I've been meaning to write this post for some time. Scott Sumner's post spurs me to write it now.
First let me ask my dumb econometrics question. It's a very simple question, and I really ought to know the answer. But I don't.
Q1. If you estimate a linear regression, using Least Squares or whatever, will the estimated residuals always sum to zero? If the answer is "yes", then skip the next question. [Update: Ben, Norman, and Matthew tell me in comments the answer is "yes", provided there is a constant term in the regression, and I want there to be a constant term.]
Q2. If the answer is "no", would the gods of econometrics be very upset if an econometrician re-estimated that linear regression subject to the constraint that the estimated residuals sum to zero? If the answer to this question is "yes, very upset!", then you should probably stop reading this post, and try to explain to me why they would be very upset.
Q3. Has anyone ever done the following? I should probably know the answer to this question too, but I don't do micro public finance (with one exception where Frances was with me).
Get a random sample of Canadian (or whatever) individuals (or households). For each individual, get data on market income Y, and on net taxes (taxes minus transfer payments) T. Estimate a linear regression of T on Y, subject to the constraint, if necessary (see Q1 above), that the estimated residuals sum to zero.
The intercept of that regression (which would presumably be negative) tells us the Guaranteed Annual Income/Negative Income Tax we can afford, given a linear income tax rate equal to the slope of that regression, under the assumption that behaviour does not change. We know we can afford that GAI/NIT, because the residuals sum to zero by construction. For every dollar of positive residual where the deficit would increase with a GAI and linear tax, there must be a dollar of negative residual where the deficit would fall. The estimated tax/transfer system would be revenue-neutral by construction, provided behaviour did not change.
Now, will behaviour change? Almost certainly yes. Those who face a higher Marginal (net) Tax Rate under the new system will presumably choose to earn less than before, and those who face a lower MTR will presumably choose to earn more. But unless the first group has a systematically higher elasticity of response than the second group, the existence of the Laffer Curve tells us the net effect should be revenue-positive. (Jensen's Inequality, right?)
If I am right in the above, that simple linear regression should give us a conservative (i.e. lowball) estimate of the GAI we could afford to pay with a linear flat tax rate equal on average to the MTR we currently have.
The key to understanding GAI/Negative Income Tax is to understand that we already have a GAI. We call it "welfare". It's just a rather messy GAI, with lots of special cases and lots of very peculiar MTRs that are sometimes very high and sometimes very low.