Chapter Three Econometric Model

Transcription

1 Chapter Three Econometric Model Methodology of Estimation and Data 3.. Introduction In chapter two we have presented a detailed survey of existing literature on the various aspects of crop insurance and its effects on agriculture. In this chapter we shall deal with the presentation of econometric model of crop insurance and the corresponding method of estimation and data. This chapter is organized as follows. In section 3. the descriptive statistics on area, output, yield rate and use of fertilizer for Aman Paddy, Boro Paddy and Potato have been considered. The descriptive statistics on the total area under cultivation, irrigation, related issues of crop insurance participation and revenue have been discussed. We have discussed the analytical model and methodology for growth rate in section 3.3. The section 3.4 is based on the analysis of the structural shift due to insurance participation. We have considered the model of profile of correlation coefficient in the production of crops in section 3.5. In section 3.6 the analytical model of area and output on insurance participation has been explained. We have explained the test of mean difference of insurance participation in section 3.7. In section 3.8 panel data regression model is considered. We have discussed the methodology of data collection in section 3.9. The specification of the variables has been presented in the section 3.0. In section 3. specifications of the econometric models for the crop insurance have been considered. On the other hand, in section 3. specification of hypothesis has been analyzed. Finally in section 3.3 conclusion of this chapter is considered. 69

2 3.. Descriptive Statistics We would like to present descriptive statistics by general statistical rule. We want to calculate the mean, median, mode, standard deviation, coefficient of variation, maximum and minimum values and standard error. The mean value helps us understand about the picture of the gross value of the variables. On the other hand the coefficients of variation help us explain the consistence or inconsistence of the different variables. By the descriptive statistics we also explain the nature of the distribution of variables. We want to calculate the descriptive statistics about area, production, yield, fertilizers consumption, irrigation facilities, crop insurance participation and total revenue for Aman Paddy, Boro Paddy and Potato Analytical Model and Methodology for Growth Rate We want to measure the growth rate of our explained variables during the period 990 to 00 from our collected secondary data from the different issues of district statistical hand books in the district of Hooghly. The growth rate of all variables (area of under cultivation, output, yield, total and per acre NPK consumption under principal crops, irrigated land as proportion to total land and total revenue) during the period can be measured simply by taking a log linear trend equation. The log linear trend equation can be written as follows where ln y = β + βt+ u ; t =,,..., n (3.3.) t 0 t ut satisfy all the assumptions of the classical linear model. Therefore we apply simple method of least square technique to estimate the time coefficient ( β ) which gives the growth rate of all specified variables in our models. The growth rate area of under cultivation, output, yield, total and per acre NPK consumption under principal crops, irrigated land as proportion to total land and total revenue has been measured for Aman Paddy, Boro Paddy and Potato by using the above equation Model and Methodology of Structural Shift due to Impact of Crop Insurance The Comprehensive Crop Insurance Scheme (CCIS) was introduced in Indian agriculture on and from st April 985 by the General Insurance Corporation of India (GIC) in collaboration with State Governments. The Comprehensive Crop Insurance Scheme (CCIS) included loanee farmers. The National Agricultural Insurance Scheme (NAIS) was introduced in Indian 70

3 agriculture from Rabi season ( ) by replacing the Comprehensive Crop Insurance Scheme (CCIS). In West Bengal the National Agricultural Insurance (NAIS) or the Rashtriya Krishi Bima Yojana (RKBJ) was introduced since Rabi season. Before the introduction of crop insurance the farmers also took crop loan from different financial institutions. So they became loanee farmers. But there is no compulsion of crop insurance. That implies that after crop damage there is no chance of receiving indemnity from insurer. But after the introduction of crop insurance since Rabi season all loanee farmers became compulsorily insured. In that situation after crop damage due to natural calamities they received indemnity from insurer and also from both the Central and the State Government. For this reason it is called the crop insurance. To analyze the impact of crop insurance we use simple spline function approach which is developed by Poirier in 974. The entire study period (990-00) can be divided into two parts. One is pre-crop insurance regime (PREINSREG) from to and other is crop insurance regime (POSTINSREG) from to Assuming a linear trend, the postulated model is Pre-crop insurance regime: ln Y = α + βt+ u for t 000 t Crop insurance regime: ln Y = α + β t+ u for 00 t 00 Let us define the following variables: w t { < } = t; w = if t (3.4.a) t t t t and reparameterise the function as lny t α δw t δw t u t t t (3.4.) = (3.4.) The expression ( ) exp βi 00 will yield the percentage growth rate of all selected variables for the pre-crop insurance and crop insurance regimes ( i =, ), where β = δ and β = δ + δ. Equation (3.4.) will be used to compute the growth rates of all selected variables for pre-crop insurance and crop insurance regimes. This model is applied for analyzing the impact of crop 7

4 insurance on area under cultivation, yield rate, fertilizer consumption, irrigated land as proportion to total land and total revenue from Aman Paddy, Boro Paddy and Potato Profile of Correlation Coefficient in the Production of Crops The correlation coefficients between two specific variables have been computed only for the observations during the crop insurance regime to The total area of a crop depends on a set of number of variables such as insurance participation for a crop, total suminsured and total premium collected. We want to verify if there is any significant relation among them. This is tested from the profile of the pearsonian correlation coefficient matrix. Similarly, the total production of a crop is stimulated by a set of variables such as an insurance participation, total insured farmer, total sum-insured, total premium collected, premium rate and price level. These variables are also known as explanatory variables. Therefore, by the profile of coefficient of correlation matrix we want to test which variables are significantly related to each other. In this section we analyze the profile of correlation coefficient matrix in the production of Aman Paddy, Boro Paddy and Potato in the district of Hooghly Analytical Model of Area and Output on Insurance Participation Total area of any crop is a quantitative variable. It is also a dependent variable in our model which is the explained variable. Thus, the total area of a crop is symbolized as TAREA. This explained variable depends on the three important explanatory variables. These explanatory variables are (i) insurance participation (INPARTC), (ii) total sum-insured (TOLSUMIN) and (iii) total premium collected (TPRECOL). The symbolized function can be written as Total Area under Cultivation = f(crop Insurance Participation, Total Sum-Insured, Total Premium Collected and Error Term) On the other hand, as an analytical model for the estimation of the total production of the three crops such as Aman Paddy, Boro Paddy and Potato, we consider a log-linear function that would assess the total production by the balanced panel least squares technique. The total production is also an important explained variable. We can symbolize the total production as TPRODUCT. 7

5 This explained variable is also a quantitative variable and it also depends on the same explanatory variables as total area. This function can be written as Total Production= f(crop Insurance Participation, Total Sum-Insured, Total Premium Collected and Error Term) Pooling or combining all observations for all crops, we can write the required equation as ln( Y ) = β + β ln( X ) + β ln( X ) + β ln( X ) + u (3.6.) it it 3 3it 4 4it it where i stands for the i th cross-sectional unit and t for the tth time period. In this case each cross-sectional unit has the same number of time series observations; such a panel data is called a balanced panel. The above equation is applicable both the dependent variables like total area (TAREA) under cultivation and total production (TPRODUCT) for all the three crops such as Aman Paddy, Boro Paddy and Potato Test of Mean Difference of Insurance Participation The test of mean difference is a vital test in order to verify if there is any significant difference between crops for a specific farm and between farm-size for a specific crop. The mean differences have been tested on the basis of the test statistic t. The test statistics can be defined x x by the following formulat = SE. x x n n ( ) t + ; where x and x are respectively the mean value of the insurance participation for the first and second crop for a particular farm-size. This formula will also be used for the test of mean difference of the insurance participation between two specific farm-sizes for a particular crop Panel Data Regression Models We will estimate the area under cultivation, total production, yield and the cost of different factors of production of different farm-size on the basis of our collected primary data directly from field survey. We have collected the data of different farm-size for the period We shall use the panel data regression models to analyze the different characteristics of different farm-size. In panel data the same cross-sectional unit (say farm-size) is surveyed over time; that is, panel data have space as well as time dimensions. 73

6 We have collected data about three hundred fifty five farms of five different sizes for Aman Paddy, Boro Paddy and Potato. The collected data about farm have been classified into five farmsize such as marginal farm (less than one acre of land), small farm, medium farm, semi-medium farm and large farm on the basis of area of cultivable land. Therefore, one cross-section includes three hundred fifty five observations (355). The total panel (balanced) observations for the five years (006-0) for all farms taken together are one thousand seven hundred seventy five (775). Pooling or combining, all one thousand seven hundred seventy five (775) observations, we can write the equation as ( ) ( ) ( ) ln Y = β + β ln X + β ln X + β t+ u (3.8.) it it 3 3it 4t it ( it ) (0, ) Eu N σ where i =,,...,355 and t =,,3, 4,5. We assume that all coefficients are constant across time and individuals and apply simplest OLS method to estimate the equation (3.8.). This model is known as restricted model. If we assume that all slope coefficients are constant but the intercepts varies across individuals, we can rewrite the above equation (3.8.) as ( ) ( ) ( ) ln Y = β + β ln X + β ln X + β t+ u (3.8.) it i it 3 3it 4 it ( it ) (0, ) Eu N σ where i =,,...,355 and t =,,3, 4,5. This model (3.8.) is known as fixed effects (regression) model (FEM). The term fixed effects is due to the fact that, although the intercept may differ across individuals (here the five farmsizes), each individual s intercept does not vary over time; that is, it is time invariant. In order to estimate the model we introduce the differential intercept dummies and OLS method. Therefore, we rewrite the equation (3.8.) as ( ) ( ) ( ) ln Y = α + α D + α D + α D + α D + β ln X + β ln X + β t+ u (3.8.3) it i 3 3i 4 4i 5 5i it 3 3it 4t it Eu N σ ( it ) (0, ) where i =,,...,355 and t =,,3, 4,5. 74

7 The model (3.8.3) is also known as least-squares dummy variables (LSD) model. We introduced the individual dummies in an additive manner. This model (regression equation) can also be estimated by the OLS method. We can easily extend our LSD model. In that situation we have multiplied each of the farm-size dummies by each of the explanatory variables or regressors or independent variables. Therefore, the model or regression equation (3.8.3) can be written in the following form Yit = α+ αdi + α3d3i + α4d4i + α5d5i + βxit + β3x3it + β4tt + γ( Di * Xit ) + γ( D3i * Xit ) + γ3( D4i * Xit ) + γ4( D5i * Xit ) (3.8.4) + γ5( Di * X3it ) + γ6( D3i * X3it ) + λ7( D4i * X3it ) + γ8( D5i * X3it ) + γ ( D * t) + γ ( D * t) + γ ( D * t) + γ ( D * t) + u ( it ) (0, ) Eu N σ 9 i 0 3i 4i 5i it where i =,,...,355 and t =,,3, 4,5. Here, the coefficients γ ' s are the differential slope coefficients andα, α 3, α4 andα 5 are the differential intercepts. If one or more of the γ coefficients are statistical significant, it will tell us that one or more slope coefficients are different from the base group. Thus we remark that if all the differential intercept and all the differential slope coefficients are statistically significant, the marginal farm, small farm, medium farm and semi-medium farm are said to be different from the large farm. Differentiating equation with respect to X ( j =,3) we get the effect of change in X jit on Y it. Thus we have the marginal effect of Xit, X 3it and t on Y it as respectively jit Y X it Y X it it 3it = β + γ D + γ D + γ D + γ D i 3i 3 4i 4 5i = β + γ D + γ D + γ D + γ D 3 5 i 6 3i 7 4i 8 5i (3.8.5) Y it t = β + γ D + γ D + γ D + γ D 4 9 i 0 3i 4i 5i Putting D = D3 = D4 = D5 = 0 we get the marginal effects of the concern variables for large farm i i i i which are respectively Y X it it = β, Y X it 3it Y = β3 and it = β4 t (3.8.5a) 75

8 Similarly the marginal effects of the concern variables for medium farms are found by putting D =, D = D = D = 0 as respectively i 3i 4i 5i Y X Y X it it it 3it = β + γ = β + γ 3 5 (3.8.5b) Y it t = β + γ 4 9 Similarly the marginal effects of the concern variables for semi-medium farms are found by putting Di = 0, D3i =, D4i = D5i = 0 as respectively Y X it Y X it it 3it = β + γ = β ++ γ 3 6 (3.8.5c) Y it t = β + γ 4 0 Similarly the marginal effects of the concern variables for semi-medium farms are found by putting Di = 0, D3i = 0, D4i =, D5i = 0 as respectively Y X it Y X it it 3it = β + γ 3 = β + γ 3 7 (3.8.5d) Y it t = β + γ 4 Putting Di = D3i = D4i = 0, D5i = we get the marginal effects of the concern variables for marginal farm which are respectively Y X it it = β + γ 4 Y X it 3it = β + γ 3 8 (3.8.5e) Y it t = β + γ 4 76

9 Equations (3.8.5a), (3.8.5b), (3.8.5c), (3.8.5d) and (3.8.5e) referred to the marginal effects of change in concerned variables on Y it for large, medium, semi-medium, small and marginal farms respectively Methodology of Data Collection The study has been conducted in the district of Hooghly in the state of West Bengal. There are nineteen districts in the state of West Bengal. We have chosen only Hooghly district purposively. The rationale behind the choice of the district of Hooghly lies in the effectiveness of the National Agricultural Insurance Scheme (NAIS) or the Rashtrio Krishi Bima Yojona (RKBJ). The district of Hooghly is economically more advanced and prosperous in respect of agriculture, industry and infrastructural aspect of development. The RKBJ was introduced in West Bengal from Rabi Season (00). The crops which have been included under this scheme are Aman Paddy (Kharif Season), Boro Paddy (Rabi Season), commercial crops like Potato (Rabi Season), Mustard, Wheat, Jute, Maize, Barley, Sugarcane, etc. We have chosen Aman Paddy at the Kharif season, because there are no insured farmers under the Aus Paddy in the entire district. Among the Rabi season crops, we have chosen only two crops such as Boro Paddy and Potato. There are no insured farmers under Wheat, Barley, Maize, and other cereals, Gram, Tur, Jute, Mesta, other Fibers and Sugarcane. In the case of Rapeseeds and Mustard seeds there are very small number of insured farmers for one year only (008) under the crop insurance scheme which is therefore of little significance in our study. So we have considered three important crops, namely Aman Paddy, Boro Paddy and Potato. For analyzing the impact of crop insurance we have selected eighteen blocks of the district and three important crops such as Aman Paddy (Kharif Season), Boro Paddy (Rabi Season), and Potato (Rabi Season). 77

10 These three crops are produced by the farmers of the Hooghly district. The major insured farmers mainly produce these three important crops. But the district of Hooghly is in the top position in Potato production. The Potato is an important commercial crop to the farmers of this district. All types of crop insurance policies such as Rashtrio Krishi Bima Yojan (RKBJ) and Weather Based Crop Insurance Scheme (WBCIS) are based on area approach. These schemes have covered these three crops. There are two types of insured farmers such as loanee and non-loanee farmers. From the collected secondary data we have got the information that there are the farmers who are loanee are compulsorily insured. The loanee farmers take loan from different institutional sources (Co- Operative Bank, Agricultural Development Bank, Allahabad Bank etc.) for cultivating these crops. The non-institutional sources of agricultural (relative, money lender etc.) credit or loan does not provide insurance facility. The loanee farmers come under NAIS or RKBJ scheme Nature and Sources of Secondary Data We have collected the secondary data on area under cultivation, total production and yield rate at block level during the year to from the various issues of District Statistical Hand Books. The crop insurance related secondary data has been collected during the period 00-0 to from the Hooghly District Central Co-operative Bank Limited and the Regional Office of Agriculture Insurance Company of India Limited in the Kolkata. From the Regional Office of Agriculture Insurance Company of India Limited (AICIL) in the Kolkata we have collected various important crop insurance related data such as Number of Insured farmers (Small/Marginal and Others), Insured Acres, Sum Insured, Total Amount of Premium Collected, Threshold Yield (TY), Actual Yield (AY), Number of Affected Area by Natural Calamities, Number of affected farmers by the Natural Calamities, Total Amount of Claim or indemnities paid to the affected farmers, loss-ratio, Premium Rate (Rate Interest of 78

11 Crop Loan) and Indemnity Limit of the different crops that is fixed by the insurers own confidential rule at the Block level of Hooghly district. We have collected these data at the block level from 00-0 to The secondary data on the use of fertilizers (NPK) per acre, total amount of the use of NPK according to the different crops of different years at the district level, on area of production and yield rate for three (007-08, , 009-0) years have been collected from Principal of Agricultural Office (PAO) and Rice Research Centre (Chinsurah, Hooghly). The price data (Wholesale Price) of these three important crops have been collected from principal markets by Agmark of India and also from businessmen of different blocks. The data about the use of fertilizer and pesticides (average) per acre during the period to has been collected from the businessmen of fertilizer and pesticides, farmers, different issues of District Statistical Hand Books, Economic Review of West Bengal and also from the Statistical Abstract of West Bengal. The data of price of fertilizer and pesticides has been collected from the Benefed Office, the sales man of fertilizer and the farmers of different blocks. We have also collected the data about the total area under cultivation and the total irrigated area in the district of Hooghly during the period to form the different issues of District Statistical Hand Books, Economic Review of West Bengal and also from the Statistical Abstract of West Bengal Nature and Sources of Primary Data We have collected the primary data about the fertilizer cost and pesticides cost per acre at the farm-size level for the crops under study such as Aman Paddy, Boro Paddy and Potato. We have also collected the information about the irrigation cost, labour cost, seed cost per acre at the farmsize level during the period by field survey. The primary data for our study has been collected by field survey with the help of suitable questionnaire for these three crops (Aman Paddy, Boro Paddy and Potato) from the insured farms of the district Hooghly during the period The following information of a specific crop of an individual insured farm has been collected. 79

12 ALOATAFARM= Amount of Loan taken by farms (in Rupees) INAREA= Insured Area (in Acre) INSPARTC =Insurance Participation AMANLAND= Total cultivable land under Aman Paddy ( in Acre) BOROLAND= Total cultivable land under Boro Paddy ( in Acre) POTATOLAND= Total cultivable land under Potato ( in Acre) TPRODUCT= Total Production (in Quintal) YIELD= Yield (Quintal/ per acre) LABOURCOST= Labour cost (in rupees) SEEDCOST= Seed cost (in Rupees.) IRRIGATIONCOST= Irrigation cost (in rupees) FERTILISERCOST= Fertilizer cost (in rupees) PESTICIDECOST= Pesticide cost (in rupees) EDUCATION= Education level of the farmers. We have followed the multi-stage sampling process for the collection of data about the farms. First of all we have selected the district of Hooghly purposively among the nineteen districts of the state of West Bengal. In the district of Hooghly there are eighteen Blocks of which we have selected two Blocks, namely Arambagh and Ghogat purposively. The Arambagh Block is agriculturally more prosperous than Ghogat (I and II) Block. In these two Blocks together there are thirty Gram Panchayates of which Arambagh Block contains fifteen Gram Panchayates and Ghogat (I and II) Block contains fifteen Gram Panchayates. From each of the Blocks we have chosen the five Gram Panchayates randomly. Thus total ten Gram Panchayates (GPs) are selected. From each of the Gram Panchayates (GPs) we have collected twenty farms randomly using the random number table in a particular year. Thus in 006 we got 400 farms from all the randomly selected Gram Panchayates of the purposively selected Blocks in the district of Hooghly. These 400 farms have been divided into five broad categories according to land size, namely, marginal farms (less than one acre), small farms (one to two acre), medium farms (two to four acre), semi-medium farms (four to ten acre) and large farms (above ten acre). Since out of these 400 farms, 45 farms were not able to furnish with the related and adequate information 80

13 required for our study, we have dropped them. Thus finally we have fixed the number of farms to 355 in which farms of different sizes are considered to be equal in number. Thus we have 7 farms for each of five different sizes. Therefore, in the every year the total number of cross section is three hundred and fifty five (355). During the period 006-0, the total number of (balanced) panel observations is one thousand seven hundred and seventy five (775) Process of Data Collection on Price The Potato is an important commercial crop to the farmers in the district of Hooghly. The price of Potato varies from day to day. The harvesting of Potato starts from the end of March and completes in April in every year. Therefore, for analytical simplicity we have collected average wholesale price of potato as on April from principal markets of all Blocks of Hooghly district. Similarly the price of Aman Paddy and Boro Paddy also varies from month to month but we have considered the average wholesale price during the harvest of crops. There are different types of Aman rice and Boro rice, but we have considered the average wholesale price of common Aman and Boro rice. For Aman rice, we have considered the average wholesale price as on February and for Boro rice as on May-June in every year. The cost of all factors of production for the period has been calculated at the market price in 006. Since we want to analyze the impact of crop insurance (that is the effect of the insurance participation) on the use of inputs of production, this has been done by examining the impact of crop insurance on the cost of input use, where the cost of all inputs over the period , has been calculated at the constant input price concerned of the base year 006. Let pi0 be the base price of input x of the year 006 and i0 x be the quantity of input used in the same year. Therefore, pi0xi0is the cost of use of input x in 006. Therefore, pi j x ij (i = labour, seed, irrigation, fertilizer and pesticide; j =006,., 00) stands for the cost of use of i-th input in j- th year. We have computed pi j x ij (the cost of use of i-th input in j-th year) in terms of the base price of the year 006 by deflating i j p x ij by ( ij i0 ). i0 p p This implies that ( ) i j ij i0 ij pij give the cost of i-th input in j-th year at constant base input price of the year 006. Thus, if the 8 p x p = p x will

14 impact of crop insurance raises the cost of inputs (calculated at base price), this is indicative of the fact that input use has been increased due crop insurance Processing and Analysis of Data After the accomplishment of data collection we turn our attention towards verification, processing and analysis of these data. The task of verification, processing and analysis of these data involve a number of closely associated operations. These are followed with a view to summarizing the collected data in such a manner that they can yield trustworthy answer to relevant questions to focus on the insurance participation for crop, production and cost of inputs of farm. In this respect, first we perform the task of examining the secondary data and primary data collected from various sources in order to detect errors and omissions. We try to correct the error of the data by suitable technique. For cross-check, we have collected the data on fertilizer consumption per acre from businessman. In order to verify these data we collect same information from the farmers also. Similarly we have collected average wholesale price of the crops from various principal markets to verify these data (price data). We have collected the same type of data from businessman of agricultural product and by field survey from farmers. We have also collected the information about the loanee farmers/farm from the field survey. Now in order to verify their information we have consulted with the respective bank and tried to minimize the errors by cross checking method. In this way we can get an accurate, consistent and complete data as far as possible. In the second phase, with a view to getting meaningful relationship we have divided the collected secondary and primary data into different groups. This task involves classification of collected data into different crops, different blocks, and different categories or classes according to the common characteristics possessed by different crops and different blocks as well as different farmers/farm. We also observed that the insurers have classified all the farmers into two groups such as small/marginal farmers and other farmer. On the other hand, according to our own choice 8

15 we have classified all the farms into five different farm-size from our collected primary data. Such type of classification prepares the ground for enabling comparison and analysis of data. In the third phase we perform the task of tabulation of data according to crops and according to farm-size. It is a technical process of logical and systematic arrangement of the collected data in compact form. The statistical tables simplify the presentation and facilitate of comparison. The statistical tables help us draw our attention to important features of data and readily detect the errors so we can easily omit the error from table. After the statistical tabulation of the data, the next stage involves the statistical analysis of data. In our study, we have analyzed the data on the basis of computation and various statistical tools and got an idea about the impact of crop insurance on fertilizers consumption, area under irrigation and total revenue. We also analyze the effect of the insurance participation for a crop on area under cultivation, production and yield. We get also idea about the impact of crop insurance on production and cost of inputs for loanee farms Specification of the Variables We have considered the analytical frame work of the models related to several issues of the crop insurance. We need to specify the actual models employed for the empirical estimation of the impact of crop insurance on the different aspect of the three selected crops, such as the Aman Paddy, Boro Paddy and Potato. We want to specify and define the variable that had been included in our model of impact of crop insurance on area under cultivation, output, output per acre, use of fertilizers, insurance participation and related issues of the three crops. We also need to specify and define the variables in the model of the impact of crop insurance on the use of irrigation and on total revenue from Aman Paddy, Boro Paddy and Potato. Some variables will be common in all the models. Among all the variables, some variables will be explained variables and other will be explanatory variables. First of all we will define the variables related to the models of impact of crop insurance on area, output, yield rate, fertilizers consumption and irrigation. 83

16 () Total Area Under Principal Crops (TAREAUPC) In the District of Hooghly, the area which is used for the production of principal crops is called total area under principal crops. The area is measured in acres. () Total Area of Production (TAREA) The total area of production means the total area under cultivation of a crop of a year in the Hooghly district and also for a farmer in the same district. The total production area is changed in every year for a specific crop. It includes both insured and non-insured area. (3) Total Production (TPRODUCT) or total output (TOUTPUT) The total production of a crop means the total production of a crop of a farmer for a year in the district of Hooghly. The production of a crop varies from year to year. The production of a crop of the different years is an important factor for determining Threshold Yield (THRYILD) or Guaranteed Yield. This will be discussed in the analysis of the indemnity factor. The total output is measured in quintal. (4) Output Per Acre or Total Yield Rate (TYIELD) The output per acre or the total yield rate (TYIELD) means the output per acre of selected crops in the district of Hooghly during the period to The yield rate for a farmer is the total production per acre for a crop. The yield rate is measured in quintal per acre. (5) Total NPK consumptions (TNPK) The farmers use different types of fertilizers for different crops. They use mainly the following types of fertilizers, such as DAP (8:46:0), UREA (46% N), MOP (K 60%), and Phosphate (P) in the agricultural production. They use mainly NPK (0:6:6), DAP (8:46:0), UREA (N 46%) and MOP (K 46%) for the cultivation of Aman Paddy, Boro Paddy and Potato. The quantity of fertilizers consumption means the NPK consumptions. The term TNPK means the total consumption of fertilizers (total NPK) for three crops in the district of Hooghly. The total NPK is measured in quintal. 84

17 (6) Per Acre NPK consumption (PANPK) The term PANPK means the per acre NPK consumption for any specific crop in the district of Hooghly during the period to The PANPK is calculated by the ratio between the total NPK consumption for a crop and total area under that crop. The per acre NPK consumption is measured in quintal per acre. (7) IAPTAREA This means the irrigated land as proportion to total land in the district of Hooghly during the period to Second we will define the variables related to the models of insurance participation for a crop and total revenue from Aman Paddy, Boro Paddy and Potato in the district of Hooghly. (8) Insurance Participation for Crop (INPARTC) The participation is often considered as the ratio of insured acres and total acres of production. It is also considered as the ratio of actual liability and total possible liability. Suppose in Block A total cultivable land is 50 acres but the insured land is 0 acres. So Insured Acre 0 Insurance Participation= = = 0.40 that is fourty percent, Total area under cultivation 50 When the participation is considered as the ratio of actual liability and total possible liability we consider the following example. Suppose for one acre a farmer gets ten thousand (Rs. 0,000/-) crop loan. Here actual liability (for insured acre) is = 0 0,000, but the total possible liability=50 0,000. Therefore Actual Liability 0*0,000 Participation for a crop= = = 0.40 that is fourty percent Total Possible Liabilty 50*0,000 This formula also implies that the participation is forty percent (40%). The insurance participation for crop is pure-number and independent of unit of measurement. The insurance participation for a crop may increase or decrease due to increase in any one of the explanatory variable of the participation function. 85

18 (9) Premium Rate (PRERATE) It is a certain percent of money of the sum insured that is fixed by the Agriculture Insurance Company of India Limited (ACICIL). There are two types of premium rate such as actuarial rate and flat/normal premium rate. If flat/normal premium rate is less than the actuarial rate, the flat/normal premium rate is considered as the applicable premium rate. In the case of crops under this study (Aman and Boro Paddy) the normal/flat premium rate is taken as an applicable rate. But for Potato, the actuarial premium rate is an applicable rate as it is more risky and important commercial crop for the farmers of the district of Hooghly. (0) Total Premium Collected (TPRECOL) The amount of premium collected is the product of premium rate and sum insured. Premium collected= Premium Rate Sum Insured The amount of premium is collected by the loan sanctioning institution/authorities from the small and marginal and large farmers and it is deducted in advance at the stage of disbursement of loan. This amount of collected money should be sent to the Agriculture Insurance Company of India Limited (AICIL) in the due time period. () Loss-Ratio (LRATIO) The Loss-Ratio (LRATIO) is the ratio of indemnity paid to premium collected (PRECOL) or the ratio of pay-out to premium collected (PRECOL) Indemnity paid Pay-out Loss-Ratio= = Premium collected premium collected The loss-ratio is also a unit free measurement. () Total Sum Insured (SUMIN) Sum-insured means the total amount of money that a farmer (small and marginal and large) takes from institutional sources as loan. It is also the amount of loan of a loanee farmer or a insured farmer (the loanee farmer is compulsorily insured). The amount of sum-insured varies from farmer to farmer for different crops. 86

19 (3) Indemnity Paid (INDPAD) The Claim Payable (Indemnity or Compensation) is a significant factor that affects the loanee farmers or the insured farmers. The claim Payable or Indemnity procedure is explained as follows. At first Threshold Yield (THRYLD) or Guaranteed Yield (GURTYLD) in the notified Area of notified crop is to be determined. Then the compensation or Indemnity under the scheme shall be calculated and paid as per following formula: Indemnity or ClaimPayable= Example: Crop: Aman Paddy Short-fall in yield Sum-insured Threshold Yield (TY) ( short-fall in yield=threshold Yield (TY)-Actual Yield(AY) ) Notified Block / Gram Panchayet (GP)-A, Kharif Season-006, Indemnity limit-80% Actual Yield (AY) per hectare: Year Kg/ha Average yield for Aman Paddy for three years: ( )/3= 4500/3 = 500 Kg/ha The Threshold Yield (THRYLD) or Guaranteed Yield (GURTYLD) for Kharif 006: Average yield (500 Kg/ha) Indemnity limit (80%) =00 Kg/ha. Following the above procedure if in the A-Block/GP the yield for 006 becomes at least 00 Kg/ha the AICIL gives the guarantee to the farmers for the said yield per hectare. As a result farmers get his income assured. The Agriculture Insurance Corporation of Indian Limited (AICIL) determines the Actual Yield (ACYLD) through the requisite number of Crop Cutting Experiments of all notified crops in the notified insurance Units. 87

20 Suppose in Block-A in Kharif 006 the Actual Yield (ACYLD) per hectare is 000Kg. whereas the short fall of yield for Kharif 006 is equal to Threshold Yield (00 Kg/ha) Actual Yield (000 Kg/ha) =00 Kg/ha. So, the State Government declares the Block-A as either affected or not affected. The Block-A must be considered to be the short fall yielded Block on the basis of 00 Kg/ha yield as per rule of AICIL. So the amount of Indemnity or Compensation shall be (Short fall in yield (00 kg/ha)/ Threshold Yield (THRYLD)) Sum Insured. Therefore the indemnity amount= Rs The farmers don t have to put forward any documents for having Indemnity. But the Agriculture Insurance Corporation of Indian Limited (AICIL) itself takes the necessary step to provide Indemnity to the farmers of the notified Block /G.P. The admissible payouts would be made by AICIL subject to receipt of Governments Share (State Govt. + Central Govt.) of Premium Subsidy. Except the above procedure of indemnity no other method of crop loss assessment shall be constructed the basis of Indemnification under the National Agricultural Insurance Scheme (NAIS). (4) Indemnity Limit (INDLIM) The level of indemnity is fixed by insurers own rule. The process of determining indemnity limit is totally confidential subject of the Agriculture Insurance Corporation of Indian Limited (AICIL). The indemnity limit varies from crop to crop. Such as for potato indemnity limit is 80% but for Boro Paddy is 90%. The Agriculture Insurance Corporation of Indian Limited (AICIL), by using indemnity limit determined Threshold Yield (THRYLD) or Guaranteed Yield (GURTYLD). (5) Insured Acres (INAREA) A loanee farmer (Insured farmer) both small/marginal and large farmers collects loan (money) from any of the institutional sources (Co-Operative Banks, Agricultural Development Bank of India etc). He must be bound to give mortgage certain amount of land to the institutions proportionate to the loan. The amount of loan varies with the capacity of land mortgaging. The 88

21 land-less farmers are deprived from the benefit of crop loan and also from the crop insurance. The capacity of land mortgaging varies from farmer to farmer and also depends on the amount of loan. The amount of land mortgaged by a farmer against the crop loan is termed as an insured acre. (6) Total Numbered of Insured Farmers (TINFARM) The total number of insured farmers who come under the crop insurance scheme for a crop after taking the crop loan from different financial institutions. This will vary crop to crop and also Block to Block in the district of Hooghly. (7) Total Area of Production (TAREA) The total area of production means the total area under cultivation of a crop of a year in the Hooghly district and also for a farmer in the same district. The total production area is changed in every year for a specific crop. It includes both insured and non-insured acre (8) Threshold Yield (THRYLD) The Threshold Yield (THRYLD) or Guaranteed Yield (GURTYLD) for a crop in an Insurance Unit shall be the moving average based on past three years average yield in case of Rice and Wheat and five years average yield in case of other crops, multiplied by the level of indemnity. The Threshold Yield (THRYLD) = Average yield for a crop level of Indemnity. The loss-ratio and indemnity are influenced by the Threshold Yield (THRYLD). Besides, the insurance participation for crop is also affected by the Threshold Yield (THRYLD). (9) Actual Yield (ACYLD) The Actual Yield (ACYLD) is an average yield per acre. The Actual Yield (ACYLD) per acre of the insured crop for the defined or notified area (affected area by the natural calamities) is determined on the basis of requisite number of Crop Cutting Experiments (CCEs). After declaring an area as an affected area the AICIL sets a Technical Advisory Committee (TAC) for conducting requisite number of Crop Cutting Experiments (CCEs). Then, the TAC chooses a 89

22 square area for any specified insured crop for requisite number of crop cutting. Then the committee determines the Actual Yield (ACYLD) per acre. (0) Price of Agricultural Output (PRICE) We have considered the wholesale price (per quintal) of Aman Paddy, Boro Paddy and Potato. The wholesale price has been collected from various principal markets and also from the businessman of different blocks of Hooghly district. () Total Revenue (TREVENUE) and revenue per acre (REVENUEPA) The total revenue is obtained by multiplying total production of a crop with the price of that crop. The total revenue varies from crop to crop and from farmers to farmers. We have calculated the total revenue and revenue per acre from Aman Paddy, Boro Paddy and Potato. The revenue is measured in terms of rupees. Third we will define the variables related to the models of panel regression for a crop of our primary data basis in the district of Hooghly during the period () Fertilizers Cost (FERTILISERCOST) The cost of fertilizer per acre incurred by farmers has been considered. The fertilizers include only three important components such as Nitrogen (N), Phosphate (P) and Potash (K). (3) Pesticides Cost (PESTICIDECOST) The farmer uses different types of pesticides to protect their crops from various types of diseases or pests. The cost of pesticides means the total cost of pesticides which a particular farmer uses per acre. Use of pesticides varies from crop to crop. Both the price and use of pesticides are increasing day by day. (4) Seeds Cost (SEEDCOST) 90

23 We have considered the cost of seeds per acre for the crop under our study. The cost of seeds varies from farmer to farmer. In the case of potato, the cost of seeds per acre is very high compared to that of other crops (Boro Paddy, Aman Paddy). (5) Irrigation cost (IRRIGATIONCOST) The cost of irrigation means the farmer s own expenditure for irrigation per acre for different crops. It varies crop-wise and also location wise. If the cultivable land is located under river or government canal, the expenditure of farmers on irrigation is very low compared to that of other process of irrigation facility (farmers own shallow, deep tube-well organized by government or any private agency, heavy deep tube-well which is organized by government or any private agency). (6) Labour Cost (LABOURCOST) The labour cost means the total wages to be paid for the number of labour which is required for the cultivation and harvesting for any crop per acre. The wage and the number of labour are increasing in every year. The labour is measured in term of rupees. We now define the different dummies related to our panel data regression model. We have chosen four essential dummies on the basis of our classifications of the farm-size. The dummy variables are considered from the collection of our primary data directly from the field survey time to time during the period 006 to 00 in the district of Hooghly. On the basis of the farm-size, the insurers assume that how much amount of crop loan is necessary to disburse for a farm for a particular crop. It helps the insurer to fix the credit limit per acre on the basis of the cost of production of a particular crop. On the other hand, according to the farm-size, we can also think about the capability of bearing cost of production for a particular crop of the different farm. Besides, on the basis of farm-size we are able to infer the production and yield rate for a crop of the different farmers after collecting the crop loan. We are able to verify the distinction of the structure of the cost of production and production decisions of the insured farm of different farm-sizes. So, we think that the classification of the farm-size on the 9

24 basis of holding of land of different farm is very important. Therefore, the introduction of dummy variables on the basis of the different categories of farm-size is also very essential factor in our analysis. The dummy variable has been treated as an explanatory variable in our model. We have chosen four important dummies to avoid the problem of the dummy variables trap. We will explain all the dummies one by one as follows. (7) DMD The word DMD is the dummy for the medium farm. The area under cultivation for this type of farm is two acre to four acre. It takes two values, if the farm belongs to the medium farm and 0 if not., if the farm belong to medium farm DMD= 0, if the farm does't belong to the meium farm (8) DSMD The dummy DSMD implies that the dummy for the semi-medium farm. The area under cultivation of the semi-medium farm is four to ten acres. We would assign the value if the farm include under the semi-medium farm and 0 if on the other farm-sizes., if the farm include under the semi-medium farm DSMD=. 0, for otherwise (9) DSML The word DSML implies that the dummy for the small farm. In the case of the small farm, the area of land lies in between one to two acre. We assign if the farm is in the small farm and 0 if not, as follows, if the farm is the small farm DSML=. 0, for otherwise (30) DMRG 9

25 The insurance dummy DMRG point-out the dummy for the farm in the marginal farm. This explained variable in the unrestricted model of the panel regression takes the value if the farm include under the marginal farm and 0 if the farm include in the other farm-sizes., if the farm belongs to the marginal farm DMRG = 0, for otherwise (3) TIME The TIME indicates the years which we have considered for the collection of data from the field survey time to time. In this case the period of times is 006 t0 00. (3) EDUCATION The literacy is an important factor for a farm. It helps them take the decision whether they will come under the crop insurance scheme or not. In the case of the informal credit, there is no chance to include the crop under insurance in general view. The average education level for all types of farm in the different farm-size is just tenth standard. 3.. Specification of the Econometric Models for the Crop Insurance We intend in this section to develop the model for different issues related to the effects of crop insurance. Let us consider the growth rate of area under cultivation, output and yield rate for the crops under study. We would consider the econometric model to find-out the impact of crop insurance on the area under cultivation, output and yield rate of Aman Paddy, Boro Paddy and Potato during the period 990 to 00. Second, the cost and use of fertilizers in quantitative terms is continuously increasing. Therefore we consider suitable econometric models about the growth rate of total NPK consumption and per acre NPK consumption for the crops under study. The econometric models for the impact of crop insurance on the consumption of NPK have been discussed. The West Bengal has taken different steps to increase the irrigation facility. As a result both the sources of irrigation and the irrigated area increase. We also consider the econometric model about the growth rate of 93

26 irrigated land as proportion to total land during the period 990 to 00. To analyze the impact of crop insurance on the use of irrigation, the suitable econometric model has been considered. We know that the insurance participation for a crop is the key factor of the crop insurance for farmers. The insurance participation for a crop (INPARTC), total sum-insured (TOLSUMIN) of the farmers and the premium collected (TPRECOL) affect the total area (TAREA) under cultivation and also the total production (TPRODUCT) of the crops under study. The total revenue for all the crops under our study changes due to change in price or production of the crop. Therefore, the growth rate of total revenue and the impact of crop insurance on the total revenue have been discussed with the help of the suitable econometric model. We will discuss the total production and the cost of different factors of production of different farm-size on the basis of our collected primary data directly from field survey during the period We shall use the panel data regression models to analyze the different characteristics of different farm-size Specification of the Model of the Growth Rate of Area under Production, Total Output and Yield Rate In this section we want to analyze the growth rate of total area of production, total production and yield rate in entire the district for the three crops such as Aman Paddy, Boro Paddy and Potato during the period 990 to 00. We shall fit three log linear equations (using equation 3.3.) corresponding to total area of production, total production and yield rate with respect to these crops Specification of the Model of the Impact of Crop Insurance on Area under Production, Total Output, and Yield Rate We want to analyze the impact of crop insurance on the total area under cultivation, total output and total yield with the help of spline function approach for the three crops such as Aman 94

27 Paddy, Boro Paddy and Potato. For this purpose we shall use the equations 3.4., 3.4.a and Specification of the Model of the Growth Rate of Total NPK (TNPK) and Per Acre NPK (PANPK) In the present sub-section we are going to explain the growth of total fertilizer and the growth rate of fertilizers per acre of cultivable land of the three crops under our study in the district of Hooghly during the period 990 to 00. In this respect we use the simple log-linear function (3.3.) for total fertilizers and growth rate of per acre fertilizers Specification of the Econometric Model of the Impact of Crop Insurance on the use of Total NPK Consumption and the Per Acre NPK consumption We want to analyze the impact of crop insurance on the use of total fertilizers and per acre fertilizers on all crops and other three crops of our under study. In this model total NPK consumption and per acre NPK consumption are explained variables and the time is independent variable. We shall use the equations 3.4., 3.4.a and Specification of the Model of the Growth Rate of Irrigated Land as Proportion to Total Land To study the Growth Rate of irrigated land as proportion to total land in the district of Hooghly during the period 990 to 00, we want to estimate a log-linear regression equation (3.3.) and apply the lest squares method to estimate the log-linear equation Specification of the Econometric Model of the Impact of Crop Insurance on the use of Irrigation To examine the effect of crop insurance on the use of irrigation in the entire district of Hooghly we have considered spline function approach. Therefore, we shall use the equations 3.4., 3.4.a and