The equations that I use for incorporating inflation into the effective demand model are based on the relationship of labor share of income, inflation and unit labor costs.

labor share = unit labor costs/inflation

But does the data actually fit this equation?

Here is a graph of the 3 indices since 2004. (labor share and unit labor costs based on business sector. Inflation based on All items less food and energy.)

I won't go into the dynamics of how they relate. I only want to show if the above equation actually fits the data in this graph.

Here is the data of the graph plotted into a spreadsheet.

In the first four columns we have actual data from the graph above, which includes the observation dates. The last column to the right takes the unit labor costs index and divides it by the inflation index * 100. The result should be the labor share index. We then compare the last two columns for labor share by graphing the difference between them.

We can say that the lines in this graph are fairly close. And considering that we are 8 years out from 2005, which is the base year for the indices, and the lines are almost equal, we can confirm the equation above. The data for labor share, inflation and unit labor costs does follow the equation.

We can actually use the equation to double-check the accuracy for all 3 indices. If the indices don't match up just perfectly, then one, two or all 3 of them are off a little. The accuracy gets critical when we want to predict the end of a business cycle, or when we determine the interest rate for monetary policy. We need to know that the labor share index from which we calculate effective labor share (labor share index * 0.78) is correct. We could adjust the index of labor share up or down by looking at unit labor costs and inflation.

Just one last thing to say. You will see that I use effective unit labor costs in some equations. This is calculated by multiplying the unit labor cost index by 0.78, the same conversion for labor share. I am just maintaining consistency between the indices. The basic equation for being "effective" is...

inflation = effective unit labor costs/effective labor share

inflation = (unit labor costs index * 0.78)/(labor share index * 0.78)

## Comments

You can follow this conversation by subscribing to the comment feed for this post.