## PREFACE ## Source details **Canonical URL:** [PREFACE](https://www.imf.org/-/media/files/publications/tar/2025/english/tarea2025107-source-pdf.pdf) ## Other formats - [Markdown version](/-/media/files/publications/tar/2025/english/tarea2025107-source-pdf.pdf.md) - [Structured JSON version](/-/media/files/publications/tar/2025/english/tarea2025107-source-pdf.pdf.json) --- ### Preface - Mission executed in Nyköping, Sweden during the period January 6 – January 17, 2025. - Mission team: Mr. Soren Pedersen (FAD) and Mr. Tobias Gabel Christiansen (FAD short-term expert). - Mission financed by the European Union under the EC DG REFORM Program. - Purpose: assist Skatteverket to estimate the corporate income tax (CIT) gap using bottom-up techniques based on operational audits for income years 2016-2023. - Data: CIT returns, audit results, and background business information (sector codes, number of employees) prepared by Skatteverket and analyzed at Skatteverket premises. - Total audited tax returns used in analysis: 6,040 (original yearly audits by income year: 519, 1,406, 950, 735, 770, 739, 556, 365 respectively). - Draft report submitted to Mr. Damián Migueles Chazarreta and Mr. Hannes Jägerstedt on February 1, 2025. ### Executive Summary — main estimates and comparisons - Average yearly CIT gap across income years 2016-2023: - 4.9 billion SEK - 2.2 percent of potential CIT liability - Corresponds to 0.1 percent of average GDP across 2016-2023 - Yearly range for CIT gap across 2016-2023: between 1.8 and 2.6 percent of potential CIT liability. - Yearly CIT gap for 2023 in absolute terms: 6.0 billion SEK. - Historical yearly CIT gap estimates (2016-2022): 5.7 billion SEK, 5.2 billion SEK, 4.7 billion SEK, 4.9 billion SEK, 4.9 billion SEK, 4.2 billion SEK, and 3.8 billion SEK. - When all corrections from audits of company records are included (CIT gap + other corrections): - 72.5 billion SEK - 25.8 percent of potential CIT - Includes adjustments such as Personal Income Tax (PIT) of the company’s main shareholder (example: undeclared use of company car taxed as personal income). - Comparison with Skatteverket's random-audit based estimate for same period: 1.3 percent of potential CIT liability. - Difference explained by Skatteverket excluding businesses with turnover below 100,000 SEK from random audits and assuming their compliance equals audited businesses; operational-audit estimates include them directly. - Businesses with turnover less than 100,000 SEK account for approximately 90 percent of the CIT tax gap identified in this mission based on operational audits. ### Recommendations (summary with timelines where provided) - Adopt the demonstrated bottom-up methodology and continue to carry out the CIT gap estimation in coming years. - Target: January 2026 - Generate an SSC (Social Security Contributions) estimate based on provided methods and existing data regarding the PIT gap derived from CIT estimates. - Target: June 2025 - Assess existing risk indicators by integrating them with random audits to determine if identified high-risk factors yield higher hit rates and tax corrections. - Target: June 2025 - Produce a risk scoring model from the random audit program and test it within operational audit programs to build an evidence-based risk model. - Target: June 2025 - Include a more comprehensive tax gap estimate for businesses with turnover less than 100,000 SEK in published tax gap estimates, since they account for approximately 90 percent of the total tax gap. - Target: Next publication of tax gap in Sweden - Gain a better understanding of factors driving the tax gap among businesses with less than 100,000 SEK turnover because audits alone are not feasible given slightly over 166,000 such businesses. - Target: June 2026 - Operational recommendation: Skatteverket analysts can perform the analysis using provided R code and documentation; alternatively request IMF CD workshop for assisted self-assessment training. ### Introduction — scope and approach - Objective: estimate the Corporate Income Tax (CIT) gap using operational (risk-based) audits and correct for sample selection bias inherent in operational audits. - Operational audits likely over-represent higher-risk firms; random audits provide unbiased estimates but Skatteverket has moved away from random audits among SMEs. - Two modeling approaches applied: - Heckman two-step sample selection bias correction. - Machine Learning (ML) control-function approach with Random Forest algorithm following Brewer and Carlson (2024). ### Methodology and modeling details - Heckman two-step: - First stage: probit model estimating probability of audit selection using risk indicators. - LASSO used to select 38 risk indicators for the selection equation from the 500-600 available risk indicators. - Second stage: model of audit outcome using 48 variables (tax lines and risk indicators) selected by LASSO, including a regressor accounting for selection (inverse Mills ratio). - Result: IMR positive but statistically insignificant — suggests limited unobserved sample selection bias. - ML model: - Random Forest algorithm employed to predict level of non-compliance. - Input: 500-600 risk indicators and around 200 tax return lines and company characteristics. - Hyperparameters tuned using 5-fold cross-validation with grid-search to maximize R-squared on training data. - Control-function approach used to remove selection bias before training ML model (following Brewer and Carlson (2024)). - Considerations and limitations: - Audit focus narrowness can cause underestimation of CIT gap if audits miss undisclosed taxes. - Targeting specific sectors/types increases extrapolation and uncertainty when estimating population-wide gap. - Some noncompliance may be undetectable by audits (e.g., “payments under the table”), potentially leading to underestimation. ### Key Findings — detailed points - CIT gap estimation results (2016-2023): - Average yearly CIT gap: 4.9 billion SEK; 2.2 percent of potential CIT liability. - CIT gap corresponds to 0.1 percent of average GDP across 2016-2023. - Yearly range: 1.8 to 2.6 percent of potential CIT liability. - 2023 CIT gap: 6.0 billion SEK. - CIT gap + other corrections: 72.5 billion SEK; 25.8 percent of potential CIT. - Sample and trimming: - Total audited returns used: 6,040 (risk-based audits completed by mission start). - Annual audit results trimmed by removing top and bottom 1 percent for each year to avoid outsized influence from a few audits. - Selection indicators and modeling: - Audit selection modeled using 38 LASSO-selected risk indicators. - Tax correction modeled using 48 LASSO-selected variables. - Several variables selected as important for selection but not for correction — these act effectively as instruments (recommend consulting auditors to validate). - Practical implications: - Skatteverket’s published tax gap estimates should be revised to incorporate the substantial contribution from businesses with turnover below 100,000 SEK. - Audits alone are not feasible to address non-compliance among the roughly 166,000 businesses with turnover less than 100,000 SEK — alternative approaches and cross-administration learning (e.g., Danish Tax Administration) recommended. ### Next steps (operational) - Set up a team of data analysts and apply the developed model using provided R scripts and documentation. - Continue annual CIT gap estimates using bottom-up methodology. - Develop SSC estimate by adapting R scripts and methods used to derive PIT adjustments from CIT audit data. - Integrate risk indicators with random audits to validate and refine risk scoring and produce an evidence-based risk model. - Study drivers of non-compliance among micro businesses (turnover < 100,000 SEK) and consider a study visit to the Danish Tax Administration for experience-sharing. ### Data and methodology - Period covered: 2016-2023 (total of 8 years). - Number of operational audits used to estimate the Heckman model: 6,040 audits. - Adjustments made to Heckman results: - Addressed non-random selection of operational audits (sample selection bias). - One percent of audit results were trimmed in top and bottom for each year to reduce noise. - Machine learning (ML) model: - Requested by Skatteverket during the needs assessment mission in February 2024 and during mission preparation. - ML estimate is presented alongside the Heckman two-step approach for comparison. - Note on pooled model: - The Heckman model was developed using pooled data across years; annual fluctuations primarily reflect changes in economic structure of corporations. ### Key quantitative findings - CIT gap estimates (Heckman vs ML): - Heckman: 4.9 billion SEK (CIT gap alone reported in Table 1: Total = 4.9 billion SEK; 2.2 percent of CIT liability). - ML: 5.3 billion SEK (equivalent to 2.3 percent of CIT liability). - Text: "The CIT gap based on ML is estimated to be 5.3 billion SEK which is very close to the 4.9 billion SEK based on the Heckman approach." - Year-by-year similarity across 2016-2023 except for 2016 (difference likely driven by noise due to a low number of audits). - Comprehensive audit corrections: - When all corrections from audits of company records are included: 72.5 billion SEK, equivalent to 25.8 percent of potential CIT (Table 1). - Skatteverket’s random-audit based estimate: 1.3 percent of potential CIT (for comparison; note methodological differences). - 2023 specific estimate: - Estimated CIT gap in 2023: 6.0 billion SEK (measured in 2016-prices). - Equivalent to 2.6 percent of potential CIT liability. - Corresponds to 0.1 percent of GDP in 2023. - Table 1 excerpts (CIT gap alone; CIT gap + other corrections — billion SEK and percent of CIT liability): - Total (CIT gap alone): 4.9 billion SEK; 2.2 percent of CIT liability. - Total (CIT gap + other corrections): 72.5 billion SEK; 25.8 percent of CIT liability. - Notes on measurement: - The denominator in the 25.8 percent calculation only includes CIT; relevant PIT ideally also included but difficult to define. ### Sectoral and firm-size patterns - Sectoral (average 2016-2023): - Highest relative CIT gap: "Accommodation and food service". - Second-highest relative CIT gap: "Manufacturing". - Negative average gap: "Agriculture, forestry and fishing" (average over 2016-2023), explained by audit data limitations (undeclared salaries paid to employees not captured in PIT adjustments). - By number of employees (average 2016-2023): - Corporations with 0 employees: 10.3 percent of potential tax. - Corporations with 1-9 employees: -1.4 percent. - Corporations with 10-19 employees: 0.7 percent. - Corporations with 20-49 employees: 0.7 percent. - Corporations with 50-249 employees: 0.3 percent. - Relative CIT gap declines as number of employees increases. - By turnover (average 2016-2023): - Corporations with turnover < 100,000 SEK: relative CIT gap = 15.3 percent of potential tax (approx. USD 8,950). - Corporations with turnover > 10 million SEK: relative CIT gap = 0.5 percent (approx. USD 895,000). - Absolute CIT gap in corporations with turnover under 100,000 SEK: 4.4 billion SEK (about 90 percent of the total tax gap). - Implication: Non-compliance is heavily concentrated among numerous very small businesses, making audits an ineffective sole remedy. ### Comparisons and interpretation - Differences with Skatteverket random audits: - Skatteverket’s random audits initially relied solely on company accounting records without access to control materials such as bank information; deeper inspections followed only if initial checks revealed deficiencies. - The Heckman-based estimate includes audits of SMEs with fewer than 250 employees and includes smallest companies; Skatteverket’s published random-audit estimate excludes businesses with turnover less than 100,000 SEK and assumes their compliance equals those above 100,000 SEK. - Evidence from the Danish Tax Agency indicates small companies without employees account for about 60 percent of the tax gap; this supports inclusion of smallest firms in gap estimates and explains higher Heckman-based gap relative to Skatteverket’s random-audit estimate. - Audit data limitations can produce misleading sectoral results (example: negative gap in Agriculture, forestry and fishing) when certain tax effects (e.g., employees’ PIT increases) are not captured in audit records. ### Policy recommendations and next steps A. Set up a Team of Data Analysts and Apply the Developed Model - Appoint 2-3 data analysts responsible for compiling future tax gap estimations based on operational audits. - Train at least 2-3 individuals in the developed models to sustain CIT gap analysis capacity. - Allocate significant analyst time to perform good data analytics; analysts attached to the project have requisite familiarity with data analytics and econometrics. B. Other recommendations - Adopt the methodology and continue CIT gap estimation annually: - Analysts who participated in the mission can use provided R code with detailed instructions (see Annex IV) to perform analysis. - Alternatively, Skatteverket can seek IMF CD for a workshop to train more analysts in assisted self-assessment of the CIT gap. - Generate an estimate for Social Security Contributions (SSC): - Use provided methods and existing data on the Personal Income Tax (PIT) gap derived from CIT estimates. - Modify supplied R scripts and instructions to assess the SSC gap. - Produce and test a risk scoring model: - Use random audit program to create a genuine evidence-based risk model and test it within operational audit programs. - Integrate and assess existing risk indicators: - Combine existing risk indicators with random audit results to determine whether factors labeled high-risk yield high hit rates. - Include small businesses in published tax gap estimates: - Include a more comprehensive estimate for corporate businesses with turnover < 100,000 SEK (findings show these businesses account for approximately 90 percent of the total tax gap). - Study drivers of non-compliance among very small businesses: - Deepen understanding whether non-compliance is due to deliberate evasion, lack of knowledge, or complicated legislation. - Audits are infeasible for the >166,000 corporations with turnover < 100,000 SEK; explore alternative approaches. - Undertake study visit to Danish Tax Administration (DTA): - DTA faces similar challenges and could provide lessons on combating non-compliance among very small businesses. ### Annex I. Supplementary Material — Sample selection bias and the Heckman 2-step estimator - Problem statement: - Tax gap estimates from non-random risk-based audits are prone to sample selection bias because audited companies are selected based on perceived risk of non-compliance and are not representative of the general population. - Heckman 2-step estimator formulation: - Outcome equation: - Y_i = X_i β + u_i - Selection equation: - S_i = 1[Z_i δ + v_i > 0] - Assumptions: - v_i ~ N(0,1) - E(u_i | v_i) = γ v_i - Conditional expectation for observed audits: - E[Y_i | X_i, S_i = 1] = X_i β + γ · γ(Z_i δ) where γ(·) = φ(·)/Φ(·) (inverse Mills ratio) - Estimation approach: - Estimate δ from the probit selection equation, compute the inverse Mills ratio, and then regress Y_i on X_i and the inverse Mills ratio using OLS (Heckman 2-step). - Note: Standard errors are wrong when manually estimating the 2-step Heckman estimator; correct standard errors can be obtained using bootstrap. ### Annex I — Identification issues and best practices - Key identification concerns: - Avoid using the same variables in both selection and outcome models: using identical regressors makes identification rely solely on the non-linearity of the inverse Mills ratio, increasing multicollinearity and instability. - The selection model should include at least one exclusion restriction—variable(s) that affect audit selection but do not affect the level of non-compliance. - Finding valid exclusion restrictions is challenging if audits are based solely on estimated non-compliance; consultation with auditors to validate candidate instruments is recommended. - Practical note: - When the Heckman 2-step is used for prediction (rather than causal inference), accuracy depends on how well both the selection and outcome models explain the data. ### Annex I — Empirical implementation and diagnostics (CIT returns and operational audits, 2016–2023) - Data and modelling choices: - Selection model estimated using a probit with 38 risk indicators (derived from an L1-regularized probit model applied to Skatteverket’s risk indicators). - Outcome model uses 12 variables selected from a LASSO model, plus PIT risk scores and PIT risk rankings (see note: a total of 12 variables are used). - Due to hardware limitations, population downsampled to 5% for fitting; final CIT gap for full population obtained by rescaling estimates. - 1% of audit results were trimmed in top and bottom for each year (in 2016-prices). - Standard errors are computed using bootstrap. - Fit and diagnostic statistics (exact reported values): - Number of observations: - Selection model: 282,156 - Outcome model: 5,990 - R² values: - Selection model (McFadden’s Pseudo R²): 0.22 - Outcome model R²: 0.09 - Interpretation: - The selection model’s R² of 0.22 indicates it fits audit selection reasonably well but a low R² suggests substantial unexplained variation—tax authorities may use additional criteria or unobservable signals. - The outcome model’s R² of 0.09 indicates a large share of variation in non-compliance remains unexplained—a common challenge in tax evasion models due to firm-specific strategies and unobserved factors. - Inverse Mills ratio (IMR): - The coefficient on the IMR (IMR in Table A2) is reported as insignificant, indicating limited sample selection bias in this application. ### Annex I — Machine learning robustness check (Brewer and Carlson approach; Random Forest) - Implementation details: - Selection model: identical L1-regularized probit model used to compute IMR. - IMR used to partial out sample selection bias from outcome variables and covariates. - Outcome model f̂(·) modeled using Random Forest (Breiman, 2001). - Features used: a total of 500-600 risk indicators and around 200 tax lines and company characteristics. - Tuning and training: - Random Forest tuned using 5-fold cross-validation with small forests of 100 trees (for computational efficiency). - Tuned parameters: mtry (number of variables to consider at each split), min.node.size (minimum number of data points in a terminal leaf). - Final model: a large forest consisting of 1000 trees fitted with optimal parameters. - Loss function: Root-Mean-Squared-Error (RMSE) minimization used in the outcome stage. - Performance and comparison: - Random Forest obtained an R² of 0.18, providing a better fit than the Heckman outcome model (R² = 0.09). - Despite the difference in fit, the CIT gap estimated using both approaches are nearly identical, corroborating robustness of results. - Variable importance: - Figure A1 reports the 10 most important variables (importance measured by "Gain" normalized to the most important variable). ### Annex I — Empirical example: audit leading to a negative gap (Skatteverket) - Narrative summary: - An auditor found both increases and decreases across PIT and CIT bases because of deductions in company records that were treated as wages to the owner, undeclared income, social security contributions, private use of company car, a loan reclassified as dividends for the shareholder/owner, and a false credited invoice. - Skatteverket enforces taxation on PIT but does not record the PIT impact of the audit in CIT. As a result, total tax gap recorded from the audit appears negative even though the full-picture tax effect would be positive if both PIT and CIT impacts were combined. - Itemized audit effects (exact numbers preserved; columns: Item — PIT base — CIT base — PIT effect — CIT effect): - 1. Private insurance - PIT base: 446 - CIT base: -586 - PIT effect: 194 - CIT effect: -129 - 2. Undeclared income - PIT base: 20 625 - CIT base: 16 500 - PIT effect: 8 959 - CIT effect: 3 630 - 2. SSC on undeclared income - PIT base: -27 105 - CIT base: 0 - PIT effect: -5 963 - CIT effect: (blank/0) - 3. Use of company car - PIT base: 12 891 - CIT base: -2 165 - PIT effect: 5 599 - CIT effect: -476 - 4. Forbidden loan - PIT base: 124 188 - CIT base: -163 207 - PIT effect: 53 943 - CIT effect: -35 904 - 5. Credited invoice - PIT base: (blank) 100 000 (CIT base: 0) - PIT effect: (blank) 21 999 - CIT effect: (blank) - Totals (as reported): - PIT base total: 158 150 - CIT base total: -76 563 - PIT effect total: 68 695 - CIT effect total: -16 843 - Clarifying note: - “Forbidden loan” is forbidden in the sense that it should be shown as dividends, not as a loan; it is not forbidden in the sense of being illegal. ### Annex III (summary) — Measuring and combatting the shadow economy - Definitions and framing: - No standardized definition of the “shadow economy”; OECD definition cited: “Economic activities, whether legal or illegal, which are required by law to be fully reported to the tax administration, but which are not reported, and which therefore go untaxed unlike activities which are so reported.” - IMF multi-pronged approach: - Coordinate revenue administration, tax policy, and statistics components to take a holistic, whole-of-government approach (revenue, social security, labor law enforcement). - Operational tools adopted by countries include dedicated shadow economy coordination units, behavioral economics for citizen engagement, and cross-agency working groups. - RA-GAP and capacity development: - RA-GAP provides capacity development for top-down and bottom-up techniques to estimate potential vs. actual revenues. - Tools include a Value Added Tax Gap model with online training and Corporate Income Tax gap estimation using econometric and machine learning techniques. - Gap estimates inform Compliance Improvement Plans (CIPs) within a Compliance Risk Management (CRM) framework and can improve tax audit case selection. - Tax policy and statistics perspectives: - Tax policy analysis examines features that sustain the shadow economy: high burdens, complex or frequently changing rules, multiple preferential treatments, piecemeal approaches to self-employment taxation, optional business regimes. - National accounts/statistics approach seeks to improve coverage of the non-observed economy (use labor input methods to estimate undeclared workers; administrative and non-statistical sources to estimate illegal activities; use tax audits to estimate under-reporting). - Cooperation between revenue and statistical agencies is critical; IMF capacity development fosters such cooperation. *Source: IMF calculations based on data from Skatteverket.* ### PREFACE _________________________________________________________________________________________ 5 ### tarea2025107-source-pdf - PREFACE ### Preface - Mission executed in Nyköping, Sweden during the period January 6 – January 17, 2025. - Mission team: Mr. Soren Pedersen (FAD) and Mr. Tobias Gabel Christiansen (FAD short-term expert). - Mission financed by the European Union under the EC DG REFORM Program. - Purpose: assist Skatteverket to estimate the corporate income tax (CIT) gap using bottom-up techniques based on operational audits for income years 2016-2023. - Data: CIT returns, audit results, and background business information (sector codes, number of employees) prepared by Skatteverket and analyzed at Skatteverket premises. - Total audited tax returns used in analysis: 6,040 (original yearly audits by income year: 519, 1,406, 950, 735, 770, 739, 556, 365 respectively). - Draft report submitted to Mr. Damián Migueles Chazarreta and Mr. Hannes Jägerstedt on February 1, 2025. ### Executive Summary — main estimates and comparisons - Average yearly CIT gap across income years 2016-2023: - 4.9 billion SEK - 2.2 percent of potential CIT liability - Corresponds to 0.1 percent of average GDP across 2016-2023 - Yearly range for CIT gap across 2016-2023: between 1.8 and 2.6 percent of potential CIT liability. - Yearly CIT gap for 2023 in absolute terms: 6.0 billion SEK. - Historical yearly CIT gap estimates (2016-2022): 5.7 billion SEK, 5.2 billion SEK, 4.7 billion SEK, 4.9 billion SEK, 4.9 billion SEK, 4.2 billion SEK, and 3.8 billion SEK. - When all corrections from audits of company records are included (CIT gap + other corrections): - 72.5 billion SEK - 25.8 percent of potential CIT - Includes adjustments such as Personal Income Tax (PIT) of the company’s main shareholder (example: undeclared use of company car taxed as personal income). - Comparison with Skatteverket's random-audit based estimate for same period: 1.3 percent of potential CIT liability. - Difference explained by Skatteverket excluding businesses with turnover below 100,000 SEK from random audits and assuming their compliance equals audited businesses; operational-audit estimates include them directly. - Businesses with turnover less than 100,000 SEK account for approximately 90 percent of the CIT tax gap identified in this mission based on operational audits. ### Recommendations (summary with timelines where provided) - Adopt the demonstrated bottom-up methodology and continue to carry out the CIT gap estimation in coming years. - Target: January 2026 - Generate an SSC (Social Security Contributions) estimate based on provided methods and existing data regarding the PIT gap derived from CIT estimates. - Target: June 2025 - Assess existing risk indicators by integrating them with random audits to determine if identified high-risk factors yield higher hit rates and tax corrections. - Target: June 2025 - Produce a risk scoring model from the random audit program and test it within operational audit programs to build an evidence-based risk model. - Target: June 2025 - Include a more comprehensive tax gap estimate for businesses with turnover less than 100,000 SEK in published tax gap estimates, since they account for approximately 90 percent of the total tax gap. - Target: Next publication of tax gap in Sweden - Gain a better understanding of factors driving the tax gap among businesses with less than 100,000 SEK turnover because audits alone are not feasible given slightly over 166,000 such businesses. - Target: June 2026 - Operational recommendation: Skatteverket analysts can perform the analysis using provided R code and documentation; alternatively request IMF CD workshop for assisted self-assessment training. ### Introduction — scope and approach - Objective: estimate the Corporate Income Tax (CIT) gap using operational (risk-based) audits and correct for sample selection bias inherent in operational audits. - Operational audits likely over-represent higher-risk firms; random audits provide unbiased estimates but Skatteverket has moved away from random audits among SMEs. - Two modeling approaches applied: - Heckman two-step sample selection bias correction. - Machine Learning (ML) control-function approach with Random Forest algorithm following Brewer and Carlson (2024). ### Methodology and modeling details - Heckman two-step: - First stage: probit model estimating probability of audit selection using risk indicators. - LASSO used to select 38 risk indicators for the selection equation from the 500-600 available risk indicators. - Second stage: model of audit outcome using 48 variables (tax lines and risk indicators) selected by LASSO, including a regressor accounting for selection (inverse Mills ratio). - Result: IMR positive but statistically insignificant — suggests limited unobserved sample selection bias. - ML model: - Random Forest algorithm employed to predict level of non-compliance. - Input: 500-600 risk indicators and around 200 tax return lines and company characteristics. - Hyperparameters tuned using 5-fold cross-validation with grid-search to maximize R-squared on training data. - Control-function approach used to remove selection bias before training ML model (following Brewer and Carlson (2024)). - Considerations and limitations: - Audit focus narrowness can cause underestimation of CIT gap if audits miss undisclosed taxes. - Targeting specific sectors/types increases extrapolation and uncertainty when estimating population-wide gap. - Some noncompliance may be undetectable by audits (e.g., “payments under the table”), potentially leading to underestimation. ### Key Findings — detailed points - CIT gap estimation results (2016-2023): - Average yearly CIT gap: 4.9 billion SEK; 2.2 percent of potential CIT liability. - CIT gap corresponds to 0.1 percent of average GDP across 2016-2023. - Yearly range: 1.8 to 2.6 percent of potential CIT liability. - 2023 CIT gap: 6.0 billion SEK. - CIT gap + other corrections: 72.5 billion SEK; 25.8 percent of potential CIT. - Sample and trimming: - Total audited returns used: 6,040 (risk-based audits completed by mission start). - Annual audit results trimmed by removing top and bottom 1 percent for each year to avoid outsized influence from a few audits. - Selection indicators and modeling: - Audit selection modeled using 38 LASSO-selected risk indicators. - Tax correction modeled using 48 LASSO-selected variables. - Several variables selected as important for selection but not for correction — these act effectively as instruments (recommend consulting auditors to validate). - Practical implications: - Skatteverket’s published tax gap estimates should be revised to incorporate the substantial contribution from businesses with turnover below 100,000 SEK. - Audits alone are not feasible to address non-compliance among the roughly 166,000 businesses with turnover less than 100,000 SEK — alternative approaches and cross-administration learning (e.g., Danish Tax Administration) recommended. ### Next steps (operational) - Set up a team of data analysts and apply the developed model using provided R scripts and documentation. - Continue annual CIT gap estimates using bottom-up methodology. - Develop SSC estimate by adapting R scripts and methods used to derive PIT adjustments from CIT audit data. - Integrate risk indicators with random audits to validate and refine risk scoring and produce an evidence-based risk model. - Study drivers of non-compliance among micro businesses (turnover < 100,000 SEK) and consider a study visit to the Danish Tax Administration for experience-sharing. *IMF Technical Assistance Report* ### 2023. The CIT gap estimates are based on a Heckman model using operational audits conducted for the ### The CIT gap estimates are based on a Heckman model using operational audits conducted for the income years 2016-2023 ### Data and methodology - Period covered: 2016-2023 (total of 8 years). - Number of operational audits used to estimate the Heckman model: 6,040 audits. - Adjustments made to Heckman results: - Addressed non-random selection of operational audits (sample selection bias). - One percent of audit results were trimmed in top and bottom for each year to reduce noise. - Machine learning (ML) model: - Requested by Skatteverket during the needs assessment mission in February 2024 and during mission preparation. - ML estimate is presented alongside the Heckman two-step approach for comparison. - Note on pooled model: - The Heckman model was developed using pooled data across years; annual fluctuations primarily reflect changes in economic structure of corporations. ### Key quantitative findings - CIT gap estimates (Heckman vs ML): - Heckman: 4.9 billion SEK (CIT gap alone reported in Table 1: Total = 4.9 billion SEK; 2.2 percent of CIT liability). - ML: 5.3 billion SEK (equivalent to 2.3 percent of CIT liability). - Text: "The CIT gap based on ML is estimated to be 5.3 billion SEK which is very close to the 4.9 billion SEK based on the Heckman approach." - Year-by-year similarity across 2016-2023 except for 2016 (difference likely driven by noise due to a low number of audits). - Comprehensive audit corrections: - When all corrections from audits of company records are included: 72.5 billion SEK, equivalent to 25.8 percent of potential CIT (Table 1). - Skatteverket’s random-audit based estimate: 1.3 percent of potential CIT (for comparison; note methodological differences). - 2023 specific estimate: - Estimated CIT gap in 2023: 6.0 billion SEK (measured in 2016-prices). - Equivalent to 2.6 percent of potential CIT liability. - Corresponds to 0.1 percent of GDP in 2023. - Table 1 excerpts (CIT gap alone; CIT gap + other corrections — billion SEK and percent of CIT liability): - Total (CIT gap alone): 4.9 billion SEK; 2.2 percent of CIT liability. - Total (CIT gap + other corrections): 72.5 billion SEK; 25.8 percent of CIT liability. - Notes on measurement: - The denominator in the 25.8 percent calculation only includes CIT; relevant PIT ideally also included but difficult to define. ### Sectoral and firm-size patterns - Sectoral (average 2016-2023): - Highest relative CIT gap: "Accommodation and food service". - Second-highest relative CIT gap: "Manufacturing". - Negative average gap: "Agriculture, forestry and fishing" (average over 2016-2023), explained by audit data limitations (undeclared salaries paid to employees not captured in PIT adjustments). - By number of employees (average 2016-2023): - Corporations with 0 employees: 10.3 percent of potential tax. - Corporations with 1-9 employees: -1.4 percent. - Corporations with 10-19 employees: 0.7 percent. - Corporations with 20-49 employees: 0.7 percent. - Corporations with 50-249 employees: 0.3 percent. - Relative CIT gap declines as number of employees increases. - By turnover (average 2016-2023): - Corporations with turnover < 100,000 SEK: relative CIT gap = 15.3 percent of potential tax (approx. USD 8,950). - Corporations with turnover > 10 million SEK: relative CIT gap = 0.5 percent (approx. USD 895,000). - Absolute CIT gap in corporations with turnover under 100,000 SEK: 4.4 billion SEK (about 90 percent of the total tax gap). - Implication: Non-compliance is heavily concentrated among numerous very small businesses, making audits an ineffective sole remedy. ### Comparisons and interpretation - Differences with Skatteverket random audits: - Skatteverket’s random audits initially relied solely on company accounting records without access to control materials such as bank information; deeper inspections followed only if initial checks revealed deficiencies. - The Heckman-based estimate includes audits of SMEs with fewer than 250 employees and includes smallest companies; Skatteverket’s published random-audit estimate excludes businesses with turnover less than 100,000 SEK and assumes their compliance equals those above 100,000 SEK. - Evidence from the Danish Tax Agency indicates small companies without employees account for about 60 percent of the tax gap; this supports inclusion of smallest firms in gap estimates and explains higher Heckman-based gap relative to Skatteverket’s random-audit estimate. - Audit data limitations can produce misleading sectoral results (example: negative gap in Agriculture, forestry and fishing) when certain tax effects (e.g., employees’ PIT increases) are not captured in audit records. ### Policy recommendations and next steps A. Set up a Team of Data Analysts and Apply the Developed Model - Appoint 2-3 data analysts responsible for compiling future tax gap estimations based on operational audits. - Train at least 2-3 individuals in the developed models to sustain CIT gap analysis capacity. - Allocate significant analyst time to perform good data analytics; analysts attached to the project have requisite familiarity with data analytics and econometrics. B. Other recommendations - Adopt the methodology and continue CIT gap estimation annually: - Analysts who participated in the mission can use provided R code with detailed instructions (see Annex IV) to perform analysis. - Alternatively, Skatteverket can seek IMF CD for a workshop to train more analysts in assisted self-assessment of the CIT gap. - Generate an estimate for Social Security Contributions (SSC): - Use provided methods and existing data on the Personal Income Tax (PIT) gap derived from CIT estimates. - Modify supplied R scripts and instructions to assess the SSC gap. - Produce and test a risk scoring model: - Use random audit program to create a genuine evidence-based risk model and test it within operational audit programs. - Integrate and assess existing risk indicators: - Combine existing risk indicators with random audit results to determine whether factors labeled high-risk yield high hit rates. - Include small businesses in published tax gap estimates: - Include a more comprehensive estimate for corporate businesses with turnover < 100,000 SEK (findings show these businesses account for approximately 90 percent of the total tax gap). - Study drivers of non-compliance among very small businesses: - Deepen understanding whether non-compliance is due to deliberate evasion, lack of knowledge, or complicated legislation. - Audits are infeasible for the >166,000 corporations with turnover < 100,000 SEK; explore alternative approaches. - Undertake study visit to Danish Tax Administration (DTA): - DTA faces similar challenges and could provide lessons on combating non-compliance among very small businesses. *Source: IMF calculations based on data from Skatteverket.* ### Annex I. Supplementary Material ### Annex I. Supplementary Material ### Sample selection bias and the Heckman 2-step estimator - Problem statement: - Tax gap estimates from non-random risk-based audits are prone to sample selection bias because audited companies are selected based on perceived risk of non-compliance and are not representative of the general population. - Heckman 2-step estimator formulation (as presented): - Outcome equation: - Y_i = X_i β + u_i - Selection equation: - S_i = 1[Z_i δ + v_i > 0] - Assumptions: - v_i ~ N(0,1) - E(u_i | v_i) = γ v_i - Conditional expectation for observed audits: - E[Y_i | X_i, S_i = 1] = X_i β + γ · γ(Z_i δ) where γ(·) = φ(·)/Φ(·) (inverse Mills ratio) - Estimation approach: - Estimate δ from the probit selection equation (equation (2)), compute the inverse Mills ratio, and then regress Y_i on X_i and the inverse Mills ratio using OLS (Heckman 2-step). - Note: Standard errors are wrong when manually estimating the 2-step Heckman estimator; correct standard errors can be obtained using bootstrap. ### Identification issues and best practices - Key identification concerns: - Avoid using the same variables in both selection and outcome models: using identical regressors makes identification rely solely on the non-linearity of the inverse Mills ratio, increasing multicollinearity and instability. - The selection model should include at least one exclusion restriction—variable(s) that affect audit selection but do not affect the level of non-compliance. - Finding valid exclusion restrictions is challenging if audits are based solely on estimated non-compliance; consultation with auditors to validate candidate instruments is recommended. - Practical note: - When the Heckman 2-step is used for prediction (rather than causal inference), accuracy depends on how well both the selection and outcome models explain the data. ### Empirical implementation and diagnostics (CIT returns and operational audits, 2016–2023) - Data and modelling choices: - Selection model estimated using a probit with 38 risk indicators (derived from an L1-regularized probit model applied to Skatteverket’s risk indicators). - Outcome model uses 12 variables selected from a LASSO model, plus PIT risk scores and PIT risk rankings (see note: a total of 12 variables are used). - Due to hardware limitations, population downsampled to 5% for fitting; final CIT gap for full population obtained by rescaling estimates. - 1% of audit results were trimmed in top and bottom for each year (in 2016-prices). - Standard errors are computed using bootstrap. - Fit and diagnostic statistics (preserve exact reported values): - Number of observations: - Selection model: 282,156 - Outcome model: 5,990 - R² values: - Selection model (McFadden’s Pseudo R²): 0.22 - Outcome model R²: 0.09 - Interpretation: - The selection model’s R² of 0.22 indicates it fits audit selection reasonably well but a low R² suggests substantial unexplained variation—tax authorities may use additional criteria or unobservable signals. - The outcome model’s R² of 0.09 indicates a large share of variation in non-compliance remains unexplained—a common challenge in tax evasion models due to firm-specific strategies and unobserved factors. - Inverse Mills ratio (IMR): - The coefficient on the IMR (IMR in Table A2) is reported as insignificant, indicating limited sample selection bias in this application. ### Machine learning robustness check (Brewer and Carlson approach; Random Forest) - Implementation details: - Selection model: identical L1-regularized probit model used to compute IMR. - IMR used to partial out sample selection bias from outcome variables and covariates. - Outcome model f̂(·) modeled using Random Forest (Breiman, 2001). - Features used: a total of 500-600 risk indicators and around 200 tax lines and company characteristics. - Tuning and training: - Random Forest tuned using 5-fold cross-validation with small forests of 100 trees (for computational efficiency). - Tuned parameters: mtry (number of variables to consider at each split), min.node.size (minimum number of data points in a terminal leaf). - Final model: a large forest consisting of 1000 trees fitted with optimal parameters. - Loss function: Root-Mean-Squared-Error (RMSE) minimization used in the outcome stage. - Performance and comparison: - Random Forest obtained an R² of 0.18, providing a better fit than the Heckman outcome model (R² = 0.09). - Despite the difference in fit, the CIT gap estimated using both approaches are nearly identical, corroborating robustness of results. - Variable importance: - Figure A1 reports the 10 most important variables (importance measured by "Gain" normalized to the most important variable). (Specific normalized importance values and variable order are shown in Figure A1.) ### Empirical example: audit leading to a negative gap (Skatteverket) - Narrative summary: - An auditor found both increases and decreases across PIT and CIT bases because of deductions in company records that were treated as wages to the owner, undeclared income, social security contributions, private use of company car, a loan reclassified as dividends for the shareholder/owner, and a false credited invoice. - Skatteverket enforces taxation on PIT but does not record the PIT impact of the audit in CIT. As a result, total tax gap recorded from the audit appears negative even though the full-picture tax effect would be positive if both PIT and CIT impacts were combined. - Itemized audit effects (columns: Item — PIT base — CIT base — PIT effect — CIT effect). Exact numbers preserved: - 1. Private insurance - PIT base: 446 - CIT base: -586 - PIT effect: 194 - CIT effect: -129 - 2. Undeclared income - PIT base: 20 625 - CIT base: 16 500 - PIT effect: 8 959 - CIT effect: 3 630 - 2. SSC on undeclared income - PIT base: -27 105 - CIT base: 0 - PIT effect: -5 963 - CIT effect: (blank/0) - 3. Use of company car - PIT base: 12 891 - CIT base: -2 165 - PIT effect: 5 599 - CIT effect: -476 - 4. Forbidden loan - PIT base: 124 188 - CIT base: -163 207 - PIT effect: 53 943 - CIT effect: -35 904 - 5. Credited invoice - PIT base: (blank) 100 000 (CIT base: 0) - PIT effect: (blank) 21 999 - CIT effect: (blank) - Totals (as reported): - PIT base total: 158 150 - CIT base total: -76 563 - PIT effect total: 68 695 - CIT effect total: -16 843 - Clarifying note: - “Forbidden loan” is forbidden in the sense that it should be shown as dividends, not as a loan; it is not forbidden in the sense of being illegal. ### Measuring and combatting the shadow economy (Annex III summary) - Definitions and framing: - No standardized definition of the “shadow economy”; OECD definition cited: “Economic activities, whether legal or illegal, which are required by law to be fully reported to the tax administration, but which are not reported, and which therefore go untaxed unlike activities which are so reported.” - IMF multi-pronged approach: - Coordinate revenue administration, tax policy, and statistics components to take a holistic, whole-of-government approach (revenue, social security, labor law enforcement). - Operational tools adopted by countries include dedicated shadow economy coordination units, behavioral economics for citizen engagement, and cross-agency working groups. - RA-GAP and capacity development: - RA-GAP provides capacity development for top-down and bottom-up techniques to estimate potential vs. actual revenues. - Tools include a Value Added Tax Gap model with online training and Corporate Income Tax gap estimation using econometric and machine learning techniques. - Gap estimates inform Compliance Improvement Plans (CIPs) within a Compliance Risk Management (CRM) framework and can improve tax audit case selection. - Tax policy and statistics perspectives: - Tax policy analysis examines features that sustain the shadow economy: high burdens, complex or frequently changing rules, multiple preferential treatments, piecemeal approaches to self-employment taxation, optional business regimes. - National accounts/statistics approach seeks to improve coverage of the non-observed economy (use labor input methods to estimate undeclared workers; administrative and non-statistical sources to estimate illegal activities; use tax audits to estimate under-reporting). - Cooperation between revenue and statistical agencies is critical; IMF capacity development fosters such cooperation. *Source: IMF calculations based on data from Skatteverket. (Annex I. Supplementary Material, as provided in the source PDF.)* --- _Source: https://www.imf.org/-/media/files/publications/tar/2025/english/tarea2025107-source-pdf.pdf_