compensation structure and establishment quit and fire rates

Compensation Structure and Establishment Quit and Fire Rates

IRENE POWELL, MARK MONTGOMERY, and JAMES COSGROVE*

Despite the claims of efficiency wage theory, there is surprisingly little direct evidence that firms that pay higher wages have lower turnover rates than otherwise similar firms. This study uses data on 205 child care establishments to examine the influence of wages, fringe benefits, and the dispersion of wages within a skill class on establishment quit and fire rates. We separately examine one high-skill group (teachers) and one low- skill group (teacher aides). While we find that wages (alone) significantly reduce establishment quit and fire rates, the effect seems too small to be consistent with the efficiency wage hypothesis.

Introduction There is a large literature exploring the effect of wages on worker turn-

over. It is well established both theoretically (e.g., Salop, 1973) and empiri- cally (see, e.g., Parsons, 1977) that workers who receive higher wages are less likely to quit their jobs. Predicated on this result is an efficiency wage literature that assumes that establishments reduce quit and fire rates by offering above-market wages when doing so is less costly than, say, more closely monitoring workers or training new replacements. There is, however, surprisingly little direct evidence that establishments with higher wage rates do in fact have lower turnover rates. Almost all empirical studies of turnover rely on data from individual workers or from industries.

Only two previous studies have examined establishment-level quit rates,

*The authors’ affiliations are, respectively, Department of Economics, Grinnell College; Depart- ment of Economics, Grinnell College; and Human Resources Division, U.S. General Accounting Office. The authors would like to thank William Ferguson, Jack Mutti, and three anonymous referees for helpful comments and suggestions. We also would like to thank Tim Schoen for research assistance.

INDUSTRIAL RELATIONS, Vol. 33, No. 2 (April 1994). 0 1994 Regents of the University of California Published by Blackwell Publishers, 238 Main Street, Cambridge, MA 02142, USA, and 108 Cowley

Road, Oxford, OX4 lJF, UK.

229

230 / IRENE POWELL, MARK MONTGOMERY, AND JAMES COSGROVE

those of Leonard (1987) and Wilson and Peel (1991). Both of these studies focused on a single industry or industrial sector. Leonard found a significant but small effect of wages on turnover; Wilson and Peel found no statistically significant effect of wages on quit rates. These studies call into question the assumption of the efficiency wage literature that firms will find it profitable to raise wages to reduce turnover.

This paper also uses establishment-level data to analyze the determinants of establishment turnover rates. Like the previous establishment- level studies, we focus on a single industry-early childhood education- using the results of a survey of child care centers conducted by the U.S. General Accounting Office (GAO) (1990). Our data afford an opportu- nity to examine a number of issues that the earlier studies were unable to address. First, we have more detailed information on compensation structure than either of the earlier studies-we know which of a variety of fringe benefits were offered at the child care centers. Second, rather than having only average wages at the establishment, we have information on the wages, education, and experience for each individual worker in two skill classes. This enables us to observe whether the variation in wages among co-workers of a given skill influences turnover rates. Finally, un- like the previous studies, we are able to analyze quit and fire rates separately.

In addition to the general questions about the effect of compensation structure on establishment quit and fire rates, our focus on early childhood education also allows us to examine an important public policy issue in the provision of child care. Many studies (see, e.g., Whitebrook, Howes, and Phillips, 1989) have indicated that lower turnover of teaching staff is an important determinant of the quality of care received by children in child care centers. Moreover, these studies indicate that turnover is exception- ally high among child care providers and have led policy analysts to call for higher wages for child care teachers in order to bring down turnover rates (Whitebrook, Howes, and Phillips, 1989). Our study sheds light on the ability of higher pay, better benefits, and other work place characteristics to lower turnover of teachers of preschool children. Because the quality of a child’s early education has significant public good aspects, this is a legiti- mate area of concern for public policy.

Though the GAO survey did not ask this question, it is likely that nearly all of the teachers and aides are female, given the demographics of child

‘Wilson and Peel (1991) did find wages to have a negative and significant effect when they ran models of turnover and absenteeism as seemingly unrelated regressions; however, the magnitude of the effect was small, as in Leonard’s (1987) study.

Compensation Structure and Establishment Quit and Fire Rates I 231

care teachers in general. For example, Whitebrook, Howes, and Phillips (1989) found that 97 percent of the teaching staff in child care centers in their study were female. While there are differences between male-female quit behavior, previous studies (see Viscusi, 1980; Blau and Kahn, 1981; Weiss, 1984; Meitzen, 1986) have found little difference in male-female responsiveness to wages (our main variable of interest), though they have found some differences in male-female responsiveness to some other variables, such as experience or tenure.

We find that wages have a significant effect on both quit rates and fire rates for high-skill workers (teachers), and on quit rates for low-skill workers (teacher aides). The observed effects are smaller and less significant when we attempt to control for the potential endogeneity of wages. We find that neither pensions nor other types of fringes have a significant effect on turnover, nor does the dispersion of wages within a skill class. When we use our estimates to explore whether it is profitable to raise wages as a means of reducing turnover, our results are consistent with those of Leonard-it seems unlikely that establishments would find such behavior profitable as the sole reason for raising wages. Finzlly, while our observation of a low responsiveness of turnover to wages calls into question the ability of policymakers to increase the quality of child care substantially by increasing the wages of teaching staff, our results also indicate that other center characteristics that can be influenced by policymakers seem to have no consistent or significant effect on turnover either.

The Model In this study we model establishment quit rates and fire rates as functions

of average establishment wage rates, the fringe benefits offered by the establishment, and various other establishment characteristics (to be discussed below). Before discussing the determinants of establishment turnover rates, however, it seems useful to question what an establishment-level study could tell us that we do not already know from studies of individual quit behavior. It seems obvious, of course, that if higher wages reduce individual quit probabilities, then they must also reduce establishment quit rates-an establishment’s work force is comprised of individuals. But there are complications. To some extent, higher wages may be rewarding the kind of individual attributes-loyalty, perseverence, amiability-that both increase productivity and reduce the likelihood of quitting or being fired. If so, wage coefficients measured with worker data may be picking up some individual-specific effects. Thus, establishment turnover rates could be less


sensitive to average establishment wages than results from worker data suggest.

Another problem with turnover studies using worker (or industry-level) data is that they have been unable to observe the effect of compensation structure within the establishment’s work force, especially the variation in wages among co-workers of a given skill. This internal structure could be important in several ways. Workers may gather clues about whether they are well paid by comparing their wages with those of co-workers in the same, or a similar, job. Workers who rank at the bottom of an internal wage scale may feel resentment at the apparent inequity and/or interpret it as a signal that they could get better pay at another establishment. In addition, if an establishment used wage bonuses to reward good performance-a system that would increase wage dispersion-substandard employees might be induced to quit the firm. These arguments suggest that increased wage variation within a skill class will result in higher turnover.

Alternatively, wage dispersion may reflect an internal wage ladder, and may help attach the workers to the firm. There is a significant literature in support of this hypothesis. As argued by Salop and Salop (1976), employers may induce self-selection of low turnover applicants by predictably increasing wages with job tenure at the firm, resulting in greater wage dispersion. Lazear (1979, 1981) and Lazear and Moore (1984) argue that firms use steep age-earnings profiles (which would increase wage dispersion) to provide incentives to workers to increase their productivity. Col- lier and Knight (1986) find that seniority pay can function primarily as a device for reducing training costs by lowering turnover. Solnick (1988) uses data from a single firm to show that workers who were recently promoted are less likely to quit, and Blakemore, Low, and Ormiston (1987), using individual data from the PSID, estimate that performance bonuses have a larger effect on turnover than do base wages. These studies all suggest that a worker who receives a reward for “performance” in the broadest sense of the term (i.e., perhaps for simply staying with the firm) is less likely to leave the firm. However, we know of no direct observation that establishments with compensation structures that create wage dispersion among similar workers have lower overall turnover rates. Our data allow us to investigate this issue.

This paper considers the effect of wages and compensation structure on fire rates, as well as on quit rates. Efficiency wage theory argues (see Lazear, 1979, 1981; Lazear and Moore, 1984) that higher wages could be paid in order to improve performance of workers, to reduce shirking, and therefore to avoid the necessity of firing workers. Thus, efficiency wage theory predicts that wages should be negatively related to fire rates, all else

Compensation Structure and Establishment Quit and Fire Rates / 233

constant. Another possible explanation of a negative relationship, one that is not based on efficiency wage theory, is that high wages will attract better quality workers, who will be fired less often. One can think of arguments, however, that would favor a positive relationship between wages and fire rates. One way of eliminating poor workers is to pressure them to quit. A high-wage employer will have a harder time inducing quits and thus have to resort to firing more often. In general, therefore, the effect of wages on quits is not theoretically unambiguous.2

Another form of compensation that might affect turnover is fringe benefits (such as pensions, health and life insurance, reduced child care fees, etc.). Such in-kind forms of compensation could have a much different influence on turnover than could wages. For example, it has been argued that the tendency of many pension plans to vest the employer’s contribu- tion only after a certain tenure with the firm will reduce turnover by encouraging employees to stay until vesting is accomplished. We are able to treat pension benefits separately from other benefits offered by the establishment and can investigate this issue.3

Other center characteristics. To specify our empirical model we need to consider center characteristics other than compensation that could be expected to influence working conditions and thereby turnover rates. These include average hours for full-time staff, size of the establishment (measured in full-time-equivalent [FTE] children), childlstaff ratios, the percent of children served who are handicapped, average experience of the center’s director, and others. Characteristics of the local job market also could influence turnover by determining the availability of alternative employment for staff who quit or get fired. Our models include county population, and whether the center is located in an SMSA.4 Finally, not-for-profit centers might have less incentive to minimize cost by reducing turnover; thus we control for the profithonprofit status of the center.

The Data The data for this study are drawn from a 1989 survey of 205 establish-

ments providing early childhood education; all were accredited by the

2We are indebted to an anonymous referee for suggesting some alternative theories on the relation-

’Wilson and Peel (1991) considered the effect of wages and fringe benefits separately; Leonard

4Ideally we would like to include the local unemployment rate, but these figures were not yet

ship between wages and fires.

(1987) was unable to consider the effect of fringe benefits on turnover.

available for the year in question.

234 / IRENE POWELL, MARK MONTGOMERY, AND JAMES COSCROVE

National Association for the Education of Young Children (NAEYC).5 The survey questionnaire was conducted by the U.S. General Accounting Office (GA0).6 The questionnaire included questions on a number of characteristics for each teacher and teacher aide, including salary, education, and experience. The 205 centers employed a total of 3,746 teaching staff. The average center had 19 full-time-equivalent teaching staff and 81 full-time-equivalent children.

Our primary dependent variable, quit rates, is measured as the number of teachers who quit in 1989 as a proportion of the total number of teachers employed at the time of the survey. Fire rates were measured as the proportion of teachers who had been fired during the year (not including layoffs). We examined quit rates and fire rates separately for the two skill classes of workers: teachers and teacher aides, re~pectively.~ Below we describe the derivation of the variables that measure the key components of compensation structure.

Wages and wage dispersion. Respondents were asked about either the hourly wage or salary (whichever was easier to report) for each member of the teaching staff. Salaries were converted to hourly wages using reported weekly hours for each employee.* The average hourly wage for teachers was $6.90 and for aides $4.27. We use the natural log of wages as the independent wage variable in the quit and fire models. The problem of the potential endogeneity of wages is discussed in the next section.

The survey of child care establishments used in this study did not tell us whether a given establishment had a seniority pay scale or a bonus system. It did, however, give us data on pay, education, and overall experience of each worker in the two skill classes under study: teachers and teacher aides. We were able, therefore, to measure wage dispersion within a skill group after adjusting for differences in human capital characteristics. Since both seniority scales and performance bonuses will tend to increase the dispersion of wages among workers with similar skill and training, this will serve as a useful proxy for the existence and scale of any such compensa-

5NAEYC accreditation may mean that our sample is restricted to high-quality centers. Nevertheless, sample mean turnover in our sample for teachers (about 22%) and aides (about 38%) seems to be comparable for estimates of turnover in broader populations of centers. See Hartmann and Pearce (1989) for a review; they estimates an average of “perhaps 30%” from various studies on all child care workers.

6All 265 NAEYC members providing full-day, full-year care were sent surveys, and 205 responded. The original purpose of the survey was to assess the effect of various determinants of the quality of education and care on cost (see U.S. General Accounting Office, 1990; Powell and Cosgrove, 1992).

’The correlation between quit rates and fire rates for teachers was .15 and for aides was -.04. *For a very few cases, the process of computing hourly wages from salary figures yielded average

wages for aides that were below the minimum wage.

Compensation Structure and Establishment Quit and Fire Rates / 235

tion schemes at an establishment. To measure wage dispersion while controlling for human capital, we posit a model predicting the wages, wij, of individual i at center j as follows:

K

+ &(Expi) + &(EXPJ2 + &(HOURS,) +c PKXik, (1) k=l

where aj is a center-specific constant, ED, and EXPi are education and total teaching experience,g respectively, and the Xi, are dummies for whether this staff member works part-time or cares primarily for infants, toddlers, preschoolers, or school-age children. Separate equations were estimated for teachers and aides. This is a form of the familiar fixed-effects model; it allows the aj's to capture the effects of all aspects of the establishment (center) and its location on wages. Our measure of wage dispersion is the standard deviation of the error from this wage equation for all teachers (aides) at the center. A high standard error would indicate that wages among staff members differ significantly for reasons other than differences in human capital attributes. We are assuming that the bulk of this variation represents reward for either tenure with the center or quality of performance. A negative coefficient on this variable would indicate that a wage structure that more generously rewards tenure and/or performance reduces the quit rate (fire rate) at the firm.1°

Our establishment dummy coefficients explain 45 percent of the variation in wages after controlling for human capital characteristics for teachers and 30 percent of the wage variation for aides. These estimates are consistent with Groshen (1991) who estimated that establishment-based wage differentials, controlling for occupation and human capital, explain 20-70 percent of intra-industry wage variation in the six manufacturing industries she studied."

Fringe benefits. The GAO survey asked respondents about the availability of 17 different fringe benefits for teachers and teacher aides, respectively. Among these fringe benefits were such items as paid vacation, sick leave, planning time, pension benefits, health and life insurance, worker's

'Total teaching experience is measured as years of employment experience in early childhood education or development.

IOIt should be noted that wage dispersion also may pick up (1) the diversity of a center's work force with respect to unmeasured wage-relevant characteristics unrelated to performance, and (2) variation in reporting errors across centers.

"The value of the establishment dummies for teachers, for example, had a mean of 1.63, a standard deviation of .31 and ranged from .70 to 2.41. Results of the wage regressions are available from the authors upon request.


compensation, reduced child care fees, and others.12 While the survey asked about total expenditure on various individual benefits, few respondents provided detailed information of that type. Consequently, to measure the approximate amount of compensation going to benefits, we constructed a benefits index based on which benefits the center offers to each type of staff.13 To create this index, we used data from the U.S. Chamber of Commerce to weight each available benefit by the proportion of the wage bill expended on this benefit by the typical nonmanufacturing firm offering that type of benefit (as nearly as it could be matched to Chamber of Commerce benefits). Formally, our benefits index for the ith, BENEFITS', for staff of type t (t = teachers or teacher aides), is defined as

16

BENEFITS: = 2 dijwj, j=l

where

d:j = 1 if the ith center offered the jth benefit to work-

wj = the average percentage ratio of payments for ers of type t, 0 otherwise,

benefits of type j to total wages for nonmanufacturing firms (U.S. Chamber of Com- merce , 1987).

Pensions are excluded from the calculation of BENEFITS, as explained below. The mean value of BENEFITS was 18.2 for teachers and 17.8 for aides. These values can be interpreted as indicating that the average center gave teachers and aides a benefits package (excluding pensions) that cost about 18 percent of the wage bill for workers of that type.

To test the hypothesis that pension benefits in particular will reduce turnover, we separated pensions from the other 16 benefits in the BENE- FITS variable, and included a dummy variable for whether a pension benefit was offered to the type of worker in question (teachers or aides). We found that 45 percent of centers extended pension benefits to teachers, and 36 percent extended them to aides.

Other center characteristics. The survey questionnaire also asked detailed questions about the characteristics of the center, including number of children served, childhtaff ratios, proportion of children with handicap-

'*For teachers, 96 percent of the centers offered paid vacation, 45 percent offered pension benefits, 81 percent offered health insurance, and 54 percent offered reduced fees for child care.

13Respondents generally did provide information about the total payment for benefits. Imitating Wilson and Peel, we used the ratio of total benefit payments to the total wage bill as an alternative to our index variable. Substituting this variable had little effect on our results.


ping conditions, etc. Supplemental information about the characteristics of the local labor market was taken from a number of published sources as detailed below. Table 1 provides descriptive statistics for all of the variables used in the analysis.

Estimation Method Because the distributions of the dependent variables-the quit rate and

the fire rate-are truncated below at zero, the appropriate statistical model for this censored regression problem is tobit. One complication with which our tobit models must contend is the potential endogeneity of wages. If, as the efficiency wage literature assumes, firms pay higher wages to reduce turnover, then the turnover rate could be a determinant of the center’s wage rate. l4 To allow for this possibility we employed Amemiya’s efficient multistage estimator for models in which a continuous variable (wages) and a truncated variable (quit rate or fire rate) are simultaneously determined (Amemiya, 1979). The details of Amemiya’s estimator are described in the appendix.

The following variables were used as instruments for wages in the GLS models of the quit and fire rates: the average salary of public school teachers in the state, the average value of a home in the local county, per capita income in the county, the monthly tuition fee charged by the center, and the hours of training given to teaching staff in the last twelve months. The first three instruments-state teacher salary, per capita income, and average home value-are related to the local real wage for teachers. The fee charged by a center should be correlated with the quality of service provided and therefore with unobservable quality characteristics of its teaching staff, characteristics that are presumably purchased with higher wages. Monthly fee should also be related to the center’s profitability. The training given to staff should translate into higher wages unless it is entirely firm specific and entirely employer owned, which seems highly unlikely in this particular industry. This set of instruments is not ideal, especially for the quit models. We discuss this further below.

Estimation Results Tables 2a and 2b report the results of our tobit models predicting the

yearly quit and fire rates for teachers (Table 2a) and teacher aides (Table

14We assume that because benefit structures are difficult to adjust in a given year, the type and number of benefits offered does not respond to an increase in the quit rate in a given year; thus BENEFITS is not endogenous.


TABLE 1 DESCRIPTIVE STATISTICS FOR VARIABLES

~ ~ ~ ~ ~ _____

Variable Mean Standard Deviation

Dependent Variables Quit rate for teachers 20.9 25.3 Firing rate for teachers 1.3 3.8 Quit Rate for Aides 35.6 45.2 Firing rate for aides 2.9 8.0

Center Characteristics Hourly wage for teachers Hourly wage for aides Wage dispersion of teachers Wage dispersion of aides Pension dummy for teachers Pension dummy for aides Other benefits for teachers (% of wage Other benefits for aides (% of wage) Average hours of full-time teachers Average hours of full-time aides Number of children ( R E ) Children per teaching staffa Percent of children with handicaps Whether center is for-profit Whether firm has multiple centers Operating less than five years Monthly fee charged

Stuff Characteristics Average education of teachers Average education of aides Average experience of teachers Average experience of aides

6.90 4.27

.86

.21

.45

.36 18.2 17.8 36.3 31.6 80.7 9.0 4.6

.14

.06

.13 304.1

15.0 13.1 6.3 3.3

1.80 1.26 1.20 2.3

.50

.50 4.3 8.0 5.1

10.8 54.1 2.0 7.0 .35 .24 .33

93.6

1.1 2.0 3.1 3.1

Average experience of director 14.6 6.9

Local Characteristics Located in SMSA .88 .32 County population (000’s)b 242.3 296.6 State average teacher salaryc 28414 3218 County median home valueb 56070 18814 Income per capita 11859 23188

aThis is the childlstaff ratio for 4-year-olds, a group of special interest to the GAO study b S o ~ ~ ~ ~ : U.S. Bureau of the Census (1988). ‘SOURCE: U.S. Bureau of Educational Research and Development (1989).


TABLE 2a DETERMINANTS OF QUIT AND FIRE RATES FOR TEACHERS

(t-statistics are in parentheses) ~~~

Variables

Ordinary Tobit GLS Estimator

(1) (2) (3) (4) Quits Fires Quits Fires

Log of wage rate

Wage dispersion

Pension dummy

Other benefits (% of wage)

Average education

Average experience

Average full-time hours

ETE children

Children per teaching staff

For-profit dummy

Multicenter firm dummy

Handicapped children (%)

Director's experience

County population (000's)

SMSA dummy

Operating < 5 years dummy

Constant

Sample

-24.4** (-3.93) -9.03 ( - S O ) -2.40 (-.78)

.45 (1.33) 1.13 (. 80)

(-4.37)

(. 80)

(. 46)

(33)

-2.39**

.30

.01

.36

-1.14 (-.29) -3.86 (- .67) - .29

(-1.26) .27

(1.27) - ,004

(- .79)

(31) 2.32

-2.83 (- .69) 27.1 (1.01)

204

-18.1*'

-4.97

-6.63 (- 1.49)

(-2.00)

(- .20)

.03 (.08)

(-1.22)

(- .20)

-2.51

- .05

- .41 (-.78)

.05* (1.75) -.18

6.88 (1.57)

.16

- .40 (- .88) -.05

- .002 (- .29) 10.4 (1.41) 5.82

(1.25) 60.8 (1.46)

(-.lY)

(.02)

(-.20)

204

-11.0 (-.Yl)

(.35) .81

-3.39 (- 1.04)

.33

.43

-2.88**

(. 90)

(.25)

(4.52) .46

(1.03) ,009

.48 (.35)

(.70) -1.25 (-.32) -5.10 (-.87) - .28

(- 1.24) .24

.003 (- .68) - . lo

-4.48

(1.10)

(- .02)

(- 1.02)

(50) 14.3

204

-23.9 (-1.21)

(50) 10.6

-5.19 (- 1.07)

.08

-1.21 (- .46) -.32

(.IS)

(- .35) - .51

(-.86) .05*

(1.73) -.17

(-.18) 5.06

(1.15) 1.80

(1.38) -.29

(- .61) - .03

- ,002

8.79 (1.25) 6.93

(1.38) 55.1 (1.40)

(-.lo)

(-.22)

204

'Significant at .1 level; "significant at .05 level.

240 I IRENE POWELL, MARK MONTGOMERY, AND JAMES COSGROVE

TABLE 2b DETERMINANTS OF QUIT AND FIRE RATES FOR TEACHER AIDES

(t-statistics are in parentheses)

Variables

Ordinary Tobit GLS Estimator

(1) (2) (3) (4) Quits Fires Quits Fires

Log of wage rate

Wage dispersion

Pension Dummy

Other benefits (% of wage)

Average education

Average experience

Average full-time hours

R E children

Children per teaching staff

For-profit dummy

Multicenter firm dummy

Handicapped children (%)

Director's experience

County population (000's)

SMSA dummy

Operating < 5 years dummy

Constant

Sample

-11.8** (-2.29)

19.1 (1.23) 2.72

.24

3.69**

(.35)

(. 66)

(2.90) -2.51** (-2.96)

-.19 (-.51) - .01

1.97** (1.97) 2.06

8.39 (1.04) -.33

-.58* (- 1.74)

(- .37)

(.37)

(-.97)

,006 (.96) -5.17 (-.80) 8.66

(1.41) -25.4 ( - . 95 )

177

-2.78 (-.42)

12.9 (.66) -4.67 (- .61)

.12

-5.46** (. 28)

(-3.43)

(3.49) 3.72"*

-.73 ( - 1 .56)

.02

- .06 (- .06) 6.48

-4.36

(52)

(.96)

(- .37) .64*

(1.77) .46

(1.15) .003

20.1* (1.71) 11.4* (1.73) 28.4

(.38)

(.82)

177

9.73

11.9

.66

(. 62)

(.76)

(.lo) - .08

(-.23) 3.80** (2.99)

-3.01*' (- 3.17)

.63**

- .02 (- ,681 1.70* (1.65) 3.83

6.93

- .34

- .48 (-1.50)

,002

-4.13 (- .64)

(2.11)

(.65)

(35)

(- .99)

(.43)

8.28 (1.36) - 69.9* * (-2.08)

177

-8.7

9.72 (- .47)

(.47)

(-.53)

(.28)

-4.18

.13

-4.89** (-3.08) 3.43** (2.98) - .60

( - 1.26) .18

- .02

5.89

(.46)

(- .02)

(. 89)

(- .37) -4.32

.55 (1.46)

.39

,004

16.3 (1.14) 9.24

(1.41) 37.1

(.96)

(50)

(. 89)

177

*Significant at .1 level; **significant at .05 level.


2b), re~pective1y.l~ The first two columns in each table give the estimates from ordinary tobit models, while the second two columns give the results from Amemiya’s GLS estimator. First we look at the estimates for teachers, the relatively high-skilled group. As predicted by theory, the wage has a negative and significant effect on the quit rates for teachers in the ordinary tobit models. The negative and significant effect of wages on fire rates of teachers lends support to either the efficiency wage theory of improved productivity, or the human capital theory that suggests that higher wages buy higher quality workers. The unadjusted coefficients imply that a $1 increase in wages will reduce quits by about 3.5 percentage points (that is, by 3.5% of the staff) at the mean hourly wage. The effect for firings is comparable: a $1 increase in teacher’s wages reduces the fire rate by 2.8 percentage points. A more accurate estimate of the impact of wages on quits and fires is obtained using the interpretation of tobit coefficients suggested by MacDonald and Moffit (see Judge et al., 1984, p. 783).16 Using the MacDonald and Moffit formula, a $1 increase in wages reduces quits by about 2 percentage points, and reduces fires by about 1 percentage point.17

Columns 3 and 4 in Table 2a report the results for teachers from the GLS estimator. The coefficient of wages falls to about half its value in the quit equation and is insignificant. Because the error term in the quit equation is expected to be positively correlated with wages, GLS was expected to make the coefficient of wages more negative rather than less negative. It appears that the variables chosen as instruments did not do a good job in identifying the quit equation, a result of the difficulty in finding variables that influence wages but not the quit rate. Not that in the fire rate model the GLS estimator does make the wage coefficient more negative, implying that the instru-

ISThe hypothesis that teachers and aides can be pooled was rejected at the ,001 level. The correlation across occupations of quits, fires, and center-specific wage differentials were low; .15 for quit rates, .22 for fire rates, and .13 for center-specific wage differentials, again suggesting that teachers and aides are in distinct labor markets. These correlations should be viewed cautiously, however, because 30 centers are excluded from these calculations because they have no aides. This exclusion is not likely to be random; firms that hire no aides should differ systematically from those that do.

T h e estimation formula is given by

aE(Quits) z f ( 4 aF(z) -- - F(z,) pW ( 1 - - - f02 ) + E(Quits*) - , awage F(z) F(Z)* awage

where z = X p / u , pw is the tobit coefficient of wages, and f and F are the probability density function and cumulative density function, respectively, of the standard normal distribution. E(Quits*) = z + of(z)/F(z) .

T h e coefficient on wages may be biased downward if the relatively low levels of experience for workers in our sample imply that current wages are a poor estimate of expected lifetime compensation. Our inclusion of the wage dispersion variable should at least partially control for this effect.


ments perform better in that model. Even in the fire model, however, the effect of wages is not significant at conventional levels.

Next we consider the other compensation variables. Offering teachers a pension benefit has the expected negative effect, and a fairly sizeable one (especially in the fire models), but we cannot reject the hypothesis that the true effect is zero at the .05 level. Nonpension benefits have a very small and insignificant effect, which has the wrong sign. The wage dispersion variable-our measure of whether the firm rewards performance and/or job tenure-had a low level of significance in both the quit and fire models. This result implies that establishments that compensate workers for other than human capital characteristics do not thereby reduce turnover.

The only other variables to show significance in the teacher models were the average experience of the staff, which had a negative effect as expected, and the number of FTE children, which was significant in the fire models. The latter effect might be explained by the fact that larger centers had more teachers and were therefore more likely to fire one of them in a given year. The coefficient for average experience implies that an extra year of average staff experience reduced quits by 2.56 percentage points.18 A negative effect of average experience might be observed because teachers with more years of job market experience are better at identifying an appropriate match between themselves and a potential employer.

We next turn to the results for the lower-skilled teacher aides, in Table 2b. The compensation variables have effects comparable to those for the teacher models, except that the hourly wage is insignificant in the fire model. The wage effect for quits is smaller in magnitude than for teachers: in the ordinary tobit model, a $1 increase in wages lowers the quit rate by about only 1 percentage point. In the GLS models, the wage rate has the wrong sign and is insignificant, which may imply that our instruments (such as state teacher salary and median home value) had little relevance to the wages of low-skill workers such as aides. The fringe benefit variables have very low levels of significance in both the quit and fire models, and the wrong sign in some cases. The wage dispersion variable has a large effect in both models, though its significance is still fairly 10w.l~ The posi-

'*It is possible that both education and experience could be endogenous if less experienced staff had consistently higher quit rates, and if centers with high quit rates tended to be out of equilibrium-that is, if these centers had not yet replaced departing staff with teachers of comparable training and experience.

T h e s e (unadjusted) coefficients would be interpreted as follows: a mean square error of $0.50 per hour in the wage equation (about 12% of the mean average wage in the sample) would increase quits by 9.5 percentage points and increase fires by 6.5 percentage points.


tive effect for aides implies that centers with a wage structure that rewards nonhuman capital characteristics tend to fire more aides and induce them to quit more often.

Some other characteristics of the center and staff do seem to have a significant effect on quit and fire rates for aides. Higher average education corresponds to a higher quit rate and a lower firing rate. To the extent that our teacher aides are female, and to the extent that they are white and young, the result that education increases quits is consistent with findings of Blau and Kahn (1981) using individual-level data. Rela- tively more educated people in low-skill aides jobs are likely to have better alternative employment possibilities. Also, to the extent that education is correlated with such personal characteristics as perseverance, fu- ture orientation, etc., we would expect that more educated people would be fired less often.

The positive effect of average experience on firing is more difficult to explain. It may simply reflect the problem raised in note 16-that some centers are out of equilibrium in that they have not replaced all of the fired aides. If the fired aides came from the lower end of the experience distribution, we could observe high fire rates corresponding to high average experience levels.

The cost of reducing turnover through higher wages. Efficiency wage theory argues that firms will reduce both quitting and shirking by raising wages. Our results are consistent with the argument that an establishment can influence its turnover rate through wages. Such a finding does not necessarily imply, however, that firms will find it profitable to do so. Following Leonard (1987), we can use the estimated coefficients from our analysis to calculate the turnover cost that must obtain if firms are in fact using higher wages solely to reduce quits. In theory, a cost-minimizing establishment would increase wages until the marginal increment to the wage bill equaled the marginal reduction in turnover cost. At the opti- mum, therefore, letting TC be turnover cost per quit, we have

A Wage * N * H = A (Turnovers) * TC, (3) where N and H are the number of teachers and their hours worked, respectively. From the tobit models, we get

A (Turnovers) = (4)

where /3$ is the MacDonald-Moffit adjusted coefficient of the logged wage in a model of the proportion of staff quitting or getting fired. Substituting


equation (3) into equation (4) and solving for TC gives a rough measure of cost per turnover equal to (H * 100 * wage/p&). To measure this cost per turnover, we ran an unreported tobit model for teachers predicting turnover (the quit rate + the fire rate), which produced a p& of -14.3 (the raw coefficient was -27.4 with a t-statistic of -4.40). Assuming that each teacher earns the mean wage, works the mean number of full-time weekly hours, and teaches 48 weeks per year, our value of p& implies a mean yearly cost per teacher quit of more than $81,000. Thus, the cost of a quit to the firm would need to be high-improbably high-in order for it to be profitable to raise wages to avoid this quit. This result is strongly consistent with that in Leonard's study of turnover in the high-technology sector of one state; he found implied quit costs to be $57,000-far too high to be realistic. Our analysis supports Leonard's conclusion that quits are insuffi- ciently responsive to wages to justify the assertion made by the efficiency wage literature that firms are paying above-market wages solely in order to reduce turnover.20

It is possible to argue, of course, that higher wages do more than reduce turnover, so that the estimates made here, and by Leonard, are mislead- ing. There may be other effects of high wages such as sorting effects, easier filling of vacancies, reduction of absenteeism, and increased effort. Our results for fires are consistent with the contention of efficiency wage theory that higher wages increase effort and reduce absenteeism (at least for our high-skill group). However, because the magnitudes of the wage effect on fires is fairly small, and the implied costs of quits are extremely large, we do not conclude that the effect of wages on effort is sufficient to eliminate the inconsistency between our estimates of implied turnover cost and efficiency wage theory.21

Summary and Conclusions This paper is one of the very few to explore the impact of compensation

structure on establishment turnover rates, and it considered aspects of compensation structure that previous studies could not. Moreover, this study was able to distinguish between quit and fire rates. Using a sample of establishments providing early childhood education we were able to verify that higher wages are associated with lower quits for both the high-skill

"Note that we control for experience, not tenure. Low-tenure (and thus low-wage) workers may have a higher propensity to quit; thus, our results may be biased in favor of efficiency wage theory. We somewhat control for this effect by including experience and newness of the center.

21Since it is likely that effort only causes firing if effort is low and that most firing is for reasons other than low effort, it may be that wages reduce effort without affecting firing substantially.


workers (teachers) and low-skill workers (teacher aides). This result contin- ued to hold when we employed a GLS estimator to cope with the potential endogeneity of wages, though in the GLS models the effect was smaller and less significant.

Higher wages also appeared to lower the firing rate of teachers, but not teacher aides. The availability of pension benefits had a negative impact on quits and fires for teachers, but the effect was statistically insignificant. Other forms of benefits had little apparent impact. As a measure of whether the establishment rewarded performance and/or tenure, we included the dispersion of wages within a skill level, after controlling for the human capital of the workers. This measure was never significant in the quit or fire equations for either teachers or aides, though its estimated effect was very large in the aides models. We were not able to conclude with much confidence that, in this industry at least, such a reward structure is an important determinant of turnover.

Despite our finding that higher wages reduce establishment quit and fire rates, our results are not consistent with the conclusion that establishments will find it cost effective to use wages solely to reduce quits. While somewhat surprising, this result is strongly consistent with previous studies to analyze turnover at the establishment level (Leonard, 1987; Wilson and Peel, 1991). Like Leonard, our estimates imply that raising wages to reduce turnover would be profitable only if turnover costs were enormous- far larger than is plausible. Overall, therefore, while the turnover version of efficiency wage theory has some support from our analysis, the effect does not appear strong enough to be the sole explanation for the observed wage differences among centers.

In addition to what our results say about the general determinants of turnover, we think it important to consider the implications of these findings for public policy with respect to child care. High staff turnover has been identified as a major detriment to the quality of care, and govern- ment efforts to reduce such turnover might be justified on the grounds that quality of child care has significant externalities. Unfortunately, our estimates suggest that raising the wages of care providers-perhaps through direct subsidies or reduced wage taxes-would be an expensive way to reduce turnover. Cutting turnover, say, by half would require a 50 percent increase in the hourly wage for teachers. This would amount to more than eliminating all income taxes on teacher salaries, a policy that would not seem politically feasible. Equally unfortunate is our finding that none of the other center characteristics that policy might influence, such characteristics as childlstaff ratios, size of the center, fringe benefits, or hours worked, seemed to significantly influence turnover either. Thus, if policy-


makers do wish to reduce turnover rates of child care teachers, wages, though an expensive method, seem to hold the only hope.

Appendix: The Amemiya GLS Estimator This appendix describes the multistage GLS estimator developed by

Amemiya (1979), which provides an efficient unbiased estimate of the coefficient of an endogenous continuous regressor in a tobit model. For purposes of this appendix, we will let Q represent the quit rate, W the endogenous regressor wage, and X the other explanatory variables. The underlying model is

Q T = yWWi + PqXq, + eqi Wi = YqQi + P w x w i + ewi,

Q; = { Q~ if Q~ 2 o

( 4 where

0 otherwise.

The reduced form equations for this system can be expressed as

wi = ynw + vwi QT = XiIIq + vqi,

where Xi = (Xwi, X,,), and vwi and vqi are error terms. Now we can estimate IIw by ordinary least squares and IIq by tobit. Amemiya shows that-using hats to denote estimated values-the estimates of IIq and IIg have the following relationship:

4 = Y , 4 + JqPq + (4 - U q ) - yw(R - n w ) , (A3) where J, is a matrix with ones and zeros in appropriate places so that XJ, = X,. We are interested in estimating the vector aq = [y,, p,]. Using (A3), Amemiya suggests a GLS estimator for aq given by

(A4)

(A51

kq = (61 v - l G ) - l & v - q ,

v = (%% - 2$Jw&qw)(x’x)-1 + v,, where G = [IIw, Jq]. The matrix V is such that

where the d s refer to the variance or covariance of the appropriately subscripted E’S in equations (Al), and V, is the variance-covariance matrix of IIq. As above, the hats denote that these values are estimated. IIq and V, are estimated from the tobit model for the second equation of (A2). II, is from the OLS regression of W on X. uqw is estimated by


1 n &,, = - x(qieWiPi-’),

n i = l

where eWi is the ith residual from the regression of W on X, and

72 pi-L exp [ - - ] d7 -x 2a;

The value of y, is estimated as follows. Let xj be a column vector of X which is contained in X, but not X,, and let rjw and rjq be the jth elements of 17, and 17,, respectively. Then yw = r j ,Inj ,. Note that since there are several elements of X that are excluded from X, or X,, respectively, the estimator is not unique given X, Q, and W. However, we found the estimates of aq to be very robust with respect to which elements of X were used to estimate y,.

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