In the years following his initial paper in 1958, many economists believed that Phillip's results showed that there was a stable relationship between inflation and unemployment. One implication of this for government policy was that governments should tolerate a reasonably high rate of inflation as this would lead to lower unemployment - there would be a trade off between inflation and unemployment.
In the 1970s however, many countries experienced high levels of both inflation and unemployment, or stagflation. Theories based on the Phillips curve suggested that this could not happen, and the idea that there was a simple and predictable relationship between inflation and unemployment was abandoned by most economists. New theories, such as rational expectations and the NAIRU (non-accelerating inflation rate of unemployment) arose to explain how stagflation could occur.