But I want to take a step back because g > r doesn't exactly smooth over all the problems with the debt debate we've been holding.

g > r means the economy can sustain a debt burden. It does not mean that that debt burden won't cost future generations (it doesn't add any more future value costs that taxation in the current period for the same expenditure wouldn't add, of course). To make the debt expenditure itself benefit everybody its not enough that g is greater than r. The rate of return

*on the expenditure*has to be greater than r.

Think about it this way - let's say the economy was growing at g for reasons completely unrelated to the debt expenditure. If g > r then you can pay that debt, right? But if g isn't boosted by the debt expenditure then the public is still worse off than it would have been. Why not just forget the debt expenditure and just enjoy g without the debt service taken out of it?

So it's important to keep in mind that g > r is a sustainability condition, not a welfare improvement condition. To improve welfare, the expenditure has to be worth it, either because we care that much about the consumption or transfer that its supporting or because the expenditure is making an investmnet that will pay off down the road.

*****

I would point out one thing: it is a public service to explain g > r to people. If you tell the man on the street that we can run deficits every year until the end of time without increasing the burden of the debt, they typically don't respond well to that.

Simon Wren-Lewis has several good posts on this. He says you need to factor depreciation into the debt burden: like if a hospital bought with debt will last a hundred years.

ReplyDeletehttp://mainlymacro.blogspot.com/2012/05/costs-of-debt-finance-jonathan-versus.html

That there is a optimal speed of debt correction.

http://mainlymacro.blogspot.co.uk/2012/03/optimal-speed-of-debt-correction.html

And that there is an optimal level of debt.

http://mainlymacro.blogspot.co.uk/2012/05/government-debt-and-burden-on-future.html

He says r is "normally" greater than g, but I haven't seen any evidence for it. (Which is strange.) And that the amount of productive capital is less than optimal. (Don't know what this means exactly, or if it's true, but apparently related to crowding out.)

I crunched the quarterly numbers since 1962 using the FRED data. That's 201 quarters. 10-year t-note was above the YoY GDP growth rate at the end of 103 quarters. 1-year t-bill was above the YoY GDP growth rate at the end of 84 quarters. So it sounds like g<r is a fairly frequent occurrence.

DeleteJust briefly, I took the YoY NGDP growth (that's what we care about here right since the debt is also in nominal terms?) at the end of each quarter and compared it to the rate for the 10-year t-note and the 1-year t-bill at the end of the quarter.

Oh, I picked 1962 because that's when the FRED data series started for the 10-year t-note. The 1-year t-bill series starts only 2 years before that AFAICT.

DeleteAnd, predictably, the debt to GDP ratio has risen over most of this time.

DeletePrometheus: "I crunched the quarterly numbers since 1962 using the FRED data. That's 201 quarters. 10-year t-note was above the YoY GDP growth rate at the end of 103 quarters. 1-year t-bill was above the YoY GDP growth rate at the end of 84 quarters. So it sounds like g<r is a fairly frequent occurrence."

DeleteThat is also a time of increasing inequality. That stands to reason, as bondholders are siphoning off money at a greater rate than the economy grows. Are we saying that increasing inequality is normal?

@ PrometheeFeu

DeleteSorry I got your name wrong. :(

@Min:

DeleteMaybe it would help if you could show us your model which includes increasing inequality being a result of r>g...

Maybe you were just writing in shorthand, Daniel, but I don't think it's right to say that you need g>r in order to run perpetual deficits. Can't you just tell me what you want the steady-state debt/GDP ratio to be X, and then I tell you that the government can run perpetual deficits of Xg? This is independent of r, right?

ReplyDelete(Sorry if I'm being stupid.)

That last comment might have been unclear. Here's what I mean:

ReplyDelete==> Assume economy grows at 3%.

==> If you want a constant debt/GDP of 100%, then start running perpetual budget deficits of 3% of GDP.

==> If you want a constant debt/GDP of 50%, then start running perpetual budget deficits of 1.5% of GDP.

==> If you want a constant debt/GDP of 200%, then run perpetual deficits of 6% of GDP.

So in the above, we're obviously running sustainable, perpetual budget deficits, and I didn't say anything about r. It could be less than 3% or more.

Well wouldn't you want to count in the servicing costs? I imagine that's the difference. I can pull out my Wickens text. He lays out all the sustainability conditions pretty clearly.

DeleteI think what Bob might mean is that your deficit already includes the cost of servicing the debt. Whether your deficit is 6% because you spent it on roads or because you just rolled over debt doesn't matter. Your debt has grown by 6% and that is what matters.

DeleteLast sentence should be: "Your debt has grown by 6% of GDP and that is what matters."

DeleteBob, r still goes to your ability to keep the deficit at the stable level. 400% debt to gdp ratio, 3% growth, 12% deficit is stable, but what if r=28%? That's 112% of gdp that must go to debt service. (with 12% borrowed) If r goes higher than that, it's no longer sustainable.

DeleteSo the sustainability condition is r <= (g/d)+g where d is the deficit as a % of gdp. Am I missing something?