QUADRATIC ALMOST IDEAL DEMAND SYSTEM ANALYSIS OF DEMAND FOR SELECTED VEGETABLES AND FRUITS IN NIGERIA

This study analyzed the demand for selected vegetables and fruits in Nigeria. It determined price effects on demand for fruits and vegetables, examined the demographic variables influencing demand and revealed the expenditure elasticity across income quartiles and sectors. Data from the three waves of Living Standard Measurement Survey - Integrated Survey on Agriculture namely 2010/11, 2012/13 and 2015/16, were employed in the analysis. The demand for bananas, citrus, pineapples, fresh okra, onions pepper and tomatoes was examined using the Quadratic Almost Ideal Demand System. Households in Nigeria consumed more vegetables than fruits. The results revealed that the staple vegetables in Nigerian diets are tomatoes, onions and pepper. It was observed that movement in relative prices elicited high quantity response. All the fruits and vegetables included in the model were normal goods. Vegetables and fruits responded similarly to expenditure increases in urban and rural Nigeria. The own - price elasticities, both uncompensated and compensated agree with the demand theory. More consideration should be given to the intensifying production of fruits and vegetables in technology development and investment to make them available and affordable.


INTRODUCTION
Malnutrition continues to be a major burden to the international community (World Health Organization [WHO] 2020). In emerging nations, roughly 13 percent of the populace is undernourished. In 2019, two billion individuals regularly lack access to sufficient, nutritious and safe food (Food and Agriculture Organization [FAO] 2020). According to Luchuo et al. (2013), malnutrition contributes significantly to high mortality rate of children worldwide.
Nutrition is getting worse in many African nations with 19.1% of the population being undernourished (FAO 2020). Over 23% of the population (210 million) in Sub-Saharan Africa (SSA) are undernourished and poor nutrition is the leading cause of death particularly in children under the age of five (FAO 2015). In SSA, over 50% lack the resources to eat healthy diets (World Food Programme (WFP), 2020).
Fruits and Vegetables (FV) are essential components of a healthy diet. They have healthenhancing properties. According to WHO, there is inverse relationship between increased consumption of FV and increased risks of Non-Communicable Diseases (NCDs) (WHO 2020). In 2017, 3.9 million deaths were linked to insufficient consumption of FV (WHO 2020). Hence, WHO recommends consumption of more than 400g of FV in a day to enhance good health and reduce risks of some NCDs. Findings have further shown that high consumption of FV ward off chronic illnesses such as heart diseases and specific cancers (Liu 2003). Intake of fruits and vegetables has been positively linked to increase in birth weight (Rao et al. 2001;Mikkelsen et al. 2006;Loy et al. 2011).
According to Hall et al. (2009), the daily recommended amount of vegetables and fruits is not met by Africans. In contrast to high-income nations, low-income countries (including Nigeria) rely more on basic foods and less on fruits and vegetables (FAO et. al. 2020). According to Global Food Policy Report (2015), the majority of African countries' children who are stunted live in Nigeria. Therefore, going by the growing thrust to improve nutrition by 2030, which is substantiated by the second sustainable development goal (SDG 2), it is of vital importance to examine households' consumption of vegetables and fruits on a disaggregated basis in order to ensure nutrition security and healthy diet in Nigeria. This will have implications on the national food policy interventions in the country.
Hence, this study explores households' demand of selected vegetables and fruits in Nigeria. There are previous studies on fruits and vegetables demand in developed and developing countries (Mutuc et al. 2007;Tey et al. 2009;Bundi et al. 2013) to name a few. Similarly, in Nigeria, Tsegai and Kormawa (2009), Akinleye (2009), Ogundari and Arifalo, (2013), Otunaiya and Shittu (2014) have explored food demand in Nigeria with the aid of double logarithms function, double hurdle, almost ideal demand system and its variants while Obayelu et al. (2009), Fashogbon andOni (2013), Khaliukova (2013) and Obisesan (2019) used quadratic almost ideal demand system. However, these studies with the exception of Khaliukova (2013), Ogundari & Arifalo (2013), and Obisesan (2019) took into account the entire food basket and viewed FV as a group of food item in the demand system. Therefore, this study distinguishes itself from previous studies on the demand for vegetables and fruits in Nigeria by using panel data, the three waves of the Living Standard Measurement Survey-Integrated Survey on Agriculture (LSMS-ISA) namely 2010/11, 2012/13 and 2015/16. It employs QUAIDS within a panel framework to estimate the price and income elasticities of different fruits and vegetables in Nigeria following (Banks et al. 1997). However, the research issue of estimating demand elasticity of vegetables and fruits on a disaggregated basis nationally and across sectors and income quartiles is crucial in order to have a more thorough understanding of how domestic food policy initiatives affect consumption (Mutuc et al. 2007). Therefore, this study achieved the following objectives:to determine the households' demand for vegetables and fruits response to changes in income and price; to estimate the expenditure elasticity across income quartiles and sectors and to isolate the household's demographic factors influencing fruits and vegetables demand in Nigeria.

MATERIALS AND METHODS Data
The study utilized secondary data of the three waves of the Living Standard Measurement Survey-Integrated Survey on Agriculture (LSMS-ISA) namely 2010/11, 2012/13 and 2015/16 (World Bank 2017. Based on the agricultural seasons, there were two visits per year namely post-planting, September-November, and post-harvest, February-April. Detailed information were collected in the survey on the quantities of household food consumption from gifts, own consumption and purchases. The amount spent each week on food purchases by the households was reported. Prices were derived from transaction data and then used to impute values to ownproduction and gifts. The data used in this study include prices, age, household size, sex, marital status, educational attainment, households' consumption of vegetables and fruits and households' food expenditure.

Quadratic Almost Ideal Demand System
In empirical analysis, QUAIDS approximates non-linear Engel curves more accurately than other demand system analyses. Furthermore, the study used a modified routine of Poi (2012) which allows the inclusion of demographic variables to the model, and compute expenditure and price elasticities. This helps in controlling for factors such as gender, age, education and rural or urban residence which may affect the quantity of fruits and vegetables demanded. The empirical demand system which have been developed to accommodate the expenditure nonlinearity include QUAIDS model developed by Banks et al. (1997), which features budget shares that are quadrat-ic in log total expenditure. The QUAIDS model is a generalization of Price Invariant Generalized Logarithmic (PIGLOG) preferences based on the following indirect utility (V) function: ………………………………...……...Eqn 05 Where: is a set of demographic variables and w i is the budget share of the i th item. By differentiating the budget share equations with respect to ln x and ln pj, respectively, we obtain the formulas for the QUAIDS expenditure and price elasticities.
A probit regression analysis is done in order to estimate the probability that a given household consumes the individual fruit and vegetable in question. In order to address any bias that may have been caused by the presence of zero consumption, this regression is then utilized to produce the Inverse Mills Ratio (IMR) for each household. (Heien and Wessels, 1990).

………………………………………..Eqn 01
Where: x is total expenditure, p is a vector of prices (in Naira), a(p) is a function that is homogenous of degree one in prices, and b (p) and ( Where, The QUAIDS budget share equations results from the application of Roy's identity to (equation 1). The linear demographic translating method will be used to incorporate demographic variables (z) into the QUAIDS model. This controls for varying preference structures and heterogeneity across households, resulting to the following empirical specification of the QUAIDS budget share equations:

RESULTS AND DISCUSSION Fruits and vegetables consumption in Nigeria
Over 90% of the households had at least one type of FV included in their weekly food consumption in the survey period.

Variables definition
The independent variables included in the model are Sex (male-1, female-0) and age of the household head (years), household size   (2.6kg) respectively from 2010-2015. Furthermore, Table 2 reveals that households consuming the fruits and vegetables considered in the study (except okra) were higher in the urban sector than rural irrespective of the fact that their production is more concentrated in the rural areas.

Estimated parameters of the QUAIDS model
Some households in the LSMS-ISA data used in the study recorded zero expenditure in the survey. Three major factors have been identified in the literature as potential causes of zero expenditures in data at household level: households may never consume the good of interest; some households may have zero consumption of the commodity during limited survey period; thirdly due to the fact that it is not the best course of action, given the current situation with respect to prices and income, some households may chose not to report consuming the commodity (Meyerhoefer et al. 2005;Tafere et al. 2011). A two stage estimation approach was used to address this problem. The first stage involved using probit regression to capture household (h) decision to demand the specific commodity (i) or not. The Inverse Mills Ratio (IMR) for each household was later derived using the estimate of the maximum likelihood. In the second stage, in order to include the censoring latent variable in the regression, the IMR was used as an independent variable (Heins and Wessels 1990; Bundi et al. 2013) see eq. 6. From the results, the coefficients of (λ) for the different fruits and vegetables considered are significant suggesting that the QUAIDS model fits the data more accurately than the AIDS. This shows that, there is non-linear relationship between the demand for all the fruits and vegetables and a rise in total expenditure, strongly supports the rejection of the zero quadratic expenditure term hypothesis. This demonstrates how the QUAIDS model is more appropriate than the conventional AIDS model.
In addition, Table 3 showed how demographic variables affect the household's demand for the various fruits and vegetables. Thirty of the demographic factors' effect estimates (out of forty-two) are statistically different from zero. The household head's age has positive and significant effect on the demand for citrus (p<0.1), onion (p<0.01), and pineapple (p<0.1) while it has negative effect on tomatoes (p<0.05) as well as banana and okra at 5% and 10% significant level respectively. Larger households consume more tomatoes and pepper while those with small sizes consume more fruits. This is because practically all other food categories are consumed with stew made of peppers and tomatoes in Nigeria. This, however, is not in tandem with Khaliukova (2013), who claimed that consumption of tomatoes and pepper in Nigeria, decreases with family size. The low consumption of fruits by households with large size could be regarded to as economic nonconsumption that is, due to economic recession/ high poverty rate in Nigeria. This authenticates the fact that economic downturns undermine nutrition security in Nigeria.
Nearly every item's demand is positively and significantly affected by educational status. Education improves the understanding of the health advantages of fruits and vegetables.

The expenditure elasticities of demand
The expenditure elasticity of demand reveals the relationship between percentage change in good's demand and the percentage change in income. Table 4 lists the expenditure elasticities for the various vegetables and fruits.
Since every FV has positive elasticity, they are all considered to be normal goods. This 116  For banana, okra, citrus, tomatoes and pineapples, the expenditure elasticities are greater than unity, but less than unity for onions and pepper. The results indicate that onions and pepper are expenditure inelastic while others are expenditure elastic. A 10% rise in income will increase demand for banana and citrus by 17.0% and 14.9% respectively. Pineapple's high expenditure elasticity (2.09) indicates that it is a more desired fruits variety.

Expenditure elasticity across income quartiles and sectors
Considering the expenditure elasticity across the income quartiles, Table 5 shows similar but reducing expenditure elasticity for the different fruits and vegetables. In contrast to pepper and onion, which are inelastic across all the income groups, okra, tomatoes, banana, citrus and pineapple are expenditure elastic. Furthermore, the table reports similar fruits and vegetables responsiveness to expenditure increases across sector (rural and urban) and zone (north and south). However, the demand for okra (1.0606) is expenditure elastic in the rural Nigeria while it is inelastic in urban (though close to unity). In the same vein, okra (1.0727) and pepper (1.0345) are expenditure elastic in the north while they are inelastic in the south.

Own-and cross-price elasticities of vegetables and fruits in Nigeria
The compensated (Hicksian) and uncompensated (Marshallian) expenditure elasticities estimates are presented in Tables 6 & 7 respectively. The estimations on the diagonal represent the various fruits and vegetables' individual price elasticity. Negative estimates are observed for both compensated and uncompensated own-price elasticities. This demonstrates that they adhere to the demand theory. All fruits and vegetables, with the exception of pineapple, have own-price elastic demand, according to estimations of uncompensated price elasticity. According to the findings, the quantity demanded for tomatoes, peppers, and onions will decrease by 1.20,1.05, and 1.04 accordingly for every 1% increase in price. Compared to the uncompensated own-price elasticities, the compensated ones have lower absolute values ( Table 6). The degree to which demand for all fruits and vegetables responds to changes in their prices is significantly influenced by income.
The Marshallian cross price elasticities of fruits and vegetables revealed a combination of complementary and substitution relationships. For instance, pepper and tomatoes have a complimentary connection (-0.74), meaning that for every 1 percent increase in tomato price, there will be a 0.74 percent fall in pepper demand.   There is high sensitivity to price changes especially among low-income groups. Expenditure elasticity for the different fruits and vegetables was similar though reducing across the income quartiles. Although pepper and onion are inelastic across all income groups, tomatoes, okra, banana, citrus, and pineapple are expenditure elastic. There is similar fruits and vegetables responsiveness to expenditure increases across sector (rural and urban) and zone (north and south). The demand theory is supported by the fact that all own-price elasticities, both compensated and uncompensated, are negative. Changes in the price of fruits and vegetables are met with a greaterthan-proportional response from Nigerian households. Fruits and vegetables have a mix of substitutive and complimentary relation-ships. The response of demand for all fruits and vegetables to changing prices is significantly influenced by income. The study suggests interventions that stabilize prices and boost income in Nigeria. Prompt attention should be given to enhancing households' income in Nigeria especially among the lowincome groups. Consumption of fruits should be included in the school feeding programme.
The study further suggests more attention on nutrition-sensitive food system that can promote and sustain healthy and diverse diets.

ACKNOWLEDGMENTS
The author appreciates Dr. Saweda Liverpool-Tasie who initiated the AAEA Africa Early Career Scholarship mentoring programme and her mentors, Prof. Derek Byelee and Dr. Tewoja Mogues for their immense contributions to the study.

AUTHOR CONTRIBUTION
OAA designed the study, collated the data, analyzed the data and discussed the results.