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FEDS Notes

June 2, 2014

The effect of labor slack on wages: Evidence from state-level relationships


Christopher L. Smith

Introduction
Over the past several years, increases in most broad measures of wages have been quite muted, which many would consider symptomatic of weak demand for labor.  For example, in a recent speech,1 Chair Yellen suggested that, in addition to a variety of other labor market measures, wage growth may also be an important indicator for assessing the health of the labor market.2   By contrast, a distinct body of research argues that, regardless of the recent behavior of wages and prices, underlying inflationary pressures may be greater than one would expect based on the aggregate unemployment rate alone, in part because much of the still-elevated unemployment rate is attributable to the long-term unemployed (LTU), who by some estimates appear to exert less downward pressure on prices and wages than the short-term unemployed (STU). However, this inference is primarily based on analysis that uses the aggregate time-series relationship between STU, LTU, and wages or prices over the last few decades, and the aggregate STU and LTU rates have exhibited significant co-movement over this period.  More recently, inference using aggregate data is highly dependent on interpretation of the atypical movements of these variables during the last five years.

In this Note, I use cross-state variation in measures of labor slack and wage growth to estimate the historical relationship between STU, LTU, other measures of labor under-utilization, and wages.  In contrast to the studies that use aggregate data, I find a very similar relationship between a state's STU rate and wage inflation and a state's LTU rate and wage inflation, suggesting that, on average, the STU and LTU exert similar wage pressure and that the LTU should not be significantly discounted as an indicator of labor slack. These findings are robust across time periods and wage measures.  Additionally, I find suggestive evidence that some categories of non-participants also exert some downward wage pressure and might therefore be candidates for explicit inclusion in measures of labor slack used for assessing wage and price pressures.

Recent research on the relationship between labor market slack and inflation
Recent research has examined whether various measures of labor slack should be treated differently for considerations of wage or price pressures or in defining the notion of "full employment"--in particular, whether the LTU should be discounted to some extent from measures of unemployment because many LTU may be structurally unemployed and exert less wage or price pressure than the STU.3   For example, for wage or price Phillips Curves using aggregate data, in which inflation is regressed against its lag and measures of labor slack, some have found that the STU rate matters more (in an economic and statistical sense) than the LTU rate, and that wage and price forecasts using the STU rate in place of the aggregate unemployment rate perform better over recent history.4 

Despite this evidence, some other recent work disputes the idea that the LTU should be strongly discounted from measures of labor slack.  For example, Hatzius and Stehn (2014) demonstrated that inflation forecasts for the last few years do not perform better using the STU rate in place of the total unemployment rate, once one limits analysis to data since the late 1990s and accounts for price shocks such as food and energy prices.5   More generally, because the STU and LTU rates (and other aggregate measures of labor slack) have moved so closely together for much of the last few decades, it is likely difficult to statistically distinguish the inflationary effects of these various measures using aggregate data.  This observation has motivated research exploiting cross-regional variation.  For example, Kiley (2014) uses cross-city variation in CPI price inflation, STU rates, and LTU rates to show that the STU and LTU have historically exerted similar pressure on prices, and Blanchflower and Posen (2014) show that the wage level in a state is negatively related to both the unemployment rate and the non-participation rate, suggesting that over the last few decades, some element of non-participation influences the wage level.6 

Defining state-level wage inflation
In this analysis, I use microdata from the Current Population Survey (CPS) to compute state-level measures of annual wage inflation and measures of labor market slack.7 Wage information is asked for all employed respondents in the outgoing rotation groups (interview months 4 and 8) of the monthly CPS survey.  Using these data, for each state I estimate the annual percent change in its nominal median wage,8 along with the following measures of labor market slack: the unemployment rate, STU and LTU rates, the share of the employed who are part-time for economic reasons (PTER), the labor force participation rate (and non-participation rate), and the share of the population that are non-participants but report wanting jobs, are marginally attached to the labor force, or are discouraged job seekers. I describe the exact definition of these measures in greater detail later.

Estimating the relationship between wage inflation and measures of unemployment
I estimate the relationship between the percent change in annual wages and measures of labor market slack with versions of the following ordinary least squares regression:

\displaystyle \pi^w_{s,t} = \beta(slack_{s,t}) + \gamma\pi^w_{s,t-1} + \delta Z_{s,t} + \alpha_s + \theta_t + \epsilon_{s,t}    

In this regression equation,  \pi_{s,t}^w is the nominal percent change in median wages for state  s in year  t;  slack_{s,t} is a measure (or multiple measures) of labor market slack for state  s in year  t , and Z are additional controls for  s in  t ;  \alpha_s are state-specific fixed effects; and  \theta_t are year-specific fixed effects. In most theoretical specifications, wages depend on expectations and slack is measured as a "gap", i.e. relative to some structural level. As state-level expectations of wages or prices are unavailable, and estimating the structural level of state-level measures of slack is infeasible given the noisiness of the data, I control for these omitted variables with age group, gender, and education population shares, state and year fixed effects, and in some specifications, state-specific time trends.

Table 1 presents coefficient estimates (and associated standard errors) for select variables.9 To begin, I estimate over the full 1985-2013 period. Over this time, there is a strong, negative association between a state's unemployment rate and wage growth (column 1). Splitting the unemployment rate into LTU and STU over this period (column 2), the coefficients on the STU and LTU rates are very similar, and statistically indistinguishable from each other and from the coefficient on the total unemployment rate. Because some states are on different economic trajectories over this period that may be related to the evolution of wages and unemployment, I include state-specific time trends to control for any slowly evolving differences (column 3), and again the coefficients on the STU and LTU rates remain very similar to each other. Next, I limit the sample to the 1994-2007 period, dropping recessionary (and later) years and dropping the 1980s, as some have speculated the unemployment/price relationship has changed since the 1980s.10 Again, the coefficients on the STU and LTU rates are fairly similar, though statistically indistinguishable from each other or from the total unemployment rate.

Table 1: State-level regressions of annual wage growth on measures of unemployment
(1) (2) (3) (4) (5)
Dependent variable: Annual percent change in state median hourly wage
Coeff. on state-level RHS variables (all divided by labor force and mult. by 100):
Unemp. -0.56*** -0.63***
(0.07) (0.18)
STU -0.60*** -0.50*** -0.54
(0.13) (0.16) (0.36)
LTU -0.50*** -0.41* -0.82
(0.15) (0.23) (0.52)
p-value, test for coeffs STU=LTU 0.68 0.80 0.74
Time period 1985-2013 1985-2013 1985-2013 1994-2007 1994-2007
State time trends No No Yes No No

Note: Observations are at the state-year level and weighted by the state 15+ population. The sample size for regressions in columns 1-3 is 1,479 (50 states and D.C., 29 years), and 714 in columns 4 and 5 (14 years). Standard errors clustered at the state-level are in parentheses. Statistical significance at the 10, 5, and 1 percent level is indicated by one, two, or three stars, respectively. All regressions include state and year fixed effects, lagged percent change in state median wages, and other demographic controls as indicated in the text. For equations that include the STU and LTU rates, the p-value for the Wald test of equality of the coefficients is presented in the bottom line of the table. Data for all variables are author's estimates, derived from the BLS's publicly available CPS microdata.

 

Estimating the relationship between wage inflation and other measures of labor slack
Although canonical wage and price regressions generally use versions of the unemployment rate as the measure of labor slack, it may be that some persons out of the labor force (OLF) nevertheless have sufficient attachment to the labor force to also influence wages.11 To explore this possibility, I include various categories of non-participation and the PTER rate in similarly-specified wage regressions. Table 2 presents these estimates. All variables are now divided by the state population so that the coefficients have comparable interpretations (e.g. a one percentage point increase in the listed variable as a share of the population).

Table 2: State-level regressions of annual wage growth on measures of labor slack
(1) (2) (3) (4) (5)
Dependent variable: Annual percent change in state median hourly wage
Coeff. on state-level RHS variables (all divided by pop. and mult. by 100):
Unemp. -0.20
(0.42)
STU -0.71** -0.45 -0.58* 0.08
(0.27) (0.33) (0.32) (0.36)
LTU -0.67* -0.55 -0.37 0.64
(0.34) (0.33) (0.48) (0.59)
Out of labor force (OLF) -0.08
(0.08)
OLF, don't want job -0.03 -0.03 -0.08 0.01
(0.08) (0.08) (0.08) (0.15)
OLF, want job -0.80**
(0.36)
OLF, want job, discouraged -3.19 -2.83 -4.75**
(2.15) (1.98) (2.07)
OLF, want job, marg. attached, not disc. 1.45 2.09 5.12***
(1.27) (1.33) (1.83)
OLF, want job, not marg. attached -1.19** -1.62*** -2.01***
(0.53) (0.54) (0.63)
Part-time for econ. reasons -1.76*** -1.82***
(0.43) (0.52)
p-value, test for coeffs STU=LTU 0.95 0.85 0.74 0.39
Time period 1994-2013 1994-2013 1994-2013 1994-2013 1994-2007

Note: Observations are at the state-year level and weighted by the state 15+ population. The sample size for regressions in columns 1-4 is 1,020 (50 states and D.C., 20 years), and 714 in column 5 (14 years). Standard errors clustered at the state-level are in parentheses. Statistical significance at the 10, 5, and 1 percent level is indicated by one, two, or three stars, respectively. All regressions include state and year fixed effects, lagged percent change in state median wages, and other demographic controls as indicated in the text. For equations that include the STU and LTU rates, the p-value for the Wald test of equality of the coefficients is presented in the bottom line of the table. For definitions of labor slack measures, see the text. Data for all variables are author's estimates, derived from the BLS's publicly available CPS microdata.

 

Column 1 includes the STU and LTU rates and the non-participation rate. Again, the STU and LTU appear to exert similar influence on wage inflation, and non-participants in the aggregate appear to have little influence on wages. In column 2, non-participants are split into those wanting a job and those not wanting a job. The fraction of the population that is OLF but wants a job (who are likely more attached to the labor market) is negatively related to wage growth, whereas the fraction OLF but doesn't want a job has no relation to wage growth.

Column 3 splits OLF persons who want a job into three mutually exclusive categories: discouraged former job seekers, persons marginally attached to the labor force who are not discouraged, and OLF persons who want a job but aren't classified as marginally attached.12 Many of these measures of labor slack are highly correlated within and across states, so identifying the individual effects of these measures is difficult. Likely as a consequence of this multi-collinearity, when including all of these measures simultaneously, most coefficients are statistically insignificant.13 Nevertheless, in this regression, the STU and LTU, and fractions of discouraged job seekers and OLF who want a job but aren't marginally attached are negatively associated with wages.

Column 4 adds the PTER share to the regression, which is negatively associated with wage growth. However, the coefficients on STU and LTU are now positive and imprecise, though this is likely because of significant multi-collinearity in the regression, reflecting fairly strong correlation between the PTER rate and measures of unemployment (particularly after 2007). In fact, even after limiting the sample to pre-recession years (column 5), multi-collinearity still appears to limit the usefulness of this approach. Indeed, the aggregate unemployment rate--which should be meaningfully related to wages--enters with a small and imprecisely estimated coefficient, further evidence that it is difficult to simultaneously infer much about the individual influence of these various measures on wages.14

Conclusion
Some have argued that the unemployment rate may overestimate labor market slack, because the LTU are largely structurally unemployed and exert significantly less wage and price pressure. If so, then using the aggregate unemployment rate to forecast wage or price inflation may be misleading. However, this Note, along with the companion note showing that a state's LTU rate normalizes as its STU rate normalizes, and the cross-city inflation-based evidence presented in Kiley (2014), suggest against the idea that the LTU should be strongly discounted from measures of labor market slack.

This Note also provides some suggestive empirical support for possibly considering broader measures of labor market slack, such as those including non-participants who may be somewhat attached to the labor market, when assessing wage and price pressures. However, despite the empirical advantage that cross-state variation provides, it is still difficult to disentangle the separate effect on wages from various measures of slack, as many of these measures are closely related within and across states. Nevertheless, taken as a whole, these findings suggest that the LTU should not be strongly discounted from measures of slack, because they traditionally exert similar wage pressures as the STU. Moreover, because some segments of those not in the labor force also appear to generally apply downward pressure to wages as well, the unemployment rate may somewhat understate the degree of labor slack that matters for aggregate wage and price movements.



1.  "What the Federal Reserve Is Doing to Promote a Stronger Labor Market," Federal Reserve Chair Janet Yellen, March 31, 2014. Return to text

2.  In a companion FEDS Note ("Using Cross-state Variation to Assess the Potential for Additional Improvement in Measures of Labor Market Conditions"), I used cross-state variation to show that, as a state's short-term unemployment rate moved towards its pre-recession level, other measures of labor market conditions--such as the long-term unemployment rate and share of workers part-time for economic reasons--also normalized to some degree.  Following the Bureau of Labor Statistics, I define short-term unemployed as persons unemployed 26 weeks or less, and long-term unemployed as persons unemployed 27 weeks or more. Return to text

3.  The most common argument is that the LTU are structurally unemployed due to skills mismatch or skills depreciation, or because employers discriminate against LTU job applicants (even if they are observationally equivalent along other dimensions). Return to text

4.  For example: Krueger, Cramer, and Cho, "Are the Long-Term Unemployed on the Margins of the Labor Market?" Brookings Panel on Economic Activity, March 20-21, 2014; Gordon, "The Phillips Curve is Alive and Well: Inflation and the NAIRU during the Slow Recovery," NBER Working paper #19390, August 2013. Return to text

5.  Hatzius and Stehn, March 28, 2014. "Slack and Inflation: Not So Fast," Goldman Sachs Economic Research, US Economics Analyst Issue No: 14/13. Return to text

6.  Michael T. Kiley, 2014, "An Evaluation of the Inflationary Pressure Associated with Short- and Long-term Unemployment," Board of Governors of the Federal Reserve System, Finance and Economic Discussion Series 2014-28; Blanchflower and Posen, April 15 2014. "Wages and Labor Market Slack: Making the Dual Mandate Operational." PIIE Policy Brief draft, http://www.iie.com/publications/pb/pb14-10draft.pdf. Return to text

7.  All estimates are derived from the BLS's publicly available CPS microdata. Return to text

8.  Because wages are top-coded in the publicly available microdata (large responses are censored at some upper limit), my primary measure of wages is the median wage (topcoding should affect the average, not median). For workers who report being paid by the hour, I take their wage to be their reported hourly wage; for other workers, I impute their hourly wage as usual weekly wages divided by usual weekly hours. I have also tried using alternative state-year wage measures, such as the average weekly wage from the BLS's Quarterly Census of Employment and Wages, and the BEA's state-level annual estimates of the level of wages and salaries. However, these are not hourly wage measures and depend in part on average hours per week or employment, which may vary with the cycle and be correlated with wage growth. Nevertheless, using these alternative wage measures, I still find that the coefficients on the STU and LTU are similar. Return to text

9.  For ease of exposition, only the coefficients on the unemployment rate and STU and LTU rates are shown. Return to text

10.  I begin estimation starting in 1994 because additional measures of labor slack, which will be considered in the next section, are only available in the CPS for this period. Return to text

11.  Indeed, Hatzius and Stehn (2014) use aggregate data to show that the U6 rate--a broader measures of slack, which include some non-participants and PTER workers--does a better job empirically of explaining wage inflation than the STU rate or aggregate unemployment rate. Return to text

12.  Following the BLS's definition, marginally attached persons are those out of the labor force who are currently not looking for work, but indicate that they want and are available for a job, and have looked for work sometime in the past 12 months. Discouraged persons are marginally attached persons who reported a job-market related reason for not currently looking for work. Return to text

13.  For example, for the pre-recession years, the correlation between STU, LTU, the potential worker rate, and the share of marginally attached or discouraged persons was between 0.5 and 0.7. Return to text

14.  This is likely why, in the Federal Reserve Bank of Atlanta's macroblog post on April 17, 2014 ("Using State-Level Data to Estimate How Labor Market Slack Affects Wages"), researchers conclude from a cross-state analysis (including data from 2007-2013) that the STU and PTER rates--but not the LTU rate--are negatively related to wages.  Indeed, as the findings from Table 2 suggest, their conclusion may be driven by the inclusion of post-recessionary years (for which the cross-state correlation between PTER and LTU jumps significantly), making it difficult to separately distinguish the effects of PTER from other measures of slack. Return to text

Disclaimer: FEDS Notes are articles in which Board economists offer their own views and present analysis on a range of topics in economics and finance. These articles are shorter and less technically oriented than FEDS Working Papers.

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Last update: June 2, 2014