# Interest, Natural Rate of

# Interest, Natural Rate of

Economists frequently refer to the interest rate the economy will tend toward under an equilibrium with price stability as the “natural” rate of interest. This equilibrium occurs in the long run, after any existing business cycles have played out. The natural rate of interest surfaced more than a century ago in the work of Swedish economist Knut Wicksell (1851–1926), though its prominence in mainstream economic thought has waxed and waned at different periods in time. Since the 1970s, the natural rate has taken a more central role in the study of monetary economics and is seen as one of the key ingredients in determining monetary policy.

One way to think about the natural rate of interest comes from the Keynesian IS-LM model of the macro-economy. In this model, the interest rate adjusts to equate savings and borrowing decisions across the entire economy. Savings is determined by the level of output and there exists a rate of interest that clears the savings market for every level of output. The natural rate of interest is the interest rate where output is equal to potential output, with potential output defined as the level that results under full employment.

Figure 1 shows that the natural rate of interest is determined by the intersection of potential output and the IS curve. At the intersection, real GDP (gross domestic product) equals potential GDP, and the real interest rate equals the natural rate of interest. The IS curve represents all interest rate and output combinations that clear the savings market. This curve shows that output decreases as the real interest rate rises. This is due to the negative relationship between investment, a major component in aggregate demand, and the real rate of interest.

Yet another, more modern way of describing the natural rate of interest comes from the neoclassical growth model originally outlined in the works of Frank Ramsey (1903–1930), David Cass, and Tjalling Koopmans (1910–1985). In this model, households choose investment and consumption through time in order to maximize lifetime utility. The natural rate of interest in this model can be thought of as the rate that clears the capital market when the economy is growing at its natural steady rate. This rate turns out to depend inversely on the amount by which households value future consumption. If households value future consumption relatively less, then the natural rate of interest will be higher in order to compensate households that save and therefore give up current consumption in favor of future consumption.

In the United States and many other countries, the short-term interest rate is the primary monetary policy instrument. In particular, U.S. central bankers use the federal funds rate, the rate at which banks borrow from

each other, as a tool to move interest rates and therefore the economy. As the main goals of monetary policy include price stability and output stabilization, the natural rate of interest provides an obvious benchmark for interest rate targeting. By setting the federal funds rate equal to the natural rate plus an inflation target (which could be zero), a bank is essentially trying to achieve the outcome resulting under an ideal economy. Interest rates above the natural rate tend to lower inflation, while rates below are expected to increase inflation.

Interestingly, John Maynard Keynes (1883–1946) ultimately objected to the idea of a natural rate of interest. He believed that this rate depended on the level of employment in the economy. Thus, there were several possible natural rates of interest, each associated with a different level of unemployment. Keynes preferred this idea of a “neutral rate of interest,” which describes the unique interest rate that equates savings and investment at full employment.

## MEASURING THE NATURAL RATE

One of the major drawbacks in using the natural rate of interest is the inability to accurately observe or calculate it. Since the natural rate of interest can change due to persistent changes in aggregate supply or demand or even changes in the projections of federal government budget deficits, it is often hard to pin down. In addition, changes in potential GDP can affect the natural rate of interest. Thus, measuring the natural rate of interest is not straightforward, and estimation techniques must be used. If the natural rate were actually constant over time, it could be estimated by averaging past real interest rates. Various methods have been implemented to account for the changing nature of the natural rate of interest.

Some methods involve weighting the data on past real interest rates differently. For example, one simple way would be to compute averages of past values of the interest rate while putting more weight on more recent data. Despite the differential weighting, this simple method does not work well during periods of large increases or decreases in inflation—when the real interest deviates substantially from the natural rate.

More sophisticated economic models have been used to measure the natural rate of interest. These include estimating the location of the slope of the IS curve and potential output to obtain estimates of interest rates. An important statistical technique known as the Kalman filter is used in some economic models to estimate the natural rate of interest. It works by adjusting the estimate of the natural rate based on how far off the model’s prediction of output is from actual output. If actual output is higher than the prediction from the model, one possible explanation is that monetary policy was more expansionary than expected, which implies that the difference between the real federal funds rate and the natural rate of interest is more negative than expected. The estimate of the natural rate then increases by an amount proportional to the prediction error. This method allows for changes in the natural rate. The estimate of the natural rate by Thomas Laubach and John C. Williams (2003) using the Kalman filter technique was 3 percent in 2002, which is not far from the average of the historical federal funds rates. However, the estimate has varied from 1 percent in the 1990s to over 5 percent in the 1960s.

Despite its intuitive appeal, monetary policy analysis involving the natural rate of interest has serious drawbacks. There is no single agreed-upon method of estimating the natural rate, and estimates can be sensitive to the statistical method used to measure it. Nonetheless, the natural rate of interest is still an important concept for evaluating monetary policy, and central banks continue to devote attention to developing and improving estimation strategies.

**SEE ALSO** *Interest Rates; IS-LM Model; Neoclassical Growth Model; Policy, Monetary*

## BIBLIOGRAPHY

Cass, David. 1965. Optimum Growth in an Aggregative Model of Capital Accumulation. *Review of Economic Studies* 32: 233–240.

Keynes, John Maynard. 1936. *The General Theory of Employment, Interest and Money.* London: Macmillan.

Koopmans, Tjalling C. 1965. On the Concept of Optimal Economic Growth. In *The Econometric Approach to Development Planning*, 225–300. Amsterdam: Elsevier.

Laubach, Thomas, and John C. Williams. 2003. Measuring the Natural Rate of Interest. *The Review of Economics and Statistics* 85 (4): 1063–1070.

Ramsey, Frank. 1928. A Mathematical Theory of Saving. *Economic Journal* 38: 543–559.

Wicksell, Knut. [1898] 1936. *Interest and Prices (Geldzins and Güterpreise): A Study of the Causes Regulating the Value of Money.* Trans. R. F. Kahn. London: Macmillan.

Williams, John C. 2003. The Natural Rate of Interest. *Federal Reserve Bank of San Francisco Economic Letter*, 2003–2032.

*Betty T. Tao*

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