The responsiveness of tax revenue to changes in national income, as measured in terms of elasticity, is of great interest to policymakers and researchers because elasticity is measured with reference to a given tax structure. However, since legislative changes in tax structure cause such elasticity to change over time, its direct measurement from historical revenue series is often difficult because the growth in revenue results both from the growth in the base caused by the increase in income and from discretionary tax changes.
In estimating the built-in elasticity of a tax, historical revenue series must be adjusted to eliminate the effects on revenue of discretionary tax measures. The method of adjustment depends on the available data on such changes and on the type and frequency of those changes. A complete adjustment of historical revenue series is not possible in any of the major existing methods, such as (1) the proportional adjustment, (2) the constant rate structure, and (3) the dummy variable methods. 1 Moreover, a great deal of information is needed for the adjustment of data, and it is often not available over a sufficient number of years. For instance, the proportional adjustment method requires use of budget estimates of tax yield owing to discretionary changes. Such data are difficult to obtain in many countries and, if available, they are of questionable reliability, as they may differ substantially from actual discretionary outturns. Similarly, the constant structure method, which requires the use of disaggregated data on taxes or effective tax rates and on the changing composition of the bases, places heavy demands on the availability of data. 2 The dummy variable method, although it requires no adjustment of data, cannot be properly used if discretionary tax changes have been made frequently in the past.
This paper has two purposes. First, it proposes a method of estimating the elasticity of total tax yield that does not require the traditional adjustment of historical revenue to eliminate the effects of discretionary tax measures. Second, it applies this method to case studies of a few selected countries.
The proposed method of estimating the elasticity of tax revenue involves three steps. First, the effects of discretionary tax measures on revenue are estimated by an index that isolates the automatic growth of revenue from the total growth. Second, the buoyancy of tax revenue is estimated, with respect to gross domestic product (GDP) or any other aggregate income variable, by a standard regression technique. Finally the buoyancy estimate obtained in the second step is adjusted by a suitable transformation of the index of discretionary revenue, as estimated in the first step, in order to provide an estimate of the elasticity of tax yield.
The proposed method of measuring the revenue effects of discretionary changes is based on the principle of the Divisia index, which is widely used in measuring technical change. This method has two major limitations. First, despite a sound theoretical underpinning, in practical application, the Divisia index of discretionary tax change can underestimate (overestimate) the positive (negative) revenue effects of such measures. A second and related limitation is that, if discretionary changes produce very large revenue effects, this method does not give satisfactory results. 3 In this sense, this method does not replace the other existing methods. In fact, when full and reliable information about the discretionary effects is available, the proportional adjustment method should be preferred, since it can handle large or small discretionary changes without bias. The main advantage of the three-step Divisia index method is that it uses only historical data and requires no specific information on the revenue effects or on the frequency of past discretionary tax changes.
The conceptual framework required to use the Divisia index for measuring the effects of discretionary changes on revenue is discussed in Section I. This section also develops a methodology for estimating the elasticity of tax revenue by using such an index of discretionary change. Section II discusses the empirical results of the application of this methodology to the four case studies selected: the United States, the United Kingdom, Malaysia, and Kenya. In Section III, the estimates of elasticity, based on the disaggregative and aggregative versions of this methodology, are compared with those based on the constant structure method and the proportional adjustment method. A few concluding remarks are made in Section IV.
Mathematical Bases for Derivation of Divisia Index of Discretionary Tax Revenue and Properties of Constant Structure Method
In this Appendix, mathematical proofs are given for some of the statements made in the text.
Andersen, Palle S., “Built-in Flexibility and Sensitivity of the Personal Income Tax in Denmark,” Swedish Journal of Economics, Vol. 75 (March 1973), pp. 1–18.
Baas, Hessel J., and Daryl A. Dixon, “The Elasticity of the British Tax System” (unpublished, International Monetary Fund, September 23, 1974).
Bahl, Roy W., “Alternative Methods for Tax Revenue Forecasting in Developing Countries: A Conceptual Analysis” (unpublished, International Monetary Fund, October 16, 1972).
Boucher, Michel, “L’Impót canadien sur le revenu des particuliers: sa contribution à la stabilisation de l’économie,” Public Finance, Vol. 32 (No. 2, 1977), pp. 159–67.
Chand, Sheetal K., “Tax Revenue Forecasting: An Approach Applied to Malaysia” (unpublished, International Monetary Fund, March 12, 1975).
Chelliah, Raja J., Hessel J. Baas, and Margaret R. Kelly, “Tax Ratios and Tax Effort In Developing Countries, 1969–71,” Staff Papers, Vol. 22 (March 1975), pp. 187–205 (especially pp. 190–95).
Chelliah, Raja J., and Sheetal K. Chand, “A Note on Techniques of Adjusting Tax Revenue Series for Discretionary Changes” (unpublished, International Monetary Fund, 1974).
Choudhry, Nurun N., “A Study of the Elasticity of the West Malaysian Income Tax System, 1961–70,” Staff Papers, Vol. 22 (July 1975), pp. 494–509.
Christensen, Laurits R., and Dale W. Jorgenson, “U. S. Real Product and Real Factor Input, 1929–1967,” Review of Income and Wealth, Vol. 16 (March 1970), pp. 19–50.
Denison, Edward F., The Sources of Economic Growth in the United States and the Alternatives Before Us, Supplementary Paper No. 13 (Committee for Economic Development, 1962).
Jorgenson, Dale W., and Zvi Griliches, “The Explanation of Productivity Change,” Review of Economic Studies, Vol. 34 (July 1967), pp. 249–83.
Solow, Robert M., “Technical Change and the Aggregate Production Function,” Review of Economics and Statistics, Vol. 39 (August 1957), pp. 312–20.
Star, Spencer, and Robert E. Hall, “An Approximate Divisia Index of Total Factor Productivity,” Econometrica, Vol. 44 (March 1976), pp. 257–63.
Tanzi, Vito (1969a), The Individual Income Tax and Economic Growth; An International Comparison: France, Germany, Italy, Japan, United Kingdom, United States (Johns Hopkins Press, 1969).
Tanzi, Vito (1969b), “Measuring the Sensitivity of the Federal Income Tax from Cross-Section Data: A New Approach,” Review of Economics and Statistics, Vol. 51 (May 1969), pp. 206–209.
Tanzi, Vito “The Sensitivity of the Yield of the U. S. Individual Income Tax and the Tax Reforms of the Past Decade,” Staff Papers, Vol. 23 (July 1976), pp. 441–54.
Mr. Choudhry, economist in the Fiscal Analysis Division of the Fiscal Affairs Department, holds degrees in statistics and economics from the University of Dacca (Bangladesh) and the University of California at Berkeley.
For a discussion and an evaluation of these three major methods of adjustment of historical revenue for discretionary tax measures, see Chelliah and Chand (1974).
Tanzi (1969b) has developed a method of estimating the income tax elasticity of the United States that utilizes only cross-section data. Briefly, the method is based on the hypothesis that a time series of income tax revenue (T) and taxable income (TI) before and after tax, all on a per capita basis, can be simulated from data for these variables from different regions of a country. While the method is very appealing, its application is rather limited, as very few countries have such regional data. Recently, however, Tanzi’s method has been applied to estimate the elasticity of income tax in Denmark and Canada. See Andersen (1973) and Boucher (1977).
These limitations are owing to the fact that the Divisia index is a line integral. In practical applications, especially with very large changes, the discrete version does not approximate the continuous function well.
Some aggregation problems ignored in the text discussion are worth mentioning. Both the aggregate production and tax functions assume homogeneous factor inputs and bases, respectively. An immediate consequence of this assumption is that the effects of compositional shifts in factor inputs and bases are not captured by the respective aggregate functions. As a result, the measurement of technical change or discretionary tax change can be biased. For example, consider a shift in, say, income distribution in favor of upper-income groups, with aggregate taxable income and the number of taxpayers unchanged. Clearly, even with no discretionary tax action, a change in revenue will take place, since the average income tax rate has increased. Similarly, a change in output occurs if there is a shift in the composition of labor between specific industry groups even when no technical change has taken place. Shifts in the composition of nonhomogeneous bases or factor inputs, such as those that often arise in reality, cannot be accounted for by a movement along the curve. If such shifts cause a change in tax yield or output, then this is perceived as a discretionary tax change or a technical change when, in fact, there was no such change.
See Hulten (1973)), p. 1017. The works of Solow (1957), Denison (1962), Kendrick (1961), Jorgenson and Griliches (1967), and Christensen and Jorgenson (1970) are important contributions to the logical foundations of the Divisia index.
Hulten has shown that the invariance property of the Divisia index is implied by the path independence property, which asserts that the value of the index depends on the current values of the variables in the production function and not on the historical path of the variables.
See Hulten (1973, p. 1018) for these necessary and sufficient conditions. A third condition required for the Divisia index of technical change, but not for that of discretionary tax change, states that the production function f has an associated input price vector that is unique up to a scalar multiplication. This implies that the ratio of marginal product between any two factors xi and xj equals their corresponding price ratio. That is, fi/fj = pi/pj. In the Divisia index of technical change, fi and fj are replaced by the factor prices pi, and pj. In the Divisia index of discretionary tax change, prices are not involved; hence, there is no need for the third condition.
Hulten demonstrated the elimination of the linear homogeneity assumption in the context of a production function characterized by nonconstant returns to scale. In fact, he also eliminated the use of the third condition referred to in footnote 7.
For a large number of developing countries, the average tax ratio has increased from 13.6 per cent for 1961–68 to 15.1 per cent for 1969–71. For more details, see Chelliah, Baas, and Kelly (1975).
The aggregation problem encountered in T = axμ is similar to that encountered in production or consumption functions.
Notice that equation (7) can be transformed as follows:
Even in measuring technical change, the same bias occurs in estimating automatic growth of factor productivity. This is because βi(t), which is a factor share, can reflect the effects of technical change on factor productivity, which, in turn, bias (generally downward) the rate of technical change.
Usually, r is greater than, or equal to, unity. For the sake of generality, it is assumed that r > 0.
Also, if the bases grow proportionally with respect to GDP, the aggregate tax function will have the same form.
In practical application, the buoyancy μ is a function of the period [0, t].
Earlier in the paper, the possible sources of bias in the index of discretionary change were discussed. From expression (13), it follows that when discretionary changes increase revenue, the Divisia index method overestimates the size of the elasticity of tax revenue and vice versa when discretionary changes decrease revenue.
See Section 3 in the Appendix for the formulas for computing log D and log D * in order to obtain the elasticity estimates
Analytically, the Divisia index method is similar to the proportional adjustment method of estimating elasticity. Essentially, in adjusting total revenue of discretionary changes, the proportional adjustment method performs the following type of operation:
where D**(t) is an index of discretionary change that is constructed as a chain index to adjust historical revenue T(t). The aggregate tax equation in the proportional adjustment method is given by
which is similar to
of the Divisia index method. The main difference between the two methods depends on how the two indices of discretionary change (D* and D**) are constructed. It has already been noted that D* is biased in practice, since it is estimated residually from unadjusted historical data. In the proportional adjustment method, if the information on discretionary changes is reliable, then D** may be a superior estimate of such changes. Consequently, the proportional adjustment method should be used under such circumstances.
The major categories of federal/central tax revenues considered for constructing Divisia indices of discretionary revenues are those shown in published government accounts for each country. Since estate and gift taxes, which are shown as a separate category for the United States, constitute less than 2 per cent of federal tax revenue, these taxes will not be discussed further in the text of this paper.
In the United Kingdom, social insurance and employment taxes are paid in the form of national insurance contributions by the taxpayers.
It is not easy to determine just what should be the proxy base for the estate and gift taxes for the United States. Private wealth may be a close proxy base for such taxes, but such data are not available. Similarly, GDP at factor cost may not be a close proxy base for the social insurance and employment tax. This tax is generally regressive with respect to individual or personal income. Of course, one could choose individual/personal income as a proxy base; however, since individual/personal income is almost unit elastic with respect to GDP at factor cost, the use of GDP as a proxy base is just as good under the circumstances.
Tax ratios in Malaysia and Kenya rose from 16.5 per cent of GDP in 1961 and 14.1 per cent in 1962 to 21.8 per cent in 1973 and 17.0 per cent in 1974, respectively. In the United Kingdom, the tax ratio rose with some fluctuations from 32.5 per cent of GDP in 1955 to 39.5 per cent in 1974. In the United States, after a sharp decline from 20.8 per cent of GDP in 1954 to 18.0 per cent in 1955, the tax ratio recovered in 1956 and thereafter remained fairly stable at around 20.5 per cent of GDP.
The elasticity of components of tax revenue cannot be estimated by the disaggregative Divisia method because it is assumed that each base represents its own tax category.
The effects of discretionary measures on tax yield can also be inferred from the movements in the shares of the components of tax revenue. For instance, despite the presence of progressive elements in individual income taxation, the share of the individual income tax remained virtually unchanged between 1955 and 1975 at about 45 per cent of tax revenue. The share of the corporate income tax steadily fell from 27.4 per cent in 1955 to 14.9 per cent in 1975 while that of the consumption tax (excises and import taxes) showed a similar declining trend, falling from 14.9 per cent to 7.4 per cent. On the other hand, the share of social security and employment taxes rose from 12.1 per cent in 1955 to 31.4 per cent in 1975, with sharp increases since 1967.
In a recent study of the U. K. tax system, it was found that the individual income tax had buoyancies of 1.02 and 1.45 for the periods 1950/51–1970/71 and 1960/61–1970/71, respectively, while the elasticity estimates based on the proportional adjustment methods were 1.37 and 1.53. The study also noted that “without these reductions [discretionary changes] the share of income tax in total revenue would have increased markedly” (See Baas and Dixon (1974), p. 14 and Table 5, p. 16.). The increase in the estimates of the elasticity and the buoyancy in the subperiod 1960/61–1970/71, compared with that for the whole period 1950/51–1970/71, indicates that, although the discretionary measures reduced revenue, they improved the progressivity of the individual income tax system.
The elasticity of corporate income before taxes with respect to GDP is found to be 1.10 (See Table 6.). The share of corporate taxes in total tax revenue declined from 18.0 per cent in 1955 to about 8 per cent in 1974.
It should be mentioned that the smaller buoyancy of income tax in Kenya than in Malaysia reflects the differences in the responsiveness of the tax base to GDP rather than the differences in the progressivity of rate structures. In fact, the income tax system is more progressive in Kenya, but the buoyancy of the base with respect to GDP was found to be only 0.8, while in Malaysia the base-to-GDP buoyancy was found to be twice as high (See Table 6.).
In a recent study of the individual income tax utilizing cross-sectional data from each of the states in the United States, it was found that, despite revenue-reducing discretionary measures, the elasticity of individual income tax with respect to adjusted gross income gradually improved over time, from 1.37 in 1963 to 1.48 in 1972. See Tanzi (1976), p. 449, Table 4.