Fiscal multipliers in the short and long term

The United States and the European Union are implementing public investment programmes in infrastructure, the energy transition, healthcare, industry, research, training, support for young people, etc. A significant fraction of the spending (infrastructure, renewable energies, healthcare, etc.) will generate an increase in production in the short term: the short-term fiscal multiplier of the stimulus plan may be high (it involves direct public spending, not transfers to households that could be saved; the only loss would then be the import content). But the important question is the long-term fiscal multiplier: will the stimulus plans boost potential growth? It is doubtful that there is a significant link between public investment in infrastructure and potential growth. On the other hand, potential growth may react to the increase in public spending on healthcare, research and education. The trap would be if the fiscal multiplier was quite high in the short term but low in the long term: there would then be only a fleeting boost to GDP, which would then rise to a fiscal solvency problem.