# Income Tax Progressivity and Reform

By Doak, Ervin John | Atlantic Economic Journal, June 1989 | Go to article overview

# Income Tax Progressivity and Reform

Doak, Ervin John, Atlantic Economic Journal

Income Tax Progressivity and Reform

I. Introduction

The income tax system is a matter of continued controversy and debate. For example, while many, if not all, people seem to have accepted the idea that the income tax rate should rise with taxable income, at least up to some point, there is a question as to the exact pattern of progressivity. Moreover, there are the continuous complaints about loopholes and ways that the rich can escape paying their fair share of the tax burden. Recent tax reform proposals have been made in both the United States and Canada. With these in mind, this paper advances a simple theoretical model within which such issues may be discussed.

II. Basic Model (I)

The basic model assumes a certain level of national income, Y, that is distributed between two individuals, A and B, where YB > YA; T* represents the required tax revenues needed to finance government spending; X represents all tax deductions; B is the only individual who can take advantage of these deductions;1 and there is acceptance of a progressive income tax. Average tax rates are represented by tA and tB, which are determined by A's and B's respective taxable incomes, YA and (YB -- X): ti=k (Yi -- Xi).

In this case, the coefficient k is the slope of this function and measures the degree of progressivity. Its determinants also represent the first approximation to the determinants of income tax progressivity.

As can be proven, k = T*/YA2 + (YB -- X)2 and it is seen that k varies directly with T* and X, and inversely with (YA + YB) and YB.

III. Numerical Illustration Assume: T* = 300; YB = 2,000; and YA = 1,000. Then: k = 300/1000(2) + (2000 -- X)2 = 300/5,000,000 -- 4,000 X + X2

IV. Basic Model (II)

So far, taxable income has been assumed to be the appropriate tax base for discussion. However, concerns over fairness and equity often have in mind income before deductions. So, the discussion is amended in this and the next section accordingly.

For any individual, the tax rate in this case is: ti* = Ti/Yi = ti(Yi -- Xi)/Yi = k(Yi -- Xi)2/Yi As can be proven, t*B -- t*A/YB -- YA = k [YB -- 2XB + XB2/YB -- YA]/(YB -- YA)

In this connection, it is of interest to consider the following extreme cases: X = 0; and XB = YB.

If X = 0, then: t*B - t*A/YB - YA = k which is identical to the previous model. Here, taxable income is the same as income before deductions. However, this is seldom the case.

If XB = YB then t*B - t*A/YB - YA = k[YB - 2YB + YB2/YB - YA]/(YB - YA) = k[- YB + YB - YA]/(YB - YA) = k (- YA)/(YB - YA)

This shows, among other things, how a progressive income tax system may become less progressive or even regressive through a system of tax deductions2 (see Table 2). 1In assuming that Xa = 0 and Xb = maximum possible, the model reflects the fact that in Canada about 75 percent of all tax deductions are taken by the richest 33 percent of households. 2Evidence of effective taxation in both the U.S. and Canada does not suggest that tax deductions have made the general pattern regressive. See, for example, [Pechman, 1987; Auld and Miller, 1982].

V. Conflicting Objectives of the Tax

System

It should be recalled that any income tax system must satisfy a variety of tax objectives. For one thing, there is the pressure to come up with a certain level of T, which may or may not match the level of government spending. Secondly, there is the pressure coming from those asking for various kinds of tax exemptions or deductions. Thirdly, the system must be progressive. Given the level of national income and its distribution, the government must then choose between these objectives, which are also conflicting objectives. In other words, government must make some hard choices. It does not have unlimited freedom in this matter.

The foregoing points may be illustrated with the help of the model in this paper. …

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