Chapter

7 Inflation, Taxation, and the Rate of Interest in Eight Industrial Countries, 1961–82

Editor(s):
Vito Tanzi
Published Date:
June 1984
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High interest rates in recent years have given new importance to the theories of interest rate determination and to the relationship between inflation and interest rates. Questions have arisen as to the impact of differential tax treatment of interest income and expense in various countries on the real rate of interest. This paper analyzes the relationship between interest rates and inflation, as well as the effects of taxation on this relationship, for a sample of eight industrial countries during the period 1961–82.

I. BACKGROUND OF THE STUDY

The classical theories of the determination of interest rates—Ricardo’s theory of value, Wicksell and the Austrian school’s natural rate, and the Fisherian theory on the interaction between time preference of individuals and the marginal productivity of capital—dealt with the determination of real interest rates. With the introduction of money into the analysis, the loanable funds (Fisher) approach and the liquidity preference (Keynes) or portfolio approach were developed. Periods of inflation made it necessary to recognize the distinction between the nominal rate of interest and the real rate of interest.

The Fisher effect, which had first been introduced by Thornton (1802) and subsequently formalized by Fisher (1896; 1930), suggests that as individuals anticipate higher rates of inflation they expect nominal rates of interest to reflect this increase.1 However, Fisher (1930, p. 43) observed. “… when prices are rising, the rate of interest tends to be high but not so high as it should be to compensate for the rise; and when prices are falling, the rate of interest tends to be low, but not so low as it should be to compensate for the fall.” Employing a loanable funds framework, Fisher expected the anticipated inflation coefficient to be unity. When he observed a smaller coefficient, he noted that the erratic behavior of real interest rates is evidently a trick played on the money market by “money illusion” and he argued further that it was also due to “the instability of money.”

Analysis of the effect of a change in anticipated inflation on the real rate of interest was introduced by Mundell (1963) and Tobin (1965). Mundell demonstrated that a rise in anticipated inflation would result in a decrease in the real rate of interest, the rationale being that such a rise depresses the real balance of equilibrium, thus causing an increase in saving to compensate for it. Equilibrium is restored by means of a lower real interest rate, which raises the level of investment to make it equal to the higher level of savings. Tobin introduced a portfolio effect. He noted that a rise in anticipated inflation causes a shift away from money balances into real capital, thereby depressing the marginal product of capital and the equilibrium of the real rate of interest. Thus, according to Mundell, the Fisher equation,

where i is the nominal rate of interest, r is the real rate of interest, and πe is the anticipated rate of inflation, would imply that dr/dπe < 0 and di/dπe < 1 and not di/dπe = 1, as Fisher would have expected.

More recently, economists have realized that the relationship between changes in anticipated inflation and interest rates should be adjusted for the tax effect. This concept of tax effect was developed independently by Darby (1975), Tanzi (1976), and Feldstein (1976), who noted that if the pretax Fisher effect—e.g., the coefficient of πe (equation (1))—was unity, then the tax-adjusted Fisher effect should be (1/1 - τ), where τ is the effective tax rate applied to interest income. As 1 > τ > 0, then 1/1 - τ > 1 and the Fisher effect combined with the tax effect would result in a coefficient greater than unity. If a capital gains tax (θ) is introduced, the modified Fisher effect and the tax effect would be 1θ1τ, which could still be greater than unity but less than 1/1 – τ because τ is normally greater than θ.

As the Fisher equation reflects only partial equilibrium, a number of attempts have been made to develop more comprehensive models that incorporate macroeconomic effects as well as tax effects. Levi and Makin (1978) constructed a macroeconomic model wherein di/dπe was derived and was shown to depend on income, liquidity, and employment effects as well as on the taxes on interest income and capital gains. A more detailed model was constructed by Summers (1982), while Nielsen (1981) developed a general-equilibrium framework based on microeconomic optimizing behavior by both households and firms. Although he incorporated the personal income tax, the corporate income tax, and the capital gains tax into the model, his conclusions were similar to those derived earlier: that the nominal interest rate would increase by more than the pure Fisher effect but by less than would be required to keep constant the real after-tax rate of return.

Empirical studies on the relationship between interest rates and inflation with or without taxes have mainly focused on the United States rather than on other countries. This paper analyzes the various responses of interest rates to changes in expected and actual inflation rates in specific countries which have different rates of inflation and different tax treatments of interest income or capital gains. It also studies the changes in response coefficients over time as the world economy has moved from low to high rates of inflation and the effects, if any, of changes in the instruments of monetary policy on these response coefficients.

The present study is divided into three phases. In the first phase, tests are carried out on the relationship between (1) short-term and long-term interest rates, and (2) actual and expected inflation. The second phase deals with the impact of the acceleration in the inflation rate that occurred in the 1970s and the response of interest rates to inflation; it also examines the possible effects of the October 1979 change in the conduct of monetary policy on this relationship. In the third phase, the impact of taxation on the response of interest rates to inflation is studied.

The paper introduces to the literature on the Fisher effect a new technique developed by Frankel (1982) to derive a time series of expected inflation from the term structure of interest rate. The results show that the Fisher effect, based on expected inflation, was generally not significantly different from unity; the response coefficient of interest rates to actual inflation was significantly less than unity for all eight countries during the twenty-year period 1961–81. The results also indicate that the acceleration of inflation during the 1970s was accompanied by increases in these response coefficients; a slight increase was also observed following the October 1979 change in the U.S. conduct of monetary policy. The Fisher effect, adjusted for taxes on interest income and capital gains, was found to be broadly consistent with the estimated response coefficients of nominal interest rates to expected inflation.

In interpreting these results, it should be noted that in most of the sample countries interest rates have been an instrument of monetary policy. It should also be pointed out that some of the countries have employed credit rationing, while other countries have had a liberal approach to capital flows, or there has been offshore banking, which tended to “exogenize” interest rates. Thus, the response of interest rates to inflation would reflect the adjustment of interest rates by the monetary authorities to inflation in countries that have pursued monetary or interest rate controls and to external factors in countries that have pursued policies of free capital flows.

II. STRUCTURE OF THE STUDY

In studying the Fisher effect, it should be recognized that the Fisher equation relating interest rates to expected inflation is an ex post identity while ex ante it is nothing but a partial equilibrium. It is not a theory of interest rate determination in the strict sense and does not include all the variables that determine interest rates. A major theoretical issue, recognized in the literature, is the treatment of the effect of expected inflation on the expected real interest rate. In addition, methodological obstacles encountered in an empirical study of the Fisher effect are (1) the determination or measurement of expected inflation and (2) the measurement of the interaction between the expected real rate and expected inflation. The first obstacle was bypassed in a number of studies on the United States and the United Kingdom through use of the Livingston series on expected inflation or through use of actual inflation or distributed lags thereof. As for the second obstacle, attempts have been made to use proxy variables, such as capacity utilization, for this measurement, but these have raised additional methodological problems.

The present study uses a number of formulations for inflation, including actual inflation, distributed lags of present and past inflation, inflationary expectations formed by distributed lags of past inflation and monetary growth, and inflationary expectations derived from the term structure of interest rates based on the new Frankel technique.

With respect to the effect of expected inflation on the real interest rate, a number of tests are conducted in which the computed ex post real interest rate is subtracted from the nominal rate of interest so that the nominal rate of interest less the ex post real rate is regressed on actual or expected inflation rates. This is designed, in part, to take into account the effect of expected inflation on the real interest rate.

Inflation and the interest rate

As a first approximation, the actual rate of inflation is used for two reasons. First, actual inflation represents a form of rational expectations, with perfect foresight (Summers (1982, pp. 52–57)), and second, its use in testing would indicate the extent of an ex post response of interest to inflation. Thus, the estimated equation is

where it is the short-term interest rate, and πt, the rate of inflation. When quarterly data, adjusted for serial correlation in the error term are used for the period 1961–81, the estimated coefficient of it, is significant with a probability of 98 percent for seven of the eight countries—the exception being the United Kingdom (Table 1). Among the other seven countries, β1 is significantly less than unity. The highest coefficients were found for the United States (0.671) and France (0.637), while Italy, Canada, and the Federal Republic of Germany recorded coefficients of about one half; Japan and the Netherlands were well below these figures, with 0.228 and 0.147, respectively.

Table 1.Eight Industrial Countries: Regression of Short-Term Interest Rates on Inflation, 1961–811

it=βo+β1πt+ut

Countryβ0β1R¯2D-W
Canada4.3730.4910.9231.718b
(2.922)(3.055)
France2.8540.6370.9191.823b
(3.595)(6.854)
Germany, Fed. Rep.4.8240.4820.8461.470a
(3.237)(2.485)
Italy25.1040.5330.9001.922b
(2.281)(4.444)
Japan5.7990.2280.8351.355a
(7.669)(4.257)
Netherlands6.6670.1470.8611.687b
(8.765)(2.790)
United Kingdom8.5590.0610.8991.899b
(4.833)(0.818)
United States2.3030.6710.9141.786b
(3.499)(7.248)

Inflation is defined as πt = [(Pt/Pt-4) – 1) · 100. Superscripts a and b represent one-lag and two-lag autoregressive error terms, respectively, adjusted by the Cochrane-Orcutt procedure; t-values are in parentheses.

Data on short-term interest rates are available only from the first quarter of 1971 to the fourth quarter of 1981.

Inflation is defined as πt = [(Pt/Pt-4) – 1) · 100. Superscripts a and b represent one-lag and two-lag autoregressive error terms, respectively, adjusted by the Cochrane-Orcutt procedure; t-values are in parentheses.

Data on short-term interest rates are available only from the first quarter of 1971 to the fourth quarter of 1981.

As di/dπ < 1, the intercept cannot be regarded as (he real interest rate. Table 5 (in the Appendix) summarizes average short-term interest rates, average rates of inflation, and average ex post real rates of interest for the twenty-year period 1961–81 and for the ten-year subperiods 1961–70 and 1971–81. With the exception of the United Kingdom, which had negative real interest rates for the period as a whole, all other countries, on average, experienced positive real interest rates. For the breakdown of the period into two subperiods, the more than doubling of average inflation rates was accompanied by a decline in average real interest rates for all countries. These computations, however, are in no way analytical proof of the Mundell-Tobin effect, but it is interesting to observe that, along with the rise in inflation rates, ex post real interest rates tend to be lower.

Thus, a second test is designed to establish the “true” coefficient of response of interest to inflation by superimposing the ex post average real interest rate on the regression as the intercept, β0 The estimated equation is

where r¯ is the average real interest rate for the period 1961–81, defined as r¯=i¯π¯,and wherei¯andπ¯ are average interest and inflation rates, respectively. The motivation behind this formulation is that β1 reflects the response of the interest rate to changes in expected inflation most accurately when the intercept β0 is equal to the real rate of interest. Also, by computing the average ex post real rate, account is being taken of the fact that dr/dπe ≠ 0. Thus, the results of the estimation, which are summarized in Table 2, are theoretically more defensible than the results of the previous test. These results show that, for the period as a whole, the response coefficients are the highest for France (0.888) and the United States (0.876), in the range of 0.5 for the Federal Republic of Germany, Italy, and Canada, and 0.213 for the Netherlands; Japan and the United Kingdom did not record significant coefficients.

Table 2.Eight Industrial Countries: Response of Short-Term Interest Rates to Inflation, 1961–811

itr¯=β1πt+ut

CountryPeriodr¯β1R¯2D-W
Canada1961–811.0350.4250.9211.669b
(2.450)
1961–701.9930.9360.8881.881a
(11.005)
1971–810.1650.8790.8851.756b
(6.221)
France1961–810.2600.8880.9101.303b
(15.660)
1961–701.3150.4170.9381.427a
(2.129)
1971–81–0.6990.9730.8661.796b
(25.407)
Germany, Fed. Rep.1961–812.2730.5480.8431.516a
(3.051)
1961–702.4250.1700.7452.024a
(0.870)
1971–812.1351.0500.8841.930b
(6.910)
Italy1971–81–2.2200.5050.8931.895b
(4.425)
Japan1961–810.134–0.0090.5911.933a
(–0.048)
1961–700.8710.0730.9151.983a
(1.113)
1971–81–0.5380.8180.4091.979b
(3.106)
Netherlands1961–810.5270.2130.8221.404a
(3.837)
1961–702.4730.0390.6641.501a
(0.365)
1971–81–1.2420.2830.8881.524a
(4.565)
United Kingdom1961–81–1.1020.0620.8931.383a
(0.913)
1961–701.6450.0870.8151.583a
(0.786)
1971–81–3.5990.0610.8091.346a
(0.651)
United States1961–810.4390.8670.9081.785b
(12.280)
1961–701.5860.6830.9411.697b
(5.481)
1971–81–0.6030.9680.8681.831b
(14.384)

To assess the cumulative effect of inflation on interest rates, two alternative schemes of distributed tags were employed, both using the Almon lag technique, with polynomials of the third degree corrected for autocorrelation. In the first scheme,

Short-term interest rates are regressed on present and past inflation rates, with eight quarterly lags. In the second scheme,

Short-term rates are regressed on the past eight quarterly lags. The formulation of equation (4) is a form of rational expectations, with actual inflation at time t, πt representing expected inflation at time t and πt-i representing instrumental variables. Equation (5), on the other hand, represents an adaptive-distributive scheme of inflationary expectations. As could be expected, the results for ∑βi, in the rational scheme are somewhat higher than those in the adaptive-distributive one, but the sums of the coefficients are less than unity (not recorded) in both.

As noted above, a major difficulty in estimation is that of the formulation of price expectations. Papers by Lahiri (1976), Tanzi (1980), and others have introduced a number of schemes or hypotheses on the formation of expectations. These include distributive, adaptive, and extrapolalive schemes, which were then used along with the Livingston series of price expectations to generate a modified price expectations series. This last was in turn used to test the Fisher effect. In the absence of a Livingston series for countries other than the United States and the United Kingdom, variations of the above schemes, some of which have been recorded earlier, are used in the present study. All schemes were estimated by using ordinary least squares, with the possible deficiency that error terms were correlated with the explanatory variables, thus resulting in inconsistent estimates. In the following test, a two-stage least-squares estimation is carried out:

where distributed lags of past inflation and money growth, μ are employed as instrumental variables—both distributed lags of the Al-mon type with polynomials of the third degree corrected for autocorrelation (Carlino (1982)). The results, which are summarized in the Appendix, Table 6, are not as robust as those derived above by using simpler techniques. Another method, using the Fama approach of short-term interest rates as predictors of inflation, did not yield any significant results (not recorded).

A new technique for extracting a measure of expected inflation from the term structure of interest rates that was developed by Frankel (1982) is applied as described below. Proxies used as measures of expected inflation include either actual present or lagged values of inflation or survey data. The actual values of inflation do not incorporate all the pieces of information that enter into the formation of expectations, while survey data, such as the Livingston series, have been shown to contain deficiencies.

The Frankel method is based on the premise that long-term interest rates reflect expected future short-term rates and that long-term rates reflect the expected inflation rate more fully than do short-term rates. It is thus assumed that there exists a commonly held expectation (πe) as to what the long-run inflation rate is and that, in the absence of future disturbances, the real rate of interest will converge to a constant in the long run. The gap is expected to be closed at a rate δ

where it, is the short-term interest rate; πe0 is the long-run inflation rate expected at time 0; and r¯ is the long-run real interest rate.

The speed of adjustment is measured in the following way:

where itτ2 is the interest rate on τ2 (long-term) maturity bonds issued at time t,itτ1 is the interest rate on τ1 (short-term) maturity bonds issued at time t, and δ = – 12 log β. Upon estimation of the above regression, β can be used to compute the weights of the linear combination of iτ2 and iτ1 so that

and

and

Thus, from equation (9) a lime series of expected inflation (plus a constant term) can be obtained.

The above technique is used for the estimation of a time series of expected inflation for six industrial countries, based on Eurocurrency deposit rates for 1 month and 12 months. The results of the estimation of equation (8) are presented in the Appendix, Table 7, while the estimated coefficients are used to generate πte+r¯, as shown in equation (9). It is assumed that 1-month and 12-month Eurocurrency deposit rates belong to the same risk class; otherwise, πte+r¯ will contain some risk factor.2

Once a lime series of expected inflation had been obtained, two tests on the impact of inflationary expectations were conducted: in the first, short-term interest rates were regressed on expected inflation; and in the second, short-term rates minus the ex post real rate were regressed on expected inflation. The results of the first test (Appendix, Table 8) indicate β coefficients significantly greater than unity for all six countries, ranging from about 1.15 for the Federal Republic of Germany and the United States through 1.2 for the United Kingdom and the Netherlands and 1.48 for France and Japan. The results of the second test (Table 3) show coefficients of response to inflation not significantly different from unity for seven countries—all but Japan, which recorded a coefficient of 1.16.

Table 3.Eight Industrial Countries: Response of Short-Term Interest Rates to Expected Inflation, September 1973–July 19821

itr¯=βπto+ut

CountryβR¯2D-Wr¯
Canada0.9910.9691.5300.908
(0.026)
France1.0220.7542.0421.252
(0.034)
Germany, Fed. Rep.0.9910.9271.9331.715
(0.036)
Italy1.0300.7791.9701.019
(0.025)
Japan21.1620.9052.432–0.279
(0.097)
Netherlands0.9840.8811.8020.953
(0.040)
United Kingdom0.9970.8142.120–1.927
(0.021)
United States0.9930.9612.0281.027
(0.032)

The variable πe is derived by the Frankel procedure from the term structure of interest rates. One-lag autoregressive error term is adjusted by the Cochrane-Orcutt procedure; estimated standard errors are in parentheses.

November 1975-March 1982.

The variable πe is derived by the Frankel procedure from the term structure of interest rates. One-lag autoregressive error term is adjusted by the Cochrane-Orcutt procedure; estimated standard errors are in parentheses.

November 1975-March 1982.

It should be mentioned here that a number of tests were conducted on the relationships between inflation and long-term interest rates. In the first test, long-term interest rates were regressed on actual inflation, resulting in low coefficients of 0,10–0.25 for Canada, France, the Netherlands, the United States, and Italy and insignificant coefficients for the Federal Republic of Germany, Japan, and the United Kingdom (Appendix, Table 9). In the second test, long-term interest rates were regressed on expected inflation as derived by the Frankel method. The results indicate a high response coefficient (0.93), but less than unity, for the interest rate of expected inflation for the United States and 0.58 for France, while for all other countries in the sample the response coefficient fell within the range 0.1 1–0.18 (Appendix, Table 10.)

Changes over time in the Fisher effect

Tests were made to measure changes in the Fisher effect following the acceleration of inflation, as inflation rates were higher in the 1970s than in the 1960s. The study also examined possible changes in the Fisher effect following the October 1979 change in technique of monetary policy in the United States, which resulted in increased variability of interest rates.3

In the first test, the twenty-year period 1961–81 was divided into two subperiods—1961–70 and 1971–81. The main objective of this test was to observe whether, during periods of higher inflation, interest rates responded more fully to inflation, that is, whether the β was higher during the 1970s. The result (Appendix, Table 11) tends to indicate that the coefficient of response was higher in the 1970s (it is possible, however, that π was a better measure of πe in the 1970s). With the exception of the United Kingdom (which had insignificant coefficients during both decades) and Canada (which had a significant coefficient in the 1960s and insignificant coefficients in the 1970s), all other countries recorded noticeably higher β’s during the second subperiod. The most significant changes occurred in the Federal Republic of Germany, where β rose from 0.176 to 1.303, and in France, where it rose from 0.15 to 0.788; in the United States, the increase was more modest—from 0.622 to 0.808.

In the above test, there is a possibility that changes in the intercept might have affected the outcome. Although the intercept declined in most countries during the second subperiod, the likelihood that intercept variability might somewhat obscure the outcome suggests a test in which changes in the intercept would not affect the response coefficients. To deal with this potential problem, a third test was constructed in which the intercept is held constant for the two subperiods so that the change in di/dπ will fully reflect the change in the response of interest rates to inflation. Thus, equation (10) is estimated (Appendix, Table 12).

where D is a dummy; D = 1 for t 1 = 1961–70 and D = 0 for t 2 = 1971–81. This test is designed to answer the question of whether β2 is higher than β1, given the fact that inflation was higher during the second period. The results indicate a general increase in response, as β2 exceeds β1 for France, the Federal Republic of Germany, the Netherlands, and Canada, which had insignificant coefficients in the previous test; the United States records a decline with β1 = 0.772 and β2 = 0.680 (a difference slightly less than one standard error of the coefficients). Japan and the United Kingdom recorded insignificant coefficients during both subperiods. The results of this test seem to reinforce those of the previous test in indicating that, as a result of higher rates of inflation, the response of interest rates to inflation tends to be higher.

As inflation rates accelerated during the 1970s, there was a decline in the ex post average real interest rate for the eight countries in the sample (Chart 1). Moreover, during 1971–81, negative average real interest rates were experienced in France, Italy, Japan, the Netherlands, the United Kingdom, and the United States, while the Federal Republic of Germany’s average real interest rate was 2.135 and Canada’s was marginally positive (Appendix, Table 5).

Chart 1.Eight Industrial Countries: Inflation and Interest Rates, 1961–82

(In percent)

In applying different ex post real interest rates for the two subperiods for all countries, a comparison between the 1960s and 1970s shows that the response coefficient is significantly higher during the latter period for France, the Federal Republic of Germany, Japan, the Netherlands, and the United States; no significant change is recorded for Canada, whereas for the United Kingdom, the coefficient is not significant (Table 2). It is interesting to note that during the period 1971–81, β1, for the Federal Republic of Germany is slightly greater than unity and for France and the United States not significantly different from unity.

In October 1979, the U.S. Federal Reserve Board changed its instrument of monetary policy from a combination of interest rates and money growth targets to one that set monetary growth targets. Changes in a similar direction occurred in the United Kingdom and in Japan, although in a considerably less pronounced manner. As a result, short-term interest rates have become more market determined while fluctuations of rates have become more pronounced. The analysis here tests whether these changes in the technique of monetary policy have affected the degree of response of interest rates to inflation.

Two tests similar to the ones above were conducted, using monthly data. The first is as follows:

where D = 1 for the period t 2 = January 1971–September 1979 and D = 0 for the period t 1 = October 1979–March 1982, The results of the estimation (Appendix, Table 13) indicate an increase in the response of interest rates to inflation in four of the eight countries in the sample: France, the Federal Republic of Germany, Italy, and the United States. Only the United States, however, recorded a significant increase (β2 being greater than β1 by one standard deviation of the mean coefficient). The second test for the period October 1979–March 1982, using monthly data, where ris the average ex post real interest rate for the period, resulted in response coefficients that are not significantly different from unity for five of the countries: Canada, France, the Federal Republic of Germany, Japan, and the United States (Appendix, Table 14). These results indicate somewhat higher coefficients than those obtained for the full period 1971–81 using quarterly data.

Impact of taxation on the Fisher effect

It is essential at this point to estimate the impact of taxation on the response of interest rates to inflation. The incorporation of tax consideration into the Fisher effect was done independently by Darby (1975), and Tanzi (1976); assuming that borrowers and lenders are concerned with the real after-tax interest, the formulation of the Fisher equation was modified to

where τ is the effective personal tax rate applied to interest income. Feldstein (1976) and later Gandolfi (1982), in two different analytical frameworks, introduced the corporate sector as a borrower and investor in the capital market, whose effective capital gains tax rate (θ) resulted in a further modification of the Fisher equation

The expression derived by Levi and Makin (1978) from their macroeconomic framework was

where L is a term incorporating liquidity, income, and employment effects. Computing the magnitude of di/dπe for the United States (assuming that τ = 0.5), they found a range of 0.750–1.285, depending on the paremeters in L. Neilsen’s (1981) general-equilibrium model based on micro-optimization behavior of households and firms included (in addition to personal income lax and capital gains tax) company income tax, τ1. Neilsen derived an expression for di/dπ that was shown as a range, depending on the relative magnitudes of all three tax rates

The tax treatment of interest income and interest expense for the household sector, on the one hand, and corporate taxation on the other hand, varies quite substantially from country to country.4 Preferential tax treatment of interest income of the household sector differs from country to country. It is most generous in Japan, where interest income of the equivalent of US$56,000 per taxpayer is tax exempt; it is estimated that average tax payments on interest income during the 1970s were about 7 percent. Interest income is incorporated into total individual income and treated as part of global income in Canada, the Federal Republic of Germany, the United Kingdom, and the United Slates, while France, Italy, and Japan permit the nominal withholding taxes on interest income to become final taxes.

Deductibility of interest payments is most liberal in the Netherlands and in the United States, because it extends to general consumer credit and mortgages. Steuerte (1982) suggests that only 30 percent of income from capital in the United States is subject to individual income taxation; he estimated that about 80 percent of the assets held by individuals has been in forms for which there has been a tax preference arising from capital gains tax rates, exclusions, or some other means of nontaxation of some or all of the income from the assets. Interest payments on home mortgages are also deductible in Canada, France, and the United Kingdom, while in the Federal Republic of Germany and Japan, less generous schemes apply. In the Federal Republic of Germany, there are taxes on the imputed income of owner-occupied housing. Although many industrial countries tax long-term capital gains of individuals, either under a separate tax (e.g., the United Kingdom) or under the regular income tax after exempting a certain proportion of the gains (e.g., Canada and the United States), most industrial countries apply lower tax rates on long-term capital gains than on ordinary income. With respect to corporate taxation, double taxation exists in the United States at shareholder levels. In the Federal Republic of Germany, shareholders receive full credit for the tax paid by the corporation on dividends distributed; in other countries, there are partial imputations.

Acknowledging the difficulties in quantifying effective tax rates on interest income, company income tax, and capital gains tax for the countries in the sample, the author presents in the Appendix, Table 15, an estimate of average effective rates of interest income of individuals and corporations during the subperiod 1971–81. Tax rates on interest income of individuals for Canada, the Federal Republic of Germany, the Netherlands, the United Kingdom, and the United States represent the percentage ratio of tax paid to taxed income of “representative” taxpayers (defined as individuals whose assessable income constitutes about one third of the total taxed income in the highest-income brackets). For France and Italy, the rates are final withholding tax rates; for Japan, the rate represents the average ratio of interest income tax to interest income5 With respect to capital gains tax rates, owing to difficulties in obtaining effective rates, statutory rates have been chosen; as effective capital gains tax rates would be somewhat lower, the computed (1 –θ)/(l–τ) could be somewhat biased downward.

On the basis of these tax rate computations, the Fisher effect adjusted to the tax on interest income alone shows coefficients ranging from 1.075 for Japan and 1.299 for the United States to about 1.5 for France and the Federal Republic of Germany (Table 4). If both the individual interest income tax and the capital gains tax are taken into account, the tax-adjusted Fisher effect is less than unity for all but France (1.124) and Italy (1.072); it ranges between 0.847 for the Netherlands and 0.964 for the Federal Republic of Germany. However, since the capital gains tax rates used are the statutory rates, these tax-adjusted Fisher effects would be somewhat higher. If these are compared with the β’s obtained for expected inflation, the two sets tend to be fairly consistent for France, the Federal Republic of Germany, the Netherlands, the United Kingdom, and the United States. For Japan, the tax ratio is less than unity while the response coefficient is significantly greater than unity. If the response coefficient of interest rates to actual inflation in Japan is compared with the tax ratio, the two will be similar in order of magnitude—0.818 and 0.857, respectively.

Table 4.Eight Industrial Countries: Impact of Taxation on Adjustment of Interest Rates to Inflation, 1971–81
Country11τ1θ1τ11θ1τβ(of πe)β(of π)
Canada1.1761.0690.9060.9910.879
France1.4931.1361.1201.0220.973
Germany, Fed. Rep.1.5151.0670.9700.9911.050
Italy1.4291.0001.0721.0300.505
Japan1.0750.9880.8601.1620.818
Netherlands1.2990.9840.283
United Kingdom1.3160.7950.9210.9970.061
United States1.2991.0610.9090.9930.968
Source: Tax rates are based on those of Table 15 in the Appendix. β(of π) and β(of πe) are regression coefficients of Tables 2 and 3, respectively.
Source: Tax rates are based on those of Table 15 in the Appendix. β(of π) and β(of πe) are regression coefficients of Tables 2 and 3, respectively.

The application of the Neilsen range shows that only in the United Kingdom di/dπe was between 1/1 – τ and (1 -θ)/(1 -τ1); in all the other countries, both di/dπand di/dπe were smaller than the lower bound of the range.

In sum, when only personal interest income tax is used, the Fisher effect is expected to be greater than unity. Empirical results that tend to support a response coefficient of interest rates to expected inflation of greater than unity were obtained when a regression of the type it=β0+β1πt+ut was used without correcting for the effects of expected inflation on the real rate of interest. When both types of tax (interest income tax and capital gains tax) are taken into consideration, the tax-adjusted Fisher effect can be greater or less than unity. In fact, it was found to be greater than unity for France and Italy and less than unity for all other countries. These tax-adjusted coefficients for the Fisher effect were found to be consistent with the estimated response coefficients of nominal interest rates to expected inflation for France, the Federal Republic of Germany, the Netherlands, the United Kingdom, and the United States; they were found to be consistent with β’s of actual inflation for Canada, the Federal Republic of Germany, Japan, and the United States.

III. CONCLUSION

The results of the tests conducted in the present analysis can be summarized in three parts:

  • 1. The response coefficient of nominal short-term interest rates to expected inflation, derived from the term structure of interest rates and based on a new technique that had been developed by Frankel (1982), was significantly greater than unity in Japan (1.16) but not significantly different from unity for all other countries. The same test, without adjusting for real interest rates, resulted in response coefficients significantly greater than unity for all sample countries—about 1.15 for the United States and the Federal Republic of Germany, about 1.20 for the Netherlands and the United Kingdom, and about 1.50 for France and Japan.

    The results indicate that the response of nominal short-term interest rates to actual inflation for the period 1961–81 was significantly less than unity for all eight countries. France and the United States recorded coefficients of about 0.90, the Federal Republic of Germany, Italy, and Canada about 0.45–0.55, and the Netherlands 0.21, while Japan and the United Kingdom had insignificant coefficients.

    As for long-term interest rates, the response coefficient to expected inflation was high for the United States (0.93) and France (0.58) and in the range of 0.10–0.20 for the Federal Republic of Germany, Japan, the Netherlands, and the United Kingdom. The response coefficient of long-term interest rates to actual inflation was found to be 0.10–0.25 for Canada, France, Italy, the Netherlands, and the United States, and insignificant for the Federal Republic of Germany, Japan, and the United Kingdom.

  • 2. The acceleration of inflation from the 1960s to the 1970s was generally accompanied by increases in the response coefficient of short-term interest rates to inflation. The change of instruments of monetary policy that occurred in October 1979 in the United States was accompanied by some increase in the Fisher coefficient to actual inflation, especially in the United States, Canada, and the Federal Republic of Germany.

  • 3. The Fisher effect, adjusted for the interest income tax and the capital gains tax, can be greater or less than unity; it was found to be greater than unity for France and Italy and less than unity for all the other countries in the sample. These tax-adjusted Fisher effects were found to be consistent with the estimated response coefficients of nominal interest rates to expected inflation for France, the Federal Republic of Germany, the Netherlands, the United Kingdom, and the United States; they were found to be consistent with the response coefficient of short-term interest rates to actual inflation for Canada, the Federal Republic of Germany, Japan, and the United States.

    In interpreting these results, it should be noted that monetary policies of most countries have used interest rates as a major instrument, while in other countries free capital flows or the existence of offshore banking tended to make the determination of interest rates exogenous. Consequently, the response of interest rates to actual or expected inflation could reflect adjustments by the monetary authorities to inflation, on the one hand, or adjustments stemming from external factors, on the other hand.

Appendix
Table 5.Eight Industrial Countries: Mean Inflation and Short-Term Nominal and Real Interest Rates, 1961–811
CountryPeriodi¯π¯r¯
Canada1961–816.7685.7331.035
1961–704.7242.7311.993
1971–818.6268.4610.165
France1961–817.4227.1620.260
1961–705.3544.0391.315
1971–819.30210.001–0.699
Germany, Fed. Rep.1961–816.2163.9432.273
1961–705.0122.5872.425
1971–817.3105.1752.135
Italy1961–819.377
1961–70
1971–8112.08114.301–2.220
Japan1961–815.8785.7440.134
1961–704.9134.0420.871
1971–816.7547.292–0.538
Netherlands1961–817.8637.3360.527
1961–708.2385.7652.473
1971–817.5238.765–1.242
United Kingdom1961–817.9779.079–1.102
1961–705.7094.0641.645
1971–8110.04013.639–3.599
United States1961–815.9925.5530.439
1961–704.3502.7641.586
1971–817.4858.088–0.603

The variables i¯,π¯, andr¯ denote average nominal short-term interest rate, average inflation, and average real interest rate, respectively. Inflation is measured as πt=[(Pt/Pt4)1]. 100, where Pt is the quarterly average consumer price index.

The variables i¯,π¯, andr¯ denote average nominal short-term interest rate, average inflation, and average real interest rate, respectively. Inflation is measured as πt=[(Pt/Pt4)1]. 100, where Pt is the quarterly average consumer price index.

Table 6.Eight Industrial Countries: Two-Stage Least-Squares Estimation of Impact of Inflation on Short-Term Interest Rates, 1961–811

(1)πt=α+i=18δiπt1+j=18γjμtj+εt

(2)it=β0+β1πt+ut

Countryi=18δii=18γjβ0β1R¯2D-W
Canada0.9130.0019.681–0.0680.9131.648b
(10.143)(0.293)(3.316)(–0.987)
France0.9170.0401.4770.7990.6621.871b
(11.615)(0.583)(1.526)(6.847)
Germany,0.844–0.0027.029–0.0790.8482.052b
Fed. Rep(8.636)(–0.040)(6.306)(–2.283)
Italy0.8900.32513.4430.0220.8701.857b
(9.761)(2.299)(5.677)(0.508)
Japan0.660–0.0416.772–0.0510.6241.828a
(3.015)(–0.326)(6.061)(–1.133)
Netherlands0.7710.1167.961–0.0230.8351.706b
(7.216)(1.920)(10.136)(–1.196)
United0.4680.4309.482–0.0090.8991.901b
Kingdom(2.361)(2.050)(4.927)(–0.465)
United0.7380.3316.9080.1010.9061.795b
States(10 .720)(3.535)(3.757)(1.118)

The two instrumental variables are Σi=18πti andΣj=18μtj, where the latter is the rate of growth of Mt; the t-values are in parentheses. The error term is autoregressive with one and two lags (superscripts a and b, respectively).

The two instrumental variables are Σi=18πti andΣj=18μtj, where the latter is the rate of growth of Mt; the t-values are in parentheses. The error term is autoregressive with one and two lags (superscripts a and b, respectively).

Table 7.Eight Industrial Countries: Estimation of Speed of Adjustment, September 1973–July 19821

(itτ2itτ1)=α+β(it1τ2it1τ1)+ut

CountryαβR¯2D-Wδ2
Canada0.0300.7660.5821.5303.200
(0.064)(0.064)
France0.1500.3870.1412.0334.948
(0.248)(0.090)
Germany,0.1250.6000.3571.9102.658
Fed. Rep.(0.085)(0.077)
Italy–0.1810.3690.1210.95011.900
(0.269)(0.095)
Japan30.2050.6940.4782.2621.906
(0.133)(0.083)
Netherlands0.1320.6720.4501.8042.071
(0.109)(0.072)
United0.0960.5470.3112.0473.148
Kingdom(0.139)(0.078)
United0.1020.7570.5642.0331.453
States(0.083)(0.064)

The variables iτ1 and iτ2 represent 1-month and 12-month Eurocurrency deposit rates, respectively. Estimated standard errors are in parentheses; the technique of estimation is ordinary least squares.

The speed of adjustment is δ = – 12 log β

November 1975–March 1982.

The variables iτ1 and iτ2 represent 1-month and 12-month Eurocurrency deposit rates, respectively. Estimated standard errors are in parentheses; the technique of estimation is ordinary least squares.

The speed of adjustment is δ = – 12 log β

November 1975–March 1982.

Table 8.Six Industrial Countries: Response of Short-Term Interest Rates to Expected Inflation, September 1973–July 19821

it=β0+β1πte+Ut

Countryβ0β1R¯2D-W
France–4.6361.4810.7981.983
(1.152)(0.094)
Germany, Fed. Rep.0.6151.1430.9311.881
(0.389)(0.063)
Japan2–4.2901.4770.9301.937
(0.566)(0.077)
Netherlands–1.2371.2320.8891.821
(0.725)(0.090)
United Kingdom–5.0761.1970.8192.055
(1.521)(0.099)
United States–0.8761.1540.9641.990
(0.571)(0.054)

The variable πe is derived by the Frankel procedure from term structure of interest rates. One-lag autoregressive error term is adjusted by the Cochrane-Orcutt procedure; estimated standard errors are in parentheses.

November 1975–March 1982.

The variable πe is derived by the Frankel procedure from term structure of interest rates. One-lag autoregressive error term is adjusted by the Cochrane-Orcutt procedure; estimated standard errors are in parentheses.

November 1975–March 1982.

Table 9.Eight Industrial Countries: Inflation and Long-Term Interest Rates, 1961–811

it=βo+βπt+ut

Country/Periodβ0β1R¯2D-W
Canada
1961–8127.43(2.30)0.172(1.84)0.9511.90
1961–703.58(4.35)0.250(4.22)0.9691.87
1971–8130.41(2.10)0.103(0.691)0.9001.89
France
1961–8120.63(2.12)0.225(3.47)0.9771.97
1961–7011.51(2.85)0.35(0.476)0.9291.98
1971–8111.90(2.16)0.324(3.33)0.9531.94
Germany, Fed. Rep.
1961–817.78(13.33)0.023(0.37)0.9121.78
1961–707.30(16.25)–0.045(–1.08)0.9031.80
1971–816.65(6.61)0.229(1.76)0.8871.80
Italy
1961–8134.58(2.26)0.100(2.82)0.9831.76
1961–707.33(13.88)–0.069(–1.49)0.9201.88
1971–8131.05(2.22)0.121(2.53)0.9721.74
Japan
1961–8110.64(5.13)0.012(0.308)0.9591.93
1961–708.21(6.06)0.012(0.59)0.9781.89
1971–819.62(5.79)0.094(0.706)0.8411.94
Netherlands
1968–817.36(15.72)0.062(2.70)0.9002.05
1968–708.04(18.57)–0.0008(–0.83)0.9801.54
1971–817.36(13.20)0.077(2.71)0.8922.04
United Kingdom
1961–8115.25(3.54)0.037(0.840)0.9601.96
1961–709.286(3.66)0.132(2.42)0.9511.77
1971–8113.28(8.36)0.036(0.565)0.8391.99
United States
1961–813.61(4.18)0.136(2.55)0.9761.98
1961–703.43(31.24)0.528(16.45)0.9532.03
1971–8133.35(2.61)0.133(1.55)0.9391.95

The t-values are in parentheses. The Durbin-Watson statistics are adjusted for serial correlation by the Cochrane-Orcutt procedure.

The t-values are in parentheses. The Durbin-Watson statistics are adjusted for serial correlation by the Cochrane-Orcutt procedure.

Table 10.Six Industrial Countries: Expected Inflation and Long-Term Interest Rates, September 1973–July 19821

it=β0+β1πte+ut

Countryβ0β1R¯2D-W
France14.450.580.9572.17
(3.09)(3.59)
Germany, Fed. Rep.5.1780.1770.9601.90
(8.44)(8.72)
Japan24.920.1410.8881.97
(10.70)(6.82)
Netherlands6.900.1120.9471.97
(14.57)(9.09)
United Kingdom8.1840.1260.6581.99
(6.88)(4.84)
United States13.130.9250.9781.76
(3.33)(8.39)

The t-values are in parentheses; the Durbin-Watson statistics are adjusted for serial correlation.

First quarter of 1976 to first quarter of 1982.

The t-values are in parentheses; the Durbin-Watson statistics are adjusted for serial correlation.

First quarter of 1976 to first quarter of 1982.

Table 11.Eight Industrial Countries: Regression of Short-Term Interest Rates on Inflation, 1961–70 and 1971–811

it=βo+β1πt+ut

CountryPeriodβ0β1R¯2D-W
Canada1961–703.0170.6530.8921.970b
(5.876)(4.452)
1971–818.1240.2700.8931.638b
(2.018)(0.877)
France1961–707.4010.1500.9331.325a
(2.786)(1.134)
1971–811.3150.7880.8681.823b
(0.865)(5.492)
Germany, Fed. Rep.1961–705.8060.1760.7242.030b
(3.516)(0.877)
1971–810.7111.3030.8591.248a
(0.286)(3.407)
Italy1971–815.1040.5330.9001.922b
(2.281)(4.444)
Japan1961–707.0110.0500.9172.038b
(4.501)(0.737)
1971–814.9610.2920.8921.461a
(4.239)(4.797)
Netherlands1961–707.2700.0640.9181.956a
(3.672)(0.945)
1971–816.1920.1590.9062.286b
(5.947)(2.420)
United Kingdom1961–705.7440.0990.8221.530a
(5.631)(0.887)
1971–8111.2620.0600.8131.284a
(3.911)(0.625)
United States1961–702.7540.6220.9401.776b
(6.119)(4.708)
1971–810.9490.8080.8681.800b
(0.602)(4.634)

Inflation is defined as πt = [(Pt/Pt-4) - 1] · 100. Superscripts a and b represent one-lag and two-lag autoregressive error structures, respectively, adjusted by the Cochrane-Orcutt procedure; the t-values are in parentheses.

Inflation is defined as πt = [(Pt/Pt-4) - 1] · 100. Superscripts a and b represent one-lag and two-lag autoregressive error structures, respectively, adjusted by the Cochrane-Orcutt procedure; the t-values are in parentheses.

Table 12.Seven Industrial Countries: Regression of Short-Term Interest Rates on Inflation for Two Subperiods, 1961–70 and 1971–811

it=β0+β2πt2(1D)+ut

Countryβ0β1β2R¯2D-W
Canada4.2780.4400.5120.9221.720b
(2.977)(1.552)(3.158)
France3.0010.5890.6270.9181.824b
(3.328)(3.431)(6.455)
Germany, Fed. Rep.4.6130.4500.5440.8441.455a
(3.167)(2.064)(2.381)
Japan6.8220.018–0.0910.6181.806a
(3.941)(0.084)(–0.386)
Netherlands6.6210.1190.1690.8601.675b
(8.398)(1.690)(2.769)
United Kingdom8.4320.0080.0710.8991.899b
(5.131)(0.065)(0.946)
United States2.1270.7720.6800.9131.794b
(3.110)(4.758)(7.406)

Inflation is defined as πt = [(Pt/Pt-4) - 1] · 100; D denotes dummy variable D = 1 for t 2 = 1971–81; the t-values are in parentheses.

2 The one-lag and two-lag autoregressive error structures are represented by superscripts a and b, which are both adjusted by the Cochrane-Orcutt procedure.

Inflation is defined as πt = [(Pt/Pt-4) - 1] · 100; D denotes dummy variable D = 1 for t 2 = 1971–81; the t-values are in parentheses.

2 The one-lag and two-lag autoregressive error structures are represented by superscripts a and b, which are both adjusted by the Cochrane-Orcutt procedure.
Table 13.Eight Industrial Countries: Regression of Short-Term Interest Rates on Inflation for Two Subperiods, January 1961-September 1979 and October 1979-March 19821

it=β0+β1πt1D+β2πt2(1D)+ut

Countryβ0β1β2R¯2D-W
Canada10.189–0.0550.1420.9791.886b
(0.121)(0.139)
France4.5080.5120.5510.9521.948b
(0.184)(0.179)
Germany, Fed. Rep.5.4160.4080.5520.9641.231a
(0.184)(0.196)
Italy9.8850.2700.3020.9751.989b
(0.092)(0.093)
Japan7.105–0.010–0.0440.7451.980b
(0.024)(0.061)
Netherlands7.472–0.001–0.0060.9732.099b
(0.002)(0.005)
United Kingdom10.2930.0400.0140.9601.956b
(0.065)(0.069)
United States4.6180.3670.5150.9391.858b
(0.150)(0.149)

Monthly data are used. The standard errors of coefficients are in parentheses. For the period t 2 = October 1979–March 1982. D = 1. Superscripts a and b represent one-lag and two-lag auto-correlated error terms, respectively, adjusted by the Cochrane-Orcutt procedure.

Monthly data are used. The standard errors of coefficients are in parentheses. For the period t 2 = October 1979–March 1982. D = 1. Superscripts a and b represent one-lag and two-lag auto-correlated error terms, respectively, adjusted by the Cochrane-Orcutt procedure.

Table 14.Eight Industrial Countries: Response of Short-Term Interest Rates to Inflation, October 1979–March 19821

itr¯=β1πt+ut

Countryr¯β1R¯2D-W
Canada3.8760.992(0.069)c0.8431.993b
(14.280)d
France0.2730.997(0.099)0.8101.834b
(10.099)
Germany, Fed. Rep.4.9130.974(1.150)0.7581.594a
(6.497)
Italy–0.9540.244(0.120)0.8941.904a
(2.032)
Japan4.1390.917(0.130)0.1341.850a
(7.071)
Netherlands2.7630.649(0.148)0.8671.680a
(4.387)
United Kingdom–0.7440.239(0.125)0.7841.493a
(1.913)
United States1.1531.004(0.176)0.5581.722b
(5.705)

Monthly data are used. Superscripts a and b represent one-lag and two-lag autocorrelated error terms, respectively; superscripts c and d represent standard errors of coefficients and t-values, respectively.

Monthly data are used. Superscripts a and b represent one-lag and two-lag autocorrelated error terms, respectively; superscripts c and d represent standard errors of coefficients and t-values, respectively.

Table 15.Eight Industrial Countries: Statutory and Estimated Effective Tax Rates, 1971–81(In percent)
CountryPersonal Income

Tax1

(τ)
Corporate Income

Tax2

t)
Capital Gains

Tax3

(θ)
Canada152823
France333425
Germany, Fed. Rep.344036
Italy302525
Japan742920
Netherlands23
United Kingdom241830
United States233430
Sources: For personal income tax: reports from the income tax departments of individual countries. For corporate income tax in France, the Federal Republic of Germany, Japan, the United Kingdom, and the United States: Thomas Horst, Income Taxation and Competitiveness (Washington: National Planning Association, 1977); in Canada: Statistics Canada, Corporation Taxation Statistics 1977 (Ottawa, March 1980).

Tax rates for countries other than France and Italy represent the percentage ratio of tax paid to taxed/assessable income of “representative” taxpayers, defined as individuals whose taxable/assessable incomes constitute, say, about one third of the total taxed/assessed income in the highest-income brackets. For France and Italy, the rates are final withholding tax rates.

For countries other than Canada, Italy, and the Netherlands, effective tax rates are those calculated by Thomas Horst on the basis of differences in corporate income tax rates, depreciation allowances, and tax credits. For Canada, effective tax rates represent the percentage ratio of corporate income tax assessed to taxable corporate profits; for Italy, they represent the statutory rate.

Statutory rates.

Average ratio of interest income tax to interest income.

Sources: For personal income tax: reports from the income tax departments of individual countries. For corporate income tax in France, the Federal Republic of Germany, Japan, the United Kingdom, and the United States: Thomas Horst, Income Taxation and Competitiveness (Washington: National Planning Association, 1977); in Canada: Statistics Canada, Corporation Taxation Statistics 1977 (Ottawa, March 1980).

Tax rates for countries other than France and Italy represent the percentage ratio of tax paid to taxed/assessable income of “representative” taxpayers, defined as individuals whose taxable/assessable incomes constitute, say, about one third of the total taxed/assessed income in the highest-income brackets. For France and Italy, the rates are final withholding tax rates.

For countries other than Canada, Italy, and the Netherlands, effective tax rates are those calculated by Thomas Horst on the basis of differences in corporate income tax rates, depreciation allowances, and tax credits. For Canada, effective tax rates represent the percentage ratio of corporate income tax assessed to taxable corporate profits; for Italy, they represent the statutory rate.

Statutory rates.

Average ratio of interest income tax to interest income.

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See Chapter 2 (paper by Ben-Zion) for a survey of the literature on the Fisher effect.

Ideally, rates for short-term and long-term government bonds of fixed maturities would be used, but these could not be obtained for all countries in the sample.

See Chapter 4 (paper by Matin and Tanzi).

See Modi(1983) for a survey of the tax treatment of investment income and expense in industrial countries.

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