An empirical study on the cointegration between major domestic market prices and imported redgram prices in India

Introduction

Redgram is commonly known as Tur or Arhar in India and is the second important pulse crop in the country after gram (chana). The ability of redgram to produce high economic yields under soil moisture deficit makes it an important crop in rainfed and dry land agriculture. World major redgram producing countries are India (42.20 lakh tonnes), Malawi (4.47 lakh tonnes), Myanmar (3.27 lakh tonnes), Tanzania (1.64 lakh tonnes) and Kenya (0.83 lakh tonnes). Area under redgram reported during 2025-26 was 42.42 lakh ha (104.82 lakh acres) as against 46.50 lakh ha (114.90 lakh acres) during the same period in 2024-25. In India, major redgram cultivating states are Karnataka 12.62 lakh ha (31.18 lakh acres), Maharashtra 10.83 lakh ha (26.76 lakh acres), Madhya Pradesh 3.70 lakh ha (9.14 lakh acres), Uttar Pradesh 3.33 lakh ha (8.23 lakh acres), Telangana 1.99 lakh ha (4.92 lakh acres) and Gujarat 1.94 lakh ha (4.79 lakh acres) According to Government 3 rd advance estimates, all India redgram production in 2024-25 is at 3.56 million tonnes.

Review of Literature

Goletti and Babu (1994) [9] studied the extent of market integration of maize markets in Malawi in order to understand how it had been affected by market liberalization. Several measures of integration were used to analyze both the co movement of prices and the price adjustment process over time using monthly retail prices of maize at eight main locations over the period between January 1984 to December 1991. The study concluded that liberalization increased market integration. Afolami (2001) [1] investigated the degree of cowpea market integration in Uganda using such measures as bi variate correlation coefficients, co-integration and Granger-Causality. Campiche et al. (2007) [4] studied the relation between crude oil prices and variation of agricultural commodities using a vector error correction model. Co integration results showed that corn and soybean prices were co integrated with crude oil price during 2006-2007. Awal and Sabur (2009) [2] examined the pricing efficiency of exportable fresh vegetables markets in Bangladesh and its export markets by using Engle-Granger (EG) test, Co integration Regression for Durbin Watson (CRDW) test and Error Correction Methods (ECM). Zhang et al. (2010) [15] used VEC model and Granger test on the monthly data from 1989 to 2008 and reported that there was no long run and short-run causality between the fuel (oil, gasoline and ethanol) and agricultural commodity (corn, soybeans, wheat, sugar and rice) prices. Nazlioglu et al., (2013) [14] investigated the relationship between the world oil prices and the agricultural commodity www.extensionjournal.com prices by using the monthly data from 1980 to 2010 and the panel co-integration and the Granger causality techniques. The results of their study showed that the change in oil prices and the weak dollar have a strong impact on many agricultural commodity prices. Esposti and Listorti (2013) [7] investigating on national and international markets observed that trade policy regime had an important role in price transmission mechanisms and they put forward a trade policy intervention to mitigate the impact of price exuberance. The authors analyzed agricultural price transmission during price bubbles, in particular, considering Italian and international weekly spot (cash) price data over years 2006-2010. Kumari et al., (2019) [13] examined cointegration of major redgram markets and price movement in major markets in India using econometric tools like Augmented dickey-fuller (ADF), Johansen's cointegration test, granger causality test and vector error correction model (VECM). Kumari et al., (2022) [12] studied Co-integration and causality analysis of castor markets in Telangana state, the results showed that Devarakadra market influenced the prices in the other three major markets i.e., Badepalli, Gadwal and Narayanpet.

Materials and Methods

For price integration, simple bivariate correlation coefficients measure price movements of a commodity in different markets. This is the simplest way to measure the spatial price relationships between two markets. However, this method clearly has some limitations, as it cannot measure the direction of price integration between two markets. The co-integration procedure measures the degree of price integration and takes into account the direction of price integration. This econometric technique provides more information than the correlation procedure does, as it allows for the identification of both the integration process and its direction between two markets.

Market Integration Test

Market integration is tested using the cointegration method, which requires that • Two variables, say P it and P jt are non-stationary in levels but

Stationary in first differences i.e. P it ~ I (1) and P jt ~ I (1).

• There exists a linear combination between these two series,

Which is stationary i.e. ʋ it (=P it P it ) ~ I (0).

So the first step is to test whether each of the univariate series is stationary. If they are both I (1) then we may go to the second step to test cointegration. The Engle and Granger (1987) [6] procedure is the common way to test cointegration.

Unit root test

The regression analysis of non-stationary time series produces spurious results, which can be misleading (Ghafoor, et al., 2009) [8] . The most appropriate method to deal with non-stationary time series for estimating long-run equilibrium relationships is cointegration, which necessitates that time series should be integrated of the same order. Augmented Dickey-Fuller (ADF) and Phillips-Perron test (PP) is used to verify the order of integration for each individual series. The ADF test, tests the null hypothesis of unit root for each individual time series. The rejection of the null hypothesis indicates that the series is non-stationary and vice-versa (Dickey and Fuller, 1981) [5] . The number of the appropriate lag for ADF is chosen for the absence of serial correlation using Akaike Information Criterion (AIC). The ADF test is based on the Ordinary Least Squares (OLS) method and requires estimating the following model.

Where, P the price in each market, Δ is the difference parameters (i.e., ΔP 1 = P t -P t-1 , P t-1 = P t-1 -P t-2 and P n-1 = P n-1 -P n-2) and so on, is the constant or drift, t is the time or trend variable, q is the number of lags length and is a pure white noise or error term.

Johansen Cointegration

The maximum likelihood (ML) method of cointegration is applied to check long-run wholesale prices relation between the selected Sesamum markets of India (Johansen, 1988; Johansen and Juselius, 1990) [10] . The starting point of the ML method is vector autoregressive model of order (k) and may be written as:

Where, (n-1) denotes the vector of non-stationary or integrated at order one, i.e., I (1) prices series. The procedure for estimating the cointegration vectors is based on the Vector error correction model (VECM) representation given by: Where,

Both Γi and Пi are the n*n matrixes of the coefficient conveying the short and long run information respectively, μ is a constant term, t is a trend, and is the n-dimensional vector of the residuals that are independent and identically distributed(i.i.d). The vector ΔP t is stationary P t is integrated at order one I(1) which will make unbalance relation as long as П matrix has a full rank of k. In this respect, the equation can be solved by inversing the matrix П -1 for P t and as a linear combination of stationary variable (Kirchgässner, et al., 2012) [11] . The stationary linear combination of the Pt determines by the rank of Π matrix. If the rank r of the matrix П r=0 the matrix is the null and the series underlying is stationary. If the rank of the matrix П is such that 0 < rank of (П) = r < n then there are n × r cointegrating vectors. The central point of the Johansen's procedure is simply to decompose Π into two n × r matrices such that Π=αβ'. The decomposition of Π implies that the β'Pt are r stationary linear combination. Johansen and Juselius, (1990) proposed two likelihood ratio test statistics (Trace and Max Eigen test statistics) to determine the number of cointegrating vectors as follows:

Where, r is the number cointegrated vector, is the eigen value and is the (r + 1) th largest squared eigen value obtained from the matrix П and the T is the effective number of observations. The trace statistics tested the null hypothesis of r cointegrating vector(s) against the alternative hypothesis of n cointegrating relations. The Max Eigen statistic tested the null hypothesis (r =0) against the alternative (r + 1).

Vector Error Correction Model (VECM)

If price series are I (1), then one could run regressions in their first differences. However, by taking first differences, we lose the long-run relationship that is stored in the data. This implies that one needs to use variables in levels as well. Advantage of the vector error correction model (ECM) is that it incorporates variables both in their levels and first differences. By doing this, VECM captures the short-run disequilibrium situations as well as the long-run equilibrium adjustments between prices. Even if one demonstrates market integration through cointegration, there could be disequilibrium in the short-run i.e. price adjustment across markets may not happen instantaneously. It may take some time for the spatial price adjustments. VECM can incorporate such short-run and long-run changes in the price movements. A VECM formulation, which describes both the short-run and long-run behaviors of prices, can be formulated as: (6) In this model, is the impact multiplier (the short -run effect) that measures the immediate impact that a change in will have on a change in . On the other hand, is the feedback effect or the adjustment effect that shows how much of the disequilibrium is being corrected, that is the extent to which any disequilibrium in the previous period effects any adjustment in the period of course and therefore from this equation we also have being the long-run response.

Granger Causality Test

If a pair of series is cointegrated then there must be Granger causality in at least one direction, which reflects the direction of influence between series (in our case prices).

Theoretically, if the current or lagged terms of a time-series variable, say , determine another time-series variable, say , then there exists a Granger causality relationship between and , in which is Granger caused by . Bessler and Brandt (1982) [3] firstly introduced this test into research on market integration to determine the leading market.

From the above analysis, the model is specified as follows:

The following two assumptions are tested using the above two models to determine the Granger causality relationship between prices.

Data and Methodology

Gulbarga, Mumbai, Indore, Vijayawada and Tandur are the five domestic redgram market prices and imported prices selected for the study. The required secondary data on redgram prices in the above markets were collected for the period from September, 2020 to August, 2025 from websites www.agriwatch.com, tgmarketing and www.commerce.gov.in The statistical analysis was carried in three steps. The first step involves testing for the order of integration, with time series data on price of redgram in each market at the levels and first differencing, using the Augmented Dickey-Fuller (ADF). Conditional on the outcome of the tests, the second stage involves investigating pair-wise redgram market time series prices co-integration utilizing the Johansen's maximum likelihood approach. If pair-wise markets cointegration exists, however, there is no guarantee that the two markets belong to one market (the law of one price). On the basis of the pair-wise redgram market co-integration results in the third stage Vector Error Correction Model (VECM) was used to examine interaction effects, taking the error term from this co-integrating regression as a measure of the VECM term to capture the short run dynamics and causality of the model. The necessary condition for doing the co-integration analysis is to determine, whether the two price series are stationary or not.

Results and Discussion

It is evident from Figure 1 that all major markets of redgram in the country were found to be highly integrated with regard to price movement. And imported prices also integrated with domestic market prices. www.extensionjournal.com

References

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