Final answer:
The statement that US public debt as a share of GDP historically increases during wars and recessions and subsequently declines is true, with examples including post-war periods and the aftermath of the 2008-2009 recession. Public debt dynamics are influenced by the relationship between government spending and economic growth.
Step-by-step explanation:
Historically, it is true that the US public debt as a share of GDP has increased during wars and recessions but has subsequently declined. Wars and recessions typically necessitate increased government spending which can lead to larger budget deficits and an increase in public debt.
However, following such periods, efforts to reduce debt have often been employed during times of economic recovery, although the dynamic can change based on various economic and policy factors.
For example, during the 1960s and 1970s, despite the government often running small deficits, the debt was growing more slowly than the economy, which resulted in a declining debt/GDP ratio. Conversely, during the 2008-2009 recession, the debt/GDP ratio rose sharply.
Moreover, while federal spending has grown in recent decades, the statement that defense spending is higher now than ever is false in terms of GDP share. Additionally, federal deficits have indeed been very large for the last two decades, and the accumulated federal debt as a share of GDP is near an all-time high.