Chris Dillow fails

Stumbling and mumbling tackles the relationship between growth and interest rates. He wants to determine if England can outgrow its interest expenses. So he compares the interest rate and the growth rate:

Debt & deficits: the maths

Do we need a budget surplus to get the ratio of government debt to GDP down? There seems to be some confusion on this, so let me clarify. George Osborne said today: Government must ensure that debt continues to fall as a percentage of GDP, including using surpluses in good years for this purpose. That word "including" is doing some work here, because surpluses are not always necessary to get the debt-GDP ratio down. A simple formula tells us this. It says the primary budget balance compatible with a stable debt-GDP ratio is equal to: d * [(r-g)/(1+g)] where d is the debt-GDP ratio, r is the long-term real interest rate and g the long-term real growth rate.

But he does not specify the interest rate to use. When England has a 50% debt/gdp ratio, then most of its debt is around the five year rate, England does borrow long at higher rates.  If England tries to dump 50% of gdp onto the short end of the curve, to get lower rates, it will invert the curve and recession follows.

Nor does he mention that rates are a function of nominal growth, the two grow together.