Taylor Rule

Taylor Rule Formula

The Taylor rule formula is as follows:

\(i=p + 0.02 + 0.5y + 0.5(p - 0.02)\)

Where:

\(i\) - the nominal Fed funds rate

\(p\) - the rate of inflation over the previous four quarters

\(y = \frac {Y-Y_p} {Y_p} \) - percentage difference between real output and full employment output.

When adjusting for the formula and moving \(p\), which is the inflation rate, on the left-hand side of the equation, we get the real federal funds rate, \(i-p\).

The formula then becomes:

\(i-p=0.02 + 0.5y + 0.5(p - 0.02)\)

That means that the real federal funds rate should respond to the difference between output and full-potential output and between inflation and target inflation. The target inflation in the Taylor rule formula is taken as 2%.

The idea behind the Taylor rule formula suggests that the federal reserve and central banks of other countries target the real interest rate rather than the real money supply in the economy. The real interest rate serves as an intermediate target through which the real money supply in the economy is influenced.

Note that when the economy is at its full potential output level and the inflation target equals 2 percent, the equation becomes as follows.

\(i-p = 0.02 \)

• Because under full employment, \(y=0 \). There is no difference between potential output and real output.
• Also the term \((p-0.02) = 0\). Because there is no difference between the inflation target and the real inflation in the economy.

Now that means that in such a scenario, the real federal funds rate is equal to the inflation target of 2%.

On the other hand, if the economy is showing signs of weakness, such as output being below its level at which full employment is possible and inflation is below its target, the Taylor rule indicates that the real Fed funds rate should be reduced below 2%, which will result in the loosening of the monetary policy. Both replies adhere to the customary procedure followed by the Fed.

Taylor Rule of Monetary Policy

Taylor's rule of monetary policy is a set of prespecified rules that the Fed should follow when it adjusts the monetary policy instruments. Taylor's rule does not prevent the Fed from responding to different shocks in the economy for as long as the response is in line with the rules.

The Taylor rule suggests that the Fed should take into account the inflation rate and the difference between potential output and real output (output gap) when setting the interest rate in the economy.

Taylor Rule of Monetary Policy: Taylor Rule Inflation Rate

Taylor's rule inflation rate suggests how the Fed should design a monetary policy to tackle inflation. According to Taylor's rule of monetary policy, the Fed should raise the federal funds rate when the inflation rate is higher than the inflation target the Fed has set. On the other hand, when the inflation rate is below the inflation target, the Fed should respond by lowering the federal funds rate.

Fig. 1 - Taylor rule inflation

Figure 1 shows how the Taylor rule works using the AD-AS model. When the inflation rate in the economy is high at P₁, and the Fed wants to reduce inflation to P₂, it should increase the federal funds rate according to the Taylor rule. The federal funds rate makes borrowing more expensive, reducing the total investment in the economy. This then shifts the aggregate demand curve from AD₁ to AD₂, resulting in a lower price level.

Taylor Rule of Monetary Policy: Taylor Rule Output gap

Taylor rule output gap suggests how the Fed can use monetary policy to tackle output gaps.

When the real GDP growth exceeds the economy's full potential, the Taylor rule calls for a higher interest rate. On the other hand, when real GDP is below levels of total employment output, the Fed should respond by lowering the interest rate according to the Taylor rule.

Fig. 2 - Taylor rule recessionary gap

Figure 2 shows an economy experiencing a recessionary gap meaning that real GDP (Y₁) is below potential GDP. Taylor argues that the Fed should lower the federal funds rate to fix the recessionary gap. This makes borrowing cheaper, increasing the total investment in the economy. As a result, the aggregate demand curve shifts from AD₁ to AD₂, and the real output Y₁ increases to Y_p at the equilibrium point E2.

Taylor Rule Examples

One of the primary examples of the Taylor rule and its application in the economy is the example of the United States. In the United States, the federal funds rate and the Taylor rule federal funds rate have followed a similar pattern for most periods, except for times of economic and financial crisis such as the one in 2008.

Fig. 3 - Federal Funds Rate and the Taylor Rule rate. Source: FRED Economic Data¹

Figure 3 shows a comparison between the predicted federal funds rate using the Taylor rule and the actual federal funds rate for the period starting in 1990 and continuing through the end of 2022 in the U.S. The pink line represents the Federal Funds Rate that would be according to the Taylor rule, whereas the green line presents the actual Federal Funds Rate.

As can be seen in Figure 3, the decisions that the Fed made from 1990 all the way up to 2010 were comparable to those predicted by the Taylor rule. The Taylor rule was closely predicting a decrease or an increase in the federal fund rate, which was the case regardless of the fact that the Taylor rule was not in effect.

The Federal funds rate and the rate set by the Taylor rule maintained a tight connection all the way up to the point where the Taylor Rule called for negative interest rates. However, the Fed did not engage in a negative discount rate as it is limited by the zero lower bound.