Simple description of how interest impacts inflation

I always was taught that inflation is impacted by interest like so:

Lower interest rate => Loaning money is cheaper => More money in the system => Higher inflation

However recently I am also hearing opposite theories as to how lower interest rate can lead to lower inflation.

I found some discussions and explanations but all of them stretch several paragraphs. Is there a short and easy to follow logic like the one I just quoted that can explain this directional impact?

I won’t prevent people from adding context or evaluation as to when each direction is relevant, but please make sure this is clearly separated from the actual impact explanation.

• Can you please add sources for the statement that lower interest rate can lead to lower inflation? Where did you hear such theories. 1. Prima facie the statement seems absurd and contradicts general evidence. 2. I suppose there could be some special rare situation where there are some complex and weird expectational effects but then it would be important to see the details of the argument to evaluate it, taken at face value the statement is absurd
– 1muflon1
Jan 1 at 14:13
• It's Neo-Fisherism: Stephen D. Williamson has a simple article explaining the basics. It's mainly about causation. From the nominal interest rate to inflation (Neo-Fisherism) or the other way around ("conventional" view). Primary determinants of long-term equilibrium real rates are mostly non-monetary: potential growth rates; demographics; risk preferences in portfolios. Now look at the Fisher equation: r = i - pi. If real rates r are determined by fundamentals, increasing i can only be causing inflation to increase as well. Jan 1 at 20:39
• stlouisfed.org/publications/regional-economist/july-2016/… It is discussed quite frequently with aggregate supply as defined by J. Galí: Monetary policy, inflation, and the business cycle: An introduction to the new Keynesian framework, Princeton 2008, Princeton University Press. or P. De Grauwe: The scientific foundation of dynamic stochastic general equilibrium (DSGE) models. Jan 1 at 20:45
• You can read J. Cochrane: Monetary policy with interest on reserves, in: Journal of Economic Dynamics and Control, Vol. 49, 2014, pp. 74-108; J. Cochrane: Whither Inflation?, 31 August 2015, The Grumpy Economist; S. Schmidt-Grohé, M. Uribe: The making of a great contraction with a liquidity trap and a jobless recovery, NBER Working Paper No. 18544, 2012. to get a more thorough discussion of the Neo-Fisherian theory. Jan 1 at 20:49
• Stephanie Schmitt-Grohe has some papers like the ECB conference on monetary policy on her website (columbia.edu/~ss3501/research/schmittgrohe.html). That particular conference also references her work with Uribe. Ultimately, I think you read some already and all you wanted is a simply "one-liner" logic, which is the fisher equation from above (with reverse causation of i and inf). It is not mainstream, yet discussed frequently among all major central banks (FED,BOE, ECB...). It is mainly relevant for liquidity traps (zero lower bounds) in combination with low inflation expectations. Jan 1 at 20:58

The theory is called Neo-Fisherishm. The Fisher equation states $$r \approx i - \pi_e,$$

where $$r$$ is the real interest rate, $$i$$ the nominal, and $$\pi_e$$ the expected inflation rate.

Primary determinants of long-term equilibrium real rates are mostly non-monetary: potential growth rates; demographics; risk preferences in portfolios.

Real rates $$r$$ are determined by fundamentals: increasing $$i$$ => Higher inflation

There are a lot of nuances and details for this to "hold". However, the same is true for

Lower interest rate => Loaning money is cheaper => More money in the system => Higher inflation

• Thanks, still digesting but it seems like this is what I was looking for. Jan 8 at 8:37
• And I acknowledge there are serious assumptions behind each theory, but at least now I know what theories there are. Jan 8 at 8:47