Introduction

World rice production from 2016 to 2022 registered an average annual growth rate (AAGR) of 0.8%, which meant an increase of 36.1 million metric tons (Mt) during the period. China has historically been the world’s leading rice producer. In 2022, global rice production surpassed 776.4 million Mt, with China and India being the main producers with 26.85 % and 25.27 %, respectively, followed by Bangladesh (7.37 %), Indonesia (7.05 %), Vietnam (5.5 %), Thailand (4.42 %), Myanmar (3.18 %), the Philippines (2.54 %), Cambodia (1.5 %), Pakistan (1.41 %), Brazil (1.39 %), and Japan (1.33 %). Mexico accounted for only 0.03% of global production. Among these countries, India recorded the highest AAGR (2.98 %) from 2016 to 2022, followed by Cambodia (2.62 %) and Bangladesh (2.11 %), while Myanmar experienced the lowest rate (-0.92 %) (^{Food and Agriculture Organization of the United Nations (FAO), n. d.}).

In 2022, rice exports from the five main exporting countries reached 2.78 million tons, which represented only 0.36 % of global production. The United States led the export market with 31.55 %, followed by Brazil (30.8 %), India (15.1 %), Uruguay (9.38 %), and Paraguay (4.29 %). Regarding imports, the top five importing countries in 2022 acquired 1.99 Mt (0.26 % of global production), with Vietnam (18.9 %), Nepal (14.77 %), Mexico (13.53 %), Venezuela (9.62 %) and Costa Rica (5.73 %). From 2016 to 2022, Vietnam experienced the highest AAGR in imports at 72.32 %, followed by Nepal (25.82 %) and Costa Rica (9.53 %), while Mexico registered a decrease in its import growth rate of 8.53 % (^{FAO, n. d.}).

In Mexico, the area planted with rice in 2022 was 37994 ha, of which 78.51 % was under irrigation and the rest was planted under rainfed conditions. The largest irrigated area was recorded in Nayarit (37.41 % or 11160 ha), followed by the states of Campeche (19.61 %), Michoacán (12.96 %), Jalisco (10.83 %), Veracruz (6.52 %), and Tamaulipas (6.15 %), totaling 27887 ha. The largest rainfed areas were in Campeche (30.74 %), Veracruz (23.41 %), Colima (22.4 %), Nayarit (15.52 %), and Tabasco (3.64 %), which together accounted for 7815 ha (^{Servicio de Información Agroalimentaria y Pesquera (SIAP), s. f.}).

In 2022, Mexico’s rice production reached 246317 t, with 84.83 % coming from irrigated areas and 15.17 % from rainfed areas. The leading irrigated producers were Nayarit (32.7 %), Campeche (16.32 %), Michoacán (16.01 %), Veracruz (10.8 %) and Jalisco (10.27 %), producing a total of 179913 t. The main rainfed producers were Campeche (32.75 %), Colima (26.27 %), Veracruz (21.92 %) and Nayarit (14.54 %), contributing a total of 35683 t (^{SIAP, s. f.}).

In terms of yield per hectare of rice in 2022, the national average was 7.6 t/ha for irrigated rice and 3.71 t/ha for rainfed. There were significant yield differences among producing states within each water regime, The irrigated yield range was 6.27 t/ha (Veracruz 11.6 t/ha and Colima 5.33 t/ha), while the rainfed range was of 3.71 t/ha (Colima 5.37 t/ha and Chiapas 1.66 t/ha) (^{SIAP, s. f.}).

From 2016 to 2022, both the planted area and rice production in Mexico experienced declining AAGRs of 1.44 and 0.51 %, respectively, which indicates an increased dependence on foreign rice. In 2022, the agricultural sector’s total national production in Mexico reached 884876 million pesos, with rice accounting for only 0.17%. While these figures indicate a low economic importance of rice in Mexico, it ranks fourth among dietary staples (after corn, wheat, and beans), with an annual per capita consumption of 8.9 kg (^{SIAP, s. f.}). This also reflects the country’s dependence on imports, registering 431,427 tons in 2022, which represented 1.75 times the national production (^{FAO, n. d.}). This highlights the need to strengthen trade relations with supplier countries such as Uruguay, Paraguay, India, Thailand, and Cambodia, with which Mexico still maintains tariff barriers, and to improve internal productivity conditions (^{Favila Tello & Herrera Corral, 2023}).

The hypothesis was that the supply of irrigated and rainfed rice is positively influenced by producer prices, water availability for irrigation, and average rainfall, and negatively affected by the prices of competitive products and inputs, with the effect on price transmission being less than proportional. The objective of this study was to evaluate the factors affecting rice production in Mexico by technology type, differentiating between irrigation and rainfed systems.

Materials and methods

A dynamic simultaneous equations model was formulated, composed of two Nerlove supply equations, three price transmission models, and an identity. It used annual data from 1980 to 2022 on rice production in Mexico (differentiated by technology type), as well as the prices of competing products, tradable inputs, and the climatic variables that determine them.

Newlove’s dynamic econometric models are autoregressive (AR) and/or distributed lag (DL) models. A distributed lag model is a regression analysis that contains time series information, where the regression model incorporates both the current values and lagged (past) values of the explanatory variables (equation 1). An autoregressive model includes one or more lagged values of the dependent variable among its explanatory variables (equation 2) (^{Gujarati & Porter, 2010}):

Y _t = α + β ₀ X _t + β ₁ X _t-1 + β ₂ X _t-2 + _ut equation 1

Y _t = α + βX _t + γY _t-1 + u _t equation 2

Both are considered dynamic models because they track the trajectory of the dependent variable over time, relative to its past values, a common practice in econometric analysis.

In economics, the effect of a variable Y (dependent) on another variable X (explanatory) is rarely immediate and requires time to manifest. Y responds to X after a period called a lag. It represents the effect of a unitary change in X on Y at time t and in subsequent periods (equation 3) (^{Gujarati & Porter, 2010}):

Y _t = α + β ₀ X _t + β ₁ X _t-1 + β ₂ X _t-2 + … + β _k X _t-k + u _t equation 3

The above function represents a distributed lag model with a finite lag of K periods. The coefficient β₀ is the short-run or impact multiplier, showing the change in the average value of Y caused by a unit change in X within the same period. If X remains unchanged, (β₀ + β₁) represents the average in Y in the next period, (β₀ + β₁ + β₂) in the subsequent period, and so on. This is referred to as the long-run or total distributed lag multiplier. A system of simultaneous equations can be expressed in condensed matrix form (equation 4), as proposed by ^{Gujarati & Porter (2010}).

ΓY _t + ΒX _t = Ε _t equation 4

Where: Y_t = Vector of endogenous variables of the model; X_t = Vector of predetermined variables, plus the ordinate to the origin; G = Matrix of structural parameters associated with the endogenous variables; B = Matrix of structural parameters associated with the predetermined variables; E = Vector of random error terms. The vectors Y_t and E_t are of order m x 1, where m is the number of endogenous variables in the model. For its part, G is a square matrix of order m x m. In turn, B is a matrix of order k+1 x m, where k is the number of lagged exogenous and endogenous variables of the model plus the ordinate to the origin; In general, k may or may not be equal to m. Since the inverse of G exists, it is possible to derive the reduced model of the system (equation 5).

Y _t = ΠX _t + V _t equation 5

Where: Π = -Γ^-1 B is the matrix of the parameters of the reduced form; Vt = -Γ^-1 Et is the matrix of the perturbations of the reduced form.

Results

The five regression equations exhibited high adjusted coefficients of determination (R2 Adjusted) ranging from 0.87 to 0.94. The F-test results were significant at the 0.01 level, indicating the overall robustness of the models. The Durbin-Watson (WS) statistic values (1.99 to 2.38) indicate a low autocorrelation between the time series, while the Shapiro-Wilk (SW) values per variable (0.94 to 0.99) imply a near-normal distribution. The intercepts of the two supply equations are negative, which indicate the deficit in national rice production (Tables 1 and 2).

The coefficients of the reduced form of the model in relation to the total quantity of rice produced (QPA) are reported in Table 3. The Student’s t-test indicates that the exogenous variables’ coefficients are statistically significant, with signs consistent with the microeconomic theory of supply.

Discussion

Regarding short-run elasticities (2 to 3 years), those calculated in this work were consistent with the aggregate elasticities of agricultural products (including rice) in the short term from 1958 to 1982 obtained by ^{Rao (1989}) for developed and developing countries such as China, India, Bangladesh, Thailand, Malaysia, Turkey, Sudan, the Philippines, Japan, and the United States, which were in the order of 0 to 0.8. Although these are not price elasticities per se, but elasticities respecting the cultivated area, which were higher than the elasticities calculated in relation to the yield.

Based on the economic elasticities estimated in this study with respect to PMRARIR and PMRATER in the short term, if their Average Annual Growth Rates (AAGRs) observed from 2016 to 2022 (7.54% and 8.60%, respectively) continue, irrigated and rainfed rice production are projected to increase by 5.27% and 3.33%, respectively, resulting in overall increases in total rice production in Mexico of 3.47% and 1.14%.

Between 2016 and 2022, PMRMRIR and TEMP recorded AAGRs of 11.79% and 1.02%, respectively, which would lead to reductions in QPA of −7.67% and −3.47%. The negative impact of exogenous variables under irrigation technology-such as PMRFRIRL, PMRLRIR, PMRTRIR, and PMRGRIR-is significantly greater than the effect of their counterparts under rainfed conditions.

It is worth noting that although water is essential for rice cultivation, as rice is known to be a semi-aquatic crop, Mexico faces a significant water scarcity issue. As a result, rice varieties that do not require constant flooding are cultivated, and in rainfed areas, varieties adapted to such water conditions are used.

The price elasticity of irrigated rice production was found to be more inelastic compared to the price elasticity of beans (0.9087) estimated by ^{Guzmán-Soria et al. (2019}), and similar to the elasticity calculated for rainfed bean production (0.3771).

The price elasticity of rainfed rice production was found to be close to the aggregate elasticity of food crops, including rice, which ^{McKay et al. (1999}) found for Tanzania at 0.35 and to the same type of aggregate elasticity calculated by ^{Mundlak et al. (1989}) for Argentina in the period from 1913 to 1984, which was 0.43. Although this comparison between results that are not entirely equivalent is limiting, in terms of economic elasticities, it helps measure the magnitude of change between variables.

In Colombia, ^{Ramírez-Gómez et al. (2004}) found a price elasticity of production for rice of 0.28, using a logarithmic model and annual information from 1970 to 2002; the result of this calculated elasticity is closer to the respective elasticity calculated here for rainfed rice production.

Compared to maize cultivation, the price elasticity of supply of rainfed rice is close to that reported by ^{Cutts and Hassan (2003}) for Zimbabwe (0.3605) and is much higher than that reported for Malawi (0.0924), Mozambique (0.0439), Tanzania (0.0631), South Africa (0.0938) and Zambia (0.0708). The comparison between the economic elasticities of production of maize and rice lies in their importance in the national diet.

Of the price elasticities for wheat, maize and soybean production calculated by ^{Cap et al. (2006}) for some MERCOSUR (South American Common Market) countries, the one calculated for wheat in Argentina (0.429) and maize in Brazil (0.28) are the closest to that found in this work for rainfed rice production and the one calculated for maize in Bolivia (0.62) and wheat in Brazil (0.86) are the closest to that found in this work for irrigated rice production. For 10 Asian countries, ^{Imai et al. (2011}) found price elasticities of supply for agricultural commodities in the range of 0.015 to 0.309, the upper limit of this range being somewhat lower than the two calculated in this work.

Regarding long-run elasticities (5 to 6 years), calculated for aggregate prices (including rice) and individual prices of some agricultural products reported for the period 1958 to 1982 in developed and developing countries such as China, India, Bangladesh, Thailand, Chile, Malaysia, Turkey, Sudan, Argentina, the Philippines, Japan and the USA, ranges from 0.3 to 1.2 (^{Rao, 1989}). The own-price elasticity of rainfed rice supply calculated here was within the range, but the irrigated rice supply was higher (1.4197).

For Tanzania and Argentina, long-run aggregate supply price elasticities of food crops (including rice) were found to be 0.98 and 0.99 (^{McKay et al., 1999}; ^{Mundlak et al. 1989}), which differs from the two larger price elasticities of rice supply calculated in this study; 1.1455 for irrigated rice production and 1.4197 for rainfed rice production. This comparison helps understand the impact and magnitude between these variables.

On the other hand, for Colombia, a long-term price elasticity of rice production of 0.93 was calculated using a logarithmic model (^{Ramírez-Gómez et al., 2004}). This elasticity is closer to the calculated for irrigated rice production in Mexico, which was 1.1455.

Finally, it is worth highlighting that the two long-term own price elasticities calculated in this work (1.1455 and 1.4197) are significantly higher than those for Zimbabwe (0.4484), Malawi (0.1331), Mozambique (0.0667), Tanzania (0.1339), South Africa (0.1519) and Zambia (0.1694) reported by ^{Cutts and Hassan (2003}).

The econometric analysis of rice production in Mexico is relevant, considering that it is the fourth most consumed staple food in the country, and this directly relates to national food security.

Conclusions

The rice supply, both irrigated and rainfed, respond positively to changes in producer prices, water availability for irrigation, and average annual rainfall recorded in the country. Conversely, negative responses were observed to changes in producer prices of competitive goods such as beans, corn, wheat, lentils and chickpeas, as well as inputs such as the price of pesticides and fertilizers.

The total supply of rice in Mexico responds inelastically to changes in the producer price for rice produced under irrigation and rainfed conditions, which partly reflects producers’ inability to increase their rice supply in response to increased demand during the analysis period. The level of own-price inelasticity was found to be higher in the supply of rice under irrigation than in rainfed conditions. This inelastic supply of rice in the country demonstrates that irrigated and rainfed producers are unable to adjust their production in response to price changes. Furthermore, the changes in producer prices of competitive elements that affect the total supply of rice are primarily those registered for corn and wheat, produced under irrigation.

The price transmission effect indicates less than proportional adjustments for the wholesale price on the producer price of irrigated rice and on the producer price of rainfed rice. Significantly, international price changes exert a smaller influence on the wholesale price of rice compared to the impact of transportation costs. Despite the limited influence that the wholesale price or transportation costs have on the producer price of rice, these factors do not constitute sufficient incentives given the limitations on adjusting production capacity in the country.

The research tested the hypothesis that the supply of irrigated and rainfed rice is positively influenced by producer prices, water availability for irrigation, and average rainfall, and negatively affected by the prices of competitive products and inputs, with the effect on price transmission being less than proportional. Based on the results of the model, the hypothesis could not be rejected.

Interests conflict

There is no conflict of interest.