This paper provides some short term ex ante forecasts of Malaysian crude palm oil prices. The forecasts are derived from a multivariate-autoregressive-moving average (or MARMA) model which integrates the normal autoregressive-integrated-moving average (ARIMA) model for the residuals into an econometric equation estimated beforehand. The MARMA and econometric models are estimated and tested individually in terms of their comparative forecasting accuracy. The results seem to indicate that the MARMA model produces a relatively more efficient forecast than the econometric model. The MARMA model is then used to generate ex ante forecasts for the period of January 1999 to June 1999. The forecast figures are then discussed in relation to the current and expected fundamentals of the palm oil market.

One of the salient features of the oils and fats market, palm oil in particular, is price variability and volatility as depicted in Figure 1. Larson (1991) and Fatimah (1991) suggest that selected vegetable oils – such as soybean, palm oil, groundnut and coconut – exhibit significant volatile behaviour as measured by the instability index. The instability index for palm oil is estimated at 2.24 compares to cocoa 1.46 and rubber 1.42. Fatimah (1991) indicates that the Mac Bean Index for palm oil stands at 2.1 compares to 1.7 and 0.9 for rubber and timber respectively. The price instability and hence uncertainty pose a significant challenge to decision makers in coming up with proper production and marketing plans to minimise risk. Price forecast therefore, is vital to facilitate efficient decisions as there is a time lag between making decisions and the time at which the outputs flowing from these decisions reach the market place. An efficient decision is when the forecast prices and quantities correspond to realised market prices and quantities.

Like any other fats and oils, palm oil price is a function of both fundamental and technical factors; ie. price is determined by the interaction of market forces as well as nonmarket forces and barriers to trade. The interplay of market forces is characterised by the unique features of the fats and oils complex. Among these features are: extent of substitutability and interchangeability of fats and oils and the technological improvements in refining and use of fats and oils. The complexity of the interplay of a number of market variables causes the instability of the fats and oils prices.

Visual examination of the price trend of palm oil between 1980 – 98 suggests some significant observations. Firstly, in the last two decades there is no clear increasing trend for palm oil prices. The price ocsillates around RM1000/tonne. Secondly, the price series exhibit a number of prominent short term peaks around 1983-84, 1988-89, 1994-95 and lately 1997-98. Currently palm oil is enjoying high price at RM2138 (as at 21 January 1999 (PORLA 1999)). Short term troughs are also prominent in the series.

In the short term, price movements of fats and oils (including palm oil) mainly reflect changes in weather conditions, in inventories, in exchange rates, and in the prices of substitutes. The two major peaks observed in the series are in 1983-84 and 1997-98. The earlier peak was the result of several coincidental factors, including (a) the sharp drop in the US soybean crop in 1983 stemming from the Payment in Kind (PIK) programme and the prolonged hot and dry weather and (b) the reduction of in Malaysian palm oil output due to combination of overstressed palms following the introduction of pollinating weevils from Cameroon, reduction of fertilizer application due to poor palm oil prices earlier; and (c) the fall in copra output in the Phillipines following a long period of drought and effects of typhoons.

The year 1997-98 saw another significant peak for palm oil price where it reached RM2400 in May 1998. This was the period where Malaysia and her neighbours suffered the worst financial crisis ever recorded. Despite the crisis, most oils have held up relatively well. Soybean and coconut prices rose 11-12% and palm oil prices were up a whopping 34% compared to the previous year. The short term factors that contributed to the increase can be summarised as: oil stocks are low, reduction in the soy bean productivity (despite ample supply) which is inadequate to compensate the current supply lossses in palm oil, uncertainty in the crisis-stricken country such as Indonesia and its negative bearings on her palm oil investment and weather abnormalities particularly the impact of El Nino which resulted in unprecedented dryness in Malaysia, Indonesia and the Phillippines. Besides, the weak Ringgit boosted palm oil export prices in Ringgit equivalent as all exports are quoted in US dollars.

Clearly the latest price increase in palm oil begs the question whether it is sustainable at least in the short run. This paper aims at answering this question, ie. providing some short term forecasts of palm oil price taking into account some of the major market factors that are crucial in the price determination.

Forecasting involves making estimates of the future values of variables of interest using past and current information. There are a number of methods to generate prediction ranging in intuitive judgements through time-series analysis to econometric models. Technical analysis is another popular alternative despite its major inherent weaknesses: it lacks sound theoretical foundation and does not provide economic explanation of its forecasts. Nevertheless each forecasting technique has its own strength and weaknesses. For instance, the Box-Jenkins univariate procedure is noted for its accuracy but was criticised as void of theoretical explanation. An econometric model provides a better alternative as it has the properties of being able to incorporate the structural relationship between a number of variables into the equation and reflects their influence on the forecasted variable.

A number of studies have indicated that a combination of econometric and univariate approaches into a composite model yields efficient forecast (Bates and Granger, 1969, Granger and Newbold, 1977, Brandt and Bessler 1981, Blisard, 1984 and Mad Nasir et al., 1993). The rationale for this combination is to retain the structural relationship extracted from the econometric method while using the time series model to explain the residuals. Another modification is the integration of econometric with the time series model for the residual series which is known as transfer function model or multivariate autoregressive-moving average (MARMA) model. According to Ludwig (1974), this model can provide efficient forecast as it includes a structural explanation of that part of the variance of forecasted values that can be explained structurallly and time series "explanation" that cannot be explained structurally. Mad Nasir (1993) has indicated that MARMA’s forecasts outweigh the individual forecasts of each of the other models in terms accuracy and efficiency.

This paper attempts to apply MARMA modelling on palm oil price analysis to generate short term price forecast. The following paragraphs describe the MARMA method. This is followed by the discussion of the results and conclusion.

MARMA Model

The multivariate autoregressive-moving-average (MARMA) model is well documented in Box and Jenkins (1976), Madridakis and Wheelwright (1978) and Pindyck and Rubinfeld (1981). A brief description of the model is discussed below.

Suppose that one would like to forecast a variable y_t using an econometric model. Presumably such a model would include explanatory variables which could provide an explanation for movements in y_t but which are not themselves collinear. Let us suppose that the econometric model contains two explanatory variables, x₁ and x₂, as follows:

y_t = a₀ + a₁x_1t + a₂x_2t + e_t (1)

This equation has an implicit additive error term that accounts for unexplained variance in y_t, i.e., it accounts for that part of variance of y_t that is not explained by x₁ and x_2. The equation can then be used to forecast y_t. One source of forecast error would come from the noise term whose future values cannot be predicted.

By substracting the estimated values of y_t from the actual values, a residual series which represent unexplained movements in y_t can be calculated. An ARIMA model for the residual series can be constructed and used to make a forecast of the error term e_t. The ARIMA model provides some information as to what future values of e_t are likely to be. By substituting the ARIMA model for the error term in equation (1), we obtain,

y_t = a₀ + a₁x_1t + a₂x_2t + f ^-1(B)q (B) h _t (2)

where h _t is a normally distributed error term which may have a different variance from et. Equation (2) is likely to provide much better forecasts than the econometric equation (1) alone or a time-series alone since it includes a structural (economic) explanation of that part of the variance of y_t that can be explained structurally, and a time-series "explanation" of that part of the variance of y_t that cannot be explained structurally.

Equation (2) is referred to as a transfer function model or, alternatively, a multivariate autoregressive-moving-average (MARMA) model.

Econometric Model

A monthly Malaysian palm oil market model is formulated. The model consists of three behavioural equations and an identity (refer to Mad Nasir et al., 1993 for further details). The behavioural equations describe the production, consumption and price. The identity defines the stock level.

Supply

The specification of supply relationship is based on the model developed by Meganathan (1983). The supply of palm oil is postulated to be a function of lagged output prices and a time trend in an attempts to capture the intensity of harvest.

PRPO_t = f (PPO_t-i, T, S, E₁) (3)
where,

PRPO = production of palm oil (‘000 t)

PPO = price of palm oil (RM/t)

T = time trend

S = seasonal shifters

E₁ = error terms

The trend term reflects the technological factors that affect yield. Both of the yield and the varietal effects which increase the intercept of the yield function are jointly embedded in the time trend. It also accounts for the effect of mature trees becoming economically productive the first time.

The seasonality of the CPO production will be reflected through the seasonal shifters. Production of CPO exhibits a seasonal pattern which lasts about a year besides the increasing trend. In fact its seasonality index indicates a clear pattern where production normally reaches its peak in September (where the index stands at 133.98) and drops significantly in January (the index falls to 76.68). Early months of the year is characterised by slow growth in production. Hence, variables S which is a seasonal shifter is included to reflect the seasonality in the CPO production. Prices of alternative crops are not included as they represent longer-run considerations compared with the resource fixity of the short-run analysis.

Demand

Demand for palm oil is a derived demand as it is used as an input in the production of final products. The demand equation is derived based on the theory of the firm. It can be specified as follows,

Q_i = f (P_i, P_yi) i = 1,2,......,n (4)

where,

Q_i = quantity of input i demanded
P_i = price of input i and related inputs
P_yi = price of output

Thus the demand for palm oil can be specified as,

DPOt = f (PPOt, PSBOt, IPIt, T, St, E2) (5)

where,

PSBO = price of soy bean oil
IPI = index of industrial production

The index of industrial production represents the effect of changes in economic activity on the demand for palm oil-using manufacturers. A time trend is introduced in the equation to represent growth trends exhibited by individual end-use items. These have largely been the result of technological factors (i.e., demand augmenting technological change through the discovery of new uses), population and income. Soybean oil is assumed to be a substitute product for palm oil in some uses.

Price

The price determination equation follows the model developed by Hwa (1979) and adopted by Tan (1984) and Mad Nasir, et. al., (1988). The price equation can be expressed as,

PPO_t = f (SPO_t, DPO_t, PPO_t-1, PPO_t-2, S_t, E₃) (6)
where,

SPO = stock of palm oil (‘000 t)

The price of palm oil is a function of the level of stock, consumption and the price in the previous periods. The price is expected to have positive relationship with consumption and one-period lagged price and negative relationship with stock and two-period lagged price. There exists an inverse relationship between CPO prices and stock levels the two variables, ie prices tend to peak during low level of stocks and vice versa.

Closing Identity

The model is closed by an identity,

SPO_t = SPO_t-1 + PRPO_t - DPO_t (7)
Equations (3), (5) and (6) are estimated using two-stage least squares. The sample period is from January 1981 to November 1998. The data is obtained from Palm Oil Update, PORLA, Oil World and Monthly Bulletin of Statistics, United Nations Statistical Office.

ARIMA Model

The autoregressive-integrated-moving average (ARIMA) model is discussed in detail in Box and Jenkins (1976) and O’Donovan (1983). Briefly, this technique is a univariate approach which is built on the premise that knowledge of past values of a time series is sufficient to make forecasts of the variable in question.

Box and Jenkins (1976) set four steps for this approach: model identification, parameter estimation, diagnostic checking and forecasting. The identification step involves the comparison of estimated autocorrelation and partial autocorrelation functions of known ARIMA processes. Given a class of ARIMA models from the first step, their parameter values can be estimated from the historical series using nonlinear least squares. Diagnostic checks are then applied to determine any possible inadequacies in the model, and the process is repeated if any are found. Finally, having arrived at an adequate model, "optimal" forecasts are generated by recursive calculation.

The general multiplicative seasonal autoregressive-integrated-moving average (ARIMA) model for a seasonal Zt = 1, 2,.....T with a known period S can be written as,

Æ _p (B) f _p (B^s) (1-B)^d (1-B^s)^DZ_t = q _q (B) q _Q (B^s) + e_t (8)

where,
e_t = a random disturbance assumed to be distributed as N(0, s ²)
B = a backward shift operator such that BZ_t = Z_t-1 and B^kZ_t = Z_t-k
Æ _p(B) = the regular autoregressive operator of order p,

i.e, Æ _p(B) = (I - Æ ₁B) - Æ ₂B² - .....Æ _pB^p)^p

f _p(B) = the seasonal autoregressive operator of order P

d = numder of regular differences

D = number of seasonal differences

q _q(B) = the regular moving average operator of order q,

i.e, q _q (B) = (I - q ₁B - q ₂B² - .....q _qB^q)

q _Q(B) = the seasonal moving average operator of order Q

s = the order of the seasonal difference 

Equation (8) is an ARIMA model of order (p, d, q) (P, D, Q)_s. 

Econometric Model
 
The estimation of the monthly palm oil model are presented in Table 1. The figures in parantheses are t-values of the estimated coefficients. The model as a whole appears to fit the data well, as evidence by R² and the t-value.

In the supply equation, the explanatory variables explain about 95 per cent of the variation in the monthly palm oil supply. The price variable is significant at the 5 per cent level. The model indicates a clear seasonality in CPO supply as evidenced by the statistical significance of the monthly seasonal shifters.

The estimates obtained for the demand relation are consistent with a priori expectations. The price of palm oil is at the 1 per cent level. The industrial production index variable and the price of soybean are significant at the 5 and 10 per cent levels respectively. Four seasonal shifters (February, August, September and October) are significant. The equation as a whole explained about 92% of the variation in demand.

Table 1: Estimated Structural Equations

PRPO_t = -21.278 - 0.018 PPO_t-4 + 0.954 PRPO_t-1 - 3.966 FEB + 57.958 MAR
                                    (2.072)                 (7.994)                 (-0.282)             (3.783)

                    + 45.902 APR + 51.903 MAY + 38.848 JUN + 76.704 JUL + 74.181 AUG
                            (3.265)             (3.690)             (2.765)             (5.461)             (5.253)

                     + 72.293 SEP + 11.304 OCT - 39.289 NOV - 54.794 DEC
                            (5.071)                 (0.782)         (-2.728)             (-3.802)
R² = 0.947 h = 0.166
DPO_t = -32.799 - 0.051 PPO_t + 0.053 PSBO_t + 0.248 DPO_t-1 + 1.825 IPI_t
                                (-3.329)             (1.788)                 (3.869)                 (2.455)

                    + 1.370 TIME - 76.700 FEB + 2.016 MAR + 2.024 APR
                            (4.445)             (-4.742)             (0.110)             (0.125)

                    + 12.639 MAY - 15.132 JUN + 20.202 JUL + 57.572 AUG
                            (0.779)             (-0.931)             (1.235)               (3.522)

                    + 50.039 SEP + 55.032 OCT + 10.664 NOV + 19.762 DEC
                            (2.986)             (3.282)                 (0.634)             (1.191)
R² = 0.923 h = 0.272

PPO_t = 113.427 - 0.149 SPO_t + 0.233 DPO_t + 1.125 PPO_t-1 - 0.191 PPO_t-2
                                    (-2.946)             (3.316)             (16.327)         (-2.749)

                        - 53.242 FEB - 115.794 MAR - 55.451 APR - 60.185 MAY
                                    (-1.576)         (-3.228)         (-1.644)         (-1.791)

                        - 99.243 JUN - 128.257 JUL - 80.943 AUG - 56.938 SEP
                                    (-2.986)         (-3.834)         (-2.373)         (-1.706)

                        - 44.495 OCT - 5.593 NOV - 26.346 DEC
                                    (-1.337)         (-1.167)     (-0.781)
R² = 0.944 h = 0.316
SPO_t = SPO_t-1 + PRPO_t - DPO_t
Note: Numbers in parentheses are t-values

All the estimated coefficients in the price equation show the expected signs. The results suggest that the price of palm oil is highly dependent on the stock level, demand and the price in the previous periods where they are significant at the 1 per cent level. The coefficients of the seasonal shifters are negative and significant at the 5 per cent level, except for February, April, May, September, October, November and December. This implies that the price of palm oil in January is generally higher than the rest of the months in a particular year.

Model Evaluation

In this section, the estimated econometric model is evaluated to ascertain the adequacy of the model in forecasting. It is first simulated during the estimation period to produce what is called as historical simulation. Secondly, the model is simulated forward in time beyond the estimation period or ex post simulation. The forecasting ability is tested based on the root mean square per cent error (RMSPE) and Theil’s inequality coefficients (U) criteria.

Historical Simulation

The results of the historical simulation are presented in Table 2. The RMSPE of all the endogenous variables are all small (less than one per cent). The values of U are all less than one suggesting the superiority of the model over the naive no-change model. The values of U^m are all very closed to zero, indicating the non-existence of a systematic bias. Thus a revision of the model is not necessary. The values of U^s are also very small which indicate that the model is able to replicate the degree of variability in the variable of interest.

Ex Post Simulation

The estimated model is again simulated to generate ex post forecasts of crude palm oil prices from January to December 1998 (Table 2). The value of the RMSPE which measures the deviation of the forecasted value from its actual value in percentage terms is 0.1. The Theil inequality coefficient is less than one. These figures indicate that the forecasting performance of the estimated model is satisfactory.

ARIMA Model

An ARIMA models is constructed and applied to the residual series of the price of palm oil equation. After following the Box-Jenkins procedure of identification, estimation and diagnostic checking, the model of (1,0,1) was chosen.This model involves a first order differencing and a second order autoregressive element. The model is then fitted into the residual series from March January 1981 to December 1998 which yield the following estimates (with t-values in parantheses):

Æ ₁ = 1.1956 (17.841)

Æ ₂ = -0.225 (- 3.352)

The diagnostic checks indicate that none of the ACF and PACF of the residuals are significant. Thus the ACF and PACF of the residuals do not detect any model inadequacies. The Box-Pierce Chi-Square Statistic Q has the value of 22.469, which is less than the critical value of Q. This test also does not detect any model inadequacies.

The estimated model is then used to obtain the residual forecasts for the six months beginning from January 1999.

Note: U^m - fraction of error due to bias
U^s - fraction of error due to variation
U^c - fraction of error due to covariation

The ARIMA (2,1,0) model of the residual series is combined with the econometric model to produce forecast of crude palm oil prices. The results are presented in Table 3. One can observe that the forecast series are much closer to the actual series than is the case when the econometric model is used, where the RMSPE is reduced by 4.5 per cent. The values of the RMSPE and U are comparatively smaller than the values generated by the econometric model. These statistics suggest that the forecasting performance of the MARMA model is more efficient than the econometric model.

Ex ante Forecast

The projection of the exogenous variables in the econometric model are made in the following manner:
1) Technology, population and income
These variables are proxied by a time trend.
2) Industrial Production Index
The following steps are followed to arrive at the industrial production index forecasts (Meganathan, 1983). The countries selected are the major importers of Malaysian palm oil which includes China, Pakistan, India, USA, EEC, Australia and Japan. The detail calculation can be found in Mad Nasir et. al. (1993).
3) Price of Soybean Oil
The outlook for the price of soybean oil is extracted from Oil World (December 1998). World production of soybeans for the 1998/99 season is estimated at 154.8 million tonnes, down by 2.3 million tonnes from the 1997/98 season. The production of all the other 9 oilseeds, taken as a group, is esxected to increase considerably to 133.4 million tonnes, up by 5.1 million tonnes from the last season. Most of the increase will be in rapeseed, sunflower seed and groundnuts. On the demand side, world demand for soybeans increased at a robust rate throughout 1998. The opinion of Oil World is that the robust market will continue in the 1998/99 season. Total world disappearance of soybeans is projected to rise to 156 million tonnes. This will lead to a reduction of world soybean stock levels. Soybean prices are thus unlikely to decline instead it is expected to hover around the current levels of USD 615 per tonne.

The price forecasts for the months of February to June 1998 generated from the econometric and MARMA models are presented in Table 3. The price of CPO is projected to decline but remain firm to around RM2,200 per tonne in the middle of the year.

As shown in Table 2, MARMA’s ex post forecasts are more efficient measured either in terms of its statistical criteria or even by visual proximity with the actual prices. Based on its proven accuracy, the forecasts for the months of February through June 1998 are generated as summarised in Table 3. Based on these forecasts, CPO prices are expected to remain firm and will still be above RM2,000 per tonne.

These forecasts are plausible in view of the current fundamental scenario and the technical swing of the market for this commodity. The state of supply and demand for palm oil in particular and fats and oils in general is conducive towards sustaining a firm price of palm oil in next few months. Based on reports by Oil World (1998), on the supply side, supplies of edible oil is tight world wide. South East Asian palm oil production is expected to remain tight because of lagged effect of the El Nino phenomenun, the instability of the Indonesian economy and the palm oil export ban in Indonesia which is intended to increase domestic supplies and stabilize prices. The Malaysian palm oil production for the month of December 1998 was estimated to be 16% lower compared to November production (PORLA, 1999). These factors will lead to low oil stock in the short term in early 1999 before it begins to improve in the mid – or end- 1999 onward. The world oilseed production is estimated to increase by 0.9% between 1997/98 and 1998/99 period (Oil World, 1998). However the major oilseed that is soybean, is estimated to reduce its production by 2.31%. Reduction in other types of oilseed is also expected such as sesameseed, copra and castorseed.

The demand sector continues to exhibit strength despite the ASIAN crisis and a slow-down of demand in several of the affected countries. The world demand for soybean has continued at a robust rate throughout 1998 and it is expected to increase in 1999. In fact Oil World believes that the strong demand will result in a reduction of soybean stocks during the world crop season 98/99. Strong demand for soy bean will further support the firming of palm oil price at least in the short run.

BATES, J.M. and C.W. GRANGER (1969), "The Combination of Forecasting". Operation Research Quarterly, 20: 451-468.

BLISARD, WILLIAM N. (1985), A Comparison of Alternative Price Forecasting Models for Slaughter Hogs. Ph.D Dissertation, University of Tennessee.

BOX, G.E.P. and G.M. JENKINS (1976), Time Series Analysis, Revised edition, San Francisco: Holden-day.

BRANDT, J.A. and BESSLER, D.A. (1981), "Composite Forecasting: An Application with U.S. Hog Prices", American Journal of Agricultural Economics.

FATIMAH MOHD ARSHAD, MOHD SHAHWAHID OTHMAN, MAD NASIR SHAMSUDIN and ZULKIFLI SENTERI (1991), "Marketing of Agricultural Commodities – The Need for A New Approach," paper presented at the National Seminar on Agricultural Primary Commodities and Agenda for Structural Adjustment. MIER-UKM-UPM, 3-4 June, 1991. 

GRANGER, C.W.J. and P. NEWBOLD (1977), Forecasting Economic Time Series. New York: Academic Press.

HWA, E. C. (1979), Price Determination in Several International Primary Commodity Markets: A Structural Analysis, IMF Staff Papers, 26: 157-188.
 
LARSON, D. F. (1991). :A World Bank View on the Price Prospect for Palm Oil." Paper presented at the PORIM International Palm Oil Conference. Palm Oil Research Institute of Malaysia, 9-14 September 1991, Kuala Lumpur.

LUDWIG, R. S. (1974), Forecasting Short-Term Saving Deposit Flows: An Application of Time Series Models and a Regional Analysis, Unpublished Master’s Thesis, M.I.T.

MAD NASIR SHAMSUDIN, ZAINAL ABIDIN MOHAMED and FATIMAH MOHD. ARSHAD, (1988), "Selected Factors Affecting Palm Oil Prices", Malaysian Journal of Agricultural Economics, 5(1): 20-29.

MAD NASIR SHAMSUDIN and FATIMAH MOHD. ARSHAD (1990), "Composite Model for Short-Term Forecasting for Natural Rubber Prices", PERTANIKA, 13(2): 283-288.

MAD NASIR SHAMSUDIN and FATIMAH MOHD. ARSHAD (1991), "Short Term Forecasting of Crude Palm Oil Prices", in Yusof Basiron and Ahmad Ibrahim (eds), Proceedings of 1991 PORIM International Palm Oil Conference.

MAD NASIR SHAMSUDIN and FATIMAH MOHD. ARSHAD (1993), "Short Term Outlook of Crude Palm Oil Prices," paper presented at the PIPOC 1993 PORIM International Palm Oil Congress – Update and Vision", 20-25 September 1993, Kuala Lumpur.

MAD NASIR SHAMSUDIN (1993), "A Short-Note on Forecasting Natural Rubber Prices Using a MARMA Model", Malaysian Journal of Agricultural Economics.

MAKRIDAKIS, S. and S.C. WHEELWRIGHT (1978), Forecasting Methods and Applications, New York: John Wiley and Sons.

MEGANATHAN, S. (1983), "Monthly World Natural Rubber Model", Kajian Ekonomi Malaysia, Vol XX, No. 2.

O’DONOVAN, T.M. (1983), Short Term Forecasting: An Introduction to the Box- enkins Approach. New York: John Wiley & Sons.

Oil World (1998), The Weekly Forecasting and Information Services for Oilseeds, Oils, Fats and Oilmeals, December 11,Vol. 41(50):427-35.

PORLA (1999), http://161.142.157.2/home2/home/pr210199.htm, PORLA PALM OIL MARKET REPORT ON 21/01/99.

PINDYCK, R.S. and D. L. RUBINFELD (1981), Econometric Models and Economic Forecasts, McGraw-Hill.

TAN, C.S. (1984), World Rubber Market Structure and Stabilization: An Econometric Study, World Bank Staff Commodity Papers, No. 10.

Fma/pipoc99.doc/26jan99