The Committee for a Responsible Federal Budget has a great breakdown of why this is so. There are layers upon layers of problems with forgiving student debt to boost the economy, especially during the short term in light of COVID-19.
First and most obviously, debt is paid off in installments, sometimes over the course of several decades. So forgiving $X in debt today reduces payments by far less than $X in the near term. Some people might spend more today because their overall debt burden is lower, but research suggests this effect is small.
Second, if the debt relief is taxed (which will hinge on the government’s interpretation of obscure tax statutes), the extra taxes will cut into even this short-term boost.
Third, when you want to inject money into the economy, you give it to the folks most likely to spend an extra dollar. People with debt from college are not, by and large, in this category:
Over 70 percent of current unemployed workers do not have a bachelor’s degree, including 43 percent who did not attend college at all. Meanwhile, less than one-third of all student debt is held by households without a bachelor’s degree and less than a tenth is held by those with no college education. Indeed, about two-fifths of all student debt is held by households with graduate degrees. That group makes up less than a tenth of the total unemployed.
Finally, even if we do want to enable folks with student loans to spend more while the economy is struggling, we can get a similar effect for a fraction of the cost by extending the current pause on payments rather than forgiving the debt entirely.