On the Determinants of Employer Demand for Part-Time Workers

On the Determinants of Employer Demand for Part-Time WorkersAuthor(s): Mark MontgomerySource: The Review of Economics and Statistics, Vol. 70, No. 1 (Feb., 1988), pp. 112-117Published by: The MIT PressStable URL: http://www.jstor.org/stable/1928156 .

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NOTES

ON THE DETERMINANTS OF EMPLOYER DEMAND FOR PART-TIME WORKERS

Mark Montgomery*

Abstract-This paper uses a survey of private establishments to examine the determinants of the firm's relative demand for part- and full-time workers. The elasticity of substitution of part-time for full-time workers is about 1.5, considerably lower than previous estimates with aggregate data. The results indicate that the quasi-fixed labor costs have a negative impact on the proportion of part-timers in a firm's work force.

Introduction

Nearly one-fifth of the U.S. labor force voluntarily works less than 35 hours per week (Deuterman and Brown (1978)). Though there has been substantial analysis of the individual's choice between part-time and full-time work, particularly among women (Jones and Long (1980), Morgenstem and Hamovitch (1976)), very little study has been made of the firm's choice between part-time and full-time workers. The only statistical analysis of demand for part-time labor was conducted by Owen (1978) who used CPS data on individuals to examine how relative wages and other factors influenced the proportion of part-time workers in each of a set of industry/occupation categories. No statistical study of demand for part-timers has yet been conducted with data on individual employers.

This paper uses the results of a 1980 survey of more than 5000 private establishments to examine the determinants of an employer's choice between part-time and full-time workers. Section I provides a theoretical framework for examining this issue and section II presents empirical models of the probability that a firm will use part-time workers and of the proportion of the firm's labor force which works part-time.

I. Theoretical Framework

The combination of part- and full-timers which a firm hires will depend upon the relative cost of providing labor services with each type of labor. The relative labor cost will be determined by the relative wages of part and full-timers, the per-person labor cost, and the rela-

tive productivity of part-timers and full-timers in the job. Below we consider these factors in turn.

Rosen (1978) shows that workers of a given quality sort themselves into a set of interconnected markets each related to a different work schedule. The equi- librium wage structure among these markets yields a function relating wages to hours of work. In a competi- tive labor market this function is parametric to the firm. Characteristics of the firm and the job to be filled will determine which wage-hours combination the firm selects. For example, firms which invest more heavily in training will favor longer shifts. The relative cost of part- and full-timers, however these are defined in terms of relative weekly hours, will depend upon the slope of the wage-hours function, which will in turn depend on the demographic structure of the labor force. For example, an increase in the proportion of part-time job seekers will lower wages for short-hours jobs relative to long-hours jobs.

Oi (1962) demonstrated that in addition to hourly wages, firms bear per-person (quasi-fixed) costs of labor. Quasi-fixed costs comprise (i) the administrative cost of supervising and maintaining records for each worker; (ii) the cost of searching for, hiring, and training a new worker; and (iii) those components of fringe benefits which are unrelated to hours worked. Higher quasi-fixed costs should reduce the proportion of part'timers at a firm. Replacing one full-timer with, say, two half-timers involves twice the level of quasi-fixed cost. In his model of demand for part-timers Owen (1978) posited a distribution of jobs in order of rising quasi-fixed cost and derived a critical level of these costs below which level jobs go to part-timers and above which they go to full-timers. The higher is the median level of quasi-fixed cost for the jobs in this distribution, the smaller is the proportion of jobs going to part-timers.

The distribution of quasi-fixed cost is related to vari- ous characteristics of the firm. Because firms tend to invest less in training low-skill production and clerical workers than those in high-skill positions, firms with high proportions of low-skill jobs will find part-timers relatively more attractive. The size of the firm may also influence quasi-fixed cost because large firms may experience higher supervisory costs per worker. Heavily unionized firms may endure higher administrative and supervisory costs due to formalized rules and proce- dures for transferring, disciplining or firing workers.

Received for publication August 27, 1986. Revision accepted for publication May 14, 1987.

*Mount Holyoke College. I would like to thank Irene Powell, Robert Robertson, Mike

Podgursky, Paul Swaim, Kathy Krynski, June Lapidus and two anonymous referees for helpful comments. All remaining er- rors are mine.

[ 112 ] Copyright (C 1988



NOTES 113

TABLE 1. -PART-TIMERS AS A PERCENTAGE OF WORKERS IN SKILL CATEGORY: MEANS FOR ESTABLISHMENTS HIRING SOME PART-TiMERS (proportion of establishments in cell hiring part-timers)

Size of All No. of Establishmenta Managers Sales Craft Clerical Operators Laborers Skills Establishments

1-20 53.4 63.0 66.3 59.4 64.6 72.2 32.2 2869 (0.05) (0.11) (0.17) (0.07) (0.07) (0.20) (0.47)

21-50 38.0 34.4 42.6 38.1 43.1 49.9 18.4 742 (0.05) (0.09) (0.22) (0.07) (0.10) (0.33) (0.51)

51-100 24.7 37.0 30.7 33.5 36.9 42.4 14.8 395 (0.09) (0.08) (0.28) (0.12) (0.15) (0.35) (0.53)

101-500 18.9 36.0 21.5 30.3 32.8 39.1 15.2 397 (0.07) (0.09) (0.28) (0.08) (0.09) (0.27) (0.46)

over 500 2.4 159b 7.3 5.7b 13.9 23.7b 4.0 82 (0.16) (0.07) (0.34) (0.02) (0.11) (0.16) (0.46)

Note: The total number of establishments was 4,519. aSize is measured in FTE employees. b Cell contains less than 20 establishments hiring part-timers.

Finally, the length of the full-time shift may interact with quasi-fixed cost in determining demand for part- timers. The more part-timers required to replace a full- timer, the greater the extra per-person cost.'

A caveat should be stated regarding the fringe-benefit component of quasi-fixed costs. Part-timers are often ineligible for some benefits. Daski (1974) shows that medical insurance, life insurance and retirement benefits are likely to be offered only to full-timers, while paid holidays and vacations are roughly as likely to be pro- rated by hours worked as offered only to full-timers. Unfortunately, eligibility is difficult to predict because no study has yet been made of which types of firms are likely to offer benefits to part-time workers.

Finally, the relative productivity of part- and full- timers should vary among industries. For example, Owen (1978) argues that part-timers are relatively less attractive in highly capital intensive industries and more attractive in industries where demand varies predictably over the work week (as in retail trade and some service industries). Also, in industries such as retailing and restaurants where operating hours are not easily divided into shifts of standard length, use of part-timers avoids having overlapping shifts of full-time workers.

II. An Empirical Model of Relative Demand for Part- and Full-Time Workers

This section presents an empirical evaluation of the factors affecting (a) whether the firm uses part-timers (in significant numbers) and (b) the proportion of the firm's labor force which is part-time. The first question is examined using a probit model of the likelihood that

part-timers would constitute at least 5% or 10%, respectively, of the firm's work force. Regression analysis was then used to examine the effect of establishment characteristics on the part-time labor force as a percentage of total establishment employment. The estimation was carried out on a usable subsample of 2,509 firms from the survey.2

A. The Data

The data used in this analysis come from a survey of employers, in 28 geographic sites, conducted in 1980 by the Institute for Research on Poverty at the University of Wisconsin. The 28 locations in the survey were Employment Opportunity Pilot Project (EOPP) sites. They overrepresent the Southeast (especially the Gulf Coast) and underrepresent the Northeast. The probability that a firm in a site would be sampled was positively related to the level of employment at the firm. At the time of the interview (first quarter 1980) firms were asked how many part-time and full-time workers (in terms of weekly hours) they employed in each of 6 skill categories during a reference pay period in mid-Decem- ber 1979.

Table 1 reports the mean proportion of part-timers in each of the six skill classes for those establishments hiring some part-timers. The proportion of establishments in each cell which hired some part-timers is in parentheses. Roughly half of the firms in each size category hired some part-timers. For all skill classes, however, the mean proportion of part-timers falls with the size of the establishment. The average weekly hours of part-timers (not shown) was very close to 20 hours

1 It should be noted that because part-time hours are a substitute for full-time hours, we may observe a shorter full-time shift when part-timers are hired even when quasi-fixed costs are not important.

2A large number of firms (about 1500) were excluded because they failed to answer all the questions needed to compute HIRECOST, described below. Rerunning the models without this variable and including the excluded firms has only a minor effect on the coefficients.



114 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE 2.-DEFINITIONS OF INDEPENDENT VARIABLES

Variable a

1. WA GE Ratio of earnings (in %) of part-timers to full-timers at the site 48.8 5.5 (persons with 4 years of high school).a b

2. BENEFIT Ratio of fringe benefits to payroll (industry).b 33.6 3.0 3. HIRECOST Residual from regression predicting log of person-hours spent 0.3 1.5

hiring and training last hired worker. 4. SIZE Log of the number of FTE workers. 2.8 2.7 5. UNION Percentage of non-supervisory workers covered by collective

bargaining agreements. 10.4 27.8 6. SEASON Predicted percent deviation of December employment from

average yearly employment in 2-digit industry at the site. 5 2.6 Predicted by regressing monthly employment on a quadratic 0 time trend and a dummy for December: 1975-1985c

7. OFFICE Percentage of total employee hours worked by office/clerical 17.1 23.2 workers.

8. LABORS Percentage of total employee hours worked by laborers/service 26.8 32.7 workers.

9. FTA VHR Average weekly hours of full-time workers.d 40.5 4.5 10. FT> 40 Equals FTA VHR if FTA VHR > 40, otherwise 0. 8.7 18.4 11. EGROWTH % change in firm employment 7/79-12/79. 0.8 28.3 12. EXPGROW % expected change in firm employment in 2 years. 17.8 36.9 13. MKTSIZE Log of total employment at the site.e 11.4 1.3

Note: Included but not reported in table 3 were (i) a set of industry dummies for durable and nondurable manufacturing, construction, wholesale and retail trade, restaurants, finance, transportation and communications, and (for probit models only) mining and oil & gas; (ii) the local unemployment rate, (iii) dummies for the use of state or industrial category data when local 2-digit data were unavailable for SEASON.

aCensus of Population; Detailed Population Characteristics, table 296, (1980). bEmployee Benefits 1980, Chamber of Commerce of the United States. CIndustry Employment, Hours, and Earnings: States and Areas; Bureau of Labor Statistics. d110 of the establishments in the regression sample hired all part-timers. For these observations, FTA VHR was set at 40. eAmerican Statistical Index; CETA Area Employment and Unemployment Statistics (1979).

per week, and showed little variation across skill categories, size categories, or industries.

Table 2 provides definitions and descriptive statistics for the independent variables used to test the hypotheses developed in section I. Some variables of central interest are discussed here.

We are unable to observe the wage-hours schedule that a firm faces in its local labor market, and our survey did not ask respondents about wages paid to part- and full-timers. The best data available on relative wages were the ratio of weekly earnings of high-school graduates working part-time (34 or fewer hours per week) to those of high-school graduates working full- time at the geographic site. These numbers were taken from the 1980 Census.

It was argued in section I that given a distribution of quasi-fixed cost among jobs at a firm, an increase in the median level of these costs should reduce the proportion of part-timers in the firm's work force. Recruiting and training costs are an important component of quasi-fixed costs. Our survey provided detailed information about the last worker hired by the establishment, including the number of hours spent recruiting and training that individual. This information can be used to draw in- ferences about the median hiring and training costs incurred by the firm.

The cost of hiring the last worker is not itself a good proxy for the median hiring cost. Bishop (1985) shows

that there is a large variation in the amount of time spent training different workers within a firm. Much of the variation in hours spent hiring the last worker would be attributable to the type of job filled (a high-skill job versus a low-skilled one) and the characteristics of the hiree (an experienced worker versus an inexperi- enced one). Therefore, to remove the noise from this variable, the log of the person-hours spent recruiting and training the last worker was regressed on a set of characteristics of that worker and the job for which she was hired. These characteristics included age, sex, education, months of previous job experience, the starting wage of the job, a set of DOT occupation dummies and a set of industry dummies. The residual from that regression represents a measure of whether the firm incurs higher (a positive error) or lower (a negative error) recruiting and training costs than the typical firm hiring a similar worker for the same type of job. This variable is called HIRECOST. Holding constant the skill distribution of the firm's work force, a higher level of HIRECOST should correspond to a higher median level of recruiting and training cost.

The fringe benefit component of quasi-fixed costs is also of central interest. The ratio of the values of fringe benefits to the yearly payroll for two-digit SIC manufacturing industries, and industrial category for other industries (e.g., Construction, Services), was obtained from a 1980 report by the U.S. Chamber of Commerce. We



NOTES 115

TABLE 3.-EMPIRUCAL RESULTS

Probit Models Regression Models

Pr(PT 2 5%) Pr(PT 2 10%) OLS WLS WLS

WA GE - 0.003 -0.015 a - 0.43a -0.19 - 0.33a (-1.45) (-2.34) (-3.33) (-1.59) (-2.93)

BENEFIT -0.15a -0.002 1.24a 1.79a 1.60a (-2.35) (-0.35) (2.99) (6.02) (6.90)

HIRECOST -0.01 -0.014 a -1.58a _1.62a -2.07a (-1.35) (-2.16) (-3.32) (-3.58) (-4.43)

SIZE -0.033a -0.049a -7.88a _8.73a -8.15a (-4.23) (6.41) (-14.55) (-15.32) (-15.54)

UNION - .oo1a - 0.0004 -0.27 -0.02 1.09 (-2.39) (-0.90) (-0.92) (-0.60) (1.32)

SEASON 0.002 0.007 0.03 0.00 - 0.02 (0.28) (1.38) (0.08) (0.00) (-0.08)

LABORS 0.016 0.015 0.26a 0.49a 0.28a (0.77) (0.72) (9.82) (8.13) (8.72)

OFFICE 0.014 0.042 0.07 0.05 0.14a (0.33) (-0.68) (1.84) (1.36) (4.37)

FTA VHR 0.003 0.002 0.57a 0.79a a

(0.09) (0.74) (2.80) (4.41) FT> 40 -0.001 -0.001 - 0.14a -0.19a -

(-1.49) (-1.29) (-2.57) (-3.75) EGROWTH 0.002a G.oola - 0.05a -0.04 -0.02

(4.12) (2.00) (-1.99) (-1.59) (-0.92) EXPGROW -0.003 -0.002 0.02 0.00 -0.01

(-1.16) (-0.65) (1.05) (0.02) (-0.74) MKTSIZ - 0.037a - 0.032a -0.02 0.76 0.70

(-4.03) (-3.96) (- 0.04) (1.54) (1.49) X - _ 17.53a 22.21a 31.01a

(3.86) (5.01) (5.70) ------------------------------------------------------

Sample 2509 2509 1322 1322 1322 x2 (30 d.f.) 559.1 551.3 - - - R 2 - - 0.385 0.340 0.356 Mean Dependent 0.40 0.32 26.7 26.7 26.7

Variable aSignificant at the 0.05 level. bSignificant at the 0.10 level.

call this BENEFIT. Because all benefits are included, rather than just those unrelated to hours worked, this variable is measured with some error.

B. Results

Table 3 presents the results of our empirical analysis of the allocation of jobs between part- and full-timers. Columns 1 and 2 show the results from probit models predicting the likelihood that part-timers constituted at least 5%, or at least 10% respectively, of the establishment's work force. Columns 3, 4 and 5 list the coefficients from regressions predicting the percentage of part-timers in the establishment's labor force.

First we consider the probit models. For ease of interpretation the numbers shown are the first partial derivatives of the probability evaluated at the means of the independent variables. SIZE, which was hypothesized to be correlated with monitoring and administrative costs, had the expected negative effect and was

highly significant in both models. Doubling the number of PTE employees reduced the probability that 5% or more workers are part-time by 0.033 (about 8% of the mean probability) and that 10% were part-time by 0.5 (15% of the mean probability). Both the WAGE and HIRECOST variables are negative and significant in the 10% model, though neither was significant in the 5% model. UNION and BENEFIT were negative in both models but significant only in the 5% case.

As expected, the industry dummies (not reported due to space limitations) show that firms in capital-intensive industries such as manufacturing and construction are significantly less likely to use part-timers than service firms (the excluded category). Restaurants are more likely to use part-timers.

Next we consider the regression models. Because about half the sample hired no part-timers, Tobit is the appropriate estimation technique for this type of problem. However, doing Tobit with a large number of observations and variables is computationally quite dif-



116 THE REVIEW OF ECONOMICS AND STATISTICS

ficult. Fortunately, Heckman (1976) shows that unbi- ased coefficient estimates can be made by treating the problem as the well-known one of having a censored sample. This familiar technique involves running regressions on a sample including only firms which hired some part-timers, and included among the regressors the inverse of Mill's ratio, X. The X term is a particular function of the probability of having some part-timers and is estimated using a probit model.

It was hypothesized that the regression model would suffer from heteroskedasticity from several sources. First, the variance of the percentage of part-timers was expected to be higher for smaller firms, and for firms with greater proportions of low-skilled jobs. Second, Heckman (1976) shows that including the X term in a regression equation generates heteroskedasticity. The hypothesis of heteroskedasticity from these sources was tested using a procedure developed by Glejser (1969). The absolute value of the ordinary least squares (OLS) residual was regressed on SIZE, OFFICE, LABOR and on the variable ( - X yXi + X'i) where Xi and y are, respectively, the vectors of independent variables and coefficients from the probit which predicts the likelihood sample inclusion (Heckman (1976)). The hypothesis of homoskedasticity could be rejected at the 0.001 level. Therefore, the coefficients from the residual regression were used to construct weights for a weighted- least-squares (WLS) model, the results of which appear in column 4. Column 5 reports a WLS model in which the potentially endogenous variables FTA VHR and FT > 40 are omitted.

In all of the regression models the HIRECOST variable is negative and highly significant. The coefficient implies that doubling the number of person-hours de- voted to recruiting and training a typical worker re- duces the proportion of part-timers by about 1.6 percentage points (or about 6% of the mean of 26.7% part-timers.) The WAGE variable is highly significant in the OLS models, but less so in the WLS equation. The WAGE coefficient yields an elasticity of substitution of -1.5 in the OLS model and -0.67 in the WLS model, both considerably lower than the -4.3 estimated by Owen (1978) using aggregate data.

It is interesting to note that the BENEFIT variable is highly significant in the regression equations, but has a positive sign-the opposite of that in the probit model. One potential explanation is the uncertain nature of part-time eligibility for benefits. Firms in high-benefit industries would be less likely to hire part-timers if they are eligible, and more likely to hire them if not eligible. But the firms in the regression sample have all hired some part-timers. A firm which is in both the regression sample and a high-benefit industry is more likely to be one which is not paying fringes to part-timers, and

therefore finds them attractive. It should be recalled, however, that this variable contains much measurement error.

Large, heavily unionized firms were hypothesized to bear higher supervisory and administrative costs per worker. SIZE was negative and highly significant in all of the models, though UNION was significant in only the 5% probit model.

The FTA VHR variable is unexpectedly positive and significant in the regression models. One possible explanation for this result is that firms respond to slack demand by reducing the hours of full-timers while lay- ing off part-timers. In this case, as full-time hours fall the proportion of part-timers falls, implying a positive relationship between the dependent variable and FTA VHR.

The industry dummies indicate that firms in all the industries hire significantly fewer part-timers than service firms, except for retail stores and restaurants which hire significantly more. The industry dummies did not capture a large proportion of the variation in the dependent variable. Omitting them reduced the ad- justed R2 by only 0.04.

III. Summary and Conclusions

This paper attempted to fill a gap in the literature on labor demand by exploring the determinants of the demand for part-time workers using establishment data. Evidence from a large employer survey showed that a high proportion of firms hire some part-timers (about half in our sample) with smaller firms tending to have greater proportions of them in the work force. Regres- sion and. probit analysis confirmed the expectation that high quasi-fixed labor costs decreased the relative at- tractiveness of part-time workers. The cost of recruiting and training was shown to be a significant impediment to the hiring of part-timers, a fact which helps explain why they find advancement within a company more difficult. To the extent that jobs which offer higher pay and better opportunities for advancement are also jobs which involve more recruiting and training costs to the firm, such positions are less likely to be filled by part- time workers.

An important caveat should be noted regarding the results of this paper, however. Though the nature of the data used here allowed the model to focus on the role of quasi-fixed labor costs, some of these findings are con- sistent with other hypotheses involving variables which we have been unable to observe. For example, the negative impact of firm size, and some of the industry dummies, could reflect, in part, the higher costs of worker monitoring and/or worker mistakes in large,



NOTES 117

capital-intensive firms. Such firms may encourage production efficiency and worker attachment by paying higher wages. However, if part-time jobs are inherently less important to their holders than full-time jobs, the wage increase necessary to attach part-timers may be greater than that for full-timers, making the former relatively more costly. Without further data we cannot disentangle these effects. Similarly, special characteristics of the people who supply part-time work may explain some of the effects detected in this study. Most part-time workers are married women or teenagers (Deuterman and Brown, 1978). These workers may tend to prefer flexible work schedules or loose attachment to the firm, arrangements which are often more easily obtained in the comparatively informal atmosphere of small firms. Our data did not provide evidence on this and other aspects of the work environment, some of which may influence the sorting of part-time and full- time workers among firms.3 The inability of this study to address all of these issues illustrates the paucity of information about the demand side of the part-time labor market.

3Several suggestions about alternative interpretations of the results were made by an anonymous referee whom I wish to thank.

REFERENCES

Bishop, John H., "Impacts of Training," in John Bishop, Suk Kang, John Wilke and Kevin Hollenbeck, Training and Human Capital Formation (report to the U.S. Depart- ment of Labor) (Columbus: National Center for Re- search in Vocational Education, 1985).

Daski, Robert S., "Area Wage Survey Test Focuses on Part- timers," Monthly Labor Review (Apr. 1974), 60-62.

Deuterman, W. V., and S. C. Brown, "Voluntary Part-time Workers: A Growing Part of the Labor Force," Monthly Labor Review (June 1978), 3-10.

Glejser, H. "A New Test for Heteroskedasticity," Journal of the American Statistical Association 64 (1969), 316-323.

Heckman, James J., "The Common Structure of Statistical Models of Truncation, Sample Selection, and Limited Dependent Variables and a Simple Estimator for Such Models," The Annals of Economic and Social Measure- ment 5 (1976), 475-492.

Jones, Ethel B., and James E. Long, "Part-Week Work by Married Women," Southern Economic Journal 46 (Jan. 1980), 716-725.

Morgenstem, Richard D., and William Hamovitch, "Labor Supply of Married Women in Part-Time and Full-Time Occupations," Industrial and Labor Relations Review (Oct. 1976), 59-67.

Oi, Walter, "Labor as a Quasi-Fixed Factor," Journal of Political Economy 70 (1962), 538-555.

Owen, J. D., Working Hours (Lexington, MA: D.C. Heath, 1978).

Rosen, Sherwin, "The Supply of Work Schedules and Employ- ment," in Work Time and Employment (Washington D.C.: National Commission on Manpower Policy, 1978).

LABOR TURNOVER BIAS IN ESTIMATING WAGES

John J. Beggs and Bruce J. Chapman*

Abstract-Cross-sectional earnings function analyses typically do not recognise the potential for misrepresentation arising from a relationship between unobserved ability and the probability of labor turnover. Our point is that if individuals staying with the firm for relatively long periods of time are more, or less, able on average than recent hires, the coefficient

estimated on tenure is necessarily biased. This is an important issue for wage determination modelling given the relevance of tenure to wages. In this note we examine the theoretical basis of our claim, and propose and implement a solution to the problem with a novel use of instrumental variables on a large sample of workers employed in the Australian government.

I. Introduction

In this note it is postulated that previous cross-sectional research using the earnings function is inadequate in its treatment of the relationship between unobserved ability and the probability of labor turnover. This relationship implies that individuals observed at a point in time are an unrepresentative sample of the cohort origi- nally joining the firm, because of the nature and inci- dence of past quits and permanent lay-offs. Ordinary regression estimates of the earnings function are therefore inconsistent. In particular, this is the case for the time-on-the-job coefficient, one of the more important

Received for publication February 24, 1986. Revision accepted for publication April 30, 1987.

*Australian National University. We wish to thank the Australian Public Service Board, Dr.

George Rothman in particular, and Sue Richardson of the University of Adelaide, for provision of the data. This work benefited from a grant from the Australian Bureau of Labour Market Research, although the Bureau is in no way responsible for the views expressed. Participants in a seminar delivered at the Research School of Social Sciences, Australian National University, made useful comments on an earlier draft, as did two anonymous referees. Paul Cheung provided excellent research assistance and Marti Pascall was terrific in production help.

Copyright K) 1988



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On the Determinants of Employer Demand for Part-Time Workers