Introduction to Computable General Equilibrium Model (CGE)

Transcription

1 Introduction to Computable General Equilibrium Model (CGE Dazn Gillig & ruce. McCarl Department of gricultural Economics Texas &M University

2 Course Outline Overview of CGE n Introduction to te Structure of CGE n Introduction to GMS Casting CGE models into GMS Data for CGE Models & Calibration Incorporating a trade & a basic CGE application Evaluating impacts of policy canges and casting nested functions & a trade in GMS Mixed Complementary Problems (MCP

3 Tis eek s Road Map Fundamental relationsips in a simple CGE model Incorporating taxes Including demand for products and factors Interpretation of results Comparative analysis 3

4 Fundamental Structure CGE models typically involve determination of economy wide levels of. commodity prices based on consumer demand and production possibilities/costs. factor prices based on supply and production possibilities/product prices 3. factor usage 4. production levels 5. income to ouseolds and resultant demand 6. Government balance 4

5 Fundamental Structure asic relationsips for a simple CGE. Supply Demand identities for factors & products. Zero profit condition for producing Industries 3. Factor demand by producers 4. Product demand by ouseolds 5. Income balance constraint for ouseolds 6. Government balance 7. Trade balance closed economy xx 5

6 Fundamental Structure asic caracteristics of CGE model solutions: set of non-zero prices, consumption levels, production levels, and factor usages constitutes an economic equilibrium solution (also called a alrasian equilibrium and a solution to a CGE of te situation if. Total market demand equals total market supply for eac and every factor and output.. Prices are set so tat equilibrium profits of firms are zero wit all rents accruing to factors. 3. Houseold income equals ouseold expenditures. 4. Government transfer payments to consumers equals taxes revenues. 6

7 Edgewort ox Pure Excange Economy O I I ω O 7

8 8 O Edgewort ox Pure Excange Economy O ω MRS MRS P/P Z I I / 0 0. P P λp λp P P P P s t Max > > U U U and U U / 0 0. P P λp λp P P P P s t Max > > U U U and U U

9 9 Edgewort ox Pure Excange Economy Implications: Feasible allocation Excess demand udget constraints 0 ( ( 0 ( ( 0 ( ( 0 ( ( Z Z 0 Z P Z P P P P P P P P P 0 ( ( 0 ( ( P P P P alras aw For any price vector P, PZ(P 0; i.e., te value of te excess demand, is identically zero, (Varian, page 37 0 ( ( ( ( P P P P alras aw

10 Fundamental Structure asic caracteristics of CGE model solutions: set of non-zero prices, consumption levels, production levels, and factor usages constitutes an economic equilibrium solution (also called a alrasian equilibrium and a solution to a CGE of te situation if. Total market demand equals total market supply for eac and every factor and output.. Prices are set so tat equilibrium profits of firms are zero wit all rents accruing to factors. 3. Houseold incomes equal ouseold expenditures. 4. Government transfer payments to consumers consumptions equal taxes revenues. 0

11 Fundamental Structure asic relationsips for a simple CGE. Supply Demand identities for factors & products. Zero profit condition for producing Industries 3. Factor demand by producers 4. Product demand by ouseolds 5. Income balance constraint for ouseolds 6. Government balance

12 Fundamental Structure asic notations: Sectors denoted by Houseolds denoted by Factors denoted by and and are owned by ouseolds is te production of goods by te t sector P is te price of goods produced by te t sector a, is te amount of goods used from sector wen producing one unit of goods in te t sector is te usage of labor by te t sector is te price of labor (te wage rate is te usage of capital in te t sector is te price of capital

13 Fundamental Structure. Supply-Demand identities for factors & products a. Factor market: Total demand is less tan or equal to total supply in every factor market or te excess demand in te factor market is less tan or equal to zero. 0 0 Total supply is te sum across te ouseold endowments 3

14 Fundamental Structure. Supply-Demand identities (con t b. Product or output market: Total demand in every output market including consumer and intermediate production usage is less tan or equal to total supply in tat market or te excess demand in eac output market is less tan or equal to zero. X a, 0 Consumer consumption (ff Intermediate usage Total production (ff 4

15 Fundamental Structure. Zero profits in eac sector P P a, Revenues Costs Note tat: CRS Perfect Competition Unit price unit cost 5

16 Fundamental Structure 3. Houseold income identity Tis relationsip implies tat ouseold exausts its income. Income Note tat: Houseold consumptions (X are a function of price and income. Maximize U(X s.t. P X Income 6

17 Complementarity Recall: alras aw: For any price vector P, PZ(P 0; i.e., te value of te excess demand, is identically zero, (Varian, page 37 Namely, if total demand is less tan total supply for te factor/commodity markets ten te price in tat market must be zero; oterwise, prices will be nonzero only if supply equals demand Tis implies PRICE OR EXCESS DEMND 0. Tis leads to te following complementary relationsips. 7

18 Complementarity (con t In a CGE model, a set of prices P and quantities are defined as variables suc tat D S (alras aw Implications: (s-dp 0 (Pd-Pd 0 (Ps-Ps 0 Eac equation must be binding or an associated complementary variable must be zero. IF P > 0 ten s d IF d > 0 ten Pd P, IF s > 0 ten Ps P, and Tis is similar to T conditions of te following optimization model. 8

19 Complementarity (con t Max 6d-0.5d s. t d s 0 s 0.s Pd 6-0.3*d Ps 0.*s d, s 0 were P is te dual variable associated wit te first constraint. 9

20 Complementarity (con t representing complementary relationsip Factor prices must be zero if factors are not all used up. Non zero prices exist if factors all are consumed.. 0 P X a, 0 Product prices must be zero if products are not all consumed. Non zero prices exist if products all are consumed. 0

21 Complementarity (con t 3. 0 P Pa, Firm profits must equal zero and a non-zero production level is acieved. Firm profits can be less tan costs witout te firm producing Income Income Houseold incomes must be non-zero if expenditures exaust incomes.

22 Complementarity (con t 5. Factor demand by producers identity (functional forms: CES, Cobb Douglas, eontief? /( ( ( ( φ /( ( ( ( φ 0 0

23 Complementarity (con t 6. Product demand by ouseolds identity (functional forms: CES, Cobb Douglas, ES? 0 X X P α ( Income ( ( α P 3

24 Incorporating Taxes asic caracteristics of CGE model solutions: set of non-zero prices, consumption levels, production levels, and factor usages constitutes an economic equilibrium solution (also called a alrasian equilibrium and a solution to a CGE of te situation if. Total market demand equals total market supply for eac and every factor and output.. Prices are set so tat equilibrium profits of firms are zero wit all rents accruing to factors. 3. Houseold income equals ouseold expenditures. 4. Government transfer payments to consumers equal taxes revenues. 4

25 Incorporating Taxes (con t Fundamental structure. Supply-Demand identities. Zero profits in eac sector 3. Houseold income-expenditure balance 4. Government tax revenue balance Tis relationsip implies tat te government satisfies its budget constraint wen total revenue is positive. 5

26 Incorporating Taxes (con t ssumptions:. Total tax revenues are a. redistributed to ouseolds in te form of transfer payments (TR at te rate (s > TR OR b. expended on government purcase of goods (GP. Government purcases are proportional to tax revenues at te rate (s > s s GP 3. t percent is imposed on ouseold income t f percent is imposed on factor f in sector F is a total deduction imposed on ouseold s R s R 6

27 Incorporating Taxes (con t Modification. Te market balance : include government purcases transformed to be in a quantity unit X 0. Te zero profit condition a, s R / P : include a tax effect as a cost of doing business P P a t l t, k 7

28 Incorporating Taxes (con t 3. Te ouseold income equation : include tax effects to reflect tax incidence and tax revenue redistribution ( t ( F R Income s 4. dd te government tax revenue balance : apply te ouseold income tax (t to gross revenue less deductions, and te factor tax (t f R t ( F t t l k 8

29 Incorporating Taxes (con t 5. Complementary 0 R R t l t ( F t k te government satisfies its budget constraint wen total revenue is positive. 9

30 Including Demand for Products and Factors Specification of product and factor demand functions sould be consistent wit teory but analytically tractable. (. Teoretical approac coosing functional forms tat satisfy : classical restrictions i.e. nonnegative, continuous, and omogenous degree zero in price : alras s law > te value of market excess demands equals zero at all prices (. nalytically tractable coosing functional forms tat are easy to evaluate e.g. eontief, CD, CES, ES, etc. 30

31 3 Including Demand for Products and Factors Factor demand derived from CES function : Production function /( / ( / ( ( ( φ : Factor demand /( ( ( ( φ /( ( ( ( φ Douglas to Cobb - ten CES tends to eontief ten CES tends 0 Note tat:

32 Including Demand for Products and factors Houseold product demand from CES Utility function Maximize Utility U ( / α ( X ( / /( s.t P X Income Yields Demand Curve X P α ( Income ( P ( α 3

33 Numerical Example Symbol α rief Description Elasticity of substitution in ouseold CES Consumption sare in ouseold CES, a, φ s s Houseold endowments of factors Use of goods in sector wen producing in sector Scale parameter in CES production function Distribution parameter in CES production Elasticity of production factor substitution Houseold sare of tax disbursements Government goods purcase dependence on revenues t t f F Houseold tax level Tax on factor f in sector Houseold tax exemptions 33

34 Parameter Specification Example of simple xx CGE (Soven and alley 984 Production Parameters Sector ( φ Food Non-Food t f abor Capital Consumer Parameters Houseold ( s t F Farmer Non-Farmer α Endowments Food Non-Food abor Capital Farmer Non-Farmer Government Food 0.0 Non-Food

35 Equilibrium Results. Total demand for eac output exactly matces te amount produced X P α ( Income ( ( α P φ ( ( / ( ( / /( Recall: X X a, 0 35

36 Equilibrium Results (con t. Producer revenues equal consumer expenditures P X P 36

37 37 Equilibrium Results (con t 3. abor and capital are exausted /( ( ( ( φ /( ( ( ( φ

38 Equilibrium Results (con t 4. Unit cost selling price > zero profits wl rk From model solutions 38

39 Equilibrium Results (con t 5. Consumer factor incomes equal producer factor costs

40 Equilibrium Results (con t 6. Houseold expenditures exaust teir incomes P X 40

41 4 Introducing Socks (. Imposing a 50% tax on a capital used in a food sector Production Parameters φ t Food Non-Food Sector ( t f abor Capital /( ( ( ( ( k t φ /( ( ( ( ( k t φ

42 Introducing Socks. Te market balance X s R /. Te zero profit condition l P 0 P (X t ( t k 3. Te ouseold income equation ( Xt ( F R Income i s 4. dd te government tax revenue constraint ( F R Xt Xt l t k 4

43 Introducing Socks (. t equilibrium, transfer payments tax revenues TR s R R Xt Xt l ( F t k 43

44 Comparative nalysis Taxrate("capital","Food" 0.5 ; SOVE CGEModel USING MCP ; Note tat: Tax revenue under non-cge excluding a tax including tax * 6. * 0.5 $4.65 VS. CGE tax revenue $.8 Factor Cost Factor Tax level uantity 44

45 Comparative nalysis (con t. Unit cost selling price > zero profits Relative pricep/p.40/.09.8 (no tax.47/.0.45 (wit tax 45

46 Comparative nalysis. Total demand for eac output exactly matces te amount produced 46

47 Comparative nalysis (con t 3. Producer revenues equal consumer expenditures 47

48 Comparative nalysis (con t 4. abor and capital are exausted 48

49 Comparative nalysis (con t 5. Consumer factor incomes equal producer factor costs 49

50 Comparative nalysis (con t 6. Houseold expenditures exaust teir incomes 50

51 rap Up Overview of CGE Fundamental relationsip of simple CGE model Interpretation of results Incorporating socks (Taxes Comparative analysis Next: Using GMS for CGE Modeling at is GMS? GMS IDE Dissecting GMS Formulation 5

52 References McCarl,.. and D. Gillig. Notes on Formulating and Solving Computable General Equilibrium Models witin GMS. Ferris, M. C. and J. S. Pang. Engineering and Economic pplications of Complementarity Problems. SIM Review, 39:669-73, 997. Soven, J.. and J. alley. pplying general equilibrium. Surveys of Economic iterature, Capters 3 and 4, 998. Soven, J.. and J. alley. pplied General-Equilibrium Models of Taxation and International Trade: n Introduction and Survey. J. Economic iterature, :007-05,