CHAPTER III

METHODOLOGY AND

DATA BASE

METHODOLOGY

This chapter deals with the brief description of the study area and

the techniques used in the selection of sample and processing of data under

the following headings.

3.1 Description of the Study Area

3.2 Sampling Design.

3.3 Collection of Data

3.4 Method of Analysis.

3.1. DESCRIPTION OF THE STUDY AREA:

3.1.1. Location of the Study Area:

The study was conducted in Hassan District of Karnataka, which is

situated in the South-Western part of the state. The District has an

eventful and rich history. In the past it reached the height of its glory

during the rule of the Hoysalas who had their capital at Dwarasamudra, the

modern Halebid in Belur Taluk. The District is noted for its enchanting

natural scenery of Malnad, is also a veritable treasure house of the

Hoysala architecture and sculpture, the best specimens of which are at

Belur and Halebedu.

82

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Map No. 3.1: Karnataka State

83

Map No. 3.2: Hassan District

84

Boundary:

The district lies between 12° - 30^ and 13° - 31* north latitude and

75° - 31* and 76° - 38* east longitude. The greatest length of the district

from north to south is about 80 miles or 129 kilometers and its greatest

breadth from east to west is about 72 miles or 116 kilometers. The district

is surrounded by Chickmagalur, Mandya District in South and Dakshina

Kannada and Madikere in the West.

Area:

The geographical area of the district is 6, 62,602 hectares consisting

of eight Taluks and 2369 inhabited villages, 38 hobalies and 259

punchyathis. Hassan Taluk is situated in the center of the district with

geographical area of 942 sq. kms, while Belur Taluk is in the border of

Chickmagalur district with the geographical area of 845 sq. kms. Other

Taluks have the geographical area of 432.5 sq km for Alur, Arkalagudu

(675 sq. km), Arsikere (1271 sq. km), Channarayapatna (1044 Sq. km )

respectively (Table - 3.01 & 3.02).

Population and Density:

The population of the district according to 2001 census was

1,7,21,319 with 0.49 : 0.51 male to female ratio. In this district Hassan

Taluk has the highest population 363.03 with 21 percent of the total

district. Followed by Arsikere (17.6%), Chanarayapatna (16.2%),

85

Arkalagudu (11.6%) and Belur (16.25). Out of the total population 83.3%

percent were live in rural area and only 17.7 percent in urban area. The

overall population in density of this District is 2.53 per square kilometer.

The literacy rate of the population was 68.75 percent, while 78.29 percent

were male and 59.32 percent were females.

Table- 3.01

Taluk Wise Area of Hassan District

SI. No. Taluks Area (in sq. kms) Percentage

1 Alur 432 6.30

2 Arkalgodu 675 9.86

3 Arsikere 1271 18.60

4 Belur 845 12.34

5 Channarayapattana 1044 15.25

6 Hassan 942 13.80

7 Holenarispura 602 8.80

8 Sakaleshpura 1034 15.10

TOTAL 6845 100.00

Source: Hass Hassan 2003.

an District at a glance: 2002-03, District Statistical Office, pp-4.

86

Table- 3.02

Taluk Wise Population of Hassan District

SI. No. Taluks Population (in 1000) Percentage

1 Alur 86.13 5.00

2 Arkalgodu 199.24 11.60

3 Arsikere 303.00 17.60

4 Belur 183.08 10.60

5 Channarayapattana 278.11 16.20

6 Hassan 363.03 21.00

7 Holenarispura 175.07 10.17

8 Sakaleshpura 133.7 7.80

TOTAL 1721.3 100.00

Source: Hassan District at a glance: 2002-03, District Statistical Office, Hassan 2003. pp-4.

3.1.2 Agriculture and Agricultural Development:

Agriculture in this district is noted for its diversity. Being the

primary and very important sector in the present stage of development in

the District it contributed Rs.98190 lakh 39 percent to the District income.

Where the total income of the District from all sectors was Rs.2,57,062

lakhs during 2000 - 01.

Net Sown Area:

Out of the total geographical land of 6,62,602 hectares and 62.48

percent of land is used for cultivation. The net sown area during 2002-03

87

was 370 thousand hectares (55.90%) in the total geographical land. The

area sown more than once is 6.58 percent. Table 3.3 shows the net sown

more than once in district. Arsikere Taluk highest net sown area 21.85

percent followed by Chanarayapatna (14.21%), Hassan (13.36%), Belur

(12.3%) during 2002 - 03.

Table - 3.03

Net Sown Area in Different Taluks of Hassan District 2001-02

SI. No. Talul(s Area (in sq. km) Percentage

1 Alur 18748 5.06

2 Arkalgodu 41520 11.20

3 Arsikere 80972 21.86

4 Belur 45653 12.3

5 Channarayapattana 52660 14.21

6 Hassan 51361 13.56

7 Holnarispura 34868 9.41

8 Sakaleshpura 44655 12.05

TOTAL 370437 100.00

Source: Hassan District at a glance 2002-03, District Statistical Office, Hassan 2003. pp-8.

Size of Holding:

The size of cultivated holdings may be taken as an index of the size

of farm business and consequently of the economic position of cultivators.

The two factors that determine the size of holdings are the pressure of

88

population on land and the area of cultivable land available. Table 3.04

shows the land holding pattern in the district.

Table -3.04

Distribution of Land Ownership and Farm Size in the Hassan District

SI. No. Farm Size No. of Holdings Area (hectares) SI. No. Farm Size Number

(000) Percentage No. of ha.

(000) Percentage

1 < 1 - 0 219.35 60.0 99.02 22.2

2 1 - 2 90.93 24.9 129.2 29.03

3 2 - 4 40.20 10.99 107.97 24.2

4 4 - 1 0 13.30 3.4 74.7 16.8

5 > 10 1.72 0.53 34.3 7.7

TOTAL 365.48 100 445.2 100

Source: Hassan District at a glance 2002 - 03, District statistical office, Hassan 2003, pp-8-9.

In the district marginal farmers (below one hectare) were 60 percent

which had 22.25 percent in total cultivated land, small farmers

(1-2 hectares) who are 90935 (24.88%) have a land of 1,29,226 hectares or

29.03 percent is total cultivated land. Semi medium and medium farmers

who are only 14 percent in number have a 40 percent in the total cultivated

land. Number of large farmers who have more than 10 hectares were very

less (0.53%) in total cultivated land. It shows that majority of farmers in

this district are small farmers with a very small size of holding.

89

3.1.3 Cropping Pattern:

Table 3.05 and 3.06 shows the cropping pattern in Hassan district

during 2002-03, it is evident from the table that area is used for cultivation

purpose in total geographical land Paddy, Ragi, Jower, Maize, Green and A

Tur were major food crops, sugarcane, cotton, oilseed, potatoes are the

major commercial crops of the districts during 2002-03.

3.1.4 Potato Cultivation in Hassan District:

The cultivation of potato as a subsidiary food crop is gaining

popularity among the Cultivators of the district. All the taluks except

Sakaleshpur grow potato in this district. Hassan (56.5%), Belur (15.6%)

and Arkalagudu (15.3%) are the major potato growing Taluks in the

District. The popular varieties of potato in the District are Kufri Joythi,

Kufri Chandramuki, Kufri Kuber, Kufri Sinduri, Kufri Badhshaha and the

local variety is called Chikkaballpur variety. Potato is grown both in

Kufri and Rabi seasons. Arsikere, Belur, and Channarayaptna Taluks grow

potato in both irrigated and rainfed conditions, remaining taluks including

Hassan grow potato only in rainfed condition. Table 3.07 shows the area

under potato in Hassan District.

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Table -3.07

Taluk Wise Distribution of Area Under Potato in Hassan District, 2003 - 04

SI. No. Taluks Area (in hectares) Percentage

1 Alur 1520 4.30

2 Arkalgudu 5395 15.27

3 Arsikere 630 1.80

4 Belur 5518 15.60

5 Channarayapatna 1300 3.70

6 Hassan 19956 56.50

7 Holenarsipura 1005 2.85

8 Sakleshpur - -

TOTAL 34054 100.00

Source:- Hassan District at a glance during 2003 - 04. Hassan District Horticulture Office, 2003 - 04.

3.1.5 Irrigation:

Irrigation can afford security against the vagaries of rainfall. As the

district comprises Malnad and semi Malnad and Maidan parts, the sources

and the systems of irrigation also vary. In Malnad and semi Malnad areas

there are a number of small dams, tanks and pick-ups constructed across

the rivers. In the maidan parts tank irrigating is predominant. About

80398 hectares (19 %) of the net sown area in the district is under

irrigation. During 2001-02 the area irrigated by canals is 2700 hectares

(33.6%) tanks 30304 hectares (37.7%) wells 2771 hectares (2.7%). There

has been a gradual increase in the irrigated area of the district. Different

sources of irrigation in the district are shown in table 3.08. The

93

contribution of tanks is comparatively high, 37 percent followed by canals

(33.6%) and tube wells (18.85%). Belur (18.4%) and Arakalagodu

(14.0%) use tank irrigation more compared to other taluks. Canal irrigation

contributes more to Holenarsipura (32.7%) and Arakalagodu (33.4%)

taluks.

3.1.6 Co-operatives and Banking:

Credit outlets are one of the important factors for agricultural

developments. Banks co-operatives play an important role in this respect.

Hassan district had a good credit outlet in terms of number of bank

branches in proportion to the population. It had 157 commercial Banks, 44

Rural banks, 25 co-operative branches and 8 PLD and also co-operative

societies for agriculture and other purposes.

94

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3.1.7. Agricultural Produce and Regulated Markets:

Marketing also one of the important factors which effect on

agricultural development. In this respect Hassan district has a good

number of regulated markets. Which is relatively more than other

districts. During 2001-02 it had 6 main and 16 sub total 22 regulated

markets. Each taluk has one main regulated markets, Arsikere,

Channarayapatna and Holenarsipura taluk-each has 4 sub markets.

The general indicators of development like per-capital consumption

of electricity and length of percapita road per 100 kilometers of area give

highly varied picture or the taluks. This district has good communication

and Transportation facility.

3.1.8. Climate:

The district has an agreeable climatic condition. The summer in the

district is from March to the end of the May followed by the south-west

monsoon season lasting upto the end of September, October and

November may be termed the past monsoon season, followed by winter in

December and January but extending upto February. The temperature of

the district increases steadily from February. April is the hottest month

with a mean daily maximum temperature of 33.5°C with the advance of

monsoon, early in June. December is generally the coldest month with the

mean daily maximum temperature at 26.9°C and mean daily maximum at

14.3°C.

96

3.1.9. Rainfall:

The average annual rainfall in the district is 1031.71 mm and actual

rainfall in the year 1997-98 it is 1284 mm and in 1999-00. It was 1090

during 2000-01 it is only 810 mm during 2002-2003. It is decreased nearly

21 percent to the actual rainfall. Most of the rainfall in the district is

confined to the period from May to October, July being the heaviest

rainfall month. The rainfall during south-west monsoon (June -

September) constitutes about 60% of the annual precipitations. While the

rest of it is received during the post monsoon months of October -

November and the pre-monsoon months of April - May.

3.1.10. Soil:

The soil of the district in general red and sandy. In Western taluks

viz., Alur, Sakleshpur and Belur, the depth is shallow to medium, colour

red at surface and red to motted red and yellow at depth highly leached

and poor in bases. This soil is suitable for irrigated and plantation crops

like coffee, tea, pepper, cardamom, areca, barely and sugarcane. The soils

of eastern taluks comprising Hassan, Channarayapatna, Arsikere and

Holenarsipur are red sandy soil. The soils are red to brownish in colour,

shallow to fairly deep shallow, loamy to sandy loamy in texture intermixed

with fairly large amounts of course gravely and pebble. They are well

drained but poor in base and water holding capacity which are favourable

for growing crops like paddy, sugarcane, coconut, potato, vegetables and

97

plantation crops under irrigated conditions and ragi millets, pulses,

groundnut, cotton, potato and jowar under rainfed conditions. The large

areas of the district contain alkaline soils, nearly 63 percent of the land

has PH hanging from 8.0 to 9.0. About 9 percent of the soils in Belur and

Sakleshpur taluk are acidic in nature. Again the organic matter is low in 42

percent of the soils, chiefly in the western taluks which are poor in the

availability of potash. Almost all soils are poor in available phosphorous.

Only 5 percent of soils being sufficient in this regard.

3. 2.1. Sampling Design:

To evaluate the objective of the study, purposive stratified random

sampling design was adopted. In the first stage, taluks are selected, in the

second stage villages are selected from each taluk and in the third stage

farmers growing potato were chosen.

3.2.(a). Selection of Study Region:

Hassan District was purposefully selected for the present study, as it

has a relatively larger area under potato and ranks first in both area and

production in Karnataka state. The District accounted for 37.1 percent

(14.230 hectares) of the total area under potato with 31.4 percentage of

production (1,42,180 tonnes) in the state.

98

3.2.(b). Selection of Sample Taluk:

Potato crop was grown in all the Taluks except Sakaleshpur during

2003 - 04. However Hassan and Belur taluks were selected purposefully

since potato was grown extensively in these taluks. The area devoted to

potato crop in these taluks was 19.956 hectares and 5395 hectares

respectively and all these taluks together had 35,324 hectares during

2003 - 04. These two taluks together contribute 73 percent of area under

potato in this district.

3.2.(c). Selection of Villages:

Each taluk has^rvejioblies, namely Kasaba, Salegame, Dudda, and

Shanthigrama, Kattage in Hassan and Kusaba, Halebidu, Madihalli,

Bikkodu, Arechalli in Belur taluk respectively. To give a better

representation, two hobalies, salegame (4850 hectares) and Dudd (4871

hectares.) in Hassan taluk and Kasuba (2230 hectares), Madihalli (1689

hectares) in Belur taluks were selected purposefully for the study. Again

two villages, which had the relatively larger area under potato, were

selected purposefully from each hobli. Thus totally 8 villages were

selected for this study.

3.2.(d). Selection of the Sample Farmers:

The farmers of the sample villages were divided into 3 size groups

based on the size of their holding, namely small (upto 0 to 5 acres).

99

medium (above 5 to 10 acre) and large (above 10 acres). In each village a

list of farmers who had grown potato during 200J - Otf was prepared.

From this list 30 farmer in each village as area under potato were

randomly selected and interviewed. In total number of 240, farmers, 80

respondents were small farmers, 80 were medium and 80 were large

formers. They were chosen for detailed investigation on cost of

production, quantity produced and sold, sales prices, cost of marketing,

problems faced in the production of potato etc.

The details of respondents, villages and hoblies, taluks selected for

the study in Hassan District is presented in table 3.09 and 3.10

Table- 3.09

Details of Respondents Villages and Hoblies in Hassan Taluk of Hassan District.

SI. No. Hoblies Villages Respondents

1 Dudda

(10454 acres)

1. Somanahalli (1310 acres)

2. Krishnapura (820 acres)

30

30

2 Salegame

(7.905 acres)

1. Ramaderar (627 acres)

2. Sigegudda (650 acres)

30

30

TOTAL 2 4 120

Note:- Figures in parentheses shows the area under potato in village

100

Table - 3.10

Details of Respondents Villages and Hoblies in Belur Taluk of Hassan District.

SI. No. Hoblies Villages Respondents

1 Kasaba

(2280 acres)

1. Hanike (465 acres)

2. Gottavalli (310 acres)

30

30

2 Madhihalli

(1689 acres)

1. Shivapur (320 acers)

2. Bebbidu (230 acres)

30

30

TOTAL 2 4 120

Source: Field Survey Note: Figures in parentheses shows the area under potato in village.

3.2.2. Selection of Market Intermediaries:

In this section, the method used for sampling of the potato market

intermediaries is presented in brief.

While interviewing the growers of potato, details regarding the

names and addresses of the agencies to which they sold, quantity sold,

price received and other details were collected. Thus a list of 24 village

level traders was prepared from the selected 8 villages; from this list 10

village level traders were selected randomly.

With the help of the sample farmers and also Hassan Regulated

Market committee staff, a list of 15 commission agents was prepared.

From this list 4 were selected in Hassan and 6 were selected in Bangalore

market and interviewed. These commission agents and subsequent market

intermediaries helped to prepare a list of 10 wholesalers, 10 retailers and

101

10 cart vendors. Totally 10 from each category in both Hassan and in

Bangalore market were selected and interviewed. The relevant

information regarding the marketing of potato was obtained from them.

All these intermediaries were almost regular agents who operate at the

APMC Hassan and Bangalore.

The details of market intermediaries in IHassan and Bangalore market are

presented in table 3.11.

Table-3.11

Details of Market Intermediaries in Hassan and Bangalore Market.

SI. No. Particulars Hassan Market Bangalore Total

1 Village level trader 10 - 10

2 Commission agents 4 6 10

3 Retailer 7 3 10

4 Wholesaler 4 6 10

5 Cart veneder 5 5 10

Source: Field Survey

3. 3. COLLECTION OF DATA:

For evaluating the specific objectives of the study necessary primary

data were obtained from the selected farmers through personal interview

method with the help of pre-tested and structured schedule. Farmers were

asked question in Kannada using the local language. In order to ensure

102

accuracy and reliability of data the respondent farmers were assured that

the collection of data had nothing to do with land revenue or agricultural

tax policy of the government and the study was undertaken purely for

research purpose. The data collected refer to agricultural year 2005 - 0^.

On the basis of enquiry mode with the farmers of the study area and also

agricultural assistants, it is found that ragi is the competing crop with

potato.

The data collected from the farmers related to the variety of seeds

used, costs incurred on the purchases of factors, inputs, total production,

storage facility and it's cost, the time of sale, price received the problems

faced in the potato cultivation etc.

For eliciting the information on the problems in the cultivation of

potato and measures to overcome these problems, farmers were asked to

answer a few questions relating to these aspects. The information on the

marketing problems of potato and measures to overcome those problems of

potato were obtained by putting relevant questions to the farmers.

In addition to primary data collected from sample farmers,

secondary data were also obtained. Secondary data on area production and

productivity of potato in world, India, Karnataka and District wise

collected from various secondary sources.

103

3.4. METHOD OF ANALYSIS:

The method of analysis of the data keeping in view of the objectives

of the study is presented as follows.

3.4.1 Growth and instability of Area, production and

productivity of potato.

3.4.2 Economics of potato and ragi cultivation

3.4.3 Resource productivity, allocation efficiency technical

efficiency. Decomposition of output growth in potato.

3.4.4 Marketing aspects of potato

3.4.5 Growth and trade direction in potato export.

3.4.6 Behaviour of potato prices in Hassan and Bangalore

Markets.

3.4.1. GROWTH AND INSTABILITY ASPECT:

3.4.1. A. Growth Performance of Potato:

In growth measurement exercise of choice of appropriate equation

from amongst the available alternatives is very crucial. Many equations

were tried to fit and finally exponential function was selected, to know

about growth rates in area, production and productivity of potato for

different states in India, districts in Karnataka and different taluks of

104

Hassan district. The different functional fcwms providing comparatively

better fits than coefficient of multiple determinations (R^) and Standard

Error or t-Value ever selected and fitted for estimating the growth

performance of potato. The study period was 1970-71 to 2001-02 for all

states, districts and taluks.

The functional form was,

Y = AB' . . (1)

Where

Area, Production, Yield

Constant

B Regression Coefficient

t Time period from 1970-71 to 2001-02.

The compound growth rate (r) and standard error has been worked

out as follows.

C.G.R = Antilog ( B-1) X 100 •(2)

The student - t distribution is used to test the significance of

compound growth rate such as

105

t= (3) S.E (r)

S.E(r) standard error for R^ was computed with the help of following

formula.

S.E (r) = 100 X AL (log b) /E(logy)^ - S (logy)^ - (logb)^-

0.43429 / n

(n-2) (Zt^ - (St) n

3.4.1.(b). Instability Analysis:

The relevant methodology is built upon the lines of the work by

Hazell (1922). An attempt is made to break up the growth of production of

potato in state wise (India) district wise (Karnataka) and taluk wise

(Hassan) during the period 1970-71 to 2001-02.

The data on area, yield and production of potato growing states,

districts, taluks were de-trended by using a quadratic trend equation. The

quadratic equation was preferred in this regard since it is more flexible.

Besides, it was found that the trend component of time series data

appeared not to fall in a straight line. The significance of estimated

parameters was tested by the ' t ' test. If the estimated parameters are found

to be non significant, then the original raw data on area production and

yield were used as the working series.

106

Instability is measured as the variability of total production for

India, Karnataka, Hassan which is equal to the sum total of the

production variances of individual and the sum of the covariance between

yield and area in different districts.

Procedure for decomposing the Variance:

Let Q denote production, A denote area sown and Y denote yield.

Then total production, Q = AY, A change in any of these components

(A,Y) will lead to a change in Q. The variance of production can be

expressed as

V(Q)= A V(Y) + YV (A) + 2 AY Cov (A,Y) - Gov (A,Y) + R

The above equation indicates that the variance of production is a

function of variance of yields and area sown and also of the mean area and

yield as well as covariance between area and yield. Changes in the

interaction terms between these components also cause changes in

variance of production.

To begin let A and Y denote the mean area and yield. They are

calculated from the detrended or raw of area and yield over time. Ai, Yj

are the mean area and mean yield. Any change in the area (A) can be

expressed in terms of Aj.

A A = A - A

107

Similarly any change in the yield is the outcome of the difference

Y-Y. By squaring the deviations of area and yield over period (AA) and

(AY) are arrived at. The detrended/raw data were used to calculate the

variance. Similar procedure is followed to calculate the yield variance.

The change in the production can be decomposed into four

constituent components. Two parts viz., A AY and Y AA arise from

changes in mean yield and mean area which are called the pure effects.

The term AA AY is an interaction effect which arises from simultaneous

occurrence of change in the mean yield and the mean area. The last term A

Cov (A, Y) arises from change in co variability of area and yield.

The details of the decomposition of output is presented in Tables

3.12

Table 3.12

Components of Change in the Average Output

SI. No. Source of Change Symbols Components

1 Change in mean Yield AY A x AY

2 Change in mean area AA Yx A'A

3 Interaction between changes in mean

area and mean yield

AA AY AAx AY

4 Change in area yield covariance ACov

(AY)

ACov (A,Y)

108

3.4.2. Economics of potato and Ragi Cultivation:

Tabular analysis was used for estimating the input utilization

pattern, costs and returns. Different concepts of costs and returns used in

the study are presented in this section.

3.4.2.1 Cost Return Concepts:

The total costs were divided into two broad categories

a. Variable costs b. Fixed costs

A. Variable Costs: Include costs incurred on seed, FYM, fertilizer,

human labour, bullock labour, tractor power plant protection

chemical (PPC), pesticides, irrigation and interest on operational

capital.

B. Fixed Costs: It includes the costs of depreciation land revenue.

Depreciation was consider 5% for the variable cost. Land revenue

was charged at the rates levied by the Government.

Returns:

Both value of main product and by product (straw) are considered

for Ragi crop. For potato only main tuber is considered.

109

3.4.3.(a). Resource Productivity of Potato Cultivation:

The main objective of any firm is to co-ordinate and utilize the farm

resource in the production process so as to obtain maximum output. It is in

this context that the study of productivity of various resources becomes

relevant. The functional approach was employed to study the productive

efficiency in potato cultivation, wherein a modified form of the Cobb-

Douglas production function was fitted separately for potato and its

competing crop ragi both in irrigated and rainfed condition to the whole

farm data.

The function employed in the study was of the form:

Y = a X i •'^' X2 "'• X3 " ' X 4 "''Xs •'^'Xfi '"'• X7 "'' Xg '"'' X9 '"• e"

Where,

A

Y= Output of the farm in quintals.

Xi = Acres of land

X2 = Quantity of seeds in quintals

X3 = Value of Farm Yard Manner in rupees

X4 = Quantity of Fertilizer in quintals

X5 = man days of human Labour

Xs = Bullock pair days

X7 = value of pesticides in rupees.

110

Xg = value of Irrigation in rupees

X9 = value of plant protection chemical in Rupees

u = error term

The above function was estimated in the log-linear form:

A

in Y= In a + bi Inxi+b2lnx2+b3lnx3+b4lnx4 H-bglnxg+u

The principle of least squares was adopted while fitting the

functions.

In order to know the goodness of fit, the coefficient of multiple

determination adjusted for sample size (R^) was calculated using the

formula,

n-1 | 2 _ 1 / I r>2> R' = 1- ( l -R^

n-p

Where

R^ = The coefficient of multiple determinations adjusted for sample size.

R^ = The coefficient of multiple determination given by

Regression sum of squares

Total sum of squares

n = Number of observation in the sample

p = Number of parameters in the function, including the intercept.

I l l

3.3.2.(a). Returns to Scale Test:

The returns to scale which is given by the sum of elasticity

(Regression) coefficients in a Cobb-Douglas production function shows

the effect of a proportionate increase in all the inputs on output. If the sum

of elasticity coefficients is equal to one it indicates a constant return to

scale. If it is less than one it is decreasing returns to scale, and if it is

greater than one if it is increasing returns to scale.

The Cobb-Douglas production function is a homogeneous function

of degree one that means the sum of elasticities should add up to one.

Seldom do the eleasticities add up to exactly one. The sum is statistically

significantly different from one or not can be tested by the returns to scale

test (Rao and Miller, 1971) using the test statistic of the form:

I * . - . t = L.^^ k

i - I SE ( X ( * , )

Where

Sbi = Sum of production elasticities of individual inputs included in the

function

k SE(^b,)=\Tvsxb, +2j;^Cov.bibj

V1-1 « >

K = the number of explanatory variables

112

The resulting ' t ' (computed) value is compared with t (n.k) critical

values at 5 percent level.

3.4.3.(b). Allocative Efficiency:

The Allocative Efficiency was studied by comparing the marginal

value product of each of the input with its marginal, factor cost.

The marginal value product (MVP) is obtained by the product of

marginal product of each input with the unit price of output (price per

quintal).

i.e., MVP = M P P . P Y

The price considered here was the weighted arithmetic mean, with

the quantity which was sold at a particular price being the weight.

The marginal products were estimated at the geometric mean levels

of the inputs using the formula.

Y Marginal product of the X;"" input = bi ~

Xi

Where

bi = Elasticity co efficient (Regression coefficient)of the i""

independent variable

Y = Geometric mean of output

Xj = Geometric mean of input

113

3.4.3.(c). Technical Efficiency of Potato Cultivators:

The production function approach does not indicate anything about

technical efficiency. Thus it can be used to study only the allocative

efficiency. In order to study the technical efficiency of the farmers the

frontier production approach was used.

The concept of production efficiency was first introduced by Farrell

(1957). He rejected the idea of an absolute measure of efficiency based on

some pre-defined ideal situation and instead he proposed that efficiency be

measured in a relative sense, as a deviation from the best performance in a

representative peer group. He also introduced the distinction between

technical efficiency and allocative efficiency. Technical inefficiency arises

when less than maximum output is obtained from a given bundle of factors

and allocative inefficiency arises when factors are used in proportions

which do not lead profit maximization.

The idea of the frontier production function was built around the

concept of efficiency adduced by Farrell (1957) and it stresses on

technical effiecincy. Timmer (1971) modified the procedure in a number

of ways, he imposed Cobb-Douglas type of specification on the frontier

and compute an output based measure of efficiency.

In 1981, Kopp suggested a different approach within the Farrell

frame work. This involved the econometric estimation of a parametric

114

frontier followed by the algebraic identification of the efficiency standard

for each data point.

The approach followed here was that fixed parameters frontier

amenable to statistical analysis is specified which takes the form:

Y = f (x )e" u ^ O

and the Cobb-Douglas form would be,

n

In Y = a + Sb j In Xj + u where u ^ 0

In estimating the above equation, Corrected Ordinary Least Squares

(COLS) regression was used. That is as a first step, ordinary least squares

is applied to the equation to yield best linear unbiased estimates of the bj

coefficients. The intercept estimated is then corrected by shifting the

function until no residual is positive and one is zero. In 1980, Green had

shown that a consistent, though biased, estimate of the intercept, which

imposes the sign uniformity on the residuals will be generated by this

procedure.

The new production function with the shift in intercept would

give the maximum output obtainable for given levels of input and it would

be of the form.

In Y* = a + Sbj In X: + u where u ^ 0

115

3.4.3.(c). i . Timer Measure of Technical Efficiency:

The Timmer measure of technical efficiency of farm ' i ' is the ratio

of actual output to potential output, given the level of input use on farm

' i ' . It thus indicates how much extra output could be obtained if farm ' i '

were on the frontier

i.e., the timer technical efficiency = Y i =

Where,

Yi = Actual output of i farm

Yi* = The maximum out put obtainable by the i"* farm for given

levels of input.

3.4.3.(c). ii. Kopp Measure of Technical Efficiency:

The Kopp measure of technical efficiency compares the actual

level of input use to the level which could be used if farm ' j ' was located

on the frontier, given the actual output of farm ' i ' and given the same

ratios of input usage.

That is, if

In Y = a' + bi lnxi+ b2 lynx 2 + +e

116

and if

Xi X3 X4 An Rl= ^2= R3 Run =

X2 X2 X2 X2

And X|i*, X2i*, X3J* , Xing* denote the optimum use of inputs on

farm ' i ' for output level Yi then,

(in Yi - a' - bj Tn Rj - b2 In R2 ... ban in Run) inX2i* = S

Sbi i=l

The values of lynx*iid, In X^i* In Xjng* are calculated in a

similar way. Then the kop technical efficiency is given by:

KoppTEi = ^ 2 i * X , i * Xing*

X * V * Y 2i -^li ^int

*

When the actual usage is compared with the frontier usage, the

extent of over use in resources is obtained.

In the present study the production function which was used in the

study of resource productivity was used for the study of technical

efficiency wherein the beta coefficients were obtained by the Ordinary

Least Squares method and then the intercept estimate was corrected by

shifting the function with the largest error term.

117

The net return was computed by subtracting the total cost of

cultivation from the gross income (return) for each sample farmer as well

as averages for sample groups.

3.4.3.(d). Decomposition of tlie Output Growtti:

One important method to identify the sources of out put growth so

as to gauge whether it is the increase in inputs or increase in input use

efficiency or improvements in technology contribute more to output

growth is decomposition. The conventional production frontier method

popularized by augural (1977) and Museum and Van Den Brock (1977) and

Cobb Douglas technology was used to know the decomposition the output

growth for irrigated and rainfed potato

The cob-Douglas functional form is

T K

InY „ = a ,, + Y, y ji ^ ji + E « *'/ ^"^ kit J=2 ^ = 2 ( 1 )

i = 1 N,

t = 1 4

Where,

E (U „) = 0, E (V,) = 0, E iV„) = 0

118

Var (U , )= a 2

"J'' for j = k and 0 other wise and

Var (v )= <7 ^ ^ *' ^ "* for j = k and 0 other wise

Var (w ^= a ^ V J, ) " .jk for j = k and 0 other wise

With these assumptions model (1) can be written as

IJu = « . + Z y , ^ ; , + i a . / n ^ *„ + E ( 2 ) j = l k = 2 ki

Where

X = I U^InX „ + X V.InX „ + ^^ W,D ., + U, + V„ Id k = 2 k = 2 J = 2

£(S«) = o for all i and k

k k T

Var{EY, ) = (yln + c^Jn + Z ^ i ^ ' ^ ' ^ - t . + X^v**^«'^fav + E^^^-t ki k=l j=l j-^1

CoV (X , , , 5 ; , ) = 0 for k ?!: j

Following the estimation procedures suggested by Hundredth and

Houck (1968) the mean response efficient cT'S y^*, and the various can be

estimated and the individual response co-efficients a' jS and YJJ S can be

obtained as described in Griffiths (1972).

119

Drawing on kalirajan and owana (1994) the assumptions underlying

model (2) are as follows.

a) Technical efficiency, which is defined as the ability and willingness

of the firm to produce the maximum possible output from the given

set of inputs and technology, is achieved by adopting the best

practice techniques which involve the most efficient use of inputs.

Technical efficiency stems form two sources.

1) The efficient use of the each input which contributes individually to

technical efficiency and can be measured by the magnitudes of the

varying slope efficients a j * and

2) Any other firm-specific internsic characteristics which are not

explicitly included but may produce a combined contribution over

and above the individual contributions. This lumpsum contribution,

if any can be measured by the varying intercept term and YJJ

b) The highest magnitudes and each response coefficient and the

interest represent the production responses of following the best

practice techniques, and they constitute the production coefficients

of the potential frontier function. Let S and Ysb the estimates of the

coefficients of the potential frontier production functions that is,

a*k,= Max i^i^N {a^u}; Y*=Max i ^ I ^ N {yji}; K=l,—- k:j, i=l —-N

and t,j = 2 T

120

Now the potential frontier output for individual observation can be

calculated as,

In Y*it= a*i, + sr'" Y*Dji+ z:, a*k, X^i.; I„Xki,; i=l, ..N & t = .... T (3) j=2 k=2

Where,

Xkit is the actual level of K-th input used by the ith firm for potato.

Measure of technical in efficiency denoted by say, TE can be defined as;

TEi, = (InY'i, -In Y^) (4a)

And alternatively a measure of technical efficieny denoted by EFjt

can be defined as

Yi, EFu = (4b)

exp (In Y*,)

Where the numanetor refers to the realized out put and the

denominator shows the potential frontier output calculated from model. (3)

Figure (3.1) illustrate the Decomposition of total output growth into

input growth, technical progress and technical efficiency improvement.

For irrigated and rainfed, faces production frontiers Fl and F2

respectively. If a given firm has been technically efficient, output would

be y*,l for irrigated potato and Y2 for rainfed potato, On the other hand,

if the firm is technically inefficient and does not operate on its frontier,

then the firms realized output is Yl, for irrigated and Y2 for rain fed

121

potato. Technical inefficiency (TE) is measured by the vertical distance

between the frontier output and the realised output of a given firm, that is ,

TEi for irrigated and TE2 for rainfed respectively. Hence, the change in

technical efficiency is the difference between TEj and TE2. If here is

technical progress, due to the improved quality of human and physical

capital, so a firm's potential forntier shifts to T2 for rainfed.

Figure 3.1 Decomposition of output Growth

y*2

y2

y 1

y*i

yi

« y 2

TE2 F2

y2 .C..- .^

B/ Fi

/A / TEi

yi

0 Xi

If the given firm keeps up with the technical progress, more output

is produced, form the same level of input. So, the firms output will be YI

122

from XI input shown in figure. Technical progress is measured by the

distance between two frontiers (yl**-yl*) evaluated at XI (fig- ).Denoting

the contribution of input growth to output growth as Yes the total output

growth (Y2-Y1) can be decomposed into three components; input growth,

technological progress and technical efficiency change.

Referring to figurel the decomposition can be shown as follows;

D = Y2 -Yi

A+B+C

[ Yi* -Yi] + [ Y/'-Yi*]+ [ Ys-Yi"]

[ Yi' -Yi] + [ Yi'*-Yr] + [ Y2'-Yi**] - [ Y2*-Y2]

{[ Y ; -YJ] - [ Y ; * - Y ; ] } + [ Y / ' - Y / ] + [ Ya'-Y,**] .. ( 5)

{ TEi - TE2} + Tc +AY

Where Y2-Y1 = output growth

TEi-TE2= technical efficiency change

TC = Technical change and

AYx = output growth due to input growth

The decomposition in model (5) enriches Slow's dichotomy by

attributing observed output growth to movements along a path on or

beneath the production frontier (input growth) movements towards or away

123

from the production frontier (technical efficiency change) and shifts in the

production frontier (technological progress)

Out growth was calculated by using the computer program TERAN

the stochastic varying coefficients frontier is estimated separately.

3.4.3.(e). Logit Analysis:

The logit model is used in capturing the qualitative responses in the

dependent variable. In the present study it is employed to know the effect

of age, education family size on potato production. When the dependent

variable is dichotomous in nature, application of linear regression model

leads to erroneous results. Under such circumstances binary-choice models

are used and assume that individuals are faced with a choice between two

alternatives and that the choice they make depends on the characteristics

of the individuals. The purpose of these models is to determine the

probability that an individual with a given set of attributes will choose one

or the other alternative. The simplest form of the model involves the

dependent variable assuming a binary response, which takes values of 1

and 0. The commonly used qualitative response model in economic

analysis is the linear probability model, the logit model and probit model.

Liner Probability Model (LPM)

The regression form of the model is,

Y= a + p xi + ui (1)

124

It is estimated through Ordinary Least Squares (OLS) method which

suffers from some disadvantages which are as follows:

1) The variance of the disturbance (Ui) will not be homoscedastic (E

(ui)=0) which is against one of the assumptions of OLS.

2) The assumption of normality is no longer tenable for LPM - because

like y, Ui takes only two values.

3) Estimated probabilities lie outside the range of 0 and 1.

Further, the estimation of probability of OLS assumes that the

probability increases linearly with the explanatory variable, i.e., the

marginal or incremental effect of the explanatory variable remains

constant throughout, which will not happen in reality.

To overcome these discrepancies, the logit and the probit models are

preferred. These models are developed based on the logistic cumulative

distribution function and normal cumulative distribution function,

respectively.

In the present study, the logit model is preferred to the probit model

owing to the computational ease.

The logit model based on the logistic probability is specified as

1 Pi= F (zj) = F ( a + E piXi) = (2)

'= 1+e -''

125

Where,

Zi= a + piXi

After simplifying the above formula for estimation purpose, one can

write the logit model as

Zi = In (Pi /(1-Pi) = a + Pi Xi = Li (3)

Pi = probability that the age, education, land will effect on potato

production.

1-Pi = probability that the age, education and land will not effect on

potato production.

Pi = coefficient to be estimated

Xi = Independent variable

E = Base of the natural logarithms, which is approximately equal

to 2.72.

Li is called the logit as it follows logistic regression.

Pi / (1-Pi) is the odds ratio in favour of age, education and land size

on potato production - the ratio of the probability that age, education ,

land size will effect on production and will not effect on production.

Given the limitations of OLS. The maximum likelihood techniques

was used in estimating the logit co-efficient. One model was fitted to each

126

variable. The marginal effect of the itch variable on Pj is given by the first

derivative of P with respect to Xi.

dp/dxi= Pi(l-Pi)

Thus the elasticity of this probability is

Epi = Pi (l-Pi)Xi

The independent variables considered in the model are described below.

1) Xi Average education in the family

2) X2 Average age of the family

3) X3 size holdings of the family

4) X4 average family size

3.4. Marketing Aspects of Potato:

Different marketing intermediaries considered in the study are,

village level trader (VLT) commission agents (CA), wholesales (WSL),

retailers (RTS), cart venders (CVS).

Market intermediaries are those individuals who specialize in

performing various marketing functions involved in purchase and sale of

goods as moved from producers to consumers.

127

Marketing Costs:

Based on the information obtained from the farmers market

intermediaries average marketing costs were worked out for all the

categories of farmers and also for different market intermediaries. The

major marketing cost incurred by farmers and market intermediaries were,

expenses on Gunny Bags, Bagging Transportation, Loading and Unloading,

Commission Charges, Marketing Cess and Miscellaneous Expenses.

Marketing Channel:

Marketing channel consists of various agencies, who perform the

various marketing functions in sequence as the produce moves from the

producers to ultimate consumers.

Marketing Margin:

This refers to the costs and net share to the different market

functionaries as a particular produce.

Producers Share in the Consumer Rupee:

This refers to the farmer's net price expressed as percentage of the

retail price of the produce.

Price Spread:

This refers to the difference between the net price the farmers

receives and the retail price of the produce.

128

The marketing season of potato grown in Hassan during 2004

started from the third week of August and lasted up to the end of

November, peak arrival month being September.

3.4.5.(a). Growth and Trade Direction of Potato Export:

The exponential function which used to know the growth rate in area

production and yield that it sold is used to know the CGR for potato

export.

3.4.5.(b). Markov Chain Analysis:

The trade directions of Indian exports were analyzed using the first

order Markov Chain approach .Central to Markov Chain analysis is the

estimation of the transitional probability matrix P. The elements Pjj of the

matrix P indicates the probability that export will switch from country i

with the passage of time. The diagonal elements of the matrix measure the

ability that the export share of the country will be retained. Hence, an

examination of the diagonal elements indicates the loyalty of an importing

country to a particular country's export. The export data from 1993-2002

were used for the analysis.

In the context of the current application, six major importing

countries of potato were considered. The average exports to a particular

country was considered to be a random variable which depends only on

the past exports to that country, which can be denoted algebraically as

129

r

Ejt = S Eit -1 X Pij + ejt j=i

Where

Ejt = Exports from India to j " " country during the year t.

Ej, = Exports to i"" country during the period t-1

Pjj = Probability that the exports will shift from i"* country to j " *

country.

ejt = The error term which is statistically independent to Eit-1.

T = Number of years considered for the analysis

R = Number of importing countries.

The transitional probabilities Pij which can be arranged in a (c*r)

matrix, have the following properties.

0 '6 Pij ^ 1

S Pij i = 1 for all; i=l

Thus, the expected export shares of each country during period ' t '

wee obtained by multiplying the export to those countries in the previous

period (t-1) with the transitional probability matrix.

There are several approaches to estimate the transitional

probabilities of the Markov Chain Model such as unweighted restricted

130

least squares,unweighed restricted least squares, unweighed restricted

least squares, Bayesia maximum likelihood, unrestricted least squares, etc.

In the present study, minimum absolute deviations (MAD) estimation

procedure is employed to estimate the transitional probabilities which

minimizes the sum of absolute deviations. The conventional linear

programming technique was used, as this satisfies the properties of

transitional probabilities of non-negativity restrictions and row sum

constraints in estimation.

The linear programming formulation is stated as

Min OP* + le

Subjected to

XP' + V = Y

GP* = 1

P* > 0

Where,

0 - is the vector zerores

P* - is the vector is which probability Pij are arranged

1 - is an apparently dimensioned Vector of area

E - is a Vector of absolute error (IVI)

131

Y - is a the vector of export each country.

X - is the block diagonal matrix of lagged values of V

V - is the Vector of errors

G - is the grouping matrix to add the row

Elements of a p arranged in P* to Unity.

3.4.6. BEHAVIOR OF POTATO PRICES:

To know the Behavior of prices ARIMA model and co integration

method was used.

3.4.6.1. Box - Jenkins (ARIMA) Model:

Forecasting and control ushered in a new generation of forecasting

tools, popularly known as the Box-Jenkins (BJ) methodology, the

emphasis of this new methodology is not in constructing single equation or

simultaneous equations but on analyzing the probabilistic or stochastic

properties of economic time series on their own under the philosophy

"let the data speak for themselves".

The acronym ARIMA stands for "Auto Regressive Integrated

Moving Average" Lags of the differenced series appearing in the

forecasting equation are called "Auto-Regressive" terms. Lags of the

forecast errors are called "Moving-Average" terms and a time series which

132

needs to be differenced to be made stationary is said to be an "Integrated"

version of a stationary series.

ARIMA method is an extrapolation method from forecasting and

like any other such method it requires only the historical time series data

on the variable under forecasting. Among the extrapolation methods, this

is the sophisticated method for it incorporates the features of all such

methods, which does not require the investigator to choose the initial

values of any variable and the values of various parameters a priori or

through interaction and it is robust to hand any data pattern.

3.4.6. (a). Definitions of the Terms:

Auto - Correlation: This term is used to describe the association or

mutual dependence between values of the time series at different time

periods. It is similar to correlation, but relates the time series for different

time lags. The patterns of auto-correlation co-efficient are frequently used

to determine the presence of seasonality in the data (and the length of that

seasonality) and to identify appropriate time series models for specific

situations.

Partial auto-correlation: This measure of correlation is used to identify

the extent of relationship between current values of variables with the

earlier values of the same variable (values for various time lags) while

holding all the other effects of time lag constant.

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Lag: The lag is the number of time periods by which the lagged variable is

offset from the variable being constant. It is frequently useful in time

series forecasting to relate the variable of the forecast to the lagged values

of itself or other variable.

Auto - Regression (AR) Auto - regression is a form of regression, but

instead of the dependent variable (the time to be forecast) being related to

the independent variable, it is related to the past values of itself at varying

time lags. Thus, auto regressive model would express the forecast as a

function of the previous values of that time series.

Auto-Correlated Residuals: When the residual or the error term

remaining after application of the forecasting method is auto-correlated, it

indicates that the forecasting method has not removed the entire pattern

from the data. When auto-correlation of the residuals is random, it

suggests that in fact the forecasting method has effectively identified the

entire pattern contained in the data.

Auto-Correlation Function (ACF) Plot: it is merely a chart of the

coefficients of correlation between a time series and lags of itself. ACF

plot is used to identify the number of MA (q) terms in the identification of

the ARIMA model.

Partial Auto-Correlation Function (PACF) Plot: it is the plot of the

partial auto correlation coefficients between the series and the leg itself. A

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PACR plot used to identify the number of AR (p) terms in the

identification of the ARIMA model.

Moving Average: The single moving average is obtained by finding the

average for a set of values. Then using that average as a forecast for the

coming period. It is often used as a basis for eliminating the seasonality in

the data. The term moving or rolling is used because each new observation

becomes available. A new average is computed that excludes the oldest

value previously included and adds the most recently observed value.

Auto-Regressive Moving Average (ARMA) Sclieme: This type of time

series forecasting model can be auto-regressive (AR) in form. Moving

average (MA) in form, or a combination of the two ARIMA. In an ARIMA

model, the series to be forecast is expressed as a function of both previous

values of the series (AR terms) and previous error values from forecasting

(MA terms)

Stationary : A stationary means that there is no growth or decline in the

data. The data must be horizontal along x-axis. In other words, at

stationary time series is the one that oscillates around a constant mean,

independent of time, thus, it contains to trend, stationary can be achieved

by using the method of differencing.

Differencing: The method of differencing converts a non-stationary time

series into a stationary one. It consists of subtracting successive values of

a time series from adjacent value. And using that difference as a new

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series. Higher order of differencing (differencing different series) is done

for higher order trends.

3.4.6.(b). Box Jenkins (BJ) Methodology:

The first step in developing a box - Jenkins model is to determine if

the series is stationary and if there is any systematic seasonality that needs

to be modelled. Both the stationary and seasonality can be assessed from

an ACF and PACF plots. Stationary can be achieved through the method of

differencing and the seasonality through seasonal differencing.

The main stages in setting up a Box - Jenkins forecasting model are as

follows:

1. Identification of the model.

2. Estimation of the parameters.

3. Diagnostic checking of the model, and

4. Forecasting.

3.4.6.(c). Identification of the Model:

Identification is concerned with deciding the appropriate values for

p.d.q.P.D and Q where,

p = Order of the non seasonal AR term

d = Non-seasonal differencing

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q = Order of non-seasonal MA terms

P = Order of the seasonal AR terms

D = Seasonal differencing

Q = Order of the seasonal MA terms

Before identifying the model, identify the characteristic of the time

series such as stationary and seasonality as said above and the same must

be removed. Once they have been addressed, the next step is to identify

the order of the AR (p) and MA (q) terms. This is done by examining the

sample ACF (to identify the number of MA (q) terms) plots of differenced

series Y,. Usually ACF and PACE are calculated up to a maximum of 16

lags (k). The AR (p) and MA (q) terms are simply the number of

correlations, which are significantly different from zero at 95 percent

confidence interval on the sample plots. Both ACF and PACF are used as

the aid in the identification of the appropriate models. There are several

ways of determining the order type of process, but still there is no exact

procedure for identifying the model.

3.4.6.(d). Estimation of the Parameters:

After identifying the suitable model, the next step is to obtain the

least square estimates. The parameters such that the sum of squares is

minimum.

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n

S (9, O) = E et^ (9 O) t=i

Where, t= 1, 2...n,

The values of ' e ' for any given values of 9 , may be calculated

recursively by using the above equation.

Estimating the parameters of the Box - Jenkins model is a quite

complicated non-linear estimation problem. For this reason, using many

commercial statistical software programmer does the parameter estimation

model.

Fundamentally, there are two ways of getting estimates for each

parameter.

• Trail and error method: examines many different values and chose

the set of values that minimizes the sum square of residuals.

. Iterative method: chose a preliminary estimates and let a computer

programme refine the estimates it iteratively.

3.4.6.(e). Diagnostic Checking:

After having estimated the parameters of a tentatively identified

ARIMA model, it is necessary to do diagnostic checking to verify that the

chosen model is adequate. This is why Box-Jenkins model is more an art

than science. Considerable skills are required to choose the right ARIMA

model.

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Examining the ACF and PACF of the residuals can show up an

adequacy or inadequacy of the model. If it shows random residuals, then it

indicates that the tentatively identified model is adequate. When

inadequacy is detected, the checks should give and indicating of how the

model needs to be modified, after which further checking takes place.

Diagnostic checking helps us to identify the differences in the

model, so that the model could be subjected to the modification if needed.

3.4.6.(f). Forecasting:

After satisfying about the adequacy of the model, it can be used for

forecasting one of the reasons for the popularity of ARIMA modelling is

its success in forecasting. In many cases forecasting obtained by the Box -

Jenkins method are reliable than those obtained from traditional

econometric modelling.

ARIMA models are developed basically to forecast the

corresponding variable. There are two kinds of forecasts: sample period

and post sample period forecasts. The former are used to develop

confidence in the model and the latter to generate genuine forecasts for use

in planning and other purposes. The ARIMA model can be used to yield

both these kinds of forecasts.

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3.4.6.2. Co-integration Analysis:

The agricultural prices vary between different markets and regions

due to localization or rationalization or production, market segmentation,

variation in weather and other factors. Differences in marketing channels

and the methods also cause the prices to vary from one market to another

and from region to region. In a perfectly competitive system, the prices in

different markets are not expected to differ much except by reasonable

transporting and handling costs.

However, imperfections in the market, particularly those arising

from the activities of the trades are generally taken as important causes for

the existence of differential price movements in different markets. It is

believed that prices quoted are a reflection of the conditions prevalent in

the markets. Therefore, if there are imperfections in the form of either

oligopoly power among buyers or unequal information among sellers, then

it is expected that buyers will be able to reap abnormal returns and

subsequently, wide intra-regional price differentials exist in the market.

This objective will determine whether the prices of potato in a

market are in parity with the reference market. In order to do this, it is

necessary to compare the prices of potato in one market with the prices in

the reference market. Co-integration tests are applied to special price

relationship between the two markets for potato.

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Spatial price relationships have been widely used to indicate overall

market performance. The usual definition in the literature is that integrated

markets are those where prices are determined interdependently. This has

been generally assumed to mean that the price changes in one market will

be fully transmitted to the other markets. Markets that are not integrated

may convey inaccurate price information that might distort marketing

decisions and contribute to inefficient product movements.

The basic relationship that is commonly used to test for the

existence of market integration is

Pi, = ao + tti Pj, + e, (1)

Where,

Pi and Pj = are series of a specific commodity in two markets i and j .

8t = residual term assumed to be distributed identically and

interdependently.

tto = domestic transportation costs, processing costs, sales cost etc.

The test of market integration is straightforward if Pj and Pj are

stationary variables. However, often, economic variable are non-stationary

in which case the conventional tests are biased towards rejecting the null

hypothesis. Thus, before proceedings to further analysis, it is important to

check for the stationary of the variables.

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Stationary series is defined as one whose parameters that describe

the series (namely mean,. Variance and auto correlation) are

interdependent of time or rather exhibits constant mean and variance and

have auto correlation that is in vibrant through time.

Once the variable is non-stationary, then the test for co-integration

is applied only variables that are of the same order of integration may

constitute a potential co-integration relationship.

Co-integration between the prices of the two markets was evaluated

by regressing the prices on potato in India with that of the prices in

Hassan. The residuals were examined for the order of integration.

Stationary series is defined as one whose parameters that describe

the series (namely the mean, variance and autocorrelation) are independent

of time; or rather exhibit constant mean and variance and have

autocorrelation that are invariant through time. Once the non-stationary

status of the variables is determined, the next step is to test for the

presence of co-integrating (long run equilibrium) relationship among the

variables.

The augmented Dickey Fuller (1979) test is used (ADF test) to

determine the stationary of a variable. The test is based on the Dickey

Fuller value statistic of Bl given by the following equation.

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Ap,=po+PiPt-i +X5kAP ,.k +11, (1) k = l

Where

AP,=Pt-P..i

The test statistics is simply the t statistic, however, under the null

hypothesis it is not distributed as student - t: But this ratio can be

compared with critical values tabulated in Fuller (1976). In estimating

Equation (1), the null hypothesis is Ho: P, is I (1), which is rejected (in

favor of I (0) ) if Pi is found to b negative and statistically significant. The

above test can also be carried out for the first difference of the variables.

That is, we estimate the following regression equation:

N

A^Pt = 00+ GiA P,.i + I(t)kA^ P t-k +lAt (2) k = l

Where the null hypothesis is Ho: P, is I (2) which is rejected [in

favor of I (1)] if 0i is found to be negative and statistically significant. In

general, a series, P, is said to be integrated of order *d', if the series

achieves stationary after differencing d times, denoted P, ~ I (d).

Consequently, if Pt stationary after differencing once, this we may denote

Pt ~ I (1).

Having established that the variables are non-stationary in level, we

may then tests for co integration. Only variables that are of the same order

of integration may constitute a potential co-integrating relationship.