## wpiea2024110-print-pdf — References

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### References and appendices (inventory)
- References section listed with page number "28".
- Appendices listed with titles and page numbers:
  - A. The MIMIC Model — 31
  - B. Estimation of the Augmented Factor Model — 32
  - C. Relationship between WBES and Other Survey Data — 33
  - D. Adding Nighttime Lights — 33
  - E. Country Groups — 36
- List of Tables (enumeration) includes Table 1 through Table 10 with specific focuses (country coverage, causes and indicators, projections, weights, estimated informality, nighttime lights, country lists, income groups).
- List of Figures (enumeration) includes Figure 1 through Figure 10 covering estimated informality, PPCA, country decompositions, medians, comparisons 2002 vs. 2021, and nighttime lights robustness.

### Introduction — scope, approach, and key methodological points
- Problem statement:
  - The informal economy's size is often unfathomable and definitions vary widely.
  - Two broad existing approaches: (1) empirical micro-data estimates (limited by infrequent micro data), (2) statistical latent-variable models (sensitive to specification, calibration, and coverage).
- New approach developed:
  - Augmented factor model approach that marries direct survey measures and a statistical model, combining micro and macro data.
  - Builds on augmented factor models from Fan, Ke, and Liao (2021).
  - Two parts:
    - A factor model of indicators of the informal economy augmented by its observable causes.
    - A function mapping the estimated factors to direct survey measures.
  - Result: estimated degree of informality directly comparable to survey results and interpretable.
- Definition used:
  - Focus on World Bank Enterprise Surveys (WBES) questions about competition against unregistered or informal firms.
  - Definition follows OECD (2002): "productive activities conducted by unincorporated enterprises in the household sector that are unregistered and/or are less than a specified size in terms of employment, and that have some market production."
- Relation to MIMIC and prior literature:
  - MIMIC recognized as superior to single-indicator approaches, but has limitations, particularly interpretability of the latent variable.
  - The augmented factor model generalizes MIMIC; shows MIMIC is a special case where the latent variable is the first principal component under strong assumptions.
  - Empirically, the first principal component is often not a useful predictor of survey-measured degree of informality.
- Advantages of the augmented factor model:
  - Projected principal component analysis clarifies channels linking indicators to causes.
  - Mapping into survey data removes need for fragile normalization and calibration required in MIMIC.
  - Allows decomposition of estimated degree of informality into contributions by factors and by projected indicators.
- Data note:
  - Uses WBES covering "154 countries" between "2006-2022" (WBES coverage details appear in Section IV).

### III. Measuring the informal economy: an augmented factor model approach (framework and estimation)
- Framework equations and relations:
  - Observed indicators y_t (P×1) relate to K latent factors f_t via y_t = Λ f_t + u_t.
  - Latent factors relate to observable causes x_t (Q×1) via f_t = g(x_t) + v_t, where g(x_t) = E(f_t | x_t).
  - The augmented factor model generalizes the MIMIC model: MIMIC is a special case with K = 1, linear g(·), and diagonal covariance of u_t.
  - Identification: Λ and g(x_t) can be identified up to an orthogonal rotation; estimation via projected principal component analysis (project indicators on causes, then PCA on fitted/projected indicators).
- Mapping factors to survey data (stepwise outline)
  - Step 1. Transform indicators y_t into growth rates (first difference in log levels).
  - Step 2. Regress {y_t} on {x_t} (include country fixed effects), obtain fitted/projected indicators {ŷ_t}, then standardize ŷ_t to mean zero and variance one.
  - Step 3. Obtain explained components ˆg_t via projected PCA: ˆg_t := ˆΛ′ ˆy_t, where ˆg_t = (ˆg_1t, …, ˆg_Kt)′.
  - Step 4. Construct level indices: for each factor k, ˆs_kt = ∑_{t′=1}^t ˆg_kt′.
  - Step 5. Map indices to survey-based informality z_t by panel regression z_t = β′ ˆs_t + ζ_0 + ε_t; predicted ˆz_t = ˆβ′ ˆs_t + ˆζ_0 provides estimated degree of informality for all countries and times.
- Advantages vs. MIMIC:
  - Allows K > 1 factors and nonlinear g(·), relaxing MIMIC’s strong assumptions.
  - Mapping to survey data makes estimates robust to choices of causes/indicators because indices act as predictors disciplined by survey observations.
  - Improved transparency: decomposition by indices and by projected indicators is straightforward (equation (6): ˆz_t = (ˆβ′ ˆΛ′) ˆy^c_t + ˆζ_0, where y^c_pt is cumulative projected indicator p).

### IV. Data and stylized facts
- Survey data (WBES)
  - World Bank Enterprise Surveys (WBES) used to map indices to survey measures; focus on firm perspective.
  - Two WBES questions used:
    - Does this establishment compete against unregistered or informal firms?
    - Number of permanent, full-time employees at the end of last fiscal year.
  - Degree of informality defined as the adjusted measure: fraction of workers in registered firms that compete with unregistered firms (adjusted by firm size).
  - Coverage: WBES covers 154 countries between 2006-2022; about two thirds of countries have at least two waves.
  - Table 1 summary (from source):
    - coverage by year: e.g., 2006: 27 countries; 2007: 12; …; 2022: 4 (as presented in the source table).
    - coverage by country: At least 1 survey: 154; At least 2 surveys: 101; At least 3 surveys: 50; 4 surveys: 2.
- Other survey measures
  - Labor-based informality measures from Ohnsorge and Yu (2022): SEMP, Infemp, Infsize, Pension.
  - These measures have limited coverage and tend to have low correlations with WBES-based degree of informality.
- Causes and indicators (selection and panels)
  - Causes (examples): PPP GDP per capita, unemployment rate (World Development Indicators); governance measures (Worldwide Governance Indicators); trade openness, tax-to-GDP, government consumption-to-GDP (WEO).
  - Indicators (examples): PPP GDP per capita, currency in circulation (IFS), labor participation rate (aged 15–64), electricity consumption (WDI), nighttime lights (Beyer, Hu, and Yao (2022); Hu and Yao (2022)).
  - Panel: 154 countries spanning 1996–2021 for causes/indicators; governance available biannually before 2002 implies panel covers 1996, 1998, 2000, 2002, and each year after.
  - 126 countries have all causes/indicators and at least one WBES wave (listed in Appendix E).

### V. Unveiling the informal economy — empirical results
- Projected principal component analysis (PPCA) — key numerical results
  - Transformation: indicators → growth rates (first difference in log levels); projection of indicators on causes including country fixed effects; PCA on projected indicators.
  - Table 3 selected projection coefficients (standard errors clustered at country level; Observations = 2,985 for each regression; Adjusted R^2s: currency 0.04; labor participation 0.05; GDP per capita 0.15; electricity 0.10):
    - Trade openness positive and significant for all four projected indicators: currency in circulation (0.057**), labor participation rate (0.0057***), GDP per capita (0.048***), electricity consumption (0.023*).
    - (log) PPP GDP per capita negative and significant for currency (-0.10***) and electricity (-0.028***); muted for labor participation (0.0035) and GDP per capita (-0.023**).
    - Unemployment rate negative and significant for labor participation (-0.065***), GDP per capita (-0.18***), electricity (-0.18***).
    - Government effectiveness: negative and significant for currency (-0.057**) and positive for labor participation (0.0046**).
  - PPCA eigenvalues and factor interpretation (Figure 2 and Table 4):
    - At least two factors recommended: first two eigenvalues > 1; first two principal components explain about 67% of variance of projected indicators.
    - Factor 1 correlations with indicators: currency 0.78; labor -0.47; GDP per capita 0.57; electricity 0.67 (Factor 1 reflects overall physical/economic activity).
    - Factor 2 correlations with indicators: currency 0.16; labor 0.74; GDP per capita 0.68; electricity -0.25 (Factor 2 captures co-movement of formal and informal activity).
- Mapping indices to survey data (Table 5 results — exact reported coefficients and fit)
  - Two cumulative indices constructed from Factor 1 and Factor 2.
  - Selected regression coefficients (standard errors clustered by country; Obs and Adjusted R^2 as reported):
    - Column (1) WBES (adjusted): Index 1 = 0.097 (0.47); Index 2 = -0.85*** (0.30); Obs = 209; Adjusted R^2 = 0.16.
    - Column (2) WBES (unadjusted): Index 1 = 0.092 (0.41); Index 2 = -0.51* (0.27); Obs = 209; Adjusted R^2 = 0.18.
    - Column (3) SEMP: Index 1 = -0.017 (0.047); Index 2 = -0.11** (0.056); Obs = 150; Adjusted R^2 = 0.96.
    - Column (4) Pension: Index 1 = 0.13 (0.33); Index 2 = -0.23 (0.56); Obs = 80; Adjusted R^2 = 0.93.
    - Column (5) Infemp: Index 1 = -0.24 (0.21); Index 2 = -0.42 (0.29); Obs = 153; Adjusted R^2 = 0.94.
    - Column (6) Infsize: Index 1 = -0.094 (0.29); Index 2 = -0.80*** (0.29); Obs = 300; Adjusted R^2 = 0.92.
  - Key insight: Index 2 (co-movement factor) is often more predictive and statistically significant across multiple survey measures than Index 1 (overall activity). This implies the MIMIC model (K = 1) can miss an important channel captured by additional factors.
- Weights on projected indicators (Table 6 — exact weights)
  - Estimated weights on projected indicators in the linear combination for the estimated degree of informality:
    - currency in circulation: -0.04
    - labor participation rate: -0.30
    - GDP per capita: -0.25
    - electricity consumption: 0.11
  - Interpretation: Negative weights for currency, labor participation, and GDP per capita indicate association with lower informality; electricity consumption has a positive weight; labor participation rate and GDP per capita have larger absolute weights.
- Country examples and decompositions (selected findings)
  - Three broad patterns across six illustrative countries (Figure 3):
    - Increasing informality over past two decades: Afghanistan, India.
    - Decreasing informality: China, Türkiye.
    - Strong cyclical behavior: Greece, Italy.
  - Decomposition by indices (Figure 4):
    - For Afghanistan, India, China, Türkiye, Index 2 (co-movement) is quantitatively more important.
    - For Greece and Italy, Index 2 drives cyclical movements.
  - Decomposition by projected indicators (Figure 5):
    - Afghanistan & India: labor participation rate is the leading indicator for rising informality; electricity consumption also contributes for Afghanistan; in India, rising GDP per capita signals decline but is insufficient to offset falling labor participation.
    - China & Türkiye: per capita GDP growth dominates (strong formal-sector growth indicates declining informality).
    - Greece: late 2000s rise in labor participation implied fall in informality; early 2010s declines in labor participation and official GDP growth imply rise in informality.
    - Italy: weak GDP growth and rising labor participation point in opposite directions and largely offset.
- Causes and cross-country patterns (Table 7 and Figures 6–7 — reported regression coefficients and significance)
  - Regressions of estimated informality on causes (country fixed effects; standard errors clustered at country level; Obs = 2,498 in reported specifications):
    - Column (1) government size: tax-GDP ratio = -1.75 (5.12); government consumption-GDP = 0.93 (2.58) — not statistically significant.
    - Column (2) development status: (log) PPP GDP per capita = -3.14*** (0.83); trade openness = -2.39*** (0.73); unemployment rate = 0.25*** (0.053).
    - Column (3) governance: rule of law = -2.11* (1.09); government effectiveness = -1.40* (0.75); regulatory quality = -1.26* (0.72); voice and accountability = 2.15** (0.83).
    - Column (4) all causes included: (log) PPP GDP per capita = -3.09*** (0.94); trade openness = -2.61*** (0.67); unemployment rate = 0.23*** (0.050); voice and accountability = 1.83** (0.73).
  - Interpretation:
    - Tax revenue and government consumption are not statistically significant determinants in these specifications.
    - Better formal-sector performance (higher PPP GDP per capita, greater trade openness, lower unemployment) reduces the degree of informality.
    - Governance matters: rule of law, regulatory quality and government effectiveness associated with lower informality; voice and accountability shows a positive association.
- Cross-country trends (subset of 104 countries with estimates 2002–2021: 21 AEs, 50 EMDEs, 33 LIDCs)
  - Median degree of informality declined between 2002 and 2013 but stalled after 2013; slowed decline during 2008–2010 Global Financial Crisis and a slight increase during the COVID-19 pandemic.
  - By group (Figure 6(b)): AEs and EMDEs show declining informality over the past two decades; LIDCs show an increase in informality.
  - Figure 7: for most LIDCs, the degree of informality is larger in 2021 compared to 2002.

### Appendix summaries and robustness (A–E)
- Appendix A. The MIMIC model
  - Structural equation: y∗t = α′xt + vt; Measurement equation: yt = β y∗t + ut.
  - Disturbance assumptions: E(vt u′t) = 0′, E(vt^2) = σ^2, E(utut′) = Θ^2 with Θ^2 diagonal.
  - Identifying restrictions: Π = β α′ has rank one; Ω = σ^2 β β′ + Θ^2.
  - Normalization typically assumes first indicator shares units with y∗.
  - Augmented factor model generalizes MIMIC by allowing multiple factors and nonlinear g(·), and not imposing structure on Θ^2.
- Appendix B. Estimation steps (concise)
  - Step 1: Transform indicators into growth rates.
  - Step 2: Regress indicators on causes; standardize fitted/projected indicators.
  - Step 3: PCA on projected indicators to estimate Λ and ĝ(xt).
  - Step 4: Construct cumulative indices ŝkt = ∑ ĝkt′.
  - Step 5: Regress survey data zt on indices with country fixed effects; predictions ẑt = β̂′ ŝt + ζ̂0 are estimated informality.
- Appendix C. Relationship between WBES and other survey data
  - Ohnsorge and Yu (2022) measures: SEMP (1990-2018), Infemp (2000-2018), Infsize (1999-2018), Pension (1990-2010 transformed).
  - Empirical finding: WBES-based degree of informality is only weakly correlated with labor-based measures (Figure 8).
  - Methodological note: the augmented factor approach fits the survey in use; alignment depends on chosen survey.
- Appendix D. Adding nighttime lights (harmonization and results)
  - Nighttime lights harmonized by dividing pre-2013 growth by 1.3 (Hu and Yao, 2022) and by 1.55 (Beyer, Hu, and Yao, 2022) to obtain a unified measure.
  - Principal component results with nighttime lights:
    - Optimal number of principal components remains two.
    - Second factor’s loading on nighttime light is almost zero.
    - Second factor remains more important in predicting degree of informality.
    - Estimated degree of informality with nighttime lights is well aligned with estimates without nighttime lights (Figure 10).
  - Table 8 reports Index 1 and Index 2 coefficients consistent with prior mappings; Index 2 shows strong negative and sometimes significant coefficients (e.g., -0.83***, -0.50*, -0.80***).
- Appendix E. Country groups
  - Table 9: list of 126 countries with full data and at least one WBES wave.
  - Table 10: list of 104 countries with full data between 2002 and 2021 and at least one WBES wave; countries organized by income group labels AEs, EMDEs, LIDC.
  - Note in source: # countries = 215033 (as listed in notes).

### VI. Conclusion (empirical summary)
- Methodological contribution:
  - The augmented factor model combines macro indicators, observable causes, and sparse survey data to estimate a mapped degree of informality for all countries and years.
- Key empirical findings:
  - Two factors (at least) are empirically relevant: one reflecting overall activity (currency/electricity) and one capturing co-movement of formal and informal activity (labor participation and GDP per capita).
  - The co-movement factor (Index 2) is often more predictive of survey-based informality measures than the overall-activity factor (Index 1), indicating limitations of K = 1 MIMIC approaches.
  - Development status (higher PPP GDP per capita, greater trade openness, lower unemployment) and certain governance measures (rule of law, regulatory quality, government effectiveness) are associated with lower estimated informality; voice and accountability shows a positive association in these specifications.
  - Over 2002–2021, informality declined for AEs and EMDEs but increased for LIDCs.

*Source: wpiea2024110-print-pdf - REFERENCES (IMF working paper content provided).*

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

### wpiea2024110-print-pdf - References .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .

### References and Appendices (inventory)
- References section listed with page number "28".
- Appendices listed with titles and page numbers:
  - A. The MIMIC Model — 31
  - B. Estimation of the Augmented Factor Model — 32
  - C. Relationship between WBES and Other Survey Data — 33
  - D. Adding Nighttime Lights — 33
  - E. Country Groups — 36

### List of Tables (enumeration)
- Table 1. Country and Year Coverage of the WBES — 14
- Table 2. Causes and Indicators of the Informal Economy — 16
- Table 3. Projection of Indicators on Causes — 18
- Table 4. Relationship between Estimated Factors and Indicators — 18
- Table 5. Survey Data and Estimated Factors — 20
- Table 6. Estimated Weights on Projected Indicators — 20
- Table 7. Estimated Informal Economy and Causes — 25
- Table 8. Survey Data and Estimated Factors with Nighttime Lights — 35
- Table 9. List of Countries with Causes, Indicators, and WBES Data — 36
- Table 10. List of Countries in Each Income Group — 37

### List of Figures (enumeration)
- Figure 1. Estimated Degree of Informality from the WBES — 15
- Figure 2. Projected Principal Component Analysis. — 19
- Figure 3. Degree of Informality: Selected Countries — 21
- Figure 4. Decomposition of the Degree of Informality by Contribution of Factors: Selected Countries — 22
- Figure 5. Decomposition of the Degree of Informality by Contribution of Indicators: Selected Countries — 23
- Figure 6. Median Degree of Informality — 26
- Figure 7. Degree of Informality: 2002 vs. 2021. — 26
- Figure 8. Degree of Informality in Survey Data: WBES vs. Labor Surveys — 34
- Figure 9. Projected Principal Component Analysis with Nighttime Light — 35
- Figure 10. Estimated Degree of Informality with and without Nighttime Light — 35

### Introduction — scope, approach, and key methodological points
- Problem statement:
  - The informal economy's size is often unfathomable and definitions vary widely.
  - Two broad existing approaches: (1) empirical micro-data estimates (limited by infrequent micro data), (2) statistical latent-variable models (sensitive to specification, calibration, and coverage).
- New approach developed:
  - Augmented factor model approach that marries direct survey measures and a statistical model, combining micro and macro data.
  - Builds on augmented factor models from Fan, Ke, and Liao (2021).
  - Two parts:
    - A factor model of indicators of the informal economy augmented by its observable causes.
    - A function mapping the estimated factors to direct survey measures.
  - Result: estimated degree of informality directly comparable to survey results and interpretable.
- Definition used:
  - Focus on World Bank Enterprise Surveys (WBES) questions about competition against unregistered or informal firms.
  - Definition follows OECD (2002): "productive activities conducted by unincorporated enterprises in the household sector that are unregistered and/or are less than a specified size in terms of employment, and that have some market production."
- Relation to MIMIC and prior literature:
  - MIMIC (multiple indicators multiple causes) has been leading statistical model since Frey and Weck-Hanneman (1984).
  - MIMIC recognized as superior to single-indicator approaches (currency-demand, electricity-consumption), but has limitations, particularly interpretability of the latent variable.
  - The augmented factor model generalizes MIMIC; shows MIMIC is a special case where the latent variable is the first principal component under strong assumptions.
  - Empirically, the first principal component is often not a useful predictor of survey-measured degree of informality.
- Advantages of the augmented factor model:
  - Projected principal component analysis clarifies channels linking indicators to causes.
  - Mapping into survey data removes need for fragile normalization and calibration required in MIMIC.
  - Allows decomposition of estimated degree of informality into contributions by factors and by projected indicators, increasing transparency.
- Data:
  - Uses WBES covering "146 countries" at infrequent intervals between "2006-2022".
  - Approach not limited to WBES; WBES chosen for wide country coverage and long time span.
  - Also considers other labor-related measures of informality as robustness checks.
- Broad empirical patterns from estimates:
  - Countries such as Afghanistan and India: informal economy increasing in past two decades; falling labor participation rate plays a dominant role.
  - Countries such as China and Türkiye: informal economy declining; strong growth of the formal economy is dominant indicator.
  - Countries such as Greece and Italy: informal economy displays cyclical behavior driven mostly by interplay between labor participation rate and GDP growth.
  - Indicators like currency in circulation and electricity consumption play a lesser role in indicating dynamics.
- Stylized findings on groups and trends:
  - Economic development status and governance matter for dynamics of the informal economy.
  - Size of the government plays a relatively minor role.
  - Heterogeneity is large across country groups.
  - Past two decades:
    - Advanced economies and emerging markets: degree of informality in overall economic activity steadily declining.
    - Low-income and developing countries: degree of informality experienced the opposite trend.

*Source: wpiea2024110-print-pdf - References .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . .*

### Section III, we introduce the augmented factor model approach. Section IV describes the

### Section III–V: Augmented factor model, Data, and Empirical Findings

### III. Measuring the informal economy: an augmented factor model approach
- Framework
  - Observed indicators y_t (P×1) relate to K latent factors f_t via y_t = Λ f_t + u_t.
  - Latent factors relate to observable causes x_t (Q×1) via f_t = g(x_t) + v_t, where g(x_t) = E(f_t | x_t).
  - The augmented factor model generalizes the MIMIC model: MIMIC is a special case with K = 1, linear g(·), and diagonal covariance of u_t.
  - Identification: Λ and g(x_t) can be identified up to an orthogonal rotation; estimation via projected principal component analysis (project indicators on causes, then PCA on fitted/projected indicators).
- Mapping factors to survey data (outline)
  - Step 1. Transform indicators y_t into growth rates (first difference in log levels).
  - Step 2. Regress {y_t} on {x_t} (include country fixed effects), obtain fitted/projected indicators {ŷ_t}, then standardize ŷ_t to mean zero and variance one.
  - Step 3. Obtain explained components ˆg_t via projected PCA: ˆg_t := ˆΛ′ ˆy_t, where ˆg_t = (ˆg_1t, …, ˆg_Kt)′.
  - Step 4. Construct level indices: for each factor k, ˆs_kt = ∑_{t′=1}^t ˆg_kt′.
  - Step 5. Map indices to survey-based informality z_t by panel regression z_t = β′ ˆs_t + ζ_0 + ε_t; predicted ˆz_t = ˆβ′ ˆs_t + ˆζ_0 provides estimated degree of informality for all countries and times.
- Advantages vs. MIMIC
  - Allows K > 1 factors and nonlinear g(·), relaxing MIMIC’s strong assumptions.
  - Mapping to survey data makes estimates robust to choices of causes/indicators because indices act as predictors disciplined by survey observations.
  - Improved transparency: decomposition by indices and by projected indicators is straightforward (equation (6): ˆz_t = (ˆβ′ ˆΛ′) ˆy^c_t + ˆζ_0, where y^c_pt is cumulative projected indicator p).

### IV. Data and stylized facts
- Survey data (WBES)
  - World Bank Enterprise Surveys (WBES) used to map indices to survey measures; focus on firm perspective.
  - Two WBES questions used:
    - Does this establishment compete against unregistered or informal firms?
    - Number of permanent, full-time employees at the end of last fiscal year.
  - Degree of informality defined as the adjusted measure: fraction of workers in registered firms that compete with unregistered firms (adjusted by firm size).
  - Coverage: WBES covers 154 countries between 2006-2022; about two thirds of countries have at least two waves.
  - Table 1 summary (from source):
    - coverage by year: e.g., 2006: 27 countries; 2007: 12; …; 2022: 4 (as presented in the source table).
    - coverage by country: At least 1 survey: 154; At least 2 surveys: 101; At least 3 surveys: 50; 4 surveys: 2.
- Other survey measures
  - Labor-based informality measures from Ohnsorge and Yu (2022): share of self employment (SEMP), share informal employment (Infemp), share employment outside formal sector (Infsize), share not contributing to pension (Pension).
  - These measures have limited coverage and tend to have low correlations with WBES-based degree of informality.
- Causes and indicators (Table 2 variables; data sources)
  - Causes (examples): PPP GDP per capita, unemployment rate (World Development Indicators); governance measures (Worldwide Governance Indicators); trade openness, tax-to-GDP, government consumption-to-GDP (WEO).
  - Indicators (examples): PPP GDP per capita, currency in circulation (IFS), labor participation rate (aged 15–64), electricity consumption (WDI), nighttime lights (Beyer, Hu, and Yao (2022); Hu and Yao (2022)).
  - Panel: 154 countries spanning 1996–2021 for causes/indicators; governance available biannually before 2002 implies panel covers 1996, 1998, 2000, 2002, and each year after.
  - 126 countries have all causes/indicators and at least one WBES wave (listed in Appendix E in source).

### V. Unveiling the informal economy — empirical results
- Projected principal component analysis (PPCA)
  - Variables transformed into growth rates (first difference in log levels); indicators projected on causes (country fixed effects included) to form projected indicators; PCA applied to projected indicators.
  - Table 3 (selected projection results; standard errors clustered at country level):
    - Trade openness positive and significant for all four projected indicators: currency in circulation (0.057**), labor participation rate (0.0057***), GDP per capita (0.048***), electricity consumption (0.023*).
    - (log) PPP GDP per capita negative and significant for currency (-0.10***) and electricity (-0.028***); muted for labor participation (0.0035) and GDP per capita (-0.023**).
    - Unemployment rate negative and significant for labor participation (-0.065***), GDP per capita (-0.18***), electricity (-0.18***).
    - Government effectiveness: negative and significant for currency (-0.057**) and positive for labor participation (0.0046**).
    - Observations: 2,985 for each regression; Adjusted R^2s: currency 0.04; labor participation 0.05; GDP per capita 0.15; electricity 0.10.
  - PPCA results (Figure 2 and Table 4):
    - At least two factors recommended: first two eigenvalues > 1; first two principal components explain about 67% of variance of projected indicators.
    - Factor 1 loadings/high correlations: currency in circulation growth and electricity consumption growth (Factor 1 correlations with indicators: currency 0.78; labor -0.47; GDP per capita 0.57; electricity 0.67).
    - Factor 2 loadings/high correlations: labor participation rate growth and GDP per capita growth (Factor 2 correlations with indicators: currency 0.16; labor 0.74; GDP per capita 0.68; electricity -0.25).
    - Interpretation: Factor 1 reflects overall physical/economic activity (currency/electricity); Factor 2 captures co-movement of formal and informal activity.
- Mapping indices to survey data (Table 5 results)
  - Two indices constructed as cumulative sums of Factor 1 and Factor 2.
  - Regressions of survey measures on indices (standard errors clustered by country):
    - Dependent variables: WBES (adjusted degree), WBES (unadjusted), SEMP, Pension, Infemp, Infsize.
    - Coefficients (Index 1, Index 2) with standard errors:
      - Column (1) WBES: Index 1 = 0.097 (0.47); Index 2 = -0.85*** (0.30); Obs = 209; Adjusted R^2 = 0.16.
      - Column (2) WBES (unadjusted): Index 1 = 0.092 (0.41); Index 2 = -0.51* (0.27); Obs = 209; Adjusted R^2 = 0.18.
      - Column (3) SEMP: Index 1 = -0.017 (0.047); Index 2 = -0.11** (0.056); Obs = 150; Adjusted R^2 = 0.96.
      - Column (4) Pension: Index 1 = 0.13 (0.33); Index 2 = -0.23 (0.56); Obs = 80; Adjusted R^2 = 0.93.
      - Column (5) Infemp: Index 1 = -0.24 (0.21); Index 2 = -0.42 (0.29); Obs = 153; Adjusted R^2 = 0.94.
      - Column (6) Infsize: Index 1 = -0.094 (0.29); Index 2 = -0.80*** (0.29); Obs = 300; Adjusted R^2 = 0.92.
  - Key insight: Index 2 (co-movement factor) is often more predictive and statistically significant across multiple survey measures than Index 1 (overall activity). This implies the MIMIC model (K = 1) can miss an important channel captured by additional factors.
- Weights on projected indicators (Table 6)
  - Estimated weights on projected indicators in the linear combination for the estimated degree of informality:
    - currency in circulation: -0.04
    - labor participation rate: -0.30
    - GDP per capita: -0.25
    - electricity consumption: 0.11
  - Interpretation: Higher currency in circulation, labor participation, and GDP per capita associate with lower informality (negative weights), while stronger electricity consumption associates with higher informality (positive weight); labor participation rate and GDP per capita have larger absolute weights.
- Country examples and decompositions
  - Six illustrative countries show three broad patterns (Figure 3):
    - Increasing informality over past two decades: Afghanistan, India.
    - Decreasing informality: China, Türkiye.
    - Strong cyclical behavior: Greece, Italy.
  - Decomposition by indices (Figure 4):
    - For Afghanistan, India, China, Türkiye, Index 2 (co-movement) is quantitatively more important.
    - For Greece and Italy, Index 2 drives cyclical movements.
  - Decomposition by projected indicators (Figure 5; indicator contributions computed using cumulative standardized projected indicators and Table 6 weights):
    - Afghanistan & India: labor participation rate is the leading indicator for rising informality; electricity consumption also contributes for Afghanistan; in India, rising GDP per capita signals decline but is insufficient to offset falling labor participation.
    - China & Türkiye: per capita GDP growth dominates (strong formal-sector growth indicates declining informality).
    - Greece: late 2000s rise in labor participation implied fall in informality; early 2010s declines in labor participation and official GDP growth imply rise in informality.
    - Italy: weak GDP growth and rising labor participation point in opposite directions and largely offset.

- Causes and cross-country patterns (Table 7 and Figures 6–7)
  - Regressions of the estimated degree of informality on causes (country fixed effects; standard errors clustered at country level; Obs = 2,498 in reported specifications; Adjusted R^2s high by construction):
    - Column (1) government size: tax-GDP ratio coefficient = -1.75 (5.12); government consumption-GDP = 0.93 (2.58) — not statistically significant.
    - Column (2) development status: (log) PPP GDP per capita = -3.14*** (0.83); trade openness = -2.39*** (0.73); unemployment rate = 0.25*** (0.053).
    - Column (3) governance: rule of law = -2.11* (1.09); government effectiveness = -1.40* (0.75); regulatory quality = -1.26* (0.72); voice and accountability = 2.15** (0.83).
    - Column (4) all causes included: (log) PPP GDP per capita = -3.09*** (0.94); trade openness = -2.61*** (0.67); unemployment rate = 0.23*** (0.050); voice and accountability = 1.83** (0.73); several governance measures retain significance or sign as in column (3).
  - Interpretation:
    - Tax revenue and government consumption are not statistically significant determinants of the degree of informality in these specifications—distinguishing “unregistered productive activity” from purely tax-evasion underground activity is important.
    - Better formal-sector performance (higher GDP per capita, higher trade openness, lower unemployment) reduces the degree of informality.
    - Governance matters: rule of law, regulatory quality and government effectiveness are associated with lower informality; voice and accountability shows a positive association with informality in these regressions.
  - Cross-country trends (subset of 104 countries with estimates 2002–2021: 21 AEs, 50 EMDEs, 33 LIDCs):
    - Median degree of informality declined between 2002 and 2013 but stalled after 2013; slowed decline during 2008–2010 Global Financial Crisis and a slight increase during the COVID-19 pandemic.
    - By group (Figure 6(b)): AEs and EMDEs show declining informality over the past two decades; LIDCs show an increase in informality.
    - Figure 7 contrasts 2002 vs. 2021: for most LIDCs, the degree of informality is larger in 2021 compared to 2002, diverging from some previous MIMIC-based studies.

### VI. Conclusion (empirical summary)
- The augmented factor model combines macro indicators, observable causes, and sparse survey data to estimate a mapped degree of informality for all countries and years.
- Key empirical findings:
  - Two factors (at least) are empirically relevant: one reflecting overall activity (currency/electricity) and one capturing co-movement of formal and informal activity (labor participation and GDP per capita).
  - The co-movement factor (Index 2) is often more predictive of survey-based informality measures than the overall-activity factor (Index 1), indicating limitations of K = 1 MIMIC approaches.
  - Development status (higher PPP GDP per capita, greater trade openness, lower unemployment) and certain governance measures (rule of law, regulatory quality, government effectiveness) are associated with lower estimated informality; voice and accountability shows a positive association in these specifications.
  - Over 2002–2021, informality declined for AEs and EMDEs but increased for LIDCs.

*Source: IMF staff analysis — Sections III–V from the provided IMF working paper content.*

### REFERENCES

### wpiea2024110-print-pdf - REFERENCES

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### Appendix A. The MIMIC model
- Purpose: prevailing modeling approach to estimate the size of the informal economy by linking multiple observable indicators to multiple observable causes through a latent variable y∗t (scalar latent index).
- Structural equation: y∗t = α′xt + vt, where vt is a scalar structural disturbance.
- Measurement equation: yt = β y∗t + ut, where yt = (y1t, …, yPt)′.
- Disturbance assumptions:
  - E(vt u′t) = 0′, E(vt^2) = σ^2, E(utut′) = Θ^2, where Θ^2 is diagonal.
- Reduced-form: yt = β α′ xt + (β vt + ut).
- Two identifying restrictions in reduced form:
  - Π = β α′ has rank one.
  - Ω = σ^2 β β′ + Θ^2 (covariance structure: sum of rank-one and diagonal).
- Normalization: typically assume first indicator shares units with y∗, i.e., y1t = y∗t + v1t.
- Estimation: maximum-likelihood estimation (see Jöreskog and Goldberger (1975)).
- Comparison: augmented factor model generalizes to multiple factors, allows nonlinear relationship between factors and causes, and does not impose structure on Θ^2.

### Appendix B. Estimation of the augmented factor model
- Step 1: Transform all indicators yt into growth rates (first difference of log levels).
- Step 2: Regress {yt} on {xt} and obtain fitted values {ŷt} = estimator of E(yt | xt). {xt} include country fixed effects. Standardize {ŷt} to mean zero and variance one; denote standardized projected indicators still by {ŷt}.
- Step 3: Estimate factor loadings Λ and explained components g(xt) via principal component analysis of {ŷt}.
  - Let Σy|x = E(E(yt | xt) E(yt | xt)′); estimate by Ŝ Σy|x = (1/T) ∑t (ŷt ŷt′).
  - Columns of Λ̂ are eigenvectors of the first K eigenvalues of Σ̂y|x, ranked high to low.
  - ĝ(xt) = Λ̂′ ŷt.
- Step 4: Construct indices as cumulative sums of explained components:
  - ŝkt = ∑t′=1^t ĝkt′, for k = 1,...,K, where ĝkt = ĝk(xt).
- Step 5: Regress survey data {zt} on indices including country fixed effects:
  - zt = β′ ŝt + ζ0 + εt, where ζ0 is country-specific intercept.
  - Predictions ẑt = β̂′ ŝt + ζ̂0 are the estimates of the size of the informal economy.
- Note: country subscript i omitted for notation ease; when computing Σ̂y|x averages are taken over countries and time.

### Appendix C. Relationship between WBES and other survey data
- Data source: Ohnsorge and Yu (2022) database based on labor force surveys with four measures:
  - SEMP: share of unemployment in total employment (1990-2018).
  - Infemp: informal employment (2000-2018).
  - Infsize: employment outside the formal sector (1999-2018).
  - Pension: share of labor force that does not contribute to a retirement pension (transformed from original measure for 1990-2010 to be increasing in informality).
- Empirical finding: scatter plots (Figure 8) show the degree of informality from WBES is only weakly correlated with these labor-related measures, suggesting different concepts of the informal economy.
- Methodological note: the augmented factor approach is designed to fit the data, so estimated degree of informality will be closely aligned with the survey data in use.

### Appendix D. Adding nighttime lights
- Motivation: satellite-recorded nighttime lights used as alternative indicator of economic activity.
- Data sources: Hu and Yao (2022), and Beyer, Hu, and Yao (2022).
- Harmonization: because nighttime light data are from different satellite systems before and after 2013, unify by dividing nighttime light growth by 1.3 (Hu and Yao, 2022) before 2013 and by 1.55 (Beyer, Hu, and Yao, 2022) to obtain a unified measure.
- Principal component results with nighttime lights:
  - Optimal number of principal components remains two.
  - Second factor’s loading on nighttime light is almost zero.
  - Second factor is more important in predicting degree of informality (see Table 8).
  - Estimated degree of informality with nighttime lights is well aligned with estimates without nighttime lights (Figure 10).
- Table 8 (selected reported results):
  - Index 1 (cum. sum of Factor 1): values reported include 0.066, 0.077, -0.023, 0.12, -0.260, 0.062 with standard errors in parentheses (0.46)(0.41)(0.045)(0.35)(0.21)(0.32).
  - Index 2 (cum. sum of Factor 2): values reported include -0.83***, -0.50*, -0.12**, -0.28, -0.40, -0.80*** with standard errors (0.30)(0.28)(0.056)(0.57)(0.28)(0.29).
  - Obs: 209, 209, 150, 8150, 13300 (as listed).
  - Adjusted R^2: 0.16, 0.18, 0.96, 0.93, 0.94, 0.92.
  - Notes: WBES = degree of informality adjusted by firm size; WBES (unadjusted) = fraction of firms claiming competition with unregistered firms; SEMP, Pension, Infemp, Infsize from Ohnsorge and Yu (2022). Standard errors clustered at country level. ∗p<0.10, ∗p<0.05, ∗∗∗p<0.01.

### Appendix E. Country groups
- Table 9: list of 126 countries for which all cause and indicator variables are available and there is at least one wave of WBES. (ISO codes excerpt shown in source.)
- Table 10: list of 104 countries for which all cause and indicator variables are available between 2002 and 2021 and there is at least one wave of WBES; countries organized by income group labels: AEs, EMDEs, LIDC.
  - # countries = 215033 (as listed in notes).
- Notes: Tables present country ISO codes and grouping into AEs = advanced economies; EMDEs = emerging markets and developing economies; LIDC = low income and developing countries.

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