Introduction

The pecan nut (Carya illinoensis Koch.) is native to northern Mexico and southeast of the United States of America (^{Gray, 1973}). For many years, walnut was one of the main foods of American Indians (^{Tait, 1996}). It is currently used to make a wide variety of products such as sweets, jams, pies, cakes, cookies, ice cream, snow, ingredient for gourmet cooking and traditional cuisine (^{COMENUEZ, 2017}). It maintains a strong competition in the market with substitute nuts such as almond, walnut ‘nuez de castilla’ and hazelnut ‘avellana’ (^{COMENUEZ, 2017}).

The world production of pecan nuts in the 2016-2017 cycle was 118 200 t (peeled base). Mexico is the world’s largest producer of pecan nuts with a total of 58 970 t (peeled base), representing 50% of world production, followed by the United States of America with 52 400 t, representing 44% of the total, both countries participate, together, with 94% of world production (^{INC, 2018}). In Mexico, the states of Chihuahua, Sonora, Coahuila and Durango stand out in nut production with relative shares of 63.14%, 13.39%, 10.83% and 5.74%, respectively (^{SIAP, 2018}).

Mexico is the world's leading exporter with an amount of 34,882 t (peeled base) representing 63% of the total followed by the United States of America with 35% (^{INC, 2018}). In the United States of America, the states of Georgia, New Mexico, Texas, Arizona and Oklahoma stand out with 36.4%, 31.30%, 12.93%, 9.52% and 4.76%, respectively (^{USDA-NASS, 2018}). Faced with the growing demand for walnuts at the global level promoted by China and the increased competition from producer states in Mexico and other countries, it is necessary to improve the production of the Comarca Lagunera and maintain the competitiveness of the region.

However, there are no studies that indicate the factors that need to be strengthened to boost production in the region. It is based on the hypothesis that there are several socioeconomic factors such as training, financing and the size of the garden that directly impact variables such as yields, price, gross income, infrastructure for harvesting and marketing. The Comarca Lagunera, composed of ten municipalities in the northeast of the state of Durango and five in the southwest of the state of Coahuila, contributes 9.5% of the national nut production (^{SAGARPA-LAGUNA, 2018}).

The first plantations of the walnut in the Comarca Lagunera were established in 1948 and the introduced varieties were Western, Wichita, Burkett, San Saba improved, Stuart, Barton and Mahan, predominating the first two (^{Medina and Cano, 2002}). Despite its importance, in Mexico there is very little socioeconomic research in this crop and what exists is a descriptive type. Some are characterization studies of producers (^{Orona et al., 2006}; ^{Luna et al., 2013}; ^{Orona et al., 2013}; ^{Cervantes et al., 2018}), others are profitability studies (^{Lopez et al., 2011}; ^{Retes et al., 2014}) and strategic planning (^{Ojeda et al., 2010}). It is necessary to carry out inferential explanatory studies that allow identifying factors that are related to variables such as income, income, infrastructure and marketing.

In agriculture, as in other economic activities, technological developments are constantly emerging that allow increasing productivity. One way to get these developments to farmers is training. According to ^{Nakano et al. (2018)} training is an effective method to disseminate new technologies, increase productivity and reduce rural poverty. Given that the training has a high cost, the challenge for these authors is to choose the best method at the lowest cost to bring the knowledge to farmers (^{Nakano et al., 2018}). ^{Roco et al. (2012)} identified training as a factor that influences the adoption of agricultural practices for soil and water conservation.

For their part, ^{Pan and Zhang (2018)} state that training in the use of fertilizers is a prerequisite for their scientific management, avoiding excessive applications. One of the dissemination methods followed by international organizations is the preparation of training manuals to improve the productivity and quality of farmers’ products (^{FAO, 2015}). ^{Baloch and Thapa (2016)} assert that the increase in yields depends on many factors, but in particular training increases skills to improve productivity. They affirm that in addition to the extension there are other factors that influence the yields, highlighting the availability of financing to acquire the inputs, availability of labor and the size of the farm.

Similarly, ^{Wossen et al. (2017)} indicate that there is a positive and significant effect of training in technology adoption and family welfare, asserting that the impact is greater when producers have access to formal financing.

The lack of financing is one of the main limitations for the modernization of agriculture, ^{Juarez et al. (2005)} state that financing is of cardinal importance in economic policy to increase production and productivity of the various sectors of the economy and to achieve social welfare. ^{Guirkinger and Trivelli (2006)}; ^{Cieza (2012)} argue that limitations in financing hinder the development of agriculture. On the other hand, ^{Chen et al. (2015)} have found that commercial banks have little participation and low interest in financing agriculture, so financing, in terms of provision of inputs and services, comes mainly from the value chain itself.

In that same sense, ^{Trzeciak-Duval (2003)} indicates that for the banking sector to have a greater participation in the economy, it requires favorable macroeconomic conditions, highlighting stability in inflation and in the currency. ^{Tiffen (2006)} mentions that there is also the problem of the culture of non-payment, which is coupled with the absence of incentives for private banks to finance agriculture. ^{Kopparthiy and Kagabo (2012)} argue that access to credit is necessary to acquire inputs, as a way to increase productivity and eradicate poverty.

Another factor of importance in the determination of yields and income is the size of the farm, in our case the size of the garden. ^{Campos and Chaves (2012)} assert that some of the weaknesses of the agrarian sector are the dispersion of supply and the small size of farms. Therefore, they propose the figure of cooperatives in order to concentrate production and obtain economies of scale. ^{Van et al. (1995)} found that large farms tend to make greater use of capital-intensive technologies and have higher management skills, while small ones are labor-intensive, so the former can achieve economies of scale by reducing the costs of production.

In this same sense ^{Sheng et al. (2014)} found that larger units have higher productivity, but not by scale but by changes in production technology. As can be seen, it has been found in various countries and crops that the variables of training, financing and scale of production have an influence on the results of agricultural enterprises. However, in Mexico, in the cultivation of walnut, the existing studies do not address these aspects beyond the descriptive analysis.

The objective of this work was to analyze the relationship of various socioeconomic factors such as training, financing and the size of the garden and its relationship with variables such as yields, price, gross income and infrastructure in the cultivation of walnut and propose measures of public policy to encourage its growth.

Materials and methods

The Comarca Lagunera is located in North-Central Mexico. It is composed of ten municipalities of the Northeast region of the state of Durango and five of the southwest of the state of Coahuila. It is located at an average altitude of 1 139 meters above sea level, a dry desert climate or warm steppe with summer rains and cool winters; the average annual rainfall is 258 mm and the average temperature is 22.1 °C, with ranges of 38.5 °C as the maximum average and 16.1 °C as the minimum average (^{García et al., 2009}).

To obtain the information, a survey was applied in 2014 to a random sample of 27 gardens distributed in the municipalities of Francisco I. Madero, San Pedro de las Colonias, Torreón and Matamoros, in the state of Coahuila and in Tlahualilo, Gómez Palacio, Lerdo, Nazas and Rodeo of the state of Durango. The sample was taken from the pattern of walnut producers obtained from the Local Plant Health Board of SAGARPA. The questionnaire was composed of 23 questions, divided into the following blocks: general characteristics of the garden, technological aspects of the management of the garden, training received, infrastructure available, financing for production and marketing, organization of producers and marketing.

Simple random sampling (^{Fuller, 2009}) was used to calculate the sample.

Where: n= sample size; t= 1.96 with α= 0.05; S²= 13 022 is the variance obtained from data from a previous sample of the price variable of the nut to the producer; d= 1.5 is the level of precision of the estimate or the distance desired by the researcher who, at most, moves away from the reference variable, in this case the producer price and N= population size (396 orchards). The calculation of the sample was 21 questionnaires; however, 27 were applied to improve the level of precision of the results.

The data were analyzed using the one-way analysis of variance. The following factors were used as factors: 1) training (receives vs. does not receive training); 2) financing (receives vs does not receive financing); and 3) the size of the garden. In the latter case, two strata were managed: a) up to three hectares; and b) more than three hectares. These strata are the ones that, according to field extension technicians and inferential statistics, showed that they made the difference between the variables analyzed. Of the 27 questionnaires applied, 16 went to orchards of up to three hectares and 11 to orchards of more than 3 ha. Following the stratified sampling, this keeps proportionality with the pattern of orchards of the Comarca Lagunera where 63% are up to 3 ha and 37% more than three hectares, with a small difference in relation to the sample due to adjustments at the time of work of field.

According to ^{Lind et al. (2004)} and ^{Levin and Rubin (2010)} when the samples are small (less than 30 observations) it is recommended to use the student’s ‘t’ statistic with (n₁+n₂)-2 degrees of freedom, where n₁ and n₂ are the sizes of the two samples and since the information was obtained by means of a survey, a maximum significance level α= 0.1 was used (^{Kazmier, 1998}). The calculations were made in the statistical package SPSS version 20.0.

Results and discussion

According to the theory, variables such as training, financing and the size of the garden are determining factors for aspects such as yield, sale price, marketing method, infrastructure and income, among others. The results of the analysis for the walnut in the Comarca Lagunera are presented below.

Conclusions

Receiving training is a significant factor in the variables of sales price, proportion of walnut sold in bulk and infrastructure for marketing. In the cases of the means of yield and income per hectare, they were also higher for orchards that received training, although without being significant, but of economic importance for the producers.

The most important factor was financing. In four of the five contrast variables, highly significant statistical differences were found, highlighting sufficient and timely resources to have a better management of the orchard, which in this case was reflected in a yield that almost doubles that of those orchards without financing. The orchards that received financing presented higher revenues, better infrastructure and higher percentage of walnut sold in a selected way. The orchards of size superior to 3 has, registered superior values in the sale price, the proportion of walnut commercialized in bulk of form selected and the infrastructure for commercialization. The means of yield and income per hectare were also higher for large orchards, although without being statistically significant.

The relevance of the size of the orchard makes it possible to recommend to the small ones, who need to organize themselves to achieve economies of scale, to make consolidated purchases of inputs and to increase the negotiation capacity in the sale of walnuts. The results obtained from the orchards that received training and financing make it possible to recommend to public institutions and producer organizations to strongly promote training and obtaining financing, especially for small producers, which will result in higher nut yields, an increase in the sale price and in better income for the producers.