# Differences

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 final_demand [2019/05/29 15:35]jfoure ↷ Page name changed from final_demand to final_demand_1.1 final_demand [2019/06/03 08:16] (current)jfoure created 2019/06/03 08:16 jfoure created2019/05/29 15:35 jfoure ↷ Page name changed from final_demand to final_demand_1.1 2019/06/03 08:16 jfoure created2019/05/29 15:35 jfoure ↷ Page name changed from final_demand to final_demand_1.1 Line 1: Line 1: + ====== Final demand ====== + [{{ ::​utility.png?​300|Utility function}}] + + Final consumption is modelled in each region through a representative agent, whose utility function is intratemporal. A fixed share of the regional income is allocated to savings, the rest is used to purchase final consumption goods. The saving rate follow projections by [[MaGE model|EconMap]]. + + Government and final consumers are modelled with the same demand function and aggregated in a single regional representative agent. This agent therefore both pays and earns taxes, and no public budget constraint has to be taken into account explicitly: this constraint is implicit to meeting the representative agent'​s budget constraint. Unless otherwise indicated (modelling a distorsive replacement tax does not raise any technical problem), this implicitly assumes that any decrease in tax revenues (for example as a consequence of a trade liberalisation) is compensated by a non-distorsive replacement tax. However, the magnitude of the tax revenue losses is an interesting information,​ provided in standard result tables. + + ===== Calibration of utility parameters ===== + + + ==== Data ==== + + Utility parameters (minimal consumption level, elasticity of substitution) are calibrated using [[https://​www.ers.usda.gov/​data-products/​commodity-and-food-elasticities/​|USDA Commodity and Food Elasticities]]. LES-CES can only accommodate positive income elasticities,​ so we change all + negative income elasticities to a very low value, namely 0.025. + + ==== Calibration procedure ==== + + All the parameters are calibrated at the same time within an optimization + procedure. It consists in minimizing the discrepancies between target and + calibrated own-price elasticities subject to the respect of the initial consumption + and the income elasticities. The calibration must be done on the consumption per + capita. There are usually several solution that minimise the objective (same final + own-price elasticities,​ but different set of parameters),​ so the initial values + matter a lot for the calibration. These multiple solutions correspond to the same + initial behavior but to different behavior after a change in prices or income. + + + The calibration follows for each country the program + $$\min_{\sigma_{i},​0\le\bar{c}_{i}\le C_{i}^{t},​\alpha_{i}} \sum_{i} \frac{P_{i} C_{i}^{t}}{I}\left(e_{ii}-e_{ii}^{t}\right)^{2}$$ + Subject to + $$+ \begin{gather} + C_{i}^{t}=Pop_{i}\left(\bar{c}_{i}+\frac{\alpha_{i}\left(I-\gamma\right)}{Pop_{i} + P}\left(\frac{P}{P_{i}}\right)^{\sigma_{i}}\right)\\ + \eta_{i}^{t} = + \frac{\alpha_iI}{P_iC_i^{t}}\left(\frac{P}{P_i}\right)^{\sigma_{i}-1}\\ + e_{ii}=-\frac{\alpha_i}{C_i^{t}}\left(\frac{P}{P_i}\right)^{\left(\sigma_{i}-1\right)}\left(C_i^{t}+\sigma_{i}\left(\bar{c}_i-C_i^{t}+\frac{I-\gamma}{P_i}\right)\right) + \end{gather} +$$ + with $e_{ii}^{t}$,​ $\eta_{i}^{t}$ and $C_{i}^{t}$ the target uncompensated + own-price elasticity (this is only for illustration,​ we use the type of + own-price elasticity corresponding to the elasticities sources), the target + income elasticity and the target consumption level (from the GTAP database). The + parameters are calibrated in consumption per capita.