gender differences in observed and offered wages in canada, 1980

Gender Differences in Observed and Offered Wages in Canada, 1980Author(s): Paul W. MillerSource: The Canadian Journal of Economics / Revue canadienne d'Economique, Vol. 20, No. 2(May, 1987), pp. 225-244Published by: Wiley on behalf of the Canadian Economics AssociationStable URL: http://www.jstor.org/stable/135358 .

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Gender differences in observed and offered wages in Canada, 1980 PAUL W. MILLER Brunel University and Australian National University

Abstract. According to the 1981 census of Canada, the female rate of pay is 30 per cent less than the male rate. The average female wage offer, however, is only around one-half of that received by males, other things the same. Slightly more than one-half of the difference in observed wages can be explained by differences in wage-related characteristics between males and femnales. Two-fifths of the disparity between wage offers can be explained by the same set of factors. Analysis of the distribution of wage offers indicates greater wage inequality in the Canadian labour market than is suggested by study of observed wages.

Diff&rences entre les salaires observes et offerts pour les hommes et les femmes au Canada, 1980. Selon le recensement de 1981 au Canada, le taux de remuneration des femmes est 30 pourcent de moins que celui des hommes. Le salaire moyen offert aux femmes est cependant seulement la moitie de ce qui est requ par les hommes. Plus de la moitie de la difference entre les salaires observes est attribuable 'a des caracteristiques reliees au niveau de salaire entre hommes et femmes. On peut expliquer 40 pourcent des differences entre salaires offerts 'a l'aide des mermes facteurs. L'analyse des salaires offerts montre une plus grande inegalite de salaires dans le marche du travail au Canada que celle suggeree par l'analyse des salaires observes.

INTRODUCTION

Variations in earnings among individuals in Canada are substantial. Perhaps the largest difference occurs between men and women. Data from the 1981 census of Canada show that, on average, women earn around 70 per cent of the male rate of pay. This earnings differential may reflect either productivity differences or discrimination (or choice). The source of the differential is

I am indebted to Veena Mishra for research assistance. Helpful comments from Glenn MacDonald and two anonymous referees are gratefully acknowledged. Work on this study was undertaken while I was at the University of Western Ontario. Research for this paper was financed in part by the Leverhulme Trust.

Canadian Journal of Economics Revue canadienne d'Economique, xx, No. 2 May mai 1987. Printed in Canada Imprime au Canada

0008-4085 / 87 / 225-244 $1.50 ? Canadian Economics Association



226 Paul W. Miller

important. If it arises from discrimination, then it implies an economically inefficient allocation of resources. But should the differential be explained by differences in productivity, then attempts to close the male-female earnings gap themselves would impair economic efficiency.

Differences in the economic positions of men and women in the Canadian economy have been examined in a number of studies, including Gunderson (1979), Holmes (1976), Robb (1978), and Shapiro and Stelcner (1981). These studies show that once account is taken of differences in productivity-related characteristics between males and females, the gender earnings gap is narrowed considerably. The fraction of the earnings gap attributable to differences in average characteristics is estimated at between 25 and 47 per cent.' The remaining proportion of the earnings gap is attributable to discrimination or differences in preferences between the sexes.

The purpose of this paper is threefold. First, it uses data from the 1981 Census to provide a more recent account of male-female earnings differentials in the Canadian labour market. Second, the study modifies the specification of the estimating equation along the lines of Polachek (1975a) to reflect family responsibilities. Third, by incorporating the selectivity bias correction developed by Heckman (1979) the wage-offer distribution among the female labour force is more accurately estimated, thereby eliminating one potential source of bias in the wage comparisons.

The paper begins with a brief review of previous research. In the third section the methodology is outlined and the data are described. The empirical analyses are presented in the fourth and fifth sections. Some concluding comments are offered in the final section.

REVIEW OF PREVIOUS RESEARCH ON GENDER WAGE DIFFERENCES

Gender wage differences have been the subject of a number of studies (Gunderson, 1975, 1979; Holmes, 1976; Robb, 1978; and Shapiro and Stelcner, 1981). Each study emphasizes the human capital approach to explaining the gender gap in wages and employs the framework popularized by Blinder (1973) and Oaxaca (1973). The studies differ, however, in terms of their geographical focus and specification of the model of the wage generation process. Even with these differences there is a surprising degree of uniformity across the conclusions.

Gunderson (1979) examines gender differences in earnings among civilian members of the full-time, full-year, paid labour force in 1970. Earnings functions were estimated for all Canada in semi-logarithmic form, with education, experience, training, marital status, language, region, province, hours worked, occupation and industry as explanatory variables. It was

I Many studies distinguish between two levels of discrimination: wage discrimination (or unequal pay for equal work) and an all-encompassing labour market discrimination concept of unequal pay for equal productivity characteristics. The figures cited are for the first concept.



Gender differences 227

established that males have earnings 51 per cent higher than females, and 19 percentage points (37 per cent) of this differential was attributed to differences in wage-related characteristics, specifically, males have more experience, have a higher probability of being married, and are concentrated in the higher-paying industries and occupations. The residual (unexplained) earnings gap of 32 percentage points (63 per cent) may be attributed to discrimination or differences in preferences between the two groups. The main avenues through which this gap occurs are differences in returns to education, experience, and marital status.

The geographical focus of Robb's study was the urban Ontario labour market. Two comparisons were presented: all males versus all females, and all males versus single females. Forty-one per cent of the earnings gap between males and females in Ontario arises from differences in their productivity-related characteristics. However, for the comparison of all males with single females, 85 per cent of the earnings gap derives from this source, a fact that highlights the importance of family responsibilities in the earnings comparisons.

Shapiro and Stelcner (1981) build upon the analyses presented by Gunderson (1979) and Robb (1978) by conducting an analysis for the Quebec labour market, and examining the female/male earnings differential in both the public and private sectors. Their results show that the factors contributing to wage differences are similar across these submarkets.2

Holmes (1976) estimates that the fraction of the gender earnings gap associated with differences in average characteristics is around one-quarter, which is slightly lower than in other studies. In part this finding may be associated with a number of methodological differences. For example, earnings rather than the natural logarithm of earnings are used as the dependent variable, and there is a focus upon potential lifetime earnings rather than actual annual earnings. It is noted, however, that the nature of the male advantage in wage-related characteristics is similar to that reported by Gunderson (1979).

METHODOLOGY AND DATA

The method used to analyse the gender wage differential follows that developed by Oaxaca (1973). The relationship between wages and observed characteristics may be expressed in semi-logarithmic form as

In W{ = Xi: + Ej (1)

where W denotes the hourly wage rate, Xi is a vector of characteristics for the ith individual, ,B is a vector of coefficients, and Ei is a normally distributed error term.

2 Shapiro and Stelcner also refine the specification of the language variables by combining aspects of ethnicity (mother tongue) and current language facility (the basis of Gunderson's 1979 language variables).



228 Paul W. Miller

If equation (1) is estimated for males (m) and females (f), the observed wage differential between the groups can be decomposed as follows.

- A - A A 2 1n W,, - In W = (Xm - Xf )/ m + Xf (/ m 1f)- (2)

The left-hand side of equation (2) (approximately) equals the observed percentage wage differential between the groups. The first term on the

- A

right-hand side, (Xm - Xf)13m, is the difference in wages due to differences in - A

average characteristics. The second term, Xf(/gm - 8f3), is the component of the wage gap attributable to differences in the estimated coefficients of the wage equations for the groups.3

There are several aspects of this technique that should be considered. First, the technique assumes that the proxies of productivity differences (X) are adequate and exhaustive. If the proxies mismeasure true productivity, then the problem of errors in variables occurs. The recent literature on reverse regression (Kamalich and Polachek, 1982; Goldberger, 1984) has attemnpted to illustrate the gravity of this problem. If the X vector does not exhaust all possible productivity-related factors, then there may be omitted variables bias. This situation is recognized in studies such as that of Daymont and Andrisani (1984), where the earnings function is augmented with more refined productivity measures not usually available on census files. A further deficiency of the decomposition technique is that it ignores questions concerning the cause of any underlying differences in characteristics. Thus, the feedback effects of labour market discrimination on the acquisition of human capital skills is neglected (Welch, 1975; Jain and Sloane, 1981). Because of these caveats, the wage decomposition technique should be viewed as providing only a broad indication of the bases of pay differences.

Computations using equation (1) are performed with data from the 1 per cent Household/Family File of the Public Use Samples from the 1981 Canadian census. This data set was chosen because it contains details on the age characteristics of children in the household for females and males that are not available on the Individual Sample File.

All analyses reported are for native-born persons aged twenty-five to sixty-four years.4 Overseas-born persons have been excluded to permit measurement of the sex differential in earnings without the compounding influence of discrimination on the basis of nativity. Within the adult native-born population, only civilian wage and salary earners with positive

3 Equation (2) uses the male wage structure as the non-discriminating norm (see Gunderson, 1979). Alternative decompositions can be utilized. Largely because the female age-earnings profile is relatively flat, and males have more labour market experience than females, adopt- ing the female pay structure as a non-discriminating norm produces a lower estimate of the wage gap because of differences in characteristics.

4 Analysis of the earnings of fifteen to twenty-four year olds would appear to require explicit recognition of the schooling alternative in the model of the selection criteria used in the fifth section. This might be achieved through a multivariate extension of the familiar bivariate probit model. Given the tentative nature of the results established for the older age groups, this more complex analysis was not attempted.




TABLE I

Definitions of variables and mnemonic names

Mnemonic Definition

Dependent variable LNW Natural logarithm of hourly earnings (income from wages and salaries

plus income from self employment) in 1980

Human capital EDUC Years of Schooling UNIDEG Possesses a university degree TRADCERT Possesses a trade or non-university certificate EXP Years of labour market experience = (age - EDUC - 6)

Marital status MARRIED (Reference group) SINGLE Never married DIVSEP Divorced, separated or widowed

Province ONT Ontario (reference province) ATL Atlantic provinces (Newfoundland, Nova Scotia, New Brunswick) QUE Quebec PR Prairie provinces (Manitoba, Saskatchewan, Alberta) BC British Columbia

Size of Place NONCMA Not a resident of a Census Metropolitan Area

Ethnicity and language FRETHN French ethnic origin (single or multiple origins) ENGONLY Speaks only English (Reference group) FRONLY Speaks only French BILENG Speaks both English and French, mother-tongue English BILFR Speaks both English and French, mother-tongue French BILOTH Speaks both English and French, mother-tongue other than English or

French NENF Speaks neither English nor French

Family structure YEARSMAR Years married CHILD < 6 Number of children living at home < 6 years of age CHILD 6-14 Number of children living at home aged between 6 and 14 years CHILD 15-25 Number of children living at home aged between 15 and 25 years

Occupation CLERICAL (reference group), MANAGEMENT, SCIENCE, social SCIENCE, TEACHING, HEALTH, ART and RECreation, SALES, SERVICES, PRIMARY, PROCESSING, CONSTRUCTION, TRANSPORT, OTHER

Industry GOVERNMENT (reference group), PRIMARY, MANUFACTURING, CONSTRUCTION, TRANSPORT, TRADES, FINANCE, SERVICES

earnings are considered. The possibility that these represent a non-random sample of the population is taken into account in the fifth section. The variables employed in the study are defined in table 1. Means and standard deviations for selected variables are presented in appendix table Al.



230 Paul W. Miller

To derive estimates of the relationships between earnings and the characteristics noted in table 1, conventional human capital earnings functions (Mincer, 1974) are estimated. Following previous research, two specifications of the earnings equations are presented. The first includes only direct productivity-generating characteristics as independent variables. These include years of schooling, two 'certification' variables representing possession of trade certificates or university degrees, potential labour market experience and its square, marital status, family characteristics, measures of facility in the official languages and locality (province and size of place). The focus of this equation is the discrimination concept (using Shapiro and Stelcner's 1981 terminology) of 'unequal pay for equal productivity-generating characteristics.' The second specification augments this basic equation with variables for occupation and industry. The incorporation of these work-type variables reorientates the focus to a second discrimination concept, 'unequal pay for work of equal value.'

These specifications differ from those used in previous studies in that a number of family characteristics, namely number and age structure of children and years married, are included in both the male and the female earnings equations. This specification is based on Polachek (1975a), who suggests that different market values of initial stocks of human capital together with differences in non-market productivities leads to a 'general division of labour perpetuated over the marriage such that married males specialise more in market activities than either their single counterparts or their wives' (214). Polachek's empirical work establishes that the number and age structure of children and the number of years married are significant determinants of both male and female earnings.

The above discussion suggests a further modification of the decomposition technique. Equation (2) presumes that the impact of each variable is in the same direction in both the male and the female earnings equations. That is, for example, additional years of education are expected to be associated with higher earnings for both males and females. However, the model presented by Polachek (1975a) predicts opposite signs for the family characteristics variables in the male and female equations. Therefore, partitioning the vectors of characteristics and coefficients into two, denoting the first subset relating to non-family characteristics by the subscript 1 and the second relating to family characteristics by the subscript 2, the earnings gap is appropriately decomposed as follows:

_ _ ~A _ A_ A

In W, - In Wf = (XI,m - Xlf)13 m + (X2mnJ2m - X2f1 2f)

+ Xf(1If m -AM PO) (3) In equation (3) the sum of the first two terms on the right-hand side

represents the difference in wages due to differences in wage-related characteristics. The final term is the portion of the wage gap due to differences in the estimated coefficients of the wage equation.5

5 The differences between males and females discussed by Polachek (1975a) are treated as fol-




DECOMPOSITION OF THE WAGE GAP: CONVENTIONAL METHODS

Columns (1), (2), (5), and (6) of table 2 list results for regression equations that provide a link with the research methodology used in earlier studies. Columns (1) and (5) report results for males and females, respectively, for full-time (thirty-five to forty-four hours per week), full-year (forty-nine to fifty-two weeks per year), wage and salary earners age fifteen or more years. This selection rule is similar to that employed by Gunderson (1979). These estimates show that 12 percentage points (28 per cent) of the 42 per cent gender wage gap are attributable to differences in average characteristics. Decomposing the gender wage gap using the Individual Sample File of the 1981 census yields similar results.6 Gunderson estimated that in 1971 19 percentage points (37 per cent) of a 51-percentage-point earnings differential could be explained by differences in productivity-related characteristics. Thus, three points are evident. First, the gender wage gap has narrowed over the decade of the 1970s.7 Second, the fraction of the earnings gap attributable to differences in average characteristics has declined. Third, calculations based upon the Family file yield results reasonably similar to those derived from the Individual File.

The remaining columns of table 2 present results for all twenty-five to sixty-four year old workers. For this sample there is a gender wage gap of 35 per cent; 8 percentage points of this gap derive from differences in the variables traditionally included in the earnings function (columns (2) and (6) ).8

Columns (3), (4), (7), and (8) present results for the model that include variables for family responsibilities. Columns (3) and (7) present estimates for the extended model (work-type included), while columns (4) and (8) present estimates with the occupation and industry variables omitted. According to the colunm (3) estimates, 19 percentage points (55 per cent) of the gender gap in wages is attributable to differences in characteristics. As illustrated in table 3, two-thirds of this explained difference is associated with the family characteristics variables. Thus, family characteristics, whether reflecting changed investment patterns among family units or lessened work experience among females, or both, are quite important to understanding wage differences between males and females. The other major contributors to the explanation of the gender gap in wages are the different distributions of the male and female work forces across occupations and industries.

When the emphasis is on the discrimination concept 'equal pay for equal

lows: the initial husband-wife wage gap is viewed as discrimination, while other family varn- ables are treated as proxies for productivity differences that derive from differences in human capital investment and/or reduced work experience.

6 The sample derived from the Individual File differs from that taken from the Family File in two respects: it is, on average, younger and has a higher representation of the non-married.

7 See also Boulet and Lavalle (1984), table 2.8. 8 Tests show that the lower fraction of the earnings gap explained in this sample derives from

the exclusion of fifteen to twenty-four year olds.



232 Paul W. Miller

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TABLE 3

Decomposition of gender gap in wages

OLS Selectivity Corrected

(1) (2) (3) (4) (5)

Difference in observed wages 0.351 0.351 0.351 0.351 na Difference in selection bias na na 0.315 0.281 na Difference in wage offers na na 0.666 0.632 0.726 Due to differences in following

characteristics Education -0.006 -0.007 -0.007 -0.008 0.021 Experience 0.003 0.003 0.000 0.000 0.000 Marital Status 0.000 0.001 0.003 0.004 -0.003 Family Structure 0.126 0.154 0.209 0.231 0.257 Ethnicity and Language 0.001 0.000 0.001 0.001 0.001 Province 0.000 0.000 0.000 0.000 0.000 Size of Place -0.004 -0.003 -0.005 -0.005 -0.001 Occupation 0.025 na 0.022 na na Industry 0.047 na 0.046 na na TOTAL 0.192 0.148 0.269 0.223 0.274 Per cent 54.7 42.2 40.4 35.3 37.9

NOTES

na = not applicable Education includes EDUC, UNIDEG, and TRADCERT

(4) = decomposed using mean values of the characteristics of the selected sample (5) decom-posed using the methods outlined in fn 12 SOURCE: (1) = table 2, columns (3) and (7); (2) = table 2, columns (4) and (8); (3) = table 4, columns (1) and (3); (4), (5) = table 4, columns (2) and (4)

productivity generating characteristics' (colunm (4)), 15 percentage points (42 per cent) of the gender gap in wages can be attributed to differences in productivity-related characteristics. Family characteristic variables are again dominant in the explanation of gender differences in observed wages.

DECOMPOSITION OF THE WAGE GAP: SELECTIVITY CORRECTED ESTIMATES

Since the pioneering work of Gronau (1974) it has been recognized that wage comparisons based upon a sample of employed persons may provide a suspect basis for analysing the comparative labour market positions of secondary labour market groups. Specifically, the theoretical analysis of discrimiination defines wage discrimination on the basis of sex as differences in the wage-offer distributions of males and females exceeding productivity differences. Tradi- tional measures of discrimination, however, have relied upon analyses of observed wage distributions which constitute only part of the wage-offer function. Gronau suggests that such measures will tend to understate the wage-offer differentials between males and females.




The methods for distinguishing between observed-wage and wage-offer functions are now well established in the literature and only a brief exposition is provided.9

Market wages can be computed only for the group of individuals included in the sample.'0 Therefore, the regression equation for the selected sample may be expressed as

E(In W4 I Xi, sample selection rule) = Xj, + E(Ej1 sample selection rule). (4)

Using the procedures developed by Heckman (1979) the wage equation to be estimated can be written as

In W4 = XJ3 + YXy + ViJ (5)

where X is the inverse of Mill's ratio term which may be estimated from a probit analysis of the probability of being included in the observed wage sample." I

Incorporation of the selectivity correction into the analysis requires a straightforward extension of the conventional wage gap decomposition outlined above. Equation (3) may be modified as follows:

A A A

+ Xlf ( I m - if) -(yf -f YmAmj)* (6)

The first four terms in this equation have been discussed earlier. The final term, ('fXf - YmXm), is the part of the difference in the observed wage rates that is due to the difference in the average selectivity bias between the groups. It is convenient to rewrite equation (6) in the following form:

( A _ A In Wm - In Wf + (9jf f- YmXm) = (XIm Xlf)8 im

- ( A -~ + (X2mfl2m X2f 1/2) + Xlfj(18m I3P)o (7)

In this form the right-hand side provides a measure of differences in the

9 This presentation is based upon Reimers (1983). 10 To be included in the wage sample a person must be a civilian wage and salary earner. In

other words, both the self-employed and non-participants are excluded. Accordingly, the reduced form probit equation which predicts inclusion in the observed wage sample is not a labour force participation rate equation (see Reinr,rs, 1983). It is also noted that industry and occupation variables that enter into one specification of the mnarket wage equation are not available for non-participants. Although these should be included as arguments in the reduced form probit, they have, of necessity, been omitted.

11 The following variables were entered into the reduced form probit used to determine the probability of sample inclusion: province, size of place, marital status, number and age structure of children, years married, education, the two certification variables, 'trade certificate' and 'university degree', age (and its square), language, French-ethnic origin, family income, and spouse's education (where applicable). This specification is based largely upon the model developed by Nakamura and Nakamura (1979, 1981). Although it is not a labour supply function as such, the estimated coefficients resemble those derived by Nakamura and Nakamura (1979, 1981).



238 Paul W. Miller

offered wage (sum of the observed wage term and the selectivity bias term), and this is decomposed into the components identified by Oaxaca (1973).12

A number of previous studies have utilized the selectivity correction in the analysis of wage differences. These studies confirm that traditional regression methods may distort measurement of the wage gap. Gronau (1974) found that while the female market wage was 66 per cent of the male rate of pay, the median offered wage was only around 45 per cent of the male wage rate. Reimers (1983) reports marked differences between the observed and offered wages for groups of white non-hispanics and minority males. The values of the selectivity-correction term in the analyses presented by Smith (1979) and Corcoran (1979) also imply large divergences between the observed and offered wage distributions.

Smith (1979), however, expresses caution over the reliability of his estimates. Part of his scepticism derives from the magnitude of the coefficient of the selectivity-correction term.13 The selectivity-bias correction term may be highly correlated with market wage determinants such as experielnce (Heckman, 1976), and this may distort measurement of differences in the offered wage distribution under the variant of the wage gap decomposition outlined above.14 Moreover, Olsen (1982) demonstrates that the solution to the sample selection problem depends upon the structure imposed on it. One implication is that the results reported may reflect the normality assumption made.15 Findings derived from selectivity-corrected estimates should therefore be interpreted with caution.16

Table 4 presents regression equations for males and females that have been corrected for the probability of sample inclusion. The selectivity correction factor is significant in each case. The difference in the average selectivity bias in the male and female samples implies a considerable divergence between observed and offered wages. In general, while there is a difference of around 0.35 in the mean logarithm of observed wages of males and females, the difference in the mean logarithm of wage offers is around 0.65. These estimates imply a differential of about 30 per cent in observed wages and a 48 per cent

12 Equation (7) utilizes the mean values of the characteristics of the selected sample. As a referee pointed out, an alternative method would use the mean characteristics of the entire sample (without the product of lambda and its coefficient). This exercise produces results similar to equation (7); see table 3.

13 Smith, for example, reports values for the coefficient on the Mill's ratio term of 0.196 for white females and -0.49 for black females. Corcoran reports a value of -0.27, while Nakamura and Nakamura (1981) report significant values of this coefficient ranging from -0.22 (for twenty-five to twenty-nine year olds) to 0.90 (for fifty to fifty-four year olds).

14 If the estimated coefficient on the selectivity-correction term overestimates the true parameter, then it is likely that other estimates understate the true parameter values.

15 In some cases the results of the wage gap decomposition could be more sensitive to the distributional assumptions than to the omitted variable bias associated with failure to deal with the sample selection issue.

16 Hirsch and Addison (1986) claim that estimates derived using the selectivity adjusted approach are so highly variable that they cannot be regarded as reliable.




TABLE 4

Regression analysis of earnings of adult males and females in Canada, 1980 (dependent variable: natural logarithm of earnings; estimation method: selectivity corrected estimates)

Males Females

(1) (2) (3) (4)

Constant 1.381 1.303 0.884 0.370 (37.39) (40.26) (11.52) (4.95)

EDUC 0.037 0.045 0.045 0.080 (19.31) (24.32) (12.30) (22.91)

UNIDEG 0.129 0.188 0.196 0.334 (9.08) (14.12) (8.12) (14.56)

TRADCERT 0.065 0.082 0.001 0.039 (7.83) (9.87) (0.06) (2.45)

EXP 0.025 0.027 0.030 0.036 (16.27) (17.25) (10.93) (12.78)

EXPSQ -0.00045 -0.00048 -0.00058 -0.00066 (15.32) (16.12) (9.65) (10.62)

SINGLE -0.122 -0.140 0.016 0.005 (7.18) (8.11) (0.67) (0.20)

DIVSEP 0.011 0.006 -0.059 -0.086 (0.59) (0.31) (2.28) (3.24)

FRETHN 0.025 0.023 -0.019 -0.030 (1.79) (1.61) (0.77) (1.23)

FRONLY -0.043 -0.048 -0.013 0.027 (1.95) (2.15) (0.36) (0.71)

BILENG -0.027 -0.024 0.015 0.007 (1.78) (1.55) (0.60) (0.27)

BILFR -0.016 -0.015 0.084 0.106 (0.87) (0.77) (2.67) (3.29)

BILOTH -0.082 -0.091 0.041 0.057 (1.43) (1.55) (0.49) (0.66)

NENF 0.079 0.011 -0.152 -(.119 (0.30) (0.04) (0.34) (0.26)

ATL -0.101 -0.100 -0.087 -0.084 (7.88) (7.64) (4.01) (3.74)

QUE 0.021 0.025 0.026 0.045 (1.46) (1.69) (1.07) (1.76)

PR -0.001 0.(08 0.050 0.042 (0.07) (0.75) (3.14) (2.59)

BC 0.126 0.124 0.139 0.122 (10.84) (10.46) (7.22) (6.14)

NONCMA -0.093 -0.091 -0.111 -0.112 (11.40) (11.05) (8.28) (8.13)

MANAGEMENT 0.277 (a) 0.228 (a) (17.81) (10.03)

SCIENCE 0.216 (a) 0.213 (a) (11.53) (4.44)

SOC. SCIENCE 0.185 (a) 0.131 (a) (5.41) (3.06)

TEACHING 0.321 (a) 0.432 (a) (13.62) (17.82)



240 Paul W. Miller

TABLE 4 concluded

Males Females

(1) (2) (3) (4)

HEALTH 0.132 (a) 0.095 (a) (2.30) (1.91)

ART & REC. 0.065 (a) 0.183 (a) (2.00) (3.49)

SALES 0.060 (a) -0.089 (a) (3.59) (4.40)

SERVICES 0.005 (a) -0.287 (a) (0.29) (13.16)

PRIMARY -0.038 (a) -0.037 (a) (1.54) (5.48)

PROCESSING 0.066 (a) -0.075 (a) (4.35) (2.63)

CONSTRUCTION 0.107 (a) -0.129 (a) (5.99) (1.26)

TRANSPORT -0.008 (a) -0.117 (a) (0.42) (2.02)

OTHER 0.062 (a) -0.075 (a) (3.39) (1.87)

PRIMARY 0.071 (a) -0.046 (a) (3.47) (0.89)

MANUFACTURING -0.024 (a) -0.054 (a) (1.78) (2.06)

CONSTRUCTION 0.035 (a) 0.079 (a) (1.99) (1.85)

TRANSPORT 0.032 (a) 0.037 (a) (2.18) (1.32)

TRADES -0.151 (a) -0.179 (a) (10.06) (7.78)

FINANCE -0.022 (a) -0.026 (a) (1.17) (1.04)

SERVICE -0.175 (a) -0.090 (a) (12.27) (4.16)

CHILD < 6 0.008 0.010 -0.092 -0.076 (1.42) (1.69) (3.91) (3.14)

CHILD 6-14 0.019 0.024 -0.068 -0.067 (4.38) (5.25) (6.65) (6.33)

CHILD 15-24 0.017 0.023 -0.036 -0.040 (3.83) (5.01) (4.66) (5.08)

YE-ARSMAR 0.005 0.005 -0.004 -0.005 (6.60) (6.67) (3.91) (5.00)

LAMBDA 0.190 0.200 0.423 0.393 (6.39) (6.61) (7.45) (6.71)

R2 0.1545 0.1172 0.1796 0.1231 Sample size 26,099 26,099 14,167 14,167 Observed wage gap 0.351 0.351 Offered wage gap (per cent) 0.666 0.632 Difference due to characteristics 0.267 0.223

(per cent) 40 35

NOTES

(a) = variable not entered; t statistics in parentheses SOURCE: 1981 census of Canada




differential in wage offers.17 As noted above, the selectivity-adjusted estimates should be interpreted cautiously, owing to the nature of the econometric techniques employed. Nevertheless, they should provide some indication of the relative labour market standings of the two groups.

Between 35 and 40 per cent of the gender gap in offered wages is explained by the variables in the estimating equation. The family characteristics variables are important contributors to this wage difference. ThUis finding is consistent with the emphasis on intermittent labour force participation of females in the discrimination literature (Polachek, 1975b; Zabalza and Arrufat, 1985). Table 3 summarizes the findings.

The earnings decompositions (table 3) show that differences in characteristics explain a smaller fraction of the gender gap in offered wages than of the difference in observed wages. This fact, together with the relatively larger gender gap in offered wages implies that the absolute size of the unexplained portion of the offered wage gap is considerably greater than the unexplained portion of the observed wage gap. Thus, if the unexplained portion of the offered wage gap is used as evidence of discrimination, then this problem is more acute than suggested by the traditional earnings decomposition.

CONCLUSION

Differences between males and females in observed and offered wage functions are considerable. On average, the female rate of pay is 30 per cent less than the male rate. The average female wage offer, however, is only around one-half of that received by males, other things being the same. Slightly more than one-half of the difference in observed wages can be explained by differences in productivity-related characteristics between males and females. Forty per cent of the disparity between wage offers can be explained by the same set of factors. Family characteristics variables that are thought to capture differing investment patterns within the family unit and/or lessened work experience among females account for the major part of the explained portion of the gender gap in wages.

The fraction of the gender gap in observed wages that can be explained by differences in wage-related characteristics declined slightly between 1970 and 1980. At the same time, however, the gender wage gap narrowed by several percentage points. The net result is a slight decline in the magnitude of the unexplained wage gap, which may translate into evidence of reduced levels of discrimination.

Perhaps the most important consideration is that analysis of the distribution of wage offers indicates greater wage inequality in the Canadian labour market than is suggested in the literature relating to observed wage distributions.

17 For large values of the difference in the mean logarithm of wages the appropriate percentage difference is calculated as [1 - antilog (estimate) ]. Hence, 30 per cent = (1 -e 035) and 48 percent = (I -e- 66)



242 Paul W. Miller

REFERENCES

Blinder, A.S. (1973) 'Wage discrimination: reduced form and structural estimates.' Journal of Human Resources 8, 436-65

Boulet, Jac-Andre and Laval Lavalle (1984) The Changing Economic Status of Women (Ottawa: Supply and Services Canada)

Corcoran, Mary E. (1979) 'Work experience, labour force withdrawals, and women's wages: empirical results using the 1976 Panel of income dynamics.' In Cynthia B. Lloyd, Emily S. Andrews, and Curtis L. Gilroy, eds, Women in the Labour Market (New York: Columbia University Press)

Daymont, Thomas N. and Paul J. Andrisani (1984) 'Job preferences, college major and the gender gap in earnings.' Journal of Human Resources 19, 408-28

Goldberger, Arthur S. (1984) 'Reverse regression and salary discrimination.' Journal of Human Resources 19, 293-318

Gronau, Reuben (1974) 'Wage comparisons - a selectivity bias.' Journal of Political Economy 82, 1119-43

Gunderson, Morley (1975) 'Male-female wage differentials and the impact of equal pay legislation.' Review of Economics and Statistics 62, 462-9

- (1979) 'Decomposition of the male/female earnings differential: Canada 1970.' This JOURNAL 12, 479-85

Heckman, J. (1976) 'The common structure of statistical models of truncation, sample selection and limited dependent variables and a simple estimator for such models.' Annals of Economic and Social Measurement 5, 475-92

- (1979) 'Sample selection bias as a specification error.' Econometrica 47, 153-61 Hirsch, Barry T. and John T. Addison (1986) The Economic Analysis of Unions: New

Approaches and Evidence (Boston: Allen and Unwin) Holmes, R.A. (1976) 'Male-female earnings differentials in Canada.' Journal of

Human Resources 11, 109-17 Jain, Harish C. and Peter J. Sloane (1981) Equal Employment Issues: Race and Sex

Discrimination in the United States, Canada and Britain (New York: Praeger) Kamalich, Richard F. and Solomon W. Polachek (1982) 'Discrimination: fact or fic-

tion? An examination using an alternative approach.' Southern Economic Journal 49, 45061

Mincer, Jacob (1974) Schooling, Experience and Earnings (New York: National Bureau of Economic Research)

Nakamura, Alice and Masao Nakamura (1981) 'A comparison of the labour force be- haviour of married women in the United States and Canada, with special atten- tion to the impact of income taxes.' Econometrica 49, 451-90

Nakamura, Alice, Masao Nakamura and Dallas Cullen (1979) 'Employment and earnings of married females.' Catalogue No. 99-760E (Ottawa: Minister of Supply and Services)

Oaxaca, Ronald (1973) 'Male-female wage differentials in urban labour markets.' International Economic Review 14, 693-709

Olsen, Randall J. (1982) 'Distributional tests for selectivity bias and a more robust likelihood estimator.' International Economic Review 23, 223-44

Polachek, Solomon William (1975a) 'Potential biases in measuring male-female discrimination.' Journal of Human Resources 10, 205-29

-(1 975b) 'Discontinuous labour force participation and its effects on women's market earnings.' In Cynthia Lloyd, ed., Sex, Discrimination and the Division of Labor (New York: Columbia University Press)




Reimers, Cordelia W. (1983) 'Labour market discrimination against Hispanic and black men.' Review of Economics and Statistics 65, 570-9

Robb, Roberta Edgecombe (1978) 'Earnings differentials between males and females in Ontario, 1971.' This JOURNAL 11, 350-9

Shapiro, Daniel and Morton Stelcner (1981) 'Male-female earnings differentials and the role of language in Canada, Ontario and Quebec, 1970.' This JOURNAL 14, 341-8

Smith, James P. (1979) 'The convergence to racial equality in women's wages.' Edited by Cynthia B. Lloyd, Emily S. Andrews and Curtis L. Gilroy, eds, Women in the Labour Market (New York: Columbia University Press)

Welch, Finis (1975) 'Human capital theory: education, discrimination and life cycles.' American Economic Review 65, 63-73

Zabalza, A. and J.L. Arrufat (1985) 'The extent of sex discrimination in Great Britain.' In A. Zabalza and Z. Tzannatos, Women and Equal Pay: The Effects of Legislation on Female Employment and Wages in Britain (Cambridge: Cambridge University Press)

APPENDIX

TABLE Al

Means and standard deviations of variables for adult males and females, 1981 census

Males Females

Standard Standard Mean deviation Mean deviation

Dependent variable LNW 2.283 0.58 1.932 0.72

Human capital EDUC 11.190 3.10 11.546 2.62 UNIDEG 0.140 0.35 0.125 0.33 TRADCERT 0.242 0.43 0.176 0.38 EXP 22.770 12.01 21.678 11.49

Marital Status SINGLE 0.083 0.28 0.118 0.32 DIVSEP 0.059 0.24 0.146 0.35

Ethnicity and language FRETHN 0.335 0.47 0.307 0.46 FRONLY 0.128 0.33 0.130 0.34 BILENG 0.061 0.24 0.061 0.24 BILFR 0.165 0.37 0.134 0.34 BILOTH 0.003 0.06 0.005 0.07 NENF 0.000 0.01 0.000 0.02

Province ATL 0.092 0.29 0.086 0.28 QUE 0.280 0.45 0.249 0.43 PR 0.177 0.38 0.187 0.39 BC 0.111 0.31 0.111 0.31



244 Paul W. Miller

TABLE Al (concluded)

Males Females

Standard Standard Mean deviation Mean deviation

Size of Place NONCMA 0.513 0.50 0.461 0.50

Occupation MANAGEMENT 0.143 0.35 0.071 0.26 SCIENCE 0.062 0.24 0.014 0.12 SOC. SCIENCE 0.012 0.11 0.019 0.14 TEACHING 0.046 0.21 0.121 0.33 HEALTH 0.004 0.06 0.013 0.11 ART&REC. 0.013 0.11 0.012 0.11 SALES 0.113 0.32 0.114 0.32 SERVICES 0.067 0.25 0.105 0.31 PRIMARY 0.039 0.19 0.010 0.10 PROCESSING 0.191 0.39 0.067 0.25 CONSTRUCTION 0.101 0.30 0.003 0.05 TRANSPORT 0.074 0.26 0.010 0.10 OTHER 0.061 0.24 0.021 0.14

Industry PRIMARY 0.059 0.24 0.021 0.14 MANUFACTURING 0.249 0.43 0.141 0.35 CONSTRUCTION 0.084 0.28 0.020 0.14 TRANSPORT 0.141 0.35 0.066 0.25 TRADES 0.156 0.36 0.205 0.40 FINANCE 0.051 0.22 0.105 0.31 SERVICE 0.149 0.36 0.342 0.47

Family Structure CHILD < 6 0.354 0.67 0.195 0.49 CHILD 6-14 0.549 0.86 0.497 0.82 CHILD 15-24 0.444 0.85 0.460 0.84 YEARSMAR 14.193 11.17 12.772 11.59

LAMBDA 0.491 0.21 0.965 0.32

SOURCE: 1981 census of Canada



gender differences in observed and offered wages in canada, 1980

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