Simple stock-flow consistency and the debt-to-GDP ratio

 

 

Ideally, we would prefer to measure either a stock relative to a stock or a flow divided by a flow.

- Cecchetti, Mohanty and Zampolli, 2011

 

 

Going by this annual GDP Deflator, the inflation rate for 1978 was 7.0%, a nice round number. I want to look at that year.

The GDP for 1977 was 2,081.826 billion dollars. The debt, domestic nonfinancial debt for 1977, was 2,895.413 billion. For 1978 GDP was 2,351.599 and debt was 3,290.005.

For debt, I can subtract the 1977 number from the 1978 number to find the amount of debt that was added to the debt accumulation during 1978. For GDP I don't have to do that, because GDP starts every year at zero. Why are they different? It's a "stock vs flow" thing. Debt is a "stock". GDP is a "flow".

In terms of annual data, inflation is a "current-year" phenomenon. It affects current-year transactions, not transactions of prior years. Inflation changes stocks and flows in different ways because flows measure only "current-year" transactions, while stocks measure both current-year and prior-year transactions.

The GDP for 1978 was entirely sold (and mostly produced) in 1978, so the inflation of 1978 inflated all of GDP. But it is different for debt. Only the 1978 increase in debt was inflated by the inflation of 1978. The debt that was existing before the start of 1978 was already existing when the ball dropped at midnight, and the 1978 inflation could not change it. But the inflation of 1977 did inflate the 1977 addition to accumulated debt, and the inflation of 1976 inflated the 1976 addition, and like that for prior years going back to the oldest debt in the accumulation.

For debt, each year's increase -- and only the increase -- is inflated by that same year's inflation. It works for the increase just like it works for GDP, because the increase in debt is a flow, just like GDP is a flow. But the accumulation of debt is a stock, an accumulation created over many years. And the inflation in any one of those years inflated only that one year's contribution to the total. If you have to read this paragraph 20 times before it sticks in your head, do it.

We will look today only at 1978, the debt and GDP for 1978. We have the end-of-year values for 1978. But we also have the start-of-year values. For debt, the start-of-year 1978 value is equal to the end-of-year 1977 value (because debt is a stock). For GDP, the start-of-year 1978 value is zero (because GDP is a flow).

Don't worry about what the numbers are, when you read this. Just look at what I'm doing with them. Pretty soon maybe you will be figuring it the way I do.

GDP went from zero to $2351.6B during 1978. Economists figure inflation affected the whole thing, our nice round 7.0% inflation. So I would say that the $2351.6 B number is 107.0% of what GDP would have been if there was no inflation in 1978. With no inflation that year, GDP would have been 2351.6 divided by 1.07, or $2197.8 B.

Nonfinancial Debt increased from $2895.4B to $3290.0B during 1978. The inflation of 1978 inflated the difference, the $394.6B that was added to the accumulation during 1978. The 7.0% inflation makes the $394.6B 107% of what the increase would have been if there had been no inflation. With no inflation that year, the increase in debt would have been $368.8B. Add this to the starting value ($2895.4B) to get a number for what domestic nonfinancial debt would have been if there was no inflation in 1978. The number I get: $3264.2B.

Using FRED's source data as a place to start, I get debt-to-GDP ratios of 1.391 for 1977 and 1.399 for 1978. We could round them both to 1.4.

Using my numbers, figuring zero inflation in 1978, I get 1.391 for 1977 (same as above) and I get a ratio of 1.485 for 1978.

With seven percent inflation in 1978, FRED's number, we got a debt-to-GDP ratio of 1.399. With zero inflation in 1978, we would have got a debt-to-GDP ratio of 1.485.

Rounded to two decimal places, 1.40 versus 1.49. Rounded to one decimal place, 1.4 versus 1.5. The difference: one tenth of a percentage point. In ten years, it could amount to a whole percentage point increase in the debt-to-GDP ratio. In the 20 years of the Great Inflation, perhaps a 2-point increase in the ratio. In other words, from a so-called stable 1.4 at the beginning of the Great Inflation, the debt-to-GDP ratio might have increased to 2.4 -- a ratio not seen in reality until 2008!

I'm not saying my estimated debt-to-GDP ratio is realistic. Far from it; we only looked at 1978. What I'm saying is: Inflation makes a big difference in the numbers. It looks like what I did -- taking the inflation out of the numbers -- is what made the difference. In the real world, inflation going into the numbers is what made the difference. Inflation was the intruder. Inflation came along, inflation so severe that economists started calling it "great", and it started changing the numbers. In particular, as we have seen here, the inflation changed the debt-to-GDP ratio and changed it severely.

Inflation invalidates the simple debt-to-GDP calculation because debt is a stock and GDP is a flow, and inflation changes stocks and flows in different ways.

Let me make my point clear. I took inflation out of the GDP for one year only: 1978. And I took inflation out of one year's increase in debt for the same year, 1978. But I did not change the number for debt accumulated before 1978. This is the only thing I did that is unique: I assumed that the inflation of 1978 affected only the addition to debt in 1978. Not to the whole of that debt.

The way debt-to-GDP is usually figured, nominal values are used for both debt and GDP. Inflation is in both the numerator and the denominator of the ratio. Therefore, inflation divides itself out of the calculation: out of GDP, and out of the year's increase in debt, and out of the starting balance of debt. With my calculation, I made sure the 1978 starting balance was not adjusted for the 1978 inflation. That's the only difference.

It makes a world of difference.