My post yesterday claimed that
"if the government were, as I suggest, to fund a £30 billion (2% of GDP) investment programme, and fund it by borrowing through issuing long-term index-linked gilts, the cost to taxpayers - the interest on those gilts - would be something like £150 million a year."
David Smith, however, tweeted repeatedly that this was wrong, arguing (for example)
"No, again, £150 million of revenue doesn't give £30 billion of funding. £1 billion - real yield plus inflation - might."Why is David wrong? Well, as the chart in the post showed, real interest rates for very long term index linked gilts have been hovering around the 0.5% mark for the last couple of years. Indeed, they are currently lower, and recently the government has actually auctioned index-linked gilts at real rates of basically zero, but lets take 0.5% as the government's current real borrowing rate. David hasn't argued with that.
What does that mean? It means that if the government borrowed £30 billion at 0.5% real, then it would have to pay interest of £150 million per year, uprated for inflation for the term of the debt. See here for an explanation. So, in year 2, it would have to pay £150 million uprated for inflation between year 1 and year 2, and so on. So David's tweet is simply wrong - £150 million per year of revenue (uprated for inflation) perfectly well could yield £30 billion of funding at current market real interest rates, consistent with the results of recent government bond auctions. David may think the markets are somehow "wrong", but those are the rates at which they are currently lending to government.
What about when the debt comes due? At the end of the term, it would have to repay the £30 billion, uprated for inflation (ie an amount worth £30 billion in today's prices). But alternatively, and more likely, it could refinance the debt. Assuming real interest rates are the same then as now (and the yield curve is actually downward sloping at the far end, implying that as far ahead as the markets can see they will be falling not rising), then it could be refinanced again, with annual interest payments again being £150 million at today's prices, uprated for inflation. Of course market prices could change and real interest rates could rise - but again, this is what the markets are saying now.
In other words, £150 million per year, uprated for inflation, and payable for ever, is sufficient to fund borrowing and spending now of £30 billion. Is this surprising? Not at all, given current market real interest rates; it's just arithmetic. Indeed, this is an absolutely standard textbook result from the basic macroeconomics of public finance, generally known as the intertemporal government budget constraint, and summed up in this equation: