The theory that national saving equals domestic investment in an open economy is a fundamental concept in macroeconomics. The key factors that determine whether this equality holds true include the degree of capital mobility, trade balances, and fiscal policies. An open economy refers to an economy that interacts freely with other economies around the world through trade, foreign direct investment, and financial flows. In a closed economy, domestic investment is constrained by domestic saving. But in an open economy with perfect capital mobility, domestic investment can be financed by both national saving as well as foreign saving flowing into the country, allowing domestic investment to exceed national saving. However, persistent trade deficits over time can lead to growing external debt burdens for a country that can eventually constrain its ability to attract foreign financing, causing the equality between national saving and domestic investment to reassert itself. Fiscal policies also play a crucial role, with budget deficits reducing national saving, while incentives for domestic investment like investment tax credits can influence the direction and degree of any imbalances between the two sides of the equation.

Over long periods, national saving and domestic investment revert back to equilibrium
While the saving-investment identity can diverge over shorter periods due to capital mobility, trade imbalances, and public sector deficits, the equality tends to reassert itself over longer intervals. No country can permanently consume more than it produces, nor invest more than it saves. Countries that try to sustain excessive domestic investment funded predominantly by foreign borrowing eventually hit external debt ceilings that force downward adjustments in their investment spending.
On the national saving side, if inadequate domestic saving is constraining investment, governments may undertake reforms to develop their local capital markets and promote higher saving rates. Over time, market forces tend to bring saving and investment back into balance. The correlation has held up remarkably well empirically, with national saving and domestic investment levels moving in tandem over multi-decade intervals across countries despite periodic divergences over shorter cycles.
The theory that national saving equals domestic investment in an open economy with perfect capital mobility does not always hold on a year-to-year basis. Differences can arise due to trade imbalances and fiscal deficits or incentives. However, current account and fiscal deficits cannot diverge from GDP indefinitely. Over long periods, market discipline and policy adjustments tend to reequilibrate saving and investment levels.