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Mean reversion in agricultural commodity prices in India.

Abstract This paper deals with the analysis of several commodity prices in India using an approach based on fractional integration and focusing on the degree of persistence of the series. We examine seven agricultural prices: rice, wheat, maize, bajra, jowar, black gram and arhar. The results can be summarized as follows: in five of the series examined (rice, wheat, maize, bajra and jowar) we find evidence of mean reversion with the effect of the shocks disappearing in the long run. On the contrary, in two of the series (black gram and arhar) we cannot reject the null of a unit root with the implication that shocks have a permanent nature. Thus, in the event of a negative shock, strong measures must be adopted in these two series since the effect of the shocks will persist forever.

Keywords Persistence * Commodity prices * Unit roots * Long memory

JEL Classification C22 * 013


Adequately modelling the order of integration in a given economic time series is an important issue since it can tell us how persistent the series is. Nevertheless, this is an issue that has not yet been resolved empirically. Since the 1980s, many economic time series have been modelled in terms of unit roots. Therefore, taking first differences has been a standard practice, especially after the influential paper of Nelson and Plosser (1982). These authors found evidence of unit roots in 14 US macroeconomic variables. The existence of unit roots implies that the series are nonstationary I(I), with the mean and the variance increasing without limits over time, the precision of the forecast error being unbounded, and shocks persisting forever. An alternative approach consists of the so-called trend-stationary models, where the raw series is described as an I(0) process plus a deterministic trend (often a linear function of time). Here the meaning of the series is described by the trend function, the variance of the forecast error remains finite and shocks have only transitory effects. Therefore, the issue of nonstationarity I(1) versus trend-stationarity I(0) has important implications for our understanding of the economy and economic planning. Shocks in an I(1) series will result in permanent changes in the level of the series so that strong policy actions will be required to bring the variable back to its original long term projection. On the other hand, in I(0) contexts, fluctuations will be transitory and there exists less need for policy action since the series will return to its original trend sometime in the future in any case.

However, the order of integration of a time series may not necessarily be an integer value. It can be a fractional value. In such a case the series is said to be fractionally integrated or I(d) where d can be a value between 0 and 1, or even above 1. Then, the higher the value of d is, the higher the level of dependence is and more persistent the series is.

Agriculture plays an essential role in the process of economic development in India, where about 72% of the total working population are engaged in agriculture. The appropriate major policy measures, i.e., land development, irrigation and extension, promotion of agricultural infrastructure, mechanisation and technological upgrading, crop diversification, storage, marketing and management, and appropriate pricing policies play an extremely crucial role for the success of agriculture in India. The policy failure in the aforementioned fronts may create imbalances and bottlenecks in the commodities market. Among all these policy measures, pricing of agriculture commodities has a pervading impact on society, government and institutions.

The price of food and other essentials has been rising consistently in India and the current food inflation level is the highest witnessed since November 2004. There is a sharp increase in, rice, wheat, maize, bajra, jowar, black gram and arhar prices that has led to food price inflation rising to about 20% in early 2010. Comparing the rise in food grain prices in May 2010 to that of May 2007, it is evident that the price of arhar has gone up by 90% followed by rice to the tune of 66%, black gram by 63%, bajra by 59% and jowar by 45%. The price of wheat has gone up by only 18% at all Indian levels over the same period.

Not only is the consistent rise in food grain prices a growing concern for India but the volatility of food grain prices is also a concern as well. Despite using a wide array of policy measures to control the rise in prices and price fluctuations of such essential food grains, the government has utterly failed in its attempts. The ban on commodity futures trading is one of such important measures in this direction which has not been able to realise its impact. Rather it is the price volatility that creates additional risks and is a particular burden for low income producers who, along with poor consumers, are less able to hedge against these fluctuations. Increased volatility tends to lead to greater government intervention in agricultural markets, often with sizeable fiscal costs. Corporate houses and retail chains have been allowed to buy products from farmers, to hoard, and to manipulate the market. The farmers gain nothing in the process as they are paid relatively lower prices than those quoted by the corporate houses on the futures exchanges or in the spot market, or those sold by the retail chains to the consumers. Clearly, it was appropriate to do everything possible to burst the speculative price bubbles, especially for rice, since reversing the dynamics of rising price expectations, and the private hoarding that exacerbated them, brought dramatic price relief in just a few months.

Being sufficiently motivated we have made in this paper an attempt to examine whether market forces are capable of bringing about long run mean reverting food grain prices in India over time. We examine which essential food grains are not guided by such long term mean reverting properties and what kind of policy response is desired in this critical juncture of the escalating food grain price regime in India.

Materials and Methods

For the purpose of the present paper we define an I(0) process as a covariance stationary process where the infinite sum of the autocovariances is finite. Thus, it includes the white noise case but also many other processes allowing for (weak) autocorrelation, e.g., the class of stationary auto-regressive moving average (ARMA) processes. Having said this, a process is said to be I(d) if it can be represented as

[(1 - L).sup.d][x.sub.t] = [u.sub.t], t = 1,2, ... , (1)

with [x.sub.t] = [u.sub.t] = 0 for t [less than or equal to] 0, where d can be any real value and [u.sub.t] is supposed to be I(0). Thus, the value of d may be 0, a fraction between 0 and 1, 1, or even above 1. When d is not an integer value, the process is said to be fractionally integrated. In this context, the parameter d plays a crucial role to determine the degree of persistence of the series. If d=0 in (1), [x.sub.t] = [u.sub.t], and the series is stationary I(0). If d belongs to the interval (0, 0.5) the series is still covariance stationary but the autocorrelations take a longer time to disappear than in the I(0) case. If d is in the interval [0.5, 1) the series is no longer stationary, however, it is still mean-reverting in the sense that shocks affecting the series disappear in the long run. Finally, if d[great than or equal to]1 the series is nonstationary and non-mean-reverting.

Let us suppose now that [y.sub.t] is the time series we observe, which is described throughout the following regression model,

[y.sub.t] = [[beta].sub.0] + [[beta].sub.1]t + [x.sub.t], t = 1, 2, ... (2)

where [[beta].sub.0] and [[beta].sub.1] are the coefficients corresponding respectively to the intercept and a linear trend, and the regression errors [x.sub.t] follow an I(d) process of the form as in (1). This is a very general specification that includes the "trend stationaty" representation (in case of d=0 in (1)) and the nonstationary "unit root" models (with d=1) advocated by many authors in the literature.

The I(d) process in (1) can be represented in terms of an infinite AR process, noting that the polynomial in the left hand side in (1) can be expanded for all real d as


implying that

[(1 - L).sup.d][x.sub.t] = [x.sub.t] - d[x.sub.t-1] + d(d-1) / 2[x.sub.t-2]-....

Thus, if d is an integer value, [x.sub.t] will be a function of a finite number of past observations, while if d is non-integer, [x.sub.t] depends upon values of the time series far away in the past, and the higher the d is, the higher the level of dependence is between the observations. Also, the same process can be described in terms of an infinite MA process, noting that [x.sub.t] can also be expressed as [x.sub.t] = [[infinity].summation over (j=0)][[psi],sub.j][u.sub.t-j], where [[psi].sub.j] = [GAMMA](j+d)/[GAMMA](j+1)[GAMMA](d), and [GAMMA](x) representing the gamma function. Thus, impulse responses can be easily obtained from the above expression.

The methodology employed in the paper to estimate the fractional differencing parameter d is based on the Whittle function in the frequency domain (Dahlhaus 1989) along with two procedures developed by Robinson (1994, 1995). The first is a very general method that allows us to parametrically test the null hypothesis Ho: d=d0 in the model given by (1) and (2) for any real value of do, including thus stationary ([d.sub.o]<0.5) and nonstationary ([d.sub.o][great than or equal to]0.5) hypotheses. The functional form of this procedure can be found, for example, in Gil-Alana and Robinson (1997). A semiparametric local Whittle estimate of d (Robinson 1995) will also be implemented in the paper.

Results and Discussion

We examine seven agricultural wholesale price series: rice, wheat, maize, bajra, jowar, black gram and arhar. The price series have been collected from the publications of the Central Agricultural Produce Marketing Committee (APMC), Ministry of Agriculture, Government of India. The data include monthly wholesale prices from January 2003 to May 2010. Per quintal price of commodities are quoted in Indian Rupee terms. The rationale of using wholesale price data is justified on 3 grounds: (i) non-availability of systematic retail price data on primary commodities in India, (ii) random fluctuations in retail wheat prices owing to varieties of retail formats and (iii) retail prices being determined by the wholesale prices of the commodities. Furthermore, the rationale of using wholesale price series data over the spot/futures market data is justified due to the commodity trade ban on some major commodities in futures market of India. This data limitation has forced us to include the wholesale prices for all the commodities under the study.

Figure 1 displays the time series plots. We observe that in most of the series, the values increase across the sample period. Taking first differences, the series might be stationary but the correlograms of the first differenced data, displayed in Fig. 2, suggest that some of the series may now be over differenced (rice, wheat, maize, bajra and jowar).

The fust thing we do in this section is to perform several standard unit root testing procedures. In particular we conduct ADF (Dickey and Fuller 1979), Phillips and Perron (1988), Kwiatkowski et al. (1992) and Elliot et al. (1996) methods, and the results, though not reported strongly support the view that the series are I(1) in the majority of the cases. Nevertheless these results should be taken with caution noting that these methods have very low power if, among other things, the alternatives are of a fractional form (see, e.g., Diebold and Rudebusch 1991; Hassler and Wolters 1994; Lee and Schmidt 1996).

Table 1 displays the Whittle estimates of d in a model given by (1) and (2) for the three standard cases of no regressors (i.e., [[beta].sub.0]=[[beta].sub.1]=0 a priori in (2)), an intercept ([[beta].sub.0] unknown and [[beta].sub.1]=0 a priori), and an intercept with a linear time trend ([[beta].sub.0] and [[beta].sub.1] unknown), under the assumption that the error term ([u.sub.t] in (1)) is a white noise process. We also report in the table the 95% confidence bands of the non-rejection values of d using the Robinson (1994) parametric approach. We observe that if we do not include regressors the unit root null is rejected in favor of smaller degrees of integration in the cases of rice, wheat, maize and jowar, while this hypothesis cannot be rejected for bajra, black gram and arhar. Including an intercept and/or a linear time trend, the results are similar in the two cases and the unit mot null cannot be rejected in the cases of black gram and arhar. In all the other cases, mean reversion seems to be the case, with orders of integration significantly smaller than 1.

Table 1 Estimates of d in the case of white noise disturbances

              No regressors    An intercept      A linear time trend
Rice                  0.826            0.609                 0.613
             (0.741, 0.927)   (0.542, 0.711)        (0.532, 0.724)
Wheat                 0.827            0.637                 0.587
             (0.706, 0.988)   (0.561, 0.770)        (0.463, 0.760)
Maize                 0.764            0.694                 0.608
             (0.653, 0.912)   (0.628, 0.798)        (0.503, 0.758)
Bajra                 0.852            0.665                 0.634
             (0.734, 1.014)   (0.590, 0.775)        (0.537, 0.765)
Jowar                 0.796            0.584                 0.497
             (0.650, 0.997)   (0.523, 0.686)        (0.386, 0.659)
Black gram            1.108            1.135                 1.138
             (0.970, 1.311)   (0.979, 1.381)        (0.981, 1.380)
Arhar                 1.004            1.018                 1.019
             (0.890, 1.169)   (0.909, 1.173)        (0.903, 1.175)

The values in parenthesis refer to the 95 % confidence band of
the non-rejection values of d using Robinson (1994) parametric
approach. The specific model is the one given by (1) and (2) with
white noise [u.sub.t]

Table 2 displays the parameter estimates of the selected models according to the t-values of the deterministic terms. It is observed that the time trend is required in all except one series (black gram) and the unit root is rejected in favour of mean reversion (d<1) in five out of the seven series examined.

Table 2 Estimates of the remaining parameters in the
selected models in Table 1

                    d          Intercept    Time trend
Rice                  0.613     915.868       10.892
             (0.532, 0.724)     (8.355)      (4.333)
Wheat                 0.587     696.470        5.339
             (0.463, 0.760)    (12.377)      (4.415)
Maize                 0.608     509.094        3.544
             (0.503, 0.758)    (15.221)      (4.681)
Bajra                 0.634     425.680        4.628
             (0.537, 0.765)    (10.658)      (4.777)
Jowar                 0.497     479.705        6.222
             (0.386, 0.659)     (8.753)      (6.324)
Black gram            1.135    1923.567            -
             (0.979, 1.381)    (12.260)
Arhar                 1.019    1172.092       35.312
             (0.903, 1.175)     (6.145)      (1.725)

In parenthesis in columns 3 and 4. t-valucs. The model
is the one used in Table 1

In what follows we suppose that the error term is autocorrelated. However, instead of assuming an AR specification, we consider the exponential model of Bloomfield (1973). This model produces autocorrelations decaying exponentially as in the AR case. Another advantage of this approach is that this method is stationary for all its coefficients, as opposed to what happens in the AR model. In Bloomfield (1973) the model is exclusively defined in terms of its spectral density function, which is given by:

f ([lambda]: [tau]) = [[sigma].sup.2]/2[pi]exp(2[k.summation over (y=1)][[tau].sub.y]cos([lambda]r)), (3)

where k indicates the number of parameters required to describe the short run dynamics of the series. Bloomfield (1973) showed that the logarithm of an estimated spectral density function of an ARMA(p, q) process is often found to be a well-behaved function and can be approximated by a truncated Fourier series. He showed that (3) approximates it well, where p and q are small values, which is usually the case in economics. Table 3 reports the estimates of d and the 95% confidence band for the case of Bloomfield disturbances. Here we observe a much higher proportion of non-rejections of the I(I) case. Thus, if we do not include regressors, the only series where the I(I) case is rejected in favour of mean reversion is wheat. In all the other cases, the I(I) null cannot be rejected at conventional statistical levels. Including an intercept, mean reversion is only observed in the cases of wheat and jowar, and including a linear trend, I(d, d<1) is only observed in these two series along with maize.

Table 3 Estimates of d in the case of Bloomfield disturbances

              No regressors    An intercept      A linear time trend
Rice                  1.153            1.002                 0.999
             (0.961, 1.454)   (0.785, 1.297)        (0.791, 1.328)
Wheat                 0.731            0.607                 0.441
             (0.487, 0.985)   (0.504, 0.798)        (0.209, 0.739)
Maize                 0.749            0.759                 0.669
             (0.572, 1.018)   (0.649, 1.010)        (0.479, 0.977)
Bajra                 0.859            0.734                 0.709
             (0.657, 1.151)   (0.587, 1.001)        (0.513, 1.011)
Jowar                 0.704            0.650                 0.482
             (0.484, 1.084)   (0.552, 0.832)        (0.288, 0.801)
Black gram            0.873            0.810                 0.788
             (0.669, 1.149)   (0.658, 1.051)        (0.599, 1.053)
Arhar                 1.021            1.098                 1.102
             (0.819, 1.462)   (0.865, 1.601)        (0.841, 1.587)

The values in parenthesis refer to the 95 % confidence band of the
non-rejection values of d using Robinson (1994) parametric approach.
The specific model is the one given by (1) and (2) with
Bloomficld-typc [u.sub.t]

Table 4 focuses on the parameter estimates. We see that the time trend is required in all except two series, rice and arhar, and the estimated values of d are strictly below 1 in the cases of wheat (with an estimated value of d equal to 0.441), jowar (0.482) and maize (0.669). For the remaining four series, the I(1) case cannot be rejected and the estimates are below 1 in the case of bajra (0.709) and black gram (0.788), and above 1 in the case of rice (1.002) and arhar (1.098).

Table 4 Estimates of the remaining parameters in the selected
models in Table 3

                    d          Intercept    Time trend
Rice                  1.002     744.143            -
             (0.785, 1.297)     (5.912)
Wheat                 0.441     700.084        5.313
             (0.209, 0.739)    (15.797)      (7.216)
Maize                 0.669     518.569        3.500
             (0.479, 0.977)    (14.607)      (3.673)
Bajra                 0.709     434.491        4.752
             (0.513, 1.011)    (10.234)      (3.675)
Jowar                 0.482     477.937        6.212
             (0.288. 0.801)     (8.951)      (6.633)
Black gram            0.788    1886.290       16.623
             (0.599, 1.053)    (12.661)      (2.777)
Arhar                 1.098    1193.420            -
             (0.865, 1.601)     (6.340)

In parenthesis in columns 3 and 4, t-values. The model is the
one used in Table 3

Finally, given the monthly nature of the series under analysis, we also consider the case of seasonal (monthly) AR disturbances. In particular we consider for [u.sub.t] a process of form:

[u.sub.t] = p[u.sub.t-12] + [[epsilon].sub.t], t = 1, 2, .... (4)

Higher AR orders were also examined and the results were similar. The fractional differentiating parameters are displayed in Table 5. We observe that they are very similar to those displayed for the case of white noise errors. Focussing now on the parameter estimates, in Table 6, we see that in five of the series the differentiating parameter is strictly smaller than 1: jowar (0.464), rice (0.584), wheat (0.587), maize (0.613) and bajra (0.634), and, in the other two the unit root null cannot be rejected: arhar (1.048) and black gram (1.137).

Table 5 Estimates of d in the case of seasonal (monthly) AR(1)

              No regressors    An intercept      A linear time trend
Rice                  0.799            0.579                 0.584
             (0.708, 0.913)   (0.498, 0.689)        (0.495, 0.703)
Wheat                 0.827            0.633                 0.587
             (0.706, 0.989)   (0.554, 0.767)        (0.464, 0.758)
Maize                 0.771            0.697                 0.613
             (0.661, 0.914)   (0.632. 0.794)        (0.516, 0.750)
Bajra                 0.843            0.666                 0.634
             (0.718, 1.010)   (0.592, 0.776)        (0.537, 0.765)
Jowar                 0.784            0.565                 0.464
             (0.636, 0.984)   (0.503. 0.657)        (0.357, 0.611)
Black gram            1.108            1.137                 1.139
             (0.971, 1.311)   (0.979. 1.387)        (0.981, 1.386)
Arhar                 0.990            1.048                 1.047
             (0.877, 1.153)   (0.927, 1.217)        (0.920, 1.218)

The values in parenthesis refer to the 95 % confidence band of the
non-rejection values of d using Robinson (1994) parametric approach.
The specific model is the one given by (1) and (2) with [u.sub.t]
given by (4)

Table 6 Estimates of the remaining parameters in the selected
models in Table 5

                    d          Intercept    Time trend
Rice                  0.584     929.155       10.682
             (0.495, 0.703)     (8.770)      (4.725)
Wheat                 0.587     696.470        5.339
             (0.464, 0.758)    (12.377)      (4.415)
Maize                 0.613     509.922        3.540
             (0.516, 0.750)    (15.148)      (4.586)
Bajra                 0.634     425.680        4.628
             (0.537, 0.765)    (10.653)      (4.775)
Jowar                 0.464     475.684        6.202
             (0.357, 0.611)     (9.191)      (7.009)
Black gram            1.137    1923.580           --
             (0.979, 1.387)    (12.259)
Arhar                 1.048    1199.459           --
             (0.927, 1.217)     (6.325)

In parenthesis in columns 3 and 4, t-values. The model is the
one used in Table 5

Table 7 summarizes the estimates of d across the different types of disturbances. We see that though quantitatively there are some differences across the cases, qualitatively the results are very similar. Thus, for wheat, maize and jowar, the three types of specifications of the error term lead to mean reversion in the series. On the other hand, for black gram and arhar, the three models indicate lack of mean reversion since the I(1) null cannot be rejected at the 5% level. The only discrepancies take place with rice and bajra, where the unit root cannot be rejected with Bloomfield disturbances, and is rejected for the other two specifications of [u.sub.t].

Table 7 Estimated values of d depending on the specification
of the error term

Series          White noise  Bloomfield      Seasonal AR(1)
Rice               0.613       1.002*            0.584
Wheat              0.587        0.441            0.587
Maize               0608        0.669            0.613
Bajra              0.634       0.709*            0.634
Jowar              0.497        0.482            0.464
Black gram        1.135*       0.788*           1.137*
Arhar             1.019*       1.098*           1.048*

* and in bold: Evidence of unit roots at the 5 % level

In spite of the similarities in the results presented across the different specifications for the error term, we also conducted a semiparametric approach, where no functional form is required for the I(0) term [u.sub.t]. We employ here a methodology proposed by Robinson (1995) that is based on the Whittle function in the frequency domain, using only a band of frequencies that degenerates to zero, and though there exist further refinements of this procedure, these methods require additional user-chosen parameters and then, the results about the estimation of d may be very sensitive to the choice of these parameters. In this respect, the "local" Whittle method of Robinson (1995) seems computationally simpler.

Figure 3 displays the results based on the above method. The horizontal axis refers to the bandwidth number while the vertical one refers to the estimated value of d. We also display in the figure the 95% confidence intervals corresponding to the I(1) case. We find that the results are consistent with those based on the parametric models. Thus, the only two series where we do not find any evidence of mean reversion are black gram and arhar. For rice and bajra, evidence of mean reversion only takes place for large bandwidth numbers and strong evidence of mean reversion is clearly observed in the remaining three series.

Figure 4 displays the first 60 impulse responses for each series using the model with fractional integration and seasonal AR disturbances. In doing so the responses are formed by the contribution of the fractional differencing parameter (d in (1)) and that of the seasonal AR coefficient ([rho] in (4)). We observe that, as expected, the responses are explosive in case of black gram and arhar; the strongest evidence of seasonality is observed in jowar, and mean reversion is clearly observed in this series along with rice, wheat, maize and bajra. The above results indicate that in the presence of an exogenous shock, stronger policy measures must be conducted in the cases of black gram and arhar than in the remaining series, noting that shocks in the former series are expected to be permanent. On the contrary, for rice, wheat, maize, bajra and jowar, there is no need for strong measures since the series will return to its original level sometime in the future.


In this article we have examined the degree of persistence in seven agricultural commodity prices using long range dependence techniques. In particular we have examined the following series: rice, wheat, maize, bajra, jowar, black gram and arhar, monthly, for the time period March 2001--May 2010.

The results can be summarized as follows: in five out of the seven series (rice, wheat, maize, bajra and jowar) mean reversion is observed, and the orders of integration are strictly smaller than 1, ranging from 0.464 (jowar) to 0.634 (bajra). For the other two series (black gram and arhar), the orders of integration are strictly above 1 and the unit root case cannot be rejected. Thus it is recommended that there is a need to review the commodity futures ban on food grains series that are mean reverting in nature. This is because the automatic forces of demand and supply will bring these series back into equilibrium. Hence there is no need for government intervention to ban these commodities from the futures market. Furthermore, as the food grain price series of arhar and black gram are not mean reverting by nature in the long run there is a need for government intervention to bring these series back into equilibrium and thus the ban on futures trading for these commodities is justified by the government. There is a need for strengthening the institutional mechanism in India that would bring the commodities under government's scanner and gather the evidence of speculation and spot out the illegal traders or hoarders rather than imposing ban on specific commodities futures trading. Rather the price determination in the commodity futures market would help government removing inefficiencies from the market, planning and taking control of the uncertainties. Thus, instead of imposing a ban on futures trading, the regulator should strengthen checks and balances in the existing illegal trading system in India.

Other issues such as the presence of non-linear structures, the existence of structural breaks, the co-movements across the series, and implicit heteroskedasticity in the volatility processes are clearly of interest and will be examined in future papers. Also, it might be of interest to check if the results presented in this work hold in neighbouring countries so that the same policy implementations may be adopted by these countries.

Acknowledgments The first-named author gratefully acknowledges financial support from the Ministerio de Ciencia y Tecnologia (ECO2012-2014, n.28196 ECON Y FINANZAS, Spain) and from a Jeronimo de Ayanz project of the Government of Navarra. Comments from the Editor and an anonymous referee are gratefully acknowledged.

Published online: 4 September 2014 [C] International Atlantic Economic Society 2014


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L. A. Gil-Alana ([??])

Faculty of Economics and Business Administration, University of Navarra, Pamplona E-31080, Spain e-mail: alana@unav.cs

T. Tripathy

IBS Hyderabad, Hyderabad, India
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Author:Gil-Alana, Luis A.; Tripathy, Trilochan
Publication:International Advances in Economic Research
Article Type:Report
Geographic Code:9INDI
Date:Nov 1, 2014
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