If you read Robert Murphy's blog, he has had several posts on this one particular topic. Paul Krugman originally made a claim that, essentially, the national debt does not matter because we owe it to ourselves. Krugman does not think that increasing the national debt leaves a burden to our children. Murphy was ready to defend Krugman in the sense that future generations do not actually pay off the national debt in terms of real wealth. But then Murphy listened to a couple of people and had a revelation. He now believes that future generations do pay for the debts being run up now.
In one of his latest posts (last time I checked), Murphy uses an example of consuming apples. He assumes that, on average, a person can only consume 100 apples when they are young and 100 apples when they are old. People can not save apples and use them in the future for their old age. The number of apples don't grow. If someone consumes more than his share of 100 apples, then this is at the expense of someone else.
Murphy comes to the conclusion that future generations do pay for debts run up now.
I am not sure I completely agree with his assessment on this, unless I am misunderstanding something (which is possible because I have a high regard for Murphy as an economist).
I think a better analogy for the apples is the Social Security program. If someone does not consume their full total of 100 apples in their young age, they expect to get more than 100 in their old age. But this is a Ponzi scheme. The first participants in the Social Security program received more than they originally put in. At some point, somebody is going to have to get less than what they originally put in.
The last person in Murphy's chart is the loser (Iris). That person did not get to consume 100 apples while younger, but did not gain anything in old age.
But that person is not really paying off a national debt. That young person was paying for someone else's excesses. Basically, every generation depends on the next generation to keep the system going. Once a generation says "no" or is simply unable to pay, then the generation before them will take the greatest loss.
The last person (both young and old) in Murphy's chart (Iris) could have said "no" and not paid in her younger years. This would have stiffed the second-to-last person on the chart (Hank). If the second to last person on the chart had said "no" during his younger years, then it would have been the person just above him who would have taken a loss. You can backtrack all the way up the chart.
The people who are getting stiffed the most right now from the national debt are the people who are working and paying taxes (or those holding money and having it devalued through inflation), but not receiving the benefits now or in the future. They are giving up extra capital right now to pay for the national debt, but they will not receive that same amount of capital in return (not even including interest).
Now there is one way that future generations pay and Murphy already identified this in a previous book he had written. With a higher national debt, the government is spending more and thus misallocating resources more. This causes less savings, less investment, and less capital accumulation over time. It leads to less technology being developed. This all hurts future generations.
If the U.S., along with the rest of the world, had been socialist over the last couple hundred years, then we probably wouldn't have many great things that we take for granted today. We wouldn't have big televisions and cell phones. We certainly wouldn't have iPads and digital cameras. If things were really bad, we might not have air conditioning or even electricity.
In a society with strong property rights and relative free markets, there is economic growth that compounds over time. Future generations benefit enormously from this. In that sense, our future grandchildren are paying for the current national debt because of our lack of savings and capital investment today.
In conclusion, I'm not sure if I have a disagreement here with Murphy or not. The last person on his chart certainly did pay at the expense of others. But it was done in the younger years. With Social Security, at some point the younger generation is going to say "no" to the older generation. They will decide that they do not want to participate in the Ponzi scheme. They will not be the ones paying.
At any given time, there is a certain amount of wealth. Some of it can be saved and some of it cannot be saved (like milk) for the future. We cannot consume wealth that hasn't been produced yet. We cannot consume the vegetables that will be grown thirty years from now. What we can do is save less and invest less. This might mean that there is less good machinery in the future and that they might not be able to grow as many vegetables in the future or that it will require more labor to grow vegetables than if there had been more capital investment.
I think Murphy's original instinct was right.