Hours of Part-Time and Full-Time Workers at the Same Firm

MARK MONTGOMERY *

Nearly half of all firms hire both part-time and full-time workers. This note uses the results of a unique survey of more than 5,000 establishments to examine the ratio of part-time weekly hours to full-time weekly hours at firms employing both types of worker. The distribution of relative hours appears fairly stable across industries, Regression analysis shows that higher quasi-fixed labor costs increase the ratio of part-time to full-time hours, although the effect is empirically small.

NEARLY 20 PER CENT OF THE U.S. LABOR FORCE works part time (Deuterman and Brown, 1978). Most studies of firm demand for workers and their hours assume uniform hours for all workers, or at least for all workers of a given skill. Yet, about half of all firms hire both part- and full-timers, and nearly a third have part- and full-timers in the same general skill category (Montgomery, 1988). The question of how firms set relative hours for part- and full-time workers is an interesting one which has not been explored.'

This note uses data from a unique survey of more than 5,000 private employers to examine relative hours of part- and full-timers at firms hiring both. To assess how hourly wages and per-person (quasi-fixed) labor costs determine relative hours, a model is developed in which the firm makes a joint decision establishing the number of each type of worker and the number of hours each is to work. Regression results support the hypothesis that increasing quasi-fixed costs would also increase the relative hours of part-timers; less support is found for the theoretical prediction that increasing

* Abt Associates, Washington, D.C. 'Much has been written, however, about how individuals choose their hours of work, including the

decision to work part time (Morgenstern and Hamovitch, 1976; Jones and Long, (1979, 1980). * I would like to thank Irene Powell, Nancy Fung, Robert Robertson, and two anonymous referees for

helpful comments. All remaining errors are mine.

INDUSTRIAL RELATIONS, Vol. 27, No. 3 (Fall 1988). 0 1988 Regents of the University of California 00 19/8676/88/ 1020/394/$10.00

394

Research Note I 395

the ratio of part-time wages to full-time wages would increase part-time relative hours.

A Joint Workers/Hours Demand Model The model presented here is an extension of one developed by Owen

(1978a), in which part- and full-time hours are fixed, and the firm is allowed to choose only the optimal mix of part- and full-timers in its work force. Here, the firm is allowed to choose both the mix of part- and full-timers and their relative hours. For simplicity, the model assumes that firms are seeking to minimize the costs of obtaining a fixed level of labor services, L:

where L and h refer to workers and hours, respectively, and subscripts p and f denote part-time or f~ l l - t ime .~ Because we are interested only in relative hours, we will assume that the daily shift for full-timers is fixed at 1 and let h represent the portion of the day worked by part-timers. Although this assumption is unrealistic, it greatly simplifies the analysis while still allowing us to observe the effects of various parameter changes on part-time hours as a proportion of full-time hours.

The first component of labor costs considered is wages. Rosen (1978, p. 171) shows that workers of a given quality sort themselves into “a spectrum of closely interconnected markets geared to different work schedules.” The equilibrium wage structure among these markets yields a function relating wages to hours of work. In a competitive labor market, it is the wage-hours function which is parametric to the firm rather than a particular wage. Therefore, when a firm sets hours for part-time workers it is actually choosing a wage-hours combination. We specify the wage of part- time workers as a convex function of h, the fraction of the daily shift worked by part-timers: w, = w,(h), wL(h) > 0, WE > 0. Full-timers’ wage remains fixed in this model because their hours are fixed.

In addition to wages, firms pay quasi-fixed (per-person) labor costs which do not vary with hours worked (Oi, 1962). These are comprised of hiring and training costs, certain fringe benefits, unemployment insurance taxes, and other items. Owen’s (1978a) model assumes that these costs vary among the types of jobs at the firm (some requiring more training, or more set up

3The implicit assumption here is that an hour worked by a part-timer yields the same output as one worked by a full-timer. It is straightforward to relax this assumption and define labor services in terms of effective hours E(h), where E is a function relating output per worker to hours worked, h. Then the labor requirement is E(h,)L, + E(hf)Lf = L.

396 / MARK MONTGOMERY

time, etc.), and it posits a distribution of quasi-fixed costs, a, by full-time- equivalent job, from lowest cost to highest cost; a = a(i), a’ > 0, for i = 0,L.4 In this model, it is easily shown that if all jobs have the same quasi- fixed costs, the firm will hire only one type of worker. Owen demonstrated that under certain conditions of wages and the distribution a(i), filling (some of) the low quasi-fixed-cost jobs with part-timers and the high quasi-fixed- cost jobs with full-timers will minimize costs.

The firm’s problem is to choose a cost-minimizing combination of L,, Lf, and h to satisfy its labor requirement. Given fixed L, the number of full- timers is simply (L-hL,), so the firm chooses L, and h to minimize costs:

(1) C = w,(h)hL, + wf (L-hL,) + - a(i) di + a(i)di

The first integral represents total quasi-fixed costs for the part-time jobs; the second integral is total quasi-fixed costs for the full-time jobs. Note that the quasi-fixed cost of using part-timers is l/h times that which would be incurred by filling these jobs with full-timers.

1 hLp L

h L = O L=hLp

Theoretical Results The method used to derive the effects of changes in relative wages and

the impact of quasi-fixed costs on h is the standard approach to comparative static analysis. Only the results are summarized here. (A detailed derivation of these results can be obtained from the author.)

Retatzve wage effect. Given that wf is a constant in this model, an increase in wf will represent an increase in the ratio of full-time to part-time wages at all levels of h. Totally differentiating the first order conditions for an interior minimum of (1) with respect to L,, h, and wf, and solving for ah/awf gives

where [HI is the determinant of the hessian matrix associated with (1). [HI must be positive for a unique interior cost minimum. The term a* is the quasi-fixed cost of the last full-time equivalent (FTE) job filled by part- timers. The sign of gj is theoretically ambiguous. While an increase in wf relative to wp will induce substitution of part-time services for full-time services, it could conceivably reduce part-timers’ hours relative to those of full-timers.

4By definition a(() is nondecreasing in (0, but we are also implicitly assuming that a‘ ( t ) > 0 V .C E [O,L]. This assumption is convenient but not necessary. However, to obtain a solution in which some of both types of worker are hired (i.e., 0 < L, < L), it must be the case that a’ ( e ) > 0 for some & E [O,LI.

Research Note / 397

A simple way to predict the sign of ah/awf is to use qwh, the elasticity of the part-time wage with respect to an increase in part-time hours. By substituting the first order condition for L, into (2), it can be shown that (2) implies that

(3) a h awf

3 0 if hqwh S a*/w,

The term a*/wp represents the quasi-fixed cost as a proportion of the wage for the last FTE job occupied by part-timers. If part-time wages rise rapidly with hours (qwh is large), firms are more likely to increase part-time services by raising the proportion of part-timers while lowering their relative hours.

It is worthwhile also to predict the sign of q/awf by look‘ing at some observed values of h, qwh, and a*/wp. It is shown below and elsewhere (Owen, 1978a) that, on average, part-timers work about half as many hours as full-timers; so let h = .5. Although we are unable to observe the wage- hours function, a rough approximation of q w h can be obtained from the inverse of the labor supply elasticity of part-time workers. Morgenstern and Hamovitch (1978) have estimated the part-time wage elasticity at .547. Using these two values, hTwh is approximately .91. Even a liberal estimate of a*/ wp is likely to place its value at less than .4 (Chamber of Commerce of the United States, 1981). This rough guage suggests that if full-time wages increase relative to part-time wages, we may observe a decrease in part-time hours. This somewhat surprising prediction is tested in the next section.

Quasi-fixed costs effect. Next consider the impact of an increase in quasi- fixed costs on relative hours. Because quasi-fixed hiring costs have a distribution over all jobs, an increase in these costs is represented by an upward shift in the distribution by a constant amount E on all jobs. Totally differentiating the first order conditions with respect to h, L,, and E gives an expression for ah/cre. For ease of interpretation, we again employ ywh and also define an elasticity of quasi-fixed costs with respect to FTE employment, qaL. The latter elasticity shows by what percentage quasi-fixed costs for the last job increase as we move up the employment distribution by 1 per By assumption qaL is strictly positive. Using this notation, the effect of a uniform upward shift in the distribution of quasi-fixed costs can be summarized by

(4) a1 - a€ S 0 if hqwh 2 (a*/wp) (1 -yaL)

51n the notation of this model, qaL = a’hlda.

398 / MARK MONTGOMERY

We saw above that hTwh is about .91, while a*/wp is less than .4. Given these values, an increase in quasi-fixed costs will always increase relative hours of part-time workers, because (l-qaL) is less than unity. A positive sign on ah/ac is intuitively reasonable, since spreading per-person costs over a larger number of hours reduces the disadvantage of part-time workers with respect to these costs.

Other Factors Affecting Part-Time Hours The model assumes perfect substitutability between one full-timer and

l /h part-timers (see footnote 3). It also assumes that labor requirements could be completely satisfied by full-timers working shifts of a fixed length. In actuality, the differences in production functions should cause cross- industry variation in part-time hours. For example, Owen (1978b) shows that one motivation for hiring part-timers is to avoid hiring overlapping shifts of full-timers in industries where hours of operation are not easily divided into shifts of standard length. Thus retail stores, restaurants, and some service industries might use part-timers to cuver hours which exceed the 40-hour week norm. In these cases, operating hours would be the predominant factor in determining part-time hours.

The model also assumes that the firm operates in a competitive labor market. Because part-timers are a minority in the labor force, the assumption that a firm is a wage taker (for a given h) is even more constraining in the part-time market than in the full-time market. If part-timers have few alternative, short-hours employment opportunities, a firm with monopsony power may have greater flexibility in moving workers away from their offer curves. Such a firm may pay a lower wage compensation for an increase in weekly hours.

Finally, the model assumes a fixed labor requirement. However, an unexpected change in product demand may affect a firm’s relative hours. For example, increasing the hours of full-timers in response to an unanticipated surge in product demand will generally require payment of an overtime wage. Raising part-time hours will not. By the same reasoning, expected demand changes caused by seasonal variation in demand may influence relative hours. As product demand varies over the yearly cycle, firms may find it easier to adjust part-time hours than full-time hours.

Empirical Evidence About Relative Hours Data. This section presents some empirical evidence about relative hours

at establishments hiring both part-time and full-time workers. The data

Research Note I 399

come from a unique survey of 5,000 employers, in 28 geographic sites. The study was conducted in 1980 by the Institute for Research on Poverty at the University of Wisconsin. The original purpose of the survey was to evaluate the Employment Opportunities Pilot Project (EOPP).6

The estimation samples were drawn from a usable subsample of 4,518 respondents, all of whom were for-profit employers having some employment in December of 1979. Supplemental data about the firm's location were drawn from other sources, as indicated. At the time of the interview (first quarter 1980), firms were asked how many part-time and how many full- time workers they employed in each of six skill categories during a reference pay period in mid-December 1979. The categories were (1) managerial, professional, and technical; (2) craft; (3) office and clerical; (4) operatives; (5) laborers and service workers; and (6) sales workers. Employers were asked about the average weekly hours of part-time workers in each of these skill classes and about the average weekly hours of all full-timers at the firm. On average, for firms hiring both part-time and full-time workers, about 22 per cent of the work force was part-time.

Relative hours by industry. Table 1 reports the distribution of the ratio of part-time average weekly hours to full-time average weekly hours for firms hiring both types of worker. Each row of the table gives the percentage of establishments for which part-timers worked; respectively, 1-20 per cent, 21-40 per cent, 41-60 per cent, 61-80 per cent, and 81-100 per cent of full-time hours. These means are conditional upon the firm having both part- and full-timers on the staff. The per cent of establishments in the industry hiring both part- and full-timers is reported in the table's far right column.

The numbers in Table 1 show that in all industries part-timers work on average about half as many hours as full-timers. In seven of the 11 industries, the ratio of average hours is between .49 and .51. Only in construction is the ratio less than .45. The table also reveals that among firms in a given industry there is substantial variation in relative hours. (The standard deviation of the percentage ratio for all industries was 21.5 per cent.) The distribution of ratios is similar for almost all of the industries. In no industry do more than 15 per cent of establishments have part-timers working either less than 20 or more than 80 per cent of full-time hours. In seven of the 11 industries, between 51 and 58 per cent of firms fall in the 41-60 per

hThe Department of Labor commissioned the study; Westat Inc. did the actual interviewing. The 28 locations in the survey (all EOPP sites) overrepresent rhe 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.

400 / MARK MONTGOMERY

TABLE 1 DISTRIBUTION OF ESTABLISHMENTS IN EACH INDUSTRY BY PART-TIME WEEKLY

HOURS AS A PERCENTAGE OF FULL-TIME WEEKLY HOURS?

Yo of weekly hours % of est.

hiring part- a n d full-

1-20 21-40 41-60 61-80 81-100 Mean timers

Manufacturing Nondurable 5.7 15.9 58.0 15.9 4.6 49.7 33.1 Durable 8.7 26.1 34.8 26.1 4.4 50.2 26.5

Construction 9.2 32.9 44.7 9.2 4.0 44.4 24.1 Transportation &

Communications 4.6 33.9 38.5 20.0 3.1 47.1 39.3 Wholesale trade 4.2 22.7 52.9 16.8 3.4 49.0 31.7 Retail trade 5.4 19.8 52.9 16.8 1.0 49.4 59.3 Restaurants 2.7 23.8 52.4 20.2 .9 49.7 71.5 Finance, insurance

& real estate 6.3 16.9 53.5 19.0 4.2 53.4 51.4 Services 4.6 18.8 52.0 23.4 1.1 50.5 51.7 All industries 4.9 21.0 51.9 20.3 1.9 49.8 47.7

Total number of establishrnents=4,5 18.

cent category. These industry distributions cannot be considered identical, however. The hypothesis of homogeneity of distribution among industries is rejected at the .01 level (x232 = 59.1). This holds even when durable manufacturing, which had only 23 firms hiring part-timers, is eliminated from the calculation.

The distribution of relative hours by skill class (not reported) shows a pattern similar to that across industries. The six skill categories show distributions which are very much alike.

Regression Results To test the hypotheses about the determinants of relative hours, we must

first specify a system which will identify the important effects, given the available data. In principle, a firm hiring both part- and full-timers will have separate demand functions for: (i) number of full-timers; (ii) number of part-timers; (iii) full-time hours; and (iv) part-time hours. These demand functions are interrelated; each includes the prices of both types of labor, quasi-fixed costs for both types of labor, and the prices of other factors.

The available data are insufficient to identify the four demand equations described above. Below, an alternative approach is used to estimate the two-

Research Note I 401

equation system implied by the theoretical model. We make the assumption that the ratio of part-time to full-time weekly hours (h) and the proportion of part-timers in the work force (Lp/[L,+Lf]) are independent of overall demand for labor services and other factors. Then we estimate a system in which these two ratios are jointly determined.

Independent variables. The independent variables are described below. Table 2 presents their formal definitions and descriptive statistics. We use a proxy for the relative wage cost of part- and full-timers (WAGE) because we are unable to observe the different wage-hours schedules that a firm faces in its local part-time and full-time labor markets, and the EOPP survey did not ask respondents about wages paid to part- and full-timers. The best proxy available is 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.

We argued earlier that quasi-fixed costs would vary among jobs at a firm and that part-timers would tend to populate the low end of the quasi-fixed cost distribution and full-timers the high end. A major source of variation

TABLE 2 DEFINITIONS OF INDEPENDENT VARIABLES

Variable I* a

WAGE

BENEFIT HIRECOST

SIZE UNION Percentage of nonsupervisory workers covered by collective

SEASON Predicted per cent deviation of December employment from

MKTPOWER EXCAPCTY

% PART- TIME

a Census of Population; Detailed Population Characteristics, Table 296, 1980.

Ratio of earnings of part-timers to full-timers at the site (persons with four years of high school).' Ratio of fringe benefits to payroll (industry).h Residual from regression predicting log of person-hours spent hiring and training last hired worker. Log of the number of FTE workers.

bargaining agreements.

average yearly employment in 2-digit industry at the site.c Log of firm FTE employment'log of site employmentd. Takes the value one if the firm could have handled a large increase in sales in the last quarter of 1979. Part-timers as a percentage of total employment at the firm.

Employee Benefits 1980, Chamber of Commerce of the United States. Industry Employment, Hours, and Earnings: States and Areas; Bureau of Labor Statistics American Startsrical Index; CETA Area Employment and Unemployment Statistics, 1979.

47.8 5.3

7.2 .9 .2 1.5

2.8 2.7 7.1 23.8

.8 2.9

. l l .4

.20 .40

20.2 5.8

402 / MARK MONTGOMERY

in per-person costs is the level of training given to workers. The EOPP survey gives a rare opportunity to observe the impact of this aspect of quasi- fixed costs by providing detailed information about the amount of time spent recruiting and training the last worker hired by the establishment.

Our model derives the effect on relative hours of an upward shift in the quasi-fixed cost distribution for all jobs. However, higher recruitment and training costs for the last worker do not necessarily imply a higher distribution of quasi-fixed costs. 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 inexperienced 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/he was hired. These characteristics include 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. A higher level of HIRECOST should correspond (on average) to a higher level of recruiting and training costs across the job distribution.

A second component of quasi-fixed costs involves fringe benefits. Our control variable, BENEFIT, is the average ratio of certain fringe benefit payments to payroll for the industry in which the firm operates (taken from the Chamber of Commerce of the United States, 1981).' This variable is available at the two-digit SIC level for manufacturing industries and at a broader industrial category for other industries (e.g. , construction, services). It must be noted that the impact of fringe benefits on the relative hours of part-timers is uncertain because in many firms part-timers are ineligible for some or all fringes (Daski, 1974). The ineligibility of some part-timers for benefits should reduce the influence of this variable on relative hours.

The best variable available to control for unexpected changes in product demand is a dummy for whether the establishment reported that it had excess capacity during the reference pay period. We call this dummy EXCAPCTY. Because the questions asked of the survey respondents pertained to a reference pay period in mid-December 1979, our proxy for seasonal variation in product demand is a measure of the percentage variation

'The fringes included are those judged to be largely independent of hours worked. They are: unemployment taxes, personal insurance benefits (life, medical), employee discounts, and paid meals.

Research Note i 403

of December employment around average yearly employment in the establishment’s two-digit SIC industry at the establishment’s geographic site. This variable, SEASON, was calculated by regressing monthly employment in the two-digit SIC industry at the site on a quadratic time trend and a dummy for December, for the period 1970-1985. SEASON is the value of the coefficient of the December dummy divided by average yearly employment. This shows by what per cent December employment tends to be higher or lower than average yearly employment in the local industry.

Also included as control variables are the log of total establishment employment, SIZE, and the percentage of nonsupervisory workers covered by collective bargaining agreements, UNION. Larger and more heavily unionized firms tend to have formalized rules and procedures governing such aspects of employment as discipline, discharge, and rights to fringe benefits. These factors imply higher administrative and supervisory costs, which are part of quasi-fixed costs. We hypothesize that SIZE and UNION will have a positive impact on relative hours. To control for monopsony power in the local labor market, the models include MKTPOWER, the ratio of (the log of) the firm’s FTE employment to (the log of) total employment in the local labor market. The industry dummies used correspond to those listed in Table 1.

As noted above, the relative hours regression is estimated as part of a two-equation system predicting both relative hours and the proportion of part-timers in the work force (YO PART-TIME). This was accomplished using two-stage least squares. The set of exogenous variables used to predict YO PART-TIME include the independent variable described above plus (1) the proportion of workers in low-skill, blue-collar occupations and low-skill, white-collar occupations, respectively; (2) the local unemployment rate; (3) the number of applications for employment received in December 1979 as a percentage of employment; and (4) the change in the establishment’s employment from July to December 1979. A discussion of the theoretical justification for the inclusion of these variables is presented in Montgomery (1988). Only the hours regression could be identified, given the data available from the survey.

Results Table 3 reports the regression results. Column 1 gives ordinary least

squares (OLS) estimates and Column 2 gives two-stage least squares (2SLS) estimates. The sign and magnitude of the coefficients changes little between the two specifications but the levels of statistical significance do. As expected, the cost of hiring and training new workers has a positive and significant

404 / MARK MONTGOMERY

impact upon the ratio of part-time to full-time hours in both models. The implied mean elasticity is fairly low, however, about .01 in the 2SLS model.

SIZE has a positive and highly significant impact on relative hours. Assuming part-time average hours of 20 per week, doubling the size of the firm raises part-time hours by 1.6 per week. This finding lends support to the expected effect of quasi-fixed costs because larger firms are likely to face higher supervisory and administrative costs. (Alternative interpretations of the impact of size cannot be ruled out, however.) Heavily unionized firms also were expected to bear higher quasi-fixed costs, but the coefficient on UNION is always negative and never significant.

The relative wage of part- and full-timers at the site, WAGE, had a positive effect in both models, though it was significant only in the OLS equation. This supports the finding of the theoretical model that, given prevailing measures of wage-hours elasticity for part-timers, a higher relative wage for part-timers would actually increase their hours. The implied wage elasticity of relative hours is low, however, about .003, using the 2SLS coefficient.

SEASON and EXCAPCTY had the expected signs in both models but low levels of significance. All of the other independent variables, including the industry dummies, are insignificant.

Conclusions The literature on labor demand contains no statistical analysis of how

firms set relative hours of part- and full-time workers. The theoretical model developed here predicted that increasing the ratio of part-time wages to full- time wages might (given observed wage-hours elasticities) actually increase part-time relative hours. Increasing quasi-fixed costs would also be likely to increase part-time hours. Regression results support the prediction about quasi-fixed labor costs. The prediction that increased relative wages for part- timers would increase their relative hours worked receives weak support; the impact is positive but highly significant only in the OLS equation. The estimated elasticities for both the wage and the per-person costs are very small, however.

The EOPP survey indicates that the distribution of relative hours is fairly stable across industries. This stability holds across different skill levels, too. In general, the variables used here to explain the determination of relative part-time hours did not capture a large portion of the variation in this variable. The results suggest that the way in which firms integrate part-time and full-time workers into the work force is not well understood. Further

Research Note I 405

TABLE 3 REGRESSION RESULTS~

(T-STATISTICS ARE IN PARENTHESES)

Department h,/h* h , h variables OLS 2515

WAGE

BENEFIT

HIRECOST

SIZE

UNION

SEASON

% PART-TIME

EXCAPCTY

MKTPOWER

DURABLE

NONDURBLE

CONSTRUCT

TRANSPORT

WHOLESALE

RETAIL

RESTRNT

FINANCE

.002** (2.19) - .002

(-.18) .006**

.024** (2.09)

(7.13) - .00003

(-.20) .002

(1.14) .16**

(8.18) -.013

(- 1.29) -.001

(-.14) .055

(1.25) ,017

(.76) - ,007

(-.20) ,007

.052 (1.72)

.004 (.38) - .002

(- 1.69) ,013

(56)

~ 3 0 )

.001 (1.56) .001

(-23) .006*

(1.80) .022**

(5.62) -.0001

(-.48) .002

(1.06) .077 .75

-.012 (-1.16) - .0006 - .06

.035 (.69) ,006

(.39) -.015

(- .40)

( - . O l ) .037

(1.03) .002

- .014 (- .79) - ,005

(-.16)

- ,0003

(.25)

Sample RZ

1,247 1,247 .10 .09

* Significant at the .1 level in a two-tailed test; * * significant at the .OS level in a two-tailed test. Also included were i) the inverse of Mill’s Ratio to correct for censored-

sample bias; ii) the ratio of applications to employment in December 1979; and iii) dummies to control for the use of 1-digit andor statewide data in the calculation of SEASON.

406 MARK MONTGOMERY

study in this area might make an important contribution to the literature on factor demand.

REFERENCES Chamber of Commerce of the United States. Employee Benefits 2980. Washington, DC: 1981. Deuterman, William V. Jr. and Scott C. Brown. “Voluntary Part-time Workers: A Growing Part of the

Labor Force,” Monthly Labor Review, CI (June, 1978), 3-10. Jones, Ethel B. and James E. Long. “Part Week Work and Human Capital Investment by Married

Women,” Journal of Human Resources, XIV (Fall, 1979), 563-578. --. “Part-Week Work by Married Women,” Southern Economic Journal, XLVI (January, 1980),

716725. -. “Married Women in Part-time Employment,” Industrial and Labor Relations Review, XXXIV

(April, 1981), 413-425. Montgomery, Mark. “The Determinants of Employer Demand for Part-Time Workers,” Review of

Economics and Statistics, LXX (February, 1988), 112-117. Morgenstern, Richard D. and William Hamovitch. “Labor Supply of Married Women in Part-Time

and Full-Time Occupations,” Industrial and Labor Relations Review, XXX (October, 1976), 59-67. Oi, Walter. “Labor as a Quasi-Fixed Factor,” Journal of Political Economy, LXX (December, 1962),

538-555. Owen, John D. “Why Part-Time Workers Tend To Be in Low Wage Jobs,” Monthly Labor Review,

CI (June, 1978a), 11-14. -. Working Hours. Lexington, MA: Heath, 1978b. Rosen, Sherwin. “The Supply of Work Schedules and Employment.” In Sherwin Rosen, ed., Work

Time and Employment. Washington, DC: National Commission on Manpower Policy, 1978, pp. 145-174.