## Monday, December 16, 2013

### Figuring Worst-Case Unemployment

Part five in a series that starts here.

 Graph #1: Actual and Hypothetical Unemployment Source: Erceg and Levin, via John Taylor
By "worst-case" unemployment I don't mean the worst that one can possibly imagine. I mean the worst we can reasonably expect, based on estimates and projections made by BLS and other agencies engaged in that sort of thing.

Anyway, my intent here is not to tell another discouraging story. My intent is to look at one of the discouraging stories that's out there, so as to better understand it. So as to get a feel for the validity of that story, or the lack of validity.

To duplicate the worst-case unemployment graph I need to rework the Labor Force Participation Rate. Rather than letting it fall rapidly, as it has, I want it to fall slowly, as the November 2007 BLS projection anticipated. I'm trying to mimic the negligible decline of unemployment shown in the red line on Graph #1 here, and I think the BLS number will help me get there.

A plan finally came together in my head, an overview of what I want to do:

First, use the Labor Force Participation Rate and the 2007 BLS projection to come up with numbers showing how big the labor force was expected to be, before things fell apart. Call it the Hypothetical Labor Force Participation Rate.

Second, work backwards from there to get numbers for the Hypothetical Labor Force.

Third, subtract the number of employed people from the Hypothetical Labor Force, to get the hypothetical number of unemployed persons. Use this number to determine the Hypothetical Unemployment Rate.

That's the plan.

### Step One

I went back to FRED for quarterly data on the three series used to generate the graph for Friday's post:

• Civilian Labor Force (CLF16OV)
• Civilian Noninstitutional Population (CNP16OV)
• Civilian Labor Force Participation Rate (CIVPART)

The November 2007 BLS projection (which we looked at yesterday) predicted an annual growth rate of -0.1 percent for the 2006-2016 period. A very slight decline.

I figured a quarterly growth rate that would give an annual rate of -0.1 percent. Then I took the first quarter 2006 value and, starting from there, applied my quarterly growth rate to generate the numbers.

Checking my work: BLS projected a participation rate number of 65.5% for 2016. I got 65.43% for first quarter 2016, 65.38% for fourth quarter. So I tweaked my quarterly growth rate to get the same 65.5% number that BLS got. I'm calling this number the Hypothetical Labor Force Participation Rate.

Check my work.

### Step Two

To figure the Labor Force Participation Rate (LFPR) you take the Civilian Labor Force (CLF) as a percent of the Civilian Noninstitutional Population (CNP):

You can rearrange that formula to see CLF in terms of population and participation rate:

Now I just use the Hypothetical Labor Force Participation Rate in place of the official version. The hypothetical is a significantly higher number, so it produces a significantly higher Civilian Labor Force. I am calling this number the Hypothetical Civilian Labor Force.

Check my work.

### Step Three

Okay. Now I need some more data. I need the number of people employed, so I can calculate the Hypothetical Number of Unemployed Persons. Then, using that number and the Hypothetical Labor Force I can figure the Hypothetical Unemployment Rate. And I will need the official unemployment rate, for comparison to the hypothetical number. These are numbers we looked at on Saturday.

I went back to FRED for the relevant numbers, quarterlies, and put 'em in a new spreadsheet along with my Step Two results.

The number of people in the labor force, less the number working, is the number of people out of work. Or in this case, the Hypothetical Labor Force less the number Employed equals the number of Hypothetical Unemployed.

And then, the number of Hypothetical Unemployed, as a percent of the Hypothetical Labor Force, equals the Hypothetical Unemployment Rate.

 Graph #2 Check my work

I think I duplicated their graph!