CHAPTER - II

NERLOVIAN SUPPLY MODEL USING FIRST DIFFEBENCES OF TIME SEBI~S DATA.

CHAPTER - II

NERLOVIAN SUPPLY ~lODEL USING FIRST DIFFERENCES OF TIME SERIES DATA

Nerlove•s formulation of agricultural supply response is one

of the most widely used econometric models in the empirical studies~

The survey of Askari and Cummings presents the results of weJ 1 over

one hundred studies in the Nerlovian tradi!bn~ This Chapter discusses

the basic postulates of the model to provide base for a critical

review of a few important studies. It is also proposed to use the

Nerlovian approach for estimating the relation ships between the

first differences of the time series data of the dependent and

independent variables. Some recent studies suggest that the first

differences of time series data satisfy the conditions qf stationarit~

to a large extent and hence the error term is unlikely to be

correlated in such fu:.nctions when estimated through ordinary least

squares method. The structural form of the model used has been adopted

from Jennings and Young 4 which differ from the traditional model in

the sen·se that it also incorporates a two years lagged dependent

variable (in addition to one laggee already used) as an explanat +~ 7--- ·-

variable. ;%J~·~!---\'\ ' /It \

1.

2· 3.

4.

!>. . :'a- ~ . ... , \ '1." J ., . •. )~

Marc Nerlove, The D namic s of Suo 1 : Estimation of Farmers• <~C$ Resoonse to Price The John Hopkins Press, Baltimore : 1 58 ~~/

- _.::.-

Hussein Askary and John Thomas Cummings (1976,1977), op.cit.

A stationary process(series) has a mPan, variance and auto-correlations which do not change through time.

c. w. J .Granger and P.Newbold, Fore-ca stioo, Economic Time-Series, ( Newyork :Academic Press, 1977 );P. Newbold and N. Davis, "Error-Mi S• Specific at ion and Spurious Regressions" International Economic Review, Vol.19,No.2 pp.513-19 (June 1978 ·

A.N.Jennings and R.J.Young, "Generalization of Nerlovian Supply Model usi!1:J Time-series Methodology : An application to Potato Plantin.;J in Great Britain" Journal of Agricultural Econo:nics, Vol.56, No.1, --THESIS · ·'\80 -,_,.. .. ~

338.17521 09542 J ~ Sa583 Dy ~· -"X ( J.., ~ ~; 5\•4 4 S~ c "'?)

lllllllllllllllllllllllll J tv\ 1 TH2155 ' '\:J

..

The Traditional Model

Specifically, Nerlove's supply response model is called

partial adjustment adaptive expectations (P.~.A.E) model and

as its name suggests, it is based upon two hypotheses which

he made about the area allocation behaviour of the farmers.

The expectational hypothesis

Nerlove observed that the elasticities of acreage using

previous year's relative or deflated prices5 estimated by his

predecessors were too low to explain the real situation of supply

programmes in the United States. He stated that one reason for

this may be the fact that price lagged by one year has been

identified with the price to which farmers react in their acreage

allocation decisions. He argued that the agricultural prices are

most volatile in the economy and the farmers may find themselves

with lower incomes if they revised their production in response to

wide swings that take place in the relative price of various crops.

Hence, to be rational "Farmers react not to last year's price, but

rather the price they expect, and this expected price depends only

to a limited extent on what last year price was". He further added,

"Price expectations are of-course, shaped by multitudes of influences,

so that a representation of expected price as a function of past

prices may merely be a ·convenient way to summarise the effect of

"f these many and diverse influence.

5. The change in absolute price of a crop is less important to cause change in the acreag~ under that crop if the prices of other crops also change overtime at the same rate, ceteris

peri bus. In order to convert crude prices into more meaningful ones from the point of view of acreage al.l ocation under the crop its price is deflated by the price of its competitive crop(s)OY any other deflator like consumer price inde)( orVof farm inputs.

index

23

He adapted the hypothesis of Cagon6 for price expectational ""'

behaviour of the farmers in the following manner. Each year farmers

revise the price which is expected to prevail in the coming y~ar

in proportion to the error they made in predicting price for this e

year. Let P: and Pt_1 be the expected prices for this year and

last year,respectively and Pt_1 , the actual price of last year.

The proportion of error by which the farmers revise their

expectations is a constant which lies between zero and one. Th€5

coefficient is known as the coefficient of expectation. Expressing,

the above hypothesis in Mathematical form.

( 1)

e e Similarity expressing Pt_1 , Pt_2 and so on and substituting

them in equation (1) we obtain,

The above equation represents the expected price as a weighted

moving average of past prices. The weights decline geometrically

towards zero as one goes back in time. The size of expectation

coefficient will determine the number of past years whose prices

should be included6A. Thus, the practice of representing expected

6. Philip Cagan, "The monetary Dynamics of Hyper-Inflation" in M.Friedman,Ed.Studies in g,uantity theory of Money, (Chicago University Press, C~icago: 1956)

6A. The sum of weights for a number N of past prices is 1-(1-~)n The number of past years whose prices may be included in order that the approximate error be less than or equal to some small positive amount say, ~ can be found from the formula

1 - ( 1 - ( l-¢)n

•

price by a year's lagged price is clearly a special case of this

general hypothesis•

Adjustment Hypothesis

taken by Nerlove is :

The stmple acreage response function7

•••••••• (3)

Where J\D =Area desired to be planted in time t.

P~ = expected price in time t.

The error term is not introduced here, though in orig ina 1

Ner love model it was introduced.

This equation involves two variables which are not observable.

P~ can be replaced by observab-tesr on the left hand side of equation(2).

Now, to replace desired acreage, he postulated another behavioural

principle knovm as adjustment hypothesis. Because of techno-economic

and socio-institutional constraints faced by the farmers, the

actually realized change in acreage in a year may be a fraction of

desired change which means the process of the rPalization of desired

change may be spread over a number of years. On expressing this

gradual adjustment process in the form of partial adjustment model

we obtain,

(4)

7. In actual estimated supp1y functions, the other exogeneous factors affectin;J supply of the crop concerned are also included. Usually, a simple linear relation ships is considered between acreage, prices and other relevant variables though the possibi­lity of non-linear relationships is not ruled out.

25

Where At - "t-1 = Actual change in the acreage

~ - At-1 = desired change in the acreage

8 = coefficient of adjustment

and ut = is the error term.

Noyv substitution among equations (1), (3) and (4) gives the

estimating equation.

with b0

= a0~, b1 = a1 B ~, b2 ~ ( 1-B ) +(!-~)

b3 = - ( 1-B ) ( 1-~ ) and vt = ut - ( 1 - ~) ut_1

This is the full P.A.A. E. model with stochastic term inc] uded

in the adjustment equation~ Compared to the P.A.A.E. model of 9

Nerlove, the above equation has an additional term of At_2 on the

right hand side. The parameters 9' and B enter symetrica1ly in this

8.

9.

For detailed solution see Koui:::.soyiannis, op.cit, p.315

In his original model Nerlove argued that on the basis of equations l3) the expected price-can be written as.:a..linear function of acre·age. In particularJlast year's exp;ected price

e Pt-l can be represented by last year's acreage.

At-1 ao 0t-1 Now pte-1 = ----- ---- ~

a1 a1 a1

Because At = a0

+a1 P: +Ut (Ut is error term)

Puttirg this value of P:-l in equation (1) and then substuting

P: in equation (3) he obtained.

1\ = ao + ali/l Pt-1 + al (l-i1J) ( ~~l -

or ~ = aJ!l + a1¢Pt_1+(1-¢)At,_1 +Ut - ( ·1-¢) Ut_1 Here,the desired acreage is supposed to be equal to planted acreage. The same equation can be obtained by using adjustment model and supposinc;:~ ¢ = 1, i· e. Pt_1 is taken for P: with

the difference that now B, the adjustment coefficient comes in place of ¢~the expectectational coefficient. Thus one can not identi· fy these co-efficien~ seperately.But this identification is possib~ in equation( 5),where both the above co-eff. are entering simul'b~t;l;;ous

26

equation so that it is impossible to get the estimates of their

separate values from regression coefficients. One can, however, obtain

the estimates of (¢ + B), ~B and hence ~ and B. In the P.A.;:.... E. model

either of the above coefficients is assumed unity and the value of

other can be easily calculated by substracting the regression

coefficient of ~-1 from one.

illerature Review :

Nerlove model has been used in different ways in actual

empirical studies. The explanatory variables included in some

important studies and their main conclusions are reviPwed in the

following paragraphs.

Raj Krishna10 in his pioneering study for underdeveloped

countries followed this model and besides the expected ptice variable,

he also included the variables of annual rainfall for weather, irriga­

ted area under all crops of the season for the level of irrigation and

yield level of the crop concerned. Thus, the original Nerlove model

was made more comprehensive by including the above variables. This

study covered nine main crops of undivided Punjab and it relates to

the period from 1914 to 1945. The main findings of the study arei

estimates of elasticity proved that the farmers of Punjab adjusted

their acreage under crops like maize and cotton, to price with the

same magnitude as the farmers in United States do. HoY.rAver, the

elasticities were hiqher for the cash crops like cotton, sugarcane

and barley than other foodgrain crops.

10. Raj Krishna ( 19 63 ) , . ..... OP·C~l-•

Z7

To specify the concept of price variable, Jai Krishna and M.S.

Rao11 have worked in two papers with different price formulations.

They worked on wheat acreage in Uttar Pradesh for the period from

1950-51 to 1962-63. In their first study they tried twelve equations

with average wholesale prices of the periods of different length. In

this, the best fit was obtained by using prices predicted from a linear

trend while in their second attempt with nine alternative price

specifications and six different response functions, the best results

were obtained with the average relative prices of preceeding three

years along with the relative yield and rainfall variables. They used

both the simple linear model and the Nerlove' s adjustment model

seperately for f>ach set of data and found that the latter gives the

higher explanation of the variations in acreage.

J.L.Kaul12 improved upon the rainfall variable by taking a more

appropriate measure of it, interms of rainfall for three months prior

to the sowio;J season instead of annual rainfall. His results indicated

11. (i) Jai Krishna and M.S.Rao, "Price Expectation and Acreage Response for vvh eat in Uttar Pradesh". Indian Journal of Agricultural Economics, 20(1), pp 20-25 (January-March 1965)

(ii) Jai Krishna and tt1.s.aao, "Dynamics of Acreage Allocation for ivheat in Uttar Pradesh: r\ case study in supply Response". Indian Journal of Aaricultural Economics, 22(1) pp 37-52 January - March, 1967

12. J.L.Kaul, "A study of Supply Response to Price of Punjab Crops" Indian Journal of Economics, 48(188), July 1967, PP• 25-39.

ZB

that (a) the area under foodgrains is more affected by rainfall,

and (b) the price elasticities are higher in the intensively

irrigated districts than those of mainly rainfall districts •. Perhaps,:

the result (b) is a consequence of result (a) because the irrigation rna}

not only change the cropping pattern but also the character of the

crops in terms of cash or subsistanc e crop( s).

Another bench mark study in agricultural supply response was

undertaken by Behrman for four annual crops of Thailand. The period

of the study relates to the years from 1937 to 196313 • He i-nproved

upon the Nerlovian model used by Krishna through the introduction of

the additional variables of price and yield risks, farm population

of the area and the annual malaria death rate. The specific situation

of uncertainty was incorporated in the form of standard deviation of

the preceding three years' prices and yields as explicit variables

(see further discussion in Chapter II I). However, he did not use

the irrigated area as it was not important for that region. The

results of this study support the hypothesis of positive response

to prices even in the backward economy and the negative coefficients

of standard deviation of price and yield gave evidence of risk-aversion

among the Thai farmers. Moreover, he has minutely discussed the

specification and rationality of various variables used, possibilities

of applying adaptive expectional hypothesis to other variables like

yield and the consequences of the values of adjustment coefficient

beyond the specified limit between z0ro to one. HovJever, hi$lain

contribution remains the introduction of the explicit variables of

price and yield risks as the other modification were not included

for empirical estimation.

13. J.R.Behrman, op, cit.

29

Studies undertaken by William Barber and Edwin Dean14 for

African farmers, though relatively simple in methodology than

Behrman's have already given the evidence in support of the notion

that primary· producers base their production decision partly on the

prices they receive. Dean, in his study which is confined to Tobacco

has also introduced the wage-rate abroad as an alternatively activity

to the crop and found that the two were negatively related.

Maj i, Jha and Venkataramanan15 have also studied the phenomenon

of risk aversion among Punjab farmers with the Behrman's specification.

The coefficient of price risk used by them (yield risk was not

incorporated) gave the exi stance of risk aversion among the Indian

farmers. Further,Kaul and Sidhu16 confirmed the presence of risk

aversion, in their study for five major crops of Punjab for the

period between 1960-61 to 1969-70. They used both the standard

deviation as well as coefficient of variation of preceeding three years

14.(i) William Barber, op.cit, (ii) R.Edwin Dean, op.cit.

15. c.c.Maj i, D. Jha and L. s. Venkataramanan, "Dynamic supply and demand Models for Better Estimation and Projections: An econometric study for Major Foodgrains in Punjab Region" Indian Journal of ricultural Economics, Vol.26(1)~ PP• 21-34 January - March 1971

16. J.L.Kaul and D.S.Sidhu, "Acreage Response to Price For Major Crops in Punjab - An Econometric Study" Indian Journal of, Agricultural Economics, Vol. 26(4) (January - March 1971) PP• 427 - 34.

risks alternatively to observe their relative performance. They

argued that the distribution of coefficient of variation was normal

and so it should give unbiased estimates. Their results shaved that

inc 1 us ion of coefficient of variation as a risk variable in place of

standard deviation impoved the R.2 , the coefficient of multiple

determination. Moreover, they introduced the variable of profitability.

Further, studies in India have been ext ended to more crops and

regions for recent periods. The main exphasis of these studies have

been to identify the shifter variablE·s of different crops and to

mea sure their quantitative impacts 'on their acreages over regions. The

main crops covered are cereals, pulses, sugarcane and ground nut~7

All of these studies follow the Nerlovian models used by Krishna and

Behrman though, in some of th~m estimation method other than Ordinary

least squares has been used~ 8

17. A few important of those studies are : (i) G.S.nam, HTotal Supply Response of Cereals in Different 19 states of Indian, Agricu.lt ural sit uat io,n in India, Vol.l8 No. (7) '"73

(ii)J.T.Cummings, "The Supply responsiveness of Indian Farmers in the Post-Independence period. Major Cereals and cash crops" Indian J ourpa 1 of Agricult u;rp!.._!:con9r.1ic s.J Vol.30, No.1 (Jan-Mar '75)

(iii) K. Chopra and G. Swamy, "Pulses : An ana 1 y sis of der-,and and Supply in India,1951-70" lNew Delhi: Sterling Publishers,l975)

(iv) Ram D.Singh, "Shift in Pulse r.creage: An Inter-regional Analysis of the Dynamics of Farmers' Response, Uttar Pradesh" Indian. Journal of Agricultural Economics, Vo.34, No.3(July -Sept ember 1979 )) PP• 1 - 18

(v) Dayanand Jha, "Acreage Response to Sugarcane in Factory Areas of North Bihar••. Indian Journal of AaricultJ..Jr,Pl Economics, Vol.25 No. 1 (January - M~rch 1970),pp.79- 91

••• 2

31

The volume of literature on this subject has grown quite fast

for India and other countries in recent years. It may not be possible

to discuss the totality of litrature and hence further survey is

restricted to the works related to potato and some recent studies

which have suggested improvement in the nerlove model.

As mentioned in Chapter I it self ,the crops like potato and

other Vegetables and fruits have been less attended to, to estimate

their supply elasticities. A f~ works regarding quantitative estimates

of potato supply functions, which the author could obtain relates to

countries outside India. Most of these studies are mere application

of the already developed Nerlove model to Potato.

17. Cont d.

(vi) M.L.Jhala, "Farmers' Response to Economic Incentives: An Analysis of Inter-Hegional Groundnut Supply Response". Indian Journal of Aaricultural Economics, Vol. 34, No. 1 (January - March 1979) PP• 55 - 67

(vii) s.s.sangwan, Producers Res onse to Price Cha e : A case Study of Changing Cropping Pattern in Haryana. Unpublished M. Phil·Diss.Jawaharlal Nehru University, New Delhi, 1980)

(viii) Indian Council of Social Science Research, Survey of He search in Agricultural Economics 1975, op.cit.

18.' (i) J.T.Cummings, op,cit., has used Cochrane- Orcutt iterative Method for estimation.

(ii) Shashi Kala Sawant, Supply BehaviiDur In Agricult~e : An Econometric Analy~ifo, (Bombay :Himalaya Publishing House,1978) She has tried two stage least squares method of estimation but her rPsults obtained through this method were not significantly different from one obtained by the ordinary least square method.

3Z

In case of Potato supply response, the ear 1 i est study of

Ingersent19 which was available to author, has analysed the relation­

ship between acreage planted in England and the yearly price of this

crop for the period from 1906 to 1960, through graphical presentation

and compariS.::.on. He used the price deflated by an index offgeneral

level of prices received by the farmers and other supply variables

of acreage were ·not included. Positive correspondence was indicated

between the trend corrected acreage and deflated price. In an another

study of Great Jritain, Ingersent20 has also estimated the

quantitative relationship between Potato acreage and its price for

the period between 1955 to 1968. Jv1ules and Jarret21 have also

estimated the supply elasticities of Potato earlier than the second

study of Ingersent. This study relates to South Australia for the

period between 1952-63.

19.

20·

K.Insergent, "The Responsiveness Of Potato Acreage To change In Prices"• Journal of Agricultural Economics, Vol.13,No.1 (1962) 1 PP• 1C1 - 15

" r~odels to Explain Annual Chances of Potato Acreaqe In GrPat Jritain since 1955". The Farm Economist, Vol.XI,No.10 (i969).

( ii) The other previous works on which thP author could not lay hand are : (1) C.G.MacCorkele, "Statistical Analysis of s:upply Response in late Spring Potatoes in California", Hilgardia, Vo1.24,No.16 ( 1965)

(iii) o.Hee, "The Effect of Price On Acreage And Yield of Potatoes" Aaricultural Economic RPserach Vol. X ~o. 4 (1958) - '

21. T. J. Mules and F.G. Jarret, "Supply Response in South Australia Potato Industry" Australian Journal of AOric ultural Economics Vol.X (June 1966) PP• 52-59 J

A relatively comprehensive study for Potato was undertaken

by RPvell22 for lindsey in England. 'BPsides the price of the crop,

his model has also included the explanatory variables like price of

the competitive crops, returns per hectare and rainfall of the sowing

season. Average wholesale price of three months before sowing the

crop was taken for expected price which will influence its acreage

of this season. Other features of the study are introduction of

competitive crop for potato and use of gross returns per acre, in

place of price and yield. The period of study was from 1957 to 1970

and the elasticities were obtained for the acreage under its main

crop and all potatoes. The acreage under potato gave positive

elasticities with respect to it own price a.lld. the elasticity was

negative vv ith respect to cor:1peti t ive crop( s).

In India, some papers relating to a few fruits and ltegetables

were presented in the 34th Annual conference of Indian Society of

Agricultural Economics at Akola (r~ahara~ra) in December, 197423 • All tA.re

of these paper~naive from methodological point of view and their

emphasis is on measuring the relative profitability o£ these crop

in a micro region at a point of time. The supply elasticities of

potato acreage in India have not been estimated so far. 24

22. B.J.Revell, 1'A RPgional 1-\pproach to Potato Acreage Planting Decisions" Journal of r..oricultural Economics,Vo1. 25 No.1 (January 1974) pp.53 - 63

23. Indian Society of Agricultural Economi.::s, "Economics of Commercial ._;rops 11 Indian Journal of A ricultural Economics Vol.29, Conference Number C.ecember 1974 1

24. Recently a study for Orissa, the least important state from the point of view .potato production has estimated the potato acreage elasticity with the state level data. (D.Naik and S.C.Patnaik, "Impact of Prices on Area, Production and Productivity of Potato In Orissa", Agricultural situation in India Vol.39(6) (September 1984) And another study has appeared for Ba o;~ ladesh ( s.A. Sa bur, "Acreage Response For Potato In Bangladesh" The Bangladesh Journal of Agricultural Economi:; s, Vole VI IJ No.ll (December, 1984}

From~review of above studies, it is observed that the

modifications to the model have tended to concentrate on the (a)

inclusion of extra explanatory variables of particular interest in

the situation under investigation, (b) change in the concepts of

variables used by Nerlove, (c) representing quantitative situations

not considered by Nerlove such as parennial crops and short duration

vegetable crops. However, underlying dynamic form of the model

remained unchanged.

In general, criticisms of the f'lodel have related to its

inadequate theoretical basis and statistical problems which arise

when OLS method of estimations is used to obtain estimates of the

parameters. The regression coefficients obtained from equation (5)

will be reliable only when Vt follows an independent and normal 2

distribution with zero mean and constant variance, i.e. Vt,._N(O, crv)

This requires that Ut, the disturbance term in the adjustment function

follows an auto regressive model of the form.

If this is not the case, possibilities of spurious results

exist. It has been found that regression equations of time-series

with high degree of fit as measured by the coefficient of multiple

correlation are sometimes accompanied by extremely low values of

Durbin-'tVatson 'd' statistics or high values of Durbin's 'h'

statistics~5 Consequences of such auto correlai?ed errors (indicated

25. See, Footnotes in Chapter VI.

35

by above tests) in the regression analysis are in the form of

inefficient estimates of regression coefficients, i· e. unduly large

sampling varlance of the estimates, sub-optimal forecasts based upon

regression equations, and invalidity of the usual significance tests

for estimated coefficient. 26

The solution to be adopted in each partie ular case depends on

the source of auto correlation. If the source is omitted variables,

the appropriate procedure is to include these variables. Similarly?

if the source of auto correlation is the mis-specification of the

mathematical form of the relationship the same can be rectified by

either respecification of the variable or of the initial (linear)

27 form •

When the above two sources of a uta-correlation have been ruled

out and if the error term is still seriaJly correlated, it can then,

be emphasized that this is happening purity on account of temporal

factor. For this type of autocorrelation the general procedure is

the transformation of the original data so as to incl ~de the

theoretical error structure in the model. To apply transformation,

26. (i) ..::.vv.J.Granger and P.Newbold (1974), op.cJ:i!

(ii) A.Koutsoyiannis, Theory of Econometrics.

The Macmillan, Tokyo, 1977),Chapter 10

27. Ibid

36

the investigator needs the estimates off( 1 - ~ ) (in this case)J which

is the auto regressive coefficient. Cochrane-Orcutfsiterative method

and Durbin's two step method have been used by some researchers to

estimate P and then apply OLS method to transformed variables to

obtain estimates. These methods and some other methods are well

d t d . t . t t h J h t 28 d K t · · 29 ocumen e 1n econome r1c ex s sue as o ns on an. ou soy1ann1s ~

However, in many cases too little attention has been paid to the

conceptual weakness of the structural equations (2) and (4). Both

propose that adjustment and expectations may be expressed in terms

of a geometric lag of past observations. Jennings and Young found that

the error term introduced in the adjustment equations was showing

large and negative values of co-variance with lagged observations of

acreage which suggest the mis-specification of partial adjustment

mechanism. It substantiate the argument that there is no reason to

expect i"Ls error structure to be stationary either as justified from

the point of view of economic theory or the nature of data 30

used.

28. J.Johnston, Econometric Methods, McGraw Hill, Tokyo, 1972 Eds.2 Chapters 8 and 10

29. A Kout soyiannis, Op•ill•

30. A.N.Jennings and R.J.Young (1980) Op~,p-106

To inter relate the variables in a model time series data

needs a prior analysis. Annual timP-series data mainly consist of

two component s~1 The first is that part of the series which can

be explained by its own behaviour, i.e. trend and the second is the

residual part which is to be explained by exogenous variables. Hence,

it is this residual part for which a researcher mutb look for the

sources of informations relating to time series. In a dynamic model

of time series, the quantity to be explained is the variations in

the changes and not the variations in the levels• While emphasizing

this point, Nelson says, ''The objective is often to investigate the

dynami:s of transitory movements in the system when data do consist

of deterministic function of time (trend) plus a stationary series

(of residuals component)~2

Nearly all the business and economic time series possess·

significant trend, hence a regression equation based upon the leve~ s

of time series data tends to produce dependent error term. Possibi­

lities of interpolation and smoothening process in the times series

may further increase the serial correlation when the series-------

31. In general time series of a variable is decomposed into four components, i· e. trend, cyclical'· seasonal and ace idental components, In annual data seasonal component is eliminated and cyclical and accidental components are left after the removal of trend component S•

32. c. R.Nel son and H. Kang le, "Spurious Periodicity in Inappropriately Detrended Data" Econometrica, Vol• 49, No.3 (1981)

38

representing actual levels are used. When trend component is removed.

the transformed series of the selected variables can be treated as

stationary series sine e the temporal effects are eliminated. RE=gression

equation with this stationary component will give serially uncorrelated

error terms and OLS me~hod of estimation may be applied to obtain

reliable estmates of parameters. Thus, besides the fact that the

model incorporating trend free component of the series has the

convenience of reducing or eliminating auto correlation in the

error term, it seems analytically the correct form for estimating

the annual reactions of the far~ers.

SeveraJ methods are dVailabl e in standard statistical and

econometric t est's33 to isolate the trend component of the time

series. A few important among them which are generally used in

applied work are discussed below.

a) Determine the trend equation of each series by OLS method

of estimation and then substract the trend values obtained by these

33. (i) Ya-Lun,Chou, Statistical knalysis (RineM.:rt ,New York,l975)

( ii)A Kolit soyiannis, op.cit •

39

equations from the set of respective original series. The type of

trend equation computed, i.e. simple linear,log linear, exponPntial

may depend upon the nature of the series. Then apply the method of

least squares to the computed series of deviations from the trend

in estimating the required regression equation.

(b) Another method of isolating trend is to work with the

original data set taking time as one of the explanatory variables.

The time variable captures the autonomous trend experienced by the

dependent variable. The introduction of time as an explicit variable

is equivalent to regressing each explanatory variable on time,

obtaining the residual deviations and then performing the regression

of dependent variable on the deviation~4

(c) Yet, another method which has been frequently recommended

for isolating temporal effects is the use of the first difference of

the series. Actually 1 in a model with first differences of the

variables, time is introduced implicity into the function. For

example if the original function is,

it is a 1 so true that

Substracting, we obtain,

Yt -Yt-1 ::::; cl (Xt - xt-1) + c2 ( t - t + 1) + at - at-1

::::; c2 + c1 < xt - xt-1) + wt

40

The term containing time drops out of the function and the

coefficient of time becomes the constant term of the new function

expressed in first difference of the variables. The new disturbance

term will not be serially correlated because if at in original

formulation follows first order autoregressive scheme, i.e.

Gut of the methods mentioned above, to eliminate the trend

component from time series data, the choice in applied research

will be determined by their analytical superiority. In method(a)

the trend series of deviations will differ with the type of trend

equation used for a variable and same type of trend equation may

not be equally applicable to all the variables. In that case some

variables may be given undue importance in the equation estimated

from the deviations. Moreover, the deviations from trend line may

give more weightage to extreme values of the time series. Considering

the difficulties of this method, we limit our choice to the

remaining two.

Time as an independent variable has been frequently used, in

various empirical studies, to represent autonomous growth. But time

as an independent trend variable may not be of much relevance to

explain economic logic. In many cases, the co~?fficient of time

represents, in reality not only autonol:lous growth in the dependent

variable but the joint effect of the factors which have been omitted

from the function. Time as an independent variable is also likely to

capture the effect of ~orne included explanatory variables because

there is a tendency among economic variables tc move together over

time.

On the other hand, the method of first differences has the

characteristics of implicity introducing time factor in the

regression equation. Kendall (1961) shov1ed that applying the method

of first differences is equivalent to the cipplication of moving

average method to a series of successive terms~5 Moreover, by

assuming the valuP of autoregressive coefficient P equal to one,

the first order autoregressive scheme of error term is taken into

account. This method keeps the computational problem grPatly

simplified. Owing to the logical and analytical superiorities, Fisher

has also recomrnened the use of first differences in applied

. h f t. . 36 econor.~c researc o ~me ser~es. However, when first differences

are used in a regression eqttation, correlation and significance of

regression coefficients -are likely to appear somewhat of lcwer

order than when other trend removal techniques are used. Fisher

attributes these low values as a reward for logic because time as

an independent variable is meaningless in view of economic

interpretation. In an equation using original series, the 'R2 may

turnput to be high due to an association between the trend conponents

of the dependerrt and independent variables, whereas the explanatory

power of equation with first differences is net of the trend or

temporal associations•

35.

36.

M.G.Kendall "A Theorem in Trend Analysis" Biometrice,Vol. 48, 1961

F.M.Fisher, A Prior Information and Tj.me Seties Analysis, (North Holland Publishing Co., Amsterdam, 1966)

Newbold and Davis suggest that the model with first differences

not only introduces stationarity in the applied set of series but is

also more plausible as it analyses the dynamics of phenomenon~7

Considering the possibilities of low significance of regression

coefficients of the equation with first differences, Granger and

Newbold suggest for estimation of the regression equations both with

the original data series and with the changes and then interpret

the combined results, obtained from them~8

Keepifl9 in view the above discussion, it is proposed to

estimate the supply functions of Potato acreage both with the levels

of the time-series as well as with the changes in levels, taking

their first difference. To obtain the equation with first differences,

substract from thP quation (5) for At a similar equation for At-l

which will give the following estimating equation.

(6)

Where t0

is the constant term for the implicit time variable.

But even after transformation, the coefficients of independent

variables remain unchanged, though the di st urbane e term is different.

The new error term will be at = Vt - Vt_1 = (Ut -Ut_1 ) - ( 1 - ~)

(Utl-U ) - t-2

This at may be serially independent and normally distributed,

being derived from the error term of residuals. So OLS method of

estimation can be applied to obtain reliable estimates.

37 •. P.Newbold and N.Devis (1978),op.cit.

38. Granger and Newbold (1979), op.cit. --

If equation (6) is traced back, the adjustment equation will

also consist of differences which implies that the rate of adjustment

under long-run equilibrium is now a function of last year's change

rather than last year absolute area. The degree of adjustment, the

farmer is capable of making in the current period will depend upon

the rate of adjustment, he was able to make in the previous year.

Moreover, the estimating equations (5) and (6) do away with

the usual assumption of expectional coefficient ¢, being equal to one.

The values of adjustment and expectational coefficients obtained

through manipulation of the coefficients of lagged dependent variables,

wcill enable to find out, whether farmers adopt the expected price or

adjust the desired area in allocating acreage under individual crops.

A fevv possibilities depending upon the magnitudes and significance of

co-efficients of lagged acreage variables may be as follows•

Case No.1 - hhen one year's lagged dependent variable, i· e. At-l or

('\.-l - J\_2 ) enters significantly and two period lagged area

variable does not enter or its coefficient is insignificant in the

estimated equation. Then from equation (5)

( 1 - B ) + ( 1- ¢ ) = b2 = C0

(say )

2 - ( B + ¢) = C0

8+¢=2-C0

•••••• (i)

1-\lso -(1 8)(1- ¢) = b3 = 0 ( does not enter)

1 - (B + ¢) + ~ = 0

a¢ = 2 - C0

- 1 substituting ( B + f/J ) from (1)

I?JP = 1 - c 0 • • • • • • ( ii)

Applying ( 8 - ¢)2 = ( 8 + ¢)2 - 48¢

= ( 2 - c )2 - 4 ( l - c ) 0 0

= 4 + c2 0

- 4C - 4 + 4C 0 0

B- ¢ ~ ( ... ) = + ~ ••••••••••••••• 111 - 0

If positive value of C0

is considered then from equation (i)

and (iii) we ~~all obtain

8 = 1 and ~ = 1 - C 0

It indicates full adjustment of desired area, however, the

expected price will follow the expectations model, i.e. not only

the price of previous year but also the prices of past years will

inluence the area planted under the crop as the value of ¢ is less

than one. When the negative va:ue of C0

is considered it gives¢ = 1

and 8 = ,x-c which means last year's price represents the expected 0

price and the farmers under adjust the desired area. ·

Case II : Whentwo years'lagged dependent variable, At_2 or (At_2 -At_3 )

enters significantly and one year's lagged dependent variable is

insignificant or does not enter in the estimated equation then

( 1 - 8 ) + ( 1 - ¢) = b2 = 0

B + ¢ = 2 • • • • • • ( iv)

and -(1- B) ( 1- ¢) = b3 = e1 ( say)

B¢ = (B + ¢) - 1 - c1 ~ = 2 - 1 - C (putting 8 + C/1 = 2)

s¢ = 1 - c1 • • • • • • • (v)

Applying (8-¢) 2 = ( B + ¢)2 - 4 8¢ (a - ¢) 2 = 4 - 4 + 4 c1

( B-¢ ) 2 = 4C1 .

8- ¢::; ± 2 vel •••••• (vi)

Now from ( iv) and (vi)

a = 1 ± /c1

l2J = 1 +v'c1

If positive sign is considered and c1 does not have negative

vaJ ue, the adjustment coefficient will be more than one and expecta-

tion coefficient will be less than one.

If negative sign is considered, the result will be opposite

to that of the first case. This implies that farmers always over-

react either in price expectations or in area adjustment. However,

they may not over react in both the stages. If the value of c1 is

negative the values will not be defined.

Case III : When lagged d~pendent variables of both periods_,i. e. t - 1

and t - 2 enter significantly then

( 1 - 3 ) + ( 1 - ¢ ) = b2 = c"' L

B + ¢ = 2- c2 •••••••••

and also

- ( 1-3 )( 1 - ¢ ) = b3 = c3 ( say )

(say)

(vii)

which on substitution from equation (vii)

will give B = 1 - c2 - c3 (vlll)

Now applying

( B - ¢) 2 = ( B + ¢) 2 - 4 ~ and substituting values from equation (vii) & (viii) it gives

B - ¢ = ± V C~ + 4C3

46

andVC~ + 4C2 will have real roots

If it is so then

B = =fc2 +vtc~ + 4C3 ~j 2

~ =1-c2 ! v'(C~ + 4C3)

= 2

The actual value of Band¢ will depend upon the value of

determinant v' C~ + 4C3 • '.Jo.Je shall examine these inferences in our

regression results,if any.

To sum up, the Nerlovian model of agricultural supply to be

used in this study will have the following qualities. AopJ.ication

of the full P.A.A.E. model including lagged dependent variables of

both one and two years as explanatory variables will do away with

the asunption of takirg the value of either adjustment coefficient

or expectations coefficient equal to one. In the P.A.r.o..E (Nerlove's

model, both these coefficients are not identifiable seperately,

whereas in the full P.A.A·E model both the coefficients can be

computed simultaneously. Hence, it is possible to know the extent

of price adapt at ion and area adjustment principles followed by the

farmers in allocating acreage under a crop. Moreover, in case of

some agricultural commodities such as perennial crops, live stock

the supply is influenced by their pattern of :.: ·; o-n acreage (or

production) of more than one year, so this r.todel including lagged

values of dependent variables for more than one year may be more

suitable.

47

Secondly, the proposal of esti:nating supply response with

first difference r.1ay enable us to give some interesting results.

The estimated supply function with first difference of time series

will not only be important in analysing the dynamics of change b~~

the results will also help us to empirically testify the arguments

advanced in favour of such models·