My reading of the above posts is that there are two separate issues being debated:
1. Should government spending be counted as GDP? If governments end up hiring workers to dig holes and them fill them up again, why is this considered as valuable production? This is a valid point but much broader than the current debate. I do not have strong views with respect to this point, I can imagine questioning the way we measure GDP on several grounds but this was not the main point I was trying to make. My assumption is that the government was buying goods that are valuable and therefore should be counted as GDP. But were I have strong views is that we should not confuse this argument with the one that separates the effects of changes in government consumption versus investment. Government consumption can be valuable (provision of healthcare, education and other public services) as much as government investment. It is not only government investment that should be counted as GDP. And this is where I felt that the original statement from the World Bank chief economist was not clear enough. That he seemed it imply the need to look for expenditures that raise the productivity of the economy.
2. The second debate is about the validity of the Ricardian Equivalence proposition. This proposition says something very simple: if the governments cut taxes today and does not change the path of spending, then the private sector should anticipate the future taxes required to pay for government spending and decrease consumption by exactly the same amount as the increase in government spending. In this case GDP does not change. Realize that here we are ignoring the first point and counting government spending as GDP (otherwise GDP will be falling). This result (Ricardian equivalence) does not apply to cases when government spending changes. To be more precise, depending on whether the change in government spending is transitory or permanent we get some or no effects.
The Ricardian Equivalence proposition requires many assumptions (perfect foresight, no financial constraints in the private sector, all taxes are lump sum, etc). Some believe that these assumptions are unrealistic and that is why they believe in a world where Ricardian equivalence does not apply. The assumption that I was questioning in my post was the fact that models where Ricardian Equivalence applies are models where the economy is in equilibrium. For simplicity you can think about it as the economy always being in full employment. But this is not a good characterization of many economies today. Why does it make a difference? Because with full employment, the only way to grow output and income is by increasing productivity (or by changes in the labor force participation).
What happens in a world where unemployment is high and there is a large output gap? Depending at which speed the economy returns to potential, we have a different path for income and potentially for private spending. If fiscal policy raises employment and income by closing the output gap faster, private spending will increase even if the other assumptions are still valid. Of course, this does not mean that any fiscal policy measure will do the job (if the government increases the purchases of foreign luxury cars, it will not do the trick...), but there is a potential to increase income and therefore move away from the Ricardian equivalence proposition.