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The author is very grateful to Reza Vaez-Zadeh for helpful comments and suggestions. Thanks to Costas Azariadis, Michael R. Darby, Dmitriy Gershenson, Lung-fei Lee, Axel Leijonhufvud, Seonghwan Oh, Simon Potter, Keunkwan Ryu, and seminar participants at the University of California, Los Angeles, and the Hong Kong University of Science and Technology for helpful comments and suggestions on earlier drafts. Also thanks to Jae Young Kim for the use of a program for the Phillips fractional integration estimation and Benjamin C. Fung for research assistance.
CS argue that one should take into account the substitutability between money and bonds in determining the effect of inflation on interest rates, especially because the data mainly pertain to the return on financial assets rather than to the return on capital.
Klein argues that, under specie standards that provided an anchor for the price level, there was considerable short-term unpredictability but much less long-term unpredictability of inflation. Under the fiduciary monetary system of the post-World War II period, there is no anchor for the price level. Agents have come to regard prices as largely affected by policy, and short-term unpredictability is less than before. For example, Hutchison and Keeley (1989) show that inflation evolved from a white noise process in the pre–World War I period to a highly persistent, nonstationary process in the post-1960 period, which strengthened the Fisher effect.
As Friedman and Schwartz (1982) note, improvements in short-term forecasting methods and in the sophistication and breadth of financial and capital markets shortened the forecast horizon of agents and increased their concern about whether or not high rates of inflation persist.
Gallagher (1986) points out that this testing pertains to the maintained hypothesis that πt+1 and ξt are only contemporaneously uncorrelated. Following earlier studies including CS, this paper takes the IFH as claiming that inflation and nominal interest rates are contemporaneously uncorrelated in the sense of Gallagher.
Under the standard Fisher hypothesis (α2’ = 0), the bias in the ordinary least-squares (OLS) estimator of α2’ equals
As inflation moves more persistently, it can be better forecast using the past history of inflation. Autocorrelations up to several orders of the residual, which contain information about persistence, will be reflected in this index. In general, agents would utilize the information set including indicators for inflation as well as inflation persistence.
Davies (1987) and Granger and Teräsvirta (1993) suggest using the supremum of statistics over a grid set, whereas Andrews and Ploberger (1994) suggest using the average and the exponential average of statistics.
Using the mnemonics on the FRED of the Federal Reserve Bank of St. Louis, the variable definitions are TB3MS (the three-month Treasury bill rate), CPIAUSL (the CPI-U: whole items), and PCE/PCEC92 (the personal consumption expenditure deflator). The average for each quarter is used to measure the quarterly series. All except interest rates are seasonally adjusted data.
The use of a monthly model may cause serial correlation in errors because the maturity of yield on a bill is longer than the data frequency. Suppose that the error term of equation (3′) (in a difference form) for the one-month rate is serially uncorrelated. Based on this equation, the monthly model of the three-month rate can be expressed, for example via the expectations hypothesis. Time aggregation results in serial correlation in errors.
Evans and Lewis argue that it is extremely difficult to know the appropriate tax rate on interest income for the overall economy, since the effective tax rate on interest varies tremendously across individuals, firms, and institutions. Friedman and Schwartz (1982, p. 572) suggest that, to judge from the differential return on taxable and tax-exempt securities, the relevant tax rate exceeds one-third and is quite stable over time.
The marginal tax rate was calculated as the weighted average of marginal tax rates from the social security tax, the individual income tax, and other federal taxes.
Different lag lengths are suggested by different information criteria (over rolling samples). However, choosing an alternative lag length (13 lags, for example) does not affect the estimation results of this paper qualitatively.
Both CS and Gupta obtained virtually identical results regardless of whether the levels or the first differences of the variables were chosen, with correction for first-order serial correlation for the former specification. The present investigation also found that the estimation of equation (2) using levels with correction for first-order serial correlation using the Beach-McKinnon or the Cochrane-Orcutt method provided almost the same results.
Barth and Bradley (1988) and Gupta (1991) find that estimation results for equation (3′) are not sensitive to whether or not the real rate is adjusted for taxes. Indeed, as Barth and Bradley point out, “since taxes are levied on the nominal interest rate, whether the real rate is adjusted for taxes or not, the real interest rate should vary inversely and one-for-one with the inflation rate (under the hypothesis),” unless the tax rate is correlated with inflation.
The time-varying variance fully consistent with the regime-wide heteroscedasticity, (1 − Dt)2σ12 + Dt2σ22, is not directly applicable. The identification of the time-varying variance weighted by Dt requires the ML estimation of the model for each value of τ from the grid set.
The plots of the likelihood ratio as a function of τf indicate a unique major dip in the likelihood ratio around the estimate, suggesting that two regimes are sufficient to describe the nature of the threshold effect.
This paper deals with these issues by using a monthly (or quarterly) average rate of interest rather than the rate at a specific date for quarter t, taking the rate of inflation as the average figure of the period.
The use of the rolling estimate of d presumes that the current state of inflation persistence is determined by the average sample characteristic over the most recent five years.
Fischer (1981) argues that high inflation raises the variability but not necessarily the uncertainty of inflation. According to Ball and Cecchetti (1990), inflation uncertainty pertains to the variance of unanticipated inflation, whereas inflation variability pertains to the variance of inflation. Since high inflation tends to be largely anticipated, unanticipated inflation will not be large relative to inflation, supporting Fischer’s argument. Also, Ball and Cecchetti show that inflation has much larger positive effects on inflation uncertainty at long horizons.
One may alternatively consider the possibility that there are more than two regimes. For instance, observations with moderate forecastability may be grouped between the two extreme regimes. The smooth transition treats these observations as a mix of the two regimes, weighted by the distance from each. Thereby the degree to which inflation is reflected in interest rates is a monotonic function of inflation persistence.
Consider Germany, which had significant regulation on money until very recently. In the 1957–97 period, Germany experienced low inflation (–1.3 to 8.5 percent a year) compared with the United States (–1.5 to 15.8 percent a year), and inflation showed no remarkable persistence in most periods. Again, inflation persistence and inflation are positively correlated. In this case we find that linearity testing provides no evidence for nonlinearity in the CS equation.
This is similar to the Mundell-Tobin effect that represents a portfolio substitution effect of inflation on the steady-state capital-labor ratio. However, the Mundell-Tobin effect assumes that real balances and capital are substitutes (direct financing for capital investments) so that an increase in inflation increases the portfolio demand for capital and thus the capital-labor ratio, which in turn lowers the real rate of return on assets.
Inflation persistence is not directly related to survey measures of inflation uncertainty, which depend on the short-term uncertainty of inflation, since a longer-term trend in inflation will largely be anticipated.