Interest rates: A closer look at inflation
Inflation effect: lenders want higher rates if prices are rising faster
A Simple Example
To see the impact of inflation on interest rates, let's look at a simple example. Assume you borrow $100 today and promise to pay back $105 one year from today. The lender will have been paid $5 for the use of that money for a year and the lender will use the $105 next year to buy a new pair of sneakers that cost $100 and have lunch for the $5 "profit." Everyone's happy with this mutually beneficial trade.
But what happens if the price level changes during the year? What happens if during the year prices rise by 5 percent? The mathematics of the example have been worked out below. Scenario 1 is the no inflation situation where the lender 's buying power increases by 5 percent over the year. In the second scenario we have an inflation rate of 5 percent so that the $100 sneakers rise in price by 5% to approximately $105. When the lender pays the $5 in interest, the borrower has $105 which is the price of the sneaker. The lender has made no "profit" since the prices of everything have risen by 5%. In this case where the inflation rate equals the interest rate, the lender has the same buying power at the beginning and the end so that the "real" interest rate is $0. After having lent the money for a year, the lender can still only buy the sneakers.
In scenario #3 the lender has adjusted the deal to account for inflation. The lender still wants the 5% interest rate so now the nominal rate of interest will be 10%. This rate will give the lender $110 at the end of the year, $105 to buy the sneakers at the inflated prices and $5 for lunch. In this case the nominal rate has increased to 10% and the real rate has remained at 5%.
When 5% is not 5%:
Real and nominal interest rates
scenario 1 scenario 2 scenario 3 Nominal rate 5.0% 5.0% 10.0% Inflation rate 0.0% 5.0% 5.0% Real rate 5.0% 0.0% 5.0% Loan $100 $100 $100 Interest paid $5 $5 $10 Total payment $105 $105 $110 Cost of living $100 $105 $105 Gain to lender 5% 0% 5% Column 1: you pay 5% interest in zero inflation world. When you repay $105 in one year, the lender can buy $105 worth of 'stuff'. The lender's buying power has been increased by 5% by waiting a year. The real rate of return is 5%.
Column 2: you pay 5% interest in 5% inflation world. When you repay $105 in one year, the lender can buy $105 worth of 'stuff', but the cost of living has risen 5%. This means that it now costs $105 just to stay even, to buy what we used to buy with $100. The lender's buying power has not been increased by waiting a year. The real rate of return is 0%.
Column 3: you pay 10% interest in 5% inflation world. When you repay $110 in one year, the lender can buy $110 worth of 'stuff', but the cost of living has risen 5%. This means the lender now has $110 and costs are $105 just to stay even. In this case the lender's buying power has not been increased by 5 % as a result of waiting a year ($110/$105 = 5%). The real rate of return is 5%.
Inflation and Interest Rates: The Math
Are there any generalizations we can make from our simple example? If we ignore all of the other components/dimensions of the interest rate, we can specify the relationship between real and nominal interest rates as follows:
rn = rr + ie
or
rr = rn - ie
- rr = real rate
- rn = nominal rate
- ie = expected inflation rate
Inflation and Interest Rates: The Track Record
We have now looked at the concept and the math, so let's turn our attention to the numbers. What type of relationship have we seen between interest rates and inflation rates. We can look at the relationship three ways. First, let's look at a scatter diagram - a little practice with your data analysis skills. The diagrams below are based on annual inflation rate and nominal short-term (3-month) government security rate data for the period 1953-1997. There is definitely a positive relationship between the two, but it is not a "perfect" one which suggests there are other factors that influence interest rates. When we look at the relationship between real rates and inflation, however, there is no clear relationship. The one definite here is when inflation rates are very high, real rates are in fact negative.
The positive relationship is also borne out by the summary table of interest and inflation rate data for the US economy. In the decades where inflation rates were higher, nominal rates were higher. The relationship between the two was not perfect, however, and in the 1970s when the economy experienced a sudden increase in inflation interest rates adjusted upward slowly and they adjusted slowly to the sharp decline in inflation in the 1980s. You can see this lag in the adjustment in the real rate column. Real rates actually become negative in the 1970s and then turning sharply higher in the 1980s.
We can also look at the relationship by examining the relationship between two time-series graph. In the first we see the two curves tend to move together - when inflation rates were rising in the 1970s, so were interest rates. Similarly, when inflation began to fall in the 1980s, we saw interest rates follow a downward trend.Short-term Government Rates
Nominal Inflation Real 1950-59 2.03 2.25 -0.22 1960-69 4.00 2.53 1.47 1970-79 6.32 7.41 -1.09 1980-89 8.85 5.12 3.73 1990-95 4.87 3.33 1.53
Inflation and Nominal Interest Rates
The lack of "perfect" synchronization can be seen in the second graph - real interest rates. There are some very sharp movements in the real rate suggesting these two do not follow each other extremely closely. Once again we see the slow adjustment of interest rates to inflation in the 1970s and 1980s. In the 1970s the rise in inflation was not adequately reflected in the interest rates so real rates actually went negative, while in the 1980s the reverse was true.
