## 10. Cumulative Changes in Policy Gap: Decomposition of Behavior-Inducd Changes

## Source details

**Canonical URL:** [10. Cumulative Changes in Policy Gap: Decomposition of Behavior-Inducd Changes](https://www.imf.org/-/media/files/publications/wp/2017/wp17158.pdf)

## Other formats

- [Markdown version](/-/media/files/publications/wp/2017/wp17158.pdf.md)
- [Structured JSON version](/-/media/files/publications/wp/2017/wp17158.pdf.json)

---

### Introduction and research objective
- VAT revenue volatility can exceed GDP or final consumption volatility; changes in VAT revenue as a share of GDP can be attributed to:
  - changes in the VAT standard rate (τS),
  - changes in the share of consumption in GDP (final consumption, FC),
  - changes in the C-efficiency ratio (E_C).
- C-efficiency: E_C ≡ V / PV_T, where PV_T = τS × FC (final consumption at prices exclusive of VAT).
- Main contribution: quantify short-run effects of business cycles on C-efficiency by decomposing C-efficiency into compliance and policy gaps, and using detailed VAT base and compliance data for 26 European countries and Japan (2000–2014).

### Decomposition definitions and empirical variance
- Definitions:
  - Compliance gap Γ ≡ 1 − (V / PV_C) where PV_C is potential VAT revenue under current legislation with perfect compliance.
  - Policy gap P ≡ 1 − (PV_C / PV_T).
  - Decomposition: E_C = (1 − Γ) × (1 − P); in logs: DevE_C = Dev(1 − Γ) + Dev(1 − P).
- Variance decomposition (Table 1; deviations from country mean):
  - Var(DevE_C) = 0.007400 (100%).
  - Var(Dev(1 − Γ)) = 0.003334 (45% of Var(DevE_C)).
  - Var(Dev(1 − P)) = 0.004565 (62% of Var(DevE_C)).
  - 2 × Cov(Dev(1 − Γ), Dev(1 − P)) = −0.000500 (−7% of Var(DevE_C)).
- Empirical patterns (2000–2014, 27 countries, 405 observations):
  - Deviations of C-efficiency from country means are positively correlated with output gaps (higher C-efficiency in booms).
  - Country-level C-efficiency levels range from less than 40 percent to more than 100 percent; many countries display long-run trends (> 4 percentage point change over 2000–2015).

### Compliance gap dynamics and links to business cycles
- Empirical correlation:
  - Correlation between compliance gap deviations and output gap = −0.30 (full sample, 2000–2014).
  - Interpretation: taxpayer compliance worsens in weak economic situations and improves in booms.
- Dynamic panel estimation (Table 2, OLS with country fixed effects; full sample, column [1]):
  - Compliance Gap (−1): −0.4087***.
  - ΔOutput Gap: −0.3593***.
  - ΔVAT Standard Rate: 0.0071**.
  - ΔDirect Policy Effects on Policy Gap: −0.2634 (not statistically significant in column [1]).
  - Constant: 0.0634***.
  - Observations = 378, R-squared = 0.2992.
- Interpretations and heterogeneous effects:
  - A one percentage point decrease in output relative to potential → 0.36 percentage point increase in the compliance gap in the short run (−0.3593).
  - Mean-reverting dynamics: next-year effect falls back by about 0.21 percentage point (0.36 × (1 + (−0.41))).
  - Higher VAT standard rates associated with larger compliance gaps (0.0071**).
  - Heterogeneity:
    - High-average compliance gap countries (> 15 percent): ΔOutput Gap = −0.4903***; Compliance Gap (−1) = −0.4195***; Observations = 154; R-squared = 0.3543.
    - Low-average compliance gap countries (< 15 percent): ΔOutput Gap = −0.1912***; Compliance Gap (−1) = −0.3631***; Observations = 224; R-squared = 0.213.
  - Policy-relevant interpretation: compliance response to output gap is larger where average compliance gaps are higher.

### Policy gap decomposition: direct policy effects vs behavior-induced changes
- Decomposition of yearly ΔPolicy Gap (ΔP):
  - ΔP_dp: direct policy effects from legislative rate/coverage changes (using previous-year base to isolate policy change effect).
  - ΔP_bc: behavior-induced changes from shifts in tax base composition under unchanged policy.
- Variance decomposition (Table 3):
  - Var(P) = 0.002677 (100%).
  - Var(P_dp) = 0.000579 (22% of Var(P)).
  - Var(P_bc) = 0.002363 (88% of Var(P)).
  - 2 × Cov(P_dp, P_bc) = −0.000266 (−10% of Var(P)).
- Empirical finding:
  - Behavior-induced changes drive the bulk of policy-gap variation; direct policy effects are important but concentrated in limited reform episodes.
  - Notable direct policy effect episodes (> 2 percentage points): Czech Republic (2008, 2012); Greece (2011); Hungary (2004, 2006, 2007); Japan (2004); Latvia (2003); Luxembourg (2005); Romania (2001); Slovakia (2003, 2004).
  - Notable negative direct policy changes (> 2 percentage points): Germany (2007), Finland (2009), Greece (2010), Hungary (2011), Malta (2004).

### Behavior-induced channels and VAT base composition
- PV_C components: PV_C = PV_C,fc + PV_C,ic + PV_C,cf + PV_C,adj where:
  - PV_C,fc = final consumption of taxable goods/services,
  - PV_C,ic = unrecoverable VAT on intermediate consumption by non-taxable/exempted activities,
  - PV_C,cf = unrecoverable VAT on capital formation by non-taxable/exempted activities,
  - PV_C,adj = other adjustments.
- Empirical observation: more than a third of total potential VAT revenue in the CASE (2013) sample attributable to intermediate consumption and capital formation by non-taxable and exempted activities.
- Relationship with output gap:
  - Behavior-induced index deviations are negatively correlated with output gap: in booms, policy gaps tend to fall as taxable base grows faster than total final consumption.
  - Mechanisms include cyclical shifts in consumption composition (necessities vs luxuries), purchases by non-taxable/exempted sectors, and other adjustments.

### Appendix IV — Estimation: Effects of Output Gaps on Behavior-Induced Policy-Gap Changes
- Models (OLS with country fixed effects; Table 4):
  - Final consumption channel:
    - ΔOutput Gap coefficient = −0.1569***.
    - Lagged dependent variable = −0.2880***.
    - Observations = 378; R-squared = 0.2778.
    - Interpretation: smaller policy gap during booms due to larger taxable share of final consumption.
  - Intermediate consumption channel:
    - ΔOutput Gap coefficient = 0.0192 (not statistically significant).
    - Observations = 378; R-squared = 0.0085.
    - Interpretation: intermediate consumption by non-taxable/exempted activities not clearly cyclical in relative magnitude.
  - Capital formation channel:
    - ΔOutput Gap (current) = −0.0779***.
    - ΔOutput Gap (lagged) = −0.0925***.
    - Lagged dependent variable = −0.1485***.
    - Observations = 351; R-squared = 0.1881.
    - Interpretation: effects through capital formation are negative, longer and more persistent than final consumption channel.
- VAT standard rate and direct policy effect variables were not statistically significant in these models.

### Role of VAT policy design and cross-country heterogeneity
- Heterogeneity channels:
  1. Household consumption of goods/services with reduced rates or exemptions varies across countries.
  2. Government consumption commonly non-taxable and less variable across countries.
- Evidence from Table 5 regressions (share of taxable household consumption on output gaps):
  - Countries without reduced rates on food: estimated output gap coefficient not different from zero (no noticeable business-cycle effect via this channel).
  - Countries with reduced rates on food: the channel increases the reaction of policy gaps to business cycles.
- Common factor: share of household consumption to total consumption is positively correlated with output gap; sluggish government consumption implies government share falls in booms, contributing to negative correlation between output gap and behavior-induced policy-gap changes through final consumption.
- Identified countries applying standard rate to food: Bulgaria, Denmark, Estonia, Japan, Latvia, Lithuania, Romania, and Slovakia.

### Implications for VAT revenue analysis (Appendix IV synthesis)
A. Implications for Revenue Elasticity of VAT to Output Gap
- Sample averages (27 countries): compliance gap = 16 percent; policy gap = 33 percent; C-efficiency = 55 percent.
- Full-sample illustrative impact: a 1 percentage point decrease in the output gap → 0.44 percentage point decrease in the C-efficiency ratio; decomposition:
  - Compliance gap effect = 0.24.
  - Policy gap effect (Final Consumption) = 0.13.
  - Policy gap effect (Capital Formation) = 0.07.
- Calculations (as reported):
  - Compliance gap effect (0.24) = 1 × −0.36 × (1 − 0.33).
  - Policy gap effect through final consumption (0.13) = 1 × −0.15 × (1 − 0.16).
  - Policy gap effect through capital formation (0.07) = 1 × −0.08 × (1 − 0.16).
- Elasticity of C-efficiency to output gap when C-efficiency = 55 percent:
  - Estimated elasticity = 0.79.
  - Illustrative range = 0.54–1.00.
- Comparison: these values are smaller than Sancak et al. (2010) estimate of 1.02 percent increase in C-efficiency for a 1 percentage point output gap reduction for advanced countries; differences attributed to output gap series and model specification (current-year regressions vs. short-term dynamics and mean-reverting features).

B. Implications for diagnosing VAT revenue performance and projections
- Country-specific diagnosis recommended: compare observed changes to benchmarks using decomposition into compliance and policy gaps and similar-country experience.
- If calculated compliance gap responds more strongly than benchmark (Table 2), consider deterioration in taxpayer compliance and potential structural measures.
- Caveat: net cash collections can distort calculated compliance gaps due to timing differences between payments and refunds (example cited: South Africa RA-GAP report, 2009).
- If policy gap responds more strongly than benchmark (sum of coefficients in Table 4 columns [4] and [6]), investigate direct policy effects and behavior-induced changes and decompose policy gaps into detailed tax bases.
- Projection guidance:
  - C-efficiency ratios are time-variant and strongly cyclical; assuming constant C-efficiency for short-term final consumption forecasts can be inaccurate.
  - Recommended: examine historical C-efficiency changes per country, incorporate country-specific characteristics, and use cycle averages for long-term projections.

### Key country- and channel-level observations (Appendices IV–V)
- Capital formation channel:
  - Contributed to cumulative policy-gap increases in Ireland, Greece, Spain (dwindling capital formation during financial crises).
  - Contributed to policy-gap reductions in Romania, Czech Republic, Estonia, Latvia, Bulgaria (rising capital formation post-transition).
- Luxembourg:
  - Large reduction of policy gap driven by “adjustment” component (VAT-liable exports, cross-border fuel shopping, e-VAT collections).
  - e-VAT revenue in Luxembourg rose from about 0.4 percent of GDP in 2005 to 2.3 percent of GDP in 2014; new EU rules adopted in 2008 expected to reduce Luxembourg’s e-VAT after 2015.
- Household consumption share regressions (Table 7; Appendix V):
  - [A1] Full Sample (FCH/FC):
    - Lagged Dependent Variable = −0.2382*** [0.0273].
    - ΔOutput Gap = 0.0934*** [0.0119].
    - Constant = 0.1699*** [0.0196].
    - Observations = 378; R-squared = 0.2812.
  - [A2] With Reduced Rates (FCH/FC):
    - Lagged Dependent Variable = −0.2207*** [0.0295].
    - ΔOutput Gap = 0.0965*** [0.0167].
    - Constant = 0.1558*** [0.0210].
    - Observations = 280; R-squared = 0.2528.
  - [A3] No Reduced Rate (FCH/FC):
    - Lagged Dependent Variable = −0.3054*** [0.0660].
    - ΔOutput Gap = 0.0899*** [0.0181].
    - Constant = 0.2242*** [0.0485].
    - Observations = 98; R-squared = 0.3461.
  - Significance: * p<0.1, ** p<0.05, *** p<0.01.

### Conclusion: main findings and policy insights
- Both compliance and policy gaps independently explain within-country C-efficiency movements along business cycles.
- Compliance responses to boom/bust are relatively short lived and vary across countries; countries with higher average compliance gaps show larger compliance sensitivity to output gap.
- Behavior-induced shifts dominate measured policy-gap changes; direct policy reforms with large direct effects are infrequent.
- Behavior-induced policy-gap changes are associated with business cycles: policy gaps tend to be smaller and C-efficiency larger during booms.
- Common drivers: sluggish government spending relative to total consumption and volatile non-deductible capital formation (housing construction and government investment).
- Countries with reduced rates for necessities exhibit larger policy-gap and C-efficiency cyclicality.
- Aggregate illustrative responsiveness:
  - 1 percentage point change in output gap → 0.44 percentage point change in C-efficiency (0.24 via compliance gap; 0.20 via policy gap) using full-sample estimates.
  - When C-efficiency = 55 percent, elasticity = 0.79; range = 0.54–1.00.
- Policy takeaways:
  - Use estimated coefficients as broad benchmarks for advanced economies to analyze VAT revenue performance.
  - Decompose observed C-efficiency changes into compliance and policy gaps when deviations from benchmarks are large.
  - Avoid simplified short-term VAT revenue projections that assume constant C-efficiency; incorporate cyclical variability and country-specific characteristics.

*Source: 10. Cumulative Changes in Policy Gap: Decomposition of Behavior-Inducd Changes; Appendix IV–V of wp17158.*

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

### References

### Tables
- 1. Variance of C-Efficiency, Compliance Gap, and Policy Gap ...................................................................... 11
- 2. Estimation Results Relating Compliance Gaps to Output Gaps .............................................................. 14
- 3. Variance of Policy Gap, Direct Policy Effects, and Behavior-Induced Changes ................................. 17
- 4. Estimated Effects of Output Gaps on Behavior-Induced Changes in Policy Gap ............................. 22
- 5. Regressing the Share of Taxable Consumption on the Output Gaps ................................................... 24
- 6. Illustration of C-Efficiency Ratio Change with Output Gap Change by 1% Point ............................. 25
- 7. Share of Household Consumption on Output Gaps .................................................................................... 36

### Figures
- 1. VAT Base for Taxable Consumption and Exempted Consumption ........................................................... 6
- 2. Deviations of C-Efficiency Ratios and Output Gaps ........................................................................................ 8
- 3. Evolution of C-Efficiency Ratio in 27 Countries ................................................................................................ 9
- 4. Cumulative Changes in C-Efficiency Ratio 2000-2014 ................................................................................ 12
- 5. Deviations of Compliance Gaps and Output Gaps ....................................................................................... 13
- 6. Average and Standard Deviation of Compliance Gap................................................................................. 16
- 7. Cumulative Changes in Policy Gap: Direct Policy Effects and Behavior-Induced Changes .......... 18
- 8. Deviations of Behavior-Induced Changes and Output Gaps .................................................................... 19
- 9. Potential VAT Revenues by Attributable Demand Components  in European Countries ............. 20

*Source: wp17158 - References (wp17158 - References .............................................................................................................); https://www.imf.org/-/media/files/publications/wp/2017/wp17158.pdf*

### 10. Cumulative Changes in Policy Gap: Decomposition of Behavior-Inducd Changes ....................... 35

### 10. Cumulative Changes in Policy Gap: Decomposition of Behavior-Inducd Changes

### Introduction and research objective
- VAT revenue volatility can exceed GDP or final consumption volatility; changes in VAT revenue as a share of GDP can be attributed to three factors: changes in the VAT standard rate (τS), changes in the share of consumption in GDP (final consumption, FC), and changes in the C-efficiency ratio (E_C).
- C-efficiency (E_C) is defined as V / PV_T, where V is actual VAT revenue and PV_T = τS × FC (final consumption at prices exclusive of VAT).
- Prior work: Keen (2013) finds C-efficiency movements important; Sancak et al. (2010) estimate that for advanced economies a 1 percent increase in the output gap is associated with a 1.12 percent increase in VAT revenue collections over one year (after controlling changes in final consumption), or equivalently a 1.02 percentage point increase in C-efficiency.
- This chapter’s main contribution: quantify short-run effects of business cycles on C-efficiency by decomposing C-efficiency into compliance and policy gaps, and by using detailed data on VAT base components and compliance for 26 European countries and Japan (2000–2014).

### Decomposition of C-efficiency: definitions and empirical patterns
- Definitions:
  - C-efficiency: E_C ≡ V / PV_T.
  - Compliance gap Γ ≡ 1 − (V / PV_C) where PV_C is potential VAT revenue under current legislation with perfect compliance.
  - Policy gap P ≡ 1 − (PV_C / PV_T).
  - Decomposition: E_C = (1 − Γ) × (1 − P) and in logs: DevE_C = Dev(1 − Γ) + Dev(1 − P) (covariance small so additive decomposition reasonable).
- Empirical patterns (2000–2014, 27 countries, 405 observations):
  - Deviations of C-efficiency from country means are positively correlated with output gaps (higher C-efficiency in booms).
  - Country-level C-efficiency levels vary from less than 40 percent to more than 100 percent; many countries show long-run upward or downward trends (definitions: decreasing trend > 4 percentage point decline over 2000–2015; increasing trend > 4 percentage point rise).
- Variance decomposition (Table 1, variance and covariance of deviations from country mean):
  - Var(DevE_C) = 0.007400 (100%).
  - Var(Dev(1 − Γ)) = 0.003334 (45% of Var(DevE_C)).
  - Var(Dev(1 − P)) = 0.004565 (62% of Var(DevE_C)).
  - 2 × Cov(Dev(1 − Γ), Dev(1 − P)) = −0.000500 (−7% of Var(DevE_C)).
- Interpretation:
  - Both compliance and policy gaps contribute substantially and roughly independently to within-country annual fluctuations in C-efficiency.
  - Figure 4 (cumulative changes 2000–2014) shows many large cumulative C-efficiency changes driven by policy gap movements rather than compliance alone.

### Changes in compliance gaps and links with business cycles
- Empirical correlation:
  - Scatter (Figure 5) shows a negative relationship between compliance gap deviations and output gap; correlation coefficient = −0.30 for the full sample (2000–2014).
  - Interpretation: taxpayer compliance worsens in weak economic situations and improves in booms.
- Dynamic panel estimation (model for ΔCompliance Gap):
  - Estimated specification includes lagged compliance gap, ΔOutput Gap, ΔVAT standard rate, and ΔDirect Policy Effects on Policy Gap (P_dp); country fixed effects included.
  - Key estimated coefficients (Table 2, OLS with country fixed effects):
    - Lagged Compliance Gap coefficient (Compliance Gap (−1)): −0.4087*** (column [1], full sample).
    - ΔOutput Gap: −0.3593*** (column [1], full sample).
    - ΔVAT Standard Rate: 0.0071** (column [1], full sample).
    - ΔDirect Policy Effects on Policy Gap: −0.2634 (not statistically significant in column [1]).
    - Constant: 0.0634***.
    - Observations = 378, R-squared = 0.2992.
  - Interpretation of full-sample coefficients:
    - A one percentage point decrease in output relative to potential is associated with a 0.36 percentage point increase in the compliance gap in the short run (column [1]: −0.3593).
    - With the estimated lag dynamics, shocks to compliance gaps tend to be mean-reverting: the estimated lag implies next-year effect falls back by about 0.21 percentage point (0.36 × (1 + (−0.41))).
    - Higher VAT standard rates are associated with larger compliance gaps (positive coefficient 0.0071**).
  - Heterogeneity by country groups (Table 2 columns [2] and [3]):
    - High-average compliance gap group (average > 15 percent): ΔOutput Gap coefficient = −0.4903***; Compliance Gap (−1) = −0.4195***; Observations = 154; R-squared = 0.3543.
    - Low-average compliance gap group (average < 15 percent): ΔOutput Gap coefficient = −0.1912***; Compliance Gap (−1) = −0.3631***; Observations = 224; R-squared = 0.213.
    - Interpretation: impact of output gap on compliance is larger where average compliance gaps are higher (weaker/less stable revenue administrations).
- Qualitative channels (from literature summarized):
  - During downturns: credit-constrained taxpayers may evade taxes for finance; bankruptcy risk may increase incentives to evade; shift to informal sector; reduced resource allocation to revenue administration → weaker enforcement.

### Changes in policy gaps: direct policy effects versus behavior-induced changes
- Decomposition of yearly ΔPolicy Gap (ΔP) into:
  - ΔP_dp: direct policy effects from legislative rate/coverage changes (constructed by mapping policy onto same base pre-change).
  - ΔP_bc: behavior-induced changes arising from shifts in tax base composition (final consumption, intermediate consumption, capital formation, other adjustments) without policy change.
- Variance decomposition (Table 3):
  - Var(P) = 0.002677 (100%).
  - Var(P_dp) = 0.000579 (22% of Var(P)).
  - Var(P_bc) = 0.002363 (88% of Var(P)).
  - 2 × Cov(P_dp, P_bc) = −0.000266 (−10% of Var(P)).
- Empirical finding:
  - Behavior-induced changes have driven a large part of policy gap variation; direct policy effects are important but concentrated in a limited number of reform episodes.
  - Figure 7 shows cumulative policy-gap changes are often dominated by behavior-induced components, while major VAT reforms produce notable direct policy effects in a few countries (examples in text: positive policy gap changes > 2 percentage points in Czech Republic (2008, 2012); Greece (2011); Hungary (2004, 2006, 2007); Japan (2004); Latvia (2003); Luxembourg (2005); Romania (2001); Slovakia (2003, 2004). Negative policy gap changes > 2 percentage points occurred in Germany (2007), Finland (2009), Greece (2010), Hungary (2011), and Malta (2004).)
- Behavior-induced channels and VAT base composition:
  - The actual VAT base differs from total final consumption because VAT may be levied on:
    - Final consumption of taxable goods/services (PV_C,fc),
    - Unrecoverable VAT on intermediate consumption by non-taxable/exempted activities (PV_C,ic),
    - Unrecoverable VAT on capital formation by non-taxable/exempted activities (PV_C,cf),
    - Other adjustments (PV_C,adj).
  - Total potential revenue under current policy: PV_C = PV_C,fc + PV_C,ic + PV_C,cf + PV_C,adj.
  - Behavior-induced ΔP_bc can be decomposed into ΔP_bc_fc, ΔP_bc_ic, ΔP_bc_cf, ΔP_bc_adj reflecting changes in shares of these components relative to PV_T.
  - Empirical observation: more than a third of total potential VAT revenue in CASE (2013) sample is attributable to intermediate consumption and capital formation by non-taxable and exempted activities (government, households housing construction, producers of exempted goods/services).
- Relationship with output gap:
  - Figure 8 indicates a negative relationship between the index of behavior-induced changes (deviations from country mean) and output gap: in booms, behavior-induced reductions in policy gaps occur (VAT base grows faster than total final consumption).
  - Mechanisms: composition shifts in consumption (necessities vs luxuries), changes in purchases (IC/CF) by non-taxable/exempted sectors, and other adjustments cause the effective taxable share to vary with the cycle.

### Implications and synthesis (as presented)
- Annual within-country movements in C-efficiency are substantially explained by independent movements in compliance and policy gaps; hence diagnosis of VAT revenue performance should analyze both gaps separately.
- Business cycles affect both gaps:
  - Compliance gap: weaker economic activity raises compliance gaps (estimated short-run elasticity: ΔCompliance Gap ≈ −0.36 × ΔOutput Gap in full sample; larger where compliance gaps are on average high).
  - Policy gap: behavior-induced changes account for the bulk of policy-gap variation over time and are correlated with output gaps (policy gap tends to fall in booms due to base composition shifts).
- Policy relevance:
  - Revenue administration strength matters: countries with higher average compliance gaps show larger responsiveness of compliance to output gap swings.
  - Behavioral base shifts (IC and CF purchased by non-taxable/exempted activities) are crucial drivers of short-run VAT revenue cyclicality and should be explicitly monitored when assessing VAT performance.
  - Direct policy reforms have concentrated but sometimes large effects on policy gaps; their short-run interaction with compliance is ambiguous and empirically mixed.

*Source: 10. Cumulative Changes in Policy Gap: Decomposition of Behavior-Inducd Changes (wp17158).*

### Appendix IV.

### Appendix IV

### Estimation Results: Effects of Output Gaps on Behavior-Induced Policy-Gap Changes
- Model estimated by OLS with country fixed effects; results shown in Table 4.
- Behavior-induced changes through final consumption:
  - Estimated coefficient on ΔOutput Gap = -0.1569***.
  - Lagged dependent variable (Index of Base Changes) = -0.2880***.
  - Interpretation: significantly negative correlation — smaller policy gap during a booming period and higher C-efficiency due to larger share of total final consumption being taxable.
- Behavior-induced changes through intermediate consumption:
  - Estimated coefficient on ΔOutput Gap = 0.0192 (not statistically significant).
  - Interpretation: relative magnitude of intermediate consumption by non-taxable and exempted activities to total final consumption may not be associated with business cycles.
- Behavior-induced changes through capital formation:
  - Estimated coefficient on ΔOutput Gap = -0.0779*** (current year).
  - Estimated coefficient on ΔOutput Gap (-1) = -0.0925*** (lagged).
  - Lagged dependent variable = -0.1485***.
  - Interpretation: negative coefficients for both current and previous years (-0.08 and -0.09) indicate longer and more persistent impacts compared with final consumption; effects of output fluctuation on policy gaps through capital formation are more persistent than those through final consumption.
- Table 4 model summary statistics (as reported):
  - Observations: 378 (final consumption), 378 (intermediate consumption), 351 (capital formation).
  - R-squared: 0.2778 (final), 0.0085 (intermediate), 0.1881 (capital).
- Note: The VAT standard rate and the direct policy effect did not prove to be statistically significant.

### Differences Across Countries: Role of VAT Policy Design
- Cross-country heterogeneity expected in behavior-induced final-consumption effects depending on VAT reduced rates and exemptions coverage.
- Two channels for differences in taxable final consumption share:
  1. Household consumption for goods and services with reduced rates or exemptions (expected to differ across countries).
  2. Government consumption that is commonly non-taxable (expected to be less variable across countries).
- Empirical evidence (Table 5 regressions on share of taxable household consumption relative to total household consumption on output gaps):
  - Countries grouped into: those that apply reduced rates to food and those that apply the standard rate to food.
  - For countries without reduced rates on food, estimated coefficient of the output gap is not different from zero — policy gaps not noticeably affected by changes in share of taxable consumption through business cycles.
  - For countries with reduced rates for food, the channel can increase the reaction of policy gaps to business cycles.
- Common factor across all countries:
  - Share of household consumption to total consumption (including government final consumption) is positively correlated with the output gap.
  - Sluggish government consumption relative to household consumption implies government consumption share to total consumption decreases when the output gap is positive, contributing to negative correlation between output gap and behavior-induced policy-gap changes through final consumption.
- Countries with reduced rates on basic foodstuffs exhibit larger changes in policy gaps and C-efficiency along business cycles.
- Countries applying their standard rates to food (as identified in the source): Bulgaria, Denmark, Estonia, Japan, Latvia, Lithuania, Romania, and Slovakia.

### Implications for VAT Revenue Analysis
A. Implications for Revenue Elasticity of VAT to Output Gap
- Using sample averages (27 countries): compliance gap = 16 percent; policy gap = 33 percent; C-efficiency = 55 percent.
- Full-sample illustrative impact: a 1 percentage point decrease in the output gap may result in a 0.44 percentage point decrease in the C-efficiency ratio.
  - This 0.44 is the sum of:
    - Compliance gap effect = 0.24
    - Policy gap effect (Final Consumption) = 0.13
    - Policy gap effect (Capital Formation) = 0.07
- Calculations (as reported in source):
  - Compliance gap effect (0.24) = 1 × -0.36 × (1 – 0.33).
  - Policy gap effect through final consumption (0.13) = 1 × -0.15 × (1 – 0.16).
  - Policy gap effect through capital formation (0.07) = 1 × -0.08 × (1 – 0.16).
- Elasticity of C-efficiency to output gap when C-efficiency = 55 percent:
  - Estimated elasticity = 0.79.
  - Illustrative range of possible variations = 0.54–1.00.
- Comparison with prior literature:
  - These illustrated aggregate responsiveness values are much smaller than Sancak et al. (2010) estimate of 1.02 percent increase in C-efficiency for a 1 percentage point output gap reduction for advanced countries.
  - Two reasons cited for difference: different output gap series and different model specifications (current-year regressions vs. short-term dynamics and mean-reverting features included here).

B. Implications for Diagnosing VAT Revenue Performance
- Country-specific diagnosis is critical: compare observed changes to benchmarks while considering country characteristics and similar-country experience.
- Use decomposition into compliance and policy gaps with detailed macroeconomic data to diagnose causes of observed C-efficiency changes.
- If calculated compliance gap responds more strongly to output gap changes than benchmark (Table 2), consider possible deterioration in taxpayer compliance beyond cyclical expectations and potential need for structural measures.
- Caveat on net cash collections:
  - If VAT revenues measured by net cash collections (payments minus refunds), calculated compliance gap can fluctuate for reasons unrelated to taxpayer compliance (e.g., lags between tax periods and payments/refunds or different lags between payments and refunds).
  - Example: RA-GAP report for South Africa showed decline in C-efficiency in 2009 due to large refunds corresponding to excess credit claims in previous years.
- If calculated policy gap responds more strongly than benchmark (sum of coefficients in Table 4 columns [4] and [6]), investigate direct policy effects and behavior-induced changes, further decomposing policy gaps into detailed tax bases for better projection assumptions.
- Projection guidance:
  - Recognize C-efficiency ratios are time-variant and strongly cyclical.
  - Simplified projection assuming unchanging C-efficiency for final consumption forecast can be inaccurate in short term.
  - Recommended: examine historical C-efficiency changes per country, incorporate country-specific characteristics, and use average over the cycle for long-term projection.

### Conclusion: Summary of Main Findings and Policy Insights
- Main contribution: analysis of cyclical movements of C-efficiency in advanced economies using decomposition into compliance and policy gaps and exploration of drivers of policy-gap movements.
- Key empirical findings:
  - Both compliance and policy gaps independently impact C-efficiency movements along business cycles.
  - Taxpayer compliance responses to boom/bust are relatively short lived and vary across countries.
  - Direct policy changes in the policy gap do not appear to have significant effects on the compliance gap in the short run.
  - Behavior-induced shifts are the dominant driver of measured policy-gap changes; direct policy changes with significant direct effects have been fairly infrequent.
  - Behavior-induced policy-gap changes are associated with business cycles: smaller policy gaps and larger C-efficiency during booms.
  - Common drivers: sluggish government spending relative to total consumption and volatile non-deductible capital formation (housing construction and government investment).
  - Countries with reduced rates for necessity goods and services exhibit larger changes in policy gaps and C-efficiency along business cycles.
- Aggregate illustrative responsiveness:
  - 1 percentage point change in output gap → 0.44 percent point change in C-efficiency (0.24 via compliance gap; 0.20 via policy gap) using full-sample estimates.
  - When C-efficiency = 55 percent, elasticity = 0.79; possible range = 0.54–1.00.
- Policy takeaways:
  - Use estimated coefficients as broad benchmarks (for advanced economies) to analyze VAT revenue performance.
  - Where observed C-efficiency changes significantly exceed benchmarks, further decompose compliance and policy gaps to inform responses.
  - Avoid simplified short-term VAT revenue projections that assume constant C-efficiency; incorporate cyclical variability and country-specific characteristics for accurate short-term projections.

*Source: Appendix IV of the provided IMF working paper content.*

### APPENDIX II. DESCRIPTION OF DATA USED IN FIGURES AND MODELS

### APPENDIX II. DESCRIPTION OF DATA USED IN FIGURES AND MODELS

### Data sources and definitions
- C-efficiency ratio
  - Final consumption (including household, government, and NPISH):
    - For European countries: final consumption data retrieved from the Eurostat database based on ESA 2010 (GDP and main components: nama_10_gdp).
    - For Japan: final consumption data retrieved from the national accounts database provided by the Cabinet Administration Office.

- VAT revenue
  - For European countries: VAT revenue data retrieved from the Eurostat database based on ESA 2010 (Main national accounts tax aggregates: gov_10a_main), VAT receivables.
  - For Italy (2009–14), Spain (2000–14), and the U.K. (2000–14): data in CASE (2013, 2015, 2016) are used to maintain consistency with their analyses.
  - For Italy and Spain: alternative revenue data in CASE (2016) used to reflect changes in VAT credit stocks.
  - For Japan: VAT revenue data retrieved from the national accounts database provided by the Cabinet Administration Office.

- VAT standard rate
  - For European countries: rates obtained from “VAT Rates Applied in the Member States of the European Union,” by the European Commission (EU Taxud.c.1[2017] – EN).

### Potential VAT revenues and compliance gaps (EU countries)
- Sources and adjustments
  - Potential revenues under current policy:
    - Retrieved from CASE (2016) for the period between 2010 and 2014.
    - Retrieved from CASE (2015) for year 2009.
    - Before 2008, results in CASE (2013) are used, unless there were significant revisions between CASE (2013) and CASE (2015, 2016).
  - For countries with significant revisions between CASE (2013) and CASE (2015, 2016) relating to components of potential revenues (more than 5 percent of the results compared with CASE (2013)):
    - Adjustment ratios calculated by taking the average of the ratios between 2009 and 2011, and applying them to the results in CASE (2013).
- Compliance gap
  - Calculated as the ratio of actual VAT revenue to potential VAT revenue under current legislation.

### Policy gap: definition and decomposition
- Policy gap
  - Calculated as the difference between the C-efficiency ratio and compliance gap, using the relationship below:
    -  11 C EΓP       .
  - In this decomposition, the policy gap is expressed as the ratio of actual to potential revenue under full compliance with the standard rate on all final consumption.

- Direct policy effects and behavior-induced changes of policy gap
  - Policy gaps are decomposed into:
    - Direct policy effects (ΔP_dp)
    - Behavior-induced changes (ΔP_bc)
  - The direct policy effect index and behavior-induced portion index are constructed.
    - The direct policy effect index reflects changes in VAT policy, except for the change in standard rate; the behavior-induced portion is the residual.
  - For European countries, to derive direct policy effects:
    - The “Index of Policy-Induced VAT Changes” in CASE (2013) is used (this index shows changes in VAT revenues owing to rate changes based on the structure of the VAT tax base in each country in the year 2000).
    - Indices are adjusted when standard rates have been changed to exclude effects of changes in standard rates.
    - For the period after 2012, direct policy effects are calculated using final consumption data for 65 goods and services and changes in rates applied to each good and service as presented in “VAT Rates Applied in the Member States of the European Union,” European Commission (2017).
  - For Japan:
    - Yearly incremental revenue projections due to policy changes published by the government are used.

### Output gap
- Output gap data retrieved from the World Economic Outlook (WEO) database in April 2016.
- For countries with no output gap data in the WEO database:
  - Used data from the estimations for cyclical adjustments of budget balances, Autumn 2015, by the European Commission (Latvia, 2000–2001).
  - Reference: Table 14 in ‘Cyclical Adjustment of Budget Balances’ shows the gap between actual and trend gross domestic products at 2010 reference levels, and percentages of trend gross domestic products at constant prices.

---

### APPENDIX III. DECOMPOSITION OF CHANGES IN POLICY GAP

### Definitions and decomposition
- Policy gap definition (textual from source)
  - The definition of policy gap is:
    - 1 C T PV P PV , where PV_T represents the theoretical VAT revenue under a hypothetical VAT system with a single rate applied to all final consumption, and PV_C represents the VAT revenues under current legislation with full compliance.
- Yearly changes in policy gap (ΔP)
  - Yearly changes expressed as:
    - 1 1     1 1 , CC tt t TT tt PV PV P PV PV                             
    - where PV_T and PV_C are calculated according to the VAT policies in years t and t-1.
- Decomposition into direct policy effect and behavior-induced changes
  - If PV_C*_t-1 denotes potential VAT revenues under the year t policy (after policy change) with the year t-1 base:
    - Direct policy effects (ΔP_dp) defined by:
      - * 11 * 11 _11 , CC tt t TT tt PVPV P dp PVPV                        
      - This shows effects of policy changes (in year t) on the size of policy gaps by using the value of the tax base of year t-1 (due to policy changes).
    - Behavior-induced changes (ΔP_bc) defined by:
      - * 1 * 1 _ 1 1 , CC tt t TT tt PV PV P bc PV PV                              
      - Represents effects of changes in tax bases from years t-1 to t under the same policy of year t.
  - The sum of ΔP_dp and ΔP_bc equals total changes in the policy gap (ΔP).

### Indices over time
- Two indices constructed for each country i and year t:
  - direct policy effect index
  - behavior-induced portion index
- Index construction (as in source):
  - , ,2000 ,2001 ,, 2001 __ _ _. t i t i i t k t i t i t k P dp P P dp P bc P bc        
- For EU member countries:
  - The index of policy-induced VAT changes is used to calculate PV_C*_t-1 in each year (see Appendix II).
  - This index calculated by applying the tax rate for each year to the tax base of VAT in 2000 for each country (see Box 1.1 in CASE (2013)).

---

### APPENDIX IV. DECOMPOSITION OF BEHAVIOR-INDUCED CHANGES IN POLICY GAP

### Key findings and notable features (from Figure 10 discussion)
- Channels considered for cumulative behavior-induced changes in the policy gap: FC Channel, IC Channel, CF Channel, ADJ Channel, and Cumulative Other Base Changes (as presented in Figure 10).
- Notable country-level observations:
  - Capital formation effect
    - Contributed to cumulative changes in the policy gap in Ireland, Greece and Spain, which were highly affected by financial crises caused by dwindling capital formation.
    - Contributed to reduction of policy gaps in Romania, the Czech Republic, Estonia, Latvia, and Bulgaria, where capital formation by government and households showed an increasing trend after economic transition.
  - Luxembourg
    - Significant reduction of the policy gap observed due to the “adjustment” component (reflects VAT collection not attributable to domestic final consumption, intermediate consumption or capital formation).
    - Adjustment component includes effects of VAT-liable exports, such as cross border shopping by nonresidents for fuel (“gas pump tourism”) reflecting lower VAT and excise rates than neighboring countries, and “e-VAT” collection (VAT levied on electronic commerce within EU taxed at origin rather than at destination).
    - Large amount of VAT collections from these transactions resulted in high C-efficiency ratio in Luxembourg, and recent buoyant increases in e-VAT collections caused higher C-efficiency and a lower policy gap.
      - Note: source mentions e-VAT revenue in Luxembourg increased from about 0.4 percent of GDP in 2005 to 2.3 percent of GDP in 2014, with new EU rules adopted in 2008 expected to shift VAT on e-commerce from domicile of seller to residency of purchaser and significantly reduce e-VAT collections in Luxembourg after 2015.
- Structural changes in economic situations
  - Factors related to some structural changes have contributed to cumulative changes in policy gaps and C-efficiency ratios in many countries, though not necessarily related to VAT policy changes.

---

### APPENDIX V. HOUSEHOLD CONSUMPTION RATIO ON OUTPUT GAPS

### Regression model specification
- Model estimated for the share of household consumption to total consumption (including government final consumption) on output gaps:
  - 1 12 1 , , , i t i t i i t i t i t i t FCH FCH θ ρ ρ og u FC FC                         .
  - Here:
    - FCH_i,t = total household final consumption
    - FC_i,t = total final consumption

### Key regression results (Table 7)
- For the full sample and subgroups by VAT reduced-rate legislation, the share of household consumption in total consumption is positively correlated with output gaps.
- Coefficients and statistics (exact values from Table 7):

  - [A1] Full Sample (FCH/FC)
    - Lagged Dependent Variable: -0.2382***
      - [0.0273]
    - ΔOutput Gap: 0.0934***
      - [0.0119]
    - Constant: 0.1699***
      - [0.0196]
    - Observations: 378
    - R-squared: 0.2812

  - [A2] With Reduced Rates (FCH/FC)
    - Lagged Dependent Variable: -0.2207***
      - [0.0295]
    - ΔOutput Gap: 0.0965***
      - [0.0167]
    - Constant: 0.1558***
      - [0.0210]
    - Observations: 280
    - R-squared: 0.2528

  - [A3] No Reduced Rate (FCH/FC)
    - Lagged Dependent Variable: -0.3054***
      - [0.0660]
    - ΔOutput Gap: 0.0899***
      - [0.0181]
    - Constant: 0.2242***
      - [0.0485]
    - Observations: 98
    - R-squared: 0.3461

- Significance notation:
  - * p<0.1, ** p<0.05, *** p<0.01

*Source: APPENDIX II–V, "DESCRIPTION OF DATA USED IN FIGURES AND MODELS" (wp17158).*

---


_Source: https://www.imf.org/-/media/files/publications/wp/2017/wp17158.pdf_