Hello and welcome to this lecture on the so-called Taylor rule. In this class, we will be discussing how monetary policy takes the trade-off between inflation and unemployment into account. In this context, we will examine a simple rule for interest rate setting, the Taylor rule. Let's start with the definition of the nominal interest rate. The nominal interest rate i has two components: the real interest rate, also referred to as r star and inflation Pi. Central bankers target nominal interest rates when setting the federal funds rate. They set the interest rate to fulfill their mandate. In the Federal Reserve's case, stable prices and maximum employment. But central bankers face a trade-off between unemployment and inflation. This trade-off has been formalized in the Phillips curve that we discussed in detail in a different lecture. Since Bohr's stable prices and maximum employment are mandates of the Federal Reserve, you may wonder how this trade-off is approached. For instance, should you put more weight on inflation or more weight on unemployment? To understand the decision-making process, let us start by defining some useful terms and concepts. First, there's a negative relationship between unemployment and GDP. This relationship is called Okun's law. When the economy is producing fully utilizing its resources, then economists say that the economy is producing its potential GDP. Potential GDP grows over time due to technology, education, and demographic trends. When an economy is at its potential GDP, then this typically implies full employment. Central bankers therefore want to know whether the economy is producing close to potential GDP and therefore close to full employment or not. A commonly used measure is the GDP gap, which is the percentage point difference between real GDP and an estimate of potential GDP. In the chart, you can see the Congressional Budget Office estimate for US potential real GDP up to 2030 and actual real GDP. While the two are tracking each other closely, there are notable deviations. For instance, after the 2008 financial crisis, when real GDP was much lower than potential real GDP. If you squint a little, you can also see times when real GDP is a bit higher than potential real GDP. In this graph showing the percentage point output gap, you can see that there was a positive gap in 1973. These are times when resources are used more than they will be in the long run. Examples are overtime, extra shifts, and so on. Positive gaps are uncommon and small. They indicate times of booms when the economy runs hard. Going back to unemployment. In this graph, you can see that when the gap is positive, unemployment is already low and often continues to fall. Look for instance at 1973 or 2000 or 2006 and 2007. The key insight here is that using the GDP gap as an input for monetary policy makes a lot of sense when maximum employment is one of your goals. The second part of the Federal Reserve's mandate is stable prices. What do stable prices mean? It means there is some target inflation rate Pi star. Academics such as John Taylor, who's rule we are exploring here, have used two percent for Pi star. The Federal Reserve seems to agree. Since 2012, the FOMC has announced it charged an annual rate of two percent consumer price inflation to be most consistent over the long run with the Federal Reserve's statutory mandate. Similarly, the European Central Bank works to achieve inflation below, but close to two percent. The graph shows you the annual growth rate of personal consumption expenditure inflation. As you can see, inflation was way above target in the 1970s and 1980s. However, since the mid-1990s, inflation has rarely been significantly larger than two percent. In fact, during the late 1990s and in the aftermath of the 2008 financial crisis, inflation was considerably lower than two percent. Just as with the output gap, there is an inflation gap measuring how much inflation differs from the central bank's target inflation rate. Now recall that the nominal interest rate is equal to the real interest rate r star and inflation Pi. Ideally, we would be at target inflation. The nominal interest rate at target inflation would be r star plus Pi star. But now we have to take deviations in inflation and output into account and weigh them to get a target nominal interest rate, i head for the Central Bank. Let's call the inflation rate Alpha and the output rate Beta. This equation is called the simple Taylor rule. It was proposed by John Taylor in an academic article in 1993. This rule is very parsimonious, but still captures all elements for the decision-making process of the Federal Reserve. Of course, we now have to find values for the inflation rate Alpha, and the output gap rate Beta. Economic researchers have conducted numerous studies, what these rates should be. Taylor's original recommendation was to set both 2.5. But now the consensus for the inflation rate Alpha is 1.5 while the output gap rate Beta estimates vary between 0.5 and 1. Let's have a look how this rule performs when we set Alpha to 1.5 and Beta to 1. The graph shows you the actual federal fund's rate and the target nominal interest rate implied by the simple Taylor rule. As you can see, the simple Taylor rule tracks the federal fund's rate remarkably well, even after 1993 when the original study was published. Of course, the Taylor rule is not perfect. For instance, it assumes that there is no constraint on the interest rate. Meaning that in the Taylor rule, the interest rate can go negative, for instance, in early 2009. Since the original study, several extensions were proposed, but the simple rules still captures the essence of the Federal Reserve's interest rate setting considerations well. In fact, the Federal Reserve has considered the simple Taylor rule as one monetary policy alternative in its internal forecast, the TealBook. This table from the December 2010 TealBook, shows you that the simple Taylor rule and the adjusted Taylor rule, were considered for setting future interest rates. The constraint policy refers to interest rates not going below zero, where the unconstrained policy shows that the simple Taylor rule calls for negative interest rates after the financial crisis. What have we learned in this lesson? First, central bankers consider deviations from potential output and target inflation when setting interest rates. Second, interest rates decisions can be described in a simple formula that weigh deviations from potential output and target inflation. Third, the most common formula summarizing interest rates decisions is the Taylor rule.
