1. Mankiw writes:
In many developed economies, the average growth rate over long periods has exceeded the average interest rate on government debt. In the United States, for example, average growth of nominal GDP from 1871 to 1992 was 5.9 percent, and the average interest rate on debt was 4 percent. If these trends continue, a policy of rolling over the debt (and using taxes to pay for current government services) will cause the debt to grow more slowly than GDP.
Economists (Mankiw is far from the only perpetrator) often dismiss debt burden by simply comparing interest rates and growth rates; if the latter is larger then everything is ok. This misses some important dynamics. Since Mankiw and Ball wrote this paper, the debt to GDP ratio has risen past 100% in a very low rate environment. This is because the rate of new borrowing--new principal--has exceeded GDP growth for most recent years.
The marginal productivity of debt both public and private (increase in GDP for each unit increase in debt) has declined since the 1950s and reached negative, interestingly, in 2006.
The selection of years going back to 1871 lets one capture the highest growth rates in US history into the average. The trendlines for the past 20 and 10 years respectively have been 2.6% and 1.6% respectively. It's a good thing the Fed has subsidized interest rates...what happens if they lose control?
Finally, averages of rates do not tell the whole story, because interest rates are mostly constant while GDP can fluctuate into negative territory. Even if a depression is followed by a growth spurt, GDP growth doesn't catch up the growth comes from a lower baseline than the monotonically increasing debt.
In conclusion, comparing 140-year averages of GDP growth and interest rates doesn't really provide very good support that the US government can continue its, in Mankiw's words, "Ponzi" game.
2. This is more of an ongoing criticism of the entire GDP equation that economists treat as fundamental. Mankiw writes:
When budget deficits reduce national saving, they must reduce investment, reduce net exports, or both. The total fall in investment and net exports must exactly match the fall in national saving.
This assumes a world where credit doesn't exist. In such a world, every dollar in existence must either be invested or put under a mattress, and a great many of them are earned from exports. This completely ignores the effect of private credit. In any given year, significant amounts of credit are pumped into the economy, disrupting the classic S = I + NX equation. This allows both current-year S and I to be pumped up irrespective of NX, with the caveat that a future year liability is created.
GDP equations, in my opinion, are at best incomplete as a reasoning model because of their exclusion of credit and finance. This is why the economics profession keeps being surprised by financial crises. They aren't random "black swans" or "sudden psychological collapses in aggregate demand"; they are predictable outcomes of debt-financed excess consumption and malinvestment.