ISTANBUL—The Turkish lira’s fall has been sudden and sharp. The cause traces back nearly a decade when the country’s leader decided to turn Turkey into something resembling China on a smaller scale, a world-class economy under one man’s firm control.

Eager to pull his nation out of an economic contraction that had marred much of the world at the start of 2009, Recep Tayyip Erdogan signed a decree easing access to foreign-exchange loans for Turkish companies.

The...