The first is the ratio of the US budget surplus to GDP, measured on the left axis. (Be careful— this is the surplus, not the deficit. The economy is in deficit when this series is negative.) The second is a measure of the real interest rate, measured on the right axis. The figure shows that interest rates do seem to increase when the surplus decreases andvice versa. We can compute the correlation between the surplus-to-GDP ratio and the real interest rate. For this data the correlation is −0.16. The minus sign means that when the surplus is above average, the real interest rate tends to be below its average value, consistent with the impression we get from the graph. However, the correlation is not very large. The 1980s stand out in the figure. During this period, the budget deficit grew substantially, reflecting low economic activity as well as tax cuts that were enacted during the early years of the Reagan administration. Starting in 1982, real interest rates increased substantially, just as the budget deficit was widening. This is consistent with crowding out and contrary to the Ricardian perspective. We must be cautious about inferring causality, however. It is false to conclude from this evidence that an increase in the deficit caused interest rates to increase. It might be that some other force caused high interest rates and low economic activity.  Toolkit: Section 16.13 “Correlation and Causality” You can review the definition of a correlation in the toolkit.
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US budget surplus to GDP