Assuming Your Conclusion
The latest stimulus analysis out of the Administration is yet another crock. It claims 2+ million jobs created, but has absolutely no evidence for this. All it does is take the same hypothetical Keynesian multipliers it used when it proposed the stimulus, and reapply them. In other words, the models basically say X jobs should have been created per billion dollars spent, so they run the models that then announce that X jobs must have been created per billion dollars spent. Surely. Somewhere. We swear.
This notion of confirming your original predictive model runs with new runs of the same model is the same kind of BS that has become so popular in climate science. The fact is, the net effect of the stimulus is almost impossible to measure in a complex economy where so much is changing. It's possible, perhaps (though this is surprisingly difficult to do right) to measure each person employed in a stimulus project, but this does not answer the question of how many jobs would have been created if the $800 billion had been left in the hands of private actors rather than spent by the government.