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Revista mexicana de ciencias forestales
Print version ISSN 2007-1132
Rev. mex. de cienc. forestales vol.12 n.67 México Sep./Oct. 2021 Epub Oct 25, 2021
https://doi.org/10.29298/rmcf.v12i67.983
Scientific article
Sawnwood production functions in the Community Forest Enterprise in Mexico
^{1}Universidad Autónoma Chapingo. México.
^{2}Colegio de Postgraduados. México.
Three production models for sawnwood were generated in 35 Community Forest Companies (CFEs) located in 10 states of México, which were classified based on variables related to: production inputs, continuous variables, and nominal variables that affect productivity. For Model I the variables L and K were highly significant (p-value <0.001). Variables L and VD in model II were highly significant and variable K was significant at 0.16 % (p-value <0.05). The CA, CM, CI, PO and PTD variables had no effect on productivity. For model III, high significance was obtained for the variables L and VD (p-value <0.001), K was significant at 0.95 % (p-value <0.01), Figura Legal Privada (FL2) and Figura Legal Sociedad (FL3) were significant at 0.1 % (p-value <0.001) and 2.9 % (p -value <0.05), respectively. Competitiveness in the use of resources was measured with the Marginal Product Value (MPV). The hypothesis of non-competitive use for input L in model II (0.1 %) was rejected. For Model III, Ho Pmg_{ L } -P_{ L } = 0 was rejected in the CFEs located in the states of Oaxaca and Quintana Roo (p-value <0.05) and Ho: Pmg_{ K } -P_{ K } = 0 was rejected for the CFEs located in Chiapas and Oaxaca (p-value <0.01). Finally, the MPV for VD in models II and III using aggregated data at the national level Ho: Pmg_{ VD } -P_{ VD } = 0 was rejected (p-value <0.001).
Key words: Competitiveness; Cobb-Douglas function; econometric model; productivity; performance to scale; marginal revenue product
Se generaron tres modelos de producción para madera aserrada en 35 Empresas Forestales Comunitarias (EFC) de 10 estados de México, que se clasificaron a partir de variables relativas (insumos de producción): continuas y nominales que afectan la productividad. Para el modelo I, la mano de obra (L) y el capital (K) fueron altamente significativas (p -valor <0.001); en el modelo II, lo fueron L y volumen disponible (VD); K resultó significativa al 0.16 % (p -valor < 0.05); Coeficiente de Aserrío anual (CA), Clasificación de madera anual (CM), Capacidad instalada de la industria anualmente (CI), Número de mujeres en puestos operativos al año (PO) y Número de mujeres en puestos de toma de decisiones por año (PTD) no incidieron en la productividad (p -valor > 0.05). Para el modelo III L y VD registraron alta significancia; K fue significativa al 0.95 % (p -valor < 0.01); Figura Legal Privada (FL2) y Figura Legal Sociedad (FL3), lo fueron al 0.1 % (p -valor < 0.001) y 2.9 % (p -valor < 0.05), respectivamente. La competitividad en el uso de los recursos se determinó con el Valor del Producto Marginal (VPM). Se rechazaron las hipótesis de uso no competitivo para L en el modelo II (0.1 %); para el modelo III, Ho: Pmg _{ L } -P _{ L } =0 en las EFC de Oaxaca y Quintana Roo (p-valor<0.05); y Ho: Pmg _{ K } -P _{ K } =0 para las de Chiapas y Oaxaca (p-valor<0.01). El VPM para VD en los modelos II y III, con datos nacionales, se rechazó Ho: Pmg _{ VD } -P _{ VD } =0 con un nivel de significancia de 0.1 %.
Palabras clave: Competitividad; función Cobb-Douglas; modelo econométrico; productividad; rendimiento a escala; valor del producto marginal
Introduction
There are 15 584 ejidos and forest communities in Mexico, which are called agrarian nuclei, and which are holders of 45.5 % of the total forest area of the country (62 639 719 ha) (^{Reyes et al., 2012}; ^{Conafor, 2019a}; ^{Frey et al., 2019}). These organizations create Community Forest Companies (CFE) and manage forest resources in order to generate economic, social and environmental benefits to improve their quality of life, without neglecting their financial viability, competitiveness and ecological sustainability in the long run (^{Frey et al., 2019}), so it is essential to analyze whether Mexico's CFEs fulfill these purposes.
CFEs have uses and customs that sometimes make expeditious administration difficult and do not easily access credit, so they depend on governmental support granted by the Comisión Nacional Forestal (National Forest Commission) (Conafor) to improve their competitiveness and efficiency; these focus on reducing production costs, improving the quality of processes, increasing efficiency and adding value to their products (^{PNUD, 2017}). ^{Frey et al. (2019)} assessed the effect of these supports and concluded that forest certification has a positive impact on productivity and, consequently, on the total income of the community.
Recent studies on CFE income show results differentiated by great variability, attributable to diversity in size, region, productivity and costs (^{Cubbage et al., 2011}, ^{2015a}). In general, CFEs replicate a competitive business model to generate jobs and benefits for their members and communities, and adopt strategies for innovation, certification, alliances, and continuous process improvements. Works such as those of ^{Cubbage et al. (2013}, ^{2015a}, ^{2015b)} and ^{Frey et al. (2019)} established that competitiveness is related to the ability of the company (of any type) to penetrate the market or increase its market; this can be estimated through the production costs, income, benefits and sustainability of wood harvesting, which explain its profitability and efficiency. ^{Chandra and Shishodia (2017)} and ^{Sasatani (2009)} considered that the classical financial indicators (profitability of growth, assets, capital and earnings before interest, taxes, depreciation and amortization), as well as production costs and profitability are essential to measure competitiveness with greater accuracy.
Generally, studies on business competitiveness in Mexico do not address a broad scheme that involves economic, environmental and social aspects as a whole, so the use of updated information (2017-2019) from direct sources, as well as the specification of the nature of the investments and the form of organization of CFEs in the present investigation constitute a novel approach. Its contributions will provide feedback and complement the analysis of the results of the Program for the Strengthening of Sustainable Forest Management with a Landscape Approach (PFMFSP, for its acronym in Spanish) and of other studies such as those already cited by ^{Cubbage et al. (2013}, ^{2015a}, ^{2015b}) and ^{Frey et al. (2019)}. Economic, environmental and social indicators are part of the PFMFSP strategy to increase competitiveness in a local market whose imports exceed its own supply. In fact, ^{Cubbage et al. (2015a}; ^{2015b)} identified that what puts the efficiency and sustainability of CFEs in Mexico at risk is precisely the increase in imports of sawn wood.
In the present study, the effect of several factors of the social scope (jobs, position of jobs and gender) and environmental (certification of the chain of custody of forest products and good forest management) on the production and productivity of forest products was measured. CFEs through the theory of the company and sustainable forest development. The first objective of this research consisted in determining Cobb-Douglas type production functions to measure the effect of the variables that affect productivity. The second was to measure competitiveness from the Marginal Product Value and determine performance to scale for such inputs as labor, capital and available volume.
Materials and Methods
Materials
The information came from Conafor's PFMFSP for the years 2017 to 2019, it corresponded to 35 CFEs located in 10 states of Mexico: Chiapas, Chihuahua, Durango, State of Mexico, Jalisco, Michoacán, Oaxaca, Puebla, Quintana Roo and Veracruz, in addition of subsidies that were assigned to CFEs in the same years (^{Conafor, 2017}; ^{2018}; ^{2019b}). The measurement and monitoring of the PFMFSP indicators were grouped into three criteria, which served to identify improvements in competitiveness, market access and gender equality according to the United Nations Development Program (UNDP) (^{PNUD, 2017}).
The subsidies corresponded to the National Forest Program (Pronafor, for its acronym in Spanish) through direct support for investment in the forest industry and commerce, administration, production and marketing, and integration and organization of forest value networks, as well as indirect subsidies for operating expenses, national certifications and international and marketing (^{Conafor, 2017}; ^{2018}; ^{2019b}).
Production functions
The Cobb-Douglas production function (Q) was used with two production factors: capital (K) and labor (L) given by the model:
Where:
K = Product of the annual installed capacity (in feet table shift^{-1}) by the wear of capital, referred to the machinery depreciation (20 %) and was obtained from the unit production cost ($ pt^{-1}) in the sawmill process
L = Number of direct jobs per 8-hour shift for 240 working days per year
Model (1) can be linearized by applying the natural logarithm (ln), with which the following was obtained:
Given a set of observations of the Q, K and L variables, in
Where:
The adjustment of the mixed model (3) was carried out with the lme4 package of the R statistical program (^{R Core Team, 2020}). The Shapiro-Wilk test and the homogeneity of variance of the errors with the Barttlet and Levine homoscedasticity tests were used to verify normality.
The base Model (1) was extended to include other continuous and categorical variables that affect the level of production. In general, the proposed production function, according to ^{Frey et al. (2019)} was:
Where:
Q = Produced quantity in thousands of board feet (Mpt = 1 000 pt) per year
β_{ 0, } β_{ i, } γ_{ j } , δ_{ k } = Function parameters
X_{ i } = Production input quantities
Y_{ j } = Continuous variables that affect productivity
Z_{ k } = Nominal or ordinal variables that affect productivity
Model (4) is an empirical variation of the Cobb-Douglas functional form (^{Frey et al., 2019}) that becomes the linear model of the form:
Based on expression (5), three labeled models are defined in order of complexity. With model (6) it is possible to determine the effect of the K and L production factors; in Model (7) the factors related to the technological level, the availability of wood and the inclusion of women in the production process are added. With Model (8) the effect of subsidies, wood certification and the legal figure with which the CFE is constituted, is evaluated. Thus, by dispensing with the subscripts to simplify the notation, the structure of the regression models to be estimated as extensions of the original model (Eq. 1) is presented below:
Where:
Q = Annual production (Mpt)
L = Work (total jobs per year)
K = Annual capital (Mexican pesos)
VD = Annual available timber volume (roundwood m^{3})
CA = Annual sawmill coefficient (%)
CM = Annual timber classification (%)
CI = Annual industry installed capacity (pt shift^{-1})
PO = Number of women per year in operational positions
PTD = Number of women per year in decision-making positions
S = Concept of PRONAFOR subsidies (number of supports year^{-1})
CERT = CoC Certification (0, 1)
FL= Legal figure (FL1= Ejido or Community, FL2 = Private and FL3 = Society)
To quantify the production of physical units in the sawmill process, the production function was modeled from the models (6, 7 and 8).
Marginal Product Value
In microeconomic theory, a firm is competitive if the marginal product value (MPV) of each input is equal to its price. MPV is the additional income that a company obtains for hiring an additional unit of work (L) and/or a unit of capital (K). That is, if CFEs seek maximum competitiveness, the income generated by an additional unit of input should be equal to its cost; that is, the MPV of the input minus the price will be zero (^{Salvatore, 1983}; ^{Mas et al., 1995}; ^{Varian, 2006}). From Equation (4), the competitiveness hypothesis in terms of the value of the marginal product is given by:
Where:
P_{ Q } = Market price of sawn wood weighted to the national price ($ pt^{-1})
P_{ f } = Input price ($ salary^{-1}, $ capital^{-1}) obtained from the production cost (30 % of the production cost for salary and 20 % of the production cost for capital)
β_{ 0 } , β_{ f } , γ_{ j } , δ_{ k } = Function parameters
From Equation (4), it is also possible to construct the competitiveness hypothesis of the CFE as a function of the MPV for labor (L):
In a similar way, the competitiveness hypothesis for the CFE as a function of the MPV for capital (K) is:
Where:
PL = Labor price
PK = Capital price
PVD = Price of unit of wood volume
With expressions (11) and (12) the hypotheses for MPV of inputs L and K and VD were tested to determine national and state competitiveness, respectively. To contrast the hypotheses, the Wald test for non-linear restrictions (^{Greene, 2011}) was used by means of the R statistical program (^{R Core Team, 2020}).
Additionally, the hypotheses of Ho: β_{ k } +β_{ L } = 1 were tested to determine constant returns to scale for inputs K and L (^{Salvatore, 1983}; ^{Gould and Lazear, 1998}).
Results
Production functions
The expressions of the final production functions derived from models 6, 7 and 8, given by models I, II and III are listed below:
The values of the parameters per variable for the production functions, the level of significance, the result of the statistical tests and the hypotheses are shown in Table 1; the p-value is indicated in parentheses.
Variable/test | Model | ||
---|---|---|---|
I | II | III | |
ln L | 0.690 (0.0)*** | 0.475 (0.0)*** | 0.442 (0.0)*** |
ln K | 0.795 (0.0)*** | 0.320 (0.0016)** | 0.252 (0.0095)** |
ln VD | 0.481 (0.0)*** | 0.520 (0.0)*** | |
FL1 | 0.267 (0.0801) | ||
FL2 | 0.781 (0.001)*** | ||
FL3 | 0.369 (0.029)* | ||
Constant | -10.371 (0.0)*** | -6.382 (0.0)*** | -5.724 (0.0)*** |
Statistics | |||
R^{2} | 0.816 | 0.848 | 0.845 |
F_{ 0 } ^{ a } | 0.988 (0.503) | 0.990 (0.635) | 0.984 (0.248) |
Bartlett/Levine^{ b } | 14.685 (0.1) | 1.475 (0.168) | 1.323 (0.235) |
Stadistical test | |||
F_{ 1 } ^{ c } | 23.86 (0.0)*** | 2.93 (0.0865) | 8.56 (0.005)** |
IMg_{ L } -P_{ L } ^{ d } | 2117.497 (0.392) | 642.42 (0.012)* | 297.183 (0.138) |
IMg_{ K } -P_{ K } ^{ d } | 5.962 (0.471) | 0.752 (0.181) | 0.752 (0.960) |
IMg_{ VD } -P_{ VD } ^{ d } | -708.236(0.0)*** | -828.57 (0.0)*** |
^{a}F_{ o } = Shapiro-Wilk normality test, normality is not rejected (p-value> 0.001); ^{b}Homoscedasticity test of variances that indicated that the variance of the residuals is constant (p-value> 0.001), for models II and III the hypothesis of homoscedasticity is not rejected; ^{c}Hypothesis test Ho: β_{ L } + β_{ K } = 1; ^{d}Hypothesis test: PmgL-P = 0 for aggregated data at the national level; * p <0.05; ** p <0.01; *** p <0.001.
The statistics of the hypothesis test for the MPV at the state level for the labor (L) and capital (K) variables of Model I, are shown in Table 2, with Ho: Pmg_{ L } -P_{ L } = 0 and Ho: Pmg_{ K } -P_{ K } = 0, respectively.
State | MPV _{ L } estimation (p-val) | MPV _{ K } estimation (p-val) |
---|---|---|
Chiapas | 1 115.438 (0.358) | 3.710 (0.497) |
Chihuahua | 1 034.867 (0.362) | 6.386 (0.443) |
Durango | 4 031.075 0.397 | 7.680 (0.471) |
Edo. México | 3 147.397 (0.397) | 11.999 (0.430) |
Jalisco | 2 219.260 (0.372) | 5.462 (0.479) |
Michoacán | 1 943.497 (0.390) | 4.186 (0.504) |
Oaxaca | 1 624.518 (0.424) | 1.440 (0.637) |
Puebla | 2 365.610 (0.385) | 6.181 (0.469) |
Quintana Roo | 3 153.318 (0.373) | 7.020 (0.466) |
Veracruz | 3 092.774 (0.390) | 8.878 (0.449) |
*p<0.05; **p<0.01; ***p<0.001.
The statistics of the hypothesis test for the MPV at the state level for the labor (L), capital (K) and VD variables of Model II, are shown in Table 2, with Ho: Pmg_{ L } -P_{ L } = 0 and Ho: Pmg_{ K } -P_{ K } = 0, respectively.
Table 4 shows the hypothesis test statistics for MPV at the state level for the L, K and VD variables of Model III, with Pmg_{ L } -P_{ L } = 0; Ho: Pmg_{ K } -P_{ K } = 0; Ho: Pmg_{ VD } -P_{ VD } = 0, respectively. Unlike Model II, in this model the effect of the legal figure variable at the state level was tested and it was statistically non- significant.
State |
MPV
_{
L
} estimation (p-val) |
MPV
_{
K
} estimation (p-val) |
MPV
_{
VD
} estimation (p-val) |
---|---|---|---|
Chiapas | 195.653 (0.040)* | -0.1744 (0.491) | -346.505 (0.0009)*** |
Chihuahua | 320.119 (0.053) | 0.884 (0.132) | -408.536 (0.0005)*** |
Durango | 1 178.74 (0.006)** | 1.0442 (0.150) | -716.938 (0)*** |
Edo. México | 377.987 (0.195) | 1.2909 (0.075) | -46.939 (0.799) |
Jalisco | 356.280 (0.045)* | 0.0578 (0.876) | -53.295 (0.723) |
Michoacán | 507.136 (0.014)* | 0.1563 (0.698) | -648.341 (0)*** |
Oaxaca | 461.268 (0.001)*** | -0.4049 (0.056) | -776.435 (0)*** |
Puebla | 609.375 (0.005)** | 0.6137 (0.205) | -787.506 (0)*** |
Quintana Roo | 927.197 (0.001)*** | 0.8459 (0.146) | -4007.601 (0)*** |
Veracruz | 784.274 (0.009)** | 1.2457 (0.064) | -791.833 (0)*** |
*p<0.05; **p<0.01; ***p<0.001.
State | MPV _{ L } estimation (p-val) | MPV _{ K } estimation (p-val) | MPV _{ VD } estimation (p-val) |
---|---|---|---|
Chiapas | 63.298 (0.383) | -0.538 (0.002)** | -537.153 (0)*** |
Chihuahua | 147.292 (0.227) | 0.091 (0.827) | -557.230 (0)*** |
Durango | 698.691 (0.057) | 0.293 (0.595) | -771.934 (0)*** |
Estado de México | -208.213 (0.213) | -0.017 (0.963) | -591.969 (0)*** |
Jalisco | 91.627 (0.471) | -0.4343 (0.069) | -402.964 (0.004)** |
Michoacán | 267.964 (0.116) | -0.2887 (0.334) | -760.214(0)*** |
Oaxaca | 378.242 (0.016)* | -0.548 (0.004)** | -758.686(0)*** |
Puebla | 283.657 (0.122) | -0.044 (0.901) | -896.420(0)*** |
Q. Roo | 525.086 (0.033)* | 0.122 (0.777) | -4253.510 (0)*** |
Veracruz | 248.478 (0.272) | 0.201 (0.653) | -945.969 (0)*** |
*p<0.05; **p<0.01; ***p<0.001.
Discussion
In Model I the L and K variables in the group of production factors were highly significant (p-value <0.001). In addition, in Model II, other variables of this type that determined productivity in the CFEs were VD and L, while variable K was significant at 0.16 % (p-value <0.05). CA, CM, CI, PO and PTD had no effect on productivity (p-value> 0.05), which could be explained by the fact that they do not have a direct relationship with productivity, as they rather refer to the result of market strategies, of technological improvements and gender quota.
The coefficients in a function of the Cobb-Douglas type are the elasticities of the inputs L and K in Models I, II and III (Table 1), and represent the percentage change in the level of output (Q) versus percentage changes in labor and capital. The elasticities of inputs L and K to produce a level of output Q (Model I, Table 1), show greater statistical significance than when other variables such as VD that affect production and productivity are added to the model (Model II, Table 1). This is relevant if it is decided to use models with more variables that explain the effect on the production of inputs as possible productive improvements in the use of factors. The statistical significance of K variable decreases when adding other variables such as VD and FL (models II and III, Table 1).
For model III, the factors related to the legal figure (private property and society) represent the percentage increase in the production of sawn wood of an CFE, so that for private companies: (e^{0.781} - 1) 100 = 118 % , while for the CFE with a legal status of society: (e^{0.369} - 1) 100 = 44 %. This is relevant since ejidos and forest communities gather more than 85 % of the forest property regime, in regard to small property and society. The variables FL1, S, and C had no effect on the productivity of the CFE (p-value> 0.05). In future analyzes of this type, it is recommended that monetary values be used for S instead of the number of subsidies.
Regarding the analysis of the MPV for L and K with the data added at the national level, the hypothesis Ho was rejected: Pmg_{ L } -P_{ L } = 0 for Model II (Table 1) with a level of significance of 0.1 % (p-value < 0.05). It was also determined that there is no statistical significance for the hypotheses Ho: Pmg_{ L } -P_{ L } = 0 and Ho: Pmg_{ K } -P_{ K } = 0 (p-value> 0.05) in the analysis of MPV at the state level (Model I, Table 2). For Model I (Table 3) when determining the competitiveness of the CFEs, Ho was rejected: Pmg_{ L } -P_{ L } = 0 in the CFEs of the states of Chiapas, Jalisco and Michoacán (p-value <0.05), Durango, Puebla and Veracruz (p-value <0.1), Oaxaca and Quintana Roo (p-value <0.001). When obtaining an estimated value greater than zero (Table 3), the interpretation is that these are EFCs that are not competitive and underuse input L, which means that the MPV of L is higher than the market price of resource L. For Model III, Ho is rejected: Pmg_{ L } -P_{ L } = 0 in the CFEs located in the states of Oaxaca and Quintana Roo (p-value <0.05). In a similar way, Ho: Pmg_{ K } -P_{ K } = 0 is rejected for the CFEs located in Chiapas and Oaxaca (p-value <0.01).
Regarding the analysis of MPV for VD in Models II and III with data added at the national level, Ho is rejected: Pmg_{ VD } -P_{ VD } = 0 with a significance level of 0.1 % (p-value <0.001). Specifically, for Model II, Ho is rejected: Pmg_{ VD } -P_{ VD } = 0 for all states (p-value <0.001), except the State of Mexico and Jalisco, in which no statistical significance was obtained.
The CFEs located in the states of Chiapas, Chihuahua, Durango, Michoacán, Oaxaca, Puebla, Quintana Roo and Veracruz when obtaining an estimated value lower than zero (Table 3) it is interpreted an overuse of the VD input, which means that the MPV of VD is lower than the market price of the VD resource. For Model III, Ho is rejected: Pmg_{ VD } -P_{ VD } = 0 for the CFEs located in the states of Chiapas, Chihuahua, Durango, State of Mexico, Jalisco, Michoacán, Oaxaca, Puebla, Quintana Roo and Veracruz (p-value <0.001) therefore, such CFEs are not competitive in the use of the VD resource (Table 4).
The relationship of the MPV and the cost of the factor is useful to determine the competitive use of resources, although no statistical significance was found to determine that there is non-competitive use of input L and K at the national level for Models I and III, also for input K of Model II. This suggests that there is no evidence of the under or overuse of both inputs in the production process, consistent with the maximization of the company's income. This result contrasts with that obtained by ^{Frey et al. (2019)}, who determined that CFEs are competitive in resource use and performance at scale.
The statistical results of variance of the aggregated data and at the state level indicate that they are not significant. However, when comparing the aggregated data by state for model II, it was observed that Chiapas, Jalisco and Michoacán maintain the significance in the use of L at 5 % (p -value <0.5); while Durango, Puebla and Veracruz increase the level of significance to 1% (p-value <0.1) and Oaxaca and Quintana Roo to 0.1 % (p-value <0.001). The State of Mexico and Jalisco in particular do not record statistical significance in the analysis of MPV for VD (p-value> 0.05). The other states keep significance at 0.1 % (p-value <0.001) in a similar way as for the aggregated data. In Model III, only Oaxaca and Quintana Roo preserve significance at 5 % (p-value <0.05) in the MPV analysis for L. Contrary to the statistical results of the aggregated data, Chiapas and Oaxaca registered significance in the MPV analysis for K of 1 % (p-value <0.01); all the states are significant at 0.1 % (p-value <0.001) in the analysis of the MPV for the VD variable.
This behavior may be due to the wide dispersion in the values of the variables as a result of grouping the CFEs by state. For example, for Chihuahua, the annual Q value was: maximum = 4 709.88, minimum = 94.89 and mean = 2 392 Mpt year^{-1}; which is noticeably higher than the production in Puebla whose annual Q value was: maximum = 1 332.02, minimum = 402.70 and average = 771.051 Mpt year^{-1}. While for the 35 CFEs, Q was: maximum = 6 952 380, minimum = 90 956 and mean = 1 613 229 Mpt year^{-1}.
The hypothesis test Ho: β_{ k } +β_{ L } = 1 to determine non-constant returns to scale for inputs L and K and the results of the elasticities of the factors of production L and K, reflect that no model has constant returns to scale (Statistical F_{ 1 } in Table 1). In fact, for Model I an increasing yield to scale was obtained (β_{ L } + β_{ K } < 1); however, it decreases when adding continuous variables (VD, CA, CM, CI, PO and PTD) and nominal (S, CERT and FL) that affect productivity in Models II and III, respectively, so the returns are decreasing to scale for (β_{L} + β_{K} < 1), which means that, on average, CFEs may be operating under diminishing returns to scale in the short term, a trend similar to that described by ^{Niquidet and Nelson (2010)}.
In this study there was high variability of the information of the CFEs analyzed, similar to that mentioned by ^{Cubbage et al. (2015b)}; the only variables with little variability between companies were CA (μ = 0.518, σ = 0.051) and CM (μ = 0.062, σ = 0.083). It is possible that the said variability between companies associated with CI, CO, PO, PTD, CERT influenced so that they had no impact on productivity. For example, the variable CA in Model II had no effect on production; the only continuous variable with an effect on productivity was VD, which is close to that obtained by ^{Frey et al. (2019)} for the variable total inventory of pine and oyamel wood to be used in the CFEs in Mexico.
It must be noted that government support through subsidies and forest certification had no effect on production, which coincides with the results obtained by ^{Frey et al. (2019)} for harvested volume. Although the information of the present study had high variability, the goodness of fit was good for the models, since it fluctuated between 81.60 and 84.60 %.
Conclusions
The Cobb-Douglas model as a particular expression of the production function is useful for constructing economic models that represent production, such as sawn wood in physical units. The economic models developed I, II and III can help define policies to promote the timber industry through the factors with the greatest impact, such as Labor, Capital and Available volume of wood.
It was determined that there is no competitive use of L, K and VD resources for the 35 CFEs analyzed and located in 10 of the Mexican states.
The VD and FL variables (FL1, FL2 and FL3) had an effect on productivity for Models II and III, respectively. The CFEs formed as private companies and social companies provide 118 % and 44 % of the production, respectively. The legal figure of ejido contributes only 30 % in production.
The production functions generated are homogeneous of degree n> 1 with increasing returns to scale for Model I and homogeneous of degree n <1 with decreasing returns to scale for Models II and III.
The continuous variables CA, CM, CI, PO and PTD and nominal (S, CERT) had no effect on productivity. Although the sawing coefficient and installed capacity are related to the technological level of the industry, they did not contribute to increasing productivity. The wood classification variable is more of a strategy to increase the value of wood with little practical effect. The operational positions for women and positions for women in decision-making that are relative to the gender quota, did not affect productivity either; however, in investment projects supported by the World Bank and Conafor those that comply with the certification of good forest management and the gender quota are privileged.
It was not possible to identify the effect of subsidies integrated into a single concept on production because a short period of time (3 years) was analyzed and direct and indirect supports take longer to mature.
Acknowledgements
The first author thanks Conacyt for the scholarship granted to carry out doctoral studies. To Ing. Mario A. Mosqueda Vázquez of the Production and Productivity Coordination in the National Forest Commission (Conafor) who provided part of the information to carry out this investigation.
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Received: November 27, 2020; Accepted: July 27, 2021