# Real value of debt

The Wikipedia article for real value says

In economics, a nominal value is an economic value expressed in historical nominal monetary terms. By contrast, a real value is a value that has been adjusted from a nominal value to remove the effects of general price level changes over time and is thus measured in terms of the general price level in some reference year (the base year).

Here the Wikipedia link for general price level changes takes me straight to the article for inflation. But then the Wikipedia article for deflation says

Economists generally believe that deflation is a problem in a modern economy because it increases the real value of debt

This sounds like a contradiction to me, because by the first definition, the real value of debt remains constant under deflation.

Can someone explain this?

If you take s loan for one million dollars at a certain point - deflation will mean one million dollars is now worth more than when you loaned it, but you still owe a million dollars (assuming you didn't return any back) therefore the value of your debt is now increased. That being said you can always take loans adjusted for inflation - where you return the real value of your loan regardless of the value of the currency.

There is actually a big argument whether deflation is good or bad - the Keynesians think it's bad - mainly because they think it reduces spending and results in a recession. The Austrians on the other hand think it is nonsense and deflation is good because it means the price of goods is lowered. *this was a great simplification, but the point is still there.

• A fine example of how real value actually factors in general price level changes over time, rather than remove it. Again, contrary to the definition on Wikipedia. – user3985 Feb 17 '15 at 19:31
• No, real value is the value when adjusted for inflation - exactly what they say in Wikipedia - if my loan is adjusted to inflation I return the real value of my debt not necessarily a million dollars, when it isn't I return the nominal value - a million dollars plus interest regardless of the value of currency. – gilmishal Feb 17 '15 at 19:38
• Thanks, I understand. It appears I misinterpreted the meaning of the word remove in the definition. But I suppose that a-b == a+(-b) – user3985 Feb 17 '15 at 19:59

There is no contradiction. Call $p$ the price level and $D$ the nominal debt level. Then, the real value of debt is given by

$$\frac{D}{p}$$

The debt level, divided by the current price level. When we have deflation, that means that $p$ decreases. A decrease in the denominator, $p$, means that the total value increases.

Perhaps an example helps. You started a debt contract in 1960, for 100 USD. That money was worth a lot back then. Suppose you would have to pay that money back now (without interest). In nominal terms, $D$ is still 100. Assuming that we had average inflation of 5 percentage points (pulling numbers from my head just for the example), the value of the currency decreased around 11.5 times (not real number) during that interval. That is, your real debt is only around 8 USD. Had the inflation over the period been higher, your real debt would be even smaller. The other way around: if there was deflation over that period, your real burden would be higher!

• What you seem to be saying is that, contrary to the Wikipedia definition, real value actually accounts for the general price level changes over time. I still need clarification. – user3985 Feb 17 '15 at 19:30