Wikipedia:Reference desk/Archives/Humanities/2025 February 22

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February 22

Curve relating interest rate and inflation rate

One of the principal objectives of monetary policy is to regulate the inflation rate, so the relationship between the interest rate and the inflation rate is obviously very important. Does this curve have a name in economics? 101.119.84.115 (talk) 08:02, 22 February 2025 (UTC)

Did you mean Fisher equation? i ≈ r + 𝜋^e Stanleykswong (talk) 10:21, 22 February 2025 (UTC)

No. The Fisher equation is a relationship between the real interest rate and the nominal interest rate. What I meant was how the inflation rate varies as a function of the interest rate. After all, central banks try to control the inflation rate by setting the interest rate. The interest rate is the independent variable, the inflation rate is the dependent variable. 101.119.84.115 (talk) 10:28, 22 February 2025 (UTC)

Without addressing the specific question, I suggest that there is likely no exact real-world equation because many other variable factors likely also affect the inflation rate. (Just my annualized 2%.) {The poster formerly known as 87.81.230.195} 94.8.123.129 (talk) 11:05, 22 February 2025 (UTC)

That's true of virtually every relationship in economics, yes. 101.119.84.115 (talk) 11:19, 22 February 2025 (UTC)

I am not sure what interest rate you are referring to? Nominal interest rate or real interest rate? Stanleykswong (talk) 13:18, 22 February 2025 (UTC)

The Fisher equation expresses the relationship between nominal interest rates, real interest rates, and inflation. In the equation, nominal interest rate (i) is the dependent variable, both real interest rate (r) and inflation rate (𝜋) are independent variables.

If you rearrange the equation, it becomes, approximately, 𝜋 ≈ i - r, i.e. inflation rate (𝜋) being the dependent variable, both nominal interest rate (i) and real interest rate (r) being the independent variables. Stanleykswong (talk) 13:25, 22 February 2025 (UTC)

Basically I was interested in a relationship roughly of the form $\pi =f(i)$.

The Wikipedia article on Fisher equation exposed me to the "Fisher hypothesis", which I didn't know about. If the Fisher hypothesis is true, then it makes sense for $\pi$ to vary linearly with $i$.

But if the Fisher hypothesis is false, then in general $r$ can be a function of $i$. So declaring $\pi =i-r(i)$ just begs the question. What is $r(i)$?

I don't know what the accepted status of the Fisher hypothesis is. 101.119.84.115 (talk) 13:52, 22 February 2025 (UTC)

If the formula of π = f(i) is what you want, I think the simplest way is starting with a basic relationship of π=α+βi, and then use the historical data to find out the best-fit curve and hence the values of α and β. Stanleykswong (talk) 16:04, 22 February 2025 (UTC)

The key interest rate set by the decision makers of a central bank depends on:

• their forecast of the development of the inflation under unchanged policy;
• their inflation target (which in the US may depend on the saltiness of the water);
• the current interest rate.

If their forecast is considerably higher than the target, they may increase the key interest rate. If it is considerably lower, they may decrease the key interest rate. It cannot be expected that this can be captured in a formula π = f(i); it should be more like Δi = g(π _fcst − π _targ), in which π _fcst is the forecast and π _targ the target. If this (very simplified) picture is basically correct, a scatter plot of π versus i will not resemble a simple curve.  ‑‑Lambiam 20:11, 22 February 2025 (UTC)

The Taylor rule Stanleykswong (talk) 20:43, 22 February 2025 (UTC)

This is a model of the behaviour of a central bank. I was interested just in how the inflation rate of a currency depends on its interest rate. 101.119.124.17 (talk) 00:38, 23 February 2025 (UTC)

Let me put it this way. Assume a rule of the form π = f(i) to hold. Under the reasonable assumption that f is a monotonic and continuous function, it has a functional inverse, say g, so i = g(π). This would give the central bank people a very simple rule: set the key interest rate to i = g(π _targ), and bingo, the inflation target will be met. The fact that they use much more complicated rules, also involving the actual rate of inflation, strongly suggests it ain't so easy.  ‑‑Lambiam 07:32, 23 February 2025 (UTC)

Yes, besides the actual and target inflation rates, they also need to consider factors, such as actual and target GDPs, actual and target unemployment rates, etc... Stanleykswong (talk) 10:54, 23 February 2025 (UTC)

If you used the US interest rate and inflation historical data to plot their trends, you will see that inflation is a leading variable and interest rate is lagging. My interpretation is the central banks set the interest rates to control the inflation (they also consider other factors such as GDP). In this case, empirical data shows that interest rate is the depending variable (not the independent variable as you said). Of course, you may argue that the two variables are affecting each other and, yes, in most cases, they are. Stanleykswong (talk) 10:21, 23 February 2025 (UTC)