## wpiea2019205-print-pdf

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---

### Overview and research question
- Research question: behavior of firms around the VAT registration threshold (the VAT “notch”), combining theoretical modeling and empirical analysis using UK administrative data.
- Stylized facts established:
  - Evidence of bunching below the registration threshold via reported turnover manipulation.
  - On average 43 percent of firms with turnover below the current-year threshold were registered for VAT over the period 2004-2014.
- Context:
  - UK VAT registration threshold cited as £85,000 ($110,000).
  - VAT rates in many EU countries often exceed 20 percent.

### Theoretical framework and core intuition
- Model structure and key requirements:
  - Firms make both B2C (sales to final consumers) and B2B (sales to VAT-registered businesses) sales.
  - Use intermediate inputs in production, requiring at least three stages of production (upstream input production, small-firm production, large downstream firm).
  - Two-stage production models are insufficient to generate coexistence of voluntary registration and bunching.
- Pricing and demand parameters:
  - Small firms can price-discriminate between B2C and B2B customers (prices p_C(a), p_B(a)) unless e_C = e_B.
  - λ measures final demand by households for goods produced by small firms (share of B2C sales).
  - Baseline technology: constant-returns fixed-coefficients; one unit of output for an a-type firm requires ω/a units of the input and (1−ω)/a units of labour.
- Comparative static predictions:
  - Voluntary registration more likely when:
    - (i) input cost relative to sales ω is high;
    - (ii) proportion of B2C sales λ is low;
    - (iii) markets are less competitive (higher mark-ups / higher Lerner index).
  - Bunching at the registration threshold more likely when:
    - (i) ω is low;
    - (ii) λ is high;
    - (iii) markets are more competitive (lower Lerner index).
  - Allowing for evasion responses does not change these qualitative predictions.

### Empirical strategy and data
- Data:
  - Administrative dataset linking population of VAT and corporation tax records in the UK for the period 2004-2014.
  - Advantage: in the UK, businesses below the VAT registration threshold are not subject to any other tax that replaces the VAT.
- Empirical approach:
  - Document stylized facts (bunching and voluntary registration).
  - Test model predictions by relating voluntary registration and bunching to firm-level characteristics: share of B2C sales, input-cost ratio, and industry competition (Lerner index).
  - Partition sample into groups based on predicted likelihood of voluntary registration to examine heterogeneous bunching responses.
  - Investigate mechanisms: under-reporting of sales (evasion) and dynamic regressions addressing persistence versus inertia.
- Sample and construction:
  - Companies binned into £1,000 turnover bins.
  - Final analysis sample: 3,461,247 company-year observations with 968,353 unique companies between 2004/2005 to 2014/2015.
  - Data pooled from fiscal year 2004/05 through 2014/15.

### Estimation method for bunching
- Bunching measure:
  - B = ∆s∗ h(s∗), with h(s∗) the counterfactual density of firms over the bunching interval (assumed constant).
  - Empirical measure:
    - b = (sum_{j=s∗}^{s∗−} (c_j − ĉ_j) / N) / (sum_{j=s∗}^{s∗−} ĉ_j)
    - c_j: actual number of firms in each £1,000 turnover bin.
    - ĉ_j: counterfactual bin count without the notch.
    - Excluded range (s∗−, s∗+) chosen so excess mass left of notch equals missing mass right of notch; s∗− set where excess bunching starts; s∗+ estimated iteratively.
- Counterfactual density:
  - Fit a flexible polynomial of order 5 (also tried orders 4–7) excluding the excluded range following Chetty and others (2011) and Kleven and Waseem (2013).
  - Excluded range used in main specification: -£14,000 to £24,000.

### Key empirical findings and magnitudes (numeric fidelity preserved)
- Aggregate bunching:
  - Bunching estimate: 1.361 (std. error: 0.202).
  - Interpretation: total excess bunching mass is almost 1.4 times the average height of the counterfactual over the excluded range.
- Voluntary registration:
  - On average 43 percent of firms with turnover below the current-year threshold were registered for VAT over 2004-2014.
- Determinants of voluntary registration (marginal effects reported):
  - A one-standard deviation (s.d.) decrease in the share of B2C sales increases the probability of voluntary registration by 4 percentage points.
  - A one-s.d. increase in the input-cost ratio increases the probability of voluntary registration by 4.9 percentage points.
  - A one-s.d. decrease in the Lerner index of competition increases the probability of voluntary registration by 3.9 percentage points.
- Heterogeneous bunching (predicted-not-register vs predicted-register):
  - For firms predicted to be less likely to register voluntarily, larger bunching responses occur when:
    - (i) proportion of B2C sales is low;
    - (ii) cost of inputs relative to sales is high;
    - (iii) Lerner index of their industry is low (more competitive).
  - For firms predicted to be highly likely to register voluntarily, bunching patterns are unrelated to these three characteristics.
- Summary statistics (selected exact values):
  - Total Turnover: Mean 74.694; St.Dev. 48.881; p10 19.88; p50 62.70; p90 151.80; Observations 3,461,247.
  - Trading profit: Mean 21.882; St.Dev. 7.250; p10 0.00; p50 11.82; p90 59.71; Observations 3,461,247.
  - Total Input Costs (CT600): Mean 52.814; St.Dev. 4.271; p10 12.04; p50 36.55; p90 123.46; Observations 3,461,247.
  - Input-Cost Ratio (CT600): Mean 0.71; St.Dev. 0.28; p10 0.28; p50 0.78; p90 1.00; Observations 3,461,247.
  - Share of B2C Sales: Mean 0.55; St.Dev. 0.24; p10 0.29; p50 0.45; p90 0.91; Observations 3,461,247.
  - Lerner Index: Mean 0.75; St.Dev. 0.11; p10 0.58; p50 0.77; p90 0.90; Observations 3,461,247.
  - VAT Registered: Mean 0.63; St.Dev. 0.4830; Observations 1,134,612,47? (as presented in source table).

### Mechanisms, robustness, and dynamics
- Evasion and misreporting:
  - Suggestive evidence that part of bunching is driven by evasion in the form of under-reporting of sales (Appendices B and D).
  - Appendix D graphical diagnostics:
    - Salary-exclusive input-cost ratio: registered firms show larger input-cost ratio than non-registered firms below the VAT notch; non-registered series smooth across notch.
    - Salary-inclusive input-cost ratio: sharp increase in average input-cost ratio for non-registered firms just below the VAT notch, consistent with turnover misreporting where salary is harder to underreport.
- Dynamics and persistence:
  - Transition probabilities (Table A.1):
    - Firms initially registered in 2004/05: 82.23% remained registered a year later.
    - For non-registered firms, 81.44% remain unregistered after 5 years; 64% of registered firms remain registered after 5 years.
  - Dynamic fixed-effect Probit and average partial effects (Appendix E):
    - Lagged Registration (Rt-1): coefficient ~3.700*** in many specifications.
    - For firms registered in previous year, falling below deregistration threshold lowers probability of current registration by 5.57 percentage points (0.0557***).
    - For firms not registered in previous year, going above registration threshold increases probability of registration by 70.4 percentage points (presented as 0.704*** and similar avg partial estimates).
    - One-standard-deviation effects on predicted probability:
      - B2C + σ_B2C: average predicted probability falls by 0.0028***.
      - ICR + σ_ICR: increases probability by 0.0073***.
      - Lerner + σ_Lerner: decreases probability by 0.0058***.
- Robustness:
  - Voluntary registration results robust to linear probability and fixed-effects logit specifications, and to inclusion of controls such as distance to the VAT threshold.

### Optimal VAT threshold and cross-country evidence
- Theoretical optimal threshold (Appendix C):
  - Revenue-maximizing first-order condition (C.38):
    - ∂R/∂s* = (t ω â / (s* p(s*)) − t(1−β)s* + A) ∂â/∂s* + tβ(â−a*) + t e/(e−1) ω p(s*) ln(â/a*) = 0.
  - Special case reproducing Keen and Mintz (2004) when e=0 and β=0 yields s* = A / (t v) (C.40).
  - Generalized formula (C.41):
    - s* = [A + t( β(â−a*) + e/(e−1) ω p(s*) ln(â/a*) ) / (∂â/∂s*)] / [t(v−β)]
  - Intuition: presence of B2B sales (β>0) tends to raise optimal threshold s*; behavioral responses (e>0) and input-intensity effects can also raise threshold.
- Cross-country empirical pattern (Figure 7, 103 countries, 2017):
  - Panel A (controls for GDP per capita): estimated slope coefficient = 0.06, significant at the 10 percent level (p−value = 0.089).
  - Panel B (controls for size of informal sector via share of agriculture): estimated slope coefficient = -0.03, highly significant (p−value = 0.005).
  - Interpretation: VAT threshold tends to be higher with higher compliance and administration costs (proxied by larger informal sector) and less direct selling to consumers.

### Contributions and conclusions
- Conceptual contribution:
  - Unified model explaining both voluntary VAT registration and bunching via a three-stage production structure.
  - Formal derivation of how input intensity ω, B2C share λ, and competition (demand elasticities and Lerner index) affect voluntary registration and bunching.
- Empirical validation:
  - Comprehensive UK administrative data support theoretical predictions:
    - Voluntary registration more likely with a low share of B2C sales, a high input-cost ratio, and more competition.
    - Clear evidence of bunching at the VAT threshold.
    - Heterogeneity in bunching across firms matches model predictions.
- Policy-relevant insight:
  - Optimal VAT threshold should account for B2B sales and behavioral responses; presence of B2B sales tends to increase the optimal registration threshold.

*Source: wpiea2019205-print-pdf - https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019205-print-pdf.pdf*

### 1.    Estimation Method    .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .    32

### 1.    Estimation Method    .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .    32

### Overview
- Research question: behavior of firms around the VAT registration threshold (the VAT “notch”), combining theoretical modeling and empirical analysis using UK administrative data.
- Key stylized facts established:
  - Evidence of bunching below the registration threshold via reported turnover manipulation.
  - A large fraction of firms with turnover below the current-year threshold are registered for VAT (on average 43 percent, over the period 2004-2014).
- Contextual details:
  - In the EU, a large majority of countries currently have a registration threshold; the UK threshold cited is £85,000 ($110,000).
  - VAT rates in many EU countries often exceed 20 percent, producing salient tax notches.

### Theoretical framework and intuition
- Model requirements:
  - To explain coexistence of voluntary registration and bunching within a sector, firms must:
    - Make both B2C (sales to final consumers) and B2B (sales to VAT-registered businesses) sales.
    - Use intermediate inputs in production (necessitating at least three stages of production).
  - Two-stage production models (e.g., Keen and Mintz (2004); de Paula and Scheinkman (2010)) are insufficient to explain both phenomena.
- Core theoretical insights:
  - Voluntary registration is attractive when firms can claim substantial input VAT and/or pass output VAT to VAT-registered buyers.
  - If firms make only B2C sales, voluntary registration costs exceed benefits.
  - With only B2B sales, voluntary registration is weakly optimal absent compliance costs, and strictly optimal if the firm uses inputs on which it can claim input VAT.
- Model predictions (signs and mechanisms):
  - Voluntary registration is more likely when:
    - (i) the cost of inputs relative to sales is high;
    - (ii) the proportion of B2C sales by the firm is low;
    - (iii) markets are less competitive (firms have higher mark-ups).
  - Bunching at the registration threshold is more likely when:
    - (i) the cost of inputs relative to sales is low;
    - (ii) the proportion of B2C sales is high;
    - (iii) markets are more competitive (lower Lerner index).
  - Extending the model to allow for evasion responses does not affect these qualitative predictions.

### Empirical strategy and data
- Data:
  - Administrative dataset linking the population of VAT and corporation tax records in the UK for the period 2004-2014.
  - Advantage: in the UK, businesses below the VAT registration threshold are not subject to any other tax that replaces the VAT, providing a cleaner test environment.
- Empirical approach:
  - Document stylized facts (bunching and voluntary registration).
  - Test model predictions by relating voluntary registration and bunching to firm-level characteristics: share of B2C sales, input-cost ratio, and industry competition (Lerner index).
  - Partition sample into groups based on predicted likelihood of voluntary registration to examine heterogeneous bunching responses.
  - Investigate mechanisms: under-reporting of sales (evasion) and dynamic regressions addressing persistence versus inertia in registration decisions.
- Appendices and supplementary analyses referenced:
  - Appendix A: theoretical proof that firms with only B2C sales will not voluntarily register.
  - Online Appendices B and D: details on evasion evidence.
  - Online Appendix E: dynamic regressions of voluntary registration.
  - Additional appendices: B. Extended Model with VAT Evasion; C. The Optimal VAT Threshold; D. Evidence of Bunching via Turnover Misreporting; E. Dynamic Regressions of Voluntary Registration; F. Data construction.

### Key empirical findings (numeric fidelity preserved)
- Aggregate patterns:
  - Strong evidence of bunching at the VAT registration threshold.
  - On average, 43 percent of firms with turnover below the current-year threshold were registered for VAT over 2004-2014.
- Determinants of voluntary registration (marginal effects reported):
  - A one-standard deviation (s.d.) decrease in the share of B2C sales increases the probability of voluntary registration by 4 percentage points.
  - A one-s.d. increase in the input-cost ratio increases the probability of voluntary registration by 4.9 percentage points.
  - A one-s.d. decrease in the Lerner index of competition increases the probability of voluntary registration by 3.9 percentage points.
- Heterogeneous bunching results:
  - For firms predicted to be less likely to register voluntarily, larger bunching responses occur when:
    - (i) the proportion of B2C sales is low;
    - (ii) the cost of inputs relative to sales is high;
    - (iii) the Lerner index of their industry is low (i.e., more competitive).
  - For firms predicted to be highly likely to register voluntarily, bunching patterns are unrelated to these three characteristics.

### Mechanisms, robustness, and dynamics
- Evasion:
  - Suggestive evidence that part of the bunching response is driven by evasion in the form of under-reporting of sales (details in online Appendices B and D).
- Dynamics and persistence:
  - Dynamic regressions suggest some persistence in registration behavior but indicate that voluntary registration is not entirely driven by inertia or failure to deregister (see online Appendix E).
- Robustness:
  - Results for voluntary registration are robust to linear probability and fixed-effects logit specifications, and to inclusion of controls such as distance to the VAT threshold.

### Contributions and positioning in literature
- Novelty:
  - Provides a unified model that explains both voluntary VAT registration and bunching at the registration threshold through a three-stage production structure.
  - Formally derives predictions about how input intensity, B2C share, and competition affect both voluntary registration and bunching.
  - Provides empirical validation using comprehensive UK administrative data.
- Relation to prior work:
  - Contrasts with Keen and Mintz (2004) and related models that allow only for final consumer sales and thus cannot explain voluntary registration.
  - Builds on informal predictions in the literature (e.g., Brashares and others (2014)) and extends understanding of the role of market competition and firm heterogeneity.

*Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019205-print-pdf.pdf*

### Section IV.A below. In a related paper, Brashares and others (2014) use a calibrated formula

### Section IV.A

### Key modeling choices
- The model allows small firms to price-discriminate between B2C and B2B customers (prices p_C(a), p_B(a)), because if e_C ≠ e_B the small firm prefers to price-discriminate; ruling out price discrimination is not tractable unless e_C = e_B.
- The homogeneous good Y may be subject to VAT or not; the parameter λ measures final demand by households for goods produced by small firms (the share of B2C sales).
- The model assumes constant-returns fixed-coefficients technology for small firms (one unit of output for an a-type firm requires ω/a units of the input and (1−ω)/a units of labour), following Keen and Mintz (2004).
- Three stages of production are required to generate voluntary registration in equilibrium: upstream input production, small-firm production, and a large downstream firm buying inputs (i.e., at least three stages).
- The model treats the large downstream firm as operating at a scale where non-registration for VAT is never profitable (it is always VAT-registered).
- For tractability in the remainder of the theoretical section the authors set e_C = φ and e_B = γ so that A_C = 1 and A_B = (1+t)^−e_B ((e_B−1)/e_B)^e_B, making demand parameters exogenous.

### Rationale for modeling choices and scope
- Allowing price discrimination is justified because when e_C ≠ e_B the firm prefers to price discriminate, and price-discrimination eases tractability. Some results (Proposition V.B parts (c) and (d), Propositions V.C–B) assume e_C = e_B so the price-discrimination assumption is without loss of generality for those results.
- Compliance costs to VAT registration are not included in the baseline model for simplicity; the authors note these costs are relatively small for the UK (around 1.5% of turnover at the registration threshold, declining to 0.1% or less for large companies, Federation of Small Businesses, 2010) and are included later in Section V.D.
- Exports can be interpreted in the model as equivalent to domestic B2B sales for the supplier, since exporters do not bear the burden of output VAT; the model could cover the exporter case by replacing 1+t in ((3)) with 1+t* where t* is the foreign VAT rate.
- The baseline model does not allow for evasion to avoid overloading analysis; evasion is introduced in Section B (online appendix).

### Comparison with prior models and necessity of three stages
- When λ = 1 the model is closely related to the Keen and Mintz model: both have firm heterogeneity, labor and intermediate inputs, and when all sales are B2C voluntary registration is not desirable.
- The de Paula and Scheinkman (2010) model has only two stages of production (upstream and downstream firms) and hence cannot generate voluntary registration in equilibrium because voluntary registration cannot occur in equilibrium with only two stages; this is why de Paula and Scheinkman (2010) is not suited to the authors’ investigation.
- The authors emphasize that at least three stages are required to generate voluntary registration in equilibrium; with only B2C sales (λ = 1) voluntary registration never occurs, and with only B2B sales (λ = 0) all firms register voluntarily (so no bunching). Thus coexistence of voluntary registration and bunching requires 0 < λ < 1.

### Implications for analysis and comparative statics
- The model embeds parameters measuring: (i) input cost ratio ω (intensity of input use), (ii) share of B2C sales λ, and (iii) demand elasticities e_C, e_B (and competition measured by e).
- Equilibrium is defined by: (i) price P for the homogeneous product given by the mark-up equation P = γ/(γ−1) C; (ii) for each a ∈ [a, a], prices p_C(a), p_B(a) and registration decision I(a) that maximize firm profit given A_C, A_B; (iii) demand shifts A_C, A_B as functions of p_C(a), p_B(a), I(a) via ((6)) and ((5)).
- Results and comparative statics are examined conditional on fixed values of λ, ω, e_C, e_B; these parameters will be varied to study effects on voluntary registration and bunching.

*Source: Section IV.A of the supplied content unit.*

### 1.  Estimation Method

### 1.  Estimation Method

### Estimation approach and empirical measure of bunching
- Bunching is expressed as B = ∆s∗ h(s∗), where h(s∗) is the counterfactual density of firms over the bunching interval (assumed constant).
- Empirical measure of bunching used:
  - b = (sum_{j=s∗}^{s∗−} (c_j − ĉ_j) / N) / (sum_{j=s∗}^{s∗−} ĉ_j)
  - c_j is the actual number of firms in each £1,000 turnover bin.
  - ĉ_j is the counterfactual bin count without the notch.
  - The excluded range (s∗−, s∗+) specifies turnover bins around the notch where bunching occurs and are excluded from predicting the counterfactual distribution.
  - s∗− is set at the point where excess bunching starts.
  - s∗+ is estimated iteratively to ensure excess mass below the VAT notch equals the missing mass above.
  - N is the number of bins in the excluded range (s∗−, s∗+).
- Interpretation: equation ((24)) measures excess mass as the difference between predicted and actual mass of firms in the excluded range, divided by the average counterfactual density of firms in that range.

### Counterfactual density estimation
- Companies are grouped into bins of £1,000.
- Counterfactual distribution is estimated by fitting a flexible polynomial of order 5 to the empirical distribution, excluding a range around the VAT notch, following Chetty and others (2011) and Kleven and Waseem (2013).
- Regression specification used:
  - c_j = sum_{l=0}^q β_l (s_j)^l + sum_{i=s∗−}^{s∗+} γ_i I{j=i} + ε_j
  - c_j: number of companies in turnover bin j.
  - s_j: distance between turnover bin j and the VAT notch s∗.
  - q: order of the polynomial.
  - I{·}: indicator function for excluded bins.
  - ε_j: error term reflecting misspecification of the density equation.
- Robustness checks:
  - Polynomial orders between 4 and 7 were tried; results are not significantly changed.
  - The excluded range used is -£14,000 to £24,000, which ensures excess mass left of the notch is almost identical to the missing mass to the right.

### 2.  Graphical Evidence

### Main sample and visualization
- Sample: companies with turnover in the range between £45,000 below and £100,000 above the registration threshold.
- Data pooled from fiscal year 2004/05 through 2014/15.
- Counterfactual distribution estimated by fitting a 5th-order polynomial excluding a range around the VAT notch.

### Key empirical findings
- Bunching is evident below the VAT threshold.
  - Bunching estimate: 1.361 (std. error: 0.202).
  - Interpretation: total excess bunching mass is almost 1.4 times the average height of the counterfactual over the excluded range.
- There is only a small hole in the distribution above the VAT notch compared with the large spike below.
- The paper does not attempt to estimate optimization frictions implied by the missing mass to the right due to reasons discussed in Section IV.
- Both evasion and real responses may drive observed bunching; no decomposition is attempted because no variation allows separation.
- The online appendix contains suggestive evidence that misreporting of turnover may partly explain bunching behavior.

### 3.  Heterogeneity in Bunching

### Identification strategy for heterogeneity
- Challenge: some firms voluntarily register and are indifferent to the VAT threshold.
- Approach:
  1. Regress voluntary registration status on three key variables (share of B2C sales, input cost ratio, Lerner index) using only firms below the turnover threshold.
  2. Use estimated coefficients to obtain a predicted probability of voluntary registration for each firm i in year t.
  3. Divide firms into two groups depending on whether predicted probability is above or below the median (predicted to register voluntarily vs. predicted not to register).

### Heterogeneity by B2C share
- Firms divided into quartiles of the B2C share distribution.
- For firms predicted to not register voluntarily (VAT notch binding):
  - Bunching estimate by quartile: Q1 = 0.5; Q4 ≈ 1.4.
  - Bunching estimate is positively correlated with the share of B2C sales.
- For firms predicted to register voluntarily:
  - Bunching estimates are consistently low, between 0.3 and 0.6, with no clear pattern across quartiles.

### Heterogeneity by product market competition (Lerner index)
- Lerner index measured at 4-digit industry level (defined as one minus the average profit margin; higher values imply more competitive industry).
- For firms predicted to not register:
  - Strong positive correlation between bunching and degree of competition.
  - Bunching estimate for Q4 = 1.7.
- For firms predicted to register voluntarily:
  - Consistently low bunching estimates across quartiles without a specific pattern.

### Heterogeneity by input cost ratio
- Input cost ratio constructed using information from the FAME subsample.
- For firms predicted to not register:
  - Degree of bunching generally decreases with the input cost ratio, though not fully monotonic (first quartile estimate relatively low).
- For firms predicted to register voluntarily:
  - Bunching estimates are flat across quartiles.

### 4.  Implications for VAT Threshold Design

### Theoretical refinement and B2B sales
- The paper develops a formula for the optimal threshold in the model (online appendix) that:
  - Accounts for a behavioral response specific to the model.
  - Allows for B2B sales (λ<1), a feature absent in Keen and Mintz (2004).
- Finding: the optimal threshold in the presence of B2B sales (λ<1) is higher than in the absence of B2B sales.
- Intuition: only B2C sales by small firms above the threshold are taxed in the model; B2B sales to the large firm are eventually taxed because the large firm’s sales are taxed. Therefore raising the threshold forgone revenue cost is smaller when the small firm’s sales are more B2B.
- A second indirect mechanism: increasing the threshold raises prices that small firms charge for inputs to the large firm, which is passed on by the large firm, increasing the VAT base (details in online Appendix C).

### Cross-country empirical evidence
- Constructed cross-country relationship between average ratio of B2C sales and the ratio of the VAT threshold in year 2017 over GDP per capita (adjusts for relative size of turnover by small businesses).
- Proxy for informal sector: share of the agricultural sector in GDP (following Keen and Lockwood, 2010).
- Empirical pattern (Figure 7):
  - Panel A: positive correlation between average B2C ratio and VAT threshold/GDP per capita.
    - Estimated slope coefficient = 0.06, significant at the 10 percent level (p−value = 0.089).
  - When controlling for size of the informal sector:
    - Relation becomes negative.
    - Estimated slope coefficient = -0.03, highly significant (p−value = 0.005).
- Interpretation: VAT threshold tends to be higher with higher compliance and administration costs (proxied by larger informal sector) and less direct selling to consumers.

### 5.  Conclusions (selected)
- Conceptual framework requires at least three stages of production with intermediate-stage firms selling to final consumers and other firms; predicts coexistence of voluntary registration and bunching.
- Comparative statics: voluntary registration more likely, and bunching less likely, when:
  - (i) input costs relative to sales are high,
  - (ii) proportion of B2C sales is low,
  - (iii) level of product market competition is low.
- Evasion opportunities generally make voluntary registration more likely and have an ambiguous effect on bunching.
- Empirical evidence from linked UK corporate income and VAT records:
  - Voluntary registration is more likely with a low share of B2C sales, a high input-cost ratio, and more competition in the industry.
  - Clear evidence of bunching at the VAT threshold.
  - Heterogeneity in bunching matches theoretical predictions: bunching increases with B2C sales ratio and decreases with input-cost ratio and level of competition.
- Discussion and cross-country evidence provided on implications for optimal VAT threshold design.

*Source: wpiea2019205-print-pdf - 1.  Estimation Method*

### REFERENCES

### REFERENCES (Content Unit: wpiea2019205-print-pdf - REFERENCES)

### Key literature cited
- Empirical and theoretical studies on VAT, thresholds, notches, and bunching:
  - Almunia, Miguel; Lockwood, Ben; Scharf, Kimberley, 2017.
  - Almunia, Miguel; Lopez-Rodriguez, David, 2018.
  - Asatryan, Zareh; Peichl, Andreas, 2016.
  - Best, Michael; Kleven, Henrik J., 2018.
  - Best, Michael Carlos; Brockmeyer, Anne; Kleven, Henrik Jacobsen; Spinnewijn, Johannes; Waseem, Mazhar, 2015.
  - Brashares, Edith; Knittel, Matthew J.; Silverstein, Gerald; Yuskavage, Alex, 2014.
  - Chetty, Raj; Friedman, John N.; Olsen, Tore; Pistaferri, Luigi, 2011.
  - de Paula, Aureo; Scheinkman, Jose, 2010.
  - Devereux, Michael P.; Liu, Li; Loretz, Simon, 2014.
  - Ebrill, Liam P.; Keen, Michael; Bodin, Jean-Paul; Perry, Victoria P., 2001.
  - Emran, M. Shahe; Stiglitz, Joseph E., 2005.
  - Federation of Small Businesses, 2010.
  - Harju, Jarkko; Matikka, Tuomas; Rauhanen, Timo, 2016.
  - HM Revenue and Customs, 2015.
  - Kanbur, Ravi; Keen, Michael, 2014.
  - Keen, Michael; Lockwood, Ben, 2010.
  - Keen, Michael; Mintz, Jack, 2004.
  - Kleven, Henrik, 2016.
  - Kleven, Henrik Jacobsen; Waseem, Mazhar, 2013.
  - Kopczuk, Wojciech; Munroe, David, 2015.
  - Liu, Li; Lockwood, Ben, 2015.
  - Onji, Kazuki, 2009.
  - Saez, Emmanuel, 2010.
  - Slemrod, Joel, 2010.
  - Vesal, Mohammad, 2013.
  - Waseem, Mazhar, 2016.
  - Wooldridge, Jeffrey M., 2005.

### Empirical findings and statistics (from tables and figures)
- Distribution and bunching evidence:
  - Figure 1: histogram of companies’ turnover net of current-year VAT registration threshold (normalized VAT notch), pooling 2004/05-2014/15; bin width £1,000.
  - Figure 2: transition probabilities for firms voluntarily registered during 2004/05-2009/10 to remain registered and below the threshold, registered and above the threshold or deregistered in following years.
  - Figures 4–6: bunching estimates around the VAT notch across quartiles of B2C share, Lerner Index, and Input-Cost Ratio for pooled dataset 2004/05-2014/15; panels distinguish firms predicted to register voluntarily (nonbinding threshold) and not predicted to register voluntarily (binding threshold).
  - Figure 7: cross-country evidence on VAT threshold and B2C ratio across 103 countries in 2017; Panel A controls for GDP per capita (VAT threshold as fraction of GDP per capita); Panel B further controls for size of informal sector by regressing VAT threshold fraction on share of agriculture and plotting residual vs B2C ratio.
- Table 1: effect of competition on sufficient statistic T across elasticity of demand (e), B2C share (λ), and input cost ratio (ω). Example entries:
  - ω=0.9, λ=0.1: e=2? table entries listed as 1.039 1.408 1.967 2.361 1.564 0.678 (presented as sequence under heading e25102050100).
  - ω=0.9, λ=0.9: 0.826 0.796 0.739 0.629 0.381 0.164.
  - ω=0.1, λ=0.1: 0.898 0.786 0.530 0.148 0.001 0.000.
  - ω=0.1, λ=0.9: 0.714 0.444 0.199 0.039 0.000 0.000.
- Table 2: UK VAT system (selected rows):
  - Fiscal Year 2004-05: Registration Threshold (£) 58,000; Deregistration Threshold (£) 56,000; Standard Rate (%) 17.5; Flat-Rate Scheme Threshold (£) 150,000.
  - Fiscal Year 2014-15: Registration Threshold (£) 81,000; Deregistration Threshold (£) 79,000; Standard Rate (%) 20.0; Flat-Rate Scheme Threshold (£) 150,000.
- Table 3: Summary statistics (top variables in thousands of pounds):
  - Total Turnover: Mean 74.694; St.Dev. 48.881; p10 19.88; p50 62.70; p90 151.80; Observations 3,461,247.
  - Trading profit: Mean 21.882; St.Dev. 7.250; p10 0.00; p50 11.82; p90 59.71; Observations 3,461,247.
  - Total Input Costs (CT600): Mean 52.814; St.Dev. 4.271; p10 12.04; p50 36.55; p90 123.46; Observations 3,461,247.
  - Input-Cost Ratio (CT600): Mean 0.71; St.Dev. 0.28; p10 0.28; p50 0.78; p90 1.00; Observations 3,461,247.
  - Share of B2C Sales: Mean 0.55; St.Dev. 0.24; p10 0.29; p50 0.45; p90 0.91; Observations 3,461,247.
  - Lerner Index: Mean 0.75; St.Dev. 0.11; p10 0.58; p50 0.77; p90 0.90; Observations 3,461,247.
  - VAT Registered: Mean 0.63; St.Dev. 0.4830; Observations 1,134,612,47? (note: table shows 113461247 as concatenation).
  - Note: 1 GBP = 1.29 USD as of September 2018.
- Table 4 (Determinants of Voluntary VAT Registration, binary choice model, equation (23)):
  - Share of B2C Sales coefficients: -0.233***, -0.167***, -0.025**, 0.008 (standard errors shown).
  - Input-Cost Ratio coefficients: 0.153***, 0.204***, 0.064***, 0.064***.
  - Lerner Index coefficients: -0.417***, -0.356***, -0.195***, -0.214***.
  - Observations vary across columns (e.g., 2405144, 213... entries appear; preserve as in table).
  - Controls, Year FE present; Firm FE added in columns (5)-(8).
  - Significance: *, **, *** denote 10%, 5%, 1%.
- Table 5: robustness of determinants using other input-cost measures (CT600 vs FAME), similar sign patterns; observations and cost-ratio source indicated.

### Theoretical results and model structure (Appendix A, B, C)
- Appendix A: Theoretical proofs (Propositions V.A–V.C) on firms’ registration incentives and bunching:
  - Key analytical results preserved:
    - For λ=1 (only B2C), prices are mark-ups p_C = e_C/(e_C−1) c(I;a) and profit expressions π(0;a) and π(1;a) given in (A.1); voluntary registration not profitable under stated restrictions.
    - Derivations produce conditions like inequality forms ((16)), ((18)), and expressions such as A.3, A.4 for π(1;a), π(0;a).
    - Proposition V.C yields bunching condition expressed via equation ((21)) after manipulations in (A.13).
    - Comparative statics: dx/dλ < 0, dx/dω > 0; bunching increases if T_e < 0.
- Appendix B: Extended model with VAT evasion (under-reporting of sales):
  - Evasion parameters: non-registered firms hide share ν_N of B2C sales; registered firms hide share ν_R of B2C sales, with 0 ≤ ν_R ≤ ν_N < 1.
  - VAT sufficient statistic with evasion: T(ν) = (1−Δ_d(ν_R))(1+Δ_c)^{e−1}, Δ_d(ν_R) = λ(1−(1+(1−ν_R)t)^{−e}) / [λ+(1−λ)A_B] (equation B.17).
  - Adjusted bunching tax term: T̂(ν_N,ν_R) = [(1−ν_N)λ+(1−λ)A_B] / [λ+(1−λ)A_B] × T(ν_R) (equation B.18).
  - Qualitative implications summarized:
    - Increase in ν_N increases bunching.
    - Increase in ν_R increases voluntary registration likelihood and reduces bunching.
    - Evasion does not change qualitative effects of λ (B2C fraction) and ω (input-cost ratio) on voluntary registration and bunching.
- Appendix C: Optimal VAT threshold (revenue-maximizing):
  - VAT base B and revenue R definitions: B = PY + ∫_{a}^{â} p(a)x(a) da + ω ∫_{a}^{â} [x(a)+y(a)]/a da (C.27); Revenue R = tB − (a−â)A (C.28) where Γ>0 compliance cost and A>0 administration cost.
  - Equilibrium price schedule p(a) piecewise given in (C.29).
  - First-order condition for revenue-maximizing threshold (C.38):
    - ∂R/∂s* = (t ω â / (s* p(s*)) − t(1−β)s* + A) ∂â/∂s* + tβ(â−a*) + t e/(e−1) ω p(s*) ln(â/a*) = 0.
  - Special case reproducing Keen and Mintz (2004) when e=0 and β=0 yields s* = A / (t v) (C.40).
  - Generalized formula (C.41):
    - s* = [A + t( β(â−a*) + e/(e−1) ω p(s*) ln(â/a*) ) / (∂â/∂s*)] / [t(v−β)]
  - Interpretations:
    - B2B sales (β>0) tend to raise optimal threshold s*; behavioral response (e>0) generally raises threshold.

### Empirical diagnostics and dynamics (Appendices D, E, F)
- Appendix D: Evidence on bunching via turnover misreporting:
  - Figure A.9 (Panel A & B): compares average input-cost ratio for registered vs non-registered firms across £1,000 turnover bins around normalized VAT notch.
    - Panel A (salary-exclusive input-cost ratio): registered firms consistently show larger input-cost ratio than non-registered firms below the VAT notch; non-registered series smooth across notch.
    - Panel B (salary-inclusive cost ratio): sharp increase in average input-cost ratio for non-registered firms just below the VAT notch, consistent with turnover misreporting hypothesis and salary being harder to underreport due to third-party reporting.
  - Conclusion: Panel A and B provide suggestive but not conclusive evidence that part of bunching is due to turnover misreporting.
- Appendix E: Dynamic regressions of voluntary registration:
  - Transition matrix (Table A.1): substantial persistence in registration status; examples:
    - Firms initially registered in 2004/05: 82.23% remained registered a year later (t=1).
    - For non-registered firms, 81.44% remain unregistered after 5 years; 64% of registered firms remain registered after 5 years.
  - Dynamic fixed-effect Probit model (equation E.42) includes lagged registration R_{i,t−1}, (1−R_{i,t−1}) IR_{it}, R_{i,t−1} ID_{it}, and controls B2C_{jit}, ICR_{it}, L_{jit}, distance to threshold, year FE, firm FE.
  - Table A.2 (coefficients highlights):
    - Lagged Registration (Rt-1): coefficient ~3.700*** in many specifications.
    - Initial Reg Status (R0): positive and significant (e.g., 0.937***).
    - (1−R)*IR: large positive coefficients around 4.7–5.2***.
    - R*ID: positive coefficients around 0.96–1.84***.
    - Average Share of B2C Sales: negative and significant (e.g., -0.598*** in some specs).
    - Average Input-Cost Ratio and Average Lerner Index: negative and significant in mean-characteristic terms.
  - Table A.3 (average partial effects):
    - For firms registered in previous year, falling below deregistration threshold lowers probability of current registration by 5.57 percentage points (0.0557***).
    - For firms not registered in previous year, going above registration threshold increases probability of registration by 70.4 percentage points (0.704***; presented as 0.782*** avg partial in table context).
    - One-standard-deviation increases:
      - B2C + σ_B2C: average predicted probability falls by 0.0028***.
      - ICR + σ_ICR: increases probability by 0.0073***.
      - Lerner + σ_Lerner: decreases probability by 0.0058***.
  - Interpretation: persistence exists but registration reacts strongly to current turnover relative to thresholds and to fundamental determinants (B2C share, input-cost ratio, Lerner index).
- Appendix F: Data construction and sample:
  - Data sources combined: Corporation Tax returns (CT600), VAT returns, FAME, and annual sector-level B2C ratios (ONS Input-Output tables).
  - Linkage and sample sizes:
    - CT600 merged with FAME: 7,914,902 company-year records covering April 1, 2004–April 4, 2015; 93% merge rate for CT600 with FAME (12-month accounting period).
    - After merging with VAT returns and applying exclusions, merged dataset for industries with B2C ratios: 6,536,170 company-year observations.
    - Final analysis sample (turnover between €10,000 to €200,000): 3,461,247 company-year observations with 968,353 unique companies between 2004/2005 to 2014/2015.
  - Sample exclusions: groups, zero-length registrations, non-corporate status, measurement errors (input VAT > input value), non-profit entities, LLPs, public investment trusts, financial services industry under SIC.

*Italic: Source: wpiea2019205-print-pdf - REFERENCES (imf.org PDF content provided).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019205-print-pdf.pdf_