# A model for low inflation due to low unit labor costs and labor share

Inflation is low and has been declining for years. I want to present a model to explain a dynamic between inflation and unit labor costs.

First let’s look at a chart of the two of them over the years. (semi-annual data, % change from year ago) They move together with more noise in the unit labor costs (blue line). I hope you notice that unit labor costs tend to peak before a recession. That is an important clue to seeing the connection between the two, because the natural level of output is reached before a recession.

### Setting up the model

The model to explain this effect is an alternative version of the AS-AD model (aggregate supply – aggregate demand). The model uses effective demand instead of aggregate demand. So it is the AS-ED model. I am the only one who has ever used it.

The AS-ED model still puts price level on the y-axis and output on the x-axis. Yet the AS curve and the ED curve have different equations than what is normally seen.

Inflation rate for AS curve = ulce(3400 + real GDP – Potential real GDP)/(3400 * cu) – 1

Inflation rate for ED curve = real GDP * ulce/(ED*cu*(1-u)) – 1

Both equations use unit labor costs (ulc). In this model, the effective unit labor cost is used, which is the index of ulc * 0.76. I won’t go into this conversion here. cu is capacity utilization. u is the unemployment rate. ED is the effective demand limit. 3400 is a business cycle amplitude constant in 2009 billion dollars. Potential real GDP refers to the center of the business cycle and is determined by effective labor share.

Note: Inflation rate for AS curve uses real GDP on x-axis. As real GDP increases, inflation would rise holding all else equal. Inflation rate for ED curve uses effective demand (ED) on x-axis. As ED increases, inflation rate would fall holding all else equal. The model looks like a normal AS-AD model. Yet the lines always cross at the LRAS curve, which is the natural level of output. In the first graph above I pointed out that the natural level of output is reached before a recession. These lines determine that natural level.

GDP moves with the AS curve below the ED curve. GDP does not like to rise above the ED curve. Profits decrease. The implication is that inflation is thus limited below the ED curve. So when we drop unit labor costs, holding all other variables constant, the top limit upon inflation drops.

As unit labor costs fall, the natural level of output does not change, but the inflation limit of the economy will fall. So as we see in the first graph, the trend of lower unit labor costs has brought down the inflation upper limit.

I will point out that unit labor costs have a connection to labor share too. I add yearly % change of labor share in this graph. In some years, the movement of unit labor costs (blue line) moves with inflation (red line) and in other years moves with labor share (green line). We could generally say that when inflation expectations are low or falling, unit labor costs tend to move with labor share.

### The result is stubborn low inflation

Currently we have a situation where labor share has been falling since 2001. Inflation expectations are still low, even though they are higher than actual inflation. Unit labor costs are trending low with labor share. Unit labor costs went negative after the last 2 recessions. The effective demand limit is weighing down upon inflation as shown by the AS-ED model. The result is a dynamic for stubborn low inflation.

### Lowering wages is not the solution

The problem is that business has the attitude that it must lower unit labor costs. Here is common advice to small businesses from an online source… (Bryan Keythman)

“An increase in your small business’ unit labor cost means your productivity is decreasing. Productivity is the efficiency with which you generate output using certain inputs. The increase in unit labor cost may result in higher expenses compared to revenue. Unless you decrease other expenses or increase your selling prices to increase your revenue, your profit will decrease. Investigate the cause to determine how you can decrease your unit labor cost and regain your previous level of productivity.”

The statement in bold is wrong… decreasing unit labor costs does not mean raising productivity. It may just mean lower wages.

unit labor costs = wage rate / productivity

It is true that raising productivity will lower unit labor costs, but many businesses just hold down wage increases thinking that will increase productivity. But that is not correct.

The key is to raise productivity, which many times involves raising compensation to workers… as this video refreshingly shows. (from Labor Performance) The video says that it is a “common misconception that if you pay more money, your labor costs go up.”