Why labor force participation (usually) increases when unemployment declines.

Hornstein, Andreas

During the Great Recession, the unemployment rate increased rapidly within two years from about 4 percent in 2007 to about 10 percent in 2009. Yet over the ensuing recovery, the unemployment rate has declined only gradually and, more than four years after the end of the recession, it now stands at about 7 percent. At the same time, the labor force participation rate has declined steadily over this time period and now stands at about 63 percent, a level comparable to the early 1980s. Many observers view the decline in the labor force participation rate as an indication that further declines in the unemployment rate will come only slowly. The expectation is that if the labor market improves, many participants who have left the labor market will return and contribute to the pool of unemployed, and many unemployed participants will no longer exit the labor force but continue to search for work. (1)

Past business cycles have indeed been characterized by a negative correlation between the unemployment rate and the labor force participation (LFP) rate, that is, as the unemployment rate declines, the LFP rate increases. In this article we use observations on gross flows Content not available due to copyright restrictions.

[FIGURE 1 OMITTED]

In this article we argue that observations on transition probabilities obtained from gross flow data are inconsistent with the IU hypothesis. In fact, the opposite is true: As the labor market improves, unemployed workers become more likely to exit the labor force and inactive workers become less likely to join the labor force as unemployed. This pattern for IU transitions would result in a positive correlation between the unemployment rate and the LFP rate. The observed negative correlation between unemployment and LFP must then result from patterns in the EU and IE group transition rates. We calculate the contributions of cylical variations in the transition rates for the three groups--IU, IE, and EU--and indeed find that the variations in the IE and EU group transition rates generate a negative co-movement of the unemployment and LFP rates that dominates the positive co-movement generated by the IU group transition rates. This suggests that an increasing LFP rate is more the by-product of an improving labor market rather than a brake on the declining unemployment rate.

This article is based on a line of research that accounts for changes in labor market ratios through changes in the rates at which labor market participants transition between labor market states. Early work in this literature mostly ignored variations in the LFP rate and focused on variations in transition rates between the two labor market states--employment and unemployment--for example, Elsby, Michaels, and Content not available due to copyright restrictions. they are not employed, whether they want to work and are actively looking for work. The latter are considered to be unemployed, and employed and unemployed household members constitute the labor force. Household members that are not employed and that are not actively looking for work are considered to be not part of the labor force, or inactive for short. The unemployment rate is the share of unemployed workers in the labor force, and the LFP rate is the share of the labor force in the working age population. (5)

The unemployment rate tends to be more volatile than the LFP rate in the short run, but changes in the LFP rate tend to be more persistent over the long run. Figure 2, panels A and B, display quarterly averages of monthly unemployment and LFP rates for the period from 1948 to 2012. The unemployment rate increases sharply in a recession, and then declines gradually during the recovery. Shaded areas in Figure 2 indicate periods when the unemployment rate is increasing, and these periods match periods of National Bureau of Economic Research (NBER.) recessions quite wel1. (6) Even though the average unemployment rate appears to be somewhat higher than usual in the 1970s, considering the magnitude of short-run fluctuations in the unemployment rate, the average unemployment rate does not change much over subsarnples of the period. The 2007-09 Great Recession stands apart by the magnitude of the increase of the unemployment rate and the rather slow decline of the unemployment rate from its peak.

The LFP rate does not display much short-run volatility, rather it is dominated by long-run demographic trends. Starting in the mid-1960s, the LFP rate increased gradually from values slightly below 60 percent to reach a peak of 67 percent in 2000. This slow but persistent increase of the LFP rate can be accounted for by the increasing LFP rate of women and early on by the baby boomer generation entering the labor force. Since 2000, the LFP rate has declined, first gradually, then at an accelerated rate since the Great Recession and is now at about 63 percent. The gradual decline in the LFP rate can be attributed to the aging of the baby boomer generation and declining LFP rates for women and the young (less than 25 years of age). (7) In general, there is not much short-run volatility in the LFP rate, the recent accelerated Content not available due to copyright restrictions. aftermath significantly increases the measured volatility of the unemployment rate and LFP rate, but, again, it does not much affect the measured negative correlation between the two variables. (12) Finally, the cyclical co-movement between unemployment and LFP is similar for men and women, but the unemployment rate is relatively more volatile for men, the LFP rate is relatively more volatile for women, and the LFP rate is lagging the unemployment rate more for men than for women.

We now study if this negative correlation between the unemployment rate and the LFP rate can be accounted for by inactive workers becoming more likely to enter the labor force and unemployed workers becoming less likely to exit the labor force.

2. TRANSITIONS BETWEEN LABOR MARKET STATES

The CPS household survey not only contains information on how many people are employed, unemployed, and inactive in any month, but it also contains information on how many people switch labor market states from one month to the next. We can use these gross flows between labor market states to calculate the probabilities that any one household member will, within a month, transition from one labor market state to a different state. This information can be used to see if, for example, variations in the transition rates between inactivity and unemployment are consistent with the usual interpretation of the negative co-movement of the unemployment rate and the LFP rate.

Households are surveyed repeatedly in the CPS. In particular, the survey consists of a rotation sample, that is, once a household enters the sample it is surveyed for four consecutive months, then it leaves the sample for eight months, after which it reenters the sample and is once more surveyed for four consecutive months. Thus, in any month, for three-fourths of the household members in the sample, we potentially have observations on their current labor market state and their state in the previous month. We can use this information to calculate the gross flows between labor market states from one month to the >Content not available due to copyright restrictions. be unemployed in the next month. Regions that are (not) shaded denote periods when the unemployment rate increases (declines). The trend for each transition probability is calculated using the same band-pass filter as in the previous section, and it is displayed as a dashed line in Figure 3. In Table 2, we display the average transition probabilities, the standard deviations of the detrended transition probabilities, and their cross-correlations with the detrended unemployment rate for the total working age population, and for men and women separately.

[FIGURE 3 OMITTED]

An increase in the unemployment rate is associated with more churning in the labor market: Employed workers are more likely to Content not available due to copyright restrictions. major source of unemployment volatility. Looking at panels IU and UI, we can see that as the unemployment rate declines, it becomes more likely that an unemployed worker exits the labor force and less likely that an inactive worker joins the labor force as unemployed. This pattern is confirmed by the cross-correlations for the detrended rates in Table 2. Thus, the cyclical pattern of the transition rates between inactivity and unemployment is exactly the opposite of what the IU hypothesis proposes as an explanation of the negative correlation between the LFP rate and the unemployment rate. However, the transition probabilities between inactivity and employment do have a cyclical pattern that supports a negative co-movement between the unemployment rate and the LFP rate. As the unemployment rate increases it becomes less likely that people make the transition from inactivity to employment. It also becomes less likely that employed workers leave the labor force, but this probability is always quite low and it is not very volatile over the cycle. The cyclical properties of the transition probabilities for all three groups, EU, IU, and IE, are roughly the same for men and women. The only exception is that transition probabilities for women tend to be somewhat less volatile overall, and that men's transition probabilities from employment to inactivity appear to be acyclical.

So far we have shown that the direct evidence on labor market transitions does not support the IU hypothesis of why the LFP rate increases as the unemployment rate declines. In particular, as the labor market improves and the unemployment rate declines, participants become less likely to make the transition from inactivity to unemployment and they become more likely to make the transition from unemployment to inactivity. So what accounts for the negative correlation of unemployment and the LFP rate?

3. SOURCES OF CO-MOVEMENT

Recent research on labor markets using the stock-flow approach points to the importance of variations in the job finding rate and job loss rate for the determination of the unemployment rate. We now argue that variations in the job finding and job loss rates are also important for the cyclical co-movement between the unemployment and LFP rates. As a first step, note that the exit rate from the labor force is an order of magnitude smaller for employed workers than it is for unemployed workers (see Table 2). This means that as the unemployment rate declines, the average exit rate from the labor force declines, and the LFP rate increases. Furthermore, as we have just seen, when the unemployment rate declines, more people join the labor force without Content not available due to copyright restrictions. lines). (17) These are the three counterfactuals for the trend deviations of the unemployment rate and LFP rate, and they approximately add up to the overall trend deviation of the two rates. In Table 3, we calculate the cross-correlations between the counterfactual unemployment and LFP rates implied by these experiments.

Table 3 Cross-Correlations between Unemployment Rate and LFP Rate for
Counterfactuals, Deviations from Trend, 1992:Q1-2007:Q4

                          Corr( u(t), l(t+s) ) for s=

           -4     -3     -2     -1      0      1      2     3      4

UE and   -0.20  -0.40  -0.58  -0.74  -0.87  -0.95  -0.99  -0.97  -0.91
EU

IU and    0.15   0.31   0.48   0.64   0.82   0.89   0.92   0.90   0.84
UI

UE, EU,   0.41   0.37   0.32   0.24   0.23   0.13   0.04  -0.02  -0.07
UI, and
IU

IE and   -0.33  -0.50  -0.66  -0.86  -0.99  -0.83  -0.65  -0.55  -0.43

Actual   -0.10  -0.22  -0.40  -0.55  -0.65  -0.71  -0.70  -0.69  -0.68

Notes: Cross-correlations of trend deviations for the unemployment
rate, u, and the LFP rate, l. The first four rows represent
counterfactuals for u and I, and the last row represents actual
values for u and I. For a counterfactual all monthly transition
rates, except for the ones listed in the counterfactual column, are
kept at their trend values. Statistics are calculated for quarterly
averages of counterfactual monthly time series. Detrended
unemployment rate and LFP rate are level deviations from trend.

Past research has shown that variations in the transition probabilities between employment and unemployment are a major determinant of the unemployment rate, e.g., Shimer (2012) or Elsby, Hobijn, and Sahin (2013). This observation is confirmed by Figure 4, panel A, in that variations in these probabilities account for a substantial part of the unemployment rate variation. Figure 4, panel B, demonstrates that these variations also introduce substantial volatility into the LFP rate. In fact, the counterfactual LFP rate is more volatile than the actual LFP rate. Furthermore, variations in the transition probabilities between employment and unemployment generate a strong negative Content not available due to copyright restrictions. to their steady-state values, u* respectively l*,

u* = [[lambda].sub.EU] / [[lambda].sub.EU] + [[lambda].sub.UE] and l* = [[1 + [[lambda].sub.UI] / [[lambda].sub.IU]u].sup.-1].

In the data, monthly unemployment and LFP rates tend to be close to the steady-state values implied by their monthly transition rates.

This special case illustrates three points. First, the unemployment rate would be independent of transitions between the labor force and inactivity, if it was not for transitions between inactivity and employment. Similar to a simple two-state model of the labor market that ignores variations in the LFP rate, the unemployment rate would be determined by the transition rates between employment and unemployment. Second, even with an unemployment rate that is "exogenous" to the LFP rate, the LFP rate does depend on the unemployment rate and transition rates between unemployment and inactivity. In particular, a lower unemployment rate implies a higher LFP rate, which helps generate the observed negative correlation between the unemployment rate and the LFP rate. Third, the observed cyclical movements in the transition rates between unemployment and inactivity imply that the ratio of [[lambda].sub.UI] to [[lambda].sub.IU] is decreasing as the unemployment rate u increases, thereby introducing a positive correlation between the unemployment rate and the LFP rate and dampening the co-movement. Thus, transitions between employment and inactivity have to be considered if one wants to account for the co-movement between unemployment and LFP.

4. CONCLUSION

Many observers of the U.S. labor market perceive the LFP rate to be below its long-run trend and the unemployment rate to be above its long-run trend. In fact, the low cyclical LFP rate is seen as keeping the cyclical unemployment rate from being even higher, because poor employment prospects have induced discouraged unemployed workers to leave the labor force and have prevented marginally attached inactive participants from a return to the job search. In this article, we have documented that direct observations on transition rates between unemployment and out-of-the-labor-force are inconsistent with this perception. It turns out that at times of high unemployment, unemployed workers are less likely to exit the labor force and inactive workers are more likely to return to the labor force as unemployed. This pattern would have introduced a positive correlation between cyclical movements of the unemployment rate and the LFP rate. Yet we have observed a negative correlation between the two rates. We have shown Content not available due to copyright restrictions. people in labor market state i at time t -- 1 is

[s.sub.i, t - 1] = [summation over k] [f.sub.ik, t] = [summation over k] [f.sub.ik, t-2]. (1)

The probability that a participant makes the transition from state i in period t -- 1 to state j in period t is simply

[p.sub.ij,t] = [f.sub.ij, t] / [s.sub.i, t-1]. (2)

The unemployment rate and LFP rate are

[u.sub.t] = [s.sub.U,t] / [s.sub.U,t] + [s.sub.E,t] and [l.sub.t] = [s.sub.U,t] + [s.sub.E,t] / [s.sub.U,t] + [s.sub.E,t] + [s.sub.I,t]. (3)

Conditional on initial values for the stocks, [s.sub.i0], we can obtain the sequence of future stocks from the sequence of transition probabilities by iterating on the equation

[s.sub.i,t] = [summation over k][p.sub,ji,t][s.sub.j,t-1]. (4)

This defines a mapping from the sequence of transition probabilities, p, to the sequence of stocks, s,

s = G (p; [s.sub.0]), (5)

conditional on initial stocks so. Suppose we have a series for the trend transition probabilities, [p.sub.ij,t.sup.T]. Then we can use the above mapping to construct the implied trend values for stocks

[s.sup.T] = G([p.sup.T]; [s.sub.0]), (6)

and we calculate the implied trend values for the unemployment rate and LFP rate, [u.sup.T] and [l.sup.T].

In order to evaluate the contribution of a group of transition probabilities to the overall variation of the unemployment rate and LFP rate, we simply construct a counterfactual path for the stocks where we keep all but the probabilities of interest at their trend values and set the probabilities of interest to their actual values. For example, in order to evaluate the contribution of variations in the k-th transition probability, we construct the series

[s.sub.k.sup.CF] = G([p.sub.k], [p.sub.-k.sup.T]; [s.sub.0]) (7)

with implied series for the unemployment rate and LFP rate,[u.sub.k.sup.CF] and [L.sub.k.sup.CF]. The contribution of the k-th probability to unemployment rate variations is then defined as [u.sub.k.sup.CF] - [u.sup.T].

The actual implementation of the procedure in Section 3 is slightly more complicated in that we allow for inflows and outflows to the working age population, and we replace the discrete time month-to-month Content not available due to copyright restrictions. steady-state unemployment rate and LFP rate is a bit messy, but it simplifies considerably if we assume that transitions between in- and out-of-the-labor-force have to proceed through unemployment, that is, [[lambda].sub.EI] = [[lambda].sub.IE] = 0. For this case we find that the steady-state unemployment rate and LFP rate are

u* = [[lambda].sub.EU] / [[lambda].sub.EU] + [[lambda].sub.UE] and l* = [[1 + [[lambda].sub.UI] / [[lambda].sub.IU]u].sup.-1].

For this special case, the unemployment rate is independent of transitions between the labor force and inactivity. Similar to a simple two-state model of the labor market that ignores variations in the LFP rate, the unemployment rate is determined by the transition rates between employment and unemployment. On the other hand, the LFP rate does depend on the unemployment rate and transition rates between unemployment and inactivity. In particular, a lower unemployment rate implies a higher LFP rate, which helps generate the observed negative correlation between the unemployment rate and the LFP rate. From Section 2 we have that the transition rates from unemployment to inactivity (inactivity to unemployment) are negatively (positively) correlated with the unemployment rate. This would imply that the LFP rate increases as the unemployment rate increases. Thus, the movements in the transition rates between in- and out-of-the-labor-force alone would yield a counterfactual positive correlation between the unemployment rate and the LFP rate.

This is a. revised version of an article previously titled "The Cyclicality of the Labor Force Participation Rate." I would like to thank Marianna Kudlyak, John Muth, Felipe Schwart man, and Alex Wolman for helpful comments. .Any opinions expressed are those of the author and do not necessarily reflect those of the Federal Reserve Bank of Richmond or the Federal Reserve System. E-mail: andreas.hornstein@rich.frb.org.

REFERENCES

Aaronson, Stephanie, Bruce Fallick, Andrew Figura, Jonathan Pingle, and William Wascher. 2006. "The Recent Decline in the Labor Force Participation Rate and Its Implications for Potential Labor Supply." Brookings Papers on Economic Activity 37 (1): 69-134.

Content not available due to copyright restrictions.

Abowd, John M., and Arnold Zenner. 1985. "Estimating Gross Labor-Force Flows." Journal of Business & Economic Statistics 3 (July): 254-83.

Frazis, Harley J., Edwin L. Robison, Thomas D. Evans, and Martha A. Duff. 2005. "Estimating Gross Flows Consistent with Stocks in the CPS." Monthly Labor Review 128. (September): 3-9.

Fujita, Shigeru, and Garey Ramey. 2009. "The Cyclicality of Separation and Job Finding Rates." International Economic Review ,50 (2): 415-30.

Hatzius, Jan. 2012. "Still Lots of Slack in the Labor Market." US Economics Analyst 12/41. New York: Goldman Sachs Economics Research (October 12).

Hodrick, Robert J., and Edward C. Prescott. 1997. "Postwar U.S. Business Cycles: An Empirical Investigation." Journal of Money, Credit, and Banking 29 (February): 1-16.

Poterba, James M., and Lawrence H. Summers. 1986. "Reporting Errors and Labor Market Dynamics." Econometrica 54 (November): 1,319-38.

Shimer, Robert. 2012. "Reassessing the Ins and Outs of Unemployment." Review of Economic Dynamics 15 (April): 127-48.

Tankersley, Jim. 2013. "Vanishing Workforce Weighs on Growth." Washington Post (April 6). Available at www.washingtonpost.com/business/economy/vanishing-workforce-weighs-on-growth/2013/04/06/2bc46116-9e20-11e2-9a79-eb5280c81c63_story.html?tid=pm_business_pop.

Toossi, Mitra. 2012. "Labor Force Projections to 2020: A More Slowly Growing Workforce." Monthly Labor Review 135 (January): 43-64.

(1.) For example, see Daly et al. (2012), Hatzius (2012), Davidson (2013), or Tankersley (2013).

(5.) Households are asked about other fat their labor market status, but the questions about employment and active search for work when not employed are the main questions of interest for determining the unemployment rate mid the LFP rate. For a detailed description of the survey and the methods used, sec Bureau of Labor Statistics (2012).

(6.) The business cycle dates provided by t he NBER are a widely accepted measure of the peaks and troughs of U.S. economic activity.

(7.) For example, see Aaronson et al. (2006). unemployment rate and the LFP rate. We calculate transition rates from data on gross flows for I he period after 1990, and again we discard some of the beginning and end of sample data on deviations from trend to minimize the problems arising from an ill-defined trend.

(12.) Related to the discussion in footnote 9, we should note that if the unemployment rate continues to decline, then future measures of the trend unemployment rate that include these data points will indicate a lower trend unemployment rate I hatt do our current measures. Thus, our current measure very likely understates the cyclical deviations from trend for the unemployment rate.

(17.) Since our trend is a symmetric moving average filter, we face a problem at the beginning and end of our sample period (see footnote 9). If for this part of the sample the deviations from a presumed trend are very large, such as is the case for the years 2007 12, then this problem is even more pronounced and our adjustment to the filter will understate deviations from trend. For this reason, we replace the calculated trend values from 2008 on with the trend values in the fourth quarter of 2007. This essentially keeps the trend unemployment rate fixed at 6.2 percent and the trend LFP rate fixed at 65.5 percent from 2008 on. Thus, our procedure is likely to overstate deviations from trend from 2008 on, especially for the LFP rate.

Table 1 Cyclicality of Unemployment and Labor Force Participation

Sample           [[sigma].sub.u]  [[sigma].sub.l]

                                                     -4    -3

                                            Total

1952:Q1-2007:Q4          0.89         0.29         -0.09  -0.20

1952:Q1-1991:Q4          0.93         0.31         -0.09  -0.19

1992:Q1-2007:Q4          0.79         0.21         -0.08  -0.21

1992:Q1-2013:Q1          0.98         0.33          0.08  -0.07

                                             Men

1952:Q1-2007:Q4          1.01         0.28        -0.03  -0.18

1952:Q1-1991:Q4          1.04         0.28        -0.09  -0.22

1992:Q1-2007:Q4          0.92         0.27         0.14  -0.03

1992:Q1-2013:Q1          1.19         0.41         0.07  -0.09

                                            Women

1952:Q1-2007:Q4          0.77         0.36        -0.16  -0.22

1952:Q1-1991:Q4          0.81         0.40        -0.13  -0.20

1992:Q1-2007:Q4          0.65         0.23        -0.26  -0.30

1992:Ql-2013:Ql          0.77         0.32         0.07  -0.04

Sample                      Corr(u(t), l(t + s)) for s=

                   -2      -1     0      1      2      3      4

1952:Q1-2007:Q4   -0.30  -0.38  -0.45  -0.52  -0.55  -0.54  -0.48

1952:Q1-1991:Q4   -0.29  -0.37  -0.43  -0.49  -0.53  -0.51  -0.44

1992:Q1-2007:Q4   -0.39  -0.55  -0.65  -0.71  -0.70  -0.69  -0.68

1992:Q1-2013:Q1   -0.24  -0.41  -0.53  -0.63  -0.70  -0.75  -0.75

1952:Q1-2007:Q4   -0.30  -0.39  -0.45  -0.52  -0.55  -0.55  -0.48

1952:Q1-1991:Q4   -0.34  -0.41  -0.46  -0.52  -0.55  -0.53  -0.44

1992:Q1-2007:Q4   -0.27  -0.48  -0.61  -0.70  -0.74  -0.77  -0.77

1992:Q1-2013:Q1   -0.27  -0.45  -0.57  -0.67  -0.73  -0.78  -0.78

1952:Q1-2007:Q4   -0.28  -0.34  -0.37  -0.42  -0.45  -0.43  -0.37

1952:Q1-1991:Q4   -0.25  -0.32  -0.35  -0.41  -0.45  -0.43  -0.36

1992:Q1-2007:Q4   -0.38  -0.43  -0.43  -0.46  -0.38  -0.35  -0.31

1992:Ql-2013:Ql   -0.17  -0.29  -0.39  -0.49  -0.58  -0.63  -0.64

Notes: Standard deviations and cross-correlations of detrended
unemployment, u, and labor force participation rate, l. for total,
men, and women. The trend for each variable is calculated as a
Baxter and King (1999) bandpass filter with periodicity more than
12 years for monthly data, from January 1948 to March 2013.
Unemployment and LFP rate are in percent, and detrended values
are the difference between actual values and trend. Statistics
are calculated for quarterly averages of monthly data for the
indicated subsamples.