3 Age Adjusting our Data

Age adjustment is a statistical procedure used to compare data for populations that have different age structures. It is meant to eliminate the confounding effects of age when comparing rates of events (like disease, death, injury, etc.) across different populations, or in our case, over time. In effect, it standardizes age structure across populations so we can ensure that trends/differences in our statistics do not emerge ONLY from the fact that one population is older/younger than the other.

3.1 Why do we age adjust our data?

Older people more often have disabilities, and the U.S. population is older on average than it was a decade ago. We age adjust our data to ensure that the changes we observe in the disability rate are NOT due only to the fact that the American population is older in 2025 than it was prior to the pandemic. When we age adjust, we standardize the age structure of the US population to a base year (2019).

Note: In this project, we standardize both the age and sex structure of the population. The sex adjustment does virtually nothing to our results because the sex distribution of the population has not changed significantly over time.

Age Adjusted or Age-Sex Adjusted?

You’ll notice that the “main analysis” is age-sex adjusted, but almost all of the breakdowns are just age adjusted. That is out of laziness on my part (sorry 😔😔). But as I said above, the sex adjustment does virtually nothing.

3.2 How do we age adjust our data?

To age-adjust our data, we first calculate age-specific rates for our statistic of interest. We then determine the share of the population that is each age for a base year (2019). For each age, we multiply its specific rate by its share of the 2019 population. Finally, we sum these products to get the age-adjusted rate.

Take the disability rate as an example.

  • We begin by calculating the share of the population in our base year that is each age. For this project, we use 2019 as a base year. Let’s call this \(S_i\), where \(i\) is age. Then, \(S_{18}\) is the share of the population in 2019 that is 18.
  • Next, we calculate the labor force participation rate for each specific age and for each year-month date in the CPS (recall that the CPS is a monthly survey and we want to accurately compare data over time). Let’s call this \(P_{i,t}\) where \(i\) is age and \(t\) is a variable for time. Then, \(P_{18,2009/2}\) is LFPR for 18-year-olds in February 2009.
  • To age adjust, we need to multiply the age-specific participation rate by that age’s population share in the base year:
    • \(S_18*P_{18,2009/2}\)
  • The age adjusted participation rate is the sum of this product for every age:
    • \(\sum_{i=1}^{n} S_i*P_{i,t}\)
  • We calculate this rate for each \(t\), the year-month date. We use the age-specific participation rates for each year-month date, but always the age shares from 2019.

Again, keep in mind that our data is also sex adjusted (it’s the same procedure but with two age distributions (one for each gender)).

3.2.1 Age Adjusting Our Population Breakdowns

To age-adjust for population subgroups–such as by educational attainment–we calculate separate age distributions for each group. Take education as an example: if we want to examine disability incidence among individuals whose highest level of education is a high school diploma, we need to fix the age structure of that specific subgroup. To do so, we calculate the age distribution of the population with a high school diploma in 2019 and use those age shares to weight our data. We would use a separate age distribution for the population that has a college degree, or no high school degree, or some college, etc.