AN ECONOMETRIC ANALYSIS FOR THE IMPACTS OF CLIMATE
CHANGE ON CASH AND FOOD CROP PRODUCTION IN THE
GAMBIA∗
Bukhari M. S. Sillah
Department of Economics, College of Business
Administration, King Saud University, Riyadh
Tel: +966 4167 9905
e-mail:[email protected]
2009
∗
The author acknowledge the assistance of Fafanding Fatajo, Ministry of Agriculture, the Gambia, for
compiling crop and rainfall data.
1
AN ECONOMETRIC ANALYSIS FOR THE IMPACTS OF CLIMATE CHANGE
ON CASH AND FOOD CROP PRODUCTION IN THE GAMBIA
Abstract
This paper employs pooled and de-pooled data econometrics method to analyze the
impacts of climate change on cash and food crop production in the Gambia. The depooled method is EGSL panel data method with random time effect. It finds that land
size and rainfall ultimately determine changes in the crop production; the crop
production does not robustly respond to changes in its own price changes. But it
robustly responds to the yield changes. Yields and not own prices are found to the
right incentives to drive farmers to undertake crop cultivation. Groundnut and rice
productions are found to respond positively to new variety introduction, whereas
cotton, maize and sorghum productions have fallen in response to new variety
innovations.
1. Introduction
This paper attempts to investigate analytically how the climate changes are being
translated into the changes of cash and food crop production in the Gambia. Cash crop
production has a long standing tradition in the Gambia, and it has been the backbone
of the local economy giving employment and living to more than 70% of the
population. This tradition has been perceived to largely at the expense of food
production that the Gambia has become a net food importer. This has been the
situation since 1904 as the feeling can be read from this excerpt, “It is a difficult
matter in a small colony like the Gambia to deal year after year with the question of
agriculture. The groundnut is the main product, and the export has so often been
described that there is nothing fresh to add beyond once again stating that the welfare
of the colony depends on this crop. The people devote almost their whole attention to
it, only growing small quantities of millet, Koos, and corn for food.”1But as people
stick to the tradition and resist the change, the climate never stays the same. Here we
define climate to consist of rainfall and the variability of rainfall. We define the cash
crop to be the groundnut and the food crops to be paddy rice, sorghum, millet and
maize. This definition is also in accordance with what obtains in the National
Agricultural Statistics. The paper develops a production function for the crops, and
then analyzes how the crop production responds to the climate variable changes. The
study is driven by the desire to ascertain the responses of these agricultural crops to
1
The Colonial Report of the Gambia 1904, p.16
2
climate changes, so that since climate change mitigation takes both long time and
global effort, the Gambia farmer, can be advised correctly based on evidence on how
to adopt their agricultural traditions to climate change. The paper will be the first of
its kind in the Gambian context that will provide such econometric evidence for the
relationships between agricultural crops and the climate change in the Gambia. The
evidence can be put with other evidence around Africa to draw country case studies
that can inform the Africans of policies of climate change adoption. the study is
organized as section 2 gives a background review of the variables in the national
context, section 3 reviews some relevant literatures, section 4 presents the models,
section 5 presents the findings and the analysis, and section 6 concludes and derives
the policy implications. The research is constrained by data; we wish to start the
analysis from around 1843 when the groundnut trade was introduced in the Gambia,
but the data would not permit us. The data on the factors of productions of the crops
are not adequately available to allow us to conduct this study; instead we have
contented ourselves with the producer prices to capture the information about factors
of productions other land, which has been explicitly included in the model.
2. Background
In this background review, we take stock of the crop production and the climate
change from 1974 to 2007. The groundnut has more than a century observations; thus
a good picture can be drawn from it. The other crops have only recently been given
attention; there are limited observations on them. The climate change has been taken
for granted, very recently the national statistics has started documenting it; thus, the
paper, to some extent, has to make use of the international records on the climate
variables.
2.1 Crop productions
For the period 1974 – 2007, groundnut recorded the highest output of 151400 tons
and the highest yield of 1.537 tons per hectare in 1982. The lowest output for the
groundnut production was in 1996 at 45800 tons. Rice experienced the highest output
in 1980 at 42700 tons and the highest yield of 2.364 tons per hectare in 1995; and rice
is the only crop that registered a yield of more 2 tons per hectare. Its production
dropped to the lowest in 2007 at 11400 tons. Sorghum registered the highest
3
production and the highest yield in 2001 at 33400 tons and 1.275 tons per hectares
respectively. The highest millet production was seen in 2004 at 132500 tons, and its
highest yield was seen in 1983 and 2003 at 1.09 tons per hectares. Maize’s highest
output was recorded in 2003 at 33400 tons and its highest yield was recorded in 1974
at 1.982 tons per hectare. In terms of output variability, millet recorded the highest
among the crops at 0.6312 standard deviations per mean value; and rice recorded the
lowest output variability at 0.263standard deviation per mean value. Millet production
is often forgone for the sorghum and maize production, and that could be reasons for
its high output variability. Rice production is relatively stable as the traditional swamp
rice fields have been fairly cultivated annually; it experiences shocks when upland
and irrigation schemes are added. Upland rice fields heavily depend on rainfall, and
irrigation schemes rely on the machines and fuels, which are often unreliable.
Rainfalls and inputs other land do explain variations in the output; but farmers also
vary the land allocated to a specific crop resulting in the crop output variations. In
term of land use, Millet has the highest land use variability of 0.567standard deviation
per mean value; and groundnut has the lowest land use variability of 0.202standard
deviation per mean value. This confirms our initial observation that millet is a crop
that farmers easily forgo for other crops; its land use could be varied easily to satisfy
the land allocation of other crops. This is not the case with groundnut, which is the
cash source for the farmers; thus, the opportunity cost associated with groundnut
production is higher than that of the other crops. There is declining trends in the yields
of the crops. The other observation is that no single year has experienced highest
outputs for all the crops or lowest outputs for all the crops. Though there were climate
variations in this study period, there was no one year that was best or worst for all the
crops. Thus crops could respond differently to climate changes, crop specific effects
could be present and farmers’ behaviours in response to crop price changes could all
explain these differing output variations in the crops. This strengthens our choice of
panel data econometrics to be able to identify particularly crop specific effects. The
farmers’ behaviours are studied in the time series model to be able to identify the
substitution effects and cross price elsatcities of the crops.
2.2 Climate Changes
4
The Gambia has a semi-arid climate with two seasons, rain and dry seasons. The rain
season starts from June to October, and the dry season goes from November to May.
In December, the temperature falls as low as 13 Celsius degrees; it peaks up in the
months of April and May exceeding 40 Celsius degrees in some climatic zones. On
average, the temperature stands at 28 Celsius degrees. The country is 200km from the
tropical forests and 300km from the Northern Desert. It has three climatic zones
namely Sahelian, Sudanian-Sahelian and Sudanian-Guinean zones. According to
Trolldalen(1991), the rainfalls vary from zone to zone. For the Sahelian zone, the
rainfall can exceed 600 millimetres per annum; it ranges from 600 – 900 millimetres
for the Sudanian-Sahelian zone and 900 -1200 millimetres for the Sudanian-Guinean
zone. Similarly, the crop duration varies as 79 days, 71 – 119 days, and 120 – 150
days for the three climatic zones respectively, Trolldalen (1991). As the rainfall
varies, the crop durations vary and consequently the crop yields vary. The country has
been experiencing decreasing rainfalls. Trolldalen(1991) finds that Gambia has been
experiencing an average annual decrease of 15.5 % in the rainfall from 1886 to 1977.
For the period, 1990 – 2007, the highest annual rainfall was recorded in 1999 at
1174.76 millimetres, and the lowest was recorded in 2002 at 597.84 millimetres. In
this period, the annual rainfall declined eleven times from its previous year and
increased only six times. If this fact can be projected into the future, then we can say
there is 64.7 per cent chance that the annual rainfall will be lower in the next year than
this year with annual average decline rate of 10.1 per cent, and only 35.3 per cent
chance that it will be higher with an annual average increase rate of 27.9 per cent. The
high increase rate results from sudden jumps in the annual rainfalls following a series
of consecutive declines. Thus, from these rainfall patterns, we can infer that there is a
higher chance for a rainfall decline in the future than for an increase, and when it
increases, it is also likely to cause flooding.
3. Literature
Climate has direct linkage with the plants. The type of climatic zones also determines
the types of the plants. For plants to grow, they require essentially four major
resources, water, nutrition and temperature and light, Saugier(1996). Farmers can, to a
great extent, control the nutrition resource, and in the case of the Gambia light
resource is available all the year around, while temperature averaging 28 Celsius
5
degrees is suitable for the crops the farmers plant in the country. Thus, it remains
there only water resource that is beyond the control of the farmers, and which
eventually determines the crop yield in the country assuming the plant disease and
pests constant. In fact a major plant pest, locus, is dependent on the water (rainfall)
availability in the sub-region of West Africa. In a climatologically modelled study,
Jamieson, et. al (1996a) and Jamieson, et. al (1996b) find that causes of variations in
crop yields are largely due to temperature and rainfall. In an historical survey of the
agriculture in the Gambia from 1948 to 1983, Trolldalen (1991) find that “the food
problem and failed agricultural projects were explained as ecological degradation”
and “drought is a constant menace.” That is, it is rainfall that in fact determines the
entire health of the country, if it does not rain, it will be aid. The country will sustain
itself if it rains, and it will need aid, if it does not rain. Trolldalen then applies a
geographical model to evolution of the environment and agricultural production in the
Gambia and finds a correlation coefficient of 0.47 between cash crop and the
precipitation, a correlation coefficient of 0.47 between upland cereal crops (sorghum,
millet and maize) and the precipitation, and a correlation coefficient of 0.1 between
rice and the precipitation. Rice is grown in three areas upland, swamp and irrigated
fields. The irrigated fields depend less on the rainfall, but the upland and swamp rice
depend largely on the rainfall. However, in the long run, , all rice production depends
on the rainfall as the level of rainfall also determines the extent of salt intrusion inland
through the river flows from the Atlantic coast, Trolldalen(1991), causing damages
to the reverie rice fields of swamp and irrigation. The upland rice depends entirely for
water on the rainfall. In a cross country panel data for the Sub-Sahara Africa, Barrios
et. al (2008) find that rainfall and temperature have significant impacts on agricultural
production. The study does not spell out the responses of various country specific
crops to the climate change. Our current paper attempts, among other things, to fill in
this gap for the Gambia. The paper estimates the dependency relationships between
the rainfall and the various crops produced in the Gambia. Since the rainfalls can be
forecasted with great accuracy, then knowing the dependency degrees of various
crops on the rainfall will help the farmers choose an optimal combination of the
agricultural planting. This paper attempts to contribute this valuable information.
4. Theoretical Framework and the Econometric Model
6
We assume the crop production follows the Cob-Web theory, where this year’s
planting will depend on the last year’s produce price. We treat the supply of crop
output and the production to be the same, what is planted and harvested (production)
is also what is supplied as output; one is to be offered for sale, which is the cash crop
and the other to be supplied for food consumption and that is the food crop. But at the
beginning of planting, the decision about the size of area to plant and the variety of
the crops to plant can be influenced largely by prices obtained in the last trading
season. Thus, we generalize this functional relationship between output and price as,
Yit = f ( Pit −1 )
Where Y= crop output measured in tons
P=price per ton
i=1, 2… 5 (groundnut, cotton, rice, sorghum, and maize).
If the last year’s price was high, this year’s planting will be more ambitious than that
of the last years and hence this year’s output will increase. As much as last year’s
price determines this year’s output, this year’s climate condition will affect directly
this year’s output. In this model, we reduce the climate change to be the rainfall.
Given the climatic zone of the Gambia, rain is a major climatic variable that
determines the growth of plants including the cash and food crops, see section 3 for
the details. Total rainfall is crucial for the crops, likewise the distribution of the annul
rainfall, for example scarce rains in the beginning of the planting stunt the growth and
result in poor yields, whereas late rains into the time of harvesting spoil the harvest
and result in lower output. However, in a whole, it is the change in the annual rainfall
that this paper assumes ultimately matters to the agricultural production in the
Gambia. In addition, the technology of production is slash and burn, which implies
that more output is expected when more lands are cleared. Thus, land inputs are
relevant for explaining changes in the agricultural output in the Gambia. With the
rainfall, R, land inputs, L, and yield, our functional relationship will be res-specified
as, Current season output = F (last season price, last season yield, current season level
of rainfalls, current season rainfall variability, and current season land use)
We compact this relation respectively as
Yit = f (Pit −1 , YDit −1 , Rt , S t , Lit )
7
i= individual crops (groundnut, cotton, rice, sorghum, and maize)
P = price per metric ton
YD = yield per acre
R = annual rainfall in millimetres
S = within season rainfall variability
L = land use in acres
t= time period from 1990 – 2007. The explanatory variables are as defined
respectively above.
In an EGSL panel method with random time effect, I write specifically the above
relation after taking the natural logarithm of the variables as,
LnYit = c + µ i + ν t + β1 LnPit −1 + β 2 LnYDit −1 + β 3 LnRt + β 4 LnS t + β 5 LnLit + ε it
Where c is the regression constant, µ is the individual cross section effect, ν is the
time period effect, and ε is the random error term of the model. The error term and
the time period effects are assumed to be random and independent and normally
distributed; their sum will be random, independent and normally distributed. Let their
sum be υ . Then the model is,
LnYit = c + µ i + β1 LnPit −1 + β 2 LnYDit −1 + β 3 LnRt + β 4 LnS t + β 5 LnLit + υ it
The model has five explanatory variables that are expected to impact relevantly on the
crop output in the Gambia. The crop output is what has been announced and reported
in the national statistics appendices of the Gambia to the international Monetary Fund,
and various Central Bank Bulletins. This variable is measured in metric tons and it is
produced in five months from June to October every year. The model considers five
important input variables, which are two climate variables (level of rainfall and
rainfall variability), land use and two incentive input variables (last season price and
last season yield) to encourage farmers to continue undertaking farming activities.
Land and rain could be available, but without incentive to undertake farming, there
will be no crop produce. The model has limitation with respect to information on farm
labour and fertilizer. There is limited farm labour data and no farm labour
8
disaggregated data with respect to the various crops in the model. Officials are often
fond of stating that 75% of the population is engaged in farming and fully and
annually employed; we find that puzzling since the farming activity is effectively for
five months. Thus, 75% employment of the population is not for the full year, but at
most two-thirds of the year. Given these two reasons (non-available disaggregated
farm labour for the various crops and seemingly puzzling total farm labour), the
model cannot include farm labour input as one of the explanatory variables. Similarly,
the researcher cannot find reliable and complete disaggregated fertilizer data on the
crops. Nevertheless, apart from incentive to farming, it is rain and land that matter the
most in the traditional farming of the Gambia. More land use also embodies
information on farm labour, as increased population increases the use of land and the
data on land use are disaggregated with respect to the various five crops in the model,
and they are sourced from the National Statistics Appendices to IMF and various
Central Bank Bulletins.
This panel data model will produce the responses of the crops to their prices and the
rainfall. It will give us individual effects on each crop type.
Expected Signs of the Coefficients
The paper expects the model to exhibit positive sings for the coefficients of last
season's price per ton, last season's yield per acre, the level of land use and the level of
rainfall, whereas a negative sign is expected for the variability of rainfall. Higher last
season's price and yield are incentives for the farmers to undertake farming activities,
they are rewards for farming. I use the last season's rewards for the reason that current
season's rewards are unknown at the planting time; up to the time of planting the best
reward information available to the farmers is that of the last season; and this in
accordance of Cob-Web agricultural production theory. The price per metric ton used
in this paper is the trade season producer price announced and reported by the Gambia
Produce Marketing Board. Its name has changed many times, but its function
basically remains the same, which is to announce at every trade season the producer
prices of the produce, and buy whatever amount it could buy on either cash basis or
credit basis. In cases where I could find the producer prices of the Board, I
supplement the data with the similar produce prices in the IMF International Financial
Statistics. This latter has little direct bearing on the local farmers, who never
participate directly in selling their produce to the outside world. The Produce
9
Marketing Board interface between the local farmers and the rest of world; and it is a
monopsonist to a great extent. Thus its offer prices are less efficient that what would
obtain in the rest of the world, and hence distorting to the planting decision of the
farmers; and farmers could treat these prices irrelevant or disturbing to their farming
decisions. Nevertheless, farmers have to plant and farm to survive. They have few
alternatives to farming when it rains; there are few other employment opportunities
that they can substitute for farming. It is not the cash prices, which they often
reluctantly accept, that encourage them to undertake farming, but the yields that make
them subsist through the year. Therefore, I expect that the higher the last season's
yields were, the more ambitious the farmers became this season in their farming
activities, and consequently leading to higher output this season. Prices and yields are
rewards and incentives that determine whether or not the farmers would plant large
farm size or small farm size. These decisions are constrained only by the availability
of land and rain in this modelling of a traditional farm setting. Thus, in this setting,
more land, ceteris paribus, means higher output. The level of rainfall is expected to
have a positive impact on the current output, whereas the variability of rainfall is
expected to depress the current output, because it disrupts the season's flow of
farming activities. The rainfall is measured in millimetres, and is sourced from the
Department of Planning, Ministry of Agriculture. I calculate the variability from the
monthly data on rainfalls from June to October.
10
5. Results
Table 1 and 2 present the pooled data estimation and the EGSL panel method with
random time effect results respectively.
Table 1: Pooled Data Estimation
Variable
Coefficient
Std Error
T-Statistic
Probability
C
-1.676027
1.275743
-1.313765
0.1927
LnP(-1)
0.097291
0.045361
2.144812
0.0350
LnYD(-1)
0.142976
0.082770
1.727386
0.0880
LnR
0.737543
0.25469
2.895849
0.0049
LnS
-0.280193
0.205304
-1.364772
0.1762
LnL
0.734988
0.029932
24.55519
0.0000
R-squared
0.971632
0.969836
S.E of
regression
F-statistic
0.271648
Adjusted Rsquared
Sum squared
resid
Prob (Fstatistic
541.159
5.829639
0.0000
Durbin-Watson 1.662235
Statistic
11
Table 2: De-pooled Data Estimation: Panel EGLS (period random effects)
Variable
Coefficient
Std Error
T-Statistic
Probability
C
0.137512
1.069655
0.128557
0.8981
LnP(-1)
-0.10520
0.092179
-1.141368
0.2573
LnYD(-1)
0.146081
0.081015
1.803124
0.0754
LnR
0.973730
0.189225
5.145891
0.0000
LnS
-0.517972
0.140188
-3.694838
0.0004
LnL
0.657303
0.059149
11.11266
0.0000
R-squared
0.981304
0.97906
S.E of
regression
F-statistic
0.225957
Adjusted Rsquared
Sum squared
resid
Prob (Fstatistic
437.3917
3.82924
0.0000
Durbin-Watson 2.016033
Statistic
Cross Section Fixed Effects
Groundnut
Cotton
Rice
Sorghum
Maize
0.580767
-0.472549
0.080993
-0.02873
-0.012873
There are certain major differences between the two models:
I.
Lagged price variable has a correct expected sign and it is significant in
table 1; whereas it has a wrong expected sign and it is insignificant in
table 2.
12
II.
The sum squared residual of the regression is higher in table 1 and lower
in table 2. The adjusted R-squared is relatively higher in table 2 and
lower in table 1.
III.
Durbin-Watson statistic of table 1, and that of table shows no presence
of autocorrelation.
IV.
Rainfall variability has a correct expected sign but it is insignificant in
table 1, whereas it has a correct expected sign and it is significant in
table 2
The other explanatory variables, log rainfall, log last season yield, and log land
variables are significant and they the correct expected signs in both tables. These
variables have positive significant impacts on the crop output. When season's yield
last is high and land is available, then when it rains large farm sizes will be planted
and consequently the current season crop output will be high. The results show clearly
that last season's yield is relevant rewards for the farmers to further undertake farming
activity, whereas the producer price offered by the Gambia Produce Marketing Board
is irrelevant and distorting to the planting decisions of the farmers as table 2 shows.
More rainfalls means more crop output as indicated by both tables, it has the highest
individual impact on the crop output. This positions the climate impact as the most
important explanatory for the crop output in the Gambia in this study period. More
land also means more crop output. But slash and burn technology to increase land has
a limit as arable land is fixed in size. Thus, better technologies, which will not require
increased land, should be encouraged to boost the land productivity.
Panel data estimation with fixed individual effects and random time effects produced
interesting results. The land inputs and rainfall influence significantly the crop
production in both the pooled and de-pooled data estimation. Whereas, the
information about the past selling prices of the produce is found irrelevant, and has a
wrong sign. We interpret the individual effects as the crop specific effects in terms of
new variety and technological innovations introduced to influence the production of
the crops. Groundnut and rice have positive individual effects, while cotton, sorghum
and maize have negative ones. It can be inferred from these effects that groundnut and
rice have been responding positively to new variety introduction and technological
innovations, while cotton, sorghum and maize have responded negatively. This
explains to some degree why the farmers have been shunning the cultivation of
cotton. Groundnut is the most responsive crop to the new variety introduction and to
13
the technological innovations, whereas the cotton is the least responsive; the response
of the rice is also not encouraging. Recently, new variety and technology have been
introduced for rice cultivation, and this is reflected by the estimation in terms of the
positive cross section effects for rice. However, the new variety and technology have
not been more important for the agricultural production than the land size and the
rainfall. The estimation shows that farming is still largely land intensive and rain
dependent. 1% increase in the annual rainfall, holding other things constant, leads on
average to 0.738% increase in the crop production in table 1 run and a 0.974%
increase in table 2. On the other hand, a 1% increase in the land size, holding other
things constant, leads on average to a 0.735% increase in the crop production in the
table 1 and a 0.6573% increase in table 2. These two important determinants of the
agricultural output in the Gambia are also the most fast diminishing factors of
productions. Land size for the land intensive crops is shrinking due to the
encroachment of industrial projects and housings on the fertile lands. Whereas,
rainfalls are determined by the global climatic conditions, which have been
worsening, and as a result the country has been experiencing declines in the rainfalls;
the decline rate is estimated to be 15.5% per annum for the period 1886 - 1977,
Trolldalen (1991).
6. Conclusions and Policy Implications
The production of groundnut and coarse grains is significantly determined by the land
size devoted to them and the annual rainfalls. The groundnut and rice are found to
positively respond to new variety introduction and technological innovations, whereas
the cotton, sorghum and maize have been negatively responding. There are three
implications from the research findings. One, the individual effects, which are
interpreted here as crop specific effects such as new variety and technological
innovations, should be intensified for the groundnut and rice as they are found to
positively respond to these specific effects. The new variety introduction and
technological innovations for cotton, sorghum and maize should be revisited because
the current specific effects are found yielding negative results. Second, the land size
and rainfall ultimately determine the agricultural output. But land size is fixed, the
fertile land size in the country is estimated at 550,000 hectares, and in 2007, an
estimate of 34.95% of it was cultivated, and the cultivated area has been increasing on
14
average for the period of the study at a rate of 5.4% per annum. If this rate continues
for the next twenty years from 2007, the total arable land will be all cultivated. In
other words, in the next twenty years, assuming other things constant, the total arable
land will be slashed and burned for the crop cultivation of the land intensive crops.
Thereafter the production of the land intensive crops will be stunted unless the
technological innovations are added to the land. These technological innovations are
not expected to take place in the next twenty years, since the slash and burn
technology has been around for more than a century with negligible technological
improvements, and we cannot expect this old habit to die in the next twenty years.
The recommendation is that the agriculturalist scientists and the policy makers should
intensify the innovations and adoption of labour intensive crops, such as vegetables
and fruit plants that require relatively small land size to produce high output to boost
the total agricultural output of the country and minimize the slash and burn impacts on
the arable lands. This recommendation is further reinforced by the fact that rainfall is
both decreasing and highly variable, and production of land intensive crops cannot be
done by irrigation. The final implication from this study is that farmers do not
robustly respond to changes in the crop-own prices. That is, the produce own prices
have been distorted, and cannot function as a market signal for the farmers to change
their planting decisions. These distortions should be lifted to link accurately the
farmers to the world market price changes, so that resources can be better allocated
between the agricultural sector and the other sectors of the economy.
References
Balestro, P., Nervlove, M., (1996), Pooling cross-section and time series data in the
estimation of a dynamic model: The demand for natural gas, Econometrica, 34, 585 –
612.
Baltagi, B., Econometric Analysis of panel data, 3rd ed., (2005), John Wiley and
Sons, Chichester.
Barrios, Salvador; Outtara, Bazoumana, & Stroble, Eric, (2008), the impact of climate
changes on agricultural production: is Africa different? Food Policy August 2008, 33
(4), 287-298.
Branch, William A., (2002), local convergence properties of cobweb model with
rationally heterogeneous expectations, Journal of Economic Dynamics and Control,
27, Iss. 1, 63 – 85.
15
Curran, Sara R. et al. ed., (2009), the Global Governance of Food, Routledge
Publication.
Ferguson, C.E., (1960), learning, expectations, and cobweb models, Journal of
Economics, 20, no. 3- 4, 297 – 315.
Jamieson, P.D., Brooking, I.R., and Porter, J.R., (1996a), A new model of spring
wheat phenological response to temperature and day-length, Proc 8th Aus Agron
Conf, Brisbane, 337-340.
Jamieson, P.D., (2000), crop responses to water shortages, Journal of Crop
Production, Vol. 2, Iss. 2, 71 – 83.
Jamieson, P.D., Martin, R.J., Francis, G.S., and Porter, J.R., (1996b), Analyzing
wheat biomass and grain yield response to drought using AFRCWHEAT2, Proc 8th
Aus Agron Conf, Brisbane, 669.
Kaldor, Nicholas, (1934), a classificatory note on the Determinateness of Equilibrium,
the Review of Economic Studies, 1, No. 2, 122 – 136.
Marc, Nerlove, (1958), adaptive expectations and cobweb phenomena, Quarterly
Journal of Economics, 73, 227 – 240.
Matyas, L. Svestre, P., (1996), the econometrics of panel data, Handbook of theory
and applications, 2nd ed., Kluwer Academic Publishers, Dordrecht.
Mitra, Sophie & Boussard, Jean-Mar, (2008),
a non-linear cobweb model of
agricultural commodity price fluctuations, Department of Economics, Fordham
University, NY, U.S.A, discussion paper 2008- 11.
Peter, D.; Maracchi, G. & Ghazi, A. , ed., (1996), Course on Climate Change Impact
on Agriculture and Forestry, proceedings of the European School of Climatology and
Natural Hazards Course held in Volterra, Italy, March 16 – 23.
Saugier B., (1996), the evapotranspiration of grasslands and crops, C. R. Acad. Agric.
Fr. 82, 133-153.
Trolldalen, John Martin, (1991), on the fringe: a system approach to the evolution of
the environment and agricultural production in the Gambia, West Africa 1948 – 1983,
NORAGRIC Occasional paper series C, Agricultural University of Norway,
Development and Environment No. 10.
16