Rising inflation and the Taylor Rule

June 28, 2022

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I recently noticed that in the last few months, my favorite pack of oatmeal went up in price by 40%, from 50 cents to a whopping 70. Not only that, but the beers at the ‘Negende Cirkel’ have probably increased as well (I have to check it when I am sober, though). Actually, life just got more expensive in general, as in May and April price levels were 10.2% and 11.2% higher than last year, respectively. But what drove the recent spikes in inflation and what is the role of central banks when it spirals out of control?

Contemporary rising inflation

On September 15, 2008, the collapse of Lehman Brothers, the fourth-largest investment bank in the USA, signaled the start of a (especially for some people such as Michael Burry) long expected financial crises. In fact, it became the largest crisis we experienced since the Great Depression between 1929 and 1939. Sadly, the economy never fully recovered from the subsequent events in 2008 and we entered a decade of low inflation and low economic growth. And as the economy seemed (this is course a not an opinion shared by all economists) to be doing better, several factors drove up both prices of supermarket goods and electricity. The current invasion in Ukraine and the resulting lack of gas supply from Russia, combined with supply chain problems stemming from the COVID policy in China will most likely worsen the economic conditions.

A little bit of inflation itself is not too much of a problem, but it is a fine line between deflation and spiking inflation. With deflation, consumers postpone purchases as they expect tomorrow prices will be lower, whereas with high levels of inflation living becomes too expensive for many people, shifting the standard of living up and thereby driving more people into poverty.  

The central banks have numerous ways to combat inflation issues. One is raising interest rates, which recently have dropped to record-time lows, even falling below zero. In the last three months, the Federal Reserve (Fed) announced three serious increases by levels not seen since 1994. The main purpose is to drive inflation back from the current 8.6% to the ‘magical’ 2% level. But what are the mechanisms behind setting inflation levels?

The Taylor Rule

In 1993, Stanford economist John Taylor came up with his famous rule in order to analyze the behavior of central banks. The main idea is that the central banks should adjust nominal (not adjusted for inflation) interest rates in a consistent and predictable manner to economic conditions, instead of it being either without purpose or not responding to economic conditions at all. Taylor postulated a simple rule of the following form:

(1)   \begin{equation*} i_t = r^n+ \phi_{\pi}(\pi_t-\pi^*) + \phi_y (\ln (Y_t) - \ln (Y_t^n) ), \end{equation*}

where i_t denotes the nominal interest rate at time t, r^n denotes the real interest rate when output (Y_t) equals the natural level of output, \phi_{\pi} and \phi_y denote the weights attached to deviations from ‘natural’ inflation and output levels, respectively, and Y_t^n is the ‘natural’ level of output at time t. That is a lot to process at once, so I will illustrate what this formula actually implies and possible shortcomings that come with Taylors proposed formula..

Let us consider the example provided by Taylor, who sets the following values for the parameters: \phi_{\pi}=1.5, \phi_y=0.5 and r^n=\pi^*=2%. This implies that the central bank should adjust the nominal interest i_t more more than in a one-to-one relation with an deviation of inflation from its natural level, \pi_t-\pi^*. Furthermore, nominal interest rates should rise (drop)  when output exceeds (falls below) its natural level. A simple rule, but (adjusted) versions of the Taylor rule are still quite common in monetary theory. In fact, the parameterization proposed by Taylor tracks the monetary policy of the Fed quite well, at least for the period from 1985 until the early 2000’s.

As with any economic theory, several caveats should be considered. For instance, the Taylor rule assumes there is no uncertainty regarding future inflation levels and output levels, and that there is ‘some’ natural level of output and inflation. Furthermore, the real interest rate is assumed to be constant over time instead of time-varying. On top of that, when neglecting measurement errors stemming from both the natural levels of output and inflation, the weights attached to deviations, \phi_y, should be adjusted accordingly with maybe a more aggressive stance towards deviations from natural output levels. When we do consider measurement errors,  \phi_y actually lines up quite well with Taylors ideas.

Perhaps the most interesting critique is that interest rates should be forward-looking, instead of only depending on past levels of inflation and output. For one, Clarida, Gali, and Gertler (2000) consider a rule of the following form:

(2)   \begin{equation*} i_t = r^n+ \phi_{\pi}(E_t[\pi_{t+k}]-\pi^*) + \phi_y E_t[\ln (Y_{t+k}) - \ln (Y_{t+k}^n)], k>0, \end{equation*}

where E_t denotes the expectation operator, i.e. the expected value of a random variable (in this case inflation or output) given the information available at time t, and k is the horizon at which the central bank is looking ahead. Typically, the horizon is either one quarter, which is most instructive, or a year, which is most likely the timeline at which we will see effects of raising interest rates materialize. Introducing the expectation operator gives rise to a small but important distinction, as in this case the central bank should adjust their interest rates to the expected inflation k periods ahead, instead of the observed inflation, which is deemed to be unaffected by raises interest rate. The paper by Clarida et al (2000) shows a nice empirical test of the Fed’s monetary policy from 1960 until 1996. However, that is homework left for the reader.

Back to the real world

Compared to the Eurozone, monetary policy for the Fed is relatively ‘easy’ as it does not have to deal with fragmented and underdeveloped regions. The Fed’s interest rates are expected to rise for the coming months. For the European Central Bank (ECB), things are more difficult as the Eurozone consists of several vulnerable states such as Spain, Greece and Italy. In the case of the latter, rising government debt has reached more than 150% of its Gross Domestic Product (GDP). Furthermore, Italy was struck hard by the pandemic and its dependence on outside sources of gas make it even more difficult to get out of the troublesome situation. Increases in interest rates for countries in debt will only worsen their situation. In an ideal world, the ECB would support suffering countries by buying government debt, but this would put downward pressure on interest rates. In these turbulent and future times, let us hope the Italians remain resilient and the elections next year will yield new and better times.

I hope you enjoyed this article and learned something about inflation and the role of central banks. Good luck with the final resits and have a nice holiday!

Sources:

Taylor, J.B., 1993, December. Discretion versus policy rules in practice. In Carnegie-Rochester conference series on public policy (Vol. 39, pp. 195-214). North-Holland.

Clarida, R., Gali, J. and Gertler, M., 2000. Monetary policy rules and macroeconomic stability: evidence and some theory. The Quarterly Journal of Economics, 115(1), pp.147-180.

Romer, D., 2012. Advanced Macroeconomics, 4e. New York: McGraw-Hill.

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