matherto
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The sequence of events for most countries goes like this:
I. First the creditors (market) start to doubt the future ability to pay of the government, and therefore the rates on rolling debt go up. At this point to cover the additional interest expense the government must either raise taxes or decrease expenditures elsewhere. Or as often happens, they do neither and the snowball starts increasing.
II. The size of the cuts required to right-size the out-of-control budget becomes politically impossible to achieve. At this point if the country has debt issued in non-domestic currency (Greece) they either need the IMF to bail them out, or they're going to default and be unable to borrow for a long time (and the companies in the country will probably also face challenges). The default also probably causes significant losses to domestic investors and possibly the banks.
III. If all of debt is in domestic currency, here is where you usually get what becomes the only politically feasible solution: the treasury issues more money to pay for the debt. Might sound clever, but this causes rising inflation (i.e. the government is taking wealth from anyone who has currency). This is another snowball that usually starts at inflation a bit higher than before, but soon spirals into 100% a year, 1000% a year. The currency also devalues by similar proportions. Although inflation would seem most detrimental to those who hold the most wealth, keep in mind that real assets retain their value well, capital is quickly moved abroad and into other currencies, and even the domestic banking system soon adapts to where its main service provided is inflation protection (see Brazil 1980s). The people most affected are those that most use paper currency vs the banking system: poorer people.
In summary, although the US and other developed countries with high debt aren't even yet at step I (everyone thinks their ability to pay is fine), there would be some level at which this would start to be questioned (and in my mind fundamentally it is developing countries that can justify running public sector deficits due to investments, developed countries have no reason for doing so for as long as they have). And you will pay eventually, hopefully with higher taxes in the future, but most likely via inflation.
Cheers for this @MTF. Makes it a lot easier to understand.