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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
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 +====== 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.