Athreya, Owens, and Schwartzman (2017) (Does redistribution increase output? The centrality of labor supply.)

The goal of this paper is to understand what impacts a redistribution from rich to poor has on short run output. The authors want to understand the mechanisms or model assumptions that lead to quantitatively significant effects.

The standard thinking is that a transfer from rich to poor will stimulate the economy, because in general the poor have a higher marginal propensity to consume out of wealth. The main finding of this paper is that this line of thinking is only correct and significant

Model

Continuum of infinitely lived agents with utility defined over consumption and leisure. Time is discrete. Households differ in initial wealth and labor productivity. Labor productivity is subject to idiosyncratic shocks.

Households can trade in risk free bonds and are subject to an exogenous budget constraint.

There is a unit mass of differentiated goods, each produced by a different firm. Intermediate goods producers operate a liner technology in labor. They sell their goods in a monopolistically competitive market, but are subject to nominal pricing frictions: a constant fraction of randomly chosen firms are allowed to change their price at the beginning of each period. Firms redistribute all profits back to households in equal shares.

The final goods producer combines a CES aggregate of the intermediate goods with physical capital to produce the final good. This final good is used for household consumption, government spending, and investment in capital by the final goods producer.

The government levies lump-sum taxes on households, issues risk free bonds, implements wealth contingent transfers amongst households, and has an exogenous spending level. Government spending is not valued by households or firms. The government’s budget is balanced period by period.

Experiment

With this model in mind, the authors consider how outcomes to a particular experiment change with different assumptions about preferences and technologies.

The experiment is that

• at time 0 the economy is in a steady state where transfers to individuals are 0
• At time one there is an un-anticipated redistribution across agents with different wealth levels. The transfer is revenue-neutral for government.
• At all subsequent periods there are no transfers and the economy settles back into steady state

The experiment was designed to isolate the role of heterogenous marginal propensity to consume that is what motivates the classical argument in favor of redistribution from rich to poor.

Results

Note that capital is pre-determined, so there is no time 1 response in capital. Any response in production of the final good must come through adjustments to labor. So what we are really after is understanding which model features or assumptions generate a change in labor supply or demand in response to the wealth transfer.

The authors consider main different specifications for nominal rigidities, consumer preferences, and the goal of the monetary authority. I’ll talk about a baseline case, then summarize the other main findings.

Consider a case without price frictions (all firms set the same price) and GHH preferences. In this case labor supply will not be altered by the wealth transfer (GHH). If labor supply is the same in periods 0 and 1, and prices can freely move, the market clearing wage will also be the same. When wages, capital, and labor supply are the same, so is output and total expenditure. In other words, the transfer didn’t stimulate the economy.

Now, let’s consider some variations:

• prices are sticky, but the monetary authority achieves stability in aggregate prices. In this case real wages will not change. If real wages don’t change and agents have GHH-like preferences, the transfer will not stimulate output or expenditure.
• Cobb Douglass preferences. In this case we loose the GHH property of no wealth effects of labor supply. The wealth transfer will impact labor supply, which can lead to effects on aggregate output and expenditure. The key factor that determines the size of these aggregate effects is the distribution of propensity to work over the wealth distribution. If the negative transfer to the wealthy entices them to work more than the positive transfer to the poor causes them to choose leisure, output and expenditure will both rise.

That’s the main point of the paper. The authors have a call to action for economists to do empirical studies on the propensity to work as a function of wealth. They argue that understanding this propensity is key to understanding how transfer-like policies will impact the economy.