Does GDP growth influence population growth?

For 22 years beginning in 1952, the economy grew at something like a 4% annual rate. For 24 years beginning in 1984, the economy grew at something like a 3% annual rate. And for all the years since 2009, the economy has grown at something like a 2% annual rate:

Graph #1

Assume it is true that population growth influences economic growth. Suppose it is also true that economic growth influences population growth, and look at the graph.

The graph shows the beginning of a very long long-term decline.

// The Excel file