Testing market integration and convergence to the law of one price in Indian onions

Spiraling prices of onions in India undermine the sustainability of current economic growth process and raised the question of price integration among the spatially separated markets. Co-integration test has been used to identify whether onion markets in India share a common linear deterministic trend and the law of one price holds true in view of rising prices in the recent past. The study sourced the wholesale daily prices of major onion markets across the country from January 2010 to March 2011. Augmented Dickey Fuller test statistic has been used to check the presence of a unit root in the time series data. Empirical results indicated the presence of unit root and a strong spatial integration between major markets. The study also confirms the law of one price in Indian onions.


INTRODUCTION
Onion (Allium cepa) is being used as a vegetable and spice for thousands of years by many cultures around the world, and it has immense medicinal and therapeutic value (Sendhil, 2012).It is cultivated across different states in India for domestic consumption and international trade.Among them, Maharashtra accounts for about 40% of India's onion output.Rajasthan is the next major producer followed by Karnataka, Andhra Pradesh and Tamil Nadu.Onion is a commercial crop in India, but the crises of 1998 and 2010 played spoilsport in the economy and the welfare of the producers (Sendhil, 2012).Price surge during the crises led to many economic as well as political implications.The prices have hit the roof across the entire nation and the absence of timely intervention to control them resulted in an explosive situation of prices (Nayyar, 2011).Prices rose by 600% from INR 12 to 18 per kg to INR 60 to 100 per kg during December, 2010 across different markets in the country.Even in the recent past, the wholesale prices hit a two-and-a-halfyear high bringing tears in the eyes of millions (Reuters, 2013).Following a 50% increase in the monthly wholesale prices, retail prices increase by cent percent particularly in Indian metros with a wide range of prices across major cities.In comparison to the last year, the reported price rise was about 500% in Lasalgoan in Maharashtra, Asia's biggest market.Though supply shock arising from excessive rainfall or drought that spoils the bulbs was a major reason for the spiraling prices, it undermined the sustainability and efficiency of public management in controlling the price of the commodity.The difference in prices that prevailed across onion markets in India raised the question of price integration among the spatially separated markets.
Spatial market integration is a situation in which prices of a commodity in spatially separated markets move together due to arbitrage and the price signals and information are transmitted smoothly across the markets.With the free flow of information in a competitive market, the difference in prices of a product in the two markets would be equal to or less than the transportation cost between them.Empirical studies on market integration of agricultural products typically use bilateral price relationships as an indicator of market integration.This methodology falls under the law of one price (LOOP), which states that if the commodity prices are converted to a common currency, then the particular commodity should be sold at the same price in each country or region.
However, in practice is a very rare case.In case of onions too, there is a great likelihood of market integration and price transmission between markets in India, if the markets are efficient and competitive.In this case, a causal relationship between prices in different spatial markets can be measured (Moodley et al., 2000).Market integration also means that a measurable longrun relationship exists between spatially separated prices for the same product.Thus, even when prices temporarily deviate from each other in the short-run, the differentials should eventually converge in the long-run and the speed of price convergence indicates the degree of market integration.In this context, an attempt has been made with the objective finding the extent of market integration within India and whether the LOOP holds true in the case of onions across different markets in India.

MATERIALS AND METHODS
The study is based on time series data on wholesale daily prices of onion collected from the AGMARKNET portal from January 2010 to March 2011.The data set can be used to analyze the price instability which occurred during 2010 to 2011.

Instability in prices
Instability index was used to examine the extent of variation and risk involved in prices.It was measured by Cuddy-Della Valle Index (Cuddy and Della Valle, 1978;Anuja et al., 2013) which is given as, . Where, CV is the coefficient of variation in per cent, and 2 R is the coefficient of determination from a time trend regression adjusted to its degrees of freedom.

Market integration and price transmission
Estimation of bivariate correlation coefficients between price changes in different markets has been employed as the most common methodology for testing market integration (Cummings, 1967;Lele, 1967Lele, , 1971)).But it indicates the integration of markets only in the short-run.Economic theory often suggests that certain pairs of economic variables should be linked by a long-run equilibrium relationship.Despite price series move away from the equilibrium point for a while, economic forces may be expected to act so as to restore equilibrium.Granger (1981) proposed the concept of co-integration which states that even though several price time series have unit roots, a linear combination of them would not have a unit root.Since the introduction of co-integration techniques by Engle and Granger (1987), Johansen (1988Johansen ( , 1991Johansen ( , 1994Johansen ( , 1995)), Johansen and Juselius (1990), and Goodwin and Schroeder (1991) researchers have applied it on non-stationary data.The Engle and Granger method is basically a bi-variate approach that accommodates relationships only between two price series.
As a result, this shortcoming does not lend itself well to analyzing multivariate systems that characterize, for example, markets with many sellers and buyers.In addition, the results are sensitive to which price series is used to normalize the other.Hypothesis testing on the estimated co-integration vector is also not possible under this approach.The Johansen method is preferred over the Engle and Granger approach and has proven to be popular in the recent literature on market integration (Kumar and Sharma, 2003).Before testing for co-integration, the time series has to be checked for its stationary property.The stationarity properties and the exhibition of unit roots in the time series are substantiated by performing the Augmented Dickey-Fuller (ADF) test.This test is conducted on the variables in level (original price series) and first differences.Price series co-integration arises when the variables are integrated of the same order against the unit root test which identifies the variables that are integrated of order one, or I (1).In a co-integrated equation system: where Y t is the price time series,  is the first difference operator (Y t -Y t-1 ) and matrix the number of linear independent co-integration relations in the vector space of a matrix.The Johansen's method of co-integrated system is a restricted maximum likelihood method with rank restriction on matrix '    (Anuja et al., 2013).The rank of  can be determined by using  trace or  max test statistics.Integration between two markets can be checked in a similar fashion through bi-variate Johansen's test.Since the test is very sensitive to price lag, the choice of lag length should be determined well.After testing for co-integration, the residuals show the deviation from equilibrium and this equilibrium error in the long-run tends to zero.Vector errorcorrection model (VECM) can be used to capture the deviations from the long-run equilibrium (Brosig et al., 2011).The model is represented as: Where, A t is the price of market 'A', B t is the price of market 'B' and u t is the co-integration vector.The coefficient (α 2 ) of the errorcorrection term (u t-1 ) indicates the speed at which the series returns to equilibrium.If it is less than zero, the series converge to long-run equilibrium and if it is positive and zero, the series diverges from equilibrium.

Law of one price (LOOP) analysis
LOOP analysis tests the hypothesis on the coefficients of both α and β using likelihood ratio tests as outlined in Johansen and Juselius (1990).To test for the LOOP, restrictions can be placed and tested on the parameters in the β matrix.In the case of a bivariate system where two price series are examined, the rank of π = αβ' is equal to one, and the dimensions of α and β matrices are 2 x 1. LOOP is tested by imposing the restriction β' = (1, -1)'.Since the matrix β contains long-run parameters in the system of equations, the test can be considered as a valid one for LOOP in the long-run.

Price behavior of onions in major Indian markets
The price behaviour in major onion markets in India, selected on the basis of production and consumption criteria, (Table 1) was studied with respect to the direction of movement in prices.The price behavior in different markets across the country is depicted in Figure 1.The figure shows the symmetric pattern in the movement of prices in all the markets of the country with peak prices during the months of December (2010) and January (2011) confirming a similar pattern identified by Reddy et al. (2012) in metro cities of India.The plausible reason was supply shock due to unexpected rainfall during the months of September -October which affected the production exhaustively in the major onion growing belts of the country.Chennai being a region of high consumption of onions with little production, the commodity has to be transported from different parts of the country.Hence, the maximum wholesale price of INR7000/quintal (Table 2) prevailed there which is due to the transportation cost.As expected, the minimum price prevailed in Lasalgaon (INR361/quintal), the Asia's biggest onion market.The average price during the study period was high in Chennai and low in the case of Nasik.As expected, standard deviation and variance was higher in the case of Chennai market.All the markets exhibited a positively skewed distribution.Excluding Chennai and Jaipur, the rest of the markets showed a leptokurtic (slim or long tailed) pattern of probability distribution.

Onion markets integration and price transmission
Market integration is the co-movements or long-run relationship between the spatial prices.The selected markets are tested for co-integration analysis using Johansen's approach.Before co-integration, correlation between different onion markets was carried out to know the short-run integration (Table 3).Correlation analysis revealed a positive co-movement between the onion price series, apriori.The results indicated a high degree of significant positive correlation between all the major onion markets that are spatially separated.Before testing for co-integration relationship between different onion market prices, it is mandatory to check the order of integration of the level variables.Hence, for each nonstationary variables, unit root test at their levels as well as first differences were conducted for each market after converting the original series to natural logarithms (Table 4).The results indicated the presence of a unit root at their levels that is, non-stationarity of each market price time series.However, all the non-stationary variables are found to be stationary at their first differences, and therefore, are integrated of order one, I(1) corroborating with the findings of Sidhu et al. (2010) that employed the Augmented Dickey-Fuller (ADF) statistic while studying the integration of wholesale market prices for onions within Punjab state of India.This conformation that each level series is I(1) allows to proceed with the Johansen's co-integration test (Table 5).
The co-integration test revealed the Eigen value and the trace statistic for each market.The test rejected the null hypothesis of no co-integration relationship between the onion market (r = 0 to r ≤ 4) at 5% level of probability indicating the presence of five co-integration vectors between those markets in the long-run (Table 5).The purpose of this analysis was to know whether the onion markets in India are integrated, and thereby price transmission takes place.These findings are also supported by Sidhu et al. (2010) despite their use of Augmented Engle and Granger co-integration test.Yogisha et al. (2006) employed a distributed lag model and found that onion markets in Kolar district of Karnataka were highly integrated attributing to the timely available information on prices.Reddy et al. (2012) also confirmed a high degree of price integration for a majority of the onion markets and they indicated that inter alia, prices are governed not only based on market arrivals but also several factors prevailing in other markets like varieties, appearance, moisture content, colour, size and shape of the produce.However, the flow of market information across markets will help to realize the law of one price in onions and the speed of flow can be estimated through the VECM.For this, bi-variate (2 markets) co-integration analysis has been done and the integrated markets were tested with error-correction mechanism.The results of the VECM indicated that most of the estimated coefficients were negative for market 1 and positive for market 2 (Table 6).This indicated that those series with positive coefficients diverge from equilibrium and negative coefficients converge to equilibrium in the short-run.However, further changes in the subsequent periods help the price series to achieve equilibrium in the long-run.The vector error-correction coefficient was estimated at -0.1467 for market 1  (Bangalore) and 0.1761 for market 2 (Chennai).This indicated the speed at which Chennai and Bangalore prices adjust towards the equilibrium in case of any price shocks in other markets.In other words, the coefficient measures the ability of the prices to incorporate shocks or price news available in the market.In this case, Chennai and Bangalore markets absorb 17.61 and 14.67% respectively to bring about the equilibrium in prices.The information flow is more in Chennai market as evident by the magnitude of the coefficient (0.1761).
Hence Chennai is more efficient than the Bangalore market in terms of reaction to news on price.Similar kind of interpretation can be done for rest of the markets.

Law of one price (LOOP)
Trace tests showed one co-integrating vector for all the selected markets, the number of common stochastic trends turned out to be one for these markets (Table 7).The number of common stochastic trends was determined by subtracting the number of co-integrating vectors from the dimension of the impact matrix given by the number of variables (n) included in the co-integration test.The findings of n -1 co-integrating vectors implied that all the prices contain the same stochastic trend and so they are co-integrated in pairs.This suggested that the LOOP holds true for the onion markets across India.

Conclusions
The study of past price behavior and price co-movement in major onion markets in India conclusively support the existence of an integrated market in the commodity.Several conclusions follow from this result.Price transmission occurs between geographically separated markets in onion due to market information flow through diverse channels.
However, the speed of convergence of onion prices to equilibrium depends on the speed of information dissemination, the government's control over the commodity, time-to-time regulations and policy harmonisation within the regions of the country.One of the reasons for market integration is the efficient functioning of markets itself which is clearly evident from the realisation of law of one price.Therefore, commodity based analysis on marketing integration and market research are better suited to understand the price behaviour of different agricultural commodities.This kind of studies is equally important as they provide policy makers with better information on expected market behaviour which will enable the decision making process on resource allocation.More resources should be allocated to those markets having a higher degree of integration and market efficiency.This will help in enhancing the overall efficiency of the marketing function in agricultural commodities and reduce market distortions.

Figure 1 .
Figure 1.Price behaviour (INR/quintal) of onion in different markets of India.

Table 1 .
Selected onion markets from different states/union territory.

Table 2 .
Summary statistics of onion market prices.

Table 3 .
Price correlation between major onion markets in India.
* indicates the significance of Spearman's correlation coefficient at one per cent level of probability.

Table 4 .
Estimates of ADF test for unit root and lag length based on Akaike Information Criterion (AIC).
* indicate significance at one per cent level of MacKinnon (1996) one-sided p-values.

Table 5 .
Estimates of Johansen's multivariate co-integration test.Trace test indicates five co-integrating equation(s) at the 0.05 level, * denotes rejection of the hypothesis at the 0.05 level and ** shows the MacKinnon-Haug-Michelis (1999) probability values.

Table 6 .
Estimates of Johansen's bivariate co-integration analysis and error correction model.

Table 6 .
Contd.denotes rejection of the null hypothesis at 5 % level of MacKinnon-Haug-Michelis (1999) probability values.The critical value for rejecting the null hypothesis at 5% , H 0 : r=0 is 15.49 and r ≤ 1is 3.81.Figures in parenthesis indicate the standard errors. *

Table 7 .
LOOP analysis for onion markets.