DOES COBWEB PHENOMENON EXIST IN RICE MARKET OF PAKISTAN? A TIME SERIES ANALYSIS
K. Mehmood ^{1}, M. ul. Hasan^{2} and A. Khan^{1,}*
^{1}Adaptive Research Farm, Sargodha, Directorate General Agriculture (Extension and Adaptive Research), Government of Punjab, Pakistan
^{2}Department of Economics, University of Sargodha, Sargodha, Pakistan
*Corresponding Author’s Email: ammaras94@yahoo.com
ABSTRACT
This study investigates the rice price dynamics and their impacts on demand and supply over the time in agricultural markets of Pakistan. Time series data on production and prices for the period 19842018 were used to study the cobweb phenomenon in local rice markets. Linear demand and supply models were used to examine the unstable ricemarket. Price dynamics were examined through identifying the time path of difference equation derived from demand and supply functions. The results inferred that market prices of rice have remained unstable in agricultural markets of Pakistan over the history. Furthermore, rice prices exhibited damped oscillations towards stable market equilibrium over last three decades in Pakistan. It is suggested that the government may respond promptly to the instability of rice markets by formulating the appropriate agricultural policies, developing stateoftheart storage facilities and ensuring the steady transmission of market information across the national as well as international rice markets. The study provides deep insights into understanding the ongoing and future trends of price fluctuations with respect to demand and supply shocks in rice market of Pakistan. It would greatly help the stakeholders and policy makers in forecasting and stabilizing the rice markets, and alleviating the food insecurity.
Keywords: cobweb model; rice; demand; supply; price fluctuations
https://doi.org/10.36899/JAPS.2022.5.0542
Published first online April 26, 2022
INTRODUCTION
Rice is an important cereal crop which supports a large population of the world as a staple food (Greenland, 1997; Maclean et al., 2002). The geographical, ecological and climatic conditions of many countries support the rice production. Particularly in Asian region, nutrientsrich and fertile lands in addition to the high monsoon rainfalls produce favourable environment for rice crop (Khan et al., 2019). Rice is extensively grown in certain areas of Pakistan which include the fertile lands of Punjab, Sindh and Baluchistan, where large number of famers rely on rice cultivation for their livelihoods.
According to Food and Agricultural Organization (FAO), the global paddy production and yield per hectare have significantly increased over the past decade. The total rice area over the world has also increased but it experienced large fluctuations over the years as shown in Fig. 1. According to the estimates of FAO, China, India, Indonesia, Bangladesh and Vietnam collectively contribute more than 70% to the global rice production of about 755 million tons (Table 1). In 2019, Pakistan produced about 11.1 million tonnes of paddy and secured 9^{th} position in top ten rice producing countries (Anonymous, 2019; FAO, 2019).
Table 1. Paddy area, production and price in major world producers for the year 2019
Country

Area
(Million Ha)

Production
(Million Tonnes)

Productivity
(Kg/Ha)

Producer Price Index (20142016 = 100)

China

29.96

211.41

7056.2

100.3

India

43.78

177.65

4057.7

109.8

Indonesia

10.68

54.60

5113.7

58.0

Bangladesh

11.52

54.59

4739.8

101.2

Viet Nam

7.47

43.45

5816.5

102.6

Thailand

9.72

28.36

2918.8

119.0

Myanmar

6.92

26.27

3795.7

92.0

Philippines

4.65

18.81

4044.9

111.6

Pakistan

3.03

11.12

3663.7

60.4

Cambodia

3.00

10.89

3627.1



Japan

1.54

10.53

6826.8

122.9

Brazil

1.71

10.37

6063.3

122.9

Source: Food and Agricultural Organization Statistics (FAO, 2019)
Huong et al. (2017) and Khan et al. (2019) reported that the unstable market conditions pose a number of challenges to the agricultural markets, especially of small producers. Therefore, it is imperative for Pakistan – a predominantly agrarian economy – to respond promptly to the unstable market conditions by devising and adjusting its agricultural policies (Khan et al., 2019). At present, the policy reaction has become more crucial in the wake of global price hikes due to the outbreak and prevalence of Covid19.
In developing countries, price instability has significant impact on the human development indicators such as health (Jensen, 2000), economic growth (Myers, 2006), food security (Mitra and Boussard, 2012) and welfare of people (Chaudhry and Miranda, 2017). However, controlling the price fluctuations has been a matter of great concern over the time for policy makers. Understanding the mechanism and causes of price instability is quite imperative for market stabilization.
The dynamics of price instability have been divided in two major categories: the exogenous factors which may include the weather shocks and any other causal agent outside the economic settings (Williams, 1936; Gustafson, 1958; Scheinkman and Schechtman, 1983; Deaton and Laroque, 1992, 1996); and the endogenous factors which are the erroneous expectations of the suppliers regarding the future prices which perturb the supply (Ezekiel, 1938; Finkenstädt and Kuhbier, 1992; Boussard, 1996; Hommes, 1998; Athanasiou et al., 2008). Particularly, Scheinkman and Schechtman (1983) have comprehensively discussed the exogenous factors disturbing the supply.
An inelastic or steeper demand augments the price instability in a market (Chaudhry and Miranda, 2017). Under the exogenous explanation, a number of policy measures including insurance schemes, stockpiling and widening the markets are effective tools to mitigate price volatility. In the endogenous case, in contrast, government intervenes through production quotas and supply management to stabilize the prices. In agriculture sector, the supply decisions of the farmers depend on the expected future prices of the produce (Anokye et al., 2014). Therefore, the knowledge of price dynamics of rice will enable the farmers to take informed decisions for sowing the crop in the coming season (White and Dawson, 2005).
To illustrate the price dynamics in the sense of endogenity, Ezekiel (1938) presented cobweb model which explains that the fluctuations primarily arise due to the erroneous expectations of the farmers which cause the under or oversupply. The cobweb model (Ezekiel, 1938; Nerlove, 1958) is an economic model which explains why prices might be subject to periodic fluctuations in certain types of markets. It explains recurrent demand and supply in a market where the quantity to be produced must be chosen before prices are observed.
The demand and supply curves are nonlinear in more realistic economic models. Nonlinearities are generated endogenously due to the tradeoff among various expectation regimes in the conventional cobweb model, which leads to chaos (Chaudhry and Miranda, 2017). The literature on chaotic cobweb models primarily focused on the effect of nonlinearity on cobweb model because nonlinearity is necessary but not a sufficient condition for chaos. Jensen and Urban (1984) and Chiarella (1988) studied chaotic dynamics in a cobweb model with nonlinear supply and linear demand functions. Finkenstädt (1995) penned a book on nonlinear dynamics in economics with respect to agricultural markets and discussed demand and supply functions. Hommes (1991) studied linear demand and nonlinear supply models. Ma and Mu (2007) framed a cobweb theory based on real estate nonlinear model, where the demand and supply are quadratic functions.
This paper examines the price dynamics of rice in the Pakistan using cobweb model. It investigates whether the rice market of Pakistan exhibits the cobweb phenomenon. This study will be worthwhile to the stakeholders and policy makers in stabilizing the market prices and ensuring the food security.
MATERIALS AND METHODS
Study Area: The study was conducted in Pakistan, the 5^{th} most populous country of the world with more than 215 million population. The area of Pakistan is 796096 squarekm which is bordered by India to the east, Afghanistan to the west, Iran to the southeast and China to the northeast. Rice is an important staple food as well as cash crop of Pakistan, which largely contributes to the exports volume of the country. According to the recent estimates, rice has been grown on an area of 3335 thousand hectares in Pakistan which accounts for more than 14% of total cultivated area (Anonymous, 2021).
Data: To achieve the research objectives, time series data were used which included historical average prices and production of rice in Pakistan. The required data for a period of 35 years (19842018) were retrieved from the statistical supplements issued by the Ministry of Finance, Pakistan, various issues of Pakistan Economic Surveys and the official website of Agricultural Marketing Information Services (AMIS) Pakistan. In addition, the data on global rice production, prices and average yield was also collected from FAO (2019). The nature and properties of data were carefully examined prior to the analysis. The data on rice production was found stationary at level, whereas, price series was stationary at first difference. So, the price series was used in transformed form i.e., as the first differenced series to avoid the unit root problem.
Methods
Cobweb Model: Cobweb model explains that the price fluctuations primarily arise due to the erroneous expectations of the farmers which cause the under or oversupply (Ezekiel, 1938; Nerlove, 1958). It explains recurrent demand and supply in a market where the quantity to be produced must be chosen before prices are observed. The cobweb model has been constructed under the naïve expectations hypothesis to derive timedelay difference equation characterized by the price fluctuations in rice market (Chaudhry and Miranda, 2017). It is assumed that there is an economic system with a single commodity. The cobweb model employs the supply and demand functions of price curves to determine the change in price P_{k} at time k from the price P_{k1} at time k1. This study follows the methods of Anokye and Oduro (2013), Anokye et al. (2014) and Khan et al. (2019) to develop the cobweb model. The Market Clearing Equation (MCE) is the first order nonhomogeneous difference equation which describes this process (Nicholson, 1972). Given an initial price P_{k1}, the market responds at time k with a quantity D_{k} determined by the supply curve S_{k}. Therefore, market demand determines the current price P_{k}.Linear demand and supply curves are given as:
where α represents intercept while β represents the slope for the demand function, and also δ and γ respectively represent the intercept and slope of the supply function.
At the MCE, D_{k} = S_{k} which implies that,
Assuming and , the equation (3) can be written as:
Solving the of difference equation (4), we get:
where, and
Equation (5) can be transformed by putting the values of A & B as:
In equation (6), the term is very important as it explains the time path of difference equation. There are three conditional explanations for absolute value of the term regarding price dynamics:
i) If , there are damped or convergent oscillations in prices towards stable equilibrium (
ii) Fig. 2).
iii) If , there are continuous price fluctuations i.e., price oscillates in period2 cycle, also called “hog cycle”.
iv) If , there are exploding or divergent oscillations and the prices will move away from the equilibrium level (
v) Fig. 2).
Fig. 2. Convergent Oscillations
Fig. 3. Divergent Oscillations
Time series data may encounter number of problems including small sample size, nonstationarity (or unit root), autocorrelation and endogeniety etc. The stationarity was checked through Augmented Dickey Fuller (ADF) and PhillipsPerron (PP) unit root tests. In the primitive demand and supply functions as given in Equation 1 & 2, the Durbin Watson (DW) statistic was about 1.23 which showed the existence of endogenity problem. Lagged dependent variable has been included in models to redress the endogenity and autocorrelation problems. The demand and supply functions with lagged dependent variables are given as:
where ϑ and ρ are the parameters of lagged dependent variables.
RESULTS AND DISCUSSION
Autocorrelation and Stationarity Diagnosis: Autocorrelation was tested through DW test with and without incorporating the lagged dependent variable as predictor. In former case, DWtest statistic was 2.66 (with pvalue 0.97) & 2.61 (with pvalue 0.96) for demand and supply functions, respectively, which implies that the problems of autocorrelation and endogeniety were resolved by use of lagged dependent variable in both demand and supply models.
Time series data often contains the problem of nonstationarity. So, we employed the Augmented Dickey Fuller (ADF) and PhillipsPerron (PP) unit root tests to detect the stationarity in data. The data of production was found to be stationary at level, whereas price series was stationary at first difference. The results of unit root test are presented in Table 2.
Table 2. ADF and PP Unit Root Test Results
Time Series

ADF Test Statistic

pvalue

PP Test Statistic

pvalue

Result

Production

3.743

0.036

26.995

0.010

Stationary

Price

1.186

0.889

4.629

0.8384

NonStationary

Diff(Price,1)

4.088

0.018

41.857

0.01

Stationary

Note: Alternative hypothesis: Stationary. Source: Author’s own calculations
Fig. 3. Graphical illustration of production and prices of rice in Pakistan (19842018)
The graphical presentation of production and price data is given in Fig. 3. Production and price both series are clearly showing an upward trend. The variance of price series has increased with the passage of time, so it is found nonstationary at level. There are significant fluctuations in production and prices of rice in Pakistan over the time.
Descriptive Summary: Table 3 presents the descriptive statistics of the variables used in cobweb model of rice. From 1984 to 2018, the minimum, average and maximum production of rice in Pakistan was 2919, 4873 and 7202 metric tonnes, respectively. Similarly, minimum, average and maximum prices per kilogram of rice were Rs. 5.88, Rs. 42.91 and Rs. 124.22, respectively.
Table 3. Descriptive Statistics of Rice Data in Pakistan (19842018)
Variable

Minimum

Mean

Maximum

Std. Deviation

Production (‘000’ Tonnes)

2919

4873

7202

38.861

Price (PKR Per Kg)

5.88

42.91

124.22

1414.527

Source: Pakistan Economic Survey: Various issues
Demand and Supply Functions: The cobweb model has been constructed under the naïve expectations hypothesis to derive timedelay difference equation characterized by the price fluctuations in rice market. The results of demand and supply functions are presented in Table 4. The signs of parameters are according to the expectations. In both models, the coefficients of price are insignificant, whereas those of lagged dependent variable are significant. The later reveals the existence of endogenity in model. The signs of estimated parameters are consistent with literature (Anokye and Oduro, 2013; Anokye et al., 2014; Khan et al., 2019).
Table 4. Results of Demand & Supply Functions for Agricultural Markets of Pakistan
Variable

Units

Demand of Rice

Supply of Rice

Intercept

(‘000’ Tonnes)

316.69 (423.39)

503.52 (406.253)

Diff(1)_Price_{k}

PKR per Kg

17.512 (11.923)



Diff(1)_Price_{k1}

PKR per Kg



2.652 (11.717)

Production_{k1}

(‘000’ Tonnes)

0.923*** (0.084)

0.873*** (0.081)

Adjusted R^{2}

0.7922

0.7849

FStatistic

61.98***

61.19***

No of observations

34 [19842018]

34 [19842018]

DWStatistic

2.66

2.61

Note: S.E reported after the coefficients in parenthesis. Significance Codes: ‘***’ = 0.01 ‘**’ = 0.05 ‘*’ = 0.1
The resultant demand and supply functions are given in equation 9 and 10, respectively.
D_{k} = 316.69  17.512 P_{k }+ 0.923 D_{k1} (9)
S_{k} = 503.52 + 2.652 P_{k1 }+ 0.873 S_{k1} (10)
From Equations 9 and 10, we have whereas . Hence, we have the ratio that is less than one.
The slope of supply function is smaller than that of demand function. The time path analysis of difference equation suggests the existence of cobweb phenomenon in the rice market of Pakistan. The resultant ratio detects the damped or convergent oscillations in rice prices towards the stable equilibrium level. The presence of convergent price oscillations in Pakistan’s rice market is in contrast to the divergent oscillations in Ghana’s tomato market (Anokye and Oduro, 2013) and maize market (Anokye et al., 2014). The possible reasons of contradictory results are the distinct characteristics of agricultural markets in terms of difference among the countries, crops, marketing structures and systems.
Pakistan’s rice market has been improved to an extent over the time in terms of facilities, structure, information transmission system and equilibrium attainment. However, a number of shortcomings still exist in rice market which need attention of the concerned government bodies and policy makers. The peculiar characteristics of agricultural markets such as bulkiness, varietal differences, dispersed production, processing requirements and seasonality lead to the complicated marketing system and ultimately the market prices of farm commodities remain unstable. In general, farmers disposeoff their farm commodities in raw form immediately after harvesting without processing and therefore, many intermediaries are involved between the producer and the end consumer.
It is crucial to take certain measures to mitigate the fluctuations in rice prices and supply shocks in Pakistan’s agricultural markets. Anokye and Oduro (2013) analysed Ghana’s tomato market and found that the appropriate storage facilities can help stabilizing the prices. Promoting the private sector trade of agricultural products can also increase the price stability (Dorosh and Salam, 2008). Swift price transmission and efficient market integration – both horizontal and vertical – can increase the speed of price adjustments in agricultural markets (Zafar et al., 2020). The price and supply shocks may be buffered by adopting suitable policies, promoting trade facilities, developing appropriate market structure especially storage facilities and improving the market information system in rice market of Pakistan.
Conclusion and Policy Suggestions: Rice is an important cereal crop of Pakistan. Unstable market conditions raise many challenges for small growers. This paper attempted to study the price dynamics of rice in Pakistan using the cobweb model. The official estimates revealed that rice price have fluctuated between a minimum level of Rs. 5.88 per kg and a maximum level of Rs. 124.22 per kg during the period 19842018. The study concludes that cobweb phenomenon exists in local rice market of Pakistan. However, price fluctuations are convergent towards stable equilibrium in rice market of Pakistan over the past three decades. To minimize the price and supply shocks, it is suggested as policy measures that the government may respond promptly to the instability of rice markets through formulating the appropriate agricultural policies, developing advanced storage facilities and improving the market information system for steady transmission of market information across the national as well as international rice markets. This study provides useful insights into understanding the dynamics and performance of local rice markets which will be worthwhile to the stakeholders and policy makers in respect of forecasting and stabilizing the market prices, and alleviating the food insecurity.
Conflicts of Interest: The authors declare no conflict of interest.
REFERENCES
 Anokye, M. and F.T. Oduro (2013). Cobweb model with buffer stock for the stabilization of tomato prices in Ghana. J. Manag. Sustain.3: 155165.
 Anokye, M., F.T. Oduro, J. AmoahMensah, P.M. Osei and E.O. Aboagye (2014). Dynamics of maize price in Ghana: linear versus nonlinear cobweb models. J. Econ. Sustain. Dev.5(7): 813.
 Anonymous. (2019). Economic Survey, Economic Affairs Division, Govt. Pakistan., Islamabad.
 Anonymous. (2021). Economic Survey, Economic Affairs Division, Govt. Pakistan., Islamabad.
 Athanasiou, G., I. Karafyllis and S. Kotsios (2008). Price stabilization using buffer stocks. J. Econ. Dyn. Control.32(4): 12121235.
 Boussard, J.M. (1996). When risk generates chaos. J. Econ. Behav. Organ.29(3): 433446.
 Chaudhry, M.I. and M.J. Miranda (2017). Complex Price Dynamics in Vertically Linked Cobweb Markets in Less Developed Countries. AEDE, The Ohio State University, USA, (online available at https://aede.osu.edu/): 136.
 Chiarella, C. (1988). The cobweb model: Its instability and the onset of chaos. Econ. Model.5(4): 377384.
 Deaton, A. and G. Laroque (1992). On the behaviour of commodity prices. Rev. Econ. Stud.59(1): 123.
 Deaton, A. and G. Laroque (1996). Competitive storage and commodity price dynamics. J. Polit. Econ.104(5): 896923.
 Dorosh, P. and A. Salam (2008). Wheat markets and price stabilisation in Pakistan: An analysis of policy options. Pak. Dev. Rev.47(1): 7187.
 Ezekiel, M. (1938). The cobweb theorem. Q. J. Econ.52(2): 255280.
 FAO. (2019). FAOSTAT, Food and Agricultural Organization, United Nations. Retrieved on 26/12/2020 from http://www.fao.org/faostat/en/#data/QC .
 Finkenstädt, B. (1995). Nonlinear dynamics in economics: a theoretical and statistical approach to agricultural markets. 1st Ed. SpringerVerlag Berlin Heidelberg. 166 p.
 Finkenstädt, B. and P. Kuhbier (1992). Chaotic dynamics in agricultural markets. Ann. Oper. Res.37(1): 7396.
 Greenland, D.J. (1997). The sustainability of rice farming. Cab Int. & Int. Rice Res. Inst. Wallingford (UK). 273 p.
 Gustafson, R.L. (1958). Carryover levels for grains: a method for determining amounts that are optimal under specified conditions. Technical Bulletin No 1178. US Deptt. Agric. Washington DC.URL: https://EconPapers.repec.org/RePEc:ags:uerstb:157231.
 Hommes, C.H. (1991). Adaptive learning and roads to chaos: The case of the cobweb. Econ. Lett.36(2): 127132.
 Hommes, C.H. (1998). On the consistency of backwardlooking expectations: The case of the cobweb. J. Econ. Behav. Organ.33(34): 333362.
 Huong, N.T.L., Y.S. Bo and S. Fahad (2017). Farmers’ perception, awareness and adaptation to climate change: evidence from northwest Vietnam. Int. J. Clim. Chang. Str.9(4): 555576.
 Jensen, R. (2000). Agricultural volatility and investments in children. Am. Econ. Rev.90(2): 399404.
 Jensen, R.V. and R. Urban (1984). Chaotic price behavior in a nonlinear cobweb model. Econ. Lett.15(34): 235240.
 Khan, S.U., M.A. Faisal, Z.U. Haq, S. Fahad, G. Ali, A.A. Khan and I. Khan (2019). Supply response of rice using time series data: Lessons from Khyber Pakhtunkhwa Province, Pakistan. J. Saud. Soc. Agric. Sci.18(4): 458461.
 Ma, J. and L. Mu (2007). Complex dynamics in a nonlinear cobweb model for real estate market. Discret. Dyn. Nat. Soc.2007(Art. ID 29207): 114.
 Maclean, J.L., D.C. Dawe, B. Hardy and G.P. Hettel (2002). Rice almanac: Source book for the most important economic activity on earth. 3rd Ed. CABI Publishing, UK. 253 p.
 Mitra, S. and J.M. Boussard (2012). A simple model of endogenous agricultural commodity price fluctuations with storage. Agric. Econ.43(1): 115.
 Myers, R.J. (2006). On the costs of food price fluctuations in lowincome countries. Food Policy31(4): 288301.
 Nerlove, M. (1958). Adaptive expectations and cobweb phenomena. Q. J. Econ.72(2): 227240.
 Nicholson, W. (1972). Microeconomic theory: basic principles and extensions. 6th Ed. The Dryden Press, Fourt Worth.
 Scheinkman, J.A. and J. Schechtman (1983). A simple competitive model with production and storage. Rev. Econ. Stud.50(3): 427441.
 White, B. and P. Dawson (2005). Measuring price risk on UK arable farms. J. Agric. Econ.56(2): 239252.
 Williams, J.B. (1936). Speculation and the carryover. Q. J. Econ.50(3): 436455.
 Zafar, M., N. Hamid and F. Arshad (2020). Are Agricultural Markets in the Punjab Technically Efficient? Lahore J. Econ.25(1): 89138.
