Sure, a temporary increase in useless government expenditure, even under Ricardian Equivalence, will give a bang for the buck. But it's a totally useless bang. No Keynesian economist would recommend it, even if there were no useful alternatives. And useful government expenditure will not only give a useful bang for the buck, it will give a bigger bang for the buck.
The intuition is simple. Paying unemployed resources to do something totally useless is equivalent to giving them a transfer payment. A transfer payment is equivalent to a tax cut. A tax cut has no effect under Ricardian Equivalence.
[Update: Paul Krugman responds.]
Assume, for simplicity, that the marginal propensity to consume out of permanent income is one. Ignore interest rates, exchange rates, and supply-constraints.
A permanent $100 increase in government expenditure will have zero effect on output, if it causes an equal $100 increase in permanent taxes, and so an equal $100 decline in consumption.
A temporary $100 increase in government expenditure will cause output to increase by less than $100, because it causes permanent taxes to increase by less than $100, and so consumption to decline by less than $100.
In the limit, as the $100 increase in government spending becomes purely transitory, we can ignore any offsetting effect of increased present value of taxes on current consumption. So output increases by $100. Just like the balanced budget multiplier in the old Keynesian Cross.
Now assume that the $100 increase in government expenditure is spent on something totally useless, like digging a hole and filling it in again. Which is what Justin Yifu Lin assumed. Does output really increase by $100?
Well, if you count that totally useless hole-digging-and-filling exercise as part of GDP, then yes, GDP does increase. And if you don't, it doesn't. And National Income Accountants can have great fun discussing whether the true value added of a filled hole is any different from the value added of a hole that doesn't exist because it was never dug in the first place. But it's still a totally useless activity. And no reasonable measure of output would include digging a hole and filling it in again for no purpose whatsoever. Its market value is precisely zero.
Now suppose the government spends the same $100 to dig a hole, plant a seed in the hole, and fill it in again. And the seed grows into a tree, and the tree produces exactly enough apples to repay the $100 the government borrowed including interest. So the government never needs to raise taxes. And people know this. What's the effect on output?
At a minimum, output increases by $100. And it really is a $100 increase in useful output. Unemployed resources, that would otherwise have produced $0, now produce something worth $100. And since that $100 increase in real wealth causes an additional increase in consumption expenditure, there will be a multiplier effect bigger than one.
Now suppose the government plants a tree at the cost of the same $100, but the tree now yields enough fruit to pay back double what it cost to plant. So the government can actually cut future taxes. You get the same direct effect as before, but real wealth has now increased by $200, which induces an even bigger additional increase in consumption expenditure, and an even bigger multiplier.
That's what Justin Lifu Lin is saying. (OK, that's a reasonable interpretation of what he's saying). He's right. If Ricardian Equivalence is true, then useless government expenditure, even if temporary, even if there are zero other sources of crowding out, will have a multiplier effect on useful output of precisely zero. And useful government expenditure, which requires no increase in present or future taxes, will have a bigger multiplier. And if it's even more useful, and allows a cut in future taxes, or an increase in future disposable income, it will have an even bigger multiplier.
Useful government expenditure doesn't just create a useful bang for the buck; it creates a bigger bang for the buck.