## wpiea2022184-print-pdf - References

## Source details

**Canonical URL:** [wpiea2022184-print-pdf - References](https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022184-print-pdf.pdf)

## Other formats

- [Markdown version](/-/media/files/publications/wp/2022/english/wpiea2022184-print-pdf.pdf.md)
- [Structured JSON version](/-/media/files/publications/wp/2022/english/wpiea2022184-print-pdf.pdf.json)

---

### Introduction and objective
- Policymakers seek combinations and sequences of structural reforms to aid crisis recovery and stimulate economic growth.
- Challenge: structural reforms are hard to measure; survey-based and policy-change indicators have biases and limited coverage.
- Approach: use a machine learning method (Partial Least Squares, PLS) to construct synthetic structural scores from a large set of structural indicators to:
  - account for correlation/redundancy,
  - weight indicators by predictiveness for future per capita GDP, and
  - reduce subjective bias.

### Data and structural categories
- Data source: IMF’s Structural and Financial Indicators database (draws from several sources).
- Coverage: 275 structural indicators from 126 countries.
- Structural areas and indicator counts:
  - Financial system (77)
  - Trade and openness (28)
  - Legal system (37)
  - Labor markets (74)
  - Business environment (45)
  - Tax policy (14)
- Sample construction:
  - Time windows: 2000-04, 2005-09, 2010-14, 2015-19.
  - Sample size referenced: 504 (126 countries and 4 time periods).
  - Missing-value procedure: five-year averages starting in year 2000, retain data every five years, exclude indicators missing more than 20% of values, impute remaining missing values by a multiple imputation procedure (see Appendix).
  - Note: indicators include World Bank Doing Business data.

### Machine learning method: Partial Least Squares (PLS)
- Motivation:
  - Many indicators (275) relative to sample size.
  - Indicators are highly correlated and potentially redundant.
  - Need predictors that are informative for high future per capita GDP.
- PLS properties:
  - Combines dimensionality reduction with prediction focus (improves on PCA by requiring predictiveness).
  - Allows many predictive indicators (unlike LASSO which assumes sparsity).
  - Accounts for correlation among indicators and redundancy.
- Estimation details:
  - Outcome: five-year-ahead per capita GDP (log, PPP).
  - Use largest possible sample with indicators from 2000-2010 to estimate predictive model.
  - Number of components chosen via leave-one-out cross-validation: eight components.
  - Operational implementation: plsr R library; iterative 4-step PLS procedure (component formation, OLS coefficient on component, update predicted outcome, orthogonalize inputs).
- Construction of synthetic scores:
  - Synthetic structural score for 2000-2015 in category c is the predicted value from the PLS model using the 2000-2015 indicators.
  - Scores standardized to have zero mean and unit variance for comparability across structural areas.

### Key empirical findings — growth impacts
- General result: using synthetic structural scores, significant 5-year cumulative growth impacts found for certain areas and complementarities across areas.
- Magnitudes (summary statements in text):
  - One standard deviation improvement in product, labor, financial markets and legal system reform areas raises cumulative 5-year growth by 2 to 6 percent (as stated earlier).
  - Conclusion section states the 5-year cumulative impact ranges from 2½ to 6½ percentage points depending on the structural area.
- Cross-country regression estimates (Table 3: coefficients measure 5-year cumulative GDP growth impact per one standard deviation increase in composite):
  - Business environment: 0.0321**, 0.0333**, 0.0330***, 0.0230** (columns 1–4; robust standard errors reported)
  - Financial markets: 0.0196**, 0.0193**, 0.0182**, 0.0189**
  - Labor markets: 0.0546***, 0.0543***, 0.0640***, 0.0640***
  - Legal system: 0.0338**, 0.0315**, 0.0330***, 0.0238**
  - Tax policy: 0.00120, 0.000372, 0.0125, 0.00659 (statistically insignificant)
  - Trade & openness: 0.00945, 0.00607, 0.00641, 0.00864 (statistically insignificant)
  - Observations: 251 (columns 1–2), 224 (columns 3–4)
  - R-squared: 0.094, 0.099, 0.363, 0.487 (columns 1–4)
  - Significance notation: *** p<0.01, ** p<0.05, * p<0.1.
- Reform-episode analysis (discrete large changes):
  - Definition: “reform episode” = improvement in top 10 percentile of positive changes in composite scores ΔS.
  - “Reversed reform episode” = top 10 percentile positive change followed by top 10 percentile negative change.
  - Distribution (Table 4):
    - Each structural area around 37–38 episodes; TOTAL 227 episodes; Reversed 51.
    - By period: 2005-2009 = 82, 2010-2014 = 78, 2015-2019 = 67.
  - Growth impact of reform episodes (Table 5):
    - Business environment: Reform episodes 0.0718**; Non-reversed -0.0419 (standard errors shown)
    - Financial markets: 0.0270; Non-reversed -0.0364
    - Labor markets: 0.0321**; Non-reversed 0.00814
    - Legal system: -0.0269; Non-reversed 0.0524*
    - Tax policy: 0.0193; Non-reversed -0.0373
    - Trade & openness: 0.0251; Non-reversed -0.00225
    - Observations: 224; R-squared: 0.483; Time FE YES; Country group FE YES; Controls YES.
  - Interpretation: business environment and labor market reform episodes have significantly positive impact; legal-system reforms only significant when not reversed.

### Synergies and interaction findings
- Method: create threshold dummy D for being in top tercile in composite S_z, interact with change in composite ΔS_s.
- Three main synergy findings:
  1. Positive synergy between business environment and labor market: reforms strengthening business environment have larger growth impact when labor market structural performance is strong, and vice versa.
  2. Business environment reforms have larger growth impact when legal system is strong (property rights enforcement).
  3. Labor-market reforms are less effective where openness to trade and capital flows is high; business-environment reforms are more effective with openness/high FDI access.
- Selected coefficients (Table 6 examples; robust standard errors shown):
  - Business environment baseline coefficients across columns include 0.0327; 0.0491*; 0.0469**; 0.00971; 0.0461*.
  - Labor markets when threshold is Business environment column: 0.0579* (standard error 0.0305).
  - Trade & openness interactions show negative coefficients for labor markets (e.g., -0.0619*).
  - Observations: 224 for each regression; R-squared range ~0.494–0.506; Time FE YES; Controls YES; Country group FE YES.

### Role of structural performance during crises
- Recessions identified: 124 recessions in dataset (negative annual growth, excluding repeated within five-year interval).
- Method: local projections (Jordà, 2005) to estimate dynamic impact of pre-crisis structural performance on post-recession growth for h = 1,2,3,4 years.
- Key crisis-recovery findings:
  - Strong business environment: differential recovery — 3% increase in the year following recession and cumulatively a 5% increase after four years; impacts statistically significant at the 5% level.
  - Trade and openness: suggestive evidence that high trade openness may reduce resilience — 2.5% decrease in growth rate in the year following the onset of the recession (cumulative impact statistically insignificant).
  - Other structural areas: impacts not statistically distinguishable from zero in the crisis-recovery analysis.

### Robustness, limitations, and interpretability
- PLS advantages over alternatives:
  - PLS weights indicators by covariance with outcome, guarding against duplication bias and redundancy while retaining predictive power.
  - PCA maximizes variation but can be distorted by redundant indicators; LASSO may over-shrink in this setting.
- Data limitations:
  - Coverage varies across countries and years; missingness is systematic (not missing-at-random) due to update frequencies and start dates.
  - Indicators excluded when missing more than 20% of values; imputation used for remaining missing data.
  - Inclusion of Doing Business indicators noted; Doing Business suspension mentioned as a data caveat.
- Interpretability:
  - Table 1 lists subgroups with large weights that align with IMF (2019) assessments, supporting the credibility of PLS-derived composites.

### Appendices — imputation and comparison with simple-average composites
- Appendix B — Imputation:
  - Imputation method: iterative PCA procedure (Josse and Husson, 2013) implemented with imputePCA in R.
  - Indicators rescaled to be between zero and one; first principal component used iteratively to impute missing values; imputed data standardized to mean zero and standard deviation one.
  - For indicators with a high missing rate, quality of imputation is lower as reflected in deflated variance.
- Appendix C — Comparison with simple-average composite:
  - Simple-average composite: within each structural category, average of indicators, standardized to zero mean and unit variance.
  - Empirical comparison:
    - Simple-average composite shows no deterioration in the legal system, while indicating more substantial improvements in business environment, financial system and taxation system compared to PLS.
    - Repeating growth analysis using simple averages yields that the effect of structural reforms on growth becomes statistically insignificant for most structural areas.
  - Table C1 (growth impact of structural reforms using simple-average composites; coefficients with robust standard errors in parentheses):
    - Business environment: 0.000919 (0.0211); 0.00692 (0.0239); 0.000222 (0.0234); 8.21e-05 (0.0204)
    - Financial markets: 0.00810 (0.0135); 0.00652 (0.0138); 0.0170 (0.0126); 0.0105 (0.0119)
    - Labor markets: 0.00350 (0.0127); 0.00394 (0.0126); -0.00818 (0.0136); -0.0125 (0.0149)
    - Legal system: 0.0319* (0.0175); 0.0283 (0.0189); 0.0170 (0.0175); 0.0272 (0.0166)
    - Tax policy: -0.00225 (0.00653); -0.00183 (0.00656); 0.00243 (0.00659); -0.00323 (0.00551)
    - Trade & openness: 0.0582*** (0.0189); 0.0562*** (0.0190); 0.0321* (0.0194); 0.0378* (0.0206)
    - Observations: 251; 251; 224; 224
    - R-squared: 0.088; 0.090; 0.295; 0.457
    - Time FE: NO; YES; YES; YES
    - Country group FE: NO; NO; NO; YES
    - Controls: NO; NO; YES; YES
    - Note: Robust standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1

### Policy implications and conclusions
- Machine learning (PLS) provides a scalable approach to quantify structural performance by aggregating diverse indicators and extracting the components most predictive of future per capita GDP.
- Empirical implications:
  - Reforms in business environment, labor markets, financial markets, and legal system show meaningful positive 5-year cumulative growth impacts (magnitude reported across sections: "2 to 6 percent" and "2½ to 6½ percentage points").
  - Reforms in tax policy and trade & openness show statistically insignificant average growth effects in baseline specifications.
  - Complementarities matter: business environment and labor-market reforms are complementary; property-rights enforcement increases returns to business-environment reforms.
  - Sustained (non-reversed) reforms can be important, especially for legal-system reforms.
  - Strong pre-crisis business environment supports faster recovery from recessions.
- Research and operational recommendations:
  - Use machine learning to construct composites for finer structural areas to provide more empirical support for reform priorities.
  - PLS-derived composites can inform prioritization: target areas and sequences where reforms are both effective and complementary.

*Source: wpiea2022184-print-pdf - References*

### References .............................................................................................................

### wpiea2022184-print-pdf - References

### Introduction and objective
- Policymakers seek combinations and sequences of structural reforms to aid crisis recovery and stimulate economic growth.
- Challenge: structural reforms are hard to measure; survey-based and policy-change indicators have biases and limited coverage.
- Approach: use a machine learning method (Partial Least Squares, PLS) to construct synthetic structural scores from a large set of structural indicators to (i) account for correlation/redundancy, (ii) weight indicators by predictiveness for future per capita GDP, and (iii) reduce subjective bias.

### Data and structural categories
- Data source: IMF’s Structural and Financial Indicators database (draws from several sources).
- Coverage: 275 structural indicators from 126 countries.
- Structural areas and indicator counts:
  - Financial system (77)
  - Trade and openness (28)
  - Legal system (37)
  - Labor markets (74)
  - Business environment (45)
  - Tax policy (14)
- Sample construction:
  - Time windows: 2000-04, 2005-09, 2010-14, 2015-19.
  - Sample size referenced: 504 (126 countries and 4 time periods).
  - Missing-value procedure: five-year averages starting in year 2000, retain data every five years, exclude indicators missing more than 20% of values, impute remaining missing values by a multiple imputation procedure (see Appendix).
  - Note: indicators include World Bank Doing Business data.

### Machine learning method: Partial Least Squares (PLS)
- Motivation for PLS:
  - Many indicators (275) relative to sample size.
  - Indicators are highly correlated and potentially redundant.
  - Need predictors that are informative for high future per capita GDP.
- PLS properties highlighted:
  - Combines dimensionality reduction with prediction focus (improves on PCA by requiring predictiveness).
  - Allows many predictive indicators (unlike LASSO which assumes sparsity).
  - Accounts for correlation among indicators and redundancy.
- Estimation details:
  - Outcome: five-year-ahead per capita GDP (log, PPP).
  - Use largest possible sample with indicators from 2000-2010 to estimate predictive model.
  - Number of components chosen via leave-one-out cross-validation: eight components.
  - Operational implementation: plsr R library; iterative 4-step PLS procedure (component formation, OLS coefficient on component, update predicted outcome, orthogonalize inputs).
- Construction of synthetic scores:
  - Synthetic structural score for 2000-2015 in category c is the predicted value from the PLS model using the 2000-2015 indicators.
  - Scores standardized to have zero mean and unit variance for comparability across structural areas.

### Key empirical findings — growth impacts
- General result: using synthetic structural scores, significant 5-year cumulative growth impacts found for certain areas and complementarities across areas.
- Magnitudes summarized in paper:
  - One standard deviation improvement in product, labor, financial markets and legal system reform areas raises cumulative 5-year growth by 2 to 6 percent (as stated earlier).
  - Conclusion section states the 5-year cumulative impact ranges from 2½ to 6½ percentage points depending on the structural area.
- Cross-country regression estimates (Table 3, coefficients measure 5-year cumulative GDP growth impact per one standard deviation increase in composite):
  - Business environment: 0.0321**; 0.0333**; 0.0330***; 0.0230** (columns 1–4; standard errors shown)
  - Financial markets: 0.0196**; 0.0193**; 0.0182**; 0.0189** 
  - Labor markets: 0.0546***; 0.0543***; 0.0640***; 0.0640*** 
  - Legal system: 0.0338**; 0.0315**; 0.0330***; 0.0238** 
  - Tax policy: 0.00120; 0.000372; 0.0125; 0.00659 (statistically insignificant)
  - Trade & openness: 0.00945; 0.00607; 0.00641; 0.00864 (statistically insignificant)
  - Observations: 251 (columns 1–2), 224 (columns 3–4)
  - R-squared: 0.094, 0.099, 0.363, 0.487 (columns 1–4)
  - Robust standard errors reported; significance: *** p<0.01, ** p<0.05, * p<0.1.
- Reform-episode analysis (discrete large changes):
  - Definition: “reform episode” = improvement in top 10 percentile of positive changes in composite scores ΔS.
  - “Reversed reform episode” = top 10 percentile positive change followed by top 10 percentile negative change.
  - Distribution (Table 4): each structural area around 37–38 episodes; TOTAL 227 episodes; Reversed 51; by period: 2005-2009 = 82, 2010-2014 = 78, 2015-2019 = 67.
  - Growth impact of reform episodes (Table 5):
    - Business environment: Reform episodes 0.0718**; Non-reversed -0.0419 (standard errors shown)
    - Financial markets: 0.0270; Non-reversed -0.0364
    - Labor markets: 0.0321**; Non-reversed 0.00814
    - Legal system: -0.0269; Non-reversed 0.0524* 
    - Tax policy: 0.0193; Non-reversed -0.0373
    - Trade & openness: 0.0251; Non-reversed -0.00225
    - Observations: 224; R-squared: 0.483; Time FE YES; Country group FE YES; Controls YES.
  - Interpretation: business environment and labor market reform episodes have significantly positive impact; legal-system reforms only significant when not reversed.
- Synergies (interaction analysis, Table 6):
  - Method: create threshold dummy D for being in top tercile in composite S_z, interact with change in composite ΔS_s.
  - Three main synergy findings emphasized:
    1. Positive synergy between business environment and labor market: reforms strengthening business environment have larger growth impact when labor market structural performance is strong, and vice versa.
    2. Business environment reforms have larger growth impact when legal system is strong (property rights enforcement).
    3. Labor-market reforms are less effective where openness to trade and capital flows is high; business-environment reforms are more effective with openness/high FDI access.
  - Selected coefficients from Table 6 (examples; robust standard errors shown):
    - Business environment baseline coefficients across columns include 0.0327; 0.0491*; 0.0469**; 0.00971; 0.0461*.
    - Labor markets when threshold is Business environment column: 0.0579* (standard error 0.0305).
    - Trade & openness interactions show negative coefficients for labor markets (e.g., -0.0619*).
  - Observations: 224 for each regression; R-squared range ~0.494–0.506; Time FE YES; Controls YES; Country group FE YES.

### Role of structural performance during crises
- Recessions identified: 124 recessions in dataset (negative annual growth, excluding repeated within five-year interval).
- Method: local projections (Jordà, 2005) to estimate dynamic impact of pre-crisis structural performance on post-recession growth for h = 1,2,3,4 years.
- Key crisis-recovery findings:
  - Strong business environment: differential recovery — 3% increase in the year following recession and cumulatively a 5% increase after four years; impacts statistically significant at the 5% level.
  - Trade and openness: suggestive evidence that high trade openness may reduce resilience — 2.5% decrease in growth rate in the year following the onset of the recession (cumulative impact statistically insignificant).
  - Other structural areas: impacts not statistically distinguishable from zero in the crisis-recovery analysis.

### Robustness, limitations, and interpretability
- PLS advantages highlighted over PCA and LASSO:
  - PLS weights indicators by covariance with outcome, guarding against duplication bias and redundancy while retaining predictive power.
  - PCA maximizes variation but can be distorted by redundant indicators; LASSO may over-shrink in this setting.
- Data limitations:
  - Coverage varies across countries and years; missingness is systematic (not missing-at-random) due to update frequencies and start dates.
  - Indicators excluded when missing more than 20% of values; imputation used for remaining missing data.
  - Inclusion of Doing Business indicators noted; Doing Business suspension mentioned as a data caveat.
- Interpretability: Table 1 lists subgroups with large weights that align with IMF (2019) assessments, supporting the credibility of PLS-derived composites.

### Policy implications and conclusions
- Machine learning (PLS) provides a scalable approach to quantify structural performance by aggregating diverse indicators and extracting the components most predictive of future per capita GDP.
- Empirical implications:
  - Reforms in business environment, labor markets, financial markets, and legal system show meaningful positive 5-year cumulative growth impacts (magnitude reported across sections: "2 to 6 percent" and "2½ to 6½ percentage points").
  - Reforms in tax policy and trade & openness show statistically insignificant average growth effects in baseline specifications.
  - Complementarities matter: business environment and labor-market reforms are complementary; property-rights enforcement increases returns to business-environment reforms.
  - Sustained (non-reversed) reforms can be important, especially for legal-system reforms.
  - Strong pre-crisis business environment supports faster recovery from recessions.
- Research and operational recommendations:
  - Use machine learning to construct composites for finer structural areas to provide more empirical support for reform priorities.
  - PLS-derived composites can inform prioritization: target areas and sequences where reforms are both effective and complementary.

*Source: wpiea2022184-print-pdf - References*

### References

### References

### Key citations
- Acemoglu, Daron, Simon Johnson, and James Robinson. 2005. "The Rise of Europe: Atlantic Trade, Institutional Change, and Economic Growth." American Economic Review, 95 (3): 546-579.
- Alesina, A., Furceri, D., Ostry, J., Papageorgiou, C. and Quinn, D., (2020), Structural Reforms and Elections: Evidence from a World-Wide New Dataset, No 14371, CEPR Discussion Papers, C.E.P.R. Discussion Papers.
- Ari, A., Lev., R and Chen, S. (2021). The dynamics of non-performing loans during banking crises: a new database with post-COVID-19 implications. Journal of Banking and Finance, forthcoming.
- Ari, A., Bartolini, D., Boranova, V., DiBella, G., Dybczak, K., Hongjo, K., Huidrom, R., Jobst, A., Jovanovic, N., Ozturk, E., Papi, L., Sola, S., Stone, M., Topalova, P., "Infrastructure in Central, Eastern, and Southeastern Europe: Benchmarking, Macroeconomic Impact, and Policy Issues," IMF Departmental Papers / Policy Papers 2020/011, International Monetary Fund.
- Ari, A. and Pula, G. (2021). Assessing the Macroeconomic Impact of Structural Reforms in Ukraine, IMF Working Papers, 2021(100).
- Romain Duval & Davide Furceri, 2018. "The Effects of Labor and Product Market Reforms: The Role of Macroeconomic Conditions and Policies," IMF Economic Review, vol. 66(1), pages 31-69, March.
- Egert, B., and Gal, P. (2016). The quantification of structural reforms in OECD countries: A new framework. OECD Economics Department Working Paper No. 1354.
- Egert, B. (2017). The quantification of structural reforms: Extending the framework to emerging market economies. OECD Economics Department Working Paper No 1442.
- Furceri, D., Loungani, P. And Ostry, J.D. (2019), The Aggregate and Distributional Effects of Financial Globalization: Evidence from Macro and Sectoral Data. Journal of Money, Credit and Banking, 51: 163-198.
- Hastie, T., Tibshirani, R., and Friedman, J.H. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction (Springer).
- International Monetary Fund (2015). Structural reforms and macroeconomic performance: Initial Considerations for the Fund. Staff Report. November 2015.
- International Monetary Fund. 2014. World Economic Outlook: Legacies, Clouds, Uncertainties. Ch. 3 “Is it Time for an Infrastructure Push? The Macroeconomic Effects of Public Investment.” Washington, DC, October.
- International Monetary Fund. 2019. World Economic Outlook: Global Manufacturing Downturn, Rising Trade Barriers. Ch. 3 "Reigniting Growth in Low-Income and Emerging Market Economies: What Role Can Structural Reforms Play?" Washington, DC, October.
- Jordà, Òscar. 2005. "Estimation and Inference of Impulse Responses by Local Projections." American Economic Review, 95 (1): 161-182.
- Josse, J. and Husson, F. (2013). Handling missing values in exploratory multivariate data analysis methods. Journal de la SFdS. 153 (2), pp. 79-99.
- Josse, J. and Husson, F. (2016). missMDA: A Package for Handling Missing Values in Multivariate Data Analysis. Journal of Statistical Software, 70 (1), pp 1-31.
- Prati, Alessandro & Massimiliano Gaetano Onorato & Chris Papageorgiou, 2013. "Which Reforms Work and under What Institutional Environment? Evidence from a New Data Set on Structural Reforms," The Review of Economics and Statistics, vol. 95(3), pages 946-968, July.
- Reinhart, Carmen M., and Kenneth S. Rogoff. 2011. "From Financial Crash to Debt Crisis." American Economic Review, 101 (5): 1676-1706.
- Rodrik, Dani. 2010. "Diagnostics before Prescription." Journal of Economic Perspectives, 24 (3): 33-44.
- Warner, Andrew. 2014. “Public Investment as an Engine of Growth.” IMF Working Paper 14/148, International Monetary Fund, Washington.

### Appendix A — List of structural indicators (selected highlights by category)
- Legal system:
  - Bribery incidence (% of firms experiencing at least one bribe payment request)
  - Bribery index (% of gift or informal payment requests during public transactions)
  - Control of Corruption: Percentile Rank
  - Firms expected to give gifts in meetings with tax officials (% of firms)
  - Informal payments to public officials (% of firms)
  - Percent of firms identifying corruption as a major constraint
  - Business costs of crime and violence, 1-7 (best)
  - Voice and Accountability: Percentile Rank
  - Rule of Law: Percentile Rank
- Product markets:
  - Burden of government regulation, 1-7 (best)
  - Cost of business start-up procedures (% of GNI per capita)
  - Procedures to register property (number)
  - Time required to get electricity (days)
  - Time required to start a business (days)
  - Time spent dealing with the requirements of government regulations (% of senior management time)
  - Effectiveness of anti-monopoly policy, 1-7 (best)
- Financial system:
  - Account at a financial institution (% age 15+) [w2]
  - Borrowed from a financial institution (% age 15+) [w2]
  - Depth of credit information index (0=low to 8=high)
  - Domestic credit to private sector (% of GDP)
  - Outstanding mortgage (% age 15+) [w2]
  - Percent of firms identifying access to finance as a major constraint
  - Private credit bureau coverage (% of adults)
  - Time to resolve insolvency (years)
  - Geographical Outreach: Number of ATMs per 100,000 adults; Number of commercial bank branches per 100,000 adults
- Trade and openness:
  - Average time to clear exports through customs (days)
  - Burden of customs procedure, WEF (1=extremely inefficient to 7=extremely efficient)
  - Cost to export (US$ per container)
  - Cost to import (US$ per container)
  - Tariff rate, applied, simple mean, all products (%)
  - Tariff rate, applied, weighted mean, all products (%)
- R&D:
  - Capacity for innovation, 1-7 (best)
  - Company spending on R&D, 1-7 (best)
  - PCT patents, applications/million pop.
  - Quality of scientific research institutions, 1-7 (best)
- Taxation system:
  - Corporate income tax rate, statutory top central
  - Percent of firms identifying tax rates as a major constraint
  - Labor tax and contributions (% of commercial profits)
- Labor markets:
  - Percent of firms identifying labor regulations as a major constraint
  - Paid annual leave for a worker with 1 year of tenure (in working days)
  - Paid annual leave for a worker with 5 years of tenure (in working days)
  - Fixed-term contracts prohibited for permanent tasks
  - Notice period for redundancy dismissal (for a worker with 1 year of tenure, in salary weeks)
  - Redundancy costs, weeks of salary
  - Severance pay for redundancy dismissal (for a worker with 1 year of tenure, in salary weeks)
  - Maximum working days per week
  - Minimum wage for a full-time worker (US$/month)
  - Flexibility of wage determination, 1-7 (best)

### Appendix B — Description of imputation for missing indicators
- Imputation method:
  - We impute the rest of the missing data using a multiple imputation procedure called the iterative PCA procedure (Josse and Husson, 2013).
  - Iterative PCA aims to preserve the variance of each indicator and the correlation between indicators during imputation, compared to imputation based on linear interpolation.
- Implementation details (procedure as described):
  - Iterative PCA performed using the imputePCA package in R.
  - Indicators rescaled to be between zero and one.
  - The first principal component is used to impute the missing indicator iteratively.
  - At the start of each iteration, PCA is performed on the dataset with missing values replaced with the mean of the variable plus some Gaussian noise.
  - At the end of each iteration, missing values are replaced with the predicted value from the PCA.
  - The imputed data are standardized to be mean zero and standard deviation one.
- Empirical note:
  - For indicators with a high missing rate, the quality of imputation is lower as reflected in deflated variance.
  - Compared to linear interpolation, multiple imputation is more robust to missing rates as the variance of the imputed indicator stays aligned to that of the non-imputed indicators, even for indicators with a high missing rate.

### Appendix C — Comparison between the PLS structural score and simple-average score
- Construction of the simple-average composite:
  - Within each structural category, for a given country and year, the simple-average composite is the average of indicators in the dataset.
  - The simple-average composite is standardized to have zero mean and unit variance across all countries and years.
- Empirical comparison (summary):
  - The simple-average composite presents a different picture regarding time profiles of structural performance compared to the PLS score.
  - Specifically, the simple-average composite shows no deterioration in the legal system, while indicating more substantial improvements in business environment, financial system and taxation system.
  - Repeating the growth analysis using simple averages yields that the effect of structural reforms on growth becomes statistically insignificant for most structural areas, consistent with concerns that the simple average assigns larger weights to noisy indicators than the PLS score.
- Table C1 — Growth impact of structural reforms (coefficients with robust standard errors in parentheses)
  - Dependent variable: GDP growth
  - Columns: (1) (2) (3) (4)
  - Business environment: 0.000919 (0.0211); 0.00692 (0.0239); 0.000222 (0.0234); 8.21e-05 (0.0204)
  - Financial markets: 0.00810 (0.0135); 0.00652 (0.0138); 0.0170 (0.0126); 0.0105 (0.0119)
  - Labor markets: 0.00350 (0.0127); 0.00394 (0.0126); -0.00818 (0.0136); -0.0125 (0.0149)
  - Legal system: 0.0319* (0.0175); 0.0283 (0.0189); 0.0170 (0.0175); 0.0272 (0.0166)
  - Tax policy: -0.00225 (0.00653); -0.00183 (0.00656); 0.00243 (0.00659); -0.00323 (0.00551)
  - Trade & openness: 0.0582*** (0.0189); 0.0562*** (0.0190); 0.0321* (0.0194); 0.0378* (0.0206)
  - Observations: 251; 251; 224; 224
  - R-squared: 0.088; 0.090; 0.295; 0.457
  - Time FE: NO; YES; YES; YES
  - Country group FE: NO; NO; NO; YES
  - Controls: NO; NO; YES; YES
  - Note: Robust standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1

*Structural Reforms and Economic Growth: A Machine Learning Approach — References (wpiea2022184-print-pdf).*

---


_Source: https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022184-print-pdf.pdf_