Data for Germany, Britain and the United States are used to investigate the hypothesis that women, especially married women, are less responsive than men to expected occupational wage differentials.

Geraint Johnes

English

Research Papers in Economics

 
 
 
 
 
 
 
Lancaster University Management School 
Working Paper  
2000/001 
 
 
 
 
 
Wage Differentials and the Responsiveness of Labor Supply: 
An International Comparison  
 
 
 
 
 
Geraint Johnes 
 
 
 
The Department of Economics                        
Lancaster University Management School 
Lancaster LA1 4YX 
UK 
 
 
©Geraint Johnes  
All rights reserved. Short sections of text, not to exceed 
two paragraphs, may be quoted without explicit permission, 
provided that full acknowledgement is given. 
 
The LUMS Working Papers series can be accessed at http://www.lums.co.uk/publications
LUMS home page: http://www.lums.lancs.ac.uk/ 
 
 
  
 
 
 
 
 
WAGE DIFFERENTIALS AND THE RESPONSIVENESS OF LABOR 
SUPPLY: AN INTERNATIONAL COMPARISON 
 
 
by 
 
 
Geraint Johnes 
 
Department of Economics 
The Management School 
Lancaster University 
Lancaster LA1 4YX 
United Kingdom 
 
Voice: +44 1524 594215 
Fax: +44 1524 594244 
E-mail: G.Johnes@lancaster.ac.uk 
 
First version: 14 February 2000 
 
 
 
ABSTRACT 
 
 
Data for Germany, Britain and the United States are used to investigate the hypothesis that 
women, especially married women, are less responsive than men to expected occupational 
wage differentials. 
 
 
JEL Classification: J0, J3, J7 
Keywords: Participation, Occupational Choice, Discrimination, Bivariate Probit Models, 
Selectivity. 
 
The author is grateful to colleagues, both at Lancaster and at Dartmouth College where much 
of this work was carried out, for useful discussions. Thanks are also due to the Data Archive 
and to the Zentralarchiv für Empirische Sozialforschung for making the ISSP data available. 1. Introduction 
 
It is widely held that occupational segregation accounts for much of the gender gap in 
remuneration. This finding results from numerous studies which examine the role played by 
occupational selection in determining remuneration (see, for instance, Dolton et al., 1989). In 
this note, I approach the question of the gender-specific determination of occupation from a 
different angle: the responsiveness of different demographic groups to expected inter-
occupational wage differentials is assessed. In so doing, I develop a model of the 
simultaneous determination of labor market participation and occupation. 
 
Previous studies of female labor market participation have touched on some, but not all, of the 
issues discussed here. In particular, the literature on part time work exemplified by Blank 
(1989, 1990) and by Nakamura and Nakamura (1983) considers female labor market decision-
making in a limited dependent variable framework bearing a family resemblance to that 
adopted in the sequel. Here, though, greater emphasis is placed on the occupational regime 
into which each worker is placed. In the latter respect, the paper bears some resemblance to 
the work of Schmidt and Strauss (1975) and of Brown et al. (1999). Perhaps the most obvious 
antecedent of the present work, however, is provided by Dolton and Makepeace (1993) who 
examine the supply to the labor market of female teachers. 
 
 
2.  Method and data 
 
The approach pursued is to construct a bivariate probit model of participation and 
occupational regimes. Three stages may be identified. In the first, I consider two latent 
variables,  
 
 P*i = Xiϕ + ε1 i          (1) 
and  
 S*i = Yiξ + ε2 i          (2) 
 
These underpin individuals’ observed behavior as regards labor market participation (Pi=1 iff 
P*i>0, otherwise Pi=0) and occupation (Si=1 iff S*i>0, otherwise Si=0), where P and S are 
both binary and represent employment and skilled occupation respectively. Explanatory 
variables are denoted by the vectors Xi and Yi and the ε denote residuals. The set of variables 
included in Yi include inter alia all measurable determinants of occupation-specific earnings, 
so the model may usefully be thought of as a reduced form. Since Si is observed iff Pi=1, this 
is a censored (bivariate) probit model of the type discussed by Meng and Schmidt (1985).  
 
The second stage involves the estimation of occupation-specific earnings equations which, 
following Heckman (1979) and Lee (1983), correct for sample selection bias. This is done by 
deriving, from the reduced form bivariate probit, a pair of sample selection terms, λpi and λoi, 
respectively representing the otherwise unobserved impact of participation and occupational 
choice on the ith individual's earnings. Ahn (1992) shows that these selection terms may be 
defined as 
 
λpi = φ(Xiϕ) Φ[(Yiξ - ρXiϕ)/(1-ρ2)½] / F(Xiϕ, Yiξ, ρ)    (3) λoi = φ(Yiξ) Φ[(Xiϕ- ρYiξ)/(1-ρ2)½] / F(Xiϕ, Yiξ, ρ)    (4) 
 
where φ is the density of the standard normal, Φ  is the standard normal distribution function,  
F is the bivariate standard normal distribution and ρ is corr(ε1,ε2). Hence, in occupation j = 
u,s, the gender-specific earnings equations to be estimated are given by 
 
 ln wji = αj + Z+iβ+j + γjλpi + δjλoi + ε3 j i       (5) 
 
where Z+i is a vector of the ith individual's characteristics. The standard errors attached to the 
estimated coefficients of these earnings functions must be adjusted using the method of Ham 
(1982). 
 
The third stage of the modelling procedure is to estimate the system given by (1) and the 
followng equation (2’). 
                 ∧ 
 S*i = Y+iξ+ + κ(ln wsi - ln wui) + ε'2 i       (2’) 
 
The λ terms are set to zero in using (5) to calculate the expected relative wage which appears 
in (2’). The vector Y+i contains all variables in Yi with the exception of some or all of the 
variables which comprise Z+i.  
 
Put simply then, a structural form of the bivariate probit is used to analyse participation and 
occupation, where occupation is hypothesised to be responsive to variations in the expected 
relative wage. Of especial interest is a test of the sign and significance of  κ and of the 
associated marginal effects, and how the latter vary across demographic groups.  
 
 
3. Results 
 
The data used in the analysis reported below refer to the Federal Republic of Germany, Great 
Britain, and the United States of America over the period 1988-91. They come from the 
International Social Survey Program (ISSP), and so have been collected on as consitent a 
basis as possible. Additional data, on local unemployment rates, have been grafted on to the 
ISSP data set from three sources: the US Statistical Yearbook, the Statistiches Jahrbüch, and 
Regional Trends. 
 
The choice of countries is intended to reflect a variety of labor market types – from the 
relatively free market of the US to the more regulated market of Germany, with Britain 
coming somewhere in the middle. The choice of period captures a time frame during which 
Britain was moving rapidly into recession, while macroeconomic conditions in the other two 
countries were somewhat more stable.
1  
 
The analysis is conducted separately for men, single women and married women in the 21-55 
age group, and coefficients are estimated separately for each of the three countries. The 
                                                           
1 As ever, the choice of both countries and period was dictated also, to an extent, by data availability.  
 specification of the preferred model described here, however, is identical across countries and 
demographic groups. 
 
The selectivity-corrected earnings functions take a simple Mincerian form; the dependent 
variable is the log hourly wage, with years of schooling, potential experience, experience 
squared, a part-time dummy, and year dummies as regressors.
2 The reduced form bivariate 
probits also include all of these as explanatory variables in the occupation equation, plus a set 
of region dummies. In the participation equation, the explanatory variables are potential 
experience, household size, the local unemployment rate, and year dummies. For reasons of 
space, the reduced form probits and the earnings equations are not reported here.
3  
 
Two features of the earnings equations are worth reporting, however. First, the coefficient on 
part-time work is positive (often significantly so) for all demographic groups, occupations and 
countries with one exception (skilled married women in the USA). This is a rather surprising 
result, in that is suggests that part-time workers are not underpaid relative to their full-time 
counterparts, though it is consistent with the finding of Blank (1990) that the rate of return to 
education for part-time workers is relatively high. It seems that, when the different 
propensities of part-time and full-time workers to enter different occupations is accounted for, 
the apparent penalty associated with membership of the former group vanishes. Secondly, the 
local unemployment rate does not appear as a regressor in the wage equations because it was 
found to be nowhere significant. Once allowance has been made for sample selection bias, the 
robustness of the wage curve comes into question. 
 
Tables 1 through 3 give the results of the structural model in each country and for each of the 
demographic groups. A number of consistent patterns emerge. The coefficient on household 
size is positive in the participation equation for men in all countries, but is negative in the 
equations for both single and married women. With the exception of males and married 
females in the US (where the relevant coefficients are insignificant), the log of local 
unemployment has a negative coefficient in the participation equation. In the occupational 
choice equations, the sign on the expected relative wage coefficient is always positive for men 
(significantly so in Germany and Britain), and always negative (sometimes, surprisingly, 
significantly so) for married women. 
 
The coefficients evaluated in a bivariate probit are not easily interpreted, however, and it is 
often more useful to examine the marginal effects. These may be calculated using the method 
of Christofides et al. (1997), and are reported in Table 4 for the coefficient on the expected 
relative wage variable. It is easily seen that, in each country, men respond to expected wage 
differentials across occupations so that, ceteris paribus, they are more likely to enter a given 
occupation when the wage differential is relatively large in favor of that occupation.  
 
                                                           
2 For Germany, no data on years of schooling are given in the ISSP for 1989, so these had to be estimated using 
information about highest level of schooling completed.  
 
3 The interested reader may, however, refer to them at http://www.lancs.ac.uk/people/ecagj/wagediff.html, where 
further information on the definition of variables is also available. 4. Conclusions 
 
The results reported above suggest that males are more responsive than females to changes in 
the expected relative wage across occupations. The pattern is remarkably consitent across 
countries in Europe and North America. While there exists a variety of explanations for this 
observation, it is consitent with the widespread presence of gender based occupational 
segregation – women may simply not be able to respond to occupational wage differentials 
because their access to certain occupations remains limited.  
 
 
References 
 
Ahn, S.C., 1992. The LM test for a model with two selectivity criteria. Economics Letters 38, 9-15. 
 
Blank, R.M., 1989. The role of part-time work in womens’ labor market choices over time. American Economic 
Association Papers & Proceedings 79, 295-299. 
 
Blank, R.M., 1990. Are part-time jobs bad jobs? In: Burtless, G. (ed.) A Future of Lousy Jobs? Brookings, 
Washington. 
 
Brown, C.J., Pagan, J.A., Rodriguez-Oreggia, E., 1999. Occupational attainment and gender earnings 
differentials in Mexico. Industrial and Labor Relations Review 53, 123-135. 
 
Christofides, L.N., Stengos, T., Swidinsky, R., 1997. On the calculation of marginal effects in the bivariate 
probit model. Economics Letters 54, 203-208. 
 
Dolton, P.J., Makepeace, G.H., Van Der Klaauw, W.,1989. Occupational choice and earnings determination: the 
role of sample selection and non-pecuniary factors, Oxford Economic Papers 41, 573-594. 
 
Dolton, P.J., Makepeace, G.H., 1993. Female labour force participation and the choice of occupation: the supply 
of teachers. European Economic Review 37, 1393-1411. 
 
Ham, J.C., 1982. Estimation of a labour supply model with censoring due to unemployment and employment. 
Review of Economic Studies 49, 335-354. 
 
Heckman, J.J., 1979. Sample selection bias as a specification error. Econometrica 47, 153-161. 
 
Lee, L-F., 1983. Generalized econometric models with selectivity. Econometrica 51, 507-512. 
 
Meng, C-L. and Schmidt, P., 1985. On the cost of partial observability in the bivariate probit model. 
International Economic Review 26, 71-85. 
 
Nakamura, A., Nakamura, M., 1983. Part-time and full-time work behavior of married women: a model with a 
doubly truncated dependent variable. Canadian Journal of Economics 16, 229-257. 
 
Schmidt, P.J. and Strauss, R., 1975. The prediction of occupation using multiple logit models. International 
Economic Review 16, 471-486. Table 1 
Structural bivariate probit estimates of the participation and occupational choice equations: Federal Republic of Germany 
 
  males  single females  married females 
  occupation participation occupation participation occupation participation 
        
constant  -3.738 0.695 0.565 0.792 0.990 0.761 
 (8.85)  (4.23)  (0.35)  (3.21) (1.39) (3.78) 
        
expected relative 
wage 
4.888  1.098  -4.651  
  (10.89)   (2.56)  (3.66)  
        
experience  0.009 0.038 -0.088 0.001 -0.020 -0.010 
 (1.75)  (14.66)  (7.36)  (0.30) (1.27) (2.82) 
        
household  size   0.087  -0.052  -0.284 
   (3.59)  (1.14)  (9.13) 
        
log of the local 
unemployment 
rate 
 -0.028  -0.035  -0.003 
   (2.02)  (1.67)  (0.22) 
        
ρ  -0.995 -0.005 0.820 
 (126.947)  (0.00) (2.77) 
        
log likelihood  -1129.088  -564.533  -964.313 
        
Note: t statistics appear in parentheses. The occupational choice equation also includes regional dummies; the participation choice equation also 
includes year dummies. Table 2 
Structural bivariate probit estimates of the participation and occupational choice equations: Great Britain 
 
  males  single females  married females 
  occupation participation occupation participation occupation participation 
        
constant  -0.377 1.759 2.579 1.153 1.510 0.962 
 (3.40)  (6.38)  (1.31)  (3.01) (2.40) (4.41) 
        
expected relative 
wage 
5.716  -0.977  -0.903  
  (13.37)   (0.94)  (2.60)  
        
experience  -0.023 -0.007 -0.073 -0.014 -0.061 -0.009 
 (5.51)  (1.50)  (2.47)  (2.07) (6.49) (2.40) 
        
household  size   0.055  -0.045  -0.113 
   (1.67)  (0.81)  (3.37) 
        
log of the local 
unemployment 
rate 
 -0.069  -0.042  -0.010 
   (3.08)  (1.35)  (0.63) 
        
ρ  0.956 -0.008 -0.011 
  (1.10) (0.00) (0.01) 
        
log likelihood  -981.926  -343.418  -1151.235 
        
Note: See note to Table 1. Table 3 
Structural bivariate probit estimates of the participation and occupational choice equations: USA 
 
  males  single females  married females 
  occupation participation occupation participation occupation participation 
        
constant  0.877 0.730 1.316 0.927 0.637 0.721 
 (0.49)  (2.54)  (1.89)  (2.96) (0.62) (2.33) 
        
expected relative 
wage 
0.012  -0.930  -0.582  
  (0.13)  (3.26)    (1.63)  
        
experience  -0.098 0.013 -0.045 -0.006 -0.059 -0.014 
 (3.52)  (3.56)  (5.27)  (1.26) (3.02) (3.02) 
        
household  size   0.014  -0.068  -0.040 
   (0.49)  (2.11)  (1.26) 
        
log of the local 
unemployment 
rate 
 0.020  -0.013  0.009 
   (0.43)  (0.25)  (0.19) 
        
ρ  0.003 -0.003 -0.005 
  (0.00) (0.00) (0.00) 
        
log  likelihood  -999.704 -712.970 -911.569 
        
Note: See note to Table 1. Table 4 
Marginal effects of the expected wage variable 
 
 Germany  Great  Britain  USA 
     
males 1.128  0.26 x 105  0.001 
single females  0.089  -0.188  -0.39 x 10-13 
married females  -0.25 x 10-8  -0.066  -0.17 x 10-13 
 

Are part-time jobs bad jobs?

Estimation of a labour supply model with censoring due to unemployment and employment.

Female labour force participation and the choice of occupation: the supply of teachers.

Generalized econometric models with selectivity.

Klaauw, W.,1989. Occupational choice and earnings determination: the role of sample selection and non-pecuniary factors,

Occupational attainment and gender earnings differentials in Mexico.

On the calculation of marginal effects in the bivariate probit model.

On the cost of partial observability in the bivariate probit model.

Part-time and full-time work behavior of married women: a model with a doubly truncated dependent variable.

Sample selection bias as a specification error.

The LM test for a model with two selectivity criteria.

Wage differentials and the responsiveness of labor supply: an international comparison

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Wage differentials and the responsiveness of labor supply: an international comparison

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