Maybe the boys and girls in Congress will never muster the will to provide the stimulus to get the economy moving. Perhaps Bernanke and the Fed crew will never get over their fear of inflation even as it turns to deflation. And, Washington politicians are too macho to say that we actually need the dollar to fall (i.e. a weak dollar) to get our trade deficit in line.

But, at least we have the pleasure of watching the leading lights of the anti-stimulus crew flailing in the cyberspace of the NYT, trying to pretend that their case makes sense. And no one does this better than University of Chicago economist Casey Mulligan.

Professor Mulligan thinks that he can show that stimulus does not work by examining the job impact of the workers temporarily employed to carry through the 2010 Census. Mulligan notes the assumption of stimulus proponents that the there would be a multiplier effect of 1.6 for each job directly created by the stimulus. This means that for every person directly employed as a result of stimulus spending there would be 0.6 jobs created as a result of the spending out of this worker’s wages.

Mulligan applies this arithmetic to the hiring of temporary Census employees earlier this year. Census employment peaked at just under this 600,000. The 0.6 multiplier would imply a jump in 360,000 non-Census related jobs. Mulligan looks at the data and cannot find any evidence of this sort of jump and believes that he has an important piece of evidence against the stimulus.

Let’s think about this a bit more closely. The Census jobs were very temporary and part-time jobs. There was a short spike in Census employment that then fell off very rapidly. Employment peaked at 586,000 in the first week in May, but the peak four-week average employment was just 571,000. The average for the prior four weeks was 156,000, and in the subsequent four weeks employment was 376,000, falling to 188,000 in the next four week period. So the vast majority of Census workers were employed for less than two months.

What sort of multiplier impact should we have expected? Census jobs paid an average of around $15 an hour. This is around 70 percent of the economy-wide average of $22.50 an hour. Furthermore, Census jobs were part-time jobs. If we assume that the average worker put in 25 a week, that is about 75 percent of the 34.2 hour average workweek. Adjusting for the somewhat lower pay and shorter hours, we should expect each Census job to generate roughly 0.32 (0.6*0.7*0.75) non-Census jobs.

For the peak four-week period, this would imply roughly 180,000 non-Census jobs (roughly 0.13 percent of total employment). Do we see this and should we expect to?

On the first question, Mulligan is almost certainly right. There is no evidence of a spike in employment in May or June when Census employment was at its peak, nor is there a notable falloff in the July/August data.

The second question is whether this should disappoint stimulus advocates? There are two parts to this question. Do we think that employees immediately adjust their spending in accordance with the pay of what they know to be a temporary job? In other words, does a person who knows they will only be working for a month spend their pay at the same rate as someone who expects to be collecting the same check for the indefinite future?

This probably depends on the person’s situation. Someone who is the sole earner in their household, with no significant savings, probably will spend their paycheck pretty quickly. However, a person who is the second earner in a household, or who is temporarily taking a second job, may spend out their 4-8 weeks of Census earnings over a much longer period of time.

The second part of the story is how firms respond to a temporary increase in demand. Suppose that the surge in Census hiring in May led to a corresponding rise in demand at firms. We might expect the immediate response to this uptick to be an increase in hours, since it would take firms some period of time to hire, even if they expected the increase in demand to be sustained.

If we look at the index of aggregate weekly hours, it actually did jump in May, rising from 91.9 to 92.2, an increase of 0.33 percent, more than twice the predicted multiplier impact of Census employment. The index fell back to 92.0 in June, but then rose to 92.4 for both July and August.

So, are the stimulus proponents vindicated? Well, if we’re being serious on this one, we would be more likely to see a movement in hours than jobs in response to such a short-term change in demand.

However, if we’re being really serious, we will note that we are trying to find evidence of a very short-term increase in demand equal to roughly 0.13 percent of GDP. This impact is likely to be swamped by factors like the surge in homebuying (and subsequent plunge) associated with the expiration of the homebuyers tax credit in April or the state and local budget cutbacks associated with the start of the new fiscal year in July.

So, if we want the find the evidence for the multiplier impact of the stimulus it is there, but in reality, this is not a very serious test. In short, might Casey has struck out again.