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--- the_complete_and_consistent_data_base_coco_for_the_national_scale [2020/02/13 08:04] – [COCO2: Data Preparation] matsz
+++ the_complete_and_consistent_data_base_coco_for_the_national_scale [2020/02/13 08:33] – [COCO2: Estimation procedure] matsz
@@ Line 552: / Line 552: @@
 ====COCO2: Estimation procedure====
+**Include file //‘coco2_def.gms’//**
+The approach to determine consumer prices is to distribute food expenditure on groups with consumption quantities given from COCO1 results such that endogenous consumer prices link endogenous expenditure with exogenous quantities. Deviations of estimated expenditure and consumer prices from their supports is penalised in an entropy framework. Estimation is done year by year, starting with the most recent year where hard data are usually available to a greater extent than for the oldest years in the database. Including consumer price changes (always relative to the previously solved year) serves to stabilise the results to some extent such that the objective does not only have supports for the consumer prices, but also for their changes. The entropy problem is solved by maximizing:
+\begin{align}
+\begin{split}
+max_t &- \sum_{m,j,k} CPS_{m,j,2}*HCOM_{m,j,k}/1000/TOFO_{m,t}*\\
+&PE_{m,j,k}*LOG(PE_{m,j,k}/PQ_k)\\
+&-\sum_{m,j,k} CPS_{m,j,2}*HCOM_{m,j,k}/1000/TOFO_{m,t}*\\
+&PED_{m,j,k}*LOG(PED_{m,j,k}/PQ_k)\\
+&-\sum_{m,FOPOS,k} EXS_{m,FOPOS,2}/TOFO_{m,t}*\\
+&PEX_{m,FOPOS,k}*LOG(PEX_{m,FOPOS,k}/PQ_k)\\
+&-\sum_{m,j,k} PFAC_{m,k}*LOG(PFAC_{m,,k}/PQ_k)*1000\\
+\end{split}
+\end{align}
+where //m// represents the region, //j// the food item with consumer price, FOPOS the food group, //t// stands for the current estimation year, t_1 for the year estimated before and k for the number of support points (=3).
+Parameters are
+| \(HCOM_{m,j,t}\) |Human consumption, result from COCO1
+|-
+|UVADm,j,t_1	Consumer price from last simulation of year t+1
+CPSm,j,k		Support points for consumer prices
+DCPSm,j,k	Support points for consumer price changes
+EXSm,FOPOS,k	Support points for group expenditures
+TOFACSm,k	Support points for total food expenditure slack
+PQk		A priori probabilities for support points
+TOFOm,t	Total food expenditure
+and entropy variables
+PEm,j,t		Probability of support points for consumer prices
+PEDm,j,t		Probability of support points for consumer price changes
+CPm,j		Consumer prices
+DCPm,j		Consumer price changes
+PEXm,FOPOS,t	Probability of support points for group expenditure
+PFACm,k	Probability of support points for food expenditure slack
+EXmFOPOS	Group expenditures
+TOFACm	Food expenditure slack