B i o - b a s e d a n d A p p l i e d E c o n o m i c s BAE Bio-based and Applied Economics 10(3): 219-238, 2021 | e-ISSN 2280-6172 | DOI: 10.36253/bae-10488 Copyright: © 2021 W. Britz. Open access, article published by Firenze University Press under CC-BY-4.0 License. Firenze University Press | www.fupress.com/bae Citation: W. Britz (2021). Estimating a global MAIDADS demand system considering demography, climate and norms. Bio-based and Applied Eco- nomics 10(3): 219-238. doi: 10.36253/bae- 10488 Received: February 22, 2021 Accepted: July 19, 2021 Published: January 11, 2022 Data Availability Statement: All rel- evant data are within the paper and its Supporting Information files. Competing Interests: The Author(s) declare(s) no conflict of interest. Editor: Fabio Gaetano Santeramo. ORCID WB: 0000-0002-8532-3823 Estimating a global MAIDADS demand system considering demography, climate and norms Wolfgang Britz Institute for Food and Resource Economics, University of Bonn, Germany Abstract. Based on data mainly from the International Comparison Program for 156 countries, we conduct a global cross-sectional estimation of an extended rank-3 MAIDADS demand system for nineteen commodity groups including agri-food detail for integration in a Computable General Equilibrium model. We render both marginal budget shares and commitment terms depending on the implicit utility level and con- sider age shares on the population, the Gini-Coefficient, the share of Islamic popula- tion, a sea access indicator and mean temperatures as further explanatory variables. We find that especially demographic factors, the share of Islamic population and mean temperature considerably improve model selection statistics and the fit of commodity groups with a low fit in a variant where prices and income only are used. Graphics of the estimated Engel curves, with details for agro-food commodity groups, highlight income dynamics of budget shares. Keywords: demand system estimation, AIDADS, General Equilibrium Modelling. JEL codes: D12, C33, C68. 1. INTRODUCTION Partial and Computable General Equilibrium Models (CGE) are widely used tools for policy impact assessments, but simulated outcomes depend on model structure and parameterization. In their review of how final demand is modelled in long-term analysis, Ho et al. 2020 underline the importance of the choice of functional form for final demand. They find differences in baseline results for 2050 for an otherwise identical CGE model of up to fac- tor two between a Linear Expenditure System (LES), a Constant-Differ- ence-in-Elasticity (CDE) demand system1 and an AIDADS specification for single sectors, and still for up to 11% in total global aggregated output, all calibrated against the same data and own and income elasticities. Similarly, Britz and Van der Mensbrugghe 2018 compare outcomes of different model configurations and find sizeable differences in comparative-static analysis under a trade liberalisation shock between variants using different functional forms, calibrated against the same data and elasticities. But besides moving to more flexible functional forms, especially with regard to Engel curves, also 1 The CDE demand system underlies the widely used GTAP Standard model. http://creativecommons.org/licenses/by/4.0/legalcode 220 Wolfgang Britz Bio-based and Applied Economics 10(3): 219-238, 2021 | e-ISSN 2280-6172 | DOI: 10.36253/bae-10488 the parameterization of the demand systems in equilib- rium model can certainly be improved. The widely used GTAP model, for instance, depicts up to 65 sectors, but its demand system is parameterized drawing on an esti- mation with ten aggregated sectors, only (Hertel and Van der Mensbrugghe 2019), such that elasticities for many sectors are identical. This paper focuses on improved representation of final demand in equilibrium models for long-run analy- sis, specifically on the GTAP model and its variants, as the most widely used CGE models globally. The GTAP Data Base covers in its latest version 10 141 single coun- tries or group of countries for which consistent long- term time series on final demand, related price and income are not available. A country specific estimation of parameters is therefore not feasible, such that the established practise estimates generic demand systems at global level, based on cross-sectional analysis, such as in Seale et al. 2006, Reimer and Hertel 2004, Preckel et al. 2010, Roson and Van der Mensbrugghe 2018, Britz and Roson 2019. Given the large differences in per capita income across countries at global level and high projected income dynamics for current low and middle income countries, flexibility in Engel curves is deemed impor- tant during estimation and simulation. Here, an AID- ADS system with its exponential Engel curves is often found as a sensible choice (cf. Rimmer and Powell 1996) and also used to estimate the current GTAP parameter (Hertel and Van der Mensbrugghe 2019). Ho et al. 2020 stress additionally in their review that demography, income distribution and other factors such as religious norms are found as important drivers of consumption choices in many micro-level studies, but are basically not considered as consumption drivers in any of the global CGE models. Against this background, we aim at an improved final demand representation in CGE models in several directions, by (1) extending the sectoral detail in the global cross-sectional estimation of the AIDADS system, by (2) moving to a more flexible MAIDADS specification where also the commitment terms change with income, and by (3) controlling for additional factors which are likely to shape preferences such as religious norms. The resulting demand system is then integrated in the G-RDEM model (Roson and Britz 2019) for construction of long-run baseline, as a module of the flexible platform for CGE modelling CGEBox (Britz and Van der Mens- brugghe 2018). But the findings in here are also of rel- evance of partial equilibrium models focusing on spe- cific sectors, or more generally of interest to economists interested in income dynamics of demand. The paper is organized as follows. We first motivate the use and detail the extended MAIDADS demand sys- tem and the estimation approach before we present key results. Next, we discuss key findings with a focus on differences across variants which consider additional drivers such as demography or income distribution. Finally, we summarize and conclude. 2. METHODOLOGY 2.1 Extended MAIDADS demand system We empirically estimate an extended AIDADS (An Implicit Additive Demand System, Rimmer and Powell 1996) demand system for nineteen product groups: ten broader non-food groups and nine food categories, where the extension refers to utility depending commitment terms. Detail for food is introduced as income effects are here especially relevant such as expressed, for instance, by Bennet’s law (Bennet 1941). The AIDADS system can be understood as a generalization of a LES demand sys- tem where marginal budget shares are not fixed, a prop- erty also described as a rank three demand system with regard to income effects. Other rank three candidates are, for instance, the Quadratic Expenditure System (QES, Pollak and Wales 1978) and the quadratic AIDS (QUAIDS, Banks et al. 1997). Cranfield et al. 2003 esti- mated all three demand systems based of an older ver- sion of the data set employed in here with less demand categories, and compared them against the rank-two systems LES and AIDS from which they are derived. In their comparison, AIDADS and QUAIDS performed best and they recommend AIDADS if the income differences in the estimation or later simulations are high. One rea- son for this recommendation is the global regularity of AIDADS. Specifically, compared to QUAIDS, it ensures that marginal budget shares stay between zero and unity. Moreover, compared to the quadratic marginal budget shares of for instance a QUAIDS or QES specification, the exponential marginal budget shares of an AIDADS system might be considered more appropriate when covering a data set with extreme per-capita differences (Rimmer and Powell 1996). In the AIDADS demand system, the marginal budg- et shares are a linear combination of two vectors, depict- ing the marginal budget structure at very low and very high utility (income) levels. A logistic function depend- ing on the implicit utility level determines the linear combination. Given that the marginal budget shares in each of the two vectors fulfil the adding up condition to 221Estimating a global MAIDADS demand system considering demography, climate and norms Bio-based and Applied Economics 10(3): 219-238, 2021 | e-ISSN 2280-6172 | DOI: 10.36253/bae-10488 unity, any linear combination of the two also leads to regular budget shares. We follow Preckel et al. 2010 who extend the original Cranfield approach by rendering also the commitment terms depending on income, to what they call the MAIDADS for modified AIDADS demand system. With regard to the estimation strategy we fol- low Cranfield et al., 2000 who improve on the original Rimmer and Powell 1996 approach by developing an estimation method that does not rely on an approxima- tion of utility. As usual, the independent data in estima- tions are the per capita incomes Y and consumer pric- es p for countries c and commodity groups i,j, and the dependents the budget shares w. Equation (1) determines the estimated budget shares w*c,i. It is identical to a LES specification with the exception that the marginal budg- et shares δ and commitment terms γ are not fixed, but depend on the endogenously determined utility level. The marginal budget shares δi are expressed in (2) as a linear combination of two vectors δlo and δhi driven by a logistic function depending on the utility level u, implicitly defined by (5): (1) (2) can be interpreted as the marginal budget share at minimum utility level, i.e. very low per capita income, while is the share at very high incomes. The util- ity level uc is calculated at the given δc,i and γc,i in (5). It drives in (2) a logistic function with the parameters ωδ>0 and κ∂ which in turn determines the marginal budget share; this shows the implicit utility definition. At the point where the expression ωδuc-κ∂ is zero, the average between the two marginal budget share vectors is chosen, based on (5), that point is defined by κ∂. For larger negative ωδuc-κ∂, the exponent term approaches zero and the lower δc,i share is chosen; for larger positive ones, the exponent term approaches infinity such that is selected. In opposite to the original Rimmer and Powell 1996 proposal and subsequent work, we also con- sider a multiplicative factor ωδ. Different from previous work with AIDADS or MAIDADS specifications we are aware off, the two vectors δlo and δhi are country specific in here as they depend on a set f of further country specific attributes a as detailed below, see equation (3). (3) γ are the constant terms, typically termed commitments. As suggested by Preckel et al. 2010, we render also the commitment terms an exponential function of utility, see equation (4). This allows especially better differenti- ating price sensitivity across income differences. (4) Equation (5) defines the additive utility from the consumption bundle and is identical to the LES defini- tion2: (5) Besides considering additional factors in the deter- mination of the marginal budget shares, our approach is therefore slightly more general compared to Preckel et al. 2010 who, first, have κ identical in determining δ and γ, and, second, introduce ω into (4), only. 2.2 Estimation approach We follow closely Cranfield et al. (2000) and Preck- el et al (2010) in our estimation by performing a log- likelihood estimation on cross-sectional data from the International Comparison Program (ICP) referring to the year 20113 which provides a harmonized data set on expenditures (2), consumer prices and purchasing pow- er parities. However, we don’t use the publicly available data, only, but based on an agreement with the ICP, add more detail for food. 2 The usual definition of the implicit utility definition in the (M)AIADS is δc,iln(xc,i-γc,i)-ln(A)-uc=1 with δ and γ expressed by (2) and (4). Our formulation is equivalent as the term (-ln(A)-1) could be recalculated from the expressions ωγuc-κγ and ωδuc-κδ. 3 The current GTAP Data Base versions in use are Version 9 for 2011 and Version 10 for 2014, which fits to the year of the ICP data. Long- run baseline construction with recursive-dynamic CGE models projects decades into the future. With regard to consumption behaviour, this is only defendable if one assumes that observed differences in consump- tion patterns across countries with different per capita income level provide guidance of how pattern might change in future under stronger income dynamics. If using data from 2014 instead of 2011 would lead to distinct differences in the estimated parameters, the assumption would be challenged. But as we don’t have access to newer data, we leave such evaluations to other scholars. 222 Wolfgang Britz Bio-based and Applied Economics 10(3): 219-238, 2021 | e-ISSN 2280-6172 | DOI: 10.36253/bae-10488 As Preckel et al. (2010) we define a quadratic covar- iance matrix E of dimension (n-1)×(n-1) comprising the error terms ec,i from (1). Dropping the last column and row reflects that budgets shares and their error terms are linear dependent due to adding up. Assuming nor- mally distributed error terms e, their concentrated log- likelihood function becomes -½ln|E*| which elements defined as (6) Where C is the number of countries observed. In order to improve estimation speed, we follow Preckel et al. 2010 and apply a Cholesky decomposition E*=R’R which eases defining the log of the determinant of E due to ln|E|=2ln|R|. The decomposition does not itself con- strain the estimation outcome as the (reduced) covari- ance matrix E* is by definition positive definite. The decomposition is defined as: (7) The Cholesky matrix R as an upper triangu- lar matrix comprises with (n-1) (n-1+1)/2 elements far less elements than E*. The lower triangular part of the matrix R with elements rkl=0∀k>l must be set to zero while for the diagonal elements non-negativity is required to guarantee finiteness. This requires small positive bounds, here chosen as 1.E-8 which turned out to not become binding (this would imply perfect fit). The overall concentrated log-likelihood to maximize is derived from the diagonal elements of R: (8) Exhaustion of income requires adding up of the marginal budgets to unity. This leads to the following adding up restrictions during estimation: (9) As seen from equation (9), the regression coeffi- cients αi,f and βi,f, must add up to zero to maintain the adding up condition as they update marginal budget shares at low and high utility depending on country spe- cific additional factors in equation (3). As some of these regressions coefficients are therefore necessarily nega- tive, we restrict all estimated marginal budget shares to be non-zero. In order to prevent negative estimates in later simulations with the CGE model, we introduce two artificial observations at 75% of the lowest income and 125% of the highest one. These two observations do not impact the estimated log-likelihood directly as there are no error terms attached to them, but the estimator needs to ensure that the estimated budget shares for these two observations are between zero and unity. Moreover, we ensure that the estimated commitment terms don’t exceed 95% of the estimated demand at the minimum and maximum observations additionally introduced, beside an observation at the mean income of the sam- ple. This provides additional safeguards against implau- sible outcomes when simulating with the system in later applications. These details clearly ref lect the specific aims of the exercise4. The use of the exp function can provoke mathemati- cal overf lows during estimation and simulation. We therefore replace is with the following smooth quadratic exponential function: (10) Where S is a smoothing factor chosen here as S=10. The usefulness of this smoothing approach becomes obvious if we consider the point x = 100. The exponen- tial function will yield ~2.7E+43 while the smoothed one results in ~1.E+8. For the resulting linear combina- tion of the estimated parameters in (2) and (4), differ- ences in values of this dimension are irrelevant for any reasonable estimate. This becomes visible if we consider their bounds. The marginal budget shares δ are bound- ed by [0,1] and the γlo,i by [0,Ymin] where the minimum yearly per capita income Ymin is around 250 USD. This acts as a maximal bound for commitment terms as util- ity in (5) is only defined if xc,i> γc,i such that even with a budget share of 100%, γlo,i can never exceed the mini- mum income level observed. Setting γup,i to its lowest possible value of zero and γlo,i at its possible maximum yields an commitment parameter of γc,i= [1+sqexp(x)] driven by utility based on x = ωγuc-κ∂. That means that if 1+sqexp(x)>> for larger values of u, the resulting mar- ginal budget share will be, as desired, almost zero. As exp(10) ~ 5.5E4, that is already given at the point where the smoothing starts to make a difference with the γlo,i and γup,i at their most critical values for the approxi- 4 For the selected model, none of these additional safeguards became active during estimation and impacted the estimates. 223Estimating a global MAIDADS demand system considering demography, climate and norms Bio-based and Applied Economics 10(3): 219-238, 2021 | e-ISSN 2280-6172 | DOI: 10.36253/bae-10488 mation. More generally, one could define demand sys- tems similar to the (M)AIDADS based on any function returning values on the domain [0,1] for any value of utility u. We estimate different variants of the model by con- sidering besides price levels and income further coun- try specific attributes relating to income distribution, religious norms, climate, access to sea and demography, separately or jointly. Such additional controls are often found in demand system estimations drawing on house- hold samples, where such attributes refer to individual households and not, as in here, to a country. Adding these controls aims at insights if and to what extent these drivers systematically improve the fit, both with respect to the overall model and to indi- vidual categories, and reflects that these attributes have been found in micro studies as relevant to explain dif- ferences in demand behaviour (Ho et al. 2020). The use- fulness of integrating further explanatory factors might deserve some discussion. In our and similar exercises, the utility structure of the representative household of any country is assumed to be identical. This implies, for instance, that consumers in a country with a main- ly Islamic population would spend as much on bever- ages and tobacco as the ones in a country dominated by Christians when facing the same prices and enjoying the same income level. This is not very likely as consuming alcohol is often forbidden in countries where the Islamic belief dominates. Such impacts might be only partially captured by price differences in goods. Similarly, a larger share of older people might imply different expenditures on health at the same prices and identical average per capita income, motivating the use of demographic fac- tors. Demand system estimations based on a cross-section of country data set might face collinearity issues. First, price levels for some of the aggregated commodities are likely related in a systematic way to income levels, while we miss variability over time as found in a panel data set to dampen this effect. For instance, the so-called “Beaumol”-disease stipulates that labour-capital substi- tution is harder in certain service sectors, such that in countries with higher wages (and income levels), some services are systematically more expensive, the costs of a hair-cut serve often as an archetypical example. Indeed, we find R2 values for a simple regression of prices on the logarithm of per capita income (see Table 3) for non-food groups in the range of 50-60% with the exemption of communication (~30%). For agri-food groups, the corre- lation between income and prices is still high (>40% R2) for meats, fish and other food, and otherwise quite small. Any estimation using cross-country data with larger income differences will likely face these issues. In our estimation, some additional factors are also correlated to income, especially demographic factors with R2 values of 60% and 70%, using again logarithms of income levels as explanatory factors. The problem is hence of a similar magnitude as for prices and will hinder a clear separation of demographic factors from income level effects. The R² for other factors are below 25% and give little reason for concern. Still, if additional factors systematically improve model selection criteria despite collinearity issues, they contribute to a better explanation, but collinearity will make it harder to tell income and price effects apart from the influence of these additional factors. We will come back to that point when discussing which of the differ- ent model variants to use for actual simulation purposes with the CGE model. Technically, we implement the estimator in GAMS, updating and improving the codes by Britz and Roson 2019 which draws on the ones originally used by Reimer and Hertel 2004. The use of GAMS is motivated by an estimation which comprises highly-nonlinear equa- tions and constraints, such as the endogenous Cholesky- Decomposition in (7). This asks for robust non-linear programming solvers such as CONOPT4 employed here which are not available in statistical packages. GAMS is not a specialized statistical package which implies that any statistics and tests need to be pro- grammed manually. Beside these technical issues, we see several reasons why we don’t develop code to esti- mate p-values for the individual parameters. First, in our demand system estimation, dropping prices or income as independents is impossible, due to constraints, the same holds for dropping additional factors in individual equations. Even for additional factors, single p-values can therefore not guide the selection of these controls. Second, even in the models with many additional fac- tors, we still have thousands of degrees of freedoms. This renders it likely that p-values always suggest most parameters significantly different from zero, even if their relevance might be low. Moreover, the interpretation of p-values is challenging in the context of parameter restrictions. We instead carefully discuss the trade-off between considering more additional factors and model selection statistics such as the Akaike’s Information Cri- terion when deciding which of the model variants to choose for simulation. 2.3 Data As other global exercises, we draw on data by the ICP as it provides standardized and consistent observations on many countries with different per capita income levels. 224 Wolfgang Britz Bio-based and Applied Economics 10(3): 219-238, 2021 | e-ISSN 2280-6172 | DOI: 10.36253/bae-10488 This should help to find a robust representation of glob- al, country-wide Engel curves. As our ultimate aim is to integrate the estimates into the GTAP derived G-RDEM model, we aggregate detailed ICP data on food expendi- tures covering 34 items to (aggregates of) GTAP sectors and keeping otherwise the ICP classification for non-food as shown in Table 1. Per capita demands are real expendi- tures in U.S. dollars, the prices are derived from these and nominal expenditure per capita in U.S. dollars. The GTAP data base differentiates between wheat, paddy rice and other coarse grains which are potential substitutes in consumption. Keeping here more detail likely violates the assumption of additive utility such that we rather aggregate here to a category “cereals”. The same holds for the two GTAP sectors ruminant meat and other animal products, the latter comprising pig and poultry meat and eggs. Moreover, the “Other meats and meat preparations“ reported by the ICP might comprise both ruminant and non-ruminant meat and can there- fore not clearly be linked to individual GTAP sectors. The reader might wonder why we don’t consider bread and pasta under the cereals product aggregate. The rea- son is that in the GTAP SAM, cereals refer to primary production and thus the farm scale, while bread or pasta as processed product are reported under the other food industry sector which comprises many more products such as ready-to-eat menus etc.. Britz and Roson 2019 therefor argue that the input coefficients of this food processing industry aggregate are likely depending on per capita income, as empirical analysis consistently shows that bulk calorie products such as cereals, bread or potatoes are inferior goods while convenience food is a rather a luxury good. We aim with the aggregation shown in Table 1 above to get a good match between the definitions in the ICP data set and the GTAP data base which motivates this specific aggregation scheme. An overview on key metrics of the budget shares as the dependent variables provides Table 2 below. We observe that for the non-food items shown in the upper part, with the exemption of costs related to housing, the minimum shares are all below 1.5%. The maxima reveal that the categorisation of non-food items is rather balanced, with the exemption of housing, they are all in the 10-20% range. The same holds, with the exemp- tion of vegetables oils and sugar for the food categories, also. Here, all minima are, with the exemption of the other food category, all close to zero. The R2 of a simple regression on log of income reaches up to 33% of cere- als, but is in most case in the 10-20% range which leaves ample room for improvement by a demand system esti- mation. Table 3 reports key metrics for the prices and income levels as key independents. The spread of prices is astonishingly high which can also seen from their standard deviation. There is also a stronger impact of the income level on the prices, a point touched upon before. When moving from the lowest income of around 250 USD to the maxima of around 55.000 USD, the regressions suggest that prices of non-food items would increase by 0.36 to 0.45 (note that the US price is set to unity and serves for normalization). Data on demography are taken from the IASSA data repository5 for the Socio-Economic Pathways which ensures that the same data can be used in model appli- 5 https://tntcat.iiasa.ac.at/SspDb/dsd?Action=htmlpage&page=about Table 1. Commodity groups in estimation and ICP detail. Commodity group ICP Identical Clothing and footwear Housing, water, electricity, gas and other fuels Furnishings, household equipment and maintenance Health Communication Recreation and culture Education Restaurants and hotels Miscellaneous goods and services Cereals Rice; Other cereals; Flour and other products Meats and eggs Beef and veal; Lamb, mutton and goat; Pork; Poultry; Other meats and meat preparations; Eggs and egg-based products Fish Fresh, chilled or frozen fish and seafood Dairy Fresh milk; Preserved milk and other milk products; Cheese; Butter and margarine Vegetable oil and cakes Other edible oils and fats Fruits and vegetables Fresh or chilled fruit; Fresh or chilled vegetables other than potatoes; Fresh or chilled potatoes Sugar Sugar Beverages and tobacco Spirits; Wine; Beer; Mineral waters, soft drinks, fruit and vegetable juices; Coffee, tea and cocoa; Tobacco Other food processing Food products nec; Narcotics; Preserved or processed fish and seafood; Frozen, preserved or processed vegetables and vegetable-based products; Frozen, preserved or processed fruit and fruit-based products; bread; Other bakery products; Pasta products; Jams, marmalades and honey; Confectionery, chocolate and ice cream 225Estimating a global MAIDADS demand system considering demography, climate and norms Bio-based and Applied Economics 10(3): 219-238, 2021 | e-ISSN 2280-6172 | DOI: 10.36253/bae-10488 Table 2. Statistics on budget shares derived from ICP data. Mean Min Max Std.Dev R2 on log(Y)1 Clothing and footwear 0,047 0,010 0,145 0,023 0,11 Housing, water, electricity, gas and other fuels 0,153 0,049 0,389 0,057 0,11 Furnishings, household equipment and maintenance 0,049 0,009 0,132 0,020 0,00 Health 0,076 0,009 0,197 0,035 0,22 Transport 0,092 0,014 0,183 0,034 0,02 Communication 0,028 0,001 0,098 0,015 0,16 Recreation and culture 0,045 0,004 0,112 0,028 0,29 Education 0,072 0,013 0,178 0,028 0,05 Restaurants and hotels 0,045 0,000 0,141 0,032 0,18 Rest 0,077 0,015 0,194 0,044 0,08 Cereals 0,049 0,001 0,311 0,063 0,33 Meats, eggs 0,053 0,006 0,239 0,035 0,03 Fish 0,013 0,000 0,103 0,016 0,14 Dairy 0,026 0,001 0,108 0,019 0,14 Vegetable oils 0,011 0,000 0,047 0,010 0,20 Fruit & veg 0,049 0,006 0,210 0,037 0,28 Sugar 0,008 0,000 0,038 0,008 0,20 Other food 0,060 0,020 0,159 0,031 0,10 Beverages and tobacco 0,048 0,009 0,149 0,023 0,00 Source: ICP 2011, aggregated according to Table 1. Notes: 1 Linear regression with log of income per capita as independent. Table 3. Statistics on income and prices. Mean Min Max Std.Dev R2 on log(Y)1 Income 9.030 220 55.835 12.196 Clothing and footwear 0,771 0,229 2,053 0,368 0,61 Housing, water, electricity, gas and other fuels 0,540 0,074 2,400 0,413 0,55 Furnishings, household equipment and maintenance 0,853 0,422 1,778 0,288 0,63 Health 0,439 0,098 1,678 0,328 0,65 Transport 0,943 0,385 2,349 0,380 0,54 Communication 0,678 0,101 1,742 0,288 0,31 Recreation and culture 0,768 0,330 1,948 0,323 0,59 Education 0,313 0,037 1,905 0,320 0,55 Restaurants and hotels 0,799 0,265 2,240 0,341 0,55 Rest 0,640 0,233 1,993 0,333 0,69 Cereals 0,916 0,258 3,588 0,395 0,15 Meats, eggs 0,994 0,277 3,313 0,467 0,51 Fish 0,593 0,155 1,723 0,289 0,53 Dairy 1,080 0,412 2,159 0,293 0,02 Vegetable oils 1,386 0,719 2,331 0,325 0,04 Fruit & veg 0,732 0,234 2,614 0,356 0,39 Sugar 0,915 0,239 2,329 0,304 0,06 Other food 0,844 0,268 1,902 0,297 0,33 Beverages and tobacco 0,716 0,128 2,289 0,329 0,33 Source: ICP 2011, aggregated according to Table 1. Notes: Price of United States = 1, 1 Linear regression with log of income per capita as independent. 226 Wolfgang Britz Bio-based and Applied Economics 10(3): 219-238, 2021 | e-ISSN 2280-6172 | DOI: 10.36253/bae-10488 cations for long-run analysis. We use the shares of two age groups as additional factors which can be expected to be not part of the working population (<15 and > 65 years). Not only are these age groups likely to show consumption patterns different from other age groups, they also might (indirectly) control for differences in household sizes, especially the share of <15 years old. As some household expenditures comprise a fix-cost share, household size at the same average per capita income of the household members is likely to change budget shares (Deaton and Paxson 1998). We took access to sea into account especially in the hope to better control for spending on hotels and restaurants, and to explain fish consumption. Mean temperature as the climatic vari- able chosen not only could impact the food consump- tion bundle, for instance with regard to dairy, but also impact housing and clothing expenditures (Sheth 2017). To check for the influence of different income distribu- tions, we use Gini coefficients taken mostly from the CIA factbooks, a few missing observations were filled by data from Liberati 2009. Data on the share of Islamic population were taken from a study by the Pew center, 2011 (Pew center 2011). In total, we observed for C=156 countries budget shares, prices and additional factors. The 19 commod- ity groups lead to 2,964 observations. The extended AIDADS model where also the commitment terms depend on the utility level has four vectors of param- eters (α, β, γlo, γhi), two utility multiplier κ and two exponents ω, considering the adding up conditions, this implies m = (2*n + 2*(n-1) + 4) = 78 parameters for the MAIDADS variant without additional factors. Each additional explanatory variable adds two addi- tional vectors of marginal budget shares at low and high income, again considering adding up, that means for each factor 2*(n-1) = 36 additional parameters to estimate. For the model considering all six addi- tional independents, we hence estimate 294 param- eters. This reduces the degrees of freedom more than a QUAIDS system which would estimate m = (3 * (n-1) + (n-1)*(n-1)/2 = 192 parameters. But the full model is not used for simulation in here, but rather serves as a benchmark to select a suitable set of additional factors beyond per capita income and price levels. 2.4 Integration in the CGE Using the estimation results for benchmarking of a CGE model is far from straightforward as observed budget shares for a country or country aggregate might deviate considerably from what the econometric model suggests. Additionally, with the exemption of the agri- food sector, the commodity groups are still rather aggre- gated compared to, for instance, the 57 sector resolution of the GTAP 9 data base or the 65 sectors of GTAP 10. During estimation and later simulation, the utility is implicitly driven by the demands which depend on the marginal budget shares and commitment levels which are functions of utility. In order to ease benchmarking, we follow therefore the approach of Britz and Roson 2019 which perform a regression of the estimated utility levels from (5) on per capita income and add here as fur- ther independents the additional factors. The estimate of the utility level allows deriving an estimate of the coun- try and sector specific δc,i and γc,i for benchmarking. We cannot introduce the error term in the simulation model directly. Instead, we have, as usual for benchmarking with CGE models, to correct some of the parameters in order to line up the observed data with the estimated ones. The errors cannot be simply added to the commit- ment terms γc,i as this changes non-committed income as well. Doing so also runs the risk to introduce rather curious elasticities in the model. This becomes visible from the Marshallian demands in equation (11). (11) If, for instance, the observed x is large compared to what the estimations suggests as x*, simply increas- ing the related commitment term will mean that income and price effects are considerably dampened compared to the estimation. Increasing the marginal budget shares at unchanged commitment terms will instead increase price and income responsiveness. We therefore suggest first scaling both vectors of estimated parameters by the relation between the observed and the estimates, next scale the commitment terms such that they add up to unity and finally penal- ize squared deviations from the original estimates and under adding up conditions. Table 4. Additional factors considered. Factor Variable(s) Income distribution Gini Coefficient Religious norms Share of islamic population Climate Mean temperature Sea access Coast line relative to country size [m/skm], in log Demography Share of persons < 15 year Share of persons > 65 years 227Estimating a global MAIDADS demand system considering demography, climate and norms Bio-based and Applied Economics 10(3): 219-238, 2021 | e-ISSN 2280-6172 | DOI: 10.36253/bae-10488 3. RESULTS 3.1 Fit of different model variants In order to assess the different model variants, we compare the value of the likelihood function, the Akai- ke’s Information Criterion, the information inaccuracy, the Schwartz’s Criterion and the system wide Root Mean Squared Error. The calculation of the statistics follows Cranfield et al. 2003, i.e. the Root Mean Squared Error for the estimation of the budget shares w for the products i is calculated as RMSEi=[1/C ωic-ω*ic with C being the number of countries and the system wide RMSE by using the mean budget share as weights, i.e. SMRSE= RMSEi. The value of the likelihood function is defined as LLF=-1/2Cln|E*|, the information inaccuracy as IIA=1/C ωc,i(ωc,i/ω*c,i), Akaike’s Information Criterion as AIC=2/ Cm+ln|E*| and the Schwartz’s Criterion as SC=1/Cln(T) m+ln|E*|. We calculate a system wide R² by weighting the individual R² with the budget shares. The full model which uses all additional explicatory factors clearly has the best fit with a likelihood function value of 11.472 and a system R wide ² of 54,2%, see Table 5. It shows also the best IIA value, but the AIC and SC statistics suggests that it might be over specified when compared to other variants. Specifically, it adds 6 times 2 parameter vectors to the base model, such that we esti- mate (around) ten parameters for each commodity from 156 observations. Both in the groups of model variants using one factor or two factors, the religious norm and the demographic variables tend show the best values for the model selection statistics. Overall, the three factor model using the religious norm, the climate factor and demographic attributes gives the best AIC criterion. Its LLF and the system wide R² are close to the full model, but its AIC and SC selec- tion criteria are considerably better. We therefore con- sider it the most suitable candidate based on the model selection statistics. The SC criterion would favour the model without any additional factors. But, as expected, the System wide R² and the value of the likelihood func- tion put it on the last position. Table 5. Model selection statistics. LLF System R² SRMSE AIC IIA SC Base 11.219 45,3 2,86 -142,9 9,47 -141,4 Norms 11.295 48,6 2,75 -143,4 9,01 -141,3 Demography 11.326 49,5 2,75 -143,3 8,83 -140,5 Sea access 11.252 46,5 2,82 -142,8 9,22 -140,7 Climate 11.275 47,7 2,80 -143,1 9,07 -141,0 Gini 11.260 47,1 2,82 -143,0 9,26 -140,8 Norms + Demography 11.379 51,3 2,68 -143,6 8,53 -140,0 Norms + Sea acess 11.328 49,7 2,72 -143,4 8,74 -140,5 Norms + Climate 11.345 50,5 2,71 -143,6 8,68 -140,7 Norms + Gini 11.328 50,0 2,73 -143,4 8,82 -140,5 Demography + Sea acess 11.360 50,5 2,72 -143,3 8,60 -139,7 Demography + Climate 11.367 50,8 2,72 -143,4 8,54 -139,8 Demography + Gini 11.359 50,6 2,72 -143,3 8,62 -139,7 Sea acess + Climate 11.302 48,7 2,77 -143,0 8,86 -140,2 Sea acess + Gini 11.290 48,2 2,79 -142,9 9,04 -140,0 Climate + Gini 11.300 48,6 2,78 -143,0 9,12 -140,1 Norms + Demography + Sea acess 11.413 52,4 2,66 -143,5 8,28 -139,3 Norms + Demography + Climate 11.425 52,6 2,65 -143,7 8,25 -139,4 Norms + Demography + Gini 11.405 52,2 2,66 -143,4 8,34 -139,2 Demography + Sea acess + Climate 11.395 51,6 2,70 -143,3 8,39 -139,0 Demography + Sea acess + Gini 11.390 51,5 2,70 -143,2 8,40 -139,0 Sea acess + Climate + Gini 11.327 49,6 2,75 -142,9 8,78 -139,3 Full 11.472 54,2 2,62 -143,4 7,99 -137,7 Source: Own estimation. Notes: Numbers in bold indicate the best statistic in the group of models and red ones the overall best model. 228 Wolfgang Britz Bio-based and Applied Economics 10(3): 219-238, 2021 | e-ISSN 2280-6172 | DOI: 10.36253/bae-10488 While the overall model statistics are reported in Table 5, the tables shown in the following report the R2 for the individual equations as a widely used and easy to interpret statistics to compare the fit, here both across estimated equations in the systems and across compet- ing model variants. For comparison, we add always the system wide R2. Table 6 reports in the column “Base” a model using prices and income levels only as independent variables, i.e. the slightly extended MAIDADS model as proposed by Preckel et al. 2010. The best fit is found for “Recrea- tion and culture” with 81% as a clear luxury good, fol- lowed by “Fruits and vegetables” by 76%. As seen from Table 6, these product groups also include staple food such as potatoes or root and tubers as classical examples of Barnett’s law. This might explain the relatively high fit for that category. Disappointing is the fact that “Fur- nishings, household equipment and maintenance” even has a negative R2 while for “Beverages and Tobacco”, 8% only of the variance are explained. Similar low fits are also reported in Britz and Roson 2019. The low explanatory power of the base model for some of the categories motivates considering additional factors which might drive consumption patterns. In order to assess how the additional factors impact results, we estimate versions where each factor is considered without the others, any combination of two or three factors and a full model comprising all of them. Note here that we always consider the two demographic variables jointly. We first find that adding any additional factor to the base model improves the fit as seen from Table 5. Demography gives the best results of the models with single factors, but is actually introducing two additional dependents variables in the model. While it improves the fit for each single product group compared to the base model, it is not always better than model variants using another additional factor. The best results for any model variant considering one additional factor only are shown in bold in Table 6. This highlights that for eleven out of the nineteen product groups, the two demograph- ic factors give jointly the highest R2. The share of Islamic population follows with seven groups. Sea, access, cli- mate and the Gini coefficients trail both with regard of the overall fit and with regard to categories where they provide the best fit. However, one needs to consider that demography is based on two additional dependents. The bad performance of the Gini coefficient - we also tested a variant using logs instead of the linear model for which results are reported – might come as a sur- prise. One might have assumed that, for instance, higher Table 6. Fit of different model variants by commodity group, single factors. Base Norms Demography Sea access Climate Gini System wide R2 45,3 48,6 49,5 46,5 47,7 47,1 Clothing and footwear 13,4 18,2 18,4 13,7 14,8 17,3 Housing, water, electricity, gas and other fuels 45,4 51,3 48,7 46,7 46,8 45,7 Furnishings, household equipment and maintenance -0,5 1,5 9,9 0,3 4,8 3,1 Health 65,7 71,5 71,6 66,1 70,2 66,5 Transport 32,5 33,7 38,2 33,4 36,0 36,5 Communication 26,4 30,6 30,2 27,4 30,4 30,3 Recreation and culture 80,9 85,3 84,1 81,2 81,5 81,3 Education 29,9 33,6 35,8 30,0 31,6 31,7 Restaurants and hotels 34,4 38,3 35,5 37,2 37,9 35,7 Rest 74,4 76,0 76,4 74,5 75,1 74,5 Cereals 73,1 74,4 74,6 73,4 73,5 73,2 Meats, eggs 49,4 49,6 49,5 52,6 49,5 49,6 Fish 33,2 34,0 34,4 38,7 37,6 35,0 Dairy 34,7 38,9 36,0 36,7 39,9 40,6 Vegetable oils 63,0 63,7 63,1 63,2 63,3 63,2 Fruit & veg 63,7 65,2 64,8 63,9 65,1 64,2 Sugar 60,9 61,2 65,2 62,3 61,3 60,9 Other food 61,6 61,8 64,1 63,6 62,5 65,6 Beverages and tobacco 8,5 16,5 23,5 14,2 16,5 14,1 Source: Own estimation. Notes: Numbers in bold indicate the best fit in the group of models. 229Estimating a global MAIDADS demand system considering demography, climate and norms Bio-based and Applied Economics 10(3): 219-238, 2021 | e-ISSN 2280-6172 | DOI: 10.36253/bae-10488 income inequality at low income levels might increase the observed budget share of luxury goods. A potential explanation why the Gini coefficient does not improve the fit strongly might be that the impact of, for instance a small group of rich households, on average spending shares of the aggregate might still be rather limited.6 Results for individual commodity groups of the models which consider two factors jointly are shown in Table 7. Here, combining the two demographic variables with the share of Islamic population gives the best fit based on the system wide R², closely followed by adding the mean temperature to them. Equally, the best fit found for any of the different product groups is more equally distributed over the different model variants. While the best model considering one of the factors adds around 4% to the overall R2 of the base model (see Table 6), con- sidering two jointly improves at best by around 6%. Results for the models which consider three factors jointly are shown in Table 8. Perhaps as expected from the results found for single additional factors, combining 6 We also tested with gini coefficient provided by UN with quite similar results. the share of the Islamic population with the two demo- graphic variables and the mean temperature to control for climate effects gives the best fit. It misses the fit of the model will all factors (i.e. adding the Gini coefficient and the sea access indicator as well) by less than just 2%. This full model performs considerably better for “Cloth- ing and footware” (+5%), “beverages and tobacco” (+4%) and “Meat and eggs” (+4%) compared to this best candi- date model with three additional factors. It is interesting to see that simpler models give a better fit in two cases compared to the full specification, for which the fit is shown in bold if it is better than any other specification. Besides considering the model selection statistics from Table 5 and considerations of the fit for individ- ual model groups, the choice of a suitable model vari- ant depends also on how its estimates can be integrated into long-run simulations with a CGE. Suitable variants comprise factors which are likely rather stable over time or are explicitly controlled by dynamic updates. As the IASSA data base reports projections of the demographic composition of the population for all countries and the different SSPs, the two demographic factors are obvi- ous candidates. They also have shown to improve con- Table 7. Fit of different model variants by commodity group, two factors. Norms Demog Norms Sea acc Norms Climate Norms Gini Demog Sea acc Demog Climate Demog Gini Sea acc Climate Sea acc Gini Climate Gini System wide R2 51,3 49,7 50,5 50,0 50,5 50,8 50,6 48,7 48,2 48,6 Clothing and footwear 18,7 18,4 18,7 19,9 19,3 20,6 19,9 15,3 18,0 17,7 Housing, water, electricity, gas and other fuels 51,9 51,7 51,5 50,9 49,0 49,0 48,9 47,4 46,9 46,9 Furnishings, household equipment and maintenance 10,4 2,0 6,7 4,2 10,4 12,0 11,4 5,9 3,6 6,0 Health 73,1 71,4 72,9 71,1 71,8 72,5 71,9 70,4 66,6 70,1 Transport 40,3 34,5 37,6 37,3 38,8 38,9 39,0 38,3 37,5 37,7 Communication 31,4 32,1 33,4 32,8 30,9 33,2 32,0 30,3 30,9 32,0 Recreation and culture 86,4 85,6 85,4 85,3 84,3 84,2 84,2 81,8 81,6 81,6 Education 37,2 34,1 34,9 35,4 35,9 36,7 36,8 32,4 31,8 32,4 Restaurants and hotels 38,6 42,0 44,6 39,8 39,5 43,9 39,0 39,3 37,8 38,1 Rest 76,9 76,0 76,2 75,8 76,3 76,3 76,5 75,3 74,7 75,0 Cereals 76,6 75,0 74,8 74,7 75,5 75,5 75,4 74,1 73,5 73,9 Meats, eggs 50,2 52,7 49,9 49,8 52,5 50,2 50,7 52,1 52,6 49,7 Fish 35,2 40,1 38,5 35,5 39,4 39,5 37,0 40,1 39,7 38,3 Dairy 42,9 41,0 45,1 42,2 37,6 39,5 41,9 40,2 41,5 42,8 Vegetable oils 64,2 63,7 64,1 64,3 63,1 63,4 63,2 63,8 63,3 63,8 Fruit & veg 67,6 65,6 66,3 66,3 65,3 66,0 65,9 64,8 64,6 65,8 Sugar 66,0 62,6 61,5 61,4 66,3 66,6 65,5 62,2 62,4 61,5 Other food 64,4 64,1 62,6 66,0 67,1 64,7 67,2 64,2 67,0 65,8 Beverages and tobacco 25,2 20,6 21,5 21,4 26,9 24,7 24,3 19,6 18,4 17,9 Source: Own estimation. Notes: Numbers in bold indicate the best fit in the group of models. 230 Wolfgang Britz Bio-based and Applied Economics 10(3): 219-238, 2021 | e-ISSN 2280-6172 | DOI: 10.36253/bae-10488 siderably the fit either alone or combined with others. The share of the Islamic population in a country could clearly change when simulating over multiple decades into future, but cultural habits related to current or former shares of Islamic population are properly more stable. It seems therefore defendable to use the share of Islamic population as well as an additional control. Finally, mean temperatures can be either considered sta- ble or updated according to climate change projections. Considering both factors besides the demographic ones clearly could improve the model selection satistis and the fit of most commodity groups. While in some cas- es, considering the Gini coefficients gave best results for certain categories, the Gini coefficient is likely to change if average per capita income increase considerably over the projection period and is therefore here excluded. Sea access seems mostly to impact fish consumption and it is likely that the benchmarking process will address outli- ers here anyhow. Based on these arguments and the model statistics, we opt for the model specification with uses the two demographic factors, the share of Islamic population and the climate variable as additional explanatory variables. Table 9 reports the estimated parameters. Quantities during the estimation are expressed in USD dollars per capita and corrected for differences in prices, setting the US price to unity. The commitment terms are all mod- est to low, when considering that income reaches up to around 55,000 USD in the sample. Generally, the reader should keep in mind the difference between expenditure levels and budget shares. Let us take education as an example: the expenditure at low income levels (250 USD) is based on budget share of around 7%, plus forty dollars committed, i.e. around sixty dollars. At 50,000 USD, the about 5% marginal budget share implies an expenditure of 2,500 USD plus 2,000 USD of committed income, i.e. 4,500 USD. But, production costs and thus prices for educational services are also generally higher in high income countries. Scatter plots are shown in Figure 1 for non-food and in Figure 2 for food-items jointly with logarithmic regres- sion lines dependent on income. Note that the income axis is logarithmic. The plots highlight two observations. First, the variation in the observed budget shares in coun- tries of the same income range can be rather large, as seen for instance from the panel for the housing costs. There Table 8. Fit of different model variants by commodity group, three and all factors. Norms Demog Sea acc Norms Demog Climate Norms Demog Gini Demog Sea acc Climate Demog Sea acc Gini Sea acc Climate Gini Full System wide R2 52,4 52,6 52,2 51,6 51,5 49,6 54,2 Clothing and footwear 20,4 20,6 20,4 22,9 21,5 18,3 25,2 Housing, water, electricity, gas and other fuels 52,0 52,5 52,3 48,9 49,2 47,4 52,5 Furnishings, household equipment and maintenance 10,9 12,8 12,6 12,4 12,0 7,3 15,8 Health 73,1 74,1 73,2 72,8 72,2 70,4 74,5 Transport 40,8 41,6 40,5 40,7 39,7 40,1 43,2 Communication 32,3 34,2 32,5 33,4 32,4 31,9 35,1 Recreation and culture 86,4 86,5 86,3 84,4 84,4 81,8 86,4 Education 37,7 37,9 38,5 36,6 36,8 33,1 39,4 Restaurants and hotels 43,0 46,5 40,4 45,0 41,8 39,5 47,9 Rest 76,9 76,7 77,0 76,1 76,4 75,2 76,6 Cereals 77,0 77,3 76,8 76,2 75,9 74,5 78,0 Meats, eggs 53,7 50,6 51,1 52,9 53,3 52,2 54,6 Fish 40,6 40,4 37,3 41,0 41,4 41,0 42,9 Dairy 45,5 47,0 46,0 39,4 42,8 43,1 49,2 Vegetable oils 64,3 64,7 64,9 64,1 63,3 64,4 66,1 Fruit & veg 67,8 68,3 67,9 66,0 66,4 65,7 68,4 Sugar 67,0 67,5 66,3 67,4 66,5 62,4 68,4 Other food 67,4 65,1 68,1 67,4 69,4 67,6 70,3 Beverages and tobacco 28,3 26,8 26,5 28,4 28,0 20,8 30,7 Source: Own estimation. Notes: Numbers in red indicate the best fit in the group of models. Results in bold indicate best value including the full model. 231Estimating a global MAIDADS demand system considering demography, climate and norms Bio-based and Applied Economics 10(3): 219-238, 2021 | e-ISSN 2280-6172 | DOI: 10.36253/bae-10488 are some observations in the 500 USD range where just 5% are spent on housing, whereas the average household in others countries spends 30%. At the same time, esti- mates also scatter around the simple logarithmic regres- sion line which reflects the impact of price differences across countries, but also of the other explanatory factors. The diagrams also highlight the usefulness of the using the exponential marginal budget lines of the AIDADS system to capture, for instance, the clear saturation effect seen for cereals in Figure 2. For meats and eggs as well as dairy, the plots suggest that budget shares first increase up to around 2000 USD to drop afterwards. Figure 3 shows the expenditure shares resulting from the AIDADS estimation, for income levels between 250 and 50,000 USD evaluated at mean prices and mean explanatory factors. At very low income levels, more than a third of the income is dedicated to food (37%), around 13% is spent on housing and 8% on transport, 5% on furnishing, household equipment and mainte- nance and 2% on health. At very high expenditure lev- els, the share for food drops to about 17%, while shares for housing increase moderately to around 16%. Shares for health care are more than tripling, reaching 11%, whereas for restaurants and hotels they increase by a fac- tor five, from 1.7% up to 7%. A similar large increment is observed for “Recreation and culture” growing from less than 1.6% to over 7%. An interesting observation is the rather drastic change in budget shares for some product groups when moving from 250 USD to 1000 USD per capita and year. Housing cost half from 37% to 18%, while expenditures for food change only slightly. Instead, budget shares for health (1.7% versus 5.6%), communication (0.08% to 2.3%), Furnishings (2.2% to 4.3%), Transport (2.8% to 6.7%), Recreation and culture (0.5% to 2.3%) and other items (0.9% to 4.6%) increase substantially. That under- lines that at very low incomes, expenditures are con- centrated on food, shelter and utilities, where the later might serve also as input into, for instance, food prepa- ration in the household, which is outsourced at higher income levels. Figure 4 below provides more detail for food cat- egories in the AIDADS system by reporting shares on total food expenditure. At very low income levels, cere- als have the highest shares with around 28%, followed by the other food category (19%) which comprises, for instance, bread, and 12 % are spent on fruits and veg- etables. Expenditures on meat in total food consump- Table 9. Estimated base coefficients for selected model. Alpha Beta Gamma, lo Gamma, high Clothing and footwear 4% 5% 6 136 Housing, water, electricity, gas and other fuels 1,00E-07 20% 121 1.354 Furnishings, household equipment and maintenance 5% 6% 1 158 Health 4% 9% 781 Transport 2% 13% 3 423 Communication 2% 3% 290 Recreation and culture 1,00E-07 6% 133 Education 7% 5% 39 2.037 Restaurants and hotels 0% 6% 5 181 Miscellaneous goods and services 1,00E-07 12% 252 Cereals 10% 1,00E-07 19 Meats, eggs 12% 3% 203 Fish 3% 1% 1 Dairy 8% 2% 84 Vegetable oils 4% 0% Fruit & veg 15% 1% 131 Sugar 2% 1% Other food 13% 3% 7 209 Beverages and tobacco 9% 3% 10 301 Food (sum of the categories above) 76% 15% 37 928 Source: Own estimation. Note: Model considers two demographic factors and temperature as additional explanatory variables. The gamma parameters are expressed on a per capita basis. 232 Wolfgang Britz Bio-based and Applied Economics 10(3): 219-238, 2021 | e-ISSN 2280-6172 | DOI: 10.36253/bae-10488 0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 100 1000 10000 Bu dg et s ha re Income Clothing and footwear obs est Log. (obs) 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 100 1000 10000 Bu dg et s ha re Income Housing, water, electricity, gas and other fuels obs est Log. (obs) 0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 100 1000 10000 Bu dg et s ha re Income Furnishings, household equipment and maintenance obs est Log. (obs) 0 0,05 0,1 0,15 0,2 0,25 100 1000 10000 Bu dg et s ha re Income Health obs est Log. (obs) 0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 0,18 0,2 100 1000 10000 Bu dg et s ha re Income Transport obs est Log. (obs) 0 0,02 0,04 0,06 0,08 0,1 0,12 100 1000 10000 Bu dg et s ha re Income Communication obs est Log. (obs) 0 0,02 0,04 0,06 0,08 0,1 0,12 100 1000 10000 Bu dg et s ha re Income Recreation and culture obs est Log. (obs) 0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 0,18 0,2 100 1000 10000 Bu dg et s ha re Income Education obs est Log. (obs) 0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 100 1000 10000 Bu dg et s ha re Income Restaurants and hotels obs est Log. (obs) 0 0,05 0,1 0,15 0,2 0,25 100 1000 10000 Bu dg et s ha re Income Miscellaneous goods and services obs est Log. (obs) Figure 1. Scatter plots, Non-Food items. 233Estimating a global MAIDADS demand system considering demography, climate and norms Bio-based and Applied Economics 10(3): 219-238, 2021 | e-ISSN 2280-6172 | DOI: 10.36253/bae-10488 -0,1 -0,05 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 100 1000 10000 Bu dg et s ha re Income Cereals obs est Log. (obs) 0 0,05 0,1 0,15 0,2 0,25 0,3 100 1000 10000 Bu dg et s ha re Income Meats and eggs obs est Log. (obs) -0,02 0 0,02 0,04 0,06 0,08 0,1 0,12 100 1000 10000 Bu dg et s ha re Income Fish obs est Log. (obs) 0 0,02 0,04 0,06 0,08 0,1 0,12 100 1000 10000 Bu dg et s ha re Income Dairy obs est Log. (obs) -0,01 0 0,01 0,02 0,03 0,04 0,05 100 1000 10000 Bu dg et s ha re Income Vegetable oils obs est Log. (obs) 0 0,05 0,1 0,15 0,2 0,25 100 1000 10000 Bu dg et s ha re Income Fruits and vegs obs est Log. (obs) -0,005 0 0,005 0,01 0,015 0,02 0,025 0,03 0,035 0,04 100 1000 10000 Bu dg et s ha re Income Sugar obs est Log. (obs) 0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 0,18 100 1000 10000 Bu dg et s ha re Income Other food obs est Log. (obs) 0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 100 1000 10000 Bu dg et s ha re Income Beverages and Tobacco obs est Log. (obs) Figure 2. Scatter plots, Food items. 234 Wolfgang Britz Bio-based and Applied Economics 10(3): 219-238, 2021 | e-ISSN 2280-6172 | DOI: 10.36253/bae-10488 tion are estimated at 10%, while dairy accounts for 7% at such low income levels. There is again a distinct differ- ence between the 250 USD to the 1000 USD consump- tion pattern, as the cereals share is halved to 14%, while the share of meat (+6% to 16%) and dairy (+3% to 10%) increase considerably. At very high incomes, other food (22%) followed by meat (18%) and beverages and tobacco (18%) are the largest expenditure groups inside the food bundle. The cereal shares on total food expenditure is still 3%, but the overall drop of the budget share of food implies that a very high income levels, less than 1% of the income is spent on cereals. The income dynamics become also visible from the Engel curves shown in Figure 5. Recreation and culture as well as the other service category show very high Engel elasticities at low income in the range of five. Interestingly, at high income levels, education and com- munication have elasticities below unity, different from all other non-food items. For the food items, cereals show negative Engel elasticities over a wider ranger of the income variation. Below 100 USD, basically all food items besides cere- als are luxury goods, as indicated above, this becomes possible by a quite low income elasticity for housing expenditure, also visible from the upper panel. But food item elasticities drop rapidly below 0.5 around 1000 USD, with the exemption of beverages and tobacco as well as meat and eggs, and increase slightly again up to income levels around 5.000 USD. A potential reason is the falling elasticity for housing costs suggested by the upper panel. Above 1000 USD yearly per capita income, none of the food items is a luxury good any longer and the crop based food items with the exemption of sugar have elasticities below 0.5. The reader should keep in mind that these estimates also capture the effect of com- positional changes, for instance, the average household in a rich country spent income on imported fresh fruits and vegetables, while in poor countries, this product 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 25 0 15 00 27 50 40 00 52 50 65 00 77 50 90 00 10 25 0 11 50 0 12 75 0 14 00 0 15 25 0 16 50 0 17 75 0 19 00 0 20 25 0 21 50 0 22 75 0 24 00 0 25 25 0 26 50 0 27 75 0 29 00 0 30 25 0 31 50 0 32 75 0 34 00 0 35 25 0 36 50 0 37 75 0 39 00 0 40 25 0 41 50 0 42 75 0 44 00 0 45 25 0 46 50 0 47 75 0 49 00 0 Clothing and footwear Housing, water, electricity, gas and other fuels Furnishings, household equipment and maintenance Health Transport Communication Recreation and culture Education Restaurants and hotels Miscellaneous goods and services Food Figure 3. Simulated expenditure shares, non-food items and total for food. Note: Calculated at mean sample prices and mean sample values of the additional factors. 235Estimating a global MAIDADS demand system considering demography, climate and norms Bio-based and Applied Economics 10(3): 219-238, 2021 | e-ISSN 2280-6172 | DOI: 10.36253/bae-10488 group might mainly comprise locally available roots and tubers. 6. DISCUSSION A suitable specification for aggregate household demand in a CGE model needs to reflect the targeted applications. For detailed policy analysis such as chang- ing subsidies and/or taxes differentiated across ener- gy carriers, income changes are mostly limited and the focus is rather on own and cross price effects. This motivates the use of nested demand systems e.g. in the GTAP-E (McDougal and Golub 2007) model to capture in detail substitution effects between different energy carries. We focus instead on long-run analysis with large income dynamics which motivates the use of the MAID- ADS functional form. Stronger Hicksian substitution effects between the commodity groups considered in here are not very like- ly such that second-order flexibility with regard to pric- es is probably not needed to identify the Engel curves. This motivates also the use of a simpler additive utility function. In this respect, we don’t follow the argumen- tation line of Reimer and Hertel 2004 who consider the AIADS as not appropriate for more than ten product categories in estimation, an argument which would also apply to an LES or CD specification. As the G-RDEM model as our main application target also uses CES nests to substitute between dif ferent cerea ls and between different meats, we deliberately aggregate here beyond the individual GTAP sectors in the estimation as discussed above. Differentiating to individual cere- als or meats would indeed render the use of an additive demand system dubious. An estimation exercise of an MAIDADS system for food only by Gouel and Guim- bard 2019 estimates calorie demands for seven food categories, introducing hence similar detail for food as in our exercise, however estimating demands based on producer prices. 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 25 0 15 00 27 50 40 00 52 50 65 00 77 50 90 00 10 25 0 11 50 0 12 75 0 14 00 0 15 25 0 16 50 0 17 75 0 19 00 0 20 25 0 21 50 0 22 75 0 24 00 0 25 25 0 26 50 0 27 75 0 29 00 0 30 25 0 31 50 0 32 75 0 34 00 0 35 25 0 36 50 0 37 75 0 39 00 0 40 25 0 41 50 0 42 75 0 44 00 0 45 25 0 46 50 0 47 75 0 49 00 0 Cereals Meats Fish Dairy Vegetable oils Fruits and vegetables Sugar Other food Beverages and tobacco Figure 4. Expenditure shares for food categories. Note: Calculated at mean sample prices and mean sample values of the additional factors. 236 Wolfgang Britz Bio-based and Applied Economics 10(3): 219-238, 2021 | e-ISSN 2280-6172 | DOI: 10.36253/bae-10488 We opted in here to render marginal budget shares depending on additional factors besides prices and income. Alternatively, the commitment terms could be updated. Using the marginal budget shares has the advantage that additivity can be imposed on the impact of these additional factors. This at least prevents that more unusual observations for the additional factors can provoke e.g. negative consumption quantity estimates, or that the non-committed income overshoots the observed one when commitment terms are increased. The esti- mates for the commitment terms (see Table 9) suggest that they are all mostly small compared to income levels. At least for the vector at low utility, that is not an aston- ishing outcome as estimation of negative budget shares is not allowed even at the quite low minimal per capi- ta income levels in the estimation. Here, neither larger increases of the commitment terms nor larger decreases are able without violating the non-negativity condition, while updates to the marginal budget share cannot pro- voke problems in that respect. 0 1 2 3 4 5 6 100 1000 10000 Clothing and footwear Housing, water, electricity, gas and other fuels Furnishings, household equipment and maintenance Health Transport Communication Recreation and culture Education Restaurants and hotels Miscellaneous goods and services -1 -0,5 0 0,5 1 1,5 2 2,5 100 1000 10000 Cereals Meat and eggs Fish Dairy Vegetable oils Fruits and vegetables Sugar Other food Beverages and tobacco Figure 5. Estimated Engel elasticities at mean prices. Note: Calculated at mean sample prices and mean sample values of the additional fac- tors. Formula based on Preckel et al. 2010. 237Estimating a global MAIDADS demand system considering demography, climate and norms Bio-based and Applied Economics 10(3): 219-238, 2021 | e-ISSN 2280-6172 | DOI: 10.36253/bae-10488 Switching to, for instance, a QUAIDS to better cap- ture cross-price effects while also considering some addi- tional factors would introduce many new parameters in the estimator. The review of Ho et. al. 2020 of demand systems in CGEs mentions only one example (Jorgenson et al. 2013, a dynamic single country CGE for the US) where a rank 3 Translog demand system is used which gives also flexibility for coss-price effects, however for four aggregate expenditure groups, only, which are further dis-aggregated to more detail based on homothetic func- tions. Given the non-homothetic character of e.g. food expenditure groups above, a nested approach where the lower nests assume homotheticy is probably less appropri- ate for our exercise. Vigani et al. 2019 estimate a QUAIDS for Kenya with detail for food, but only mention that this can improve economic models without discussing how. It is also interesting to see that in their estimation, the QUAIDS gives for most product and product groups income elasticities quite close to unity. Their hierarchical demand system layout might render it hard to link their results into CGE models, especially if flexible aggregation with regard to commodity is maintained, as in case of the GTAP family of CGE models. Furthermore, given the often high correlation between prices and income levels in our cross-sectional data where time variability of prices is missing, it could be challenging to introduce a non-addi- tive demand system with full flexibility for price effects Several statistic packages allow estimation of a (non- linear) system with parameter restrictions. For highly non-linear specifications such as in here, convergence and feasibility issues with the solvers inbuilt in these packages are not uncommon. It is therefore not astonishing that all authors estimating (M)AIDADS systems (Reimer and Her- tel 2004, Preckel et al. 2010, Roson and Van der Mensbrug- ghe 2018, Britz and Roson 2019) rather use GAMS to access robust NLP solvers such as CONOPT. Estimating one of the more detailed systems in here requires up to 10 minutes of computing time using the parallelism of CONOPT4 on a fast four core machine. We consider a larger-scale boot- strapping exercise to determine the distribution of the parameters and p-values as not feasible. Arata and Britz 2019 propose instead to construct a Fisher information matrix by simulating the error terms at changed parame- ters. While this would be computationally feasible, we don’t consider that the additional coding efforts would help us in better assessing the choice of models. SUMMARY AND CONCLUSION We present an estimation of an extended MAIDADS demand system from global cross-sectional data. Exist- ing literature in this field is extended in multiple dimen- sions. Compared to Britz and Roson 2019 who use the same data set, we integrate the extension proposed by Preckel et al. 2010 to render the commitment terms depending on utility. In both Britz and Roson 2019 and Preckel et al. 2010, only prices and income are used as independents while we now also consider demographic factors, the share of Islamic population to control for religious norms and cultural habits, mean temperature to check for climatic influences and test if access to sea and the Gini coefficients have a systematic impact on consumption shares. According to our knowledge, this is the first time that the (M)AIDADS specification is extended in these respects. Compared to Reimer and Hertel 2003 or Preckel et al 2010, we also introduce more detail for food expenditure and render the func- tional form somewhat more flexible. We find that espe- cially demography, religious norms and temperature considerably improve the fit in our global cross-sectional analysis. We compare different model variants, con- sidering only one, two or three factors in combination compared to the base model and a variant with all fac- tors. Considering model selection statistics and the need to integrate estimates into long-run dynamic long run analysis with a CGE model, we opt for a version where demography, religious norms and mean temperatures are maintained as additional factors. Data selection and definition of food categories in here reflects our aim to integrate the estimates in a global dynamic CGE mod- el. We deliberately removed some detail for food avail- able from the underlying data set to render Hicksian substitution effects between groups less likely, to better motivate the use of an additive demand system. Sub- stitution effects are instead considered by CES nests in our simulation model. Our estimation has the potential to improve the representation of demand dynamics in global long-run analysis. Further work could introduce more detail in so far more aggregated consumption cat- egories such as the costs of housing. REFERENCES Arata, L., and Britz, W. (2019): Econometric mathemati- cal programming: an application to the estimation of costs and risk preferences at farm level, Agricultural Economics, 50(2): 191-206 Banks, J., Blundell, R., and Lewbel, A. (1997). Quadratic Engel curves and consumer demand. Review of Eco- nomics and statistics, 79(4), 527-539 Bennett, M.K. (1941). Wheat in national diets. Wheat Studies, 18(2), 37–76. 238 Wolfgang Britz Bio-based and Applied Economics 10(3): 219-238, 2021 | e-ISSN 2280-6172 | DOI: 10.36253/bae-10488 Britz, W., and Roson, R. (2019): G-RDEM: A GTAP- Based Recursive Dynamic CGE Model for Long- Term Baseline Generation and Analysis, Journal of Global Economic Analysis, 4(1): 50-96 Cranfield, J. A., Eales, J. S., Hertel, T. W., and Preckel, P. V. (2003). Model selection when estimating and pre- dicting consumer demands using international, cross section data. Empirical Economics, 28(2): 353-364. Cranfield, J. A., Preckel, P. V., Eales, J. S., and Hertel, T. W. (2000). On the estimation of ‘an implicitly addi- tive demand system’. Applied Economics, 32(15), 1907-1915. Deaton, A. and Paxson, C. (1998). Economies of scale, household size, and the demand for food. Journal of political economy, 106(5): 897-930 Gouel, C., and Guimbard, H. (2019). Nutrition transition and the structure of global food demand. American Journal of Agricultural Economics, 101(2): 383-403. Hanoch, G. (1975). Production and Demand Models with Direct or Indirect Implicit Additivity. Econometrica 43 (3): 395-419 Hertel, T.W. & Tsigas, M.E. (1997). Structure of GTAP, in: T.W. Hertel (ed.), Global Trade Analysis: Modeling and Applications, Cambridge University Press Hertel, T.W. & van der Mensbrugghe, V. (2019). Chap- ter 14: Behavioral Parameters, in: GTAP 10 Data Base Documentation, available at: https://www.gtap. agecon.purdue.edu/resources/download/9557.pdf Ho, M., Britz, W., Delzeit, R., Leblanc, F., Roson, R., Schuenemann, F. and Weitzel M. (2020). Modelling Consumption and Constructing Long-Term Base- lines in Final Demand. Under second review in the Journal of Global Economic Analysis Jorgenson, D., Richard G., Mun H. and P. Wilcoxen (2013). Double Dividend: Environmental Taxes and Fiscal Reform in the U.S., The MIT Press, Cambridge, MA. Liberati, P. (2015). The world distribution of income and its inequality, 1970–2009. Review of Income and Wealth, 61(2): 248-273 McDougall, R., and Golub, A. (2007). GTAP-E: A revised energy-environmental version of the GTAP model. GTAP Research Memoranda 2959. Center for Global Trade Analysis, Department of Agricultural Econom- ics, Purdue University Pollak, R. A., and Wales, T. J. (1978). Estimation of com- plete demand systems from household budget data: the linear and quadratic expenditure systems. The American Economic Review, 68(3), 348-359 Pew center (2011): The Future of the Global Muslim Population, available at https://web.archive.org/ web/20110202043556/http://pewforum.org/The- Future-of-the-Global-Muslim-Population.aspx Preckel P.V., Cranfield J.A.L., and Hertel T.W.A. (2010). Modified, Implicit, Directly Additive Demand Sys- tem. Applied Economics, 42(2):143–155 Reimer, J.J., and Hertel. T.W. (2004). Estimation of Inter- national Demand Behavior for Use with Input-Out- put Based Data. Economic Systems Research, 16(4): 347-66. Rimmer, M. T., and Powell, A. A. (1996). An implicitly additive demand system. Applied Economics, 28(12), 1613-1622. Roson, R. and van der Mensbrugghe, D., 2018. Demand- Driven Structural Change in Applied General Equi- librium Models. In The New Generation of Comput- able General Equilibrium Models (39-51). Springer, Cham. Seale, J.L., and Regmi A. (2006). Modeling International Consumption Patterns. Review of Income and Wealth, 52(4): 603-24. Sheth, J.N. (2017). Climate, Culture, and Consumption: Connecting the Dots. In The Routledge Companion to Consumer Behavior (14-18). Routledge Vigani, M., Dudu, H., Ferrari, E. and Causape, A.M. (2019). Estimation of food demand parameters in Kenya. A Quadratic Almost Ideal Demand Sys- tem (QUAIDS) approach (No. JRC115472). Joint Research Centre (Seville site). Volume 10, Issue 3 - 2021 Firenze University Press The Bioeconomy in economic literature: looking back, looking ahead Davide Viaggi1,*, Fabio Bartolini2, Meri Raggi3 The contribution of research to agricultural policy in Europe Alan Matthews Drinking Covid-19 away: wine consumption during the first lockdown in Italy Giulia Gastaldello*, Daniele Mozzato, Luca Rossetto Estimating a global MAIDADS demand system considering demography, climate and norms Wolfgang Britz The evolution of organic market between third-party certification and participatory guarantee systems Gianluca Iannucci1, Giovanna Sacchi2,*