Vintage production approach to perennial crop supply

Journal

of Econometrics

36 (1987) 133-161.

North-Holland

VINTAGE

PRODUCTION APPROACH TO PERENNIAL CROP SUPPLY An Application to Tea in Major Producing Countries* T. AKIYAMA The World Bunk, Wushington, DC 20433,

USA

P.K. TRIVEDI Indianu New planting and replanting perennial producers and in development. In this paper which links the producer’s production in Kenya, India supply responses.

Unic~ersity. Bloomrngton,

IN 47405,

USA

decisions play a key role in determining the long-run response of accounting for observed differences in the patterns of agricultural a framework based on the vintage production model is proposed, short-run and long-run decisions. The empirical applications to tea and Sri Lanka illustrate the diversity of mechanisms determining the

1. Introduction Tree crop commodities such as cocoa, coffee, tea, rubber, palm oil and many others comprise an important source of export revenues and employment in many LDC’s. For example, in 1981-1983 average annual export value of these commodities for all LDC’s was US $16 billion. Hence it is extremely important to understand the mechanism of perennial crop supply and its interactions with policies targeted on the suppliers. A number of approaches have been developed in the past to model econometrically the behavior of suppliers, but these suffer from well-known defects. The present paper reexamines some of the issues and puts forward an alternative approach which has features absent from earlier work. For example, within our framework it becomes possible conceptually and empirically to distinguish between short-run and long-run elasticities and to identify the effects of local institutional features and incentives that play a key role in determining long-run resources. Our approach explains why supply elasticities cannot be treated as time-invariant and how the integration of the production * This paper is based on research conducted both individually and jointly by the two authors in the Commodities Studies Division of the World Bank. The authors gratefully acknowledge the comments and assistance of numerous colleagues, including especially Ronald Duncan and Alan Bowers. However, the authors are solely responsible for the contents of the paper.

0304-4076/87/$3.500

1987, Elsevier Science Publishers

B.V. (North-Holland)

134

T. Aki.vama and P.K. Trivedi, Analysis of perennial crop supply

and investment decisions of suppliers helps to understand better the supply response in total. Section 2 begins with a review of some of the time-series approaches used in the past, especially those of Wickens and Greenfield (1973) and French and Matthews (1971). The assumptions, definitions, concepts and methods underlying our own approach are given in section 3, followed by application to the case of tea in section 4. 2. Review of literature on perennial crop supply A major difficulty with earlier analyses of perennial crop supply is their failure to distinguish clearly between the long-run and short-run dimensions of the producers supply decisions. They have estimated a single, reduced-form output function that combines the long-term investment decision and the short-term harvest decision in a single equation. When this is done, it is usually not possible to analyze separately the individual effects of harvest and investment decisions on crop output. Below, we discuss in some detail earlier analyses of perennial crop supply. Bateman (1965) began by assuming that farmers maximize the present value of expected profits with respect to planted acreage. Thus, acreage planted to cocoa becomes a function of the present value of expected real prices, expected marginal yields per acre, and expected marginal costs. Bateman assumed the price term would dominate, so he specified area planted as a function of the discounted value of the expected own- and substitute-prices. Price expectations were assumed to be formed adaptively and the models respecified in terms of output rather than planted acreage for which data were not readily available. But output is also a function of yields, which in turn depend on the age of the trees. After taking first differences (to avoid a nearly infinite time horizon) and combining output and planting equations, Bateman finally obtained his reduced-form estimating equation in which output is a function of lagged own- and cross-prices, lagged rainfall, and lagged output. Behrman (1968) also took a similar approach in his study of cocoa; however, he began not with the planted acreage but with the desired acreage. Thus the desired acreage is specified as a function of own- and cross-prices. Behrman also transforms this acreage equation to an output equation because of lack of data, the latter being based on a Nerlovian model of area adjustment. In this case, output becomes a function of own-prices (current and lagged) and an infinite summation of yield multiplied by lagged area. On taking first differences, output reduces to a function of lagged own- and substitute-prices and lagged output. Ady (1968) followed Bateman and Behrman in that she estimated, in first difference terms, output as a function of lagged prices and lagged output; but she also included a world price term, an index of agronomic factors, and an

T. A k&ama and P. K. Tri’uedi, A nu(vsis

ofperennial

crop supp!v

135

index of other economic factors. Nonetheless, the basic model remains the Nerlovian adjustment scheme based on planted acreage (or on tree stocks) and on prices, leading to a single reduced-form equation in terms of first differences of output. Stern (1965) made an advance on this approach as he had available new planting data on cocoa for Nigeria. He estimated a new planting equation using lagged prices as explanators. But for those countries where such data were not available he estimated (again in first difference terms) output as a function of current and lagged own-price. French and Matthews (1971) provided a more complete model of supply response comprising of five equations: one explains new planting and another replacement, and these two are combined to give desired bearing acreage. A fourth equation explains variations in yields, and the last specifies the relationship between unobserved expectational variables and observed data. A further identity makes output the product of area and yield. The solved model produces a single reduced-form equation for output. French and Matthews attempt to quantify separately the investment and harvest components of the output decision. However, as in earlier work, lack of data constrains their estimated reduced-form equation to take a very familiar form: in first difference terms, acreage is specified simply as a function of lagged prices deflated by an index of farm wage rates and average acreage harvested in different periods. This equation is then estimated using OLS. However, the estimated coefficients could not be used to recover the structural parameters as the model remained underidentified. Thus the effect of harvest and investment decisions could not be separately quantified. Wickens and Greenfield (1973) also attempted to quantify investment and harvest decisions separately, but ended up estimating a final reduced-form output equation based on a distributed lag model. Their model consisted of three equations:

(1)

fY,+zL

qr=Yo+Y14P+

i=o

where qf denotes production potential, q, actual production, Z, investment, and P,producer price. Eq. (2) the investment function, is derived from a neoclassical adjustment cost model which gives the standard result that optimally investment will take

T. Akiyomu and P.K. Trivedi, Anulysis

136

ofperennialcrop supply

place at a rate which equates the marginal cost and the expected discounted marginal revenue of investment. Wickens and Greenfield used a distributed lag model of prices to proxy net expected revenue in the actual estimation. Eq. (1) specified the ‘potential’ output as a function of past investment and a yield term 6; which measures the present yield of the past plantings. Their original model could be specified to include both embodied and disembodied technical progress on yields, but the former is ignored for simplicity. Consequently, potential output becomes a function only of the number of productive trees. It is assumed that labor and land are always used in fixed proportions to capital and that the supplies of land and labor are unlimited. Once again, these assumptions are made to keep the model tractable. The final equation (3) is the output equation. Output depends upon potential output (past investment) and harvest decisions which are proxied by a distributed lag on own-prices. An additional term was included in this equation to capture the biennial bearing cycle for coffee trees. On substituting eqs. (2) and (1) into eq. (3) and solving for output the estimated equation becomes a distributed lag function of prices and lagged areas; viz.

C &p,-, +

qr =

(1 + al)qr_i

- cy,q,_2 + constant,

(4)

i=O

where P,

=

Y2

=-t

+

I+2

Q,Y&&

i =

>

+ Q,Y&&-

0,

QIY~+~, i= l,...,m,

=Q~Y,%,+I -QlY,+,,

i=m+l,

= Q,Y;4,

i=m+2,...,m.

This approach encounters several problems: (i) It is not possible to derive coefficients of the three structural equations from the reduced form. (ii) It is difficult to include non-price explanatory variables in the planting equation [if, for example, one term (~~2~ is added to the right-hand side of eq. (2) it appears as a distributed lag in eq. (4)]. (iii) The yield curves of perennial crops are not necessarily well approximated by the polynomial form used. Thus weights of lagged prices attained statistically could be quite different from the yield curve. And (iv), empirically, the sum of the coefficients for q1_1 and ql_2 seldom comes close to unity, which violates a theoretical constraint on this specification. Conventionally, a distinction is drawn between the short-run producer decision regarding the intensity of usage of variable inputs, for given quanti-

T Akiyama and P. K. Trivedi, Analysis

ofperenniul crop supp!)

137

ties of fixed inputs and technical conditions of production, and the longer-term decision involving the quantities of fixed factors and the choice of technique of production. The supply response in the former case is measured by the short-run supply elasticity, holding constant the capital input. The typically larger long-term elasticity is the sum of the short-run elasticity and the elasticity of capital stock with respect to the output price multiplied by the elasticity of supply with respect to the capital stock [Binswanger et al. (1985)]. The latter is usually neglected in empirical work when the focus is on short-run output and price determination. However, the short-run supply function, being indexed by quantities of fixed factors, shifts as these factors undergo adjustment in response to changes in the long-term profitability of the crop. To separate these short-run and long-run responses or to produce estimates of long-run supply elasticity, a model of the adjustment of cropped area to variations in profitability is required. Empirical studies which model supply as a long distributed lag on prices, without explicitly modelling the adjustment of fixed inputs will confound short-run and long-run responses. In any case, an attempt to measure the long-run supply elasticity is not meaningful unless it can be shown that the capital stock adjusts in a determinate manner. In dealing with perennial crops an allowance must be made for the heterogeneity of capital arising both from a changing age-distribution of trees and from varietal change. From a priori considerations alone it is not clear that there will always exist a heterogeneous capital stock of unique composition corresponding to a given configuration of prices. If this is not the case, long-run supply elasticity is not a well-defined concept. The relationship between investment and output prices is essential for estimating the long-term supply elasticity if that concept is meaningful. To some extent such a relationship subsumes within it the choice of technique of production. This should be especially obvious in cases where technical change is of the embodied variety, as in the case of high-yielding varieties, so that it cannot be implemented without investment. Understanding of the process of diffusion of technological change and of investment are closely related. An understanding of the determinants of new planting and replanting investment decisions of the producer is of key importance when trying to account for the observed difference in the patterns of development and change. This requires a comprehensive analytical framework within which one can examine producer’s short-run decisions such as the utilization of factor inputs, as well as long-term decisions such as the choice of technology and the level of new planting and replanting. Motivation for studying the supply response comes in a large measure from the desire to analyze the short-run and long-run impact of subsidies and taxes on producers. Many countries have used new planting, replanting and infilling subsidies as incentives to stimulate stagnant tree-crop sectors. Although the precise reasons for such stagnation and/or decline are unclear, candidate

138

T. A ki@tna und P. K. Trivedi, Analysis of perennial crop supp!v

variables include factors such as the perceived reduction in the expected profitability of production brought about by, inter alia, aging capital stock, declining productivity and ‘over-taxation’ of sales revenues (often through export taxes). The operation of the mechanism through which these variables affect producer decisions, as well as the quantitative magnitude of their impact will remain a major issue for some time. To resolve them, however, various elements which go on to make up the supply decision such as new planting, replanting, uprooting and harvesting should be carefully disentangled and the policy variables should be directly related to the relevant decision variables rather than indirectly to final output. [See Nerlove (1979) and Trivedi (1986) for a longer discussion of this issue.] Ultimately, therefore, detailed structural models provide the only way out of the impasse. An example of a modelling exercise which moves in this direction is the recent study of Hartley, Nerlove and Peters (1985) in which the authors have studied new planting, replanting, and production decisions for the case of rubber in Sri Lanka using a variant of the Wickens-Greenfield model. In their case, new planting was a negligible component of total area so the authors concentrated on modelling the uprooting-replanting decision, concluding that for understanding the supply response treatment of the relation between production and the stock of trees was considerably more complex than specified by the Wickens-Greenfield model. Specifically, steady varietal improvement resulting in higher-yielding trees was thought to be very important in their case. To conclude: from the viewpoint of a structural model capable of providing insights into the operation of policies, most of the econometric formulations of perennial supply are deficient. However, each crop has its own special features such that the importance of various general criticisms made in this section will vary on a case-by-case basis. In what follows we provide an empirical illustration which provides some indications of potentially fruitful directions for future research. 3. Supply behavior 3.1. General considerations In the case of most tree crops, careful attention has to be paid in modelling the supply side to four features of the production process: (i) the existence of a biologically-determined gestation lag between planting and obtaining yield, (ii) the dependence of current production on current as well as previous levels of outputs, (iii) the existence of significant costs of adjustment in respect of the planting and removal of trees, and (iv) the constraints on planting and removal resulting not only from past decisions but also from the existence of binding non-negativity constraints related to the adjustment process. Features (i)-(iv) imply, individually and jointly, that investment behavior of the productive firm cannot be myopic. Features (i) and (ii) imply that the relevant

T. Aki?/ama and P. K. Triuedi, Ana!ysis of perennial crop supp!y

139

supply theory is intrinsically dynamic. More specifically, if for given levels of other variable inputs the productivity of trees varies with age, then the age distribution of trees as well as the total stock of trees becomes important in determining feasible levels of production. Thus in general the capital stock should be regarded as heterogeneous with respect to yield. Since the productivity of a tea tree declines very slowly with age [Etherington (1973)] - the biologically productive period can be 90-100 years - to achieve minimum differentiation one should classify the stock of trees into three categories: less than five years old, between five and ten years old and more than ten years old. Furthermore, in the case of countries like India and Sri Lanka, which have been growing tea for a long time, it would be helpful to disaggregate the last category further into trees less than and more than (say) 60 years old. A further source of heterogeneity in the stock of trees derives from the introduction of VP varieties which have been increasingly adopted since the 1960s. Given heterogeneity in the capital stock, a major potential misspecification may be avoided by adopting the vintage capital approach to investment and production behavior.

3.2. Dejinitions,

assumptions

and basic concepts

For simplicity a two-factor production function is postulated. Production possibilities are characterized by a vintage production function F[ K( t, u), L(t, u)], where K(t, u) denotes ‘capital’ of vintage used at time t and L(t, u) denotes ‘labor’ combined with K(t, u). ‘Capital’ means homogeneous land planted with trees with some specified density and requiring fixed levels of other inputs such as fertilizers and pesticides. The variable ‘labor’ refers to all non-capital inputs which are used in fixed proportion to labor. Output is produced only by mature vintages and is assumed to be homogeneous. Total output Q(t) is defined by

(5) where

q(t, 0) = F[K(t, u), L(t, u>l.

(6)

Average productivity, or yield per unit of capital, is given by q(t, u)/K(t, Assuming constant returns to scale, this can be derived from (6),

s(t,u)=-

4k4 K(t, u)

=F

u).

L(t,u)

___

[ K(o)

1’

(7)

140

T. Akiyuma und P. K. Trivedi, Analysis of perennial crop supply

In general, 8(t, u) would depend special cases are

upon the wage-rental

s(t,u)=s(t-U),

ratio. Two interesting

(8)

and s(t,

u) = y(t)b(r

- u).

(9)

In the case of (8) productivity depends only on the age of the trees, denoted t - u, and not upon the time at which they were planted. In the case of (9) the productivity of trees of age (t - u) changes smoothly with time at a rate determined by the function y(t) which may be given a specific parametric form. Capital stock of vintage u at the end of period 1, denoted K(t, u), obeys the capital depletion equation K(t,u)=K(t-l,u)-

u(t,u),

(10)

where U( t, u) denotes uprootings or remouals of vintage u capital in period t. By definition, K(t, t) = N(t), where N(t) denotes new plantings (or new investment). One may distinguish between additions to the capital stock from new plantings from those which come about from replanting currently uneconomic area under the same crop or under a different crop. Taking account of replantings, we obtain K(t,

t) = N(t)

+ R(r),

(11)

where R(t) denotes replantings. U(t, u), N(t) and R(t) are all non-negative. Trivedi (1986) presents a model of a competitive firm which chooses levels of U( t, u), N(t), R(t) and L(t, u) to maximize net discounted revenue. The optimization also involves the choice of the subset of mature vintages denoted V, u E V, which are economic in the sense that they earn non-negative quasi-rents. The remaining vintages are termed ‘uneconomic’. The vector { K(t, u)} where u belongs to the set of uneconomic vintages, denoted v, is termed the ‘stock of uneconomic vintages’. Define the total feasible output,

QfW, by Q’(t)

=

x8(t,

u)K(t,

u),

Vu.

(12)

Total planned output, denoted QP(t), is the profit-maximizing level of output which the firm plans to produce given its expectations about the product and input prices expected to prevail in period t. Given (i) the gestation lag for

T. Aki~vumaand P. K. Triuedi, AnaJvsis

ofperennialcrop supply

141

capital to become productive and (ii) the assumption that the adjustment costs associated with new planting, uprooting and replanting are convex, it follows that the scale of these activities is determined jointly by expected future profitability and past investment decisions; see Trivedi (1986). Expected future profitability in turn depends upon expected future net real product prices and net real input prices. For any given time path of all such prices, there will be profit-maximizing levels of all inputs and the associated set of economic vintages. These in turn would imply a profit-maximizing level of output which we shall call planned output, denoted QP(t). That is,

Q'(t)= CF[K*(t, 4, ~*(t, u)],

v,

uE

(13)

where asterisks denote profit-maximizing levels. Actual production will differ from planned production both because of stochastic supply shocks and because expectations will not be realized on all occasions. Consider the log-linear identity Q(t)

Q(t) = Q'(t)e’(t) i

04) 1

and let

(15) where u(t) is the supply disturbance and P( t)/P’( t) denotes the relative error of expectation. Then combining (14) and (15) and taking logs, we obtain

lnQ(t)=lnQP(t)+ln

+ In u(t),

(16)

whence we obtain the long-run and short-run supply elasticities, denoted T$,, p and vi, p, respectively. qs,p reflects the effect of an unanticipated price change on current output and can be expected to be positive if the suppliers have some margin for adjustment of output, for example, as a result of more intensive application of variable inputs, even when the capital stock is completely determined by previous planting decisions. This is the so-called harvesting decision. The long-run elasticity, $, p, is given by

%.p=

alnQP -.alnp’

JlnP” JInP

8 lnMP/P’)I +

JlnP

’

(17)

142

T. A k&mu and P. K. Trivedi, Analysis of perenniul crop supply

The first derivative on the right-hand side depends, of course, on the sensitivity of new plantings and replantings to variations in price; the second depends on the elasticity of variable factors with respect to errors of expectations. If either is negligible, nb,P and n& will be close. In Binswanger et al. (1985) the elasticity of supply is shown to depend upon the elasticity of supply of variable inputs. Such a formulation helps to explain why $, P may be small in size in any given situation. Eq. (16) is the generic form of the supply equation used in this paper. The exact variant used in explaining supply for any country will depend upon the way in which an equation for Qp is specified and on the assumption made about Pe. In turn this requires that we specify the links between the production process and related investment decisions. Some differences can be expected in the specifications used for different countries due to institutional and intercountry differences in organization of production and land-labor constraints. These will be reflected primarily in the investment decisions which we shall examine first.

3.3. Some models for new planting

decisions

Nickel1 (1985) has shown that adjustment equations consistent with the error correction model (ECM) can be derived from a dynamic cost of adjustment model similar in spirit to that used in theoretical models of perennial crop supply in Trivedi (1986). We shall apply two variants of the basic error correction model to new plantings and uprootings/replanting decisions, the choice of the specific alternative depending upon the producing region concerned, for it is the case that the relative importance of uprooting vs. new planting of tea varies considerably as between the old established producers such as India and Sri Lanka on the one hand and a relatively new and fast growing producer like Kenya on the other. In the case of Kenya much of the ‘action’ relates to new plantings. If in the aggregate new planting is positive and uprootings/replanting can be neglected, then the following ECM can be expected to provide a starting point. The ECM (variant I) is specified as follows: N(t)-N(t-1)=&v*(t)-Aqt-l)] 1 > a1 > 0,

+&v(t-l)-N*(t-l)],

a2 IO,

or N(t)

= a,AN*(t)

+ ( al-

CY&v*(t

- 1) + (1 - (Yi+ a&v(t

- l), (18)

T. Ak(yuma

and P. K. Trivedi, Anu~$sis

ofperenniulcrop

supp(v

143

where N *(t) denotes the desired level of new plantings in period t that will yield desired level of capacity output QP(t + G) in period t + G, G being the gestation lag. By assumption QP(t + G) has been calculated conditionally on expectations about future profitability. If no new planting were undertaken between t and t + G, the feasible level of production would depend upon the current feasible production level, Q’(t), and on the additional production from currently planted but immature vintages. The profitable level of production would be at most equal to Q’(t), and the profitable level anticipated at t would depend upon expected future prices. Denote this level by Q’(t). Specify that if QP(t + G) > dP(t), then the rate of new plantings is an increasing function of the expected shortfall in profitably-usable capacity; that is N*(t)

=/3[QP(t+

G) - h”(t)]>

Let Qp( t + G) be linear 2, which are determinants linear in Z,; that is,

where ji,

(19

D’o.

in two sets of as yet unspecified of expected future probability,

variables 2, and and let QP(t) be

Q”(t + G) =fiZ,(t) + gA(d,

(20)

Q”(t) =M&h

(21)

j2 and g, are vectors of parameters.

N(t) = &o-i +

-fd[W)

- -z& -

Combining

(18)-(21)

111 +&J-w)

b, - %>P[(fl -f2,>W- 1)+&Z*(t -

+ (1 - (Yi+ a&v(t

- 1).

leads to

- z,(t- 111 1>1 (22)

Note that if corresponding elements of vectors ji and ji have the same sign a priori, the coefficients of levels as well as the first differences of Z, will be ambiguous in sign. Those of Z,(t) - Z,(t - 1) and Z,(t), however, are not. The variables which influence expected future profitability include, inter alia, the expected real price of the product received by the producer and the expected real unit cost of production. The first will be positively related to both the desired level of future production and to the profitable level of production from the existing capital stock. That is, an increase in future expected product price will raise desired capacity output and thereby stimulate new planting, but it may also make the existing capital more profitable and cause previously unprofitable capital to become profitable and hence to lead to some postponement of uprootings and replantings. Thus the net efect on the level of new plantings may be indeterminate. If the existing capital stock is large

T. Aki.vuma and P.K. Trwedi, Analysis ofperenniul crop supp(y

144

relative to the level of new plantings, the negative effect may well dominate. Analogously, an increase in the unit real cost of production will depress both the required future capacity and the level of output from the existing capital stock. This may lead to scrapping of existing uneconomic capacity to such an extent that the net effect may well be to stimulate new plantings. Factors which will affect QP(t + G), but not QP(t), include new planting subsidies and embodied technological progress, since they tend to reduce the marginal cost of new planting. It would be desirable to also include in 2, those variables which reflect physical and economic obsolescence. Some empirical short-cuts may be necessary if the data on real unit cost of production are not available. One possibility is to assume that Q”(t) = k& f(t ), where Q’(t) could be measured by substituting an estimated 8(t, u) in (19). Given

of(t)

the estimating

equation

Nd = 4fiPd4 +

-

will have the following

form:

-at- 1)) + ET,{-w>- z&

h - Gwiw

- 1) +hw

- 1))

- 1>1

-cy,pk{Qf(t)-Qf(t-l)}-((Yi-(Y*)k&f(f-l) +

(1 -

a1 +

a*)Nt-l.

(23)

If (Yi > (Y*, both of(t) and do’(t) will enter the equation with a negative sign. Q’ is not directly observable and will tend to move in a manner determined by the time path of scrapped capacity. Therefore, the use of Q’ as a proxy for Qp may involve an important measurement error. Note that (23) incorporates a complex dependence between the existing capital stock and new plantings. This is captured directly via the Q” variable in (23) and indirectly via variables which influence the rate of discarding of old capacity in (22). It is known that the ECM (variant I) does not have the property of trend neutrality and hence is unsuitable for modelling a situation in which new plantings have shown steady growth, as in the case of smallholders in Kenya. To overcome this limitation a variant of the ECM (variant II) for the rate of growth of new plantings expressed as a proportion of existing smallholder area, denoted r(t), is specified as follows: r(t)-r(t-l)=yl{r*(t)-r(~-l)}+Y~{r(~-l)-r*(~-l)}~

or r(t)

= {r*(t)

- r*(t

+(I--r,+y,)+-11,

- 1)) + (Yi - Yz)‘*(t

- I) (24)

T AkQwm~ and P. K. Trivedi, Ana(wis of perennial crop supplr

145

where a priori yr > 0, ya < 0 and r(t) = N(t)/A(t - l), A(t - 1) being the total area under smallholder production at t - 1. r*(t) denotes the desired rule of expansion, whose precise specification is not needed at this juncture. This model does have the property of trend neutrality. If variant 1 is adopted when N*(t) incorporates a trend component, the model may imply that once any discrepancy between N(t) and N *(t) arises, it would never be removed. In contrast (24) applies the partial adjustment principle only to the deviations from the trend growth rate. Note also that (24) implies costs of adjustment arise from growth of new plantings exceeding or falling short of the optimal rate Y*(t) whereas (22) implies that they arise from N(t) being different from N*(t).

3.4. A model for interdependent

replanting and uprooting decisions

Theoretical analysis shows that planned uprooting and replanting are interrelated decisions not only in the sense that uprooting (U) precedes replanting (R), but in the more substantial sense that they are jointly determined and a sequence of planned {R(t)} implies a corresponding sequence of {U(t)}. On the other hand, actual { R(t)} is likely to be closely related to previous actual levels of uprootings. For this reason we shall develop a behavioral model for {u(t)} and relate {R(t)} to (U(t)} through a simple distributed lag model. An estimating equation for either U(t) or R(t) can be derived from a vector error correction model (VECM) which incorporates dynamic interdependence between U(t) and R(t). Let

[::;:))I

= j:::

;;;I[

+ ]

;:;:;:$I:;]

1’

U(t-l)-u*(t-1)

Ull

v1*

v21

vz2 I] R(t-l)-R*(t-1)

(25)

the desired rate of uprooting and where U * and R* denote, respectively, replanting. Planned uprooting followed by replanting depends upon the stock of currently uneconomic capital and on the expected future profitability of production. As before we shall subsume these variables in the vector Z(t) and assume linearity, i.e., U*(t) = h;Z(t) and R*(t) = h$Z(t). Substituting these into (25) and expanding we obtain the following equation for U*(t): U(l)

= [l-Q14

+P&;l{w

-z(t-

+ th4 + Pd; - VII4-

1))

52h;lZ(t

- 1)

+(I - VII- PII>~(~ - 1) + (~12- ~L12)R(l- 1).

(26)

146

T. A kiyama and P. K. Trivedi, Analysis of perenniul crop supply

[A similar equation can be obtained for R(t) if desired.] Note that R(t - 1) has an ambiguous coefficient. The expected future profitability variables subsumed in Z appear in the level form and as rates of changes. If the off-diagonal terms in the p and v matrices are not too large, and if pii and vii are positive, then the coefficients of Z(t) and AZ(r) have their signs determined by the signs of the corresponding elements of h; and h; which (we expect) share the same sign. For example, an increase in the expected future price or in the uprooting-replanting subsidy will affect U(t) and R(t) in the same direction. As in the case of N*(t), the ultimate objective of uprooting and replanting is to eliminate the gap {Q *(t + G) - QP(t)}. Therefore, the determinants of U *(t ) and R * (t ) should be the same as those of N *(t >, with the qualification that the subsidy variable in the former case would be specific to uprooting and replanting. Furthermore, to eliminate the unobserved variable QP(t) will require approximations as in the case of the N(t) equation. 3.5. The supply equation The basic equation: Eq. (16) provides the starting point. that actual and potential output are related by the following

First, we assume equation:

6

Q(t)

=A’{ Q'(t)}

i

$$ j u(t),

(27)

where A’ is an unknown scale factor and t9 is the unknown elasticity of Q with respect to P. If P’(t) in (17) is the very same P’(t) that determines QP(t), then P’(t) = P(t) would imply equality of Q(t) and QP(t) apart from the scale factor A’ and the supply shock u(t). Since neither QP(t) nor P”(t) are directly observable, additional assumptions are required to reduce (27) to an estimable form. Begin with the identity Qp(t>

=

Qf(t)QP(t) Q'(t)

(28)

’

Let Q’(t) denote measured feasible output calculated under the assumption of given (not necessarily profit-maximizing) age-yield profile and assume that (i)

Q’(t)

= k,{ $‘(t)}‘,

k,, E ’ 0,

(29)

and (ii)

Q’(t) Q’(t)

=k,fiP(t-i)“, i=O

P,lO.

(30)

T. A ki~vamuund P. K. Trivedi, A nuly~is of perennial crop supply

147

The difference between Q f and Qf arises from the possible error in calculating Qf from an ‘average’ rather than optimal age-yield profile. The justification for (30) is that the profit-maximizing level of output is an increasing function of the producer price, whereas Q’(t) is definitionally determined, given past decisions. Lags in (30) take account of the dependence of current yield on past inputs such as fertilizers. The integer m is likely to be small, perhaps 1 or 2 (years), the issue being empirical. Combining (27)-(30) and taking logs we obtain the basic supply equation: lnQ(t)=ln(A’k,k,)+elnQ’(t)+(&,+B)lnP(t)

-8lnP’(t)+

fpIlnP(t-i).

(31)

r=l

To convert this to an estimating equation we need to (a) either make specific assumptions about the relation between d’(t) and observable variables such as past new plantings or to precalculate o’(t), (b) make a specific assumption about how expectations are formed, and (c) fix the value of m. With respect to (a) we take one of three possible approaches, depending on the data constraints; with respect to (b) we assume that Pe is a linear function of past values of P; and, finally, with respect to (c) we take an empirical approach and fix m at 1, 2, or 3. Alternative specificntions for Bf(t): To take into consideration the differences in the average productivity of capital of different ages and the effects of disembodied technological change on the age-specific yields, we distinguish known total productive capacity (feasible output) existing at some arbitrary origin, denoted Q(O), from the subsequent additions to that capacity arising from new planting and replanting in subsequent periods. Let Q(t) denote the former and en’(t) the latter; and d’(t)

= Q”‘(t)

+

Qnf(t).

(32)

Assume that old capacity Q(0) is changing at an unknown proportionate rate x *, which reflects the joint effects of disembodied technological change and of the reduction in productivity due to aging; i.e., Qof( t) = e”z’Q(0). Given data on total newly planted and replanted areas from given the normalized age-yield profile S(t - v) known to constant /3(O) [i.e., P(O)s(t, u) gives the productivity in capital of age (t - u) in period 01, it is possible to construct productive capacity contributed by addition to the planted

(33) t = 1 onward, and a proportionality physical units of an index of the area since time 0.

T. Akiyama and P. K. Trivedi, Analysis of perennial crop supply

148

Denote

this by

p(0)

qt-“)N+(t-u),

i t-v=1

where N+(t - u) is the cumulated sum of new plantings and replantings of age (t - u) at time t. p(O) is the productivity of a mature vintage in period 0. Finally assume that 6(t - u) is also subject to disembodied technical change at a constant proportionate rate A, (A, > 0 if productivity is increasing). That is, (34) Combining

(31)-(34)

yields variant

I of the ‘vintage’

supply

function,

+(&+0)lnP(t)-BlnP”(t)

+

jglB,ln p(t- j> + u(t),

(35)

which is non-linear in the unknown parameters (A, /3(O), A,, A,, 13). The expression inside the square brackets is analogous to the shift term representing the heterogeneous stock of capital. The remaining terms are analogous to the price variable of the textbook supply function. Given data on N+, s(t - u), Q(0) and an appropriate proxy for P’(t), (34) can be estimated by non-linear least squares. Data permit such estimation for two major producers, India and Sri Lanka, whose age-yield profiles appear to have changed through time. A special case of (35): If (a) Q(0) = 0 and (b) the age-yield profile is approximately constant such that A, = 0, (35) simplifies to the log-linear variant of the vintage supply function; viz. InQ(t)=lnA+ln[~8(t-u)N+(t-u)] -8lnP’(t)

+ C&lnP(t-i)

+(p,+e)lnP(t) +u(t).

(36)

In certain cases (e.g., Kenya estates) it was necessary to allow for changing yields through time. We were able to construct three time-series corresponding to planted areas in three age classes - less than 5 years old, between 5 and 10 years and more than 10 years old. Using data on normalized yields ( = 1 in the

149

T. Aki~vvamu und P.K. Triuedi, Analysis of perennial crop supply

age class ‘older than 10 years’), a weighted area measure, denoted WAREA, was constructed. Then, a further vintage supply function, which may be thought of as the ‘yield equation’, was derived on the assumption that all age groups share equi-proportionally in the increase in yield, i.e.,

Q(r) WAREA(

t)

= Aehl’{ P(t)/P’(t)}“u(t).

(37)

This concludes our discussion of the interrelationships between various parts of the production sector. We can now proceed to the discussion of empirical results.

4. Empirical results Computation of the index of feasible production: To calculate QE( t) as defined in (32)-(35) involves the unknown parameters p(O), A, and A,. But the first task is to construct an index of the productive capacity added by new plantings and replantings, denoted Es< t - u)N’( 1- u). The coefficients in the sequence 6(t - u) denote the proportion of peak yield obtainable at different ages prior to full maturity.This profile will, of course, vary between countries and over time. Our information concerning the base period, derived from World Bank project reports, is summarized in table 1. It is assumed that in those countries such as India and Kenya, where the yields are rising, the increase is spread over all age groups. The base period profile is taken to be the same in India and Sri Lanka. New planting and replanting equations: In India and Sri Lanka, the rate of new planting and replanting as a proportion of total planted area has varied considerably over the last 20 years. The range of variation is between 0.8 and 1.8 percent in India and 0.9 to 1.4 percent in Sri Lanka. (The figures for Sri Table 1 Base period age-yield 01

profiles

2

3

4

5

6

I

8

India

1952

(a)” (b)b

0 0

0 0

0.074 70

0.299 281

0.449 422

0.599 563

0.749 704

0.899 845

1 939

Sri Lanka

1956

(a) (b)

0 0

0 0

0.074 76

0.299 303

0.449 445

0.599 608

0.749 760

0.899 912

1 1014

0

0

0

0.199 206

0.399 412

0.399 412

0.798 824

0.899 928

0.899 928

Kenya’

I;‘,

‘Proportion of peak output at different ‘Yield in kg/hectare at different ages. ‘Applies to smallholders only.

ages prior to full maturity.

150

T. Akiyama and P. K. Trivedi, Analysis

4ooo,

Sr i Lankan

ofperennialcrop

Tea

supply

P I ant i ngs

Replantings 3000

0 L~zL~~~____L__ I956

i 960

--_1__1964

I968

I972

1976

1980

I984

YearFig. 1

4000 r ___~___~ Indian

Tea

Plantings

Replantings

,,:I I953

I 957

1961

1905

1969

Year Fig. 2

I973

1977

IQ81

I 985

T. Aki_vamu and P. K. Trivedi, Ana(wis

Kenyan

Sma

of perenmal

I I ho

151

crop supp!v

( der

6000

i

5500 !

New Plantings

5000

i

/A

4500 1

\

4000 i i

(II 3500

if ,o 3000 $2500

I

\

f/l

i 1 1

/’

/’

A\i

b

\\ \

‘, L-,

/

2000 1 1500

/’

/:

‘I>, ‘/

I/

‘\

IO00 ‘;

_I__.-m

,O; L-__.d-~ 1963 >

1966

I969

1972

I975 'Ye a r

i

_ p_.imm_L I 978

r9al

I 984

Fig. 3

Lanka may reflect inaccuracies in estimates of planted area.) In contrast, the annual average growth rate of planted area for Kenyan smallholders was about 17 percent over the period 1963-83, having declined to around 4 percent in the last five years. In both India and Sri Lanka new planting and replanting are subsidized. Information about the subsidies in India remains sketchy and new planting and replanting equations may need revision when detailed and accurate information has been obtained. In the case of Sri Lanka, uprooting and replanting subsidies are more important relative to the new planting subsidies. (See notes to table 2 for additional information.) In Kenya it is important to distinguish between the behavior of smallholders and estates. The smallholder sector accounts for nearly 2/3 of the area and most of the growth in area whereas the estates which have registered rapid growth in yields dominate the growth of production [Etherington (1973) Schluter (1982) Lamb and Muller (1982)]. An explanation of new plantings in Kenya is essentially a model of smallholder sector which has shown a strong trend-like behavior. It cannot be readily understood without reference to the historical and institutional factors discussed by Etherington (1973) and Lamb and Muller (1982). Etherington has stressed the stimulative effects of the removal of legal restrictions on the cultivation of tea by smallholders on their

T. Akiyumu

152

and P. K. Trivedi, Analysis of perennial crop supply Table 2

New planting,

replanting

and production Kenya

KSHNPRT

equations

- Smallholder

for Kenya,

India and Sri Lanka.

new plantings

= -0.1127 + 0.7487 PRK( - 1) + 0.2009 A KEXPPH (2.4076) (- 1.3569) (1.3074) + 0.2077 KEXPPH( (2.9789)

- 1) + 0.5052 KSHNPRT( (3.3228)

- 1)

+ 0.0379 A PRK (0.7936) ?? = 0.894

DW=

SEE = 0.29772E-01 Kenya

1.85

Period = 1966-82

- Estates weighted

F(5,ll)

= 22.943

F(l,lO)

= 286.742

area

9.6823 + 0.0196 TR61 LN ZKEA W = (469.939) (16.9918) SEE = O.l3813E-01

x2 = 0.963

D W = 1.97

Kenya YLDKES

Period = 1972-83

- Estates yield

= - 1.4695 + 0.0997 TR61 t 6.6698 PRK (2.4712) (- 2.3435) (6.1015) + 6.7935 PRK( - 1) + 8.4269 PRK( - 2) (3.0969) (2.5902)

i? = 0.782

SEE = 0.14438

DW=

Kenya LN QKSH

1.86

- Smallholders

Period = 1972-82

F(4,6) = 9.982

production

= 4.5995 + 0.7314 LN QKSE + 0.1708 LN PRIKTDAR (1.2894) (7.0572) (18.2242) + 0.22789 LN PRIKTDAR(-1) (1.7189)

x2 = 0.968

SEE = 0.93797E-01

D W = 1.92

Period = 1971-83

F(3,9) = 120.756

India - Supply equation LN QIND =

0.303 + LN [l.O exp (0.0118t) (15.17) (17.66)

TPRODI

+ exp

(O.O118t)283500] (17.66)

+ 0.115 LN PRI( - 1) (3.45) li2 = 0.9822

SEE = 0.0266

Period = 1959-83

Sri Lanka

- Supply equation

LN QSL = 1.00 + LN[0.8 exp (0.0095f)TPRODSL (0.97) -

F(2,22)

= 532.25

+ exp ( - O.O2105t)230420] (5.45)

0.4861 LN QSL( - 1) + 0.5060 LN QSL( - 2) (5.08) (4.91)

+ 0.0346 LN RA TPC( - 1) - 0.1405 DM83 (5.08) (1.45) E2 = 0.9162

SEE = 0.0644

Period = 1965-83

F(5,13)

= 40.65

T. Akiyama

und P.K. Trivedi, Analysis of perennial crop supply Table 2

153

(continued)

India - Extensions AIEXT

= 9889.8164 (2.1743)

+ 0.4085 AIEXT( (2.0153)

- 1) + 13240.4561 PREI( - 1) (2.0144)

+ 2624.8991 A PREI + 614.6401 TR51 (2.2529) (0.2445) _

x2 = 0.538

0.0471 TPRODCI( ( - 2.2338)

SEE=

462.11

DW=

- 2) -

1.57

0.0491 ATPRODCI( ( - 1.2400)

Period = 1959-82

- 1)

F(6,17)

= 5.463

India - Replantings AIREPL

= 294.6120 + 0.6393 AIREPL( (0.5272) (3.7826) + 2252.3240 PREI( - 1) (1.0344)

x2 = 0.752

SEE = 185.17

DW=

1.77

Sri Lanka SRINEWP

=

- 1) -

0.0001 TPRODCI( (-0.1852)

- 2)

1817.5537 A PREI (- 0.4508) Period = 1959-82

F(4,19)

= 18.397

- New plantings

- 811.3419 - 0.3108 SRINEWP( (2.2003) (1.3598) + 33626.1953 APRES (3.8431)

- 1)

+ 23842.2539 ACOPSLR( (2.2507)

- 1)

+ 15003.5449 PRES( - 1) + 8665.0684 COPSLR( (1.8374) (1.8873)

- 2)

+ 534.5070 A PRS (1.6844) x2 = 0.725

SEE = 195.41

DW=

2.39

Sri Lanka SRIUP

0.9836 SRIREPL( (- 1.6652)

=

2’ = 0.968

= 8.023

- Uprootings

- 1) + 179.9945 RSSLREAL( (3.1637)

+ 37472.8594 APRES (1.3144)

+ 118.8185 ARSSLREAL (3.8879)

SEE=

1.88

314.93

DW= Sri Lanka

SRJREPL

F(6,lO)

= - 1589.8682 + 0.5055 SRIL’P( - 1) + 3851.3064 PRES( - 1) (- 0.8483) (1.0557) (0.2245) +

z2 = 0.816

Period = 1966-82

Period = 1967-82

- 1)

F(6,9) = 12.053

- Replantings

- 118.9512 + 0.4716 SRIUP (- 1.7587) (7.9319)

+ 0.2110 [SRIUP( (7.4639)

- 1) + SRIUP(

SEE = 145.56

Period = 1958-82

F(2,22)

DW=

2.04

- 2)]

= 368.433

T. Akiyumu und P. K. Trivedi, Analysis of perennial crop supp!~

154

Variable

Table 2

(continued)

Glossary

of variables

Description

units

Source”

All India extensions

Hectares

ITC

AIREPL

All India replantings

Hectares

ITC

PREI

Three-year moving average of producer price of tea in India, lagged 3 years, deflated by the Indian CPI (CPIIND, 1975 = 100)

Rup/kg

ITC

PRI

Deflated

TRODCI

1.1942*(1.0* TPRODI + 183500.0) * exp(0.00994 * TREND)

Hectares

TPRODI

India new planting production capacity ‘The price’ of tea is taken to be value share weighted average of auction price of leaf tea in Calcutta and Co&in inclusive of export taxes and cesses

Hectares

India A IEXT

retail tea price

Rw/kg

ITC Constructed using TPRODI ITC

Kenya KEXPPH

Per hectare real direct development expenditure on extensions and services, CPIKEN = 100 in 1975, by KTDA

KSHNP

Kenya smallholders’ (calender year)

KSHREAT

Total smallholders’

KSHNPRT

KSHNP/KSHREAT(

PRIKTDAR

Adjusted real producer green leaf by KTDA

K.sh/hect. 1975 prices

KTDA Annual Report

new plantings

Hectares

KTDA Annual Reports/ Schluter

area under tea

Hectares

-ditto-

Sh/kg

KTDA Annual Reports

payment

for

PRK

Real Mombasa

QKES

Estates

QKSE

Total estimated production

QKSH

Total estimated production

YLDKES

Kenya estates tea production = QKES/ZKEA W

yields

Mt/hect.

ZKEA

Kenya estate total equivalent maturity area = 0.12 (Area < 5 yrs.) + 0.76 (Area < 10 yrs.) + 1.0 (Area > 10 years)

Hectares

W

auction

- 1)

price

Sh/rg

ITC

1000 kg

EPDCS

feasible smallholder

1000 kg

EPDCS

feasible estate

1000 kg

EPDCS

tea production

in Kenya

KTDA/WB

155

T. A kivama und P. K. Triuedi, Analysis of perenniul crop supp&

Table 2

(continued)

Sri Lanka COPSLR

Sri Lanka cost of production of tea based on sample survey deflated by Sri Lanka CPI. = COPSL/CPISL

b/kg

PRS

Tea price at Colombo auction sales tax, cess and export tax deflated by Sri Lanka CPI

b/k

PRES

Three year moving average of real producer tea price in Sri Lanka. lagged three years

QSL

Sri Lanka

RA TPC

= PRS/COPSL

RSSL

Replanting

tea production

subsidies

RSSLREAL

= RSSL/CPISL

SRINE

New plantings

WP

paidb

with

Mt

Rp mill

Central Bank Abstracts and Reports ITC & FAO

ITC

Central Bank Review

Hectares

ITC

in Sri Lanka

Hectares

ITC

in Sri Lanka

Hectares

in Sri Lanka

SRIUP

Uprootings

SRIREPL

Replantings

TPRODSL

Sri Lanka total estimated feasible production

Mt

ITC ITC/EPDCS

“ITC = International Tea Council, IFS = International Financial Statistics, KTDA = Kenya Tea Development Authority, EPDCS = Economic Projections Division Commodity Section (World Bank), WB = World Bank. ‘Subsidy schemes for tea planting in Sri Lanka. The figures for replanting subsidies were derived from the following publications and they pertain to four planting subsidy schemes, viz., Tea Replanting Subsidy Scheme (TRSS), Tea Newplanting Subsidy Scheme (TNSS), Rubber into Tea Replanting Subsidy Scheme (RTRSS), Tea Infilling Subsidy Scheme (TISS): Annual Report - Central Bank of Sri Lanka; Bulletin of the Central Bank of Sri Lanka, various issues between 1960-83; Performance Report of The Ministry of Plan Implementation, 1980. TRSS was begun in late 1950’s and continues as the major subsidy scheme for the planting of tea. Initially it covered only large estates (over 100 acres) and later was extended to smallholdings. RTRSS was started in 1962, and TNSS in 1977. TISS appears to have been started after Tea Rehabilitation Subsidy Scheme was abolished in 1967. The actual details of the operation of schemes are not easily found but it appears that payments are frequently made on an installment basis.

adoption of tea as an alternative cash crop; Lamb and Muller have detailed the important role played by the Kenya Tea Development Authority (KTDA) in the provision of extension services and a network of factories which provided the necessary infra-structure for the smallholder sector and which increased the profitability of tea production to the smallholder. A measure of this role is the KTDA expenditure on nurseries, tea stumps, field and factory development per hectare of smallholder planted tea area. This variable has a role similar to but not identical with that of subsidies in other countries.

156

T. Akiyuma ond P.K. Trivedi, Analysis of perennial crop supply

For Kenya smallholders the model used is (24). Specify r*(t) to be linear and increasing in (i) real per hectare investment expenditure by KTDA, denoted E(t), and (ii) the real producer price PR(t). That is, r*(t) = a,,?(t) + a,PR(t) + a,, and r(t)=yI[aI{E(t)-E(t-1)) +(yl

+

(1 -

+u*{PR(t)-PR(t-I)}]

-y&@(t-2) y1 +

+G’R(t-l)]

Y2)r(t - 1) + (ul - Y2)ao.

(38)

A justification for this specification is that the Kenya smallholders did not face land constraint in this period and that the critical limitation arose from access to planting material, credit facilities, factories for processing tea leaves and expertise in the marketing of the leaf. The provision by the KTDA of these facilities made it easier for the smallholder to take up growing tea. We postulate that by maintaining a constant real rate of development expenditure per hectare the KTDA would enable more smallholders to undertake tea production and to maintain a steady growth in new plantings. But this assumption is reasonable only as long as the availability of suitable land is not a binding constraint. If the constraint changes, so does the adjustment cost function. The net new planting of estates in Kenya has been small and highly variable compared with that of the smallholders. We hypothesize that estates act at the intensive margin and the smallholders at the extensive margin. Specifically, an improvement in expected profitability, arising from (say) an increase in the real price of tea, causes more smallholders to enter tea production, whereas it causes estates to increase production by greater use of yield-increasing agricultural practices. (Elsewhere in this paper we have discussed the yield-price relationship.) A general model of production and demand for inputs allows for the possibility that a firm may respond to higher product prices by raising its production through more intensive utilization of variable inputs. Given high adjustment costs of fixed inputs this may be an optimal response. The empirical fact that the yields per hectare on Kenya estates have increased in a spectacular fashion, while the area under production has increased rather slowly, suggests that the hypothesis proposed is reasonable. To obtain the estimating equation we have combined a variant of (18) with the following specification of N *(t ), N*(t)=c,+c,YLD(t), Note which lagged The (new

Cl co.

(39)

that YLD(t) is an endogenous variable. This leads to an equation in new plantings depend upon the yield and the change in yield as well as values of new planting. estimated equations for India (extensions and replantings), Sri Lanka plantings, uprootings and replantings), Kenya smallholders (rate of

T. A ki&wna und P. K. Trivedi, Anulysis of perennial crop supp!v

157

growth of area planted), Kenya estates (net change in planted area) are given in table 2. In the case of Sri Lanka planned replantings and uprootings are assumed to be jointly determined, but actual R(t) is specified as a finite distributed lag on current and lagged values of U(t) to capture the mechanics of replanting and the installment method of subsidy payment. That is, the uprooting equation is ‘behavioral’ and the replanting equation is ‘mechanical’: thus

R(t) =

c

w,U(t-i).

(40)

r=O

For India the specification of the replanting equation is similar to (26), no account having been taken of the interdependence between U(t) and R(t) as no data on uprootings are available. In general terms, the econometric results we have obtained are consistent with the error correction models described earlier. However, the statistical adequacy of the equation varies. For example, the Indian new planting equation has heteroscedastic residuals, and the fit of the equation is not good. Let us consider the role of ‘expected’ future producer price, denoted generically as PRe. We model producer’s price expectations in terms of perceived ‘normal’ p+ which is assumed to be a simple function of realized current and lagged prices. For India and Sri Lanka, it is a simple moving average of PR( t - l), PR(t - 2) and PR( t - 3). For Kenya, current and/or one or two lagged values have been used. A broad finding is that uprootings in Sri Lanka and replanting in India show little price responsiveness. On the other hand, new plantings in all three countries show statistically significant price responsiveness. The short-run elasticity of new plantings with respect to PR or PR’ varies from about 0.5 for India and Kenya to a figure between 1.5 and 2.0 for Sri Lanka. It is intuitively reasonable that economic incentives for exploiting the extensive margin of production would be greater in countries which are relatively unconstrained by availability of suitable land (i.e., the cost of adjustment factor). Then relatively new producers would show the largest price elasticities, whereas the long established producers that have ‘used up’ the most suitable land would respond to the price incentives at the intensive margin. For these countries we would expect the elasticity of N(t) with respect to PR(t) to be relatively low. Our finding of a relatively high value for Sri Lanka and a relatively low one for Kenya is, therefore, a surprise. On the other hand, note that for the Kenya estates’ net new planting is negatively related to yield per acre, which enters as a determinant of N*(t) and the latter is positively related to PR. It appears that the impact of changes in real producer price on production takes place, in the short run mainly through the changes in the level and intensity of factor use, but in the long run through a mixture of new planting and replanting at unchanged levels of utilization and

J.Econ

F

158

T. A kiyamu and I? K. Trivedi, Ana&

of perennial crop supple

variation in the intensity of factor use without any additional new planting. Consequently, the exact size of the long-run production response will vary between countries and time periods. Price insensitivity of uprooting and replanting may be rationalized by recalling our earlier discussion where it was argued that improvement in future expected price on the one hand tends to make previously uneconomic vintages economic, and thereby reducing uprooting and replanting, while on the other it raises the expected rate of profitability on new investment. Our results show that subsidy is an extremely important determinant of uprootings in Sri Lanka. The short-run elasticity of uprooting with respect to real subsidy is close to 2. The long-run effect is less certain as the coefficients on lagged uprooting (SRIUP_,) have large standard errors. The importance of subsidy in Sri Lanka is not surprising since it is evident that the average yield is low and falling, possibly due to the old age of the tree stock. For Kenya smallholders the level of KTDA development expenditure per hectare (KEXPPH) has been a highly significant factor in the expansion of production. Indeed the contribution of price to the explanation ‘would be negligible before 1975 [Etherington (1973)], while the KEXPPH would provide most of the explanatory power. Finally turning to the discussion of ‘other factors’, note that in the case of India the size of existing total feasible output (TPRODCI), which can be regarded as a proxy for the heterogeneous capital stock, enters the equation with a statistically significant negative coefficient. The variable TPRODCI is not directly observed and was calculated using the expression in the square brackets in (34) multiplied by A with non-linear least squares estimates of A, p(O), h, and A, substituted. Intuitively, large existing capacity should have a depressing influence on new plantings. For Sri Lanka we used the unit cost of production instead of a capacity variable since costs affect the rate of scrapping, the cost of production is related to the level of potential production. Since the unobservable Qp rather than Qf is the relevant variable, and the former would be in part determined by the average cost of production, we have included lagged real unit production cost (COPSLR) as an explanatory variable. The results indicate that the net effect of an increase in unit production cost is to stimulate new planting. This outcome is possible if the reduction in capacity due to scrapping is substantial. The observed decline in production and yield in Sri Lanka is consistent with the hypothesis that the scrapping effect is substantial. In the uprooting equation the use of COPSLR did not yield significant results - possibly because of the shortness of the time series but also because the replanting subsidies have had a dominant role since 1967. For Kenya we found very weak evidence that the rate of the smallholders’ new plantings was significantly affected by the existing productive capacity. The variable QKSE which proxies Qf does not, therefore, appear in our equation. Once again, this reflects an important difference between relatively new producers and the established ones.

T. A k&mu

und P. K. Trivedi, Analysis of perennial crop suppb

159

Suppll,, equations: The estimated supply functions have been specified as follows: those for India and Sri Lanka are based on (39, those for Kenya on (36) and (37). Variations from the basic specification take three forms. First, the manner in which P/P’ is proxied varies. For India P’ is moving average of three lagged values, P(t - 5), P(t - 6) and P(t - 7); for Sri Lanka P/P’ is proxied by the ratio of price to the cost of production. For the rest a simple distributed lag has been used. Hence the supply equation ends up as a function of trend, a proxy for potential or feasible output, and current and/or lagged prices. The reported specifications incorporate restrictions which appear empirically reasonable in the light of specification searches. In all cases the price variable is intended to be the real local producer price, net of taxes. For India, Sri Lanka and Kenya this variable can be constructed from the averages of auction prices. (In the case of India the price variable is a value-share weighted average of leaf and dust prices at Calcutta and Cochin auctions.) The second variation arises from the need to include lagged values of Q(t) in some countries (e.g., Sri Lanka) to take into account dynamic dependence in production in successive periods, e.g., a biennial cycle. The third variation comes from the need to include the effects of known supply shocks, e.g., drought in Sri Lanka in 1983. In estimating (35) by non-linear least squares a major difficulty arose from the flatness of the residual sum of squares surface so that the major parameters of interest A, p(O), X, and X, could not be estimated both freely and precisely. This is essentially an identijication problem. After some experimentation, which suggested that free estimation of all unknown parameters was not feasible, we treated the problem as one of estimation-calibration of the unknown parameters and not of estimation alone. The values of p(O) (and also of A in the case of Sri Lanka) was fixed and the remaining parameters were estimated. For India p(O) was fixed 1.00 (peak yield per hectare in 1952 = 1 metric ton) and for Sri Lanka at 0.80. The scale parameter for Sri Lanka was also fixed at unity. The estimates of X, and h, for India were constrained to be equal - this restriction is consistent with the data. The estimate indicates that the productivity of new plantings as well as the base period capacity has been increasing at an exponential rate of between 1.0 and 1.5 percent per annum. This could come about from a more intensive utilization of available inputs or better agricultural practices. By contrast, the value of X, for Sri Lanka is insignificantly different from zero whereas that of h, is negative and this implies zero increase in the productivity of new plantings, a decline in productivity of the base period output at the annual rate of just over 2 percent - a result which is consistent with observation. The supply equations for major producers appear to fit reasonably well, subject to the qualification that there is some evidence of heteroscedastic residuals, which could reflect in part the ubiquity of supply shocks, but in part also the effects of m&specification. Each country is in some sense a special case and the adopted specification reflects this. For example, in the case of Sri

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T. Akiyuma

und P. K. Trivedi,

Analysis

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crop supply

Table 3 Short-run

price elasticities

India Sri Lanka Kenya: Smallholders” Estatesh

0.12 0.04 0.17-0.40 0.26-0.86

“The range covers one- to two-year responses. bThe numbers are calculated at mean values of price, weighted area and quantity produced in 1972-1983.

Lanka there is a curious biennial production cycle which we capture through the inclusion of Q(t - 1) and Q(t - 2) as explanatory variables. In the case of Kenya estates there is evidence of some outliers (1973,1976) which contribute significantly to the lack of a good fit. The only satisfactory resolution of these difficulties is to obtain additional information about the special circumstances of the producers in these countries and, where necessary, to respecify the equation. This avenue could be explored in the future. For those countries where an estimate 0’ could be constructed, its explanatory variable was extremely high - see the equation for India and for Kenya smallholders. Similarly the weighted area measure, WAREA, based on data on planted area distinguished by age class is also a useful explanatory variable. The alternative of using time trends to proxy the feasible output variable Q’ the estimated equations will have an acceptable performance in the sample period but would be unsatisfactory in general. Short-run price elasticities calculated from these after ignoring short lags are shown in table 3. These are in the range 0.05-0.12 for India and Sri Lanka, a rather larger value is being obtained for Kenya. The calculation of long-run supply elasticities requires us to use the estimates the price elasticity of new plantings and the elasticity of potential output to changes in new plantings. Such calculations are best done in the context of the complete model simulations taking into account the endogeneity of the price variable. However, the elasticities for new planting and replantings with respect to real price will vary over time and region, and consequently, the long-run supply elasticities will not be time-invariant.

6. Conclusion The old Nerlovian approach [Nerlove (1958)] to modelling the supply response of perennial crops is unsatisfactory [Nerlove (1979)] essentially because it neglects the detailed structure of the investment process. Despite useful insights of Wickens and Greenfield (1973) the vintage approach which seems germane to the problem has not been applied systematically. In this

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paper we have made a modest beginning within a vintage framework which can be used to interpret the behavior of perennial producers in economically interesting and insightful ways. Our empirical results throw up a diversity of response which we believe will also characterize other perennial crops. Our suggestions for modelling the various elements of supply should likewise apply to other perennials. As always, better and more detailed data are essential for progress in econometric modelling. References Ady, P., 1968. Supply functions in tropical agriculture, Oxford Institute of Statistics Bulletin 30, 157-188. Akiyama, T. and A. Bowers, 1984, Supply response of cocoa in major producing countries, EPDCS working paper no. 1984-3 (The World Bank, Washington, DC). Akiyama, T. and P.K. Trivedi, 1986, A new global tea model: Specification estimation and simulation, EPD working paper no. 1986-3 (The World Bank, Washington, DC). Bateman, M.J., 1965, Aggregate regional supply functions for Ghanian cocoa, 1946-62. Journal of Farm Economics 47, 384-401. Behrman, J.R., 1968, Monopolistic cocoa pricing, American Journal of Agricultural Economics 50, 702-719. Binswanger, H., Y. Mundiak, M.-C. Yang and A. Bowers, 1985, Estimation of aggregate agricultural supply response from time-series of cross-country data, EPDCS working paper no. 1985-3 (The World Bank, Washington, DC). Etherington, D.M., 1973, Smallholder tea production in Kenya: An econometric study (East African Literature Bureau, Nairobi). French, B.C. and J.L. Matthews, 1971, A supply response model for perennial crops, American Journal of Agricultural Economics 53, 478-490. Hartley, M.J., M. Nerlove and R.K. Peters, Jr., 1985, The supply response for rubber in Sri Lanka: A preliminary analysis. World Bank staff working paper no. 657 (The World Bank, Washington, DC). Lamb, G. and L. Muller, 1982, Control, accountability and incentives in a successful development institution: The Kenya tea development authority, World Bank staff working paper no. 550 (The World Bank, Washington, DC). Nerlove, M., 1958, Distributed lags and estimation of long-run supply and demand elasticities: Theoretical considerations, Journal of Farm Economics 40. 301-310. Nerlove, M., 1979. The dynamics of supply: Retrospect and prospect, American Journal of Agricultural Economics, 874-888. Nickell, S.J., 1985, Error correction mechanisms, partial adjustment and all that: An expository note, Bulletin of the Oxford Institute of Economics and Statistics 47, 119-136. Ramanujam, P., 1984, The world tea economy: Supply, demand and market structure, Ph.D. thesis (Australian National University, Canberra). Schluter, M., 1984, Constraints on Kenya’s food and beverage exports, Research report no. 44 (International Food Research Institute, Washington, DC). Stern, R.M.. 1965, The determinants of cocoa supply in West Africa, in: R.G. Stewart and H.W. Ord, eds., African primary products and international trade (Edinburgh University Press, Edinburgh). Trivedi. P.K., 1986, A framework for studying the supply response of perennial crops, Commoditv Studies and Projections working paper- no. 1986-i @he World Bank, Washington, DC). . Wickens, M.R. and J.N. Greenfield, 1973, The econometrics of agricultural supply: An application to the world coffee market, Review of Economics and Statistics 55, 433-440.