• TABLE OF CONTENTS
HIDE
 Main
 Front Cover
 Acknowledgement
 Table of Contents
 List of Tables
 List of Figures
 Introduction
 Objectives
 Review of literature
 Theoretical considerations
 Economic and other variables in...
 Economic models
 Statistical procedures
 Empirical results
 Forecasting United States imports...
 Results of the forecasts
 Summary and conclusions
 Appendix
 Bibliography






Group Title: Agricultural Economics report 28
Title: An econometric analysis of United States import demand and prices of natural rubber
CITATION PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00027480/00001
 Material Information
Title: An econometric analysis of United States import demand and prices of natural rubber
Physical Description: iv, 54 l. : illus. ; 28 cm.
Language: English
Creator: Ahmad Mahdzan Ayob
Prato, Anthony ( joint author )
Publisher: Dept. of Agricultural Economics, University of Florida
Place of Publication: Gainesville
Publication Date: 1971
 Subjects
Subject: Rubber industry and trade -- United States   ( lcsh )
Genre: bibliography   ( marcgt )
statistics   ( marcgt )
non-fiction   ( marcgt )
 Notes
Statement of Responsibility: by Ahmad Mahdzan Ayob and Anthony Prato.
Bibliography: Bibliography: leaves 53-54.
General Note: Cover title.
General Note: Based on Ayob's M.S. thesis, University of Florida.
Funding: Florida Historical Agriculture and Rural Life
General Note: Agricultural economics report - University of Florida ; 28
 Record Information
Bibliographic ID: UF00027480
Volume ID: VID00001
Source Institution: Marston Science Library, George A. Smathers Libraries, University of Florida
Holding Location: Florida Agricultural Experiment Station, Florida Cooperative Extension Service, Florida Department of Agriculture and Consumer Services, and the Engineering and Industrial Experiment Station; Institute for Food and Agricultural Services (IFAS), University of Florida
Rights Management: All rights reserved, Board of Trustees of the University of Florida
Resource Identifier: aleph - 001615811
oclc - 00571396
notis - AHP0252
lccn - 72612048

Table of Contents
    Main
        Main
    Front Cover
        Front Cover
    Acknowledgement
        Page i
    Table of Contents
        Page ii
    List of Tables
        Page iii
    List of Figures
        Page iv
    Introduction
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
    Objectives
        Page 6
    Review of literature
        Page 6
        Page 7
    Theoretical considerations
        Page 8
    Economic and other variables in the rubber market
        Page 9
        Page 10
    Economic models
        Page 11
        Page 12
        Page 13
        Page 14
    Statistical procedures
        Page 15
        Page 16
        Page 17
    Empirical results
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
    Forecasting United States imports and RSS #1 prices of natural rubber
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
    Results of the forecasts
        Page 35
        Page 36
        Page 37
        Page 38
    Summary and conclusions
        Page 39
        Page 40
        Page 41
        Page 42
        Page 43
    Appendix
        Page 44
        Page 45
        Page 46
        Page 47
        Page 48
        Page 49
        Page 50
        Page 51
        Page 52
    Bibliography
        Page 53
        Page 54
Full Text





HISTORIC NOTE


The publications in this collection do
not reflect current scientific knowledge
or recommendations. These texts
represent the historic publishing
record of the Institute for Food and
Agricultural Sciences and should be
used only to trace the historic work of
the Institute and its staff. Current IFAS
research may be found on the
Electronic Data Information Source
(EDIS)

site maintained by the Florida
Cooperative Extension Service.






Copyright 2005, Board of Trustees, University
of Florida




jiO

A gust 1971 Ag. Econ. Report 28


An Econometric Analysis

of United States Import Demand

and Prices of Natural Rubber


A. UI ~"


Department of Agricultural Economics
College of Agriculture
Institute of Food and Agricultural Sciences
University of Florida, Gainesville


Ahmad Mahdzan Ayob
Anthony Prato


- I I I L~ I ~ L I~ I I




OCT 1 1971




















ACKNOWLEDGEMENTS

The authors wish to extend their sincere appreciation to Carlton Davis,
Bob Emerson and W. W. McPherson for their constructive review of earlier
drafts of this manuscript. Special thanks go to the Ford Foundation for
supporting Ahmad Ayob's graduate studies and M.S. thesis research.








TABLE OF CONTENTS


ACKNOWLEDGEMENTS . . . . . . .
LIST OF TABLES . . . . . .
LIST OF FIGURES . . . . . . .
INTRODUCTION . . . . . . .
OBJECTIVES . . . . . . .
REVIEW OF LITERATURE . . . . .
THEORETICAL CONSIDERATIONS . . .......
ECONOMIC AND OTHER VARIABLES IN THE RUBBER MARKET . .
ECONOMIC MODELS . . . . . .
Model I: Simultaneous Equations Model . . .
Model II: Single Equation Model . . .
Import demand equation . . . .
Price equations . . . . .
STATISTICAL PROCEDURES . . .. . .

Functional Forms of the Models . . . .
Identification . . . . . ..
Measurement of Variables ..................
Observation Interval and Period of Study .. ..

EMPIRICAL RESULTS . . .. . . .

Summary of Model I .....................
Results: Import Equation Model II . . .
Predictive Ability of Import Equation . . .
Results: Price Equations Model II . . .
Predictive Ability of Price Equations . . .

FORECASTING UNITED STATES IMPORTS AND RSS# 1 PRICES OF
NATURAL RUBBER . ...... .

Forecasting with Stochastic Models . .....
Forecasting the Predetermined Variables . . .

Imports . . . . . .
Prices . . . . . .

RESULTS OF THE FORECAST . . . . . .
SUMMARY AND CONCLUSIONS . .. . . ..


Summary ........ . . ..
Conclusions . . .


Page

i
iii
iv
1
6
6
8
9
11
11
13
13
14
15

15
16
17
18

18

20
20
23
23
29


29

31
33

33
34

35
39


39
42










TABLE OF CONTENTS
Page


APPENDIX . . . . . . . 44
Results for Model I . . . . ... .45
BIBLIOGRAPHY . . . . . . 53


LIST OF TABLES
Table Page


1 Regression coefficients and related statistics of import
equation, Model II . . . . ... 21

2 Regression coefficients and related statistics of price
equation, Model II, Version 1 . . . . 26

3 Regression coefficients and related statistics of price
equation, Model II, Version 2 . . . . 27

4 Forecasts of natural rubber, variance of forecast errors and
tolerance intervals, 1969-80 . . . . 36

5 Forecasts of RSS#1 price, variances of forecast errors and
tolerance intervals, 1969-80 .. .. . . . 37


Appendix Tables

1 Regression coefficients and related statistics for natural
rubber . . . . . . . 47

2 (X'X)- Matrix for natural rubber import equation ..... 48

3 (Z'Z)-1 Matrix for natural rubber price equation, Version 2 48

4 Forecasted value of the predetermined variables used to forecast
imports and prices of natural rubber . . . 49

5 Data used in estimation of import demand and price equation
for natural rubber . . . . ... .50










LIST OF FIGURES


Figure Page

1 United States imports of natural rubber, 1947-69 . 3

2 United States consumption of natural rubber as a percentage
of all new rubber consumed, 1947-69 . . . 4

3 Annual average price of RSSf# natural rubber in New York,
1947-69 . . . ... .. . 5

4 Actual and predicted United States imports of natural rubber,
1948-1968 . . . . ... ....... 24

5 Actual and predicted RSS#1 prices in New York, 1948-68 . 30

6 Actual United States imports of natural rubber, 1948-68; and
forecasted imports, 1969-80 . .. . . 38

7 Actual average price of RSS#1 natural rubber in New York,
1948-68; and forecasted prices, 1969-80 . . .. 42










AN ECONOMETRIC ANALYSIS OF UNITED STATES
IMPORT DEMAND AND PRICES OF NATURAL RUBBER*


Ahmad Mahdzan Ayob and Anthony Prato



INTRODUCTION


"One of the threats to the exchange earnings of developing countries
in recent years has come from competition of synthetics with agricultural
raw materials, principally cotton, wool, jute and allied fibres, hard
fibres (mainly abaca), and rubber" [10,p.l].
Natural rubber is the most important source of foreign exchange
earnings and government revenues for Malaysia, and an important one for
Indonesia, Thailand and Ceylon. Some countries in Tropical Africa and
Latin America also export natural rubber. The Malaysian rubber industry
provides about 40 percent of the world's supply of natural rubber, employs
more than 500,000 workers and generates about M$1,300 million in foreign
exchange earnings yearly [11].
Natural rubber is a raw material used to manufacture tires and tire
products, beltings, footwear, hoses, gloves and hundreds of other con-
2
summer and industrial goods. The largest single user of natural rubber
is the tire manufacturing industry.
Natural rubber is produced in the developing countries and marketed
in the highly industrialized economies of the world such as the United
States, the United Kingdom, France and Germany. However, in recent years


This report is based on a M.S. thesis prepared by Ahmad Mahdzan Ayob [2].

MS$ denotes Malaysian dollars, M$1.00 = US $0.33.

A complete listing of products made of rubber is given in [29].


Ahmad Mahdzan Ayob is lecturer in agricultural economics at the College
of Agriculture, Malaya. Anthony Prato is assistant professor of agricultural
economics at the University of Florida.










consumption of natural rubber has been increasing in countries of the Soviet
Bloc, mainland China and Japan.
A crucial turning point for natural rubber occurred during World
War II when for the first time synthetic rubber was produced in the United
States on a commercial scale in an effort to alleviate the shortage of
natural rubber supplies from Southeast Asia. Since World War II the United
States, which is the largest single importer of natural rubber, has re-
duced its imports of rubber both in absolute terms and relative to world
imports. Of the 1,232 thousand tons of total world imports in 1947 the
3
United States imported 711.5 thousand tons, or about 58 percent. In
1969 the United States imported only 585 thousand tons, or 23 percent of
the 2,550 thousand tons of world imports (see Fig. 1).
United States consumption of natural rubber was 775 thousand tons
in 1941 as compared to consumption of only 6,259 tons of synthetic rubber.
In 1969 synthetic rubber consumption was 2,001 thousand tons whereas consump-
tion of natural rubber was only 588 thousand tons, or about 24 percent of
total new rubber (synthetic plus natural rubber) consumption, compared
with 99 percent in 1941 (Fig. 2).
As is common with many primary commodities that enter world trade the
price of natural rubber as represented by the price of RSS#1 has been
extremely volatile (Fig. 3). In contrast, the price of synthetic rubber
has remained relatively stable at about 20 cents per pound ever since syn-
thetic rubber plants came into operation under direct auspices of the
United States government. Low and stable prices for synthetic rubber
have made synthetic rubber competitive with natural rubber.
An econometric analysis of United States import demand and prices
of natural rubber has practical value for at least three reasons. First,
the United States is the largest single user of natural rubber. Conse-
quently, information concerning the determinants of and future changes
in United States import demand and prices of natural rubber is of vital
concern to natural rubber producing countries. Secondly, the United
States rubber industry provides the best example of a market that has


Tonnage as used here is the long ton which equals 2,240 pounds.

Ribbed-smoked sheet, No. 1 Grade, the best grade of natural rubber.

















































51 53 55 57 59 61 63
Figure l.--United States imports of natural rubber, 1947-69
Source: [28]


850


800


750


700


650


600


550


500


450


400


350


300















100


90


80


70


60


w 50
50


40


30


20


10


0
1947 49 51 53 55 57 59 61 63 65 67 69

Figure 2.--United States consumption of natural rubber as a percentage of all
new rubber consumed, 1947-69


Source: [281






































30


25


20


15
1947


49 51 53 55 57 59 61 63 65
Figure 3.--Annual average price of RSS#1 natural rubber in New York, 1947-69
Source: [28]










been converting rapidly from natural rubber to synthetic rubber. A
better understanding of this conversion process will provide valuable
insight into the impact of technical progress on the demand for agricultural
raw materials produced in developing countries. Finally, a study of the
United States rubber market will provide a useful reference for future
studies of other major rubber markets.


OBJECTIVES

This study focuses on the following set of objectives:
1. To identify the major factors that influence the volume of natural
rubber imported (demanded) by the United States and to measure the re-
lationships between these factors and imports.
2. To identify the major factors that influence the New York price
of natural rubber and to measure the relationships between these factors
and price.
3. To utilize these relationships and other information to forecast
United States imports and price of natural rubber for the period 1969-80.


REVIEW OF LITERATURE

Most studies related to natural rubber are of the historical type.
Even though these studies have contributed to the understanding of the
natural rubber market they do not provide quantitative information about
the economic relationships among important market variables. However,
there are three quantitative studies which have a direct bearing upon
the present study.
The first study by Horowitz [13] is mainly concerned with the supply
and demand for synthetic rubber, although the model included a supply
relation for natural rubber. Using quarterly data for 1948-60 (exclud-
ing the first quarter of 1948), Horowitz estimated the elasticity of supply
(imports) of natural rubber with respect to price to be 0.4461 which in-
dicates that supply is relatively inelastic. The price elasticity of
supply of synthetic rubber, on the other hand, was found to be 1.4914,
which indicates that supply of synthetic rubber is rather elastic. The
long run price elasticity of demand for synthetic rubber was -.8408, in-
dicating that demand for synthetic rubber is relatively inelastic.










been converting rapidly from natural rubber to synthetic rubber. A
better understanding of this conversion process will provide valuable
insight into the impact of technical progress on the demand for agricultural
raw materials produced in developing countries. Finally, a study of the
United States rubber market will provide a useful reference for future
studies of other major rubber markets.


OBJECTIVES

This study focuses on the following set of objectives:
1. To identify the major factors that influence the volume of natural
rubber imported (demanded) by the United States and to measure the re-
lationships between these factors and imports.
2. To identify the major factors that influence the New York price
of natural rubber and to measure the relationships between these factors
and price.
3. To utilize these relationships and other information to forecast
United States imports and price of natural rubber for the period 1969-80.


REVIEW OF LITERATURE

Most studies related to natural rubber are of the historical type.
Even though these studies have contributed to the understanding of the
natural rubber market they do not provide quantitative information about
the economic relationships among important market variables. However,
there are three quantitative studies which have a direct bearing upon
the present study.
The first study by Horowitz [13] is mainly concerned with the supply
and demand for synthetic rubber, although the model included a supply
relation for natural rubber. Using quarterly data for 1948-60 (exclud-
ing the first quarter of 1948), Horowitz estimated the elasticity of supply
(imports) of natural rubber with respect to price to be 0.4461 which in-
dicates that supply is relatively inelastic. The price elasticity of
supply of synthetic rubber, on the other hand, was found to be 1.4914,
which indicates that supply of synthetic rubber is rather elastic. The
long run price elasticity of demand for synthetic rubber was -.8408, in-
dicating that demand for synthetic rubber is relatively inelastic.










Horowitz concluded that even though natural rubber prices might stabil-
ize and decline, rubber manufacturers will continue to turn to synthetic
rubber. Two reasons were given for this belief [13,p.345]:
1. The stability of the price of synthetic rubber.
2. The "prospect that eventually it may surpass the natural product
in the technical qualities that it [synthetic rubber] offers."
In a second study by FAO [8,pp.316-25] the demand for natural rubber
was projected to 1975 in each of several countries. Based on assumptions
about future growth of population and national income, time series data
for the period 1954 to 1963 were used to derive the elasticity of demand
for all rubber with respect to income and these elasticities were then
used to project total rubber consumption to 1975 for each country. Con-
sumption of natural rubber was projected to 1975 by estimating its propor-
tion in projected total rubber consumption. On the assumption that natural
rubber's share will be 20 percent of all new rubber consumption in 1975,
United States consumption (not imports) of natural rubber was projected
to have a range of 528,000 to 580,000 tons depending on whether low or
high income growth rates are assumed.
A third study made by the United Nations Conference on Trade and
Development (UNCTAD) [27] focused on constructing a world model. The
model attempted to explain the New York price of RSS#1 natural rubber in
terms of total world consumption of elastomers (synthetic and natural
rubber), world supply of natural rubber and the ratio of natural rubber
consumption to total world elastomer consumption lagged one year. In
the other equation, total world consumption of natural rubber was expressed
as a function of total world elastomer consumption, the ratio of natural
rubber consumption to total elastomer consumption lagged one year, and the
New York RSS#1 price. The study was based on annual data for the period
1954-66.
In their analyses UNCTAD found, inter alia, that an increase of one
thousand tons in total elastomer consumption was associated with an in-
crease of 280 tons in natural rubber consumption. The regressions showed
that a decline in the ratio of natural rubber to total elastomer consump-
tion of one percentage point was associated with a decline of about 19
thousand tons in natural rubber consumption in the following year. A one
cent per pound decrease in RSS#1 price was associated with a 14 thou-
sand ton rise in natural consumption.











THEORETICAL CONSIDERATIONS

Economic theory states that a firm's demand for an input in a pro-
duction process depends upon the prices of all inputs as well as the price
of the output. The underlying assumptions of this theory are that the
entrepreneur is rational, striving to maximize profit, and operating in
a perfectly competitive market. Under these assumptions the ith firm's
demand for an input, say X., would be a function of the prices of all
inputs and output, viz.,

X.. = X. (Pj P', P ) i=l, ..., m; j=l, ..., n;

where P. = price of the jth input;

P' = vector of input prices excluding P.;

P = price of the output.
y

The above input demand function is derived from the technical pro-
duction function of the firm, which expresses total physical product as
a function of all inputs. From the production function and the price of
the output we can derive a value marginal product curve (VMP) for each
input. Profits are maximized when purchases of each input are at the level
at which the VMP of the input equals the price of the input. A change
in technology alters one or more of the parameters of the production func-
tion which in turn causes a movement in the VMP curves for the variable
inputs affected by the change in technology. Since the firm's input demand
function is derived from the VMP curves, changes in technology can be
expected to shift the level and/or alter the slopeafi the firm's demand
curve for one or more inputs.
The input demand function for the industry is obtained by horizontal
summation of the individual firm's input demand functions. Hence, the
industry demand function for X. is:
mJ
Xd m j=l, ..., n.
j i=1 ij

The last equation embodies the traditional economic theory of indus-
try demand for an input and follows logically from the underlying assump-










tions of the theory. In reality, the assumption of perfect competition
in the rubber industry in untenable, for it has been estimated that the
four major United States rubber companies purchase about 65-70 percent
of the natural rubber entering the country [l,p.8]. In addition, con-
tinuous technological change, sudden appearance of exogenous shocks in
the economic system, spreading of "mischievous" rumors in the market,
imperfect knowledge and increasing government action make the above model
inadequate for explaining input demand in the real world. When analyz-
ing the import demand for natural rubber, a commodity which is sensitive
to all these phenomena, the researcher must take cognizance of these
"extraneous" factors. It is unrealistic to think that prices of inputs
and output are the only factors influencing the demand for natural rubber.


ECONOMIC AND OTHER VARIABLES IN THE RUBBER MARKET

According to several writers, the price of natural rubber plays only
a minor role in determining the quantity imported. For example, Phillips
stated that "...historically, changes in rubber prices have had little
effect upon the quantities of rubber consumed by industry. General econ-
omic conditions that influence the purchase of consumer goods, particularly
automobiles, determine how much rubber will be purchased annually" [22,p.105].5
Notwithstanding remarks of this kind, which are unsupported by empirical
evidence, the present study will initially assume that price is a factor
to be considered in analyzing import demand for natural rubber. In other
words, it is hypothesized that price and imports are related.
Since World War II, United States import demand for natural rubber
has been under constant pressure from the increased use of synthetic
rubbers. Technological change in the synthetic rubber industry has been
taking place so rapidly that synthetic rubber has been able to replace


5See also [30,p.10] and [18,p.76].











the natural product in many end uses. This substitution is a crucial
factor which has affected imports of natural rubber.
On the other hand, natural rubber is definitely superior in certain
products where high resilience and low heat build-up are necessary, e.g.,
in airplane and heavy-duty truck and bus tires. Substitution of existing
synthetic rubbers for natural rubber in these products is not technically
feasible [21;26,p.96]. In other words, the demand for natural rubber used
in these products is largely based on technical rather than economic consi-
derations. The utilization of natural rubber in these products is ulti-
mately derived from consumer demand for goods and/or services connected
with these products, e.g., the demand for bus transportation creates a
demand for natural rubber imports.
Import demand for natural rubber is somewhat complicated by its dual
relationship with synthetic rubber. In some end uses the two are com-
plementary (as in the latex products), and in other uses they are sub-
stitutes (as in passenger car tire carcasses, truck tire treads, etc.).
This poses a conceptual and empirical problem in terms of the relation-
ship between the price of natural rubber and the consumption of synthetic
rubber.
Concerning the "exogenous shocks" in the rubber market, one can cite
the following: the Korean War, closure of the Suez Canal, dock strikes,


By technological change is meant the emergence of new end products
using synthetic rubber, new forms of synthetic rubber (especially stereo-
regulars) and new ways of processing synthetic rubber. It should be noted
that synthetic rubber is not one chemical substance; it is a generic name
encompassing several different products. Styrenebutadiene, often referr-
ed to as SBR, is a general-purpose rubber and, therefore, the most used
synthetic rubber. In 1968, 68 percent of all synthetic rubber used in
the U.S. was SBR.

On the other hand, the demand for synthetic rubber is complicated
by the fact that a substantial amount of it is consumed by the producers
themselves. This is a captive sale, and the price is entirely an internal
book operation, which does not lend itself to any sort of tight marketing
analysis. Moreover the listed price is negotiable. Negotiation between
seller and buyer can drive down the listed price from 10 to 30 percent,
depending on the market situation, especially the price of natural rubber
of equivalent grade. (Natural Rubber Bureau, Malaysian Rubber Fund Board,
Washington, D. C., personal communication)











strikes within the rubber manufacturing industry itself, announcements
of United States stockpile releases, etc.


ECONOMIC MODELS

The two models formulated in this study represent alternative struc-
tures for United States import demand and prices of natural rubber. The
models use different sets of explanatory variables and assumptions to
explain import demand and prices of natural rubber.

Model I: Simultaneous Equations Model
The first model is a system of simultaneous equations in which im-
ports and prices of natural rubber are jointly determined. The demand
and supply equations for natural rubber are as follows:

P = P(QMd, QAt, QRt, AIt, ut) (demand)

QM = Q(P Pt-' QEt' vt) (supply)


QM = QMs (market equilibrium condition)
t t
where P = price of RSS#1 rubber in the New York market;

QM = quantity demanded of natural rubber by the United States;
QA = quantity consumed of synthetic rubber in the United States;
QR = quantity consumed of reclaimed rubber in the United States;
AI = net changes in commercial inventories of natural rubber;

QMs = quantity supplied of natural rubber to the United States;
QE = total world exports of natural rubber;
u & v = stochastic disturbance terms.
The rationale for looking at United States imports instead of con-
sumption of natural rubber is that imports are deemed to be of more direct
concern to natural rubber producing countries than actual utilization.
The variable QA is intended to reflect the effects of the substitution
of synthetic rubber for natural rubber on the price of natural rubber.
It is hypothesized that as synthetic rubber consumption increases the
demand and price of natural rubber decrease. That is, synthetic rubber
and natural rubber are viewed, for the most part, as substitutes. Reclaim-
ed rubber, QR, is expected to be complementary with natural rubber; hence,












price of natural rubber is expected to vary directly with the consumption
of reclaimed rubber.8
AI is intended to reflect the effects on price of net changes in commer-
cial inventories of natural rubber. A positive (negative) AI indicates
a net increase (decrease) in commercial inventories. Two hypotheses about
the relationship between net changes in inventories and natural rubber
prices can be postulated. First, net decreases in inventories could de-
crease the demand for rubber imports and thereby reduce the price of natural
rubber, i.e.,inventories are substituted for imports. Conversely, net in-
creases in inventories could increase the demand for imports and thus
increase the price of rubber, i.e., increased inventory requirements could
enhance the demand for rubber. This hypothesis would imply a positive re-
lationship between AI and rubber prices. Alternatively, decisions to

increase or decrease rubber inventories may be influenced by the price of
natural rubber. During periods of low natural rubber prices, inventories
may be replenished, whereas during periods of high natural rubber prices
inventories may be diminished. This hypothesis implies that AI and rubber
prices are inversely related. If the second hypothesis obtained AI or
I would become a dependent variable in the model. The contradictory con-
sequences of these two hypotheses make it difficult to anticipate the sign
of the coefficient of AI. This difficulty could perhaps be alleviated by
a more sophisticated treatment of inventory decisions in the model. Such
treatment was not considered worthwhile in the present study because the
annual data used in estimation more than likely obscure the effects of
inventory decisions on import demand and prices of natural rubber.
Although the theoretical input demand function previously discussed
includes the price of the output, the inavailability of data on prices
of finished rubber products made it necessary to ignore output prices when
estimating import demand for natural rubber.
On the supply side it was assumed that rubber exporters are respon-
sive to current as well as lagged prices. It is expected that supply



Based on theory, a change in the price of X. with respect to a change
in the consumption of Xk is negative if the products are substitutes and
positive if they are complements, other things held constant.










will be directly related to current and lagged prices. QE reflects world
availability of natural rubber. Quantity supplied to the United States
is expected to vary directly with total world exports of natural rubber.
It should be noted that the supply equation is really an aggregation
of the supply equations for each country exporting rubber to the United
States. Similarly, the demand equation is an aggregation of the demand
equations for all U.S. firms importing natural rubber.

Model II: Single Equation Model
In Model II the assumption that prices and imports are jointly deter-
mined was dropped. The decision to drop this assumption was based on
the statistically insignificant relationship between imports and prices of
natural rubber in the demand equation estimated by Model I (see Appendix).
In attempting to explain prices and imports of natural rubber, Model II
9
gives greater attention to variables at the macroeconomic level. Three
equations are formulated: one to explain imports and two alternative
equations to explain price.

Import demand equation
The import demand equation is specified as follows:

QMt = F(Rt, Wt, TBt, RGSt, ut

where R = ratio of synthetic rubber consumption to total consumption of
new rubber;
W = zero-one dummy variable to account for war years, 1 in 1950,
1951 and 1952; and 0 otherwise;
TB = production of trucks and buses;
RGS = releases of natural rubber from U.S. government strategic stock-
pile;
u = stochastic disturbance term.
The variable R is intended to reflect the effect of synthetic sub-
substitution (or technological change) upon the demand for natural rubber.



Wright stated that "...specific raw materials are used in so many
businesses that the demand for such commodities can be estimated with
reasonable accuracy by correlating past usage of the product with national
income, industrial production, disposable income or other comprehensive
measurements of activity on a national basis" [31,p.117].











The inclusion of the variable TB may be justified on the grounds that the
largest single use of natural rubber is in manufacturing of heavy-duty
tires for trucks, buses and airplanes. The variable RGS is included be-
cause it is known that announcements by the United States government of
releases of natural rubber from its strategic stockpile have influenced
decisions of rubber manufacturers regarding demand for imports.10

Price equations
Version 1 of the price equation is:
P = G (P R ICR IAP RGS v )
Pt = G1 (Pt-l' Rt-l' ICRt-' IAPt' RGS' Vlt)

where P = price of RSS#1 rubber in the New York market;
ICR = ratio of commercial inventories of natural rubber at the beginn-
ing of the year to consumption of natural rubber in the previous
year;
IAP = index of automotive production (1957-59 = 100);
v1 = stochastic disturbance term.

It is not known how lagged price affects current price, but it is
assumed that the bargaining that occurs in the market is affected by the
lagged price.
A one year lag for the ratio of synthetic to total rubber consump-
tion (R t) is based on the assumption that price adjustments resulting
from synthetic substitution take about one year. It is hypothesized that
increases in Rt depress the current price.
The variable ICR1 reflects the effect of natural rubber inventories
on the price of natural rubber. It is hypothesized that the higher the
beginning inventories relative to consumption in the preceding year, the
lower the price manufacturers are willing to pay for imports of natural
rubber.
To show the effect of industrial activities (especially automobile
production) upon the price of natural rubber, the index of automotive
production is included as an explanatory variable. It is expected that



1For example, FAO stated that "...there was a 3,000 ton rise in U.S.
imports [1967] largely due to the slower rate of releases from the stra-
tegic stockpile" [9,p.420].











RSS#1 price will vary directly with the index of automotive production.
The variable RGS has been included because it is felt that releases
of natural rubber from the U.S. government stockpile have an important
effect on RSSI# price. Rubber from the stockpile is sold at rather low
prices, and these sales could depress the market price of natural rubber
imports. Thus, by including RGS in the model it is possible to test the
hypothesis that releases of rubber from the stockpile depress the price
of natural rubber in the New York market, as claimed by government offi-
cials and industry leaders in natural rubber producing countries.

Version 2 of the price equation is:
t = G2(Pt-' Rt- t-l' IAPt, QRt v2t)

where QR = quantity consumed of reclaimed rubber in the United States.
v2 = stochastic disturbance term.

In Version 2, releases of rubber from the government stockpile, RGS,
is replaced by consumption of reclaimed rubber, QR.1


STATISTICAL PROCEDURES

To determine the appropriate statistical procedures for measuring
the relationships given by the economic model, it is necessary to specify
the model in the form of precise mathematical equations and to state the
statistical assumptions concerning the distributions of all variables.

Functional Forms of the Models
While economic theory provides qualitative information about certain
price slopes and elasticities, it provides little information about the
algebraic form of demand and price relationships. In this study two al-
ternative functional forms were estimated, namely, a linear relationship



1Reclaimed rubber is obtained by extracting the rubber content of
scrap or worn out rubber products after treatment to eliminate the fiber
content and to "devulcanize" the rubber atoms by removing their sulphur
content. Reclaimed rubber has an important and proper place in manufac-
turing certain rubber products, particularly where maximum tensile strength
is not needed, but resistance to abrasion is required [24,p.14]. RGS
was replaced by QR, because the former was not statistically significant
in Version 1 (see Table 2).










in the actual variables (actual variate form) and a linear relationship
in the logarithms of the variables '(double-log form). Estimation in the
actual variate form implicitly assumes constant slopes whereas in the
double-log form constant elasticities (or flexibilities) are assumed.
By measuring relationships in both forms, comparisons can be made of
the estimated elasticities and the goodness of fit. In fitting the
double-log form, zero-valued observations were coded as 1 and all ratio
variables were multiple by 100. Relationships containing variables with
negative values were not estimated in the double-log form.

Identification
Model I has the following mathematical form:

Pt = a + alQM + a2QAt + aQRt + AlAI + ut (demand)

QM = b + blP + b P + b QE + v (supply)
t 0 1 t 2 t-l 3 t t

QMs = QMd (market equilibrium condition)
t t
Each equation of Model I consists of two endogenous variables, namely
in the demand equation, the quantity of natural rubber demanded, QMd and
RSS#1 price, P; and in the supply equation, the quantity of natural rubber
supplied, QMs, and RSS#1 price, P. Applying the necessary and sufficient
condition for identification, shows that the demand and supply equations
are both overidentified. In order to estimate the structural parameters
of Model I, one of the methods for estimating parameters of overidentified
equations must be used. The method of two-stage least squares was used
in this study.
In Model I consumption of synthetic rubber is assumed to be predeter-
mined. This assumption is not unrealistic considering that commercial
production of synthetic rubber in the United States was started in an effort
to overcome shortages brought about by war, and not as a response to rising
natural rubber prices. Consumption of reclaimed rubber is also assumed
to be predetermined because it depends, for the most part, on past con-
sumption of new rubber. Net changes in inventory are also considered to be
predetermined although it may be argued that the inventory policy of man-
ufacturers does take into consideration current RSS#1 price (and prices
of other grades of natural rubber). Lagged price in the supply equation











is predetermined because it cannot be influenced by variables in the
current period. Total world exports of natural rubber, QE, is clearly
determined by conditions outside the United States.
Each disturbance term in Model I is assumed to be normally and inde-
pendently distributed with zero mean and finite and constant variance.

Measurement of Variables
In Model I the price of RSS#1 in the New York market is measured in
dollars per ton and deflated by the Industrial Wholesale Price Index
(1957-59 = 100). Unfortunately, the RSS#1 price corresponds to the best
grade of rubber whereas total United States imports, QM, include all
12 13
types and grades3 of natural rubber. Since data on prices and imports
of the various grades of rubber are not available (nor is total value of
natural rubber imports available) it is impossible to derive a weighted
average price of all grades of natural rubber that would more nearly corres-
pond with total rubber imports. Hence, the authors were compelled to
follow the practice of previous writers by using the RSS#1 price of natural
rubber. It may be noted that the price of RSS#1 is regarded as the gen-
eral indicator of natural rubber prices. All quantity variables are meas-
ured in long tons.
In estimating Model II undeflated prices of RSS#1 rubber, in cents
per pound were used since prices in current dollars were judged to be more
14
relevant to natural rubber producers than deflated prices.4 Imports of
natural rubber, QM, consumption of reclaimed rubber, QR, and releases
from government stockpile, RGS, are measured in thousands of units.


12
1The principal source of natural rubber is the Hevea tree, but a
small quantity is derived from the Guayule bush, Parthenium argentum,
cultivated mainly in South America. Both types of natural rubber are
imported by the United States although the bulk of rubber imported is the
Hevea product. It should also be noted that imports of natural rubber
include latex, which is always expressed in terms of the solid rubber
content.
13
1There are listed 31 recognized International Grades of natural
rubber. The differences in the values of the many grades are not fixed
but their prices follow the general price level in the market [4,p.527].
14
1The same argument may be given for Model I. In fact, the undeflated
price was also tried for that model.










Observation Interval and Period of Study
All variables correspond to an annual time interval. Even though
an analysis of annual data obscures intra-year changes in the relation-
ships such loss of information is not considered serious, in view of the
fact that the main concern of this study is to estimate annual relation-
ships that can be used to forecast long-run movements in prices and im-
ports of natural rubber. Also an annual time interval is considered long
enough to allow the market to represent a state of equilibrium which is
a necessary requirement for the application of the models. Each model
was estimated with data for different time periods. Model I was estimated
with data for the period 1948-50 and 1961-69.15 The war years, 1941-47
and 1951-52, were excluded because for those years the United States govern-
ment fixed the price of natural rubber. Prior to World War II no syn-
thetic rubber was produced commercially, hence this period was deemed
inappropriate for purposes of this study. Model II was estimated using
observations for the entire period 1948-68. Zero-one dummy variables
were used to account for possible intercept changes in the relationships
during the Korean War years, 1950-52.16 Data for 1969 are incomplete
in that no figures are available for production of trucks and buses
and the index of automotive production. The data used in estimation
are presented in Appendix Table 5.


EMPIRICAL RESULTS

Ordinary least squares regression requires, among other things, that
one endogenous variable be expressed as a linear function of predetermined


15Perhaps observations for 1950 should also be discarded because it
was the year the Korean War broke out. However, because free trading
was not suspended until March 31, 1951, it was decided to include obser-
vations for 1950.

16Kogiku writes: "In the period following the outbreak of the Korean
conflict, the raw materials market underwent some shocks. There was a
strong demand for materials for stockpiling especially in the U.S., add-
ing to the pressure of commerical demand for raw materials. Prices of
raw materials rose sharply. Purchases for the stockpile continued through
1952, but in the first half of 1953 substantial concellations of stock-
pile obligations occurred" [19,p.116].










or exogeneous variables. Since this requirement is not satisfied for
Model I, two-stage least squares as well as ordinary least squares esti-
mation methods were applied to Model I. The F-test is used to test for
the significance of the coefficients of multiple determination (R2) ob-
tained for the ordinary least squares regressions, and the t-test is used
to test for the significance of individual regression coefficients. The
authors recognize that the t-test is valid only when the assumptions of
ordinary least squares estimation are satisfied.
The Durbin-Watson (D-W) statistic is used to test for serial corre-
lation in the unexplained residuals. However, the Durbin-Watson test is
inappropriate for testing serial correlation in equations containing one
or more lagged endogenous variables as explanatory variables. Durbin
[6] has developed a test of serial correlation which can be applied in
such cases. To illustrate, assume:
Yt = B + B2 Y + B3 Zt + ut t=l, ..., n

where Y is the dependent variable and Z is strictly exogenous. The first
step is to estimate the above equation by ordinary least squares regression
and compute the residuals, et (t=l, ..., n). The residuals are then re-
gressed (beginning with e2) on the one-period lagged residuals (when testing
for first-order autocorrelation) and all explanatory variables:
e = a + a et_ + a Yt-i + a Z + E t=2, ..., n

where E is spherical normal. If the coefficient of et-1 (i.e. a2) is
not significantly different from zero (based on the t-test), the hypo-
thesis that et has zero serial correlation is not rejected. In this study
Durbin's test is applied to the residuals of the two price equations.
Regression results will also be evaluated in terms of the consistency
between the observed signs of the regression coefficients and the signs
implied by economic theory and a priori information.
It is noted that the regression coefficients in the actual variate
form are estimates of the partial slopes of the function under considera-
tion with respect to the particular independent variables. These coeffi-
cients measure the effect on the dependent variable of a unit change
in the independent variable when all other variables are held constant
(ceteris paribus condition). In the double-log form, regression coe-
fficients are estimates of the elasticities or flexibilities, as the










case may be.

Summary of Model I

Based on the above criteria, Model I does a poor job of explaining
the demand and supply structure for natural rubber. A discussion of the
salient features and the statistical results of Model I are given in the
Appendix. In general the results suggest that imports and RSS#1 price
are not jointly determined. The model is also very sensitive to speci-
fication. Consequently, Model I is not used to forecast United States
imports and prices of natural rubber.

Results: Import Equation Model II

The regressions for the import equation in the actual variate and
double-log forms are given in Table 1.17 All variables in the actual
variate form are statistically significant at the one percent level.
In the log form all variables except Rt are statistically significant
at the one percent level. R is significant at the 10 percent level.
t 18
The actual variate regression shows that an increase of one unit in
the ratio of synthetic rubber consumption to total new rubber consump-
tion is associated with a reduction in natural rubber imports of 516 tons.
Thus, as synthetic rubber's share of the market (measured by Rt) increases,
natural rubber imports decrease, as expected. Such reductions in natural
rubber imports result from the substitution of synthetic rubber for nat-
ural rubber. The variable R also reflects changing technologies in the
synthetic rubber industry. As technology advances, we can expect this
ratio variable to increase. If this ratio stabilizes, then natural rubber
imports can be expected to stabilize also, other things remaining un-
changed.


17The import equation for Model II was also estimated with RSS#1 price
as an independent variable but this variable was found to be statistically
insignificant at the 10 percent level.

18Interpretations of the coefficients of ratio variables are slightly
different from those of ordinary variables. In this study essentially
two ratios were used, namely, Rt (Rt-1 in price equations) and ICR 1
These ratios lie between zero and one. A unit increase in each ratio
is defined as an increase of .01. This definition is used throughout
this study.













Table 1.-Regression coefficients and related statistics of import equa-
tion, Model II


Independ- Actual variate Double-log
ent Beta Average Regression
varia- Regression coeffi- elas- coeffi-
bles coefficients clients ticities cientsa


Constant
term 624.2095 4.5780 3.3790

R -516.0433*** -.4358 -.5915 -.2314*
t (121.1738)b (.1267)

W 140.9436*** .3706 .0361 .1544***
(30.1309) (.0528)

TB .2320*** .4680 .5513 .5644***
t (.0574) (.1193)

RGS -1.6630*** -.6148 -.1146 .0979***
(.4035) (.0158)



R2 .9183 .9265
D-W 1.597C 2.092C
Est. Var(u) 1897.9583 .0058
F(4, 16) 44.9776*** 50.3920***



All ratio variables have been multiplied by 100, prior to regression
in this form.

Standard error of the estimate.

CNo serial correlation

***Statistically significant at the one percent level.

Statistically significant at the 10 percent level.












Some caution is required in interpreting the dummy variable coeffi-
cient. Since the variable W takes on a value of zero or one, the coeffi-
cient of W measures the average increase for the war years in the inter-
cept of the import equation. The model assumes that partial slopes with
respect to non-dummy variables remain unchanged during the Korean War
years. The coefficient of 140.9436 associated with the dummy variable
means that, on the average, the United States imported about 141 thousand
tons more rubber per year during the war years than during non-war years.
However, circumstances surrounding the Korean War are special and need
not emerge again in future wars. Hence, it should not be construed that
future wars involving the United States are going to increase natural
rubber imports and thereby benefit natural rubber producing countries.
For one thing, technological advances and excess capacity in the synthetic
rubber industry may more than offset any future shortages of natural rubber
in the United States. Moreover, during national emergencies inferior
rubber is better than no rubber at all.
The regression coefficient with respect to the production of trucks
and buses (TB) indicates that an increase of one thousand units in the
production of these heavy vehicles is associated with an increase of
232 tons in natural rubber imports. The elasticity with respect to pro-
duction of trucks and buses, computed at the means of the variables, is
similar to the regression coefficient of TB in the log form equation.
These elasticities indicate that a one percent increase in production of
trucks and buses is associated with .55 to .56 percent increase in natural
rubber imports. Assuming that there are no major breakthroughs in the
use of synthetic rubber for heavy duty tires in the immediate future, natur-
al rubber imports can be expected to increase in order to meet the demand
from manufacturers of heavy-duty tires.
The negative coefficient of RGS seems to support claims made by FAO
concerning the detrimental effects of stockpile releases on manufacturers'
decisions to import natural rubber. The results indicate that a one
thousand ton release from the government stockpile is associated with
a 1,660 ton decrease in natural rubber imports. Certainly, one thousand
tons from stockpile cannot replace 1,660 tons of natural rubber imports.
Perhaps the deficit in natural rubber supply is made good by domestic pro-
duction of synthetic rubber.









19
The beta coefficients9 indicate that variations in stockpile releases
account for most of the variation in imports: one standard deviation in-
crease in stockpile releases is associated with .6148 standardized unit
reduction in imports. Next in importance in explaining imports is the
production of trucks and buses, with a beta coefficient of .4680. Dis-
regarding the war dummy variable, W, the ratio variable, R, contributes
least towards explaining imports, even though, statistically, it is high-
ly significant.

Predictive Ability of Import Equation
Figure 4 illustrates the relationship between the observed values of
natural rubber imports and the predicted values obtained from the actual
variate form of the price equation. Unexplained residuals are relatively
large for 1952, 1961, 1963, and 1966. For other years the predicted im-
ports are fairly close to actual imports. Theil [24,pp.31-2] has given
a statistical criterion for "judging the quality of time series forecast."
This is the inequality coefficient, U.

/1 n 2
SE (A P
n i i


U n n
U = / n 2 1 n 2
A + E P
n i1 i n i=


where Ai is the ith actual observation on the dependent variable, Pi is
the predicted value of the ith observation on the dependent variable, and
0 < U <1. If U = 0 there is a perfect forecast and if U = 1 there is a
poor forecast. For the actual variate import equation the value of U
is .146. Since this value is close to zero the predictive ability of the
import equation is fairly good.

Results: Price Equations Model II
Price regressions, Versions 1 and 2, are given in Tables 2 and 3,


19For a discussion of the use of beta coefficients, see [12,pp.197-200].












actual
----------predicted




















- -


Ij


800




700




600




500




400




300
1948


50 52 54 56 58 60 62 64

Figure 4.--Actual and predicted United States imports of natural rubber, 1948-68










20
respectively.20 In Version 1 (Table 2) the estimated average flexibility
of current price with respect to lagged price in the actual variate form
is similar in sign but larger than the regression coefficient in the log
form. The direct relationship between current price and lagged price lends
support to Adams' observations. According to Adams, "...it has been suggest-
ed that one of the causes of price instability associated with consumer
buying policy is that if for some reason there is a fall in price and the
market appears weak, there is a tendency for consumers to reduce their
purchases in case the price should fall even further, and by reducing their
purchases at that time a further fall is thereby made more probable.
Similarly when prices begin to rise consumers may fear even higher prices
and may in consequence rush in to buy and in so doing exaggerate the up-
ward movement of price" [l,p.9]. In the actual variate form a one unit
increase in the lagged ratio of synthetic to total rubber consumption
(R t) depresses current price by approximately one cent per pound. In
other words, the effect of the increasing share of synthetic rubber in
total new rubber consumption in the preceding year (or synthetic substitution)
is to depress RSS#1 price in the current period as expected.
The estimated flexibilities of current price with respect to ICRt-
in the actual variate and log forms are similar in their signs; but in
magnitude, the flexibility in actual variate form is larger in absolute
value. In the actual variate form an increase of one unit in the ratio
of beginning year inventories to previous year's consumption of natural
rubber depresses RSS#1 price in the current year by 1.63 cents per pound.
This implies that when inventories are high on January 1 relative to con-
sumption of natural rubber in the previous twelve months, manufacturers
bid down the price they are willing to pay for natural rubber imports.
This finding is consistent with a priori expectations and in agreement
with Horowitz's finding, even though Horowitz's basic time unit was the
quarter [13,p.334]. Typically, a manufacturer's policy is to maintain


20
Versions 1 and 2 were also estimated including imports as a regress-
or. In neither case was the import variable significantly different from
zero at the 10 percent level. It is noted that because the price equations
are auto-regressive models (they include a lagged endogenous variable as
a regressor) the least squares estimates will be biased but consistent
and efficient in large samples [12,pp.272-74].










Table 2.--Regression coefficients and related statistics of price equation,
Model II, Version 1



Independ- Actual variate Double-log
ent Regression Beta Average Regression
varia- coefficients coeffi- flexi- coefficients
bles clients abilities


Constant
term 79.9997 8.047 5.9792
P .4832*** .481 .4839 .4484**
t-1 b
t- (.1008) (.1572)
R -97.2249*** -.978 -2.0252 -1.1865***
t- (12.1848) (.3327)
ICR -163.1490*** -.057 -.9810 -.9162***
t (23.5173) (.2167)
IAP .2502*** .819 .9371 .7536***
t (.0575) (.2409)

RGS -.0507 .026 -.0646 -.0633*
t (.0291) (.0317)

R2 .9260 .8646
Est. 9.7437c .0162d
Var(v1)
F(5,15) 37.5703*** 19.1581***


aAll ratio variables have been multiplied by 100, prior to regression in
this form.
Standard error of the estimate.

cNo serial correlation in vl at the five percent level (Durbin's test).

Serial correlation not tested.
***
Statistically significant at the one percent level.
Statistically significant at the five percent level.
Statistically significant at the five percent level.
Statistically significant at the 10 percent level.









Table 3.--Regression coefficients and related statistic of price equation,
Model II, Version 2



Independ- Actual variate Double-log
ent Regression Beta Average Regression
varia- coefficients coeffi- flexi- coefficients
bles cents abilities


Constant
term 37.5750 3.781 -1.8231
.P .3566*** .354 .3562 .3386***
t (.1030)b (.1455)

Rt1 -65.8616*** -.740 -1.3719 -.7403*
(16.8214) (.3494)
ICRt-1 -115.6909*** -.404 -.6957 -.4946**
(26.3856) (.1852)
IAPt .1099* .360 .4117 .1889
(.0518) (.2210)
QRt .1178** .321 1.0551 1.3654***
(.0435) (.4259)

R2 .9397 .8969
Est. 7.9449c .0123d
Var(v2)
F(5,15) 46.7558*** 26.1127***


aAll ratio variables have been multiplied by 100, prior to regression in
this form.

Standard error of the estimate.

CNo serial correlation in v2 at the five percent level (Durbin's test).

Serial correlation not tested.

Statistically significant at the one percent level.
**
Statistically significant at the five percent level.
Statistically significant at the 0 percent level.
Statistically significant at the 10 percent level.










a minimum size of inventory relative to requirements. Although rubber
is not a perishable good, there is always a high risk of fire accompanied
with rubber stocks. Moreover, inventory is a form of tied up capital, and
rational manufacturers would want a minimum amount of money invested in
this form.
An increase of one unit in the index of automotive production (1957-
59 = 100) is associated with a .25 cent per pound increase in RSS#1 price.
This finding provides some empirical evidence that general economic con-
ditions, particularly automobile production, do influence the price of
natural rubber. Releases of rubber from the government stockpile, RGS,
was not statistically significant in the actual variate form and significant
at only the 10 percent level in the double-log form.
Version 2 of the price equation (Table 3) was estimated after dropping
RGS from Version 1 and adding reclaimed rubber consumption, QR, as an ex-
planatory variable. Although the addition of QR increases R2 slightly,
IAP is not significant in the log form, and significant only at the 10
percent level in the actual variate form. The regression coefficient of
QR indicates that a one thousand ton increase in reclaimed rubber consump-
tion is associated with an increase of approximately .12 cents per pound
in RSS#1 price. This suggests a complementary relationship between nat-
ural rubber and reclaimed rubber. Measures of price flexibility with res-
pect to QR (1.0551 in the actual variate, and 1.3654 in the log form)
indicate that a one percent increase in the consumption of reclaimed rubber
is associated with slightly greater than one percent increase in RSS#1
price.
The regression coefficients of P t-l Rt- ICR t- and IAP in Version 2
are smaller in absolute values than the same coefficients in Version 1.
The average flexibility with respect to lagged price in the actual variate
form (.3566) is similar in magnitude and sign to the regression coeffi-
cient of lagged price in the log form (.3386). The average flexibility
with respect to Rt- in the actual variate form is almost twice as large
as the coefficient of Rt- in the log form. However, in the log-form
t--l
Rt- is significant at the 10 percent level, which is not a particularly
acceptable level of significance.












An increase of one unit in the.ratio of beginning year inventories
to natural rubber consumption in the previous twelve months depresses current
RSS#l price by 1.16 cents per pound. Flexibility estimates with respect
to ICRt are similar in sign in both forms of Version 2. The coefficient
of the index of automotive production indicates that an increase of one
unit in this index is associated with about .11 cents increase in RSS#1
price. Natural rubber producing countries can derive some comfort from
this result.
Beta coefficients are computed only for the actual variate form of
the price equations. In both versions, variations in Rt- account for
most of the variation in RSS#1 price. This result is not surprising, and
merely shows that synthetic substitution has had the greatest impact on
natural rubber prices. Next in importance for Version 1 is the index
of automotive production. For Version 2, ICRt_ supersedes IAP in ex-
plaining RSS#1 price variations. In Version 1,RGS is the least important
determinant of current RSS#1 price, and in Version 2 the variable QR is
the least important. The last finding is not surprising because reclaimed
rubber consumption did not vary a great deal during the sample period.

Predictive Ability of Price Equations
Figure 5 illustrates the correspondence between the observed values
of RSS#1 price and values predicted by Version 2 of the price equation.
Unexplained residuals are rather large for 1953, 1958, 1959, 1964 and
1968. Their absolute values range from 3.58 cents to 4.56 cents per pound.
The predicted values for other years are fairly close to the observed
values. Applying Theil's criterion, gives values for U of .138 in Version 1
and .125 in Version 2. Thus it may be concluded that the predictions
obtained from the price equations estimated in this study are fairly good.
Version 2 will be used to forecast RSS#1 price.


FORECASTING UNITED STATES IMPORTS AND RSS#1
PRICES OF NATURAL RUBBER

As previously mentioned a knowledge of the size of the United States
natural rubber market and prices of natural rubber in future years is of
vital importance to natural rubber producing countries. The purpose of
this section is to utilize the empirical results of the previous section















actual
-----------predicted


60






| 50


0

CO

S40






30






20



19Z


50 52 54 56 58 60 62

Figure 5.--Actual and predicted RSS#1 prices in New York, 1948-68











to forecast United States imports and RSS#1 prices of natural rubber for
the years 1969 through 1980.

Forecasting With Stochastic Models
The objective of forecasting in time series analysis is to estimate
the value of a random variable in a future period based on relationships
obtained from sample observations. As Klein [17,p.13] states, "[A forecast]
can be formulated as an unqualified statement about the future, regardless
of external or exogenous events. This is called unconditional [forecast],
while a [forecast] that is qualified by assuming that some exogenous events
must simultaneously occur is ... conditional [forecast]. Forecasts made
in this study fall in the second category, namely, conditional forecasts.
The general linear model used in this study represents the relation-
ships between a random dependent variable, y, and a set of independent
variables, X2, X3, ... Xk, which are known constants. The relationship
between y and the X 's are assumed to be linear in the actual variables,
as given below:

yt = 1 + B2X2t + kkt + ut' t=l, ..., n.
Having obtained the least-squares estimates, bl, b2, ..., bk of the para-
meters, 1, B2' "..., k we may write the estimated relationship between
21
y and the X 's as follows:

yt = bl + b2X2t +...+ bkkt + et, t=l, ..., n;
where e is the unexplained residual.
F
Letting the value of y in forecast period T be y and given forecasted
22
values of the X.'s, the following relationship holds:
F F F F
T = 1 + 2T +" + kkT + uT,
F 2
where uT is assumed to have zero mean and constant variance (a ).
T F u
Taking the conditional expectation of y for a given set of forecasted
values of the Xi's gives:


21
2The discussion which follows is based, in part, on [12,pp.168-170]
and [17,pp.255-57].
22
It is assumed that the i's remain unchanged during the forecast
period.











E(yTl2 = 2 "'' Yk 1 + 2XT + + 'kiT .

By the Gauss-Mar1off theorem the heat linear unbiased estimate of this
function is:

yT bl +b2X2T +...+ bkT = Tb,

where yT is the forecasted value of yT with variance XF EbbXT and b is
the least-squares estimate of 8. Zbb is the variance-covariance matrix
of b (see Appendix Tables 2 and 3).
In using the linear model to forecast the dependent variable, it is
assumed that during the forecast period the structural relationships of
the model are the same as during the sample period.23 This essentially
means that the intercept and the coefficients of the independent varia-
bles do not change during the forecast period. Two other assumptions are
F
that the forecast disturbances, u are normally and independently dis-
tributed with zero mean and finite and constant variance, and that these
disturbances are independent of the bi's (i=1, 2, ..., k).
The error of forecast is defined as:
F ^F

HF F F
fT = YT YT.

Hence, fT ( b) (2 b2)XT +.+ (B bk)Xt + u

or in matrix notation:

f = X.' ( b) + u.
The expected value of the forecast error is:

E(f) XF' E( b) + E(uF) = 0

The variance of forecast error is:

Var(fT) = E(fT) [E(fT)] = E(f)2


F, F 2
= XT h XT u
^F
= Var(y)T + var(u)


23
2For a discussion of forecasting under unchanged structure, see [13]
and [19,pp.266-273].










Thus the variance of forecast error is made up of two components -- the
variance of yand the variance of u. The latter is estimated by SSE/n-k.
Letting s^F be the estimated standard error of forecast, the tolerance
T ^F ^F
interval of the forecast, y T is defined as: y + ks^F.
T- YT
The value of k depends on the percentage, p, of future observations which
lie in the interval, on the probability, y, of obtaining this percentage,
24
and on the sample size, n.24 In the present study the value .95 was chosen
for y. Three alternative values for p were chosen: .75, .90, and .95.
The values of k for y = .95, n 21 at the three different levels of p
are as follows [3,p.102]:
p = .75 ; k = 1.599
p .90 ; k = 2.286
p = .95 ; k = 2.723

Forecasting the Predetermined Variables
The method of forecasting the predetermined variables requires some
explanation. The forecasted values of the predetermined variables are
given in Appendix Table 4.

Imports
Recall that the major determinants of United States imports of natural
rubber were identified as: the war dummy variable (W), the ratio of syn-
thetic to total rubber consumption (R), production of trucks and buses
(TB) and releases of rubber from the government stockpile (RGS). For the
purpose of forecasting imports it is assumed that no major war will occur
during the period of forecast. The ratio variable, R, is forecasted to
reach .80 in 1970 and remain at this level through to 1980. Figure 2
(page 4) shows that this value is not too unrealistic because the ratio
of natural rubber consumption to total rubber consumption appears to be
approaching, asymptotically, the twenty percent level, in which case, R
wouLd approach the eighty percent level. The production of trucks and
buses is forecasted to increase at the rate of three percent per year
from 1969 to 1980. This forecasted rate of growth is equal to the average


2k increases with p and y, and decreases with n [17,p.257]. For a
thorough treatment of the concept of the tolerance interval, see [3].










growth rate during the five year period, 1964-68. As for the variable
RGS, it is assumed that no more rubber will be released from the stockpile
after 1970.

Prices
Determinants of RSS#1 price of natural rubber include: Pt-,l Rt-l'
ICRt_1, IAPt and QRt. There is no need to forecast the initial value
for lagged price because the actual value is available. The value of
P for 1969 is the observed 1968 price. From 1970 to 1980 the lagged
t-l
prices are the forecasted prices obtained from the price equation. If
a large error is made in forecasting 1969 price this error will be compound-
ed in subsequent years because of the auto-regressive nature of the fore-
cast price equation. Hence, the forecasts become less and less reliable
as we go further and further into the future. This problem is recognized
by the authors but no suggestion can be given to circumvent it. The lagged
price will be treated as any other predetermined variable.
The values for R t are based on the values of Rt used-to forecast
imports. The ratio of beginning inventories to consumption of natural
rubber in the previous year, ICRtl, is forecasted to remain constant
at .18, which is the simple average of ICRt_1 for the sample period.
This is no doubt an oversimplification. Historically, the ratio has
ranged from .1238 (in 1951) to .2683 (in 1949). In 1969 it was .1853.
Because the ratio did not exhibit any secular trend during the sample
period (see Appendix Table 5), there was no basis for assuming it to be
a function of time.
The forecasted values for the index of automotive production were
derived from extrapolations of the line fitted by hand to IAP data for
the ten years beginning with 1959. As for reclaimed rubber consumption,
this too did not show any secular trend. It ranged from 222,700 tons
to 346,100 tons during the sample period (see Appendix Table 5), having
a mean value of 270,000 tons. This average value was considered too high
to use for forecasting, compared with the average value for the last five
years. The forecasted value of reclaimed rubber consumption for the en-
tire forecast period is the average of QR for the last five years (1965-
69), namely, 253,000 tons. During those five years reclaimed rubber con-
sumption ranged from 239,000 tons to 269,500 tons.











RESULTS OF THE FORECASTS

The results of the forecasts are given in Tables 4 and 5. No attempt
was made to use other forecasts of the predetermined variables in fore-
casting RSS#1 prices and imports of natural rubber.
Some salient features of the results of the forecasts can be pointed
out. Forecasted imports (Table 4) increase steadily over the entire fore-
cast period, i.e., from 1969 to 1980 (see Figure 6). The increases in
imports are of course conditional upon the materialization of the assumed
values of the predetermined variables, the accuracy of the forecast model
and the assumption of an unchanging structure. Because the present attempt
is not to make point forecasts (which are average values of the dependent
variables, given certain levels of the predetermined variables) greater
attention should be given to the tolerance intervals than the point fore-
casts. Notwithstanding the last remark, the forecast imports do look a
bit high (Figure 6). For the years 1978-80 the point forecasts lie well
beyond the range of the sample data. The highest level reached for im-
ports was 806,600 tons in 1952. The point forecast for 1980 imports is
850,540 tons. Perhaps the lower limit of the tolerance interval for
p = .75 would be a more realistic figure, that is, 671,000 tons.
For the sake of comparison and validation, we note that actual imports
in 1969 were 585,300 tons. The forecasted 1969 imports, based on actual
values of all predetermined variables, are 623,990 tons with a tolerance
interval (p = .75) of 520,570 to 727,410 tons. The observed quantity does
lie within this tolerance interval.
In Table 5, forecasts of RSS#1 price of natural rubber are presented
along with the variances of forecasts and the tolerance intervals. The
forecast value of RSS#1 price for 1969 is 18.77 cents per pound, which
is 7.43 cents lower than the observed value of 26.20 cents per pound.
This relatively large error may have originated from the low value of
IAP forecasted for 1969. This index was 174.2 in 1968, but in 1967 it
was only 149.1 (see Appendix Table 5). The forecasted value for IAP in
1969 was 153.0. It is not until 1973 that the forecasted level of IAP
surpasses the actual 1968 level (see Appendix Table 4). Because the

1969 forecast price is well below the actual, i.e., observed price, all
subsequent price forecasts will be underestimated.








Table 4.--Forecasts of natural rubber imports, variances of forecast errors and tolerance intervals,
1969-80




Forecasts Variance Tolerance intervals (y = .95)
Year of imports of
[E(QMIX')]a forecasts p = .75 p = .90 p = .95
E(fT)2 Lower Upper Lower Upper Lower Upper
limit limit limit limit limit limit


-----------------------------1,000 long tons------------------------------------

1969 623.99 4,183.34 520.57 727.41 476.14 771.85 447.87 800.11
1970 675.54 6,094.27 550.71 800.37 497.08 854.00 462.97 888.11
1971 690.79 6,521.78 561.66 819.92 506.18 875.40 470.89 910.69
1972 706.54 6,990.00 572.85 840.23 515.42 897.66 478.88 934.20
1973 722.79 7,501.51 584.30 861.28 524.80 920.78 486.95 958.63
1974 739.54 8,058.97 596.00 883.09 534.99 944.76 495.09 983.99
1975 756.79 8,665.12 607.94 905.64 543.99 969.59 503.32 1,010.27
1976 774.54 9,322.81 620.15 928.93 553.82 995.26 511.62 1,037.46
1977 793.70 10,034.90 633.52 957.88 564.70 1,022.70 520.92 1,066.47
1978 811.54 10,804.50 645.33 977.75 573.92 1,049.16 528.50 1,094.58
1979 830.79 11,634.60 658.32 1,003.26 584.21 1,077.37 537.08 1,124.50
1980 850.54 12,528.30 671.56 1,029.50 594.67 1,106.41 545.76 1,155.33


aX' is a vector of forecasted predetermined variables.










Table 5.--Forecasts of RSS#1 price, variances of forecast errors and tolerance intervals, 1969-80


------------- per pound---------------------------------------
18.77 9.42 13.86 23.68 11.75 25.79 10.41 27.13


1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980


20.19
19.41
19.62
20.19
20.83
21.61
22.39
23.10
23.90
24.63
25.38


9.47
9.61
9.69
9.78
9.97
10.36
10.89
11.51
12.42
13.35
14.50


15.27
14.45
14.64
15.19
15.79
16.47
17.11
17.68
18.27
18.79
19.29


25.11
24.36
24.60
25.19
25.88
26.76
27.66
28.52
29.54
30.47
31.47


13.16
12.32
12.50
13.04
13.62
14.26
14.84
15.35
15.85
16.28
16.68


27.22
26.49
26.74
27.34
28.05
28.97
29.93
30.84
31.96
32.98
34.09


11.81
10.97
11.14
11.67
12.24
12.85
13.40
13.86
14.31
14.68
15.01


28.57
27.85
28.10
28.71
29.43
30.38
31.37
32.34
33.50
34.58
35.75


aZ' is a vector of


forecasted predetermined variables.













900



850



800



750



700



650



600



550



500



450



400


350

194


Sia
'I\

\ I aI
I







a

a


\ 'I'
'1~
~ a


, I'I


\I \
'I



%

*% '


I
/

I

I

\ I
\7


76 78 80


I


8


50 52 54 56 58 60 62 64 66 68 70 72 74

Figure 6.--Actual United States imports of natural rubber, 1948-68.
and forecasted imports, 1969-80


I ; i l I I I I .


,
r



r'/
r


i i











Figure 7 illustrates themagnitudes of-the forecasted prices and the
observed prices for the sample period.


SUMMARY AND CONCLUSIONS

This study has attempted to identify the economic variables that
influence United States import demand and prices of natural rubber, and
to measure import demand and price relationships for the period 1948-68.
Another objective was to make conditional forecasts of United States imports
and CRSS#l) prices of natural rubber for the period 1969-80 based on the
estimated demand and price relationships. Two models were formulated to
explain import demand and price. Model I contains two simultaneous equa-
tions in which imports and RSS#1 prices of natural rubber are jointly
determined. Estimation of this model was by the method of two-stage
least squares. In Model II demand and RSS#1 price relationships were
estimated independently by ordinary least squares.

Summary
Model I did not adequately explain the demand and supply of natural
rubber. On the basis of Model I the hypothesis of simultaneous determina-
tion of imports and prices of natural rubber was rejected. Model II
provided better explanation of import demand and RSS#1 price. The results
from Model II formed the basis of all conclusions drawn in this study.
The results showed that the major fact rs which influenced imports were
the ratio of synthetic to total new rubber consumption (percentage share
of the market), the war dummy variable, the production of trucks and
buses and releases of natural rubber from the United States strategic
stockpile. These four variables explained about 92 percent of the varia-
tion in imports during the period 1948-68. Of these variables, stock-
pile releases contributed most toward explaining imports. A one thousand
ton increase in stockpile releases was associated with a 1,660 ton reduction
in natural rubber imports.
The production of trucks and buses was next in importance in explaining
imports. A one thousand unit increase in the production of these heavy
vehicles was associated with a 232 ton increase in natural rubber imports,
indicating the importance of the heavy tire industry as a major user of
natural rubber.
















I\
Il

-I i
I i






I


i

I I'
I
II
I I
I I
I I
I
'I


I


- I
I
I
I
I
I
4.
4.-
4.... ~
4.


I i


j a i i I I a I a a I I A M"I 2
1948 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80

Figure 7.--Actual average price of RSS#1 natural rubber in New York, 1948-68,
and forecasted prices, 1969-80


I
I

S I

/
F:

hI










Excluding the war dummy variable, the ratio of synthetic to total new
rubber consumption, although highly significant in the statistical sense
appeared to contribute least towards explaining imports. A unit increase
in this ratio (or an increase of .01) was associated with a 516 ton reduc-
tion in imports. This finding demonstrates the impact on natural rubber
imports of the various technological advances in the synthetic rubber
industry.
The coefficient of the war dummy variable indicated that, on the
average, the United States imported about 141 thousand tons more rubber
per year during the Korean War years than during other years. This find-
ing implies there was an increase in demand for natural rubber during
the Korean War.
On the price side, the results (based on Version 2 of the price
equation) showed that the lagged ratio of synthetic to total rubber con-
sumption was the most important variable influencing RSS#1 price of natural
rubber. A unit increase in this lagged ratio was associated with a .66
cent per pound reduction in current RSS#1 price.
A one unit increase in the ratio of beginning inventories of natural
rubber to natural rubber consumption in the preceding year was associated
with a 1.16 cents per pound reduction in RSS#1 price. An increase of
one unit in the index of automotive production was associated with a
.11 cent increase in RSS#1 price, implying that general economic conditions
do influence RSS#1 price. RSS#1 price in the previous year also influenced
current RSS#1 price. A one cent increase in RSS#1 price in the previous
year was associated with a .35 cent increase in the current year's price.
There was some empirical evidence to support the claim that releases
from the United States strategic stockpile have a dampening effect on
natural rubber prices in the New York market.
The significant and positive coefficient of reclaimed rubber suggested
that reclaimed rubber is complementary with natural rubber in the produc-
tion of rubber products. A one thousand ton increase in reclaimed rubber
consumption was associated with a 117.8 ton increase in natural rubber
imports.
The forecast results showed that United States imports and RSS#1
price are likely to increase from 1969 to 1980. The increase in imports
are conditional upon increases in the production of trucks and buses,












while the increases in RSS#1 price are dependent upon continued increases
in the index of automotive production and the cessation of U.S. stockpile
releases of rubber after 1970.

Conclusions

Some rather general conclusions can be drawn from the results of
this study. The level of imports and prices of natural rubber in the
United States appear to be determined for the most part by general econo-
mic conditions in this country implying that natural rubber producing
countries must accept the New York price of natural rubber as given.
In addition, the demand for natural rubber in the United States appears
to be infinitely inelastic with respect to RSS#1 price.
Net foreign exchange earnings to natural rubber producing countries
depend on the volume imported and the difference between the prices re-
ceived for natural rubber and the costs of production. Since producers
of natural rubber apparently have little control over the volume imported
and cannot influence the prices received for rubber in the United States,
they should strive to increase foreign exchange earnings by reducing their
cost of production. Great progress has already been, and will continue
to be, made in reducing costs of producing natural rubber. Replanting with
higher yielding clones, adoption of improved tapping systems, application
of yield stimulants, e.g., ethrel applied to the bark of rubber trees,
are some ways of reducing production costs and/or increasing the yield of
rubber trees. These measures have either been successfully applied or have
a great potential for successful application.
Another avenue which can be exploited more fully is in the marketing
of natural rubber. In this respect, the introduction of the Standard
Malaysian Rubber (SMR) scheme, in which natural rubber is graded according
to technical specifications, rather than the conventional visual standards,
is perhaps one of the greatest achievements of the rubber industry in
Malaysia. This major breakthrough is the result of years of research under-
taken by the Rubber Research Institute of Malaysia. This method of grading
will place natural rubber on an equal footing with synthetic rubber as
far as technical qualities are concerned. The SMR scheme should of course
be expected to include a greater proportion of the natural rubber exported.
The present study has concentrated only on the United States rubber
market, and has attempted to identify the determinants of imports and RSS#1












price of natural rubber. It is also the first study of its kind. Future
economic research should focus on measuring the basic economic relation-
ships in other major world markets, such as France, Germany and the
socialist countries. Studies of this type would hopefully provide natur-
al rubber producing countries with more complete information on the world
market for natural rubber. With this information natural rubber pro-
ducing countries might be in a better position to establish a pattern
of exports to consuming countries that would increase their foreign
exchange earnings. The present study, although limited in nature and
scope, provides an important beginning to more extensive studies of the
major natural rubber markets of the world.





































APPENDIX










Results for Model I

The regression equations and related statistics obtained for
Model I are given in Appendix Table 1. The demand equation esti-
mated by two-stage least squares (column 1) shows there is an insig-
nificant relationship between RSS#1 price and quantity demanded
of natural rubber. In the supply equation, RSS#1 did have a sig-
nificant effect on quantity supplied, but the coefficients of the
remaining variables have unexpected signs even though they are
statistically significant. Other versions of Model I were esti-
mated but the results did not improve. In fact, Model I was rather
sensitive to slight changes in specification, a characteristic which
sheds considerable doubt on the validity of Model I.
On the basis of the results given by the two-stage estimation
of Model I, the assumption of joint determination of prices and
imports appeared untenable. Accordingly, Model I was reestimated
by ordinary least squares methods (last two columns of Table 1).
The results did not improve. The coefficient of imports in the
demand equation and the coefficient of price in the supply equation
were both statistically insignificant.
Ordinary and two-stage least squares estimation in the double-
log form also gave poor results. On the basis of the results ob-
tained from the various estimations of Model I, it was concluded
that Model I was a poor representation of the natural rubber mar-
ket in the United States. Clearly, Model I is inadequate for pur-
poses of forecasting United States imports and prices of natural
rubber as evidenced by the poor fits obtained for the reduced form
equations. Moreover, Model I seems to suggest that prices and
quantities imported of natural rubber are not jointly determined.











Appendix Table l.--Regression coefficients and related statistics for natural
rubber, Model I


Structural
Explan- equations a Reduced-form
atory Demand Supply equation
variables (Pt) (QM) (P)


Constant
term 515.653 1012.112 -1041.061
d
QMt .489
(.639)

P .398***
t (.174)

QA .116 -.980***
t (.170) (.280)

QE -.233** 1.340***
t (.082) (.454)

AI -.135 --1.421
t (2.555) (2.243)

P .427*** .270
t-i (.142) (.240)


2
.5132

D-W n.c. n.c. n.c.


Continued










Appendix Table l.--Regression coefficients and related statistics for natural
rubber, Model I--Continued



Structural
Explan- Reduced-form equations
atory equation Demand Supply
variables (QMd) (P) (QMS)
t ~t


625.510


Constant
term

QMd
t


QAt


QEt


-.402**
(.174)

.300
(.282)

1.540
(1.390)

-.340***
(.149)


P
t-1


.5858

1.1184d


707.367


.220
(.385)


1213.915





.188
(.123)


-.158
(.103)


.274***
(.084)


.242
(2.466)


-.407**
(.152)


.261

1.952c


.509

.963d


R2

D-W


aIn actual variates, by two-stage least squares.

Standard error of the estimate.

CNo serial correlation.

dThe test was inconclusive.

eBy ordinary least squares.

n.c.Not computed.

***Statistically significant at the one percent level.
** Statistically significant at the five percent level.











Appendix Table 2.--(X'X)-1 Matrix for natural rubber import equationa


5.924 -5.4107 .313002 -.002403 .188433
8.21968 -.0000245 .0005818 -.016056
.508239 -.0003683 -.002671
.0000018 -.0000094
.0000911



aRequired to obtain an estimate of the variance-covariance matrix of
the regression coefficients; est. Var(u) = 1897.958.


Appendix Table 3.--(Z'Z)- Matrix for natural rubber price equation,
Version 2


42.406 .03652 -24.075 -51.997 .04161
.00131 -.12586 .03565 .00047
29.8962 19.3259 -.08497
94.2094 -.01676
.00031


-.08745
-.00021
.05638
.08721
-.00013
.00021


aRequired to obtain an estimate of the variance-covariance matrix of the
regression coefficients; est. Var(v2) = 7.9449.











Appendix Table 4.--Forecasted values of the predetermined variables used
to forecast imports and prices of natural rubber





Year R TB RGSt ICRtI IAPt QRt
t t t t-L t t
(1,000) (1,000 (1957-59 (1,000
long = 100) long
tons) tons)


1969 .7729a 1,982.0a 34.758a .18a 153.0 242.4a
1970 .80 2,041.0 0 .18 162.5 253.0
1971 .80 2,102.0 0 .18 167.0 253.0
1972 .80 2,165.0 0 .18 171.5 253.0
1973 .80 2,230.0 0 .18 176.0 253.0
1974 .80 2,297.0 0 .18 180.0 253.0
1975 .80 2,366.0 0 .18 185.0 253.0
1976 .80 2,437.0 0 .18 189. 253.0
1977 .80 2,510.0 0 .18 193.0 253.0
1978 .80 2,585.0 0 .18 198.0 253.0
1979 .80 2,662.0 0 .18 202.5 253.0
1980 .80 2,741.0 0 .18 207.0 253.0


aActual values.











Appendix Table 5.--Data used in estimation of import demand and price
equations for natural rubber





N.Y. NR SR RR World Beg. End.
Year RSS#1 cons. cons. cons. NR NR NR
price (1,000 (1,000 exports exports inven. inven.
(cents/ long long (1,000 (1,000 long tons)
pound) tons) tons) long
tons)


1947a
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969


20.8
21.9
17.6
41.3
60.0
38.6
24.1
23.4
39.0
34.3
31.1
28.2

36.5
38.5
29.6
28.5
26.3

25.2
25.7
23.6
19.9
19.8
26.2


562.7
627.3
574.5
720.3
454.0
453.7
553.5
596.3
634.8
562.1
538.8
484.5
555.0
479.0
427.3
462.8
457.2
481.5
514.7
545.7
488.8
581.9
588.0


442.1
414.4
538.3
758.9
806.9
782.1
636.7
894.9
874.5
925,9
879.9
1072.7
1079.2
1102.2
1255.9
1306.8
1451.5
1540.0
1666.0
1628.0
1896.0
2001.0


261.1
222.7
303.7
346.1
280.0
285.1
249.0
312.8
270.5
266.9
248.2
290.4
276.5
250.3
263.4
263.7
263.2
269.5
264.5
239.3
250.4
242.4


1457.5
1440.0
1785.0
1822.5
1715.0
1640.0
1727.5

1842.5
1787.5
1830.0
1845.0
2005.0
1883.0
2010.0
1993.0
1960.0
2098.0
2190.0
2228.0
2295.0
2453.0
2550.0


129.0
141.5
106.6
89.2
76.6
95.3
112.3
104.5
110.1
166.5
101.4
77.8
79.4
77.3
68.0
70.2
60.0
86.8
100.0
91.6
111.7
107.8


Source: [28] unless stated otherwise.

aRequired for lagged variables only.


141.5
106.6
89.2
76.6
95.3
112.3
104.5
110.1
116.5
101.4
77.8
79.4
77.3
68.1
70.2
60.6
86.8
100.0
91.6
111.7
107.8
103.5


Continued













Appendix Table 5.--Data used in estimation of import demand
equations for natural rubber--Continued


and price


Year Ind'l NR SBRc Prod'nd Indexe
Whole- imports cons. of of
sale (1,000 (1,000 trucks auto-
Price long long tons) & buses motive
Index tons) (1,000) prod'n.
(1957-59= (1957-59=
1.0) 100)


1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969


.817
.800
.829
.915
.894
.901
.904
.924
.965
.992
.995
1.013
1.013
1.008
1.008
1.007
1.012
1.025
1.047
1.063
1.090
1.127


735.3
660.6
802.2
734.7
806.6
647.5
597.2
637.2
579.3
553.7
475.2
573.6
410.7
390.9
421.5
379.5
441.2
445.3
431.6
452.8
540.2
585.3


345.3
321.1
416.2
626.4
666.4
624.2
500.3
742.0
724.0
767.2
730.2
886.3
904.4
895.0
979.1
974.1
1056.4
1096.2
1152.5
1106.3
1280.8
1302.2f


1369
1132
1344
1412
1218
1204
1023
1246
1104
1090
871
1140
1198
1128
1254
1463
1561
1785
1764
1585
1951
1982g


d


b[7] d[23]
c[23] n.a. not available


72.6
72.0
90.6
80.1
72.1
91.3
85.0
118.3
97.8
105.2
86.0
108.1
123.2
111.8
131.1
131.1
145.1
167.2
163.0
149.0
174.2
n.a.


Continued











Appendix Table 5.--Data used in estimation of import demand
equations for natural rubber--Continued


and price


Year U.S. Ratio of Ratio of
stockpile SR cons. beginning
releases to total inventory
(1,000 new rubber to NR cons.
long cons. in previous
tons) (Rt) Year (ICRt_1)


1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969


0
0
0
0
0
0
0
0
0
0
0
6.786
88.937
25.770
56.097
84.191
95.974
119.660
154.686
96.884
78.615
34.758


.4987
.4134
.4190
.4277
.6257
.6401
.5850
.5164
.5850
.6087
.6321
.6449
.6590
.6926
.7206
.7307
.7408
.7509
.7495
.7533
.7691
.7652
.7729


.2292
.2683
.1855
.1238
.1687
.2100
.2029
.1752
.1734
.2073
.1882
.1606
.1431
.1614
.1594
.1517
.1325
.1803
.1943
.1679
.2285
.1853


e[29]

fComputed from figures given in [15].









BIBLIOGRAPHY


[1] Adams, P. F. Memorandum on the Fluctuations in the Price of Natural
Rubber. Kuala Lumpur: Malaysian Government Printer, 1958.

[2] Ayob, A. "An Econometric Analysis of United States Import Demand
and Prices of Natural Rubber" (unpublished M.S. thesis, Univ-
ersity of Florida, 1971).

[3] Bowker, A. H. "Tolerance Limits for Normal Distribution," in Eisen-
hart, C., M. Hastay and W. A. Wallis (Eds.). Techniques of
Statistical Analysis. New York: McGraw-Hill Book Co., 1947,
pp.97-110.

[4] Burgess, J. V. "The Case for the Rubber Market," Rubber and Plas-
tics Age, May 1965, pp. 527-9.

[5] Council of Economic Advisers. Economic Report of the President.
Washington: U. S. Government Printing Office, 1969.

[6] Durbin, J. "Testing for Serial Correlation in Least Squares Re-
gression When Some of the Regressors are Lagged Dependent
Variables," Econometrica 38: 410-20, May 1970.

[7] Economic Statistics Bureau of Washington D. C. The Handbook of
Basic Economic Statistics. Vol. 24, No. 1. Washington,
January 1970.

[8] Food and Agriculture Organization, United Nations. Agricultural
Commodities Projection for 1975. Vol. 1. Washington,


[9] Commodity Review 1968. Rome, 1968.

[10] Synthetics and Their Effects on Agricultural Trade. Commodity
Bulletin Series No. 38. Rome, 1964.

[11] Federal Department of Information, Malaysia. Malaysia in Brief.
Kuala Lumpur, 1967.

[12] Goldberger, A. S. Econometric Theory. New York: John Wiley & Sons
Inc., 1964.

[13] Horowitz, Ira. "An Econometric Analysis of Supply and Demand in the
Synthetic Rubber Industry," International Economic Review
4: 325-45, September 1963.

[14] Hurwicz, L. "Prediction and Least Squares," in Koopmans, T. C. (Ed.).
Statistical Inference in Dynamic Economic Models. New York:
John Wiley & Sons, Inc., 1950, pp. 266-273.

[15] International Rubber Study Group. Rubber Statistical Bulletin. London,
August 1970.










[16] Klein, Lawrence R. A Textbook of Econometrics. Evanston, Illinois:
Row, Peterson & Co., 1953.

[17] An Essay on the Theory of Economic Prediction. Chicago:
Markham Publishing Co., 1971.

[18] Knorr, K. E. World Rubber and Its Regulations. Palo Alto, California:
Stanford University Press, 1945.

[19] Kogiku, K. C. "A Model of the Raw Materials Market," International
Economic Review 8: 116-20, February 1967.

[20] Koopmans, T. C. "Measurement Without Theory," Review of Economics
and Statistics 29: 161-72, August 1947.

[21] McHale, T. "Changing Technology and Shift in Supply and Demand for
Rubber: An Analytical History," Malayan Economic Review
9: 24-48, October 1964.

[22] Phillips, C. F., Jr. Competition in the Rubber Industry. Chapel Hill:
University of North Carolina Press, 1963.

[23] Rubber Manufacturers Association. Rubber Industry Facts. New York,
1969.

[24] The Rubber Industry in the U. S. A. New York, undated.

[25] Theil, H. Economic Forecasts and Policy. Amsterdam: North-Holland
Publishing Co., 1958.

[26] The Natural Rubber Producers' Research Association. Rubber Develop-
ments. Vol. 23, No. 3. Hertfordshire, England, 1970.

[27] United Nations Conference on Trade and Development. "A Provisional
Model of the World Rubber Market," in Review of Problems and
Policies for Specific Commodities Facing Competition from Synthe-
tics and Substitutes. Geneva, 1968.

[28] U. S. Department of Commerce. Current Industrial Report, Rubber:
Supply and Distribution for the U. S. Various issues.

[29] U. S. Office of Statistical Standards. Standard Industrial Classi-
fication Manual 1967. Washington: U. S. Government Printing
Office, 1967.

[30] Wilson, Joan. The Singapore Rubber Market. Washington: Eastern
Universities Press, 1969.

[31] Wright, W. Forecasting for Profit: A Technique for Business Manage-
ment. New York: John Wiley & Sons, Inc., 1947.




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