The concept of inflation and interest rate is interlinked and this connection constitutes the
major part of monetary policy in macroeconomics.

Inflation is the rise in the general price level of goods and services over time.

In India, the interest rate, the rate at which lender offers money to a borrower, is based upon the following:- Cash Reserve Ratio, Statutory Reserve Ratio, Repo Rate, and Reverse Repo Rate. It is regulated by the Reserve Bank of India.

To know a bit more about it, let’s dig into some history. The relationship between interest rate and inflation is known as Fisher Effect. This idea was proposed by Irving Fisher which states that the real interest rate has no dependence on monetary measures, nominal interest rate. The equation given by Fisher was: r = i − π, where (r) stands for real interest rate, (i) for the nominal interest rate and inflation (π). Some people over the years have employed Mathematical tools this equation now looks like r = i – 𝛽ℼ + ε where 𝛽<1 and ε is the error term.

Now this tells us that, if we the real interest rate is to be kept constant, then an increase in the inflation rate should require a proportional change in nominal interest rate. The Fisher Effect proposes that, in the long run, purely monetary measures will not affect the economy’s relative prices. Though, the effect is not always seen in short run because in case of unexpected inflation, nominal interest rate may take time to adjust.

The theory suggests as interest rates are lowered, it increases credit availability and more people spend on consumption which causes the economy to expand and also causes inflation to rise. This is practiced in expansionary monetary policy. Conversely, in a contractionary monetary policy, as interest rates are increased, there is a corresponding effect on credit availability i.e. less money is available to spend which in turn causes less consumption spending and causes price to fall (deflation). This is possible due to the fractional-reserve banking system which we follow.

The question is how to establish it that interest rate and inflation are related with each other, thus, using some data we will establish some evidence which may be convincing.

To establish the relationship between interest rate and inflation, we have employed data from 1st January, 2018 to 31st December, 2018. The interest rate consists of Repo Rate, and Reverse Repo Rate, the corresponding inflation levels are taken through CPI with base year 2012. We will use correlation analysis between interest rate and inflation to measure the viability of Fisher Effect in the short run.

For a better understanding, let us define some terms.

Repo Rate or Repurchase Rate: It is the rate at which the central bank lends to commercial banks for short periods in lieu of government bonds. The data has been sourced from http://www.ceicdata.com.

Month of 2018	Repo Rate
January	6.000
February	6.000
March	6.000
April	6.000
May	6.000
June	6.250
July	6.250
August	6.500
September	6.500
October	6.500
November	6.500
December	6.500

Reverse Repo Rate: It is the rate at which the central bank borrows from commercial banks for short periods.

Month of 2018	Reverse Repo Rate
January	5.750
February	5.750
March	5.750
April	5.750
May	5.750
June	6.000
July	6.000
August	6.250
September	6.250
October	6.250
November	6.250
December	6.250

Both of the above Rates are meant to restrict the flow of credit from financial institutions to the people, which in turn reduce their ability to spend, and which further helps to decrease prices as the demand falls.

Consumer Price Index: an index used to calculate the price changes of a basket of goods and services. It is a measure of inflation. Here, CPI growth is measured on a Year to Year basis. The data has been sourced from http://www.ceicdata.com

Month of 2018	Consumer Price Index Growth Rate (Base 2012=100)
January	5.065
February	4.441
March	4.278
April	4.577
May	4.871
June	4.924
July	4.173
August	3.693
September	3.698
October	3.380
November	2.326
December	2.114

Now, since we have data, let’s define how we are going to find evidence for a relationship. For this purpose we are going to use Correlation Analysis.

We first find the correlation between CPI (x) and Repo Rate (y) using Karl Pearson’s correlation coefficient. Thus, using these parameters we get a correlation coefficient of r_xy= -0.7906106559. This is a moderately negative relationship.

Similarly, when calculating the correlation coefficient between CPI (x) and Reverse Repo Rate (y), we (coincidentally) get the same value of r_xy = -0.7906106559.

Thus, we observe that in both cases a negative relationship exists between interest rates and inflation. Thus, in the short run, the Fisher Effect applies.

Also, recently State Bank of India decided to link the interest rates on its account and short-term loans to Repo Rate of the RBI. Thus, we see our banking system heavily relies on this relationship and forms an important part of macroeconomic policy.

This, provides enough evidence to prove that Inflation and Interest Rates are related.

Sources:
https://www.livemint.com/money/personal-finance/sbi-new-rule-on-savings-accounts-short-term-loans-1556607290081.html
Data on Economic Indicators, Indian Economy Indicators Data & Charts www.ceicdata.com