The government has announced a big investment in infrastructure - to start in 2014. If you believe the OBR's forecast for economic recovery, this means the investment will come just after the economy most needs a boost.So much for Keynesianism.

This set me pondering. Just how counter-cyclical has public investment in infrastructure been in the past?

My chart suggests: not much. If spending were counter-cyclical, you'd expect to see a negative correlation between gross public investment as a share of GDP and the output gap, with recessions causing high spending and booms lower spending. But in fact, there's no such relationship. According to Treasury/OBR data, the correlation was zero between 1963 and 2010*.

You might find this surprising, because you don't need to be a Keynesian to believe that infrastructure spending should be countercyclical. If real interest rates fall in recessions, you only have to think it's a good idea to borrow more when interest rates are low to want a negative correlation between the output gap and infrastructure spending.

So, why haven't we had one? Anti-Keynesians could argue that it's just impossible for governments to behave in a Keynesian way.The time lags involved in finding and planning big investments mean they cannot be started when the economy is weak. Alternatively, perhaps investment decision have been driven more by politicians'vanity - a desire for grand projects such as Concorde - than by economic logic.

Good points. But they run into a problem. If we split our data sample into three periods, we find different, and negative, correlations: -0.1 for 1963-79;-0.56 1979-97;and -0.85 for 1997-2010.

What we have here is an example of Simpson's paradox.

In other words, both the Thatcher/Major governments and New Labour behaved Keynesianly, having higher investment in booms and slumps. For example, Thatcher cut infrastructure spending as the economy moved from recession in 1981-82 to boom in 1988-89.

If anything, it was the pre-1979 governments that were not so Keynesian, having only a weak correlation between the output gap and investment. The golden age of Keynesianism was no such thing.

In this sense, Cameron's announcement of rail investment represents a return to pre-Thatcherism.

* In theory, this could be because governments have seen recessions coming and increased investment in anticipation of them with the result that recessions haven't materialized, and so there's been no correlation between spending and the output gap. But I don't think anyone thinks this has been the case in practice.