To introduce the theoretical foundations linking productivity to wages, several complementary frameworks explain how compensation levels relate to worker and firm performance. Human capital theory argues that individual productivity, and consequently wages, derives from investments in education, training, and work experience (Schultz, 1961; Mincer, 1974). These investments increase skills and capabilities, producing enduring benefits not only for workers but also for firms through higher efficiency and improved task performance.

Efficiency wage theory, as formulated by Shapiro and Stiglitz (1984) and expanded by Akerlof and Yellen (1986), emphasizes the strategic role of compensation. Firms may deliberately set wages above the market-clearing level to discourage shirking, reduce turnover, and stimulate motivation, thus highlighting the endogenous relationship between remuneration and output. Together, these theories provide a basis for understanding why wages may reflect both the productive potential of workers and managerial choices aimed at improving firm performance. Importantly, this theoretical link also implies a bidirectional relationship: higher wages may themselves increase productivity through motivational channels, a possibility we address explicitly in our empirical strategy (see Empirical Model section).

Building on this foundation, insights from firm heterogeneity and industrial organization literature broaden the discussion by situating productivity within a wider set of market and managerial factors. Syverson (2011) notes that differences in technology adoption, market structure, managerial quality, and access to inputs generate significant productivity gaps among firms operating in similar environments. These findings suggest that productivity does not stem solely from individual characteristics but also from firm-level strategies and competitive pressures that shape the efficiency of resource allocation. As a result, wage determination is influenced not only by the capabilities of workers but also by the organizational and structural conditions under which firms operate.

Incorporating gender economics and labor market segmentation further enriches these models by revealing how institutional and structural biases shape productivity outcomes. Occupational segregation, unequal access to training, and limited promotion prospects systematically distort productivity measures when labor is treated as a homogeneous input (Blau & Kahn, 2000; Seguino, 2000; England and Folbre, 2002; Kabeer, 2016). A growing body of feminist economics shows that women are frequently concentrated in lower-paid sectors or occupations, creating a persistent gap between their actual contribution to output and their remuneration (Becker, 1971; Goldin, 2014). Moreover, recent evidence suggests that even when female-intensive firms achieve high productivity, the transmission of that productivity into wages tends to be weaker, pointing to the influence of structural factors (Rivera-Lozada et al., 2024).

The empirical evidence on gender and productivity presents mixed findings. Tsou and Yang (2019) show that Chinese firms with higher proportions of female workers often display lower productivity than male-intensive firms. Nonetheless, when women possess higher educational attainment, they significantly enhance firm productivity, particularly in small private and foreign enterprises. Pfeifer and Wagner (2014) similarly report contrasting outcomes across estimation methods: under OLS, female -intensive firms appear less productive, yet a GMM framework reverses these findings. Such inconsistencies underscore the importance of methodology and the operational definition of ‘female-intensive’ firms.

Most existing studies focus on the gender of CEOs or owners, whereas our work, constrained by the structure of the EAM survey, classifies firms as female-intensive or male-intensive according to the proportion of women or men in their workforce. Following Tsou and Yang (2019) and Pfeifer and Wagner (2014), we adopt the term female-intensive firms to describe establishments where women represent 50% or more of the total workforce, and male-intensive firms for those where men predominate. This classification reflects labor force composition, not ownership or management structure, a distinction that, as we argue, captures broader organizational practices and sectoral norms that may be invisible in leadership-based classifications.

These dynamics are particularly relevant in emerging economies such as Colombia, where industries including garments, textiles, and pharmaceuticals employ a large share of women (Ñopo and Gallardo, 2009). Recent Colombian data reinforce this paradox: women-led firms identified in the Unified Business and Social Registry (RUES) represent 59% of the 1.2 million registered enterprises, and according to the Emicron Survey (2022) and WCP (2024), these firms show slightly higher productivity (34.3% compared with 33.25% for male-led firms) and greater efficiency improvements (25.8% versus 17.9%). Nevertheless, wage differentials continue to exceed productivity gaps, suggesting that structural factors, rather than productivity differences alone, account for the persistent disparity.

Lastly, merging these perspectives reveals that the decoupling between wages and productivity, well documented in advanced economies since the 1970s and linked to globalization, declining bargaining power, and labor market segmentation (Feldstein, 2008; Meager & Speckesser, 2011), acquires a distinctive gendered dimension in emerging economies. In Colombia, this divergence appears amplified for female-intensive firms, suggesting that gender-based wage disparities are embedded in the very mechanisms connecting productivity and remuneration. Understanding these linkages is therefore essential for designing policies that promote fair compensation, enhance firm efficiency, and reduce structural gender inequality.

TFP disaggregated by gender follows the two-equation system proposed by Wooldridge (2009). This framework facilitates GMM estimation, improving the efficiency of standard error estimation and eliminating the need for bootstrapping. Specifically, we assume the production process follows a linearized Cobb-Douglas production function:

where yit denotes firm i's production in period t; litw is female labor; litm is male labour; kit is capital stock; mit is materials consumption; and eneit is electric energy consumption. ωit is firm productivity, unobservable to the econometrician but predictable by the firm, and εit is an idiosyncratic error term.

Following Olley and Pakes (1992) and Levinsohn and Petrin (2003), capital stock is a state variable determined in the previous period, so current productivity shocks do not affect capital. Labor by gender and energy consumption are treated as freely variable inputs chosen in the current period. However, Ackerberg, et al. (2015) demonstrate that these input choices are correlated with ω_it, rendering OLS, fixed effects (FE), and instrumental variable (IV) estimators biased and inconsistent.

To address this, we use materials demand as a proxy for unobserved productivity (Levinsohn and Petrin, 2003). Inverting this demand function yields an expression of productivity in terms of observables, which is substituted back into Equation (1) and proxied by third-degree polynomials. Introducing the law of motion of productivity as a Markov process (Wooldridge, 2009), the two-equation system estimated jointly under GMM is:

where vit is a composite error term ( ξit+εit ). Once the system is estimated, TFP is recovered as the residual:

Our key methodological innovation consists in disaggregating the labor factor by gender, estimating separate output elasticities for female labor ( βlw ) and male labour ( βlm ). To our knowledge, this extension of Wooldridge’s (2009) approach to gender-specific TFP has not been implemented in prior studies. This allows us to assess whether women contribute differently to firm output and whether any differential is reflected in wages.

Regarding the limitations of TFP as a measure, we acknowledge the critiques raised by Shaikh (1974), Felipe and McCombie (2020), and related literature. These authors argue that TFP as a residual measure can capture factors beyond technological progress, including income distribution shifts and market power changes. Nonetheless, these critiques operate primarily at the macroeconomic level. Our analysis focuses on firm-level productive efficiency, where TFP is the standard performance measure (Syverson, 2011). At the microeconomic level, modern production function estimators, including Olley and Pakes (1992), Levinsohn and Petrin (2003), and particularly the two-equation system of Wooldridge (2009), were developed precisely to address endogeneity between inputs and unobserved productivity shocks, yielding more robust and consistent TFP estimates than earlier approaches.

The data come from the Annual Manufacturing Survey (EAM) and the Technological Development and Innovation Survey (EDIT), both published by Colombia’s National Statistics Department (DANE) for the period 2013–2020. After merging eight waves of EAM and EDIT, we obtain an unbalanced panel of 59,355 observations. The panel includes 9,715 firms (T = 7 periods on average), covering 23 manufacturing sub-sectors classified according to ISIC Revision 2.

All monetary variables as output, materials, capital, and wages, are deflated to constant 2015 prices using the Industrial Producer Price Index (IPP) for output and material inputs, and the Gross Fixed Capital Formation deflator for capital. Wages are deflated using the Consumer Price Index (CPI, base 2014).

The key variable of interest is the gender composition of the firm’s workforce. Following Tsou and Yang (2019) and Pfeifer and Wagner (2014), and consistent with the classification framework proposed in our methodological note, we define the female intensity index (fem_index) as the proportion of women in total employment. We classify a firm as female-intensive if fem_index ≥ 0.50, and as male-intensive otherwise. Robustness checks with alternative thresholds (54.5% and 60%) are reported in the Appendix.

Table 1 presents the estimates of labor product elasticities using three different methods: Ordinary Least Squares (OLS), Generalized Least Squares (GLS), and Wooldridge’s (2009) two-step method. These estimates are analyzed under two scenarios: one considering the firm's total labor force (Labor) and the other distinguishing employees by gender (women and men’s labor).

As expected, the results generally reveal that all methods yield positive and statistically significant elasticities. Nevertheless, without distinguishing by gender, the product elasticity under Wooldridge’s (2009) method is 0.286. In contrast, the OLS and GLS methods tend to overestimate this figure, likely due to biases from unaddressed endogeneity issues in the Cobb-Douglas production function. When gender is considered, Wooldridge’s (2009) method shows that the product elasticity of women’s labor is 0.136, while that of men’s labor is 0.132. The remaining elasticities corresponding to capital (0.093), materials (0.690), and energy (0.045) fall within the ranges reported by empirical studies on the industrial organization in Colombia (Gómez-Sánchez et al., 2022; Llopis et al., 2022; Sanchis Llopis et al., 2024).

The significance of our findings extends beyond the absolute size of the elasticity gap. The results’ econometric significance stems from their statistical significance and consistency across different model specifications. While the use of logarithmic transformations and monetary variables in U.S. dollars may compress the apparent magnitude, these differences translate into substantial economic effects when converted to Colombian pesos. Furthermore, our findings reveal that the higher output elasticity of female labor is a general characteristic of the Colombian manufacturing industry. This is due to that only one of the twenty-three sectors deviates from the overall pattern.

The differential in labor product elasticities between men and women is noteworthy: the elasticity of female labor is higher, implying that women’s average contribution to the firms’ output surpasses that of men. However, it is possible that women’s wages do not correspond to this greater contribution to production. In this regard, we present additional descriptive analyses to explore this idea.

Figure 1 shows that male-intensive firms have higher average log-wages (13.52) than female-intensive firms (13.09). Besides, in terms of average product of labor (APL), male-intensive firms exhibit higher productivity (11.598) than female-intensive firms (11.127), seemingly aligning with the prediction of neoclassical theory.

However, more precisely, measures of a firm’s productivity suggest different results. In the TFP scenario, female-intensive firms outperform male-intensive firms, with values of 2.554 and 2.476, respectively. Furthermore, in TFP weighted by gender (TFPwm), female-intensive firms also perform better (2.622) compared to male-intensive firms (2.566). Whilst further analysis is required to establish causality, these findings advise a potential productivity advantage when gender weighting is considered.

Table 2 presents wages and different productivity measures broken down by manufacturing sectors to deepen our analysis. In our preferred scenario (TFPwm), the numbers reveal that in industrial sectors such as Food, Textiles, Leather, Publishing, Coking, chemicals, Electric motors, Vehicles, and Machine Maintenance, female-intensive firms’ productivity displays higher productivity than male-intensive firms. However, wages are lower for female-intensive firms compared to salaries in male -intensive firms. In the remaining sectors, there is a clear correspondence between productivity and wages, that is, the more productive the higher the wages, regardless of firms’ gender orientation.

Other productivity measures, such as TFP, are consistent with the observed results for TFPwm. Nonetheless, APL estimates indicate that both productivity and wages are higher in male- intensive firms than in female-intensive firms across all industries except the Garment sector.

To examine the relationship between firm productivity and wages by gender composition, we estimate a dynamic generalized least squares (GLS) model with random effects (RE) for panel data. All variables are expressed in natural logarithms except dummy variables. To address simultaneity, that is, the possibility that wages contemporaneously affect productivity through efficiency wage mechanisms and vice versa, all covariates are lagged one period. The model is:

where lwit is the firm’s average real wage (in logs); findxit−1q,r is the female intensity index (continuous or dichotomous); lprodit−1h,j,p denotes firm productivity (h = aggregate TFP, j = gender-weighted TFP, p = APL); and Zit−1 is a vector of firm-level controls. The lagged dependent variable lwit−1 captures wage persistence, that is, firms with higher (or lower) wages in the past continue to display higher (or lower) wages in the present (Roberts and Tybout, 1997). In our context, this persistence may reflect structural gender-based disparities, as firms that historically paid lower wages to workers in female-intensive firms continue to do so. The term pre_lw2013 (pre-sample means of wages, Blundell and Bond, 1998) controls for long-run unobserved firm heterogeneity correlated with wage levels.²

The vector Zit−1 includes firms characteristics such as firm size (SMEs dummy, ≤200 employees); employee skills (number of workers with master’s degrees) as a proxy for human capital (Schultz, 1961; Mincer, 1974); export status and innovation activities (process and product combined) as internationalization and innovation proxies (De Loecker, 2013; Crepon et al., 1998); the Herfindahl-Hirschman Index (HHI) for market concentration; firm-level mark-up; and firm age. We also control for location loc _j (Bogotá D.C.), macroeconomic shocks (year fixed effects, year _t), and sector characteristics (industry fixed effects, ind _j).

Specification Tests and Robustness

Our estimation strategy was subject to three complementary specification tests regarding the econometric justification for the random-effects specification.

Serial Correlation Test

As a first diagnostic, we apply the Wooldridge (2002) test for first-order serial correlation in panel data. Results show strong evidence of autocorrelation in the static (non-dynamic) models for all three productivity specifications, TFPwm (p < 0.001), aggregate TFP (p < 0.001), and APL (p <0.001). This finding validates our dynamic specification. The strong serial correlation in wages, consistent with wage rigidity documented across labor markets, provides direct empirical justification for including the lagged wage lwit−1 as a regressor. Our dynamic model absorbs this autocorrelation, ensuring residuals are serially uncorrelated and estimates are consistent.

Hausman Test

Table A1 reports the Hausman specification test comparing fixed-effects (FE) and random-effects (RE) estimators for the preferred TFPwm specification. The test formally rejects RE in all three subsamples, full sample, female-intensive, and male-intensive all with p < 0.001. Nevertheless, this test result must be interpreted with caution in dynamic panel models.

When the lagged dependent variable lwit−1 is included as a regressor, the within (FE) estimator is also inconsistent, this is the well-known Nickell (1981) bias. The bias arises because the within-group transformation creates a negative correlation between lwit−1 and the transformed error term, which remains even as N tends to infinity and disappears only as T tends to infinity.

With T = 7 periods in our sample, this bias is non-trivial. The evidence is visible in Table A1 because the lagged wage coefficient under FE (0.33–0.38) is lower than under RE (0.59-0.67), a discrepancy of approximately - 0.29 that is Nickell bias rather than a structural difference between estimators. As a result, the Hausman test is comparing two inconsistent estimators, and is therefore uninformative in this context (Wooldridge, 2010).

Correlated Random Effects (CRE)

To provide a valid test of the RE orthogonality assumption, we follow Mundlak (1978) and Chamberlain (1980) framework and estimate Correlated Random Effects (CRE) models. This approach is appropriate precisely in dynamic panel settings where the standard Hausman test is invalid (Wooldridge, 2010). The CRE model relaxes the strict RE assumption by modelling the correlation between unobserved firm heterogeneity ( ui ) and time-varying regressors explicitly:

where X¯i are firm-level time averages of all time-varying lagged regressors (productivity, skills, market concentration, mark-up, exports, innovation, age, and firm size) and vi is orthogonal to regressors by construction. Including X¯i in the RE model yields estimates that are consistent even if ui is correlated with Xit . A joint Wald test on the coefficients of X¯i provides the specification test, that is, non-rejection supports the original RE specification; rejection indicates correlated heterogeneity but does not invalidate the CRE estimates themselves.

Table A2 in the appendix reports RE and CRE estimates side by side for the preferred TFPwm specification. Three findings are noteworthy. First, the joint Wald test strongly rejects the null that all Mundlak terms are zero, that is, chi2(8) = 1,320.30 (full sample), 395.15 (female-intensive), and 977.63 (male-intensive), all p < 0.001. This confirms that unobserved firm heterogeneity is correlated with time-varying regressors, as expected in any sample of heterogeneous manufacturing firms. The primary driver of this rejection is between-firm variation in productivity (m_ltfp_wm = −0.216*** to −0.319***), market concentration (m_lihh = 0.071***−0.079***), and mark-up (m_lmarkup = 0.247***−0.289***). These between-firm differences are large and structurally determined, reflecting persistent sorting of firms into different productivity and wage regimes.

Second, and crucially for our main argument, the key coefficient ltfp_wm_(t-1) in the CRE model reveals an asymmetry by gender composition. For male-intensive firms, the within-firm (transitory) effect of TFP on wages becomes non-significant in the CRE model (0.018, p > 0.10), indicating that the RE estimate was partly driven by between-firm heterogeneity. For female-intensive firms, the within-firm effect remains statistically significant and is in fact larger in the CRE model (0.087*, p < 0.10) than in the RE estimate (0.057*). This finding strengthens the paper’s core argument, as the productivity-wage link is not only weaker for female-intensive firms in cross-sectional terms but also operates through a distinct dynamic channel within firms over time.

Third, the wage persistence is strong and positive in all specifications, also SMEs pay lower wages than large firms, besides skills, innovation, and geographic location significantly affect wages, lastly the differential between female-intensive and male-intensive firms in the productivity-wage link is robust.

Robustness to Alternative Classification Thresholds

Table A3 of the appendix presents the main coefficient of interest ( ltfp_wmt−1 ) under alternative thresholds for classifying firms as female-intensive (≥50%, ≥54.5%, ≥60%). For male-intensive firms, results are virtually identical across all thresholds (0.061–0.062***), demonstrating full robustness. For female-intensive firms, the coefficient ranges from 0.057* to 0.047 across thresholds. The slight loss of significance at higher thresholds reflects reduced sample sizes (13,658 to 10,887 to 8,768 observations) rather than structural instability, as the point estimates remain close. This pattern is consistent with a productivity-wage link in female-intensive firms that becomes harder to estimate precisely as the sample falls.

The difference in the productivity-wage elasticity between male-intensive firms (0.062%) and female-intensive firms (0.057%) implies that, for every 1% increase in TFP, male-intensive firms transfer approximately 0.005 percentage points more into wages. Expressed in Colombian pesos, given average TFP and wage levels in the sample, this differential amounts to a meaningful and economically relevant gap, reinforcing the hypothesis of gender-based wage disparities.

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