Economic and predictive analysis of millet cultivation in India

Introduction

Millets are small-seeded grasses that can grow in arid and semi-arid regions. They are also referred to as dryland cereals or nutri-cereals. In rainfed farming, millets are resilient to stress and drought and a good source of minerals and nutrients. Millets can survive in a wide range of natural situations. Based on the size of the grain, millets are categorized as Major Millets and Minor Millets such as Sorghum (Jowar), Pearl Millet (Bajra), and small millets such as Kodo Millet (Kodon), Proso Millet (Cheena), Little Millet (Kutki), Finger Millet (Ragi), and Foxtail Millet (Kakun) (Gowri, U.M. et al., 2020) [4] . They are a good source of phytochemicals, minerals, and protein and high in dietary fibre. Millets have a composition of 7-12% protein, 2-4% fat, 65-75% carbohydrates, and 15-20% dietary fibre (Saravand et al., 2022) [16] . Compared to rice, wheat flour, and maize, which provide 64-68 grams of carbohydrates per gram, millets have 60-70 grams. From the perspective of sustainable development, millets have shown to be supportive in reducing the effects of SDG 1: No Poverty, SDG 2: Zero Hunger, SDG 3: Good Health and Well-Being, SDG 5: Gender Equality, SDG 8: Decent Work and Economic Growth, SDG 12:

Responsible Consumption and Production, and SDG 13: Climate Action (Kumari. P. et al., 2023) [11] . India stands as the leading global producer of millets, with 19% of the global production share in 2022. In 2022-23, the cultivated area of millets in India was 12.45 million hectares, with a production of 15.53 million metric tons and an average yield of around 1,247 kg per hectare (Agriculture Statistics at a Glance 2022) [1] . Rajasthan has the highest area under millets cultivation (29.05%) followed by Maharashtra (20.67%), Karnataka (13.46%). In India, per capita millet consumption has decreased significantly from 30.94 kg per year in 1960 to 3.87 kg per year in 2022-2023(FAO, USDA 2023). After the introduction of the National Year of Millets the export value reached from US$ 59 million to US$ 75 million between 2019-20 and 2022-23. During 2022-2023 India experienced a 29.56% increase in export quantity over the previous year (WITS 2023). According to APDA's 2023 report, the UAE ranked first among the top five export destinations in terms of value, with USD 13.33 Mn (17.76%), followed by Saudi Arabia with USD 10.39 Mn (13.67%), Nepal with USD 5.57 Mn (7.35%), Bangladesh with USD 3.69 Mn (4.92%), and Japan with USD 3.37 Mn (4.43%). The year 2018 was designated as the National Year of Millets in an effort to increase promotion and demand. Millets were renamed "Nutri Cereals" in April 2018. On March 5, 2021, the United Nations adopted a resolution designating the year 2023 as the International Year of Millets, with support from 72 nations. (PIB.gov.in.2023) The potential of millets to improve food and nutritional security is not being fully realized, and their cultivation and consumption are decreasing in many countries. With growing emphasis on the consumption of nutritious food on the consumption side, sustainability on the supply-side production, there is a need to highlight the nutritional and environmental benefits of millet to producers, consumers, and decision-makers (Joshi, P.K. et al., 2005) [9] . Analyzing growth trends is important for ensuring a stable supply of millets, evaluating the economic impact on farmers, safeguarding food security, and developing effective agricultural policies (Umagowri et al., 2020) [18] . The instability index addresses challenges related to fluctuating yields and helps to build strength against climatic variations, supporting agricultural diversification and food security initiatives (Jainuddin S. M. et al., 2019) [8] . In India, where the economy heavily relies on agricultural production, making timely and reliable forecasts is essential for stakeholders to make informed decisions (Bellundagi et al., 2016) [2] . Hence, forecasting crop production and productivity is crucial for India's agriculture commodities, as it aids in planning and policy making for future food distribution, export and import decisions, pricing, and administrative measures for storage and marketing of agriculture commodities. The autoregressive integrated moving average (ARIMA) (Paswan et al., 2022) [14] model is widely used for forecasting agricultural produce and prices, which gives accurate and unbiased forecasts. Therefore, the present study was conducted with the following objectives: 1. To assess the growth trends and instability of the millets area, production and productivity in India. 2. To forecast the area, production and productivity of millet in India up to 2023.

Methodology

The data on production were taken from Agriculture Statistics at a Glance 2022 [1] and examined for the period from 1971-72 to 2021-2022. Over the years, India's millet cultivation has faced a significant challenge characterized by declining cultivation area.

The study used the compound annual growth rate (CAGR) and the Cuddy Della Valle instability index of millet cultivation in India.

Trend analysis:

The exponential growth function was used to estimate the growth rates of the selected economic variables and the model is

Yt:: Dependent variable for which growth rate of increase/decrease is estimated (area, production, and yield) A: Intercept (constant) B: Regression coefficient T: Years which take values, 1, 2, …, n Ut: Disturbance term for the year t

The equation Yt = ab t ut was transformed into log linear form for estimation purpose and was estimated using the Ordinary Least Square (OLS) technique. The compound growth rate (g) in percentage was then computed from the relationship, g = (Antilog of ln b-1) * 100

The significance of the regression coefficient was tested by using the 't' test

Instability analysis

In order to study the variability in the area, production and yield of millets, an instability index suggested by Cuddy and Della (1978) was used: The CDVI shows trends and the exact direction of the instability. ARIMA model: The ARIMA model was first introduced by Box and Jenkins in 1976; as a result, this approach is commonly referred to as the Box-Jenkins method in academic literature. The analysis and forecasting of univariate time series data utilizing the ARIMA model are most frequently used. It makes a prediction in response to the linear combination of the values from its own historical time series. Time series models are typically considered to be stationary, meaning that the series mean, variance, and covariance are all constant throughout time. It can be concluded that ARMA (p, q) is used if the time series is stationary. If the series is not stationary, it can be made stationary by differencing it "d" times, in which case the model is known as ARIMA (p,d,q).

Auto-Regressive (AR) Model

The AR model expresses the current value of a time series as a linear combination of its past values (response variable at time lags). The equation for an AR(p) process is:

▪ Yt is the value of the variable (production in '000 tonnes) at time ▪ µ is constant mean ▪ 𝜑1, 𝜑2, . . ., 𝜑p are the autoregressive coefficients to be estimated for lags 1 to p. ▪ Yt-1, Yt-2..., Yt-p are the response variable values at the respective time lags. ▪ 𝜀t represents a predicted error at time t.

Moving Average (MA) Model:

The MA model models the current value of a time series as a linear combination of past forecast errors. The equation for an MA(q) process is:

▪ δ1, δ2, . . . δ q are the moving average coefficients to be estimated for lags 1 to q. ▪ 𝜀t-1, 𝜀t-2, . . ., 𝜀t-q are the error terms from the previous time periods.

ARIMA Model

ARIMA combines both AR and MA models with an integration (I) component to handle non-stationarity. The ARIMA model equation is:

▪ The letters 'p' stands for the number of autoregressive terms, ▪ 'q' stands for the number of lagged forecast errors and ▪ d represents the order of difference or the degree of time series differencing.

A model should be extended with seasonal parameters known as the seasonal ARMA (in the case of stationary time series) or SARIMA (in the case of non-stationary time series) if the model has a seasonality component. SARIMA (p, d, q) (P, D, Q) is an abbreviation for them, where P denotes seasonal autoregressive order, D denotes seasonal differencing number, and Q denotes seasonal moving average order. Time-series data can be fitted to an ARIMA model using the procedures listed below: (Kathayat & Dixit, 2021) [10] .

Identification: Since only stationary data series can be used for estimation, this is the initial step in determining the stationarity of the data series. The arrangement of autocorrelation and partial correlation coefficients gives insights into whether stationarity is present. If the analysis indicates that the model lacks stationarity, the data series can be made stationary through differencing.

Model identification:

To find the values of p and q, analyze the autocorrelation function (ACF) and partial autocorrelation function (PACF). Then, from the set of models, using Akaike's information criterion (AIC) with correction (AICc), choose the optimal ARIMA model. [13] .

The statistical software tool R was used to conduct the statistical analysis for the present study. The ideal ARIMA model was chosen using R's auto.Arima () function. The unit root test and AICc minimization are used in this function to create an ARIMA model using the Hyndman-Khandakar algorithm (Hyndman & Khandakar, 2008) [6] . The Hyndman-Khandakar method only uses the first two stages described above, thus we carried out the other steps on our own. In addition, we tested further models based on the ACF and PACF graphs using the R software.

Results and Discussion

Trends in area, production and productivity of millets. As seen in Figs. 1,2, and 3, the millets when compared to rice and wheat, millets continuously showed declining output and cultivated area growth, while rice and wheat showed increasing trends. Despite government efforts to promote millet cultivation for nutritional value, negative growth in millet cultivation area may be attributed to changing farmer cropping patterns and the millets' lesser significance in consumption practices. It is found that the studies conducted by (Sharma et al., 2022) [17] and (Kumar et al., 2022) [12] also had comparable findings.

CDVI Instability Index

According to the study, compared to rice and wheat, millets such as ragi, sorghum, small millets, and bajra show more variability in area, production, and yield. More instability is seen in area of cultivation of ragi (9.016) and the sorghum (6.858), followed by small millets (5.988) and bajra (5.786) presented in Table 3. Production instability in sorghum (10.613) and ragi (15.04) is almost three times higher than in rice and wheat. Unlike other cereals, this instability is mostly related to decreased growing area and inadequate adoption of improved varieties. Additionally, the yield instability of millet (11.0) is twice as large as that of major cereals (~4), highlighting the technological and variety advances in major cereals compared to millets. The results align with the research conducted by (Gowda et al., 2019) [3] and (Kumar et al., 2023) [11] .

ARIMA model: The data has been analyzed and graphically plotted using the R program. Box-Jenkins ARIMA Modeling was used to predict the series under investigation.

Verification of the stationarity of the data

The ACF (autocorrelation function) and PACF (partial autocorrelation function) graphs are used to determine whether the data is stationary. The graphs below show how the data is related to its previous values at various time lags. Figure 4 shows that the ACF plot is gradually diminishing, implying that the data's correlation with its previous values decreases as time goes on. This decline suggests that the mean value of the data is changing over time, indicating that the time series data is not stationary.

Fig 4:

The correlogram of millet production of (ACF) and (PACF) before differencing

The Augmented Dickey-Fuller (ADF) test is used to check if a time series is stationary. The null hypothesis (H0) assumes that the time series is non-stationary, while the alternative hypothesis (Ha) assumes that the time series is stationary.

In Figure 5, the ADF test results show that when the p-value is higher than 5%, we can accept the null hypothesis, indicating that the time series is non-stationary. However, to determine if the data is actually stationary, the first difference in the data is calculated. After calculating the first difference, the p-value of the ADF test falls below 5% as shown in Figure 6. As a result, we reject the null hypothesis, implying that the data is stationary. (Haerani & Nugraha, 2022) [5] . Figure 7 shows the production series becomes stable after the first difference. p, d, andq) and fitting the model to the study The autocorrelation and partial correlation functions were examined, and multiple ARIMA models were fitted with various significant values of p and q, such as (2,1,2), (0,1,0), (1,1,0), (0,1,0), (1,1,1), (0,1,2), (1,1,2), and (0,1,1).

ARIMA (0, 1, 1) with drift was chosen as the optimal model for production ('000 tonnes) based on the RMSE, BIC, and AIC minimum values as given in Tables 4 and5. Table 6 shows the highly significant estimates of the ARIMA (0, 1, 1) with drift model parameters for production. H1: The residuals do not contain white noise (the residuals are correlated). Figure 12 shows the findings of the Ljung-Box tests. These results demonstrate that the p-value actually exceeds the level of significance (alpha = 5%), demonstrating that H0 is satisfied.

Forecasting

The millet production determined by the ARIMA (0,1,1) model and the outcome of the forecasting for the next 6 years is given in table 7. The selection of optimal ARIMA models was determined through an analysis of autocorrelation and partial autocorrelation functions at various lags. The forecasting accuracy of these models was assessed based on minimum AIC, RMSE, MAE, MAPE, and maximum R values. the future trends in cultivation area, production, and yield for all millets in India have been predicted with a 95 percent accuracy level.

Conclusion

Utilizing the ARIMA approach, the study forecasts a decline in millet cultivation area while anticipating an increase in production and productivity over the next eight years. Despite this projected rise, sustained government investment, farmer encouragement, and effective policies are crucial to securing favourable land tenure systems for millet cultivation. This proactive approach aims to ensure consistent production surpassing consumption, mitigating the need for wheat imports, and preventing potential economic repercussions such as heightened millet prices and increased inflation. Additionally, it sheds light on the concerning negative trends in millet cultivation, emphasizing the necessity for targeted interventions to address instability and sustain farming systems.

References

1. Government of India, Department of Agricultural, Cooperation and Farmers Welfare, Ministry of Agricultural and Farmers Welfare. Agricultural Statistics at a Glance 2022.
2. Bellundagi V, Umesh KB, Ravi SC. Growth dynamics and forecasting of finger millet (Ragi) production in Karnataka. Economic Affairs. 2016;61:195.
3. Gowda HR, Amrutha T, Raghavendra KJ, Kumar S. Millet's production and prospects in India: An economic overview. Green Farming. 2019;10:300-305.
4. Gowri UM, Shivakumar KM. Millets -miracle grains: growth trends and cost effectiveness in India. Agricultural Research Journal. 2020;57:805-812.
5. Haerani SLS, Nugraha ES. ARIMA Model in predicting Jakarta Composite Index. Journal of Actuarial, Finance. 2022;27-35.
6. Hyndman RJ, Khandakar Y. Automatic time series forecasting: The forecast package for R. Journal of Statistical Software. 2008;27:1-22. https://doi.org/10.18637/jss.v027.i03
7. Indian Institute of Millets Research (IIMR). Vision 2050. Hyderabad: IIMR; 2015.
8. Jainuddin SM, Seema, Suhasini K, Lavanya. Determinants of growth and instability of groundnut in Karnataka: Evidence from Hazel's decomposition model. Economic Affairs. 2019;65:649-661.
9. Joshi PK, Singh NP, Singh NN, Gerpacio RV, Pingali PL. Maize in India: Production Systems, Constraints, and Research Priorities. Mexico, D.F.: CIMMYT; 2005.
10. Kathayat B, Dixit A. Paddy price forecasting in India using ARIMA model. Journal of Crop and Weed. 2021;17:48-55. https://doi.org/10.22271/09746315.2021.v17.i1.1405
11. Kumar P, Sonnad JS, Yeledhalli RA. A study on trend in area and production of major millets in India. Journal of Farm Sciences. 2023;36:290-294. https://doi.org/10.61475/JFS.2023.v36i3.13
12. Kumar S, Lad YA, Mahera AB. Trend analysis of area, production, and productivity of minor millets in India. Biological Forum-An International Journal. 2022;14:14-18.
13. Mishra P, Yonar A, Yonar H, Kumari B, Abotaleb M, Das SS, Patil SG. State of the art in total pulse production in major states of India using ARIMA techniques. Current Research in Nutrition and Food Science. 2021;4:800-806. https://doi.org/10.1016/j.crfs.2021.10.009
14. Paswan S, Paul A, Paul A, Noel AS. Time series prediction for sugarcane production in Bihar using ARIMA & ANN model. The Pharma Innovation Journal. 2022;11:19471956.
15. Sankar TJ, Pushpa P. Stochastic ARIMA Model for Pennisetum glaucum production in India. International Journal of Agricultural and Statistical Sciences. 2023;19:373. https://doi.org/10.59467/ijass.2023.19.373
16. Saravand MJ, Rebasiddanavar RM, Relekar SP, Thakar KP. Forecasting of pearl millet production in North Gujarat by using ARIMA model. The Pharma Innovation Journal. 2022;11:672-677.
17. Sharma S, Meena L, Sharma LG, Singh H, Chaudhary R. Growth and instability in area, production and yield of major millets in Rajasthan. The Pharma Innovation Journal. 2022;11:1536-1543.
18. Umagowri M, Shivakumar KM. Millet scenario in India. Economic Affairs. 2020;65:363-370.