## wpiea2019048

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---

### Key findings and interpretation
- Definition used: “...The shadow economy includes all economic activities which are hidden from official authorities for monetary, regulatory, and institutional reasons. Monetary reasons include avoiding paying taxes and all social security contributions, regulatory reasons include avoiding governmental bureaucracy or the burden of regulatory framework, while institutional reasons include corruption law, the quality of political institutions and weak rule of law. For our study, the shadow economy reflects mostly legal economic and productive activities that, if recorded, would contribute to national GDP....” (Medina and Schneider (2018) definition used).
- Main empirical finding: identification of a U-shaped relationship between the size of the shadow economy and the level of economic development using a panel dataset covering 158 countries from 1996 to 2015.
- Interpretation of the U-shaped relationship:
  - At low levels of development the relationship between the shadow economy (SE) and GDP per capita is negative; development and stronger institutions/social infrastructure tend to shrink the shadow economy.
  - Beyond a threshold in GDP per capita the relationship reverses and the size of the shadow economy rises with per capita income as higher human capital, greater financial freedom, technology innovation, and preferences for work flexibility encourage participation in informal activities.
  - Two competing forces—downsizing via public goods/institutions and upsizing via higher incomes and technological/occupational choice—determine the net effect across the development path.
- Micro-level channel: educational attainment, especially college degree or above, plays a vital role in improving GDP per capita and helps explain the mechanism underlying the U-shaped pattern.
- Distributional note: most countries lie on the downward (declining-SE) part of the U-shaped curve; a few countries lie on the upward part, notably four oil-exporting countries: BRN, ARE, KWT and QAT.

### Data, sample and variables
- Sample: 158 countries or regions; panel period 1996 to 2015.
- Averages used:
  - 20-year averages (cross-sectional regressions).
  - 10-year averages (robustness checks).
  - 5-year averages (panel regressions).
- Shadow economy measures:
  - Primary: Medina and Schneider (2018) MIMIC-based estimates (revision uses light intensity).
  - Robustness: Elgin and Oztunali (2012) estimates.
  - Reported summary: estimated average size of the shadow economy in 158 countries over 1991 to 2015 is 31.9 percent relative to GDP.
- GDP per capita measures:
  - PPP-based constant 2011 international dollars (used in figures).
  - Constant 2010 US dollars (main series for major finding).
- Institutional control: Political stability index (WGI), original range -2.5 to 2.5 rescaled to 0 to 100.
- Other controls (WDI unless noted): GDP per capita growth (national currency), CPI inflation (percent), Trade openness (percent), Financial depth (domestic credit to private sector), Tax burden (robustness), Education (primary, high school, college and above), Capital stock (IMF ICSD).

### Benchmark empirical results (static cross-sectional, 20-year averages)
- Main result: U-shaped relationship between shadow economy size and GDP per capita; squared GDP per capita significant in main regressions.
- Institutional and financial factors:
  - Political stability coefficient: consistently negative.
  - Financial depth coefficient: negative (financial development dampens shadow economy).
- Selected coefficients and statistics (Table 1, average of 1996-2015):
  - Dependent variable: GDP_PPP$
    - GDP_PPP$: -5.314*** (1.142)
    - (GDP_PPP$)^2: 0.352*** (0.110)
  - Dependent variable: GDP_2010$
    - GDP_2010$: -5.611*** (1.238)
    - (GDP_2010$)^2: 0.398*** (0.123)
  - Institutional factor:
    - PolStability: -0.129** (0.0570), -0.114* (0.0585), -0.0848 (0.0567) across specifications
  - Non-institutional factors:
    - GDPGrowth: -0.310 (0.367), -0.362 (0.363), 0.00131 (0.376)
    - Inflation: 0.109 (0.113), 0.115 (0.115), 0.0514 (0.122)
    - Openness: 0.0168 (0.0114), 0.00458 (0.0109), 0.00981 (0.0117)
    - FinDepth: -0.0581** (0.0278), -0.0479* (0.0279), -0.0624** (0.0271)
  - Constants and fit:
    - Constant: 45.23*** (2.613), 43.82*** (2.689), 44.26*** (2.626)
    - R-squared: 0.574, 0.569, 0.556
    - Observations: 152, 152, 147
    - F-test: 44.03, 56.07, 43.69

### Long-run determinants of GDP per capita (Table 2, average of 1996-2015)
- Specification guided by production function: physical capital, human capital (education), technology; inflation included.
- Education effects:
  - College: 0.0787** (0.0309)
  - HighSch: 0.00682 (0.0132)
  - PrimSch: 0.0196* (0.0110)
- Inflation: -0.0868*** (0.0311)
- Capital stock: CapStock: -0.000232 (0.00014) — not significantly different from zero.
- Fit:
  - Constant: 1.796* (0.976)
  - R-squared: 0.306
  - Observations: 70
  - F-test: 13.86
- Interpretation: education, capital stock and inflation explain about 30.6 percent of GDP per capita; a large share remains unexplained.

### Robustness checks and extensions
- Robustness approaches:
  1. Control for tax burden and country group heterogeneity (dummies and separate estimations).
  2. Use 10-year averages (1996-2005 and 2006-2015).
  3. Use 5-year averages and panel regressions (FE and RE, with lag specifications).
  4. Drop four oil-exporting countries (Brunei, United Arab of Emirates, Kuwait, Qatar) and/or change GDP per capita measurement to constant 2010 US$.
- Selected robustness results:
  - With tax burden included (Table 3):
    - GDP_PPP$: -5.301*** (1.143)
    - (GDP_PPP$)^2: 0.352*** (0.110)
    - TaxBurden: 0.00461 (0.0184)
    - R-squared: 0.574; Observations: 152; F-test: 39.33
  - Country-group regressions (Table 4):
    - AEs: GDP_PPP$: -8.954*** (2.771); (GDP_PPP$)^2: 0.555** (0.224); R-squared: 0.623; Observations: 34
    - non-AEs: GDP_PPP$: -4.081*** (1.302); (GDP_PPP$)^2: 0.249* (0.126); R-squared: 0.310; Observations: 184
    - HICs: GDP_PPP$: -6.728*** (2.309); (GDP_PPP$)^2: 0.426** (0.179); R-squared: 0.517; Observations: 91
    - non-HICs: mixed results; R-squared reported: 0.155; Observations: 103
  - 10-year averages (Table 5):
    - 1996-2005: GDP_PPP$: -6.510*** (1.358); (GDP_PPP$)^2: 0.458*** (0.137); R-squared: 0.601; Observations: 144
    - 2006-2015: GDP_PPP$: -5.088*** (1.062); (GDP_PPP$)^2: 0.306*** (0.0853); R-squared: 0.552; Observations: 149
  - Panel FE and RE (5-year averages, Tables 6–8):
    - Panel FE:
      - GDP_PPP$: -11.59*** (1.640)
      - (GDP_PPP$)^2: 0.838*** (0.215)
      - PolStability: -0.0559* (0.0336)
      - Inflation: 0.0704*** (0.0221)
      - Openness: -0.0476*** (0.0148)
      - Constant: 52.02*** (3.032)
      - Observations: 558; F-test: 25.50
    - Panel RE:
      - GDP_PPP$: -8.755*** (1.141)
      - (GDP_PPP$)^2: 0.656*** (0.157)
      - Inflation: 0.0846*** (0.0185)
      - Observations: 558
    - Lagged specifications (one-period lags):
      - GDP_PPP$(-1): -9.444*** (1.391) / -7.814*** (0.934)
      - (GDP_PPP$(-1))^2: 0.665*** (0.173) / 0.565*** (0.122)
      - Observations: 414
    - Two-period lags:
      - GDP_PPP$(-2): -4.636*** (1.754) / -6.294*** (1.138)
      - (GDP_PPP$(-2))^2: 0.717*** (0.210) / 0.465*** (0.139)
      - Observations: 266
    - Robustness conclusion: panel regressions and lag specifications support the U-shaped relationship.
  - Impact of four oil-exporting countries:
    - Concern: BRN, ARE, KWT, QAT lie on upward part and could influence results.
    - Alternative GDP per capita measure (constant 2010 US$) moves these four countries to the downward part; regressions with this measure support U-shaped relationship (Table 9).
    - Dropping the four outliers yields the same U curve though at a less significant level.

### Labor market, welfare roles, and policy implications
- Labor market rigidity and flexibility:
  - Labor market flexibility indicator (GCI, scale 1-7) used; higher values mean more flexibility.
  - Labor market flexibility helps reduce the size of the shadow economy in the long run although not significantly.
  - Inclusion of labor market indicator does not remove significance of squared GDP per capita.
- Selected coefficients when labor market indicator included (average of 1996-2015, dropping four oil exporters in one specification):
  - GDP_PPP$: -6.086*** (1.310)
  - (GDP_PPP$)^2: 0.413*** (0.124)
  - PolStability: -0.125** (0.0614)
  - FinDepth: -0.0544* (0.0292)
  - LabMarket: -0.205 (1.606)
  - Constant: 47.81*** (7.582)
  - R-squared: 0.578; Observations: 139; F-test: 34.75
- Welfare and economic roles of the shadow economy:
  - Negative effects:
    - Threat to fiscal revenue collection and public goods provision.
    - Firms in shadow economy are smaller and less productive.
    - Limited information for authorities weakens economic monitoring.
    - The shadow economy evolves, requiring ongoing policy adaptation.
  - Positive/mitigating roles:
    - Provides temporary and low-paid jobs when social safety nets are weak.
    - Serves as an untapped reservoir of labor that allows rapid scaling-up of production during demand shocks.
- Labor force composition and research directions:
  - Gender participation and other composition factors may influence shadow economy size; Goldin (1994) referenced for U-shaped female labor participation pattern.
  - Further research suggested on symmetry/asymmetry of the non-monotonic relationship before and after the GDP per capita threshold and on productivity dynamics in the shadow economy as development advances.

### Policy recommendations
- General caveat: harsh eradication of the shadow economy is not a first-best solution; policy appropriateness depends on level of development.
- When economy is less-developed (shadow economy expected to downsize with development):
  - Promote financial development.
  - Contain inflation.
  - Stabilize the political situation.
  - Expand educational spending.
- When the economy has reached the GDP per capita threshold and the relationship turns positive:
  - Make formal-sector employment more beneficial:
    - Reduce labor market rigidities.
    - Simplify tax compliance procedures using technology innovations.
- Specific recommendations:
  - Strengthen capacity in data collecting and processing:
    - Exploit all available data sources, especially given rapid growth of the digital economy.
    - Government agencies should work collectively to cross check data quality.
    - Authorities should measure policy impact accurately and adjust policies accordingly.
  - Streamline administrative procedures to reduce compliance costs and make public goods/services more accessible leveraging technology.
  - Continue educating people to improve human capital and teach about the role of the shadow economy:
    - Promote healthy social norms and advise firms and households on merits/risks of the shadow economy to foster positive attitudes toward formal jobs and transparency.

### Paper-level conclusion
- Main empirical result: a long-run U-shaped relationship between GDP per capita and the size of the shadow economy using a dataset of 158 countries for 1996–2015.
- Additional finding: the share of the population with a bachelor’s degree or above plays a vital role in promoting average productivity.
- The U-shaped pattern warrants further exploration, including potential asymmetry and mechanisms driving productivity changes in the shadow economy as development advances.

*Source: wpiea2019048 (IMF working paper; INTRODUCTION, LITERATURE REVIEW, METHODOLOGY AND DATA, and 4.4 Policy Discussion sections; average period 1996–2015).*

### INTRODUCTION ______________________________________________________________ 3

### wpiea2019048 - INTRODUCTION

### Introduction: key findings and interpretation
- Definition used: “...The shadow economy includes all economic activities which are hidden from official authorities for monetary, regulatory, and institutional reasons. Monetary reasons include avoiding paying taxes and all social security contributions, regulatory reasons include avoiding governmental bureaucracy or the burden of regulatory framework, while institutional reasons include corruption law, the quality of political institutions and weak rule of law. For our study, the shadow economy reflects mostly legal economic and productive activities that, if recorded, would contribute to national GDP....” (Medina and Schneider (2018) definition used).
- Main empirical finding: identification of a U-shaped relationship between the size of the shadow economy and the level of economic development using a panel dataset covering 158 countries from 1996 to 2015.
- Interpretation of the U-shaped relationship:
  - At low levels of development, the relationship between the shadow economy (SE) and GDP per capita is negative: economic development (productivity improvement, technology advance) and stronger institutions/social infrastructure tend to shrink the shadow economy as households and firms move into the formal sector.
  - Beyond a threshold in GDP per capita, the relationship reverses: the size of the shadow economy rises with per capita income as higher human capital, greater financial freedom, technology innovation, and preferences for work flexibility encourage participation in informal activities.
  - The two competing forces—downsizing via public goods/institutions and upsizing via higher incomes and technological/occupational choice—determine the net effect across the development path.
- Micro-level channel highlighted: educational attainment, especially college degree or above, plays a vital role in improving GDP per capita and helps explain the mechanism underlying the U-shaped pattern (skilled workers remain formal at lower income levels; at higher income levels, household financial sufficiency can increase demand for informal work for flexibility or perks).
- Additional observation: most countries lie on the downward (declining-SE) part of the U-shaped curve; only a few countries lie on the upward part, notably four oil-exporting countries: BRN, ARE, KWT and QAT. The paper examines robustness by dropping these four countries.

### Literature review: context and contribution
- Estimation approaches for SE cited: survey-based methods, observable-variable methods, and model-based methods (Multiple Indicators Multiple Causes (MIMIC) approach noted).
- Reference estimate: Medina and Schneider (2018) find an estimated average size of the shadow economy in 158 countries over 1991 to 2015 of 31.9 percent relative to GDP.
- Categorization of SE causes: economic, policy-related, and regulatory and institutional factors.
- Typical prior assumption: most studies assume or identify a linear (monotone) relationship between SE and its determinants, often implying a shrinking SE with development; this paper departs by explicitly testing nonlinearity (U-shaped) via inclusion of squared GDP per capita.
- Contribution:
  - First attempt (per paper) to investigate the non-linear long-run trend of the shadow economy with explicit focus on a U-shaped relationship between SE and GDP per capita.
  - Explores long-run determinants of GDP per capita and highlights the role of educational attainment (college degree or above).
- Comparisons with prior work:
  - Buehn and Farzanegan (2013): find higher education decreases SE in strong institutional environments via interaction terms; the present paper’s results differ.
  - Elgin and Erturk (2016): support a negative relationship between education and SE; methodological differences noted (longer SE series; fixed effects used).
  - Elgin and Birinci (2016): investigate SE impact on GDP per capita growth and find an inverted-U between SE and growth of GDP per capita; no direct inference to the present paper’s level relationship between SE and GDP per capita.

### Methodology: empirical specifications and estimation strategy
- Sample and data construction:
  - Annual cross-country panel data covering 158 countries or regions from 1996 to 2015.
  - Variables used as 20-year, 10-year, or 5-year averages: 20-year and 10-year averages used in cross-sectional regressions; 5-year averages used in panel regressions.
  - Shadow economy data source: Medina and Schneider (2018) (revision of MIMIC using light intensity instead of GDP as an indicator variable). Robustness check uses Elgin and Oztunali (2012) shadow economy data.
  - Note: “Most of the key time series are from 1990 to 2015 except for the World Governance Index which starts from” (text is truncated in source).
- Benchmark cross-sectional regression (equation (1) as presented in the paper):
  - Dependent variable: percentage ratio of the shadow (or informal) economy relative to GDP of country i.
  - Key regressors: GDP per capita and squared GDP per capita to test for nonlinearity; additional control variables x_n,i included.
  - Purpose of squared GDP per capita: check potential nonlinear relationship between size of informal economy and GDP per capita.
- Robustness strategy and additional estimators:
  - Cross-sectional regressions using 20-year averages.
  - Robustness checks include:
    - (i) controlling for country group effects via dummy variables and separate regressions by country group;
    - (ii) regressions on variables of 10-year averages;
    - (iii) panel regression method with 5-year averages, including regressions with one-period lagged variables to control for endogeneity;
    - (iv) regressions controlling for other potential economic and institutional factors.
- Panel regression specification (equation (2) as presented in the paper):
  - Includes country and time dummies to reflect country and time effects.
  - Both fixed-effect and random-effect estimators are reported in the paper.
  - Panel notation indicates use of 5-year averaged variables, country effects (alpha_i) and time effects (gamma_t), and error structure with epsilon_i,t.
- Endogeneity considerations: use of lagged variables in panel regressions to control for endogeneity in robustness checks.

### Data and variables: exact sample and constructs
- Sample size and period:
  - 158 countries or regions.
  - Panel period 1996 to 2015 for the primary regressions.
- Averages constructed:
  - 20-year averages (used in cross-sectional regressions).
  - 10-year averages (robustness check).
  - 5-year averages (used in panel regressions and further robustness checks).
- Shadow economy measurement:
  - Primary series: Medina and Schneider (2018) MIMIC-based estimates (revision uses light intensity as indicator).
  - Robustness series: Elgin and Oztunali (2012) estimates.
  - Reported summary from Medina and Schneider (2018): estimated average size of the shadow economy in 158 countries over 1991 to 2015 is 31.9 percent relative to GDP.
- GDP per capita:
  - Proxy for level of development.
  - Note on figures: Figure 1 uses GDP per capita as the average value of PPP-based constant 2011 international dollars from 1996 to 2015; axis labels reflect “The shadow economy, in % of GDP” and “GDP per capita, in 10 thousands of PPP-based constant 2011 intl dollars.”

### Robustness and extensions highlighted in the paper
- Robustness checks undertaken (as summarized in paper structure and tables):
  - Robustness check I: controlling for tax burden and for country groups.
  - Robustness check II: 10-year averages.
  - Robustness check III: 5-year averages.
  - Robustness check IV: panel regressions (including fixed/random effects).
  - Robustness check V: panel regression with one-period lags.
  - Robustness check VI: panel regression with two-period lags.
  - Robustness check VII and VIII: averages of 1996-2015 (further robustness checks).
  - Robustness also includes dropping four oil-exporting countries (BRN, ARE, KWT, QAT) to examine sensitivity of U-shaped relationship.
- Findings from robustness narrative:
  - The squared GDP per capita term is significant in main regressions and subsequent robustness checks, supporting the nonlinearity result.
  - Educational attainment (college degree or above) remains an important long-run determinant of GDP per capita in the regressions examined.

*Source: IMF working paper (INTRODUCTION, LITERATURE REVIEW, METHODOLOGY AND DATA sections; dataset and figures/tables referenced are from the paper text).*

### 1996. Therefore, our regressions change the sample period to the range of 1996 to 2015.

### wpiea2019048 - 1996. Therefore, our regressions change the sample period to the range of 1996 to 2015.

### Data and control variables
- Sample period: 1996 to 2015.
- Shadow economy estimates: Medina and Schneider (2018) (used in benchmark) and Elgin and Oztunali (2012) (series spans 1950 to 2014).
- GDP per capita measures:
  - PPP-based constant 2011 international dollars (WDI).
  - Constant 2010 US dollars (WDI) — main series for major finding.
- Institutional control:
  - Political stability index (WGI), original range -2.5 to 2.5 rescaled to 0 to 100.
- Non-institutional controls (WDI unless noted):
  - GDP per capita growth (national currency).
  - CPI inflation (percent).
  - Trade openness = (exports + imports of goods and services) / GDP (percent).
  - Financial depth = domestic credit to private sector provided by financial corporations.
  - Tax burden = ratio of taxes and mandatory contributions payable to commercial profits (used in robustness checks).
- Education variables (WDI): percentages completing primary school only, completing high school only, and completing college and above (note: high-school-or-above data largely available only after 2012).
- Capital stock (IMF ICSD): public capital + private capital + public-private-partnership (PPP) capital = total capital stock.

### Benchmark empirical results (static cross-sectional, 20-year averages)
- Main finding: U-shaped relationship between shadow economy size and GDP per capita — shadow economy shrinks with GDP per capita up to a threshold, then increases with further GDP per capita growth.
- Statistical significance: positive coefficient on squared shadow economy size identified at the 1-percent significance level in three benchmark specifications.
- Political stability: coefficient consistently negative (institutional factors help contain shadow economy expansion).
- Financial depth: estimated negative coefficient — financial development dampens shadow economy activities.
- Selected coefficients and statistics from Table 1 (average of 1996-2015):
  - Dependent variable: GDP_PPP$
    - GDP_PPP$ coefficient: -5.314*** (1.142)
    - (GDP_PPP$)^2 coefficient: 0.352*** (0.110)
  - Dependent variable: GDP_2010$
    - GDP_2010$ coefficient: -5.611*** (1.238)
    - (GDP_2010$)^2 coefficient: 0.398*** (0.123)
  - Institutional factor:
    - PolStability: -0.129** (0.0570), -0.114* (0.0585), -0.0848 (0.0567) across specifications
  - Non-institutional factors:
    - GDPGrowth: -0.310 (0.367), -0.362 (0.363), 0.00131 (0.376)
    - Inflation: 0.109 (0.113), 0.115 (0.115), 0.0514 (0.122)
    - Openness: 0.0168 (0.0114), 0.00458 (0.0109), 0.00981 (0.0117)
    - FinDepth: -0.0581** (0.0278), -0.0479* (0.0279), -0.0624** (0.0271)
  - Constants and fit:
    - Constant: 45.23*** (2.613), 43.82*** (2.689), 44.26*** (2.626)
    - R-squared: 0.574, 0.569, 0.556
    - Observations: 152, 152, 147
    - F-test: 44.03, 56.07, 43.69

### Long-run determinants of GDP per capita (Table 2, average of 1996-2015)
- Regression specification guided by production function: physical capital, human capital (education), technology; inflation included following Barro (2013).
- Education effects:
  - College and above major contributor to GDP per capita increases.
  - Coefficients:
    - College: 0.0787** (0.0309)
    - HighSch: 0.00682 (0.0132)
    - PrimSch: 0.0196* (0.0110)
- Inflation: negative and significant
  - Inflation: -0.0868*** (0.0311)
- Capital stock: not significantly different from zero
  - CapStock: -0.000232 (0.00014)
- Constant and fit:
  - Constant: 1.796* (0.976)
  - R-squared: 0.306
  - Observations: 70
  - F-test: 13.86
- Interpretation: education, capital stock and inflation explain about 30.6 percent of GDP per capita; a large share remains unexplained.

### Economic intuition linking education, GDP per capita, and the shadow economy
- Formal sector productivity is higher; as education rises, firms hire skilled workers in the formal sector, reducing shadow economy size.
- Beyond a threshold of education and GDP per capita, informal-sector wages and household income rise; higher household revenue and reduced financial pressure can increase willingness to accept flexible, temporary unregistered work, expanding the shadow economy — explaining the upward part of the U-shaped relationship.

### Robustness checks (Section 4.3)
- Four types of robustness tests implemented:
  1. Control for tax burden and country group heterogeneity (dummies and separate estimations).
  2. Use 10-year averages (1996-2005 and 2006-2015).
  3. Use 5-year averages and panel regressions (FE and RE, with lag specifications).
  4. Drop four oil-exporting countries on the upward part of the U curve (Brunei, United Arab of Emirates, Kuwait, Qatar) and/or change GDP per capita measurement to constant 2010 US$.

- Robustness check I — controlling for tax burden and country groups (Table 3):
  - With tax burden included:
    - GDP_PPP$: -5.301*** (1.143)
    - (GDP_PPP$)^2: 0.352*** (0.110)
    - PolStability: -0.129** (0.0571)
    - FinDepth: -0.0577** (0.0281)
    - TaxBurden: 0.00461 (0.0184) — positive but insignificant
    - R-squared: 0.574; Observations: 152; F-test: 39.33
  - With dummy for AEs / dummies for HICs and LICs:
    - GDP_PPP$ coefficients: -4.562*** (1.181), -3.769** (1.474)
    - (GDP_PPP$)^2 coefficients: 0.286** (0.111), 0.239* (0.125)
    - Dummy AE: -3.987* (2.251)
    - R-squared: 0.581, 0.580; Observations: 152

- Robustness check II — separate regressions by country group (Table 4):
  - For AEs:
    - GDP_PPP$: -8.954*** (2.771)
    - (GDP_PPP$)^2: 0.555** (0.224)
    - R-squared: 0.623; Observations: 34
  - For non-AEs:
    - GDP_PPP$: -4.081*** (1.302)
    - (GDP_PPP$)^2: 0.249* (0.126)
    - R-squared: 0.310; Observations: 184
  - For HICs:
    - GDP_PPP$: -6.728*** (2.309)
    - (GDP_PPP$)^2: 0.426** (0.179)
    - R-squared: 0.517; Observations: 91
  - For non-HICs:
    - GDP_PPP$: -4.549 (5.626)
    - (GDP_PPP$)^2: 0.590 (2.331)
    - Alternative non-HIC specification: GDP_PPP$: -3.345* (1.773)
    - R-squared for non-HICs reported: 0.155; Observations: 103
  - Interpretation: squared GDP per capita significant for AEs, non-AEs, and HICs; non-HICs show predominantly linear negative relationship (many non-HICs lie far from threshold). R-squared values for AEs and HICs above 50 percent; for non-AEs and non-HICs below 50 percent.

- Robustness check III — 10-year averages (Table 5):
  - 1996-2005:
    - GDP_PPP$: -6.510*** (1.358)
    - (GDP_PPP$)^2: 0.458*** (0.137)
    - PolStability: -0.112** (0.0548)
    - FinDepth: -0.0610** (0.0302)
    - Constant: 47.09*** (2.679)
    - R-squared: 0.601; Observations: 144; F-test: 55.83
  - 2006-2015:
    - GDP_PPP$: -5.088*** (1.062)
    - (GDP_PPP$)^2: 0.306*** (0.0853)
    - PolStability: -0.109* (0.0573)
    - FinDepth: -0.0585** (0.0250)
    - Constant: 45.05*** (2.695)
    - R-squared: 0.552; Observations: 149; F-test: 35.91
  - Conclusion: nonlinear relationship stable in the medium term.

- Robustness check IV & V — 5-year averages, panel regressions, and lagged specifications (Tables 6–8):
  - Panel FE (5-year average):
    - GDP_PPP$: -11.59*** (1.640)
    - (GDP_PPP$)^2: 0.838*** (0.215)
    - PolStability: -0.0559* (0.0336)
    - Inflation: 0.0704*** (0.0221)
    - Openness: -0.0476*** (0.0148)
    - FinDepth: -0.0136 (0.0119)
    - Constant: 52.02*** (3.032)
    - Observations: 558; F-test: 25.50
  - Panel RE (5-year average):
    - GDP_PPP$: -8.755*** (1.141)
    - (GDP_PPP$)^2: 0.656*** (0.157)
    - PolStability: -0.0418 (0.0292)
    - Inflation: 0.0846*** (0.0185)
    - Openness: -0.0308*** (0.00995)
    - FinDepth: -0.0278** (0.0122)
    - Constant: 46.89*** (2.079)
    - Observations: 558
  - Panel with one-period lags (robust FE with lags / robust RE with lags):
    - GDP_PPP$(-1): -9.444*** (1.391) / -7.814*** (0.934)
    - (GDP_PPP$(-1))^2: 0.665*** (0.173) / 0.565*** (0.122)
    - GDPGrowth(-1): -0.317*** (0.0847) / -0.331*** (0.0723)
    - Inflation(-1): 0.0770*** (0.0191) / 0.0828*** (0.0172)
    - FinDepth(-1): -0.00410 (0.0118) / -0.0223* (0.0123)
    - Constant: 43.24*** (2.817) / 42.13*** (1.717)
    - Observations: 414
  - Panel with two-period lags (robust FE with lags / robust RE with lags):
    - GDP_PPP$(-2): -4.636*** (1.754) / -6.294*** (1.138)
    - (GDP_PPP$(-2))^2: 0.717*** (0.210) / 0.465*** (0.139)
    - Inflation(-2): 0.0776*** (0.0221) / 0.0641*** (0.0150)
    - Constant: 33.29*** (3.822) / 39.51*** (1.837)
    - Observations: 266
  - Robustness conclusion: panel regressions (including lagged specifications) support the U-shaped relationship; FE and RE estimators presented though Hausman test suggests RE may be inconsistent.

- Robustness check VI — impact of four oil-exporting countries (Brunei, United Arab of Emirates, Kuwait, Qatar):
  - Concern: these four countries lie on the upward part of the curve and could disproportionately affect results.
  - Alternative GDP per capita measure (constant 2010 US$) moves these four countries to the downward part of the U curve; regression with this measure supports U-shaped relationship (Table 9).
  - Dropping the four outliers while using the same measurement yields the same U curve, though at a less significant level.

### Summary of substantive findings and implications
- The relationship between shadow economy size and GDP per capita is nonlinear and U-shaped across the 1996–2015 sample: shadow economy shrinks with increasing GDP per capita up to a threshold, then expands with further GDP per capita increases.
- Institutional strength (political stability) and financial depth consistently associate with smaller shadow economies.
- Education — especially college and above — raises GDP per capita and influences shadow economy dynamics: rising education initially reduces informality but beyond a GDP per capita threshold can be associated with an expanding shadow economy due to higher incomes and preferences for flexible informal work.
- Robustness: the U-shaped relationship holds across multiple robustness checks (tax burden controls, country group analyses, 10-year and 5-year averages, panel estimators, lag specifications, and exclusion of four oil-exporting outliers), with variations in coefficient magnitudes and significance but persistent nonlinear pattern.

*Source: wpiea2019048 (average period 1996–2015).*

### 4.4 More Discussions on Labor Market and Policy Implications

### 4.4 More Discussions on Labor Market and Policy Implications

### Labor market rigidity, labor market flexibility, and robustness checks
- One view: labor market rigidity lengthens job search and matching, discouraging firms from registering newly hired workers and causing workers, especially migrant workers, to prefer informal jobs.
- The paper controls for institutional effects of labor market rigidities using the indicator of labor market flexibility from the World Economic Forum Global Competitiveness Index (GCI).
  - Indicator scale: 1-7 with high values meaning more flexibility.
- Empirical findings (Table 10 and subsequent robustness checks):
  - Labor market flexibility helps reduce the size of the shadow economy in the long run although not significantly.
  - The coefficient of squared GDP per capita remains significant, supporting the U-shaped curve relationship between GDP per capita and the shadow economy.
- Selected regression coefficients and statistics (as reported):
  - From robustness check (average of 1996-2015) using GDP per capita in PPP-based $ and dropping four oil exporting countries:
    - GDP_PPP$: ‐5.391*** (1.294)
    - (GDP_PPP$)^2: 0.256* (0.154)
    - GDP_2010$: ‐5.611*** (1.238)
    - (GDP_2010$)^2: 0.398*** (0.123)
    - PolStability: ‐0.114* (0.0585) and ‐0.129** (0.0569) (institutional factor)
    - GDPGrowth: ‐0.362 (0.363) and ‐0.251 (0.379)
    - Inflation: 0.115 (0.115) and 0.117 (0.112)
    - Openness: 0.00458 (0.0109) and 0.0205 (0.0124)
    - FinDepth: ‐0.0479* (0.0279) and ‐0.0452 (0.0282)
    - Constant: 43.82*** (2.689) and 44.48*** (2.603)
    - R-squared: 0.569 and 0.585
    - Observations: 152 and 148
    - F-test: 64.946 and 4.94
  - With labor market indicator included (reported coefficients):
    - GDP_PPP$: ‐6.086*** (1.310)
    - (GDP_PPP$)^2: 0.413*** (0.124)
    - PolStability: ‐0.125** (0.0614)
    - GDPGrowth: ‐0.594 (0.573)
    - Inflation: 0.0480 (0.128)
    - Openness: 0.0179 (0.0121)
    - FinDepth: ‐0.0544* (0.0292)
    - LabMarket: ‐0.205 (1.606)
    - Constant: 47.81*** (7.582)
    - R-squared: 0.578
    - Observations: 139
    - F-test: 34.75

### Economic roles and welfare implications of the shadow economy
- Negative effects highlighted:
  - Severe threat to fiscal revenue collection, undermining government's ability to provide public goods and services.
  - Firms in the shadow economy are smaller and less productive than those in the formal sector.
  - Authorities have limited access to information related to the shadow economy, weakening economic monitoring and management.
  - The shadow economy evolves and adapts, requiring policymakers to update knowledge regularly.
- Positive/mitigating effects noted:
  - The informal sector supports workers' ability to make a living by providing temporary and low-paid jobs when social safety nets are weak.
  - The informal sector provides an untapped reservoir of labor supply that allows rapid scaling-up of production when demand shocks occur.

### Labor force composition and further research directions
- Labor force composition (e.g., gender participation) may influence the relative size of the shadow economy.
  - Reference: Goldin (1994) finds a U-shaped curve between female labor participation and economic development; if true, more male individuals may tend to work informally with economic development.
  - The paper suggests this as a topic for further investigation, conditional on data availability.
- Additional research question raised in conclusion:
  - Whether the non-monotonic relationship before and after the GDP per capita threshold is symmetric or asymmetric.
  - Possible scenario: productivity increase of the shadow economy may accelerate when development exceeds a stage, due to industrial advancement in the formal sector and technological innovation.

### Policy implications and recommendations
- General caveat:
  - Taking harsh measures to dramatically reduce or eradicate the shadow economy is not a first-best solution; appropriateness depends on the level of economic development.
- When the economy is less-developed or in a catch-up phase (shadow economy expected to downsize):
  - Authorities can harness the trend to attract firms and workers out of the shadow economy by:
    - Promoting financial development.
    - Containing inflation.
    - Stabilizing the political situation.
    - Expanding educational spending.
- When the economy has reached the GDP per capita threshold and the relationship turns positive:
  - Authorities should put additional efforts to make formal-sector employment more beneficial, for example by:
    - Reducing labor market rigidities to improve market efficiency.
    - Simplifying tax compliance procedures using recent technology innovations.
- Specific policy recommendations listed:
  - Strengthen capacity in data collecting and processing:
    - Exploit all available data sources, especially given rapid growth of the digital economy.
    - Relevant government agencies should work collectively to cross check data quality.
    - Authorities should be able to measure policy impact in a relatively accurate way and keep adjusting policy to achieve better outcomes.
  - Streamline administrative procedures to reduce compliance costs of firms and households and make public goods and services more accessible by leveraging technology innovations:
    - Revise policy measures to create a business-friendly environment and ensure firms and workers can obtain digital advantages and stay or move to the formal sector.
  - Continue educating people to improve human capital and teach about the role of the shadow economy:
    - Promote healthy social norms to positively influence economic behavior.
    - Advise firms and households on the merits and risks of the shadow economy and foster a positive attitude toward formal jobs and transparency for economic monitoring and policy design.

### Conclusion (paper-level)
- Main empirical result: a long-run U-shaped relationship between GDP per capita and the size of the shadow economy using a dataset of 158 countries.
- Additional finding: the share of the population with a bachelor’s degree or above plays a vital role in promoting average productivity.
- The U-shaped pattern warrants further exploration, including potential asymmetry and mechanisms driving productivity changes in the shadow economy as development advances.

*Source: wpiea2019048 - 4.4 More Discussions on Labor Market and Policy Implications (IMF working paper content provided).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019048.pdf_