Our estimation employs a standard statistical modeling technique called reduced form estimation in which underlying structural equations may be combined into one multivariate regression model (Greene, 1999). Our reduced form model determining the profit rate thus incorporates factors influencing both demand and supply for the output of the firm. The profit rate is considered a function of four groups of variables. Two of them, capital intensity and work-family benefits, represent the firm's supply curve. In addition there are two series of dummy variables, one series for years (representing changes in demand) and a second series for firms, thus accounting for industry differences, demand factors and market structure. Note that labor intensity is not included as a regressor since this is a reduced form model and labor intensity is endogenous to the production decision. Since we have no reason to believe that work-family programs and the productivity enhancements they may generate have an impact on such costs as interest expenses or income tax expenses, the measure of profit rate chosen is operating income divided by sales. Operating income is defined as net sales from which the cost of goods sold as well as general and administrative expenses have been deducted. [3]
The model which forms the basis of our analysis therefore is:
[[pi].sub.it] = [[beta].sub.0] + [[beta].sub.1](K/[S.sub.it]) + [[beta].sub.2t]([WF.sub.hit]) + [[beta].sub.3h]([DY.sub.t]) + [[beta].sub.i]([DF.sub.i]) + [[epsilon].sub.it] (2)
where i = firms 1 through n
t = time periods 1 through T
h = specific work-family benefits 1 through k
[pi] = profit rate, which is calculated as real operating income as a fraction of sales for firm i in time period t
K/S = capital intensity, which is calculated as the value of property, plants and equipment as a fraction of sales for firm i in period t
WF = a vector of work-family benefits for the firm i in period t
DY = a vector of dummy variables denoting years
DF = a vector of dummy variables denoting firms
[[epsilon].sub.it] = a classic error term
As it is necessary to control for firm-specific variation in the profit rate (Greene, 1999; Hsiao, 1986), two options are available: using a fixed effects or a random effects model. Both models allow the researcher to account for unobservable factors (such as corporate culture, the nature of the industry, market structure and demand for product) which contribute to differences in the profit rate between firms. The fixed effects model achieves this by allowing for differences across firms in the constant term of equation (2) as represented by our vector of dummy variables denoting firms (DY). On the other hand, a random effects model assumes a second error term which varies by firm.
The fixed effects model was felt to be appropriate for two reasons (Hsiao, 1986). First, the fixed effects model has the flexibility of not assuming that the individual effects are uncorrelated with the other regressors in the model. Such an assumption would be restrictive in our case since it is possible that individual effects may in fact be picking up unobserved productivity factors such as management techniques and the integration of technology into the workplace. If so, one may conceive of firms, progressive in leadership styles and uses of technology, also being progressive with respect to work-family programs. Second, the data do not come from a random sample but rather from the companies that provide the "best" work-family programs in the country. Random effects models are considered appropriate when the data are drawn randomly from a large population, an assumption that we did not feel was warranted. However, for completeness, we did attempt to estimate a random effects model. We estimated the error term and the firm disturbance term by using data from the within-cell regression and the between-cell regression. The resulting negative estimate for the firm disturbance term provided further evidence that the random effects model is inappropriate for these data (Greene, 1999).
Data Used in the Analysis and Descriptive Statistics
The data used in this study come from Working Mother magazine's annual survey of "The 100 Best Companies for Working Mothers" (Moskowitz and Townsend, 1991-1995). The editors of Working Mother rank the top 100 companies based on their responses to questions on the various programs they offer and the programs' usage. As a result, these data are not taken from a random sample of companies but are derived from a sample of only those firms that have the most extensive work-family programs in the country. Clearly, the results of our study may not be generalized to all firms, but are, nevertheless, useful in understanding companies already committed to offering such wide-ranging work-family programs. Furthermore, while it is not appropriate to apply our point estimates to the entire universe of firms, one generalization may yet be possible. If a work-family benefit is under-provided by a firm in this sample consisting of firms highly committed to providing such benefits, a reasonable inference is that such a benef it is under-provided by firms in general.
The Working Mother survey covers a wide variety of programs such as after-school and holiday programs, information and referral services for child and elder care, alternative work schedules, subsidized onsite child care, family leave, and assistance to parents adopting a child. Due to data limitations, however, we are limited to studying a subset of the full range of benefits. As a result of a significant increase in the variety of programs since the beginning of the Working Mother surveys in 1986, we are constrained to examining the years 1991 through 1995 during which time we can observe the same 9 programs for all companies. We also limited the analysis to publicly traded companies, due to inadequate availability of financial data for private firms. These restrictions yield 245 observations over five years (1991 through 1995) for 95 different firms. This is, perforce, an unbalanced panel since every firm does not appear every year.
The work-family benefit programs which are included are: paid leave for a family member's illness, maternity leave beyond 12 weeks, adoption assistance, subsidized onsite child care, permitting work at home, job sharing, flex-time, compressed workweek, and part-time work. Instead of merely indicating whether a program was offered or not, our analysis is enriched by the fact that, for several specific work-family programs, our data allow us to include a measure of the extent to which each program is used. This is of vital importance to an understanding of the effect of work-family benefits on firms' income given that the cost to the company of an unused service is expected to be small. Hence, a company whose culture discourages the use of work-family programs can profitably offer a wide variety of programs, knowing that few employees will use those programs to avoid the risk of being labeled as disloyal or non-career oriented (Ferber and O'Farrell, 1991).
Table 1 contains the descriptive statistics of the variables used in the analysis. It is useful to compare this sample of firms to the experience of workers in all firms, since the companies represented in the Working Mother survey are in the forefront of implementing these work-family programs. For instance, the average firm in our sample provides subsidized onsite child care for 63 children, with 43% of employees eligible for this benefit. Subsidized onsite child care is far more prevalent in our survey than in the economy as a whole, where only 8% of full-time employees are eligible for such childcare. Adoption assistance is also more common in the Working Mother sample than in the population overall, with 64% of workers in the sample eligible for such a benefit as compared with 11% of employees economy-wide (Bureau of Labor Statistics, 1997a).
We next examine the extent to which employees use alternative work schedules such as working at home, job sharing, flex-time, compressed workweeks and part-time work. Although media coverage of such programs has been extensive, the typical firm in this survey has no employees using these alternative schedules. The most popular of the alternative scheduling programs is flex-time, with an average firm participatory rate of 10% of the work force. The compressed workweek and part-time scheduling are the least common, with a usage by approximately 0.6% of the work force.
The average extent of participation, however, masks the nonuniform distribution of the use of these programs across firms. The large standard deviations of some of the benefits (e.g. adoption assistance, subsidized onsite child care, paid sick days) emphasize the sizeable degree of variability between firms. Since mean values are sensitive to extreme values, median values are also presented. Though the firms in this survey have the greatest number of programs in the country [4], in the majority of them only a few employees participate in these programs. For instance, 31 out of 51 firms sampled in 1995 offered some flex-time benefits. For these 31 firms, on the whole, 37% of employees reported taking advantage of this benefit, but in 8 firms, over 75% of the work force reported working flexible hours.
Empirical Results
Table 2 reports results from two different fixed effects models. In Model 1, the work-family benefits were entered as dummy variables equaling "1" if the firm had any participation in that program and "0" otherwise. One interpretation is that work-family benefits have a positive impact on income through a labor market reputation effect. This implies that the very presence, rather than the actual use, of such programs attracts better employees and decreases worker stress, thereby increasing productivity. Model 2 specifies the extent to which each program is used or offered. This model recognizes that a firm may formally offer a program, yet subtly discourage its use. Ideally, we would have measures of program participation for all work-family benefits in our study. Data limitations, however, allow us to test the hypothesis that work-family benefits must actually be used by employees to improve their work performance only for a selected subset of benefits. We actually have data on program usage for the followi ng variables: subsidized onsite child care, working at home, job sharing, flex-time, compressed workweeks and part-time work. For the remaining benefits (paid sick days, maternity leave and adoption assistance) we can only observe the generosity of the firm's benefit. Although not a perfect proxy for usage (since a firm could offer very generous benefits and still discourage their use), we feel that measuring the number of allowable days of sick and maternity leave and the amount of adoption assistance available does provide some sense of whether higher levels of benefits affect productivity.




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