Relationship between production and price of garlic in ... - J-Stage

Bull. Inst. Trop. Agr., Kyushu Univ. 38: 31-38, 2015

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Relationship between production and price of garlic in Bangladesh: an analysis by using distributed lag model Md. K. Hasan and K. M. Khalequzzaman

Abstract The study was conducted to aim at the relationship between production and price of garlic in Bangladesh. The experiment was carried out by using garlic production and prices data from Bangladesh Bureau of Statistics (during 1974-2011). The Koyck model of distributed lag models was used. According to the results, garlic production in Bangladesh has been influenced by the lag value of average price formed in the market. The most striking result of the study is the time required for the changes in the garlic prices in Bangladesh to an effect on garlic production of 32.33 years. This result also shows that the farmers are very enthusiastic for growing this crop, which is largely grown as a major spice crop. The value of coefficient indicated that the changes in lag values of the prices had a positive influence on production, but this influence was getting smaller. To reduce the risk and uncertainty of the price of garlic, sustainable garlic farming and establishment of an efficient marketing organization is necessary.

Key words: Garlic production, Garlic prices, Distributed lag model, Koyck model

Introduction Garlic (Allium sativum) is one of the most important bulb crops grown and used as a spice or a condiment in various ways in all curries, fried, and for other purposes in Bangladesh. It also adds flavour of distinctive pungency and has medicinal values. Garlic stands third among the spice crops in considering area (42.02 thousand ha) and second in production (2.09 lac m. tonnes) (BBS, 2011). In Bangladesh, the yield (4.97 t/ha) of garlic is very low as compared to the other developed countries like; Netherlands (48 t/ha), Jordan (33.84 t/ha), Egypt (22.68 t/ha), Tajikistan (20.00 t/ha) and China (17.14 t/ha) (Bonde and Prakash, 2006). The reasons behind such low yielding due to lack of sufficiency of improved varieties and practice of unimproved cultural method was followed by the farmers. Problems in weather conditions, pests and diseases, storm etc. negatively affect to the production. The national productivity of garlic was also significantly low level in Bangladesh before introducing improved variety (2.80 t/ha in 2003). The trend of area and production are increasing after 2003-04 because of introducing new improve varieties of garlic and getting higher income to the farmer. Growing area of garlic increased 12.73 thousand hectares of land in 1994-95 to 42.02 thousands hectare in 2010-11. On the other hand, production increased 41.44 thousand metric tonnes in 1994-95 to 2.09 lac metric tonnes in 2010-11 Senior Scientific Officer, Spices Research Centre, Bangladesh Agricultural Research Institute, Shibgonj, Bogra, Bangladesh Corresponding author: [email protected]

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(BBS, 1997 and 2011). Garlic is the crop in Bangladesh whose price is increase and decrease randomly. Therefore, this crop is faced with the highest risk and uncertainty. Resulting this, prediction is not possible on production correctly. Besides, problems in garlic pricing also negatively affect to the production, since the garlic prices are generally determined under market conditions without the effect of the producers. However, there is not an effective organization in the production and marketing of garlic in Bangladesh. Price of garlic is formed in domestic market conditions expending upon the supply. Changes in the garlic prices result in fluctuations in the production. For this reason, farmers have to take the prices formed by the market as information and to make production plans accordingly. Prices in the market are formed based on supply and demand principles rather than production costs. The sensitivity of garlic farmers to prices in Bangladesh was measured. Establishing the interaction between agricultural production and price via a distributed lag model, this model can significantly contribute to the literature. Indeed, we have not come across with such an investigation into the subject. Farmers are not well organized in input and produce markets. All these factors make price uncertainties for the farmers in garlic market. Farmers consider the previous years’ price when planning the production. Such a planning causes big price and production fluctuations in garlic production markets. This is called Cobweb theory in economy literature, often encountered in agricultural production and has been the subject of the investigations about relationship between production amount and price. Because of this structural feature of garlic produces, relationship between the amount of production and the price can be studied using a distributed lag model., If the model uses not only the present values but also the delayed past values of the defining variable, this model is defined as distributed lag model in the regression models in which time series data is used (Gujarati, 2005). Two major problems arise in distributed lag models. One is multicolinearity and the other is the increasingly lower degrees of freedom as lag length increases. In order to overcome these problems, Koyck model has been developed for the estimation of parameters in distributed lag models. In a study conducted by Yurdakul (1998) in Turkey, relationship between the production and price of cotton crop in 1985-1997 was studied using Koyck approach. In another study by Dikmen (2005), production and price relationship for tobacco crop in 1982-2003 was analyzed using Koyck model. Eraktan et al. (2004) used Koyck model to investigate the relationship between Direct Income Support and a financial support paid by government to the farmers based on their agricultural land in Turkey, and value added produced. The study by Erdal (2006) dealt with the production and price in tomato crop in 1975-2004 using Koyck approach. Ozcelik and Ozer (2006) reported relationship between production and price of wheat in 1973-2004 using Koyck approach. Erdal and Erdal (2008) analyzed the relationship between dry onion production and price in 1975-2006 via Koyck approach. These research works have not so far been conducted in Bangladesh. So, the study was undertaken to study the relationship between production amount and price of garlic which is a staple spices to a large extent in Bangladesh by using Koyck model.

Relationship between production and price of garlic in Bangladesh

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Materials and Methods The experiment conducted with data of garlic production amounts and prices was obtained from records of Bangladesh Bureau of Statistics (BBS, 1975 - 2011). Garlic production and price data were arranged yearly in 1974-2011. These data were subjected to regression analyses using Koyck distributed lag model. Theoretical Framework Distributed lag models has a special place in literature of economics in that they can allow the analyzing the behaviors of economical units (consumer, producers, etc.) based on appropriate dynamic models. This model is studied and used for the first time by Irving Fisher (Isyar, 1999), taking the distributed lag models into account not only the present year value but also the previous year values of defining variable. If how far back into the past will be gone for defining variable is not described, this is called an “infinite lag model” and shown as follows: Yt = α + β0Xt + β1 Xt-1 + β2 Xt-2 + …+ ut ...................................................... (1) On the other hand, if the number of years to go back is defined as k for defining variable, it is called “finite distributed lag model” and has been defined as: Yt = α + β0Xt + β1Xt-1 + β2Xt-2 +…+ βkXt-k + ut ............................................ (2) In this model, dependent variable Y (Yt … Yt-k) is not only influenced by the present day value (Xt) but also by the past day values (Xt-1 ……. Xt-k) of defining variable. Most often, Y responds to X after some time, and the time to respond is called “lag period” (Dikmen, 2005). Unknown parameters in distributed lag models (α, α0, …, α k) can be estimated using the classical least squares method (Alt, 1942; Tinbergen, 1949). Model-specific estimates in distributed lag models have certain drawbacks (Gujarati, 2005). One is the lack of a pre-information in the model about the length of lag period. Another is a data set that can estimate the lag period is not set up, degree of freedom is increasingly decreased in statistical significance tests of parameters. Yet another, but the most significant, drawback variables decided as defining variables are in a multiple linear relationships. In order to overcome the above mentioned drawbacks, we used the distributed lag model developed by Koyck (1954). Based on the assumption that lags in independent variable affect the dependent variable to some extent and the weight of these lags decrease geometrically, model is reduced and thus made to estimate the regression equation (Dikmen, 2005). In order to obtain the reduced model, Koyck assumed that all β’s in an infinitely distributed lag model had the same signs and geometrically decrease as shown below: βk = β 0 λ k k = 0,1 ........................................................................................... (3) In the Koyck model, a sensible range for λ would be the interval between 0 and 1. One possibility, involving the entire distribution over λconsider the class of “sup test statistics”, corresponding to the highest value of the original test statistic within the range for α. This approach is advocated by Davies (1987), Hansen (1996) and Carrasco (2002). βk is the lag coefficient. Lag coefficient βk varies by λ as well as by β 0. The closer λ to 1, the less the decrease in βk. On the other hand, the closer λ to zero, the greater the decrease in βk (Gujarati, 2005).

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In other words, λ values close to 1 mean that values of defining variables in remote past have a significant effect on dependent variable, and λ values close to zero mean that values of the defining variable in the remote past rapidly lose their effects of dependent variable. Mean lag number is the weighted average of all lags and is calculated for Koyck model as shown in Equation (4).

Mean lag number =

λ 1- λ

................................................................

(4)

Mean lag number showing the time period is necessary for a one unit change in X defining variable to have a detectable effect on dependent variable Y (Dikmen, 2005). In view of these explanations, infinite lag model is formed using OLS method as shown in Equation (5). Yt = α + β0Xt + β0λXt-1 + β0λ2Xt-2 + ….+ ut ................................................. (5) Linear regression solution cannot be applied to regression Equation (5) since infinite lag and λ coefficients are not linear. In order to solve this problem, the model has been taken one period back and the following regression model has been developed: Yt-1 = α + β0Xt-1 + β0λXt-2 + β0λ2Xt-3 + ….+ ut-1 ............................................. (6) When the equation (6) is multiplied by λ, the Equation (7) is obtained; λYt-1 = λa + λβ0Xt-1 + λ2β0Xt-2 + λ3β0Xt-3 +...+ λut-1 ........................................ (7) When the Equation (7), whose lag is taken one period back, is subtracted from Equation (5), whose lag is infinite, the following Equation is reached: Yt - λYt-1 = α (1- λ ) + β0Xt + (ut - ut-1 ) ......................................................... (8) If the Equation (8) is reorganized, Equation (9) is obtained; Yt = α (1- λ) + β0Xt + λYt-1 + v t ..................................................................... (9) In Equation (9) v t = ( ut - λut-1 ), it is the moving average mean of ut and ut-1. The procedure explained above is known as Koyck transformation. Equation (9) is described as Koyck model. In Koyck model, variables that consist of lag values of defining variables are not defined. Thus, multiple relationship problems are in a sense solved. On the other hand, while infinitely distributed lag model is necessary to predict infinite number of β using α, Koyck model distributed lag model can be resolved only through estimating α, β0 and λ.

Results and Discussion In order to determine the relationship between garlic prices and production at the studied period, a correlation analysis was performed. A correlation coefficient of 0.79 was found, indicating a high level of relationship between the two variables. This result indicated that the relationship between production amount and price r can be studied using Koyck model. Distributed lag model was formed as follows: Qt = α + β0 Pt + β1 Pt-1 + β2 Pt-2 + ……….+ βk Pt-k + ut ............................. (10) In the model, Qt is garlic production (ton) in period t, and Pt is garlic price in period t (Tk/ton). In order to form Koyck model, it is necessary to determine lag value of garlic price series of lag length. In a distributed lag model, Schwarz criterion is used to determine the lag length (Dikmen, 2005).


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Schwarz proposes reduction of Equation (11) to the lowest: SK = ln σ2 + m ln n ..................................................................................... (11) Here, σ2 is the highest probability estimate of σ2 = (RSS/n), m is length of the lag, n is the number of observations and RSS is the residual sum of square. In summary, a regression model is used along with some lag values (=m), and m value that makes the value of Schwarz criterion of the lowest is selected (Gujarati, 2005). At this stage, without making any limitation to the form of the distributed lag, a very large k value length of the lag is used at the start. Then, when the duration of lag is shortened, whether the model goes wrong is checked (Davidson and Mackinnon, 1993). Values for Schwarz criterion determined at different lag lengths for Equation (10) is given in Table 1. From Table 1, the lowest Schwarz value (24.28) was obtained from lag length K=1. Thus, effect of garlic prices on the production is zero after one year. According to the determined lag lengths, the relationship between garlic production and price has been estimated using the classical least squares method given in Equation (10). The results of the model are given in Table 2. Table 1. Lag length values based on Schwarz criterion Sl. No. 1. 2. 3. 4.

Lag length K=1 K=2 K=3 K=4

Schwarz values 24.28 27.81 31.28 34.69

Table 2. The results of distributed lag model Items

Coefficient t-values Probability

Constant 4230.59 0.354 0.726 R 2=0.68

Qt = 4230.59+ 1.71Pt + 0.55Pt-1 + 0.88Pt-2- 0.28Pt-3 Lag length t t-1 t-2 1.71 0.55 0.88 2.499 0.568 0.806 0.018 0.575 0.426 F=15.50

t-3 0.28 -0.289 0.775 P=000

According to the results of Table 2, garlic prices in the period t and one period earlier (t-1) and two periods earlier (t-2) positively affected the garlic production while garlic prices three periods earlier (t-3) negatively affected the production. Partial regression coefficients in the model except (β0) have been statistically insignificant. Model, as a whole, is also statistically significant. Multiple determination coefficient of the model is 0.68, which means that 68% of the changes in garlic production can be explained through changes in garlic price and its distributed lag values. Although statistically significant as a whole, the model has to be questioned in terms of reliability for two points related to distributed lag models. The first is the multiple relationship problems as a result of the fact that lag values of price variable was used in the model. The second problem is the loss of observations occurred in lag value set. If the number of data in formed series is not large, estimated values can be inconsistent due to lags. In order to overcome these two major problems, estimations were made using Koyck model. Estimation results of regression equation given in Table 2 based on Koyck model are given in Table 3.

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Table 3. The results of Koyck model Items Constant α) -4168.29 -0.995 0.327

Coefficient t-values Probability

Qt =- 4168.29 + 0.52 Pt + 0.97Qt-1 Lag length t β) 0.52 2.599 0.014 F=225.33

Qt-1 λ) 0.97 12.164 0.000 P=000

R 2=0.93 Mean lag 32.33333 Note: Qt is garlic production in period t, Pt is garlic price in period t and Qt-1 is garlic production in one period earlier than t. λ

Mean lag =

1- λ

Koyck model given in Table 3 was statistically significant at 1 % level of probability. According to the model results, a one taka increase in garlic price increased the garlic production by 0.52 tonnes. An increase of one tonne of garlic production in the previous period increased the garlic production by 0.97 tonnes. According to mean lag number, the time required for changes in garlic prices to have a significant and detectable effect on garlic production was 32.33 years. This result shows that Bangladesh farmers, who most often grow garlic as a staple spice crop, are very enthusiastic for growing garlic. Different crops the time required for the prices to considerable changes is 1.19 years for tobacco (Dikmen, 2005), 18 years for tomato (Erdal, 2006), 0.83 years for wheat (Ozcelik and Ozer, 2006) and 1.19 years for dry onion (Erdal and Erdal, 2008) in Turkey. In Koyck model Qt = α + β0 Pt + λ Qt-1+ ut and βk = λ k β0 Since 0 < λ < 1, using the following calculations Equation (10) is reached; βk = λ k β0 β0 = λ0 β0 = (0.97)0 (0.52) =0.520 β1 = λ1 β1 = (0.97)1 (0.52) = 0.504 β2 = λ2 β2 = (0.97)2 (0.52) =0.489

α0 =

α 1- λ

=

-4168.29 1-0.97

= -138943

When the regression formulae derived from Koyck model is rewritten using this results, equation (12) is obtained; Qt = -138943 + 0.520Pt + 0.504 Pt-1 + 0.489Pt-2 ....................................... (12) In Equation (12), which represents a distributed lag model derived from Koyck model, it is seen that lag garlic prices have a decreasing effect on garlic production, since 0 < λ < 1. Decreasing effects of lag price parameters result from the fact that λ coefficient exerts an effect which was limited in the model. According to Equation (12), a one-unit increase of garlic prices in Bangladesh increased the production by 0.52 tons in that year, while a one-unit increase of the previous year increased the production by 0.504 tons. In addition, a one-unit price increase for two years ago increased the production by 0.489


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tons. Although the changes in lag values of the prices had a positive influence on production, this influence was getting smaller. Conclusions and Suggestions In this study, relationship between amount and price of garlic, all under domestic market economy conditions, were studied. This relationship was studied using Koyck model, one of distributed lag models. The study dealt with the period of 1974-2011. At the studied period, there was a correlation of 79% between amount produced and the price. This coefficient showed that Koyck model was appropriate for studying the relationship between production amount and price of garlic crop. For the estimation of unknown parameters in the model, lag length determined using Schwarz criterion was calculated. This means that garlic production is influenced by the prices of up to past one year in Bangladesh, based on the data from studied period. On the other hand, according to Koyck model, the time required for the changes in garlic prices to a significant and detectable effect on garlic production was calculated as 32.33 years. For the studied period, a one-unit increase in garlic prices increased the garlic production by 0.52 tons in that year; while a one-unit increase in the previous year increased the production by 0.504 tons. In addition, a one-unit increase in the prices of two years ago increased garlic production by 0.489 tons. Thus, it can be said that each additional lag value results in a smaller effect on garlic production. Considering the average lag number, it can be stated that garlic producers in Bangladesh is very enthusiastic about growing garlic. However, price uncertainties resulted in fluctuations are present in the production of this crop in Bangladesh. For sustainable garlic farming in Bangladesh, establishment of an efficient marketing organization is necessary. Garlic product in Bangladesh does not go beyond a registration process in trade stock markets. In this context, lack of crop-specific stock markets is a major drawback for Bangladesh. At this point, farmer unions have significant roles in protecting the farmer against the risks and uncertainties appeared under market conditions. For the garlic crop, it is necessary to conduct a contract based production system. Policies are needed to be developed for efficient, profitable and sustainable garlic farming. Thus, price uncertainties that the producers face can be overcome, and contribution of this major spice crop to national economy can be increased.

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