The natural rate of unemployment hypothesis was advocated by Milton Friedman. According to this hypothesis, there is a natural rate of unemployment that exists in an economy, which is a result of structural factors such as mismatch between the skills of workers and the skills needed in the job market. This natural rate of unemployment is considered to be the non-accelerating inflation rate of unemployment (NAIRU).

Option 2, A. W. Phillips, is not the correct answer. A. W. Phillips introduced the Phillips curve, which shows the relationship between inflation and unemployment, but he did not advocate for the natural rate of unemployment hypothesis specifically.

Option 3, J. M. Keynes, is also not the correct answer. J. M. Keynes is known for his Keynesian economics, which focused on government intervention and fiscal policies to manage unemployment and stimulate economic growth.

Option 4, R. G. Lipsey, is not the correct answer either. R. G. Lipsey is an economist who has contributed to the field of international economics and trade, but not specifically to the natural rate of unemployment hypothesis.

Therefore, the correct answer is option 1, Milton Friedman.