Simon Wren-Lewis wrote about Aggregate Demand and the Labour Market. He shows that an aggregate demand constraint can keep employment from reaching its natural rate. He is essentially describing Keynes' effective demand in his post. So I have made 2 changes to his title in the title of this post. I have changed aggregate demand to effective demand. Also I have changed the spelling of labour to labor, which is the American way to spell it. (When I was young I used to spell it labour because of my family's Canadian background.)
He presented a graph with real wages on the y-axis and labor on the x-axis. He then drew the normal supply and demand curves in the labor market. The two lines cross at the natural rate of employment. Then he drew a vertical line to the left of the crossing point showing an aggregate demand constraint that can keep employment from reaching the natural rate.
I determine effective demand by labor share. I will change his graph by putting labor share on the y-axis instead of real wages. Then you not only reflect real wages but also the inverse relationship to productivity. What would the diagram look like with labor share on the y-axis?
Real wage = labor share * productivity
Labor share = real wage/productivity
So in my graph, if you hold productivity constant, the demand and supply curves are the same as Mr. Wren-Lewis'.
The labor share of natural employment
In this graph, the horizontal dashed line shows that the current labor share will allow the labor market to clear at the natural rate of employment.
Yet, you might be asking about productivity. How does productivity fit in?
The data shows that productivity will increase when labor employment falls to the left of the effective demand vertical line (green). But when labor employment returns to the vertical line, productivity stops increasing. So at the effective demand limit (green line) his graph and my graph are essentially the same.
That makes sense because being more productive at the effective demand limit creates production that may not be sold at a sticky real wage. So we solve a portion of the productivity puzzle there.
Now what happens if labor share falls below this natural level?
We move down the labor supply curve, people drop out of the labor force and there is less overall employment. Employment will not return to its natural level because the effective demand limit based on labor share moved left. Mr. Wren-Lewis makes the same case. Moving up the labor demand curve, firms would be willing to hire that level of labor at a much higher labor share, but they are enjoying greater profits, so why fix something that is not broken.
The solution is to raise labor share back up to the level where we find the natural rate of employment. The key to that is raising real wages as productivity becomes sticky at the effective demand limit which is below full employment.
Now what if labor share is above the natural employment level?
Employment still falls below its ideal natural level. Yet, now more workers are willing to work. If the power of workers in this situation is great enough to demand more work, we might firms hiring more workers beyond the green effective demand limit. This could represent part of the 1960's and 1970's when employment was pushed higher and inflation resulted.
To summarize, labor is employed at whichever is lower, labor demand or labor supply. Since labor share has fallen over 6% since the crisis in the United States, this model explains the decrease in labor force participation and the lower level of employment.
UPDATE: The ultimate solution is to give labor more power to bargain a higher labor share. If labor is weak, firms have a profit incentive to keep labor share low.