PRMTR - Trade Policy Simulation Course Maros Ivanic 5 May 2010

Transcription

1 PRMTR - Trade Policy Simulation Course Maros Ivanic 5 May 2010

2 Overview Structure of the model Consumer behavior Producer behavior Government behavior International trade and investment Solution software Construction of the model Solving the model

3 Consumer behavior A set of equations determining the consumption behavior of the private households Single consumer per region CDE demand system Two estimated parameters per commodity Flexible definition Domestic and foreign goods are imperfect substitutes Other systems can be implemented (AIDADS) Demand for a specific commodity is affected by Change in the other commodity prices Change in the consumer income Income derived from Returns to factors (land, labor, capital, natural resources) Taxes and transfers

4 Consumer decision Good 1 Utility Good 2 Good 3 Domestic Foreign Domestic Foreign Domestic Foreign

5 Producer behavior Production exhibits constant returns to scale Doubling of all inputs doubles output Production earns no profit All revenue is returned to the owners of the factors (labor, land, capital) Production is double-nested Output is produced using value-added Labor, capital, natural resources, land Inputs Foreign and domestic

6 Production nest Value added Land Labor Natural resources Production Input 1 Domestic Foreign Capital Input 2 Domestic Foreign Input Domestic Foreign

7 Government behavior Government expenditure is modeled in a neutral way Share of government income from GDP remains constant Budget share of individual good consumption remains constant Treats domestic and foreign goods as imperfect substitutes It is not necessarily tied to the collection of taxes Level of government spending can be changed

8 International trade Countries in the model trade with each other Trade follows Armington s assumption Each country trades with another (no zero flows) The same good (e.g. rice) from different countries are imperfect substitutes Substitution parameters empirically estimated Substitution is low for Fish 2.5 Substitution is high for Natural gas 34.4 International margins are also modeled on bilateral basis The model considers individual margin providers for specific flows

9 Import structure Source 1 Demand Imports Domestic Source 2 Source 3 Source

10 Investment The model assumes that capital is invested to equate returns on investment Regional savings are collected in a global bank Investment is distributed across regions to equate returns to investment Modifications to the assumption are possible

11 Construction of the model Model is stored as a set of Parameters (estimated and assumed fixed) Sets (countries, commodities, factors, etc.) Variables Equations Linking variables together with parameters The most common software package is GEMPACK with its Tablo editor Equations are linearized (percentage changes) It is possible to run GTAP in other software packages (GAMS)

12 Linearization of equations Variables in the model are recorded as linear transformations (percentage changes) Consider equation R = Q x P R=revenue Q=quantity P=price Linearized form: r = q + p The percentage of the increase in revenue is approximately the sum of the percentage increases in quantity and price The model is translated into a matrix of parameters and variables

13 Example of the Tablo syntax Definition of a set Set REG # regions in the model # maximum size 10 read elements from file GTAPSETS header "H1"; Definition of a coefficient/parameter Coefficient (parameter)(all,i,trad_comm) ESUBD(i) # region-generic el. of sub. domestic/imported for all agents #; Read ESUBD from file GTAPPARM header "ESBD"; Definition of an equation Equation IMPORTDEMAND # regional demand for disaggregated imported commodities by source# (all,i,trad_comm)(all,r,reg)(all,s,reg) qxs(i,r,s) = qim(i,s) - ESUBM(i) * [pms(i,r,s) - pim(i,s)];

14 Model closure In order to be able to run a model we need to specify Exogenous variables which can be changed Endogenous variables which are solved for Parameter values Levels of substitution among inputs Mobility of factors etc. Sets and data Which regions, factors and commodities are included What are the values of all coefficients

15 How is the model specified? Consider a set of two equations A w + B v + C x + D y + E z = 0 F w + G v + H x + I y + J z = 0 Where x, y, z are the variables The model is internally represented as This model cannot be immediately solved: the number of variables is greater than the number of equations 0 0 z y x w v J I H G F E D C B A Parameters Variables

16 A model must be square to be solved! We need to specify a set of exogenous variables If we have n equations we need to have exactly n free variables E.g. we can choose w, x, z and to be exogenous 0 0 z y x w v J I H G F E D C B A z x w J H G E C B y v I F D A z x w J H G E C B I F D A y v 1

17 Solving the model The solver has to invert a potentially huge matrix Often hundred of thousands of elements The model is solved numerically with varying levels of accuracy using various methods Linear method (Johansen) Newton method (Euler) Gragg method (Gragg) The model is capable of separating the impacts of various shocks (subtotals) The model can be solved stochastically (sensitivity analysis)

18 Subtotals We are able to separate easily each exogenous variable s individual impact on the results z x w J H G E C B I F D A y v 1 z J E I F D A x H C I F D A w G B I F D A y v Impact of variable w Impact of variable x Impact of variable z

19 Sensitivity analysis The model can also take stochastic shocks as inputs E.g. the productivity is expected to change by 5% with standard deviation of 3 percentage points Solution method: Guassian Quadrature The model is run twice as many times as the number of shocks E.g. if five variables change, the model is run 10 times GQ algorithm prepares representative shocks for each run The 2n results are interpreted into Means Standard deviations

20 Conclusion Questions?