This analysis is a companion piece to my Atlanta Fed colleague John Robertson's recent macroblog post. John's blog highlighted some findings of a recent New York Fed study by Samuel Kapon and Joseph Tracy on the employment-to-population (E/P) ratio. Their work has received considerable attention in the media and blogosphere (for example, here, here, and here). Kapon and Tracy's final chart (reproduced below) has received particular scrutiny.
The blue line represents the authors' estimate of the demographically adjusted E/P ratio purged of business-cycle effects. This line can be thought of as "trend." The chart shows that as of November 2013, the E/P ratio was only –0.7 percentage point below trend. Was the "gap" between actual and trend E/P really this small?
Attempting to answer this question requires digging into the details of Kapon and Tracy's method for estimating trend. One key excerpt is the following:
To overlay our demographically adjusted E/P ratio with the actual E/P ratio, we need to adopt a normalization… [W]e adopt the normalization that over the thirty-one years in our data sample [1982–2013] any business-cycle deviations between the actual and the adjusted E/P ratios will average to zero.
This methodology seems reasonable since one might typically expect business cycle effects to average out over 30 years. However, the 1982–2013 sample period is somewhat unusual in that the unemployment rate was elevated at both the starting and ending points.
The chart below shows estimates of three labor market gaps derived from the Congressional Budget Office's (CBO) estimates—released on February 4, 2014—of the potential labor force and the long-term natural rate of unemployment. (This rate is often referred to as the nonaccelerating inflation rate of unemployment, or NAIRU, and refers to the level of unemployment below which inflation rises.)
On average, the trend E/P ratio is below the actual rate by 0.86 percentage point. If one were to normalize the Kapon and Tracy E/P trend so that its average value was equal to CBO's trend, then the November 2013 E/P gap is about 1.5 percentage points. Whether or not the CBO estimate is the right benchmark is a matter of taste. CBO's recent estimate of NAIRU in the fourth quarter of 2013—5.5 percent—is lower than the 6 percent median estimate from the Survey of Professional Forecasters in the third quarter of 2013.
A second, more subtle issue in the Kapon and Tracy analysis is their treatment of cohorts:
We divide these individuals into 280 different cohorts defined by each individual's decade of birth, sex, race/ethnicity, and educational attainment. We assume that individuals within a specific cohort have similar career employment rate profiles. We use the 10.2 million observations [of CPS microdata] to estimate these 280 career employment rate profiles.
A well-known 2006 Brookings paper by Stephanie Aaronson and other Fed economists modeled trend labor force participation rate(LFPR) using birth-year cohorts. With estimates of trend LFPR and NAIRU, we can back out a trend E/P ratio. The chart below, adapted from Aaronson et al., plots age-group LFPRs against birth year.
We see that successive birth-year cohorts born between 1925 and 1950 had steadily increasing labor force attachment. Attachment for more recently born cohorts has leveled off and even declined slightly. People born in the 1990s have very low labor force attachment by historical standards. The inclusion of the "1990s—decade of birth" dummy variable in the Kapon and Tracy research probably implies that their model is interpreting much of this decline as structural. However, an alternative interpretation is that the decline is cyclical, because persons born after 1990 have been in an environment of high unemployment for most of their short working lives.
To gauge the sensitivity of trend or structural LFPR to how the youngest cohorts are treated, I used a stripped-down version of a model similar to Aaronson et al. Monthly LFPRs are modeled as a function of age, sex, birth date, and the CBO's estimate of the output gap during the January 1981 to January 2014 period. Time series published by the U.S. Bureau of Labor Statistics for 30 different age-sex cells are used so that the regression has 11,550 observations. Structural LFPR is constructed with the fitted values of the regression with a value of 0 percent for the output gap at all points in time. The trend E/P ratio is then backed out with the CBO's estimate of NAIRU.
The model is run with two different assumptions: First, following the approach of Aaronson et al., people born after 1986 have the same birth-year cohort effects as those born in December 1986. Second, no constraints are placed on birth-year cohort effects. Trend values of LFPR and E/P (taking on board the CBO's NAIRU) are plotted in the two charts below:
The January 2014 E/P gap with unconstrained cohort effects, as in Kapon and Tracy, is –1.0 percent, well below the –1.7 percent gap in the model with constrained cohort effects. Ultimately, both models are still very consistent with Kapon and Tracy's bottom line:
It is important to control for changing demographic factors when looking at the behavior of the E/P ratio over time. This step is particularly important today when these demographic factors are exerting downward pressure on the actual E/P rate, suggesting that the recent lack of improvement in the E/P ratio does not imply a lack of progress in the labor market. The adjusted E/P rate corroborates the basic picture from the unemployment rate that the labor market has been recovering over the past few years, but that it still has a ways to go to reach a full recovery.
By Pat Higgins, senior economist in the Atlanta Fed's research department