To introduce the theoretical foundations on productivity and wages, several approaches explain how pay levels relate to worker performance. Human capital theory argues that individual productivity, and consequently wages, derive 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 better task performance.

Besides, 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, lower 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 performance.

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 labour market segmentation further improves 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 labour 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 actual productivity and wages ( Becker, 1971; Goldin, 2014). Moreover, recent evidence suggests that even when female workers or female-dominated firms achieve high productivity, wage transmission tends to be weaker, pointing to the influence of structural discrimination ( Rivera-Lozada et al., 2024).

These dynamics are particularly relevant in emerging economies such as Colombia, where industries like garments, textiles, and pharmaceuticals employ a large share of women ( Ñopo and Gallardo, 2009). Integrating gender-sensitive approaches into productivity analysis thus allows for a more nuanced understanding of how institutional barriers and social norms interact with firm performance and wage setting.

The empirical evidence on gender and productivity present mixed findings. Tsou and Yang (2019) show that Chinese firms with higher proportions of female workers often display lower productivity than those with more male workers. Nonetheless, when women possess higher levels of education, they significantly enhance firm productivity, particularly in small private and foreign firms, whereas the effect is weaker or absent in medium and large public enterprises. Pfeifer and Wagner (2014) similarly report contrasting outcomes: under an OLS approach, female-dominated firms appear less productive than male-dominated ones, yet a GMM framework reverses these results. Such inconsistencies underscore the importance of methodology and the operational definition of “female 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 or male according to the proportion of women or men in their workforce. This distinction is important because the composition of employees can reflect broader organizational practices, sectoral norms, and institutional barriers that leadership-based classifications may overlook.

In Colombia since early stages of industrialization, women have contributed actively to manufacturing, particularly in food and textile sectors, often as a means to supplement household income ( Santos, 2017; Arango, 1991). Historically, their work was associated with low pay, shaped by religious norms and disciplinary practices that undervalued female contributions ( Arango, 1991). Over time, women have strengthened their position in the economy by investing in education and acquiring skills that match or even surpass those of men ( Goldin, 2014).

Despite these advances, wages still fail to adequately reward women’s resilience and investment in human capital, and gender wage gaps remain pervasive worldwide ( World Bank, 2024). 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 firms and around 1.8 million microenterprises. 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. Santos (2017) highlights three factors behind this persistence.

First, firms often perceive female labour as costlier due to assumptions about motherhood and absenteeism, even when they lack systems to measure labour costs by sex ( Todaro et al., 2002). Second, some women-led firms may capitalize on relatively lower wages to increase profits, diverging from the predictions of efficiency wage theory. Third, occupational segregation by sector confines many women to specific industries, perpetuating unequal pay structures ( Goldin, 2014).

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 labour market segmentation, acquires a distinctive gendered dimension in emerging economies. In Colombia, this divergence is amplified for women-led or female-intensive firms, suggesting that wage discrimination is embedded in the very mechanisms that connect productivity and remuneration. Understanding these linkages is therefore essential for developing policies that promote fair compensation, enhance firm efficiency, and reduce structural gender inequalities in the labour market.

TFP broken down by gender follows Wooldridge’s (2009) method. This framework takes advantage of the GMM estimation to shorten the standard error calculation and avoid using bootstrapping techniques. Expressly, we assume that the production process follows a linearised Cobb-Douglas production function: y it = β 0 + β lw l it w + β lm l it m + β k k it + β m m it + β e ene it + ω it + ε it (1)

y it denotes firm’s i production in period t; l it w is the women labor; l it m is the men labor; k it is the firm’s capital stock; and, m it is the materials consumption, and ene it is the electric energy consumption. Besides, ω it is the firm’s productivity, which is only observable or predictable by the firm. As well, ε it represents an error term unobserved or unpredictable by firms.

Olley & Pakes (1992) assume that capital stock evolves according to the perpetual inventory method, and it is determined in the previous period (state variable). Therefore, current productivity shocks do not affect capital stock ( Eslava et al., 2013). We also assume that labor by gender and firm’s energy consumption are chosen in the same period, as they are consumed (freely variable factors). However, Ackerberg, et al., (2015) demonstrate that these choices are correlated with ω it , so the equation (1) cannot be estimated by ordinary least squares (OLS), fixed effects (FE), or instrumental variables (IV). In this sense, Levinsohn and Petrin (2003) suggests using the materials demand function as a proxy for unobserved productivity. The demand for materials is as follows: m it = m t ( k it , ω it , ene it ) (2)

According to Levinsohn and Petrin (2003), this demand is monotonically increasing in productivity, so we can invert this function to express firms’ productivity in terms of observables: ω it = m t − 1 ( k it , ω it , ene it ) = h t ( k it , ω it , ene it ) (3)

h t is an unknown function of k it ; m it ; k it ; ω it ; and ene it . Replacing (3) in (1): y it = β 0 + β lw l it w + β lm l it m + β k k it + β m m it + β e ene it + h t ( k it , ω it , ene it ) + ε it (4)

h t ( ∙ ) is unknown, so it is proxied by third-degree polynomials in the respective arguments. Nevertheless, β m and β k are collinear with h t ( ∙ ) , so we cannot to identify these parameters. Following Olley & Pakes (1992), and Levinsohn and Petrin (2003), it is necessary to introduce the law of motion of productivity as a Markov process: ω it = E [ ω it | ω it − 1 ] + ξ it = f ( ω it − 1 ) + ξ it (5) where f ( ∙ ) is an unknown function that join productivity in t and in t − 1 plus an innovation term, ξ it , which is uncorrelated to k it . By replacing (5) in (1), we get: y it = β 0 + β l l it + β k k it + β m m it + β e ene it + β w wat it + f ( ω it − 1 ) + ξ it + ε it (6)

Furthermore, by lagging and replacing equation (3) into (6), we get: y it = β 0 + β lw l it w + β lm l it m + β k k it + β m m it + β e ene it + h ( k it − 1 , m it − 1 , ene it − 1 ) + v it (7) where v it is a composed error term ( ξ it + ε it ) . Because h ( ∙ ) is an unknown function, it is proxied by third degree polynomials in the arguments. Equations (4) and (7) are the two-equation systems proposed by Wooldridge (2009); they are jointly estimated by using the GMM method with suitable instruments and moment conditions showed for instance by Gómez Sánchez (2020). Once we estimate equation (1), we get the TFP as a residual by using output elasticities: y it − ( β ̂ 0 + β ̂ lw l it w + β ̂ lm l it m + β ̂ k k it + β ̂ m m it + β ̂ e ene it ) = ω ̂ it (8) where ω ̂ it is the TFP estimated in logs for firm i at time t .

It is important to mention that we acknowledge the historical and theoretical critiques of Total Factor Productivity (TFP), particularly those raised by authors such as Shaikh (1974), or Felipe & McCombie (2020). Their arguments, which question the ability of TFP to isolate technological progress from other factors, are fundamental in the macroeconomic debate. However, it is crucial to distinguish these objections from their applicability to firm-level productivity analyses. Our research focuses on the productive efficiency at the firm level, where TFP is the standard performance measure. Unlike macroeconomic models, our analysis is focused on how the gender composition of the workforce affects productive efficiency and wages within the firm. Furthermore, the initial critiques of TFP, such as those by Shaikh (1974), precede the key methodological innovations in production econometrics. Modern approaches, such as those by Olley and Pakes (1992); Syverson, (2011) and in particular, the two-step method of Wooldridge (2009), were developed to deal with endogeneity problems. These advancements allow us to obtain more robust and consistent TFP estimates by controlling for the correlation between inputs and unobserved productivity shocks. Our main methodological contribution is an extension of the Wooldridge (2009) approach to disaggregate the labor factor by gender, allowing us to estimate the output elasticity of female and male labor separately.

In the next section, our estimation results consistently show that the output elasticity of female labor exceeds that of male labor. This differential is obtained prior to the calculation of TFP, reinforcing the reliability of our production function estimates. The stability of these parameters indicates that the subsequent TFP measure provides a valid and accurate representation of firm-level efficiency and productivity differences.

This section describes some key variables used in this study that provide insight into the empirical model. We specifically examine the output elasticity of labor without considering gender and with gender taken into account, as well as the linkage with firms’ salaries, analyzed for the entire sample and by manufacturing sectors.

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 firms have higher average log-wages (13.52) than female firms (13.09). Besides, in terms of average product of labor (APL), male firms exhibit higher productivity (11.598) than female 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 firms outperform male firms, with values of 2.554 and 2.476, respectively. Furthermore, in TFP weighted by gender (TFPwm), female firms also perform better (2.622) compared to male 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 firms’ productivity displays higher productivity than male firms. However, wages are lower for female firms compared to salaries in male 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 firms than in female firms across all industries except the Garment sector.

To explore the effect of female firm productivity on a firm’s wages, we offer a dynamic generalized least squares model (GLS) with random effects for panel data. The variables are in natural logs except for dummy variables. In addition, we lagged all covariates in one period to deal with possible simultaneity, except factor variables such as time, industry, and firm localization. The model is as follows: lw it = φ 0 + α 0 lw it − 1 + α 1 findx it − 1 + α 2 lprod it − 1 h , j , p + γ k Z it − 1 + pre lw ¯ + loc j + year t + ind j + ε it (9)

Where lw it signifies the firms wages; findx it − 1 q , r represents the female firm’s index with q ∈ continuous index and r ∈ dichotomous index. Besides, lprod it h , j , p denotes firms productivity; with h ∈ full TFP; j ∈ TFP by gender; and p ∈ APL. Supported in Roberts and Tybout (1997), we introduce the term lprod it − 1 h , j , p to capture firm’s wages persistence, that is, firms with higher (lower) wages in the past; currently continue to show higher (lower) wages. In this sense, here persistence aims to capture potential gender discrimination. That is, it examines whether firms that paid lower salaries in female firms in the past continue to do so in the present.

The vector Z it − 1 includes firm’s control variables according to industrial organisation. It includes the firm’s classification as SMEs (SMEs), to capture if a firm's size influences wages. In line with Schultz (1961), Mincer (1974), and others, we incorporate employee skills ( skills) as a proxy for human capital, as higher levels of education and/or training are associated with increased wages. Specifically, skills are the number of employees with master’s degrees. Export ( exp it ) and innovations activities ( inn it ) are included as a part of firm’s internationalisation strategies, as highlighted by De Loecker (2013) and Crepon, Duguet & Mairesse, (1998). According to Schank et al., (2010), firms with strong international trade connections and innovation efforts tend to be more productive and efficient, which typically results in higher employee wages. It is worth mentioning that due to the limited introduction of innovations in Colombian manufacturing, we combine both process and product innovations to achieve accurate statistical representativeness.

As well, the vector Z it − 1 accounts for market concentration proxied by Herfindahl-Hirschman index ( lihh), and firm’s mark-up ( lmarkup). We also include the firms’ age ( lage) because, according to the ILO (2015), young small enterprises in Latin America significantly contribute to job creation. On the other hand, following Blundell and Bond (1998), we include pre-sample means of the dependent variable ( pre _ lw 2013 ) to deal with correlated unobserved firm heterogeneity in the model estimation. Note that we also control for geographic firm localization (loc), macroeconomic shocks ( year), and sector characteristics ( ind). Finally, ε it is a composed the error term that consist of a fixed effect of firms ( u i ) and an idiosyncratic error term ( η it ) .

We adopt a random effects specification because our framework requires simultaneous control for industry-specific characteristics and macroeconomic shocks, which are introduced through sector and time dummies. In a fixed effects specification, these variables would be eliminated, thereby removing crucial cross-sectional variation that is essential for our analysis. For this reason, the Hausman test is not applied, since its conventional interpretation in this context could lead to a misrepresentation of the underlying economic rationale. Consistent with the practice in industrial organization research, the random effects model provides a more suitable framework for capturing the interaction between firm productivity, workforce gender composition, and wage outcomes.