## Statistical Modelling for Production, Cost and Profit Functions of Foodgrains: A Quantile Regression Approach

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##### Date

2018-06

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Sher-e-Kashmir University of Agricultural Sciences and Technology of Jammu, Jammu

##### Abstract

Ordinary least square method (OLS) is an efficient method for estimating the parameters under the presence of assumptions of error term. Moreover, the problems like multicollinearity, auto-correlation, outliers, influential observations, heteroscedasticity etc., do occur and then OLS estimates are less efficient. Under these conditions, different regression techniques are advisable but not simultaneously applied. So, in the presence of these circumstances, the most suitable regression technique i.e., Quantile regression(QR) is advisable which have been shifted from mean to the median as a measure of centrality first introduced by Koenkar and Bassett (1978). In this study, the estimation of production, cost and profit functions of rice, wheat and maize crops at national level and in Jammu region have been done through QR due to the presence of outliers, multicollinearity etc. using Cobb-Douglas and also compared with OLS.
The significant parameters obtained from the quantile regression estimation at τ= 0.90 revealed that for production of rice data, the variables area under rice (AUR), quality seed of rice (QSR) and sale of power tillers (SPT) may be maximizing the production of rice; for the cost of cultivation, the variables cost of machine labour (CML) and cost of insecticide (COI) may minimize the overall cost of cultivation of rice. Further, the results for QR profit function at τ = 0.75 revealed that by minimizing the cost of variables i.e; cost of seed (CS), cost of insecticide (COI) and fixed cost (FC), the profit of rice may be maximized. In case of wheat at τ = 0.90, the variables area under wheat (AUW), fertilizer consumption (FC) and electricity consumption (EC) may be maximizing the production. For the cost of cultivation at τ = 0.75, the variables cost of machine labour (CML), cost of seed (CS) and irrigation charges (IC) will minimize the overall cost. And, by minimizing the cost of variables cost of seed (CS) and irrigation charges (IC), the profit of wheat may be maximized. The production function of maize at τ = 0.90 indicated that the variable annual rainfall (AR) may be maximizing the production of maize but it was not possible to increase the annual rainfall, so in alternate to that we have to focus on improving the irrigation facility by making small ponds, canals, tanks etc.; for the cost of cultivation, the variables cost of fertilizer and manure (CFAM), cost of insecticide (COI) and irrigation charges (IC) will minimize the overall cost of cultivation of maize at τ = 0.75. By minimizing the cost of variable fixed cost (FC), the profit may be maximized at τ = 0.90.
Similarly, same methods have been applied for analyzing primary data on two patterns: rice-wheat and maize-wheat. Firstly for rice-wheat pattern, the significant parameters obtained from quantile regression estimation revealed that the variable area under rice (AUR) and will maximize the production of rice at τ = 0.95. The variables cost of transplanting (COT) and cost of fertilizer (COF) may minimize the overall cost of cultivation of rice at τ = 0.90. And, by minimizing the variables cost of harvesting, threshing and winnowing (CHTW) and COF, the profit of rice may be maximized. In case of wheat crops the variables area under wheat (AUW) and fertilizer consumption (FC) may maximizing the production of wheat at τ = 0.95. And, by minimizing the variables COF and cost of labour (COL) the overall cost of cultivation of wheat may be minimized; for profit COF and cost of herbicide (COH) may maximize the profit. In case of maize-wheat pattern, for production, cost and profit functions of maize revealed that the variable fertilizer consumption (FC) will maximize the production of maize at τ = 0.90; cost of seed (COS) may minimize the overall cost of cultivation at τ = 0.90; COS and COF may maximize the profit at τ = 0.95. In case of wheat, the variables area under wheat (AUW) and fertilizer consumption (FC) may maximize the production τ = 0.90; CHTW and COS will minimize the cost at τ = 0.95 and the variables CHTW and COL will maximize the profit of wheat at τ = 0.95.It has been observed that the estimates of parameter through QR are more efficient than the estimates from OLS on the basis of sign, size and significance. Further the constraints have been identified through Garrett ranking. The Box-Jenkins methodology has been applied on the secondary data of production, cost and profit of rice, wheat and maize crops. The different time series models have been developed and best model was selected on the basis AIC and SBIC. For rice production, the model was ARIMA (0 2 2), for cost it was ARIMA (0 1 1) and for profit it was ARIMA (0 1 1). The time series model(s) for production, cost and profit of wheat were ARIMA (1 2 2), ARIMA (0 1 1) and ARIMA (0 1 1) resp. However, the model(s) for production, cost and profit of maize was ARIMA (0 2 2), ARIMA (0 1 1) and ARIMA (0 1 1). The forecasted values for the production, cost and profit of rice for the year 2020-21 may be 110.64 MT, Rs 60495.90 per hectare and Rs 72646.71 per hectare; for wheat it maybe 102.98 MT, Rs 55631.66 per hectare and Rs 13571.49 per hectare; for maize it may be 36.12 MT, Rs 68682.53 per hectare and Rs 43169.25 per hectare.

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