Samaneh Namdari·Kamran Adeli·Soleiman Mohammadi Limaei·Zahra Bahramabadi

Abstract Linear risk programming was used to determine the optimum cultivation pattern to increase incomes of poplar farmers.Seven clones of Populus deltoides Bartr.ex Marsh.were examined in Guilan province,northern Iran.Growth and price data were taken from previous research at the Safrabaste Poplar Research Station and in interviews with farmers.The Lingo software was used to analyze the data in different forms of E.The results show that when risk was considered,the optimal solution included the clones Pd63/51-x1,-Pd72/51-x3,Pd73/51-x4 and Pd79/51-x6.There was a high growth fluctuations of the clones Pd69/55-x2,Pd77.51-x5,and Pd caroliniensis-x7 and were not included in cultivation plans.Furthermore,the existing farm plans executed by local farmers,is neither profitoriented nor efficient in terms of income risk management according to risk efficient frontier.These results could help farmers with different levels of risk-aversion to select proper planting plans.

Keywords Populus deltoides·Farmers·Linear risk programming·Optimum cultivation patterns

Introduction

Forest plantations are subject to various risks in the form of price instability in the market and instability due to changes in rainfall patterns and other natural phenomena(Payn et al.2015).These risks lead to farmers’income instability and consequently affect household subsistence levels.Small-scale farmers are notably vulnerable to any shocks due to their high dependence on farming livelihoods.Therefore,any crop productivity reduction can have significant impact on incomes and welfare(Harvey et al.2014).Overlooking risk in a classic model of linear programming has often led to results that differ from what farmers have done in reality(Taghizadeh et al.2011).In considering this problem and noting the risk factor,several models have been applied to optimize the farming system such as quadratic programming(QP),stochastic dominance(SD),expected mean-variance(EMV),minimization of the total absolute deviation(MOTAD)and target-MOTAD. Among these, the MOTAD model has been widely used over the last two decades for specifying optimal cultivation patterns.Kehkha et al.(2005)applied this model to study the effects of risk on cropping patterns and farmers’income on farms in Fars province.Taghizadeh et al.(2011)used the model for determining the optimum cultivation patterns under water deficits.Daneshvar-Kakhki and Ghodrati-Azadi(2009)used the target-MOTAD model to develop a cultivation plan for oilseed cropping.Abdeshahi and Soltani(2000)investigated farmers’risk behavior using the safety first rule(SFR),generalized stochastic production function(GSPF)and target-MOTAD models.Singh and Singh(1999)investigated production and income and showed that cultivation programming increased production from 60 to 96% and net income from 23 to 26% .The aim of this research is to determine the effects of risk on farm incomes as well as the optimal cultivation pattern considering risk using the MOTAD model.Furthermore,high risk and low risk poplar clones were identified to poplar farmers in the study area.

Materials and methods

Study area

The study area is located in the Astaneh-ye Ashrafiyeh district,Guilan province,northern Iran at 49°57′to 49°60′E longitude and 37°19′to 37°22′N latitude(Fig.1).Based on 30-year statistics (1985 to 2014)from the Astaneh-ye Ashrafiyeh weather station,the average annual rainfall was 1200 mm and average annual temperature 11.6°C.Minimum and maximum annual temperatures were 2.4°C and 20.2°C in December and July,respectively.In addition,soil moisture was udic,common to soils of humid climates,and the regime,mesic(General Office of Natural Resources and Watershed of Guilan province 2015).Different land uses in the area include mixed stands of poplar(Populus deltoides) and alder (Alnus subcordata C.A.Mey.)in different ratios,pure stands of alder and spruce,bald cypress(Taxodium distichum(L.)Rich.plantations and rice paddy fields.

Data collection

Growth data

Seven pure clones of Populus deltoides,commonly grown by local farmers at a 5 m×5 m spacing,were selected(Table 1).These seven clones-Pd63/51,Pd69/55,Pd72/51,Pd73/51,Pd77/51,Pd79/51,and Pd caroliniensiswere used as decision variables.

Fig.1 Map of Astaneh-ye Ashrafiyeh,Guilan province in northern Iran

Table 1 Names and number of clones studied(decision variables)

Average annual growth data for the clones were taken from a research project in Safrabaste Poplar Research Station during the period 2002-2012 (Fig.2) (Karimi 2015).

Estimation of the stumpage price equation of Populus deltoides clones

Stumpage price data of the different clones were gathered through interviews with farmers and sawmill personnel over 1990-2009.The data were adjusted to the Consumer Price Index(CPI)of Iran for the base year 2004,Eq.(1)and Fig.3(Central Bank of Iran 2015).

where Pris the real price,Ptthe price in year t,ytthe price index in year t,and 100 the price index in the base year(Branson 1979).

Economists have generally applied two approaches to estimate stumpage prices.According to the first approach,prices follow a stationary autoregressive model so that price changes over a period will have no significant effect on prices in the next period.Therefore,the best method for forecasting prices is to calculate the average of the previous prices.In this way prices can be estimated using the following formula:Pt+1=α+βP where 0＜β＜1.

In the second approach,prices are non-stationary and do not follow the aforesaid stationary condition.In this situation,prices in the next year or period completely depend on prices in the previous year or period.Price in this approach can be evaluated as Pt+1=βP， β=1(Mohammadi Limaei 2006).

In this study,the price data followed a stationary and autoregressive model,and this approach was applied toestimate the parameters,Eq.(2)(Mohammadi Limaei and Lohmander 2007).

Fig.2 Average annual growth of clones over 2002-2012

Fig.3 Nominal(non-adjusted)and real(adjusted)prices of Populus deltoides in the considered period

Here it is assumed that εtis a sequence of errors with a normal distribution,a mean of zero and zero autocorrelation.pt+1is the price in year t+1 and ptthe price in year t.The expected mean stumpage price is calculated as follows:

According to the results and at value confidence level of 95% ,there was a significant correlation between parameters Pt+1and Pt.Moreover,the results of this analysis revealed that β varied between 0 and 1,and a stationary condition was observed(Table 2).

The price predicting equation for Populus deltoides clones was calculated using the parameters obtained from the regression analysis,and by substituting the values of the parameters in Eq.(2)as follows:

Using Eq.(3),the expected mean stumpage price of Populus deltoides clones was calculated as 218,950 IRR(US$7.30)per m3.

Gross income of Populus deltoides clones

This was calculated by multiplying the expected mean stumpage price by the average annual growth over the period 2002-2012.In the next step,in order to calculate the average gross income in this period,the income of different years discounted to year zero and the average gross incomes of the different clones were eventually calculated(Table 3).It should be noted that the market prices of all poplar clones were very similar.Hence,we considered an identical price for all of the clones.Furthermore,due to the fact that the government provides free saplings to farmers and the average annual rainfall is 1200 mm,farmers do not need irrigation.Therefore,variable costs are insignificant and not considered in the calculations.

The MOTAD model

The MOTAD programming model is a linear approximation of the Quadratic Risk Programming(QRP)model.To solve the problem of estimating the variance-covariance matrix for QRP,Hazel and Norton(1986)applied the Mean Absolute Deviation (MAD) of crop returns from their average returns.Therefore,in the MOTAD method,risk calculation depends on the mean absolute deviation.This criterion can easily be inserted in the linear programming pattern.If the incomes of the farmers have a normal distribution,by changing the expected income of the MOTADpattern in a parametric way,we can derive similar answers as the QRP.

Table 2 Estimated parameters using autoregressive analysis

Table 3 Gross income of Populus deltoides clones in different years(Iranian Rials per ha)

The general form of the MOTAD model

where Z is the sum of the gross income modulus of a different range of activities from their mean values;is the negative modulus of total gross income deviations in year h from their mean output;xjis the production activity level j;aijis item j level for each unit from i activity;bjis the supply of the available source j;Chiis the programmed i activity output in year h;giis the mean amount of gross output of i agricultural or livestock activity;fiis the programmed i activity output and E is the constant parameter of zero to Z of the total expected gross output.

In this study,the limitations exerted on the farm include land,labor and capital.These limitations are defined as follows.

Land limitations

xiis the area cultivated by clone i;piis the coefficient of area cultivated by clone i(considered one ha for all types of clones);and plantation is the total area currently available for afforestation in Astaneh-ye Ashrafiyeh district

Labor limitation

Liis the number of laborers needed to plant each hectare of clone i;labor is the maximum person/day labor available in Astaneh-ye Ashrafiyeh district.

Limitation of capital

Ciis the required capital for planting one hectare of clone i;capital is the total available assets and includes cash,machinery,and other equipment used in the whole process of planting and harvesting.

Limitation of negative deviation from the average return

Chiis the programmed i activity output in year h;giis the mean amount of gross output of clone i;is the negative modulus of total gross income deviation in year h from their mean output.

The parametrical limitation of the model

fiis the programmed i activity output and E is the constant parameter of zero to z of the total expected gross output.

The MOTAD model was coded in Lingo software considering the previously noted function objectives and constraints (supplementary appendix 1). The estimated coefficients and Right Hand Side(RHS)of the MOTAD model are shown in Table 4. These coefficients were extracted by interviewing poplar growers and by collecting the data regarding land and capital from the General Office of Natural Resources and Watershed of Guilan province(2015).As shown in Table 4,12 laborers were required per day in order to plant the different clones at 5×5 m spacing per hectare.The number of available labor in the study area was 62,736 people.The coefficient of cultivated area considered one hectare for all the clones and the total area for reforestation was 8460 ha.The cost of planting each hectare of different clones was determined to be a US$400(12 million IRR).The total amount the government allocates for reforestation in the area is US$16,000(480 million IRR).After calculating the average gross income of different clones, the negative deviation was calculated from the average gross income in different years.

Results and discussion

Using standard linear programming,the maximum value of E or Z was calculated as US$329,364(9880.920 million IRR), the maximum level of income obtainable. By changing the value of E(from zero to Z),different plans with various levels of risk were determined(Table 5).These results enable the farmers and producers to choose a risk efficient farm plan with regards to their risk-averse behavior.In this study,risk taking households will choosefarm plan X with higher expected incomes and associated with larger variance in incomes.As we move from plan X to plan I,risk aversion increases and plans are selected by risk-averse households.Risk neutral households will most likely select farm plans between the two extremes,i.e.,plan V.

Table 4 Coefficients and variables of the MOTAD model

Table 5 MOTAD model results(risk minimized solutions)

In plan X,5228.0 ha should be allocated to clone Pd63/51.If farmers would like to be a little more certain and to minimize risk(for instance,from US$1,631,136 to US$1,371,115.67[48,934.08 to 41,133.47 million IRR]),they could allocate 3951.3 ha to clone Pd63/51,and 1276.7 ha to clone Pd79/51,and an income of US$300,000(9000 million IRR)could be expected.Moreover,by increasing the expected income or minimizing risk,low risk clones with a higher average return and lower fluctuations in gross income are added to the farm plan,while high risk clones with lower average returns and fluctuations higher in gross income are omitted.Abdeshahi and Soltani(2000)and Torkamani and Kalai(1999)confirmed this observation.

Clones of Pd69/55-x2,Pd77.51-x5 and Pd caroliniensisx-7-with an average gross incomes of US$38.89,29.2 and 3.17(1,166,503,875,934 and 954,151 IRR,respectively),and variation coefficients of 56.36,66.08 and 53.36% (Table 6)respectively,are not recommended under any circumstances due to lower gross incomes and higher income fluctuations.These clones are high risk with most income volatility.Among the four remaining clones,-Pd73/51-x4 with a return of US$19.02(570,667 IRR)and lowest coefficient of variation(50.47% )will be omitted from the plan by increasing the expected income to US$233,333.33 USD(7000 million IRR),and will be substituted by Pd72/51-x2 with a gross income of US$41.91(1,257,353 IRR)(Tables 5,6).

With an increase in the expected income from US$233,333.33 to US$300,000(7000 to 9000 million IRR),and an increase in minimum risk from US$978,682.33 to US$1,371,115.67(29,360.47 to 41,133.47 million IRR),the Pd63/51-x1,Pd72/51-x2 and Pd79/51-x6 clones with the highest gross income remain in the farm plan.Furthermore,Pd73.5-x4 and Pd63/51-x1 can be identified as low-risk and high-risk clones,respectively.

Figure 4 represents the MOTAD results in terms of the efficient frontier between expected incomes and associated risk levels.The efficient frontier as a portfolio technique helps farmers to choose the maximum possible expected income associated with lowest level of risk.Therefore,all the points on the frontier line are considered as efficient.As seen in Fig.6,the actual plan of farmers is implemented with lower levels of income at higher risk levels.This means that the exiting plan is neither profit-oriented nor efficient in term of income risk management.According to Kaseva(2013)and Brunette et al.(2017),under this classic pattern,farmers are forced to take a higher level of risk for receiving a considerably lower level of income.The plans extracted from the MOTAD model are more reliable than the actual plan due to the reduction of the negative effects of risk to farmers and producers.

Fig.4 Risk efficient frontier for the selected clones(million IRR)

Sensitivity analysis

In this study,we applied reduced costs and dual prices from the‘‘Lingo Report’’for the sensitivity analysis.As shown in Table 7,the shadow value of land and capital constraints equal zero for all of the plans under consideration and these constraints are nonbinding.This means that increasing or decreasing these constraints by one unit will have no effect on the objective value or risk value.The labor force is the only constraint that affects the objective function value in plan I to plan VI.For instance,at the expected income level of US$6000,the objective function value or the amount of risk decrease by 0.61 units if the labors force constraint is increased by one unit.

If there is a variable with a reduced cost,a penalty would be paid as much as the reduced cost to introduce that variable into the optimal solution.The optimal solution includes the clones with reduced cost to zero and eliminates the clones with reduced non-zero cost.For instance,clone Pd 69/55 associated with reduced non-zero cost was eliminated from the optimal solution,as well as clone Pd79/51 due to reduced cost zero presented in all of the plans(Tables 7,8).

Table 6 Coefficient of variation and average gross income from different Populus deltoides clones

Table 7 Dual price values of land,capital and labor constraints(US$)

Table 8 Reduced cost value of clones

Conclusions

This research determined the effects of risk on farm incomes as well as optimal cultivation patterns in the Astaneh-ye Ashrafiyeh district using the MOTAD model.High risk and low risk poplar clones for local farmers were identified. The MOTAD results and the risk efficient frontier showed that the actual plan farmers are presently implementing results in lower levels of income with higher levels of risk;the existing plan is neither profit-oriented nor effective in terms of income risk management.Moreover,by increasing expected income or reducing risk,the low risk clones with a higher average incomes and lower income fluctuations(such as Pd63/51)are added to the farm plan,while high risk clones with lower average incomes and higher income fluctuations(such as Pd73/51)are omitted.These findings can be of great importance to farmers with different levels of risk-taking for improving their incomes.In the end,due to farmers’risk-aversion in producing crops,it is suggested that the government provide some assistance such as subsidies and crop insurance.

AcknowledgementsOur grateful thanks to Safrabaste Poplar Research Station for providing us with data and information.Also we should be thankful to the Indigenous people,especially the poplar farmers,of Astaneh-ye Ashrafiyeh for their compassion in cooperation with us.