Economica (1993) 60, 125-42

The Employer Size-Wage Gap: Evidence for Britain By BRIAN G. M. MAIN and

BARRY REILLY

. University of Edinburgh and University of Sussex Final version received 5 May 1992. This paper presents estimates for the employer plant size-wage gap for Britain. Using an ordered probit model, selectivity-corrected wage equations are estimated for three plant size categories. In a comparison between plants with more than 500 workers and those with less than 100, a wage gap estimate of over 17 per cent is detected. The wage effects of unionization in plants with more than 500 workers is reported as insignificant. In contrast to evidence provided by Idson and Feaster (1990) for the United States, no evidence of non-random sorting of workers across plant size is detected. .

INTRODUCTION

The relationship between employer size and wages has been the subject of empirical investigation since Lester's (1967) seminal contribution.' Masters (1969), Haworth and Reuter (1978) and Pugel (1980), using industry-level data for the United States, detected a strong positive relationship between the proportion of workers in 'large' plants and the industry wage. This employer size-wage relationship was confirmed by Mellow (1982), Podgursky (1986) and Evans and Leighton (1989), using individual-level data-sets for the Uhited States. The clear message that emanates from these studies is that workers employed in 'large' plants earn higher wages than workers employed in 'small' .plants. Though the empirical existence of a wage premium for employees working in 'large' plants appears well established, explanations as to why there exists such a premium remain the subject of much debate. Brown and Medoff (1989) considered a number of possible explanations for the employer size-wage gap. Prominent among the neoclassical explanations for this phenomenon are differentials in labour quality between 'large' and 'small' plants (arising from the relatively higher capitar intensity of 'large' plants) and compensating differentials (arising from the fact that employees in 'large' plants are subjected to less pleasant working conditions and, as a consequence, earn a compensating differential). Brown and Medoff (1989) also considered institutionally oriented explanations for the size-wage gap. One such explanation relies on the assumption that 'large' firms or plants follow a strategy of 'positive labour relations' and pay higher wages to deter unionization at their plants. Another such explanation focuses on product market power as a source of higher wages in 'large' plants. This explanation rests on the assumptions that 'large' firms operate in product markets that are characterized by inelastic demand and the employers are willing to share the accruing monopoly rents. Another possible explanation is linked to the inability of the larger, impersonal, firms to accurately monitor workers' efforts. Efficiency wage considerations lead to the payment of a higher wage in a 'large' relative to a 'small' firm for a given quality of worker. Garen (1985) details a theoretical model © The London School of Economics and Political Science 1993

126

ECONOMICA

[MAY

which, though not piedicted in tenns of efficiency wiiges, possesses the interesting implication that 'large' plants/firms rely more heavily on external indicators of ability (for example, schooling) to assess worker productivity than do 'small' plants or firms. One final explanation, presented by Brown and Medoff (1989) but without any supporting empirical evidence, suggested that the size-wage gap may be explained by the fact that 'large'firmspay higher prices for their labour inputs because their other inputs are relatively cheaper (owing, for example, to lower interest rates on borrowed funds). No explanation is given, however, as to what incentives exist for 'large' firms to pay these higher wages for the labour input in the first place. More recently. Green et al (1992) provide an explanation for the size-wage effect couched in terms of a monopsonistic model. However, the authors concede that models of monopsony require a lot more investigation concerning their assumptions and conclusions. This development in theoretical explanations of the employer size-wage gap has not been accompanied by equivalent progress in techniques of estimating the wage gap. Most of the empirical research that has investigated this phenomenon has used the econometric framework adopted in early empirical studies of the union-wage gap. In the industry-level studies cited above, for example, the proportion of workers in 'large' plants provided the appropriate size variable in wage equations. In individual-level studies, the size effects were picked up by a set of exogenous intercept dummies. Idson and Feaster (1990) justifiably argue that employer size is a decision variable based on an interaction between employer demand and workers' labour supply decisions. Thus, failure to account adequately for the potential non-random sorting of workers across different sizes of firms may lead to biased estimates of the employer size-wage gaps. Idson and Feaster (1990) employ an extension of the Heckman (1979) procedure to address this problem. An ordered probit model is used to predict firm size attachment, and these predictions are then used to construct the truncated means necessary to correct the wage equations for selectivity bias. Up to now, the issue of the employer size-wage gap appears to have been a relatively neglected area of investigation in Britain, with a recent exception provided by Green et al. (1992). The purpose of this papei is lo examine the phenomenon using data for the United Kingdom derived from the Economic and Social Research Council's 'Social Change and Economic Life Initiative' data-set of 1986. Three plant size classes are used for the analysis: 'small', 'medium' and 'large'. More explicit information on this breakdown is provided in a later section. Separate wage equations for these plant size classes are estimated with an appropriate correction for selectivity bias. It is hoped that the wage equation estimates will provide not only a feel for the magnitude of the employer size-wage gap (in particular, that between 'large' and 'small' plants), but also empirical information that can shed some light on possible explanations for the wage gap itself. The organization of this paper is as follows. Section I details the data-set to be employed in the analysis, paying particular attention to a number of the key variables used, such as employer size and unionization. Section II outlines the econometric model that deals with the problem of selectivity bias in the © The London School of Economics and Political Science 1993

1993]

EMPLOYER SIZE-WAGE GAP

127

context of an ordinal latent dependent variable. Section III provides the empirical estimates, and Section IV offers some conclusions.

I. DATA

The data employed in the following analysis were collected under the Economic and Social Research Council's 'Social Change and Economic Life Initiative' in 1986. In each of six local labour markets (Aberdeen, Coventry, Kirkcaldy, Northampton, Rochdale and Swindon) 1000 individuals, aged between 20 and 59, were randomly selected for an interview of some one-and-a-half hours' duration. From each respondent, detailed information was collected on current labour market situation, educational background and workhistory since leaving full-time education. For those in employment, information concerning hours of work, pay and job characteristics were also collected.^ For the purposes of this study, only male full-time workers employed in the private sector are used in the analysis.^ The size categorization variable is based on a question asking how many people were employed 'at or from the establishment' where the individual worked, and respondents were given a limited number of size categories. From the responses to this question, we can allocate workers to three broad sizes of categories: up to 99 workers (defined as 'small'), 100-499 workers (defined as 'medium') and 500+ (defined as 'large'). Since the survey did not ask a question on company size, it would be misleading to refer to these size categories as firm or company size categories.^ Thus, the terms 'plant' or 'workplace' will be used below when referring to these categories. In those cases where companies or firms are single-plant entities, all these terms, of course, are synonymous. Table Al in Appendix A contains a brief description of all the variables used in the analysis. Two variables are worthy of some additional comment. A union representation rather than a union membership variable is used in this analysis. This variable is constructed from responses to a question that asked 'Where you work, are there any trade unions representing people who do your kind or work?' The TUREP variable thus captures trade union power at the workplace and overcomes the problems posed by using a trade union membership variable, where non-union members benefit from the exertion of union power.' The WAGE variable is the natural log of the basic hourly wage. The basic hourly wage rate is defined by the gross wage or salary in the last pay period divided by the number of hours worked in that period, with overtime being weighted time and a half. As will be shown below, the substantive results of this paper are not affected by making alternative assumptions about the payment of overtime hours. Table A2 in Appendix A reports the means for the relevant variables broken down by the employer size categories. The number of individuals used in the analysis is 905, with 466, 220 and 219 observations in the 'small', 'medium' and 'large' plant size categories, respectively. Since little is known about the properties of the type of two-step estimators to be outlined below, the usual caveats regarding small samples must be inserted. © The London School or Economics and Political Science 1993

128

ECONOMICA II.

ECONOMETRIC

[MAY

METHODOLOGY

An ordered probit model provides the appropriate framework in which to examine the determinants of an individual's attachment to a given plant size. A latent dependent variable model can be defined as:

(1)

n

where Yf is unobservable, Z contains the set of determining variables, y is an unknown parameter vector and u,~7V(0,1).* More precisely, if: (2a)

y* < 0,

the individual works in a 'small' sized plant;

(2b)

0{,i

and for 'large' sized plants as: (7c)

\2

where (-) and (•) are the standard normal density and distribution functions, respectively. . The fi and the y vector of parameters are obtained by maximum likelihood techniques. The likelihood function for the ordered probit model, used in this study, is given by:

(8)

L= n «I>(-Z'r) n

Xn y=2

where the subscripts on the Y variable are suppressed. The maximum likelihood estimates for fi and the y vector are then used to construct the truncated means in (7a)-(7c). These constructed variables are then inserted into the wage equations and OLS estimation is performed. However, the standard errors must be corrected to account for both heteroscedasticity and the use of predicted selectivity variables. Greene (1981) suggests a procedure to correct the standard errors which is followed here and is detailed in Appendix B.

lir. EMPIRICAL RESULTS

Table A2 in Appendix A provides the mean values for the variables used in the analysis. For convenience, the comparison that follows is effected only ijetween 'large' and 'small' workplaces. Workers employed in 'large' plants earn on average over 25 per cent more than \vorkers employed in 'small' plants. It is also evident from Table A2 that workers in 'large' plants, on average, are more educated, possess higher labour force experience and have shorter lengths of past unemployment than workers in 'small' plants. Furthermore, over 74 per cent of workers in 'large' plants are represented by unions at their workplaces as compared with just under 34 per cent of workers in 'small' plants. Over 43 per cent of all 'large' plant employees work in the metal goods, and © The London School of Economics and Political Science 1993

130

ECONOMICA

[MAY

engineering industries, and nearly 2S per cent of all 'large' plant workers reside in Coventry. This summary glance at the raw data is only intended to highlight the contrast in worker characteristics across plant size and to motivate an interest in the subsequent empirical estimates. The reduced-form estimates for the ordered probit model are reported in Table A3 of Appendix C and are not the subject of extensive discussion h«e. Note, however, that the identification of the selectivity variables in the wage equations is achieved through the inclusion in the ordered probit (and the exclusion from the wage equations) of a set of variables that capture the effects of some family characteristics (dummies for the number of dependent children and their age groups). Their inclusion in the size attachment equation is rationaUzed by the assumption that workers with dependent children are more likely to choose larger plants given their presumed employment stability. However, it could be argued that such variables should also enter the wage equations. This is the standard problem with such selectivity models where the identifying restrictions can appear somewhat ad hoc. As a rough test for whether the family background variables should be included in the wage equations, a Lagrange multiplier test was estimated using the OLS residuals from the three wage equations. The LM tests for the 'small' and 'large' sized categories were not significant at conventional levels, but that for the 'medium' sized category was.^ This tentatively suggests that the restrictions for identifying the selection effects in the 'small' and 'large' plant size wage equations are adequate. This is regarded as salutary, since most of the emphasis in this paper concerns a comparison of wage estimates for the 'large' and 'small' employer sizes. Finally, as the footnote to Table A3 shows, the identifying set of dummy variables are jointly significant in the ordered probit equation. In general, the signs on the significant variables in the reduced-form ordered probit are what wouW be expected a priori. Although the family background variables are not individually significant, they are, as pointed out above, significant as a set. In the interests of brevity. Table A4 provides only the impact effects for the different family background variables. With the exception of the categories for dependent children of primary school age, the impact effects are in line with ones' priors. For instance, the more dependent children of pre-school age an individual has, the greater the probability of attachment to a 'large' sized plant. A similar result is obtained for individuals with dependent children of secondary school age. In contrast, however, the probability of 'large' size plant attachment for an individual with dependent children of primary school age declines as the number of such children increases. This, one has to accept, is not consistent with ones' priors but may be linked to the small number of observations in the KIDSPRIl (2-9 per cent) and KIDSPRI3 (5-9 per cent) categories. In addition, the coefficient on the KIDSPRI3 variable is poorly determined, and this ihay also be a contributory factor to this ostensibly perverse result. Attention now focuses on Table 1 and the reported estimates for the selectivity-cortecled wage equations. The estimated Tet\iins to education are highest in 'small' plants with the effect in iarge' plants reported as insignificant. However, statistically, these effects are not significantly different from each other on the basis of a t-test. Thus, there appears minimal evidence in favour © The London School of Economics and Political Science 1993

1993]

131

EMPLOYER SIZE-WAGE GAP TABLE 1 WAGE EQUATION ESTIMATES BY EMPLOYER SIZE

Small Medium Large (1-99 workers) (100-499 workers) (500+ workers)

Constant

0-4998** (0-1274)

1-3051** (0-3536)

0-8314 (0-5078)

(0-0127) 0-0338** (0-0057) -0-0006** (0-0001) -0-0726** (0-0308) 0-0045 (0-0063)

0-0441** (0-0193) 0-0104 (0-0099) -0-0002 (0-0002) 0-0083 (0-0673) -0-01771 (0-0190)

0-0260 (0-0181) 0-0284** (0-0104) -0-0005** (0-0002) -0-1066** (0-0429) 0-0158** (0-0072)

0-1653** (0-0734) 0-0174 (0-0379) 0-0384 (0-0367) 0-0038 (0-0668) 0-0485 (0-0349) -0-0176 (0-0524) 0-0842** (0-0390)

-0-1528 (0-1233) 0-0327 (0-0582) 0-0528 (0-0566) -0-0709 (0-1043) 0-1333** (0-0546) 0-0479 (0-0881) 0-0800 (0-0597)

-0-1392 (0-1229) 0-1399** (0-0548) 0-1156** (0-0554) 0-0036 (0-0826) 0-0102 (0-0560) 0-0710 (0-0720) 0-0488 (0-0560)

0-3670** (0-1383) 0-2931** (0-1134) 0-2530** (0-1152) 0-2968** (0-1020) 0-1597 (0-0943) 0-1551 (0-1058) 0-2426** (0-0955)

-0-1756 (0-2120) -0-0947 (0-1844) -0-1145 (0-1808) 0-0360 (0-1753) 0-1289 (0-1545) 0-1745 (0-1649) -0-0427 (0-1725)

0-0323 (0-2039) 0-0395 (0-1764) 0-0379 (0-1760) -0-0775 (0-1806) -0-0004 (0-1590) -0-0762 (0-1830) 0-1880 (0-1600)

0-2384** (0-1514) 0-0561 (0-1466) 0-0075 (0-1582)

0-4409** (0-1379) 0-4327** (0-1393) 0-2049* (0-1267)

Personal characteristics 0-0514** EDUC EMP

EMPS UNEMP UNEMPS Job characteristics

TUREP SUP

TDUR SHIFT CALLOUT NIGHT SKILL Industry INDl IND2 IND3 IND4 IND5 IND6 IND7 Occupation OCCl OCC2 OCC3

0-1570 (0-0930) 0-2135** (0-1065) -0-0784 (0-0843)

© The London School of Economics and Political Science 1993

132

[MAY

ECONOMICA

TABLE 1—continued

Small Medium Large (1-99 workers) (100-499 workers) (500+ workers)

Occupation OCC4 OCC5 OCC6

0-1398 (0-1091) -0-0350 (0-0743) -0-0312 (0-0776)

0-0328 (0-1609) -0-0363 (0-1160) -0-1035 (0-1224)

0-2853 (0-1596) 0-2305** (0-1147) 0-1625 (0-1179)

0-0301 (0-0812) 0-0750 (0-0826) -0-0007 (0-0870) -0-0415 (0-0864) -0-0988 (0-983)

0-1214 (0-0895) -0-0012 (0-0864) 0-1211 (0-0899) 0-0518 (0-0965) 0-0254 (0-1062)

Area of residence

ABERD KIRK COV

SWIN NORTHN Selection term A P a R^ N Wald test xl Wald test xl Wald test xl Wald test xl Wald test xl

for joint for joint for joint for joint for joint

0-1036** (0-0490) 0-0300 (0-0525) 0-0844 (0-0553) 0-1518** (0-0588) 0-1404** (0-0611)

0-0776 -0-2127 -0-0306 (0-1462) (0-1828) (0-1503) 0-2516 -0-7329 -0-1014 0-2902 0-3022 0-3085 0-3474 0-3964 0-3922 466 220 219 significance of experience terms 35-791** 2-189 7-855** significance of unemployment terms 13-262** 4-669* 6-196** significance of industry dummies 15-417** 7-225 5-051 significance of occupation dummies 22-313* 10-036** 15-931** significance of area of residence dummies 9-177* 3-048 4-873

The standard errors, in parentheses, are corrected using the procedure outlined by Greene' (i981), which is detailed in Appendix B. ** denotes significance from zero at the S per cent level using two-tailed tests; * denotes significance from zero at the 10 per cent level using two-tailed tests; c is corrected for selection bias.

of Garen's (1985) hypothesis that 'large'firmsare more likely to use indicators such as education in evaluating worker productivity. On the basis of the Wald statistics, the labour force experience terms are jointly significant in two of the three equations. The estimated returns to labour force experience, when evaluated at 10 years of experience, are highest, at 2-1 per cent per annum, for workers in 'small' plants. The comparable estimates for 'medium' and 'large' plants are, respectively, 0-7 and 1-7 per cent per © The London School of Economics and Political Science 1993

1993]

EMPLOYER SIZE-WAGE GAP

133

annum. On the basis of a t-test, there exists no significant difference between the returns in the 'small'-sized plant and those in the 'large' plant. One of the most interesting features of Table 1 is the insignificance of the union representation variable (TUREP) ih both the 'medium' and 'large' plants. This result is in contrast to the significant 'mark-up' of almost 18 per cent obtained for union-represented workers in the 'small' category. Thus, despite the fact that ov-er 74 per cent of workers in 'lai'ge' workplaces are represented by unions, no significant wage advantage is obtained relative to their non-union represented counterparts in 'large' workplaces. This finding is similar to that of Blanchfiower (1991), who, using OLS and a union membership dummy, detected an insignificant wage effect for individuals employed in plants of 500 or more workers.^ The SHIFT, NIGHT, CALLOUT and SKILL variables are included in the wage equations to shed some light on the 'compensating differentials' argument referred to in the Introduction. Workers subjected to frequent shift work and/or night work or who are on call should, it is argued, receive a wage premium to compensate for the unpleasant nature of this type of work. This effect should be more prevalent in the 'large' plants. As is evident from Table 1, no 'compensating differential' effects are detected in the 'large' workplaces.' The only significant 'compensating differential' variable is the CALLOUT variable in the 'medium' category, where the estimated premium is reported at slightly over 13 per cent, and the SKILL variable in the 'small' category, where the estimated effect is 8-8 per cent. Thus, little empirical evidence is found here to support one of the neoclassical explanations, alluded to by Brown and Medoff (1989), for the existence of higher wages in 'large' plants. However, some of the other job characteristics exhibit greater statistical significance in the 'large'-plant wage equation. For example, supervising responsibilities (SUP) are better rewarded in 'large' plants where the estimated eSect is 15 per cent. The TDUR variable, which captures the ejects of having had training on the job for six or more months, also registers a robust effect, estimated at over 12 per cent in the 'large' plant category. A striking feature of Table 1 is the fact that the industry dummies, both individually and as a set, are important only for employees working in 'small' plants. In contrast, the occupation effects are important, as a set, in all three categories but appear more important individually for employees in 'large' plants. This may be attributable to the fact that 'large' plants/firms are more able to delineate internal labour markets which broadly approximate occupational groupings. On the basis of the magnitudes of the individual occupational coefficient estimates, a clear and intuitive structure emerges. The top earners are management and professional workers, followed by the intermediate nonmanual group, foremen, skilled manual workers, junior non-manual workers, semi-skilled workers and, finally, the unskilled workers. Although some of these estimates may not be statistically different from each other, a comparable order or structure does not emerge for the other plant-size categories under consideration. ' There is evidence of regional variation in wages for 'small' plants on the basis of a Wald statistic. No such evidence emerges for the 'medium' or 'large' categories of plant size. This suggests that 'small'.firms may be more sensitive to local labour market conditions than the other two categories. © The London School of Economics and Political Science 1993

134

ECONOMICA

[MAY

Finally, none of the selection variables is significant. Thus, in contrast to Idson and Feaster (1990), no evidence of non-random sorting of workers across the different sized plants emerges. This is a surprising result, given the marked differences in employee characteristics observed in Table A2. To facilitate the interpretation of these results. Table 2 shows estimates for employer size-wage gaps under a number of alternative assumptions. The notes in this table report how the various differentials are calculated. In order to examine whether the differentials are sensitive to the weighting procedure adopted for the payment of overtime hours, alternative estimates are presented. It should be recalled that overtime hours in the construction of the hourly wage variable were weighted time-and-a-half, and the wage equation estimates reported in Table 1 are based on the use of this variable. Since it is not always

TABLE 2 EMPLOYER SIZE PERCENTAGE OF WAGE GAP ESTIMATES Large/small

Medium/small

Selectivity-corrected" with overtime weighted Time-and-a-half 17-7 Normal 16-5 OLS* with overtime weighted Time-and-a-half 134 Normal 12-5 OLS' with overtime weighted Time-and-a-half 25-5 Normal 25-3 Full sample** with overtime weighted Time-and-a-half 179 Normal 17-3

10-6 12-3 4-5 40 10-5 107 7-9 7-8

" This differential is calculated on the basis of the vector of mean characteristics, for the full sample of individuals, and is interpreted as an unconditional differential; i.e. the selection terms are set to zero. The differentials are calculated by taking the difference ih coefficients between the 'large' and 'small' firms reported in Table 1 and weighting them by the vector of mean characteristics. Taking the exponent of the resultant scalar and subtracting 1 yields the estimated percentage wage gap reported in the first column. A similar exercise is carried out for the coefficients of the 'medium' and 'small' firms. The differential estimates are calculated under two different assumptions about overtime hours: one assumes that they are valued at time-and-a-half (as reported in Table I); the other assumes they are valued at the normal rate. ** These OLS differentials are calculated on the basis of the 'large' and 'medium'-plant-size mean characteristics. 'These OLS differentials are calculated on the basis of the 'small'plant-size characteristics. " These estimates are based on the OLS estimation of the full sample of workers with intercept dummies for large and medium-sized firms included. The reported estimates are the exponents of the dummy coefficients less 1. All wage equation estimates not reported in the text are available from the authors on request. © The London School of Economics and Political Science 1993

1993]

EMPLOYER SIZE-WAGE GAP

135

the case that overtime is paid according to this criterion, it is reasonable to present a set of differential estimates with overtime not given extra weight. Thus, in each case two sets of differential estimates are provided. The first is based on the wage estimates from Table 1, whereas the second is based on wage specifications identical to those reported in Table 1 but with the hourly wage variable treating overtime hours as normal (i.e. with no extra weights). The first row of Table 2 reports unconditional estimates based on the wage coefficients of Table 1. These estimates, though conditional on the X vector, are unconditional on the sector of attachment. They illustrate what an individual with mean characteristics from the sample as a whole would get in one sector (a 'large* plant) relative to what the same individual would get in any other sector (for example a 'small' plant). Reimers (1983) outlines the concept in greater detail. The mean estimate, in a comparison between 'large' and 'small' plants, suggests a differential ofl7-7 per cent. In the context of 'medium' and 'small' plants, the point estimate is 10-6 per cent. These estimates are not dramatically different from those reported for the equations where the hourly wage variable treats the overtime component as normal. The relevant estimates, for purposes of comparison, are 16-5 and 12-3 per cent respectively. The differences between the overtime and normal estimates ofthe differentials appear negligible for almost all the etimates reported in Table 2. Discussion, therefore, will now focus only on the time-and-a-half weighted overtime estimates.'" The difference in wage offers (i.e. the difference in observed wages corrected for the effects of selectivity bias) between 'large' and 'small' plants is 27-6 per cent." The 17-7 per cent unconditional estimate introduced above suggests that the greater part of the wage offer differential (of 27-6 per cent) is not accounted for by differences in worker quality. Thus, another neoclassical explanation for the employer size-wage gap fails to find empirical support in the data. The other estimates reported in Table 2 are derived from OLS estimates that do not control for selectivity bias.'^ The first column and the third and fourth rows of this table report estimates that evaluate the differentials at the means of the 'large'-plant characteristics. The second column and the third and fourth rows provide estimates that calculate the differentials on the basis of the 'medium'-plant-size characteristics. Finally, the fifth and sixth rows provide estimates evaluated on the basis of the 'small'-plant characteristics. These differentials are interpreted as conditional, since they are evaluated conditional on the sector of attachment. Given the lack of selectivity bias in the wage equations, the estimate of 13-4 per cent for the 'large'/'small' comparison is not surprising. Using 'small'-plant mean characteristics, the estimate rises to 25-5 per cent. The variation in the estimates may be viewed as attributable more to variation in the mean characteristics used to evaluate them than to variation in the coefficient estimates. The penultimate row of Table 2 contains estimates obtained from using dummy variables in a fullsample OLS wage equation. In general, all the estimates reported in Table 2 for the 'large' versus 'small' comparisons are of broadly similar dimensions, and our conclusion, therefore, must be resonant of Brown and Medoff (1989), that the employer size-wage gap is 'sizeable' and 'omnipresent'. © The London School of Economics and Political Science 1993

136

ECONOMICA IV;

[MAY

CONCLUSIONS

This paper employed an ordered prob|it selectivity model to examine the niagnitude of the employer size-wage gap. An unconditional estimate based on a comparison between 'large' and 'small' plants, and evaluated at the means ofthe data, suggested a wage gap of 17-7 per cent. Conditipnal OLS estimates ranged between 13-4 and 25-5 per cent, depending on the vector of means at which they were evaluated. In contrast to Idson and Feaster (1990), no evidence of non-random sorting of workers across different plant sizes was detected. The magnitude of the size-wage gap between 'large' and 'small' plants is somewhat higher than the estimates cited in the literature for the union-wage gap (see e.g. Stewart 1983,1990,1991; Green.1988; Symons and Walker 1990). The existence of such a large wage gap, even in the absence of an institution whose main objective is to raise the wage, remains an unresolved puzzle. This paper found little empirical support for those neoclassical explanations predicated on the existence of differentials in worker quality and compensating differentials. Other explanations, however, remain untested. The roles ofthe product market and of firms' profit margins on wage levels need to be investigated more thoroughly. The suggestion by Brown and Medoff (1989) that the higher wages associated with 'large' plants may be due to the relative cheapness of other inputs (like capital) is also worth further examination. In a similar vein, there is ample scope for work along the lines of Green et al. (1992), who develop a model based on monopsony power. , , , . : Finally, the absence of a statistically significant trade union effect among 'large' plants lends support to the idea of a positive face to trade unions as portrayed by Freeman and Medoff (1984). The wage effects of unions are subordinated to their role of providing an institutionalized collective voice for their membership in 'large' plants. In terms of the monopoly supply effects of unions, they appear more in evidence in 'small' plants.

APPENDIX A TABLE

Al

VARIABLE C O D E S WITH

Variable

,

DESCRIPTION

Description

Job and personal characteristics SIZE = 0, if works in 1-99 size plant = 1, if works in 100-499 size plant = 2, if works in 500+ size plant WAGE Natural log of hourly wage with overtime weighted time-and-a-half EMP Years of employment , . EMPS EMP-squared UNEMP Years of unemployment or years out of the labour force UNEMPS UNEMP-squared ^ EDUC Years of post-compulsory education • • TUREP = 1, if union representing worker at the workplace SUP = 1, if holding supervisory job . TDUR = 1, if the job took at least 6 months to learn SHIFT = 1, if job involves shift work CALLOUT = 1, if job involves being on call © The London School of Economics and Political Science 1993

1993]

137

EMPLOYER SIZE-WAGE GAP

TABLE Al—continued

Variable

Description

Job and personal characteristics NIGHT =1, if job involves night work SKILL = 1, if job involves a certain skill to do Area of residence ABERD = 1, if resides in Aberdeen KIRK = 1, if resides in Kirkcaldy COV = 1, if resides in Coventry SWIN = 1, if resides in Swindon NORTHN =1, if resides in Northampton ROCHD = 1, if resides in Rochdale Industries INDl = 1 Energy & Mineral Extraction IND2 = 1 Metal Goods & Engineering IND3 = 1 Construction IND4 = 1, Other Manufacturing IND5 = 1 Distribution & Hotels IND6 = 1 Transport & Communication IND7 = 1 Banking & Finance IND8 = 1 Other Services Occupations OCCl = 1, management and professional OCC2 = 1, intermediate non-manual 0CC3 = 1, junior non-manual OCC4 = 1, foreman, etc. OCC5 = 1, skilled manual 0CC6 = 1, semi-skilled manual OCC7 = 1, unskilled Family characteristics KIDSPREl

= l,if one child 0-4 years old

KIDSPRE2 = 1, if two children 0-4 years old KIDSPRE3 = 1, if three or more children 0-4 years old KIDSPREl = 1, if one child 5-12 years old KIDSPRE2 = 1, if two children 5-12 years old KIDSPRI3 = 1, if three or more children 5-12 years old KIDSSECl = I, if one child 13-18 years old KIDSSEC2=l, if two children 13-18 years old KIDSSEC3 = 1, if three or more children 13-18 years old

TABLE A 2 S U M M A R Y STATISTICS FOR W A G E E Q U A T I O N

VARIABLES

(Sample Means) . Small Medium Large (1-99 workers) (100-499 workers) (500+ workers) Job and personal characteristics SIZE 0-5149 0-2431 WAGE 1 2731 1-4199 0-8474 EDUC 1-0784 EMP 18-7600 20-0550 EMPS 496-6900 532-4300 © The London School of Economics and Political Science 1993

0 2420 1-5298 1-0676 22-0630 615-0000

138

ECONOMICA

[MAY

TABLE A2—continued

Small Medium Large (1..-99 workers) (100-499 workers) (500+ workers) Job and personal characteristics 0-514S UNEMP 1-3455 UNEMPS TUREP 0-3391 SUP 0-3991 TDUR 0-5922 SHIFT 0-1288 0-3154 CALLOUT 0-1395 NIGHT SKILL 0-7339

0-4716 1-1219 0-6182 0-3727 0-5045 0-2727 0-3091 01500 0-7046

0-4387 1-2818 0-7443 0-3973 0-5160 0-3059 0-2648 0-2192 0-7078

0-0536 0-2275 0-1223 0-1223 0-2382 0-0665 0-1395 0-0301

0-1227 0-3591 0-2318 0-0500 0-0545 0-0500 0-0319

0-1324 0-4338 0-2100 0-0411 0-0594 0-0365 0-0594 0-0274

0-1931 0-0515 0-1330 0-0365 0-3820 0-1545 0-0494

0-2500 0-1136 0-0409 0-0454 0-3273 0-1773 0-0454

0-2374 0-0822 0-1233 0-0365 0-3059 0-1689 0-0458

0-2253 0-1502 0-1502 0-1416 0-1588 0-1739

0-1591 0-1182 0-1864 0-1682 0-1682 0-1999

0-1644 0-1416 0-2466 0-1507 0-1872 0-1095

-0-5859

0-1714

1-0745

Industry INDl IND2 IND3 IND4 IND5 IND6 IND7 IND8^

0 - 1 0 0 0 '••

Occupation

OCCl OCC2 OCC3 OCC4

0CC5 OCC6

occr

Area of residence

ABERD KIRK COV

SWIN NORTHN ROCHD' Selection term A

* Omitted in estimation.

APPENDIX B: VARIANCE-COVARIANCE MATRIX FOR THE ORDERED PROBIT SELECTION MODEL This appendix is based on Greene (1981, 1990). Recall equation (6): where i indexes the individuals and j indexes the firm size. If we define bj = pjo-j, then we can express the consistent estimate of the error variance of this equation as:

© The London School of Economics and Political Science 1993

1993]

139

EMPLOYER SIZE-WAGE GAP

where n is the number of observations,

i

n i-i

and

The squared correlation coefficient between the error term in the ordered probit and the 7th wage equation is given by pj = b^oj. The corrected standard errors for the regressions and the correlation coefficients are reported for the various equations in Table 1. If we augment the X matrix to include the column of Ay observations and redefine it as X^, the expression for the variance-covariance matrix of the full set of wage equation parameters is given by (with the j subscripts suppressed): Var (ft 6) = «r^(X;X^)-'[X; diag (1 - p^S,)X^ + Q ] [ X ; X » ] - ' where Q = p\X'^,Z) Var-Cov (y)(Z'XJ and Var-Cov (y) is the asymptotic variancecovariance matrix of the ordered probit coefficients, excluding the threshold parameter fi. The Q term is designed to account for the fact that the same y is used to estimate A for each individual observation.

APPENDIX C TABLE A3 R E D U C E D - F O R M O R D E R E D PROBIT

(Maximum Likelihood Estimates) Constant Personal characteristics EDUC EMP EMPS UNEMP UNEMPS Job characteristics TUREP SUP TDUR SHIFT CALLOUT NIGHT SKILL Industry INDl IND2 IND3 IND4 IND5 IND6 IND7 Occupation OCCl OCC2 OCC3 OCC4 OCCS OCC6 Area of residence ABERD KIRK

-1-7366**

(0-3678)

01001** 0-0450** -0-0008** -0-1342* 0-0293**

(0-0275) (0-0170) (0-0004) (0-0755) (0-0116)

0-8236** -0-0708 -0-1797* 0-4433** -0-0883 -0-1045 -0-0716

(0-1006) (0-1106) (0-0990) (0-1391) (0-1029) (0-1512) (0-1109)

1-1054** 0-8682** 0-8272** 0-3088* -0-0153 0-1674 -0-1047

(0-2738) (0-2588) (0-2621) (0-2930) (0-2676) (0-3178) (0-2692)

0-4685* 0-3195 0-1985 0-0562 -0-0088 0-0525

(0-2600) (0-2832) (0-2554) (0-3242) (0-2340) (0-2406)

0-1623 0-0389

(0-1547) (0-1569)

© The London School of Economics and Political Science 1993

140

ECONOMICA

[MAY

T A B L E A3—continued

Area of residence COV SWIN NORTHN Family characteristics" KIDSPREl KIDSPRE2 KIDSPRE3 KIDSPRIl KIDSPRI2 KIDSPRI3 KIDSSECI KIDSSEC2 KIDSSEC3 Threshold estimate M

0-2437 0-2716* 0-4436** -0-3061 0-2305 0-5912 0-3253 -0-1827 -0-3157 -0-2557 0-1628 0-4120

(0-2028) (0-1696) (0-3691) (0-2229) (0-1514) (0-3978) (0-1575) (0-2064) (0-4286)

p-8367**

Log L (unrestricted) Log L (restricted)

(0-1558) (0-1513) (0-1453)

(0-0507) -781 -02 -931 -19 300 -34** 60 -3% 905

Correct predictions Observations

Asymptotic standard errors appear in parentheses. ** denotes significance from zero at the 5 per cent level using two-tailed tests; * denotes significance from zero at the 10 per cent level using two-tailed tests. * Denotes the identifying variables that enter the ordered probit attachment equation but not the wage equations. A likelihood ratio test was employed to test for their overall significance. The resultant test statistic was calculated as 15-85 and with 9 degrees of freedom is significant at the 10 per cent level or better. TABLE A4 IMPACT EFFECTS FOR FAMILY CHARACTERISTICS BASED ON THE ORDERED PROBIT MODEL"

KIDSPREl KIDSPRE2 KIDSPRE3 KIDSPRIl KIDSPRI2 KIDSPRU KIDSSECI KIDSSEC2 KIDSSEC3 where:

APROB(Yi=0)

AJ PROB(Yi = l)

0-0207 -0-0248 -0-0848 -0-0379 0-0137 0-0211 0-0180 -0-0166 -0-0515

-0-0177 0-0202 0-0661 0-0306 -0-0116 -0-0180 -0-0154 0-0136 0-0411

APROBiY, = 2) -0-0030 0-0046 0-0187 0-0073 -0-0021 -0-0031 -0-0026 0-0030 0-0104

A QD/^Df \

APROB{ 1' = l ) = [4>(/t —Z'y) —4>(—i?r)] -[(M-Z* ^7)-