This includes different supply response models( Nerlovian models) for annual and perennial crops and need of these models in econometrics

2. NERLOVIAN SUPPLY RESPONSE MODEL
Speaker: Samriti (F-17-05-D)
Department of Social Science
Dr YSP UHF Nauni, Solan

3. Supply: Supply of a commodity refers to the quantity of a commodity
that is offered for sale in market at a given price during a particular
period of time.
The definition of supply is complete when it has the following
elements:
(i)Quantity of a commodity offered for sale.
(ii)Price of the commodity.
(iii)Time during which the quantity is offered.
Law of supply: law of supply states that, other things remaining
constant, there is a positive relationship between price of commodity
and its quantity supplied. Thus more is supplied at higher price and
less at lower price.

4. Supply Response Function:
The supply response function shows the functional relationship between price of
the commodity and quantity supplied on the assumption that other determinants
of supply are held constant. These other determinants are rainfall, fertilizer
prices of competing crops, wages etc.
When the 'ceteris paribus' assumption is not met then there will be shifts in the
supply curve. As such the 'ceteris paribus’ assumption is not satisfied and the
simple relationship extend to a multivariate one.

5. Need for the supply response function
 Supply responses of primary producers vary considerably according to the
characteristics of the crops analyzed.
 Annual/seasonal and perennial crops have different characteristics and present
different conceptual problems. Therefore, they require the use of different models.
 Most of the econometric studies on supply responses have been carried out on
annual/seasonal crops. These crops form the staple foods of most underdeveloped
countries and as self-sufficiency in food became the overriding aim of most of the
underdeveloped countries, emphasis was placed on such crops.
 Policies which could encourage greater production of these staple crops were
required and formulation of these policies necessitated supply response studies on
such crops. What therefore, needed is a comprehensive supply model which can
incorporate the various alternative opportunities open to the farmer.

6. RESPONSIVENESS OF PERENNIAL CROPS
Some of the models combining planting - decisions with output - planting
relationship in order to estimate the price responsiveness of producers are;
 The Batesman Model
 The Ady Equation
 The Behrman Equation
The time horizon involved for the producers of perennial crops is much
longer than that of annual crops. For perennial crops yield are dependent
upon age of the tree, previous output and current as well as previous level of
input.

7. Responsiveness of Annual Crops

The aim of all supply response
studies is to find out how a farmer
intends to react to movements in the
price of the crop he produces.
When more than one crop is being
cultivated the aim is to find out how the
farmer intends to reallocate his efforts
between the various crops in response to
changes in the relative price levels.
In attempts to quantify such price responsiveness, acreage planted
should be used as the dependent variable because actual output is not a
good proxy for intended output. The acreage planted would give a better
indication of the farmer's intention as he has greater control over this
variable.

8. Some of the supply response function models used for annual crops.
The simple Koyck
distribution lag
model
Native
expectation model
The
Extrapolative
Expectation
Model
The Partial
adjustment model
Adaptive
expectation model
The complex
Nerlovian
expectations
model

9.  According to Koyck, current value of a variable say A (area) depends on many
lagged values for another variable (price) Pt, Pt-1, Pt-2, Pt-3 ….etc. it is normally
expected that more remote values would tend to have smaller influence than
more recent.
 In the Native Expectation Model (i.e., the Cobweb model) the current
expected price P*
t is assumed to be equal to the previous period's actual price
(Pt-1). This is usually done in the case where agricultural markets are
controlled by the government and future prices are announced prior to planting
time.
 The Extrapolative Expectation model (Goodwin, 1947) It assumes the
expected price to be a function of the lagged price plus or minus some fraction
of the price change in the previous two periods.
P*
t = Pt-1 + β (Pt-1 - Pt-2)

10. The Nerlovian model is considered one of the most influential and
successful models used to estimate agricultural supply response among
all the econometric models.
The reduced form of the
Nerlovian model is an
autoregressive model because it
includes lagged values of the
dependent variable (output)
among its explanatory variables.
The Nerlovian model is a
dynamic model, stating that
output is a function of expected
price, area adjustment, and some
exogenous variables.

11. Nerlovian model was given by Marc Leon Nerlove in 1958
who is an American economist specialized in agricultural
economics and econometrics.

12. Nerlovian models are built to examine the farmers’ output reaction based on
price expectations and area adjustment.
. Time series data are often used for the commodity under study to capture the
dynamics of agriculture production.
The Nerlovian supply response approach enables us to determine short- run
and long-run elasticities..

13. This is the simplest version, with one determinant
and the assumption of a linear relationship, which is
based on the hypothesis that desired level of area A*t
in period t depends on the price at time t-1.
A*t = b0 + b1Pt-1 + ut
Partial Adjustment

14. As A*
t is desired area under cultivation at time t and is
unobservable, equation cannot be estimated. Therefore,
At - At-1 = α (A*
t – At-1) + ut ; 0≤ α ≤ 1
= α [ (b0 + b1Pt-1 + ut) – At-1]+ ut
= α b0 + α b1Pt-1 + α ut - α At-1 + ut
At = α b0 + α b1Pt-1 + (1- α) At-1 + α ut + ut
or At = π1 + π2 Pt-1 + π3 At-1 + ut
Where,
 At = actual area under cultivation at time t
 At-1 and A*
t-1 = actual and desired area at time t-1
 Pt-1 = actual price at time t-1
 ut = unobserved random factors affecting the area under cultivation
 α = adjustment coefficient ( α = 1 when actual area = desired area & α = 0
when actual area at time t = observed area at t-1).

15. This model is based on the following behavioural
hypothesis: The value of area in any one period t
depends not on the actual value of Pt but on the
expected level of P at time t, say P*
t.
Adaptive Expectation

16. This model has become popular because it can deal with
“expectation” (about future factors) whose importance in
economic behaviour is being increasingly recognised.
At = b0 + b1P*
t + ut
P*t - P*t-1 = ɤ (Pt-1 – P*
t-1) ; 0≤ ɤ ≤ 1
P*
t = P*
t-1 + ɤ (Pt-1 – P*
t-1)
where ɤ is coefficient of expectation
 P*
t = -b0/b1 + At/b1 - ut/b1
 P*
t-1 = -b0/b1 + At-1/b1 - ut-1/b1 (lagged one period)
Thus area under cultivation at time t is
 At = (ɤ b0) + ɤ b1Pt-1 + (1- ɤ) At-1 + {ut – (1- ɤ) ut-1}
or At = π1 + π2 Pt-1 + π1 At-1 + ut

17. Thus Nerlovian expectations model is
supposed to reflect the way in which past
experience determines the expected prices
and other expectational variables which in
turn determine the acreage planted.

18. COMPLEX EXPECTATION MODEL

19. As full adjustment to the desired allocation of land may not be
possible in the short run, the actual adjustment in area will be only a
fraction α of the desired adjustment.
At – At-1 = α (A*
t - At-1 ) + vt ……………..(2)
( α is partial adjustment coefficient)
The price that the producer expects to prevail at harvest time
cannot be observed. Therefore, one has to specify a model that explains
how the agent forms expectations based on actual and past prices and
other observable variables.

20. For eg., farmers adjust their expectations as a fraction of the deviation
between their expected price and the actual price in the last period, t-1.
P*t - P*t-1 = ɤ (Pt-1 – P*
t-1 ) + wt
P*t = ɤ Pt-1 + (1- ɤ) - P*
t-1 ; 0 ≤ ɤ ≤ 1 ……………(3)
( ɤ is the adaptive-expectations coefficient)
Since A*
t and P*t are unobservable we eliminated them from the system and
substitution of Equation (1) and (3) into Equation (2)
αA*
t = At - At-1 +α At-1 – ut
A*
t = (1/ α )At + (α -1/ α)At-1 – (1/ α)ut

21. By putting the value of A*
t in equation 2
(1/ α)At + (α -1/ α)At-1 – (1/ α)ut = b0 + b1P*
t
P*
t = (1/b1 α)At + (α -1/b1v)At-1 – (1/b1 α)ut – b0/b1
If equation is lagged by 1 therefore equation becomes:
P*
t-1 = – b0/b1 + (1/b1 α)At-1 + (α -1/b1 α)At-2 – (1/b1 α)ut-1
P*
t - P*
t-1 = ɤ( Pt – P*
t-1)
[(1/b1 α)At + (α -1/b1α)At-1 – (1/b1α)ut – b0/b1 ] – b0/b1 + (1/b1α)At-1 +
(α -1/b1)At-2 – (1/b1 α)ut-1
= ɤ [ Pt– (b0/b1 + (1/b1α)At-1 + (α -1/b1α)At-2–(1/b1α)ut-1]

22. Thus rearrangement gives the reduced form
At = π1 + π2 Pt-1 + π3 At-1 + π4 At-2 + π5 Zt + et
……………(4)
This equation is the estimable form of the supply response model.
Where;
• π1 = b0ɤα
• π2 = b1ɤ α ; short run coefficient of supply response
• π3 = (1- α) + (1-ɤ)
• π4 = - (1- α) (1-ɤ)
• et = vt - (1- ɤ)vt-1 + α ut - α(1- ɤ)ut-1 + b1 α wt
Since only the actual output rather than the optimal output is observed in reality.
The reduced form is a distributed lag model with lagged dependent variable.

23. The short-run price response of each explanatory variable is estimated directly
by its coefficient.
The long-run price response is obtained by dividing short-run
elasticities by an adjustment coefficient (the coefficient of the lagged dependent
variables).
The short run elasticity can be calculated from;
e = π2 .P/ A
where P and A are mean price and acreage respectively.
and π2 is regression coefficient.
The long run elasticity can be calculated as;
e = π2/1- π3 – π4 × P/ A
The short run and the long run elasticities of supply with respect to the
other determining variables are obtained in the same way.

24. Case study:
Leaver Rosemary (2003) studied an estimate of the price
elasticity of supply for tobacco output in Zimbabwe using an
adapted Nerlovian model and covered the period 1938 to
2000.
The supply response equation is expressed as:
LOUTPUTt = b0 + b1LREALPRICEt-1 + b2LOUTPUTt-1 +
b3 LOUTPUTt-2 + b4 QUOTA + b5 RAINt-1 +
b6 TIME + b7 TIME2 + Ut

25. The results show that price lagged one period, output lagged both
one and two periods, and the simple time trend all exert a positive
influence on tobacco production.
The negative coefficient of the quadratic time trend variable implies
that unspecified effects are causing tobacco output to increase,
although at a decreasing rate.
These variables together explain about 96 percent of the variation in
Zimbabwean tobacco output.

26. REGRESSION RESULTS FOR THE TOBACCO SUPPLY RESPONSE FROM 1938-2000

27. CONCLUSION
This Nerlovian Model has become popular because it
can deal with ‘expectations’ (about future factors)
whose importance in economic behaviour is being
recognised. And Nerlovian Complex Expectation
model contains an additional variable At-2 when
compared with Partial Adjustment and Adaptive
Expectation models which gives more reliable results

28. Thank
you