## _wp9121

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### Summary: purpose and main results
- The paper analyzes the implications of widespread exemptions in developing-country value-added tax (VAT) systems.
- Two basic adjustments to the base of a VAT with exemptions:
  - subtract the value of sales to consumers of exempt goods and services; and
  - add the value of the sales of taxable inputs used in the production of exempt goods and services.
- Derives a formula, with the aid of an input-output table, to determine the impact of a given list of exempt activities on the size of the tax base.
- Obtains an expression for the elasticity of a VAT with exemptions with respect to aggregate consumption and illustrates implications of changes in an economy’s productive structure for the VAT base.

### I. Introduction: context and scope
- Developing-country VAT systems typically exempt a large share of economic activity, chiefly for administrative expediency.
- Estimating the VAT base with exemptions requires information beyond final sales of exempt goods and services; it requires the economy’s productive structure to account for taxed inputs used by exempt sectors.
- The procedure to estimate the base of a VAT with significant exemptions can be quite complicated.
- The paper: discusses rationale for exemptions; examines how exemptions affect the VAT potential base; derives the formula for estimating the potential base; and examines economic implications of a VAT with exemptions.

### II. Exemptions in the Developing Countries Context
- Zero-rating purges tax embodied in inputs and is superior to exemption for distributive goals, but zero-rating is administratively complex and usually confined to exports and some sensitive goods/services; exemption is more common domestically and in developing countries.
- Common exemptions in developing countries include basic foodstuffs, newspapers and books, and selective taxation of services (reference to Tait (1988)).
- Equity and administrative expediency can justify exempting basic foodstuffs where agricultural output is hard to tax and such commodities represent an important share of poor households’ budgets.
- Some countries adopt a VAT restricted to the manufacturing-import stage (a manufacturing-import sales tax with a tax credit feature) to reduce tax collection points and administration/compliance costs.
  - Risks: manufacturers may understate manufacturing-stage sales, integrate vertically, or use transfer pricing; direct sales from manufacturer to retailers/final consumers complicate matters.
  - Alternative: exempt traders below a stipulated minimum (size-of-trader exemption) can pressure small producers to register; policing exemption limits is difficult.
- Proliferation of exemptions of manufactured goods can erode the tax base with little administrative savings; many exemptions may lack economic or administrative justification.

### III. The Impact of Exemptions on the Base of a VAT
- A consumption-type VAT without exemptions and with zero-rating for exports has base equal to final sales of consumer goods and services.
- Total value of sales in the economy (intermediate + final) is expressed as:
  - Cd + Id + x + ISd + ISm + Im + Cm (equation (1), variables defined in text).
- When exemptions exist, intermediate sales can generate net tax liabilities because purchaser credits may be absent for exempt purchasers.
- Matrix of technological coefficients A partitioned by exempt (1) and taxed (2) sectors:
  - A = [ A11  A12
          A21  A22 ] (equation (4))
  - A11: k by k matrix, exempt→exempt intermediate requirements
  - A12: k by n-k matrix, exempt→taxed requirements
  - A21: n-k by k matrix, taxed→exempt requirements
  - A22: n-k by n-k matrix, taxed→taxed requirements
- Two adjustments to aggregate consumption to account for exemptions:
  1. Subtract value of exempt consumer goods (final sales of exempt goods).
  2. Add value of intermediate sales of taxed industries to the exempt sector.
- Additional adjustments noted:
  - add purchases of taxed capital goods by the exempt sector (treated as intermediate sales because exempt purchasers do not receive credits);
  - include the component of sales value that represents tax on inputs to exempt sectors if their products are sold to taxed sectors.
- Formula for the base of a consumption-type VAT that zero-rates exports and exempts certain industries (equation (7), notation preserved in source).

- Two-sector closed-economy numerical example (Table 1):
  - General case (upper panel):
    - Exempt sector:
      - purchases of intermediate inputs from exempt = 60
      - purchases of intermediate inputs from taxed = 90
      - final demand = 170
      - gross output = 380
      - value added = 230
    - Taxed sector:
      - sales to exempt = 90
      - sales to taxed = 100
      - final demand = 390
      - gross output = 580
      - value added = 330
    - Total value added = 560 = total final demand; VAT base without exemptions = 560.
    - With exemptions: subtract exempt consumption 170; add sales of taxed to exempt 90; VAT base = 480.
  - Special case (no intermediate sales from exempt to taxed; lower panel):
    - Exempt sector final demand = 270
    - taxed→exempt sales = 90
    - VAT base after adjustments = 380 which equals value added of taxed sector.
- General result:
  - The VAT base with exemptions will be greater than the value added of the taxed sector and the reduction to the base from exempting part of the economy is less than the value added of the exempt sector, except in the special case when exempt sectors make no intermediate sales to taxed sectors.

- Practical data issues and workarounds:
  - Industry definitions in input-output tables may not map exactly to exempt/taxed classifications (e.g., food preparation may contain taxed and exempt subindustries).
  - Suggested workaround: estimate base assuming entire industry exempt, then assuming entirely taxable, then take a weighted average using available information on subindustry sales.
  - Small trader exemptions (across industries) require additional data, possibly industry surveys on distribution of sales by firm size.

### IV. Some Implications of a VAT with Exemptions
- Elasticity properties:
  - The potential base of a consumption-type VAT with no exemptions has elasticity of one with respect to aggregate consumption.
  - With exemptions, elasticity of the potential base with respect to aggregate consumption may differ from one; it depends on:
    - elasticity of exempt consumption with respect to total consumption (E_cl);
    - elasticity of taxed consumption with respect to total consumption (E_c2);
    - shares of exempt and taxed consumption in total consumption; and
    - extent to which exempt sector relies on taxed inputs (productive structure).
- Input-output relationships and notation:
  - A0 GO + FS = CO (equation (8))
  - FS = [I-A] GO (equation (9))
  - GO = [I-A]^-1 FS (equation (10)); denote B = [I-A]^-1.
  - Restatement of the VAT base using B (equation (11)) and further transformations yield expressions (12), (13), (14).
  - Definitions:
    - k1 reflects demand for taxed-sector inputs generated by final sales of exempt products.
    - k2 reflects demand for taxed-sector inputs generated by final sales of taxed products.
- Elasticity of the tax base with respect to total consumption (E_tb) (equation (15), symbolic form preserved):
  - E_tb = [ (1+k2) C2 + k1 C1 ]^-1 [ k1 C1 * E_cl + (1+k2) C2 * E_c2 ]
- Observations from formula (15):
  - k1 and k2 are greater than zero but less than 1.
  - For given k1 and k2, elasticity of the base varies positively with share of taxed goods in total consumption, provided average E_c2 exceeds E_cl.
  - Expression (15) is a weighted average of the elasticities of consumption of exempt (E_cl) and taxed (E_c2) goods with respect to aggregate consumption.
  - If share of taxed products in total consumption generally exceeds 50 percent and k1 does not exceed (1+k2), the weight on the elasticity of taxed goods will exceed that on exempt goods.

- Approximation when A is unavailable:
  - The elasticity of the tax base with respect to aggregate consumption could be approximated by the elasticity of taxed consumption with respect to aggregate consumption; approximation error depends on k1, k2, and shares of exempt consumption.
  - Numerical illustration (two-sector example, upper panel of Table 1; assume 30 percent share of exempt products):
    - Matrix A elements: a11 = 0.158; a12 = 0.259; a21 = 0.237; a22 = 0.172.
    - Matrix B elements: b11 = 1.302; b12 = 0.407; b21 = 0.373; b22 = 1.325.
    - Resulting k1 = 0.31 and k2 = 0.10.
    - Table 2 (derived from the general case assuming a 30 percent share of exempt products) reports elasticities; example entries:
      - when elasticity of exempt goods = 0.00 and elasticity of taxed goods = 1.44, elasticity of tax base = 1.28 (difference 0.16)
      - when elasticity of exempt goods = 0.50 and elasticity of taxed goods = 1.22, tax base elasticity = 1.14 (difference 0.08)
    - The approximation error falls as elasticity of taxed goods declines and elasticity of exempt goods rises; the error increases with either the share of exempt consumption in total consumption or larger k1.

- Technological change effects:
  - Even if shares of exempt and taxed consumption remain constant and both elasticities equal one, the elasticity of the potential base can differ from one if productive structure evolves (i.e., technological coefficients a_ij change).
  - If a_ij values fall over time (reduced input requirements), elements of B and terms in formula (11) fall, reducing the potential base; faster falls in a_ij yield greater effects on the potential base.

- Practical conclusion:
  - Estimating the VAT base with exemptions must account for sales of taxed industries to exempt industries.
  - Applicability and practical significance depend on quality of economic statistics and relative size of exempt industries.
  - In practice, estimating final sales of exempt products may be easier than estimating sales of taxed industries to exempt industries, but the latter must be taken into account for accurate base estimation.

*Source: _wp9121*

### Introduction

### _wp9121 - Introduction

### II. Exemptions in the Developing Countries Context
- Section title: "Exemptions in the Developing Countries Context"
- No further content provided in source.

### III. The Impact of Exemptions on the Base of a VAT
- Section title: "The Impact of Exemptions on the Base of a VAT"
- No further content provided in source.

### IV. Some Implications of a VAT with Exemptions
- Section title: "Some Implications of a VAT with Exemptions"
- No further content provided in source.

### Tables
- Table 1: "Examples of VAT Base Calculation"
- Table 2: "Elasticities of VAT Base and Taxed Consumption with Respect to Aggregate Consumption"

*Source: _wp9121 - Introduction*

### References

### _wp9121 - References

### Summary
- The value-added tax (VAT) has already been adopted by many deve loping countries and is being actively considered by others.
- These countries typically exempt a large number of goods and services from this tax.
- Exemptions are most readily justified on grounds of administrative expediency or equity.
- Two basic adjustments must be made to the base of a VAT with no exemptions:
  - subtract the value of sales to consumers of exempt goods and services; and
  - add the value of the sales of taxable inputs used in the production of exempt goods and services.
- The paper derives a formula, with the aid of an input-output table, to determine the impact of a given list of exempt activities on the size of the tax base.
- The paper obtains an expression for the elasticity of a VAT with exemptions with respect to aggregate consumption and illustrates implications of changes in an economy’s productive structure for the VAT base.

### I. Introduction
- Developing-country VAT systems typically exempt a large share of economic activity, chiefly for administrative expediency.
- Estimating the VAT base with exemptions requires information beyond final sales of exempt goods and services; it requires the economy’s productive structure to account for taxed inputs used by exempt sectors.
- The procedure to estimate the base of a VAT with significant exemptions can be quite complicated.
- The paper: discusses rationale for exemptions; examines how exemptions affect the VAT potential base; derives the formula for estimating the potential base; and examines economic implications of a VAT with exemptions.

### II. Exemptions in the Developing Countries Context
- In a costless-administration world, exemption would be unnecessary except perhaps where value added is hard to define; zero-rating is superior to exemption for distributive goals because zero-rating purges tax embodied in inputs.
- Zero-rating is administratively complex and in most VAT systems is confined to exports and some sensitive goods/services; exemption is more common domestically and in developing countries.
- Common exemptions in developing countries include basic foodstuffs, newspapers and books, and selective taxation of services (reference to Tait (1988)).
- Equity and administrative expediency can justify exempting basic foodstuffs in developing countries where agricultural output is hard to tax and such commodities represent an important share of poor households’ budgets.
- Some developing countries adopt a VAT restricted to the manufacturing-import stage (a manufacturing-import sales tax with a tax credit feature) to reduce tax collection points and administration/compliance costs.
  - Risks: manufacturers may understate manufacturing-stage sales, integrate vertically, or use transfer pricing; direct sales from manufacturer to retailers/final consumers complicate matters.
  - Alternative: exempt traders below a stipulated minimum (size-of-trader exemption) can pressure small producers to register; policing exemption limits is difficult.
- Proliferation of exemptions of manufactured goods can erode the tax base with little administrative savings; many exemptions may lack economic or administrative justification.

### III. The Impact of Exemptions on the Base of a VAT
- A consumption-type VAT without exemptions and with zero-rating for exports has base equal to final sales of consumer goods and services.
- Total value of sales in the economy (intermediate + final) is expressed as:
  - Cd + Id + x + ISd + ISm + Im + Cm (equation (1), variables defined in text)
- When exemptions exist, intermediate sales can generate net tax liabilities because purchaser credits may be absent for exempt purchasers.
- The matrix of technological coefficients A can be partitioned into four sub-matrices reflecting exempt (1) and taxed (2) sectors:
  - A = [ A11  A12
           A21  A22 ] (equation (4))
  - A11: k by k matrix, exempt→exempt intermediate requirements
  - A12: k by n-k matrix, exempt→taxed requirements
  - A21: n-k by k matrix, taxed→exempt requirements
  - A22: n-k by n-k matrix, taxed→taxed requirements
- By partitioning gross output and final sales similarly, formula (3) is restated as formula (5) with the intermediate sales separated into four categories: exempt→exempt; exempt→taxed; taxed→taxed; taxed→exempt.
- Two adjustments to aggregate consumption to account for exemptions:
  1. Subtract value of exempt consumer goods (final sales of exempt goods).
  2. Add value of intermediate sales of taxed industries to the exempt sector.
  - Additional noted adjustments: add purchases of taxed capital goods by the exempt sector (treated as intermediate sales because exempt purchasers do not receive credits); and include the component of sales value that represents tax on inputs to exempt sectors if their products are sold to taxed sectors.
- Formula for the base of a consumption-type VAT that zero-rates exports and exempts certain industries (equation (7), notation preserved in source).
- Two-sector closed-economy example (Table 1) illustrates calculations:
  - General case (upper panel):
    - Exempt sector: purchases of intermediate inputs from exempt = 60; from taxed = 90; final demand = 170; gross output = 380; value added = 230.
    - Taxed sector: sales to exempt = 90; to taxed = 100; final demand = 390; gross output = 580; value added = 330.
    - Total value added = 560 = total final demand; VAT base without exemptions = 560.
    - With exemptions: subtract exempt consumption 170; add sales of taxed to exempt 90; VAT base = 480.
  - Special case (no intermediate sales from exempt to taxed; lower panel):
    - Exempt sector final demand = 270; taxed→exempt sales = 90; VAT base after adjustments = 380 which equals value added of taxed sector.
- General result: the VAT base with exemptions will be greater than the value added of the taxed sector and the reduction to the base from exempting part of the economy is less than the value added of the exempt sector, except in the special case when exempt sectors make no intermediate sales to taxed sectors.
- Practical data issues:
  - Industry definitions in input-output tables may not map exactly to exempt/taxed classifications (e.g., food preparation may contain taxed and exempt subindustries).
  - Suggested workaround: estimate base assuming entire industry exempt, then assuming entirely taxable, then take a weighted average using available information on subindustry sales.
  - Small trader exemptions (across industries) require additional data, possibly industry surveys on distribution of sales by firm size.

### IV. Some Implications of a VAT with Exemptions
- The potential base of a consumption-type VAT with no exemptions has elasticity of one with respect to aggregate consumption.
- With exemptions, elasticity of the potential base with respect to aggregate consumption may differ from one; it depends on:
  - elasticity of exempt consumption with respect to total consumption (E_cl);
  - elasticity of taxed consumption with respect to total consumption (E_c2); and
  - shares of exempt and taxed consumption in total consumption; and
  - extent to which exempt sector relies on taxed inputs (productive structure).
- Relationship between gross output and final sales:
  - A 0 GO + FS = CO (equation (8))
  - FS = [I-A] GO (equation (9))
  - GO = [I-A]^-1 FS (equation (10)); denote B = [I-A]^-1.
- Restatement of the VAT base using B (equation (11)) and further transformations yield expressions (12), (13), (14).
  - Definitions:
    - k1 = sum over i,j of C_i^-1 a_ij ... (as defined in source; preserved symbolically)
    - k2 analogous (see source)
  - k1 reflects demand for taxed-sector inputs generated by final sales of exempt products.
  - k2 reflects demand for taxed-sector inputs generated by final sales of taxed products.
- Elasticity of the tax base with respect to total consumption (E_tb) is given by equation (15):
  - E_tb = [ (1+k2) C2 + k1 C1 ]^-1 [ k1 C1 * E_cl + (1+k2) C2 * E_c2 ] (preserved symbolic form from source)
- Observations:
  - k1 and k2 are greater than zero but less than 1; for given k1 and k2, elasticity of the base varies positively with share of taxed goods in total consumption, provided average E_c2 exceeds E_cl.
  - Expression (15) is a weighted average of the elasticities of consumption of exempt (E_cl) and taxed (E_c2) goods with respect to aggregate consumption.
  - If share of taxed products in total consumption generally exceeds 50 percent and k1 does not exceed (1+k2), the weight on the elasticity of taxed goods will exceed that on exempt goods.
- Approximation note:
  - If technological coefficients matrix is unavailable, the elasticity of the tax base with respect to aggregate consumption could be approximated by the elasticity of taxed consumption with respect to aggregate consumption (approximation error discussed).
  - Numerical illustration using the two-sector example (upper panel of Table 1) with 30 percent share of exempt products:
    - Matrix A elements: a11 = 0.158; a12 = 0.259; a21 = 0.237; a22 = 0.172.
    - Matrix B elements: b11 = 1.302; b12 = 0.407; b21 = 0.373; b22 = 1.325.
    - Resulting k1 = 0.31 and k2 = 0.10.
    - Table 2 (derived from the general case assuming a 30 percent share of exempt products) reports elasticities:
      - Example entries: when elasticity of exempt goods = 0.00 and elasticity of taxed goods = 1.44, elasticity of tax base = 1.28 (difference 0.16); when elasticity of exempt goods = 0.50 and taxed goods = 1.22, tax base elasticity = 1.14 (difference 0.08).
    - The approximation error falls as elasticity of taxed goods declines and elasticity of exempt goods rises; the error increases with either the share of exempt consumption in total consumption or larger k1.
- Technological change effects:
  - Even if shares of exempt and taxed consumption remain constant and both elasticities equal one, the elasticity of the potential base can differ from one if productive structure evolves (i.e., technological coefficients a_ij change).
  - If a_ij values fall over time (reduced input requirements), elements of B and terms in formula (11) fall, reducing the potential base; faster falls in a_ij yield greater effects on the potential base.
- Practical conclusion:
  - The derived formula for the base of a VAT with exemptions illustrates the need to account for sales of taxed industries to exempt industries when estimating the size of the tax base.
  - Applicability and practical significance depend on quality of economic statistics and relative size of exempt industries.
  - In practice, estimating final sales of exempt products may be easier than estimating sales of taxed industries to exempt industries, but the latter must be taken into account for accurate base estimation.

*Source: _wp9121 - References*

### References

### _wp9121 - References

### Cited works

- Aguirre, Carlos A., and Parthasarathi Shome, "The Mexican Value-Added Tax (VAT): Methodology for Calculating the Base," National Tax Journal, Vol. XLI, No. 4 (19881, pp. 543-54.  
- Ahmad, Ehtisham, and Nicholas Stern, "The Reform of Indirect Taxes," Chapter 7 in The Theory and Practice of Tax Reform in Developing Countries (Cambridge, United Kingdom, forthcoming).  
- Bird, Richard M., "A New Look at Indirect Taxation in Developing Coun- tries," World Development, Vol. 15, No. 9 (1987), pp. 1151-61.  
- Casanegra de Jantscher, Milka, "Problems of Administering a Value-Added Tax in Developing Countries," IMF Working Paper 86/115 (Washington: International Monetary Fund, 1986).  
- Newbery, David, and Nicholas Stern, The Theory of Taxation for Developing Countries (International Bank for Reconstruction and Development, 1987).  
- Stern, Nicholas, "Aspects of the General Theory of Tax Reform," Chapter 3 in The Theory of Taxation for Developing Countries, ed. by David Newbery and Nicholas Stern (International Bank for Reconstruction and Development, 1987).  
- Tait, Alan A., Value-Added Tax--International Practice and Problems (International Monetary Fund, 1988).  

*Source: _wp9121 - References*

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