I asked it at tutor2u, About: Economics and economicshelp.org
Only one site has responded yet, however, other two might answer it later, so maybe I will post the answers on my blog.
So, the answer from economicshelp.org:
The Phillips curve originated out of analysis comparing money wage growth with unemployment. The findings of A.W. Phillips in The Relationship between Unemployment and the Rate of Change of Money Wages in the United Kingdom 1861–1957 suggested there was an inverse correlation between the rate of change in money wages and unemployment. For example a rise in unemployment was associated with declining wage growth and vice versa
This analysis was later extended to look at relationship between inflation and unemployment. Again the 1950s and 1960s showed there was evidence of this inverse trade off between unemployment and inflation.
Phillips Curve Diagram
However, Monetarists have always been critical of this Phillips curve trade off. They argue that in the long run there is no trade off as LRAS is inelastic.
Is there still a Phillips Curve Trade Off?
Evidence from the 1970s suggested the trade off had broken down. The 1970s witnessed a rise in stagflation - rising unemployment and inflation.
However, others argued there was still a trade off - the phillips curve had just shifted to the right giving a worse trade off.
In the early 2000s, the trade off seemed to improve. Helped with low global inflation. Unemployment in UK fell without any rise in inflation. Some argued this period of stability had ended boom and bust cycles with the classic trade off between inflation and unemployment.
Since the mid 2008s we have seen a rise in the unemployment rate and a fall in inflation. Part of this fall in inflation is the drop in oil prices. But, it also reflects the fact as the economy enters into recession we get a rise in unemployment and inflationary pressures fall away.
There are many factors affecting inflation and unemployment. At the very least the Phillips curve is not stable. The trade offs between inflation and unemployment are often changing due to supply side factors.
I think most economists would agree there is a trade off, at least in the short term. If you boost aggregate demand then unemployment will fall, but at the cost of higher inflation.