Economics question

[RandBlade]

Be curious if anyone can answer, from either US or UK perspective.

Interest is paid on national debt by the government, but so long as borrowing is kept below both the rate of inflation and the rate of GDP growth then the debt burden as a ratio of debt:GDP falls. Most of the time since WWII until Brown the UK national debt:GDP has been falling despite frequently running a deficit.

I'm curious if there's data out there: how often have interest rates on government bonds been above or below the combination of interest rates and real GDP growth and what sort of margin has historically been normal?

[earthJoker]

Be curious if anyone can answer, from either US or UK perspective.

[wiggin]

To be honest I'm not 100% sure what you're asking. (I think you use 'interest rate' when you mean 'inflation rate' in the last sentence, but I'm not really sure.) It's pretty easy to get historical GDP growth numbers in real terms (i.e. with inflation stripped out) as well as gov't budget deficit numbers as a percentage of GDP. I believe if the former is larger than the latter, you're good, yes? I don't know where interest rates really figure in, though - most gov't deficits include borrowing costs, so it's already built in. Oh, you can always look at primary balance, but I never thought that was relevant. A government with no deficit in its primary balance could easily still have an increasing debt-to-GDP ratio if interest rates are high or growth is low.

So... what do you actually want? Data on this is widely available and easy to plot (for most large economies).

[RandBlade]

Interest (bond) rates on government debt.

What I'm curious about is not the deficit (which is a function of over-spending/less tax receipts) but the interest on new and existing debt. The latter is the burden for having debt in the first place.

[wiggin]

So all you want is interest payments as a percentage of GDP, correlated against rates? I'm just not sure exactly which metric you want. I can easily put together a few graphs once I know.

[RandBlade]

I think I've gotten ahead of myself with mixed messages.

What I'm curious about is:
1: The nominal interest (bond) rates applied on government debt.
2: The rate of inflation.
3: The rate of real GDP growth.

Then 1 plotted against 2+3

[wiggin]

Over time? Or do you just want a scatterplot for a sampling of the last, say, 90 years? I could also plot 1 and 2+3 against a time independent variable...

[RandBlade]

Either/or? Or both? Whatever's easiest.

[wiggin]

Okay, I'm doing some data analysis now on something else but I can def. get to this over the weekend.

BTW, I assume I could just choose a convenient maturity date for which I have data for the interest rate? I was thinking 5 or 10-year T-notes to start with for the US. I'd have to look at gilts more closely, but I imagine something on the longer end (10 years?) is better due to the very long average maturity of gilts.

[RandBlade]

Yes I think 10 years seems very reasonable, thank you for this .

[wiggin]

Hmm, there's another wrinkle in the data now that I think about it. So, in terms of gov't debt interest rates, there's a number of ways to look at it. One could look at market rates for a specific security, which is easiest but probably least informative. After all, if the government has low turnover on their debt it doesn't matter what the prevailing interest rate is on the market. It probably makes more sense to look at Treasury auctions, but that's messy discrete data that won't tell you much.

So, I propose to instead look at an aggregate interest rate paid by the government - look at interest payments and total debt (I'll include public and intragovernmental for simplicity's sake) and calculate an interest rate. I'm not sure what kind of detail I'll want, since the data gets pretty granular at the month level - I might just look at annual data and hope it isn't too far off. (edit: the US has this data available, but only for the last decade. I'm going to have to reconstruct the rest from other sources...)

[RandBlade]

Thank you very much for the amount of effort you're putting into this

[wiggin]

Okay, I'm rather tardy in putting this up (last week was crazy, I'm afraid), but the basic data is plotted below. If you need higher res, I can probably try uploading a larger image - I haven't ever used tinypic for sharing graphs before, so it's a bit off.





Some notes: My data sources are thus:

For annual real GDP growth data, I used data straight from the Bureau of Economic Analysis. Although their annual data goes back to 1930, I only used postwar data. Quarterly data began in the postwar period but is not included here for simplicity.

For inflation rate data, I used the Bureau of Labor Statistics' CPI data. Again data goes back very far (1914), but I only used the postwar period. I did not get into other price indices - such as the PPI, core CPI, or other variants - since the CPI is a good general measure.

For interest rate data, I used a bit of a kludgy method since it is not officially published by the Treasury going back before 2001. I took gross debt (including intragovernmental debt) of the US from each Dec. 31, averaged it, and took the interest paid during that year as a percent of the total. It is obviously a bit shaky, but a quick look at the published Treasury data showed it normally falls in the same range (within 0.1-0.2% for the year). Note that this is an approximation of the total interest rate the government was actually paying on its debt for the year, not the auction or market rate for US securities at the time. New debt auctioned in a given year may be quite a bit higher or lower than the current average interest rate due to average maturity and the interest rate environment. Nevertheless, there is a clear trend obvious from the data which is largely divorced from such annual fluctuations. I got my data on interest expenditures from the White House's Office of Management and Budget, with data going back to 1962.

If you want anything else - or replotted data of any sort - just let me know.

[wiggin]

I also did a scatterplot of the two against each other as you suggested. There isn't a particularly large correlation there (though the interesting outlier of the recession is quite instructive); a quick linear fit gives an R^2 of only 0.08.