A new global tea model : specification, estimation, and simulation

A0b& New Tea Mod&3 INTERNATIONAI. BANK RECONSTRUCTION NI) DEVEl.OPMENT Specification, Estimation, and Simulation MAY 4 1987 Takamasa Akiyama and Pravin K. Trivedi WORLDBAN_K STAFF _COMM_ _D_n_ WO_NG_ _ 9198 H ***iD9198 .A2 A424 1987 c.2 aA2 A new global tea model speciication, estimation, and simu A424, 11111 I c. H HLC H30040 Lc..2 SLCO30040  WORLD BANK STAFF COMMODITY WORKING PAPERS 1. The World Tin Economy: An Econometric Analysis (out of print) 2. International Cotton Market Prospects 3. An Econometric Model of the World Rubber Economy (out of print) 4. Industrial Processing of Natural Resources 5. The World Sugar Economy: An Econometric Analysis of Long-Term Developments 6. World Bank Commodity Models (2 volumes) 7. Analysis of the World Coffee Market 8. Analysis of the World Cocoa Market 9. The Outlook for Primary Commodities 10. World Rubber Market Structure and Stabilisation: An Econometric Study 11. The Outlook for Primary Commodities, 1984 to 1995 12. The Outlook for Thermal Coal 13. Jute Supply Response in Bangladesh 14. Prospects for the World Jute Industry 15. The World Copper Industry: Its Changing Structure and Future Prospects 16. World Demand Prospects for Jute  kit) WORLD BANK STAFF COMMODITY WORKING PAPERS ' f} Number 17 C,Z A New Global Tea Model Specification, Estimation, and Simulation Takarnasa Akiyama and Pravin K. Trivedi The World Bank Washington, D.C., U.S.A.  The International Bank for Reconstruction and Development / THE WORLD BANK 1818 H Street, N.W. Washington, D.C. 20433, U.S.A. All rights reserved Manufactured in the United States of America First printing March 1987 Commodity Working Papers are not formal publications of the World Bank, and are circulated to encourage discussion and comment and to communicate the results of the Bank's work quickly to the development community; citation and the use of these papers should take account of their provisional character. 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The latest edition of each of these is available free of charge from the Publications Sales Unit, Department F, The World.Bank, 1818 H Street, N.W., Washington, D.C. 20433, U.S.A., or from Publications, The World Bank, 66, avenue d'1ena, 75116 Paris, France. Takamasa Akiyama is a senior economist in the Commodity Studies and Projections Division of the World Bank. Pravin Trivedi is a professor of economics at Indiana University; this work was completed while he was on sabbatical leave and working as a consultant for the World Bank. Library of Congress Cataloging-in-Publication Data Akiyama, T. (Takamasa), 1944- A new global tea model. (World Bank staff commodity working papers, ISSN 0253-3537 ; no. 17) Bibliography: p. 1. Tea trade--Mathematical models. I. Trivedi, P. K. II. Title. III. Series: World Bank staff commodity working paper ; no. 17. HD9198.A2A424 1987 382'.41372 87-6238 ISBN 0-8213-0868-8  - iii - ABSTRACT This econometric model of the world tea economy represents an advance on previous models for perennial crops in several respects: (i) the use of a conceptual framework based on the vintage production model; (ii) the detailed indelling of the supply side to incorporate new planting decisions in three laading producing countries (this specification makes it possible to distinguish explicitly between the long-run and short-run producer responses t) changes in exogenous variables); and (iii) the use of a market-clearing rational expectations approach to modelling the "world price" of tea, which lsads to a "forward-looking" price equation for tea. The specification of the supply side is more detailed for the four leading producing and/or exporting c,untries, viz., India, Sri Lanka, Kenya, and Malawi, since there is some attempt to model long-run decisions, such as new planting, replanting, and uprootings. For the remaining producer countries in the model the specifica- tion is simpler. There are sound a priori reasons for expecting that the laading producers/exporters will show substantial divergences in their long- run responses to external stimuli. The empirical results support these a priori expectations in that the long-run response in "newer" producer countries, like Kenya and Malawi seems to be different in kind and magnitude from that in the "older" producing countries such as India and Sri Lanka. Specification of demand is based on fairly conventional demand equations for tea. Compared with previous models, this paper has greater disaggregation by country or geographicaL zone. There is also a greater attempt to use the appropriate retail price variable in place of the producer price that is often used in demand equations. Price determination is based on a simplified linear rational expectations model in which a market clearing price is established in each period. The model consists of a supply and demand relation and an inventory demand equation which closes the model. Inventory demand comprises speculative and transactions components, both of which involve expectations of future prices. The insight provided by the analog model--that price depends upon expectations of future values of exogenous variables--provides the basis for specifying and estimating a "world price" equation which plays an extremely important role in the model. The "world price" is linked to the producer prices and retail prices in individual countries through price linkage equations. The results of simulation exercises are presented to exhibit the properties and weaknesses of the model. In the estimated model, equilibrium is established very rapidly following an initial shock. This characteristic reflects the market clearing assumption and the absence of lags in price determination. More significantly, the dynamic simulation of the model based on such an assumption portrays the historical behavior of price's reasonably accurately, in the specific sense that the spike-like behavior of the price of tea can be reproduced by the model.   TABLE OF CONTENTS ABSTRACT ............................................................. iii ]. INTRODUCTION ......................................................... 1 I.1 An Overview of Some Published Tea Models ........................ 1 I.2 Distinguishing F'eatures of the Present Model .................... 4 TI. STRUCTURE OF THE MODEL ............................................... 8 --II. SUPPLY BEHAVIOR ........................................................ 11 III.1 General Considerations ........................................ 11 III.2 Definitions, Assumptions and Basic Concepts ................... 12 III.3 Specification of New Plantings and Replantings ................ 20 III.4 The Supply Equation ........................................... 29 III.4.1 The Basic Specification ........ :t .................... 29 III.4.2 Alternative Specifications for Q (t) .... ............ 31 III.4.3 A Special Case of (3.29) ............................. 33 III.5 Empirical Results .. 34 III.5.1 Compultation of the Index of Feasible Production ...... 34 III.5.2 New Planting and Replanting Equation ................. 35 III.5.3 Supply Equations ..................................... 49 IV. FINAL DEMAND FOR TEA ................................................. 54 IV.l The Demand Specification ........................................ 54 IV.2 Empirical Results ................................................ 58 V. PRICE DETERMINATION ......................................... I ......... 67 V.1 The Specification of the Price Equation .......................... 67 V.2 Linear Analog Model ............................................. 69 V.3 Solution of the Model ........................................... 72 V.4 Derivation of the "Structural" Equation ......................... 74 V.5 Empirical Application ........................................... 75 V.6 Price Linkage Equation .......................................... 79 VI. MODEL SIMULATIONS .................................................... 85 VI.l Results of Ex-Post Simulation .................................. 85 VI.2 Results of Base Ex-Ante Simulation .............................. 97 VI.3 Evaluation of Some Key Elasticities ............................ 98 VI.4 Simulation of a One Time Supply Shock .......................... 110 VII. CONCLUSIONS AND SUGGESTIONS FOR FURTHER RESEARCH ..................... 114 GLOSSARY OF VARIABLES ..................................................... 118 REFERENCES ............................................................ 129  - vi - LIST OF TABLES AND FIGURES Table 1. A Tabular Summary of Some Tea Models ................................. 2 2. Base Period Age-Yield Profiles ...................................... 35 3. Estimated Equations for Supply Block ................................ 40 4. Short-Run Price Elasticities ........................................ 53 5. Estimated Equations for Consumption Block ........................... 59 6. Price and Income Elasticities of Demand for Tea ..................... 65 7. Price and Linkage Equations ......................................... 80 8. Results of Ex-Post Simulation ....................................... 86 9. Results of Ex-Ante Simulation ....................................... 99 10. Changes in Key Variables in case World Price is Increased by 10% During 1990-2000 .......................... 111 11. Simulation Results with 200,000 mt World Production Decline in 1990. 112 Figure 1. A Schematic Representation of Production Process and Decisions in a Price-Taking Producing Country ................................. 18  I. INTRODUCTION The model of the world tea economy described herein has a number of g;eneral features which are shared by other econometric commodity models. The *tylized version of an econometric agricultural commodity market model usually contains supply equations for the major producers, demand equations for major consumers and either inventory demand equations or price equations. However, within this general structure there are usually many variations. To give the reader some appreciation of these in the specific case of globaL econometric tea models the paper begins with a brief overview of the relevant literature. 1.1 An Overview of Published Tea Models The tea models hitherto estimated and published tend to have the !;tructure of market-clearing commodity models. Some of these models are briefly discussed here and their main characteristics are summarized in TabLe which is adapted from Ramanujam (1984). One of the earliest model for tea was developed by Murti (1966). In this model the demand for tea was disaggregated and equations were estimated for eight countries or regions. On the supply side only India and Sri Lanka were considered separately and the rest grouped together. An equation explaining the average price of tea in the London market was specified and estimated. Two price-linkage equations modelling the relationship between the London auction price and the internal price of tea in India and the unit value of imports of tea in the United States were also estimated. Finally, the model included identities for total demand, total supply and stocks.  Table 1: A TABULAR SUMMARY OF SOME TEA MODELS Model & Year of Murti Behrman & Adams Tyler UNCTAD/FAO Cheong7Hoy & Ukpong Publication 1966 1976 1975 1978 1981 1. Type of data Annual Annual Annual Annual Annual period covered or used in estimation 1948--961 1956-1971 1958-1971 1960-1977 1957-1978 method of estimation OLS OLS OLS OLS & OLS & Cochrane Orcutt Cochrane Orcutt Procedure Procedure 2. Main equations Supply, Demand & Supply, Demand & Exports, imports, Supply, Demand, Stocks Acreage Response, Yield, Response Price Price Price & Stocks Price Linkages Supply, Demand, & Price 3. Countries covered India, Sri lanka & Developed Countries, India, Sri Lanka, India, Sri Lanka, Kenya, Total Industrialized Countries, in supply Rest of World Developing Countries Indonesia, Kenya, Other Africa, Bangladesh, Total Centrally Planned, Total Centrally Planned East Africa & Argentina, Indonesia, & Developing Countries, Asia, India, Rest of World Rest of World Sri Lanka, Indonesia, Other Asia, Africa, Kenya, Tanzania, Uganda, Other Africa & Latin America 4. Countries covered UK, US, Canada, EEC Same as above 37 Countries UK, US, India, Other UK, US, Canada, Japan, Australia, Developing Countries & Other Industrialized Countries, Eastern Europe India, Sri Lanka, Indonesia, Iran, Pakistan, Kenya, Latin America, Other Developing Countries, China, USSR, Other Centrally Planned 5. Price variable London Auction Price London Auction London Auction Average Price of four London Auction Average Price employed in for Indian & Ceylon Average Price Average Price Auction centers, Colombo, Tea Calcutta, Cochin & Mombasa (a) Supply (b) Demand London Auction Same as above Same as above Same as above Same as above Average Price 6. Market structure Competitive Competitive Competitive Competitive Competitive 7. Any other features Lagged adjustments Arbitrary selection Price lagged one year Price determined by Fixed gestation period. Supply of supply with of different lags on in the supply equilbrating supply estimated in two ways: Supply adaptive expectation different supply ftnctions and demand Acreage & Yield Response; and of price functions Supply separately  -3- Adams & Behrman (1976) analyzed the world tea economy in a regional framework. This was one of the seven models they estimated for different commodities with a general specification. They specified three supply and three demand functions for three groups of countries. The price equation was estimated in two ways, in terms of the actual price and the deflated price-- both prices were related to stocks and with an assumption of lagged adjustment. Tyler (1975) designed his world tea model to have all imports and exports determined only by the average London price of tea and a time trend. The equilibrium price of tea for any year was specified, as that price which ensures total import demand equals total available exports. The inclusion of a time trend as the only other explanatory variable is clearly a simplification. The trend in exports represents the combined effects of assumed steady trends in the productivity of existing estates and smallholdings and in the extension of acreage. The import trend represents secular influences on the demand side. FAO and UNCTAD (1979) jointly constructed an econometric model of the world tea economy to analyze the prospective supply/demand balance of tea and the implications of an international buffer stock arrangement and an export quota system. The model consists of eight supply equations, six demand equa-' tions, eight price-linkage equations and two inventory equations (one for the supply side and one for the demand side). Total supply is defined as sum of total production and carry-over stocks, while total demand is defined as the sum of world consumption and the demand for inventories. There is no explicit equation for price, which is determined by equilibrating total demand and total supply. Supply is considered to be a function of real price and a time trend. Demand is a function of own price, the price of substitute and a time trend.  -4- Cheong-Hoy and Ukpong (1981) developed an econometric model of the world tea economy for the Worid Bank. They estimated supply functions for some individual tea producing countries and others were aggregated according to geographical and/or economic regions. The supply functions were somewhat different from the earlier models. The authors attempted to distinguish between long-term effects of investment and short-term price effects on yields. The model included 14 country- or region-specific demand functions. The demand for tea was postulated in per capita terms as a function of the relative price of tea with respect to coffee and per capita GDP. The price equation was estimated with the London auction average price as a function of the proportion of implied stocks to total world tea consumption, the ferti- lizer price and the price of coffee. I.2 Distinguishing Features of the Present Model In this section, some of the important differences between the model estimated in this paper and previous tea models are summarized. Several of these differences also apply to previous models of perennial crops. Broadly speaking, the major differences of conceptual and operational nature between the present model and earlier work is in the specification of the producers' supply decisions and in the specification of the price equation. The treatment of the demand equations is largely conventional. A major difficulty with earlier models of perennial crops is their failure to distinguish clearly between the long-run and the short-run dimen- sions of the producers' supply decisions. Conventionally, in dealing with the short-run decision the capital stock is taken as given and attention is con- centrated on the producers' decision concerning the changes in utilization of  variable inputs (and consequently output) induced by changes in prices. Such ain analysis yields a measure of the short-run elasticity of production. To obtain a measure of long-run elasticity, it is necessary to model the response of fixed and quasi-fixed factors to changes in prices. Few global models of ?erennial crops have attempted this despite the fact that the literature is Eull of conjectures about the size of the long-run elasticity. The usual approach of specifying an area equation with a distributed lag on prices and of deriving from it both a short-run and a long-run price response has some- what vague conceptual foundations (Trivedi 1985). In this paper the issue is resolved in the following way: (i) The conceptual framework is based on the vintage prc.duction model (See Trivedi (1985)). Within this framework it is possible to distinguish between actual output, feasible output and potential output in an empirically useful way. Such a framework also explains the components of short-run price response. (ii) For the major producing countries equations are developed for new plantings and replantings which highlight the role of producer price expectations in the determination of investment decisions. These equations also are potentially valuable for analyzing long-run supply responses. They already incorporate, or given additional data can be made to incorporate, very important iocal institutionel features and incentives that have a key role in determining long-run responses. Moreover, they are consistent with the theoretically more flexible notion of time-variant, long-run supply elasticities. (iii) For the major producing countries data on new plantings and average age-yield profiles are combined to construct measures of feasible  - 6 - output which play an important role in the short-run supply equa- tions. Moreover, the measures of feasible output contribute to the ease of interpretation of the supply equations. By contrast, (planted) area equations comprising distributed lags on producer prices are difficult to interpret. (iv) Both theory and empirical observation suggest that there are impor- tant differences between old established producers and newly emerging ones in their supply response to prices. The specification of the tea model exploits this feature at several levels. For example, the new planting and replanting equations and short-run supply equations allow for the differences between countries and, in a few cases, between different types of producers in the same country. Finally, it is to be noted that the disaggregation by countries is much more extensive than in most previous work. Coming now to the issue of price determination, a major limitation of previous modelling has been the lack of emphasis on the role of forward- looking variables. The main reason for this lies in the conventional treatment of inventories. In a typical econometric inventory equation the role of expected future prices is not emphasized. It can be shown (see Section V below) that if inventory demand is comprised of a speculative component which depends upon the difference between the expected future price and the spot price and on a transactions component which depends upon expected future demand, and if the market-clearing price is established within each period, this price will depend upon the expected future values of exogenous variables that drive aggregate demand and supply. The derivation of the price equation exploits this feature. The issues involved in estimating such an equation are  - 7 - discussed below and this discussion makes clear the role of factors such as inflation and exchange rates in commodity price determination. Global commo- dity modelling has to date not paid adequate attention to these important variables. Although the treatment of demand for tea is fairly conventional, it needs to be said that previous work in the area has been somewhat cavalier in the choice of the price variable. Often the London auction price has been used in all demand equations whereas a more appropriate variable is the local retail price which would reflect local taxes, margins and the exchange rate. In this model demand for tea is disaggregated to a greater extent than pre- viously. This is desirable because of the important changes in t:he pattern of consumption that are currently under way. For example, per capita consumption is growing relatively rapidly in India and the Middle East - a factor that has important implications for price behavior. The rest of the paper is organized as follows. Section II provides an overview of the model and an outline of important features of the data used in estimation. Section III sets out the theoretical specification and the empiri- cal estimates of the supply side. Sections IV, V and VI deal, respectively, with the demand side, price determination and the simulation properties of the model. Section VII concludes. The estimated econometric equations appear in two places, first in the relevant parts of the main body of the paper and again in the Appendix where they have been collected together. Definitions of the variables are also in the Appendix.  -8- II. STRUCTURE OF THE MODEL The basic structure of the model consists of supply, demand, price and stock blocks. A schematic view of the model is given in Figure 1. The supply block covers production of 15 countries/regions--India, Sri Lanka, Turkey, Bangladesh, Indonesia, Iran, exports of black tea from China, rest of Asia, Kenya, Malawi, Uganda, rest of Africa, USSR, Argentina and rest of Latin America. Of the 15 countries/regions, behavioral equations were estimated for eight regions and the rest were treated as exogenous. The demand block covers demand for 24 countries/regions--United Kingdom, rest of Western Europe, USSR, Eastern Europe, United States, Canada, Australia, New Zealand, South Africa, Pakistan, Saudi Arabia, Arab countries (Abu Dhabi, Bahrain, Oman, Qatar, Dubai, Kuwait and other Arabian states), Iran, Iraq, Syria, Turkey, Afghanistan, North African countries (Algeria, Libya and Tunisia), Egypt, India, Sri Lanka' Indonesia, Chile and rest of world. Of the 24 countries/ regions, behavioral equations have been estimated for all except Indonesia, Afghanistan, Iran and Iraq which are treated as exogenous variables. There is one behavioral price equation which determines the world price and 13 price- linkage behavioral equations linking the world price to the major auction prices in producing countries and retail prices in major consuming countries. All the statistics used are from the various issues of International. Tea Council (ITC) publications except for the data on stocks, retail prices, subsidies and'other s'uch variables. Efforts have been made to exclude green and other teas from the statistics. (i) Production: Data for each country are from ITC. From the world total, Indonesian smallholders production' in Java and Sumatra, and produc- tion in China and Japan has been excluded from the world totals, as  -9- most of this output is of green tea. Exports of black tea from China are treated as part of the world production in the model. This convention allows exclusion of production and consumption of tea in China from the model without causing distortions. (ii) Demand: The statistics used are those of ITC "Tea Imports for Consumption" and "Consumption of Tea in Producing Countries" with few exceptions. For the United Kingdom, "Apparent Consumption" is used. For Pakistan and the United States, net imports of green and other teas are excluded. Morocco is excluded from the model- as it mainly imports green tea for consumption. (iii) Prices: The "world" price is a value-share weighted sum of 4 major auctions (Calcutta, Cochin, Colombo and Mombasa) including sales tax, cesses and export duties. Prices used in supply equations are either auction prices excluding sales tax, cesses and export duties or the "world" price adjusted by exchange rates. Prices used in demand equations are retail prices for the United States, United Kingdom, India, Australia and Canada. In those cases where retail price data are not available the "world" price adjusted by exchange rates has been used. (iv) Stocks: "World stocks" used in the price equation is a simple sum of stocks held in United Kingdom, India and Sri Lanka, and denoted by TWS. In the simulation runs of the model, however, the world stocks are calculated as: WK = WK-1 + QW - CW where WK = End-of-year World Stocks QW = World Production CW = World Consumption  - 10 - The calculated values of WK for the period 1971-83 showed a correla- tion coefficient of 0.83 against TWS suggesting that treating TWS as world stocks is not inappropriate. In the ex-post simulation run, an error correc- tion term has been added to adjust the historical discrepancies between WK and TWS. For the ex-ante simulation runs, the discrepancy in 1983, the last year for which data are available, is assumed to persist throughout the period simulated.  - 11 - III. SUPPLY BEHAVIOR III.1 General Considerations This section deals with issues relating to the specification and estimation of relationships which jointly determine the production of tea in the world on an annual basis. The material is divided into three subsections. Sections III.2 to III.4 deal with, respectively: the general issues of speci- fication without emphasis on country-specific detail; the empirical results, on a country basis; and finally the comparison of behavior across countries-- at least in respect of certain key parameters. The empirical results are contained in Subsection III.5. In the case of tea, as also in the case of most tree-crops, when modelling the supply side careful attention has to be paid to four features of the production process: (i) the existence of a biologically-determined gestation lag between planting and obtaining output (ii) the dependence of current production on current as well as on previous levels of inputs; (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. 1/ 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 supply theory is intrinsically dynamic. More specifically, if the productivity of trees varies with the age, for given levels of other variable inputs, then the age distribution of the 1/ When dealing with aggregate data, feature (iv) may not be ELS important as it would be in a microeconometric study.  - 12 - trees becomes important in determining feasible levels of production. The average yield curve for tea shrubs approximates a logistic curve, with the asymptote corresponding to maximum yield obtainable approximately 10 years after planting in the case of the traditional hybrid variety (slightly earlier for vegetatively propagated (VP) clones). There is no significant output in the first four years and yields gradually increase subsequently. 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 the stock of trees should be classified into three categories; less than five years old, between five and ten years old and more than ten years old. Furthermore, for countries like India and Sri Lanka which have been growing tea for a long time it would be helpful to disaggre- gate 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 these sources of heterogeneity in the capital stock, a major potential misspecification may be avoided by adopting the vintage capital approach to investment and production behavior. This point has been discussed at length in Trivedi (1985). In the next sub-section some of the implications of this approach are spelled out. III.2 Definitions, Assumptions and Basic Concepts Production possibilities are characterized by a vintage production function F[K(t,v),L(t,v)] where K(t,v) denotes "capital" of vintage v used at time t and L(t,v) denotes "labor" combined with K(t,v). "Capital" means  - 13 - homogeneous land planted with trees with some specified density and requiring fixed levels of other inputs such as fertilizers and pesticides. 1/ 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. 2/ Total output Q(t,v) is defined by Q(t,v) =Iq(t,v) (3.1) v where q(t,v) = F[K(t,v), L(t,v)]. (3.2) Average productivity or yield per unit of capital is given by q(t,v)/K(t,v). Assuming constant returns to scale, this can be derived from (3.2), 6(t,v) K(t,v) K(t,v) (3e3) In general 6(t,v) would depend upon the wage-rental ratio. Two interesting special cases are 6(t,v) = 6(t-v) (3.4) and 1/ In practice the issue is complicated by the existence of mixed stands of trees resulting from infilling of existing area. Removal and replacement of aged or damaged trees by younger trees means that a "capital" unit cannot be regarded as homogeneous. 2/ In the case of tea the assumption of homogeneous output is a simplifica- tion. Q(t,v) in equation (3.1) should be thought of as measured in units of "standard" quality. If the relative prices of different types of tea vary a lot, aggregation into "standard" units will be difficult.  - 14 - 6(t,v) = X(t)6(t-v). (3.5) In the case of (3.4) productivity depends only on the age of the trees, denoted t-v, and not upon the time at which they were planted.. In the case of (3.5) the productivity of trees of age (t-v) changes smoothly with time at a rate determined by the function X(t) which may be given a specific parametric form. Capital stock of vintage v at the end of period t, denoted K(t,v), obeys the capital depletion equation K(t,v) = K(t-1, v) - U(t,v) (3.6) where U(t,v) denotes uprootings or removals of vintage v capital in period t. By definition, K(t,t) = N(t) (3.7) 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 leads to a modified version of (3.7), viz. K(t,t) = N(t) + R(t) (3.7a) where R(t) denotes replantings. U(t,v), N(t) and R(t) are all non-negative.  - 15 - Trivedi (1985) presents a model of a competitive firm which chooses levels of U(t,v), N(t), R(t) and L(t,v) to maximize net discounted revenue. The optimization also involves the choice of the subset of m<ature vintages denoted V, v 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,v)} where v belongs to the set of uneconomic vintages, denoted V, is termed the 'stock of uneconomic vintages'. If v is the marginal vintage, then under certain conditions all vintages older than v will be uneconomic. 1/ The total feasible output, Q (t), is defined by Q f(t) = I 6(t,v)K(t,v) , v c V U V. (3.8) v 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 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 (1985). 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 1/ A more general possibility is that the subset of uneconomic vintages can belong-to any age class. Various possibilities are considered in Trivedi (1985).  - 16 - economic vintages. These in turn would imply a profit-maximizing level of output which is called planned output, and denoted QP. That is, *~~~~~~~~~ Qp(t) = F(K(t,v), L (t,v)) , v e V (3.9) v where asterisks denote profit-maximizing levels. Actual production will differ from planned production both because of stochastic supply stocks and because expectations will not be realized on all occasions.-Consider the log-linear identity Q(t) = Q(t) ( ) | Q(t) = QP(t)(Q( ) (3.10a) Qp(t) Q Ct) and let Q(t)IQp(t) = f(P(t)/Pe(t))u(t) (3.10b) where u(t) is the supply disturbance and P(t)/Pe(t) denotes the relative error of expectation. Then combining (3.10a) and (3.10b) and taking logs we obtain log Q(t) = ln Qp(t) + In (f(P(t)/Pe(t)) + ln u(t) (3.11) from which can be used to derive the long-term and short-run supply elastici- L S S ties, denoted 1Q p and Q p, respectively. nQ 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. The long-term elasticity, n is given by Q,P' sgvnb  - 17 - L = a In QP a In Pe a l (f(P/Pe)) Q Q in pe a ln P a ln P The first derivative on the right-hand side depends, of course, on the sensi- tivity of new plantings and replantings to variations in price and the second L S on the elasticity of expectations. If either is negligible, nQ1p and nQ p will be close. Equation (3.11) is the generic form of the supply equation used in this paper. The exact variant used in any equation explain-ng the supply response of any country will depend upon the way in which an equation for QP is specified and on the assumption made about pe. Figure 1 which follows gives a schematic representation of the links between the production process and related decisions. It should be read in conjunction with the notes that follow the diagram. Given the immediately preceding general outline and Figure 1, the immediate task now is to develop estimating equations for the main endogenous variables that appear on the supply side of the model. There will be some differences in the specifications used for different countries, since it is wished to incorporate both the institutional differences within a country and differences in constraints which apply to different countries.  Figure 1: A SCHEMATIC REPRESENTATION OF PRODUCTION PROCESS AND DECISIONS IN A PRICE-TAKING PRODUCING COUNTRY |Cpllmar kets D lnstitutionssanSUprooting/ infrastrucLurc- replanting _ _ _ - 1 ~~~~~~~subsi dies Nev plan ing Expected future subsidies profitability Productiveroorldpric Neo plcn acnge u Replratings rd eprocesions pi A r~~~~~~~otal hearia8 . ~~~~~~& non-bearinE {BiologicLl ageiia CurrenL |process Fu2nconomic 3 Technical Currernt Real labour improvemen t productive cotC stock - |Productive | |orld price| capacity | Exchange rate d i I I I~~~Local Ltxes I Elogenous Actheual currenA cre |supply t production rc  - 19 - Notes: Figure 1 is designed to explain the principle linlkages between zariables that appear in the supply side of the model. For the main producing aind exporting countries, viz., India, Sri Lanka, Kenya and Malawi, these are ti) new plantings, (ii) uprootings, (iii) replantings, (iv) the current ieasible level of production and (v) the actual level of production. Where data limitations are an operating constraint, or where the producing country is not 'large' in the relevant sense, only some of these equations have been fitted. The schematic representation of Figure 1 should be followed from the top and centre. Exogenous or pre-determined variables are arranged on the Extreme left and right and linked to the important endogenous variables in the centre. Several of these including, for example, the variable 'currently unprofitable bearing area' are not directly observed and the model does not have equations corresponding to them. Nevertheless, for expository reasons they# have been included in the diagram. The symbol (L) represents either a simple or a distributed lag.  - 20 - III.3 Specification of New Plantings and Replantings The task of specifying suitable models for explaining new plantings is complicated both by the diverse economic environments to which the model is intended to apply and by inter-country differences in data availability. The available data permit estimation of new planting equations for India, Sri Lanka, Kenya and Malawi. 1/ The first two are long established producers which have experienced little or no growth for a considerable period whereas the last two, especially Kenya, have shown a steady growth in production since the early 1960s. Production in Sri Lanka stagnated in the mid-1960s and has since declined. Production in India has continued to rise ,but not anywhere near as fast as in Kenya. Furthermore, most of the growth in new plantings in Kenya has occurred amongst the smallholders, 2/ who are probably subject to different economic constraints from the older and more established estate plantations in the same country. In general, it could be expected that the constraints on expansion would be rather different for new emerging producers than for the long established ones. Given these differences, a flexible model to explain new plantings is needed. The model which seems suitable for India and Sri Lanka is an error correction model (ECM) which is known to be consistent with decision equations 1/ The data from India distinguish between 'extensions' which represents increases in area and 'replacements' which represents new planting on virgin land. In the case of Kenya and Malawi the available data refer to the net change in the planted area; no separate figures for new plantings and uprootings are available. 2/ See Schluter (1982).  - 21 - derived from dynamic optimization in the presence of convex adjustment costs.l/ Specifically, N(t) - N(t-1) = al(N (t) - N(t-1)) + a2(N(t-1) - N*(t-1)) N(t) = a1AN (t) + (al - a )N (t-1) + (1-a + a )N(t-l). (3.12) 1 ~~1 2 1 2 A priori it is expected that 1>a >0, a2<0 provided N(t) is always positive. The fact that N(t) can be zero whenever a corner solution is optimal is a p)roblem. N *(t) denotes the desired level of new plantings in period t. The objective of new plantings is to obtain some desired level of capacity output i.n period t+G where G is the-gestation lag. Denote this level by QP(t+G) and assume that it has been calculated conditionally on expectations about future profitability. If no new planting were undertaken between period t and period t.+G, the feasible level of production would depend upon the current feasible production level, Qf(t), and on the additional production from currently planted but immature vintages. The profitable level of production would be at nost equal to Qf(t), and the profitable level anticipated at t would depend upon expected future prices. Denote this level by QP(t). Specify that if QP(t+G) > QP(t), then N (t) = O[Qp(t+G) - Qr(t)], 6>0 (3.13) which means that the rate of new plantings is an increasing function of the eKpected shortfall in profitably-usable capacity. Once again, the presumption L/ See Nickell (1985).  - 22 - that N*(t) is non-negative is troublesome, since the expected shortfall in capacity can be negative. If the shortfall is negative there may be an incentive for uprooting or replanting of unprofitable trees. Let QP(t+G) be linear in two sets of variables Z, and Z2 which are determinants of expected future profitability and which will be specified later, and let Qp(t) be linear in ZI; 1/ that is, Qp(t+G) = f Z (t) + g Z ( (3.14) 1 1 g1Z2(t Qp(t) = f2ZI(t) (3.15) where fl, f2 and g, are vectors of parameters. Combining (3.12) - (3.15) leads to, N(t) = aI[6(f -f2) (Z1(t) - z (t-1)) + og1(z2(t) - Z(t-) + (ai-a2) K[(f -f2) Z1(t-l) + g Z2( t-)] + (1-ac +a2) N(t-1). (3.16) which is the type of equation estimated for Sri Lanka. 1/ Slightly greater generality can be achieved by allowing QP and Qp to depend upon, respectively, Z1 and Z2 and Z, and Z3. That is, Z1 is the common subset of variables and Z2 and Z3 are specific toQP and QP, respectively.  - 23 - As usual in error correction models, the right-hand side variables appear in first difference and also in (lagged) level form. Notea also that if corresponding elements of vectors f, and f2 have the same sign a priori, the coefficients of levels as well as the first differences of Z, are ambiguous in sign. Those of (Z2(t) - Z2(t-1)) and Z2(t-1), however, are not. The broad concept of variables which influence expected future profitability subsumes a variety of specific factors and can accommodate a number of ways in which those specific variables can be introduced into the equation. Two determinants of expected profitability are 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 plantings, but it may also make the existing capital more profitable and cause previously unprofitable capital to become profitable and hence lead to postponement of uprootings and replantings. Thus the net effect on the level of new plantings may be unclear. If the existing zapital stock is large relative to the level of new plantings, the negative effect may well dominate. In the same way 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 could lead to scrapping of exist- ing capacity to such an extent that the net effect may well be to stimulate new plantings. There are some factors, subsumed under Z2, which will affect QP(t+G) but not .QP(t). Examples are new planting subsidies and embodied technological progress, both of which will reduce the marginal cost of new planting and hence stimulate it.  - 24 - 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 the unobservable variable Qp(t) is proportional to Q (t)--e.g., Qp(t) is k times Qf(t). The latter denotes estimated feasible output which could be measured using (3.8), given 6(t,v), although in general this would lead to a measure- ment error. If this assumption is employed, the estimating equation will have the following form: N(t) 1f(zl(t) - Yt-1)) + g1(Z2(t) - Z2(t-1)) + (a1 1Z(t-1) + g Z2(t-1)] - a1Ik(QV(t) - Qf(t-l)) - (Ct1-a2 )kQ (t-l) + (l-a 1+a2)N t-l (3.17) (This is the type of equation used for India for which no data are available on cost of production.) If a >a2' both Q (t) and AQ (t) will enter the equation with a negative sign. The use of Q in place of Qf (3.17), however, will involve a misspecification error (due to the use of the proportionality assumption) whenever the scrapping of capacity moves in a highly variable fashion. Before proceeding to another variant of the new planting equation it is worth noting that equation (3.17) incorporates a complex dependence between the existing capital stock and new plantings. This is captured directly via the proxy for the QP variable in (3.17); in (3.16) it is captured indirectly  - 25 - via variables which influence the rate of discarding of old capacity. However, since the magnitude of the unprofitable productive capacity is not directly Dbservable, it seems desirable to include variables which would capture the effects of both physical and economic obsolescence. Equation (3.16) does not adequately capture the first and equation (3.17) does not adequately capture the second. Consider now the variants of the new planting equation which have ibeen used for Kenya. In this case the specification for the smallholders is different from the rest. Since the new plantings of smallholders in Kenya ;hows a strong trend-type behavior, the ECM specification developed above iieeds to be modified. An ECM model for the rate of growth of new plantings expressed as a proportion of existing smallholder area, denoted r(t), seems riore appropriate (see below for the rationale) r(t) -r(t-1) = y(r'(t)-r(t -1)) + y (r(t - 1)-r* (t-1)) or r(t) = yI(r*(t)-r*(t - 1)) + (y -y ) r(t-l) + (1-y1+y2)r(t-1) (3.18) where a priori y>?O, Y2<0 and r(t) = N(t)iA(t-1), with A(t-1) being the total area under smallholder production at t-l. r (t) denotes the desired rate of expansion; its precise specification is not needed at this juncture. Given the strong trend in smallholders' new plantings the choice of r(t) has the merit that it ensures the model has the property of trend neutrality. This would not be so if N(t) was chosen to be the dependent variable. If the previous  - 26 - specification for N(t) were adopted, wherein N*(t) incorporated a trend component, the standard partial adjustment model would imply that once N(t) and N*(t) begin to diverge the discrepancy would never be made up. In contrast the model of (3.18) applies the partial adjustment principle only to the deviations from the trend growth rate. See Pagan (1985) for a discussion of higher-order error correction models. Note that this specification implies a different type of costs-of- adjustment specification from the one which implicitly underlies (3.16). In the present case, costs of adjustment arise from growth of new plantings exceeding or falling short of the optimal rate r (t), whereas in the former case they arise from N(t) being different from N (t). This latter specifica- tion seems appropriate in certain cases such as for Kenya smallholders. Theoretical analysis shows that planned uprootings and replantings are interrelated decisions not only in the sense that uprooting (U) precedes replanting (R) but also in the more substantial sense that they are jointly determined--i.e., 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 the preferred strategy would be to develop a behavioral model for {U(t)} and relate {R(t)} to {U(t)} through a simple distributed lag model. Unfortunately, however, data on both U(t) and R(t) are available only for Sri Lanka. For India, data are available only for R(t). For relatively new tea producers such as Kenya and Malawi, for which only the data on net new plantings are available, uprootings and replantings are not thought to be important. An estimating equation for either U(t) or R(t) can be derived from a vector error correction model (VECM) as follows:  - 27 - AU(t) U7 1 2 l(t)-U(t-l)l l 91 1V U(t-l)-U*(t-l)" 1 ~~12 1~~ 1(3.19) AR(t) 21 I22 it (-R(t-l) *21 22 R(t-l-R (t-l) where U and R denote, respectively, the desired rate of uprooting and replanting. Planned uprooting followed by replanting depends upon the stock of unieconomic capital and on the expected future profitability of production. As before, these variables- are subsumed in the vector Z(t) and it is assumed that U (t) and R*(t) are!both linear in Z(t), i.e., U (t) = h Z(t) and R (t) = hZ(t). Substituting these into (3.19) and expanding, the following 2 ecuation for U *(t) is obtained: U(t) [ 11 h+ p12h21 (Z(t) - Z(t-1)) + I I 11 1 -12h2 v 11h1 1 v12h2] Z(t-l) + (1-v11 - "ll) U(t-l) + (v12 12) R(t-). (3.20) A similar equation can be obtained for R(t) if desired. The main difference between this and the scalar ECM is the appearance of R(t-l) in the equation with 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 ifp.11 and v 1 are positive, the coefficients of Z(t) and AZ(t) have their signs determined * I by the signs of the corresponding elements of h and h which (it is expected) 1 2  - 28 - 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. Now consider the determinants of U (t) and R*(t). As in the case of N (t) the ultimate objective of uprooting and replanting is to eliminate the gap (Qp(t+G) - QP(t)). Therefore, variables which enter the U(t) and R(t) equations should be the same as those in the N(t) equation, with the qualifi- cation 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 is the case in the N(t) equation. (See discussion immediately preceding equation (3.17).)  - 29 - I]I.4 The Supply Equation III.4.1 The Basic Specification The supply equation for the model is based on (3.11). However, more detailed discussion needs to be provided about the calculation of QP(t) and the choice of a suitable functional form. Both these steps involve important simplifications and approximations. Details vary considerably even for the three major produ'cers--India, Sri Lanka and Kenya. For the remaining countries the specification of the model is rather crude. First, it is assumed that actual and potential output are related by the following equation: Q(t) = A'(Qp(t)) (P(t)/Pe(t))8u(t) (3.21) where A is an unknown scale factor and 0 is the unknown elasticity of Q with respect to P. If Pe(t) in (3.21) is the same Pe(t) that determines QP(t), then Pe(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 Pe(t) are directly observable, additional assumptions are required to reduce (3.21) to a suitable form for estimation. Begin with the identity QP(t) = Qf(t)QP(o/Qf(t)- (3.22) Let Q (t) denote measured feasible output calculated under the assumption of a given (not necessarily profit-maximising) age-yield profile and assume that (i) Q (t) = kl(Qf(t)) , k1, c>O (3.23)  - 30 - and GO fP = k 2IT P(t-i) i, B. > O. (3.24) Q (t) i=O f f The difference between Qf and Q arises from the possible error in calculating Q from an "average" age-yield profile. The justification for (3.24) is that the profit-maximising level of output is an increasing function of the pro- ducer price whereas Qf(t) is definitionally determined, given past decisions. Furthermore, lags are introduced in (3.24) to take account of the dependence of current yield on past inputs such as fertilizers. Whereas it is expected that the unknown value of m would be a small integer such as 1 or 2, the issue is empirical. Combining (3.21) - (3.24) and taking logs we obtain the basic supply equation: ln Q(t) = ln(A k k2) + e ln Q (t) + (a0+e) ln P(t) m - ln Pe(t) + l in P(t-i). (3.25) i=l1 To convert this equation to a form suitable for estimation the following steps are necessary: (a) either make specific assumptions about the relation between Q (t) and observable variables such as past new plantings or precal- culate Q (t); (b) make> a specific assumption about how expectations are formed; and (c) fix the value of m. With respect to (a) the premise approach on takes will depend on the data constraints; with respect to (b) it is assumed *that In pe is a linear function of past values of P which is, strictly speaking, inconsistent with the approach elsewhere in the paper  - 31 - end, finally, with respect to (c) an empirical approach is taken and m is fixed at 1, 2 or 3. 1/ III.4.2 Alternative Specifications for Q (t) Since it is desired to take into consideration the differences in the average productivity of capital (trees) of different ages and the effects of disembodied technological change on the age-specific yields, a distinction is made between known total productive capacity (feasible output) existing at some arbitrary origin, denoted Q(O), and the subsequent additions to that capacity arising from new planting and replanting in subsequent periods. Let Q)f(t) denote the former and Qnf(t) the latter; then If ~ f t 4 nf Q(t) (t) + Qnf(t) . (3.26) A:;sume that old capacity Q(O) is changing at an unknown proportionate rate X>, which reflects the joint effects of disembodied technological change and oi the reduction in productivity due to aging; Qof (t) = ex2tQ(O). (3.27) Given data on total newly planted and replanted areas from t=l onwards, and given the normalized age-yield profile 6(t-v) known up to a proportionality ccnstant B(0) (i.e. 8(0)&(t,v) gives the productivity in physical units of capital of age (t-v) in period 0), it is possible to construct an index of the ptoductive capacity contributed by additions to the planted area since time 0. t Denote this by B(0) I 6(t-v)N (t-v) where N (t-v) is the cumulated sum of new t-v=l 1/ A consequence of this approach is that coefficients of P(t-l)*, P(t-2),... P(t-m) could be ambiguous in sign. Empirically, it is found that these coefficients are usually positive when statistically significant.  - 32 - plantings and replantings of age (t-v) at time t. I/ O(0) is the productivity of mature vintages in period 0. Finally, assume that &(t-v) is also subject to disembodied technical change at a constant proportionate rate X (>O if pro- ductivity is increasing). That is, Q (t) = B(O)exlt(I 6(t-v)NW(t-v)). (3.28) Combining (3.25) - (3.28) yields Variant 1 of the "vintage" supply function. In Q(t) = In A + In t(0) I(t_v)N+(v) X e Q() m + (s +0)ln P(t) - 0 ln P (t) + . ln P(t-i) + u(t) (3.29) which is nonlinear in the unknown parameters .(A,B(O), X1, X2, 0). The expres- sion inside the square bracket 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 , 6(t-v), Q(O) and an appropriate proxy for Pe(t), (3.29) can be estimated by nonlinear least squares. Data permit such estimation for two major producers, India and Sri Lanka, whose age-yield profiles appear to have changed through time. Though straight-forward in principle, the estimation of (3.29) in practice poses difficult problems of identifiability, as will be seen in Section TT1.5. 1/ There could be an important aggregation problem here if different kinds of trees are planted at different times.  - 33 - III.4.3 A Special Case of (3.29) If (a) Q(O) = 0 and (b) the age-yield profile is approximately constant such that Xi= 0, (3.29) simplifies to the log-linear equation which is Variant 2 of the vintage supply function: ln Q(t) = ln A + In [E 6(t-v)N (t-v)] + (8+0) ln P(t) - 0 ln Pe(t) + Ea. In P(t-i) + u(t). (3.30) I In certain cases (e.g., Kenya estates) it was necessary to allow for changing yields through time. It was possible to construct with Kenyan data ttiree time series corresponding to planted area 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 age-class 'older than 10 years'), a weighted area measure, denoted WAREA, was constructed. Then, variant 3 of the vintage supply function which may be thought of as the 'yield equation', was sDecified as follows: Q(t) Ae 1 (P(t)/pe(t))Ou(t). (3.31) WAREA(t (pe 3.1 (Note that this assumes that all age-groups share equi-proportionally in the increase in yield.) For the remaining countries the quality and quantity of data do not permit estimation of anything much more than simple variants of (3.25), u:;ually based on the assumption that Qf(t) is a function of a linear or quadratic time trend. This specification will be referred to a Variant 4 of the basic specification. It makes essentially no use of any data of a vintage nature.  - 34 - III.5 Empirical Results III.5.1. Computation of the Index of Feasible Production To calculate Qf(t) as defined in (3.26) - (3.29) involves the unknown parameters B(0), X1 and X2.The first task is to construct. an index of the productive capacity added by new plantings and replantings, denoted ZE(t-v) N+(t-v). The coefficients in the sequence R(t-v)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. Available information concerning the base period, derived from World Bank project reports, is summarized in Table 2. It is assumed that in those countries such as India, Kenya and Malawi where the yields are rising 1/ the increase is spread over all age groups. The base period profile is taken to be the same in India and Sri Lanka. In India and in 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 from 0.8 to 1.8 percent in India and from 0.9 to 1.4 percent in Sri Lanka. (The latter figure should be treated with caution because of uncertainties about the planted area.) In contrast, the annual average growth rate of planted area for Kenya smallholders has been at nearly 17 per cent over the period 1963-83; though the rate has declined to around 4 per cent in the last five years. 1/ Such information as is available fails to distinguish between the productivity of new VP varieties and the older hybrids.  - 35 - Table 2: BASE PERIOD AGE-YIELD PROFILES 0 i 2 3 4 5 6 7 8 India 1952-(a) 0 0 .074 .299 .449 .599 .749 .899 1 -(b) 0 0 70 281 422 563 704 845 939 Sri Lanka -(a) 0 0 .074 .299 .449 .599 .749 .899 1 L956 -(b) 0 0 76 303 455 608 760 912 1014 Kenya -(a) .199 .399 .399 .798 .899 .899 -(b) 0 0 0 206 412 412 824 928 928 (a): Proportion of peak output at different ages prior to full rnaturity. (b): Yield in Kg/hectare at different ages. k: Applies to smallholders only. III.5.2 New Planting and Replanting Equations In both India and Sri Lanka new planting and replanting are subsi- dized. Information about the subsidies in India remains very sketchy and it is hoped that the estimated new planting and replanting equations cam be revised at a later date when more detailed and accurate information has been obtained. There are indications that such respecification and reestimatiort is required. In the case of Sri Lanka, uprooting and replanting subsidies are more important relative to the new planting subsidies. However, there are a number of subsidy schemes in existence and they have changed considerably over the years, so the computation of total value of subsidies is a somewhat involved matter. In Kenya it is important to distinguish between the behavior of smallholders, who account for nearly two-thirds of the area but only one-third of the production, and that of the. estates which have been producing tea for several decades. (Etherington 1973; Schluter 1982; Lamb and Muller 1982). Net new plantings have thereEore. been disaggregated into smallholder and estates  - 36 - categories. The former (but not the latter) shows a strong trend-like behavior which cannot be readily understood without reference to the historical and institutional factors. These have been studied by Etherington (1973) and by Lamb and Muller (1982). The former author has stressed the stimulative effects of the removal of legal restrictions on the cultivation of tea by smallhoLders at a time when tea was an alternative cash crop; the latter 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 infrastructure and increased the profitability of tea production to the smallholder. The specification used here, therefore, pays. attention to these factors. 1/ A measure of this role is KTDA development expenditure (including the expenditures 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. For Kenya smallholders the model used for replanting is equation (3.18). To complete it a specification of r (t) is needed. Specify r'(t) to be linear and increasing in (i) real per hectare investment expenditure by the KTDA, denoted E(t), and (ii) the real producer price PR(t). That is, r (t) = a1E(t) + a2PR(t) + ao, and r(t) = y1[alE(t) - E(t-l)) + a2(PR(t) - PR(t-l))] 1/ From an analytical viewpoint such factors are akin to subsidies which increase the net producer price and hence the actual and expected profitability.  - 37 - + Y2) [a1E(t-L) + a2PR(t-1)] + (l-y1, 4 y2)r(t-1) + (y1-Y2 0. (3.32) rhe main justification for this specification is that the Kenya. smaliholders probably did not face an area constraint in this period and that: the critical Limitation arose from access to planting material, credit facilities, fac- tories for processing tea leaves and expertise in the marketing of the leaf. ro the extent that the KrDA provided these facilities, it made it easier for the smallholder to take up growing tea. It is postulated that by maintaining a constant real rate of development expenditure 1/ per hectare the KTDA would enable more smallholders t,o undertake tea production and to maintain a steady growth in new plantings. Of course, this assumption is reasonable only as long as the availability of suitable land is not a binding constraint. Eventually, such a constraint will become binding and this would imply a different kind of adjustment cost function. Consider now the net new plantings of Kenya estates. In absolute terms new planting activity of the estates is small compared with that of the Kenya smallholders. It is also highly variable. The main difference between the behavior of the estates and smallholders in the specification is that it is hypothesized the former to be active at the intensive margin and the latter at the extensive margin. Specifically, any improvement in expected profit- ability, arising from (say).an increase in the real price of tea, causes more 1/ Actual real rate of expenditure per hectare (KEXPPH) declirned after 1969 but stabilized after 1980.  - 38 - smallholders to enter tea production, whereas, it causes estates to increase production at the intensive margin by greater use of yield-increasing agricul- tural practices. (The yield-price relationship has been discussed elsewhere.) A general model of production and demand for inputs clearly does not rule out the possibility that a firm may respond to higher product prices by raising its production through more intensive utilization of variable inputs. Given sufficiently high adjustment costs of fixed inputs this may be an optimal response. 1/ The empirical fact that in the case of the estates in Kenya yields per hectare 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, a variant of (3.12) has been combined with the following specification of new plantings N (t), N (t) = c0 + c YLD(t) (3.33) 0 1 cl<O. Note that YLD(t) is an endogenous variable. This leads to an equation in which new plantings depend upon the yield and the change in yield as well as lagged values of new plantings. In the case of Malawi a similar equation has been used but it has also been assumed that the yield is a function of past real producer prices and a time trend. The justification for specifying the Malawi equation in the same way as for Kenya estates is that the estates in Malawi account for a 1/ Although no concrete data is available, land prices in Kenya have been increasing at a rate much faster than the general consumer price index in recent years.  - 39 - predominant part of total output 1/ and, it is assumed, most of the rather small absolute amount of new plantings. The estimated equations for India (extensions and replantings), Sri Lanka (new plantings, uprootings and replantings), Kenya smallholders (rate of growth of area planted), Kenya estates (net change in planted area) and Malawi ,net increase in planted area) are given in Table 3. For Sri Lanka actual R(t) is specified as a finite distributed lag on current and lagged values of U(t); thus, m R(t) =I w U(t-i) (3.34) i=O where