## Thursday, December 1, 2016

### A new "real debt" calculation

 Nominal (blue) and Real (red) Ratios of Debt-to-GDP
I thought of an easier way to do the "real" calculation for data that accumulates over multiple years. Debt is the obvious example of something that accumulates over multiple years.

Here's the calculation:

Take the change in debt as a share of nominal GDP, multiply it by the real GDP value for that period, and add the previous period's Real Debt value. That's it. That's the whole calculation.

It's a proportions thing. The change in debt is re-sized from a certain proportion of nominal GDP to the same proportion of real GDP. The purpose of the exercise is to determine the real (inflation adjusted) purchasing power of the additions to debt over time. This is a key part of the puzzle when one is considering economic growth.

The only data series needed are nominal GDP, real GDP, and the debt series you want real values for. Three columns of data. And you can do the calculation in a single step if you want, so just one column is required for that.

To me this seems a simple calculation -- at least compared to my old method. Let me go over it again:

Figure the change in debt relative to NGDP, then multiply by the RGDP value, and add up the values as you go. This gives you inflation-adjusted debt. If instead you figure the change in debt relative to NGDP, multiply by the NGDP value (instead of RGDP), and add up the values as you go, you get your nominal debt series back. The calculation works as it should.

If I was looking at consumer debt I'd want to use Disposable Income and Real Disposable Income instead of NGDP and RGDP. The method is flexible that way.

Also, you can use quarterly data. With my old method I was stuck using annual data for some reason.

And you don't need to use the GDP Deflator series. The new calculation uses the nominal and real GDP values instead. That's an improvement because the deflator creates rounding errors. If you use the deflator to figure real GDP, your values will differ a bit from the real GDP you get from FRED. Using the new calculation, the rounding error would show up in our deflator, if we calculated one. Since we don't need to show a deflator, the rounding error goes away.

Here's a usage tip: Insert a blank row between the data labels row and the first row of data. This way, you can use the same "change-in" calculation for the first data item and all the rest in that column. The first "change-in" value will be the first given value minus zero, which is exactly what you want.

And remember that for the base-year part of the calc, you probably need a dollar sign before the row number, so the row number doesn't change.

For those who may be interested, my first hard look at the inflation-adjustment of debt is in a series of five short posts beginning with an unnumbered intro. (The last post in series is number 4.)

My second hard look at it (four posts) begins here.

Here is a post that links to a spreadsheet with my old calculation.

And here is an Excel file that uses the new calculation.