Why is the Correlation between Interest Rates and Inflation positive?

I regressed quarterly CPI on lagged quarterly (from 1 to 8 quarters) 10-year Treasuries, and found that with data from roughly 1990, the coefficient of the lagged rates tends to be positive. This implies that as interest rates rise, inflation also rises. Excluding the earlier data and using only more recent data results in a negative coefficient. I thought this might be due to the ineffective use of interest rates following the oil crisis in the 70s, but the 80s also follow this trend.

P.S. Using the Federal Funds Rate results in a positive coefficient no matter what.

• en.wikipedia.org/wiki/Fisher_effect Jul 20, 2022 at 17:37
• CPI is not inflation but price level, looks like a unit root spurious correlation Jul 20, 2022 at 18:47
• Could you please provide links to the data you use and minimal working example?
– 1muflon1
Jul 20, 2022 at 19:43

The answer is that what you are getting is bias from naive regression and there isn't a positive relationship, careful empirical studies using appropriate models show the relationship is negative. If you are running simple naive regression you will get biased results due non-stationarity of the series and endogeneity. Hence your positive correlation is caused by bias and is no indication of what the relationship between the two variables is.

To examine relationship between interest rates and inflation you need some model that can handle both endogeneity, and series being non-stationary and in this case actually not just non-stationary but also cointegrated. An one alternative is to run Vector Error Correction (VEC) Model. VEC similarly to VAR solves endogeneity problem and it allows for non-stationary and cointegrated variables (see Verbeek A Guide to Modern Econometrics 3rd ed ch 9.5).

Empirical studies such as Booth & Ciner (2001) show that there is a negative relationship between interest rates and inflation around the world:

If there would be Fisher effect present the relationship would be positive in the cointegrated models above. In naive regression you just get positive results because of endogeneity and stochastic trends that create spurious correlation.

• I used a vecm model to check for cointegration and at the 1% critical levels there is no case for rejecting stationarity, but there is at the 5%. As far as I understand it, it's obviously up to me how much precision I need. Can you explain where you see a negative relationship in the Booth & Ciner study? I only see negative std. Jul 26, 2022 at 0:04
• @PostScriptum VECM is not test for stationarity, I am not sure how you used it to test for stationarity. Std here is not standard deviation, btw standard deviation cannot even be negative that’s impossible, std here stands for standardized, in VECM you always have to standardize your coefficients otherwise they are hard to interpret
– 1muflon1
Jul 26, 2022 at 1:49
• Part of the process of creating a vecm model is testing for stationarity, because if it's not present it's just a var model then. I did this in r with the ca.jo function. Yeah ok standard deviation can't be negative, what would the -1.5 for Belgium mean? Jul 27, 2022 at 5:51
• @PostScriptum but ca.jo function does not test for stationarity. The -1.5 is the standardized effect between inflation and interest rates
– 1muflon1
Jul 27, 2022 at 11:50
• I meant the cointegration test. Jul 28, 2022 at 16:21