Managerial Economics

Analysis of the factors influencing the quantity imported of common wheat

Contents
Introduction 3

Literature revue 3

Panos Konandreas, Peter Bushnell and Richard Green (1978) 4
Won W. Koo (1984) 5
Daniela Kopp and Iain Wallace (1990) 6
Franqois Ortalo-Magne and Barry K. Goodwin (1990) 7
William W. Wilson (1994) 10
James N. Barnes and Dennis A. Shields (1998) 11
S. D. Rozelle and J. Huang (1998) 14
Samarendu Mohanty and E. Wesley F. Peterson(1999) 15
M. Uzunoz and Y. Akcay (2009) 16
L. J. S. Baiyegunhi and A. M Sikhosana (2012) 18
Methodology and results 18

Explanation of coefficients: 27
Elasticity Analysis : 30
Conclusion 32

References 33

Appendices 35

Introduction

Food habits vary in finction of countries and regions. In Morocco, the wheat production have reached 3400 million metric tons in 2012 ("Index mundi," ), which makes Morocco wheat production ranked in the 24th place, excluding EU.

All over the world, people consumption of wheat has increased in the majority of countries. Wheat is more and more used in every meal.

Due to its importance in the Moroccan alimentation, we decided to to conduct a study related to the imported quantity of common wheat. The objective of this study is to determine the factors influencing the quantity demanded of common wheat in Morocco.

In this project, we will make use of statistical tools like regression analysis. Our analysis will be through time for the period 1961-2010. Before to start this study, we expect to find a negative relationship between the quantity demanded and the price of wheat and a positive relationship between the dependent variables and the price of substitute, the GDP per capita and the total population.

Literature revue

Wheat is one of the most important commodities in the world. It is consumed worldwide under several forms: bread, pasta, breakfast cereals…(Baiyegunhi & Sikhosana, 2012). In 2011-2012, the world consumption of wheat attained 692 million tons. Total world production was 694 million tons ("International grains council," ). According to International Grains Council, China is the most important supplier with 169.4 million tons in 2010-2011, followed by the EU-27 with 157.6 million tons ("International grains council," ). Among different possible aspect to study the wheat market, the demand estimation including import and export is one of the most studied subjects for decades. In this literature review, we will present studies done in different countries, related to the demand of wheat or its pricing.

Panos Konandreas, Peter Bushnell and Richard Green (1978)

The objective of this paper is to estimate the export demand function for US wheat for five world region. The estimates of the influence of income, price and non-price variables on US wheat exports are obtained using various econometric procedures.

The authors adopt the following methodology:

• Specification of a model for the export demand for US wheat :

Mkt = a0 + a1 (PUSt / Pwt) + a2 (P’t / Pwt) + a3 (Pkt / Pwt) + a4 Ykt + ut

Mkt is the commercial import demand for US wheat by the kth country. It is assumed to be a function of that country’s domestic wheat price Pkt , world price of wheat Pwt, US export price PUSt , the world price of a substitute commodity for wheatP’t , and the country’s per capita real income Ykt .

• The estimation of the model using econometric methods incorporating extraneous information on the income coefficient of export demand;

• Derive the price and exchange rate elasticities and the policy implications of the results are analyzed.

The estimation uses data collected via annual observations from 1954-1972 for US wheat exports. Due a problem of availability of data, the food price index, expressed with a base of 1958=100 was used as a proxy variable for domestic wheat prices in the importing countries. The export demand functions were estimated by ordinary least squares, a mixed estimation procedure developed by Theil and Goldberger, and conditional least squares.

The major result of this study reflects the substantial effects of exchange rate on US wheat exports.

Won W. Koo (1984)

The author uses a spatial equilibrium model for the US wheat industry, developed on the basis of a quadratic programming algorithm. The model:

• Has transport and storage activities in shipping wheat from producing areas to domestic and foreign importing countries;

• Incorporates export supply equations at US export ports and import demand equations in importing regions;

• Has a basic structure similar to those developed by Furtan et al. with one difference: the model of this study includes domestic transportation activities associated with wheat shipments from producing regions to domestic consuming regions and export ports, and excludes wheat trade activities associated with other wheat export countries;

• Includes 49 domestic wheat producing regions and 23 domestic consuming regions. The study includes 12 export ports.

The study includes three different classes of wheat: winter, spring and durum. For modes of transportation are included: rail, truck, barge, and ocean vessel and 40 water access points as inland water ports on the river system. The social payoff function is calculated on the basis of wheat export supply equations for the three classes of wheat at each US export port and import demand function for the three classes in each importing region. The net social payoff, the objective function of the model, is equal to the social payoff less transportation costs in shipping wheat from producing regions to domestic consuming and export regions.

The data used for this model are:

• Demand for wheat in domestic consuming regions;

• Supply of wheat in producing regions;

• Transportation costs in shipping wheat from producing regions to domestic consuming and foreign importing regions.

• Export supply equations in US export are derivatives from export supply elasticities of US wheat at average export quantity and price levels;

• Import demand equations for each of the three classes of wheat are derived from import demand elasticities at average import quantity and price levels in each importing region;

• Domestic demand and supply of each class of wheat used in the model a three-year average of the data from 1978 to 1980 obtained from Wheat Situation.

• Transportation costs for rail, truck, barge, and ocean vessel are estimated on the basis of information obtained from industrial sources.

The study shows that under a free market system, the West Coasts ports have the highest price for winter and spring wheat ant the great Lakes have the lowest prices. Durum wheat price is higher at the Great Lakes and Gulf ports than at the West Coast. The geographic differences in price are due to trade restrictions and volatilities in transport costs.

The study also finds that tariffs imposed by European Economic Community EEC are absorbed more by the customers. Changes in ocean freight rate influence wheat price at US ports more than it impact importing countries.

Daniela Kopp and Iain Wallace (1990)

This article has as subject the import of wheat for non-traditionally wheat producing countries. The authors in this article identify countries whose imports of wheat are important but in which the crop has played a marginal role in domestic agriculture based on the following criteria:

• The country has to import more than 500000 tons of wheat in 1985;

• Wheat must have been sown on less than 10% of their arable land in 1960 and 1984;

The authors retain 60 states that fulfill these conditions and which accounted for 25% of world wheat imports in 1985. These nations are very diverse. The income levels, population density, the availability of agricultural land, the degree of urbanization, the identity of the traditional dietary staple and the significance of wheat in the contemporary diet differ markedly and unrelatedly among the sixteen countries. The diversity of the origins of imported wheat and the supply linkage stability are considerably different too.

The demand of wheat for countries reared on a different staple is influenced by a certain number of sometimes conflicting considerations: colonization, the westernization of lifestyles, the consideration of the wheat consumption as a symbol of modernization, the intervention of subsidies that have made wheat the cheapest marketed foodstuff. In addition, the states that import wheat are generally aid-dependent and have low prices for nutritional elements based on wheat (bread for example). The demand for wheat also reflects the ease of household preparation.

Another reason for the high bread import in the world is the use of this type of crop as a humanitarian aid initiative. Other factors presented by the authors that influence the import of wheat is that the majority of countries studies have coastal zone which simplifies the provision of imported wheat and the distribution of its product. Poor farm-to-market- systems of transportation, the lack of inland grain handling and storage facilities, and often the inferior baking qualities of local strains of wheat, have restricted government efforts at import displacement.

The implications of sizeable wheat imports vary and they affect both the national development goals and the country’s freedom of action in international affairs. If the import of wheat, especially from a single supplier, is significant for the country staple food supply, the country becomes vulnerable to the external pressures and to the threat of “the food weapon”. In general, the US government and transnational grain companies tend to counter the efforts of importing countries to weaken the growth of wheat consumption.

Franqois Ortalo-Magne and Barry K. Goodwin (1990)

The objective of the study is to determine the gluten wheat demand in United State. An econometric analysis has been done to evaluate the quantity demanded of gluten wheat. The variables that are taking in consideration are the price of flour, income, and protein amount for domestic harvest wheat harvest.

The study was motivated by the fact that the United State has made considerable investment in the gluten wheat over the past few years. The overcapacity of production of Gluten wheat in United State leads European countries to import from United State. This overcapacity of production is now higher than the quantity exchanged on the international market. U.S. imports play in the international market for wheat gluten; it is of interest to empirically examine factors that are related to the demand for imported wheat gluten in the U.S.

The model is estimated using monthly data over a l4-year period, from 1974 to 1987. The time series data start in 1974 because it represents the year of change in the presentation of import data. Therefore, the model is based on 168 monthly observations

Wheat gluten is mainly used as a protein complement in flour. As the protein amount of the wheat harvest increases, the need for gluten, and therefore, the quantity imported decrease.

The economic model is:

The dependent variable is the quantity of wheat gluten imported by the U.S.

The Independent variables are:

• Lagged import

• Price

• Price of complement

• Income

Other Explanatory and Policy Variables:

The objective is to incorporate within the model the various factors specific to the wheat gluten market that influences the U.S. import demand for this commodity. The previous analysis of this market leads to consideration of an average protein amount of the wheat harvest. This factor has been identified as the main factor influencing the demand for wheat gluten (Hesser, 1989(a); Pudden, 1989).

The chosen indicator is a weighted average of the protein amount of the wheat harvest in North Dakota and Kansas. North Dakota is the main state for the production of Hard Red Spring Wheat, the strongest wheat in protein produced in the U.S. Kansas is the main state for the production of Hard Red Winter Wheat, which ranks second as far as protein level is concerned. The weights are the amounts of each one of these wheat categories harvested. The value taken is the one calculated for the previous season. The value of "Pa" is calculated as:

Pa - «Pnd * HRSW) + (Pks * HRWW» / (HRSW + HRWW)

Pnd : Protein percentage of the wheat harvest in North Dakota

HRSW : Amount of the harvest of Hard Red Spring Wheat Protein

Pks : percentage of the wheat harvest in Kansas

HRWW : Amount of the harvest of Hard Red Winter Wheat

Relation between the Dependent and Independent Variables:

• The lagged import is positive

• The price is negative

• The price of complement is negative

• The income is positive

• Protein Amount of the Wheat Harvest is negative

The authors find that the U.S. import demand for wheat gluten is significantly influenced by the price of a complementary product (flour), by income, and by the domestic availability of wheat protein. The results also reveal that the import demand for wheat gluten is very price inelastic.

William W. Wilson (1994)

The consumption of different wheat depends on multitude of factors including income, relative prices, and taste, which are influenced by tradition and culture. There are also factors that influence substitutability among wheat include products consumed, technology used in processing, and institutional impacts of buying agencies. The objective of this study is to estimate wheat class demand functions for Pacific Rim countries. The model used is a conditional demand model which is derived from a transcendental logarithm functional form an expenditure function.

Most of the international wheat trade approves perfect substitutability across classes and origins. However, other studies show an imperfect substitutability of wheat among exporting countries. Substitution is important to understand wheat import demand and the potential impact of particular policies on trade. Other literature method are used to identify the price response in international trade is the elasticity of substitution model in which logarithms of relative import ratios are regressed on logarithms of income and relative prices.

This study uses the dual approach to specify the demand functions because it offers computational advantages without scarifying theoretical integrity. Duality has been used in many studies; such as, energy substitutability. It has been also used to derive transport demand functions.

The study uses TL demand functions derived from dual relationships. Using TL demand system will allow cross-elasticities to vary across pairs of imports, and also to permit to expenditures to have a nonlinear impact on distribution of import .by using the dual approach to derive demand functions is good to analyze imports of wheat classes.

The TL functional form (Christensen, Jorgenson, and Lau) was chosen because it results in a more general system than either the Armington or the AIDS model. Differentiation of the cost function yields a demand system, which has a flexible functional form and has several important characteristics. It is linear in parameters and satisfies all the general demand restrictions: homogeneity, symmetry, and adding-up constraints.

TL demand function is as:

S = x + B1log (M) + /B2log (M) ² + SUM Y log (P1)

Where S is the share of expenditures made on the import of wheat class , M is real expenditures on wheat imports, and P is the import price for class. The TL demand system is similar to the AIDS specification except the latter does not include the second- order logarithmic term of expenditures, i.e., log (M) ²

A separate model was estimated for each of nine Pacific Rim countries. The Pacific Rim is an important region to analyze for a number of reasons: countries in this region have been and are expected to be important growth markets, they import from multiple origins, and, in general, they are cash customers. Each of these countries has a history of purchasing multiple classes of wheat from multiple sources. Consequently, intense international competition exists in these individual markets. Specific countries chosen in this study include Hong Kong, Indonesia, Japan, Republic of Korea, Malaysia, Philippines, Singapore, Tai- wan, and Thailand. These countries are a subset of "Far East Asia" as defined by the International Monetary Fund (IMF). A number of countries in this region were not included in the analysis for one of three reasons: they were not wheat importers, they were large domestic wheat producers, or they had centrally planned economies. Wheat producing countries were deleted because of simultaneity problems not dissimilar from those encountered in Diewert and Morrison. Countries that are centrally planned also were deleted since they would not necessarily have objectives compatible with expenditure minimization.

Results indicate that the quantity demanded level has a significant impact on import shares in five countries. In these countries, income has a nonlinear impact on wheat class import demand.

This model was estimated for a group of 9 countries for Pacific Rim and the conclusion that we draw from the study is that quantity impacts across wheat classes and importing countries. The result also indicates a shift in preferences in five countries toward the wheat that contains high protein. The quantity demanded that vary from country to another is due to the expenditure, and the market share of wheat

James N. Barnes and Dennis A. Shields (1998)

The use of wheat grew dramatically especially for domestic food. It reached 880 million bushels during 1997. However, exports of wheat’s represented 23% since the 70’s and the demand grew rapidly in the 80’s and peaked 1.88 billion bushels. So, the exports have fluctuated under the influence of international supply and demand conditions and government policies.

In general, demand has grown faster for domestic food especially, for white wheat and durum than other classes. Between the 70’s and 90’s, the durum and white wheat rose 112%, and this is explained by the growing consumption of pasta products and the availability of white wheat. Another point that explain the growing consumption of white wheat is the increasing population, the preferences have changed, the relative prices of other food and income levels. For most of the 20th century, the wheat based food consumption declined because consumer starts to purchase more expensive food such as meat due to the rose of income.

The growing health awareness have made customer to care more about their health and moved to change their eating behavior. The medical community has long encouraged reduced fat consumption and increased in eating the wheat flour, which accounts for three quarter of total U.S grain. Another factor that affects the increase consumption is the availability of products. During the last several years, manufacturers have launched production of wheat based of wheat (pita bread, snack food, bagels, and variety bred ).

The lifestyle changed over the past three decades, people spent less energy and time to make bread because restaurant and bakery make the bread accessible and cheaper for two-income families, which represent 46% in 1996 in contrast of 28% in 1965. Wheat is used heavily and extensively in United States to satisfy the demand of household. `

The bread, cookies, pasta, noodles are made from different classes of wheat; such as, hard red winter (HRW), hard red spring (HRS), soft red winter (SRW), white and durum. In order to estimate the total U.S demand of wheat, the study suggests including all the different classes because by ignoring or excluding one of them risk creating a biased results. For the study, they used OLS (ordinary least square method) and SUR (seemingly unrelated regression). By using these two approaches, we can estimate the quantity demanded for each class. The OLS will be used to estimate the by-class wheat food demand equation individually. However, the SUR will estimate by-class wheat food demand using a 5-equation system. These two equations will provide the total U.S wheat food demand, the cross price elasticity and identifying the demand factors.

The OLS shows that the most elastic market of the five classes is the HRW. However, the food demand for HRW is still considered inelastic. Seemingly Unrelated Regression (SUR) results indicate white is the most inelastic market. Both techniques agree that all five classes of wheat are inelastic as the own- price elasticities for each class are less than unity. Both equation-by-equation OLS and SUR noticed the correct negative own-price signs.

The estimated OLS HRW demand equation suggests HRS is more substitutable for HRW than SRW. When there is a shortfall in HRW production, HRS can be substituted as long as protein specifications are met. SRW is not as substitutable as HRS because of the protein needs associated with HRW’s end uses (primarily for bread flour, which requires more protein than SRW can provide). Also, HRS is more substitutable for HRW than HRW is for HRS. It appears HRS is more substitutable for durum than durum is for. This result could be associated with the different blending requirements to produce durum food products versus HRS products.

The SUR econometric procedure provides a “system frame- work” for evaluating just how substitutable each class is with respect to the others. The estimated price elasticities of demand. It appears that HRW is more substitutable for HRS than HRS is for HRW. Other cross-elasticities of interest also include white and HRW. It appears HRW is five times more substitutable for white than white is for HRW.

Consumer taste and preferences have changed over time. Marketers understand which type of wheat to blend in order to satisfy the demand. Both econometric procedures yield similar results for this study. Both agree that by-class food demand is inelastic. Although these procedures differ based on substitutability estimates between classes such as HRW and HRS, the most probable case seems to favor HRS having more substitutability for HRW than HRW has for HRS because it is easier to blend down for protein than up. OLS estimates of substitutability support this as the cross-price elasticity for HRS is statistically significant at the 5-percent level where as the SUR estimate of the cross-price elasticity for HRW is not statistically significant at the 5-percent level.

This study also found positive per capita income elasticities for all classes of wheat. These estimates differ from previous research results where representative wheat food products such as bread were found to exhibit a negative or inferior relationship. The introduction of a wider variety of “wheat-based” products available for consumption at both the retail level and in fast food restaurants may help explain this finding. Specifically, both econometric techniques found durum to have the largest per capita income elasticity (ranging from 1.23 to 1.27) which is to say durum food demand will increase the most if per capita incomes continue to rise in the United States.

S. D. Rozelle and J. Huang (1998)

The objective of the study is to determine the features and characteristics of China’s wheat economy and increase the understanding of its domestic wheat sector and its current and future participation in global markets. The study provide a comprehensive, transparent and empirically sound basis for assessing the future growth of china for whet supply, demand, and trade needs.

The first step in this study was to examine the grain balance sheet of the country and evaluate a series of elements, a part income and prices, which may have a significant influence on Chinese grain demand and supply. The authors established a wheat supply and demand projections model including important structural factors and policy variables (urbanization and market development on the demand side, technology, agricultural investment, environmental trends, and institutional innovations on the supply side).

After the revision of baseline assumptions and forecasts, the results of the baseline projections are presented. After this, alternative scenarios with different growth rates in income, population, and investment in research and irrigation are examined. Policy implications are derived from these scenarios.

The results of this study shows that under the most plausible expected growth rates in the important factors, the Chinese demand for imported wheat will increase somewhat in the late 1990s before peaking and gradually declining through 2020. The increase in wheat importation is caused by the expansion of demand and the slowing of supply due to the reduction of investments in agricultural research in the late 1980s. After 2000, the expectation for wheat import is to stabilize ad the growth of demand becomes slow due to the increase of urbanization, the decline of population growth rate, and the relative low and falling expenditure elasticities for wheat.

Samarendu Mohanty and E. Wesley F. Peterson(1999)

The objective of this study is to estimate the demand for wheat differentiated by classes using a dynamic the Almost Ideal Demand System (AIDS) model for the US and the European Union. The AIDS model is obtained by determining a cost function representing a PIGLOG1 class of preferences represented by cost or expenditure function. The preferences define the minimum expenditure needed for obtaining a specific utility level at a given price. The cost function C(U,p) for utility u and price vector p can be defined using the PIGLOG class of preferences by:

log c (u, p) = (1 - u) log a(p) + u log b (p),

where u lies between O and 1 so that the positive linear homogeneous functions a(p) and b(p) may be regarded as the costs of subsistence and bliss. The demand function is derived from the cost function:

Wit = αi + ∑λijln(Pjt) + βi ln(Mt/Pt) + ut

In this equation, we have budget shares as a function of P and M (total expenditures).

Two separate demand systems, one for durum and the other for spring and other wheat classes, were estimated for the US and the European Union. The durum demand system for the US contains two elements: durum from domestic production and imported Canadian durum. The other demand system for the U S contains domestic spring and other wheat and also imported Canadian western red spring wheat. The European Union durum demand system contains domestically produced durum, and durum imported from Canada and the United States. The other demand system for the European Union contains domestically grown common wheat, spring wheat imported from the US and Canada, and other types of wheat imported from the US.

Data on prices and quantities of wheat consumed in the US were collected from the Wheat Situation and Outlook report. The prices of US other wheat is the average of hard red winter, white, and soft wheat according to their share in consumption. The European Union domestic wheat prices for durum and common wheat were collected from Agra Europe and Agricultural Situation in the Community. A time series of delivered prices in local currencies for imports was calculated for each wheat class by taking into account FOB prices, the import tariffs and freight rates. FOB prices of wheat by classes for Canada and the United States are collected from Znternationai Wheat Statistics and International Grain Statistics, published by the International Grains Council.

The results show that in US, the imported wheat is more responsive than domestic wheat. This finding is not true for the European Union market. They also discover that in the European Union, there is a complementary relationship between spring and other wheat groups. This relationship between the lower and higher quality wheat was expected because the European Union millers blend cheaper wheat and US other wheat with high protein (spring) to obtain the preferred characteristics.

M. Uzunoz and Y. Akcay (2009)

Wheat is considered as the principal agriculture crop in Turkey. In Turkey, studies about import demand analysis for agriculture products are few. The objective of this study is to analyze the different factors that affect the import demand of wheat for the period from 1984 to2006. The authors use double logarithmic-linear function. They set the import demand for wheat of Turkey as a function of:

• Domestic price (PW);

• Gross national product per capita (GNP);

• Turkish lira-US dollar exchange rate (EX);

• Lagged import;

• Production value of wheat (PV);

• Domestic demand (DD);

• And trend factor (T).

The model used is expressen is the following general form:

IDt= f (PWt, GNPt, EXt, IDt-1, PVt, DDt, T)

Time series data is used in the regression analysis. In the estimation of the import demand schedules of agricultural products, the majority of works use a regression analysis followed by a double logarithmic-linear function.

The data of import value is collected from Food and Agriculture Organization. The authors obtain the gross national product per capita (GNP) from the Basic Economic and Social Charts of State Planning Organization. The data of domestic prices, domestic production and demand is obtained from Turkish statistical Institute. The data of Turkish YTL-US $ exchange rate is obtained from Central Bank of the Republic of Turkey. The real domestic prices (PW) of wheat are calculated by using wholesale price index. The import demand functions have included a relative price variable, real income, and dummy variables to account for unusual periods. The relative price measure is often the ratio of the import price to the domestic price index for the commodity adjusted for the exchange rate, which gives a measure of the real exchange rate.

The result shows a strong relationship between the dependent and the independent variables. The import demand of wheat in Turkey is highly affected by the change of domestic wheat prices. Turkish consumers would prefer to buy domestic wheat than import wheat gradually. Another important factor affecting the demand function is the level of GNP per capita among the consumers in market. When this factor increases, consumption will increase and vice versa. The study also shows that the import value of wheat increases with the increase of TL/USD parities. The production value has a negative impact on the imported demand. The time trend variable is used to show the impact of variables not explicit in the analysis through time. These factors are there to show the changes in the tastes and preferences of the consumers. The negative sign found by the authors reflects that consumers in Turkey prefer to buy domestic wheat than import wheat gradually.

L. J. S. Baiyegunhi and A. M Sikhosana (2012)

The objective of this study, the first of its kind, is to find the determinants of import demand for wheat in South Africa for the period from 1971 to 2007. The authors use double logarithmic linear function and secondary data. The authors are interested on wheat because it is the most important grain crop after maize in South Africa. South Africa is a net importer of wheat. In this country, demand for wheat is largely influenced by the size, composition, distribution and market behavior of the population.

In this study, authors use a common form of regression model followed by the double logarithmic-linear model.

Ln (IW) = β0 + β1Ln (GDP) + β2Ln (PIW) + β3Ln (IPPR) + β4Ln (PM) + β5Ln (PS) + β6Ln (WPNt-1) + β7 (TW) + ε

The dependent variable is IW =Quantity of imported wheat (tons). The independent variables are: GDP =Real gross domestic product per capita (Rands), PIW = Real price of imported wheat (Rands per ton), IPPR= Real import parity price of rice (Rands per ton), PM = Real domestic price of maize (Rands per ton), PS = Real domestic price of sugar cane (Rands per ton), WPNt-1= Lagged domestic wheat production (tons), and TW = Dummy variable for tariffs on imported wheat (0 – no tariffs; 1 – tariffs).

The results of this study show that there is a significant relationship between the dependent variable: the quantity of imported wheat and the independent variables: a positive relationship with income (measured by the real gross domestic product per capita), the price of imported wheat, a negative relationship with the price of sugar cane (a complement of wheat), a negative relationship between the level of domestic wheat production.

Methodology and results

In this paper, our objective is to determine the elements that influence the imported quantity of common wheat in Morocco. The hypotheses of our model are:

H0: there is no relationship between the imported quantity of common wheat and the value of wheat.

H1: there is a relationship.

H0: there is no relationship between the imported quantity of common wheat and the value of corn.

H1: there is a relationship.

H0: there is no relationship between the imported quantity of common wheat and the value of barley.

H1: there is a relationship.

H0: there is no relationship between the imported quantity of common wheat and the value of bean.

H1: there is a relationship.

H0: there is no relationship between the imported quantity of common wheat and the drought.

H1: there is a relationship.

H0: there is no relationship between the imported quantity of common wheat and the value of OATS.

H1: there is a relationship.

H0: there is no relationship between the imported quantity of common wheat and the value of sorghum.

H1: there is a relationship.

H0: there is no relationship between the imported quantity of common wheat and the value of rice.

H1: there is a relationship.

H0: there is no relationship between the imported quantity of common wheat and the annual exchange rate USD/MAD.

H1: there is a relationship.

H0: there is no relationship between the imported quantity of common wheat and the GDP per capita.

H1: there is a relationship.

H0: there is no relationship between the imported quantity of common wheat and the total population.

H1: there is a relationship.

In our analysis we will use regression analysis. We will use time series for the period from 1961-2010. The data were collected from different sources:

• World Bank;

• The United States Department of Agriculture;

• Food and Agriculture Organization of the United Nations.

At the beginning, we started with the following variables:

• Dependent variable: log of the quantity imported of common wheat;

• The independent variables:

✓ The value of wheat per tones;

✓ The value of corn;

✓ The value of barley;

✓ The value of beans;

✓ The value of Oats;

✓ The value of sorghum;;

✓ The value of rice;

✓ The annual exchange rate USD/MAD;

✓ The GDP per capita;

✓ The total population;

• Dummy variable: drought. This variable present the weather events.

Our first model is as follow :

|Coefficientsa |
|Model |

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Log Quantity of imported common wheat = α0 + α1 value of wheat per tones + α2 corn + α3 barley + α4 beans, dry value per tones + α5 drought + α6 OATS + α7 sorghum value per tomes + α8 rice + α9 annual exchange rate USD/MAD + α10 GDP per capita + α11 population, total + error

Quantity of imported common wheat = eα0 * e α1 value of wheat per tones * e α2 corn * e α3 barley * e α4 beans, dry value per tones * e α5 drought * e α6 OATS * e α7 sorghum value per tomes * e α8 rice * e α9 annual exchange rate USD/MAD * e α10 GDP per capita * e α11 population, total * e error

After running the regression analysis, we find the R square equal to 84.3% and R square adjusted of 79.7%. the overall model is good (F test 18.535 with a p-value of 0.000).

The model becomes:

|Coefficientsa |
|Model |

[pic]

[pic]

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Log Quantity of imported common wheat = 4.774 + 0.003 value of wheat per tones + 0.000 corn + 0.000 barley + 1.777E-5 beans, dry value per tones – 0.161 drought - 8.207E-5 OATS + 0.000 sorghum value per tomes - 6.302E-5 rice – 0.019 annual exchange rate USD/MAD + 0.000 GDP per capita + 6.544E-8 population, total

With this model, we find only two significant variables: the wheat value (t test equal to 2.378) and the total population (t test equal to 2.816). Consequently, we decided to change the model by eliminating some variables.

The new model is:

Log Quantity of imported common wheat = α0 + α1 value of wheat per tones + α2 barley + α3 drought + α4 sorghum value per tomes + α5 annual exchange rate USD/MAD + α6 GDP per capita + α7 population, total + error

Thanks to regression, we found the following result:

Log Quantity of imported common wheat = 4.746 + 0.002 value of wheat per tones – 5.367E-5 barley – 0.160 drought + 0.000 sorghum value per tomes - 0.029 annual exchange rate USD/MAD + α6 GDP per capita + 6.987E-8 population, total

The model has an R square equal to 83.5%, so 83.5% of the change in the log of the quantity of imported common wheat can be explained by the independent variables.

R square adjusted is equal to 80.7% which means that 80.7% of the change in the log of the imported quantity of common wheat is explained by the independent variables taking into consideration the number of the independent variables and the sample size.

Since F test is equal to 30.322, with a p-value of 0.000, the overall model significance is good. The VIF of some variables is higher than 10, but since these variables are important for our analysis and they do not have a variable that is similar in our model, we decided to keep them. (see appendices)

Our analysis found that there is five factors that influence the imported quantity of common wheat (the absolute value of t test is higher than 2):

• Wheat value; • GDP per capita; • Total population; • Drought; • And the value of sorghum.
Explanation of coefficients:

Since our quantity function is expression in terms of exponential as it is shown in the equation bellow:

We will make use of marginal analysis in order to find out the meaning of each coefficient.

We should reformulate first the quantity equation in order to ease our analysis

We have

Log(Q) = b0 + b1X1 + b2X2 + b3X3 + b4X4 + b5X5 + b6X6 + b7X7

Ln(Q)/Ln(10) = b0 + b1X1 + b2X2 + b3X3 + b4X4 + b5X5 + b6X6 + b7X7

Ln(Q) = Ln(10)*[ b0 + b1X1 + b2X2 + b3X3 + b4X4 + b5X5 + b6X6 + b7X7]

The multi-linear equation can be transformed as follow

Q = Exp( Ln(10)*[ b0 + b1X1 + b2X2 + b3X3 + b4X4 + b5X5 + b6X6 + b7X7])

Q = 10*Exp(b0 + b1X1 + b2X2 + b3X3 + b4X4 + b5X5 + b6X6 + b7X7)

In order to assess the change we will use the average of each coefficient. The results are shown in the following table where X̄ is the average of each variable and it is computed and shown in the following table but since X6 is a dummy variable we will have to analyze two cases:

When there is drought X6 = 0 and we will use this table:

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When there is no drought X6 = 1 and we will use this table:

[pic]

Now we will go analyze each coefficients alone in the following sections :

For example , In order to know by how much the quantity of wheat will be affect if there is a one unit increase of Wheat price X1 we will go through marginal analysis:

∂Q/∂X1 = 10*b1* Exp(b0 + b1X1 + b2X2 + b3X3 + b4X4 + b5X5 + b6X6 + b7X7)

∂Q/∂X1 = 10 *b1* Exp(b0 + b1 X̄1 + b2 X̄2 + b3 X̄3 + b4 X̄4 + b5 X̄5 + b6 X̄6 + b7 X̄7)

∂Q/∂X1 = 10*b1* Exp(4.746 + 0.002 *X̄1 + (-5.367E-5)* X̄2 + (-0.029)* X̄3 + 0.0003 X̄4 + (6.987E-8) X̄5 + -.160X̄6 + 0.0005 X̄7)

( b1 in this case is equal 0.002)

And this is also the formula for all other variable we only change b1 by the ( b2, …, bn)

The results are as follow;

With drought:

[pic]

X1(Price wheat)

On average if price of wheat increases by one unit, Q will increase by 10.89 Tones.

X2( price of barely)

On average if price of Barely increases by one unit, Q will decrease by 0.291 tones which means they are complements products.

X3(Exchange rate USD/MAD)

On average if exchange rate increases by one unit, Q will decrease by 147.19 tones. When exchange rate increases it becomes more costly to import wheat.

X4( GDP per Capita)

On average if GDP per capita increases by one unit, Q will decrease by (1.445).

X5( Population)

On average if population increases by one unit, Q will increase by (3.5044 *E-3). This is normal since that having more people means more demand for wheat.

X7( Price of Sorghum)

On average if price of Sorghum increases by one unit, Q will increase by 1.06 tones which means they are substitute products.

With no drought :

[pic]

X1(Price wheat)

On average if price of wheat increases by one unit, Q will increase by 9.367 Tones.

X2( price of barely)

On average if price of Barely increases by one unit, Q will decrease by 0.229 tones which means they are complements products.

X3(Exchange rate USD/MAD)

On average if exchange rate increases by one unit, Q will decrease by 125.46 tones.

X4( GDP per Capita)

On average if GDP per capita increases by one unit, Q will decrease by (1.232).

X5( Population)

On average if population increases by one unit, Q will increase by (2.98 *E-3).

X7( Price of Sorghum)

On average if price of Sorghum increases by one unit, Q will increase by 0.911 tones which means they are substitute products.

As it is shown by the different results, taking into consideration drought does not change the nature and the sense of the relationship between the dependent and the independent variable.

Elasticity Analysis :

In order to assess the elasticity we will make use of arc elasticity and take the average in order to come up with the values in the following table.

As an example for the elasticity of wheat price the formula is as follow :

(∂Q/∂X1)*( X̄1/Qbar) = [10 *b1* Exp(b0 + b1 X̄1 + b2 X̄2 + b3 X̄3 + b4 X̄4 + b5 X̄5 + b6 X + b7 X̄7)]* ( X̄1/Qbar)

(∂Q/∂X1)*( X̄1/Qbar) = [10*b1* Exp(4.746 + 0.002 *X̄1 + (-5.367E-5)* X̄2 + (-0.029)* X̄3 + 0.0003 X̄4 + (6.987E-8) X̄5 + -.160X̄6 + 0.0005 X̄7)] *[( X̄1/Qbar)]

In this case b1 = 0.002

And X̄1 = 147.58

And this is also the formula for all other variable we only change b1 by the ( b2, …, bn) and X̄1 by (X̄2, .., X̄n)

When there is Drought

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When there is no Drought

[pic]

In both cases( with and without drought) , we notice that the absolute value of all elasticity is less than zero, which means that all variables are inelastic, one unit increase in any variable does not affect much the quantity imported.

This result can be explained by the fact that wheat is one of the most important cereals in the Moroccan alimentation. It is an important part of each meal, and eaten it is part of the culture of the country. As a result, even if the price will increase, Moroccan will continue to buy it.

The histogram (see appendices) shows that the imported quantity of common wheat is normally distributed.

According to the normal P-Plot, all the points are close to the line.

In the scatter plot, there is no clear pattern, so we have homoscedascity and the model is good.

The results of our study are similar found by L. J. S. Baiyegunhi and A. M Sikhosana (2012) in South Africa. They found a significant and positif relationship between the dependent variable: the quantity of wheat imported and the price of the imported wheat. Like them, we found a negative relationship between the dependent variable and barely;

Conclusion

We conducted our study for the period between 1961 and 2010 in order to determine the factors that influence the quantity of imported common wheat in Morocco. We used regression analysis and we analyzed the arc elasticities. Some of our findings are similar to those found by authors in South Africa. We found 5 significant variables: wheat value, GDP per capita, total population, drought, and the value of sorghum. We found a positive relationship between the dependent variable and: the price of wheat, the total population, and the price of sorghum. We found a negative relationship with the price of barely, the annual exchange rate USD/MAD, and the GDP per capita.

References

Baiyegunhi, L. J. S., & Sikhosana, A. M. (2012). An estimation of import demand function for wheat in south africa: 1971-2007. African Journal of Agricultural Research, Vol. 7(37), pp. 5175-5180. Retrieved from http://www.academicjournals.org/ajar/PDF/pdf2012/25Sep/Baiyegunhi and Sikhosana.pdf

International grains council. (n.d.). Retrieved from http://www.igc.int/en/grainsupdate/sd.aspx?crop=Wheat

UZUNOZ, M., & AKCAY, Y. (2009). Factors affecting the import demand of wheat in turkey. Bulgarian Journal of Agricultural Science,, 15((No 1)), 60-66.

Koo, W. W. (n.d.). Tariffs and transport costs on u.s. wheat exports. Oxford University Press,

Wallace, I., & Kopp, D. (1990). The wheat imports of non-traditionally wheat-producing countries. Geography, 75(2), pp. 148-152.

Konandreas, P., Bushnell, P., & Green, R. (1978). Estimation of export demand functions for u.s. wheat. Western Agricultural Economics Association, 3(1), 39-49.

Rozelle, S. D., & Huang, J. (1998). Wheat in china: Supply, demand, and trade in the twenty-first century. Special Report N 3,

Mohanty, S., & Peterson, E. W. F. (1999). Estimation of demand for wheat by classes for the united states and the european union. Agricultural and Resource Economics Review,

Ortalo-Magne, F., & Goodwin, B. K. (1990). The world wheat gluten industry, an econometric investigation of the u.s. import demand for wheat gluten . Kansas Agricultural Experiment Station Contribution, Retrieved from http://ageconsearch.umn.edu/bitstream/133771/2/kansas-research-report-12.pdf

Barnes, J. N., & Shields, D. A. (n.d.). The growth in u.s. wheat food demand. Retrieved from http://www.google.co.ma/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CCMQFjAA&url=http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.46.5257&rep=rep1&type=pdf&ei=_POaULvlJqjT0QWNt4DgAg&usg=AFQjCNGAI3XvkRZ4RN05TVvInbTXCkJGgA

Wilson, W. W. (1994). Demand for wheat classes by pacific rim countries. Journal ofAgricultural and Resource Economics, 19(01), 197-209. Retrieved from http://ageconsearch.umn.edu/bitstream/31234/1/19010197.pdf

The world bank. (n.d.). Retrieved from http://data.worldbank.org/

U.s. department of agriculture. (n.d.). Retrieved from http://www.usda.gov/wps/portal/usda/usdahome

Food and agriculture organization of the united nations. (n.d.). Retrieved from http://www.fao.org/index_en.htm

Index mundi. (n.d.). Retrieved from http://www.indexmundi.com/agriculture/?country=ma&commodity=wheat&graph=production

Appendices

SPSS output of the first model

|Variables Entered/Removedb |
|Model |Variables Entered |Variables Removed |Method |
|1 |Corn, Barley, Beans, |. |Enter |
| |dry value per tonnes,| | |
| |Drought, OATS, | | |
| |Sorghum value per | | |
| |tonnes, Rice, Annual | | |
| |Exchange Rate | | |
| |USD/MAD, GDP per | | |
| |capita (current US$),| | |
| |Wheat Value, | | |
| |Population total | | |
|a. All requested variables entered. |
|b. Dependent Variable: log wheat tonnes |

|Model Summaryb |
|Model |R |R Square |Adjusted R Square |Std. Error of the |
| | | | |Estimate |
|1 |.918a |.843 |.797 |.1763181457 |
|a. Predictors: (Constant), Corn, Barley, Beans, dry value per tonnes, Drought, OATS, |
|Sorghum value per tonnes, Rice, Annual Exchange Rate USD/MAD, GDP per capita (current|
|US$), Wheat Value, Population total |
|b. Dependent Variable: log wheat tonnes |

|ANOVAb |
|Model |

|Coefficientsa |
|Model |

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|Case Processing Summary |
| |Cases |
| |Valid |Missing |Total |
| |
| |Statistic |Std. Error |
|Unstandardized Residual |Mean |.0000000 |.02195866 |
| |95% Confidence Interval for Mean |Lower Bound |-.0441276 | |
| | |Upper Bound |.0441276 | |
| |5% Trimmed Mean |.0089905 | |
| |Median |.0247655 | |
| |Variance |.024 | |
| |Std. Deviation |.15527115 | |
| |Minimum |-.67564 | |
| |Maximum |.32875 | |
| |Range |1.00439 | |
| |Interquartile Range |.16844 | |
| |Skewness |-1.613 |.337 |
| |Kurtosis |6.325 |.662 |

|Tests of Normality |
| |Kolmogorov-Smirnova |Shapiro-Wilk |
| |

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SPSS output of the second model

|Variables Entered/Removedb |
|Model |Variables Entered |Variables Removed |Method |
|1 |Sorghum value per |. |Enter |
| |tonnes, Population | | |
| |total, Drought, | | |
| |Barley, Wheat Value, | | |
| |Annual Exchange Rate | | |
| |USD/MAD, GDP per | | |
| |capita (current US$) | | |
|a. All requested variables entered. |
|b. Dependent Variable: log wheat tonnes |

|Model Summaryb |
|Model |R |R Square |Adjusted R Square |Std. Error of the |
| | | | |Estimate |
|1 |.914a |.835 |.807 |.1719750839 |
|a. Predictors: (Constant), Sorghum value per tonnes, Population total, Drought, |
|Barley, Wheat Value, Annual Exchange Rate USD/MAD, GDP per capita (current US$) |
|b. Dependent Variable: log wheat tonnes |

|ANOVAb |
|Model |

|Coefficientsa |
|Model |

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|Case Processing Summary |
| |Cases |
| |Valid |Missing |Total |
| |
| |Cases |
| |Valid |Missing |Total |
| |
| |Statistic |Std. Error |
|Unstandardized Residual |Mean |.0000000 |.02195866 |
| |95% Confidence Interval for Mean |Lower Bound |-.0441276 | |
| | |Upper Bound |.0441276 | |
| |5% Trimmed Mean |.0089905 | |
| |Median |.0247655 | |
| |Variance |.024 | |
| |Std. Deviation |.15527115 | |
| |Minimum |-.67564 | |
| |Maximum |.32875 | |
| |Range |1.00439 | |
| |Interquartile Range |.16844 | |
| |Skewness |-1.613 |.337 |
| |Kurtosis |6.325 |.662 |

|Tests of Normality |
| |Kolmogorov-Smirnova |Shapiro-Wilk |
| |

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