Savings, Interest Rates, and Money Illusion

It’s been well documented that the personal savings rate of Americans has dropped precipitously over the past few decades. The changes are shown in the chart below:

Macroeconomic theory suggests that this is related to the real interest rate (after inflation rates). A higher interest rate implies that the return on savings is higher, so that more future consumption goods can be obtained for a given sacrifice of current consumption goods.[1] Is this really the case? Is the savings rate related to real interest rates? I tested the relationship between savings and real interest rates from January 1959 to March 2012 to find out. I used the 10 Year Treasury real rate and found the correlation between the two to be 0.00. That implies that there is no relationship between real rates and savings rates.

There does, however, seem to be a stronger relationship between nominal rates and savings rates. When you take inflation out of the picture, the chart looks like this.

This implies that something called money illusion exists. Money illusion is when people mistake nominal changes for real changes. If your savings after taxes rise 2% and inflation is 2% you will think you are better off when in fact you are no better or worse off than before.

There are two main problems with this.

(1) If consumers were completely rational, they would take inflation into account when they make their consumption/savings decision. Obviously they are not completely rational as they take cues by nominal rates instead of real rates. This poses a problem for economic modeling. Should we not use nominal rates instead of real rates when modeling expected savings to get a more accurate result?

(2) When real interest rates go down savings needs to go up, not down. Consider someone facing retirement in 20 years. They want an income of $30,000 ($2,500/month) over 30 years in retirement. If their real rate of return is 5%, they will have to save up $465,704.04 in today’s dollars to make that happen.[2] They will need to save $1,940.43/month. However, if their real rate of return is 1% they will need to save up $777,267.67 in today’s dollars by retirement. That’s a monthly savings need of $2,926.89/month, a significant difference! Consider what you will need to save if the real rate of return is negative! The average American household would be hard-pressed to come up with the difference, particularly given the fact that most aren’t even saving for retirement.

To sum up: what actually happens and what needs to happen are at complete polar opposites. What actually happens is that when nominal interest rates go down, savings decreases. What needs to happen is that when REAL interest rates go down, savings needs to INCREASE.

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[1] Williamson, Stephen D. Macroeconomics. 4^th Ed. Pg 283.

[2] All projections in real terms, taxes not included, volatility not factored. Rates of return are assumed to be the same before and after retirement of illustrative purposes. I realize that retirement portfolios aren’t entirely in 10 Year Treasuries and the real rate actually experienced will differ. This was just for illustrative purposes.