Introduction

Grain corn is an important crop in human and livestock feed for Mexico, with two main types of corn being planted: yellow corn (MA) and white corn (MB), with similar biological and genetic characteristics. However, in the market they present a differentiation in terms of prices, where the price of the MA is lower than the price of the MB. Also, from an external point of view there are two approaches that influence the perception of the two types of corn, a first approach is that both types of corn are complementary and the second that they are substitutes.

Under the first approach, the MB is used primarily for human consumption, which is transformed for the preparation of inputs for food and contributes to food security, while the MA is used for the manufacture of balanced feed for livestock and use industrial (^{SIAP, 2007}), therefore, in this sense both types of corn are not replaced, but could be described as complementary.

According to ^{FIRA (2015)}, in 2014, 23.27 million tons of corn were produced in Mexico, of which 10.4% of the total production represents the MA, while 89% of the production represents the MB, the latter highlighting the almost self-sufficiency for the country and main producer in the world.

Regarding exports, Mexico in the period 2005-2016 exported 3.5 million tons of corn, of which 99.6% were MB destined mainly to Venezuela, El Salvador, the United States of America, Colombia and South Africa; while 0.4% were from MA consigned to the United States of America, Canada, Cuba, the United Kingdom and Denmark (Table 1).

On the other hand, imports for the same period were 99.7 million tons of corn, of which 92.5% correspond to MA from the United States, Brazil, Argentina, Canada and Belize, while 7.5% correspond to MB originating in the United States of America, Mozambique and South Africa, ratifying that Mexico is a net importer of MA (Table 2).

In addition, the import of MA affects the producer price in Mexico of MB (and that of MA), causing a downward effect on the domestic price of corn, determining that the MA and the MB are implicitly substitutes under the second approach (^{Contreras, 2008}; ^{García et al., 2011}; ^{Martínez and Hernández, 2012}; ^{Moreno et al., 2016}).

In order to recognize the degree of substitution between MA and MB, the present work estimates the elasticity of substitution between both types of corn. The main hypothesis to be tested is that the elasticity of substitution between MA and MB is equal to zero.

Methodology

The elasticity of substitution is a concept originally introduced by Hicks (^{Binger and Hoffman, 1998}), it establishes the proportional change in the ratio of quantities for the proportional change in the price ratio:

This is a measure of the degree of curvature of an indifference curve, by detecting the speed at which Qi is changed by Qj when Pj rises relative to Pi. When two goods are substitutes γij is delimited by (0,∞), a substitution elasticity of 0 implies that the goods Qi and Qj are foreign or are simply not substitutes, they can also be referred to as complements (^{Varian, 2010}). On the other hand, if σij is infinite this implies perfect substitution. In an empirical situation, it may turn out that σij is negative, this indicates absence of substitution or that there are complementary goods.

Table 3 shows the information obtained from SIAP regarding prices and quantities of corn by variety, the price of yellow corn is on average approximately 7% lower than the price of white corn; likewise, the amount of white corn is on average 85% of the total production for both varieties. What sustains that the corn market in Mexico is dominated by white corn.

The substitution approach is generally approached through an aggregate function, for example, that of constant substitution elasticity (^{Berndt, 1976}; ^{Caddy, 1976}). However, in the present case, the total of 15 observations obtained is limited, which prevents the estimation of the elasticity of substitution through econometric methods with an aggregate function. Therefore, a direct calculation of the quotient of logarithmic differentials was implemented in the following way:

Where: σ^ab is the elasticity of substitution of yellow corn for white of period t-1 to t, LnQa/Qbt-LnQa/Qbt-1 is the percentage change in the ratio of quantities between period t and t-1, LnPb/Pat-LnPb/Pat-1 is the percentage change in the price ratio between period t and t-1. Note that in this way, we obtain a point estimator of the substitution elasticity σ^ab for 2 periods of yellow corn for white corn, with the purpose of having a global estimator, we take the arithmetic average of the adjacent logarithmic differentials per period. Also, note that σ^ab=σ^bba; that is, the elasticity of substitution is a measure that expresses symmetry, therefore, the elasticity of substitution of MA per MB is the same as that of MB per MA.

For the first case, we have a variation period by period, the interest is to measure the distance of the average with respect to 0, this is done using a test of t under the null hypothesis that the elasticity of substitution is 0; that is, the following hypothesis set is contrasted:

A second form of estimation was obtained from the following regression (^{Battese and Sohail, 1976}; ^{Kwan, 2007}):

For this case, θ1 is the estimator of the elasticity of substitution, where both the value of the point estimator of θ1 and the contrast of the following set of hypotheses are interesting:

The estimate of θ1 was obtained through ordinary least squares, while the aforementioned hypothesis test was performed with the t statistic (^{Greene, 2004}).

Results

For the first case, the direct estimation of the estimated elasticity of substitution was obtained a point value of -7.5163, with an estimated deviation of 18.1446 and a t-statistic of -0.4142 for the set of hypotheses referred to. For the second case, the minimum quadratic estimate of the substitution elasticity estimator resulted in -0.8466 with a standard deviation of 0.902, resulting in a hypothesis of t-statistics of -0.9386 for the hypothesis set.

In both cases the null hypothesis is not rejected, that is, the elasticity of substitution from MA to MB is equal to zero. Regarding the probability value, this is 0.6854 and 0.3651 respectively, where a value higher than 0.05 is confirmed, which does not reject the null hypothesis and therefore its elasticity is equal to zero (Table 4). These results from a point of view between the use of yellow corn and white corn, allow concluding with the available data of MA and MB that these show a behavior of complementary goods. On a non-agricultural level (^{Kwan, 2007}), it obtains positive substitution elasticities for private consumption and government consumption for East Asian countries, positive and high substitution elasticities are obtained by (^{Papageorgiou et al., 2013}) for productive inputs.

According to the above, it is reaffirmed that the approach where the two varieties of corn are complementary, so the result encourages to deepen what is found with respect to the price depressant effect of corn imports, being these predominantly in MA. That is, the effect of imports primarily of MA have an effect on the domestic price of domestic MA, the effect on the price of MB is uncertain given the complementarity of varieties found here. Therefore, the effect of imports on the domestic corn price may refer to an effect on the average price of both types of corn.

Conclusions

It is necessary to have more data to give a robust answer to the problem of elasticity of substitution from MA to MB, with the available data of quantity and price it is concluded that both types of corn are characterized as complementary. This makes it imperative to refocus the problem of imports of corn and its effect on the domestic price of the same. If both types of corn are complementary and MA is primarily imported, then how is this transferred to the MB price.