1. Background
Despite a broad recovery of the U.S. economy from the depths of the Great Recession, lingering slack remains in the labor market. In particular, statistics estimated using the Current Population Survey (CPS) show that while the unemployment rate--the most prominent indicator of labor market conditions--has retreated from its 2009 high of 10 percent to 5 percent, the fraction of Americans working part time for economic reasons (PTER) remains relatively elevated.² Measurement of underemployment, i.e., working fewer hours than one is willing to, has important implications for understanding labor market conditions and the strength in the broader economy.³ In this note, we show that PTER substantially underestimates underemployment along the dimension of hours people are actually working--relative to the numbers they would prefer to work at current wages.

Textbook economic theory suggests that an individual will work until his or her marginal utility of leisure is equal to his marginal utility of consumption multiplied by his or her wage. That is, the individual should be indifferent, at equilibrium, between working an additional hour and earning extra wages compared with spending an hour on leisure activities. By this logic, underemployment occurs when some workers cannot work enough hours to satisfy this indifference condition. Indeed, people who have a full-time job, and thus are not included in the PTER statistics, may desire to work even more hours at their current wage level but are not able to for similar economic reasons that keep other people working only part time even though they would prefer full-time work.

The Bureau of Labor Statistics (BLS) defines PTER as working part time (between one and 34 hours per week) but wanting to work full time and reporting an economic reason such as slack work or unfavorable business conditions, inability to find full-time work, or seasonal declines in demand as the reason for working part time. This indicator, while capturing fairly well the trends in underemployment stemming from work-hour constraints, may understate its levels by excluding workers employed more than 34 hours per week but want to work even more hours than they do. In addition, the CPS data track the same individuals over a relatively short period compared with some other household surveys and have limited information on workers' consumption expenditure and home production.⁴

In this note, we introduce a new survey-based indicator of work-hour constraints that are available in the Panel Study of Income Dynamics (PSID) and the Health and Retirement Study (HRS) . This new indicator sheds light on measuring underemployment, helps tracking workers' transitions into and out of PTER states over the longer term, and enhances our understanding of the causes of and workers' responses to such constraints. We first show that this indicator, for involuntary part-time workers, reveals a trend similar to the PTER rate estimated using the CPS data over the past four decades. We then present evidence of work-hour constraints among a large fraction of full-time workers. Accordingly, the underlying level of underemployment due to work-hour constraints is potentially much higher than the PTER indicates, particularly during recessions. We subsequently present some suggestive evidence regarding the factors that cause work-hour constraints and how workers adjust their time use when encountering such constraints.

2. Indicators of Work-Hours Constraints
We introduce an alternative indicator of work-hour constraints using information collected in two long-running household surveys--the PSID and HRS, both managed by the Institute for Social Research at the University of Michigan. The PSID collected information from a nationwide representative sample of more than 3,000 households annually from 1968 through 1997 and every other year thereafter. The HRS surveyed a representative sample of approximately 20,000 people in America over the age of 50 biennially from 1992 onward. The two surveys collected work-hour-constraint-related information over two distinct periods, covering forty years.

From 1968 to 1986, the PSID asked heads of surveyed households the following questions:

• Would you have liked to work more if you could have found more work?
• Was there more work available on (any of your jobs) so that you could have worked more if you had wanted to?

We count a worker as facing work-hour constraints if he responded that he wanted to, but was not able to, work more hours.⁵ While the PSID discontinued these questions after 1986 due to funding constraints, from 1992 the HRS started asking essentially the same set of questions in its survey. Furthermore, the HRS also asked constrained households what their desired numbers of work hours were, which can be used to study the intensive margins of work-hour constraints. Table 1 summarizes the prevalence and intensity of such constraints and compares constrained households with unconstrained households.

As the table indicates, nearly 20 percent of household heads were unable to work as many hours as desired in an average year between 1968 and 1986 and 45 percent of all heads were subject to work-hour constraints at least once during this period. Over the most recent twenty years, the HRS data suggest that among senior workers (aged 50 and above), these shares are about 10 and 20 percent, respectively. The HRS data also indicate that the average margin of constraints is about nine hours per week (460 hours per annum). Comparing constrained and unconstrained workers, we find that, in both surveys, constrained workers worked fewer hours and earned less income than unconstrained workers.⁶ Notably, we find that among those in the PSID and HRS sample who wanted to work more hours but unable to, 72 and 81 percent, respectively, were working on average more than 35 hours per week, and thus were not captured in the BLS's PTER measure. Indeed, our estimates derived from the HRS data suggest that the additional hours the survey respondents working part-time wanted but were unable to work account for only about one fifth of those for all survey respondents.

3. Comparing the CPS PTER and Panel Data Series
To introduce the PSID and HRS data as useful additional data sources of studying labor market constraints, we show that the overlapping concepts in these two surveys and the CPS are estimated consistently. Specifically, we show that the shares of involuntary part-time workers (those who were upside constrained and working fewer than 35 hours per week) in labor force measured in the PSID and HRS resemble the PTER rates estimated using the CPS data. As shown in figure 1, during the overlapping sample period of 1967 to 1986, the CPS PTER series and the share of involuntary part-time workers in the PSID have very similar levels and fluctuations over business cycles. The correlation of the two series is about 0.66, and 0.5 for the detrended series.

Likewise, as shown in figure 2 the CPS PTER estimates of people older than 55 (a subpopulation comparable to the HRS sample) are also very similar to the share of upside constrained labor force in the HRS, and the two series have a correlation coefficient of near 0.85 (0.74 for the detrended series). In addition, the CPS PTER estimates of the entire population (the black series) shared a very similar trend as the estimates of those aged 55 and above.⁷ All told, the PSID and HRS appear to have measured involuntary part-time work in a way consistent with the CPS PTER.

Figure 3 contrasts the broader measure of work-hour constraints with the PTER series. The most striking difference is that the overall prevalence of upside hour-constraints seen in both the PSID and HRS is much higher than the PTER rates, and such a gap is quite stable over the past several decades. Second, despite the sizable gaps in their levels, the PSID and HRS work-hour-constraint estimates are highly correlated with the CPS PTER series over the respective overlapping period.⁸

4. New Insights the Survey Data May Provide
Because both the PSID and HRS are longitudinal surveys that run for multiple decades and both collect rich information on household socioeconomic and demographic characteristics, labor market experience, and health status, they can shed new light on labor market work-hour constraints. We offer three examples of the new analysis using the PSID and HRS data.⁹ First, we can study the longer-term persistence of work-hour constraints, beyond what can be done using the matched CPS data. For example, table 2 shows that the upside hour constraints are quite persistent over time. Specifically, half of the workers who are constrained in a given year will continue to be constrained next year, and the odds do not appear to diminish with the duration of being constrained.¹⁰

Second, the panel structure of the data allows us to investigate the factors associated with the constraints and their relative economic significance. For example, we estimate a logistic model of transitioning into being work-hour constrained on changes in family compositions, family income and wage rate variations, and other labor market status changes using the PSID data. The results indicate that having an additional child in the family is not predictive for such constraints (holding earnings constant), while reductions in family income or increases in wage rates are associated with a greater likelihood of being work-hour constrained. This is suggestive that constrained individuals are constrained for economic rather than non-economic reasons. However, more work is needed to further establish the causal factors of work-hour constraints.

Finally, we can explore how workers react to such constraints. Specifically, for those who cannot work as many hours in the labor market as they desire, we consider whether they increase hours on housework and home production. Both surveys offer two ways of measuring home production. First, households were asked the number of hours they spent on housework in a given year, and second, households reported expenditures separately on food consumed at home and food eaten out at restaurants. We use the ratio between eating out and total food expenditures as an approximation of home production, with more eating-out indicating less home production. We find that, in a number of different model specifications, not being able to work as many hours as desired is associated with a greater number of household work hours and a lower share of eating out. Specifically, we estimate that, on average, work-hour constrained household heads spent about 25 more hours in housework during the year and had an eating-out share one percentage point lower.¹¹

5. Conclusions
This note introduces a novel data source for measuring work-hour constraints that helps shed light on underemployment among the full-time employed. We show that two surveys--the PSID and HRS--yielded PTER estimates that are fairly close to the trend derived from CPS data, but at a much higher level. Indeed, our analysis suggests that part-time workers, as defined by the CPS' PTER, may only account for one fifth of the total additional hours that workers wanted to work but were unable to. Further research is needed to understand underemployment dynamics among the full-time employed and the policy implications. As a recent example, in June 2015, the Obama administration announced regulations to raise the maximum weekly salary under which workers are eligible to receive overtime pay (1.5 times their normal wage rate) from $455 to $970.¹² This policy change is likely to lead more full-time workers to want to work more hours.

References:
Canon, Maria, Marianna Kudlyak , Guannan Luo, and Marisa Reed (2014) "Flows To and From Working Part Time for Economic Reasons and the Labor Market Aggregates During and After the 2007-09 Recession," Economic Quarterly, Richmond Fed, Second Quarter, 2014

Cajner, Tomaz, Dennis Mawhirter, Christopher Nekarda, and David Ratner (2014), "Why is Involuntary Part-Time Work Elevated?" FEDS Notes, April 14, 2014.

Li, Geng (2009), "Do Constraints on Market Work Hours Change Home Production Efforts?" Federal Reserve Finance and Economics Discussion Series 2009-21.

Valletta, Rob and Catherine van der List (2015) "Involuntary Part-Time Work: Here to Stay?" FRBSF Economic Letter, June 8th, 2015.

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Please cite this note as:
Li, Geng and Brett McCully (2016). "Is Underemployment Underestimated? Evidence from Panel Data," FEDS Notes. Washington: Board of Governors of the Federal Reserve System, May 16, 2016, http://dx.doi.org/10.17016/2380-7172.1775.