CGE Models. Eduardo Haddad

Transcription

1 CGE Models Eduardo Haddad

2 Outlne Introducton Structure of a CGE Model The Johansen Approach Stylzed Johansen Model 2

3 What s a CGE? Computable, based on data It has many sectors And perhaps many regons, prmary factors and households A bg database of matrces Many, smultaneous, equatons (hard to solve) Prces gude demands by agents Prces determned by supply and demand Trade focus: elastc foregn demand and supply 3

4 General features of CGE models CGE models nclude equatons specfyng: market-clearng condtons for commodtes and prmary factors; producers' demands for produced nputs and prmary factors; fnal demands (nvestment, household, export and government); the relatonshp of prces to supply costs and taxes; varous macroeconomc varables and prce ndces. Neo-classcal flavor demand equatons consstent wth optmzng behavor (cost mnmzaton, utlty maxmzaton); compettve markets: producers prce at margnal cost. 4

5 CGE smplfcatons Not much dynamcs (leads and lags) An mposed structure of behavor, based on theory Neoclasscal assumptons (optmzng, competton) Nestng (separablty assumptons) Why: tme seres data for huge matrces cannot be found Theory and assumptons (partally) replace econometrcs 5

6 What s a CGE model good for? Analyzng polces that affect dfferent sectors n dfferent ways The effect of a polcy on dfferent: Sectors Regons Factors (Labor, Land, Captal) Household types Polces (tarff or subsdes) that help one sector a lot, and harm all the rest a lttle 6

7 What-f questons What f productvty n agrculture ncreased 1%? What f foregn demand for exports ncreased 5%? What f consumer tastes shfted towards mported food? What f CO2 emssons were taxed? What f water became scarce? A great number of exogenous varables (tax rates, endowments, techncal coeffcents) Comparatve statc models: results show effect of polcy shocks only, n terms of changes from ntal equlbrum 7

8 Comparatve-statc nterpretaton of results Results refer to changes at some future pont n tme C Employment Change B A 0 T years Now 2004 smulaton date 2006 (?) 8

9 Regonal modelng Intense nterest n regonal results Polces whch are good for naton but bad for one regon may not be poltcally feasble Assstance to one regon may harm naton Regonal modelng s the largest part of Fpe s Brazlan contract work More customers: 1 natonal government but 27 state governments Two approaches: Bottom-Up or Top-Down 9

10 The bottom-up approach Smply add a regonal subscrpt (or two) to each varable and data 2 sources 1 reg Natonal (c,s,) sze 7 x 2 x 7 33 reg CEER (c,s,,r) sze 7 x 34 x 7 x sources 33 locatons Database has grown by factor of [34/2]*33 = 561 Number of varables also 561 tmes bgger Solve tme and memory needs move wth SQUARE of model sze (so model needs 300,000 tmes as much memory and takes 300,000 tmes longer to solve) 10

11 Stylzed GE model: materal flows Produced nputs Demanders Non-produced nputs Producers captal, labour households domestc commodtes nvestors government mported commodtes export 11

12 You wll learn... How mcroeconomc theory cost-mnmzng, utltymaxmzng underles the equatons; The use of nested producton and utlty functons: How nput-output data s used n equatons; How model equatons are represented n percent change form; How choce of exogenous varables makes model more flexble; CGE models mostly smlar, so sklls wll transfer. 12

13 Outlne Introducton Structure of a CGE Model The Johansen Approach Stylzed Johansen Model 13

14 CGE models Defnton Analytcal and Functonal Structures Functonng Mechansms of the Economy Numercal Structure Database Pcture of the Economy 14

15 Nested structures n CGE models In each ndustry: Output = functon of nputs: output = F (nputs) = F (Labor, Captal, Land, dom. goods, mp. goods) Separablty assumptons smplfy the producton structure: output = F (prmary factor composte, composte goods) where: prmary factor composte = CES (Labor, Captal, Land) labor = CES (Varous skll grades) composte good () = CES (domestc good (), mported good ()) All ndustres share common producton structure. BUT: Input proportons and behavoral parameters vary. Nestng s lke staged decsons: Frst decde how much leather to use based on output. Then decde mport/domestc proportons, dependng on the relatve prces of local and foregn leather. Each nest requres 2 or 3 equatons. 15

16 Actvty Level Inputs to producton: Nests (example) Leontef top nest Good 1 Good G Prmary Factors 'Other Costs' CES CES CES prmary factor nest Domestc Good 1 Imported Good 1 Domestc Good G Imported Good G Armngton nest KEY Functonal Form Land Labour CES Captal skll nest Work upwards Inputs or Outputs Labour type 1 Labour type 2 up to Labour type O 16

17 Example 1: CES skll substtuton Sklled s a = s a + u a R 0 < a < 1 C A B =15 Cost=$6 Cost=$9 =10 UnSklled u 17

18 Effect of prce change Sklled s Unsklled wages fall relatve to sklled wages A B A B PR1 PR2 Unsklled u =10 18

19 Example 2: Substtuton between domestc and mported sources KEY Good 1 up to Good C Functonal Form Inputs or Outputs Armngton hypothess: CES aggregaton for dfferent sources CES CES Good-specfc parameters Same structure for all users Domestc Good 1 Imported Good 1 Domestc Good C Imported Good C 19

20 Numercal example p = S d p d + S m p m average prce of manufactures dom. e mp. x d = x - σ(p d - p) x m = x - σ(p m - p) demand for domestc manufactures demand for mported manufactures Let p m = - 10%; x = p d = 0; S m = 0.3 and σ = 2 Then, cheaper mports mply: p=-0.3(-10%) =-3% x d =-2[0-( -3%)]=-6% x m =-2[-10% (-3%)]=14% decrease n the average prce of mp. mnf. decrease n domestc demand ncrease n mport volume Effects on domestc sales are proportonal to S m e σ 20

21 Outlne Introducton Structure of a CGE Model The Johansen Approach Stylzed Johansen Model 21

22 Johansen models Class of general equlbrum models n whch a equlbrum s a vector V, of length n satsfyng a system of equatons F V 0 (1) where F s a vector functon of length m. We assume that F s dfferentable and that the number of varables, n, exceeds the number of equatons m. Johansen s approach s to derve from (1) a system of lnear equatons n whch the varables are changes, percentage changes or changes n the logarthms of the components of V. 22

23 Illustratve computatons We wll assume that the system (1) conssts of 2 equatons and 3 varables and has the form V V V 3 V V 1 and V 2 (endogenous); V 3 (exogenous) V V 1 2 V 1/ 2 3 1/ V 23

24 Illustratve computatons (cont.) Intal soluton: V I ( 3 I I I V1, V2, V ) (1,1,1) What s the effects on V 1 and V 2 of a shft n V 3 from 1 to 1.1? Johansen approach: V V Complexty and sze of the system (1) normally rule out the possblty of dervng from t explctly soluton equatons Solve a lnearzed verson of (1) 24

25 Step by step Derve from (1) a dfferental form A( V ) v 0 (2) v s usually nterpreted as showng percentage changes or changes n the logarthms of the varables V. Johansen-style computatons make use of a ntal soluton, V I, wth results beng reported usually as percentage devatons from ths ntal soluton. A( V) A( V I ) fxed matrx ("model") 25

26 Step by step (cont.) Dervaton of (2) s by total dfferentaton of (1) 2VV V Se V = V I, 2 dv dv dv I A( V ) v 0 (3) dv 1 0 dv dv

27 Step by step (cont.) On choosng varable 3 to be exogenous: 2 1 A v v a dv dv a dv dv a 0dV 1 dv ( V 1 2 I ) v A 1 2 a B( V 1 1 a I 2 1 dv ( V ) v A 0 1 I ( V 1 ) A I 0.5 dv 0.5 ) v ( V 0 1 dv I 0 3 ) v (4) (5) (6) 27

28 Any dfference? Before: V 3 10% V %, V % Now: V 3 10% V 1 5%, V 2 5% Dfferences are due to lnearzaton errors The operatons gve us the values of the dervatves or elastctes only for the ntal values, V I, of the varables. When we move away from V I, the dervatves or elastctes wll change. In percentage change form: v v 1 v v v v

29 Lnearzaton error Y J Y 1 step dy Y exact Exact Y 0 0 d F Y J s Johansen estmate Error s proportonately less for smaller changes 29

30 Breakng large changes n nto a number of steps Y J Y 1 step Y 2 Y 1 3 Y Y exact 3 step Exact Y 0 F Mult-step process to reduce lnearzaton error 30

31 Extrapolatng from Johansen and Euler approxmatons Method y Error Johansen (1-step) 150% 50% Euler 2-step 125% 25% Euler 4-step 112.3% 12.3% Euler -step (exact) 100% 0 The error follows a rule (arbtrary polynomal approxmaton of contnuous functon) Use results from 3 approxmate solutons to estmate exact soluton + error bound 31

32 Summary 1. We start wth the model s equatons represented n ther levels form 2. The equatons are lnearzed: take total dfferental of each equaton 3. Total dfferental expressons converted to (mostly) % change form 4. Lnear equatons evaluated at ntal soluton to the levels model 5. Exogenous varables chosen; model then solved for movements n endogenous varables, gven user-specfed values for exogenous varables But, a problem: lnearzaton error Mult-step, extrapolaton 32

33 Outlne Introducton Structure of a CGE Model The Johansen Approach Stylzed Johansen Model 33

34 Implementaton 1. Development of a theoretcal structure 2. Lnearzaton of the model equatons 3. Use of nput-output data to provde estmates for the relevant cost and sales shares 4. Development of a flexble computer program to manpulate the lnear system 34

35 Structure of the model Two good/sectors (1 and 2) Two prmary factors (3 and 4) One fnal user household (0) 35

36 Assumptons Household sector (0) max 0 U a a subect to P 1 10 P2 20 Y Producers ( = 1,2) mn C 4 1 P subect to A a 1 1 a 2 2 a 3 3 a 4 4 A 0, 4 1 a 1 36

37 Assumptons (cont.) Value of output equals the value of nputs C P 4 1 P, 1,2 Equlbrum condtons 2 0, 1,2 2 1, 3,4 Household budget equals factor ncome 37

38 Structural form Share of nput n total costs of ndustry a Y 0 0 P, 1,2 (1) a Q P 4 t1 P at t, 1,,4 1,2 (2) P a t t Q P, 1,2 (3) 38

39 39 Structural form (cont.) (4) (5) P 1 = 1 (6) Varables: 3,4, 1,2, Y P,4 1,,4 1, 1,2,4 1, 1,2 0

40 Percent-change equatons examples Levels form: Ordnary change form: A = B + C DA = DB + DC Convert to % A(100.DA/A) = B(100.DB/B) + C(100.DC/C) change form: A a = B b + C c Typcally two ways of expressng % change form Intermedate form: Percentage change (share) form: A a = B b + C c a = S b b + S c c where S b = B/A; S c = C/A 40

41 Percent-change equatons examples Levels form: Ordnary change form: A = B C DA = DB C + DC B Convert to % A(100.DA/A) = BC(100.DB/B) + BC(100.DC/C) change form: A a = BC b + BC c a = b + c PRACTICE: = F P e Ordnary change and percent change are both lnearzed Lnearzed equatons easer for computers to solve % change equatons easer for economsts to understand: elastctes 41

42 Percent-change numercal example Levels form Z = *Y Ordnary Change form DZ = Y*D + *DY [+ D DY] Multply by 100: 100*DZ = 100*Y*D+ 100**DY Defne x = % change n, so *x=100d Z*z = *Y*x + *Y*y Dvde by Z=*Y to get: Percent Change form z = x + y Intally =4, Y=5, so Z = *Y = 20 Suppose x=25%, y=20% [e, :45, Y:56] Lnear approxmaton z = x + y gves z = 45% True answer: 30 = 5*6 = 50% more than orgnal 20 Error 5% s 2nd order term: z = x+y + x*y/100 2nd-order Note: reduce shocks by a factor of 10, error by factor of

43 43 Lnearzed verson y x p x x,4 1,,4 1, 1,2,4 1, 1,2 0 Varables: 0 3,4 1,2 1,2 1,2,4 1, 1, p x x x x p p p p x x p y x t t t t t t a a 0,1,2 1,...,4, /

44 Intal soluton Input-output data Conventon: one unt of good or factor s the amount whch costs $1 n the base perod Parameters of the structural form: a 0, a, Q Calbraton guarantees that structural form equatons are satsfed by the suggested values for the parameters 44

45 Matrx A(V I ) Matrx A(V I ) can be evaluated usng the nput-output data Equvalent to evaluate the coeffcents of the model! Exercse: representaton of the matrx A(V I ) of the lnearzed system 45

46 46 Lnearzed verson y x p x x,4 1,,4 1, 1,2,4 1, 1,2 0 Varables: 0 3,4 1,2 1,2 1,2,4 1, 1, p x x x x p p p p x x p y x t t t t t t a a 0,1,2 1,...,4, /

47 Input-output data 47

48 17 columns 19 rows 48

49 The model A(VI) y x10 x20 x11 x21 x31 x41 x12 x22 x32 x42 x1 x2 x3 x4 p1 p2 p3 p Aalfa y x10 x20 x11 x21 x31 x41 x12 x22 x32 x42 x1 x2 p1 p2 p3 p4 Abeta x3 x Fpe 0 - Fundação 0 Insttuto 0 0 de Pesqusas 0 Econômcas

50 Soluton matrx (-)nvaalfa B(VI) y x x x x x x x x x x x x p p p p4 Fpe - Fundação Insttuto de Pesqusas Econômcas 50

51 TCL Notes and Problems n Mcroeconomc Theory Dxon, P.B.,Bowles, S. and Kendrck, D., Amsterdam, North- Holland, The lnear expendture system 4.2. Propertes of the Cobb-Douglas producton functon The CES producton functon Notes and Problems n Appled General Equlbrum Economcs Dxon, P.B.,Parmenter, B.R., Powell, A. A. and Wlcoxen, P. J., Amsterdam, North-Holland, Cap. 3. The Johansen Approach 51