Government Deficits in a Generalized Fisherian Credit Market Theory with an Application to Indexing Interest Taxation

WILLIAM. white, who joined the International Monetary Fund in 1948, spent his entire professional life in the Research Department. Present and past staff members, many of whom benefited from his advice, have asked that his contribution-to the work of the Fund should receive recognition in Staff Papers. This appreciation draws on excerpts from written recollections of some of his colleagues.

Abstract

WILLIAM. white, who joined the International Monetary Fund in 1948, spent his entire professional life in the Research Department. Present and past staff members, many of whom benefited from his advice, have asked that his contribution-to the work of the Fund should receive recognition in Staff Papers. This appreciation draws on excerpts from written recollections of some of his colleagues.

The literature on the tax-adjusted Fisher equation incorporates taxes integrally in Fisher’s analysis (1930) of interest rate determination. The argument is that an increase in inflation would tend to raise nominal interest rates by enough to compensate lenders for their extra taxes on interest income so that real aftertax interest rates would not change (Darby (1975), Feldstein (1976a), and Tanzi (1976, 1977)).1 A corollary is that indexing the tax treatment of interest income and expense to inflation would reduce nominal interest rates, from which it is inferred that government borrowing costs and the deficit would decline (Feldstein (1976b), Tanzi (1984), Walters (1984), and Makin (1985)).

The present paper shows that these conventional results are not genera], since they are based on credit market models within which is it assumed, often implicitly, that inflationary investment returns are not taxed but that nominal interest income is fully taxed and that nominal interest expense is fully deductible. If tax rates were uniform, real interest rates would be independent of inflation in such models. Hence the literature (for example, Feld-stein (1976a)) has emphasized the distorting effect of inflation as operating through unrealistic depreciation allowances, different tax rates for borrowers and lenders, and inflation-induced distortions in the demand for money. Although differences in corporate and individual tax rates as well as in portfolio adjustments may well be important, the present paper identifies additional and fundamental distortions that inflation would introduce—distortions that would affect real interest rates even if tax rates were uniform—without introducing money demand effects explicitly. Rather, the present analysis brings out the essence of the distortion that results from taxing the inflation premiums in interest rates. It is shown that, first, inflation would widen the wedge between the real rate that fully taxed borrowers pay and the after-tax real rate that is both earned by lenders and paid by borrowers whose inflation gains are not taxed and that, second, inflation would reduce both the real borrowing requirement of the government and the real interest rate at which the government’s outstanding debt is financed.

With regard to the first of these distortions, the paper shows that changes in inflation would affect real interest rates, provided that some credit demand originates from borrowers who are taxed on both their real and inflationary investment returns. By ignoring the latter, earlier analyses in general specified that inflation would reduce the after-tax real rate for all borrowers. Thus, an increase in inflation would shift the demand for credit up and the supply of credit down, raising the nominal interest rate just enough to leave the after-tax real rate and the equilibrium quantity of credit unchanged. In contrast, if inflation effects on income and expenses wash out for at least some borrowers, then an inflation-induced shift in the supply of credit would not be fully offset by an opposite shift in the demand for credit, so that the amount of credit and real interest rates would be affected. Within a generalized Fisherian credit market that includes fully taxed borrowers as well as those whose inflation gains go untaxed, the original Fisher equation and the tax-adjusted Fisher equation emerge as special cases depending on elasticities of the supply and demand for credit.

With regard to the second type of inflation distortion, the main innovation of the present paper is to introduce the real government budget into a generalized Fisherian credit market. It is shown that the real interest rate needed to finance government debt is precisely the same as the after-tax real rate that influences both lenders and untaxed borrowers. Furthermore, an increase in government spending would in general increase real interest rates; but an increase in a uniform tax rate might either raise or lower real rates, depending on whether the resultant decrease in the after-tax real interest rate reduces the net supply of private credit to government and fully taxed borrowers more than it reduces government demand for credit because of increased tax revenues. Despite the conventional argument to the contrary, the present paper shows that indexing the taxation of interest to inflation could well raise the real interest rate at which the government finances its debt and thus increase the deficit. In essence, taxing nominal investment income constitutes a real tax wedge that yields revenue to the government. Indexing interest taxation would eliminate revenues associated with taxing inflation premiums.

With respect to the empirical work on these issues, some investigations have tended to confirm the tax-adjusted Fisher equation (Peek (1982), Ayanian (1983), and Mehra (1984)), but most have not (Gandolfi (1976), Feldstein and Summers (1978), Levi and Makin (1978, 1979), Tanzi (1980), Summers (1981, 1982), and Makin (1982, 1983), among others). These negative results have been ascribed to factors that cause inflation to affect real interest rates. One is the real balance effect, attributed both to Mundell (1963), who argued that an increase in expected inflation causes a decrease in wealth that would reduce the demand for real money, thereby increasing saving and lowering real rates, and to Tobin (1965), who argued that an increase in expected inflation causes a shift out of real money into real capital, thereby lowering real rates. This effect would be augmented if inflation were not fully anticipated. Another is the relative price effect, which suggests that the increased relative price uncertainty that accompanies inflation would reduce investment more than saving and thus lower real rates (Levi and Makin (1979)). Whatever the cause, many empirical studies have found that real interest rates have been significantly variable over time (Nelson and Schwert (1977), Blinde T and Fischer (1981), Mishkin (1981), Friedman (1982), Peek (1982), Wilcox (1983), Walsh (1984), and Huizinga and Mishkin (1984)).

In the context of this literature, the present paper adds three more ways in which inflation might affect real rates: (1) by the tax distortion effect, because inflation would increase the tax wedge between the real rate paid by fully taxed borrowers and the real rate earned by lenders and paid by the government and borrowers whose inflationary gains are not taxed ; (2) by the real budget effect, because inflation would reduce the amount of real outstanding government debt to be financed; and (3) by the paradox of the thrift effect, because, if a decrease in after-tax real interest rates increases net lending, an increase in inflation would increase the supply of credit and reduce after-tax real rates. These inflationary effects on real interest rates could conceivably be eliminated by compensatory wealth effects in a Barro equivalence world (Barro (1984a)), but in any case by indexing not only the tax treatment of interest rates but also the real value of government debt to inflation.

Section I formally presents one of the standard tax-adjusted Fisherian credit market models with and without indexing, from which its author (Makin (1984)) has inferred that indexing would decrease the government deficit. Section II identifies real interest rates that would influence borrowers who maximize present values of investments under various tax regimes. Section III presents another standard tax-adjusted credit market model (Feldstein (1976a)). Section IV generalizes the credit market model with and without indexing interest taxation to incorporate borrowers whose investment returns are untaxed, those whose inflationary returns only are untaxed, and those whose real and inflationary investment returns are fully taxed. The last category is critically important to the results. Section V incorporates government deficits in the generalized credit market model with and without indexing the tax treatment of interest income and expense. Section VI presents conclusions.

I. The Makin Credit Model

The argument is widely accepted that indexing the tax treatment of interest to inflation would lower nominal interest rates and the government deficit.2 To illustrate the argument, it is assumed that the after-tax real interest rate is 3.0 percent, the tax rate is one third, and inflation is 6.0 percent. Under these assumptions, a nominal interest rate of 13.5 percent, given a one-third tax rate, amounts to a 9.0 percent after-tax interest rate. Subtracting 6.0 percent inflation from this leaves a 3.0 percent after-tax real interest rate. With the introduction of indexing, the nominal rate would fall to 10.5 percent. A 10.5 percent nominal interest rate less 6.0 percent inflation equals a 4.5 percent before-tax real interest rate that, with a one-third tax rate, leaves lenders the same 3.0 percent after-tax real interest rate as before. According to the argument, the government deficit would be reduced because the nominal interest rate would have fallen with the introduction of indexing the tax treatment of interest income and expense.

One question about this analysis is that it fails to account for the effects on government revenue of indexing interest taxation and of lower tax rates. In Section V it is shown that indexing might reduce tax revenue, so that a tax rate increase—not a decrease— could be required to maintain revenue neutrality. A second question is that the underlying credit market model used to derive the above results is not general but is based on an implicit assumption that investment returns of borrowers are not taxed, as Section II makes clear.

Table 1 formally presents this tax-adjusted credit market.3 The model is linear, with lending and borrowing measured in logarithms. Taxes are introduced on the assumptions that borrowers can deduct interest payments and that lenders are taxed on gross interest earnings. The after-tax real interest rate is i(l − τ) − π without indexing and (i − π)(l − τ) with indexing. Such an aftertax real rate is specified as the interest rate variable that would increase the supply of, and decrease the demand for, credit as recorded in Table 1. Other factors that affect the credit market are assumed to be reflected in the constants.

According to the lending equation, an increase in inflation would reduce lending unless nominal interest rates were to increase by 1/(1 − τ) times as much. An increase in the tax rate would lower the after-tax interest rate and reduce lending.

Table 1.

Makin Tax-Adjusted Credit Market With and Without Interest Taxation Indexed to Inflation

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Note: With indexing, ∂B/∂i = β1(i − π) > 0; without indexing, ∂B/∂τ = β1i > 0. For comparisons, π > 0 is assumed throughout the paper. L is real lending (logarithm); B is real borrowing (logarithm); r is the after-tax real interest rate; α and β are nonnegative parameters; i is the nominal interest rate; τ is the tax rate; π is expected inflation; i − π is the before-tax real interest rate.

According to the borrowing equation, an increase in inflation would affect borrowing through a reduction in the after-tax interest rate, which would tend to increase borrowing unless nominal interest rates increased by 1/(1 − τ) times as much. According to the tax-adjusted credit market of Table 1, if the real balance and relative price uncertainty effects of inflation on lending and borrowing are ignored, the nominal interest rate would increase by the full 1/(1 — τ) times an increase in expected inflation, which is the hypothesis of the tax-adjusted Fisher equation.

A clue that raises a question about the borrowings equation of Table 1 is that an increase in the tax rate would reduce after-tax real interest rates and increase borrowings. Increase borrowings? This implication of the model is not intuitive. Even though firms occasionally borrow to pay taxes, higher tax rates would normally reduce expected returns. The demand for credit as represented by the borrowing equation, however, is not specified to include any such direct effect of tax rates on investment but only the indirect effects of tax rates on the after-tax real interest rate at which expected returns are discounted, as will be shown in the next section. Furthermore, equilibrium credit and after-tax real rates in Table 1 are independent of tax rates and, thus, of indexing. These results merit scrutiny.

II. Present Values Under Alternative Tax Regimes

Under a tax code such as in the Netherlands, Switzerland, or the United States, interest income is taxable, and interest expense by both individuals and businesses is deductible in calculating taxable income. The tax on interest income effectively taxes saving and lending as would an excise tax, except for that portion which escapes because of evasion and the exemption of interest income from particular credit instruments (such as savings deposits in Switzerland and state and local government securities in the United States). But does interest deductibility subsidize spending and investment? The answer is partly yes and partly no. Borrowing for consumption that does not yield taxable income is actually subsidized because interest expense is deductible in calculating taxable income. Borrowing to finance investment in houses or consumer durables for personal use is also subsidized because the services of such assets are not taxed, but interest expense is deductible. Unrealized capital gains may also escape taxation temporarily. Nevertheless, consumer credit, home mortgages, and government obligations totaled only about two thirds of the funds raised in U.S. credit markets by nonfinancial sectors in 1984 (Board of Governors of the Federal Reserve System (1985)). Therefore, it is important to recognize that, for a large part of total borrowing, an increase in tax rates not only may lower the interest rate at which investment returns are discounted but also may raise the tax burden on the income that is thereby generated. It will be shown that failure to account for this heavier tax burden is what explains the result of the standard models, that a change in a uniform tax rate would not affect real variables in the credit market.

Tax rates can be introduced directly into present-value calculations on which investment decisions depend. Investments whose present values are positive would be undertaken, others abandoned. It is assumed that all investment is financed by borrowing. Hence, positive present values would increase the demand for borrowing. The question is how tax rates and inflation would affect present values under alternative tax regimes.

It is easily shown that present values would be independent of tax rates if the tax rate applicable to investment returns is the same as the tax rate applicable to interest cost deductions from taxable income. First consider an investment expected to return 1 + r dollars at the end of one period. If i is the market rate of interest, the present value of the return is

v=(1+r)/(1+i).(1)

Suppose that the cost of the investment is c. The investment would be made as long as net profit a is not negative:

a=(1+r)c(1+i)0.(2)

Equivalently, the present value must be no less than the cost of an investment:

v=(1+r)/(1+i)c.(3)

The introduction of a uniform tax rate on income, with interest as a deductible expense, would not affect this condition. After-tax profit would simply be the before-tax profit less taxes:

a=(1τ)[(1+r)c(1+i)].(4)

As before, the investment would be made as long as the before-tax profit—the term in brackets—is not negative. Thus, the investment decision would be independent of the tax rate in this simple case, as Stiglitz (1973), Auerbach (1983), and others have argued. Increasing the tax rate would reduce after-tax profits but would not affect investment or borrowing to finance investment.

Table 2 records present-value formulas under alternative tax regimes with and without inflation. Capital is assumed to yield a marginal physical product r in perpetuity and with no depreciation. Results would not be affected if the nominal interest rate is thought of as including the depreciation rate (Gandolfi (1982)). According to the table, in all cases in which taxes on real or nominal returns are matched by comparable deductions of real or nominal interest expense, present values are independent of tax rates. Regime C in Table 2 corresponds to the one-period illustration previously discussed. The after-tax real return is r(l − τ). It grows in nominal terms at a rate of only π(1 − τ) rather than π because of the tax on the inflationary gain. Discounting this nominal after-tax return at the nominal after-tax interest rate i(1 − τ) yields the same present value as under regime A, with no taxes, or regime B, with indexation of both taxable rates of return and deductible interest rates. Thus, tax rates would not influence present values, investment, or borrowing to finance investment as long as both investment returns and deductible interest expenses influence tax liabilities symmetrically.

Table 2.

Present Values Under Alternative Tax Regimes

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Note: r, i, t, and π are, respectively, the marginal physical product of capital, the nominal interest rate, the uniform tax rate on taxable income, and the inflation rate. Interest expense is deductible in calculating taxable income except in regime F. Gandolfi (1982) incorporates a comparable taxonomy including depreciation.

r = i − π/(l − τ) as in Feldstein (1976a).

r = i(1− τ)-π as in Makin (1984).

r = i/(l− τ) −π as in Fisher (1906).

Regimes D, E, and F show three tax regimes under which tax rates would affect present values and hence investment. In regime D, only real investment returns are taxed, but total nominal interest is deductible. In this case, when there is inflation an increase in the tax rate would increase the present value of a given investment because the increased tax on the real return would be more than offset by the increased deduction of nominal interest payments. Regime D corresponds to Feldstein’s model (1976a) in that Feldstein explicitly assumed that real but not inflationary returns are taxed. Under regime E, investment returns are not taxed at all. With inflation, an increase in the tax rate would therefore increase the present value of a return because of the effect of the higher tax rate in increasing deductible nominal interest expense. Regime E is the one implicitly assumed in much of the literature on the tax-adjusted Fisher equation (including Makin (1984), reported in Table 1). Regime F, under which nominal returns are taxed but interest is not deductible, seems pathological today, but when this case was discussed by Fisher (1906, pp. 398–400) there was no income tax, so that Fisher was in effect evaluating the effect of property taxes on present values.4 Tax regime F is not considered further in this paper.

III. The Feldstein Credit Model

Table 3 modifies the Makin model of Table 1 to make it consistent with Feldstein (1976a), who assumed that only inflationary capital gains are untaxed. The two models are similar to the extent that they imply that di/dτ = 1/(1 − τ). The Makin model specifies that borrowers are influenced by the same after-tax real interest rate as lenders, i(l − τ) − π (Table 2, tax regime E). The Feldstein model specifies that borrowers are influenced by i − τ/(l − τ) (Table 2, tax regime D). In the latter case, the after-tax rate earned by lenders is therefore less than that earned by borrowers by a factor of 1 − τ. Nevertheless, in both the Makin and Feldstein models, an increase in the tax rate would increase borrowing. In the Makin model, present values and hence borrowing demand would increase with an increase in the tax rate because the higher tax rate would reduce the after-tax interest rate used to discount returns, which are assumed to be untaxed. In the Feldstein model, such a decrease in the after-tax interest rate used to discount returns would only increase the present value of inflation returns, which are assumed to be untaxed.

Table 3.

Feldslein Tax-Adjusted Credit Market With and Without Interest Taxation Indexed to Inflation

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Note: With indexing. ∂B/∂τ = 0; without indexing, ∂B/∂τ = β1 π(l − τ)2 > 0. Δ = (1 − τ)α1 + β1

A critical similarity between these models is that neither a change in inflation nor the introduction of indexing the tax treatment of interest income and expense would have any effect on the real interest rates influencing borrowers or lenders and, thus, on the volume of credit. The introduction of indexing interest taxation would also unambiguously decrease the nominal interest rate in the Feldstein model, a result that lends support to his argument that such indexing would reduce interest payments on the government debt.5 Nevertheless, it is ironic to note that, in either the Makin or Feldstein models of Tables 1 and 3, the introduction of indexing the tax treatment of interest would not in itself influence the real rate that lenders earn. As Section V shows, this is also the real rate at which the government borrows; thus, indexing in the framework of the Makin and Feldstein models would not in general reduce the government deficit, as these authors have argued.

IV. The Generalized Credit Model

In the standard models of Tables 1 and 3, an increase in the tax rate or the inflation rate would not affect the after-tax real interest rate or the amount of credit. These results depend on the assumption that borrowers are not taxed on inflationary investment returns. By modifying the specification of the borrowing relationship to include fully taxed borrowers, not only tax rates but also indexing the tax treatment of interest to inflation are shown to affect both real interest rates and the amount of credit. A model yielding these results is discussed in the following subsection without indexing interest taxation, and in the next subsection with indexing. In the third subsection the model is generalized to incorporate three categories of borrowing that reflect the alternative tax regimes.

Inflation, Taxes, and Interest Rates when Nominal Investment Returns Are Taxed

Table 4 modifies the borrowing relationships of Tables 1 and 3. Borrowing is specified to be a function of the before-tax real interest rate and, thus, to be independent of the tax rate. Think of the function as involving the demand for credit, net of borrowing both for consumption and for investment not subject to taxation of inflationary capital gains. Government borrowing will be introduced in Section V.

Focusing on the results without indexing of the tax treatment of interest in Table 4, one finds that an increase in the tax rate would raise the real after-tax rate to borrowers, even as it would lower the real after-tax rate that lenders earn, and would reduce the amount of credit. Figure 1 depicts how an increase in the tax rate would both shift the lending function up to the left and increase its slope. Table 4 also shows that an increase in inflation would in general increase the real rate to borrowers, decrease the real after-tax rate to lenders, and decrease the amount of credit. Figure 2 depicts this case. The supply of credit shifts up by 1/(1 − τ) times the increase in inflation. The demand for credit shifts up by only the increase in inflation. Hence, the nominal interest rate must rise, and the amount of credit must fall. The magnitude of the effect wouid depend on the interest elasticities of the supply of and demand for credit.

Table 4.

Modified Tax-Adjusted Credit Market With and Without Interest Taxation Indexed to Inflation

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Note: rB = i − π; Δ = (1 − τ)α1 + β1.
Figure 1.
Figure 1.

increase in Tax Rate (di/dτ = α1i/Δ≥; dL/dτ= −α1 β1i/Δ ≤ 0)

Citation: IMF Staff Papers 1986, 002; 10.5089/9781451946956.024.A003

Figure 2.
Figure 2.

Increase in Inflation [1 ≤, di/dπ = (α1 + β1)/Δ ≤ 1/(1 − τ); dL/dπ = −α1 β1τ/Δ ≤ 0]

Citation: IMF Staff Papers 1986, 002; 10.5089/9781451946956.024.A003

If the interest elasticity of credit supply is low compared with the interest elasticity of credit demand, the nominal interest rate would change by approximately the change in inflation—the hypothesis of the Fisher equation. Figures 3 and 4 show two extreme cases. In Figure 3, lending is totally insensitive to the interest rate. In Figure 4, borrowing is perfectly elastic with respect to the interest rate. In both cases the borrowing relationship shifts up by the increase in inflation, which is fully reflected in the nominal interest rate.

If the interest elasticity of credit demand is low compared with the interest elasticity of credit supply, however, a change in inflation would be reflected in an increase in the nominal interest rate of approximately 1/(1 − τ) times as much—the hypothesis of the tax-adjusted Fisher equation. Figures 5 and 6 show two extreme cases. In Figure 5, borrowing is totally insensitive to the interest rate; in Figure 6, lending is perfectly elastic with respect to the interest rate. In both cases the lending relationship shifts up by 1/(1 − τ) times the increase in inflation, which is fully reflected in the nominal interest rate.

Figure 3.
Figure 3.

Lending Insensitive to Interest Rate (di/dπ = 1;dL/dπ = 0)

Citation: IMF Staff Papers 1986, 002; 10.5089/9781451946956.024.A003

Figure 4.
Figure 4.

Borrowing Perfectly Elastic with Respect to Interest Rate (di/dπ = 1;dL/dπ < 0)

Citation: IMF Staff Papers 1986, 002; 10.5089/9781451946956.024.A003

Figure 5.
Figure 5.

Borrowing Insensitive to Interest Rate [di/dπ = 1/(1 − τ); dL/dπ = 0]

Citation: IMF Staff Papers 1986, 002; 10.5089/9781451946956.024.A003

Because empirical evidence indicates that the interest elasticity of saving is comparatively low, the tax-adjusted credit market of Table 4 could be interpreted as almost reinstating the hypothesis of the Fisher equation, that nominal interest rates would change proportionately with inflation. Thus, di/dπ would equal unity not only if the tax rate is zero, as in the original Fisherian formulation, but also if either the interest elasticity of lending is zero or the interest elasticity of borrowing becomes infinitely large. That investment might be infinitely elastic with respect to the interest rate has been argued by elasticity optimists, such as Knight (1933) and Friedman (1976) for a closed economy and Dornbusch (1976) and Harberger (1980) for an open economy. According to Knight (1933, p. 336),

The supply of capital goods is the demand for savings, and is indefinitely elastic, because capital goods are indefinitely producible at substantially constant cost. Likewise the demand for capital goods is the amount of saving, which depends on individual choices between saving and spending. The supply of savings, conceived in the only proper way, as the rate of flow into the investment market, in response to various rates of interest, is certainly inelastic, quite possibly inversely elastic, under some conditions, if not on the whole.

Ironically, in light of the controversy between Fisher and Knight regarding interest rate determination (with Fisher arguing that saving behavior is a critical factor determining interest rates), a Knightian world (with the real interest rate determined by investment demand regardless of the propensity to save) would reinstate the original Fisher equation relating nominal interest rates to inflation.

In the empirical literature on the tax-adjusted Fisher equation, it has frequently been observed that nominal interest rates tend to increase by even less than increases in expected inflation—let alone by more, as is the hypothesis of the tax-adjusted Fisher equation (see, for example, the studies included in Tanzi (1984)).

Figure 6.
Figure 6.

Lending Perfectly Elastic with Respect to Interest Rate [di/dπ = 1/(1 − τ); dL/dπ < 0]

Citation: IMF Staff Papers 1986, 002; 10.5089/9781451946956.024.A003

One theoretical possibility to account for this phenomenon is an inverse relationship between credit supply and the after-tax real interest rate. Such a modified lending equation is introduced in Figures 7 and 8, on the assumption (for dynamic stability) that the interest elasticity of borrowing remains more negative than that of lending. Figure 7 depicts how an increase in the tax rate in this case would decrease the nominal interest rate as the lending function shifts up and flattens. Because lending is now assumed to be related negatively to the after-tax real interest rate, an increase in the tax rate would reduce the after-tax real interest rate and increase lending—a paradox of thrift. Figure 8 shows how an increase in inflation would increase the nominal interest rate less than proportionately. The lending function shifts up more than proportionately, but the borrowing function only proportionately, to an increase in inflation. Hence the nominal interest rate would increase less than proportionately, and the after-tax real interest rate would fall.

Figure 7.
Figure 7.

Increase in Tax Rare Under Modified Lending Equation (di/dτ = −α1i/Δ ≤ 0; dL/dτ = α1β1i/Δ ≤ 0)

Citation: IMF Staff Papers 1986, 002; 10.5089/9781451946956.024.A003

Figure 8.
Figure 8.

Increase in influiion Under Modified Lending Equation [0 ≤ di/dπ = (−α1 + β1)/Δ ≤ 1; dL/dπ =α1β1τ/Δ ≥ 0]

Citation: IMF Staff Papers 1986, 002; 10.5089/9781451946956.024.A003

Note: (α1 + β1)/Δ = 1 + α1 τ/Δ ≤ 1; since β1 > −α1(l − τ), both (α1 + β1) and Δ are nonnegative; thus, di/dπ ≥ 0.

Indexing Interest Taxation when Nominal Investment Returns Are Taxed

Figure 9 compares credit market results from Table 4 with and without indexing interest taxation. The borrowing function remains the same with or without indexing. Lending is again assumed to vary directly with interest rates. Indexing interest taxation would increase lending because it would raise the after-tax real return to tenders. Consequently, the nominal interest rate would decrease with the introduction of such indexing. Reducing the tax rate and, in the limit, eliminating taxes would further increase lending and reduce the nominal interest rate.

Figure 9 also shows that indexing interest taxation can lower rB, the real rate that fuliy taxed borrowers pay, and simultaneously raise rL, the after-tax real rate that lenders earn.6 Without indexing, the after-tax real rate i0(l − τ) − τ induces L0, lending. The corresponding real interest rate facing fully taxed borrowers is i0 − π, which exceeds the lenders’ rate by τi0−the tax paid by lenders per dollar of interest income. This real tax wedge depends directly on the tax on the inflation premium in the nominal interest rate τπ. With indexing, the lending function shifts down by τπ/(1 − τ)—the tax on the π/(1 − τ) increase in the nominal interest needed to maintain the after-tax real rate to lenders in the presence of inflation. Lending increases to L1, reducing the nominal rate to i1. The after-tax real interest rate earned by lenders rises to rL1. With indexing, the real rate facing fully taxed business borrowers can simultaneously fall. The gap between it and the after-tax real rate earned by lenders is τ(i, − π) with indexing. which is smaller than τi0 (the gap without indexing) not only because the inflation premium is not taxed but also because the nominal interest rate is reduced. Thus, indexing interest taxation to inflation not only would lower nominal and real interest rates paid by fully taxed borrowers but also would raise the after-tax real rate earned by lenders. Both lenders and fully taxed borrowers would be better off because the government would have removed an artificial wedge in the pricing of credit, allowing lenders and fully taxed borrowers to increase their use of credit to mutual advantage.

Figure 9.
Figure 9.

Modified Tax-Adjusted Credit Market With and Without interest Taxation Indexed to Inflation

Citation: IMF Staff Papers 1986, 002; 10.5089/9781451946956.024.A003

Note: B = β0 − β1(i − π); L = −α0 + α1[i(l − τ) − τ] (without indexing); L = −α0 + α1[(i − π)(1 − τ)] (with indexing); L = B. See also Table 4.

Credit Market with Three Tax Regimes Combined

Table 4 demonstrated the distortionary effect of inflation when lenders are taxed on their nominal interest income and borrowers are taxed on both real and inflationary investment returns. Table 5 generalizes the credit market to incorporate borrowers in three tax categories: (1) untaxed investment returns (Makin (1984)); (2) untaxed inflationary investment returns (Feldstein (1976a)); and (3) fully taxed returns. Qualitatively, the results are exactly the same as for the case of fully taxed returns in Table 4. The reason is that as long as there are some fully taxed borrowers (β1 ≠ 0), then the distortion of the taxation of inflationary premiums in nominal interest rates would have real effects. In particular, indexing interest taxation to inflation would have real effects because, in the presence of inflation, indexing interest taxation would reduce the tax wedge between the real rate that fully taxed borrowers pay and the real after-tax rate that lenders earn.

Table 5.

Generalized Tax-Adjusted Credit Market With and Without interest Taxation Indexed to Inflation

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Note: Δ = α1(1 − τ) + β1 + β2(l − τ) + β3 ; r1B=iπ (real rate when both nominal and real returns are taxed); r2B=rL (real rate when returns are untaxed); r3B=rL/(1τ) (real rate when only real returns are taxed).

Note that in long-run equilibrium the before-tax real returns from investment in each of the three categories would be adjusted so as to exploit any opportunity to increase utility or profits by switching from one kind of investment to another. In other words, the real effects of the differential taxation of investment returns would be reflected not in different borrowing rates but in investors’ selecting investments on the basis of the tax structure, thus affecting the composition of the capital stock.

V. Government Deficits in the Credit Market

It has thus far been assumed that the government intervened in the credit market only by defining taxable income to include interest income and certain investment returns and by allowing interest expense as a deduction. But the government borrows and lends too. It will be assumed that the government finances deficits solely by issuing interest-bearing securities and not by issuing money. Thus, the deficit is defined as the change in the amount of interest-bearing government debt outstanding:

DD1=Pγ+iD1T,(5)

where

P = the price level

γ = real government purchases of goods and services i = the nominal interest rate

Di = outstanding nominal government debt in the previous period

T = nominal government tax receipts less transfers other than interest payments.

The nominal interest rate is assumed to be the same for private borrowers as for the government, although actually the government would borrow at the lowest after-tax interest rate because of its unique powers to tax or issue money (or both) to pay its obligations. To avoid the complication of interest rates affecting the value of outstanding government debt, all such debt is assumed to be of one-period maturity. P can be thought of as a function of the amount of government demand debt outstanding.

Taxable income, defined as national income plus interest earned on government debt, is assumed to be subject to a uniform tax rate; both the tax rate and real taxable national income are considered to be autonomous:

T=τ(PY+iD1),(6)

where τ is the tax rate,7 and Y is real national income.

The deficit defined in equation (5) is in nominal terms. It must be expressed in real terms to fit into the credit market framework of the previous section. The real government deficit, Z, is simply the change in the real government debt per period (see Barro (1984a)):

Z=D/P(D/P)1.(7)

The real deficit depends on whether and how interest taxation is indexed to inflation. Consider first the case in which nominal interest income is taxed, as in the present U.S. tax system. Substitute equation (6) into equation (5) to obtain the government budget constraint:

DD1=Pγ+iD1τ(PY+iD1).(8)

Deflate both sides of the equation by P and collect terms to get

D/P(D1/P)=γτY+i(1τ)D1/P.(9)

Using the definition that P/P−1 = 1 + π, where π is the inflation rate, yields the real deficit as defined in equation (8):

Z=D/P(D/P)1=γτY+[i(1τ)π]D1/P.(10)

Note well that, without indexing of interest taxation, the real deficit to be financed in the credit market is a function of the very same rL, the after-tax real interest rate without indexing that influences lenders in the credit market. By definition, the primary deficit is γ − τY, and the financing deficit is rL D−1/P. The latter would increase with an increase in rL.

Consider next the case in which interest taxation is indexed to inflation. Only real interest income is taxed, so that the tax base is defined as PY + (i − π)D−1,. Therefore, the tax equation is

T=τ[PY+(iπ)D1].(6a)

Substituting equation (6a) into the budget equation (8) yields the real deficit under indexation of the tax treatment of interest:

Z=γτY+[(iπ)(1τ)]D1/P.(10a)

In the case of full inflation indexing, including not only indexing interest taxation but also the outstanding government debt, the real government budget deficit is

Z=γτY+[(iπ)(1τ)]D1.(10b)

It is worth emphasizing that disposable income and the real budget deficit under any mode of taxation are functions of the same after-tax real interest rate that influences the supply of credit and the demand for credit to finance expenditures that do not yield taxable income—which, after all, is what government deficits are.

Table 6 introduces the real government budget deficit into the credit market model of Table 4, which yields the same qualitative results as the generalized credit market model of Table 5. The borrowing equation for fully taxed borrowers remains unchanged. Because the real government budget deficit is a function of the same interest rate rL that influences borrowing that does not generate taxable income, it is convenient to include the real government budget surplus in the net supply of funds made available to fully taxed private borrowers, hereafter called the net supply of credit. One must also account for how government interest payments would affect real disposable income YD and, in turn, saving and lending. For simplicity it is assumed that a one-dollar increase in YD would be reflected in an α2 increase in lending. A unit increase in rL would therefore increase private lending directly by α1 and indirectly through YD by an additional α2(D−1/P), whereas government lending would decline by D−1/P for a net effect of α1 − (1 − α2)D−1/P.

In the framework of Table 6, an increase in government spending would unambiguously increase interest rates and reduce the net supply of credit to fully taxed business borrowers. The increase in government spending represents an autonomous decrease in the net supply of credit, with a resultant decrease in net lending and increase in interest rates. The analysis is more complicated with respect to tax rate changes. A tax increase not only decreases the primary deficit, as in the case of a government spending change, but it also changes the slope of the net supply of credit function, leaving the total effect of a tax rate change ambiguous.8

Under less than full indexing of the tax treatment of interest income and expense, the tax distortion effect that arises from changes in expected inflation when the inflation premium in nominal interest rates is taxed is (τ/Δ)(θ + πd θ/dπ) in Table 6. The real budget effect is − (rB/Δ)dΔ/dπ; it reflects the decreased need for the government to borrow when an increase in expected inflation has reduced the real value of the outstanding government debt to be financed (unless that debt is also indexed). If the government debt were not all of one-period maturity as assumed, such a capital gain to the government would not be realized until the outstanding debt had fully turned over.

Table 6.

Government Budget in Tax-Adjusted Credit Market With and Without Indexing

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Note:rB=iπθ=α1(1α2)D1/PP=1+πΔ=[α1(1α2)D1/P](1τ)+β1,Ω=α0+γ[α2+τ(1α2)]YΔ1=[α1(1α2)D1](1τ)+β1, where Y is real national income, YD is real disposable income, γ is real government spending, D−1/P is real government debt, and Z is the real government deficit (for definitions of other variables, see Table 1). Real disposable income in this model is national income plus interest on government debt, less taxes less the depreciation in the vaine of the outstanding government debt due to inflation: YD=(Y+iD1/P)(1τ)πD1/P=(1τ)Y+[i(1τ)π]D1/P. The real interest rate that affects disposable income is the after-tas real interest rate for lenders and investors who are not subject to taxes on investment returns.

One unambiguous theoretical result from Table 6 is that inflation indexing of the tax treatment of interest rates would reduce the negative and distorting effect of inflation on rL, the after-tax real interest rate for lenders and borrowers whose investment returns go untaxed. Indexing interest taxation would not, however, unambiguously decrease the volatility of nominal interest rates with respect to inflation changes, although this result has often been inferred in previous analyses (Feldstein (1976a), Gramlich (1976), Nielsen (1981), and U.S. Department of the Treasury (1984)).

Another unambiguous theoretical result—and the main point of the present paper—is that, under the assumptions of the analysis, indexing the taxation of interest to inflation would increase the after-tax real interest rate applicable to the net supply of credit. In essence, indexing interest taxation would reduce the real tax wedge, thereby raising the after-tax real rate that lenders earn, which is also the real rate influencing untaxed borrowers and the government as a borrower. Because the government deficit would thereby be unambiguously increased,9 to leave the deficit unchanged it would be necessary to reduce government spending, raise tax rates, or both—the opposite of the conventional conclusion drawn in the literature. Thus, although indexing interest taxation would lower nominal interest rates, it does not follow automatically that the government deficit would be reduced. With uniform tax rates and at least some fully taxed borrowers, indexing interest taxation could raise the after-tax real rate influencing government borrowing, thereby increase the deficit, and require compensating budgetary adjustments to maintain revenue neutrality.

VI. Conclusion: Inflation Indexing of Interest Taxation Might Increase the Deficit

The main theme of this paper has been to introduce the real government budget deficit into a credit market generalized to incorporate borrowers in different categories with respect to the taxation of their investment returns. The analysis aggregated the real government surplus with saving less borrowing for investment, the inflationary returns of which are not taxed. This aggregate was defined as the net supply of credit to fully taxed borrowers. The results were as follows. An increase in government spending, working as an autonomous decrease in the supply of credit to private borrowers, would increase nominal and real interest rates. Indexing the tax treatment of interest to inflation would increase the after-tax real rate that influences savers and the government, as well as other borrowers whose inflationary investment returns are untaxed. Indexing interest taxation would also increase the real government budget deficit, even though nominal interest rates would decrease.

These unambiguous results are different from those in the standard credit market analyses. Nevertheless, they make good sense. Given the assumption that inflationary investment returns are taxed, indexing the tax treatment of interest would eliminate one source of taxable income—the tax on the inflation premium in nominal interest rates—which would not only raise the after-tax real interest rate that lenders earn but also the effective real interest rate that the government pays. Although indexing interest taxation to inflation could improve economic efficiency in the sense that an artificial wedge between real rates paid by fully taxed borrowers and those earned by household lenders would be reduced, it could be expected to raise—not lower—the effective real interest rate at which the government debt is financed and thus increase the deficit.

As a matter of fact, business profits have included many inflationary elements from 1970 through 1980,10 and inflation significantly hurt corporate profits and investment. According to the analysis of the present paper, one reason for the harm would be that taxing the inflation premium in interest rates profited the government at the expense of both fully taxed borrowers and lenders. There doubtless were consumer borrowers, home purchasers, and others who benefited from the full deductibility of interest payments, but others were being seriously hurt by inflation. To the extent that there are such fully taxed borrowers, it is reasonable to conclude that indexing the taxation of interest income and expense to inflation, despite the weight of conventional wisdom and professional opinion to the contrary, might well raise the effective real interest rate at which the government borrows and thus the federal deficit. That is not sufficient reason to oppose indexing interest taxation that promises to improve the allocation of resources by taxing only real returns and allowing only real interest cost deductions in place of the existing differential taxation of nominal returns from various sources. Indexing the taxation of interest income and expense to inflation could avoid distortions in the allocation of credit and the level of real interest rates when inflation is present. But, because it might well increase government deficits, general increases in tax rates or decreases in government purchases might be needed to maintain revenue neutrality.

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*

Mr. Dewald, an economist at the U.S. Department of State, completed the research for this paper while he was a consultant in the Research Department of the Fund. He is a graduate of Northwestern University and of the University of Minnesota. He was formerly Professor of Economics and Editor of the Journal of Money, Credit and Banking at the Ohio State University, Columbus. The author acknowledges helpful criticism from his colleagues in the Fiscal Affairs and Research Departments. Earlier versions of the paper were presented at the Congressional Budget Office, George Mason University, the Eastern Economic Association Meetings, Georgetown University, the Board of Governors of the U.S. Federal Reserve System, the Brookings Institution, the American University, George Washington University, the U.S. Department of the Treasury, and the Western Economic Association Meetings (in 1985).

1

The Fisher equation (1930) is r = i − π; the tax-adjusted Fisher equation is r = i(1 − τ) − π, or r = i − π/(l − τ). where r is the real interest rate, i is the nominal interest rate, τ is the tax rate, and π is the inflation rate. In general, authors have not made clear that these two tax-adjusted Fisher equations reflect quite different assumptions about the tax system, although in both cases di/d, π= 1/(1 − τ). This point is elaborated in Section II of the paper.

2

“By allowing deduction only of real interest cost and taxing only real interest income, the Treasury plan reduces the tax incentive to borrow and the tax penalty on lending and thereby helps to produce a drop in interest rates that will reduce deficits” (Makin (1985, p. 24)). “It [indexing] would. for example, by reducing interest cost on the public debt, reduce the U.S. fiscal deficit by $8 billion, and it would reduce the cost of borrowing for developing countries by considerable amounts” (Tanzi (1984, p. 27)).

3

The model without indexing is presented in Makin (1984). A comparable model is the basis of the analysis of interest indexation by the Institute for Research on the Economics of Taxation (see Schuyler (1985)).

4

Incongruously, Brenner and Venezia (1983) specified regime F in their study of investment duration.

5

“… If adjustments for inflation were made, lenders would require smaller interest premiums during inflation; as a result, the government could pay less interest on its debt” (Feldstein (1976b, p. 80)).

6

Stiglitz (1981) also shows that indexing would affect real rates.

7

To avoid further complicating the analysis, the tax rate can be thought of as including government revenue that is associated both with the issue of government demand debt and with the taxation of inflation premiums in interest rates paid by fully taxed borrowers.

8

The present paper does not account for the feedback effects of taxation and government deficits on wealth. In a world in which decision makers have infinite horizons, tax rate changes including indexation would not affect interest rates (see Barro (1984a, 1984b)), Deficits from whatever source would induce sufficient net private saving to be self-financing without affecting interest rates. At most, a decrease in tax rates and an increase in the deficit would have a distorting effect in increasing the current supply of output and then decreasing that supply later when tax rates were increased to finance the resultant debt. The introduction of indexing the tax treatment of interest might, however, affect the allocation of credit to particular borrowers, an effect that could have positive or negative effects on real growth. There is at best ambiguity with respect to the consequences that indexing would have for long-run growth and tax revenue. Thus, it has simply been assumed in the present analysis that inflation indexing of interest taxation would not affect real output and related tax revenue at all. although the issue merits study.

9

The deficit could be further increased because of forgone revenues associated with taxing the inflationary returns of fully taxed borrowers.

10

King and Fullerton (1984) in their study of capital income taxation found that, for the 1970 tax law, an increase in inflation from zero to 6.67 percent would increase the effective tax rates by 3.5 percentage points. Feldstein and Summers (1978) found a 3.3 percentage point increase in the effective tax rate per percentage-point increase in the inflation rate.

IMF Staff papers: Volume 33 No. 2
Author: International Monetary Fund. Research Dept.
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    increase in Tax Rate (di/dτ = α1i/Δ≥; dL/dτ= −α1 β1i/Δ ≤ 0)

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    Increase in Inflation [1 ≤, di/dπ = (α1 + β1)/Δ ≤ 1/(1 − τ); dL/dπ = −α1 β1τ/Δ ≤ 0]

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    Lending Insensitive to Interest Rate (di/dπ = 1;dL/dπ = 0)

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    Borrowing Perfectly Elastic with Respect to Interest Rate (di/dπ = 1;dL/dπ < 0)

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    Borrowing Insensitive to Interest Rate [di/dπ = 1/(1 − τ); dL/dπ = 0]

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    Lending Perfectly Elastic with Respect to Interest Rate [di/dπ = 1/(1 − τ); dL/dπ < 0]

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    Increase in Tax Rare Under Modified Lending Equation (di/dτ = −α1i/Δ ≤ 0; dL/dτ = α1β1i/Δ ≤ 0)

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    Increase in influiion Under Modified Lending Equation [0 ≤ di/dπ = (−α1 + β1)/Δ ≤ 1; dL/dπ =α1β1τ/Δ ≥ 0]

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    Modified Tax-Adjusted Credit Market With and Without interest Taxation Indexed to Inflation