Impediments to the Advancement of Women in the Japanese Employment System: Theoretical Overview and the Purpose of This Book

Abstract

As the opening to the book, this chapter reviews the current situation, marked by the very slow advancement of women’s participation in Japanese economic activities despite various types of legal support. The main factor attributed to this delay in promoting women’s participation is Japanese employment practices . To better understand the historical origins of these practices and of the significant delay in women’s participation, the author clarifies economic and cultural foundations of the so-called Japanese employment system . He addresses its problems referred to in this chapter as “rationality under specific premises ,” the problem of “structural inertia” associated with the employment system constructed under the principle of “strategic rationality ,” and the problem of the “traditional division of household labor between husband and wife” as imposed by society as a complement of the employment system. Based on those discussions, the aims of this book are explained. In addition, given the book’s focus on empirical analysis, this chapter also provides an explanation of the aims of, and the methodological background for, the analytical strategies employed in the book.

Appendix: A Non-technical Explanation of Rubin’s Causal Model

Analyses in Chaps. 2–5 of this book use statistical methods that originate from Rubin’s causal model . Therefore, its characteristics are explained in non-technical terms.

1.1.1 Treatment Variable and Outcome

The “Rubin’s causal model” is a statistical causal inference approach developed by Donald Rubin and his colleagues (Rosenbaum and Rubin 1983, 1984; Rubin 1985). We consider whether the treatment variable X—assuming a value of 1 or 0—causally generate a difference in outcome Y and, thus, whether X has a causal effect on Y. However, an effect may not always exist, and therefore causality is assessed by examining whether, on average, the mean value of the outcome becomes significantly larger (or smaller) under treatment (when X = 1) than under no treatment (X = 0). Diverse examples of the model’s application include: (1) whether the introduction of the new English curriculum (X = 1) will improve students’ English ability (Y) relative to not introducing the new curriculum (X = 0); (2) whether experiencing a divorce (X = 1) will shorten life expectancy (Y) relative to not experiencing a divorce (X = 0); (3) whether municipalities administering guidance to firms to achieve numerical targets prescribed by the Act on the Promotion of Success in the Working Careers of Women (X = 1) will result in larger increases of the proportion of women in managerial positions (Y) relative to not administering guidance (X = 0); (4) whether attending a particular high school (X = 1) will increase the probability of being admitted to The University of Tokyo (Y) relative to attending another high school (X = 0).

1.1.2 Definition of Counterfactual Causality

Rubin’s causal model has two main characteristics. The first one is the use of defining the counterfactual in defining the causal effect. For hypotheses (1)–(4), referring to them in the past tense may be more easily comprehended. For example, (1) would be “whether the introduction of the new English curriculum (X = 1) improved students’ English ability (Y) compared with the outcome that would have been realized when it had not been introduced (X = 0).” Rubin’s causal model considers answers to these types of questions as causal inference. In other words, we are concerned here with an answer for the question “if the same individuals were placed, under the same conditions other than X, in the unobserved state of X = 0, instead of the observed state of X = 1, would the outcome be different?” If the answer is yes, a causal effect of X exists, and if the answer is no, no causal effect exists.⁷ However, the differences in these outcomes cannot be measured directly because although outcomes exist for which the situation was actually observed, X = 1, the outcomes for the situation that was not observed, X = 0—known as the counterfactual—do not exist.

However, the average causal effects resulting from the definition of the counterfactuals can be inferred if the situations X = 1 and X = 0 are randomly assigned to the subjects. The average refers to the mean of treatment effects when they differ by individual. It is because when subjects are randomly assigned to a treatment, the estimate for the average of Y values among sample subjects assigned X = 1 becomes the estimate for the average of Y values for the entire population. Similarly, the estimate for the average of Y values among for sample subjects assigned X = 0 becomes the estimate for the average of Y values for the entire population. As a result, the difference between the average Y value for subjects assigned X = 1 and the average Y value for subjects assigned X = 0 becomes the estimated value of the average causal effect of X in the population.

Such a random assignment can be used to examine hypotheses (1) and (3) because teaching the new English curriculum only in randomly selected classes is possible, as is making firms receive administrative guidance only in randomly selected firms. However, such random assignments cannot be employed for examples (2) and (4) because randomly selecting subjects to get a divorce or to make randomly selected subjects admitted to a particular nonexperimental high school is impossible. Furthermore, even for examples (1) and (3), complete randomization to implement the study would prove difficult because some subjects who perceive random assignments into the treatment group (X = 1) or the control group (X = 0) may not comply with the assignment.⁸

1.1.3 Nonrandom Assignment and Selection Bias

Rubin’s causal model is the approach used to carry out statistical causal inference when assignment of the treatment variable X is nonrandom. Generally, the nonrandom assignment of treatment group X = 1 is subject to selection bias for the states of X. Two types of selection biases exist: those as a result of confounding factors and those arising from reverse causation . Each is explained using previous examples.

Selection bias resulting from confounding factors refers to the biases that arise concerning the observed relationship between X and Y when variables that influence both the treatment variable X and outcome Y (i.e., confounding factors) are present and the impacts of those factors are not excluded. We use the previous example (4). As a result of Tokyo’s introduction in 1967 of the group-school-system for Tokyo metropolitan public high schools, prestigious high schools such as Hibiya High School, from which more than 100 students gained admission to The University of Tokyo prior to implementation of the system, all saw an across-the-board decline to less than 10 in the number of students admitted to The University of Tokyo from the cohorts after the implementation of this system. This fact implies that education in those prestigious high schools was not the primary reason for the large number of their graduates admitted to The University of Tokyo; rather, the major cause of their success was the pre-existing high academic ability of the students who were admitted to those high schools. To investigate whether any educational effect existed from attending Hibiya High School relative to other high schools, we must control for the confounding factors of the differences in students’ academic ability before entering high school.

Depending on the methods used to measure the effects of divorce [example (2)], in addition to the effects of selection bias attributable to confounding factors (for example, one’s health affects both divorce rate and life expectancy), another selection bias can occur. That is, if the presence of divorce experience is measured as having been divorced until the time of death, individuals who die a relatively young age may not have experienced divorce because of fewer years of exposure to the risk of divorce (they could have experienced a divorce if they had lived longer). Hence, a positive correlation between longevity and divorce experience is likely a result of reverse causation , where shorter life causes a lower probability of experiencing a divorce. Thus, causal analysis first employs an outcome measure and a treatment variable that are unaffected by a reverse causation , such as examining whether having been divorced by a certain age has an effect on the subsequent mortality rate or using divorce experience as a time-varying treatment variable of the hazard rate of death and then tries to eliminate selection bias into the states of the treatment variable.

1.1.4 Assumptions of Rubin’s Causal Inference

Rubin’s causal model is one method for reducing the selection bias resulting from a group of observed confounding variables V. Before the development of Rubin’s approach, multivariate regression analysis was often used in similar situations, and still is today in a large number of analyses. However, when using regression analysis, the manner by which outcome Y is dependent on treatment variables X and confounding variables V must be indicated in the regression equation; furthermore, various assumptions must be made, such as homogeneity of variables’ effects except for parametrically specified interactions with other variables, linear additivity of those effects, and a normally distributed error. From the author’s experience, rarely can such assumptions, especially the assumption of homogenous effects, be satisfied, and biases usually remain. In contrast, Rubin’s causal model is a “semi-parametric” statistical method, whereby no specific assumptions are made concerning the effects of X and V on outcome Y.⁹ However, the following causal order is assumed, as illustrated in Fig. 1.5.

Fig. 1.5

Order of causal relationships in Rubin’s causal model

Figure 1.5 depicts an assumption for a model whereby confounding variable group V affects both treatment variable X and outcome Y, and X affects Y. Rubin’s causal model aims at realizing in data a counterfactual situation in which the effects of confounding variable group V on X are eliminated, as illustrated by an elimination of the dotted line. Assuming V represents all of the confounding variables, when V does not affect X, a situation is created as if people are randomly assigned to the states of X. Such an assignment is difficult to realize directly. That is because when many confounding factors exist, the number of V value combinations increases similarly to a geometric progression, making it nearly impossible to find corresponding samples between the treatment group X = 1 and control group X = 0 for each combined V value. However, by doing the following, it is possible to realize the statistical independence for X and V for the given population.

Here, the unbiased estimate for the conditional probability of X = 1 for given V is denoted by $P(X = 1|{\mathbf{V}})$, and the quantity is referred to as a propensity score in Rubin’s causal model . Because V affects X, the propensity score will change according to V. However, if the value of $P(X = 1|{\mathbf{V}})$ can be made constant in the data and thereby a situation can be created where X will no longer be affected by V, the selection bias in the effect of X on Y is eliminated. Using the propensity score , two methods were devised in Rubin’s causal inference model to realize this situation: (1) matching method and (2) inverse probability of treatment (IPT) weighting method. Under the matching method , pairs of samples with the matching (or nearly identical) propensity score values are selected from the treatment group (X = 1) and from the control group (X = 0), and the data of these matched pairs are analyzed. Under method (2), the inverse probability $1/P$ of being selected for the treatment group is applied as a weight to the treatment group samples, and similarly, the inverse probability $1/(1 - P)$ of being selected for the control group is applied as a weight to the control group samples. The method utilizes the property of the weighted data attaining statistical independence between X and V. The IPT weighting method allows for the use of more samples than the matching method , and thus this book employs the IPT weighting method for all of its analyses.

1.1.5 Limitations of Rubin’s Causal Model

Rubin’s causal model has one major limitation when it is applied to cross-sectional survey data, which is the assumption that no unobservable confounding factors exist. For example, because this assumption is rather strong, the analysis in Chap. 5 using Rubin’s causal model makes an additional assumption regarding the effects of unobservable confounding factors and examines whether the causal interpretation can still be justified in their presence.

When unobservable confounding factors are present, the difference-in-differences (DID) method, commonly used in econometrics, and other panel data analysis methods may be used. The instrumental variable method, which uses a variable to satisfy specific assumptions, may also be used. To provide an example of the former, we revisit example (1). In this case, students’ English ability (Y) is surveyed at two points in time. The first time is before the introduction of the new curriculum for both the treatment and the control groups, and the second time is after the implementation of the new curriculum for the treatment group while the control group continued with the previous curriculum. The results are then examined to uncover whether differences existed in the degree of improvement in academic achievement between the two groups. Even if unobserved disparities existed from the outset in academic achievement between the two groups, the causal effect of treatment can be assessed if we further assume that the extent of academic growth under the previous curriculum was the same between the two groups.

Such an analysis has the merit of being able to eliminate the effects of unobservable confounding factors, even if they existed, if the effects of those factors on the outcome remain temporally unchanged. A similar analysis can be applied to example (3) whereby the outcomes of a company’s rate of women’s attainment of a managerial position can be observed at two points in time.

However, the DID method cannot be applied to examples (2) and (4). The DID method measures the difference in Y values at two points in time and examines whether a difference of the change over time exists between the treatment and the control groups—the “difference in differences.” However, in the case of example (2), the outcome of death can occur only once for an individual and, hence, measuring the mortality rate before and after divorce for the same individual is not possible, thus preventing a “difference in differences” value from being obtained. Similarly, measuring the before- and after-treatment outcomes at two points in time is impossible for example (4) because the rate of being admitted to The University of Tokyo cannot be measured before entering high school.

Although Rubin’s causal model has stronger assumptions than causal analysis based on panel survey data, it is particularly effective in causal analyses when data are from cross-sectional surveys and in situations such as the previous examples in which the characteristics of the outcomes do not allow for measurements of the outcome to be taken at two points in time for the same individuals.

1.1.6 Adapting Rubin’s Causal Inference Model for Decomposition Analysis

In Chaps. 2–4 of this book, Rubin’s statistical method is used not to analyze the causal relationship, but for the decomposition analysis of gender disparities in the proportion of men and women in managerial and other occupational positions, and gender disparities in income into the “explainable disparity” and the “unexplainable disparity.” Unlike causal analysis , the DFL method (explained in the appendix in Chap. 2) and the matching method developed by the author (explained in the appendix in Chap. 3; no relation to the matching method of Rubin’s causal inference model) make the following assumptions on causal order.

In Fig. 1.6, X represents gender, V is the variable for human capital and other observable intermediary variables, and Y is the variable for income or other outcomes. Comparing Fig. 1.6 with Fig. 1.5 shows that the causal order between X and V has been reversed.

Fig. 1.6

Causal relationships in the DFL method

Figure 1.6 illustrates how decomposition analysis breaks down the effects of gender X on outcome Y as indirect effects (explainable disparity) passing through intermediary variables V and direct effects (unexplainable disparity), which do not pass through V. Because the total disparity is observable, the decomposition analysis can be performed if the “unexplainable disparity” that does not pass through intermediary factors can be estimated. Thus, all we must do is create data that represent the counterfactual situation in which X has no effect on V—in other words, a situation in which X and V are statistically independent. Creating such data can be accomplished with the IPT weighting method used in Rubin’s causal model , which allows for the use of the same statistical methods for the decomposition analysis , which is not causal analysis , but without the need for the strong assumptions of a regression model.