## 12 March 2016

### Demographically Adjusting Working Age Employment

I've mentioned in the past that my preferred indicator of economic slack is the employment to working age population rate (or, equivalently, the employment rate of people between the age of 15 and 64). This measure is a lot better than the employment to population ratio for obvious reasons: it takes aging into account, which serves to explain the lack of employment growth since 2008; most of the decline in the employment to population ratio since the Great Recession is secular and solely happened because of older people retiring.

The employment to working age population ratio is not without its own problems though. Perhaps the biggest of these is the fact that it fails to take into account women entering the labor force during most of the twentieth century. Because of this, the employment to working age population ratio is skewed downward between 1970 and 1990 and skewed upward in the 1990's (because women entering the labor force enables some men to leave it).

In order to solve the gender problem, I decided to try to remove the skew created by women entering and men leaving the labor force. First, I took the male employment to working age population ratio and postulated a linear downward trend. I then determined the cyclical gap in male employment and assumed that women would experience the same cyclical underemployment as men. From this, I could determine 'equilibrium' female employment and determine a trend.

I postulated that the trend for female employment would be quadratic -- it would increase quickly at the beginning of the time series and then level out (this is technically more logarithmic, but the logarithmic function had a terrible fit). This matched pretty well with the data, so I now had a trend value for female employment.

It was now possible to determine demographically adjusted female employment by taking the actual employment rate and adding the gap between the 'full employment' rate (which I assumed to be about 80%, the male employment rate in 1990) and the trend employment rate. The same process could be done to the male employment rate and the linear downward trend.

Now, with the demographically adjusted female and male employment rates, I could determine the full demographically adjusted rate. Given that
$$\frac{E_m}{WAP_m}\frac{WAP_m}{WAP} + \frac{E_f}{WAP_f}\frac{WAP_f}{WAP} = \frac{E_t}{WAP}$$
where $E_{gender}$ is [gender] employment and $WAP_{gender}$ is [gender] working age population, I could simply multiply each gender's adjusted employment rate by their percentage of the total working age population.

Here is the demographically adjusted employment rate:
And here is the non-demographically adjusted measure: