Examples of Nerlovian Models

Supply Response: Expectations Formation and Partial Adjustment

4.4. Examples of Nerlovian Models

4.4.1. Supply Response of Maize in Thailand under Risk

An interesting extension of the Nerlovian supply model is Behrman’s (1968) study of the area response of maize in eight provinces of Thailand using time series data from 1937 to 1963. He stated a four-equation structural model as follows:

At

d a₀ a₁pt ea₂yt

ea₃_pta₄_yt a₅Mt u_1t,

d

At b₀ At1(A_t At1)u_2t,

e e e

pt c₀ p_t1(p_t1p_t1)u_3t,

ytey ˆ t, ytd₀d₁(R_tR )d₂td₃t²u_4t, where:

A^d, p^e, y^e = desired area, expected price (deflated by a price index of competing crops), and expected yield,

A_t , y_t = area and yield, respectively, = predicted yield for

y ˆ R_t R ,

_pt and _yt = standard deviations of price and yield in last three periods, M_t = malaria death rate,

R_t , R = rainfall in t and average rainfall, t = time trend.

Substituting the latter three equations in the first to eliminate all unobservable variables, the reduced form equation for area planted is of the type A = Xb + w, where the variables X are p_t1,A_t1,A_t2, ˆ y _t1, ˆ y _t2,_pt,_p,t1,_yt,_y,t1,M_t, and M_t1

to a₆,b₀,

. Behrman used a maximum-likelihood procedure to estimate this reduced form equation directly with respect to the structural form parameters a₀ ,c₀, and  . His results for maize plantation are reported in Table 4.3. Table 4.4 gives the short-run and long-run elasticities at the sample mean. As shown by the R²s, this model explains a considerable portion of the variation in planted area in all eight provinces, but this is not due to price response coefficients which are in all cases statistically insignificant. By contrast, the expected yield is a strong determinant of area planted. So is price risk which has a negative effect on area planted as greater risk in the gross return of a crop leads farmers to plant more of other crops. Area adjustment and price expectation coefficients play minor roles and were set equal to one in most provinces.

Table 4.3 approximately here

Table 4.4 approximately here

4.4.2. Supply Response under Controlled Prices in Egypt

Cuddihy (1980) estimated a model of area response for the five major crops of Egyptian agriculture: long-season berseem (Egyptian clover), cotton, wheat, maize, and rice. For price, he used revenue per feddan (1 feddan = 1.035 acres) of each crop deflated by a real wage index. Using revenue per feddan is an interesting way of combining price and yield expectations when both are assumed to be exogenous. The choice of deflator, the real wage index, is based on the fact that labor cost is a large share of the variable costs of agricultural production in Egypt. Expectations are formed with a one-year lag, as in section 4.2.4. The expected yields y_i^e of the five crops are all included in the model, and no shifter is used.

The structural form of the model is thus:

At

d ₁ _2i

i



5 pit

e _3i

i



5 yit e ut, At At1 At

dAt

 

^vt,

p_it^e  p_i,t1, i.e.,  1 (administered prices), yit

e y_i,t1, (naive expectations).

The reduced form of the model is written as:

At ₁ _2ip_i,t1 i1



5 ^3At1 _5iy_i,t1 i1



5 ^(ut vt),

where:

₁₁,

₂ ₂, short-run elasticity of supply response,

₃1,

₅₃,

₂ ₂ /(1₃), long-run elasticity of supply response.

The data set has 26 annual observations, from 1950 to 1975.

The estimation results are shown in Table 4.5. Table 4.6 presents the supply elasticities.

About one-third of the estimated coefficients are significantly different from zero at the 5%

level, and the R²s indicate that a large part of observed variation in the cultivated areas is explained by the model. An interesting aspect of Cuddihy’s model is that unlike most other studies, where crops are considered in isolation, area responses of the main crops are estimated together so that the interactions among them can be examined. However, his results have several problems, probably reflecting the fact that resource allocation in Egyptian agriculture has been highly intervened by government, leaving to revenues a relatively secondary role. The presence of some negative own-revenue effects does not make economic sense. Also, some revenue terms have been arbitrarily omitted in the equations for maize, cotton, and berseem. Finally, the cross-revenue effects are not always consistent. For example, in the estimate of the equation for wheat, one finds that maize is its competitor, while the maize equation indicates that wheat is a complement.

Table 4.5 approximately here Table 4.6 approximately here

4.4.3. Other Supply Response Studies

The adaptive expectations model has been applied to a number of specialized supply response models such as beef and tree crops. For beef, because animals are both a capital good and a product, structural models predict that the short-run supply response to an increase in the price of cattle should be negative, while the long-run should be positive (Jarvis, 1974). This is, however, not a strong conclusion and slight changes in specification of the model can lead to positive short-run supply response (Paarsch, 1985). Empirically, both negative and positive short-run supply responses have been obtained, and most frequently non-significant coefficients (Nelson and Spreen, 1978; Antonovitz and Green, 1990).

Structural models for perennial crops have stressed the determinants of new investment in tree plantations. In a model for Brazilian coffee, Wickens and Greenfield (1973) developed a three equations structural model with: (1) a vintage production function where potential production is function of the number of trees surviving and technological change, (2) an investment function where the number of trees planted is function of lagged planting and current price, and (3) a supply response equation where the proportion of potential production that is harvested is explained by lagged prices. The reduced form supply function derived from this structural model is estimated and shows the importance of longer lags in the supply of tree crops compared to field crops. For the analysis of rubber supply in Sri Lanka, Hartley, Nerlove, and Peters (1987) focused on the uprooting and replanting of trees as opposed to new plantings as in the previous study. They specify a three equations model with

replanting, production, and new plantings. Their results show a strong positive long-run response of replantings to variations in the expected price and generally insignificant response to current price.