Aguirre, Carlos A., and Parthasarathi Shome, “The Mexican Value-Added Tax (VAT): Methodology for Calculating the Base,” National Tax Journal, Vol. XLI, No. 4 (1988), 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 Countries,” World Development, Vol. 15, No. 9 (1987), pp. 1151–61.
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I am indebted to Alan Tait, Ved Gandhi, Ke-Young Chu, George Kopits, Richard Hemming, Christopher Towe, and Adrienne Cheasty for comments on an earlier version of this paper. I am responsible for any remaining errors.
Aguirre and Shome (1988) make detailed calculations of the base of the Mexican VAT, which has multiple rates and some important exemptions. The method they employ to take account of the impact of exemptions differs from the one presented here.
Thus, France exempts medical and educational services, rented housing, sports and entertainment, financial services, secondhand goods, and original art. Germany exempts the same activities exclusive of secondhand goods and original art, but also exempts museums. In neither country, however, is any domestic sector zero-rated. Portugal, Ireland, and the United Kingdom are three exceptions to this rule (Tait (1988), Table 3-1).
The theoretical base of the VAT in this case may be derived with the following formula:
GDPmarket prices + imports - exports - gross capital formation.
GDP at market prices would include indirect taxes net of subsidies but not the VAT itself, if the base is to be measured on a tax exclusive basis. The value of imports would also include customs duties because these are typically included in the base of the tax.
An additional adjustment to be made is the addition of purchases of taxed capital goods by the exempt sector. These purchases should be treated as intermediate sales because the purchaser, being exempt, does not receive credit for the tax content of the capital goods.
A qualification is necessary. If the products of an exempt industry contain taxed inputs and if these products are sold to another taxed sector, then the component of the sales value accounted for by the tax on the inputs to the exempt sector should be included in the base of the tax as well.
This follows from the relationship that the value added of the exempt sector minus intermediate sales to the taxed sector will equal final sales of the exempt sector minus intermediate purchases from the taxed sector. As long as intermediate sales to the taxed sector are positive, the reduction to the base entailed by exemptions will be less than the value added of the exempt sector.
The elasticity of the effectively exploited base with respect to consumption will differ from one if the rate of tax evasion is nonzero, provided that this rate varies from one sector to another, and also that the share in aggregate consumption of various products varies as aggregate consumption grows.
The elements of the A matrix are: a11 = 0.158; a2 = 0.259; a21 = 0.237; and a22 = 0.172. The elements of the B matrix are: b11 = 1.302; b12 = 0.407; b21 = 0.373; and b22 = 1.325.