Payroll taxes (V1)

Krugman comments on the politics around the payroll tax, and reminds us that "Milton Friedman’s permanent income hypothesis tells us that much of such cuts will be saved, not spent." This makes the case for spending based stimulus much stronger. The long term unemployed are having significant trouble finding work. After some threshold they can reasonably assume their future employment income to be zero. However, once they are back in the work force, they have reentered the ranks of the employed and can reasonably expect continuous work until their retirement. The result is that their lifetime income has increased dramatically and they can be expected to spend a large portion of their wages. There is a little model below the fold.

Here's a tiny model: consider an economy with 100 people employed all making a mean of $100 a year and 10 people long term unemployed making zero. We further assume that recent hires have a 1/2rd chance of retaining employment indefinitely after their first year of employment, and a 1/2rd chance of returning to unemployment. All citizens are 30 and expect to continue working and living to 80. The government must choose between a one $200 payroll dollar tax cut (average of $2 per employed individual), and a policy of employing four individuals at $50 each. w.l.o.g, assume a discount rate of zero. Also assume that increased economic activity will turn into future jobs (contentious)?

Under the tax cut policy, we will see increased economic activity of $200 (total tax cut)/50 (years), or $4 year, each year. By contrast, the four workers each have an lifetime income expectation of 1/2*50 (year 1) + 1/2*50^2 ($50 year for 50 years). Hence we see an first year increase in economic activity of 4 (workers) * 1/50 (years) 1/2 * 50*(50+1) = 2*51 = 102. For future years we see 2 (still employed workers) * 50 plus $2 from the $98 which was unspent in year 1. Clearly in this little world the direct hiring route generates more income in the first year, and it happens that the numbers I chose (not intentionally, I just wanted numbers that were easy to work with) created enough economic activity to sustain the 2 long term reemployed. BTW, please check my numbers, they were done on the fly.