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El—Eraky has been accepted towards fulfillment of the requirements for Ph.D. degreein Agricultural Economics WWWfl Major professor Date May 8, 1987 MS U is an Affirmative Action/Equal Opportunity Institution 0-12771 ANALYSIS OF FOOD CONSUMPTION IN EGYPT: A DEMAND SYSTEMS APPROACH By Mohamed B. El-Eraky 'A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Economics 1987 457a?/7 Copyright by Mohamed B. El-Eraky 1987 ABSTRACT ANALYSIS OF FOOD CONSUMPTION IN EGYPT: A DEMAND SYSTEMS APPROACH By Mohamed B. El-Eraky This study's approach to demand analysis is consistent with the theory of utility and with the theory of exact non-linear aggregation. Two flexible food demand systems are presented and estimated in this study, using Egyptian regional data from one budget survey. The first system is a hybrid of Working's model and the Rotterdam model, referred to here as the WTS demand system. The second is the Almost Ideal Demand System (AIDS). The analysis shows that the WTS system fits the data slightly better than the AIDS. Furthermore, the likelihood ratio tests demonstrate that the homogeneity restrictions are acceptable while the other restrictions are not. The compensated and uncompensated own—price elasticities for food groups are negative as expected. Moreover, the study indicates to the prevalence of substitutability among food groups in Egypt. Based on the expenditure elasticities, dairy products and fruit are the only luxuries among food groups in Egypt. Mohamed B. El-Eraky An important component of this dissertation is the food policy analysis. The results reveal that the annual rate of increase in the true cost of food has risen drastically after 1975. Before 1975, the food price policy was in favor of urban consumers in general and poor and large families in particular. New patterns have emerged after 1975. There is no clear differentiation between urban and rural families as before. In addition, food prices became slightly biased against poor and large urban families. This research suggests specific policies in order to mitigate the pressure on the government budget without jeopardizing the welfare of the poor: 1. The cuts of food subsidies should be directed toward the meats group rather than to the group of grains. 2. The income of the repre— sentative poor urban family should be raised by six percent in order to offset the increase in the price of meats group by 50 percent. Finally, this study shows that substituting food for nonfood is a mechanism to adjust for the increase in the household size when income is fixed. Within the food groups, the substitution is from high quality foods such as meats to lower quality foods such as grains. The estimation of adult equivalents is attempted in this dissertation.’ In addition, a scheme for income maintenance policy is suggested. ACKNOWLEDGMENTS During the development of this dissertation I have accumulated debts to many individuals and institutions. I am grateful to Dr. Lester Manderscheid, my major professor, for his invaluable guidance, encouragement, and interest in my research. Thanks are due to Dr. Stan Thompson for his willingness to help and for his interest in my progress during the past few years. I wish also to thank Drs. Harold Riely and Robert Gustafson for their helpful guidance. This dissertation would have never been completed with- out the financial and administrative support of Egypt's Cultural and Educational Bureau (ECEB) in Washington, D.C. My deep gratitude to the ECEB and to its director and staff. A special thank you goes to Mr. Zein Al-Abedin Mustafa who facilitated communications between me and the ECEB. Many thanks to my great teachers at Ain Shams University, Egypt, for their inspiration, support, and faith in me. My due respect includes Drs. Mohamed Rehan, Ahmed Goueli, Mahmoud El-Audemi, and Mahmoud El-Shahat. Finally, I am totally indebted to Dr. Sandra Hernandez for her unending moral support. She served as my special mentor and stood by me in difficult times. Moreover, she read it all and provided me with competent editorial assistance. I also want to thank Mabel Buonodono for typing some parts of the first draft and Catherine Rynbrandt for typing the final product. Finally, my thanks to Terra who put up with me while I wrote the last two chapters. vi TABLE OF CONTENTS INTRODUCTION. The Problem . Objectives of the Research. Data. . Organization of the Dissertation. THE DEMAND SYSTEMS APPROACH Introduction. Basic Concepts in the Demand Theory Restrictions on Demand Functions. Separability Conditions and Demand Sub- Systems Derivation of a System of Demand Equations . . . . Working' 8 Model . Working' 5 Model Incorporating Prices. The PIGLOG Cost Function Approach The Differential Approach ESTIMATION AND TESTING OF RESTRICTIONS. Commodity Groups. Two Demand Systems. Assumptions Underlying the Two Demand Systems . . . . . . . . Estimation Procedure. Results Estimates of Elasticities Which Demand System to Choose Testing of Further Restrictions No Compensated Cross Price Effects. - 2. Strong Separability REGIONAL AND DISTRIBUTIONAL IMPLICATIONS OF THE CHANGES IN INCOME AND FOOD PRICES Introduction. Regional Income Effects Regional Price Effects. vii Distributional Effects of Price Increases Income Distribution of Households Welfare Effects of Price Increases. Food Consumption Pattern After Price Increases . . . . . . . . . . . V. HOUSEHOLD SIZE AND FOOD CONSUMPTION Effects of Household Size Estimation of Equivalence Scales. Changes in the True Cost of Food. VI. SUMMARY AND CONCLUSIONS Summary of Methodological Conclusions Summary of Policy Conclusions . . Suggestions for Future Research . BIBLIOGRAPHY . APPENDIX . viii 106 107 110 117 125 135 142 152 154 157 159 166 L») L») wwww .10 .11 .12 .13 .14 .15 .16 LIST OF TABLES Definition of Commodity Groups The Unrestricted Parameter Estimates of AIDS The Unrestricted Parameter Estimates of WTS Demand System Testing for Homogeneity (F—Ratios) The Homogeneous Parameter Estimates of AIDS The Homogeneous Parameter Estimates of WTS Demand System Expenditure Elasticities with Respect to Total Expenditure Uncompensated Own-Price Elasticities Information Measures of Goodness of Fit Testing of Theoretical Restrictions The Symmetric Parameter Estimates of WTS Demand System Own—Price Elasticities of Symmetric WTS Compensated Price Elasticities of WTS Demand System Uncompensated Price Elasticities of Homogeneous WTS Demand System Estimates of Preference-Independent WTS Demand System Testing of Preference Independence Marginal Budget Shares for Five Regions Divisia Price Indices for the Movement from Region C to Region D ix 52 66 67 69 72 73 75 78 81 83 84 85 88 89 93 94 99 104 .10 .11 Divisia Price Indices for Seven Groups with Grains Deleted Frisch Price Index Minus Divisia Price Index for Eight Groups Frisch Price Index Minus Divisia Price Index for Seven Groups with Grains Deleted Distribution of Urban Households According to Per Capita Annual Expenditure Distribution of Rural Households According to Per Capita Annual Expenditure The Compensating Variations for Urban Families The Compensating Variations for Rural Families Percentage Change in Food Consumption for Six Representative Families as a Result of Grains Price Increase and Income Compensation for the Poor Percentage Change in Food Consumption for Six Representative Families as a Result of Meats Price Increase and Income Compensation for the Poor Estimated Average Budget Shares of Food Groups for Different Household Types When Income is Fixed Income Statistics for Different Household Types Estimates of PIGLOG Models for Urban and Rural Samples Estimates of Adult Equivalent Scales in Both Urban and Rural Samples Annual Average Percentage Rates of Increase in the True Cost of Food in Urban Areas Annual Average Percentage Rates of Increase in the True Cost of Food in Rural Areas Average Budget Shares in Five Regions X 105 108 109 115 115 119 121 127 133 140 141 145 145 166 .10 .11 .12 Expenditure Elasticities for Five Regions Uncompensated Own-Price Elasticities for Five Regions Parameter Estimates of for Urban Households Parameter Estimates of for Urban Households Parameter Estimates of for Urban Households Parameter Estimates of for Urban Households persons) Parameter Estimates of for Rural Households Parameter Estimates of for Rural Households Parameter Estimates of for Rural Households Parameter Estimates of for Rural Households persons) Composite Prices of Food Groups in Urban and Rural Areas xi Working's Model (one person) Working's Model (2—3 persons) Working's Model (4-6 persons) Working's Model (7 and more Working's Model (one person) Working's Model (2-3 persons) Working's Model (4-6 persons) Working's Model (7 and more 167 168 169 170 171 172 173 174 175 4. 5. 5 1 1 .2 LIST OF FIGURES Income Distributions of Urban and.Rural Populations 111 Working's Relationships for Four Household Types in Urban Areas 130 Working's Relationships for Four Household Types in.Rural Areas 132 xii ,. .r. 7% CHAPTER I INTRODUCTION The Problem Egypt may be one of the few countries in the world that has a ministry of supply. The primary task of this ministry is to regulate and distribute food commodities over time and space. The continuation of this establishment reflects the constant concern for food security. Food security is not a new concern in Egyptian life. In fact, ancient Egyptians were interested in securing a regular food supply from one year to another. The cause of concern, however, is different between then and now. In the past, irregular floods of the Nile were the source of food insecurity. Historians tell us about incidents of famines and hunger as a result of very low water flows. Egypt is an arid country, rainfall in the Delta is insufficient to support agriculture. As Herodotus summed it up in his famous phrase ”Egypt is the gift of the Nile.” The longstanding Egyptian desire is to bring the Nile under full control. Egypt, under Nasser, built the High Dam, thus eliminating a significant source of food insecurity. Egyptian people were especially thankful to the High Dam in 1985 when they realized that Egypt without the High Dam 2 would have been a natural extention of the African famine. Nevertheless, Egypt is still subject to other sources of food insecurity. The average self—sufficiency ratio of total cereals declined from 80 percent in 1966—70 to 63 percent in 1976-80 (Khaldi, 1984; table 22). Import dependence be- came significant in 1974 when the value of agricultural im- ports exceeded exports for the first time. Food imports rose quickly, and by 1981 Egypt was importing 48 percent of 1 Major imports are wheat, its staple food commodities. flour, maize, sugar, vegetable oil, beans, lentils, red meat, and poultry meat. This considerable degree of dependence on foreign food supply has its own political, economic, and social repercus- sions. A society cannot advance in science and technology without first satisfying the basic necessity of life, food. From the layman's viewpoint, the government is the first to be blamed for any food shortage. The political pressure on the government forces it to provide food at subsidized prices. Subsidizing imported food is becoming a burden on the government budget. Expenditures on food subsidies rose from less than one percent of total public outlays in 1970 to more than 10 percent in the second half of the decade, Alderman et a1. (1982). 1Egyptian Ministry of Agriculture and the USAID in cooperation with the International Agricultural Development Service and the USDA (1982); ”Strategies for Accelerating Agricultural Development - A Report of the Presidential Mission on Agricultural Development in Egypt.‘ 3 Moreover, the government does not have enough foreign ' . exchange to finance its food imports. Thus, Egypt depends on foreign assistance especially from the U.S.A. The American Food for Peace program to Egypt amounts to $250 million, consisting almost entirely of wheat and wheat flour. U.S. AID officials believe that as a result of this program, two out of five loaves of bread consumed in Egypt are made from American wheat. Obviously, American aid to Egypt has some political objectives. Egypt was a major recipient of U.S. food aid since the creation of PL 480 in 1954. For example, in 1964 PL 480 aid to Egypt accounted for 92 percent of Egyptian wheat imports and 53 percent of Egypt's net supply of wheat. Unfortunately, the Johnson Administra- tion decided to terminate U.S. aid to Egypt in order to pro— test Egypt's policies in the Middle East and its socialist policies, Burns (1985). The implication is that food aid is vulnerable to the political climate in both Cairo and Wash- ington. There is still some risk of not being able to procure its large food imports from the international market, assuming that Egypt has enough financial resources. That risk could be in the form of imposing a trade embargo on Egypt for some reason or insufficient food supply in the international market, say, as a result of a drought in some major producing countries. But why is the gap between domestic food supply and food demand widening? Naturally, one has to look carefully at the two sides of the equation, supply and demand. On the supply 4 side, the limiting factors are insufficient water resources “and limited arable land. There was a major effort in the sixties to increase the supply of arable land by one million feddans.2 The target was almost achieved, but further in- vestment was needed to make about one-half of the new land more than marginally productive. Unfortunately, there was no follow-up in the seventies. On the contrary, a great deal of the argicultural land has been lost to housing expansion. There are other limitations such as agricultural research, drainage projects, farm price policies, land tenure arrange- ments and extension programs. The discussion of these con- straints, however, is beyond the scope of this study. On the demand side, the population explosion is the main source of pressure on food demand. The size of popula- tion has almost doubled in 25 years from 25.7 million in 1960 to about 50 million in 1985, at an annual average rate of 2.7 percent. If this rate of population growth continues, the size of population will be 74.5 million in year 2000. That is, if there is no improvement in food production and if per capita consumption of food is maintained at the current level, Egypt will have to import about two thirds of its food needs by year 2000, compared with about one- half in 1985. Per capita food consumption is not constant. It is a function of many economic and non—economic variables. Food 2 The total supply of arable land in the beginning of the sixties was six million feddans, 1 feddan = 1.04 acres. 5 prices, consumer's income and taste, region of residence, habits, level of education, age, and religion are important determinants of food consumption. The economic variables, however, play an important role in determining the pattern of food consumption in a given society. As people get richer they tend to eat more of high quality foods like fruit, fish, milk, etc. Poor people eat less food in absolute terms, but they eat relatively more carbohydrates. In the period from 1974 to 1980 per capita consumption of wheat increased 38 percent, sugar 69 percent, white meat 67 percent, dairy products 41 percent and fish 76 percent.3 This rapid in- crease in per capita consumption is mainly the result of increased incomes, partly as an indirect effect of the oil boom in the neighbor Arab countries, and cheap food price policies. This study will concern itself to the study of food consumption at the household level. We postulate that a household's consumption of food is affected by its income, food prices, its region of residence, and its size. This study might be useful to answer questions about the govern— ment's price and income policies. The food subsidy program in Egypt is a controversial topic. Some commentators see it as a necessary caution against inflation and recommend its continuation. Others see it distorting the pricing system 3Egyptian Ministry of Agriculture and the USAID in cooperation with the International Agricultural Development Service and the USDA (1982): ”Strategies for Accelerating Agricultural Development - A Report of the Presidential Mission on Agricultural Development in Egypt.” 6 andarguethat families should be given income compensation instead of subsidizing the prices. In the midst of the debate, however, the quantitative effects of the proposed policies are hardly known. For example, we need to answer questions such as: 1. What would be the net effect of 10 percent increase in the price of grains on the consumption of all food commodity groups for different households? 2. How much income supplement is needed to compensate poor families for the price increase in order to keep them as well off as before? 3. Is the food consumption pattern for families of two persons the same as those of five persons? 4. How much money is needed to compensate a family of five persons relative to a family of two persons? The theme of this study is to try to answer questions of this kind in quantitative terms. Objectives of the Research One family budget survey will be used to estimate a complete system of demand equations for food in Egypt en- abling us to calculate a complete matrix of price and income elasticities for food commodity groups. The approach is to use two flexible demand systems based on Working's model. Then we will choose the system that fits the data better. Using a flexible demand system allows us to test any res— triction before imposing it. Otherwise, imposing restric— tions, from the outset could easily lead to misleading results. . e L. a we 3“ *9 ' is...“ 7 Specifically, we have four objectives: A. To provide a complete and reliable set of demand elasticity estimates for food commodity groups. B. To test the empirical validity of the theoretical restrictions on demand equations. Also, to test other restrictions of special interest. C. To estimate the equivalence scales for different household types. D. To study the welfare effects of government income and price policies on different household types. Data This study will depend to a large extent on the data available in one family budget survey. This survey was con- ducted by The Central Agency for Public Mobilization and Statistics (CAPMS) during the period August 1974 - July 1975. The results were published in September 1978. This survey is the third to be done on the national level in Egypt. The first was conducted in 1958/1959 and the second in 1964/1965. The stated objectives of the third family budget survey according to CAPMS are: 1) to estimate the levels of national consumption expenditure on different commodity groups. 2) To estimate the budget shares or weights which are needed to calculate various consumer price indices. 3) To estimate demand elasticities to be used to project future consumption. 4) To study the relationships between demographic characteristics and the consumption patterns. 8 According to CAPMAS (1978), the survey's sample size ‘ ‘ Q was determined, separately for urban and rural areas, using the following statistical formula: N = (1.96 o / e§)2 where N is the sample size, 2 is the average total consump— tion expenditure per household, 0 is the standard deviation of i, and e is the allowed percentage of inaccuracy in estimating E (e = 2.3% for urban areas and 2.8% for rural areas). The probability of E being within the desired accuracy of the true value is 95%. Values of i and 0 were taken from 1964/1965 family budget survey. Then, after calculating N, the number was doubled in order to assure a reasonable degree of accuracy in estimating E for every geographic region. The final number of households was 8000 in the urban areas and 4000 in the rural areas. The allocation of the total sample of Egypt's different urban and rural areas was based on the optimal allocation sampling technique. All the governorates in Egypt were covered except Port Said, Suez, Ismailia, Red Sea, New Valley, Matruh, and Sinai. Subsequently, the total sample was subdivided into four sub-groups of 3000 households. Households of each sub- group were surveyed for three months only in order to reduce respondent burden. The first sub-group was studied in the period August—October 1974, the second sub—group was studied in the next three months and so forth until the last sub- group being surveyed in the period May-July 1975. This time sequence was meant to capture the seasonal variations in consumption. Every household was visited three times. The 9 first one was to establish confidence between families and . f interviewers and to deliver some secondary questionnaires. The second visit took place at the beginning of the follow- ing month to record the actual consumption of families in the previous month of commodity groups such as food, cloth- ing, fuel and light, cleaning material, tobacco products, etc. In the third visit, two months after the second, families were to report their actual consumption for each of the last two months for all commodity groups as in the second visit. In addition, families in the third visit were asked to report their total expenditures on other commodity groups, services and durable goods, in the last twelve months, CAPMAS (1978). The available data are for the four sub-groups together. Hence the data do not show the seasonal variations from one month to another, because the monthly data are added together to give annual consumption and expenditure. House— holds are classified into likely homogeneous groups on the basis of urban areas vs. rural areas, household size, geo— graphic location, and annual total expenditure. Accordingly, this study will depend on group means rather than on individual observations as is the case for most family budget studies. This study will use the data in two sets. Firstly, regional data with price variations. Secondly, data for different sizes of households without price variations. In the first data set, the study will depend on 34 observations 10 calculated from Tables 1 and 22, CAPMS ”Family Budget Survey 1974/75" (Cairo), September, 1978. Each observation belongs to one region in Egypt. Specifically, we have data for Cairo, Alexandria, and for both the urban areas and the rural areas in another 16 governorates. Table 22 provides data on quantity consumed and value of consumption for 38 food items and three fuel and light items, hence prices can be calculated. Table ]_ provides data on total expenditure on aggregate commodity groups covering food groups such as grains, vegetables, etc. Regional price differences stem from many factors such as different agricultural production patterns, different degrees of governmental intervention in markets, transportation costs, and different market structures. The regional data will be used to estimate the price res- ponses. The second set of data will be based on tables 12 and 13 which provide data on aggregate commodity groups. The data are classified according to household total expenditure for four types of households. Households are broken down into four types according to household size. The first type is households consisting of one person, the second type of households consists of 2—3 persons, the third type consists of 4-6 persons, and the last type of households consists of seven or more persons. This data set will enable us to estimate the equivalence scales. 11 Organization of the Dissertation Chapter II examines the theoretical foundations of the demand systems approach. The restrictions derived from the utility theory and the separability conditions are explored. Four procedures to derive a complete demand system are pre- sented. Then, a model developed by Working is examined closely with special attention to its desirable properties. Working's original model does not assume price variations. To incorporate prices into Working's model, two approaches are discussed in some detail. The PIGLOG cost function approach and the differential approach are the two contenders. Demand systems that give rise to Working's model are the groundwork of this study. The Almost Ideal Demand System (AIDS) and the Working- Theil—Suhm (WTS) demand system are estimated in Chapter III. The demand systems are limited to eight food commodity groups. It is assumed that food commodities are weakly separable from nonfoods in the households' preference order- ing. The Maximum Likelihood and OLS estimates are used for the estimation purposes. Under certain conditions, the equivalance of Zellner's estimators and FIML estimators is established. Estimates of expenditure elasticities and compensated and uncompensated price elasticities are pre- sented. The performance of the two systems is assessed using the information measure of goodness of fit. Then several interesting hypotheses are tested using the Likeli- hood Ratio (LR) test. Namely, the hypotheses are homogeneity, 12 symmetry, compensated cross-price effects vanish, and strong separability. Based on the estimates of the homogeneous WTS demand system, Chapter IV investigates the regional and distributional implications of the changes in income and food prices. The regional variations in income and price responses are con— sidered. Divisia and Frisch price indices are employed in order to evaluate the effects of a household's movement from one region to another on the cost of food. Then, income distributions of both urban and rural families are discussed. According to income, households are divided into three categories: 1) Low-income households, 2) Medium-income households, 3) High-income households. The welfare effects of increasing food prices on each income category are then examined. Finally, the pattern of food consumption after price increase is predicted. Chapter V studies the relationships between household size and food consumption in Egypt. The PIGLOG cost functions are estimated for both urban and rural samples for two purposes. 1) The estimation of adult equivalent scales. 2) The assessment of how different households are affected by increases in the food cost from 1959 to 1980. Chapter VI summarizes the important findings and con— clusions of the study and some implication for future policy modifications and research needs. CHAPTER II THE DEMAND SYSTEMS APPROACH Introduction There are two main approaches to demand analysis. The first one is the single equations approach; where the demand function for each commodity is usually estimated in isolation of the other commodities and without direct reference to the economic theory of consumer behavior. The second approach is usually called the demand systems approach or, alternatively, the utility appraoch. A complete system of demand equations describes the household's allocation of expenditure among some exhaustive set of consumption categories. This does not necessarily imply that the demand system should include all consumption categories. In fact, under appropriate separability conditions, one can apply the demand systems approach to groups of goods that absorb a portion of the household's budget, say, expenditure on food. A system of demand equations is consistent with economic theory in the sense that it is derived from maximizing the consumer's utility function subject to the budget constraint. Thus the systems approach provides empirical demand analysis with a conceptual framework, namely the neoclassical utility theory, to deal with the interdependence of demand for various commodities. On the other hand, the single equation approach 13 -h 14 is usually based on ad hoc specifications which may not ad— here to economic theory. This approach, however, has great flexibility for modelling the demand for single commodities. For example, by including special explanatory variables and using different functional forms for each demand equation. In addition, data requirements for the single equation approach are less demanding. Nevertheless, the demand systems approach allows us to impose and test cross-equations restrictions such as symmetry relations. The link between utility theory and the demand systems approach proves to be useful in many policy applications. Evaluation of price and income policies is one important area of application. One can estimate the consumer's cost function in the context of a complete demand system. Then this cost function can be used to estimate the relative expenditure re— quirements of different population segments under different income and price schemes under the assumption of maintaining a constant utility. Basic Concepts in the Demand Theory The standard utility maximization problem of the con- sumer can be stated as follows: Maximize u = u (ql, qZ, qn) (2.1) Subject to: qi . (2.2) where qi is the quantity demanded of good 1, pi is the unit price of good i, x is the total expenditure on the n goods, and u is a strictly quasi-concave monotone increasing 15 utility function. The solution is the set of Marshallian demands: 1’ pn) (2.3). qi = mi (x. p The consumer's problem can be reformulated as one of selecting the quantity vector (ql, q2 qn) that minimizes the total expenditure x given that the achieved level of utility is u. Mathematically, the problem is stated as follows: Minimize x = i pi qi ' (2.4) Subject to: 11011, C12 qn) = u (2.5). The solution is the set of Hicksian or Compensated demand functions: (1 . l = hi (u, p1) pn) (2.6) Substituting the solution (2.3) into (2.1) gives the maximum attainable utility as a function of prices and total ex- penditure. u = u (q1’ q2, qn) = u [1111 (x, p1,—-—,pn),———,mn (x, pl pn)] = V (X: p1, p2,““,pn) (2.7). The function in (2.7) is known as the indirect utility function and it could be defined formally by i V (X, P1, p2,——-—,pn) = mix [u(q); pq=x] (2.8) where q and p are column vectors of quantities and prices respectively. Substituting solution (2.6) into problem (2.4) gives rise to the concept of the consumer's expenditure function, or simply the cost function. 16 q. = i pi hi (u, p) = C (u, p) (2.9) The cost function c(u, p) can be defined formally by c (u, p) = min [p' q; u (q) = u] (2.10). There are direct relationships among the three functions; the utility function, the indirect utility function, and the cost function. Deaton and Muellbauer (1980a) provide a full dis— cussion of going from one function to another and of the properties of each function. One of the important properties of the cost function is what is known as Shephard's lemma or the derivative property, that is 8 c (u, p) = h. (u, p) = q. (2.11). 1 1 8 p. 1 It states that the Hicksian demand functions are the partial derivaties of the cost function with respect to prices. Once we derive the Hicksian demands from any known cost fucntion, we can derive the Marshallian demand functions as well. Substitution of the indirect utility function u = v (x, p) in the Hicksian demands gives qi in terms of x and P, that is qi = hi (u, p) = hi [v (x, p), p] = mi (x, p) (2.12) where mi (x, p) is the Marshallian demand for good 1. Con— versly, we can derive the Hicksian demands from the Marshallian demands as follows: qi = mi (X, p) = mi [c(u, p), p] = hi (u, p) (2.13) where x is replaced by the cost function c (u, p). Differentiating the last identity in (2.13) with respect to pi gives rise to the well known Slutsky equation. Formally, 17 ami (x, p) 8 c(u, p) + 3mi(x, p) = 8hi(u, p) (2.14) 8X 8. 3. 8. p3 pJ pJ using (2.11), (2.14) can be written as sij= 8hi(u, p) = 8mi(x, p). qj + 8mi(x, p) (2.15) 8 . 8 . pJ x BpJ The term on the left of (2.15) is the substitution effect of the price change which is always negative in the case of 511' The first term on the right of (2.15) is known as the income effect of the price change which could be negative as in the case of inferior goods. The Slutsky matrix [Sij] is usually used to classify goods into complements and substitutes. According to Hicks‘sdefinition, goods 1 and j are complements if sij is negative; they are substitutes if sij is positive. Slutsky equation (2.15) can be written in elasticity form, by multiplying through by pj / qi, as follows eij = ei wj + eij (2.16) where eij is the compensated cross-price elasticity, ei is the expenditure elasticity, e is the uncompensated cross— ij price elasticity, and wj is the budget share quj/x. Finally, it is convenient to derive the budget share equation from the cost function, via Shephard's lemma (2.11), as follows: aln c (u,p) = 3c (u,p) Pi = p. 1 qi / x=wi (2.17). Bln pi Bpi x The budget share demand equation is simply the logarithmic derivative of the cost function with respect to ln pi. ; Mun-2 18 Restrictions on Demand Functions Economic theory suggests that the demand functions must satisfy certain restrictions. A background can be found, for example, in Barten (1977), Phlips (1974), and Deaton and Muellbauer (1980a). The following is a discussion of the general theoretical restrictions on the demand functions. 1. Adding—up: Both the Marshallian and the Hicksian demand functions must satisfy the linear budget constraint: i pi mi (x, p) = i pi hi (u, p) = x (2.18). The adding-up restriction (2.18) is usually expressed in terms of restrictions on the derivatives of the demand functions rather than on the functions themselves. To do so, we differentiate the budget constraint (2.2) with respect to income and p. respectively: J 1 pi qu = 1 (2.19) 1 8x i pi aqi + qj = o (2.20) Bpj Equation (2.19) is referred to as the Engel aggregation condition which can be written in elasticity form; I w. e. = l (2.21) i 1 1 where W1 is the budget share of good 1, pi qi / x, ei is the expenditure elasticity of good 1. Since I wi = 1, the i Engel aggregation condition means that the weighted average of all expenditure elasticities equals one. The weights are the corresponding budget shares. Similarly, equation (2.20) is rewritten in elasticity form as 19 i eij wi + wj = o (2.22) where eij is the cross-price elasticity of good i with respect to the price of good j. Equation (2.21), or (2.22), is referred to as the Cournot aggregation condition. In contrast to the single equation approach, the systems approach meets the adding-up restriction and hence forces recognition of the fact that an increase in expenditure on one commodity must be balanced lay a decrease in the expenditure on others. 2. Homogeneity: The homogeneity condition states that scaling of all prices and expenditure has no effect on the quantity demanded of each good. Formally, for any positive number k for all i from 1 to n, mi (kx, kp) = mi (x, p) (2.23) It follows from Euler's theorem on homogeneous functions that4 qu x + § aqi pj = o (2.24) 8 3 . x pJ or; e. + E e .. = o - (2.25). 1 j 13 That is the sum of all elasticities for any good must vanish. The homogeneity restriction is also known as the ”absence of money illusion“ since the units in which prices and total expenditure are expressed have no effect on purchases. l‘Euler's theorem states that if f(q1,q2, qn) is homo- geneous of degree h; h f(kq , kq , kq ) = k f(q , q , q ) then T 8f q 1 2 n 1 2 n j 3; J = hf(q1: qz: qn)° J 20 ” 3. Symmetryrther1x11 Slutsky matrix, whose elements are given by sij in (2.15), is symmetric. That is the cross- price derivatives of the Hicksian demands are symmetric: Bhi (u, p) _3hj (u, p) (2.26). 8 3 P1 The proof of this property follows directly from Shephard's p1 lemma in (2.11) since Bhi (u, p) 82c (u, p) 3h. (u, p) = = J 8 . 8 . 3 . 8 . 8 . PJ Pl PJ P1 P1 4. Negativity: The Slutsky matrix (s) is a negative semidefinite matrix. That is for any column vector y Y‘SY : 0 (2.27) This result follows from the mathematicl properties of concave functions (Varian 1978: 253-255). The matrix of second derivatives, 8, is negative semidefinite because the cost function is concave. In particular, the compensated own price effect is nonpositive since the substitution matrix, Slutiky matrix, is negative semidefinite and thus has non—positive diagonal terms. That is, for all i, ahi (u, p) 820 (u, p) :0 (2.28). api 3pi2 Expression (2.28) states that the Hicksian demand curve can never slope upwards. Equations (2.18), (2.23), (2.26) and (2.27) are the general restrictions that each demand system must satisfy. These restrictions are always effective irrespective of the form of the utility function. However, as Phlips (1974) argues, there is no reason why measured demand behavior should obey these restrictions, as theory is always a 21 simplification of reality. Many circumstances may prevent these restrictions from being satisfied. For example, measurement errors and aggregation over consumers, commod- ities and regions are potential problems in any applied demand study. In applied work, there are two strategies to deal with the general theoretical restrictions on demand systems. The first one is to impose all the restrictions from the out- set and then estimate the restricted model. The easiest way to do so is to derive the demand system from a specified utility function and therefore the demand equations will be such that all general restrictions are automatically satisfied. The second strategy is to test the validity of each restric- tion before imposing it. Not all demand systems are appropriate for testing restrictions. Therefore, we should use a flexible demand system to test the theory first. The first procedure preserves degrees of freedom. The advantage of the second procedure is its generality because it avoids using a particular utility function. Separability Conditions and Demand Sub—Systems In addition to the general restrictions presented in the previous section, we can impose a set of separability restric- tions on the utility function, the indirect utility function, or the cost function. We will discuss two types of separability of special interest. The first type is called strong separability under which the utility function, Goldman and Uzawa (1964), takes the form: u(q) = f[u1 (ql) + u2 (q2) + ------ +us(qs)] (2.29) 22 where ql, q2, qS are subvectors of the commodity vector q, f is an increasing function in all its arguments and uS (qS) is a function of subvector qS. The additive utility function (2.29) implies that the marginal rate of sub- stitution ui (q)/uj (q) between two commodities i and j from different commodity groups qS and qt respectively, does not depend upon the quantities of commodities outside of qS and qt; namely, a [ui (q)/u. (q)] = o (2.30) __________.l____ qu for all i e qs, j 8 qt and K t qS 0 qt (8 # t). In the case where there is only one good in each group, preferences are said to be additive or occasionally, that "wants are independent.” The terms strong separability or block additivity are usually reserved for the case of multigood groups (Deaton and Muellbauer, 1980a: 137). Strong separability implies independence of the marginal utility of commodity group i from the consumption of any other group or 'groupwise independence' (Phlips, 1974:69). Furthermore, strong separability implies that expenditure and price elasticities are approximately proportional. In the context of strong separability, inferior goods are ruled out and goods are permitted to be substitutes only (Deaton and Muellbauer, 1980azl38—141). A less restrictive type of separability is called the weak separability. Theorem 2 in Goldman and Uzawa (1964) states that: a utility function u (q) is weakly separable 23 with respect to a partition [ql, qs] if, and only if, u (q) is of the form: u (q) = f [u1 (ql), uS (qs)] (2.31) where f and ql, q2, q8 are defined as before in (2.29). Weak separability places some restrictions on the degree of- substitutability between goods in different groups. For example, if groups G and H are substitutes (complements) for one another, all pairs of goods, one from each group, must also be substitutes (complements) as the case may be (Deaton and Muellbauer, 1980a:129). One important application of the separability restric— tions is the so-called budgeting tree or multi-stage budget— ing. Consumers allocate their expenditure to broad categories of goods at the first level (food, clothing, etc.), to more detailed commodities at the second level (cereals, meat, fruit, etc.), and so on until each of the commodities is reached along one of the branches of the tree. The concept of budgeting tree allows us to break up the whole demand system into a number of smaller subsystems. Each subsystem gives rise to what is called conditional demand functions. It is conditional in the sense that the demand function for commodity i in subsystem G is a function of prices of goods in G and the expenditure on G commodities only. This budgeting procedure has obvious econometric advantages since it uses a much smaller numbercfiivariables to explain the consumer's behavior. If the utility function can be represented as indicated by (2.31), then both Hicksian and Marshallian demand 24 schedules for any good can be written as a function of the prices of only the other goods in the partition and the total expenditure made on goods in that partition (Yohe, 1984:148-155). In other words, a necessary and sufficient condition for the second stage of a two-stage budgeting procedure is that of weak separability (Deaton and Muellbauer, 1980a:123-134).. However, this separation of the allocation into two steps requires very restrictive assumptions about the error structure. In particular, covariances between error terms in different subsystems must vanish (Blackorby et al., 1978: 279). In addition, each conditional demand disturbance must be uncorrelated with all group disturbances. Finally, conditional demand disturbances in a given subsystem must be uncorrelated with the conditional demand disturbances in all other subsystems (Theil, 1980:104). The estimators of the parameters of subsystems of conditional demand functions retain their optimal properties only if those restrictive assumptions are made about the error structure. In practice, however, most demand systems studies assume separability conditions and exclude one or more commodity groups without any cOncern about the Structure of the error terms. It is a common practice to assume that preferences are weakly intertemporally separable. Demand functions in each period can be expressed as a function of total expenditure and prices in that period alone. The time dimension is very critical in the decision to spend on durable 25 goods and hence this commodity group is usually excluded from static demand systems. Also, labor supply decisions are often ignored in demand systems studies on the assumption that leisure is separable from goods. Separability conditions, without assumptions about the error structure, are assumed in many food demand subsystems, for example, Blanciforti and Green (1983), Pitt (1983), and Murray (1984). Derivation of a System of Demand Equations There are four general procedures to derive a demand system consistent with economic theory. The following is a brief discussion of each. 1. The utility function approach: One starts by spec- ifying the functional form of the utility function and then proceeds to derive the demand functions from the maximization conditions. Deaton (1978) argues that these maximization con- ditions cannot be solved explicitly for the demand functions in most cases, and when they can, the resulting equations may be difficult or impossible to estimate. Moreover, it is very difficult to incorporate empirical evidence about the con- sumer behavior into the utility function approach. The commonly used Linear Expenditure System (LES) is a good example of the utility function appraoch. LES is derived from the Klein-Rubin or Stone-Geary additive utility function U (q) = Z ai 1n (qi - bi) (2.32) 26 where the a's and the b's are parameters which satisfy ai > o, i ai = 1, and bi < q monotonic transformation of it subject to the budget con- i' Maximizing (2.32) or any straint will give, after rearrangements, p. 1 qi = bi pi + a. (x - 2K bK pK) (2.33) 1 If the bi's are nonnegative, the model (2.33) can be describ- ed as follows. First, the consumer buys bi units of the i th good, which requires Di bi‘ Having made these initial pur- chases for all goods, the remaining income x - BK bK pK which is known as ”supernumerary income" is allocated to all goods in the proportions ai. Although there is no requirement that any bi be positive, these parameters are often interpreted as the minimum required quantities or subsistence quantities. 2. The indirect utility function approach: This ap- proach, and the next one, make use of the duality theory to find new functional forms for demand systems. In this ap- proach, one starts with a specific functional form of the in- direct utility function and then applies the Roy's identity5 to derive the demand functions. For example, Houthakker de- rived the indirect addilog system from the following indirect utility function v (x, p) = a. (x/pi)bi. 1 The indirect addilog demand system imposes serious restric- Z i tions on the demand elasticities (Johnson et al., 1984:63-66). DRoy's identity state that the Marshallian demand functions can be derived from the indirect utility function v (x, p) as follows: qi = mi (x, p) = - 3 v (x, p)/3 pi for i = 1,---,n. 3 v (x, p)/3 x 27 3. The consumer's cost function approach: This ap— proach is especially advocated by Professor Deaton. The in— troduction of the cost function implies that we View the con- sumer as a producer of utility; she buys certain goods and services which he transforms into utility. In fact, it can be shown that if the budget constraint is linear, the cost func— tion provides a complete description of the consumer's pre- ferences insofar as these are relevant to behavior. The consumer's cost function approach shows quite clearly the ana- logy between the theory of the firm and the theory of consumer. Deaton and Muellbauer (1980b) used a cost function to derive their Almost Ideal Demand System ”AIDS." 4. The differential approach of Theil and Barten: This approach does not require a specification of the algebra- ic form of any of the three functions; utility function, in- direct utility function and the cost function. Rather, we de— rive a general demand system from the maximization conditions of a general utility function. The resulting demand system is a first-order approximation to any demand system and is ex- pressed in terms of the differentials rather than in the levels of the variables, Theil (1980). The Rotterdam demand system is a product of such approach. Alternatively, the Rotterdam demand system can be de— rived in the following manner. We can write the total differential of the general demand function (2.3) as dqi = qu d x + T 3 qi d pj (2.34). 8x 3 . pJ After some simple rearrangements, (2.34) can be written as d 1n qi = ei d 1n x + E eij d 1n pj (2.35) 28 where ei and eij's are as defined before. Substituting the Slutsky equation (2.16) into (2.35) gives d 1n q1 = ei (d 1n x - j wj d 1n pj) + g eij d 1n pj (2.36). Multiplying (2.36) through by wi gives the demand equation for good i in the Rotterdam demand system: J J J (2.37) wi d ln qi = 6i (d 1n x - 2 w. d 1n pj) + T flij d 1n pj where 6. = w. e. and n}. = w. e... 1 1 1 13 1 13 Further manipulations of Bi and Wij show that 9i = 8 (pi qi) and Nij = pi p. Sij' 8x x The adding up condition of the Rotterdam system can be written as E 9i = 1 (2.38), i while the new version of the homogeneity condition is given by ; nij = o (2.39). The transformation from Sij to fiij leaves the symmetry condition as n.. = (2.40). 1T.. 13 ji Finally, the requirement of non—positive diagonal terms in the Slutsky matrix means, for all i, “ii < O (2.41). I Provided that we are ready to treat the ei's and nij s as constant parameters, the Rotterdam system (2.37) can be estimated by ordinary least squares. The expenditure elasticity of good i is ei = 9i /wi. Si is interpreted as the marginal share of good i, i.e., the 29 the additional money spent on good i as a result of increas- ing total expenditure by one Egyptian pound. The compensated J- own-price elasticity of good i is eii = n '/Wi' Similarly, ii the compensated cross-price elasticity of good i with respect to the price of good j is éij = Hij/Wi' Finally, the uncom- pensated price elasticities can be calculated easily from our estimates of e..'s. 1] Working's Model H. Working (1943) was the first to propose and estimate the following model using U.S. family expenditure data. wi = ai + bi 1n x (2.42), where wi is the budget share of good i in total expenditure x. Working (1943) found this model to fit the data very well espe— cially for the food commodity group. Working (1943:45-46) notes that "The proportion of total expenditure that is devoted to food tends to decrease exactly in arithmetic progression as total expenditure increases in geometric progression. With only certain exceptions at very low levels of total expenditure, this relationship applies closely for families of every size, of every occupation, and in each type of community studied.” In spite of the simplicity of Working's model and of its almost exact fit, it was ignored in the literature of family budget studies. Twenty years later, Leser (1963) brought Working's model back into light. Leser (1963) studied four specifications of Engel curves and found that Working's model gives the best fit. Apart from the goodness of fit, Working's model has other attractive characteristics which we discuss below. 30 1. Working's model satisfies the general restrictions of demand theory: An Engel curve is a relationship between income and the expenditure on a particular commodity, all other things being equal. It is easy to show how an Engel curve can be derived from a diagram representing an in— difference map for two goods. That is an Engel curve is a demand function derived by constrained utility maximization. The constraint is that prices are constant. Therefore, all restrictions in terms of price derivatives (homogeneity, symmetry, negativity of the own substitution effect) disappear, Phlips (1974). The only restriction that remains is the adding-up condition (2.18). Moreover, the adding—up condition is reduced to Engel aggregation condition (2.21) only since Cournot aggregation condition cancels out as a result of assuming constant prices. To show our point, we multiply equation (2.42) by x; pi qi = ai x + bi x 1n x (2.43). , Then, the marginal budget share of good i, ei, is 91 = 3 (Pi qi) = pi e qi 8x 3x = a. + b. 1n x + b. 1 1 1 = w. + b (2.44). 1 i The expenditure elasticity of good i is given by ei = 8 qi x = wi + bi x 3x qi ' p1 qi = 1 + bi / Wi (2.45). Clearly, good i will be luxury if bi is positive. If bi is negative and its absolute value is less than wi, good i 31 will be normal. Good 1 will be inferior if bi is negative and its absolute value is greater than Wi’ Summation over i in equation (2.42) gives Z w. = Z a + 1n x X b. = 1 (2.46), . 1 . . . 1 1 1 1 1 since x = Z piqi. It follows from (2.46)that the ai's and i bi's are subject to the constraints 2 a. = 1, 2 b. = 0 (2.47). Condition (2.47) is the adding-up restriction under Working's model. ,Using (2.45) one can see that Engel aggregation condition 2 ei wi = 1 is satisfied. Hence, Working's model is theoretically plausible. Applying ordinary least squares, to an additive data set, to estimate Working's model will automatically satisfy the adding-up restriction (2.47). To show that, we will rewrite Working's model as: wit = ai + bi yt + ut for 1=1,--—-n and t=1,----T where wit is budget share of good i for cross-section t, yt = 1n x t’ ut is an error term, n is the number of goods, and T is the number of cross-sections (observations). OLS estimate of bi is A :w.(y—§) bi = t it t . s: :2 t_ (37-37) t=1 t _ _ 2 n = 2 (y - y ) , E (y - y ) Since E w. = 1 t t t i=1 1t 32 Similarly, i ai = i (w: - bi y) = 1. That is OLS estimation of Working's model, equation by equation, is bound to satisfy the adding—up restriction. However, the adding-up restriction is not testable. The commonly used double-logarthmic model does not satisfy the adding-up restriction unless all the expenditure elasticities are equal to unity, See Yoshihara (1969) for a proof. Thus the double-logarithmic model is not theoretically plausible and it should not be utilized in empirical demand analysis. 2. Working's model is compatible with a known set of cost functins: A by-product of the theorems in Muellbauer (1975) is the result that if the demand functions are wi = ai (p) + bi (p) 1n x (2.49), where Z a. = 1 , Z b. = o o l D l 1 1 then the cost function must be 1n c (u, p) = (l - u) 1n A(P) + u 1n B (p) (2.50), where A (p), B (p) are linear homogeneous, concave functions in the prices and u is the utility level. If the prices are assumed to be constant, the demand function (2.49) will reduce to Working's model (2.42). Hence, Working's model corresponds to optimizing consumer behavior. The direct link between preferences and Working's model is very useful in many applications, e.g., the cost of living indices. In contrast, the double logarithmic model has no reference to explicit specification of preferences. Much more, it is not compatible with utility maximization, as 33 it does not satisfy the adding-up condition. 3. Working's model allows perfect aggregation over consumers: Muellbauer (1975) considered the problem of how demand functions can be aggregated over consumers. In order to adapt Working's model to the grouped data available, we intrOduce the subscript h to denote household and a stochastic term uh to portray errors. Wih = a1 h Further, we assume that all households of a given income + bi 1n x + uih (2.51). group have identical tasts and face the same prices at any given point in time. Multiplying (2.51) by xh and summation over h gives + bi é total Z x w. = a. Z x h h 1h 1 h h Dividing (2.52) by Z Xh’ h in a given income group, gives xh 1n xh + Z xh uih (2.52). h expenditure of all households the following equation w. = a. + b. 1n x + v. (2.53), 1 1 1 o 1 where wi 3 fi pi qih / % Xh E grouped mean budget share 1n x = Z x 1n x /Z x o h h h h h v. = Z x u. /2 x (2.54). 1 h h 1h h h Define i = Z Xh/H’ H = number of households I = i (xh /Z xh) 1n (xh/x) Then, one can show that 1n x0 is equivalent to 1n x0 = g (xh /Z xh) [1n (xh x/§)] = 1n x + g (XhI/S'xh) 1n (xh)/x) = 1n E + I 34 X.O is calledrepresentative expenditure in Muellbauer's sense, while E is the average expenditure of an income group. Therefore, equation (2.53) can be rewritten as wi = ai + bi (1n E + I) + vi (2.53'), where I is a measure of income inequality for a given income group, Wi is the grouped mean budget share of good 1, § is the grouped mean total expenditure, and V1 is the new error term defined in (2.54). Usually, we do not have information about I and we end up dropping it out from equation (2.54). If I is the same for all income groups, ai would be biased while the crucial parameter bi is still unbiased (Theil and Suhm, 1981:119-120). To put the previous discussion into persepctive, we will differentiate between two types of aggregation. First, exact linear aggregation which requires that average demands should be a function of average total expenditure, ai = f (p, E). This condition means that Engel curves should be linear and have the same slope for each household. Second, exact nonlinear aggregation which requires that average bud- get share should be a function of representative level of total expenditure x0, $1 = f (p, X0). The representative ex- penditure is a function of the distribution of expenditures and of prices, Deaton and Muellbauer (1980b). Thus, Working's model allows exact nonlinear aggression since ti = f (x0). When the expenditure distributinn can vary, average expenditure, §, may only be used as a regressor if Engel curves are linear. Nonlinear aggregation goes beyond this and allows 35 nonlinear Engel curves at the price of introducing re- presentative rather than average expenditure, Mnellbauer’(l975) 4. Working's model allows the expenditure elasticities to decline with rising income: The expenditure elasticity is defined in equation (2.45) as: ei = 8i / wi = 1 + bi / Wi‘ Differentiating this expression with respect to 1n x gives _ _ 2 8 ei — wi (bi) - 9i (bi) — - (bi/W1) 8 lnx w If bi >o so that good i is a luxury, an income increase re- duces its expenditure elasticity6 in the direction of 1. If bi =¢x2 <>/‘~“x)‘2 va vi 2 h var uih (2 h h h = 02 [ E xi / (E xh )2]. h h Since families are grouped according to income, we can 37 approximate xh by E; E = Z xh / H where H is the number of families in the corresponding income bracket. Then Var (vi) can be simplified to var (vi) = 02 / H. That is vi is heteroskedastic, and efficient estimation of ai and bi requires that the group means are weighted with the square root of the number of households in the correspond- ing income bracket. Working's Model Incorporating Prices Working's model as described so far, excludes the prices on the n goods frdm the demand equations on the assumption that prices ought to be the same for all cross-sections. If we believe that prices are different we would modify Work- ing's model to include the prices explicitly. This can be done by following one of two procedures: The PIGLOG cost function approach and the differential approach. Both of them will be discussed in detail in the following two sections. The PIGLOG Cost Function Approach We stated in the previous section that Working's model is consistent with a special class of cost functions por- trayed by (2.50). This cost function has been named by Muellbauer (1975) as the PIGLOG cost function which is the logarithmic transformation of PIGL (price-independent generalized linear) cost function. PIGL cost function allows 38 the representative expenditure level xO to be price- independent and hence to be a function of the distribution of expenditures alone. These types of cost functions allow exact nonlinear aggregation over consumers. The exact form of the budget shares demand functions would depend on the algebraic specification of the two functions A(p) and B (p). Two examples are in order. Example 1: The Almost Ideal Demand System ”AIDS”. This demand system is developed by Deatbn and Muellbauer (1980a). They choose the two functions A (p) and B (p) to be as follows: ln A (p) = a0 + Z a 1n p + 1 y 1n p ln p. K K K 2 Z j+ 2 and 41 's and 39 Fij's with ltl 3 l. 11 — 13' Using time-series data, Deaton and Muellbauer (1980b) reported 66 Awwm.mo Aqmm.fiv AooK.v Aqoq.muo Aomfi. v Aoom.-o Aowo.auo Aooo.fiuv Aawo.nv Amom.fio om. omo. HHo. oHo. omo.n moo. qoo.- mmo.u omo.u oHo.u moo. oommoo now «we Ammo.mo Amfim.mo Aomm.uo AomH.Huo Amqm.no Aonm.H;V Aomn.H:o Aoqo.muv Aomq.auo Afimm.mv co. coo. HNo. qao.u «Ho.u moo.: mmo.u omo.c Hmo.u mHo.u mqfi. muoozm paw Hmwsm Amqq.mio Adam.-v Aon.o Aofiq.mo Aamm.-o Aomm.o AmHN.Nv AmHH.Huo Amfio.mo Aofim.quv mn. oNo.u Hoo.u moo. mmo. Noo.u oHo. omo. q~o.: Nqo. Hwa.n manna Amwo.auv awm.mno Ammo.v Aoow.fio AHoN.HV Awwm.uo Aoqm.auo Aoom.uo Annm.mo Ammo.muv . muosnouo mo. omo.u mmo.u moo. «mo. qao. Koo.u oqo.: HNo.u Moo. omm.- xuwmp pom xHHZ Ammo.No Awoo.o Aqom.:o ANoH.o Ammn.mo ANNK.HV Aomm.uo AmoH.mv Aqoo.uo Ammo.fio ox. Nqo. moo. mNo.u moo. omo. omo. ooo.: Hmo. ooo.; ocH. mumw pom mane Aqu.o AHMN.V Aqmq.fiuo Ammm.mv «mqo.mnv ANw¢.No AoHN.No AMKN.NIV Amqm.mv Amom.an mo. nao. ooo. oH.u mwo.u woo.u mad. NmH. oHH.: wofi. ooN.u cmflw paw umoz Ammo.N-v Amm.Huo ANKm.o AmHN.Ho Aomn.-o AmH.H:V Amm.ao Kano.v Aomw.v Afiwq.o. mm. omo.u Hmo.u HNo. mwo. . ooo.u. oNo.- omo. Hoo. «Ho. qqo. moanmuowo> pom mammm Amom.no Amfim.o Aoo.ao Amm.mlv Amaw.o Amo.auo AKH.H-V AHq.NV AHK.q-o Amm.mv om. omo.l oHo. moo. mmH.u mmo.u ooo.n moo.i omfi. HoH.n mom.H mcfimuo ,. h le NH» oar mm» «H» ow» NH» HA» H H: anouo >uapoEEoo ‘ A) -—4 (\l AmommsuConm CH modam>uuv mQH< mo mme paw mcmoo Afimm.ov mHm.H mcflmno Hm QDOMU \UHUOEEOU Ememww QZ:no Am.mv mdm2. An applica- tion of AIDS to Indian cross-section data produced 55 (out of 81) price coefficients,in the rural sector and 33 in the urban areas with ltl >1, Ray (1980). The next step is to impose the homogeneity restrictions Z y = o in the case of AIDS and Z H = o in the case of j iJ j ij WTS demand system (i, j = i, ,n). Substituting the homogeneity restriction in AIDS demand system equation (3.3) n-l gives w. = a + B m + z y E. + u. (3.15) 1r 1 i r j=l ij jr 1r A similar equation can be derived for homogeneous WTS demand systems; H.. S. + e. (3.16) where Ejr = sjr - snr , i = l, 2, ,n To test homogeneity, systems (3.15) and (3.16) are estimated, equation by equation, by OLS. F-statistics are calculated to test the validity of the restriction. F-statistics are calculated as (ESS - ESS ) /q F- R U E SSU/ (T ‘ n r 2) where ESS is the residual sum of squares under the homoge- R neity restrictions, ESS is the residual sum of squares U under the unrestricted model, q is the number of restrictions (q = l), and T and n as before. The results are in Table (3.4). 69 TABLE (3.4) TESTING FOR HOMOGENEITY (F-RATIOS) Commodity Group AIDS WTS Grains .13 .003 Beans and vegetables .03 .12 Meat and fish .20 .22 Oils and fats 6.29 2.04 Milk and dairy products 1.30 .68 Fruit 1.13 .49 Sugar and sweets 2.20 2.23 Tea and coffee .40 .54 The tabulated F (1,24) =4.26. Therefore, all commodity groups .05 demand equations, except oils and fats in the case of AIDS, are homogeneous of degree zero in prices and food expenditure. Overall, the WTS demand system conforms better to the homo- geneity restriction than the AIDS. An important conclusion of Attfield's (1985) analysis is that a test for homogeneity, with total expenditure assumed exogenous, is equivalent to a test for exogeneity of total expenditure assuming homo- geneity. Hence previous tests of homogeneity might be re- interpreted instead as rejecting the hypothesis of exogeneity of the expenditure variable where homogeneity is assumed as part_of the maintained hypothesis (Attfield, 1985:198). Accordingly, we can conclude that our assumption of exogeneous 70 total food expenditure is a reasonable one. This study is one of the few studies that does not re- ject the homogeneity restriction. This frequent rejection is somewhat surprising since the homogeneity condition im- poses one restriction only on each equation. Many research- ers refer this rejection to the violation of one or more of the assumptions underlying the classical linear regression model. One might argue that total food expenditure is likely to be measured with less error than total expenditure on all commodity groups. The latter includes expenditure on groups like housing and miscellaneous goods and services which are likely to benmasuredwith considerable error. For example, expenditure on housing might reflect the saving behavior rather flmnithe consumption behavior especially in a country like Egypt. One needs a large sum of savings in order to buy a house or to rent an apartment.8 On the other hand, expenditure on food is frequent and regular. There- fore, food demand subsystems are likely to comply to the exogeneity of total food expenditure and hence to homogeneity restriction. The OLS estimates of homogeneous AIDS and WTS demand system are represented in Tables (3-5) and (3-6) respectively. There are no sign changes between the unrestricted estimates and the homogeneous ones. However, there is a slight 8Usually one has to pay a large sum of money in advance before leasing an apartment, e.g., 30 percent of the total cost of the housing unit. At best, this money will be de- ducted from the monthly rent over, say, the next 15 years. 71 improvement in the precision of the estimates of the homo- geneous systems. There are 22 Yij's with |t| Z 2 in com- parison with 20 in unrestricted AIDS. In the WTS demand system, there is improvement from 18 Hij's with |t| i 2 and 39 with [ti 3 l in the unrestricted case to 21 with [ti 2 2 and 44 with [ti 1 1 in the homogeneous WTS demand system. Note that fiiB'S and AiS'S in Tables (3-5) and (3-6) are calculated from the homogeneous restrictions. Their vari- ances were calculated as var (118) ; var (;. ) + 2 Z cov (1 , ;. ) j=1 1j K 066 66660 100K.-0 0000.0 A0K0.00 0000.0-0 1000.0 AK00.0-0 1000.0-01000.00 0000.0-0 1000.00 00. 000.- 000. 000. 000.- 000. 000.- 000.- 0K0. K00.- 000.0 660600 00 000 K00 000 000 000 000 000 0.0.0 00 06 06660 060066660 AmomosuSonmd CH mnam>uuo mQH¢ mo mma<2HHmm mmamz 066 66660 0000.-0 0000.0 1000.00 0000.0-0 0000.00 0000.-0 0000.-0 AO0K.-0 0000.0-0 0000.00 00. 000 - 000. 000. 000.- 000. 000.- 000.- 000.- 000.- 000.0 660600 00 000 K00 00: 00 000 000 00: 00: 06 06 66600 060066660 AmmmoLuCoMMQ CH oSHm>nuo EMHmwm QZ1 in comparison with 52 in AIDS. Due to the above considerations, we will limit further analysis to WTS demand system only. We should emphasize that ¢ 82 while WTS does not clearly outshine AIDS, it does have a slightly better fit. Testing of Further Restrictions So far, we only tested the homogeneity restriction. Given homogeneity and the WTS demand system as our maintained hypothesis, we test the symmetry restriction Hij = nji (all i and j). To impose the symmetry restrictions across equations, we will use GLS estimator described in earlier sections. For testing purposes, we reestimated unrestricted WTS model (3.4) and homogeneous WTS model (3.16) using ML. The equation of tea and coffee group is dropped during the estimation in order to avoid the singularity problem of the variance-covariance matrix of the disturbances. Table (3.10) indicates that the drop in the value of log- likelihood function after imposing the homogeneity restric— tion is very small and the likelihood ratio test (LR) does not reject the homogeneity restriction. Note that -2) is asymptotically distributed as ¢2 with the degrees of freedom equal to the number of constraints, A = value of restricted log— likelihood function minus value of unrestricted log-likeli— hood function. Thus the LR test confirms the F test we did earlier on an equation by equation basis. Then we will take homogeneous WTS as the maintained hypothesis and impose the symmetry restriction. In other words, we use ML to estimate model (3.16) subject to the constraint Hij = Hji (i # j for all i and j). LR test in Table (3.10) indicates that symmetry cross-equations 83 TABLE (3.10) TESTING OF THEORETICAL RESTRICTIONS Specification Log-Likelihood Number of ~21 $2 05 value restrictions ' Unrestricted 818.295 - - - Homogeneous 811.477 7 13.636 14.07 Symmetric 773.198 21 : 76.558 32.670 restrictions are far from being acceptable. We will present the results of symmetric WTS in Table (3.11) in order to compare with previous estimates. In fact, some economists like Phlips (1974) argue that one should impose the theoretical restrictions from the outset and then proceed to estimate the final form, the symmetric WTS in our case. To Phlips (1974), one should not test these restric- tions, rather one should use demand functions obeying them theoretically. This view, however, is very restrictive because there is no reason to impose symmetry, for example, if the data do not support it. Furthermore, it is not intutively obvious why the Slutsky matrix should be symmetric. As Deaton and Muellbauer (1980az45) argue, ”it is not obvious why, for example, a compensated penny per pound increase in the price of apples should increase the number of bars of soap bought by a number equal to the number of more pounds of apples bought consequent on a compensated penny per bar increase in the price of soap.” .AN.mV manme :0 mm oEmmr 84 600006 can one 0000.0-0 mmo.l mu0®3w USN mefim 0000.0 000K.0-0 000. 000.- 60666 A000.-0 0000.00 0000.0-0 000.- 000. 000.- 66660666 00060 066 600: 0000.00 A0KK.-0 0000.-0 0000.0-0 000. 000.- 000 - 000.- 6660 066 6000 0000.-0 0000.00 0000.00 0000.-0 0000.0-0 000.- 000. 000. 000.- 000.- 6600 066 666: 0000.0 0000.00 0000.00 0000.0-0 1000.00 0000.0-0 000. 000. 000. 000.- 000. 000.- 660666606> 066 66660 0000.-0 0K00.0-0 0000.0-0 000K.00 0000.0-0 0000.-0 000K.00 000.- 000.- 000.- 000. 000.- 000.- K00. 660600 00: 00: 00: 000 000 000 00: 666000 0000660660 ZmHmwm Qz<2m9 mHS mo MMHm MIR 85 Table (3.12) shows the compensated and uncompensated own-price elasticities of the symmetric WTS demand system. TABLE (3.12) OWN-PRICE ELASTICITIES OF SYMMETRIC WTS Commodity Group Compensated Uncompensated Grains +.205 + .109 Beans and vegetables -.l75 - .304 Meat and fish -.238 - .639 Oils and fats ' -.292 - .361 Milk and dairy products -.873 -l.00 Fruit I -.S91 - .677 Sugar and sweets -.356 -.609 Tea and coffee -.690 -.726 Obviously, there is a considerable change between homo- geneous WTS estimates and the symmetric estimates. Note especially the price elasticities of grains, beans and vegetables, and tea and coffee. Also notice that compensated own-price elasticity of grains is positive which is a clear violation of the negativity condition (2.28). However, this negativity condition is maintained in both unrestricted and homogeneous versions of WTS demand system. Next, we will test the validity of the assertion that broad food commodity groups tend to be independent of each other for low income people (Abdel-Fadil, 1975:75-76). Two 86 definitions of independence in consumption will be examined: 1. The Hicksian definition that all compensated cross- price effects vanish, Phlips (1974). 2. The strong separability definition that the marginal utility of any commodity group is not affected by the consumption of other commodity groups. 1. No Compensated Cross Price Effects This restriction amounts to Hij = 0 (all i ¢ j). That is, model (3.4) becomes yir = ai + bi mr + Hii sir + eir (3.23) Model (3.23) is estimated for seven equations simultaneously using GLS. The value of the log-likelihood function is 714.448 while the value of the log likelihood function of the unrestricted model (3.4) is 818.295. Therefore, we conclude that compensated cross price effects are highly significant since ~2X = 207.694 compared with ¢205 (49) = 67.505. This conclusion is further confirmed by noting that 44Hij's (out of 64) in Table (3.6) have absolute t values greater than unity. We will use the homogeneous WTS demand system, our best model, to calculate the compensated and uncompensated price elasticities. These elasticity estimates are based on the average budget shares and are presented in Tdfles (3.13) and (3.14). According to Hicks' definicunusof substitutes and complements, i and j goods are substitutes if eij‘w) and complements if e:j Z(0 -80)s. ._ .. . .. . . 3r 3—1 13 3r 13 1 3 = 003(1-0i) Sir — Zj¢i ej Sjr] n = O. s. — Z 0. 3. ¢ 1[ 1r j=1 3 3r] n—l z ¢ 01 [Sir - %_ 83 83r - 3n Snr] 3—1 n-l n = o 1 [(s. - s ) — E a (s. - s )],51nce Z 6 = l 1 1r nr 3:1 3 3r nr le 3 n n-l ZW s=0(w+b)[(s-s)-: (w+b)(s-s)] 3:1 13 3r ir 1 1r nr 3=1 3r 3 3r nr (3.24) since 0. = w. + b. under Working's model. 1 1r 1 92 Substituting the RHS of (3.24) in WTS demand system (3.4) gives the following model —1 yir = ai + bi mr + 0 (wir + bi)[sir - (er+ bj) an'J =1 Sjr] (3.25) where, as before, sir = sir - snr , i=1, 2, ,n. Model (3.25) is the preference—independent version of WTS demand system (3.4). Model (3.25) is non-linear in 15 in- dependent parameters; 7 ai's, 7 bi's and 0. We dropped the last equation of tea and coffee and estimated model (3.25) using non—linear GLS. The results are in Table (3.15). There is a change in the signs of ai's and bi's for the last two equations under model (3.25) in comparison of those under homogeneous WTS. Estimates of bi in Table (3.15) suggest that sugar and sweets and tea and coffee are luxuries in the food budget. This result is unlikely and is in conflict with our earlier estimates. Also, we have five parameter estimates (out of 17) with absolute t-values less than unity. All of this suggest that model (3.25) is a rather restrictive one. Formally, model (3.25) is rejected against model (3.4); note that model (3.25) is nested in model (3.4) and hence the LR test can be used. Table (3.16) indicates that —21 is more than twice $2 and hence we conclude that preference independence is a rather restrictive assumption and it should be rejected. 93 TABLE (3.15) ESTIMATES+ OF PREFERENCE-INDEPENDENT WTS DEMAND SYSTEM Commodity Group ai b. Grains 1.362 (- .201) (10.353) (-8.242) Beans and vegetables .111 .002 ( 1.963) ( .160) Meat and fish - .219 .094 (-2.10 ) ( 4.840) Oils and fats .159 .012 ( 3.230) (-l.303) Milk and dairy products - .179 .046 (-2.998) ( 4.189) Fruit - .192 .044 (-5.945) ( 7.310) Sugar and sweets - .037 .019 (- .862) ( 2.319) Tea and coffee - .005 .008 (- .045) ( .571) +Asymptotic t-values in parentheses 94 TABLE (3.16) TESTING OF PREFERENCE INDEPENDENCE Specification Log-Likelihood . Number of -21 $2 Value Restrictions Model (3.4) 818.295 - - - Model (3.23) 714.448 49 207.694 67.505 Model (3.25) 737.475 55 161.640 73.29 The above conclusion implies that one should not use demand systems that imply additive preferences in modeling food demand. Such demand systems are very restrictive and give rise to unrealistic elasticity estimates. However, it is convenient to assume additive preferences because it saves a large number of parameters, 55 in our case. Theil and Suhm (1981) used model (3.25) throughout their study because of the limited number of observations they had to work with. An important by-product of estimating model (3.25) is the estimate of the income flexibilitylO parameter 0. Its t-value indicates that our estimate of the income flexibility is highly significant; Egypt's income flexibility estimate is _.636 with standard error .041 Our estimate is in excellent 10It is believed that 0 depends on the level of income. When we allowed 0 to depend on income as 0 = Co + :1 mr, and reestimated model (3.25) the results were disappointing. The estimates and their t—values were 03 = -.18 (0.197) and 01 = -.848 (-.501). Theil and Suhm (1981) reached a similar result. 95 agreement with Theil and Suhm's (1981) estimate of the in- come flexibility. The income flexibility estimate along with expenditure elasticities can be used to calculate the own-price elasti- cities, see Pigou's law (3.21) The resulting estimates are conditional on the validity of the assumption of strong separability. This study clearly indicates that strong separability is sharply rejected when applied to food commod- ity groups. It might be argued, however, that additivity is less restrictive when dealing with highly aggregated broad groups such as food, housing, clothing, and so forth. The evidence is against this. Barten (1969), Theil (1975), and Deaton (1975) do not find strong separability acceptable. Our analysis indicates that the homogeneous WTS demand system gives the best results. It fits the data better than the homogeneous AIDS. Further restrictions, beyond homo— geneity are rejected. Therefore, the estimates of the homogeneous WTS demand system are used for further analysis in Chapter IV. CHAPTER IV REGIONAL AND DISTRIBUTIONAL IMPLICATIONS OF THE CHANGES IN INCOME AND FOOD PRICES Introduction Regional variability in food consumption is notice- .able in Egypt. This variability can be attributed to many factors such as food availability, consumption habits, food prices, income and social variables which include the level of education and the occupation of the household's head. People in the cities tend to be more educated and richer than thoseixlthe Egyptian villages. Food availability differences stem from variations in the crop production patterns and the government food policy. For example, rice production is concentrated in lower Egypt and as a result people eat more rice in that part of the country than in upper Egypt. Government food policy alters the regional pattern of food availability. The ration system has some regional biases. Most households are entitled to monthly quotas of basic commodities, at low prices, such as sugar, tea, oil, and rice. Rations are larger in Cairo and Alexandria than elsewhere. Urban dwellers receive more rice and oil than rural residents, Alderman et al., (1982). The subsidy 96 97 system provides bread cheaply to urban consumers without quantity restrictions. Government food policy is often accused of distorting the regional demand for food. The introduction of rice to consumers in upper Egypt was done by the government through a system of rations and govern- ment food outlets. Consequently, consumers in upper Egypt have gotten used to the consumption of a new food and their demand for rice is stronger than ever. Regional Income Effects Average household's annual total expenditure, an income proxy, varies from one governorate to another. The average household in urban Fayom had the highest income level in 1975, while the average household in rural Asyut had the lowest income (about one third of that of Fayom's household). In general, the average urban household makes more money than the average rural household and the average household in lower Egypt makes more money than its counterpart in upper Egypt, Table A.1 in the appendix. Food budget shares and the expenditure elasticities also are regionally different. The expenditure elasticity for grains is .03 for Cairo compared with .28 for rural lower Egypt. Grains and beans and vegetables groups are consider- ed necessities all over Egypt. Meats, however, are necessities in the urban areas and have unit expenditure elasticities in the rural areas. Oils and fats, sugar and sweets, and tea and coffee are perceived as necessities in all regions. Milk and dairy products are luxuries in all 98 regions except Cairo. Furit is the only group that is a luxury throughout Egypt. Its expenditure elasticity ranges from 1.01 in Cairo to 1.65 in rural upper Egypt, see Table A.2 in the appendix for more details. Five major regions are considered in this chapter; upper11 Egypt (rural and urban), lower Egypt (rural and urban) and Cairo. PeOple in upper Egypt tend to stand out as a group on the basis of their spoken Arabic, color of skin, and habits and attitudes. Cairo will be dealt with independently because of its demographical and political importance. One fifth of the Egyptian population live h1Cairo. Political stability in Cairo is a major concern and there- fore the impact of food policies on Cairo consumers should be evaluated. Table (4.1) shows the allocation of an extra Egyptian pound devoted to the household's food budget. The biggest marginal budget share is that for the meats group. An average household in Cairo will allocate 42 piasters to the meats group and one piaster to the grains group out of each additional pound to its food budget. Out of each additional pound to the household's income, however, 25 piasters will be spent on food in Cairo while 42 piasters will be spent on food in rural upper Egypt, Table (4.1). Rural families will allocate more money, out of their extra earnings, to food than urban families and families 11Upper Egypt is the south of Egypt, south of Cairo, while lower Egypt is the north. 99 TABLE (4.1) MARGINAL BUDGET SHARES FOR FIVE REGIONS ‘Urban Rural Cairo L. Egypt U. Egypt L. Egypt U. Egypt“ Grains .009 .054 .049 .134 .114 Beans and vegetables .154 .146 .130 .144 .128 Meat and fish .424 .422 .422 .375 .387 Oils and fats .075 .075 .084 .079 .093 Milk and products .163 .138 .133 .126 .109 Fruit .106 .097 .094 .085 .078 Sugar and sweets .039 .040 .049 .033 .050 Tea and coffee .030 .028 .039 .024 .041 Food .247 .296 .308 .389 .421 SOURCE: Based on estimates in Table (3.6), Chapter 3. 100 in upper Egypt will allocate more extra money than families in lower Egypt. MOre extra money will be allocated to grains by a rural family than by an urban family. The opposite is true for the meats group. Recall from Chapter 2 that the marginal budget share (8i) under WTS demand system is 9i = wi + bi' That is the marginal budget share of good i exceeds the corresponding average budget share (wi) by bi' Regional Price Effects Absolute values of the own-price elasticities are high- er in the rural areas than in the urban areas for all food groups except that of oils and fats and tea and coffee. The biggest difference is that of the fruit group; -1.29 in rural upper Egypt versus -.762 in Cairo, see Table A.3 in the appendix for more details. This result is consistent with the assertion that low-income consumers are more responsive to price signals than high-income consumers. The previous result is not as clear when we consider other levels of regional disaggregation. For example, the price elasticity of grains is at the highest level in rural lower Egypt while rural upper Egypt has the lowest income per household. Price elasticity of tea and coffee is at its lowest absolute value in rural upper Egypt in spite of the fact that the average household in rural upper Egypt has the lowest income. In fact, rural upper Egyptians are heavy tea drinkers and therefore less responsive to its price changes. 101 Thus, own-price elasticities are affected not only by income but also by regional preferences and food habits. Preferential government treatment of urban dwellers, especially in Cairo, in the form of food subsidies and availability of other services might lead to rural-urban migration. The true cost-of-living index would be affected as a result of the movement from one region to another. A Divisia price index represents the true cost-of-living index which compares the price vectors of two regions c and d at the utility level which corresponds to the geometric means of incomes and prices in the two regions, Theil and Suhm (1981). The Divisia price index for the movement from region c to region d is given by dcd = i Wicd (In pid ‘ 1“ pic) where wicd = %~(Wic1”wid) ’ wi's are average budget shares, and pi's are the prices of commodity groups. A related price index known as Frisch price index is given by, Theil and Suhm (1981), fcd = E 6icd (1n pid ‘ 1n pic) where (I; icd = W' bi's are the income coefficients in WTS system. The Frisch price index gives more weight to luxury goods since 102 marginal budget shares (01's) for luxury goods are larger than average budget shares. The difference between Frisch price index and Divisia price index ) n w =i b. (1n pid - ln piC is positive when the prices of luxuries increase relative to those of necessities, negative in the opposite case. The effect of grains, or any other group, on the differences between the indexes can be evaluated. With grains indicated by 1, the Divisia price index for the move- ment from region c to region d is n d = I w. (n-l) i=2 T%%9 (in pid ‘ 1n pic) lcd Similarly the Frisch price index is n f = Z 0. .9 led The difference is given by !(n-1)' If Un—l is smaller than 0, it means that the tendency of luxuries to increase in price relative to necessities in the more affluent regions is mainly the result of the fact that grains tend to be relatively cheaper in high—income regions. The above indexes are calculated and presented in Tables (4.2)—(4.5). The calculations are based on the homogeneous WTS in Chapter 3. The movements are considered from less affluent to more affluent regions. The regions are listed in the order of declining income per household. 103 Table (4.2) indicates that the cost of food for any average household that moves from any region to Cairo will increase. The rate of increase is modest though. If the grains group is removed from the aggregation of food, the cost of food will increase substantially for the household that moves to Cairo. The rate of price increase will be especially high for families moving from rural lower Egypt to Cairo. This observation indicates that grains are re- .latively cheaper in Cairo than in the rest of the country. The movement from urban upper Egypt to urban lower Egypt will be beneficial for consumers in urban upper Egypt. Table (4.2) shows that the cost of food will decline by 2.49 percent for the household that moves from urban upper Egypt to urban lower Egypt. The cost of food will increase by 2.8 percent for the household that moves from rural lower Egypt to urban uper Egypt. Removing the effect of the price of grains will make the movement from urban upper Egypt to urban lower Egypt and from rural upper Egypt to rural lower Egypt more beneficial for the families that make the move. Table (4.4) shows the difference between Frisch price index and Divisia price index for the movement from one region to another. If the difference is positive it means that the prices of luxuries increase relative to those of necessities. Accordingly, the relative prices of luxuries to necessities increase as we move from any region to Cairo. Also comparing rural lower Egypt to both urban lower Egypt and urban upper Egypt, the prices of luxury foods are 104 TABLE (4.2) DIVISIA PRICE INDICES FOR THE MOVEMENT FROM REGION C TO REGION D To Cairo Urban Lower Urban Upper Rural Lower Egypt Egypt Egypt From U. Lower Egypt . 103.4 U. Upper Egypt 100.6 97.51 R. Lower ‘ Egypt 103.6 100.6 102.8 R. Upper Egypt 102.2 99.49 101.8 99.58 TABLE (4.3) DIVISIA PRICE INDICES FOR SEVEN GROUPS WITH GRAINS DELETED To Cairo Urban Lower Urban Upper Rural Lower From Egypt Egypt Egypt U. Lower Egypt 109.6 U. Upper Egypt 102.3 93.09 R. Lower Egypt 116.9 106.3 114.8 R. Upper Egypt 107.7 97.82 105.6 91.82 105 TABLE (4.4) FRISCH PRICE INDEX MINUS DIVISIA PRICE INDEX FOR EIGHT GROUPS To ' Cairo Urban Lower Urban Upper Rural Lower prom Egypt Egypt Egypt U. Lower Egypt .0640 U. Upper Egypt .0375 -.0269 R. Lower Egypt .1005 .0361 .0629 R. Upper Egypt .0616 -.0028 .0241 —.O389 TABLE (4.5) FRISCH PRICE INDEX MINUS DIVISIA PRICE INDEX FOR SEVEN GROUPS WITH GRAINS DELETED TO Cairo Urban Lower Urban Upper Rural Lower From Egypt Egypt Egypt U. Lower Egypt .0139 U. Upper Egypt .0237 .0102 R. Lower Egypt .0133 -.0011 -.0129 R. Upper ~ Egypt .0235 .0343 -.0019 .0119 106 relatively more expensive in the last two regions. More- over, the prices of luxury foods increase relative to necessities as we move from rural upper Egypt to urban upper Egypt. In general, seven entries in Table (4.4) are posi— tive, out of ten. Therefore, we might conclude that there is a tendency for the prices of luxury foods to increase relative to those of necessities when we move from a less affluent region to a more affluent region. Table (4.5) compares the Frisch and Divisia price in- dexes when the grains group is deleted. A comparision with Table (4.5) shows that most of the figures are much smaller. Thus, we may conclude that the tendency of luxury foods to increase in price relative to necessities in the more affluent regions could be the result of the fact that grains are relatively cheaper in the more affluent regions. Distributional Effects of Price Increases Welfare effects of the changes in food prices will be evaluated in this section. Specifically, we will evaluate the welfare implications of: 1. Increasing the price of grains only. 2. Increasing the price of meats groups only. 3. Increasing the prices of both groups simultane- ously while the other prices are held constant. This evaluation exercise-wi11 be done for different households in both urban and rural areas. Both urban and rural families will be grouped into three categories according to per capita income. 107 Income Distribution of Households Table (4.6) shows that 20.67 percent of urban popula- tion comes from families with a per capita income ranging from 60-80 Eyptian pounds per year. In fact, about three quarters of the urban population come from families with per capita income ranging from 40 to 150 Egyptian pounds. The weighted average of annual per capita expenditure for the urban population is L.E 103, while the modal expenditure is L.E 70. Three households are chosen to represent three income stati; poor families, middle-income families, and rich families. The per capita income of the first household ranges from L.E 40 to L.E 50. About one-fifth of the urban population have per capita incomes less than L.E 50. There- fore, the L.E 40-50 household will be representative of the urban poor. The second household of L.E 60-80 will repre- sent the urban middle-income families. About one half of the urban population have a per capita income less than L.E 80. Finally, the third household of L.E. 150-200 will be used to represent the rich families. About 16 percent of the urban population lie on the top of the income ladder with a per capita annual income equals to at least L.E 150. Table (4.7) shows that 20.36 percent of the rural population has a per capita income ranging from L.E 60 to L.E. 80. That is, the mode per capita income in both urban and rural areas is the same. However, the rural income distribution has more weight toward poverty. About one quarter of the rural population have per capita income 108 TABLE (4.6) DISTRIBUTION OF URBAN HOUSEHOLDS ACCORDING TO PER CAPITA ANNUAL EXPENDITURE Per Capita Number of Percentage of Cumulative Expenditure Households Individuals Percentate (L.E) of Individuals less than 20 26 .34 .34 20 - 129 1.95 2.29 30 - 405 6.09 8.38 40 - 733 10.99 19.37 50 - 833 11.81 31.18 60 — 1518 20.67 51.85 80 - 1161 15.03 66.88 100 - 1518 17.34 84.22 150 - 716 7.27 91.49 200 - 340 3.24 94.73 250 - 234 2.22 96.95 300 and more 380 3.05 100.00 SOURCE: CAPMAS, Family Budget Survey, 1974/75 (Cairo: CAPMAS, 1978) - Table 4. 109 TABLE (4.7) DISTRIBUTION OF RURAL HOUSEHOLDS ACCORDING TO PER CAPITA ANNUAL EXPENDITURE Per Capita Number of Percentage of Cumulative Expenditure Households Individuals Percentage (L.E) of Individuals less than 20 52 1.52 1.52 20 - 232 6.64 8 16 3O - 581 16.61 24 77 4O - 708 19.33 44 10 50 - 618 15.42 59 52 6O - 847 20.36 79 88 8O - 402 9.10 88 98 100 - 380 7.86 96 8 150 - 111 2.08 98 92 200 - 39 .57 99 49 250 - 13 .22 99.71 300 and more 19 .29 100.00 SOURCE: CAPMAS, Family Budget Survey, 1974/75 (Cairo: CAPMAS, 1978) — Table 5. 110 less than L.E 40 (in contrast to 8.38 percent of the urban population). On the other hand, about three percent of the rural population have per capita income more than or equal to L.E 150 (in contrast to about 16 percent of the urban population). The weighted average of the annual.per capita expenditure for the rural population is L.E 63.8 (less than two—thirds of the urban average). Three representative households, with similar incomes to the urban ones, will be chosen to represent the income status in the rural areas. The income distribution comparisons between urban and rural areas are clear from Figure (4.1). Both distributions have the same mode of 60 to less than 80 Egyptian pounds. Before the mode,the rural income distribution lies above the urban distribution. The urban distribution lies above the rural distribution,after the modal income. The vertical distance between the two curves is generally bigger after the mode than before. That is more concentrations of low in- come people reside the rural areas in Egypt. Welfare Effects of Price Increases The concept of compensating variations will be used to measure the welfare changes. Compensating variations are the amount of money necessary to just compensate the con- sumer for the loss of utility due to a price increase. Using the Consumer's Cost Function, the compensating variation can be defined as: cv = c(pl, uo) - c (p0, uo) 111 0292-580 .2021 oz< z7 1 2-3 4-7 Grains .11 .18 .23 .29 .18 .22 .29 Beans and vegetables .11 .13 .13 .13 .10 .12 .11 Meats .38 34 .30 .25 .32 .31 .27 Oils and fats .08 .09 .09 .08 .13 .12 .11 Milk and dairy products .12 .10 .10 .08 .08 .07 .07 Fruit .09 .07 .06 .04 .05 .05 .04 Sugar and sweets .06 .06 .06 .06 .06 .06 .06 Tea and coffee .05 .03 .03 .07 .08 .05 .05 Total Food .32 .44 .47 .51 54 .48 53 .35 .ll .25 .04 .60 *The income is fixed at per household per year. the national average of L.E. 490 128 Having the same income, urban and rural households allocate higher budget shares to grains and lower shares to meats as the household size increases. The substitution of grains for meats works as a mechanism to adjust for the increases in the household size if the income is unchanged. If the household size increases from 2—3 persons to 4-6 persons the urban household will increase its grains budget share by five percent and lower its meats budget share by four percent, Table (5.1). Furthermore, the average budget share of milk and dairy products tend to decrease with the family size. The oils and fats budget share decreases in the rural areas when the family size increases. Thus, oils and fats tend to be luxurious in the rural areas. In fact, consumption of butter and ghee is highly regarded in the countryside. Finally, note that the fruit budget share de- clines when the size of the family increases in the urban areas. Table (5.1) indicates that larger households have higher total food budget shares than smaller households in the urban areas. One person urban household allocates 32 percent of its LE 490 annual income to food, while a four to six persons household allocates 47 percent of the same in— come to food. Apart from the one person households, the same pattern of relationship exists in the rural areas. The total food budget share increases by 12 percent as the rural household size increases from four to six to seven or more persons, Table (5.1). The fitted total food budget 129 shares are depicted against the natural logs of total annual expenditures for urban and rural areas in Figures (5.1)and (5.2) respectively. The estimated food budget shares are based on Working's model estimates in the appendix. There are four lines in each figure, one for each household type. At all income levels, larger households spend higher proportions on food than smaller households in the urban areas, Figure (5.1). The three lines of one person, four to six persons, and seven or more persons are almost.parallel for the urban families. Thus the increase in the food budget share as the size of the household increases from one person to four to six persons is 15 percent at all in- come levels. Similarly, the food budget share increases by four percent as we go from four to six persons household to seven or more persons household in the urban areas. In contrast, the increments in the food budget share increase with income as we go from one person household to two to three persons household in the urban areas, Figure (5.1). This information is important in designing the government income maintenance programs. Clearly, the increase in the food budget share as the family gets larger will be at the expense of nonfood commodity groups such as clothing, medical care, and housing. To keep the budget of nonfood unaffected and maintain the household after the increase in its size, the government can raise the household's income in proportions consistent with Figure (5.1). 130 .mm (d)) where d is a vector of demographic variables, 8i (d) and m (d) are functions of the demographic variables d. This specifica- tion states that household characteristics change the prices conceived by the household from p to p* = p m (d). In Deaton and Muellbauer's (1980a) words, having chidren makes ice cream, milk and soft drink relatively more expensive and makes cigarettes relatively cheaper. In addition to chang- ing prices, demographic variables introduce a fixed cost element 2 % (d) pi into the household cost function. If 81 (d) = o (each i), Gorman's specification reduces to Barten's specification or to what Pollak and Wales (1981) call scaling. On the other hand, if mi (d) = 1 (each i), Gorman's specification reduces to what they call translat- ing. 137 The PIGLOG cost function (2.67) in Chapter 2 will be the basis of discuSsion in the following sections. To reiterate, our model's cost function is _ 8 1n c (u, p) — ZK YK ln pK + u HK pKK (5.1) The scaling procedure will be used to modify (5.1) in the following manner: In c (u, p, d) = Z y 1n mK pK + u HK (mK pK)BK (5.2) K K If mK's are the same for all commodity groups, (5.2) will reduce to 8 ln c (u, p, d) = ln m + Z YK 1n pK + u HK pKK (5.3) The demographic function m will be specified as 1n m = 81 ln 2 + 62 (1n 2)2 (5.4) where z is the household size. The demand system corresponding to (5.3) and (5.4) is given by n-l wi = Yi + Bi [ln (x/pn) - i 1K 1n (pK/pn) -6 ln 2 - 8 (1n z)2] (5 5) .1 ,2 . for i = l, 2, ------ , n-l Data and Procedures: Data on different household types in two family budget surveys, 1958/59 and 1974/75, will be used to estimate model (5.5) separately for urban and rural areas. The urban sample consists of 88 observations, 31 from 1958/59 survey and the rest from the other survey. Households in 1958/59 are classified according to size into three types: 1. Small households (1-3 persons), 2. Medium households (4—6 persons), and 3. large households 138 (7 or more persons). The same classification was carried on in the 1974/75 survey with the exception that small households were further broken down into two types: a. households consisting of one person, and b. households consisting of two to three persons. The rural sample has 87 observations, 34 from the 1958/59 survey. Households are classified in the same fashions for both urban and rural samples. Information about prices can be derived for every commodity group for every income class in both urban and rural areas. Conceptually, this would mean that prices depend on household income and therefore they should be treated as endogeneous variables in the demand system. To overcome this potential complication, each sample will have only two prices, one for each budget survey. That is urban consumers are faced with two prices for each commodity group, one price for 1958/59 observations and the other price for 1974/75 observations. A similar argument goes for the rural consumers. The definition of commodity groups is the same as in Chapter III. Moreover, the composite group prices are calculated as geometric means. Model (5.5) is chosen because of its desirable features, outlined in Chapter II; noteably the ability to identify its parameters from data with limited price variations. The specification of the m function in (5.4) could be allowed to vary from one commodity group to an- other. It can also be extended to include other demographic 139 variables such as age and sex compositions. Lack of data on such variables prevented exploring these possibilities. Specification (5.4), however, gives a direct estimate of the adult equivalent scales since 1n m = o for the re- ference household consisting of one adult. Using the cost function concept, it can be shown that 1n Equivalence Scale E 1n c (u, p, d) - 1n c (u, p, do) = ln m; which shows the needed expenditure at constant prices by a household with demographic composition d relative to that of some reference household with composition dO in order to reach the same level of utility u. Results: Non-linear FIML in TSP computer program was used to estimate model (5.5) for both urban and rural areas. The last equation, tea and coffee, was dropped during the estimation process in order to avoid a singular variance-covariance matrix. The estimates for both samples are in Table (5.3). Most of the estimates are statistically highly significant and seem reasonable when compared to expected results. The estimates of i1 and 52 are used along with formula (5.4) to calculate the estimates of adult euqivalant scales in Table (5.4). The calculations are based on the average household sizes in Table (5.4). Adult equivalent scales estimates in Table (5.4) suggest that there is more economies of size in food con- sumption in rural areas than in urban areas in Egypt. An 140 TABLE (5.3) ESTIMATES OF PIGLOG MODELS FOR URBAN AND RURAL SAMPLES (asymptotic t-values are in parentheses) Commodity Urban Sample Rural Sample Group . \{1 Bi Y i 8 - Grains 1.112 - .126 1.464 - .141 (25.73 ) (-25.72 (21.61 ) {-19.11 ) Beans and .039 .011 .075 .003 vegetables ( .95 ) ( 1.68 ( 1.92 ) ( .60 ) Meats - .220) .075 - .381 .079 (-4.26 ) ( 11.09 (-9.66 ) ( 18.45 ) Oils and .090 .0002 -.078 .022 fats ( 4.81 ) ( .06 (-3.00 ) ( 7.09 ) Milk and - .060 .022 - .053) .015) dairy (-4.40 ) ( 12.55 (-1.80 ) ( 3.96 ) products Fruit - .112 .024 - .092 .016 (-7.52 ) ( 13.91 (-7.06 ) ( 10.49 ) Sugar and .075 - .002 .044 .003 sweets (13.13 ) (- 1.86 ( 4.83 ) ( 2.16 ) Tea and .076 - .004 .021 .003 coffee” ( 6.73 ) (- 2.86 ( 1.19 ) ( 2.00 ) 61 1.052 .535 ' (11.33 ) ( 5.61 ) 62 - .061 .094 (-1.22) ( 2.41) Log of like- 1728.12 1723.04 lihood func- tion 7'~‘The adding-up restriction is used to recover the estimates of this equation. 141 TABLE (5.4) ESTIMATES OF ADULT EQUIVALENT SCALES IN BOTH URBAN AND RURAL SAMPLES Household Type Average Household Urban Rural Size Sample Sample One person 1 1 1 2-3 persons 2.5 2.49 C 1.77 4-6 persons 5 4.65 3.02 7 or more persons 8.5 7.20 4.83 unlikely explanation is that the adult proportion in an urban family is larger than that of a rural family of the same size. But, in fact, rural families tend to be extended families and are likely to have more adults. Moreover, it might be safe to assume that a two to three person family in both samples has two adults, husband and wife. Table (5.4) however, indicates that a two to three urban family is equivalent to 2.49 adults while a similar rural family is equivalent to 1.77 adults. Thus, fixing the adult pro- portion does not seem to help explaining the more efficient use of food in rural areas. Food habits are different between urban areas and rural areas. Members of the rural family usually eat together, from the same dish, the two essential meals; breakfast and supper. Waste in food consumption is likely 142 to be negligible as a result. In contrast, food waste is observable in urban areas either because of bad quality or because of the food consumption habits. Changes in the True Cost of Food Food prices are particularly important politically in Egypt. The government controls these prices through a com- plex system of rationing, subsidies, public outlets, and policing of prices. Any explicit attempt to increase food prices is usually met with unrest. Other implicit measures are often taken by the government in recent years such as reducing the weight Of bread loaves, providing a slightly better quality bread at higher prices and eventually elimi- nating the cheaper bread, and providing different types of bread for different suburbs. Household types are affected differently by increases in food prices. Evaluating these effects is crucial in understanding the impact of possible price increases on different households. The cost function concept can be used to construct what is known as economic indexes or true indexes, in contrast to the statistical indexes such as Laspeyres and Paache price indexes. The true cost-of-living index measures the relative costs of reaching a given standard of living under two different price situations. It is given by p (pl, p0; ur) = c (ur, pl)/C (ur, p0) (5.6) where ur is the reference utility level; it can be set to 143 u0 or ul. The true cost-of-living index can be calculated straight forwardly if we know the cost function c (u, p). Deaton and Muellbauer (1980a: 170-173) show that Laspeyres price index is greater than or equal to o o . . ; u ) and that Paasche price index can be no more than the current utility referenced index p (p1, p0; ul). 1 P (P : P The base-weighted, true cost-of-food index using the cost function in (5.3) is given by in p (p1, p0; u0) = Z Y (1n pl - in P0) + K K K K uO(H pieK- n p0 8K) (5.7) K where the base utility level u0 is equal to O u = [ 1n x O — ln m - Z YK ln p: ]/H pEBK, where x0 is the total expenditure on food. The true cost- of-food index is independent from variations in prices of goods outside the food commodity groups as long as weak separability is assumed (Deaton and Muellbauer, 1980a:182- 184). Weak separability is assumed in this study, see Chapter III. Given the importance of food in the budget of the Egyptian family, the true cost-of-food index might serve as a good proxy of the true cost-of-living index. The estimates of PIGLOG cost functions in Table (5.3) are used to calculate the true cost-of-food indeces, in terms of annual rates of growth, in both urban and rural areas for different household types. For comparison pur— poses, these indeces were calculated for two time periods: 1959—1975 and 1975—1980, see Table A.12 in the appendix for 144 details about the prices. For both intervals, the utility levels are the same and are evaluated at 1959 prices for each household type. The indices are calculated for four different levels of food expenditures. The results are in Tables (5.5) and (5.6) for urban and rural areas res- pectively. From 1959 to 1975 increases in the cost of food were moderate and under control. In general, rural consumers experienced higher rates of increases in food cost than urban consumers. Rates of increases in food cost were higher for high income families than for low income families in both urban and rural samples. The differentiation between high and low income families was more significant in the urban areas, Table (5.4). For example, the rate of increase for an urban family consisting of seven or more persons increased from 1.67 percent to 4.21 percent as food expenditure increased from L.E 50 to L.E 600. The corre- sponding increase in the rural sample was from 3.96 to 4.74 percent, Table (5.6). An interesting pattern of relationships existed between inflation rates and household size. There was a negative relationship between inflation rates in food cost and the household size in both urban and rural areas from 1959-1975. The decline in rates of increase in food cost 'was greater for urban families than for rural families. Table (5.5) shows that the rate declined by 2.01 percentage points for an urban family with L.E 50 expenditure on food 145 TABLE (5.5) ANNUAL AVERAGE PERCENTAGE RATES OF INCREASE IN THE TRUE COST OF FOOD IN URBAN AREAS Household Type and Annual Food Expenditure Levels (L.E) Time Interval 50 100 300 600 1959-1975: one person 3.68 4.40 5.55 6.27 2-3 persons 2.75 3.45 4.26 5.31 4-6 persons 2.12 2.82 3.95 4.66 3.7 persons 1.67 2.38 3.50 4.21 1975-1980: one person 18.98 18.97 18.69 18.57 2-3 persons 19.13 19.02 18.89 18.72 4-6 persons 19.24 19.12 18.94 18.83 3 7 persons 19.31 19.19 19.01 18.90 TABLE (5.6) ANNUAL AVERAGE PERCENTAGE RATES OF INCREASE IN THE TRUE COST OF FOOD IN RURAL AREAS Household Type and Annual Food Expenditure Levels (L.E) Time Interval 50 100 300 600 1959-1975: one person 4.45 4.67 ' 5.02 5.24 2-3 persons 4.27 4.49 4.84 5.06 4-6 persons 4.11 4.32 4.67 4.89 i 7 persons 3.96 4.18 4.52 4.74 1975-1980: ' one person .19.26 19.52 19.94 20.19 2-3 persons 19.05 19.31 19.72 19.98 4-6 persons 18.85 19.11 19.52 19.78 3 7 persons 18.68- 18.94 19.35 19.61 146 when the family size increased from one person to seven or more persons. The corresponding decline for the rural family, however, was .49 percentage points. Our discussion above suggests that Egypt's food policy favored the poor and large families in the time period 1959-1975. That policy differentiated actively between urban and rural families, low and high income families, and small and large families. The differentiation was more successful in the urban areas. Egypt's food policy decision- makers were mainly interested in protecting urban consumers in general and the urban poor in particular. Rural consum- ers were discriminated against. They usually had limited access to subsidized food and had lower quantities on their ration cards than urban consumers, (Alderman et al., 1982). The results for the time period 1975—1980 show new trends of Egypt's food policy. Inflation rates in the true cost of food are much higher than those in the earlier period. In the mid 1970's, Egypt adopted a new economic policy known as A1.Infitah or openness. The main thrust of this policy is to allow more freedom to the private sector and to encourage foreign investments in Egypt. New philos- ophies and attitudes were emerging. Basically, the free enterprise philosophy gradually replaced Nasser's socialist policies. Egypt's economic ties with western Europe and U.S.A. became more important than the traditional ties with the Eastern Block. People were encouraged not to depend on the government since one of the slogans was ”The government cannot do everything.” 147 In the food sector, private traders became active in importing food products such as chicken and in exporting some fruits and vegetables. Domestically, new private food channels known as ”Food Security Outlets” were created and promoted with the government's encouragement. Food products were usually available in these outlets at the market price. In contrast, similar food products were sold in government-owned outlets at lower prices. Buying food from government outlets was not an easy task because of supply shortages and the need to wait in long lines. Rumors were going around that subsidized goods were illegally being transferred from government outlets to “Food Security” out- lets. Judicious use of the subsidy system and its eventual elimination was considered as an essential step for economic reform. On January 16, 1977, the government revealed its intentions on national TV and announced major price in- creases to be effective the following day. The next two days marked serious street rioting in Cairo and other major cities. In response, the armed forces were called on duty to quell the riots and the price increases were cancelled. Sadat used to refer to this incident as thieves uprising while his critics called it a popular uprising. Some observers believe that this incident had major effects on Sadat's future policies including his overtures of peace toward Israel. After January 1977, the government became less vocal about its efforts to increase food prices and it usually took implicit measures to achieve its objective. 148 These new developments in Egypt's political and economic environments help to explain the high rates of increase in the cost of food during the period 1975-1980. Two more factors contributed to that phenomenon of high rates of increase in food prices. 1. The widening gap between the demand for food and the domestic supply of it. Demand for food started increasing dramatically while food production's rate of growth slowed since 1974. Rapid population growth rates and higher real incomes of millions of Egyptians,as a result of working in the rich Arab countries, explain the increased demand for food. 2. In- flation was a World-wide phenomenon in the 1970's. Crop failures in major countries like the Soviet Union and China and the increased demand for food in the oil rich countries led to unusually high food prices in the international markets. As Egypt increasingly depended upon imported food, it was difficult to insulate its citizens from the rest of the world. High income families with food expenditures of L.E 300 or L.E 600 had lower rates of increase in the true cost of food in urban areas than in rural areas during the period 1975-1980, Tables (5.5) and (5.6). However, larger and poorer families experienced higher rates of increase in the cost of food in urban areas than in rural areas. Urban families of seven or more persons and L.E 50 food budget had higher rate of increase in the cost of food than their rural counterparts during the time period 1975-1980. The 149 larger the family and the poorer it is, the higher the rate of increase in its cost of food in the urban areas from 1975 to 1980. This pattern is the opposite of that pre- vailed in the period 1959-1975. On the other hand, the rates of increase were higher for small and high income families in the rural areas than for large and poor families, Tables (5.6). This was the same pattern in the earlier period 1959-1975. Based on data from Scobie (1981), the average annual rates of increase in the food price index for the entire country are calculated. The rate of increase was 6.2 percent during the time period 1959-1975. Then the rate of increase in the food price index jumped to 13 per- cent from 1975 to 1979. Although the comparison with our estimates is not possible, the changes in the food price index give support to our finding that the cost of fOod increased at much higher rates after 1975 than before. From the analysis presented above, it seems that Egypt's food price policy was designed carefully to help the urban poor and large families during the period 1959-1975. After 1975 the differential treatment of poor against rich and large family against small family was not successful. On the contrary, the previous analysis suggests that the food price policy was somewhat biased against poor and large families during the period 1975-1980. This conclusion is consistent with Dessouki (1982)'s study of the politics of income distribution in Egypt before and after the adoption of the open-door economic policy in 1975. He concludes that 150 Egypt has experienced two processes of income distribution: the first was toward a more egalitarian structure that was the outcome of a conscious policy on the part of the govern- ment, and the second was a reverse redistributive process in favor of the more privileged groups in society (Dessouki, 1982:82). The findings in this chapter and in Chapter IV comple- ment each other. In Chapter IV the Divisia and Frisch price indices were calculated in order to evaluate the impact of the movement from one region to another on the cost of food in 1974/75. Time and income variations were not considered. It was shown that moving from rural areas to urban areas results in a slight increase in the cost of food. The analysis in this chapter indicates that the differentiation between rural and urban consumers is no longer as explicit as beflnxal975. Furthermore, urban poor and large families compared with their rural counterparts, had higher rates of increase in the cost of food during the period 1975—1980. Thus migration to the cities is not attractive anymore. In fact, there is a reverse pattern of migration from urban to rural areas in today's Egypt. We argued in Chapter IV that Egypt is heading toward the elimination of food subsidies and the income compensa- 'tion of the poor. In this chapter we show that poor and large families are going to suffer the most from the price increases. Unless they are compensated, they could be a source of political instability. Using the estimates of 151 equivalence scales and Figures (5.1) and (5.2) we know how to support a large family in relation to a small family. In Chapter IV we estimated the income compensations needed to offset the price increases according to the income level of the family. Thus, combining the results from both chapters should be of value to the policy decision-makers in Egypt. CHAPTER VI SUMMARY AND CONCLUSIONS Summary of Methodological Conclusions This study assumes that the households adopt the notion of a two-stage budgeting. In the first stage they dis- tribute their total expenditures for broad groups like food, housing, transportation, and so forth. Then in the second stage the budget of each broad group is allocated for its components. The food budget in this study is divided into eight food groups. The demand equations of these food groups are consistent with the consumer's optimization behavior. Our demand equations give rise to an empirically ex- cellent model introduced by Working (1943). A hybrid of Working's model and the Rotterdam model is derived by Theil and Suhm (1981), we refer to it as the WTS demand system. The Almost Ideal Demand System (AIDS) and the WTS demand system have similar desirable characteristics. They are flexible, relatively easy to estimate, consistent with Working's model, and allow perfect nonlinear aggregation over consumers. We estimated both systems using Egyptian regional data from one budget survey. According to the informational 152 153 measure of goodness of fit, the WTS demand system seems to fit the data better than the AIDS. This study is the first to estimate the WTS demand system without imposing the strong separability a priori. The results are very pro- mising and indicate that the WTS model is a serious con- tender of the popular AIDS. Testing of the homogeneity and symmetry restrictions shows that the WTS demand system is homogeneous but not symmetric. This is one of the few studies that accepts the homogeneity restrictions. Attfield (1985)'s analysis leads us to conclude that accepting the homogeneity restrictions implies that the exogeneity of the total food expenditure is acceptable too. Thus, the two-stage budgeting process proves reasonable. Furthermore, two tests were conducted to verify if the broad food groups are independent of each other in con- sumption. A test based on Hicks's definition of indepen- dence was rejected. Therefore, the relationships of sub- stitutability and complementarity between food groups in Egypt are significant. The second test was of the strong separability and it was rejected too. Accordingly, we recommend against the use of additive utility functions in modeling the demand for food. Our income flexibility estimate for Egypt is -.64 with standard error of .04. Theil and Shum (1981) estimate of income flexibility from a sample of 15 developed and developing countries is —.62. This study and Theil and 154 Shum (1981) found that income flexibility parameter does not depend on the level of income, in contradiction with Frisch's conjecture. Finally, this study demonstrates that Working's model can be exploited in order to make welfare comparisons. The model is used in Chapter V to estimate the increases in income needed for the maintenance of different household types. Another achievement of this study is to show that one family budget survey can be successfully used to estimate a complete matrix of demand price elasticities. Summary of Policy Conclusions The demand elasticity estimates are essential tools for food policy analysis. Estimates of the price elastic- ities are not usually available for Egypt. This study provides a good set of estimates of the price elasticities. Tables (3.13) and (3.14) present our best estimates of the compensated and uncompensated price elasticities respective— ly. The uncompensated own-price elasticities are negative as expected a priori. On the other hand, all compensated own-price elasticities are negative, in accordance with the negativity condition of the Slutsky matrix. Compared with other studies, the magnitudes of the own-price elasticities seem reasonable. The largest absolute uncompensated own—price elasticity is for fruit, -.998, while the smallest is that of grains, -.214. The compensated cross price elasticities are mostly positive, 155 indicating that the degree of substitutability is stronger than the degree of complementarity among food groups in Egypt. Based on the expenditure elasticities in Table (3.7), milk and dairy products and fruit groups can be classified as luxuries and the other groups as necessities. Furthermore, rural households allocate more money to food, out of an extra Egyptian pound in their incomes, than urban households. And the families in upper Egypt allocate more extra money to food than the families in lower Egypt. The largest portion of the increase in the food budget will go to the meats group. When we considered the impact of regional migration on the cost of food we found that the movement from any region in the country to Cairo is asso- ciated with a slight increase in the cost of food index. However, based on Divisia and Frisch price indices, we found that grains are relatively cheaper in Cairo than in the rest of the country. Increasing the price of sub- sidized grains in Cairo will make the migration to Cairo less attractive. We argued in the last two chapters that the government of Egypt is bound to increase the prices of some subsidized foods and to compensate the incomes of some segments of the population. The analysis in Chapter IV demonstrates that increasing the price of meats is preferred to increasing the price of grains. Increasing the price of meats induces less severe changes in the demand for food and hence less structural changes in the food system. Moreover, the 156 limited-income segment of the population, or the middle- income group, will be less affected by the increase in the price of meats than by the increase in the price of grains. By assumption, the poor groups are equally unaffected under both price policies since they are going to be com- pensated. The representative urban poor family should get its income raised by about six percent in order to offset the increase in the price of meats by 50 percent. On the other hand, the income of the same family should be increased by about 17 percent in order to offset the doubling of the price of grains. Therefore, increasing the prices of sub- sidized meats and compensating the poor is a sound option for Egypt's food policy. Another important factor in the design of the govern- ment welfare programs is the family size. The analysis in Chapter V shows that substituting food groups for nonfood groups is a mechanism to adjust for the increase in the household size when income is fixed. Within the food groups, the substitution will be from expensive foods such as meats to less expensive foods such as grains. For the maintenance purposes, the income of a given household should be raised by the same percentage increase in its food budget share in order to leave the budget of nonfoods unaffected. A poor urban family with annual income of L.E 148 should get its income raised by about 10 percent when its size increases from one person to 2-3 persons and by about five percent 157 when its size increases from 2-3 persons to 4-6 persons, Figure (5.1). If the interest is to keep the household as well off as before the increase in its size, the estimates of the equivalence scales should be employed. Unfortunately, our estimates of the equivalence scales for the urban sample do not look right. Generally, the estimation of the equivalences scales is not very success- ful, Muellbauer (1977 and 1980). Finally, this dissertation reveals that large and poor urban families enjoyed low rates of increase in the cost of food during the period 1959-1975. During the same period, urban families experienced lower rates of increase in the cost of food than rural familes. The pattern was reversed after 1975. There is no clear differentiation between urban and rural families as before. The rates of increase in the cost of food were almost the same, during the period 1975-1980, in urban and rural areas. Furthermore, the food price policy was slightly biased against poor and large urban families. This is further evidence why the government should offer income compensation to the poor and large families when the food subsidies are cut. Suggestions For Future Research It would be interesting to include some of the non- food groups in our demand systems. This would enable dis- covery<1fthe interrelationships between food and nonfood groups in a developing country like Egypt. Increasing the 158 cost of housing or transportation might have a profound impact on the food consumption. Also it is important to know what nonfood groups are most sacrificed when the size of the household increases. Another area of improvement would be to use better and more detailed data on the demographic variables. 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A. ”Middle-Income Classes and Food Crises: The 'New' Food-Feed Competition," Economic Develop- ment and Cultural Change, 33 (1985):463-483. 166 TABLE (A.1) AVERAGE BUDGET SHARES IN FIVE REGIONS Urban Rural Groups Cairo Lower Upper Lower Upper Egypt Egypt Egypt Egypt Grains .202 .247 .243 .327 .308 Beans and vegetables .136 .128 .113 .125 .111 Meat and fish _ .307 .305 .306 .258 .270 Oils and fats .088 .088 .099 .092 .106 Milk and products .106 .081 .075 .068 .053 Fruit .061 .052 .050 .039 .033 Sugar and sweets .059 .060 .070 .053 .070 Tea and coffee .041 .039 .044 .038 .049 Food .424 .473 .485 .566 .598 Average house- hold's annual expenditure (L.E) 610 512 469 404 311 SOURCE: CAPMAS, Family Budget Survey, 1974/75 (Cairo: CAPMAS, 1978) - Table l. APPENDIX 167 TABLE (A.2) EXPENDITURE ELASTICITIES FOR FIVE REGIONS Urban Rural Groups . Cairo Lower Upper Lower Upper Egypt Egypt Egypt Egypt Grains .03 .14 .13 .28 .26 Beans and vegetables .66 .72 .74 .79 .81 Meat and ' fish .80 .87 .88 1.00 1.00 Oils and . fats .49 .54 .56 .59 .61 Milk and products .89 1.07 1.13 1.27 1.45 Fruit 1.01 1.17 1.22 1.49 1.65 Sugar and sweets .38 .42 .46 .43 .50 Teaoand coffee .42 .45 .48 .49 .54 Food .53 .63 .64 .69 .70 SOURCE: Based on Tables (3-6) and (A.1). 168 TABLE (A.3) UNCOMPENSATED OWN-PRICE ELASTICITIES FOR FIVE REGIONS Urban Rural Cairo Lower Upper Lower Upper Egypt Egypt Egypt Egypt Grains -.187 -.20 —.198 -.244 -.232 _Beans and vegetables -.669 -.69 -.750 -.700 -.760 Meat and .fish -.711 -.711 -.710 —.720 -.71 Oils and fats -.530 -.53 —.490 -.510 -.470 Milk and products -.521 -.61 -.640 -.680 -.830 Fruit -.762 -.87 -.900 -1.110 -1.290 Sugar and sweets -.751 -.74 -.650 -.830 -.650 Tea and coffee —.398 -.42 -.380 —.420 -.350 Food -.37 -.40 -.410 -.440 -.450 SOURCE: Based on Tables (3-6) and (A.1). 169 TABLE (A.4) 7': PARAMETER ESTIMATES OF WORKING'S MODEL FOR URBAN HOUSEHOLDS (ONE PERSON) Commodity A A 2 Group ai bi R wi Grains .718 - .121 .97 .162 (24.46) (-19.15) Beans and .294 - .036 .29 .129 vegetables ( 3.91) (- 2.22) Meats - .154 .106 .83 .333 (-2.42) ( 7.76) Oils and .112 - .006 .46 .084 fats ( 2.94) (- .76) Milk and - .011 .025 .41 .104 dairy (- .27) ( 2.91) products Fruit - .098 .038 .64 . .075 (-2.57) ( 4.59) Sugar and .107 - .009 .45 .067 sweets ( 8.36) (- 3.13) Tea and .032 .003 .19 .046 coffee ( .92) ( .48) Total Food l 080 - .123 .91 .396 (17:61) (-11.33> *t values in parentheses 170 TABLE (A.5) PARAMETER ESTIMATES OF WORKING'S MODEL FOR URBAN HOUSEHOLDS (2-3 PERSONS) Commodity Group E. B. 2 WJ.- Grains .778 - .112 .90 .198 ( 14.15) (-10.68) Beans and .265 - .026 .73 .131 vegetables ( 11.42) (- 5.86) Meats - .142 .090 .95 .322 (- 4.72) ( 15.61) Oils and .089 .0001 .0002 .089 fats ( 6.46) ( .05) Milk and - .045 .028 .83 .100 dairy (- 2.41) ( 7.93) products Fruit - .095 .030 .97 .062 (-12.29) ( 20.63) Sugar and .071 - .002 .093 .060 sweets ( 7.28) (- 1.15) Tea and .079 - .008 .73 .038 coffee ( 11.62) (- 5.99) Total Food 1.089 - .105 .99 .457 ( 61.53) (-36.28) *t values in parentheses 171 TABLE (A.6) PARAMETER ESTIMATESkOF WORKING'S MODEL FOR URBAN HOUSEHOLDS (4-6 PERSONS) Commodity A A 2 Group ai bi R wi Grains 1.022 - .146 .99 .244 ( 47.71) (-36.61) Beans and .276 - .027 .85 .132 vegetables ( 15.69) (- .26) Meats - .324 .115 .97 .288 (—10.59) ( 20.17) Oils and .056 .006 .48 .086 fats ( 6.02) ( 3.33) Milk and - .121 .040 .98 .090 dairy (-12.89) ( 22.69) products Fruit '- .111 .031 .96 .052 (-1l.79) ( 17.47) Sugar and .074 - .002 .30 .062 sweets ( 13.76) (- 2.29) Tea and .128 - .017 .93 .044 coffee ( 19.16) (- 12.67) Total Food 1.187 - .115 .98 .486 ( 39.63) (-23.68) *t values in parentheses 172 TABLE (A.7) PARAMETER ESTIMATEE‘OF WORKING'S MODEL FOR URBAN HOUSEHOLDS (7 AND MORE PERSONS) Commodity A A 2 Group ai bi R wi Grains 1.087 -.144 .99 .279 ( 61.24 (-45.79) Beans and .189 - .010 .35 ' .134 vegetables ( 72.78) (- 2.29) Meats - .336 .107 .99 .264 (-21.94) ( 39.42) Oils and .027 .010 .76 .085 fats ( 2.61) ( 15.66) Milk and - .091 .031 .96 .081 dairy (- 7.81) ( 14.87) products Fruit - .083 .023. .95 .047 (- 9.26) ( 14.54) Sugar and .086 - .004 .44 .062 sweets ( 9.97) (- 2.79) Tea and .121 - .013 .66 .047 coffee ( 7.23) (- 4.42) Total Food 1.204 - .112 .98 .497 ( 41.18) (-24.36) *t values in parentheses 173 TABLE (A.8) PARAMETER ESTIMATES OF WORKING'S MODEL FOR RURAL HOUSEHOLDS (ONE PERSON) Commodity A A 2 Group‘. ai bi . R wi Grains .600 - .075 .78 .263 ( 8.80) (- 4.99) Beans and .243 - .025 .47 .13 vegetables ( 5.32) (- 2.50) Meats .127 .035 .44 .283 ( 1.87) ( 2.32) Oils and .014 .021 .68 .11 fats ( .54) ( 3.85) Milk and - .002 .014 .36 .06 dairy (- .6) ( 2.00) products Fruit - .001 .009 .30 .038 (- .05) ( 1.73) Sugar and .071 - .002 .05 .063 sweets ( 5.26) (- .61) Tea and - .052 .023 .46 .053 coffee (- 1.20) ( 2.45) Total Food .823 - .045 .35 .600 ( 7.14) (- 1.95) *t values in parentheses 174 TABLE (A.9) PARAMETER ESTIMATES" OF WORKING'S MODEL FOR RURAL HOUSEHOLDS (2-3 PERSONS) Commodity A A 2 Group a. b. R w. 1 1 1 Grains .932 - .131 .96 .287 ( 25.13) (-17.60) Beans and .182 - .011 .36 .127 vegetables ( 8.52) (- 2.62) Meats - .113 .078 .93 .268 (- 3.75) ( 12.85) Oils and — .005 .022 .58 .105 fats (- .188 ( 4.04) Milk and - .005 .014 .63 .063 dairy (- .34) ( 4.48) products Fruit - .056 .020 .69 .041 (- 2.94) ( 5.16) Sugar and .046 .003 .162 .063 sweets ( 4.24) ( 1.52) Tea and .019 .005 .012 .046 coffee ( .96) ( 1.31) Total Food 1.141 - .107 .84 .550 ( 15.10) (- 7.94) *t values in parentheses 175 TABLE (A.10) PARAMETER ESTIMATES OF WORKING'S MODEL FOR RURAL HOUSEHOLDS (4-6 PERSONS) Commodity A A 2 Group ai bi R wi Grains .916 - .112 .97 .322 ( 32.71) (~21.45) Beans and .160 - .009 .41 .112 vegetables ( 9.80) (- 3.00) - Meats - .088 .065 .79 .256 (- .76) ( 6.94) Oils and .012 .017 .76 .100 fats ( .88) (- 6.45) Milk and - .043 .021 .65 .068 dairy (- 1.89) ( 4.95) products Fruit - .035 .014 .73 .039 (- 2.76) ( 5.90) Sugar and .025 .007 .40 .062 sweets ( 1.93) ( 2.95) Tea and .053 - .003 .024 .041 coffee ( 2.67) (- .56) Total Food 1.254 - .117 .85 .55 ( 14.99) (- 8.50) *t values in parentheses 176 TABLE (A.11) PARAMETER ESTIMATES€OF WORKING'S MODEL FOR RURAL HOUSEHOLDS (7 AND MORE PERSONS) Commodity A A 2 Group ai bi R wi Grains 1.167 - .143 .89 .387 ( 14.91) (-10.09) Beans and .087 .004 .09 .108 vegetables ( 4.44) ( 1.13) Meats - .225 .083 .91 .228 (- 5.53) ( 11.27) Oils and .018 .013 .46 .089 fats ( .82) ( 3.33) Milk and .002 .011 .50 .060 dairy ( .122) ( 3.64) products Fruit - .037 .013 .69 .033 (- 2.84) ( 5.38) Sugar and - .013 .013 .50 .055 sweets (- .69) ( 3.61) Tea and .001 .006 .24 .040 coffee ( .10) ( 2.03) Total Food 1.153 — .089 .97 .624 ( 44.64) (-20.78) *t values in parentheses 177 TABLE (A.12) COMPOSITE+ PRICES OF FOOD GROUPS IN URBAN AND RURAL AREAS (L.E/KG) Group 1959 1975 1980* Urban Rural Urban Rural Grains .061 .034 .046 .055- .128 Beans and vegetables .034 .036 .08 .086 .190 Fruit .037 .033 .062 .056 .10 Meats .197 .199 .525 .501 1.930 Dairy products .075 .041 .194 .125 .301 Fats .283 .276 .490 .439 .377 Sugar and sweets .089 .087 .166 .142 .396 Tea and coffee 1.036 1.089 2.05 2.261 4.93 +The prices are calculated as the geometric mean prices of the items within each food group. 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