metadata: authors: 0: author: Trivedi,Pravin K.
count: Brazil
docna: 0: docna: A model of cocoa replanting and new planting
            in Bahia, Brazil, 1966-85
docty: Policy Research Working Paper
subtopic: Climate Change and Agriculture,Crops and Crop Management Systems,Administrative & Civil Service Reform,Public Sector Administrative & Civil
            Service Reform,Macroeconomic Management,Democratic Government,Public Sector Administrative and Civil
            Service Reform,De Facto Governments
teratopic: Finance and Financial Sector Development
abstracts: cdata!: In 1966, 90 percent of the cocoa growing
            areas in Bahia, Brazil had trees more than 30 years old. By
            1985 most of the area had been replanted or supplied with
            new trees. Throughout most of this period there were high or
            rising cocoa prices, and zero or negative interest rates.
            High prices and low interest rates directly encouraged new
            planting, but their relationship to replanting is more
            complex. In the short term, higher prices discourage
            replanting, which involves uprooting and a temporary loss of
            revenue. But over the long run, higher prices increase
            expectations of future profits and encourage replanting.
            Lowering the interest rate beloow its real level provided
            cocoa growers with a subsidy that encouraged both replanting
            and new planting.
geo_reg_key: 119228,517191
repnme: repnme: A model of cocoa replanting and new
            planting in Bahia, Brazil, 1966-85
display_title: A model of cocoa replanting and new
            planting in Bahia, Brazil, 1966-85
listing_relative_url: /research/1988/09/700656/model-cocoa-replanting-new-planting-bahia-brazil-1966-85
topicv3: Crop Production m1326627 174,Employment and Wage Data m1327013 2055,Deflation m1505334 3102
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Finance and Financial Sector Development
origu: Policy Plan & Prog Review Dept
no_of_pages: 54
author_keys: 0: author_key: 563924
model_extractions: <!-- Start of picture text --> Polac,Pnning, and R surch I<br>Intaatonal Commodity Mfiarkets|<br><!-- End of picture text -->

In 1966, 90 percent of the cocoa growing areas in Bahia, Brazil had trees more than 30 years old. By 1985 most of the area had been replanted or supplied with new trees.

Throughout most of this period there were high or rising cocoa prices - and zero or negative interest rates. High prices and low interest rates directly encouraged new planting, but their relationship to replanting is more complex. In the short terrn, higher prices discourage replanting, which involves uprooting and a temporary loss of revenue. But over the long run, higher priceb increase expectations of future profits and encourage replanting.

Lowering the interest rate below its real level provided cocoa growers with a subsidy that encouraged both replanting and new planting.

This paper is a product of the International Commodity Markets Division, International Economics Department. Copies are available free from the World Bank, 1818 H Street NW, Washington, DC 20433. Please contact Dawn Gustafson, room S7044, extension 33714.

'Ce PPR Working Paper Series disseminates the fdings of work uRnideTr way in the Bank's Policy, Plaring. and Research Complex. An objective of the scries is to get these findings out quickly, even if presentations are less than fuDy polished. The findings, interpretations, and conclusions in these papers do not necessdrily represent official policy of the Bank.

Copyright i) 1988 by the International Bank for Reconstruction and Development/Te World Bank
# CONTENTS

|I.|Introduction<br>.1........................<br>1|
|---|---|
|II.|A descriptive factual account.<br>.<br>4|
||Planted area andproduction..<br>4|
||New planting andreplantg...<br>4|
||Age distribution<br>of tree.<br>.5<br>|
||Productivity.....<br>....<br>. ...<br>.<br>5|
|III|. Analytical framework<br>.9|
||A Formal Derivation.<br>9|
|IV.|An econometric model of cocoa replanting<br>.<br>.<br>19|
||Srecification<br>of the NER(.) function<br>..<br>19|
||Specification<br>of the MCI(.) function<br>..<br>21|
||The Results.....<br>23|
||Comparison with variants<br>..<br>25|
||Elasticity of RPBAN with respect to PRICOCO<br>.30|
||Interest rate effects<br>..<br>31|
|V.|Econometric AnalysisofNew Planti<br>n<br>.<br>.32|
||Price elasticity of new planting<br>..<br>.39|
||Interest elasticity<br>..<br>37|
|VI.|Sumary and conclusions.<br>.<br>40|
||References<br>..<br>42|
ti

# TABLES

Table 1 : Summary statistics on the level and percentage change in new planting and replanting, Bahia, 1967-1985 Table 2: Estimated Age Distribution of Productive Cocoa Trees, 1936-86 Tables 3-6 : Alternative specifications ar.d tea4s of replanting equations Tables 7-8 : Alternative spectifications and tests of new planting equations Table 9 : Specification of productivity equation
iii

## FIGURES

# Figure 1 : Log of Bahia total production

Figure 2 : Log of total area under cocoa In Babia Figure 3 : New planting of cocoa in Bahia in hectares Figure 4 : New planting divided by total area or old area Figure 5 : Ratio of replanting to new planting Figure 6 : Ratic of surviving pre-1966 area to total planted area Figure 7 : Log of estimated yield on pre-1966 planted area Figure 8 : Log of real cocoa price Figure 9-12: Plots of coefficients based on recursive regression of replanting Figure 13 : Real subsidy rate and real interest rate Figures 14-18 : Plots of coefficients based on recursive regression of new planting
1

# A NODIL OF COCoA REPLANTING AND NEW PLANTING IN BANIA, BRAZIL : 1966-1985

# I : INTRODUCTION

In 1966 approximately 90 per cent of cocoa growing area in Bahia, Brazil, had trees more than 30 years old. From that date onwards the rate of replanting and new planting grew more or less steadily until about 1980. The average annual replanted and new planted hectarage during 1967-70 was about 731 and 1353 respectively, growing to 1026 and 7800 during the period 1971 to 1975, and rising still further to 4651 and 20841 during 1976-80 before declining to 3510 and 10753 during the last five year period 1981-85. As a result of this remarkable surge in replanting and new planting the ratio of surviving pre-1966 cocoa area to the total planted area was just around 45 per cent in 1985. The purpose of this study is to throw light on the factors that contributed to this post-1966 phase of extra-ordinary growth following the stagnation of the previous two decades.

Analysis of replanting and new planting lies at the heart of the longterm supply response. In the case of Derennials the short-term supply elasticity is usually rather small; hence the long-term supply elasticity depends critically on the response of replanting and new planting to price incentives (Nerlove (1979), Binswanger et. al. (1987)). However, given the relative dearth of suitable data on replantlng and new planting, such studies are difficult to carry out. The heterogeneity of the planted area and the peculiarities of perennial crop supply create challenges for both theoretical and empirical analysis. To date there has been limited progress in this area, due in large measure to the paucity of data on age-cohorts and
2 their productivity; see French, King and Minami (1985) and Hartley, Nerlove and Peters (1985) for two recent examples.

Econometric equations for replanting and new planting will be derived fros. a neo-classical cost of adjustmen. ivestment model modifled to allow for "vintage effects", viz., differences In the productivity of trees in different age-cohorts. This extends previous analyses. Using available data on new planting and replanting since 1966 and average oroductivity at different ages, and using the concepts described In Akiyama and Trivedi (1987b), it has been possible to separate the potential output attributable to pre-1968 and post-1966 planted area and to construct measures of productivity on pre-1966 area<sup>1</sup> . These measures play an essential role in explaining replanting behavior.

A fundamental difference between new planting and replanting decisions arises **from** differences in the cost of adjustment. Whereas both Involve Installation costs, replanting involves uprooting which results in a (temporary) revenue loss whose magnitude depends upon the current and future expected prices and on the average productivity of the uprooted trees. Consequently high and rising prices and productivity tend to encourage new planting and to discourage replanting.

The broad conclusion of the study is that the growth in Brazilian new planting and replanting was a response to high and rising cocoa prices and to zero or negative real interest rates that prevailed for most of our sample period. That is, the evidence is consistent with the behavior implied by the theoretical neo-classical investment model. However, in contrast to 1 This calculation, sometimes referred to as the vintage matrix method for calculating potential output is described in detail in Akiyama and Trivedi (1987a, 1987b).
3 new planting, the response. of replanting to variation in price is complex. Since the immediate effect of an increase in price Is to improve the productivity and profitability of marginal cohorts, which in turn reduces the Incentive for uprooting and replanting, replanting Is related negatively to price In the short-run; but over the long-term the positive effect of improved profitabillty dominates the short-term negative effect. The results of the analysis throw light on the efficacy of certain policies, such as the role of Interest subsidies, intended to lead to the rejuvenation of the cocoa sector, and on the prospects for future expansion of this sector in Bahia.

The resainder of this paper consists of the descriptive Section II; Section III sketches the analytical framework; Sections IV and V provide econometric analyses of replanting and new planting respectively; Section VI concludes.
4

# II A DESCRIPTIVE AND FACTUAL BACKGROUND

We preview some of the major features of replanting and new planting of cocoa in Bahia, Brazil. The area planted under cocoa before 1966 will be referred to as "old area" [OLDAREA]. Further, estimated output or output Imputed to this area using the vintage matrix method (based on estimating the separate contributions of new planting and old plantings using average age-yield profiles) will be referred to as "old output" and the estimated production per hectare from the "old area" will be referred to as "old productivity" [OLDPROD].

Planted area and Droduction: Figure 1 shows the log of total cocoa production [LTOTPRODJ in Bahia since 1966. Between 1966 and 1971 production was essentially stagnant, but since then it has risen by about 30X. Figure 2 shows log of total area (LTOTAREA] under cocoa. This aJ^o has shown consicerable growth since 1971, being especially rapid between 1977 and 1981. The total growth in area between 1966 and 1985 has been nearly 40X.

New Planting and Replanting Between 1946 and 1956 there was very little new planting. Over the next decade the pace increased somewhat, but significant Increases in planted area did not occur until after 1966. Figure 3 shows the cocoa new planting hectarage [NPBAHJ and NPBAH as a proportion of total planted area [NPBAHR] and as a proportion of old area [NPBAHR2]. The two measures move synchronously. NPBAHR rose from close to zero in 1967 to the peak of 7.4X in 1980 but declined sharply since then to just around 1X in 1985. The peak growth rate of NPBAHR is around l1l.

Figure 4 shows replanting hectarage (RPBAH]. Again note that the most rapid growth in replanting was between 1976 and 1980, and also that, like
5 new planting, replanting has declined botia absolutely and relatively since 1981.

Table 1 shows RPBAH, NPBAH and their respective growth rates for the period 1967-1985. It is clear that new planting and replanting are rather similar in their varlability. Figure 5 shows how the ratio of replanting to new planting has varied over the period. **From** 1968 to 1976 new planting rose, though not steadily, relative to replanting. However, between 1976 and 1984 this ter jency was reversed and replanting was almost 40% of new planting in 194; since 1984 replanting has once again sharply declined relative to new planting.

Age Distribution of Trees :The effect of replanting and new planting undertaken in the last two decades has been a major rejuvenation in the age structure of the cocoa tree stock. Table 2, derived from Knight (1976), shows the estimated age distribution of the Bahia tree stock between 1936 and 1966. Accordingly, nearly 60% of the tree stock in 1966 was more than 40 years old. No estimates are available of the age distribution In the recent years. As a rough index or the average age one **may** use the ratio of the surviving pre-1966 planted area to total planted area [AGEINDEX]. This is shown in Figure 6. As a consequence of the vigorous new planting and replanting program, AGEINDEX has dropped nearly 60% in just over a decade. Productivity Using information on the age distribution of trees planted since 1966, together with estimated age ,ield profile data for new plantings, the contribution of new plantJng to total production was separated. By subtraction the contribution of old area can be derived, and
6 TABLE 1 : Sumary statistics on the level and percentage change li new planting and replanting , 1987-1985.

|Variable|RPDAR|MPDAR|DLRPBRA|DLNPBAB|
|---|---|---|---|---|
|**Maximum**|8788|31568|2.93|2.63|
|**Minimum**|449|773|-1.28|-.77|
|Mean|2572|10651|<br>0.14|0.18|
|Std. dev.|2465|9098|0.97|0.74|

Notes : Fgures for RPBAH and NPBAH are In hectares. Those for DLRPBAH and DLNPBAH are annual percentage rates of change for RPBAH and NPBAN. respectively.

Table 2 : Estimated Age Distribution of Productive Cocoa Trees, Bahia, 1938-66 <!-- Start of picture text --> Age group, in yeare<br>>10 >20 >30 >40<br>Year <20 <30 <40<br>1936 88 60 44 48<br>(36.8) (25.1) (18.4) (20.1)<br>1946 116 88 60 92<br>(32.7) (24.8) (16.9) (25.8)<br>1956 11 116 88 152<br>(3.0) (31.6) (24.0) (41.2)<br>1966 33 11 116 86<br>(8.3) (2.8) (29.0) (22.0)<br><!-- End of picture text --> Notes: Figures are thousands of hectares and (in parenthesis) percentage of total. Source Knight (1976).
7 division by OLDARKA yields OLOPROD. The log of OLDPROD, defined as LOLDPROD, is shown in Figure 7. Compared with the estinates of productivity given by Knight (1973). the yield on OLDAREA shows a dramatic rise from 367 kilos/lectare in 1967/68 to about 990 kilos/hectare in the late 1970's.

The increase ii the average productivity of old trees Is an important phenomenon. Its source **may** be partly the increased use of better agricultural practices, including the use of fertilizers, and partly the high real cocoa prices that have prevailed through the 1970's. Figure 8 shows the log of the real cocoa price [LPRICOCO] rising dramatically between 1971 and 1976, and declining between 1976 and 1982 with a partial recovery between 1982 and 1984.
8

# III : ANALYTICAL FRANBUORK

The analytical framework for empirical anralysis is a neoclassical investment model with convex adjustment costs. The model also incorporates a vintage production technology, distinguishes between replanting and new planting. It **may** be regarded as an extension of the type of model In Nickell (1978) and Hayashi (1982); however, the treatment of uncertainty in our model is still rudimentary.

Notation: r(t) : real discount rate at t net of taxes or subsidies ff(t) :profit or net revenue pO(t) : real price of output net of taxes if any F(K(t,v),L(t,v);tJ : production function for vintage v capital K(t,v) : stock of capital of vintage v at time t, t > v.

L(t,v) : labor input combined with capital of vintage v.

R(t,v) : uprooting and replanting of vintage v capital at time t G(R(t.v),K(t,v)l : output losses due to removal of vintage v capital q(t) : purchase price of new capital net of grants or subsidies C(Iv(t),K(t,v)] :installation costs of new planting or replanting.

The firm's objective is to maximize the present value of future aftertax net receipts (y(t)J. The gross revenue function is the difference between the value of total output of production from all economic vintages [Po(t)EvF(K(t,v),L(t,v)] minus the total wage-bill. The convex function G(R(t,v)),K(t,v)) denotes adjustment cost, i.e. the output costs associated with investment at rate R(t,v). If R(t,v) is the rate of uprooting and replanting, then G(.) can be regarded as the loss in potential real output
9 due to the reduction in the productive capital stock. Gross revenue net of - - adjustment costs is p0 (t)[F(.) G(,)] wagebill.

An alternative or an additional cost that **may** be included in the revenue function is the convex cost of installation associated with new planting, denoted by C(I(t),K(t,v)). The total cost of new investment is the **sum** of the direct cost, denoted by q(t)I(t), and the installation cost q(t)C(.). Therefore, at time t and for vintage v, the net after-tax revenue is equal to the revenue from the output net of "lost output", minus the wage-bill, and minus the direct cost of installation of the investment goods. The decision problem is to choose the time paths of new planting and replanting and labor input to maximize the present value of net after-tax receipts, given the time-paths of prices of all inputs and output, the technology and the capital accumulation equation.

Since the general solution to this decision problem is complex, or even intractable, important simplifying assumptions are made. It will assumed that a **firm** is either replanting (uprooting and then replacing) or undertaking new planting, but does not simultaneously undertake both activities. This allows us to ignore the complication arising from possible interdependence in the cost of adjustment associated with the two types of activities. 2 It also enables us to develop the view-point that the essential difference between new planting and replanting as ways of expanding productive capacity lies in the different costs of adjustment associated with each. Specifically, it is suggested that replanting is different from new planting because it involves higher output losses in 2 While it is difficult to judge the realism of this assumption for the Bahia cocoa data, it will be a reasonable assumption if new planting and replanting is undertaken by distinctly different groups of farmers.
10 addition to Installation costs.

The net revenue function for vintage v trees in period t is - - - w(t.v) p0(t)(F[K(t,v),L(t,v)J G[R(t,v),K(t,v)]) w(t)L(t,v) - - q(t)I(t) q(t)C[I(t),K(t,v)] (1) where the first term on the right-hand side is the revenuo, net of output loss due to replanting (if any) , the second term is the wage-bill, the third term is the purchase cost of new capital, and the final term is the installation cost of newly purchased capital.1 In the case of replanting the last term will be omitted since no purchese of new capital (i.e. land is involved). In the case of new planting only the output loss function Gt.] will be omitted since no loss of potentially productive land is then Involved. It is assumed that the functions FC.], G[.] and Ct.] are linear homogeneous in their arguments. Further, the production function satisfies conventional regularity conditions in that the marginal product of "Mature" capital is positive and exhiblts diminishing returns. G].J and Ct.l are convex cost functions such that G[ . 2 0 as R(t,v) 2 0, GRt.] > 0, ORR > 0, C[.1 2 0 as 1(t) a 0. C1[.] > 0, Ci1 > 0 Firm's total profit over all productive vintages is given by w(t) - Ev w(t,v), v e V* (2) where V* is the set of currently economic (and hence productive) vintages. The stock of vintage v capital is given by K(t,v) = K(t-l,v) - R(t,v) (3) which assumes for simplicity that depreciation is zero and that there are no exogenous unplanned losses.

Capital stock of vintage v capital, K(t,t) is given by

- - K(t,t) I(t) IV(t) (4)
11 By definition. replanting means removal of uneconomic vintage v capital and replacement by trees of current vintage. That is, if the replanting option is chosen then<sup>2</sup> I V(t) = R(t.v). (5) For convenience of exposition assume that the firm replantlng and new plantlng decisions can be analyzed separately. This implies restrictions on the structure of adjustment costs.

Define the ,agrangean function H(t,v) - w(t,v) + l(t.v)tK(t,v) - K(t-l,v) * R(t,v)l + /A(t,v)(Iv(t) - R(t,v)] (6) where (l(t,v), s(t,v)) are families of lagrange multipliers which may be Interpreted respectively as the shadow prices of vintage v capital and current capital replacing R(t,v). The firm's decision problem is to choose either the replanting sequence (R(t,v)) or new planting sequence I,v (t)) so as to unconstrainedly maximize the value of V - E[Ea r(t+s)H(t+s)l 0(t-1)] (7) where E denotes the operation of taking conditional expectations given the information set Q(t-1) at t-I and the vintage v subscript is omitted for notational convenience. Because the objective is to motivate behavioral equations for aggregative analysis an interior solution is assumed and corner solutions ignored. The necessary conditions for maximization (the Ruler equations) are as follows: Btl1(Po(t+8)FL(t+8) - w(t+s)) - 0 (8) Et.1(PO(t+5)FK(t+5) - GK(t+s) - q(t+s)CK(t+s) + l(t+s)

- r(t)l(t+s+1)J - 0 (9) Et_i(-Po(t+s)GR - A(t+s) + l(t+s)] = 0 (10)
12 (11) Et-I[ -q(t+s) - q(t+s)C1 + ,(t+s)] - 0 In the Euler equations L, F K'<sup>G</sup> RP Cl, and CK denote the first partial derivative of the respective functions with respect to the subscripted variable. (These derivatives may themselves be separable functions of **time** but this feature is omitted here for convenience).

Eliminating M(t+s) from (10) and (11) yields l(t+s) = Et l(po(t+S)GR + q(t+s) + q(t+s)C 1 (12) where the sight-hand side is the expected marginal cost of replanting. Ass'iming now a constant real discount rate, say r, from (9) solve for l(t+s) to obtain

- - - l(t+s) Et_E. rs[PO(t+s)(FK GR) q(t+s)CKJ (13)

where the right-hand side is the expected discounted present value of the marginal revenue product of capital net of adjustment costs of capital.

Eliminating l(t+s) from (12) and (13) yields the basic equation from which one **may** derive the replanting and new planting equations, viz.

Et_l{po(t+s)GR + q(t+s)(1+C,)=E, r (Po(t+s)(FK-GK)-q(t+s)CK) (14) which can be regarded as a generalization of the familiar condition from the adjustment cost models of investment in which the optimal rater of investment is given by the equality of the marginal cost and present value of benefits of investment.

The desired investment equation is a closed form solution to this equation. However, such a closed form solution can only be derived after imposing restrictions on the form of the production function and the adjustment cost function and making strong assumptions about the expected time path of prices. Specifically, a necessary condition is that the production function is homogeneous and that the adjustment cost function Is
13 homogeneous and quadratic, (Nickell (1978)). Given these assumptions the above equation can be solved for I(t)/K(t,v).

Linear homogeneity implies that the first partial derivatives are functions of the ratios of their respective arguments, viz., K/L, or I/K or R/K. A further assumption is that the functions G and R are quadratic in their arguments such that the partial derivatives GR' CI are linear functions of their arguments. That is, for each vintage v, GR(t+s) = aO + a1(R(t+s)/K(t+s)) ao, a, >0 (15a) GK(t+s) - 0 - _(R(t+s)/K(t+s)) ,o 19 >0 (15b) CI(t+9) r 0 + 'r1(Iv(t)/K(t+s)) To, t1>° (15c) CK(t+s) 'I0 - d4IIv(t)/K(t+s)) do 81>0 (15d) Combining (15a)-(16d) and (14) yields Et 1 (pO(t+s)(a0 +aI(R(t+s)/K(t+s)) + q(t+s)(1+c0+cI(Iv(t+s)/K(t+s)) =Ea - r Po(t+s)(FK-.GK) q(t+s)(do+d1<sup>(lv(t+s)/K(t+s))]).</sup> (16) To derive an equation for R(t+s)/K(t4s), set R(t+s)-I,v(t+s), omit the term q(t+s) from the right-hand side and solve (16) for the replanting ratio R(t+s)/K(t+s). Under the stated assumption of linear homogeneity of F, FK along the optimal path will be a function of relative prices alone. Even with these assumptions a closed form solution for R/K seems unlikely to be obtained.

To derive the equation for Iv(t+s)/K(t+s), the same approach **may** be followed, omitting the terms involving G. In this case (16) simplifies to Et_l{fq(t+s) (I+,o+,rl(](t.+s)/K(t+s) ) = E r (Po(t+s)FK - q(t4s)(d0<sup>+dj(I(t+s)/K(t+s))]j</sup> (17) which **may** be readily solved for I v(t+s)/K(t+s).

For empirical analysis the model needs modification. For the replanting
14 equations we need to modify G[.t and Cr.] to reflect the effects of relevant exogenous variables. Specifically add to the right-hand side of (15a) and (15b) a term involving the average productivity of capital. In general this is of course endogenously deterained. However, under the assumption that tree-crops display a typical biologically determined pattern of productivity change, the output loss associated with the reduction in capital due to replanting would be related systematically to the average product of capital for that vintage. 'n many cases, the older the vintage the lower will be the loss of output due to replanting. Let PROD denote average prAductivity. Then modify (15a) to GR(t+s) - s + a1(R(t+s)/K(t+s))+ a2PROD(t+s), **o2>,** (18) which **may** be further modified to 3R(t+s) - ao + al(R(t+s)/K(t+s))+ a2(t+s)(PROD(O)), (18a) if PROD has a profile that depends upon age alone.

The function CI may also be modified to take into account exogenous variables such as implicit or explicit replanting and/or new planting subsidies designed to affect the adjustment. Denoting by Z2 the set of such variables , (15c) aay be rewritten as follows: CI(t+s) - to + rl(Iv(t+s)/K(t+s))+ r2Z2. (19) Consider soae modifications of the right-hand side of (16), interpreted as the expected net discounted marginal productivity of Investment, referred to -as HER for brevity. This depends upon the time-paths (p0(t+s),q(t+s),w(t+s)) and also on the discount rate r. Separate and distinct expectational assumptions about the time-paths of prices will lead to an empirically intractable nodel. More simply, write the MER(t+s) function in terms of average revenue per unit of capital, denoted by AR(t+s)/K(t+s) and the
15 discount rate r(t+s): NRR(t+e)- Et-,[ *o + *1(A4,(t+s)/K(t+s)) - 02r(t+s)J (20) The assumption of linearity is rather special, though similar assumptions have been made In the so-called Q-theory investment literature. Such a specification implies that the firm takes a short-cut by forming expectations directly in terms of revenue rather than separately for its components. Finally substitute the above assumptions into (16) and solve for R(t+s)/K(t+s) or I(t+s)/K(t+s). The replanting equation is ((a2p 0<sup>(t+s)</sup> + clq(t+s))(R(t+s)/K(t+s))J E StI (-aOpo(t+s) - cZPROD(t+s) - r 2 q(t+s)Z 2<sup>(t+s)</sup> + 00e+ 0 1(AR(t+s)/K(t+s))

- e2r(t+s)) (21)

The price variables enter this equation In a multiplicative fashion. A linearized version of this equation is R(t+s)/K(t+s) Et1 (-Aipo(t+s) - A2q(t+s) - A3PROD(t+s)

- c2Z2(t+s) + DI(AR(t+s)/K(t+s)) - D2r(t+s)) (22)

where all coefficients are positive a priori. Thus the replanting rate is negatively related to the expected output price, the price of new capital and the real interest rate and positively to the expected average revenue. The new planting equation is simpler since the terms- arising from G[. I do not appear. Thus we have = t(t+s)/K(t+s) - B1q(t+s) - B2Z2(t+s) + B3 (AR(t+s)/K(t+s)B4r(tes)). (23) Aefregation The derivations given above apply to planting rates relative to the stock of a single vintage, i.e., the cohort of trees planted in any one year. Thus the replanting rate would be the proportion of trees In that cohort that are replanted (compare French, King and Ninami (1985)).
16 New planting could be defined relative to the size of any cohort. But data constraints are likely to lead to aggregation of vintages. The criteria for aggregation are likely to be case dependent. However, the use of broad age classes has pragmatic appeal. Further, under average conditions productivity **may** vary systematically with age. It seems natural in such cases to aggregate across all age cohorts greater than (say) X years as If these were acceptably homogeneous. The replanting rate is sometimes defined as total replanting as a proportion of ail area older than X years. This assumes that 3 replanting have not occurred in younger cohorts. Glven suitable data, separate replanting rate for each age-class **may** be considered 4. In the case of new plantings it is not obvious which aggregate stock of capital should 5 be used to define the rate of new plantings

# 3 French, King and Minami (1985) provide examples to the contrary.

4 Often data may be available only on total replanting but it **may** be possible to separate the capital stock into at least two age classes, say pre- and post-year Y. This will provide an opportunity for estimating equations with different dependent variables.

5 One obvious alternative is to exclude only the immature vintages. A narrower aggregate is obtained by taking all vintages considerably older than even the mature vintages. Since the choice is arbitrary an econometric sensitivity analysis seems desirable.
17

# IV : AN ECONOKETRIC MODEL OF REPLANTING

The starting point of empirical analysis is the first-order condition for revenue maxilmization which states that the rate of investment must be such as to equalize the present value of net marginal expected revenue (MER) from additional investment and the marginal cost of investment (MCI). For exposition, write this In the form MER(I(t),K(t,v); Z1) = MCI(I(t),K(t,v); Z2). (24) It Is possible that the variables Z2 in the new planting and replanting equations are different.

SDecification of MER(.) function (1) MER per unit of investment is increasing in the expected net marginal revenue product of capital. Given constant returns to scale the latter can be expressed as a funct.ion of expected future taxes, wage rates and product prices. But a separate specification for each of these, leading to an average or marginal revenue specification, will lead to an overparametrized model. A simpler approach is to specify an equation for expected revenue directly.

Accordingly it will be assumed that firms base their decisions on forecasts of gross revenue per unit capital and that the expected gross marginal revenue product per unit of investment is linear In expected average gross revenue which ic turn is a linear function of lagged average gross revenue.

(2) A priori G(.) is quadratic and homogeneous and has a positive first derivative with respect to I(t)/K(t,v). A higher rate of replanting implies an initially smaller capital stock and higher immediate costs of "lost output", for a given price of output. Marginal net revenue product of
i8 a unit of replanting is decreasing in the real value of "lost output", which in turn Is Increasing in the expected real price of cocoa. For any given age structure of capital, high expected future price implies a future demand for a larger productive stock and a corresponding higher present opportunity cost of replanting.

(3) The marginal product of scrapped capital is endogenouslY determined. Economic age of capital is also endogenous. But biologicallydetermined age-related changes In the productivity of capital stock introduces an exogenous component. For example, productivity **may** decline monotonically after certain age, say 40 years. Then the marginal value of "lost output" due to replanting will be a decreasing function of the age of the scrapped capital. Such a dependence could be captured by making expected losses in revenue depend upon an index of age, e.g. AGEINDEX mentioned in an earlier section.

An alternative specification would include a variable reflecting the (unobservable) average productivity of marginal capital, i.e. capital that earns zero quasi-rents, see Hartley, Nerlove and Peters (1986). Here it will be assumed that the average productivity of marginal capital is linear in the average productivity of the "old capital", i.e pre-1966 stock of trees. A priori, "lost output" is positively related to OLDPROD; hence, the rate of replanting will be negatively related to OLDPROD.<sup>6</sup> (4) The expected marginal revenue is a decreasing function of the discount rate. The higher the discount rate used in the calculation of marginal expected revenue, the lower will be the expected revenue associated 6 Average measured productivity will generally include a component which responds to price movements.
19

# with replanting.

# sDecification of MCIUJ) function

(5) The standard convex, quadratic and homogeneous formulation of C[.J is modified by including the multiplicative variable I(t)/K(t,v)*RSUBRATE In the cost function, where RSUBRATE is Intended to account for the real subsidies per hectare given for replanting. The specific subsidy effect modelled this way is the interest rate subsidy glven by CEPLAC to cocoa producers In the period 1979 to 1985 . A priori, the partial derivative of Ct.I with respect this variable Is negative, reflecting the reduction in marginal Installation costs due to replanting subsidies.

(6) AdJustment cost models typically specify the marginal adjustment costs to be q + C1, where q Is the unit purchase price. However, since no such direct cost ot purchase of land Is involved for he replanting producer, it **may** be omitted in our model of replanting but should be Included In the model of new planting.

Linearizing equation (24) yields rn + r1GREVE - r2REALINT - r3PRIE - r4OLDPROD - r5RPBAHR2 8;+ c2RPBAHR2 - c3RSUBRATE + ERROR (25)

# where

GREVE expected gross revenue per replanted unit of capital REALINT real interest rate as proxy for the discount rate PRIE expected real cocoa price OLDPROD estimated average productivity (MT/HA) on OLDAREA RSUBRATE : real subsidy rate for replanting.

RPBAHR2 replanting divided by OLDAREA 7 CEPLAC **memo;** October 1987.
All coefficients are posltlve a priori.

Since this still involves unobservables additional simplifying assumptions are required to obtain the final estimating equations in terms of observables. GREVE is proxied by either a second-order autoregression on two past values of the variable AREVPROD, which measures gross revenue per unit of old capital, or more restrictively by a two-period moving average of AREVPROD.

GREVE(t) a aIREVPROD(t-l) + a2AREVPROD(t-2) We require a measure of expected after-tax revenue on replanted area whereas AREVPROD measures avere.- pre-tax revenue on OLDAREA. For present purposes this will be defined as the measure of real gross revenue per hectare of old area (AREVPROD] as the product of PRICOCO and OLDPROD, where PRICOCO is real price per kilo of cocoa beans, and OLDPROD is the yield per hectare. For some purposes this calculation is deficient. First, the calculation of OLDPROD includes even area which **may** be currently uneconomic to harvest. Therefore, ARLJPROD understates the revenue per unit of harvested area. Second, the measure of operating costs excludes the imputed cost of services of land which is theoretically relevant. Third, the direct costs of acquiring new land are ignored. However, this is not necessarily a serious problem if one wishes to use AREVPROD to explain replanting and it also happens to be the case that replanting and new planting are undertaken by essentially different enterprises. To the replanters the cost of new land is not a part of the costs of production and should be excluded. To the new planters who will necessarily face such a cost, AREVPROD will overstate the average revenue per hectare of old area. Its behavior is of course heavily correlated with that of PRICOCO which has a direct effect and an indirect
21 effect through OLDPROD. Excluding taxes is not serious since the producer taxes have been static for the Bahia cacoa producers. Perhaps revenue on newly planted area **may** provide a better surrogate variable. On the other hand, it can also be argued that the relevant expectations **may** be those based on the past experience of those currently replanting rather than those engaged in new planting. This would justify the use of AREVPROD.

Analogously, PRIE will be proxied by either last period's price, denoted PRICOCO(t-1) or by a moving average of two past prices, denoted MAPRI. This, of course, is a very simple assumption . However, the DickeyFuller did not reject the hypothesis that PRICOCO is first orie'r autoregressive with a unit root, which suggests that the "naive" forecasting rule assumed here is actually the optimum rule.

Combining the assumptions yields the following basic replanting equation RPBAHR2(t) = d(ro-c ) + dr a AREVPROD(t-1) + dr a2 AREVPROD(t-2)dr2REALINT(t-1) - dr3 bPRICOCO(t-1) - dr4OLDPROD(t-1) + dc3RSUBRATE(t) (26) where d=1/(c1+r4) > 0.

In summary, the rate of replanting can be expected to rise when average revenue on existing area has bean rising, and when the real subsidies are increased, but will tend to fall when the real interest or the real producer price of cocoa or the productivity of existing area rises.

8 However, using the arguments given elsewhere [see Akiyama and Trivedi (1987)1 it would appear that the relevant model of world cocoa price determination is likely to be complex in terms of its informational requirements and a simpler assumption such as that which made above has appeal in terms of the acknowledgement of the limited informational resources available to the cocoa producers.
22

# Tho Results

The estimates of the basic equation estimated for 1968-85 without the subsidy variable RSUBRATE are given In Table 3, the variant with the subsidy variable is In Table 4. All coefficients are well-determined and have a priori expected signs, with the exception of AREMPROD(-2). The fit of the equation as Judged by the R-Bar squared coefficient, the absence of serial correlation and heteroscedasticity in the residuals and the diagnostic test of the functional form, is good, perhaps surprisingly so. The graph of predicted vs. actual values for the dependent variable shows no significant episodes
23

# TABLE 3 : Basic Reolantinf Eauation

Dependent variable Is RPBAHR2 18 observations used for estimation from 1968 to 1985

|Regressor|Coefficient|T-Ratio|
|---|---|---|
|CONS|.0295<br>3|4.6063|
|AREVPROD(-1)|1995xlO 3|6.8853|
|AREVPROD(-2)|.0022xlO3|.3235|
|REALINT(-1)|-.2452xlO 3|-5.3344|
|PRICOCO(-1)|-<br>.1152xlO|-6.2994|
|OLDPROD(-1)|-.0492|-4.6606|
|R-Squared|.9664||
|F-statistic F( 5, 12)|69.0101||
|R-Bar-Squared|.9524<br>-2||
|S.1.<br>of Regression|.2038xlO3||
|Residual Sum of Squares|.0498xlO||
|Mean of Dependent Variable|<br>.00920||
|S.D. of Dependent Variable|<br>.00934||
|DW-statistic|2.1109||

# Diagnostic Score (LK) Test Statistics

|A:Serial Correlation|CHI-SQ( 1).|0.2632|
|---|---|---|
|B:Functional Form|CHI-SQ( 1)-|2.3738|
|C:Normality|CHI-SQ( 2)-|1.3139|
|D:Heteroscedasticity|CHI-SQ( 1)-|.0562|

# Notes

A:Lagrange multiplier test of residual serial correlation B:Ramsey's RESET test using the square of the fitted values C:Based on a test of skewness and kurtosis of residuals D:Based on the regression of squared residuals on squared fitted values
24 unexplained by the regression. The leverage chart shows that most of the explanatory power of the regression derives **from** post 1977 data. As was noted earlier this coincides with the period of most rapid growth In replantling.

As a part of the diagnostic checking of the equation tests of parameter stability based on the CUSUJM and CUSUNSQ of the recursive residuals were also carried out and these also Indicated that the basic equation was satisfactory. Figures 9-12 provide plots of the coefficients of 10 significant variables based on recursive regression . These plots show considerable stability in the signs of the coefficienrts post 1976.

CompR ison with some variants: Before turning to an analysis of the policy implications of the results It Is useful to compare the basic equation with some of the variants. In one two-period moving averages of PRICOCO and OLDPROD were used In place of the one-period lagged values; In another the surrogate variable AGEINDEX was substituted In place of OLDPROD. In yet another only one of the two variables REALINT and REALSUJB was tried.

First, consider the role of subsidies on Interest payments of the replanters . Observe from Figure 13 that RSUBRATE and REALINT were stziff'iy negatively related over the period of subsidy. Note that the period over which the subsidies weere given was quite short compared with the sample The results were less satisfactory when the dependent variable RPBAIRR was used, which again suggests that deflation by OLDAREA rather than TOTAREA is more appropriate.

10 See Dufour (1982) for a survey of recursive regression techniques for the regression model. The calculations reported here were executed using DATAFIT program by Pesaran and Pesaran (1987).

11 The figures for interest rate subsidies were provided by CEPLAC.
25 period. The rate of subsidy rose as REALINT fell sharply from 1977 to 1980, and fell as REALINT rose sharply between 1981 and 1985. This strong negative correlation, in conjunction with the absence of substantial variation in REALINT before 1975, makes it very difficult to separate the individual effects of the two variables. It is clear from Table 4 that REALSUB does have a strong effect on the rate of replanting provided REALINT(-i) is excluded from the equation. Nevertheless, since the diagnostic tests of the resulting equation show evidence of both serial correlation and heteroscedasticity, and, moreover, the coefficients in this variant are not uniformly precisely determined, the basic equation of given earlier seems preferable. To confirm this preference for the basic equation, non-nested hypothesis tests were run to compare the two variants. The results given in Table 5 generally favor the specification with REALINT(-1) over that with RSUBRATE. It is emphasized that even though the REALINT specification is favored, the available evidence is consistent with the hypothesis that the interest rate subsidies given by CEPLAC stimulated replanting.

Now consider the specifications based on two-period moving averages of PRICOCO and OLDPROD, denoted, respectively, by MAPRI and MAOLDPR. The estimated equation had sharply determined coefficients, but provided no improvement in the overa'l fit of the model. Actually there is a slight deterioration. Once again the basic specification is favored by the nonnested tests given in Table 6 though the margin of improvement offered by the basic model is slight.

Finally, consider the choice between two possible determinants of "lost output", AGEINDEX and OLDPROD. When AGEINDEX(-1) is substituted in place of
26

# TABLE 4 : Replanting Equation with Subsidy Variable

Dependent variable Is RPBARR2 18 observations used for estimation from 1968 to 1985 Regressor Coefficient T-Ratio CONS .0069743 3 1.1821 ARBVPROD(-1) .0828x 0<sup>3</sup> 2.9185 AREVPROD(-2) -.0057x 0-2 -.8038 RSUBRATE .1194xlO 4.1312 PRICOCO(-1) -.0366xlO -1.8451 OLDPROD(-1) -.9990X10<sup>2</sup> -1.0819 R-Squared .9532 F-statistic F( 5, 12) 48.9066 R-Bar-Squared .9337 S.E. of Regression .0024 3 Residual Sum of Squares .0694xlO Mean of Dependent Variable .0092 S.D. of Dependent Variable .00934 DW-statistic 2.7985

# TABLE 5 : Tests for Mon-Nested Regression **Models**

Dependent variable is RPBAHR2 Regressors for model MI: CONS, AREVPROD(-1), AREVPROD(-2), RSUBRATE, PRICOCO(-1), OLDPROD(-1) Regressors for model K2: CONS, AREVPROD(-1), AREVPROD(-2), REALINT(-1), PRICOCO(-1), OLDPROD(-1)

|Test Statistic<br>MI|against K2|K2 against MN|
|---|---|---|
|COX-PESARAN TEST|-4.0023|-1.3238|
|ADJUSTED COX-PESARAN|-3.0145|-. 9773|
|DAVIDSON-MACKINNON<br>J-Test|2.3284|.8935|
|ADJUSTED J-Test|2.3284|.8935|

Model MI: DW 2.7985 ;R-Bar-Squared .9337 Model M2: DW 2.1109 ;R-Bar-Squared .9524 Akaike's Information Criterion of MI versus M2= -2.9756 favours M2
27

# TABLE 6 : Tests for Non-Nested Regression Models of Replanting

# Dependent variable is RPBAHR2

Regressors for model MI: CONS, AREVPROD(-l), AREVPROD(-2), REALINT(-1), MAPRI, KAOLDPR Regressors for model M2: CONS, AREVPROD(-l). AREVPROD(-2), REALINT(-1), PRICOCO(-1). OLDPROD(-1) Teot Statistic Teot Statistic Ml agalnst M2 M2 against MI COX-PESARAN TEST -2.5758 -1.4636 ADJUSTED COX-PESARAN -1.8761 -1.0374 DAVIDSON-MACKINNON J-Test 1.6607 1.0080 ADJUSTED J-Test 1.6792 .9518 Model Ml: DV 1.9375 ;R-Bar-Squared .9459 88.4834 Model M2: DW 2.1109 ;R-Bar-Squared .9524 89.6325 Akaike's Information Criterion of Ml versus K2 - -1.1491 favours M2
28 OLDPROD(-1), there was significant deterioration in the fit of the model, though all coefficients retained their a priori expected signs. The nonnested model test comparisons unequivocally support the basic specification over the alternative.

. Hence the regression model of Table 3 is suitable for summarizing the contribution of the four determinants to changes in the rate of replanting (RPBAHR2). The changes were generally positive between 1975-1981 and generally negative subsequently. In the post-1975 period the contribution of the revenue factor has been generally negative, the exceptions being the years 1977, 1978 and 1984. The contribution of the real interest factor was positive from 1980-1982 and since then generally negative.

Over the sample period cocoa price has shown very sharp fluctuations and hence its contribution to replanting has also shown corresponding sharp variations. This contribution was large and negative in 1977 and 1978, but positive between 1979 and 1983. That is, while the revenue factor was tending to lower replanting, the lower real cocoa price tended to encourage It. To the extent that the two effects are in opposite directions the total price elasticity of replanting can be theoretically quite low and theoretically even negative when one takes into account the effect of increase in the price on the productivity of old area.

Average productivity on old area has been rising for most of the sample period, quite possibly stimulated by price increases. The contribution to replanting from improvements in productivity is positive to the extent that it improves revenue but negative to the extent that it raises the opportunity cost of replanting. The latter factor has had a negative impact throughout most of the sample period.
29

# Elasticity of RPBAH with respect to PRICOCO

The total elasticity of replanting with respect to PRICOCO depends upon (1) the (negative) direct effect of PRICOCO on replanting, (ii) the (positive) effect operating through the revenue variable and (iii) the (negative) effect operating through the productivity variable. Since the first effect operates with shorter lags than the other two, It determines the short-tera elasticity which is found to be -4.4. The revenue variable adds nearly 7.4 to this figure whereas improvement in price which causes the average yield to rise contributes -1.3. Combining the three estimates produces a total elasticity of about 1.712.

The result that the short-term price elasticity is negative and sizeable serves to emphasize the importance of the endogenous element in scrapping and harvesting decisions (see Trivedi (1987)). An increase in the real price of cocoa will encourage producers to operate at the extensive margin of production by increasing the economic life of all existing capital including capital which was previously uneconomic, thus reducing the rate of uprooting/replanting. Higher prices also encourage the producers to raise yields on all existing capital and this tends to depress replanting. For the present data set these two negative effects are found to be substantial but do not dominate the positive effect of the revenue variable. This last effect is not only statistically significant on its own, but it determines the sign of the total effect.

12 Of course such an estimate is subject to the usual estimation error which **may** be considerable in the present small sample. Further recall that theoretical arguments suggest a nonlinear response to price changes so that in any given instance the response of replanting **may** differ substantially from that estimated from a small sample.
30

# Interest rate effects

The partial derivative of replanting with respect to the real interest 1 rate is negative and highly signiticant statistically . The change In interest rate has been of the order of fifty percentage points In **some** years. e.g. 1980. and this implies a reduction In replanting of about 4035 (- 0. 2452xlO3 x50x329189) hectares. Comparison with the data in Table I shows this to be a large effect. Clearly, real interest subsidies can be expected to have significant stl-ulatory effects.

13 The interest rate elasticity calculated at the sample mean real interest rate of about -15 (see Figure 21) is 22sitive at about 0.48. Since the real interest rate has fluctuated between positive and negative values the elasticity value as such is not very meaningful.
31

# V : ICONONBTRIC ANALYSIS Of MM PLANTING

The new planting equation is derived In a manner similar to that for replanting, but the specifilcation of the costs of adjustment is different1 4 New planting decisions are based on expected profit calculations. In estimating expected gross revenue the operating costs and average yield at maturity should be those which apply to the variety being considered. It is likely that the average yield at maturity of newly planted areas may be substantially different from the yield on older areas due to differences in soil fertility, chosen varieties and the average age of planted area. Despite this the first alternative considered for proxying expected revenue of new planting is AREVPROD. Again two lagged values of AREVPROD are used to proxy GREVE. The major justification for this Is that, given the relative unimportance of new planting before 1966, and the rather low level of new planting until 1975, reliable estimates of the revenue of new planting based on the yield of newly planted area cannot be formed except for a rather small part of our sample. Estimation based on such a small sample will not yield useful results. On the other hand, it is at least plausible that the movements in the revenue of newly planted areas should closely mirror the movements in revenue of the older areas since both depend to some extent on PRICOCO.

Yet another possibility is to specify expected revenue to be a linear function of two lagged values of PRICOCO. Such a specification ignores an important component of revenue, viz, average yield, but could involve a relatively smaller error than using AREVPROD variable if the past yield on 14 It may be argued also thet the relevant measure of expected revenue also should be different.
32 OLDAREA does not properly reflect the expected future yield on new area.

Specifically, It is assumed that new planting does not involve any "lost output", i.e., the G(.) function does not appear in the specification of the net revenue function. Consequently, the variables PRIE and OLDPROD, whose inclusion in the replanting equation was justified through their relationship with the "lost output", will not appear in the new planting equation.

Adjustment costs enter the model only through the installation cost function C(.). However, we allow C(.) to include a dynamic element in the following sense. For a static convex installation cost function, CI > 0. In the case of perennial, where inelastic supply of suitable land even in the long run **may** constitute a constraint, adjustment costs will also rise over time as the supply of suitable land is depleted. The latter cost is external to the firm and will be reflected in the rising purchase price of capital. As, however, we do not have data on the price of suitable cocoa- growing land a proxy variable for the speed of depletion of suitable land is includedi viz., the total "newly installed capicity". The higher the ratio of "newly installed capacity" to total capacity, the higher will be the marginal installation cost of any further additions. To apply this idea one needs an operational definition of "newly installed". 15 Since Interest rate subsidies which apply to replanting are not available for new planting, no subsidy variable will appear in the new planting equation.

The first order condition for profit maximization for new planting is Here the capacity added after 1966 will be referred to as "new capacity".
33 that the present value of marginal expected revenue **from** new planting should 16 equal its marginal installation cost . As before a linear MER function is specified in the variables AREVPROD(-1), ARBVPROD(-2). and REALINT. The marginal Installation cost Is also linear In PLAND which is the empirical counterpart of the theoretical variable q; the rate of new planting as measured by either NPBAHR or NPBAHR2 and a variable measuring the ratio of "newly Installed capacity" to old capacity or total capacity, measured by either KNPLR, KNPLR2 or NEWCAPR2. Thus we have rO + r1 AREVPROD(t-1) + r2AREVPROD(t-2) - r3REALINT(t)

- PLAND(t) + c0 + cINPBAKR(t) + c2 KNPLR(t-1) (27) Rewriting gives an equation for new planting

NPBAHR(t) - d(r0 - c0) + drIAREVPROD(t-1) + dr2AREVPROD(t-2) - dr3REALINT(t) - dPLAND(t) - dc2KNPLR(t-1) (28) where d-l/c1.

In sumaary, the rate of new planting is related positively to the average revenue on existing planted areas, negatively to the discount rate, negatively to the price of land and negatively to the ratio of newly planted area to the old area. The variable PLAND is actually omitted from the estimated equation because of lack of data, but theoretically it should be present. Its inclusion will capture the external adjustment costs that are 17 likely to be important for the sector as a whole Two aeasures of the rate of new planting, NPBAHR and NPBAHR2, move 16 It is assumed that there Is an interior solution for the rate of new planting.

17 The seriousness of the misspecification ensuing from the omission of the price of land will be case dependent, being the greater when area expansion nears the limit of suitable available land.
34 synchronously and the regression results for the two are also rather similar, except that residual serial correlation is a more serious problem when the dependent variable is NPBAHR.

As an estimate of newly installed capacity relative to total capacity, two measures have been tried. The first Is simply the ratio of area planted after 1966 to the total area planted, denoted KNPLR, a slight variant of this being KNPLR2 where the divisor was OLDARBA. The second measure Is NEWCAPR2, the estimated proportlonal contribution to total cocoa production due to the area planted since 1966. This is based on the potentlal production calculations alluded to earlier. The regression results using the different variants are broadly similar but those based on NRWCAPR2 are marginally superior in terms of statistical fit.

The estimated equations reported here incorporate a small variation on equation (27) above. The latter **may** be properly interpreted as an equation for Planned rate of new planting. Allow the actual rate to differ from the planned rate by an amount that dep.erd2 upon the percentage error of price expectation, denoted by CHPRI, which in the present case is simply the percentage change in PRICOCO between current and last period. That is, price
35

# TABLE 7: Basic new planting equation

Dependent variable Is NPBAHR2 18 observations used for estimation froa 1968 to 1985 Regressor Coefficient T-Ratio CONS -.0163 3 3.4623 PRICOCO(-1) .0735xlO 3 5.2300 PRICOCO(-2) .0437xlO 2.6948 CHPRI .0117 -2 2.2021 kRALINT -.104x10 -10.0122 NEWCAPR2(-i) -.0198 -1.9917 R-Squared .9663 F-statistic _FP_ 5, 12) 68.7542 R-Bar-Squared .9522 s.E. of Regression .0070318 3 Residual **Sum** of Squares .5934x10 Mean of Dependent Variable .0369 S.D. of Dependent Variable .0322 DW-statistic 1.67fit R-Squared

# Diagnostic Score (LK) Test Statistics

A:Serial Correlation CHI-SQ( 1)= .2901 B:Functional Form CHI-SQ( 1)= .2783 C:Normallty CHI-SQ( 2)= .8643 D:Heteroscedasticity CHI-SQ( 1)= .7206

# TABLE 8 : Tests for Mon-Nested Models of New Planting

Dependent variable is NPBAHR2 Regressors for model M1: CONS, PRICOCO(-1), PRICOCO(-2), REALINT, NEWCAPR2(-1) Regressors for model N2: CONC, AREVPROD(-1), AREVPROD(-2). REALINT, CKPRI, NEWCAPR2(-1) CHPRI, Test Statistic Ml against K2 K2 against Ml COX-PESARAN -.6627 -1.4303 ADJUSTED COX-PESARAN -.4068 -.9602 DAVIDSON-MACKINNON J-Test .9022 1.4457 ADJUSTED JA-Test .1700 .4942 Model Ml: DW 1.6761 ;R-Bar-Squared .9522 Model K2: DW 1.5614 ;R-Bar-Squared .9482 Akalke's Information Criterion of Ml versus M2= .7343 favours Ml
36

# TABLE 9 : Productivlty Equation for OLDAREA

Dependent variable is LOLDPROD 18 observations used for estimation from 1968 to 1985

|Regressor<br>Co|efficient|T-Ratio|
|---|---|---|
|CONS|-2.8642|-6.3135|
|TR66|.0206|2.5136|
|LPRICOCO(-2)|.3905|4.4258|
|R-Squared|.7924||
|F-statistic F( 2, 15)|28.6345||
|R-Bar-Squared|.7648||
|S.E. of Regression|.1483||
|Residual Sum of Squares|.3298||
|Mean of Dependent Variable|-.4164||
|S.D. of Dependent Variable|.3057||
|DW-statistic|2.2468||

Diagnostic Score (L") Test Statistics A:Serial Correlation CHI-SQ( l)-.8410 B:Functional Form CHI-SQ( 1)=.0372 C:Normality CHI-SQ( 2)- .2994 D:Heteroscedasticity CHI-SQ( 1)= .0424
37 expectations art. assumed to be based linearly on the previous perlod's price. A priori, a positive change will provide an Incentive to raise the rate of new planting and a negative change to reduce it.

Using non-nested tests, the specifications based on AREVPROD and either NEWCAPR2 or KNPLR2 , which were generally very similar, twere compared with the results obtained with PRICOCO(-1) and PRYCOCO(-2) (Table 7) replacing AREVPROD(-1) and AREVPROD(-2), respectively. The tests given in Table 8 favor the model based on PRICOCO.

Whereas the variables AREVPROD and PRICOCO are highly correlated, the regression of AREVPROD on PRICOCO leaves a substantial unexplained variance essentially because the former depends by definition on the average yield of OLDARBA, which has shown very substantial variation. If, however, the relevant variable is the expected yield on new area, which **may** differ from that on OLDAREA. then the final choice of equation can be rationalized.

The results presented in Table 7 show that all explanatory variables have t-ratios of about 2.0 or greater. The price and the interest rate effects are precisely measured and have the a priori expected signs. The R- bar-squared statistic has a value of .9522 and the diagnostic tests presented in the lower part of Table 7 are all satisfactory. The CUSUM and CUSITMSQ plots were examined ; the former deviates markedly from the zero axis suggesting that at least some of the estimated coefficients **may** not be robust. The recursively estimated coefficients plotted in Figures 14 through 18 and these suggest that the coefficients of NEWCAPR2(-1) and CHPRI are
38 relatively the least robust<sup>18</sup> Price elasticlty of new planting :The estimated short-run elasticity of new planting with respect to price measured at the sample means is 1.60 (- 0.1172x 10<sup>3</sup> x342.42 /0.0369), about the same as the replancing elasticity. However, the dynamics of replanting are a great deal more complex and there is considerable internal evidence that the price response of replanting is somewhat nonlinear.

Interest elasticity The interest rate elasticity measured at the sample mean values is 0.42 - a value very similar to that obtained for replanting. This effect is interpreted as a cost of capital type effect. **From** 1973 through 1985 the real interest rate was negative and between 1973 and 1980 it was for the most part declining reaching about -68% in 1980, a decline of almost 60 points over the previous two years. The estimated net direct effect of such a decline would be to add about 12180 hectares of new planting, thereby strongly counteracting the negative contribution over this period from the declining average revenue per hectare. It is clear that the factors that contributed to low real Interest rates caused a very considerable growth in cocoa new planting during the 1970's1 18 Generally, the t-ratios on the estimated coefficients provides a good guide to the robustness of the coefficients to variations in the sample size.

the empirical analysis of new planting has been carried out without including the theoretically relevant price of cocoa land. Even if this were not a significant omission in the sample period, such **may** not be the case in the future so that an extrapolation based on the estimated equation should be done with care.
39 VI : SUNKARY AND **CONCLUSIONS** Specifications for replanting and new planting derived from a cost of adjustment model of investment have been estimated and tested extensively in this paper. They stand up well to a battery of specification tests and several key coefficients are robust.

The detailed and the broad conclusions of this paper support the importance of real price of cocoa as a key determinant of both replanting and new planting. Lest such a conclusion should be thought obvious, note that the channels through which this effect operates is perhaps more complex in the case of replanting than new planting. For the latter the short run response **may** be small, whereas for the former it is estimated to be negative. The long run response of both is estimated to be positive. Though elasticity estimates have been provided in the text, they must be interpreted with care both because of the small sample analyzed and the nonlinearities involved.

The analysis of replanting has been conditioned on the productivity of the pre-1966 planted area. But the latter is an endogenous variable. The average productivity of this area has shown considerable rise since 1966. but the reasons for this change do not appear to have been fully documented. Whether replanting will be stimulated in the future depends both on the movements in the real price of cocoa and the exogenous component of changes in average productivity.

Evidently the low real interest rates of the 1970's and early 1980's have stimulated new planting and also replanting. The strong collinearity between the interest subsidy provided by CEPLAC to replanters between 1977 and 1984 and the real interest rate has prevented a clear quantitative
40 conclusion about the effect of this subsidy, though Its qualitative effect seems to have been as expected a priori. By lowering the real interest even below the prevailing level which was already low, the subsidy reinforced that effect.

The surge in new planting during the last two decades has implications for future new planting. The Brazilian cocoa orchard is now considerably younger than in 1966, and the consequent increase in its production potential reduces the need for both new planting and replanting. A sharp decline in the yield of the pre-1966 planted area and/or the depletion of land suitable for new planting **may** generate new incentives for replanting. These are issues for future investigations.
41

# RIFEmECS

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___________________________ (1987b) "Vintage Production Approach to Perennial Crop Supply : An Application to Tea in Major Producing Countries", Journal of Econometrics 36, 133-161.

Binswanger, H., Y. Mundlak, N.C. Yang and A. Bowers (1985), "The Determinants of Cross-Country Aggregate Agricultural Supply". Journal of Econometrics, 36.

Dufour, J-N. (1982) "Recursive Stability Analysis of Linear Regression Relationships", Journal of Econometrics, 19, 31-76.

French, B.C., C. A. King, and D. D. Minami (1985) "Planting and Removal of Perennial Crops", American Journal of Agricultural Economics, 67, 215-223.

Hartley, M. J., M. Nerlove and R. K. Peters (1985) The SupplY ResDonse for Rubber in Sri Lanka : A Preliminary Analysis, World Bank Staff Worklnig Papers, Number 657, Washington, D. C.: The World Bank.

Hayashi, F. (1982) " Tobin's Marginal Q and Average Q : Neoclassical Interpretation", Econometrica, 50, 213-224.

Knight, P. T. (1976) "Economics of Cocoa Production in Brazil", Chapter 10 in Cocoa Production : Economic and Botanical Perspectives , John Simmons (Editor). New York : Praeger Publishers.

Monteiro, A. (1987) "Estmativas de margea bruta de producao de cacau, dos investimentos na implatacao e renovacao de lavouras decadentes nas propriedades cacaueiras de Estado da Bahia. Periodo 1965 a 1986". Unpublished CEPLAC paper.

Nerlove, M. (1979) "The Dynamics of Supply : Retrospect and Prospect", American Journal of Agricultural Economics, 61, 874-888.

Nickell, S. J. (1976) The Investment Decisions of Firms . Cambridge University Press.

Tafani, R. R. (1987) "Estimativas de producao de cacau no Brasil Para **08** proximos anos". Unpublished CEPLAC paper.

____________ (1987) "Juros Subsidiados Pela CEPLAC". Unpublished **memorandum.** Trivedi, P. K. (1986) "A Framework for Studying the Supply Response of Perennial Crops", Division Working Paper No. 1986-1, Commodity Studies and Projections Division, EPD, The World Bank
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|WPS73|Taxation and Output Growth in Africa|Jonathan SkInner|August 1988|A. Bhalla<br>60359|
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|WPS80|Emerging Issues of Privatization<br>and the Public Sector|Samuel Paul|September 1988|<br>E. Madrona<br>61711|
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