Inside the Mind of a New Keynesian

A New Keynesian’s Brain                Image Credit: FreeImages.com

[NOTE: Edited on 11/13/2015 to ensure proper interpretation of the Taylor Rule.]

There can be no doubt New Keynesian economists are very smart people. Keynesian economists of one stripe or other (the originals from the 1930s through the 1940s, neo-Keynesians  or “old” Keynesians from about 1950 to around 1980, and now the New Keynesians from around 1980 to the present) have dominated most academic economics departments from the Great Depression to the present. During all that time they have also more often than not dominated federal government economic policy. As one would expect, being responsible for describing such an incredibly complicated human invention as the world’s economies, the Keynesians have had to molt their skins and adapt their mental models of the economy as unkind economic events and observations stressed their theories. In this post our task will be to describe the ideas of the latest reincarnation of the Keynesians, the New Keynesians. If you have read the posts Blowing Up the New Keynesian Model and Bending History, you know that many think it is time to throw New Keynesianism onto the “ash heap of history”. What I would like to do is discover what about their economic models causes them to err so often. If you doubt they have such a pronounced tendency for error, read:

• Echoes of the Great Depression: America, Europe, and Japan
• Echoes of the Great Depression: Europe
• Echoes of the Great Depression: Japan
• Current Economic Effects of the Federal Reserve
• Quantitative Easing and its Effects
• Why Have ZIRP and QE Failed?
• Economic Damage Created by the Fed

As you read these posts, be aware that any errors in monetary policy were errors created by following New Keynesian monetary ideas.

In Blowing Up the New Keynesian Model we noted the New Keynesian economic model is logically divided into three pieces where each piece describes the economy in successive time periods after the beginning of a recession or depression.

1. On the short run immediately after the start of a recession/depression the original Keynesian economic model is believed to be an accurate rendition of the economy. One major assumption of the original Keynesian model is that prices are constant; there is no inflation or deflation present. This places a time limit on the accuracy of a pure Keynesian model as the period during which wages and prices are substantially constant; i.e. about a year or less.
2. In the intermediate term, between the end of a pure Keynesian model’s efficacy and a longer term when sticky wages and prices adjust to supply and demand curves and neoclassical microeconomics holds sway, is where the bulk of the New Keynesian ideas, the new neoclassical synthesis, reigns. A new tool in the form of monetary policy is given to optimize economic output, i.e. GDP. In this regime the central bank can lower interest rates to encourage growth if the GDP is below its potential; and it can similarly increase interest rates to reign in inflation if the  GDP is above its potential. Once sticky wages and prices begin to adjust to supply and demand pressures, this intermediate term is finished.
3. In the long term New Keynesians believe the neoclassical model of the economy is its best description.

In our inquiry I will restrict myself to the description of the intermediate term piece of the model, since this is the only piece that is different from the original Keynesianism and neoclassical economics.

The really big addition of this intermediate term model is the addition of inflation/deflation, and therefore of monetary policy into the model. Although a number of equations must be used to define terms and express New Keynesian assumptions, we will very quickly move to a graphical description, just as we did in describing the Solow-Swan growth model beginning with the post The Solow-Swan Model and Where We Are Economically (1).

The way any central bank works is by attempting to control interest rates by controlling the amount of money in the economy, using standard central bank operations for a short-term interest rate and using quantitative easing for a long-term interest rate. See The Federal Reserve: What It Is. To do this the central bank must decide what value of the interest rate, the interest rate target i_t, they will try to impose. The subscript t is an integer labeling a time-period, generally a year or less, for which the interest rate will apply. To decide what this interest rate should be, a central bank could use their own discretion in applying whatever “wisdom” they might have, or they can apply some general monetary rule. The U.S. Federal Reserve says that it is using its “discretion”, but I suspect more often than not they use a Taylor rule. The Taylor rule has the form

i_t = π_t + r_t* + α_π(π_t – π^T) + α_y(y_t – y*)/y*

where π_t is the inflation rate during the period, r_t* is an equilibrium real interest rate which is some long-term average of the interest rate being adjusted minus inflation, α_π and α_y are constant parameters that are often set to 0.5, π^T is the target inflation rate, y_t is the economic output of the nation during the period t (i.e. the GDP), and y* is a Keynesian construction called the potential GDP. We will eventually have a lot more to say about potential GDP. For now you can consider it to be what the GDP would be if it always grew at the same long-term growth rate The quantity (y_t – y*)/y* is called the “output gap”, and it is clearly the fractional difference of the GDP during the period from potential GDP. The Taylor rule is usually simplified by defining the real interest rate during the period as the interest rate minus the inflation rate.

r_t ≡ i_t – π_t

Then the Taylor rule becomes

r_t = r_t* + α_π(π_t – π^T) + α_y(y_t – y*)/y*

Note that because of the output gap term, the interest rates in the other terms must be fractional differences between years. To convert them into percent differences, all terms must be multiplied by 100%.

Let me now introduce some nomenclature. If the output gap is negative and the GDP is less than the potential GDP, then the output gap is said to be contractionary; if the output gap is positive with the GDP greater than potential GDP, the output gap is said to be expansionary.

Now, it may not be that the central bank is using a Taylor rule to determine target interest rates, but some other monetary rule, or even some kind of ad hoc discretionary rule. Whatever the rule, the Keynesians call the function of inflation rate and output gap that determines the real interest rate target the Policy Reaction Function, or PRF. Whatever the PRF is, it is generally a monotonically increasing function of inflation rate and output gap. In our case with the Taylor rule, the dependence on the inflation rate is linear in inflation and for fixed output gap the interest rate can be plotted versus the inflation rate as shown below.

If the inflation rate increases with a constant output gap, then the central bank will continually increase the interest rate using the policy reaction function to attempt to stop the inflation. For any particular inflation rate, the desired real interest rate can be read right off of the graph.

We will now introduce two major assumptions that nevertheless track well with reality. We assume the inflation in the present period of time depends on the inflation in the previous period and the output gap in the current period as shown below.

π_t = π_t-1 + γ(y_t – y*)/y* , γ > 0 .

Note that if the output gap is zero, the inflation will remain the same as in the last time period, a phenomena known as inflation inertia, which is caused by inflationary expectations being built into the populace. Also it is assumed that an expansionary output gap will increase the inflation rate linearly.

We now have the major building blocks to construct what is known as the aggregate demand (AD) – aggregate supply (AS) model, also know as the aggregate demand – inflation adjustment model. This is a macroeconomic analogue of the microeconomic law of supply and demand. We will finish its construction in the next post.

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