Ljungqvist and Sargent (2011) (A Labor Supply Elasticity Accord?.)

Here Ljungqvist and Sargent explain both sides of a long debated issue regarding labor supply elasticity (percent change in labor supply divided by percent change in wages) and then describe a relatively new idea that has the potential to reconcile the opposing views. The main argument from the micro-and-labor-economics camp is that the labor supply elasticity is quite low for individuals in the work force. On the other hand, macroeconomists typically say that the aggregate labor supply elasticity is large.

The classic way to reconcile these two seemingly opposing viewpoints is to allow labor supply to respond sharply on the extensive margin. This will allow workers to continue to have a small elasticity while they are working, but as individuals move in and out of work more freely the aggregate labor supply elasticity is driven up.

The benchmark way to model this flavor of environment is to follow Rogerson and use employment lotteries with perfect, competitive insurance markets for unemployment. The basic idea is that households are composed of families. Each family will choose a probability with which each of its members works in that period. If the realization of the lottery is positive, that individual supplies full labor to the market and receives wages. If the realization is negative they supply zero labor. The family then purchases an insurance claim that pays a specified amount of the consumption good if a member of the family receives a bad outcome from the employment lottery. The insurance market is competitive, which results in all agents having equal consumption after lotteries have been realized and insurance claims paid out. In this setting agents who work supply the maximum amount of labor regardless of the wage, meaning the micro labor supply elasticity is small. However as wages change, households will adjust the probability that each family member works, causing there to be some elasticity on the extensive margin.

This is commonly referred to as an aggregation theory. Micro economists have issue with this particular aggregation theory because they cannot find evidence that these sort of employment lotteries exist.

Ljungqvist and Sargent then go on to explain a new way of thinking that seeks to unify the rhetoric regarding labor supply elasticity. The main idea is that instead of thinking about the labor supply choice as a lottery played out amongst family members in a household, we can think of it as an individual making a binary labor supply decision at every instant of their life. One natural interpretation of this type of setting is that there is a lifecycle component to the model, where after some date agents enter retirement and do not supply labor any more, regardless of the wage. The fraction of the lifetime spent working has been termed the career length of the individual.

It turns out that for an interior solution for labor supply probability in the Rogerson model is identical to interior solutions for career length, when the discount factor equals the market rate of return in a deterministic setting. This means that same results for micro and macro labor supply elasticity that held in the Rogerson setting continue to hold in this lifecycle model. There are two last points I’ll make about this:

1. This type of aggregation theory has been better received by labor economists. They consider the career length choice more plausible than the employment lottery choice.
2. This does not settle the debate about whether the macro (aggregate) labor supply elasticity should be large or small: the theory could support either argument.

Recall that I said the lifecycle career-length choice was equivalent to the employment probability lottery, at interior solutions. The behavior is somewhat different at the corners.

For our discussion we can think of an agent being on corner solution as an agent who is incentivized to retire at a certain age. If a large portion of the workers in an economy are on a corner, then when wages move the aggregate response in labor supply will be dampened (people can’t come out of retirement)) and the aggregate labor supply elasticity will be low. On the contrary, if there are relatively few agents at the corner, the aggregate labor supply elasticity will be high.

The measure of agents at a corner will be crucially impacted by the government policies regarding targeted retirement age, retirement benefits or payments, and how they are financed.

Ljungqvist and Sargent conclude by suggesting that a promising area for new research will look at how to reform taxation and disability/retirement payments to minimize the deadweight loss associated with distorting the labor supply decision through taxes.