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Watson, Mark W.. "Explaining the Increased Variability in Long-Term Interest Rates." Economic Quarterly. Federal Reserve Bank of Richmond. 1999. HighBeam Research. 23 Apr. 2018 <https://www.highbeam.com>.
Watson, Mark W.. "Explaining the Increased Variability in Long-Term Interest Rates." Economic Quarterly. 1999. HighBeam Research. (April 23, 2018). https://www.highbeam.com/doc/1G1-63973154.html
Watson, Mark W.. "Explaining the Increased Variability in Long-Term Interest Rates." Economic Quarterly. Federal Reserve Bank of Richmond. 1999. Retrieved April 23, 2018 from HighBeam Research: https://www.highbeam.com/doc/1G1-63973154.html
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Monetary policy affects the macroeconomy only indirectly. In the standard mechanism, changes in the federal funds rate, the Federal Reserve's main policy instrument, lead to changes in longer-term interest rates, which in turn lead to changes in aggregate demand. But the links between the funds rate, long rates, and demand may be far from tight, and this potential slippage is a fundamental problem for monetary policymakers. In particular, long-term interest rates sometimes move for reasons unrelated to short-term rates, confounding the Federal Reserve's ability to control these long-term rates and effect desired changes in aggregate demand. Has the link between long rates and short rates weakened over time, therefore making it more difficult for the Federal Reserve to achieve its macroeconomic policy objectives through changes in the federal funds rate?
Such questions naturally arise when one observes the behavior of long-term interest rates. For example, Figure 1 plots year-to-year changes in ten-year Treasury bond yields from 1965 through 1998. (The volatile period of the late 1970s and early 1980s has been masked to highlight differences between the early and later periods.) The most striking feature of the plot is the increase in the variability of long-term rates in the recent period relative to the earlier period. Indeed, the standard deviation of long rates essentially doubled across the two time periods. What caused this increase in variability? Did a change in the behavior of short-term interest rates (caused, for example, by a change in Federal Reserve policy) lead to this dramatic increase in long-rate variability? Or, rather, is this change in variability caused by changes in factors unrelated to short-term rates, often described under the rubric of "term" or "risk" premia?
In what follows, we study the behavior of short-term interest rates over the two sample periods, 1965-1978 and 1985-1998, highlighted in Figure 1. It focuses on two key questions. First, has the short-term interest rate process changed? Second, can these changes in the behavior of short-term interest rates explain the increased volatility in long-term interest rates? The answer to both of these questions is yes; our findings suggest no weakening of the link between short rates and long rates and thus no weakening of the link between the Federal Reserve's policy instrument and its ultimate objectives.
The variability in long-term interest rates is tied to two distinct features of the short-rate process: (1) the variability of "shocks" or "innovations" to short-term interest rates, and (2) the persistence (or half-life) of these shocks. In the standard model of the term structure, changes in the variability of short-rate innovations lead to proportional changes in the variability of the long rate. Thus, holding everything else constant, doubling the standard deviation of the innovation in short-term interest rates would lead to doubling the standard deviation of long rates evident in Figure 1.
The relationship between short-rate persistence and long-rate variability is more complicated. To explain this relationship it is useful to consider an example in which the short-term interest rate process can be described by an autoregressive model with one lag (an AR(1)). Let [rho] denote the autoregressive coefficient associated with the process. When [rho] = 0, short rates are serially uncorrelated, and shocks have only a one-period effect on the short-term interest rate. In contrast, when [rho] = 1, short rates follow a random walk so that shocks to the current value of short rates lead to a one-for-one change in all future short rates. When long-term interest rates are viewed as discounted sums of expected future short-term rates, these different values of [rho] imply very different behavior for long-term rates. For example, when [rho] = 0, a change in the current short rate has no implications for future values of short rates, so long rates move very little. In contrast, when [rho] = 1, any change in the current short rate is expected to be permanent and all future short rates are expected to change. This change in expected future short rates leads to a large change in the long-term rate. Values of [rho] between 0 and 1 are intermediate between these two extremes, but in a subtle way that will turn out to be important for explaining the increased variability in long-term interest rates evident in Figure 1. In particular, for long-lived bonds, a short-rate process with [rho] = 0.9 generates long rates that behave much more like those associated with [rho] = 0 than with [rho] = 1. Put another way, changes in the autoregressive parameter [rho] have large effects on the behavior of long-term rates only when [rho] is very close to 1. Such a result is familiar from studies of consumption behavior using the present-value model, where the variability of changes in consumption increase dramatically as income approaches a "unit-root" process (Deaton 1987, Christiano and Eichenbaum 1990, Goodfriend 1992, and Quah 19 92).
As a preview of the empirical results in later sections, we find that the variability of short-term interest rate shocks was smaller in the later sample period than in the earlier period. If there were no other changes in the short-rate process, this decline in short-rate variability should have led to a fall in the standard deviation of long-term interest rates of approximately 50 percent, as opposed to the 100 percent increase shown in Figure 1. However, we also find evidence of an increase in persistence: for example, the estimate of the largest autoregressive root in the short-rate process (the analogue of [rho] from the AR(1) model) increased from 0.96 in the early period to nearly 1.0 in the later period. By itself, the increase in persistence should have led to a three-fold increase in the standard deviation of long rates. Taken together, the decrease in short-rate variability and increase in persistence explain remarkably well the increase in the variability of long rates evident in the data.
The estimated change in the persistence of the federal funds process has important implications for the Federal Reserve's leverage on long-term rates. For example, the estimated autoregressive process for the early sample period implies that a 25 basis point increase in the federal funds rate will lead to only a 3 basis point increase in ten-year rates. The autoregressive process for the later period implies that the same increase in the federal funds rate will lead to a 15 basis point increase in ten-year rates. Alternatively, the increase in persistence makes it possible to achieve a given change in the long rate with a much smaller change in the federal funds rate. The "cost" of increased leverage is the implicit commitment not to reverse changes in the federal funds rate, that is, to maintain the persistence in the short-rate process. The benefit of increased leverage is the reduced variability in the short-term rate. These costs and benefits are discussed in detail by Woodford (1999), who argues that it may be beneficial for the monetary authority to commit to making only persistent changes in its policy instrument.
The article is organized as follows. Section 1 documents changes in the variability of both long-term and short-term interest rates from the 1960s to the present. Here we document the decrease in variability of short-term interest rates (the federal funds rate and three-month Treasury bill rates) but an increased variability in longer-term rates (one-, five-, and ten-year Treasury bond rates). The relative increase in variability is shown to depend on the horizon of the interest rate--it is much higher for ten-year bonds than for one-year bonds, for example.
Section 2 studies changes in the persistence of short-term interest rates over the two sample periods. It begins by using a hypothetical AR(1) model for short-term interest rates to quantify the potential effects of short-rate persistence on the variability of long-term interest rates. …
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