Bit by bit we’re getting information on the Obama stimulus plan, enough to start making back-of-the-envelope estimates of impact. The bottom line is this: we’re probably looking at a plan that will shave less than 2 percentage points off the average unemployment rate for the next two years, and possibly quite a lot less. This raises real concerns about whether the incoming administration is lowballing its plans in an attempt to get bipartisan consensus.

In the extended entry, a look at my calculations.

The starting point for this discussion is Okun’s Law, the relationship between changes in real GDP and changes in the unemployment rate. Estimates of the Okun’s Law coefficient range from 2 to 3. I’ll use 2, which is an optimistic estimate for current purposes: it says that you have to raise real GDP by 2 percent from what it would otherwise have been to reduce the unemployment rate 1 percentage point from what it would otherwise have been. Since GDP is roughly $15 trillion, this means that you have to raise GDP by $300 billion per year to reduce unemployment by 1 percentage point.

Now, what we’re hearing about the Obama plan is that it calls for $775 billion over two years, with $300 billion in tax cuts and the rest in spending. Call that $150 billion per year in tax cuts, $240 billion each year in spending.

How much do tax cuts and spending raise GDP? The widely cited estimates of Mark Zandi of Economy.com indicate a multiplier of around 1.5 for spending, with widely varying estimates for tax cuts. Payroll tax cuts, which make up about half the Obama proposal, are pretty good, with a multiplier of 1.29; business tax cuts, which make up the rest, are much less effective.

In particular, letting businesses get refunds on past taxes based on current losses, which is reportedly a key feature of the plan, looks an awful lot like a lump-sum transfer with no incentive effects.

Let’s be generous and assume that the overall multiplier on tax cuts is 1. Then the per-year effect of the plan on GDP is 150 x 1 + 240 x 1.5 = $510 billion. Since it takes $300 billion to reduce the unemployment rate by 1 percentage point, this is shaving 1.7 points off what unemployment would otherwise have been.

Finally, compare this with the economic outlook. “Full employment” clearly means an unemployment rate near 5 — the CBO says 5.2 for the NAIRU, which seems high to me. Unemployment is currently about 7 percent, and heading much higher; Obama himself says that absent stimulus it could go into double digits. Suppose that we’re looking at an economy that, absent stimulus, would have an average unemployment rate of 9 percent over the next two years; this plan would cut that to 7.3 percent, which would be a help but could easily be spun by critics as a failure.

And that gets us to politics. This really does look like a plan that falls well short of what advocates of strong stimulus were hoping for — and it seems as if that was done in order to win Republican votes. Yet even if the plan gets the hoped-for 80 votes in the Senate, which seems doubtful, responsibility for the plan’s perceived failure, if it’s spun that way, will be placed on Democrats.

I see the following scenario: a weak stimulus plan, perhaps even weaker than what we’re talking about now, is crafted to win those extra GOP votes. The plan limits the rise in unemployment, but things are still pretty bad, with the rate peaking at something like 9 percent and coming down only slowly. And then Mitch McConnell says “See, government spending doesn’t work.”

Let’s hope I’ve got this wrong.