Reassessing the male-female wage differential: a fixed effects approach.

• Author: Choudhury, Sharmila

1. Introduction

   The vast literature on the subject of the male-female wage differential has shown that despite dramatic structural and behavioral changes in the labor supply of women, a sizeable wage differential exists |19; 2; 9; 6; 4~. O'Neill |16, S92~ finds that a sex differential of about 40% as measured by full-time annual earnings has persisted in the U.S. for the last four decades.

   But while few doubt the existence of the wage gap, there is considerable controversy regarding the role of the factors explaining the gap. The conventional approach of economists has been to estimate earnings as a function of various socio-economic characteristics.(1) The observed wage gap is decomposed into a part explained by productivity related factors and an unexplained residual, traditionally labelled as discrimination. While it is possible that the unexplained variation in earnings is the result of discrimination, it is also possibly the result of model misspecification.(2)

   In this present paper, we address the misspecification that could possibly arise from omitted variables, endogeneity and sample selection. While these issues have been considered in the context of women's labor supply functions, they have largely been ignored in studies on the wage differential |12; 13~. We approach the problem of omitted variables by formulating a Fixed Effects model. In this way, productivity related factors that are difficult to measure or have unsuitable proxies are netted out from the earnings equation. Furthermore, some of the variables that are used to explain wages are themselves the outcome of discrimination. In particular, the labor market experience of a woman is dependent on her wages earned. Here, we address the endogeneity that such a cause and effect relationship may bring about. A third difficulty arises because a typical sample of working women is a non-random selection of the female labor force giving rise to the problem of sample selection bias. Heckman's |12, 213-17~ procedure is used to formulate a sample selection model of earnings.

   The organization of this paper proceeds as follows: Section II begins with the traditional model of earnings and then develops an extended model which consolidates the issues of omitted variables, endogeneity and sample selection. Section III contains the empirical results of the models using data from the Panel Study of Income Dynamics (PSID). In section IV, a Oaxaca |15, 694-97~ style decomposition of the wage gap sheds some light on the factors that cause the wage gap. Section V ends with some concluding observations.

2. The Econometric Model

   For a sample of men and women who work, the traditional earnings model is given as:

   ln |W.sub.m~ = |X|prime~.sub.m~||Beta~.sub.m~ + |u.sub.m~ (1)

   ln |W.sub.f~ = |X|prime~.sub.f~||Beta~.sub.f~ + |u.sub.f~ (2)

   m = 1,... |N.sub.m~

   f = 1,... |N.sub.f~

   where W is a vector of wages, X is a vector of individual characteristics, N is the number of individuals, and m and f refer to men and women, respectively. The error terms, |u.sub.m~ and |u.sub.f~, are independent and identically distributed. In this case, OLS provides the best results.

   There are several unobservable variables that genuinely influence earnings. Factors such as intelligence or motivation are difficult to quantify and do not have reasonable substitutes. An important source of misspecification results from the omission of such variables from the earnings equation. These are typically innate characteristics of an individual and can be expected to be constant (more or less) over short periods of time. We, therefore, formulate a Fixed Effects model given as:

   ln |W.sub.it~ = |X|prime~.sub.it~||Beta~.sub.i~ + |A|prime~.sub.i~||Gamma~.sub.i~ + |u*.sub.it~ (3)

   where |A.sub.i~ is the individual (men and women) specific, time invariant component, t measures time and |u*.sub.it~ is the error component that varies over both individuals and time. The equation now includes A, which is the unobservable component of an individual's characteristics that affect earnings. It is a fixed effect because such characteristics are expected to be fixed for individuals over a short time period.

   Alternately, a random components model may be formulated where a particular distribution is assumed for the individual effect. According to Mundlak |14, 69-70~, such models provide efficient estimates but if the distributional assumption is incorrect, GLS as well as OLS results will be biased. Since our primary concern is with inference on |Beta~'s and not with forecasting, the use of a Fixed Effects model is preferred to a Random Effects model.

   Women's labor market experience follows a more complex pattern than that of males, who typically work on a continuous basis regardless of the wages earned.(3) There are significant costs of participation for married women in terms of money and time. This is because women have to allocate their non-leisure time between market activities and household activities associated with child-rearing. Child care arrangements are an important source of money costs of work. These costs determine her labor market behavior. The experience accumulated by married women is, therefore, a function of the wages earned and is highly correlated with the wages she commands in the market. The resulting simultaneity bias in the wage equation makes it necessary to use an instrumental variable in place of labor market experience. The econometric approach to endogeneity of experience is to replace actual experience in the women's earning equation with the predicted value of experience. Experience is defined and thereby predicted as a function of a set of exogenous variables such as individual human capital stock, marital status, parenthood and family income. This two stage least squares approach has been used by Mincer and Polachek |13, S99~ and Zabalza and Arrufat |20, 73-74~. Cain |6, 755~ states that the validity of such a technique depends on two assumptions. First, there should be at least one variable used in predicting experience that is not included in the wage equation. Second, the excluded variable must not be an outcome of labor market discrimination. Here, the additional variable used in predicting a woman's labor market experience is the family income. The few studies that have analyzed this endogeneity issue have used number of children as the excluded variable |20, 75~. An alternative approach is used by Gronau |10~ who determines earnings and experience in a simultaneous equations framework. Other variables may be endogenous too, such as education and fertility related variables. By ignoring the endogeneity that could arise from sources other than experience, the results stated here will admittedly contain a bias. However, educational and fertility decisions are made for the long term and we require a fuller understanding (than is available now) of these decision processes and their impact on the earnings equation before we can include them in our model.

   The sample of working women is essentially truncated because it ignores those who do not work. These working women are not a random selection of the workforce. Women who participate in the labor market are not representative of the entire population of women because participation is endogenous to the...