There is a connection between them. The level of savings affects demand in the short and medium term. So, savings affect the size of GDP. If demand drops, GDP will fall. At a low savings level, potentially, the country will not be able to finance its investments, and will increase foreign borrowing.
If the savings level is low, the GDP is approaching a potential maximum, and the higher the GDP, the lower the debt-to-GDP ratio.
If the level of savings increases, the GDP will decrease, the ratio of debt to GDP will increase
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