Assessment of growth rate and instability analysis of rice cultivation in some selected states of India

Introduction

Rice (Oryza sativa L.) is an important and widely consumed staple food grain crop, which is rich in carbohydrates, and several other vital nutrients. It holds an eminent position in the diet of Indian subcontinent. Kumar et al. (2025) [5] . It is most important and widely consumed staple food crop in the Poaceae family and its native is South India. is commonly grown in the foothills of the far Eastern Himalayas. Rice is rich in carbohydrates, source of protein and it contains various vitamins, such as thiamin, niacin and minerals. It is a highly nutritious cereal comprising of carbohydrate, protein, fiber and other vital nutrients. In India, it is mainly grown in kharif season. More than 80 percent of people in Asia eat rice. India is also the second largest producer and consumer of rice in the world. Sunandini et al. (2020) [14] . India is the second-largest producer of rice in the world, after China with a production of 135.76million tons, area 47.83 million hectares and yield 2.84 tons/hectare of rice during the year 2022-23. Moreover, the largest producing state of rice in India was Uttar-Pradesh (16.14 million tons) during the concerned year followed by Telangana (15.88 million tons), West Bengal (15.48 million tons), Punjab (12.99 million tons), Chhattisgarh (9.81 million tons), Odisha (8.25 million tons) and Andhra Pradesh (7.94 million tons) during the concerned year (Source: Economics, Statistics and Evaluation Division, DA&FW, Govt. of India).

The largest area of rice in India was Uttar-Pradesh (5.90 million tons) during the year 2022-23, followed by West Bengal (5.07 million hectares), Telangana (4.66 million hectares), Odisha (4.06 million hectares), Chhattisgarh (3.77 million hectares), Punjab (3.10 million hectares), and Andhra Pradesh (2.13 million hectares) during the concerned year (Source: Economics, Statistics and Evaluation Division, DA&FW, Govt. of India). The rice crop plays a vital role in global trade and significantly contributes to national economic growth. As a result, many scientists have concentrated their research efforts on studying rice cultivation. Lekshmi and Venkataramana (2020) [7] conducted a study on the growth and instability of paddy cultivation in Kerala, focusing on area, production, and productivity. They employed an exponential growth model for forecasting purposes. Sunandini et al. (2020) [14] analyzed the trends, growth patterns, and instability in the area, production, and productivity of rice in Andhra Pradesh. They applied the compound growth rate and coefficient of variation to calculate the annual growth rate and measure instability. Mishra et al. (2021) [8] employed both simple ARIMA and ARIMAX models incorporating crop inputs into the ARIMA framework to forecast rice production. The ARIMAX model outperformed the simple ARIMA in terms of accuracy. The study highlighted future trends in rice production and identified key factors influencing www.extensionjournal.com productivity. Nazir et al. (2021) [9] estimated rice yield at different phenological stages using hyper-temporal vegetation indices derived from time-series Sentinel-II satellite imagery. Various vegetation indices were employed to predict paddy yield, and the accuracy of the predictions was assessed using RMSE and MAPE statistical methods. Several other noteworthy contributions towards time series analysis of crops, other than rice have been made by Arti and Rai (2017) [2] , Sanjay et al. (2018) [12] , Kalidas et al. (2020) [3] , Wasnik et al. (2022) [15] , Singh et al. (2021) [13] , Kumar and Menon (2022) [4] , Rana and Kumar (2022) [11] , Kumar et al. (2024) [6] and Prakash et al. (2025) [10] . In recent years, time series analysis of agricultural crops has become essential for examining long-term trends in harvest patterns and for shaping policies related to bulk storage, price setting, transportation, crop insurance, and food security. With this context in mind, the present paper aims to analyze the growth rate and variability in the production, area, and yield of rice in various states of India. The objective of the present paper is to carry out comparative assessment of the instability and growth rate in production, area and yield of rice in India. The analysis is made by computing statistical measures viz., Cuddy-Della Valle (CDV) instability indices and compound growth rates (CGRs) concerning periods (2011-2022).

Data and methodology 2.1 Source of Data

For the objectives of present investigation secondary time series data on rice, belonging to the period 2011-12 to 2022-23, for the states of India are examined. The time series data is collected from the records of Economics, Statistics and Evaluation Division, DA&FW, Govt. of India.

Terminologies and Notations

In India. Also, in most of the states we observe various growth patterns of rice production, namely, increasing growth pattern, decreasing growth pattern, and constant growth pattern. For the present investigation, we have considered three rice producing states of India, viz. Punjab (S1), Andhra Pradesh (S2) and Uttar Pradesh (S3). In these states, the above-mentioned cases of growth pattern are observed. 2) Percentage share of area under cultivation in state is obtained as follows:

Statistical Measures and

3) Percentage share of yield in state is obtained as follows:

where (𝑖 = 1, 2, …, 28) as the India consists of a total of 28 states.

c) Coefficient of Variation (CV)

The coefficient of variation (CV) is a standardized measure of dispersion, and is a unit free quantity. It is generally expressed in terms of percentage as follows:

where denotes the standard deviation of the variable (which may be either of area, production or yield, as the case may be). Also, denotes the mean of the variable X.

d) Instability Index

The Cuddy-Della Valle (CDV) instability index is computed to measure the level of instability in production, area and yield of rice for the states S1, S2 and S3 of India. The instability index is obtained on using the following formula:

Where, represents the coefficient of determination, rice is obtained on fitting linear model to the concerned time series data on production, area and yield of rice for the respective states. Also, represents the coefficient of variation.

e) Compound Growth Rate (CGR)

The CGR in production, area and yield of rice is obtained on using the following formula: www.extensionjournal.com where, = observed value of production, area or yield of rice crops at time 𝑡.

= initial time series value of production, area or yield.

= compound growth rate. The compound growth rate (𝑟) is generally expressed in terms of percentage as follows:

Data analysis and results

The secondary time series data on the production, area and yield of rice in states S1, S2, and S3 of India are demonstrated in Tables 1,2, and 3 respectively. Moreover, the percentage change in production, area and yield of rice for the selected states of India are described in Tables 4, 5 and 6 respectively. It is observed from Table 4, 5, 6, it is revealed that for the year 2022, the percentage change in production of rice is more for the state S1 (i.e., 23.24%) as compared to the state S3 (i.e., 15.12%). However, the percentage change in production is negatively high for the state S2 (i.e., -38.45%). Moreover, the percentage change in area under rice cultivation is positively for the state S1 (i.e., 9.93%), However, the percentage change in area is negatively high for the state S2 (i.e., -48.05%) and S1 (i.e., -0.84%). However, the percentage change in area is negatively high for the state S2 (i.e., -48.05%) and S1 (i.e., -0.84%). From Table 6, it is revealed that for the year 2022, the percentage change in yield of rice is more for the state S2 (i.e., 18.56%) as compared to the states S3 (i.e., 16.17%) and S1 (i.e., 12.17%).

The percentage share of production, area and yield of rice for the year 2022 in various rice producing states of India are depicted graphically in Figures 1,2, and 3 respectively. The compound growth rates (CGRs) for production, area and yield of rice in the concerned states of India, are computed and the findings are presented in Table 9. From Table 9, we conclude that: 1. In state S1, there is a steady growth in production and yield of rice during the period 2011-2022. Furthermore, a slight growth in the area under rice cultivation has been observed. 2. In state S2, there is a rapid decline in production and area under rice cultivation, and a steady growth in the yield of rice has been observed. 3. In state S3, a slight decline in area under cultivation has been observed, whereas a steady growth in production and yield has been observed.

Conclusion

In the present paper, the assessment of growth rate and instability in production, area, and yield of rice is carried out for some rice growing states S1 (Punjab), S2 (Andhra Pradesh), and S3 (Uttar Pradesh) of India is considered. The secondary time series data pertaining to the period 2011-2022 is considered for the study. The percentage change in production, area and yield of rice has been evaluated, by considering the base year as 2011. It is revealed from Section 3 that among all the three states, the percentage change in production, and area of rice is positively high for the state Punjab. Moreover, the percentage change yield of rice is positively high for the state Punjab, Andhra Pradesh in the year 2022.

The percentage share of production, area and yield of rice for the year 2022 in various rice growing states of India are elaborated in Section 3. It is revealed that among all the three considered states, the percentage share of production and area of rice is highest in the state Uttar Pradesh, followed by the states Punjab and Andhra Pradesh. Moreover, the percentage share of yield of rice is highest in the state Punjab, followed by the states Andhra Pradesh and Uttar Pradesh. The level of instability in production, area and yield of rice is measured for the concerned states by using Cuddy-Della Valle (CDV) instability index. It is observed from the results of Section 3 that the production of rice in the state Andhra Pradesh is comparatively more instable as compared to the states Uttar Pradesh and Punjab. Moreover, the area of rice in the state Andhra Pradesh is comparatively more instable as compared to the states Punjab and Uttar Pradesh. However, the yield of rice in the state Uttar Pradesh is comparatively more instable as compared to the states Punjab and Andhra Pradesh. In Section 3, the compound growth rates (CGRs) in production, area and yield of rice are examined for the states considered under study. It is revealed that for state Punjab, the compound growth rates (CGRs) for production, area and yield are positive. Moreover, the state Andhra Pradesh, the compound growth rates (CGRs) for yield is positive, whereas there is a negative growth rate in area and production under rice cultivation. However, the state Uttar Pradesh, the compound growth rates (CGRs) for production and yield of rice are positive, whereas there is a negative growth rate in area under rice cultivation.

The findings of the study provide important information on www.extensionjournal.com the growth rate scenario of rice in Punjab, Andhra Pradesh and Uttar Pradesh. The study can be further extended to some other states of India. Since rice occupies a prominent place in the human diet and has nutritional benefits, potential farmers can maximize their income through rice cultivation as well as integrated farming practices.

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