# Janet Yellen is Hardly a Dove—She Knows the US Economy Needs Some Unemployment

Here is a link to my 34th column on Quartz: “Janet Yellen is hardly a dove–she knows the US economy needs some unemployment.”

October 18, 2013 Update: Given his 780,386 Twitter followers, a tweet from Ezra Klein is worth reporting. I like his modification to my tweet:

No, she’s a human being RT @mileskimball: Don’t miss my column “Janet Yellen is hardly a dove” http://blog.supplysideliberal.com/post/63725670856/janet-yellen-efficiency-wages-and-monetary-policy

Notes:

Andy Harless’s Question: Where Does the Curvature Come From? Andy Harless asks why there is an asymmetry–in this case a curvature–that makes things different when unemployment goes up than when it goes down. The technical answer is in Carl Shapiro and Joseph Stiglitz’ paper “Unemployment as a Worker Discipline Device.” It is not easy to make this result fully intuitive. A key point is that unemployed folks find jobs again at a certain rate. This and the rate at which diligent workers leave their jobs for exogenous reasons dilute the motivation from trying to reduce one’s chances of leaving a job. The discount rate also dilutes any threats that get realized in the future. So the key equation is

dollar cost of effort per unit time

=  (wage - unemployment benefit)

· detection rate

÷ [detection rate + rate at which diligent workers leave their jobs                              + rate at which the unemployed find jobs + r]

That is, the extra pay people get from work only helps deter dereliction of duty according to the fraction of the sum of all the rates that comes from the detection probability. And the job finding rate depends on the reciprocal of the unemployment rate. So as unemployment gets low, the job finding rate seriously dilutes the effect of the detection probability times the extra that workers get paid.

(The derivation of the equation above uses the rules for dealing with fractions quite heavily, backing up the idea in the WSJ article I tweeted as follows.

The Dividing Line: Why Are Fractions Key to Future Math Success? http://on.wsj.com/15rlupS

Deeper intuition for the equation above would require developing a deeper and more solid intuition about fractions in general than I currently have.)

Solving for the extra pay needed to motivate workers yields this equation:

(wage - unemployment benefit)

= dollar cost of effort per unit time

· [detection rate + rate at which diligent workers leave their jobs                              + rate at which the unemployed find jobs + r]  ÷

detection rate

In labor market dynamics the rates are high, so a flow-in-flow-out steady state is reached fairly quickly, and we can find the rate at which the unemployed find jobs by the equation flow in = flow out, or since in equilibrium the firms keep all their workers motivated,

rate at which diligent workers lose jobs * number employed

= rate at which the unemployed find jobs * number unemployed.

Solving for the rate of job finding:

rate at which the unemployed find jobs

= rate at which diligent workers leave their jobs

· number employed  ÷  number unemployed

Finally, it is worth noting that

rate at which diligent workers leave their jobs

+ rate at which the unemployed find jobs

= rate at which diligent workers leave their jobs

· [number unemployed + number employed]/[number unemployed]

= rate at which diligent workers leave their jobs

÷ unemployment rate

Morgan Warstler’s Reply: The original link in the column about Morgan Warstler’s plan was to a Modeled Behavior discussion of his plan. Here is a link to Morgan Warstler’s own post about his plan. Morgan’s reply in the comment thread is important enough I will copy it out here so you don’t miss it:

1. The plan is not Dickensian. It allows the poor to earn $280 per week for ANY job they can find someone to pay them$40 per week to do. And it gives them the online tools to market themselves.

Work with wood? Those custom made rabbit hatches you wish you could get the business of the ground on? Here ya go.

Painter, musician, rabbit farmer, mechanic - dream job time.

My plan is built to be politically WORKABLE. The Congressional Black Caucus, the Tea Party and the OWS crowd. They are beneficiaries here.

2. No one in economics notices the other key benefit - the cost of goods and services in poor zip codes goes down ;:So the $280 minimum GI check buys 30% more! (conservative by my napkin math) So real consumption goes up A LOT. This is key, bc the effect is a steep drop in income inequality, and mobility. That$20 gourmet hamburger in the ghetto costs \$5, and it’s kicking McDonalds ass. And lots of hipsters are noticing that the best deals, on things OTHER THAN HOUSING are where the poor live.

Anyway, I wish amongst the better economists there was more mechanistic thinking about how thigns really work.