Projecting food demand in 2030: Can Uganda attain the zero hunger goal?

A precarious food security situation implies that many countries in the Global South may not achieve the United Nations Sustainable Development Goal 2 (SDG2) of zero hunger by 2030. We focus on the case of Uganda and explore food demand and food security implications for 2030, where 33% (15 million) of the population of 44 million are poor. Matooke (cooking bananas) , cassava, and (sweet) potatoes are traditional foods in Uganda; however, the consumption of maize, wheat, and rice has been rising with increases in income and urbanization. Using the Living Standards Measurement Study (LSMS) datasets of Uganda, this study estimated the demand for matooke, cassava and potatoes, maize/coarse grains, wheat and rice, vegetables, and meat and fish in 2030. Our findings confirm that with increases in income and demographic changes, the demand for these food items will increase drastically. To attain SDG2 of zero hunger, as well as food and nutrition security, this study calls for further investments in Uganda’s agricultural sector to enhance domestic production capacity to meet the growing demand for food. © 2021 The Author(s). Published by Elsevier B.V. on behalf of Institution of Chemical Engineers. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )


Introduction
To achieve the United Nations Sustainable Development Goal 2 (SDG2) of zero hunger by 2030, it is imperative to ensure basic food security for millions of people in the Global South. Globally, nearly 2 billion people are moderate to severely food insecure ( FAO et al., 2019 ), of which 135 million people are severely food insecure ( FSIN, 2020 ). Those who are food insecure are mostly concentrated in Africa, Asia, and Latin America ( FAO et al., 2019 ). Since 2015, the absolute number of hungry people has increased, particularly in sub-Saharan Africa and South Asia ( FAO et al., 2017 ;WHO, 2018 ). It is thus becoming increasingly challenging for many of the countries in the Global South to eliminate hunger by 2030. Moreover, the World Food Program (WFP) has cautioned that in the absence of swift and effective action, an additional 265 million people may become severely food insecure due to COVID-19induced economic turmoil ( WFP, 2020 ). How then to ensure basic food security for people in the Global South by 2030?
For a start, we need to understand the food choices of foodinsecure populations. Food consumption patterns are contextspecific, calling for grounded, country-level case studies to examine food choices. In this study, we focus on Uganda -a rapidly developing, landlocked country in sub-Saharan Africa, where one-third of the total population is classified as poor ( World Bank, 2016a ).
Uganda is one of the fastest economically growing nations in sub-Saharan Africa and is in the midst of socio-economic transition. From 20 0 0-2019, the gross domestic product (GDP) of the country expanded on average by more than 6% per annum ( World Bank, 2020a ). Consequently, the per capita GDP reached US$ 710 in 2019, up from US$ 632 in 2011 (at 2010 prices) ( USDA, 2021 ). It is projected that from 2020 to 2031, the real GDP (at 2010 prices) of Uganda will further grow by an average of 5.6% per annum ( USDA, 2020 ), and thereby the real per capita GDP of the country will reach US$ 984 by 2031 ( USDA, 2021 ). Population growth and urbanization are also rapid in Uganda. In 2019, out of a total population of 44.3 million, 24.4% were residing in urban areas ( World Bank, 2020a ). By 2030, Uganda's population is projected to be 58-61 million 1 depending on the fertility rate assumptions ( United Nations, 2019 ), of which more than 31% will reside in urban areas ( World Bank, 2021 ). These economic and demographic changes will have significant impacts on the agricultural sector ( Alexandratos, 2005 ), generating the challenge of producing and supplying more and better food at affordable prices ( FAO, 2018 ).
The objective of this study is to assess the future demand for major food items in Uganda by 2030. The study relies on information from 8,424 households, collected through three rounds (2010-11, 2013-14, 2015-16) of Uganda's Living Standards Measurement Study-Integrated Surveys on Agriculture (LSMS-ISA). The major food items of Uganda are matooke (cooking bananas), cassava and (sweet) potatoes, and cereals such as maize, wheat, and rice. This study assessed the nation-wide demand in Uganda for matooke, cassava, and (sweet) potatoes, maize/coarse grains (including sorghum and millet), wheat and rice, vegetables, and fish and meat in 2030. To achieve this, the study applied the endogeneitycorrected Quadratic Almost Ideal Demand System (QUAIDS) estimation approach separately for rural and urban households. From the QUAIDS model, we estimated the price and expenditure elasticities for the sampled foods. We then estimated the aggregate demand in Uganda for the sampled food items considering population projections and GDP growth rates up to 2030.
The study is important for two crucial reasons: Firstly, Uganda's rapid economic growth has resulted in a marked decline in poverty -in 1993 68% of the population were living on less than US$ 1.90/day ( World Bank, 2016a ), down to 33% in 2020 (14.7 out of 44.3 million, ( World Bank, 2020b ). Nonetheless, FAO et al. (2018) found that in Uganda in the period from 2015 to 2017, 17.2 million (41.4%) people were undernourished, 0.3 million (3.6%) children under five years of age were wasted, and 2.2 million (28.9%) children under five were stunted; and in 2016, 2.6 million (37.2%) women of reproductive age (15-49 years) were anemic. In the 2020 Global Hunger Index, Uganda is classified as a country under a serious threat of hunger ( Grebmer et al., 2020 ). Understanding the future demand for major food items and investing accordingly from now on can be instrumental in ensuring the food and nutrition security of Uganda.
Secondly, Uganda aims to become a middle-income country by 2040, with zero hunger, a major share of earnings coming from the non-farm sector, and the majority of citizens residing in urban areas ( Government of Uganda, 2015World Bank, 2016a ). To achieve the status, Uganda has to secure more food with the increase in population and economic progress ( Fukase and Martin, 2017 ). As a developing nation, it is not desirable for Uganda to rely primarily on substantive imports to meet growing food demands. Supply failures can generate food price hikes and the "Ricardo-Schultz" trap, in which increased food prices can generate unrest and reduce incentives to invest in industrial development, hampering economic progress. A number of African countries, including Uganda, witnessed riots linked to food and fuel price hikes during 2007-2011 ( Kron, 2011 ;Sneyd et al., 2013 ). To avoid future food riots, ensuring food security for the urban poor is par-1 FAOSTAT, 2021c . ticularly crucial for Uganda ( Kamara and Renzaho, 2014 ), yet the COVID-19 pandemic is aggravating food insecurity in urban areas ( FEWSN, 2021 ). It is thus imperative to produce more food to avoid future food-related riots and to achieve Uganda's desire of becoming a middle-income country.
This study is organized as follows: the next section explains the conceptual framework, including a brief literature review. Section 3 presents the data and methods used for estimating the expenditure and price elasticities of the food groups and projects the aggregate demand for them by 2030. Section 4 presents the results, including general findings, estimated elasticities, and projected aggregate consumption of the sampled food items, considering the projected GDP and population rates. Section 5 presents the conclusion and policy implications.
As development progresses, with increases in income and urbanization, the lifestyle and dietary intake of households change. For example, with an increase in income and urbanization, households tend to increase their consumption of diverse and expensive foodstuffs, such as more plant-and animal-based food items ( Mottaleb et al., 2018b ;Pingali, 2006 ;Reardon et al., 2019Reardon et al., , 2012. This dietary transition is popularly known as the "nutrition transition" ( Drewnowski and Popkin, 2009 ;Jakicic and Davis, 2011 ;Pingali, 2006 ;Pingali et al., 2019 ;Popkin, 2003Popkin, , 1999Reardon et al., 2014 ;Semba et al., 2008 ). Population growth provides a further driver, by affecting the aggregate food demand both directly and indirectly through its interlinkages with urbanization and income growth. We use these stylized changes affecting food demand as our overarching conceptual framework ( Fig. 1 ), with these processes playing out differently in rural and urban settings and affecting both the aggregate food demand and the composition of food demand in the Global South.
The nutrition transition has led to calls for more diverse agrifood systems but also concerns about the environmental footprint and affordability ( Hirvonen et al., 2020 ;Willett et al., 2019 ). There are also concerns about the triple burden of undernutrition, micronutrient malnutrition, and overnutrition (overweight/obesity and non-communicable diseases ( Poole et al., 2021 ).
For most developing nations, continued population growth and the nutrition transition call for increased investment in domestic agri-food systems to enhance food security in all its dimensions: (food availability; food accessibility; utilization; stability; FAO, 2006 ). This typically requires additional investments in both energy-dense staple foods and nutrient-rich foods as complements, and increased attention for the one should not thereby replace attention for the other ( Poole et al., 2021 ). Ignoring the role of energy-dense staple foods can have devastating impacts, particularly on the food security of economically emerging and developing countries, where such staples are and remain the major sources of dietary energy.
Currently, out of the 7.7 billion global population, 821 million people (10.9%) go to bed hungry ( FAO et al., 2019 ). By 2050 the global population is expected to increase to 8.9-10.6 billion, de-  pending on the fertility rate assumptions ( United Nations, 2019 ). The concern is that under the business-as-usual scenario, the number of hungry people may increase to 2 billion by 2050. Thus, to ensure basic food security and to advance on eliminating hunger by 2030 as per SDG2, and to ensure basic food security of the burgeoning population of the world by 2050, it is imperative to supply more basic food items such as energy-dense staple foods at an affordable price. For Uganda, investing in cereals is particularly important. This is because, even though Uganda has been highly successful in fighting abject poverty by achieving rapid economic growth in recent years, 41.4% of its population is still undernourished . Also, it is projected that by 2030 the population of the country will be 58-61 million depending on the fertility rate assumptions ( United Nations, 2019 ), from 43 million in 2018 ( World Bank, 2020a ), of which more than 44% will reside in urban areas ( World Bank, 2021 ).
In Uganda, matooke (cooking bananas), cassava and (sweet) potatoes, cereals such as maize, wheat, and rice, vegetables, and fish and meat are the major food items ( FAOSTAT, 2021a ). For the triennium ending in 2018 (TE2018), the daily per capita calorie intake in Uganda was 2,012 kcal, of which 1,057 kcal (53%) came solely from matooke, cassava and (sweet) potatoes, maize, wheat, and rice ( FAOSTAT, 2021c ). In TE2018, the yearly matooke consumption was 80 kg per capita (pc), and the corresponding aggregate national consumption 3.3 million metric tons (MMT) ( FAOSTAT, 2021a ). Consumption of cassava and potatoes was 114 kg pc and the corresponding national consumption 4.7 MMT. Maize, millet, and sorghum consumption was nearly 48 kg/year/capita, and the corresponding national consumption 1.97 MMT. Wheat and rice consumption was 23 kg/year/capita and the corresponding national consumption 939 thousand metric tons. Vegetable consumption was 31.2 kg pc, and the corresponding national consumption 1.3 MMT. Finally, fish and meat consumption was nearly 23 kg pc and the national consumption 947.2 thousand metric tons ( FAOSTAT, 2021a ). As Uganda is rapidly developing economically and demographically, it is important to examine the future of the food demand in Uganda considering the economic and demographic changes.
Several studies have estimated the future demand for major staples at the global level in the context of demographic changes ( Godfray et al., 2010 ;Ray et al., 2013 ;Tilman et al., 2011 ). Projections for global food demand show increases from 70% ( FAO, 2009 ) to 110% ( Tilman et al., 2011) by 2050. Ray et al. ( Ray et al., 2013 suggested that to meet the surge in demand, average yield growth rates for any agricultural commodity should be at least 2.4% per year compared with rates in 2005. While existing studies provide broad, important insights into the future demand for agricultural commodities, conducting commodity-specific studies at the country level is imperative given the heterogeneity of dietary intake, cropping patterns, urbanization, population, and economic dynamics across countries. This study assessed Uganda's demand for major food groups: matooke; cassava and (sweet) potatoes; maize and other coarse grains; wheat and rice; vegetables; and fish and meat in 2030.
There are only a few studies that assess Uganda's demand for major food items. Boysen (2016) examined the price and income elasticities of 14 food items in Uganda using data from the 2012-13 Ugandan National Household Survey comprised of 6,887 households. The study found that for rural households in Table 2 Background information of the sampled households by their rural-urban location and by the LSMS rounds.

Household affiliation All
Rural Urban Uganda, income-elastic food items included maize, potatoes, matooke , fruit, meat, fish, milk, and sugar, whereas other cereals, cassava, legumes, and fats were income-inelastic. In contrast, for urban households in Uganda, Boysen (2016) showed that only meat, fish, and milk were income-elastic food items, whereas all other sampled food items were income-inelastic. However, Boysen's study did not assess Uganda's future food demand. The novelty of our study is that, in addition to updating estimates of price and expenditure elasticities, we examine Uganda's future demand for the major food items by 2030, using the estimated expenditure elasticities and projected population and GDP growth rates. Also, unlike that of Mottaleb et al. (2018a) , the present study follows the approach of Deaton (1990) , McKelvey (2011) , and Gibson and Kim (2013) in dealing with issues related to zero consumption and prices of the sampled food items. The world's GDP increased on average by 3.5% per annum during the period from 1961 to 2019, and consequently, the per capita nominal GDP increased from less than US$ 452 in 1961 to US$ 11,428 in 2016( World Bank, 2020a. Like Uganda, several countries in South Asia and sub-Saharan Africa have been rapidly developing economically due to high GDP growth rates and rapid urbanization ( USDA, 2021 ;World Bank, 2020a ). Nevertheless, out of the world's total population of 7.7 billion people, 821 million are extremely poor ( WHO, 2018 ) and live on less than US$ 1.90/day -86% of these reside in sub-Saharan Africa and South Asia ( World Bank, 2019a ). Alarmingly, an additional 420-580 million people may fall into poverty due to the recent COVID-19 pandemic and associated economic fallout ( Sumner et al., 2020 ). How to ensure the basic food security of the extremely poor people in economically emerging nations is a major policy issue. As in Uganda, the majority of the extremely poor in developing countries rely mainly on staples for their daily dietary energy. Thus, although this study is Ugandaspecific, the policy implications are broader and wide-ranging.

Data
The study is based on information collected from 8,424 households from Uganda. In collaboration with the Uganda Bureau of Statistics (UBOS), the World Bank collected data for the Liv-ing Standard Measurement Study-Integrated Survey on Agriculture (LSMS-ISA). This study is based on LSMS-ISA datasets 2010-11, 2013-14, and 2015-16. The LSMS-ISA survey sampled data and the sampling process can be seen in ( World Bank, 2019b, 2016b, 2014). In the case of Uganda, a questionnaire with 19 sections was used to collect household-level data on the demographic composition, labor allocation, education, and food consumption. Excluding cigarettes and alcoholic drinks, the datasets include information on weekly household-level consumption and expenditure for 66 food items. In this study, we examined the consumption of six major food items: matooke ; cassava and potatoes; maize/coarse grains; wheat and rice; vegetables; and fish and meat ( Table 1 ).
The original LSMS sample size of 2010-11 was 2,716 households, 2013-14's was 3,119 and 2015-16's was 3,305. Because of incomplete information on consumption and expenditure, this study retained 8,424 households. For sample details see Table 1 A, Annexure A. Of the total samples, 6,358 (75.5%) were from rural areas and 2,0 6 6 (24.5%) from urban areas ( Table 1 A, Annexure A). Among the households in this study, 5,726 (68%) were headed by males, and the remaining 2,698 by females (32%).
The background information of the sampled households is presented in Table 2 . In this study, all monetary values are converted from nominal to real terms using the Consumer Price Index (CPI) reported by the World Bank (2020a), setting CPI 2010 as the base ( = 100). The weekly average household-level total expenditure on food in real terms was UGX 41.3 thousand; however, there is a large gap in food expenditure between rural and urban households 2 . The weekly household expenditure on the sampled food items considered in this study was UGX 34.1 thousand, which was nearly 83% of the weekly household total food expenditure ( Table 2 ). Both rural and urban households spent at least 73% of their weekly total food budget on the sampled food items, which shows some similarity in the eating behavior of rural and urban households in Uganda. Households consisted on average of nearly six family members, household heads were older than 45 years, and spouses were older than 24 years ( Table 2 ). Nearly 80% of the sampled household heads were formally educated, and of these, nearly 55% had completed at least a primary level of education (7 years of schooling), nearly 22% had completed secondary-level schooling, and 3% had completed higher than secondary-level education ( Table 2 ). More than 50% of spouses were formally educated, of which nearly 38% had completed at least primary-level education, more than 11% had completed secondary-level education, and a little over 1% had completed higher than a secondary level of education ( Table 2 ). The percentage share of household heads and spouses who were educated up to secondary level and above was higher in urban areas than in rural areas. The share of household heads and spouses who were engaged in agriculture was also higher in rural areas ( Table 2 ). Furthermore, in general, the weekly household-level total food expenditure was higher in any given LSMS round for an urban household than for a rural one ( Table 2 ). These indicators indicate that poor and food-vulnerable people in Uganda are mostly concentrated in rural areas and are mostly engaged in agriculture. Considering these inequalities between rural and urban households in Uganda, we estimated expenditure and price elasticities of the sampled food items separately by rural and urban affiliation of the households.

Modeling of food demand
In modeling demand for the sampled food items, we followed several steps. We assumed a rational household head who allocated the daily per capita total food budget X UGX to different food items in a way that maximized utility. The allocation of the daily food budget (for the household as well as per capita) can be endogenously determined by several factors. Thus, X UGX can be a function of a number of exogenous variables. This study, therefore, considers a two-stage budgeting procedure, in which it is assumed that a household first decides on the per capita daily total food budget. In the next stage, a household decides how much of the daily per capita total food budget will be allocated to each of the six food items. We assume that prices of the food items, household demographic structure, and the major source of livelihood can affect the daily per capita budget allocation to the sampled food items. The specific functional form of the expenditure function used in the two-stage budgeting process is given below: UGXic is the daily per capita expenditure on the six sampled food items (c = 1-6), by household i, who resides in a rural (s = 1) or urban area (s = 0); ζ i is the error term; and δ 0 , δ i , σ i and θ t , are the parameters to be estimated.
Among the independent variables in equation (1) , P I is Stone's Price Index 3 calculated using six prices for six food items and the share of expenditure on each food item. H H demographics is a vector of independent variables that include: -age of the household head and spouse; -a female household head dummy that assumes a value of 1 if the head is a female, and 0 otherwise; -two primary level education dummies that assume values of 1 if the household head and, separately, spouse are educated up to primary level, or 0 otherwise; -two secondary-level education dummies that assume values of 1 if the household head and, separately, spouse are educated up to secondary level, or 0 otherwise; -two higher than secondary-level education dummies that assume values of 1 if the household head and, separately, spouse are educated above the secondary level; -two higher than secondary level education dummies that assume values of 1 if the household head and, separately, spouse are educated above secondary level, or 0 otherwise; -two livelihood dummies that assume values of 1, if the household head and, separately, spouse are engaged in agriculture, or 0 otherwise; -two year dummies for the year 2013-14 and 2015-16, setting the year 2010-11 as the base ( = 0).
It is important to mention here that the imputed sampled food prices are calculated as expenditures on a specific food divided by the quantity consumed, typically reported in kilograms. The problem is that the use of imputed prices in estimating income and price elasticities can lead to bias estimates due to the presence of selection bias and measurement errors and the problem of missing values ( Deaton, 1990 ;Gibson and Kim, 2013 ;McKelvey, 2011 ). In the sample data, consumption of vegetables was nearly universal in Uganda, but a significant share of the sampled households reported zero expenditure on five of the sampled food items (from { ln ( Price of commodity c ) × Expenditure share on commodity c } nearly a third not consuming maize/coarse grains or meat and fish to 62% not consuming wheat and rice). We elaborate on the procedure of how we dealt with the issues of imputed price and zero consumption in Annexure B. In brief, firstly we estimated a multivariate probit model, explaining the consumption choices of the sampled food items (did not consume = 1, consumed = 0) by the households ( Eq. 2B , Table 2 B, Annexure B). Secondly, after estimating a multivariate probit model (did not consume = 1, consumed = 0), we calculated five generalized inverse Mill's ratios for the five sampled food items based on whether or not that food item was consumed, following Vella's (1998) procedure (Annexure B). To deal with the imputed price issue, following Deaton (1990) , McKelvey (2011) , and Gibson and Kim (2013) , we estimated the prices of the six sampled commodities ( Table 3 B, Annexure B). In the estimation process, we plugged in six inverse Mill's ratios for six sampled food items calculated after estimating the multivariate probit model (Annexure B). After estimating price functions ( Table 3 B, Annexure B), we calculated residuals for each commodity price and added them to the reported prices of each sampled food item. Finally, we took into account the sample years for each commodity price and the rural or urban status of the sampled households in averaging the commodity prices. The Stone's Price Index used in Eq. (1) was therefore estimated using the estimated prices following the procedure elaborated in Annexure B.
In estimating Eq.
(1) , we applied the ordinary least square (OLS) estimation procedure, replicating the estimation process 100 times using the bootstrap method to correct the issues related to distorted standard errors. The estimated daily per capita expenditure on the sampled foods for rural and urban households was used to formulate the demand system separately. This process allowed us to avoid the endogeneity problem (if any) in daily per capita food budget allocation to the six foods. Finally, In modeling demand for the food items, we followed Banks et al., (1997) and Deaton and Muellbauer (1980) . Using the formula and methods in Stata software developed by Poi (2021), we calculated the expenditure, price, and cross-price elasticities.
Considering that poverty is more widespread in rural areas and that urban consumers may have more options and different preferences, we estimated the demand model separately for rural and urban households. After estimating the expenditure elasticities following Poi's (2021) specification, and using the GDP growth rate projected by USDA (2020) and the population projection by the United Nations (2019), we estimated the demand for the six foods in 2030. In projecting food demand in 2030, following Khanal et al., (2016) we applied the following formula: where C yc is the total consumption of commodity c in year y; C T E2017 is the daily per capita consumption of commodity c in TE2017 in grams; P y is the projected population in year y; r y is the annual net GDP growth rate after deducting the national savings rate; and η c is the income (expenditure) elasticity for commodity c .
In projecting the consumption of the sampled food items using Eq.
(2) , we used the population projected by the United Nations under high, medium, and low fertility rates ( United Nations, 2019 ). For the GDP growth rate ( r y ), we used USDA's ( USDA, 2015 ) projection. Fig. 2 presents the projected population and GDP growth rate (%) of Nepal until 2030. Further, we deducted the GDP growth rate from the national savings rate. The national savings rate was calculated at 18.2%, which is the average national savings rate during 2010-2019 reported by the World Bank (2020a).
It is assumed that the national savings rate will be constant at 18.2% of the GPD until 2030. We did not have disaggregated data on GDP and population growth separated by rural and ur-ban areas in Uganda. Therefore, in estimating demand for the sampled foods, we projected the demand at the national level, taking the weighted averages of the estimated expenditure elasticities for each commodity by the proportion of rural-urban samples in the LSMS datasets.

General findings
The average diet of a Ugandan household is predominantly based on matooke, cassava and (sweet) potatoes, maize/coarse grains, and vegetables ( Table 3 ). Matooke and cassava consumption have been declining in recent years ( Fig. 3 ), but they remain the major sources of daily dietary energy. On average, a household consumes nearly 51 kg of the six sampled food groups in a week (fresh weight, i.e., the marketed form, not dried to a common standard or dry matter, so including varying amounts of water), including 20 kg of matooke, an equal amount of cassava and potatoes, nearly 4 kg of maize/coarse grains, less than 1 kg of rice and wheat, nearly 5 kg of vegetables, and 1.3 kg of fish and meat ( Table 3 ). The daily per capita expenditure on the six food groups was more than UGX 1,245 of which the highest expenditure was on vegetables (UGX 309 or 25% of the total) followed by meat and fish (UGX 264 or 21% of the total, Table 3 ). This shows that rural households consumed lower quantities of food and spent less daily per capita on the sampled food items ( Table 3 ). Rural households also spent less on fish and meat ( Table 3 ). However, rural households consumed more cassava and potatoes than urban households. This indicates the importance of roots and tubers in the food security of rural households in Uganda.
The sampled households, on average, spent 17% of their daily per capita food budget on matooke, nearly 19% on cassava and potatoes, 25% on vegetables, and 21% on fish and meat ( Table 3 ). Interestingly, an average of 4% of the daily per capita food budget of a rural household was spent on wheat and rice, whereas the share was 7.5% for an urban household ( Table 3 ). This indicates a positive correlation between urbanization and the consumption of wheat and rice in Uganda. The average price of matooke in the sampled period was UGX 290/kg, UGX 367/kg for cassava and potatoes, UGX 1,530/kg for maize wheat and rice, UGX 2,114/kg for vegetables, UGX 4,850/kg for fish and meat ( Table 4 ).

Econometric findings
In projecting the 2030 demand for the sampled food items, we first estimated the daily budget ( X s UGXic ) function specified in Eq. (1) allocated to the six sampled food groups at the per capita level separately for rural and urban households. The estimated functions explaining the daily per capita expenditure on the sampled foods are presented in Table 5 .
The estimated results show that the coefficient of Stone's Price Index is positive and significant in explaining the daily per capita expenditure on the sampled foods ( Table 5 ). This indicates that the sampled commodity prices, as well as the expenditure share for the sampled food items, positively affect the daily per capita budget allocation to the foods. Interestingly, only the age of the household head affects positively the daily budget allocation to the sampled food items of rural households ( Table 5 ). Estimated functions demonstrate that the age of the spouse negatively affects the daily budget allocation for both rural and urban households ( Table 5 ). The primary level education dummy of the spouse negatively affects the daily budget allocation to the sampled foods ( Table 5 ). Household heads engaged in agriculture negatively affect the daily per capita expenditure on the six food items for both rural and urban households. This indicates that poverty in rural areas, and par-   1961 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999  ticularly among agricultural households, is widespread in Uganda.
Our estimation shows that a household in rural and urban areas spends on average UGX 1,140 and UGX 1,593 respectively on the sampled foods on a daily per capita basis ( Table 5 ).

Expenditure and price elasticities
Following Poi (2021), the calculated compensated (Hicksian) and uncompensated (Marshallian) price and cross-price elasticities for all six food items are presented separately for rural and urban households in Table 6 . The original parameters from the QUAIDS estimation procedure can be seen for rural households in Table 4 C and urban households in Table 5 C in Annexure C.
Consistent with the demand theory, the own-price elasticities of all the food items are negative ( Table 6 ), which confirms that an increase in the price of the sampled food items will lead to a reduction in the demand and vice versa ( Deaton, 2018 ). The size Table 4 Sampled commodity prices and the expenditure share (%) on the sampled food items by the sampled households by rural-urban location of the sampled households.
Reported prices (all rounds, UGX/kg) All     Estimated income (expenditure) elasticities ( η j ) for rural and urban households (expenditure endogeneity corrected QUAIDS model). of uncompensated own-price elasticities indicates the percentage change demand due to a one percent change in price. For example, for rural households, a 1% increase in the price of matooke will reduce the demand by 0.97%, and similarly by 0.80% for cassava and potatoes, and 0.61% for maize/coarse grains ( Table 6 ). Similarly, for urban households, a 1% price increase reduces demand for matooke by 1.15%, for cassava and potatoes by 0.90%, and for maize/coarse grains by 0.54% ( Table 6 ). An analysis of cross-price elasticities demonstrates that there is a substitutability relationship among matooke and all the other sampled commodities, whereas wheat and rice have a complementarity relationship with maize/coarse grains. It suggests that under certain circumstances, a price-related shock on matooke can be mitigated by substituting other food items such as cassava and sweet potatoes. We also calculated the uncompensated (Marshallian) price and cross-price elasticities for the poorest and richest households by their rural-urban status, reported in Table 6 C in Annexure C.
The estimated expenditure elasticities ( η j ) are presented in Table 7 . In addition to the overall average expenditure elasticities, we also reported expenditure elasticities by rural-urban areas and years sampled. The overall expenditure elasticities reveal that matooke , cassava, and potatoes are normal and necessary food items in rural Uganda ( Ƞ c < 1), meaning that consumption is sticky and less affected by price, albeit, for urban households, matooke is a less necessary food item ( Ƞ matooke > 1). Maize/coarse grains, wheat and rice, vegetables, and meat and fish are less necessary food items in Uganda with expenditure elasticities greater than one ( η c > 1 ) . Similar to our findings, Boysen (2016) reported that maize is a less necessary food item for rural households, and that meat and fish are luxury food items for all households in Uganda. Interestingly, in rural areas, maize/coarse grains had the highest expenditure elasticities of all the food groups. In general, these are hardly considered luxury goods but seem to be a preferred and affordable way of diversifying Ugandan rural diets from their matooke and roots and tubers base.

Food demand projections
Using the estimated expenditure elasticities and combining the projected GDP and population growth rates (see Table 8 for high, medium, and low fertility rates), this study projected the demand in Uganda for the six food groups by 2030. The daily per capita baseline consumption of the food groups (TE2018; FAOSTAT, (2021a); Table 8 ) was 221 grams of matooke, 312 grams of cassava and (sweet) potatoes, 131 grams of maize/coarse grains, 63 grams of wheat and rice, 85 grams of vegetables, and 63 grams of meat and fish ( Table 8 ).
In projecting the demand for the sampled food items in 2030, we used the weighted average expenditure elasticities in which the rural and urban sample sizes were used as weights ( Table 8 ). For example, the expenditure elasticity for matooke was 0.36 for rural households and 1.01 for urban households ( Table 7 ). Considering that 75.5% of the sampled households were from rural areas and the remaining 24.5% were from urban areas, we calculated the weighted average expenditure elasticity for matooke at 0.52 ( Table 8 ). The weighted average expenditure elasticities of all the other sampled foods are reported in Table 8 .
In TE2018 the per capita matooke consumption was around 81 kg/yearly, cassava and (sweet) potatoes consumption was 114 kg/ yearly, consumption of maize and other grains was less than 48 kg /yearly, wheat and rice consumption was less than 23 kg/ yearly, consumption of vegetables was 31.2 kg /yearly and of fish and meat 23 kg/yearly ( FAOSTAT, 2021a ). Our projection shows that in 2030, the yearly per capita matooke consumption will be 134 kg; cassava and (sweet) potato consumption will be 173 kg; maize/coarse grains consumption will be 156 kg; wheat and rice consumption will be 66 kg; vegetable consumption will be 100 kg, and fish and meat consumption will be 71 kg.
In TE2019 Uganda produced 3.5 MMT matooke from 811 thousand ha with a yield of 4.3 Mt/ha ( FAOSTAT, 2021b ). Our projections indicate that to meet matooke demand by 2030, Uganda must either increase matooke yields to 9.6-10 Mt/ha (assuming no increase in land for matooke) or expand land for matooke to 1.8-1.9 million ha (assuming no change in matooke yield). Along the same lines: -In TE2019 production of cassava, sweet potatoes, and potatoes was 4.92 MMT from 1.71 million ha of land with a yield of 3.6 Mt/ha. To meet the growing demand for cassava and sweet potatoes by 2030, either yield must be increased to 5.9-6.1 Mt/ha assuming no increase in land for the crops, or land must be expanded to 2.8-2.91 million ha assuming no change in yield. -In TE2019 production of maize/coarse grains was 3.3 MMT (1.61 million ha, 1.65 Mt/ha). Uganda is currently a net maize exporting country, exporting 0.37 MMT (TE2019). To meet the domestic demand in 2030 domestically, yields must be enhanced to 5.6-5.9 Mt/ha assuming no land expansion, or maize land must be expanded to 5.5-5.8 million ha assuming a constant yield. -The current production of rice and wheat is 258.1 thousand tons (100 thousand ha, 2.15 Mt/ha). Uganda is currently net  wheat-and rice-importing country, importing 576.5 thousand tons (TE2019). If the country continues to rely on imports to meet demand, an additional 3-3.4 million tons will have to be imported in 2030. Furthermore, our projections indicate that the demand for vegetables and fish, and meat will also increase severalfold by 2030 above the current level of consumption ( Table 9 ). The demand for fish and meat will increase by 4.3-4.5 times by 2030. Our findings on fish and meat demand are similar to those of FAO (2018), which projected that the consumption of beef will increase by 403%, mutton and goat by 347%, poultry by 419%, and pork by 412% by 2050 in Uganda compared to the 2012 consumption level.
With the nutrition transition, one would expect the consumption of luxury goods such as vegetables, meat, and fish to increase. More surprising perhaps is that the consumption of maize/coarse grains, and wheat and rice showed similar increases. These substantive increases reflect the affordability and versatility of these flexi foods. In contrast, basic foods such as cassava and sweet potatoes had relatively the lowest projected demand increases, although achieving these increases for all food crops to ensure food security remains daunting.

Table 10
Baseline and projected consumption of the sampled food items estimated only as a function of projected projections in 2030 in Uganda (million tons, assuming constant per capita consumption). As an alternative scenario, we also project future demand for the sampled food items assuming constant levels of per capita consumption and only considering population projections ( Table 10 ). This scenario shows that even if we ignore the influence of the GDP growth rate and urbanization on food consumption and only consider the projected population, it will be imperative for Uganda to supply 42-48% more matooke, 40-47% more cassava and sweet potatoes, 42-51% more maize/coarse grains, 38-48% more wheat and rice, 38-46% more vegetables, and 37-46% more meat and fish by 2030 ( Table 10 ).
To compare our elasticity estimation, we calculated the expenditure elasticities of the sampled foods applying the left-censored Tobit estimation procedure separately for rural and urban households ( Tables 7 D and 8 D, Annexure D). Similar to the expenditure elasticities reported in Table 7 after the QUAIDS model estimation, the expenditure elasticities calculated from the alternative specification of the demand model also show that the sampled foods are normal food items with positive income elasticities ( Tables 7 D and 8 D, Annexure D). The expenditure elasticities reported in Tables 7 D and 8 D are larger in absolute size than the expenditure elasticities reported in Table 7 . This is probably because the two-limit Tobit model is a single-equation model, which cannot capture the complementarity and substitutability effects among different items. Furthermore, we checked our projected per capita consumption, comparing it with the actual yearly per capita consumption (in kg) of the six food items.
The model validation graphs ( Figs. 1 E to 6E) are presented in Annexure F. Similar consumption trends during the period from 2010 to 2018 between projected and actual consumption of matooke and cassava validate our demand projection. However, the demand projections for wheat and rice, vegetables, and fish and meat seem over-projected in the long term. The seemingly overprojection of demand is a major limitation of demand forecasting using elasticities calculated applying the QUAIDS model estimation procedure. In addition, we have assumed that the estimated expenditure elasticities will be constant until 2030, which provides a linear projection of the sampled food times. In reality, expenditure elasticities can change due to different exogenous factors. Therefore, it is suggested that the future demand for major commodities at the country level should be examined regularly.

Conclusion and policy implications
This study examined projected food demand and consumption patterns in Uganda in 2030. The consumption of the six main food groups in Uganda will increase substantively in relation to increases in per capita GDP and population. To attain the SDG2 of zero hunger by 2030 it is imperative to invest more in agricultural productivity, to ensure both an adequate food supply and an adequate income for agricultural households in Uganda while staying within planetary boundaries.
Despite tremendous progress in poverty alleviation due to rapid economic growth, Uganda is still classified as a country with a serious hunger threat ( Grebmer et al., 2020 ). Currently, 33% of the total population of the country is classified as poor. As 72% of the total employed labor force of the country is directly engaged in agriculture, and as agriculture contributes nearly 24% to the GDP, investment in enhancing agricultural productivity can have a significant impact on the overall economic development of the country.
Alarmingly, while it is imperative to produce more matooke, cassava, and other agricultural commodities to ensure food security, agricultural productivity is severely challenged by land degradation, climate extremes, and rural outmigration ( Call et al., 2019 ;Call and Gray, 2020 ;Mubiru et al., 2017 ;Nkonya et al., 2008 ). In fact, the matooke and cassava yield growth rates have stagnated (reduced to -0.90% per annum for matooke and -3.1% for cassava between 1990 and 2019, compared to + 0.21% per annum for matooke and + 5.4% for cassava between 1962 and1989 ( FAOSTAT, 2021b ). As the demand for all the sampled foods will increase by 2030, and as the yield growth rate of some of the major food items is stagnating, investment in the overall agricultural sector in Uganda is needed to enhance food security and to improve the livelihoods of resource-poor farmers.
This study projected that Uganda's demand for six main food items, including cassava, maize/coarse grains, wheat, and rice, would increase in line with its projected increase in income and population. Increasing the productivity of the associated crops will be key to enhancing food security, but additional investments are warranted to enhance the nutritional value of the projected diets. Promising in that respect are the introduction and scaling of vitamin-and mineral-enriched biofortified staple foods, including cassava, maize, wheat, rice, and beans. As an emerging landlocked economy, increasingly relying on imports to meet growing food demand is not a feasible policy option. It is important to invest in the agricultural sector to ensure food and nutrition security. In addition, as more than 70% of Uganda's employed labor force is directly engaged in agriculture, revitalizing agricultural productivity and raising incomes by investing in the sector can also substantially contribute to sustainable development. This study therefore strongly urges the international donor agencies and the government of Uganda to further invest in the agricultural sector, to unleash the growth potential of the country, and to ensure its food and nutrition security.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgment
This work was supported by the CGIAR Research Programs on maize and wheat agri-food systems (CRP MAIZE and CRP WHEAT). The contents and opinions expressed herein are those of the authors and do not necessarily reflect the views of the associated and/or supporting institutions. The usual disclaimer applies.

Calculating commodity prices and dealing with zero expenditure on the sampled food items
Based on the information on the weekly household consumption expenditure on the sampled food items (in UGX), and quantity consumed in kilograms (kg), we first calculated the unit prices as follows: Where p is the per kilogram unit price of food item c ( c = 1---6) that a household h faced; xp is the expenditure on food item c, and q is the quantity consumed in kilograms (kg). After calculating the unit price, we deflated the price using the consumer price index setting 2010 = 100. The problem is that a significant proportion of the sampled households did not consume the sampled food items (zero expenditure). Table 1 B presents the information. Table B1  Table B2  Table B3 This shows that almost all the sampled households consumed vegetables, but nearly 47% of them did not consume matooke, 26% did not consume cassava or potatoes, nearly 32% did not consume maize, more than 61% did not consume wheat or rice, and 32% did not consume meat or fish ( Table 1 B). At this stage, since a number of households did not consume all food items, the missing prices ( xp i ct q i ct = 0) are replaced using the mean unit values of prices considering the year and the rural-urban affiliation of the households. These prices are defined as imputed prices.
The use of imputed prices in estimating income and price elasticities can lead to biased estimates due to selection bias, measurement errors, and the problem of missing values ( Deaton, 1990 ;Gibson and Kim, 2013 ;McKelvey, 2011 ). Moreover, as the imputed prices are the reported actual prices, these prices are the combination of both prices and the economic status of the households revealed by the product quality. To handle the issue, we estimated the prices of the six sampled commodities.
In the price estimation process, we first estimated a multivariate probit model for not consuming the sampled food items (did not consume an item = 1, consumed = 0). Symbolically: where C ic is a vector of dependent variables that assumes a value of 1 if the i th household did not consume a sampled food item c (matooke, cassava, and potatoes, maize, wheat and rice, vegetables, meat, and fish) in any of the years sampled (2010,2014,2016), and 0 otherwise. Among the independent variables, Exp includes four dummies for five expenditure quintiles based on the weekly total food expenditure in UGX at the household level, in which the poorest quintile (Q1) is set as the base (Q1 = 0). H H demographics is a vector of variables that includes the following: -the age in years of the household head and spouse; -a sex dummy of the household head that assumes a value of 1 if the head is male, and 0 otherwise; -three education-level dummies of the head that assume a value of 1 if the head is educated up to primary level (7 years); if the head is educated up to secondary level; if the head is educated beyond the secondary level; and 0 otherwise; -three education-level dummies of the spouse that assume a value of 1 if the spouse is educated up to primary level (7 years); if the spouse is educated up to secondary level; if the spouse is educated beyond the secondary level; and 0 otherwise; -a livelihood dummy of the head that assumes a value of 1 if the head is employed in the agriculture sector, and 0 otherwise; -a livelihood dummy of the spouse that assumes a value of 1 if the spouse is employed in the agriculture sector, and 0 otherwise; Year includes two year dummies for 2014 (yes = 1) and 2016 (yes = 1) setting the year 2010 as the base ( = 0).

Table B3
Estimated functions applying the Generalized Linear Model (GLM) estimation method explaining the prices of the sampled commodities. Year dummies ( Rural dummy is a dummy variable that assumes a value of 1 if a household is from a rural area, and 0 otherwise. Table 2 B presents the estimated functions applying the multivariate probit model estimation procedure explaining household consumption choices of the sampled food items. The likelihood ratio test of the joint significance of the correlation of the error terms of all the consumption equations χ 2 = 367.6, p = 0.00 indicates the suitability of the application of the multivariate probit model estimation procedure to identify the factors that affect the decision to not consume a sampled food. The estimated functions demonstrate that economically affluent households are progressively more likely to consume the sampled five commodity food items in Uganda, as the dummies for the expenditure quintiles (Q1-Q5) were highly significant and increased progressively over the quintiles. In other words, relatively economically affluent households are more likely to consume the sampled five food items than the poorest households located in the first expenditure quintile (Q1). While the age of the household and spouse are not significant determinants in deciding consumption of the sampled five food items, household heads and spouses with above a secondary level of education are more likely to consume wheat and rice, and meat and fish ( Table 2 B). The regional heterogeneity in food consumption is seen in Table 2 B. For example, compared to the households from the central and Kampala regions, households in the eastern, northern, and western regions are more likely not to consume cassava and potatoes, maize, rice, and wheat ( Table 2 B). On the other hand, households in the eastern and northern regions are more likely to consume meat and fish than households in the central and Kampala regions. Finally, while rural households are more likely to consume cassava and potatoes, they are less likely to consume other food items such as matooke, maize, wheat, rice, meat, and fish compared to urban households. This is probably because poverty in Uganda is more widespread in rural areas than in urban ones.
After estimating Eq. (2B) , we calculated five generalized inverse Mill's ratios for five food items, following the procedure suggested by Vella (1998) . Finally, we specified the price equations as follows: Where p ic is the real imputed price of food item c reported by household I; weekly food expenditure is the weekly total food expenditure at the household level in real terms. All monetary values are converted into real terms by setting the consumer price index at 2010 = 100 reported by the World Bank (2020).
In estimating Eq. (3B) we applied the Generalized Linear Model (GLM) estimation method. To correct the standard error, we bootstrapped the estimation method by replicating it 100 times. In addition, we clustered the standard error at the household level.
It is likely that the households in the same primary sample unit (PSU) may inform the same prices for the sampled food items since usually the sampled households in a PSU are surveyed at the same time ( Deaton, 1988 ). To handle this issue, we further demeaned the prices separately by year, food item, and ruralurban affiliation of the households. This estimated unit price from Eq. (4B) is used in estimating Eq. (1) to calculate price and expenditure elasticities.

Annexure C
Parameter estimation from QUAIDS model Table C4  Table C5  Table C6   Table C4 Parameter estimates from QUAIDS model for rural households.

Matooke
Cassava   Note: Values in parentheses are standard errors calculated based on the bootstrap method by replicating 50 times. * Significant at the 10% level. * * Significant at the 5% level. * * * Significant at the 1% level.    Note: Values in parentheses are standard errors calculated based on the bootstrap method by replicating 100 times. * Significant at the 10% level. * * Significant at the 5% level. * * * Significant at the 1% level.
All monetary values are in real terms converted using the Consumer Price Index 2010 = 100. Figure