Efficiency Analysis of Human Capital Investments at Micro and Large-Sized Enterprises in the Manufacturing Sector Using Data Envelopment Analysis

Abstract

Micro and large-sized enterprises are important elements to enhance the economic growth of any country, and even more so for developing countries such as Mexico. These enterprises highly contribute to job generation, competitiveness, and gross domestic product, factors that are important for the developing of a nation. The aim of this paper is to study the impact of human capital investments in the efficiency of the 21 economic activity subsectors for micro and large-sized enterprises in the Mexican manufacturing industry between 2009–2021. The database come from Mexico Annual Manufacturing Industry Survey. Four Data Envelopment Analysis models are developed to study the relationship between annual average working days, annual average wages, and annual average investment in training with average sales per year. Data indicate that, most of the micro-sized enterprises of the Mexican manufacturing sector do not invest in human capital training, contrary to their large-sized enterprises. The results show that investing in human capital training increase sales and wages in micro-sized enterprises of the Mexican manufacturing industry, but it is not evident in large-size enterprises of the Mexican manufacturing industry. The calculation of the economic activity subsectors efficiencies using the developed Data Envelopment Analysis models indicate that all the economic activity subsectors with scale efficiency equal to one optimally invest, and the average amount of investments in human capital training needed to increase the global and pure technical efficiencies of the others are calculated with the developed Data Envelopment Analysis models. In the three main economic activity subsectors of the Mexican manufacturing industry, a significant increase—in 83.33% of cases—in wages and salaries is seen in both micro and large-sized enterprises. Particularly, the results indicate that the Chemical industry economic activity subsectors show the highest efficiency in both micro and large-sized enterprises when the human capital training variable is present. This paper demonstrates the importance of investing in human capital to enhance the efficiency of micro and large-sized enterprises.

1. Introduction

An enterprise is an entity that significantly impacts a country’s economy, some of them impact the economy of multiple countries. Enterprises can be classified according with their size into three groups of enterprises: (1) micro-size enterprises, (2) small and medium-size enterprises (SME) and (3) large-size enterprises. Their group size determines the role it plays in the socioeconomic dynamics of a country. Enterprise size classification criteria are the number of employees, annual sales, income, and fixed assets (Brodny and Tutak 2022; Diario Oficial de la Federación 2019).

Micro enterprises, especially in development countries like Mexico, make significant socioeconomic contributions, because they show characteristics such as high assimilation capacity, flexibility in responding to market size, quick problem-solving due to a small number of employees, employees with great knowledge, high scalability owing to low operating costs, and rigorous control and supervision of activities. These characteristics foster synergy among workers, helping in the achievement of growth objectives (Martínez-Aparicio 2012; Peralta et al. 2023).

Despite their low impact on gross production due to their modest billing, micro companies are important gateways to labor market, mostly for youth. In Mexico, 30% of the population is conformed for young people (INEGI 2023) and micro-size enterprises are their main source of employment. This group of enterprises contributes approximately 52% to Mexico gross domestic product—GDP—, alongside with the SMEs group (García Camacho and Anido 2024).

One of the main problems faced by micro-size enterprises in Mexico is the absence of economic links between the three groups of enterprises—the group of SMEs, the group of micro-sized enterprises, and the group of large-sized enterprises—and between the Economic Activity subsectors—EAS. This problem reduces the possibility of growth for micro-sized enterprises and makes it difficult to understand business dynamics as well as to identify the reasons for the survival and success of organizations. (Martínez-Aparicio 2012).

Large companies are a small percentage compared to micro companies, it means, the group of large-size enterprises is smaller than the micro-size enterprises group. However, the group of large-size enterprises occupy a transcendental place in the economic activity due to the role that large companies play as agents that reinforce and stimulate development, these companies play an important role to bring foreign investment and, therefore, they also contribute to the global economy, increase job numbers, and GDP (Martínez-Aparicio 2012). Large-size companies are usually multinational, a condition that allows them to have easier access to financial and human resources than micro-size enterprises, reason why, large-size enterprises influence market trends, as well as government policies, despite their high number of workers. Large-size enterprises main difficulties arise in organizational management and social responsibility.

In Latin America, micro and large-size enterprises represent 88.4% and 0.5% respectively (Padilla-Angulo et al. 2023). In Mexico, based on the last economic census, it was identified that micro-size enterprises represent 94.9% and employ 37.2% while large-size enterprises represent 0.2% and employ 32.1%. In particular, the manufacturing sector plays a fundamental role in the country’s economic growth, as well as a significant contribution to employment, production, international trade, and exports. Micro-size enterprises in this sector represent 93.7%, hire 19.4% of the personnel employed in the sector, and generate 2.3% of the GDP. Large-size enterprises represent 0.8%, hire 58.1% of the personnel employed in the sector, and generate 78.2% of the GDP (INEGI 2019). In the country, the three main economic activity subsectors—EAS—based on the value of total production in the manufacturing industry are the Chemical Industry—325—the Food Industry—311—and the Transportation Equipment Manufacturing Industry—336—(INEGI 2021b; Rosales-Córdova and Carmona-Benítez 2023).

A company—regardless of its size or sector—is comprised of physical, financial, and intellectual capital, and in turn, intellectual capital consists of human, relational, and structural capital. (Al-Omoush et al. 2022). Although the survival and success of an organization depend on the proper functioning of each of its components, recent research’s (Aman-Ullah et al. 2022; Rosales-Córdova and Carmona-Benítez 2023) have identified—and therefore given much greater attention—human capital (HC) as a primary element for the performance of an organization, since its competencies have an impact directly on innovation, competitiveness, adaptability, product, service quality, and reputation of the company. These are conditions that allow companies to survive in the short term and achieve efficiency, and consequently success, in the medium and long-term (Way et al. 2018). For this reason, research on the impact of investment in HC across different sizes of enterprises is of outmost important. As the performance of HC improves, the productivity and efficiency of organizations increase, which positively affects the economic growth of any country. This benefits a developing country such as Mexico. (Bissoondoyal-Bheenick et al. 2023; Ling et al. 2024; Montejano García and López Torres 2013; Rosales-Córdova and Carmona-Benítez 2023; Rosales-Córdova and Llanos 2021).

Various studies have been conducted on HC across different sizes and sectors of enterprises (Almeida and Faria 2014; Nguyen et al. 2020; Prouska et al. 2016; Sitzmann and Weinhardt 2019; Way et al. 2018; Zhao et al. 2018). However, there is a gap in the study of the impact investment in HC has on efficiency of the EASs. Few have used Data Envelopment Analysis—DEA—models to analyze the efficiency in different company size based on HC, and fewer have been conducted at EAS level (Kalapouti et al. 2020; Monika and Mariana 2015; Rosales-Córdova and Carmona-Benítez 2023). For this reason and based on the importance of HC in the performance and efficiency of organizations, and these in turn in the country’s economy, that the aim of this paper is to study the impact of HC investments in the efficiency of the 21 EASs for micro and large-sized enterprises in the Mexican manufacturing industry for the period 2009–2021. To study so, four DEA models are developed. One DEA BCC and one DEA CCR use annual average working days, annual average salary, and annual average investment in training as input factors, and average sales per year as output factor, while one DEA BCC and one DEA CCR consider annual average working days and annual average salary as input factors and average sales per year as output factor.

This paper is organized as follows: in Section 2, a review on HC in micro and large-size enterprises, and a review about the application of DEA to analyze the performance of micro and large-size enterprises are presented; in Section 3, the inputs and output variables under study are explained, the CCR input-oriented model and the BCC input-oriented model are described, and the data are presented for the analysis of the 21 EAS that conform the micro-sized and large-sized enterprises in the Mexican manufacturing industry; in Section 4, the results and discussion about the efficiency of the 21 EAS that conform the Mexican manufacturing industry are analyzed for micro-sized enterprises and for large-sized enterprises; finally, in Section 5, conclusions are drawn, limitations and future research topics are provides.

2. Literature Review

2.1. Human Capital in Micro and Large-Size Enterprises

Mincer (1958), Schultz (1961), and Becker (1962) are the pioneers and creators of the theory of Human Capital. Over the years, their definition of HC has been complemented and refined. Now, it is accepted as a multidimensional construct composed of two main factors: cognitive and non-cognitive (Zhang et al. 2023). These factors include different dimensions. In general terms, HC can be defined as the knowledge, skills, abilities, talents, and capabilities of an individual to enhance productivity and create value to an organization (Nahuat Román 2020; Wright 2021).

The survival and success of an enterprise depend on physical, financial, and intellectual capital. The later plays an important role because the benefits of an organization increase for both the individual and the organization itself to the extent that HC is acquired and retained (Bissoondoyal-Bheenick et al. 2023). According with literature, several studies identify that investing in human capital training (HCT) increases enterprise productivity and efficiency, leading to significant improvements for both the employee—higher wages—and the organization—cost reduction, increased production, competitiveness, and sales (Bissoondoyal-Bheenick et al. 2023; Ling et al. 2024; Montejano García and López Torres 2013; Rosales-Córdova and Carmona-Benítez 2023; Rosales-Córdova and Llanos 2021). It is important to highlight the inherent difficulty in referring to a human being, as enterprises do not own them. They constantly change and are complex to understand (Ibarra-Cisneros and Hernández-Perlines 2019).

In micro-sized enterprises, the accumulation of HC and years of experience significantly impact economic performance of countries. The level of schooling—formal learning—job experience—informal learning—and HCT—non-formal learning—improves this effect (Peralta et al. 2023). The accumulation of HC is generated when the owner or microentrepreneur values the expected profitability of additional schooling degrees more than the costs associated with their realization. Education improves enterprise processes and sales management (Díaz Rodríguez et al. 2021). The longevity of micro-sized enterprises is well-defined within the first three years of operation. During this time, competitive capabilities are developed, and enough knowledge and skills for problem solution are generated (Ramírez et al. 2017). Unfortunately, in Mexico, a high percentage of micro-sized enterprises fail to surpass this time interval (INEGI 2021a). Hence, creativity, adaptability, and effective resource management are important factors for overcoming inherent challenges.

Unlike micro-sized enterprises, most of large-sized enterprises participate in both national and international markets. These types of enterprises expose their HC to external knowledge, including interactions with suppliers, clients, research centers, and financial institutions worldwide, helping them to gain competitive advantages (Perri et al. 2017). Moreover, multinational corporations increase knowledge management and diversify the professional profiles of their HC because they have access to more resources. Therefore, large-sized enterprises enable better adaptation to new technologies within the organization, thus providing HC with the necessary tools to adapt to the continuous changes in the market (Tseng et al. 2023).

HC is one of the most important factors influencing the survival and success of companies, regardless of their size (Rodríguez-Gulías et al. 2024). Consequently, understanding the optimal investment in HC is important for enhancing and assuring enterprises efficiency. This is the reason why this paper is particularly relevant, since it aims to analyze the impact of HC investments has on the efficiency and productivity of the 21 EAS within both micro and large-sized enterprises in the Mexican manufacturing industry. Moreover, while most of the research on HC focuses on SMEs without distinguishing between enterprise sizes, there are few research studying large companies and even fewer on micro-size enterprises. This is attributable to the difficulty of obtaining data from micro-size enterprises.

2.2. Data Envelopment Analysis Method in Micro and Large-Size Enterprises

Micro-sized enterprises are the main drivers of economic growth, and they are essential to boosting the capacity of a country to be competitive and innovative (Basyah and Fahmi 2024). This type of enterprises employs a maximum of 10 persons and applies family business principles (Porfírio et al. 2020). Micro-sized enterprises in Latin America often encounter a high failure rate (García Camacho and Anido 2024), primarily due to management or administrative problems, financing problems, and access to win tenders (Basyah and Fahmi 2024). Moreover, micro-sized enterprises operate in uncertain environments where available information about their performances is limited (Kononiuk 2022; Sedliačiková et al. 2024). Reason why, it is highly complex to evaluate the performance of micro-sized enterprises. Different factors have been studied, and various methodologies have been applied, leading to the conclusion that a high correlation between HC and company performance at micro-sized enterprises exist (Sedliačiková et al. 2024).

Chanda (2019) uses DEA methodology to evaluate the performance of micro-sized enterprises and SMEs at industry level. He compares the productivity of micro-sized enterprises and SMEs with large-sized enterprises. Purmiyati et al. (2019) applied the DEA VRS methodology to measure the technical efficiency (TE) of micro-sized enterprises that acquire commercial credit in 7 cities in East Java. Ayele (2021) uses a DEA model to calculate the TE and scale efficiency (SE) of 375 randomly selected micro-sized and small-sized enterprises. Boubaker et al. (2023) propose a DEA methodology to measure the efficiency performance of Vietnamese micro-sized enterprises and SMEs of its manufacturing sector. Dey et al. (2023b) apply DEA methodology to calculate the TE of 427 handloom micro-sized enterprises in the India State of Assam. Dey et al. (2023a) apply DEA a two-stage double-bootstrap DEA methodology to estimate the TE and its determinants of 340 handloom micro-sized enterprises for the three districts of the Indian State of Assam. García Camacho and Anido (2024) develops a DEA and a Malmquist index to analyze the performance of the micro-sized enterprises and SMEs in Colombia. Baruah and Saha (2024) use DEA to examines the TE of 312 micro-sized enterprises in India. Yang et al. (2024) use DEA methodology and a Malmquist index method to study the efficiency of financial funds assigned to support the technological innovation in new energy vehicle micro-sized enterprises.

Zheng et al. (1998) apply DEA methodology to analyze the TE in large-sized and medium-sized enterprises at state, collective, and township-village level. Zheng et al. (2003) use DEA to research the productivity of 600 large-sized state enterprises from 1980 to 1994. Memon and Tahir (2012) develop a DEA model to evaluate the performance of large-sized (assets over 100 million usd), medium-sized (assets between 30 million usd and 100 million usd), and small-sized (asset under 30 million usd) enterprises in Pakistan. Wang et al. (2017) develop a fuzzy DEA model to evaluate the performance of environmental regulations in 16,375 enterprises. Villa et al. (2021) develop a project selection method based on DEA methodology to determine what energy projects to prioritize regarding their economic efficiency. Cinaroglu (2021) develop a Bootstrap DEA methodology to study the efficiency of small-sized and large-sized public hospitals from 2014 to 2017. Proaño-Rivera and Feria-Dominguez (2022) use DEA methodology to calculate the TE of 24 banks in Ecuador from 2015 to 2019. Gopalkrishnan et al. (2023) develop a mix of Tobit regression and measure the operational efficiency of 26 housing finance enterprises in the Indian economy. Hooda and Sehrawat (2023) use DEA to study the overall technical efficiency (OTE), pure technical efficiency (PTE), and SE of the state transport system in the Indian State of Rajasthan. Seth et al. (2024) design a panel data fixed-effects model mixed with DEA methodology to study the efficiency of working capital management in 1,388 manufacturing firms from 2008 to 2019. Ofori et al. (2024) apply DEA methodology to study the efficiency and productivity of 749 US agricultural cooperatives from 2011 to 2015. Boubaker et al. (2024) design a composite performance index as a variable that measures bank stability. They use the dynamic weighting system of DEA to analyze the stability performance of 45 Vietnamese banks using data from 2002 to 2020. Zhu et al. (2024) apply a three-stage DEA mixed with Malmquist index to evaluate the digital inclusive financial development efficiency in 31 Northwest China provinces from 2015–2021.

It is important to mention that few papers study the impact of HC variables in EAS. From literature, the papers that apply DEA methodology to analyze the impact of HC variables in the performance of micro-sized enterprises and SMEs between EAS are Olexová (2011), Monika and Mariana (2015), Kalapouti et al. (2020), and Rosales-Córdova and Carmona-Benítez (2023). We did not find a paper that applies DEA to study the impact of HC variables between EAS for large-sized enterprises.

Rosales-Córdova and Carmona-Benítez (2023) is a very important study to this paper because they analyze the efficiency of HC in relation to sales at the EAS level for the 21 SMEs that conform the Mexican manufacturing industry. They use a DEA CCR input-oriented model to calculate the technical efficiency (TE) (Charnes et al. 1978), and a DEA BCC input-oriented model to calculate the pure technical efficiency (PTE) (Banker et al. 1984). Similar, in this paper, we analyze the efficiency of HC in relation to sales between the 21 EAS that conform the Mexican manufacturing industry, but for micro and large enterprises using the DEA CCR input-oriented model to calculate the OTE and the DEA BCC input-oriented model to calculate the PTE. Therefore, this paper complements the study published by Rosales-Córdova and Carmona-Benítez (2023) in four ways: (1) to acknowledge the effects of human capital training (HCT) have on the efficiency of micro and large-size enterprises in the Mexican Manufacturing Industry; (2) to identify the EAS that are efficient in the micro and large-sized enterprises of the Mexican Manufacturing Industry; (3) to determine the EAS that properly invest in HCT in the micro and large-sized enterprises in the Mexican Manufacturing Industry; and (4) to calculate the optimal investment in human capital (HC) that enables efficiency and consequently generates a competitive advantage for all the EAS in the micro and large-sized manufacturing enterprises of the Mexican Manufacturing Industry.

In summary, our literature review reports the application of DEA methodology to analyze the impact of HC in sales at company level for all size of enterprises, but the impact of HC variables in EAS has mainly been done for SMEs. Therefore, there is a gap in research considering the impact of HC variables in micro and large-sized enterprises.

Based on the above, the following hypotheses are proposed in this research:

H1. 

The number of micro-sized enterprises that invest in HCT is lower than the number of micro-sized enterprises that do not invest in HCT at each EAS of the Mexican manufacturing industry.

H2. 

The number of large-sized enterprises that invest in HCT is higher than the number of large-sized enterprises that do not invest in HCT at each EAS of the Mexican manufacturing industry.

H3. 

The investments in HCT increase average sales and average wages at each of the 21 EAS in micro and large-sized enterprises of the Mexican manufacturing industry.

H4. 

The correct investments in HCT increase the efficiency of the EAS in micro and large-sized enterprises of the Mexican manufacturing industry.

H5. 

The efficiencies of the three main subsectors of the Mexican manufacturing industry—the Chemical Industry (325), the Food Industry (311), and the Transportation Equipment Manufacturing Industry (336)—are above 0.50 when they invest in HCT in both micro and large-sized enterprises.

3. Methodology and Data

The aim of this paper is to study the impact of HC investments in the efficiency of the 21 EASs for micro and large-sized enterprises in the Mexican manufacturing industry. To achieve this, we analyze the efficiency of HC (investment in HCT, wages, and working days) in relation to sales within each of the 21 EASs that conform this industry. Therefore, the variables employed in each sample, as well as their definitions are:

-

Investment in HCT (input 1): payments made by a company for the training of its workers, including payments to internal and external instructors, training materials and payments to educational institutions also known as scholarships.

-

Wages (input 2): all payments and contributions, normal and extraordinary, in money and kind, before any tax deduction, to remunerate the work of the employee’s dependent on the company name, in the form of wages and salaries, social benefits, and profits distributed to the personnel, whether this payment is calculated based on a working day or by the amount of work performed.

-

Working days (input 3): counts the number of days dedicated directly to activities related to the production process of the establishment.

-

Sales (output): revenues obtained for production of goods and services.

Using these variables, the DEA methodology is applied to analyze the efficiency and productivity growth between HC investments and sales on micro and large-sized enterprises. DEA methodology creates an efficient frontier setting a target between a set of units under study making this methodology more suitable for performance measurement.

The aim of DEA models is to calculate the efficiency and productivity of various units in a set, the units are called DMUs (Martín-Gamboa and Iribarren 2021). Two types of efficiency are calculated from DEA models. The overall technical efficiency (OTE) is calculated assuming constant returns-to-scale (CRS) with DEA CRS input-oriented model (Charnes et al. 1978), and pure technical efficiency (PTE) is calculated assuming variable returns-to-scale (VRS) with the DEA BCC input-oriented model (Banker et al. 1984). A DMU produces optimally when OTE is equal to PTE because the scale efficiency (SE) is equal to 1, it means no efficiency gain is achieved if the production scale is modified.

In this paper, input-oriented models are applied to calculate OTE and PTE since micro and large-sized enterprises can control their investments on HC, but they do not have control on sales. It means they control inputs but not the output. So, input-oriented DEA models minimize inputs to produce the same level of output (Kumar and Gulati 2008). The aim of these DEA models is to measure sales efficiency in HC investments within micro and large-sized enterprises. It is an important contribution to the research in human resources management.

3.1. CCR Input-Oriented Model

Equation (1)–(5) present the CCR input-oriented model (Marjanovic et al. 2018) written into its standard form (Kumar and Gulati 2008).

$$\min {OTE}_0={\theta }_0-\epsilon \left({\displaystyle \sum _{i=1}^m{s}_i^{-}}+{\displaystyle \sum _{r=1}^s{s}_r^{+}}\right)$$

(1)

ST

$${\displaystyle \sum _{j=1}^n{\lambda }_j{x}_{ij}}+s_i^{-}={\theta }_0{x}_{i0}\hspace{1em}\hspace{1em}i=1,2,\dots ,m$$

(2)

$${\displaystyle \sum _{j=1}^n{\lambda }_j{y}_{rj}}-s_r^{+}=y_{r0}\hspace{1em}\hspace{1em}r=1,2,\dots ,s$$

(3)

$$s_i^{-},s_r^{+}\ge 0\hspace{1em}\hspace{1em}(i=1,\dots ,m; r=1,\dots ,s)$$

(4)

$${\lambda }_j\ge 0\hspace{1em}\hspace{1em}j=1,2,\dots ,n$$

(5)

where:

DMU0	unit under analysis	[-]
xij	quantity of input i used by DMUj	[units]
xio	quantity of input i used by the DMU0	[units]
yrj	quantity of output r delivered by DMUj	[units]
xro	quantity of output r delivered by the DMU0	[units]
λj	relationship importance between DMUj and the DMU0	[-]
${\theta }_o^{*}$	DMU0 optimal OTE	[-]
$s_i^{-}$	input slack variable	[units]
$s_r^{+}$	output slack variable	[units]
$\epsilon$	a small positive number	[-]

3.2. BCC Input-Oriented Model

Equations (6)–(11) present the BCC input-oriented model (Marjanovic et al. 2018) written into its standard form (Kumar and Gulati 2008).

$$\min {PTE}_0={\theta }_0-\epsilon \left({\displaystyle \sum _{i=1}^m{s}_i^{-}}+{\displaystyle \sum _{r=1}^s{s}_r^{+}}\right)$$

(6)

ST

$${\displaystyle \sum _{j=1}^n{\lambda }_j{x}_{ij}}+s_i^{-}={\theta }_0{x}_{i0}\hspace{1em}\hspace{1em}i=1,2,\dots ,m$$

(7)

$${\displaystyle \sum _{j=1}^n{\lambda }_j{y}_{rj}}-s_r^{+}=y_{r0}\hspace{1em}\hspace{1em}r=1,2,\dots ,s$$

(8)

$${\displaystyle \sum _{j=1}^n{\lambda }_j}=1$$

(9)

$$s_i^{-},s_r^{+}\ge 0\hspace{1em}\hspace{1em}(i=1,\dots ,m; r=1,\dots ,s)$$

(10)

$${\lambda }_j\ge 0\hspace{1em}\hspace{1em}j=1,2,\dots ,n$$

(11)

3.3. Data

The data used in this study comes from Mexico Annual Manufacturing Industry Survey for the period 2009–2021. Data is collected by the “Instituto Nacional de Estadística y Geografía” (INEGI SNIEG 2021) and provided based on its regulations established in its procedure for the utilization of the Annual Survey of the Manufacturing Industry, as well as for the extraction of data from its microdata laboratory, the ethical use of information, as well as its replicability and acquisition are ensured.

The Annual Survey of the Manufacturing Industry contains data about the methodology inputs and output variables allowing to study the efficiency of micro and large-sized enterprises of the Mexican industry for the 21 EAS.

The steps to clean and prepare the data and generate the sample sets are:

Step 1. Variable average values are calculated for the period 2009–2021. All observation units that report zero employees, wages, and sales are removed from the data.

Step 2. Observation units with full-time employees between 1 and 10 are classified as micro-sized enterprises, and observation units with more than 250 full-time employees are classified as large-sized enterprises (Diario Oficial de la Federación 2019). Hence, two samples are generated, one is the micro-sized enterprise sample, and the other is the large-sized enterprise sample.

Step 3. The micro and large-sized enterprise samples are divided in two sets each, by separating the observation units that report investing in HCT from those that do not. Therefore, the micro-sized enterprise—Set 1—includes observation units that invest in human capital training (HCT/Yes); the micro-sized enterprise—Set 2—includes observation units that does not invest in human capital training (HCT/No); the large-sized enterprise—Set 3—includes observation units that invest in human capital training (HCT/Yes); and the large-sized enterprise—Set 4—includes observation units that does not invest in human capital training (HCT/No).

Step 4. In the four datasets, all variables (inputs and output) are segmented by quartiles to control the variability that is inherent to data (x) which is categorized in three groups: Group 1 = first quartile (x < 25%), Group 2 = second and third quartile (25% ≤ x ≤ 75%), and Group 3 = fourth quartile (x > 75%). This study only uses data from group 2 because the variables coefficient of variation—CV—are smaller than 1. Contrary, data from groups 1 and 3 are not used because their variables CV are greater than 1, which indicate these data are not statistically acceptable.

Table 1. Average input and output variables of micro-sized enterprises from 2009 to 2021.

	HCT/Yes—Set 1—					HCT/No—Set 2—
		Inputs Variables			Output Variable		Inputs Variables		Output Variable
EAS	N	Annual Average HCT [MXN]	Annual Average Wages [MXN]	Annual Average Working Days [Days]	Annual Average Sales per Year [000 of MXN]	N	Annual Average Wages [MXN]	Annual Average Working Days [Days]	Annual Average Sales per Year [000 of MXN]
311	37	$13,757	$580,457	277.4	$6379.3	509	$224,338	292.4	$1179.6
312	21	$3810	$423,133	292.4	$3501.9	134	$167,970	298.8	$613.7
313	7	$7286	$920,429	280.7	$9012.0	103	$251,398	274.8	$1296.3
314	4	$5000	$715,333	239.0	$1936.0	69	$347,348	289.5	$1815.6
315	12	$8083	$649,750	253.7	$9053.6	142	$250,690	269.9	$915.0
316	8	$8128	$433,667	258.1	$1950.0	113	$304,770	280.4	$1402.3
321	8	$5625	$408,667	287.3	$5988.5	154	$192,844	276.0	$862.3
322	4	$39,600	$444,000	246.3	$2689.7	45	$358,333	275.9	$1596.7
323	14	$7000	$343,200	257.8	$2714.0	64	$169,803	276.1	$623.0
324	4	$8333	$897,667	327.3	$4987.0	10	$309,900	266.0	$1373.5
325	13	$39,333	$685,846	257.6	$49,418.5	73	$288,151	282.7	$1064.5
326	20	$6846	$739,235	250.8	$3915.4	128	$263,578	275.4	$1049.4
327	36	$4250	$1,120,250	299.6	$11,881.3	174	$241,810	273.7	$782.4
331	4	$27,000	$1,822,500	282.0	$71,202.4	46	$217,239	289.7	$868.9
332	23	$9217	$561,955	276.6	$5269.5	178	$174,427	278.4	$676.3
333	15	$25,750	$599,615	261.3	$5826.6	77	$331,026	267.9	$1196.6
334	4	$2250	$658,250	251.3	$3655.3	53	$321,849	278.9	$1285.4
335	6	$19,500	$1,085,833	255.0	$4270.6	50	$244,600	260.8	$969.3
336	11	$16,818	$673,500	258.5	$2793.8	78	$288,244	285.5	$1288.3
337	8	$12,500	$428,857	285.9	$3599.3	81	$206,877	300.3	$818.9
339	15	$6267	$410,938	270.4	$3371.3	129	$304,465	273.6	$1215.9

and

Table 2. Average input and output variables of large-sized enterprises from 2009 to 2021.

	HCT/Yes—Set 3—					HCT/No—Set 4—
		Inputs Variables			Output Variable		Inputs Variables		Output Variable
EAS	N	Annual Average HCT [MXN]	Annual Average Wages [000 of MXN]	Annual Average Working Days [Days]	Annual Average Sales per Year [000 of MXN]	N	Annual Average Wages [000 of MXN]	Annual Average Working Days [Days]	Annual Average Sales per Year [000 of MXN]
311	608	$262,622	$73,682.2	292.2	$449,446.5	264	$58,482.8	288.2	$272,072.5
312	148	$397,209	$80,254.6	297.1	$542,262.3	61	$65,672.2	295.3	$333,689.4
313	115	$203,800	$70,083.8	291.6	$365,709.6	59	$54,598.1	295.5	$231,402.3
314	51	$164,353	$66,276.5	273.9	$334,678.9	18	$35,922.7	286.9	$189,447.5
315	60	$60,650	$57,429.4	271.4	$147,562.6	40	$41,667.9	259.2	$110,854.9
316	31	$124,290	$39,020.1	264.9	$171,229.1	18	$44,433.3	270.6	$192,398.3
321	5	$42,600	$43,598.6	316.5	$389,412.0	1	$57,937.0	293.0	$440,158.0
322	36	$472,694	$76,552.2	334.4	$812,872.9	18	$84,373.9	349.3	$1,035,219.9
323	12	$203,000	$60,942.8	293.1	$182,428.8	6	$40,603.2	321.5	$166,881.7
324	6	$1,776,000	$134,110.0	335.7	$1,571,015.0	7	$2,018,178.1	365.0	$118,405,378.4
325	65	$814,154	$132,428.5	290.0	$1,222,906.1	31	$137,769.0	289.3	$997,483.4
326	67	$259,955	$57,455.0	296.3	$258,804.0	34	$56,478.6	301.4	$241,054.7
327	22	$252,909	$103,021.6	319.7	$544,489.9	16	$52,047.1	337.5	$260,075.7
331	25	$435,040	$89,292.1	310.5	$1,102,789.6	11	$85,060.5	310.4	$1,339,806.3
332	62	$283,323	$76,402.6	273.0	$260,697.3	12	$58,021.6	296.5	$304,894.3
333	44	$510,227	$101,412.0	283.7	$319,145.5	13	$74,514.0	277.5	$287,117.9
334	91	$366,560	$114,887.7	269.1	$259,937.9	36	$99,082.8	273.2	$238,375.0
335	67	$413,478	$100,475.4	262.5	$262,235.4	22	$84,075.5	266.1	$310,289.3
336	192	$507,995	$137,830.4	265.1	$529,175.4	85	$114,790.4	254.8	$282,766.1
337	23	$160,913	$55,799.8	275.0	$165,283.6	15	$44,507.3	270.8	$189,541.1
339	68	$342,838	$92,782.5	296.9	$249,207.2	23	$85,682.2	258.7	$163,623.9

show the average input and output variables data used for the statistical analysis (Section 4.1) and the DEA analyses (Section 4.2) of the 21 EAS for micro and large-sized enterprises respectively. These tables show the average investment done in HCT (HCT/Yes) per EAS from 2009 to 2021.

4. Results and Discussion

From the analysis of the data shown in Table 1 and Table 2, it can be observed that, in the Mexican manufacturing industry, the number of micro-sized enterprises that invest in HCT is lower than the number of micro-sized enterprises that do not; contrary to large-sized enterprises, where the number of large-size enterprises that invest in HCT is higher than the number of enterprises that do not, the reasons might be: (1) in the Mexican manufacturing industry, most of micro-sized enterprises are family-owned and live day-to-day, these make difficult for them to train their HC since they are financially limited, whilst large-sized enterprises have access to more financial resources; (2) their HC average educational level is lower in micro-sized enterprises than in large-sized enterprises, it shows a lack of awareness about the benefits of HCT, mainly due for their perception of this as an expense rather than an investment; (3) the absence of strong economic links between micro and large-sized enterprises directly impacts micro-sized enterprises organizational culture and, consequently, their acknowledge of the advantages that investment in HCT can produce. These findings are consistent with the results reported in Martínez-Aparicio (2012) and confirm the first and second hypotheses of this paper regarding the number of enterprises that provide training compared to those that do not.

4.1. Statistical Results

Table 3. Hypothesis test HCT/yes vs HCT/No of the EAS micro-sized enterprises.

	HCT/Yes—Set 1—				HCT/No—Set 2—
EAS	N	Average Employees	Annual Wages per Employee	Annual Average Sales per Year ([000 of MXN])	N	Average Employees	Annual Wages per Employee	Annual Average Sales per Year ([000 of MXN])	t Student Wages per Employee	t Student Sales
311	37	6.9 (SD = 1.7)	83,720 (SD = 27,347)	6379.257 (SD = 4081.92)	509	4.8 (SD = 1.4)	47,007 (SD = 19,421)	1179.627 (SD = 581.25)	t (544) = 10.76 *	t (544) = 25.64 *
312	21	5.5 (SD = 2.2)	76,933 (SD = 30,458)	3501.933 (SD = 3365.73)	134	3.5 (SD = 1.3)	48,683 (SD = 22,874)	613.679 (SD = 323.20)	t (153) = 5.07 *	t (153) = 9.82 *
313	7	9 (SD = 0.9)	102,270 (SD = 40,820)	9012 (SD = 4032.39)	103	5.3 (SD = 1.9)	47,693 (SD = 18,137)	1296.331 (SD = 762.71)	t (108) = 10.15 *	t (108) = 16.40 *
314	4	7.5 (SD = 2.4)	95,378 (SD = 94,443)	1936 (SD = 1801.42)	69	5.5 (SD = 1.6)	63,680 (SD = 20,959)	1815.551 (SD = 691.81)	t (71) = 2.18 *	t (71) = 0.30
315	12	7.2 (SD = 1.9)	90,663 (SD = 28,592)	9053.583 (SD = 6649.70)	142	4.3 (SD = 1.7)	58,903 (SD = 22,776)	915.007 (SD = 439.04)	t (152) = 4.54 *	t (152) = 14.73 *
316	8	5.3 (SD = 1)	81,313 (SD = 20,810)	1950 (SD = 1152.20)	113	5.5 (SD = 1.8)	55,664 (SD = 16,120)	1402.330 (SD = 902.74)	t (119) = 4.27 *	t (119) = 1.63 *
321	8	6 (SD = 1.6)	68,111 (SD = 23,762)	5988.5 (SD = 2960.41)	154	3.8 (SD = 1.7)	50,103 (SD = 24,294)	862.344 (SD = 597.68)	t (160) = 2.05 *	t (160) = 16.91 *
322	4	5.2 (SD = 2.9)	85,385 (SD = 37,979)	2689.667 (SD = 216.57)	45	6 (SD = 1.5)	59,897 (SD = 18,783)	1596.651 (SD = 849.92)	t (47) = 2.38	t (47) = 2.54 *
323	14	5.9 (SD = 1.1)	58,080 (SD = 27,483)	2714 (SD = 2195.11)	64	3 (SD = 1)	56,601 (SD = 21,778)	622.984 (SD = 278.68)	t (76) = 0.22	t (76) = 7.52 *
324	4	8.3 (SD = 0.6)	107,720 (SD = 69,774)	4987 (SD = 1347)	10	5.1 (SD = 2)	60,964 (SD = 28,428)	1373.5 (SD = 1,110.26)	t (12) = 1.85 *	t (12) = 5.20 *
325	13	2 (SD = 0.9)	351,716 (SD = 214,637)	49,418.5 (SD = 36,918.12)	73	4.1 (SD = 1.8)	69,582 (SD = 31,135)	1064.459 (SD = 794.17)	t (84) = 10.89 *	t (84) = 11.50 *
326	20	5.1 (SD = 2)	144,448 (SD = 51,387)	3915.364 (SD = 1493.57)	128	4.2 (SD = 1.7)	63,387 (SD = 25,308)	1049.411 (SD = 696.58)	t (146) = 11.27 *	t (146) = 14.13 *
327	36	5.7 (SD = 1.5)	195,772 (SD = 66,172)	11,881.250 (SD = 3926.16)	174	4.1 (SD = 1.7)	58,535 (SD = 27,895)	782.434 (SD = 496.48)	t (208) = 20.15 *	t (208) = 36.24 *
331	4	5.3 (SD = 1.7)	347,143 (SD = 178,454)	71,202.350 (SD = 64,880.67)	46	4 (SD = 1.7)	54,310 (SD = 22,228)	868.913 (SD = 434.98)	t (48) = 11.34 *	t (48) = 8.32 *
332	23	4.4 (SD = 1.8)	127,502 (SD = 54,480)	5269.5 (SD = 3297.11)	178	2.4 (SD = 1.6)	71,356 (SD = 48,301)	676.344 (SD = 492.58)	t (199) = 5.17 *	t (199) = 17.41 *
333	15	6.4 (SD = 2.4)	93,853 (SD = 32,524)	5826.560 (SD = 2731.85)	77	4.8 (SD = 1.4)	68,517 (SD = 30,296)	1196.636 (SD = 695.64)	t (90) = 2.93 *	t (90) = 11.57 *
334	4	5.8 (SD = 0.5)	114,478 (SD = 65,589)	3655.250 (SD = 2478.25)	53	4.3 (SD = 1.8)	74,458 (SD = 33,458)	1285.442 (SD = 701.16)	t (55) = 2.15 *	t (55) = 5.11 *
335	6	6.7 (SD = 2)	161,720 (SD = 57,030)	4270.6 (SD = 327.50)	50	4 (SD = 1.6)	60,888 (SD = 32,048)	969.26 (SD = 824.01)	t (54) = 6.65 *	t (54) = 9.66 *
336	11	3.2 (SD = 1.1)	210,469 (SD = 173,147)	2793.75 (SD = 1251.30)	78	4.4 (SD = 1.6)	65,960 (SD = 25,945)	1288.2693 (SD = 765.91)	t (87) = 7.06 *	t (87) = 5.59 *
337	8	6.3 (SD = 1.1)	76,818 (SD = 25,542)	3599.286 (SD = 1935.42)	81	4.6 (SD = 0.9)	44,498 (SD = 21,877)	818.876 (SD = 492.22)	t (87) = 3.93 *	t (87) = 10.37 *
339	15	6 (SD = 2.1)	68,490 (SD = 23,065)	3371.286 (SD = 1137.52)	129	5.1 (SD = 1.4)	60,092 (SD = 20,820)	1215.921 (SD = 675.29)	t (142) = 1.46	t (142) = 10.77 *

* p < 0.05.

and

Table 4. Hypothesis test HCT/yes vs HCT/No of the EAS large-sized enterprises.

	HCT/Yes—Set 3—				HCT/No—Set 4—
EAS	N	Average Employees	Annual Wages per Employee	Annual Average Sales per Year ([000 of MXN])	N	Average Employees	Annual Wages per Employee	Annual Average Sales per Year ([000 of MXN])	t Student Wages per Employee	t Student Sales
311	608	521.4 (SD = 125.5)	141,303 (SD = 43,574)	449,446.485 (SD = 225,444.282)	264	476.9 (SD = 122.7)	122,628 (SD = 40,997)	272,072.462 (SD = 131,171.846)	t (870) = 5.92 *	t (870) = 11.93 *
312	148	532.6 (SD = 131.3)	150,676 (SD = 46,034)	542,262.331 (SD = 328,690.170)	61	465.9 (SD = 84.8)	140,967 (SD = 35,510)	333,689.426 (SD = 204,532.897)	t (207) = 1.48	t (207) = 4.60 *
313	115	474.5 (SD = 107.9)	147,713 (SD = 42,662)	365,709.565 (SD = 138,858.837)	59	480.7 (SD = 122.7)	113,569 (SD = 33,299)	231,402.288 (SD = 82,801.115)	t (172) = 5.36 *	t (172) = 6.83 *
314	51	468.3 (SD = 124.8)	141,536 (SD = 49,700)	334,678.853 (SD = 160,362.891)	18	364.9 (SD = 53.9)	98,433 (SD = 14,624)	189,447.5 (SD = 84,976.839)	t (67) = 3.61 *	t (67) = 3.65 *
315	60	642.1 (SD = 144.1)	89,447 (SD = 21,825)	147,562.593 (SD = 36,757.112)	40	524.5 (SD = 106.1)	79,437 (SD = 18,582)	110,854.9 (SD = 35,918.245)	t (98) = 2.38 *	t (98) = 4.94 *
316	31	469.5 (SD = 108)	83,101 (SD = 22,238)	171,229.065 (SD = 42,402.847)	18	461.7 (SD = 139.4)	96,238 (SD = 43,084)	192,398.333 (SD = 65,697.177)	t (47) = −1.41	t (47) = −1.37
321	5	447.2 (SD = 83.4)	97,492 (SD = 36,606)	389,412 (SD = 190,732.057)	3	647 (SD = 167)	89,547 (SD = 73,212)	440,158 (SD = 381,464.114)	t (2) = 0.18 *	t (2) = −0.21 *
322	36	397.1 (SD = 66.5)	192,776 (SD = 34,066)	812,872.889 (SD = 192,339.787)	18	490.9 (SD = 98.9)	171,878 (SD = 40,902)	1,035,219.944 (SD = 450,173.286)	t (52) = 1.99 *	t (52) = −2.55
323	12	438.2 (SD = 47.6)	139,086 (SD = 40,197)	182,428.833 (SD = 80,695.894)	6	313.7 (SD = 45.5)	129,447 (SD = 24,874)	166,881.666 (SD = 38,573.758)	t (16) = 0.53	t (16) = 0.44
324	6	660.3 (SD = 230.9)	203,094 (SD = 66,651)	1,571,015 (SD = 709,867.650)	7	3881.1 (SD = 578.1)	519,996 (SD = 76,140)	118,405,378.429 (SD = 13,659,482.544)	t (11) = −7.91	t (11) = −20.79
325	65	507.7 (SD = 124.7)	260,820 (SD = 75,281)	1,222,906.092 (SD = 612,634.752)	31	514.8 (SD = 135.9)	267,630 (SD = 117,999)	997,483.388 (SD = 727,550.361)	t (94) = −0.34	t (94) = 1.59
326	67	408.4 (SD = 69.6)	140,698 (SD = 31,675)	258,803.985 (SD = 117,053.145)	34	413.8 (SD = 67.9)	136,4992 (SD = 26,632)	241,054.676 (SD = 103,581.556)	t (99) = 0.66	t (99) = 0.75
327	22	458.1 (SD = 103.7)	224,871 (SD = 84,188)	544,489.909 (SD = 393,548.433)	16	419.4 (SD = 101)	124,088 (SD = 26,603)	260,075.667 (SD = 146,586.314)	t (36) = 4.61 *	t (36) = 2.75 *
331	25	483.5 (SD = 104.2)	184,686 (SD = 72,608)	1,102,789.56 (SD = 939,653.252)	11	421.3 (SD = 123.4)	201,899 (SD = 57,163)	1,339,806.272 (SD = 783,298.827)	t (34) = −0.70	t (34) = −0.83
332	62	421.2 (SD = 75.9)	181,376 (SD = 38,769)	260,697.274 (SD = 110,550.096)	12	375.6 (SD = 72)	154,484 (SD = 54,213)	304,894.25 (SD = 157,909.320)	t (72) = 2.05 *	t (72) = −1.18
333	44	483.4 (SD = 116.4)	209,789 (SD = 67,673)	319,145.523 (SD = 97,003.389)	13	474 (SD = 90.2)	157,203 (SD = 74,385)	287,117.923 (SD = 176,555.031)	t (55) = 2.41 *	t (55) = 0.85
334	91	740.4 (SD = 254.7)	155,173 (SD = 54,097)	259,937.945 (SD = 98,727.606)	36	622.8 (SD = 202.1)	159,091 (SD = 48,571)	238,374.972 (SD = 85,468.506)	t (125) = −0.58	t (125) = 1.15
335	67	656.4 (SD = 161.9)	153,076 (SD = 33,837)	262,235.403 (SD = 80,897.799)	22	555.4 (SD = 141.4)	151,376 (SD = 41,299)	310,289.273 (SD = 177,631.239)	t (87) = 0.19	t (87) = −1.74
336	192	864.7 (SD = 304.6)	159,403 (SD = 50,555)	529,175.351 (SD = 222,897.198)	85	938.2 (SD = 380.1)	122,348 (SD = 48,631)	282,766.107 (SD = 129,216.051)	t (275) = 5.69 *	t (275) = 9.50 *
337	23	447.4 (SD = 132.3)	124,726 (SD = 28,188)	165,283.609 (SD = 38,042.089)	15	399.5 (SD = 85.5)	111,407 (SD = 39,838)	189,541.071 (SD = 101,050.865)	t (36) = 1.21	t (36) = −1.05
339	68	695.9 (SD = 276.8)	133,331 (SD = 56,867)	249,207.191 (SD = 86,374.550)	23	627.4 (SD = 219.8)	136,560 (SD = 45,976)	163,623.870 (SD = 66,581.340)	t (89) = −0.25	t (89) = 4.33 *

* p < 0.05.

conclude the third hypothesis of this paper. Table 3 results confirm Hypothesis 3 for the micro-sized enterprises of the Mexican manufacturing industry since over 85% of the EAS both average sales and average wages increase significantly when investing in HCT. Contrary, the effect of HCT on average sales and average wages is not as evident in large-size enterprises of the Mexican manufacturing industry (Table 4). However, this does not indicate that investing in HCT does not have an effect as it has been described in other papers (Bissoondoyal-Bheenick et al. 2023; Ling et al. 2024; Montejano García and López Torres 2013; Rosales-Córdova and Carmona-Benítez 2023; Rosales-Córdova and Llanos 2021) where investments in HCT generates positive effects on both organizational and personal indicators. There are some reasons for this behavior: (1) the profiles of HC change significantly in large-sized enterprises, unlike micro-sized enterprises, therefore, the objectives of HCT are different between them; (2) HCT focuses on maintaining individual skills in large-sized enterprises, this complicates the capacity to observe the effect of HCT on sales; (3) the fact that micro-sized enterprises in the Mexican manufacturing industry are flexible and have a multifaceted structure, which allows them for quick and direct improvements in HC performance through HCT, what increase sales and wages in short-term, in contrast, large-sized enterprises aim to achieve competitiveness in the market, so the effects of investing in HCT are reflected in the medium-term.

4.2. DEA Results

As it is explained in Section 3.3, the micro and large-sized enterprise samples are divided in four datasets. Set 1 contains micro-sized enterprises that include observation units that invest in human capital training (HCT/Yes). Set 2 contains micro-sized enterprises that include observation units that does not invest in HCT (HCT/No). Set 3 contains large-sized enterprises that include observation units that invest in HCT (HCT/Yes). Set 4 contains large-sized enterprises that include observation units that does not invest in HCT (HCT/No).

The size of the four datasets under analysis is justified because they fulfilled the validation rule n ≥ max {m × s; 3 (m + s)} (Cooper et al. 2007).

Table 5. Micro-sized enterprises OTE, PTE, SE and returns to scale.

	HCT/Yes—Set 1—				HCT/No—Set 2—
EAS	OTE	PTE	SE	Returns to Scale	OTE	PTE	SE	Returns to Scale
311	0.24	0.90	0.27	IRS	1	1	1	CRS
312	0.34	1	0.34	IRS	0.69	1	0.69	IRS
313	0.46	0.88	0.53	IRS	0.98	1	0.98	IRS
314	0.14	1	0.14	IRS	1	1	1	CRS
315	0.42	0.99	0.43	IRS	0.70	0.97	0.72	IRS
316	0.11	0.98	0.11	IRS	0.88	0.97	0.91	IRS
321	0.4	1	0.40	IRS	0.85	1	0.85	IRS
322	0.08	1	0.08	IRS	0.92	1	0.92	IRS
323	0.18	1	0.18	IRS	0.70	1	0.70	IRS
324	0.22	0.75	0.30	IRS	0.85	1	0.85	IRS
325	1	1	1	CRS	0.71	0.93	0.76	IRS
326	0.21	0.96	0.22	IRS	0.76	0.96	0.80	IRS
327	1	1	1	CRS	0.62	0.96	0.64	IRS
331	1	1	1	CRS	0.76	0.94	0.81	IRS
332	0.23	0.91	0.26	IRS	0.74	1	0.74	IRS
333	0.16	0.94	0.17	IRS	0.71	0.98	0.72	IRS
334	0.58	1	0.58	IRS	0.76	0.95	0.80	IRS
335	0.09	0.94	0.10	IRS	0.76	1	0.76	IRS
336	0.09	0.93	0.09	IRS	0.85	0.95	0.90	IRS
337	0.17	0.89	0.19	IRS	0.75	0.92	0.82	IRS
339	0.21	0.97	0.21	IRS	0.76	0.96	0.79	IRS

shows the results of the OTE for micro-sized enterprises. According with the DEA efficiency distribution, 18 EAS are non-DEA effective, which means they are not in optimal state, four EAS have an OTE > 0.5 (19.05%), and only three are OTE efficient (OTE = 1; 14.29%) in Set 1—325, 327 and 331—in Set 2, nineteen EAS are non-DEA effective, twenty one EAS have an OTE > 0.5 (100%), and only two of them are OTE efficient (OTE = 1; 9.52%)—311 and 314—. The results indicate that the investments in HCT are in optimal state with sales in the EAS—325, 327 and 331—in Set 1, and in the EAS—311 and 314—in Set 2. Since, these EAS define the efficiency frontier and the best practice within each set, it is possible to conclude that investing in HCT increase the differences in efficiency between EAS in micro-sized enterprises, and the efficiency gets close or similar for those EAS in micro-sized enterprises that do not invest in HCT.

Table 5 also shows the results of the PTE, SE and returns to scale for micro-sized enterprises. In this table, the global efficiency EAS are those with efficiency on the constate-return-to-scale (CRS) frontier, which means these EAS chose the optimum size for their HC investments. Hence, the efficient EAS are the Chemical Industry (325), the Nonmetallic Mineral Product the Manufacturing (327), and the Basic Metal Industry (331) in Set 1; and the efficient EAS are the Food Industry (311) and the Textile Product Manufacturing Except Apparel (314) in Set 2. All other EAS are overall technical inefficient (OTIE), they operate at suboptimal scale sizes on the increasing-return-to-scale (IRS) frontier, it means the micro-sized enterprises are too small for their scale of operations, these EAS need to develop strategies to increase productivity to gain efficiency. Since PTE > SE at these EAS, one strategy is to reorganize the utilization of their investments in HCT to achieve optimal sales, because the wrong size of their investments in HCT might be the reason of their technical inefficiency.

Table 6. Large-sized enterprises OTE, PTE, SE and returns to scale.

	HCT/Yes—Set 3—				HCT/No—Set 4—
EAS	OTE	PTE	SE	Returns to Scale	OTE	PTE	SE	Returns to Scale
311	0.58	0.94	0.62	IRS	0.08	0.99	0.08	IRS
312	0.55	0.92	0.59	IRS	0.09	0.90	0.10	IRS
313	0.55	0.94	0.59	IRS	0.07	0.88	0.08	IRS
314	0.59	1	0.59	IRS	0.09	1	0.09	IRS
315	0.39	1	0.39	IRS	0.05	1	0.05	IRS
316	0.4	1	0.40	IRS	0.07	0.96	0.08	IRS
321	1	1	1	CRS	0.13	0.88	0.15	IRS
322	0.86	0.93	0.93	IRS	0.21	0.74	0.28	IRS
323	0.28	0.9	0.31	IRS	0.07	0.89	0.08	IRS
324	1	1	1	CRS	1	1	1	CRS
325	1	1	1	CRS	0.12	0.88	0.14	IRS
326	0.37	0.90	0.42	IRS	0.07	0.86	0.08	IRS
327	0.7	0.89	0.78	IRS	0.09	0.8	0.11	IRS
331	1	1	1	CRS	0.27	0.84	0.32	IRS
332	0.33	0.97	0.34	IRS	0.09	0.87	0.10	IRS
333	0.3	0.93	0.32	IRS	0.07	0.93	0.07	IRS
334	0.28	0.98	0.28	IRS	0.04	0.94	0.04	IRS
335	0.27	1	0.27	IRS	0.06	0.97	0.07	IRS
336	0.53	1	0.53	IRS	0.04	1	0.04	IRS
337	0.29	0.96	0.30	IRS	0.04	0.96	0.08	IRS
339	0.27	0.89	0.30	IRS	0.03	0.99	0.03	IRS

shows the results of the OTE for large-sized enterprises. According with the DEA efficiency distribution, 17 EAS are non-DEA effective, which means they are not in optimal state, eleven EAS have an OTE > 0.5 (52.38%), and only four are OTE efficient (OTE = 1; 19.05%) in Set 3—321, 324, 325, and 331—whilst in Set 4, twenty EAS are non-DEA effective, the 324 EAS is the only one that has an OTE > 0.5 (4.76%), and it is the OTE efficient (OTE = 1; 4.76%). The results indicate that the investments in HCT are in optimal state with sales in the EAS—321, 324, 325, and 331—in Set 3, and in the EAS—324—in Set 4. Since these EAS define the efficiency frontier and the best practice within each set, it is possible to conclude that investing in HCT increases the differences in efficiency between EAS in large-sized enterprises, and the efficiency gets close or similar for those EAS in large-sized enterprises that do not invest in HCT. In Set 4, the efficiency of the 324 EAS is very high in comparison to all other EAS.

Table 6 also shows the results of the PTE, SE and returns to scale for large-sized enterprises. In this table, the global efficiency EAS are those with efficiency on the CRS frontier, which means these EAS chose the optimum size for their HCT investments. Hence, the efficient EAS are the Wood Industry (321), the Petroleum and Coal Products Manufacturing (324), the Chemical Industry (325), and the Basic Metal Industries (331) in Set 3; and the Petroleum and Coal Products Manufacturing (324) is the only efficient EAS in Set 4. All other EAS are OTE, they operate at suboptimal scale sizes on the IRS frontier, it means the large-sized enterprises are too small for their scale of operations, these EAS need to develop strategies to increase productivity to gain efficiency. Since PTE > SE at these EAS, one strategy is to reorganize the utilization of their HC investments to achieve optimal sales, because the wrong size of their HC investments might be the reason of their technical inefficiency.

The SE results confirm the fourth hypothesis of this paper (Table 5 and Table 6) because all the EAS with SE = 1 indicate that their annual average HCT investments are at the optimum level whilst the EAS with SE < 1 indicate investments are not at optimum level.

Figure 1 and Figure 2 show the current annual average HCT investments in orange color, the calculated investments needed to become local efficient (PTE = 1) using the DEA CCR model are shown in blue color, and the calculated investments needed to become global efficient (OTE = 1) using the DEA BCC model are shown in green color for the micro-sized enterprises of the Mexican manufacturing industry that invest in HCT (Set 1) (Figure 1) and for the large-sized enterprises of the Mexican manufacturing industry that invest in HCT (Set 3) (Figure 2).

Figure 1 confirms that all the EAS with SE < 1 must reduce their annual average amount of investments from their current annual average amount of investment (orange color) to their PTE annual average amount of investment (blue color) to become local efficient (PTE = 1) and to their OTE annual average amount of investment (green color) to become global efficient (OTE = 1). Figure 1 shows that all the EAS are over investing except—325, 327, and 331—in the micro-sized enterprises of the Mexican manufacturing industry. Moreover, the efficiency of enterprises increases when investing in HCT no matter their size (García-Zambrano et al. 2018; Nduneseokwu and Harder 2023; Rosales-Córdova and Carmona-Benítez 2023; Rosales-Córdova and Llanos 2021) since more EAS with SE = 1 exist in Set 1 and Set 3 than in Set 2 and Set 4 respectively. This happens because HCT increases performance, sales, productivity, and competitiveness, which positively impact the efficiency of any organization (Bissoondoyal-Bheenick et al. 2023; Ling et al. 2024; Montejano García and López Torres 2013; Rosales-Córdova and Llanos 2021; Słomka-Gołębiowska et al. 2023; Song 2024).

Figure 2 confirms that all the EAS with SE < 1 must reduce their annual average amount of investments from their current annual average amount of investment (orange color) to their PTE annual average amount of investment (blue color) to become local efficient (PTE = 1) and to their OTE annual average amount of investment (green color) to become global efficient (OTE = 1). Figure 2 shows that all the EAS are over investing except—321, 324, 325, and 331—in the large-sized enterprises of the Mexican manufacturing industry.

Hypothesis five is confirmed for large-sized enterprises and rejected for micro-sized enterprises. In Figure 1 and Figure 2, as well as in Table 5 and Table 6, it is observed that the efficiency of the three main EAS is above 0.5 in large-sized enterprises, a condition that only occurs in the Chemical industry—325—of micro-sized enterprises.

Identify, improve, and/or maintain high efficiencies in the three main EAS of the Mexican manufacturing industry is of utmost importance, since they represent 54% of total manufacturing production of the country (INEGI 2021b). The lack of connections (Martínez-Aparicio 2012) between micro-sized enterprises and large-sized enterprises in Mexico results in a lack of knowledge regarding the correct investment of HCT, a condition that affects both the Food industry—311—and in the Transportation Equipment manufacturing industry—336.

In the Transportation Equipment manufacturing industry—336—the efficiency of large-sized enterprises is 0.53 which is consistent with the findings of (Rosales-Córdova and Carmona-Benítez 2023) who conclude that SMEs in this EAS show a similar efficiency value of 0.43. This result is noteworthy because of the EAS contribution to the GDP and employment of Mexico. This clearly shows an area of opportunity for this EAS across the three group sizes of enterprises—SMEs, micro, and large-sized—as efficiency increases, benefits for enterprises increase too, and consequently, the GDP of any country.

The Chemical industry shows an SE = 1 in both micro and large enterprises that invest in HCT, which is equal to the SE of the SMEs in this EAS (Rosales-Córdova and Carmona-Benítez 2023). This indicates effective resource management and underscores the importance of investing in HC. It is important to highlight that efficiency in an organization positively impacts various aspects of its operation and performance, such as: (a) competitive market permanence, (b) maximization of resources, (c) Optimal product and/or service quality, (d) Greater satisfaction and retention of human capital, (e) Potential for growth and expansion, and (f) Healthy financial management.

5. Conclusions, Limitations and Further Recommendations

Micro and large enterprises contribute differently but complementarily to job creation, competitiveness, GDP, and economic growth, especially in a developing country like Mexico.

HCT plays a fundamental role in the efficiency of any enterprise, regardless of the size–SME, micro-sized and/or large-sized. With the correct management of resources, a contribution to sustainability, development, continuous improvement, and innovation can be generated, increasing the probabilities of the organization’s survival and success.

In this paper, DEA models are used to analyze the impact of HC investments on the performance of the 21 economic activity subsectors for micro and large-sized enterprises in the Mexican manufacturing industry. The results of this paper confirm that the presence of the HCT variable identifies a positive change in the efficiency of the EAS for both micro and large-sized enterprises. In general, higher efficiency values are found in the sets where enterprises invest in HCT.

Despite the recognized positive effect of HCT, in micro-sized enterprises, the number of enterprises that invest in HCT is lower than those that do not invest in HCT. Contrary, in large-sized enterprises, the number of those that invest in HCT is higher than those that do not invest in HCT.

The results show that investing in HCT increase sales and wages in micro-sized enterprises of the Mexican manufacturing industry, but it is not evident in large-size enterprises of the Mexican manufacturing industry. Specifically, in the three main EAS, it is identified that in all cases—except for the Chemical industry of large-sized enterprises—the increase is significant when investing in HCT.

It is noteworthy to mention that of the three main EAS in the Mexican manufacturing industry, 100% scale efficiency is exhibited in the Chemical industry in both micro and large-sized enterprises that invest in HCT. This highlights the importance of investing in HC and the excellent resource management within this EAS.

This paper identifies that investment in HCT is a determinant factor to achieve efficiency in both micro and large-sized enterprises, the nature and impact of training vary depending on the group size of the enterprises. It is important to emphasize that investments in HCT do not guarantee their effectiveness; investments must be properly made. Hypothesis tests generally recognize the positive effect of HCT, while DEA models identify the correct investment of HCT.

In micro-sized enterprises, their organizational culture has yet to incorporate the substantial improvements in skills and adaptability that investment in HC represents. Therefore, it is crucial to promote this culture in Mexico to boost the organization and, consequently, all EAS.

Large-sized enterprises main objectives is to maintain competitiveness in the market due to globalization. To achieve this, they employ specialized HCT and continuous improvement programs, conditions that increase HC efficiency in the long-term and foster innovation, and product quality.

The findings of this research confirm that HC is the most valuable intangible resource of a company. Investing in HC improves employees’ skills, allowing them to perform better, which in turn helps the organization achieve its goals and objectives, such as efficiency and increased sales. Additionally, employees also benefit, including a significant increase in their wages, a better work environment, and increased happiness. While, as shown in the results, investment in HC is part of the work culture in large-sized companies’, this is not the case in micro-sized enterprises, which perceive investments in HC as an expense rather than an investment.

Based on the findings of this research, the Mexican government should develop policies—such as incentive the collaboration between universities and enterprises, tax reductions, etc.—to incentive the investment in HC—particularly among owners of micro, small, and medium-sized enterprises—because the benefits are for employees, for companies, for the social realm, and for country’s economy; moreover, it helps reduce inequalities, increase quality of life, foster cultural development, and improve mental and physical health. Therefore, it is crucial to invest in HC to promote sustainable growth and national progress.

The limitations of this study are primarily twofold: (1) data must be worked in groups of companies—n ≥ 3—because of the confidentiality criteria of information managed by INEGI, and (2) data must be cluster into groups or sets because of minimize their high variability. Groups with a CV greater than 1 are excluded.

The statistical analysis and the development of DEA models to study the impact of HC investments on the efficiency of the 21 EASs opens a new line of research and, therefore, an avenue for further research, such as: (1) applying DEA models to study each of the classes within the Chemical industry EAS with the aim is to identify the causes for its 100% scale efficiency across the three size groups of enterprises; (2) Performing a deeper analysis of the behavior of HC in large-size enterprises, and (3) complementing this research with the use of output-oriented DEA models.