The human capital is considered a propitiating factor for development and economic growth. ^{Schultz (1961)} defines human capital as one that includes qualitative components such as skill, knowledge and similar attributes that affect the individual capacity to perform productive work. Knowledge is integrated into human beings through education, as well as through various forms of informal learning. Some studies indicate that the level of schooling of individuals in a country has a positive effect on the economic growth of gross domestic product (PIB, for its acronym in Spanish) (^{Barro, 1991}; ^{Mankiw et al., 1992}; ^{Benhabib and Spiegel, 1994}; ^{Cohen and Soto, 2007}).

In Mexico, studies on human capital have focused on the general level of the economy; has studied the impact of having a greater degree of studies at the income level (^{Carnoy, 1967}), the relationship between investment in human capital and wage income of individuals (^{Rojas et al., 2000}) more recently, on the significant externalities of human capital at the state level in Mexico (^{Villarreal, 2016}). The objective of this study was to analyze human capital in research and development institutions in the agricultural sector, as well as the relationship between the number of doctorates in agricultural sciences and the value of goods and services produced in the primary sector in Mexico during the period from 1994 to 2011.

Information on the number of researchers working in research and development (R+D) institutions in the agricultural sector in Mexico was obtained from the Agricultural Science and Technology Indicators (ASTI) database of the International Research Institute (IFPRI) (^{ASTI, 2016}), as well as the fact sheets on agricultural R+D indicators for Mexico carried out by Indicators of Agricultural Science and Technology of IFPRI (^{Flaherty et al., 2016}). To perform the analysis of the number of researchers in institutions in the agricultural sector, we used the concept of full-time equivalent researchers (FTE) proposed by ^{Stads et al. (2016)} which takes into account the part of the time that researchers dedicate to specific research and development activities (R+D).

The variable related to the number of human resources trained with postgraduate studies in Mexico during the period 1994 to 2011 was obtained from the censuses on science and technology of the National Institute of Statistics and Geography (^{INEGI, 2016}). While the value of gross domestic product (PIBA, for its acronym in Spanish), measured in millions of pesos at 2008 prices, was obtained from the Banco de México’s economic information system (^{BANXICO, 2016}). The PIBA of the primary sector in Mexico includes the value of goods and services of the agricultural sector: animal husbandry and exploitation, forestry, as well as fishing and hunting activities.

The average annual growth rate (TMCA, for its acronym in Spanish) was used as a tool to analyze the trend in the number of researchers involved in R+D agricultural institutions in Mexico. The formula to calculate it was: TMCA=Vf/Vi1/n-1-1*100 . Where: Vf= final value of the data series; Vi= initial value of the data series; n= total number of years that the series is evaluated.

The simple linear regression model is characterized in that only an independent or exogenous variable is used to estimate or predict the dependent variable (^{Gujarati, 1992}), the model is represented by the following equation.

For all i= 1, ..., n. Where: n= number of observations; the coefficients α and β= are the unknown parameters that indicate respectively, the ordinate at the origin and the slope or coefficient of the regression; ε= is the random perturbation that collects all those facts not observable and that, therefore, are associated with chance. The estimated model was obtained from the following equation.

Where: PIBA= is the value of the production of the gross domestic product of the agricultural sector measured in millions of pesos at 2008 prices; doc= is the number of graduate students graduated from the area of agricultural sciences in Mexico; ε= random error. The hypothesis test proposed for β1 was H0= there is no linear relation between the PIBA and the number of doctorates graduated in the agricultural sciences, against the alternative hypothesis: H1= there is a linear relation between the PIBA and the number of doctorates graduated in the sciences agriculture.

The robustness of the model was validated as follows: the absence of multicollinearity was verified using the tolerance index and the variance inflation factor (FIV). According to ^{Pérez (2005)} a large FIV and a small tolerance index may indicate possible presence of collinearity, so if the value of FIV is equal to 1 they are not correlated. To verify the serial correlation was applied of the residues the Durbin Watson test (DW) (^{Gujarati, 1992}). The ordinary least squares (OLS) method was used to estimate the model. The hypotheses were tested at the 5% level of significance. Finally, the statistical analysis was performed with the Minitab 16 statistical software.

The acquisition and availability of specialized human capital (researchers) in research and development (R+D) institutions in Mexico has suffered different impacts in recent years. On the one hand, during the period 2006 to 2013, the total number of researchers in higher education institutions increased to a TMCA of 4.51% for researchers with doctoral level and 0.67% for researchers with masters level; this represented an increase over the period of 410.3 full-time researchers who joined these institutions. In contrast, the number of researchers with a master’s degree in public research centers and the National Institute of Forestry, Agriculture and Livestock Research (INIFAP) had negative growth rates during the same period, 1.76% for public research centers and 2.67% for INIFAP. This same behavior occurred for the number of researchers with a bachelor’s degree in both R+D institutions. On the other hand, the positive TMCA of researchers with doctoral level has had an increase in the three types of institutions (Table 1).

Fuente: elaboración con base a datos obtenidos por ASTI (2016).

Table 1 Annual rowth of researchers in the agricultural sector in Mexico, 2006-2013. 

These results provide evidence to reaffirm the existence of a low number of researchers at the national level. This is in line with data from the National Council for Science and Technology (CONACYT), which states that the proportion of researchers in Mexico per thousand members of the economically active population (PEA) in 2012 was 0.9, a figure below those of advanced countries, such as Germany with 7.9, or the United Kingdom with 8.2 (^{CONACYT, 2014}).

The estimated model of the relationship between human capital and doctoral studies and the value of agricultural production in Mexico was as follows: PIBA= 1 208 385+1985*doc.

The adjusted coefficient of determination (R²) was 92.6%, which means that 92.6% of the PIBA variability is explained by its linear relationship with the number of doctorates graduated. The results obtained from the table for the Durbin Watson statistic are: Dinf=1.158 (lower limit), Dsup= 1.391 (upper limit). The DW coefficient obtained from the model was 2, which is higher than the upper limit so there is no evidence of correlation of the data. The value of FIV is equal to 1 so the data do not present multicollinearity. To verify the normality assumption, a graphical analysis and the Shapiro-Wilk test were performed, concluding that the residues follow a normal distribution (Table 2).

PIBA=variable dependiente; doc= variables predictoras: n= 18.

Table 2 Results of the application of the linear regressionmodel. 

The F-test was 213.26 and the p-value= 0, so we rejected H0 and concluded that there is a possible linear relationship between the PIBA and the number of doctorates graduated in the agricultural sciences. These results agree with a number of studies that have identified a relationship between education and the level of human capital with agricultural productivity and economic growth (^{Pudasaini, 1983}; ^{Azhar, 1991}; ^{Barro, 1991}; ^{Cohen and Soto, 2007}; ^{Islam et al., 2016}). In this way, improving and increasing the level of human capital involved in R+D institutions in the agricultural sector is relevant in order to achieve greater efficiency of resources for the primary sector in Mexico.

^{Stads et al. (2016)} points out that it is necessary to have scientists at the doctoral level to raise, manage and conduct high-quality research effectively, to communicate with policy-makers, donors and other actors, both locally and through regional forums and to increase the opportunities for institutes to obtain competing funds.