Taylor Rule

The interest rate in the economy changes. Currently, the economy's interest rate is rising, and borrowing money is becoming significantly expensive. The institution in charge of setting the interest rate is the Federal Reserve System. The Federal Reserve System sets the interest rate according to the economic conditions. Did you know that it is possible to predict when the Fed will raise the interest rate and when it will not? This would help you decide whether to take a loan now, wait for another year, or consume more and save when there is a higher interest rate. But to know that, you'll have to know the Taylor Rule and how it works. Why don't you read on and find out all there is about the Taylor rule and what it says about the interest rate?

Taylor Rule Economics

The Taylor rule in economics is a monetary policy rule that suggests that the federal funds rate should be set following inflation and economic growth levels. The federal funds rate is the interest rate at which financial institutions lend their excessive reserves to each other on an uncollateralized basis.

Taylor's rule in economics aims to elaborate on the relationship between the Federal Reserve's main policy instrument - the federal discount rate, inflation, and the gross domestic product. The Taylor Rule was developed by John B. Taylor in 1992.

The Federal Reserve uses the federal funds rate as one of the main instruments when conducting its policies. This policy instrument is essential in controlling inflation levels and ensuring healthy and steady economic growth.

The main idea behind the Taylor rule is to explain how the federal funds rate should be set to maintain economic growth and healthy inflation levels.

Taylor's rule is based on the assumption that the Federal Reserve will be willing to accept a moderate rise in the inflation rate if it helps stimulate greater production in the economy. This is the foundation upon which Taylor's rule is constructed.

• According to the Taylor rule, the Federal Reserve has a 2 percent inflation target and follows three rules when setting its federal funds rate.
  1. When the inflation target is 2 percent, and the real GDP is equal to potential GDP, then the federal funds rate should be 2 percent.
  2. If the real GDP increases above the potential GDP, meaning that there is a positive output gap, the Fed should raise the real federal funds rate by 1/2 percentage point for every 1 percent increase.
  3. If the inflation increases above its percentage target of 2 percent, then for each 1 percent increase, the Fed should raise the federal funds rate by 1/2 percentage point.

You should be aware that in the real world, the Fed doesn't strictly adhere to these rules, and it sets the federal funds rate considering other factors as well. However, in many instances, the federal funds rate suggested by the Taylor rule was close to the actual one set by the Fed.

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.