# A simple model of monetary policy and interest rates

This **comment** caught my eye:

I think it’s easier for most people (especially laymen) to understand how central banks affect interest rates than it is to understand the mechanics of the money supply and other aspects of monetary policy.

You could probably count on one hand the number of laymen who understand how monetary policy affects interest rates. Suppose you asked an average person how the Fed affects interest rates. What might they say?

Most people would have no idea how to answer this question. Better educated people would attempt an answer, but they would almost certainly be wrong. Consider some plausible explanations:

1. Changing the discount rate? Nope.

2. Changing the interest rate on reserves? OK, but *how* does that affect market rates? They might cite some sort of arbitrage condition. But from 1913 to 2008 the IOR in America was set at zero, and yet market rates were often well above zero. So that can’t be the entire explanation.

3. Pumping money into the economy? OK, but why would that affect interest rates? They might point to supply and demand. More supply of money means a lower price of money, with the implicit assumption being that interest rates are the price of money. But interest rates are *not* the price of money; they are the price of credit, and (throughout most of US history) interest rates tend to be higher when money growth rates are higher. Thus money growth sped up in the 1960s and 1970s and interest rates rose sharply. Indeed interest rates rose sharply *because* money growth sped up (leading to higher inflation.)

Here’s a simple model of money and interest rates:

i = IRG + NRI

That is, market interest rates = interest rate gap + natural rate of interest

The natural rate of interest can be defined in multiple ways, but is usually assumed to represent the risk free short-term interest rate that is consistent with some sort of macroeconomic equilibrium. For simplicity, let’s assume macroeconomic equilibrium occurs when NGDP is consistent with the public’s previous expectations. Even that’s a bit vague, as it raises the question, “Expectations formed at what time?” But it’s a reasonable approximation of what we mean by the concept.

In this model, monetary policy affects interest rates in two ways. Policy affects the natural rate of interest (NRI) and it affects the interest rate gap (IRG). Thus in the long run, a monetary policy that raises the trend rate of NGDP growth from 4%/year to 14%/year will tend to boost the NRI by 10 percentage points. You can call this aspect of policy the “NeoFisherian effect” although it includes both the (real) income and inflation effects.

The other part of policy is the liquidity effect. Because NGDP is slow to respond to changes in the supply and demand for money, policy shocks move the market interest rate away from the natural rate in the short run, producing an interest rate gap.

I cannot emphasize enough that *every single* monetary policy action influences both the IRG and the NRI; it’s just a question of how much. Furthermore, most actions (not all) push these two rates in the opposite direction. And the liquidity effect has more of an impact on short-term rates, whereas the NeoFisherian effect usually has more impact on medium and longer-term rates.

Imagine asking a layman to explain all this.

Open market purchases raise the supply of base money, creating disequilibrium (excess money supply) at the previous level of interest rates and NGDP. Because NGDP is slow to adjust, short-term interest rates immediately decline to induce the public and banks to hold larger cash balances.

A reduction in IOR reduces the demand for base money, creating disequilibrium (excess money supply) at the previous level of interest rates and NGDP. Because NGDP is slow to adjust, short-term interest rates immediately decline to induce banks to hold existing cash (i.e. reserve) balances.

It is less clear how these actions affect future expected short-term rates; the answer depends on how they influence the future expected path of NGDP, which in turn depends on the impact on the future expected path of policy.

Imagine asking a layman to explain all this!

In general, interest rate gaps move the natural interest rate in the opposite direction. Creating a positive IRG nudges the NRI downward. And in the medium to longer-term, the natural interest rate has more impact on market interest rates than does the interest rate gap. This is what Nick Rowe means when he uses the analogy that monetary policy is like riding a bike where you turn the wheel to the left when you want to go right, and vice versa. If you want lower rates in the long run, you nudge short-term rates higher, and vice versa. Usually.

Imagine asking a layman (or MMTer) to explain all this!!

In some cases (such as Switzerland in January 2015), a cut in the policy rate is associated with the natural interest rate falling, because it is associated with other *signals* that lead people to expect a more contractionary policy stance going forward. (Signals such as allowing a large upward appreciation in the franc’s exchange rate.)

Imagine asking a layman to explain all this!!!

Before trying to teach students how monetary policy affects interest rates, we should start with something easier, like quantum mechanics.