# G-RDEM: A GTAP-based recursive dynamic CGE model for long-term baseline generation and analysis¶

This section is prepared by Roberto and Wolfgang Britz, drawing on: G-RDEM: A GTAP - Based Recursive Dynamic CGE model for Long Term Baseline Generation and Analysis, in: Bocconi Working Paper Series No. 105, April 2018,

## Background and introduction¶

Due to issues such as climate change and depletion of global resources, there is an increasing demand for long-term quantitative analyses. Computable General Equilibrium models can contribute in that direction as they consistently consider the manifold interrelations occurring in the economy, while providing the often needed sectoral detail. They therefore complement approaches working at the more aggregate level (e.g. Dellink et al. 2017) or focusing in detail on specific sectors (e.g. Alexandratos and Bruinsma 2012). On the other hand, it should be noted that CGE models were not originally designed to this purpose, but rather for short-term policy assessment, like simulating the effects of a fiscal reform, or the implementation of a trade agreement. Accordingly, most parameters are usually “calibrated” to a relatively recent Social Accounting Matrix or Input Output Table, such that the observed structure of an economic system is taken as a benchmark, from which counterfactual experiments are conducted

Of course, when the economy is analysed at a horizon of 20, 30 years, or even more, the economic structure as emerging from some past national accounts, which may refer to five years back, is no more a valid starting point. One should consider trends in structural adjustment, driven by changing preferences, demographic composition, new technologies, variations in the endowments of primary resources (including human capital), etc. The whole issue is not about forecasting: nobody actually knows which “breakthrough” technologies could emerge, or which unexpected phenomena could shape the economic structure in the future. What we do know from past observation is that a number of “slow” adjustment processes are active and therefore they should be taken into account in the generation of a credible and internally consistent future baseline.

The study of time evolution of the economic structure (“structural change”) is a rather active research field in theoretical and applied economics (Matsuyama, 2008). Most of the studies in the literature, however, look at the past. Typical research questions are: the contribution of the changing industrial mix to aggregate productivity (e.g., Duarte and Restuccia 2010); the declining share of the agricultural sector in developing economies (e.g., Üngör 2013), etc., where some specific transition processes are identified. Here, rather than studying the past, we aim at drawing from some empirical findings and methodologies in this literature to infer, inside a CGE modelling framework, a possible future evolution of the economy.

To this end, a number of “unconventional” features have to be introduced into the standard CGE formulation, to create a model specifically designed for the generation and assessment of long-term economic scenarios. We present therefore in here a newly develop CGE model of this kind, termed G-RDEM (GTAP based Recursive Dynamic Economic Model). This model considers drivers of long run structural change, which we regard as especially relevant, namely: (1) non-linear Engel curves in household consumption, (2) productivity growth differentiated by sector, (3) debt accumulation from foreign savings and trade imbalances, (4) aggregate saving rates linked to population and income dynamics, and (5) time-varying and income dependent industrial cost shares.

G-RDEM extends the flexible and modular CGE modelling platform CGEBox (Britz and Van der Mensbrugghe 2016), from which it inherits some important features. Firstly, the code is open source, to ensure transparency and invite the community of modellers to use the tool and contribute to its further development. Secondly, it maintains full flexibility in sectoral and regional aggregation. Thirdly, G-RDEM as a seamless integrated module in CGEBox offers the possibility to combine it with other modules such as CO2 and Non-CO2 emissions, GTAP-Water, GTAP-AEZ etc.. All new features are based on econometrically estimated parameters, thereby making the implementation fully documented and transparent. G-RDEM is encoded in the GAMS modelling language and, as a module of CGEBox, shares its graphical user interface

## Overview¶

The construction of a long-term baseline in CGE models typically draws on population and GDP projections from other studies. Indeed, a recursive dynamic CGE only considers capital accumulation as an endogenous mechanism driving growth, while productivity changes and other drivers of structural change are usually kept exogenous. In order to let a CGE model replicate a given growth path, a total factor productivity shifter is endogenously determined during the construction of the reference baseline, by fixing GDP at each time period. In subsequent model runs and counterfactual simulations, productivity parameters are then maintained at those estimated levels, while national income is endogenously computed.

This simple methodology aligns the output of the CGE model to a pre-determined aggregate growth path, but of course does not capture some fundamental structural changes which may take place in the economy, i.e. in the composition of output and demand. Instead, we aim in here to address the key elements driving such compositional change (Figure 4).

To this end, we introduce an AIDADS demand system to consider how budget shares in household consumption adjust to the changing levels of per capita income, to capture “non-linear Engel curves”, which are a salient feature of economic development. Secondly, the economy wide total factor productivity (TFP) shifter, aligning the model to the target GDP in any period, is here differentiated by sector. These two features are introduced through specific equations directly into the CGE framework itself (red boxes in Figure 1). Other elements are activated in between the solution points (blue boxes). Therefore, the intra-periodal equilibrium computed by the model, in combination with exogenous projections from the current period t, updates some parameters for the following period t+1. The labour force (by skill category) is adjusted to population and work force projections. Next year’s capital stocks reflect last year’s ending stocks and gross investments. International capital transfers reflect past foreign savings. Saving rates adjust to population and GDP growth, and I-O coefficients (factor shares in production processes) are updated on the basis of national income.

Figure 4: Overview of the recursive-dynamic modelling framework G-RDEM

The process thus requires some exogenous projections for GDP and population. G-RDEM offers the possibility to draw on a set of projections for the so-called SSPs (Shared Socio Economic Pathways) (Riahi et al. 2016), available online from the IIASA Shared Socio Economic Pathways Database.[^9] These SSPs were developed in the context of the IPCC scientific assessment on Climate Change. For each of these five SSPs, a single population and urbanization scenario, jointly developed by IIASA and NCAR (National Center for Atmospheric Research), can be combined with GDP projections from either the OECD or IIASA. These GDP and population projections are available in 5-year steps up to 2100, at a single country basis. They are aggregated in G-RDEM to the desired regional aggregation level and interpolated to yield yearly time series. They can also be complemented by Climate Change impacts on yields for a set of RCPs (Representative Concentration Pathways) and various combinations of GCMs (Global Circulation Models) and global gridded growth models provided by the AgCLIM50 project (van Meijl et al. 2017).

A user might also add its own scenario assumptions during the construction of the baseline, such as about trade policies or alternative GDP projections. After the definition of the baseline, the software saves the resulting productivity shifters and other variables, which can subsequently be loaded as exogenous parameters for counterfactual analysis. The set of results from the baseline can also be directly employed, to get a much disaggregated definition of the economic scenario.

## Non-linear Engel curves: An AIDADS demand system with detail for food consumption¶

### Background¶

It is universally acknowledged that the relationship between consumption level and income (also known as Engel curve) can be complex and non-linear. Yet, many CGE models still adopt demand systems such as Cobb-Douglas (CD) or Linear Expenditure System (LES), having linear Engel curves. Those simplifying assumptions make the model easier to handle, but are defendable only if the model is used for simulations involving limited changes in income levels. Of course, this is not the case for long-term analyses. Keeping constant marginal budget shares would lead to an overestimation of the demand for necessities, such as food, while demand in other sectors will hence be underestimated. The consequences are implausible long-run structural changes in production, demand, and trade patterns. Some models employed for long-term analysis therefore use different demand systems and/or re-parameterize along the dynamic path. For instance, MAGNET (Woltjer et al. 2014, p. 84) incorporates a module for re-calibrating the parameters of a CDE (Constant Differences in Elasticity) demand system to given income elasticities. Nonetheless, the authors admit: “All of these parameters and functional forms are very much ad hoc, and should be improved.”.

Following Roson and van der Mensbrugghe 2018, we rather implement an empirically estimated AIDADS demand system into the G-RDEM model, for broad product groups. The AIDADS is An Implicit, Directly Additive Demand System (Rimmer and Powell 1996). It can be understood as a generalization of a LES demand system, where marginal budget shares are not fixed, but are a linear combination of two vectors, depicting the marginal budget structure at very low and very high utility (income) levels. Given that the marginal budget shares in the two vectors fulfil the adding up condition to unity, any linear combination of the two vectors also leads to regular budget shares. In order to improve the detail inside the agri-food sector, we also took econometric estimates of income dependent marginal expenditure shares for food categories from Muhammad et al. 2011, and incorporate them in the AIDADS framework.

Cranfield et al. 2000 improve on the original Rimmer and Powell 1996 approach, by developing an estimation method that does not rely on an approximation of utility. We follow their notation in the following. The demand system is defined below. Equation (1) determines the Marshallian demand, which is similar to that of a LES. Here, however, the marginal budget shares are endogenous variables, defined by (2), expressed as a linear combination of two vectors α and β, function of the utility level u, implicitly defined by (3).

    (1)


    (2)
(3)


3.2 Estimation and integration into modelling framework

We first econometrically estimated α, β, γ und u using data from the International Comparison Program ICP 2015, for ten broader expenditure categories (food, beverages and tobacco, clothing, housing, furniture, transportation, recreation, communication, health, education). The integration in the CGE model requires mapping the parameter estimates to the commodity resolution of the model. In order to get more detail for food demand, we combined estimates by Muhammad et al. 2011, taking their estimated marginal budget shares for the five lowest and highest income observations as proxies for the vectors α and β.

The demand system is calibrated against the benchmark data of regional household consumption, from the GTAP v.9 data set. To this purpose, we regressed the utility levels u from our findings to total per capita consumption expenditure Y in each region. That allows us to estimate (from (2)) the marginal budget shares in the calibration point. We then discarded the previously estimated γ and instead solve (1) for γ at given x, Y, p and the calibrated marginal budget shares. In the case that this implies a negative γ, we use a penalty minimization approach, which minimizes the difference between the estimated α, β and the “corrected” ones, such that all γ turn out to be positive.

### Technical implementation of the AIDADS demand system¶

#### Equations¶

Due to its resemblance with the LES system, which was already available in CGEBox, the code is a direct extension of the existing code both for the calibration to the benchmark and implementation of the demand system in the model’s equation (see model\cal_les.gms and model\dem_les.gms).

The demand equations for both systems are indeed identical:

The demand is equal to a constant term gammaLES per head multiplied with population plus the marginal budget share times the non-commited income yCNonCom, divided by the Armington price index for the private household aggregate, defined in the macro m_pa.

The non-committed income is the difference between the given expenditures for final consumption and the value of the commitments:

We allow for demand nests which are CES aggregates of other nests or individual commodity demands. In the case of AIDADS, the marginal budget shares alphaLES are not fixed (as in the LES), but are a function of utility:

The two vectors alphaAIDADS and betaAIDADS are the limiting cases for the marginal budget shares at very low and very high utility levels. The utility of the (representative) private household is set at one in the benchmark. In order to line up with the empirical implementation (see next section), the parameter p_uh0 is introduced. Cardinal utility is thus defined as follows:

where p_uh1 is an additional parameter in the demand system (corresponding to the parameter A in Cranfield et al. 2000, see their equation (10)). Note the equivalence of the utility definition to the one in the LES system: only consumption quantities exceeding the commitments gammaLES generate utility.

#### Calibration¶

The calibration code can be found in “model/cal_les.gms”. The estimated parameters are inserted as a table in the code:

We add to these estimates the marginal budget shares obtained by the Economic Research Service of the United States Department of Agriculture (https://www.ers.usda.gov/data-products/international-food-consumption-patterns/, see Muhammad et al. 2011). We take the five lowest and five highest per capita countries in their sample, to derive the marginal expenditure shares for food categories at low and high income, relative to expenditure on food:

The entries for “cereals” and “food_other” for the low income case where manually corrected to consider that the estimates refer to functional groups, where cereals also comprise, e.g. bread.

Integration into a GTAP model with flexible sectoral aggregation requires a mapping from these categories to the current sectors in the model. That is achieved in two steps:

The commodity groups from the AIDADS estimation and from Muhammad et al. 2011 are mapped to the 57 GTAP sectors (non-aggregated):

We link the estimates from Roson and van der Mensbrugghe 2018 of marginal budget shares relating to total final consumption by private households to the marginal expenditures from the ERS estimates relating to food expenditures as follows:

Next, the mapping mapi from the 57 GTAP sectors to the current aggregation is used to assign parameters to the commodities, as defined in the current run:

Note that the aggregation might define an intersection such that, for some aggregates, the original sectors comprised belong to multiple estimation groups. Using the benchmark consumption shares as weights corrects for that In order to ensure that both vectors fulfil the adding up condition exactly, they are then scaled to unity:

The cardinal utility level, which drives the marginal budget composition, is an estimated parameter. To this end, Roson and van der Mensbrugghe 2018 regress the estimated utility levels on real GDP per capita. Their regression results are here employed to derive the utility level at the benchmark and thus the marginal budget shares:

The obtained marginal budget shares are then used to define the commitment terms. The code is not shown here as it was already comprised in CGEBox code and it is illustrated in the associated documentation.

Whenever that calibration procedure becomes infeasible, some deviations from the given alphas and betas are allowed:

Minimizing the squared relative differences in the objective function:

Finally, a multiplier (termed A in Cranfield et al. 2000, eq 10 ) is calculated:

The code allows introducing aggregates of individual commodities under which CES-sub-nests can be defined, which comprise these individual commodities.

Table 4: Mapping between AIDADS categories and GTAP sectors

AIDADS category GTAP 9 sector Detailed description
Cereals pdr Paddy Rice: rice, husked and unhusked
wht Wheat: wheat and meslin
gro Other Grains: maize (corn), barley, rye, oats, other cereals
pcr Processed Rice: rice, semi- or wholly milled
Meats Ctl Cattle: cattle, sheep, goats, horses, asses, mules, and hinnies; and semen thereof
Other Animal Products: swine, poultry and other live animals; eggs, in shell (fresh or cooked), natural honey, snails (fresh or preserved) except sea snails; frogs' legs, edible products of animal origin n.e.c., hides, skins and furskins, raw , insect waxes and spermaceti, whether or not refined or coloured
oap Cattle Meat: fresh or chilled meat and edible offal of cattle, sheep, goats, horses, asses, mules, and hinnies. raw fats or grease from any animal or bird
Other Meat: pig meat and offal. preserves and preparations of meat, meat offal or blood, flours, meals and pellets of meat or inedible meat offal; greaves
cmt
omt
Fish fsh Fishing: hunting, trapping and game propagation including related service activities, fishing, fish farms; service activities incidental to fishing
Dairy Rmk Raw milk
mil Milk: dairy products
Oils_Fats Osd Oil Seeds: oil seeds and oleaginous fruit; soy beans, copra
vol Vegetable Oils: crude and refined oils of soya-bean, maize (corn),olive, sesame, ground-nut, olive, sunflower-seed, safflower, cotton-seed, rape, colza and canola, mustard, coconut palm, palm kernel, castor, tung jojoba, babassu and linseed, perhaps partly or wholly hydrogenated,inter-esterified, re-esterified or elaidinised. Also margarine and similar preparations, animal or vegetable waxes, fats and oils and their fractions, cotton linters, oil-cake and other solid residues resulting from the extraction of vegetable fats or oils; flours and meals of oil seeds or oleaginous fruits, except those of mustard; degras and other residues resulting from the treatment of fatty substances or animal or vegetable waxes.
Fruits_vegs v_f Veg & Fruit: vegetables, fruitvegetables, fruit and nuts, potatoes, cassava, truffles
Other Crops: live plants; cut flowers and flower buds; flower seeds and fruit seeds; vegetable seeds, beverage and spice crops, unmanufactured tobacco, cereal straw and husks, unprepared, whether or not chopped, ground, pressed or in the form of pellets; swedes, mangolds, fodder roots, hay, lucerne (alfalfa), clover, sainfoin, forage kale, lupines, vetches and similar forage products, whether or not in the form of pellets, plants and parts of plants used primarily in perfumery, in pharmacy, or for insecticidal, fungicidal or similar purposes, sugar beet seed and seeds of forage plants, other raw vegetable materials
ocr
Food_other c_b,sgr,ofd
Cothing tex Textiles: textiles and man-made fibres
wap Wearing Apparel: Clothing, dressing and dyeing of fur
lea Leather: tanning and dressing of leather; luggage, handbags, saddlery, harness and footwear
Wool: wool, silk, and other raw animal materials used in textile
wol Plant Fibres: cotton, flax, hemp, sisal and other raw vegetable materials used in textiles
pfb
Housing dwe Dwellings: ownership of dwellings (imputed rents of houses occupied by owners)
obs Water: collection, purification and distribution
wtr Gas Distribution: distribution of gaseous fuels through mains; steam and hot water supply
gdt Electricity: production, collection and distribution
Coal: mining and agglomeration of hard coal, lignite and peat
ely Oil: extraction of crude petroleum and natural gas (part), service activities incidental to oil and gas extraction excluding surveying (part)
coa Gas: extraction of crude petroleum and natural gas (part), service activities incidental to oil and gas extraction excluding surveying (part)
oil Insurance: includes pension funding, except compulsory social security
gas
isr
Furniture, Maintenance, appliances p_c Petroleum & Coke: coke oven products, refined petroleum products, processing of nuclear fuel
Forestry: forestry, logging and related service activities
frs Other Mining: mining of metal ores, uranium, gems. other mining and quarrying
omn Lumber: wood and products of wood and cork, except furniture; articles of straw and plaiting materials
Chemical Rubber Products: basic chemicals, other chemical products, rubber and plastics products
lum Non-Metallic Minerals: cement, plaster, lime, gravel, concrete
Iron & Steel: basic production and casting
crp Non-Ferrous Metals: production and casting of copper, aluminium, zinc, lead, gold, and silver
Fabricated Metal Products: Sheet metal products, but not machinery and equipment
nmm Construction: building houses factories offices and roads
i_s Electronic Equipment: office, accounting and computing machinery, radio, television and communication equipment and apparatus
nfm Other Machinery & Equipment: electrical machinery and apparatus n.e.c., medical, precision and optical instruments, watches and clocks
Other Manufacturing: includes recycling
fmp
cns
ele
ome
omf
Transport Otp Other Transport: road, rail ; pipelines, auxiliary transport activities; travel agencies
Water transport
wtp Air transport
atp Motor Motor vehicles and parts: cars, lorries, trailers and semi-trailers
mvh Other Transport Equipment: Manufacture of other transport equipment
nsurance: includes pension funding, except compulsory social security
otn Petroleum & Coke: coke oven products, refined petroleum products, processing of nuclear fuel
Isr
p_c
Communication cmn Communications: post and telecommunications
Recreation ros Recreation & Other Services: recreational, cultural and sporting activities, other service activities; private households with employed persons (servants)
Paper & Paper Products: includes publishing, printing and reproduction of recorded media
ppp
Education osg Other Services (Government): public administration and defense; compulsory social security, education, health and social work, sewage and refuse disposal, sanitation and similar activities, activities of membership organizations n.e.c., extra-territorial organizations and bodies
Health Osg See above
Restaurants and hotels Trd Trade: all retail sales; wholesale trade and commission trade; hotels and restaurants; repairs of motor vehicles and personal and household goods; retail sale of automotive fuel
Rest Other Financial Intermediation: includes auxiliary activities but not insurance and pension funding (see next)

## Differentiated productivity growth¶

### Background and literature review¶

Productivity does not vary uniformly among industries and sectors. Harberger 1998 points out that the whole dynamics of economic progress actually resembles the growth process of “mushrooms”, rather than the steady rise of “yeast”. Indeed, differential productivity growth is one key factor of structural change in the economic systems, and probably the most important one (Swiecki 2017). Several implications of different growth rates have been investigated in the literature, e.g.: relevance and empirics of the so-called “Baumol's disease” (Baumol 1986, Triplett and Bosworth 2003, Young 2014); specialization and international trade (McMillan and Rodrik 2011, Caron and Markusen 2014); “premature deindustrialization” (Rodrik 2016).

To introduce differentiated productivity growth in the G-RDEM model, we build on Roson 2018, who estimated trends in labour productivity, using the Groeningen GGDC 10-Sector Database (de Vries et al. 2015). In that study, some trends and country specific dummies for labor productivity (VA/employment) are estimated. Results are subsequently employed in a cluster analysis, where three groups of countries with similar characteristics are identified. Table 5 below shows some of the findings used to obtain parameters for G-RDEM:

Table 5: Average labour productivity growth rates

Cluster AGR MAN SER TOT

Rising 6.23 11.43 5.65 8 Steady 7 7.88 5 5.93 Lagging 5.17 5.32 2.34 3.16

Source: Roson 2018

The last column in Table 1 (TOT) displays the average (yearly) growth rate in labor productivity in each group. It refers to value added per worker or hour, so it accounts for capital deepening and similar effects. Interestingly, the differences among industries depends on how fast an economy is growing.

### Estimation of differentiated productivity growth¶

In the development of the G-RDEM model we are not concerned about labour productivity in itself, but rather on the relative differences among the three broad sectors of Agriculture, Manufacturing and Services. To this end, a correspondence between the three clusters and the annual GDP growth rates used in the SSPs was established. The distribution of IIASA SSP data (OECD) on GDP was considered, and it was assumed that the average GDP growth in the Lagging group of countries corresponds to the 20% percentile of the SSP distribution, 50% for Steady, 80% for Rising. This means 1.2%, 2.5%, and 4.9%, respectively.

Second, the ratio of each sector productivity rate, relative the slowest growing sector, which is Services, was computed. Third, for each industry a quadratic interpolation between the three multipliers and the references GDP growth rates was undertaken, thereby getting three parameters of a quadratic polynomial relationship between a sectoral productivity shifter (ratio between industry growth rate and the corresponding one in the Services) and GDP annual growth. This gives raise to the functions displayed in Figure 5.

Figure 5 : Productivity growth relative to GDP growth

The key finding is that productivity differentials are minimized (although still significant) at a moderate GDP growth of around 2%. For higher or lower rates, we can see that differences amplify, with manufacturing becoming the key sector. Notice that the shifter is a multiplier: if aggregate growth is negative, it will likely become negative for the reference slow sector as well. When the shifter for Manufacturing is high and positive, this means that productivity is decreasing there more than in the rest of the economy. In other words, productivity growth in Manufacturing appears as strongly correlated with the aggregate productivity growth, which suggests the existence of inter-sectoral externalities.

Implementation in G-RDEM is straightforward. Total factor productivity in the Services tfp® becomes endogenous during the construction of the baseline and is kept then fixed during counterfactual simulations. Total factor productivity for other sectors (indexed by i) in region r at time t+1 are defined as tfp®*sh (i,r), where the latter is determined by equations like:

(4)

Here are the estimated values for the three parameters a, b and c:

Table 6: Estimated parameter for sector specific productivity growth

    AGR        MAN


a 0.925391 2.893917 b 11.99205 -94.8599 c 291.8147 1680.554

### Implementation of the sector specific productivity shifters¶

The production shifter equation derives from the economy wide, regional specific ftp shifter axpreg sector specific shifters axp based on the quadratic function as detailed above (see model.gms):

The parameters are derived from estimates in “GTAPRDEM\diffProdGrowth.gms”:

Which requires a mapping from the original GTAP sectors iOri to the currently active sector aggregation defined in the same program, of which here only an extracted part is shown:

## Endogenous saving rates¶

### Background and literature ***r***eview¶

We aim at developing a simple but robust mechanism to render aggregate saving rates in G-RDEM endogenous. One strand of literature, relying on cross-country differences of saving rates (e.g. Kisanova and Sefton 2007), works with micro-economic survey data. It explicitly accounts for factors such as demography, welfare state, retirement behaviour, borrowing constraints, income distribution over a lifetime and its uncertainty, as well as capital gains. The focus here is on the life-cycle hypothesis, which considers the change in available income over a lifetime. While these papers give robust evidence that the factors indeed explain the saving behaviour of individuals or households, they typically offer results only for one or a smaller group of countries.

Rather, we draw here on studies which employ cross-sectional analyses over countries to evaluate the factors affecting the economy-wide aggregate saving rates. Most of these works also take the lifecycle hypotheses into account (although indirectly) and find that even in cross-country analyses larger proportions of the young and the elderly compared to persons in working age (dependency ratios) generally decrease the saving rate (Doshi 1994, Masson et al. 1998, Laoayza et al. 2000).

### Estimation¶

Instead of directly using parameter values from the literature, we carry out our own cross-section estimation, using GTAP 9 and other data used in our modelling framework, to overcome any potential divergence in definitions, measurement units etc.. The reader might note that we face a potential endogeneity issue: higher rates of GDP growth require increased capital accumulation, thus larger net investments and consequently higher saving rates. The saving rate and GDP growth are hence structurally dependent. However, this is not an issue of major concern in this context, since we are not integrating the estimated equation into the model, but only updating saving rates, given GDP projections. Hence, our aim is solely to ensure that correlation, not causation, is properly accounted for. Notice also that we obtained our estimates from a sectional data base, which would make it impossible the introduction of lagged variables as instruments.

The distribution of the national aggregate saving shares in the GTAP 9 data set reveals a large spread, as shown in the Figure 6. We regressed those saving rates with OLS against the following explanatory variables:

1. Population composition by age group from the IIASA repository for 2010 (Lutz et al. 2017)

2. GDP growth per capita from 2010 to 2011, in PPPs, from the OECD Env. Growth Model data base as found in the IIASA repository

3. Foreign savings (trade balance) relative to regional income, from the GTAP 9 data base

4. We also tested, as a potential explanatory variable, the share of government consumption on regional income, but did not find a statistically significant relation.

Figure 6 : Distribution of aggregated savings rates in GTAP 9

We found a very good fit for our sectional analysis, with a R2 at 92% and all variables (with the exemption of the young dependency rate) statistically significant at <0.1%. The young DR is nonetheless significant at the 5% level. All variables have the expected sign: dependency ratios decrease the saving rates, as postulated by the life cycle hypothesis, while a higher income per capita and a higher growth rate increase the saving rate. A positive trade surplus (i.e. negative foreign savings) also tends to increase the saving rates.

Table 7: Regression output for saving rate estimation

Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 0.2584670 0.0587350 4.401 2.22e-05 *** gdpGrowth 2.2080586 0.3902076 5.659 9.18e-08 *** GDPperCAP 0.0010213 0.0003523 2.899 0.00439 ** age_depOldSqrt -0.3640043 0.0792999 -4.590 1.02e-05 *** age_depYoungSqrt -0.1454039 0.0562902 -2.583 0.01089 * savfToRegy -0.9674676 0.0473476 -20.433 < 2e-16 *** savfToRegy2 0.3347001 0.0676960 4.944 2.30e-06 ***

Signif. codes: 0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1

The good fit of the regression stems to a large degree from the inclusion of foreign savings relative to regional income, i.e. a trade surplus indicator, (see Table 4 below), while the contributions of the dependency ratios and GDPperCAp are in a similar range, with GDP growth trailing.

Table 8: Analysis of Variance for saving rate estimation

Response: betas Df Sum Sq Mean Sq F value Pr(>F) gdpGrowth 1 0.0001 0.0001 0.0287 0.8658 GDPperCAP 1 0.5271 0.5271 151.7686 < 2.2e-16 *** age_depOldSqrt 1 0.5092 0.5092 146.6187 < 2.2e-16 *** age_depYoungSqrt 1 0.3712 0.3712 106.8974 < 2.2e-16 *** savfToRegy 1 3.8306 3.8306 1103.0480 < 2.2e-16 *** savfToRegy2 1 0.0849 0.0849 24.4447 2.297e-06 *** Residuals 131 0.4549 0.0035

Some scatter plots (visualizing the ANOVA results above) between the explanatory variables and the saving rate are shown below in Figure 7.

Figure 7 : Scatter plots of explanatory variables against the saving rate

The high contribution of the relation between foreign savings and regional income is not astonishing, because it controls for cases such as oil exporting countries (high saving rates) as well as some other countries, often developing ones, with very low saving rates. The foreign saving indicators can be hence rather understood as a control variable for country specific unobserved features (large receiver of development aid in a group a country with otherwise similar macro-economic indicators, rich oil and gas reserves, tax havens …). Accordingly, we do not use changes in the foreign savings during the process of baseline construction, to update the saving rates.

Figure 8 : Fitted against observed saving rates, GTAP region codes as labels

Note that the fitted values cannot be used as such, since we would then neglect any unexplained additional factors, which could imply large changes in the saving rates from the benchmark to subsequent simulation periods in some countries. Thus, we use relative changes in the estimates – neglecting foreign saving – to update the saving rates used in the model.

### Implementation of the endogenous saving rates¶

The GAMS code does not use the estimated intercept, but rather updates over the simulation horizon the “betas” for the individual countries in terms of the difference between two consecutive time periods.

That restrict the application to simulation exercises where a projection of the population by age group is available. Given that the IIASA repository features these projections for SSP1-SSP5, we suggest to use one of these SSPs population scenarios directly, or at least the projected age composition.

## Debt accumulation from foreign savings¶

Accounting identities in the model ensure (for each time period) that the sum of regional and foreign savings in each region equals gross investments, while foreign savings are equal to the foreign trade deficit. The latter is determined, in the GTAP model (Hertel and Tsigas 1997, Corong et al. 2017), which defines the intra-periodal equilibrium in G-RDEM) by the mechanism of regional allocation of investments. It turn, this is based on a distribution of global savings, driven by relative expected returns on capital, as it is briefly illustrated in the following.

Let denote the price of a homogeneous capital factor (services) as and as the price of investments (the cost of producing one unit of new capital good), κ the tax rate on capital earnings, fdepr the depreciation rate. The net rate of return in a region r (rorc) is defined in the GTAP model as:

    (5)


The expected rate of return rore takes into account the difference between start and end of period capital stocks, and . The logic is that investors should become more cautious when aggregate investments lead to large changes in capital stocks:

    (6)


The parameter rorFlex (whose default value is 10 for all for regions) dampens the relative differences in expected returns, thereby avoiding the generation of unrealistically large flows of (real) capital in international markets. In addition, a regional risk factor is introduced, to ensure that an arbitrage condition for the international investor holds in the calibration data set, meaning that a single global, risk-adjusted return rorg is identified:

    (7)


The condition (7) holds in all periods in G-RDEM, where rorg and rore are endogenous variables. Therefore, the relationships above drive the distribution of foreign savings fsav or, equivalently, the amount of investments in each region (which do not generally match with regional savings).

The global investor hence expects equal returns of rorg on his savings in any region. Accordingly, the returns in year t from foreign savings add up to zero as, by construction, the global economy is closed, and total investments equal total savings (equivalently, the global trade balance is zero):

    (8)


to keep track of the foreign debt dynamics, we assume that regions, which receive foreign savings (fsav > 0), will pay in any consecutive year the expected returns to their foreign debtors, while investing regions (fsav < 0) will be paid back:

    (9)


The interest payments on the stock of foreign debt enter the equation defining the regional income regy, in addition to the factor income facty and the indirect tax income yTaxInd,:

    (10)


A practical issue emerged when the mechanism above was applied to some special cases, where foreign savings account for a large share of investments or total final consumption. Examples are some developing countries, receiving large amounts of development aid or remittances, but also “tax havens” such as Malta. In such cases, we noticed that the mechanism above can lead, after some periods, to a situation where regional income gets unrealistically small. To avoid such extreme cases, while allowing for the existence of capital inflows or outflows determined by factors other than expected returns, we introduced a regional share parameter, such that only part of the debt may actually be served (see the Technical Annex for more details).

### Implementation of foreign debt accumulation¶

The debt accumulation is a more or less straightforward translation of the equations discussed in the main text into the GAMS code.

Note the scaling of p_capTrans to ensure the global expenditures to serve the debt and related revenues add up to zero.

### Background and literature review¶

If preferences are a function of income per capita, reflected in non-linear Engel curves, then the portfolio of products offered by the economy clearly changes. As Chenery et al. 1986 put it “On the demand side, a rise in income can only be sustained if the goods and services made available correspond to the proportions in which consumers wish to spend their income”. We already addressed this issue for the final demand through the introduction of an AIDADS demand system, but further adjustments are in order on the production side, to account for income-dependent variations in intermediate demand. Indeed, an often neglected aspect in CGE and input-output models is that industries internally include many diverse production processes, characterized by different technologies. Variations in demand patterns therefore occur not only between the macro-industries, but also inside them: aggregate industrial cost structures should be better interpreted as reflecting the internal composition of a sector, rather than describing the production function of a representative firm. Consequently, input-output coefficients can well evolve over time, following changes in income, prices, foreign trade, demography, etc., in a way not too different from the one affecting household final consumption.

Already Arrow and Hoiffenberg 1959 decomposed changes in input-output coefficients into variations due to real disposable income and variations due to technology and tastes. Skolka 1989 provides a structural decomposition analysis for Austria along these lines, thereby explicitly considering that I-O coefficients are not static, but actually change along the process of economic development. This contrasts with the approach followed in most dynamic CGE models, where changes in the industrial cost shares are only attributed to two causes: non-Hicksian technological progress and changes in relative prices.

To illustrate the point, consider the case of distributional services (retail trade and wholesale trade), which are a separate sector in input-output tables and SAMs. A large share of final demand expenditures of households is accounted there. However, those expenditures relates to purchases of food, clothes and other goods, all of which are accounted for separately in most household surveys, and are very likely characterized by significant differences in income elasticity. As a consequence, any shift in the pattern of household consumption should bring about a change in the structure of intermediate demand for the services sector.

We conclude that I-O coefficients should be not be considered as static in the long-term. Since the model already accounts for price-induced compositional changes in intermediate demand, and possibly Hicksian non-neutral technical progress, we concentrate here on the issue of modelling income-related variations.

### Econometric analysis¶

Our basic hypothesis is that I-O coefficients are income dependent, likewise final consumption shares. To estimate the relationship with income, however, we adopt a different strategy. This is because time series consistent with the GTAP industrial classification are not available, and input-output tables are limited. We thus test our hypothesis using a sectional approach, using again the GTAP 9 data base. To keep the analysis manageable, we first aggregated to 10 sectors, while keeping the maximum spatial detail of 140 countries and regions. We then regressed the intermediate input-output coefficients on the log of per capita income in each country, including only data entries with a median cost share of at least 1%. This leaves 65 coefficients out of the potential 100, i.e. 10 sectors times 10 commodities.

Since part of the demand stems from abroad, we constructed (for each sector) a GDP-per-capita index for the average “buyer”, as a weighted average of domestic GDP per capita and GDP per capita in export destinations, taking domestic and export sales as weights.

If input-output coefficients change in the process of economic development, we should find regression coefficients relating to per capita income with a low significance level of being zero. The distribution of these probabilities is plotted in Figure 9. Out of the 65 coefficients with a cost share of at least 1%, more than 40 displays have probabilities below 1% of being zero which supports the assumption that they have a relation with per capita income.

Figure 9: Distribution of significance levels of the regression coefficient between the IO-coefficients and GDP per capita being zero

We conclude from the analysis that fixing the I-O coefficients in long-term analysis hence will mostly likely over-estimate the intermediate demands for product groups with lower income elasticity and vice-versa. The actual estimation procedure uses a Mean-Absolute Deviation as a robust estimator, which is not very sensitive to outliers. It uses sectoral output as a weight, assuming that larger sectors are statistically better monitored and reported.

### Implementation of dynamic I-O and factor share coefficients¶

A similar approach is used to simulate possible changes in:

1. I-O coefficients

2. I-O coefficients in technology nests

3. The intermediate composite share

The estimated relationship links the I-O coefficients in the different sectors to per capita income, using production output as weight:

Using production output as weight should prevent that outliers from small sectors with suspicious values dominate the estimation outcome.

The resulting estimates are used to update the I-O coefficients:

Similar statements estimate and apply shifters for the other elements.

## Steering of G-RDEM model runs¶

The screenshot presented in Figure 10 below shows how the user can select which data base aggregation to use, decide the time horizon of the baseline as well as the report frequency. For instance, retaining the flexible aggregation approach from GTAP in G-RDEM allows the user to develop a long-term baseline with a focus on only one country, while aggregating the rest of the world into a single aggregate. So far, the G-RDEM module has been tested with resolution with up to 80 countries.

Figure 10 : Main steering panel of CGEBox

The set of years to run will always include the benchmark (t0), the last year (eq card(t)) and the first year of the simulation period, which can be used e.g. for estimations from the initialized variables.

For the above input, the resulting years to run are:

In order to construct the baseline, the user selects (Figure 11) the desired SSP scenario for population and GDP, as well some procedural modules to use.

Figure 11 : Main steering panel of the G-RDEM module in CGEBox

## Population and GDP growth from the IASSA SSPs¶

IASSA host a web application (http://www.iiasa.ac.at/web/home/research/researchPrograms/Energy/SSP_Scenario_Database.html) which gives access to model results relating to the IPCC model activities comprising GDP growth rate projection by country from a range of models and for different Shared Socio-Economic Pathways (SSPs). Some if GDP projections were downloaded in XLSX format and converted into a GDX container. That container is read by the driver program:

The labels for the country follow the same codes as for the UN population projections. As seen from above, the projections are not yearly, but by decade. In order to use them flexible with different time steps, the code first interpolates linearly between given time points:

The mapping to the regional aggregate used in CGEBox is structural identical to assigning the population projections:

For some countries, notably small islands, no projections are available. In these cases, global unweighted averages are used instead.

For use in the model, per capita growth is used:

## Using the G-RDEM generated baseline for counterfactual analysis¶

Besides analysing the baseline itself or comparing different baselines against each other, they also might serve as starting point for some counterfactual analysis. Two types of simulations are currently supported in the CGEBox platform. The first one uses the shifters generated during the baseline construction (changes in saving rates, productivity shifters, updated I-O coefficients), as well as population projections, as given parameters into a recursive-dynamic simulation. That would make only sense if the structural set-up of the model is unchanged (production function nesting, bi-lateral trade, etc.). During such a run, GDP would no longer be fixed, but endogenous and, as usual, shocks can be introduced, such as changes in policies or productivity, like climate change impacts on agricultural yields. Parameter estimates for some impacts (like those of climate) are already available in CGEBox and can be readily inserted during the simulation runs, by means of the graphical interface.

The second type of possible utilization of G-RDEM is in the provision of input data for comparative-static analysis. In this case, the global SAM and parameters for one of the simulated time points could be loaded as a replacement for benchmark data from GTAP. The full modular flexibility of CGEBox could then be exploited, allowing to modify several characteristics of the model. That approach might be also interesting to produce not a long-run, but a rather a medium-term baseline as an ex-ante benchmark, which is for instance the usual practice in partial equilibrium modelling of agri-food markets.

The first option is to use the G-RDEM module in non-baseline generation mode:

In the case, the user can select the baseline results to employ. That will load the necessary shifters and exogenous parameters into the GAMS code:

We have checked that without additional shocks, the existing baseline will be recovered without that GDP is fixed.

The second option requires that during baseline generation, altertax output is activated:

That will output the SAM and other information required for a benchmark calibration of the model are stored in “build” directory:

These benchmark data can be used similarly to the output from the data preparation step. If the user wants to use the specific module, which requires additional information (AEZ, CO2 and Non-CO2 emissions, NUTS2), these modules must have been selected during the generation of the baseline. The data can therefore be chosen as a starting point for comparative (or even recursive-dynamic) analysis:

That makes the layout of the model fully adjustable (e.g., by adding myGTAP for several household types, a different production nesting, changes in how bi-lateral trade is modelled).

## Specific nestings in G-RDEM¶

We add some specific nestings for the production function (see gams\gtaprdem\gtaprdem.gms):

GTAP-AGR has proven to work badly with some long-term projections, because of limited factor mobility between agricultural and non-agricultural sectors. Therefore, only the technology nests from GTAP-AGR are taken over:

In order to reflect stronger substitutional relations between animal and crop based products, two final demand nests are constructed:

## Endogenous non-Hicks neutral technical progress, primary factors depending on population growth and price dependent factor supply¶

In addition to price driven changes in endowments, the marginal productivity can also be rendered price dependent. In the default setting, the labour force is reacting to population changes fully, while land, irrigation water and natural resources follow to a limited extend (positive changes) in population. The other element are by default switched off.

The input from the GUI is mapped to the following symbols in the GAMS code:

We also take changes in education levels into account:

The population and factor price shifters are implemented as follows:

The resulting technical progress changes are calculated as follows:

## Analysis of G-RDEM simulation output (exploitation)¶

Loading all results from long time recursive dynamic with detailed global SAMs might require amounts of memory exceeding most personal computer configurations. Therefore, the exploitation selection allows to pick up only a few years for inspecting the results. Therefore, while all output variables are stored in the GDX repository output file, only the selected ones will be loaded into the memory.

Generally, any view existing in the exploitation tool can be changed to a time series using the pivot facility. In order to ease the exploitation, three views have been pre-configured, under the heading “Time series”:

The first one reports changes in GDP, price indices etc:

The second one focuses on the demand side:

The third one reports production quantities and related input demands:

## Computing and data base considerations for G-RDEM runs¶

Compared to a comparative-static run with the model, constructing a baseline over several decades requires many solves. As indicated above, the time resolution can be chosen by the user. While larger time steps such as five year intervals decrease the number of necessary solves, the resulting shock in each period becomes larger, which implies more time spent by the solver to find a fixed point. For a dataset larger than around 57x24, it is therefore recommended to solve at least in bi-yearly steps, whereas less detailed data sets can still solve quite fast in five year steps. Using the built-in pre-solve mechanism with at least three steps is also recommended for more detailed datasets. Furthermore, we recommend aggregating over the Armington agents, which removes the agent specific differentiation between domestic and imported shares and reduces the model complexity and rigidities in the demand composition.

Some relatively large data sets have been tested, including 33 from all 57 sectors and 80 countries from the 140 available in GTAP 9. One run over 40 years in 2 year steps with such detailed data base might require about two hours. Note that especially debt accumulation from foreign savings might lead to infeasibilities, such that it might be required to manually reduce the accounted share of related debt servings for specific regions. In the same vein, we typically used an ALTERTAX run to construct a benchmark where very high negative macro-economic saving rates are reduced (see gams\scen\user_scenarios\corr_betas.gms). These odd saving rates might point a specific problem in GTAP 9 data, as in the 2011 the global economy was still affected by an economic crisis.

More generally, it should be understood that baseline construction is only partially a process which can be delegated to a ready-to-use code. A close look at some key results, such as the evolution of foreign savings, saving rates and sectoral output per capita is recommended to rule out implausible findings. An ALTERTAX adjustment may be needed to vary the initial benchmark or it might be necessary to add specific shocks on top of the baseline mechanism. We also remind the reader that the SSP1 to 5 storylines comprise elements relating to governance such as policies to abate emissions or control land use change which are not integrated in the model structure discussed here.

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