clustered at country-level. *** p<0.01, ** p<0.05, * p<0.1.

### Robustness to industry-level variables (Table 3)
- Alternative HCI/PCI measures and specifications yield similar results:
  - Column 1: dummy variables for high HCI and PCI (median split) — interaction 푙표푔(퐿푃)×퐻퐶퐼 = -0.499*** (0.159).
  - Column 2: HCI as average years of schooling — 푙표푔(퐿푃)×퐻퐶퐼 = -0.187*** (0.070).
  - Column 3: HCI from European industries — 푙표푔(퐿푃)×퐻퐶퐼 = -2.312** (1.141).
  - Column 4: HCI from a broader sample (Shikher 2014) — 푙표푔(퐿푃)×퐻퐶퐼 = -7.082*** (2.122); note mean and standard deviation of that HCI measure reported in text as mean 0.93 and standard deviation 0.03 (Table A1) driving larger coefficient estimates in this test.
- Alternative labor productivity measures and corrections:
  - Column 5: labor productivity based on industry output instead of value added — 푙표푔(퐿푃)×퐻퐶퐼 = -1.938*** (0.740).
  - Column 6: deflate labor productivity growth by (one plus) the rate of appreciation in real exchange rate — 푙표푔(퐿푃)×퐻퐶퐼 = -2.283** (1.111).
  - Column 7: level and growth relative to same industry in the US (dropping the US from sample) — 푙표푔(퐿푃)×퐻퐶퐼 = -1.781*** (0.648).
- Industry size controls:
  - Column 8: weighted regressions using industries’ beginning-of-period value added (log) as weights — 푙표푔(퐿푃)×퐻퐶퐼 = -2.524*** (0.687).
  - Column 9: control for beginning-of-period value added share of each industry in total manufacturing — 푉퐴 푠ℎ푎푟푒 coefficient = -0.006 (0.019); 푙표푔(퐿푃)×퐻퐶퐼 = -2.017*** (0.638).
- PCI interaction coefficients across robustness columns generally remain statistically insignificant or small in magnitude (examples: -0.116 (0.137), 0.134 (0.108), -0.138 (0.109) across columns).
- Observations and R-squared across Table 3 columns:
  - Observations: 5,560 in most columns; column 5: 5,515; column 6: 5,320; column 7: 5,429.
  - R-squared ranges reported: 0.152, 0.167, 0.044, 0.190, 0.138, 0.152 across columns.
- Notes: Results based on equation 2. Standard errors clustered at country-level. *** p<0.01, ** p<0.05, * p<0.1.

### Robustness to sample composition and country sample
- Industry-composition robustness checks (Table A3, Appendix) — results hold when:
  - Dropping four industries with minimum and maximum values of HCI and PCI (column 1).
  - Excluding country-industry pairs with high and low labor productivity growth over the sample period (column 2).
  - Dropping pairs with high and low labor productivity level over the sample period (column 3).
  - Dropping the 2-digit industry with the highest coefficient estimate in industry-specific regressions (ISIC 32) (column 4).
  - Restricting to continuous sample with available data in all 4 periods (column 5).
  - Extending the sample by adding country-industry pairs with available data only for one period (column 6).
- Country-sample robustness checks (Table A4, Appendix) — results remain similar when:
  - Dropping the US (column 1).
  - Excluding G7 economies (column 2).
  - Excluding several richer and poorer (smaller and larger) economies (columns 3 and 4).
  - Extending sample to include all countries instead of dropping ones with few observations (column 5).
- Results are not driven by the Covid-19 period (Table A5, Appendix referenced).

*IMF WORKING PAPERS — What is Needed for Convergence? The Role of Capital and Finance, INTERNATIONAL MONETARY FUND*

### Appendix shows the results when the period of the analysis is restricted to 2019.

### wpiea2025112-print-pdf - Appendix shows the results when the period of the analysis is restricted to 2019.

### Industry-specific convergence
- Objective:
  - Test convergence within each 2-digit manufacturing industry across countries using the specification in equation (1).
  - Assess whether convergence is widespread across industries and whether industries that are more human capital intensive converge faster.
  - Method: obtain convergence rates from industry-specific regressions and examine correlation between those estimates and HCI and PCI.
- Key findings (Table 4):
  - Labor productivity in all 2-digit manufacturing industries converges to its own global frontier.
  - Mean value of the industry coefficient estimates: -1.96
  - Standard deviation of the coefficient estimates: 0.77
  - Correlation between industry convergence coefficients and HCI: -0.49
  - Correlation between industry convergence coefficients and PCI: 0.12
- Selected industry-specific coefficient estimates (ISIC 휷1 풊, Std. error, Observations, R-squared) from Table 4:
  - ISIC 15: -1.662*** (0.164) 317 0.186
  - ISIC 16: -0.828*** (0.290) 214 0.057
  - ISIC 17: -1.785*** (0.394) 315 0.135
  - ISIC 19: -2.023*** (0.560) 132 0.202
  - ISIC 23: -2.394*** (0.421) 225 0.149
  - ISIC 30: -2.574*** (0.626) 100 0.169
  - ISIC 32: -4.147*** (1.235) 24 0.208
  - ISIC 35: -3.729*** (0.764) 110 0.473
  - ISIC 36: -1.461*** (0.251) 312 0.122
- Interpretation:
  - Negative and statistically significant convergence coefficients across all 2-digit industries confirm widespread within-industry cross-country convergence.
  - The negative correlation with HCI (-0.49) implies industries with higher human capital intensity tend to converge faster.
  - The small positive correlation with PCI (0.12) indicates physical capital intensity alone does not strongly predict faster convergence.

### Role of financial development (industry level)
- Purpose:
  - Investigate how financial development affects convergence based on industries’ reliance on human and physical capital (Table 5; equation 3).
- Main empirical patterns:
  - Industries with higher HCI: manufacturing convergence is stronger (negative and significant interaction terms).
  - Industries with higher PCI:
    - Appear to diverge at particularly low levels of financial development.
    - Financial development reverses divergence and catalyzes convergence in high-PCI industries.
  - Thresholds for FD index effects on PCI-driven convergence:
    - Industries with higher PCI diverge when FD index < 0.17 (representing about 26 percent of the observations).
    - Industries with higher PCI start to converge when FD index > 0.61 (representing about 17 percent of the observations).
    - When FD index is between 0.17 and 0.61, PCI does not play a role in industry convergence (joint evaluation statistically insignificant).
  - Interaction evidence:
    - Positive and statistically significant coefficient of PCI×FD suggests greater financial development is associated with higher labor productivity growth in industries with higher PCI.
    - Statistically insignificant coefficients on HCI×FD interactions suggest financial development does not have a clear differential role for industries with higher HCI.
- Selected coefficient estimates from Table 5 (standard errors in parentheses):
  - log( LP )×HCI: -3.015** (1.159) [FD index column]
  - log( LP )×PCI: 0.400** (0.161) [FD index column]
  - PCI×FD: 12.440** (6.155) [FD index column]
  - log( LP )×PCI×FD: -1.316** (0.565) [FD index column]
  - Alternate specifications produce broadly similar results using FD index (residual) and Credit:
    - log( LP )×HCI: -2.356*** (0.657) [FD index (residual) column]
    - PCI×FD: 30.779** (12.842) [FD index (residual) column]
    - log( LP )×PCI×FD: -3.149** (1.283) [FD index (residual) column]
    - log( LP )×HCI: -1.932** (0.903) [Credit column]
    - log( LP )×PCI: 0.278** (0.132) [Credit column]
    - PCI×FD: 0.099* (0.056) [Credit column]
    - log( LP )×PCI×FD: -0.010** (0.005) [Credit column]
- Robustness checks:
  - Use FD index residual (FD index net of (log) real GDP per capita and country and year fixed effects).
  - Use Credit to the private sector (share of GDP) as a banking-sector-focused proxy.
  - Results on the differential role of financial development for high-PCI industries remain broadly similar across proxies.
- Conclusion from industry-level FD analysis:
  - Human-capital-intensive industries converge in productivity irrespective of financial development levels.
  - Physical-capital-intensive industries require a sufficiently high degree of financial development to converge.

### Country-level implications: structural transformation and finance
- Macro approach:
  - Test unconditional convergence in GDP per capita over time and examine role of structural transformation (shift away from agriculture toward industry and services) and financial development (equations 4–6).
- Structural transformation and per capita GDP convergence (Table 6):
  - Baseline: real per capita GDP tends to converge across countries over time.
  - Convergence is faster when countries are less intensive in agriculture and more intensive in industry and services (interaction terms).
  - Selected coefficient estimates (Table 6):
    - log(GDP per capita)×Industry: -0.033** (0.015)
    - log(GDP per capita)×Services: -0.025* (0.013)
    - Industry (level): 0.234* (0.140)
  - Convergence rate examples:
    - For a country at the 25th percentile of GDP share of industry (20.2 percent), convergence rate becomes 0.67 percent.
    - For a country at the 75th percentile of GDP share of industry (33.3 percent), convergence rate becomes 1.10 percent.
    - A country with high industry share (33.3 percent of GDP) will experience a convergence boost in per capita GDP growth 2.3 percentage points per annum compared to a country at the 25th percentile of per capita GDP (1.1×푙푛(8.4)).
    - For a country with low industry share (20.2 percent of GDP) the convergence boost would be about 1.4 percentage points (0.67×푙푛(8.4)).
  - Evidence on structural shift:
    - Poorer countries start with larger shares of agriculture but tend to shift away from agriculture faster (Figure 2; aggregate data 1980-2022).
    - This shift toward industry and services is more pronounced in poorer economies, supporting aggregate convergence.
- Financial development and per capita GDP convergence (Table 7):
  - Baseline: real per capita GDP converges across countries in the sample.
  - Greater financial development predicts faster convergence (consistent with Aghion et al. (2005)).
  - Selected coefficient estimates (Table 7):
    - log(GDP per capita): -0.193** (0.098) [column (1)]
    - log(GDP per capita)×FD: -2.196*** (0.457) [column (2)]
    - FD (level): 25.963*** (4.891) [column (2)]
  - Convergence rate examples using FD percentiles:
    - Country at the 75th percentile of FD index (index ≈ 0.34) exhibits a convergence rate of 1.01 percent.
      - This implies a convergence boost in per capita GDP growth 2.3 percentage points per annum if located at the 25th percentile of per capita GDP compared to the 75th percentile (1.01×푙푛(9.5)).
    - Country at the 25th percentile of FD index (index ≈ 0.10) exhibits a convergence rate of 0.49 percent.
      - This implies a convergence boost of about 1.1 percentage points per annum (0.49×푙푛(9.5)).
- Interpretation:
  - Structural transformation toward sectors that require more human capital (industry and services) supports faster aggregate convergence.
  - Financial development materially accelerates per capita GDP convergence across countries.

### Conclusions and policy implications
- Main conclusions (preserve wording and emphasis from the text):
  - The composition of the economy matters for convergence, as well as for which factors can accelerate that convergence.
  - Within manufacturing, labor productivity converges faster across countries and industries when there is a high reliance on human capital.
  - For industries that rely on physical capital, convergence is only observed with sufficient financial development in the country.
  - At the aggregate level, a higher share of sectors which require more human capital (i.e., non-agriculture) predicts faster per capita GDP convergence across countries over time.
  - Countries have generally been shifting from agriculture towards industry- and services-oriented economies, and this shift is occurring faster in poorer countries which initially have a higher share of agriculture in their GDP.
  - Financial development, accumulation of human capital, and fostering high human capital industries remain key elements to help growth in developing countries converge faster towards their advanced economy peers.
- Policy priorities implied by the results:
  - Invest in human capital accumulation (such as through schooling) and implement policies conducive to industries that utilize such capital.
  - Promote structural and macroeconomic policies that enable reallocation of resources from production activities that do not exhibit much convergence toward sectors that can reap growth benefits from convergence.
  - Deepen domestic financial markets to allow physical capital-intensive industries to converge (i.e., raise financial development beyond identified thresholds).
  - Pursue policies that facilitate the shift from agriculture to industry and services, particularly in poorer economies where such shifts are occurring faster and support aggregate convergence.

*Source: https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025112-print-pdf.pdf*

### References

### References (wpiea2025112-print-pdf)

### Key cited literature
- Acemoglu, Daron and Carlos Molina (2021): “Converging to converge? A comment”, NBER Working Papers No 28992.
- Acemoglu, Daron, Simon Johnson and Robinson (2005): “Institutions as a Fundamental Cause of Long-Run Growth”, Handbook of Economic Growth, Volume 1, Part A, Pages 385-472.
- Aghion, Philippe, Peter Howitt, and David Mayer-Foulkes (2005): "The effect of financial development on convergence: Theory and evidence." The Quarterly Journal of Economics 120, no. 1: 173-222.
- Alfaro, Laura, Sebnem Kalemli-Ozcan and Vadym Volosovych (2008): “Why doesn’t capital flow from rich to poor countries? An empirical investigation”, The Review of Economics and Statistics, vol 90(2): 347–368.
- Barro, Robert and Xavier Sala-i-Martin (1992): “Convergence”, Journal of Political Economy, vol 100(2): 223-251.
- Beck, Thorsten, Ross Levine and Norman Loayza (2000): “Finance and the sources of growth”, Journal of Financial Economics, vol 58 (1–2): 261-300.
- Benhabib, Jess and Mark Spiegel (2005): “Human Capital and Technology Diffusion”, Handbook of Economic Growth, vol 1(A): 935-966.
- Comin, Diego and Bart Hobijn (2010): “An Exploration of Technology Diffusion”, American Economic Review, vol 100(5): 2031-2059.
- De Gregorio, José (1996): “Borrowing constraints, human capital accumulation, and growth”, Journal of Monetary Economics, vol 37(10): 49-71.
- Duarte, Margarida and Diego Restuccia (2010): “The Role of the Structural Transformation in Aggregate Productivity”, The Quarterly Journal of Economics, vol 125(1): 129–173.
- Eaton, Jonathan and Samuel Kortum (1999): “International Technology Diffusion: Theory and Measurement”, International Economic Review, vol 40(3): 537-570.
- Galor, Oded (2005): “From Stagnation to Growth: Unified Growth Theory”, Handbook of Economic Growth, vol 1(A): 171-293.
- Gennaioli, Nicola, Rafael La Porta, Florencio Lopez-de-Silanes, and Andrei Shleifer (2013): “Human Capital and Regional Development”, The Quarterly Journal of Economics, vol 128(1): 105-164.
- Keller, Wolfgang (2002): “Geographic Localization of International Technology Diffusion“, American Economic Review, vol 92(1): 120-142.
- King, Robert and Ross Levine (1993): “Finance and Growth: Schumpeter Might Be Right”, The Quarterly Journal of Economics, vol 108(3): 717–737.
- Mankiw, N. Gregory, David Romer and David Weil (1992): "A Contribution to the Empirics of Economic Growth", Quarterly Journal of Economics, vol 107(2): 407–437.
- Solow, Robert (1956): “A contribution to the theory of economic growth”, The Quarterly Journal of Economics, vol 70: 65-94.
- Svirydzenka, Katsiaryna (2016): Introducing a new broad-based index of financial development. International Monetary Fund.

(Selected additional references listed in the source include works by Beck & Levine, Fatás & Mihov, Galor & Weil, Gollin et al., Ha et al. (2023), Hardy & Sever (2021, 2023), Herrendorf et al., Kremer et al., Levine (1997), Lucas (1988), Madsen & Timol (2011), Miles (2008), Morales (2003), Nickell (1981), Nunn (2007), Perez-Trujillo & Lacalle-Calderon (2020), Pritchett (1997), Rajan & Zingales (1998), Rodrik (2013), Shikher (2014), Tamura (2002), Xu (2000), and others.)

### Appendix — list of countries included in the industry-level analysis
- Albania, Australia, Austria, Belgium, Bangladesh, Bulgaria, Bosnia and Herzegovina, Bermuda, Bolivia, Brazil, Barbados, Canada, Switzerland, Chile, China, Cameroon, Colombia, Costa Rica, Cyprus, Czechia, Germany, Denmark, Ecuador, Egypt, Eritrea, Spain, Estonia, Ethiopia, Finland, Fiji, France, United Kingdom, Georgia, Ghana, Greece, China - Hong Kong SAR, Croatia, Hungary, Indonesia, India, Ireland, Iran (Islamic Republic of), Iceland, Israel, Italy, Jordan, Japan, Kenya, Kyrgyzstan, Korea, Kuwait, Lao, Sri Lanka, Lithuania, Luxembourg, Latvia, China - Macao SAR, Morocco, Moldova, Mexico, North Macedonia, Malta, Mongolia, Mauritius, Malawi, Malaysia, Netherlands, Norway, New Zealand, Oman, Pakistan, Panama, Peru, Philippines, Papua New Guinea, Poland, Portugal, Qatar, Romania, Russia, Senegal, Singapore, Slovakia, Slovenia, Sweden, Syria, Thailand, Trinidad and Tobago, Tunisia, Türkiye, Taiwan Province of China, Tanzania, Uruguay, USA, Venezuela, Vietnam, Yemen, South Africa, Zambia.

### Tables — key industry- and country-level statistics and regression results

Table A1: Industry-level variables: Data sources and summary statistics (selected variables)
- Human capital intensity (baseline), Source: Erman and Kaat (2019)
  - 25th ptile: 0.55
  - Mean: 0.68
  - 75th ptile: 0.78
  - Std. dev.: 0.11
- Human capital intensity (Europe), Source: Erman and Kaat (2019)
  - 25th ptile: 0.07
  - Mean: 0.11
  - 75th ptile: 0.16
  - Std. dev.: 0.05
- Human capital intensity (average years), Source: Ciccone and Papaioannou (2009)
  - 25th ptile: 11.00
  - Mean: 11.64
  - 75th ptile: 12.43
  - Std. dev.: 0.96
- Physical capital intensity, Source: Erman and Kaat (2019)
  - 25th ptile: 0.86
  - Mean: 1.55
  - 75th ptile: 2.23
  - Std. dev.: 0.80
- Human capital intensity (broader sample), Source: Shikher (2014)
  - 25th ptile: 0.90
  - Mean: 0.93
  - 75th ptile: 0.95
  - Std. dev.: 0.03
- Labor productivity (log), Based on UNIDO
  - 25th ptile: 8.96
  - Mean: 9.76
  - 75th ptile: 10.66
  - Std. dev.: 1.54
- Labor productivity growth (percent), Based on UNIDO
  - 25th ptile: 0.26
  - Mean: 4.04
  - 75th ptile: 7.54
  - Std. dev.: 8.91
- Labor productivity (based on output, log), Based on UNIDO
  - 25th ptile: 10.01
  - Mean: 10.85
  - 75th ptile: 11.73
  - Std. dev.: 1.57
- Labor productivity growth (based on output, percent), Based on UNIDO
  - 25th ptile: 0.68
  - Mean: 4.42
  - 75th ptile: 7.83
  - Std. dev.: 7.72
- Value added share (percent), Based on UNIDO
  - 25th ptile: 1.59
  - Mean: 5.69
  - 75th ptile: 6.92
  - Std. dev.: 7.25

Table A2: Labor productivity convergence (annual frequency) — selected coefficient estimates
- Dependent variables and regressions: Unconditional (columns 1–2) and Conditional (columns 3–4).
- Column (1): log(LP)
  - Coefficient: -4.124*** (0.354)
- Column (2): log(LP)
  - Coefficient: -0.296 (0.977)
- Column (3): log(LP)
  - Coefficient: -9.027*** (0.868)
- Column (4): log(LP)
  - Coefficient: -6.871*** (1.112)
- log(LP) × HCI
  - Column (1): -5.339*** (1.255)
  - Column (2): -2.838** (1.263)
- log(LP) × PCI
  - Column (1): -0.154 (0.151)
  - Column (2): -0.141 (0.185)
- Observations: 66,620 (all columns)
- R-squared:
  - Columns (1)-(2): 0.086
  - Columns (3)-(4): 0.124 and 0.124
- Notes: LP, HCI and PCI are labor productivity, human capital intensity and physical capital intensity, respectively. Standard errors clustered at the country-level. *** p<0.01, ** p<0.05, * p<0.1.

Table A3: Industry composition — selected coefficients and sample details
- log(LP) × HCI coefficients (columns 1–6):
  - Column (1): -2.473*** (0.889)
  - Column (2): -1.784*** (0.514)
  - Column (3): -1.904** (0.788)
  - Column (4): -1.908*** (0.628)
  - Column (5): -1.670** (0.724)
  - Column (6): -2.857*** (0.985)
- log(LP) × PCI coefficients (columns 1–6): values range from -0.038 (0.136) to -0.119 (0.092); none marked as significant.
- Observations by column: 4,424; 5,354; 5,322; 5,450; 3,056; 5,848
- R-squared by column: 0.152; 0.185; 0.157; 0.148; 0.164; 0.123
- Notes: Columns implement different sample restrictions (dropping extreme industries, trimming outliers in growth or levels, excluding ISIC 32, restricting to complete panel, extending by including one-observation pairs). Standard errors clustered at the country-level. *** p<0.01, ** p<0.05, * p<0.1.

Table A4: Country composition — selected coefficients and sample variants
- log(LP) × HCI coefficients across columns (1)–(5):
  - Column (1): -2.059*** (0.659)
  - Column (2): -1.953*** (0.665)
  - Column (3): -2.106*** (0.663)
  - Column (4): -2.083*** (0.662)
  - Column (5): -1.948*** (0.637)
- log(LP) × PCI coefficients range from -0.083 (0.104) to -0.045 (0.098); none marked as significant.
- Observations by column: 5,483; 5,085; 5,350; 5,373; 5,646
- R-squared by column: 0.154; 0.158; 0.156; 0.157; 0.149
- Notes: Columns drop the US, drop G7 economies, trim richer/poorer countries, trim smaller/larger countries, or extend sample to countries with few observations. Standard errors clustered at the country-level. *** p<0.01, ** p<0.05, * p<0.1.

Table A5: Labor productivity convergence — excluding the Covid-19 period (1980–2019)
- Column (1)
  - log(LP): -1.718*** (0.221)
  - log(LP) × HCI: -2.066*** (0.665)
  - log(LP) × PCI: -0.085 (0.101)
  - Observations: 5,560
  - R-squared: 0.157
- Column (2)
  - log(LP): -0.196 (0.496)
  - log(LP) × HCI: (not separately listed in column 2 notes)
  - log(LP) × PCI: (as reported above)
  - Observations: 5,560
  - R-squared: 0.158
- Notes: Results based on equations 1 and 2. LP, HCI and PCI are labor productivity, human capital intensity and physical capital intensity. The period of the analysis is 1980-2019. Standard errors clustered at the country-level. *** p<0.01, ** p<0.05, * p<0.1.

*Source: wpiea2025112-print-pdf - References*

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_Source: https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025112-print-pdf.pdf_