8 Given the fact that explanatory power of human capital variables has been di- minished, this paved a path for labour economists to integrate psychological and socioeconomic factors into the analysis of the gender pay gap. The recent advance- ments in psychology and experimental economics literature have had a significant impact on economic research (Bertrand, 2010). Among many psychological factors, risk aversion and competitiveness have been most extensively studied. Gneezy et al. (2003) observed that women are more likely to have poor performance in a competi- tive environment compared to men, however, non-competitive environments allow them to have equal performance. They conducted a lab experiment asking students to solve a maze under two possible compensation schemes: a piece rate and tourna- ment schemes. The piece rate scheme paid each student on the basis of a number of mazes solved, while the tournament scheme paid only them who solved the high- est number of mazes. In the former case, there was observed no gender difference in performance, however, in the case of the latter, a sharp increase was observed in men’s performance. These findings are in line with those of Niederle and Vesterlund (2007), who found that men and women tend to overestimate their performance rank in their group, but men do it by a greater extent. They studied compensation choices (the same schemes as in Gneezy et al., 2003) of men and women in a mixed-sex environ- ment and observed that approximately three-quarters of men choose tournament compensation scheme, while only one-third of women favoured it. The gender gap in overconfidence could explain a portion of gender difference in the compensation scheme, but not all (Bertrand, 2010). On the other hand, Manning and Saidi (2010) studied British Workplace Employees Relations Survey data and, considering litera- ture outcomes on the gender differences in risk attitudes and competitiveness, they tested a hypothesis that fewer women are employed in the establishments, which use variable pay scheme. Even though the hypothesis could not have been rejected, the difference was quantitatively very small. Likewise, Lavy (2012) did not find any significant difference in performance when the compensation was paid according to the rank in the tournament. Considering these contradictory results, it is legitimate to ask whether the findings of experimental studies can be extrapolated to on-the-job discrimination. Azmat and Petrongolo (2014) argue that to date experiments do not fully explain real-life discrimination, and how expected discrimination might affect an individual’s choices. Furthermore, while one may conclude that lab experiments have direct implication for labour market outcomes, these conclusions are based on incomplete information and require further evidence from the workplace to depict the gender differences in real markets. In addition to psychological factors, the unequal share of unpaid work and fam- ily responsibilities are supposed to contribute to the gender pay gap at larger ex- tent than differences in risk aversion and competitiveness (Ponthieux and Meurs, 2015). A family composition results in different consequences in the labour market for men and women, even though they might possess similar productive character- istics. Family status and parenthood are found to have a significant contribution to the gender pay gap. However, these factors have strictly opposite effects for men and women. Men are found to receive marriage wage premium, while there is no positive change observed for married women. One possible explanation is that since most of the domestic chores are done by women, men tend to have higher involve- ment in the labour market. A concept of wage penalty has been introduced to reflect the fact that married women or mothers receive lower wages compared to their male
- Related Literature 9 counterparts. This is easily explained by the inelastic supply of labour that puts their employers into monopsony and gives market power, which allows them to pay be- low the competitive wages. Similar results are reported by Hirsch et al. (2010) and Barth and Dale-Olsen (2009), who reported that in Germany and Norway, respec- tively, labour supply of women is more inelastic than of men’s and linked with wage discrimination. During the last decades an interesting trend has been observed: despite the decline in the gender wage gap, the wage dispersion increased between women with and without children. This phenomenon was called “motherhood wage gap”. Cukrowska-Torzewska and Lovasz (2016) studied the effects of having children on the gender pay gap in Hungary and Poland and named five possible sources of lower wages of women with children compared to those without children: 1) work- ing mothers are more likely to spend time out of the labour market due to childbear- ing, which leads to accumulated less human capital and its depreciation; 2) family responsibilities limit working mothers to seek for ‘mother-friendly’ jobs, which are typically less demanding and more convenient, resulting in wage differentials; 3) unobserved heterogeneity among women with and without children; 4) according to Becker’s work effort theory, lower wages for mothers are consequence of their re- duced productivity, which makes employers avoid their promotion; 5) discrimination- based theories. In the recent study of Viitanen (2014), it is shown that motherhood has a long lasting but small effect on compensation. On the contrary, using the same dataset as Viitanen (2014), Waldfogel (1998b) showed that motherhood results in 20% penalty for women aged between 30 and 33. Due to the "motherhood wage gap," there has recently emerged a hypothesis that women tend to postpone having children in order to accumulate human capital. Caucutt et al. (2002) showed that there is a correlation between the increase in earnings and fertility delay. These re- sults are in line with Miller (2011), who found the positive effect of fertility delay on wages. In contrast, Smith et al. (2013) argued that those women who have children at a young age are more likely to be selected as chief executive officers. Not only women are affected by family status and parenthood, as it was noted above. While there are no direct effects of having kids on men, they do receive mar- riage premium. In addition to the increased productivity argument stated above, another hypothesis contributing to the wage premium is a positive selection. Corn- well and Rupert (1997) and Nakosteen and Zimmer (1997) argued that those men, who are more productive in the labour market, are more likely to find a partner and succeed in the marriage market. However, there is no convincing evidence support- ing either hypothesis. For example, Nakosteen and Zimmer (1997) and Dougherty (2006) found the selection effect. On the other hand, Chun and Lee (2001) and Mehay and Bowman (2005) observed a positive effect of specialization. Until recently, little to no studies have been done on wealth inequality. Most likely, the explanation is a lack of appropriate statistical data. Generally, data in- cludes household level assets that are shared among the members and almost al- ways it is impossible to differentiate who owns what in the household. However, some approaches have been developed over time to partially overcome the data lim- itations, though all of them are far from being consistent. For example, one of the most widespread methodologies is to impute wealth on the individual level from the household level. This can include per capital wealth, an equal share of wealth to each partner in the couple households, etc. As it is easily noted, the assumption that all
10 household assets are owned jointly and shared equally has different consequences for different types of households, which depends on partners’ marital status and marriage agreement. However, the emerged approaches are still better than nothing and provide some interesting insights despite the bias. Sierminska et al. (2010) and Bonnet et al. (2013) used German and French data and found a significant differ- ence in wealth accumulation: in Germany there was observed almost 45% gap in net worth, favouring men, and in France, the gap was 16%, again in favour of men. The results differ not because there is less inequality in France but because Bonnet et al. (2013) did not include business assets in their study, whereas in Germany the biggest wealth gap was observed in business wealth. These results are in line with D’Alessio (2018), who found 18% gender wealth gap in Italy, and Meriküll et al. (2018), who estimated approximately 45% gender wealth gap in Estonia, the country with the largest gender wage gap in EU. Furthermore, Meriküll, et al. (2018) showed that the gender wealth gap is the largest in self-employment business wealth. Furthermore, the gender gap in pensions was neglected till the second half of the 20th century, when male breadwinner model was no longer consistent with the real- ity. Before that time, it was considered that since pensions could be considered as an outcome of wage, the wage differential would automatically result in less pensions for women than for men. In addition, the assumption of a women being married implied that the pensions were pooled and they could share their partner’s pension (Ponthieux and Meurs (2015)). Recent decreasing trends in marriage and increased rate of divorce and cohabitation changed the patterns of the gender pension gap. 3 Methodology In the paper I analyze factors contributing to the gender income gap, apply regres- sion analysis, and decompose the difference by Oaxaca-Blinder method. If the pri- mary interest of the paper were to study the impact of the explanatory variables on the average income, then the simple OLS method could have been a candidate. The reason why the simple OLS method is popular in economic studies can easily be seen from the law of iterated expectations (L.I.E.). According to the L.I.E., the mean of dependent variable, conditional on explanatory variables, averages up to the un- conditional mean: E (E(Y/X)) = E(Y), where Y could be the dependent variable and X could be a vector of explanatory variables. Due to this property, the OLS re- gression provides consistent estimates of the effect of an independent variable on the unconditional mean of the dependent variable. Since the goal of this study is to ex- amine the whole distribution of the income, methods other than simple OLS should be employed. A computation of quantiles is considered to be a convenient way to characterize the distribution of the outcome variable. This helped conditional quan- tile regression models gain popularity (e.g. see Koenker and Basser (1978), Koenker (2005)). However, the estimates of the impact of the explanatory variables on the outcome variable, derived by quantile regression, cannot be used to study their im- pact on the corresponding unconditional quantiles. This is due to the fact that the expectation of the conditional quantiles does not equal to the expectation of the un- conditional quantiles, which was the case for the conditional mean. To overcome this problem, Firpo et al. (2009) proposed the unconditional quantile regression. The rationale behind using the unconditional quantile regression is that it allows
- Methodology 11 estimation of effects of marginal changes in the explanatory variables on the uncon- ditional quantiles of the dependent variable. Borah and Basu (2013) studied the conditional and unconditional quantile re- gressions and distinguished three differences favouring the latter: (1) if the data generating process is influenced by only one covariate then both conditional and un- conditional regressions would estimate the same effect of this covariate on a specific quantile; (2) if the data generating process is influenced by several covariates, then conditional quantile regression would estimate the effect of a variable on a specific quantile of the dependent variable, conditional on mean values of other covariates. On the contarary, in case of unconditional quantile regression, the estimated effect of a covariate is generalized over the distribution of other covariates and its interpre- tation is directed to the whole population instead of a specific quantile; (3) in case of exogenous covariates, the inclusion of different sets of explanatory variables have no impact on the estimate of a covariate in case of unconditional quantile regression as a specific quantile of the distribution is not conditioned on the mean values of other covariates. The unconditional quantile regression is built on influence function, however, a slightly modified one. As Hampel (1974) described, the influence function of func- tional statistic shows how much influence each observation has on the distribution of this functional. Firpo et al. (2009) proposed a concept of recentered influence function (RIF), which is derived by adding the statistic to the influence function. For the sake of clarity, if the influence function is: IF (Y; qτ) = τ− 1{Y≤ qτ} fy(qτ) (3.1) then the recentered influence function can be written in the following way: RIF (Y; qτ) = qτ + IF (Y; qτ) (3.2) where 1{Y≤ qτ} is an indicator function, Y is a continuous random variable, qτ is τth quantile of the unconditional distribution of the dependent variable, Y, and fy(qτ) is the density of the marginal distribution of Y. In general terms, instead of qτ, there could have been any functional statistic of our interest. Modelling the expectation of the RIF , conditional of explanatory variables, is called RIF regression model. In case of quantiles, it can be considered as uncondi- tional quantile regression: E [RIF (Y; qτ)|X] = mτ(X) (3.3) It is easily observed that when mean is considered as a functional statistic, the OLS estimates of explanatory variables, X, on the dependent variable, Y, are equiv- alent to the coefficient estimates derived by regression of RIF (Y, µ) (Firpo et al. (2009)). In case of mean, the influence function is the demeaned value of the depen- dent variable. Therefore, recalling the fact that RIF is sum of IF and the functional statistic, RIF would equal to Y: 12 IF (Y; µ) = Y− µ (3.4) RIF (Y; µ) = IF (Y, µ) + µ (3.5) By plugging equation (3.4) into equation (3.5), RIF (Y, µ) = Y− µ + µ = Y. This property implies validity of OLS estimates of the impact of explanatory variables on the unconditional mean of the dependent variable, Y. However, Firpo et al. (2009) show that this property can be extended to any other distributional statistic. The central idea of the unconditional quantile regression is that any functional of the distribution can be written as a mathematical expectation. The definition of the unconditional distribution of Y implies that FY(y) = ∫ FY|X(y|X = x)dFX(x) (3.6) Firpo et al. (2009) provide the proof for the fact that the recentered influence function integrates up to the functional: ∫ RIF (y; ν)dF(y) = ∫ ν(F) + IF (y; ν)dF(y) = ν(F) (3.7) By substituting the equation (3.6) into the equation (3.7) and considering the fact that: E [RIF (Y; ν)|X = x] = ∫ y RIF (y; ν)dFY|X(y|X = x) (3.8) The following equation can be shown (Firpo et al. (2009)): ν(FY) = ∫ RIF (y; ν)dFY(y) = ∫ E [RIF (Y; ν)|X = x] dFX(x) (3.9) By comparing the equation (3.6) to the equation (3.9), it is easily seen that to de- rive the unconditional distribution of Y, it is necessary to integrate over the whole distribution in (3.6), however, when a specific distributional statistic is of an interest, integration over E [RIF (Y; ν)|X] by regression methods is sufficient. The primary goal of the unconditional quantile regression is to estimate how a small increase, t, in the explanatory variable impacts unconditional quantile of the dependent variable. This is achieved by unconditional quantile partial effect (UQPE). If Y is a function of observed X covariates and unobservable ϵ, in a form of some unknown mapping h (Y = h(X, ϵ)), then the impact on the unconditional distribution of Y, caused by an infinitesimal change in a continuous variable X on the τth quantile, is given by: β(τ) = lim t→0 Qτ [h(X + t, ϵ)]− Qτ [Y] t (3.10) where Qτ [Y] is the τth quantile of the unconditional distribution of Y. This de- picts the case when X is univariate, however, it can be extended for the case whenX is multivariate:
- Methodology 13 βj(τ) = lim tj→0 Qτ [ h( [ Xj + tj; X−j ] , ϵ) ] − Qτ [Y] tj (3.11) More formally, if a continuous variable X is increased by an infinitesimal change t, from X to X + t, the change will result in counterfactual distribution F∗ Y,t(y). If ν is any distributional statistic then the impact of the change in X on the distributional statistic ν can be written as2: β(ν)≡ lim t→0 ν(F∗ Y,t)− ν(FY) t = ∫ dE [RIF (Y; ν)|X = x] dx dF(x) (3.12) This can be extended to the case, when X is a binary random variable. Let us assume that X can be either 1 or 0, i.e. X ∈ 0, 1. If probability of X = 1 is Px then the infinitesimal change in this probability would result in the counterfactual distribution of F∗ Y,t(y). The effect of this change on the distributional statistic can be written as: β(ν)≡ lim t→0 ν(F∗ Y,t)− ν(Fy) t = E [RIF (Y; ν, F)|X = 1]− E [RIF (Y; ν, F)|X = 0] (3.13) To apply the unconditional quantile regression to this study, first, I define the recentered influence function specification for income: RIF (yi; qτ) = β0,τ + J ∑ j=1 βj,τxj i,τ + ϵi,τ (3.14) where RIF (yi; qτ) is the recentered influence function of income yi at quantile qτ; xj (j=1,...,J) are explanatory variables; β0,τ and βj,τ are coefficients of the explanatory variables on the τth quantile of income; and ϵi,τ is an error term. Firpo et al. (2011) distinguish several advantages of the recentered influence function regression due to its linearity. The most important advantage of this method is that one does not have to worry about monotonicity. This fact emerges from in- version of proportion of the interest, performed locally, which relaxes a need of eval- uating the global impact at all points of the distribution. The simplicity of regression makes it easy to interpret and the decomposition is path independent. To study the gender income gap, Oaxaca-Blinder decomposition is employed (Oaxaca (1973), Blinder (1973)). First, considering the fact that income is strongly skewed right, the sample mean is not necessarily the most informative. When the distribution is skewed right, a sample mean tends to be biased towards the right tail and the difference between mean and median increases as distribution becomes more skewed. Therefore, a great emphasis should not be placed on the sample mean, because those individuals earning high incomes would be a false representation of 2The proof is provided by Firpo et al. (2009) 14 the typical income. This might be an especially relevant issue in a country such as Es- tonia (Rõõm and Anspal (2010)), where income dispersion is high. Due to this reason unconditional quantile regression is applied. Second, the Oaxaca-Blinder decompo- sition is applied to the estimates derived from RIF-regression. The decomposition method allows writing the difference between income estimates of men and women in the following way: b∆τ M−F = XF bβM,τ −XF bβM,τ + XMbβM,τ −XF bβF,τ = XF bβM,τ −bβF,τ
- bβM,τ(XM −XF) = b∆τ S + b∆τ X (3.15) where b∆τ M−F refers to the income difference between men and women at τth quantile of the income distribution, XM and XF are sample averages of the explana- tory variables, bβM,τ and bβF,τ are respective coefficients of the explanatory variables, derived from RIF-regression for men and women separately. The first term of the right-hand-side of the equation (3.15) (b∆τ S) is called a struc- ture effect, while the second term is referred to as composition effect (b∆τ X). Structure and composition effects are also referred to as unexplained and explained parts of the differential, respectively. Since a reported gender status is considered as a group membership indicator, either male or female, its immutable nature implies that un- explained part of the differential can be attributed to the discrimination. However, in case of income, unlike the case of wages, the unexplained part is not necessarily discrimination. This unexplained part is related to the institutions to some extent, for example, how generous public transfers are towards those raising children at home. The composition effect, or the explained part of the differential, captures the gap that is due to the difference in the observed characteristics between men and women. Such characteristics could be education, field of occupation, employment status, etc. Gardaezabal and Ugidos (2004) and Oaxaca and Ransom (1999) argue that choice of base group has a large impact on the contribution of each explanatory variable to the structure effect. In this paper, men are considered as a base group. The compo- sition effect can be interpreted how income would differ between men and women, had they had different observable characteristics but same returns (i.e. returns of men) on these characteristics. On the contrary, the structure effect shows how in- come would differ between men and women, had they had the same characteristics (i.e. characteristics of women) but different returns. The rationale behind using men as a base group is the author’s expectation of the discrimination in favor of men, which makes interpretation of the structure effect of the gap straightforward. Ponthieux and Meurs (2015) highlight one classic difficulty associated with de- composition methods that "the measurement error of some key variables may be more marked for women than for men" (p. 1014). The striking example of this problem is the labour market experience, which very often is proxied as a difference of current age and school-leaving age (potential experience). Given the fact that women are more likely to have interruptions in the career, their experience is over- estimated, leading to downward bias of returns to experience and therefore upward bias of the unexplained part of the wage gap. Neumark and Korenman (1992) point