Pseudo-Panel Decomposition of the Blinder–Oaxaca Gender Wage Gap

Abstract

This article introduces a novel approach to decomposing the Blinder–Oaxaca gender wage gap using pseudo-panel data. In many developing countries, panel data are not available; however, understanding the evolution of the gender wage gap over time requires tracking individuals longitudinally. When individuals change across time periods, estimators tend to be inconsistent and inefficient. To address this issue, and building upon the traditional Blinder–Oaxaca methodology, we propose an alternative procedure that follows cohorts over time rather than individuals. This approach enables the estimation of both the explained and unexplained components—“endowment effect” and “remuneration effect”—of the wage gap, along with their respective standard errors, even in the absence of true panel data. We apply this methodology to the case of Colombia, finding a gender wage gap of approximately 15% in favor of male cohorts. This gap comprises a −5.6% explained component and a 20% unexplained component without controls. When we control by informality, size of the firm and sector the gap comprises a −3.5% explained component and a 18.7% unexplained component.

1. Introduction

Measuring wage gaps between groups over time ideally requires panel data. However, such data are often unavailable in most developing countries due to the high costs associated with tracking individuals over time. Instead, these countries typically rely on repeated cross-sectional household surveys that are representative at each point in time but do not follow the same individuals across periods. For example, Colombia conducts periodic household surveys with representative samples, but the individuals surveyed differ across survey waves.

Some researchers address this limitation by pooling cross-sectional data and including time dummies to estimate consistent parameters. However, this approach is inefficient in the presence of measurement error arising from unobserved heterogeneity that varies across time. Under these circumstances, estimators may become inconsistent, and a preferable alternative is the use of pseudo-panel data, as proposed by Deaton (1985) and further developed by Mora and Muro (2014).

Consider now the estimation of wage gaps between two groups—typically men and women—using pseudo-panel data. Measurement errors persist because gender wage gaps often reflect unobserved individual heterogeneity that varies across groups. Furthermore, these estimates may be inconsistent in the presence of selection bias.

In cross-sectional data, the Blinder–Oaxaca decomposition is commonly applied to estimate the wage gap, and adjustments for selection bias are often included. To enhance efficiency, Jann (2005) provides a method to estimate the variance–covariance matrix of the decomposition. In the context of panel data, Kröger and Hartmann (2021) present an approach that extends the Kitagawa–Oaxaca–Blinder decomposition method to analyze wage differentials over time. However, to date, no consistent and efficient methodology exists for estimating the gender wage gap and its twofold decomposition using pseudo-panel data. This is due to the fact that individuals in period t differ from those in period t − 1, and unobserved heterogeneity is not constant over time.

Wage gaps between men and women are a matter of global importance. Equal pay is one of the guiding principles of the International Labour Organization (ILO) and a key target of the United Nations Sustainable Development Goals. Moreover, Buchely (2013) argues that gender inequality in the labor market imposes inefficiencies on society, as the costs associated with women’s disadvantage are externalized through the social security system, particularly in health and pensions.

The literature on the gender wage gap is extensive. Among international studies, Paz (1998) estimates the wage gap in Greater Buenos Aires and the Northwest of Argentina using data from the Permanent Household Survey. The income disparity between women and men is 0.70 for the overall population and 0.60 among individuals with spouses. The Blinder–Oaxaca decomposition indicates that approximately 90% of the wage gap remains unexplained by differences in human capital. Di Paola and Berges (2000) analyze gender income differences in Mar del Plata, Argentina, employing the Blinder–Oaxaca decomposition and correcting for selection bias using the Heckman method. Their findings suggest that 78% of the wage gap is explained by human capital endowments, while the remaining 22% is attributable to discrimination.

Johansson et al. (2005) studied the gender wage gap in Sweden during the 1980s and 1990s using cross-sectional data from the Swedish Household Income Survey. Their results show a gap of approximately 13% in the 1980s and 15% in the 1990s, with the unexplained portion ranging between 5% and 9%. Watson (2010) analyzes the gender wage gap among full-time managers in Australia from 2001 to 2007, using data from the Household, Income and Labour Dynamics in Australia Survey. He finds that female managers earn about 27% less than their male counterparts, and that the unexplained portion of the gap—remuneration effect—ranges from 65% to 90%, depending on the decomposition method used.

Biltagy (2014) examines wage disparities in Egypt using data from the 2006 Egyptian Labour Market Panel Survey. The Blinder–Oaxaca decomposition reveals a gender wage gap of 25%, attributed entirely to discrimination against women. Blau and Kahn (2017) studied changes in the gender wage gap in the United States between 1980 and 2010 using microdata from the Panel Study of Income Dynamics. They found that the unexplained component of the wage gap—remuneration effect—declined from 49% in 1980 to 38% in 2010.

Several studies also focus on the Colombian labor market. Baquero (2001) applies the Oaxaca (1973) decomposition using data from the National Household Survey and finds a wage gap of approximately 34% in favor of men in 1999. Abadía (2005) examines statistical discrimination by gender using data from the Continuous Household Survey for the second quarter of 2003, distinguishing between public and private sector workers. While no discrimination is found in the public sector, evidence of discrimination exists in the private sector, particularly against married or cohabiting women. Bernat (2005) analyzes hourly wage differences in Colombia’s seven major cities from 2000 to 2003 and concludes, based on a Blinder–Oaxaca decomposition, that gender discrimination persists. Fernández (2006), using Quality of Life Survey data and quantile regressions for 1997–2003, shows that wage differences favoring men are concentrated in the upper percentiles of the wage distribution, while in lower percentiles, the differences tend to favor women.

This article contributes to two strands of the literature on the gender wage gap. First, it extends the Blinder (1973) and Oaxaca (1973) decomposition to pseudo-panel data, enabling analysis in contexts where traditional panel data are unavailable. Second, it adapts the correction proposed by Jann (2005) for estimating the variance–covariance matrix of the decomposition to the pseudo-panel framework. Finally, the proposed methodology is applied to the Colombian case, serving as an illustrative example for a developing country context.

The remainder of the article is organized as follows: Section 2 reviews the literature on the Blinder–Oaxaca decomposition. Section 3 presents the proposed pseudo-panel adaptation of the Blinder–Oaxaca decomposition and the corresponding variance–covariance matrix following Jann (2005). Section 4 applies this methodology to estimate the gender wage gap in Colombia. Section 5 concludes.

2. Blinder–Oaxaca Decomposition

The most widely employed technique for assessing the gender wage gap is the Blinder–Oaxaca decomposition (1973). This method disaggregates the observed wage differential into two main components. The first component reflects differences in the returns to observable productivity-related characteristics (e.g., education, experience), while the second component captures disparities due to unobservable factors, including discrimination.

Consider two groups: men and women. The first step in the decomposition involves estimating wage equations for each group g∈{m, w}, where individual wages are modeled as follows:

$$\begin{array}{r}Ln{W}_g=f\left(S_{g,},Ex{p}_g,Ex{p}_g^2\right)\\ g=men, women.\end{array}$$

(1)

In Equation (1), lnW denotes the natural logarithm of hourly wages, S represents years of schooling, Exp corresponds to potential labor market experience—calculated as age minus years of schooling minus six—and $Ex{p}^2$ is the square of potential experience. This specification follows the human capital framework proposed by Mincer (1974), who argued that the returns to education can be quantified through an income equation based on an individual’s educational attainment and work experience. The Mincer equation predicts a positive relationship between years of schooling and earnings. However, in the case of Colombia, this theoretical expectation does not fully materialize for women. Despite having, on average, higher levels of schooling than men, women continue to experience lower wages. This indicates that the returns to human capital differ significantly between men and women, suggesting the presence of structural inequalities in the labor market that may not be explained solely by differences in observable characteristics.

With respect to Equation (1), the difference in average wages between the two groups can be expressed as follows:

$$\left({\overline{w}}_m-{\overline{w}}_w\right)=\left({\overline{X}}_m-{\overline{X}}_w\right){\widehat{\beta }}_m+\left({\widehat{\beta }}_m+{\widehat{\beta }}_w\right){\overline{X}}_w$$

(2)

where ${\overline{w}}_g$ and ${\overline{X}}_g$ denote the mean of the logarithm of wages and the control characteristics for group g, respectively, and $\widehat{{\beta }_g}$ is the estimated parameter from Equation (1). The wage gap can thus be decomposed into two components: the explained component or “endowment effect”, which reflects differences in observable productive characteristics between the groups, and the unexplained component or “remuneration effect”, which captures the portion of the wage differential that cannot be attributed to such characteristics—often interpreted as a result of discrimination or other unobserved factors.

In recent decades, applications of the Blinder–Oaxaca decomposition often omitted statistical inference information, such as standard errors and confidence intervals. However, interpreting decomposition results without reference to the precision of the estimates significantly limits their reliability and analytical value.

Oaxaca and Ransom (1998) and Greene (2003) proposed methods to approximate these standard errors, assuming fixed regressors. This assumption neglects a critical source of statistical uncertainty, which may lead to biased inference in most empirical applications (Jann, 2005). In particular, treating the regressors as non-stochastic tends to substantially underestimate the standard errors associated with the explained component–endowment effect of the wage gap.

In response to these limitations, Jann (2005) developed unbiased variance estimators for the components of the Blinder–Oaxaca decomposition. Suppose that

$$\tilde{Y}={\tilde{X}}^{\prime }\widehat{\beta }$$

(3)

where $\tilde{X}$ is a vector of sample means and $\widehat{\beta }$ is a vector of regression coefficients. The sample variance $V\left({\tilde{X}}^{\prime }\widehat{\beta }\right)$ can be estimated as follows:

(a)

If the covariates are fixed, then $\tilde{X}$ has no sampling variance. If the regressors are fixed, then $\tilde{X}$ is constant. Therefore, $V\left({\tilde{X}}^{\prime }\widehat{\beta }\right)={\tilde{X}}^{\prime }V\left(\widehat{\beta }\right)\tilde{X}$.

(b)

However, in most applications, the regressors and $\tilde{X}$ are stochastic. Since $\tilde{X}$ and $\widehat{\beta }$ are not correlated (as long as this is true, then $Cov\left(ϵ, X\right)=0$), the sampling variance is as follows (Jann, 2008):

$$\widehat{V}\left({\tilde{X}}^{\prime }\widehat{\beta }\right)={\tilde{X}}^{\prime }\widehat{V}\left(\widehat{\beta }\right)\tilde{X}+{\tilde{\beta }}^{\prime }\widehat{V}\left(\tilde{X}\right)\widehat{\beta }+trace\left\{\widehat{V}\left(\tilde{X}\right)\widehat{V}\left(\widehat{\beta }\right)\right\}$$

(4)

where $trace\left\{\widehat{V}\left(\tilde{X}\right)\widehat{V}\left(\widehat{\beta }\right)\right\}$ disappears asymptotically and $\widehat{V}\left(\widehat{\beta }\right)$ is the variance–covariance matrix obtained from the regression process.

3. Pseudo-Panel Approach to the Blinder–Oaxaca Decomposition

In the absence of longitudinal panel data that track the same individuals over time, it is necessary to employ pseudo-panel data methods. Pseudo-panels consist of observations drawn from different individuals across various time periods—that is, the individuals observed at time t differ from those observed at time t − 1. Utilizing the pseudo-panel approach enables the consistent and efficient application of the Blinder–Oaxaca decomposition when only cohort-level tracking is feasible.

Deaton (1985) introduced the concept of pseudo-panels as a method for exploiting repeated cross-sectional surveys. This approach entails grouping individuals into synthetic cohorts based on time-invariant and exogenous characteristics, such as age and gender.

As previously noted, the foundational idea of pseudo-panels is to construct cohorts composed of individuals who exhibit similar behavioral patterns (Guillerm, 2017). For instance, in the case of Colombia, where the age of legal adulthood is 18, it is appropriate to form nine five-year cohorts spanning the working-age population, specifically individuals aged 18 to 63. These cohorts approximate different stages of the employment life cycle.

Estimating returns to human capital using pooled cross-sectional regressions introduces an errors-in-variables problem, primarily due to time-varying unobserved individual heterogeneity. Additionally, such estimations are subject to inconsistency in the presence of selection bias.

To address these concerns, consider the following pseudo-panel specification for estimating returns to human capital (Mincer, 1974; Mora & Muro, 2014):

$$Y_{i\left(t\right)}={\beta }_1{X}_{i\left(t\right)}+\rho {\lambda }_{i\left(t\right)}+f_i+{ϵ}_{i\left(t\right)}$$

(5)

where $Y_{i\left(t\right)}$ denotes income, $X_{i\left(t\right)}$ represents the set of explanatory variables consistent with human capital theory—namely, education and potential experience—${\lambda }_{i\left(t\right)}$ accounts for potential selection bias, and $f_i$ captures individual-specific unobserved heterogeneity. The subscripts $i\left(t\right)$ indicate that the data originate from independent, representative cross-sectional surveys in which individuals are observed only once in a single time period.

In this context, Deaton (1985) demonstrates that when individuals differ across time periods, estimations based on Equation (5) yield inconsistent results. To overcome this limitation, Deaton proposes a pseudo-panel estimation strategy that involves constructing cohorts based on invariant characteristics.

Building on this approach, Mora and Muro (2014) develop a methodology for addressing pseudo-panel data in the presence of selection bias. Specifically, they propose using the generalized method of moments (GMM) to account for the measurement error problem inherent in pseudo-panel data. This methodology, hereafter referred to as GMMC (GMM with correction for measurement error), leads to the following equation:

$$E\left[\left(Y_{it}-X_{it}^{\prime }{\beta }_1-Z_{0i}^{\prime }\delta -\rho {\lambda }_{ct}\right)h\left(Z_{0i},Z_{1it}\right)\right]=B\beta +b$$

(6)

where $Z_0$ denotes a matrix of fictitious cohort indicators; $Z_{1it}$ are instrumental variables that vary over time (they do not contain $Z_0$); $h\left(·\right)$ is a known function—typically comprising time effects and cohort-by-time interaction terms—although other time-varying variables may also be incorporated; $\beta ={\left({\beta }_1^{\prime }{\delta }^{\prime }\rho \right)}^{\prime }$; and $B$, $b$ depends on the covariance matrix of measurement errors.

Regarding the selection mechanism, a panel probit model is employed to characterize the selection process, specified as follows:

$$E\left[\left(s_{it}-Z_{1it}^{\prime }{\gamma }_t\right)A_t\right]=0$$

(7)

where $s_{it}$ is the selection process, and $A$ is a cohort mean operator, ${\left(Z_0^{\prime }{Z}_0\right)}^{-1}{Z}_0^{\prime }$.

Definition 1.

The cohort-level expression for the moment conditions specified in Equations (6) and (7) can be formulated as follows:

$$E\left[s_{ct}-Z_{1ct}^{\prime }{\gamma }_t\right]=0; t=1,\dots ,T, c=1,\dots C,$$

(8)

$$E\left[\left(\Delta Y_{ct}-\Delta X_{ct}^{\prime }{\beta }_1-\rho \Delta {\lambda }_{ct}\right)\Delta W_{ct}\right]=B\beta +b.$$

(9)

Here, $\Delta W_{ct}={\left(\Delta X_{ct}^{\prime },\Delta {\lambda }_{ct}\right)}^{\prime }$. Equation (8) is a system of $T$ cross-sectional linear regressions. First, differences from the synthetic panel (Deaton, 1985) are used in Equation (9). By substituting $\widehat{{\gamma }_{ct}}$ into Equation (9), we obtain the following:

$$E\left[\left(\Delta Y_{ct}- \Delta X_{ct}^{\prime }{\beta }_1-\rho \Delta \widehat{{\lambda }_{ct}}\right)\Delta X_{ct}\right]=B\beta +b.$$

(10)

Finally, the GMMC estimator is as follows:

$$\widehat{\beta }={\left[{\displaystyle \sum }_{c=1}^C\left(\Delta W_c^{\prime }\Delta W_c+B^{\prime }\right)D_c{\displaystyle \sum }_{c=1}^C\left(\Delta W_c^{\prime }\Delta W_c+B\right)\right]}^{-1}\left[{\displaystyle \sum }_{c=1}^C\left(\Delta W_c^{\prime }\Delta W_c+B^{\prime }\right)D_c{\displaystyle \sum }_{c=1}^C\left(\Delta W_c^{\prime }\Delta Y_c-b\right)\right]$$

(11)

where $\Delta W_c={\left(\Delta W_{c2},\Delta W_{c3},\dots ,\Delta W_{CT}\right)}^{\prime }$ and $\Delta Y_c={\left(\Delta Y_{c2},\Delta Y_{c3},\dots ,\Delta Y_{CT}\right)}^{\prime }$. The optimal choice of $D_c$ is any consistent estimator of the inverse of the covariance matrix of $\Delta W_c^{\prime }\Delta W_c$ (Hansen, 1982).

The asymptotic distribution of the GMMC estimator, for $B$, $b$, and $\Delta W_c$ known, can be derived using standard assumptions and GMM theory (Mora & Muro, 2014). Following Deaton (1985), Newey and McFadden (1994), and Mora and Muro (2014), the following is a convenient expression for an upper limit of the covariance matrix $V_{\beta }^{MM}$:

$$V_{\beta }^{MM}={\left[M_{WW}-\Sigma \right]}^{-1}\left[{\Sigma }_{WW}\left({\sigma }_{\mu }^2+{\sigma }_{00}+{\theta }^{\prime }\Sigma \theta -2{\sigma }^{\prime }\theta \right)+\left(\sigma -\Sigma \theta \right){\left(\sigma -\Sigma \theta \right)}^{\prime }\right]{\left[M_{WW}-\Sigma \right]}^{-1}+{\Pi }^{\prime }\widehat{V}\Pi .$$

(12)

In Equation (12), the first additive term corresponds to the covariance matrix associated with the pseudo-panel data model (Deaton, 1985). The second term is the correction matrix designed to adjust for selectivity bias, which is essential for obtaining consistent estimators in the pseudo-panel framework. This correction term reflects an estimated regressor—rather than the true regressor—in the second stage of the two-step generalized method of moments with measurement error correction (GMMC) estimation procedure (Mora & Muro, 2014). Moreover, the covariance matrix of the parameter estimates is further adjusted for bias using the approach proposed by Newey and McFadden (1994). A comprehensive demonstration of this methodology is provided in Mora and Muro (2014).

For instance, to estimate the returns to education within each group, extending the Mincer (1974) earnings equation to the pseudo-panel context can be expressed as follows:

$$\begin{gathered} Ln{W}_{g,ct}={\alpha }_{ct}+{\beta }_1{S}_{g,ct}+{\beta }_{2}Ex{p}_{g,ct}+{\beta }_{3}Ex{p}_{g,ct}^2+\lambda Se{l}_{g,ct}+{\mu }_{g,ct} \\ c=1,\dots ,C t=1,\dots ,T g=men, women \end{gathered}$$

(13)

$$Se{l}_{g,ct}=f(Marrie{d}_{g,ct}, Head\_Househol{d}_{g,ct}, Ch{6}_{g,ct},N\_in{d}_{g,ct}).$$

(14)

In this context, $ln{W}_{ct}$ denotes the natural logarithm of hourly wages for cohort c in year t. The variable S represents years of schooling, while Exp denotes potential labor market experience, calculated as age minus years of schooling minus six. $Ex{p}^2$ is the square of potential experience, capturing the nonlinear (diminishing) returns to experience. The term α accounts for unobserved heterogeneity across cohorts, and μ is the error term. The inverse Mills ratio λ is included in the wage equation to correct for selection bias, as wages are only observed for employed individuals. Excluding individuals who are not currently working (e.g., unemployed) but invested in human capital introduces selection bias in the estimation of returns to education.

The parameter ${\beta }_1$ captures the return to an additional year of education, while ${\beta }_2$ and ${\beta }_3$ represent the returns to an additional year of experience and its diminishing effect, respectively. Equations (13) and (14) are estimated using the GMMC approach that corrects for selection bias, as specified in Equation (11).

Regarding the selection equation, $Se{l}_{i,ct}$ is a binary indicator for labor force participation, equal to one if the individual is either employed or unemployed (i.e., actively participating in the labor market), and zero otherwise. The covariates used in the selection equation include the following: Married, a binary variable equal to one if the individual is married; Head_household, a dichotomous variable equal to one if the individual is the head of their household; Ch6, a continuous variable measuring the number of children under the age of six in the household; and N_ind, which denotes the total number of individuals residing in the household.

According to the ILO (2020b), marital status has a differential impact by gender on labor market outcomes, particularly in labor force participation, job types, and underemployment. Being the head of household entails greater financial responsibilities and thus influences the decision to participate in the labor market (Budlender, 2003). Similarly, the presence of young children1 and the overall household size are relevant determinants of labor market participation, as highlighted by Tobón and Rodríguez (2015), Cools et al. (2017), ILO (2020a), and Baranowska-Rataj and Matysiak (2022).

Definition 2.

The counterpart of the Blinder–Oaxaca (1973) decomposition in the pseudo-panel data framework for two groups is defined as follows:

$$\begin{gathered} Ln{W}_{m,ct}-Ln{W}_{w,ct}=\underset{A}{\underbrace{\left(X_{m,ct}-X_{w,ct}\right){\widehat{\beta }}_{m,ct}}}+\underset{B}{\underbrace{X_{w,ct}\left({\widehat{\beta }}_{m,ct}-{\widehat{\beta }}_{w,ct}\right)}}+\underset{C}{\underbrace{\left({ϵ}_{m,ct}-{ϵ}_{w,ct}\right)}} \\ m:men; w:women. \end{gathered}$$

(15)

In Equation (15), the first term (A) represents the explained component–endowment effect, which captures the portion of the wage differential attributable to observable differences in productive characteristics between the two groups. The second term (B) corresponds to the unexplained component–remuneration effect, which reflects differences in the returns to these characteristics and is often associated with discrimination or unobserved heterogeneity. The final term (C) tends to converge to zero, as the evaluation of Equation (15) at the mean of the logarithm of the hourly wage distribution implies that the linear combination of the error terms has an expected value of zero.

For instance, the explained component—based on education, experience, and squared experience as proxies for human capital accumulation—can be expressed as follows:

$${\tilde{\beta }}_{m,ct}^S\left({\overline{S}}_{m,ct}-{\overline{S}}_{w,ct}\right)+{\tilde{\beta }}_{m,ct}^{Exp}\left({\overline{Exp}}_{m,ct}-{\overline{Exp}}_{w,ct}\right)+{\tilde{\beta }}_{m,ct}^{Ex{p}^2}\left({\overline{Ex{p}^2}}_{m,ct}-{\overline{Ex{p}^2}}_{w,ct}\right)$$

(16)

Similarly, the unexplained component is expressed as:

$${\alpha }_{ct}^m-{\alpha }_{ct}^w+\left({\tilde{\beta }}_{m,ct}^S-{\tilde{\beta }}_{w,ct}^S\right){\overline{S}}_{w,ct}+\left({\tilde{\beta }}_{m,ct}^{Exp}-{\tilde{\beta }}_{w,ct}^{Exp}\right){\overline{Exp}}_{w,ct}+\left({\tilde{\beta }}_{m,ct}^{Ex{p}^2}-{\tilde{\beta }}_{w,ct}^{Ex{p}^2}\right){\overline{Ex{p}^2}}_{w,ct}.$$

(17)

Definition 3.

The variance–covariance matrix counterpart for the pseudo-panel data model, following Jann (2008), for two groups is specified as follows:

For the explained component–endowment effect, the variance–covariance matrix is given by the following:

$$\begin{gathered} {{\widehat{V}}^{MM}}_{explain}\left\{{\left({\tilde{X}}_{m,ct}-{\tilde{X}}_{w,ct}\right)}^{\prime }{\widehat{\beta }}_{m,ct}\right\}\approx \\ {\left({\tilde{X}}_{m,ct}-{\tilde{X}}_{w,ct}\right)}^{\prime }\widehat{V}\left({\widehat{\beta }}_{m,ct}\right)\left({\tilde{X}}_{m,ct}-{\tilde{X}}_{w,ct}\right)+{\widehat{\beta }}_{m,ct}^{\prime }\left\{\widehat{V}\left({\tilde{X}}_{m,ct}\right)+\widehat{V}\left({\tilde{X}}_{w,ct}\right)\right\}{\widehat{\beta }}_{m,ct}. \end{gathered}$$

(18)

For the unexplained component–remuneration effect, the variance–covariance matrix is given by the following:

$$\begin{gathered} {{\widehat{V}}^{MM}}_{unexplain}\left\{{\tilde{X}}_{w,ct}^{\prime }\left({\widehat{\beta }}_{m,ct}-{\widehat{\beta }}_{w,ct}\right)\right\}\approx \\ {\tilde{X}}_{w,ct}^{\prime }\left\{\widehat{V}\left({\widehat{\beta }}_{m,ct}\right)+\widehat{V}\left({\widehat{\beta }}_{w,ct}\right)\right\}{\tilde{X}}_{w,ct}+{\left({\widehat{\beta }}_{m,ct}-{\widehat{\beta }}_{w,ct}\right)}^{\prime }\widehat{V}\left({\tilde{X}}_{w,ct}\right)\left({\widehat{\beta }}_{m,ct}-{\widehat{\beta }}_{w,ct}\right). \end{gathered}$$

(19)

The  $trace\left\{ \widehat{V}\left({\tilde{X}}_{m,ct}\right) \widehat{V}\left({\widehat{\beta }}_{m,ct}\right) \right\}$ disappears when we use cohort’s as instruments and NT/C → ∞.

4. Blinder–Oaxaca Wage Gap Decomposition: The Case of Colombia

The Colombian labor market continues to exhibit significant gender disparities. For instance, according to the World Economic Forum’s (2021) Global Gender Gap Report, substantial wage differences persist between women and men in Colombia. Among 156 countries, Colombia ranks 120th on the equal pay index for comparable work, with a score of 0.56 (where 1 indicates full parity). Despite increased female labor force participation and longer average years of schooling among women, their earnings remain significantly lower than those of men. Data from the National Administrative Department of Statistics (DANE—its Spanish acronym) reveal that women’s labor force participation rate rose from approximately 46% in 1991 to 54% in 2019, while men’s participation rate remained steady at around 75%. Additionally, Piñeros (2009) notes that the educational attainment gap between men and women began to narrow in the 1970s, with women surpassing men in average years of schooling during the 1980s.

Peña et al. (2013) emphasize that the predominant emerging family structure in Colombia is the female-headed single-parent household, where gender inequalities negatively affect family income and human capital accumulation, thereby limiting social mobility for members of such families.

The gender wage gap in Colombia has been examined at various points in time using cross-sectional data (e.g., Bernat, 2005; Fernández, 2006; and Badel & Peña, 2010). For example, Fernández (2006) reports that the average wage differential was 19% in 1997 and decreased to 13% in 2003. However, a comprehensive understanding of the underlying causes for the persistence of this gap over time remains insufficient.

Badel and Peña (2010) examine the gender wage gap in Colombia’s seven largest cities using quantile regression techniques. Their findings indicate that men earn more than women, and the wage gap exhibits a U-shaped pattern, with women’s wages falling further below men’s at the extremes of the wage distribution compared to the middle. Similarly, Galvis (2011) investigates regional and gender wage differentials in Colombia employing quantile regressions. The results reveal consistent positive wage differentials favoring men. Furthermore, a Blinder–Oaxaca decomposition suggests that these wage gaps are not fully explained by observable individual characteristics; rather, they primarily arise from differences in the returns to these characteristics (e.g., education) and unobserved factors.

Mora and Arcila (2014) analyze the wage gap between Afro-descendant and White individuals in Cali, utilizing data from the 2013 Employment and Quality of Life Survey. When incorporating variables, such as migration status and perceived discrimination, into the selection equation for Afro-descendants, they estimate a wage gap of 42%, of which 9% is attributable to differences in human capital characteristics, while 33% is linked to labor market discrimination.

To the best of our knowledge, although prior studies documented the existence of the gender wage gap in Colombia (e.g., Baquero, 2001; Fernández, 2006; and Badel & Peña, 2010), the present study is the first to analyze the evolution of this gap over time. Specifically, it employs a pseudo-panel dataset combined with decomposition methods and selectivity correction techniques.

To estimate the gender wage gap over time, we constructed a pseudo-panel comprising a time series of independent and representative cross-sectional samples spanning from 2016 to 2021. This pseudo-panel is based on data from the Large Integrated Household Survey (GEIH—its Spanish acronym), a multipurpose survey conducted by Colombia’s official statistics agency, DANE. The GEIH regularly monitors the labor market and provides monthly labor statistics at the national, departmental, and major city levels.

Since the observations consist of independent cross-sectional data for each period, nine 5-year cohorts of individuals aged 18 to 63 have been defined. The sample comprises a total of 840,499 individuals.

Table 1. Number of individuals by cohort.

Cohort, Ci(t)	2016	2017	2018	2019	2020	2021	Total
18–22 years old	18,986	18,402	17,679	17,974	9138	14,750	96,929
23–27 years old	22,024	21,729	21,909	22,677	11,746	18,789	118,874
28–32 years old	20,119	20,198	20,255	21,709	11,638	18,627	112,546
33–37 years old	19,545	19,358	19,324	20,011	10,667	17,193	106,098
38–42 years old	16,405	16,449	16,954	18,636	9953	16,588	94,985
43–47 years old	16,028	15,396	14,931	16,039	8342	13,827	84,563
48–52 years old	15,814	15,448	15,432	15,601	8206	13,465	83,966
53–58 years old	15,888	16,018	16,312	17,093	9198	14,771	89,280
59–63 years old	8904	9353	9662	10,283	5600	9456	53,258
Total	153,713	152,351	152,458	160,023	84,488	137,466	840,499

Source: author’s own calculations.

displays the distribution of the sample by cohort and year. Each cohort includes more than 5500 individuals. The cohort representing the youngest age group has an average of 16,155 individuals per year, whereas the oldest cohort has an average of 8876 individuals per year.

Regarding the number of individuals per cohort, Mora and Muro (2014) assert that including at least 200 individuals per cohort is sufficient to test if there are selection bias in pseudopanel at 5% of level (p. 15). Descriptive statistics of the variables are provided in Appendix A.

Gender wage gaps in Colombia have been notable for their persistence over time. Despite increases in women’s average years of schooling and labor market participation in recent decades, empirical evidence consistently shows that men continue to receive higher remuneration than women.

Table 2. Decomposition results without selection bias correction.

Without Selection Bias
	Pool	Panel Cohort a	Pseudo Panel (Deaton)
Differential	0.12987 ***	0.14467 ***	0.20106 ***
	(0.00181)	(0.02554)	(0.0000779809)
Explained—endowment effect	−0.08622 ***	−0.05064 **	−0.02020 ***
	(0.00100)	(0.02434)	(0.0000000016)
Unexplained—remuneration effect	0.21609 ***	0.19531 ***	0.22126 ***
	(0.00152)	(0.00887)	(0.0000779794)
NT, cohorts	771,194	108	108

Note: *** Statistically significant at the 0.01 level; and ** statistically significant at the 0.05 level. Standard errors appear in parentheses. ^a Since two groups of nine cohorts each are observed over six time periods, the total number of cohort-period observations used in the decomposition amounts to 108.

presents the results of the Blinder–Oaxaca wage gap decomposition without accounting for selection bias.2 The models considered include a pooled cross-section, a pooled cohort, and a pseudo-panel with Deaton’s correction. It is important to note that without applying Deaton’s correction, the model essentially becomes an error-in-variables model, wherein all explanatory variables (except dummy variables) are subject to measurement error (Deaton, 1985).3

When calculating the wage gap in the Colombian urban labor market, it is found that women earn, on average, 13% less than men in the pooled configuration. The endowment component is approximately −8.6%, indicating that the difference in observable characteristics favors women. In this regard, women possess superior attributes that enhance productivity (e.g., human capital and work experience) compared to men. This finding corroborates previous studies that documented women’s higher average years of schooling relative to men (Abadía, 2005; Galvis, 2011).

Regarding the unexplained component, the estimated effect is 21.6%. This suggests that if men and women had equivalent endowments, a substantial wage gap would still persist, indicating that gender differences in wages cannot be fully accounted for by productivity-related attributes or other supply-side factors.

In the pseudo-panel configurations, the wage differential is 14.5% without correction for measurement error and increases to 20.1% when such correction is applied. This implies that male cohorts earn, on average, 20% more than female cohorts in the Colombian urban labor market. The endowment effect in this setting is −2%, while the remuneration effect accounts for 22%, indicating that the unexplained component exceeds the total observed wage differential between men and women cohorts.

It is important to note that these regression results are subject to bias, as they do not adjust for selection bias, given that not all individuals participating in the labor market receive wages (Heckman, 1979).

Table 3. Decomposition results with selection bias correction.

With Selection Bias
	Pool	Pseudo Panel (MH)
Differential	0.21186 ***	0.14617 ***
	(0.00203)	(0.00005)
Explained—endowment effect	−0.08622 ***	−0.05636 ***
	(0.00100)	(0.000000025)
Unexplained—remuneration effect	0.29809 ***	0.20254 ***
	(0.00179)	(0.00005)
NT, cohorts	840,499	108

Note: *** Statistically significant at the 0.01 level. Standard errors appear in parentheses.

presents the results of the wage gap estimation with correction for selection bias (Equations (11)–(19), MH):

When adjusting for selection bias, the results from the pooled configuration become more pronounced, with the total wage differential increasing to 21%. Notably, while the endowment effect remains negative, indicating that women possess, on average, more productive characteristics, the remuneration effect rises to approximately 30%. In the pseudo-panel framework, the estimated wage gap stands at 14.6% in favor of male cohorts, with the explained component at −5.6% and the unexplained component at 20%.

Including additional controls in the human capital equation is crucial for capturing sources of heterogeneity beyond education and experience—such as labor market informality, firm size, and sector of economic activity. These factors may exert independent effects on wages, and their omission can lead to biased estimates of the returns to education.

In this context, one of the defining features of the Colombian labor market is its high level of informality (Mora & Muro, 2017; Arango & Flórez, 2020), with more than half of the workforce employed in the informal sector (Mora, 2017; Sánchez, 2020) and segmentation in the Colombian labor market (Mora & Muro, 2015). Informality is linked to several structural variables, including employment status (e.g., self-employed or independent workers), firm size, and the absence of formal employment contracts or access to public welfare systems such as health care and pensions (Mora & Muro, 2017).

Moreover, reports from the Economic Studies Office of the Colombian Ministry of Commerce, Industry, and Tourism indicate that microenterprises constitute the vast majority of the country’s business structure, accounting for over 90% of all firms (Ministerio de Comercio, Industria y Turismo, 2024). According to Law 905 of 2004, microenterprises are defined as those employing no more than ten workers or possessing total assets, excluding real estate used for housing, valued below 500 monthly minimum legal wages (Congreso de la República de Colombia, 2004).

Additionally, the tertiary sector exhibits the highest rate of female labor force participation in Colombia (DANE, 2020; Confecámaras, 2024). Since the final quarter of the 20th century, there has been a sustained incorporation of women into the service sector (Maubrigades, 2020). This overrepresentation is often attributed to the prevalence of occupations traditionally regarded as ‘feminine,’ such as those in education, healthcare, and administrative support (ILO, 2018).

Accordingly,

Table 4. Decomposition results with controls.

	Without Controls	Informality	Informality, Firm Size, and the Tertiary Sector
Differential	0.14617 ***	0.15100 ***	0.15186 ***
	(0.00005)	(0.0000400258)	(0.0000394999)
Explained—endowment effect	−0.05636 ***	−0.03976 ***	−0.03541 ***
	(0.000000025)	(0.0000000607)	(0.0000000420)
Unexplained—remuneration effect	0.20254 ***	0.19076 ***	0.18727 ***
	(0.00005)	(0.0000399651)	(0.0000394579)
Cohorts	108	108	108

Note: *** Statistically significant at the 0.01 level. Standard errors appear in parentheses.

presents the results of the wage gap estimation under three model specifications: without controls; controlling for informality; and controlling for informality, firm size, and employment in the tertiary sector.

A wage differential of approximately 15% in favor of men is observed across all model specifications, with the endowment effect remaining negative and the remuneration effect ranging between 18% and 20%.

Within this context, the explained component captures gender differentials associated with variations in returns to individuals’ observable characteristics. The residual unexplained component is often interpreted as a proxy for labor market discrimination. However, it is important to emphasize that these estimates are indicative rather than definitive, since the unexplained portion may also encompass differences in unobservable attributes not captured by the model. That is, they could be affected by the impact of unobserved factors of productivity (e.g., motivation, risk aversion, and negotiation), job conditions (e.g., part-time, inflexibility), or employer-level factors (e.g., monopsony power, network benefits). In addition, discrimination itself is an immensely complex, multidimensional component that encompasses taste-based discrimination (based on employer bigotry), statistical discrimination (based on group-based assumptions), and structural discrimination (institutionalized or societal norms that hinder access/mobility).

Thus, after estimating the corresponding wag GAPs, we evaluate the statistical significance of the difference in the GAP between the models with controls and the baseline model, as well as between the two models with controls.

The difference between coefficients is assessed using the following expression (Clogg et al., 1995; Mora et al., 2022):

$$z={\displaystyle \frac{{\widehat{GAP}}_k^i-{\widehat{GAP}}_k^j}{\sqrt{{(S_{{\widehat{GAP}}_k^i})}^2+{(S_{{\widehat{GAP}}_k^j})}^2}}}$$

(20)

where i and j refer to different models, k is differential, explained, or unexplained, ${\widehat{GAP}}_k^i$ is the estimated value of the GAP in Table 4, and $S_{{\widehat{GAP}}_k^i}$ denotes the standard error of the $\widehat{GA{P}_k}$ for model i or j and GAP k. The null hypothesis states that ${\widehat{GAP}}_k^i={\widehat{GAP}}_k^j$.

Table 5. Test for the equality of regression coefficients across models.

	Informality vs. No Controls	Informality, Firm Size, and the Tertiary Sector vs. No Controls	Informality, Firm Size, and the Tertiary Sector vs. Informality
Differential	75.41 ***	89.30 ***	15.29 **
Explained—endowment effect	252,868.74 ***	428,623.47 ***	58,932.00 ***
Unexplained—remuneration effect	−184.04 ***	−239.74 ***	−62.14 **

Note: *** Statistically significant at the 0.01 level; and ** statistically significant at the 0.05 level.

reports these results.

Based on this hypothesis test, the null hypothesis that the coefficients related to the wage differential are equal between the models with controls, and the baseline model is rejected. Furthermore, the coefficients associated with the endowment effect and the remuneration effect are statistically different between the models with controls and the baseline model. Similarly, the null hypothesis that the respective coefficients are equal between the model that includes controls for informality, firm size, and tertiary sector and the model that controls only for informality is also rejected.

In this context, when informality is included as a control variable, the unexplained component decreases by approximately 1.2 percentage points compared to the baseline model without controls. Furthermore, when informality, firm size, and the tertiary sector are jointly included, the unexplained component is reduced by 1.5 percentage points.

Finally, when selection bias is present, our methodology reveals that pooling the data leads to an overestimation of both the explained and unexplained components. This overestimation arises from the failure to account for measurement errors introduced by data aggregation, as well as from neglecting changes in unobserved individual heterogeneity.

5. Conclusions

The Blinder–Oaxaca methodology is a widely recognized approach for estimating gender wage differentials between two groups. Jann (2005, 2008) enhances this methodology by providing a correction for the variance–covariance matrix, which ensures efficiency in cross-sectional estimations. While Kröger and Hartmann (2021) discuss the decomposition effects in panel data, such extensions are not directly applicable to pseudo-panel data. This limitation arises because the individuals observed in period t are not the same as those observed in period t − 1, and unobserved individual heterogeneity may vary across time.

Many developing countries, such as Colombia, lack true panel data structures, but possess independent repeated cross-sectional data. In this context, the pseudo-panel approach provides a practical alternative for analyzing labor market outcomes over time, particularly in the absence of longitudinal tracking of individuals.

As in many other countries, gender wage disparities persist in Colombia. Our empirical findings, based on a pseudo-panel configuration with corrections for both measurement error and selection bias, consistently show wage differentials favoring men in the Colombian urban labor market. The results indicate that female cohorts earn, on average, 15% less than their male counterparts. Importantly, this wage gap is not primarily attributable to differences in observable attributes such as education or experience. Instead, the bulk of the gap is explained by differential returns to these attributes and potentially by unobservable factors, suggesting that productivity-related characteristics or other supply-side determinants cannot fully explain gender differences in earnings. It may instead reflect underlying structural or institutional dynamics within the labor market.

The Colombian labor economics literature repeatedly documented that women increased their labor force participation and now exhibit, on average, higher educational attainment than men. Nevertheless, the gender gap in the returns to human capital remains significant, suggesting that women are not equally rewarded for their skills and qualifications in the labor market.

The review of previous studies and empirical evidence supports the conclusion that wage differentials between men and women persist in Colombia and that human capital endowments explain only a limited portion of this gap.

To address the gender wage gap, a range of policy interventions and institutional efforts can be implemented. These include promoting equal access to education and vocational training to ensure women acquire skills aligned with labor market demands. Scholarship programs and mentorship initiatives can also encourage women’s participation in male-dominated fields of study. Furthermore, workplace-level reforms are critical. These include the enforcement of anti-discrimination policies in hiring and compensation, as well as measures to support a work–life balance, such as flexible work arrangements and remote work options. Such policies can facilitate women’s sustained engagement in the labor market and contribute to reducing the persistent gender pay gap.