Building an Applied General Equilibrium Model

Transcription

1 Builing an Applie General Equilibrium Moel B. Essama-Nssah overty Reuction Group (RMR) The Worl Bank May, 2006

2 Forewor A logical picture iffers from an orinary picture in that it nee not look the least bit like its object. Its relation to the object is not that of a copy, but of analogy. The great value of analogy is that by it, an by it alone, we are le to seeing a single logical form in things which may be entirely iscrepant as to content. Langer (1967) 2

3 Introuction Relevance Shocks an policies may have at once macroeconomic, structural, an istributional implications working through a number of flowof-funs variables, an iniviual goo an factor markets. This creates interepenence between stabilization, structural an istributional issues an a nee for an analytical framework that accounts for this interepenence. A general equilibrium analysis offers such framework 3

4 Introuction Focus of presentation Moeling an Open Market Economy Outline The Logic of General Equilibrium Moeling Working Definition The Basic Walrasian Framework Diagrammatic Representation Circular Flow of Economic Activity Social Accounting Matrix 4

5 Introuction Numerical Implementation in EViews Specification Closure Calibration Valiation Simulations Dutch Disease Deterioration of TOT 5

6 What is a General Equilibrium Moel? A logical representation of a socioeconomic system wherein the behavior of all participants is compatible. Key moeling issues: Ientification of participants. Specification of iniviual behavior. Specification of moe of interaction. Characterization an esirability of compatibility. 6

7 Basic Walrasian Framework Template for most applie CGE moels. Two categories of agents or participants: proucers or firms an consumers or househols. 7

8 Basic Walrasian Framework Optimizing behavior Entails specification of (1) actions an economic unit can take; (2) the constraints it faces; an (3) the objective function use to evaluate iniviual actions (Varian 1984). Supply an eman behavior is thus an observable consequence of the optimization assumption. 8

9 Basic Walrasian Framework Market interaction: metho of social coorination by mutual ajustment among participants base on qui pro quo (Linblom 2001). Compatibility All markets are in equilibrium: incentive configuration is such that effective eman equals supply. Alternatively: No feasible change in iniviual behavior is worthwhile, or if a change is worthwhile, it must not be feasible. 9

10 Basic Walrasian Framework Comparative Statics entails comparison of equilibrium states associate with changes in the socioeconomic environment. Social esirability of any state epens on chosen criterion. Criterion may involve both unerlying social arrangements an outcomes from participation in such arrangements. 10

11 Basic Walrasian Framework A esirable social arrangement is a mechanism esigne to control an coorinate the behavior of participants in a way that minimizes conflict an promotes cooperation unerstoo as exchange of help (Linblom 2001) Social peace woul therefore be maintaine if the market system is accepte (by law an popular acquiescence) as the preferre allocation mechanism. 11

12 Basic Walrasian Framework areto efficiency focuses on how well the system promotes iniviual objectives. Compatibility implies no other situation (in terms of outcomes) is unanimously preferre by all participants. poverty/equity-focuse criterion: less poverty/inequality is preferre to more. 12

13 Circular Flow Chart of Economic Activity Factor services Factor markets Firms Intermeiate goos Househols rouct markets Final goos Exports Imports Rest of the worl 13

14 Social Accounting Matrix Structure of a Basic SAM for an Open Economy Activity Commoity Factor Househol Worl Total Activity Domestic Sales Exports Total Sales Commoity Intermeiate Deman Househol Consumption Total Deman Factor Factor ayments Factor ayments Househol Factor ayments Balance of Trae Total Househol Income Worl Imports Imports Total Total Cost Total Supply Factor ayments Total Househol Expeniture Foreign Exchange 14

15 Social Accounting Matrix An accounting framework that reflects the circular flow of economic activity. A square matrix, the imension of which is etermine by the number of sectors, agents an institutions consiere. Each entry represents a payment to a rowaccount by a column-account. Consistency implies that row total must equal corresponing column total. Also, if all but one accounts balance, the last one must balance as well (Walras law). 15

16 Social Accounting Matrix Analytical Expression for a Basic SAM Activity Commoity Factor Househol Worl Total Activity Commoity Factor Househol Worl Total Q q n WF X mq m WF s x X Q s q s WF s Q q f e X e x X s RS f Q q f e X e + RS f Q + Q q n WF WF + s mq m RS q f f 16

17 Numerical Implementation Specification Simple Salter-Swan one-sector moel with symmetric prouct ifferentiation for both imports an exports. Domestic an foreign goos are imperfect substitutes. A founation for the stuy of the impact of macroeconomic imbalances an ajustment policies on the real sector of a small open economy (Devarajan, Lewis an Robinson 1990). Three agents: proucer, consumer an rest of the worl. rouction sector sells output both omestically an on the worl market. 17

18 Specification roucer maximizes profit subject to technical constraints an market opportunities at home an abroa. Consumption goo is mae up of omestic goo an imports. Consumer owns all factors of prouction an maximizes utility subject to a buget constraint (or minimizes expenitures neee to achieve given level of utility). 18

19 Specification Goos an factor markets are perfectly competitive, an full employment prevails. Small country assumption: country cannot affect the terms at which it is traing with the rest of the worl. Assumption of full employment of all primary factors of prouction allows use of the prouction possibility frontier moele as a constant elasticity of transformation function (CET). 1 φ φ X A γ X + γ X s [ ] φ = x e e 19

20 Specification Optimal behavior of proucer represente by CET revenue function: [ ] 1 s ω (1 ω) ω (1 ω) (, ; ) = γ + γ (1 ω) e Xs e e Ax R X where ω=1/(1+ ϕ) stans for the elasticity of transformation. Supply of exports an that of omestic sales are erive from this revenue function by application of the Envelope theorem. 20

21 Specification Envelope Theorem Optimization assumption implies that the maximum value attainable by the objective function can be expresse in terms of various parameters that enter both the objective function an the constraints. This expression is the maximum value function (Dixit 1990). Accoring to the envelope theorem, the change in in the objective function inuce by a change in a parameter while the choice variable ajusts optimally is equal to the partial erivative of the maximum value function with respect to the parameter (Varian 1984). 21

22 22 Specification Export supply function is the partial erivative of the revenue function wit respect to the omestic price of exports. Similarly for omestic sales ( ) ) (1 1 1 ) / ( ω ω ω ω ω ω ω γ γ γ + = e e e e x s e A X X ( ) ) (1 1 1 ) / ( ω ω ω ω ω ω ω γ γ γ + = e e x s A X X

23 Specification Domestic price of export GD eflator x e s = Rπ X = + e ( e X e X The consumer is assume to minimize the cost of a composite consumption goo efine as a constant elasticity of substitution (CES) aggregate of imports an omestic goos (Armington aggregation). Q s [ ] ρ ρ β Q + β D ρ = Bq m m x 1 ) 23

24 24 Specification The corresponing optimal level of expeniture is: The elasticity of substitution is: Deman for omestic goo ( ) ) (1 1 1 ) / ( σ σ σ σ σ σ σ β β β + = m m q s x B Q D [ ] s m m q s m Q B Q E ) (1 1 ) (1 ) (1 1 ) ;, ( σ σ σ σ σ β β + = ρ σ + = 1 1

25 Specification Deman for imports Q m Domestic price of imports Total expeniture on the composite consumption goo Q = Q + D ) q s Househol income h x m s = σ Rπ Y = X + RS σ σ 1 σ σ 1 σ ( β + β )(1 ) βm ( Q / ) σ s Bq m m m = m ( m m x f 25

26 Specification Deman for composite consumption goo (assuming no savings) Q = Goos market equilibrium Q = Q D x Balance of trae Y h q X = s π Q π X = S m m e e f 26

27 Closure EViews requires a one-to-one mapping between equations an enogenous variables. The process of etermining which variables to make enogenous an which exogenous is known generally as closure. In the Walrasian framework, only relative prices matter. If we multiply the price of omestic goo an the exchange rate by a constant, all nominal values will be multiplie by the same constant an real variables will remain unchange. Hence the system is sai to be homogeneous of egree zero. 27

28 Closure We can therefore choose a numéraire goo an fix its price exogenously. We select the price of the composite goo Q, an make it exogenous. Full employment assumption means real GD can be mae exogenous. The small country assumption implies that worl prices are exogenous. Finally, we make the balance of trae exogenous as well. 28

29 Closure The moel also respects Walras law: if all economic agents satisfy their buget constraints an all, but one, markets are in equilibrium, then the last market must also be in equilibrium. Alternatively, if all markets are in equilibrium an all, but one, buget constraints are bining, then the last buget constraint is bining as well (Dinwiy an Teal 1988). Hence, we can rop one equilibrium conition from the system an it will still solve. We rop the househol buget constraint by assigning to it a ummy enogenous calle WALRAS. This ummy must equal zero when the law is satisfie by a solution of the moel. 29

30 Closure The Core Moel of an Open Economy in EViews XQ = ces * ( betam * XM^(-rho) + beta * XD^(-rho) )^(-1 / rho) E = EXR * WE M = EXR * WM X * XS = (E * XE + D * XD) D * XD = (Q * XQ - M * XM) XE = (XS / cet) * (gammae / E )^omega * ( gammae^omega * ( E)^(1 - omega) + gamma^omega * (D)^(1 - omega) )^(omega / (1 - omega)) XD = (XS / cet) * (gamma / D )^omega * ( gammae^omega * ( E)^(1 - omega) + gammad^omega * (D)^(1 - omega) )^(omega / (1 - omega)) XM = (XQ / ces) * (betam / M )^sigma * ( betam^sigma * ( M)^(1 - sigma) + beta^sigma * (D)^(1 - sigma) )^(sigma / (1 - sigma)) YHH = X * XS + EXR * BOT WALRAS + Q * XQ = YHH EXR * WM * XM = E * XE + EXR * BOT 30

31 Calibration To make the moel fully computable we resort to calibration. This process solves the relevant equations for values of the parameters that are consistent with base year ata. For the parameters of the CET aggregation function: Assume a value for ω an compute ϕ=(1- ω)/ ω The share parameters a up to one γ e + γ =1 31

32 32 Calibration Share parameter The shift parameter of the CET is compute as: ω ω ω γ = + = e e e e e e e X X X X X X [ ] φ φ φ γ γ + e e X X 1 = s x X A

33 33 Calibration Calibration of the parameters of the Armington aggregation is entirely analogous: σ σ ρ = 1 =1 + β m β σ β = x m m m D Q [ ] ρ ρ ρ β β 1 + = x m m s q D Q Q B

34 Calibration Baseline Data Activity Commoity Househol Rest of Worl Total Activity Commoity Househol Rest of Worl Total Source: e Melo an Robinson (1989) 34

35 Calibration Calibration of the Core Moel of an Open Economy in EViews MODEL CALIBER omega.fill -0.2, -0.5, -2, -5, -500 sigma.fill 0.2, 0.5, 2, 5, 5 CALIBER.AEND gammae=1/(1 + ( D/E)*(XE/XD)^(-1/omega) ) CALIBER.AEND gamma=(1 - gammae) CALIBER.AEND phi=(1-omega)/omega 'Exponent in the CET function CALIBER.AEND cet=xs/( gammae*xe^(-phi) + gammad*xd^(-phi) )^(-1/phi) CALIBER.AEND betam=1/(1 + ( D/M)*(XM/XD)^(-1/sigma) ) CALIBER.AEND beta=(1 - betam) CALIBER.AEND rho=(1-sigma)/sigma 'Exponent in the CES Armington function CALIBER.AEND ces=xq/( betam*xm^(-rho) + betad*xd^(-rho) )^(-1/rho) CALIBER.SCENARIO ACTUALS CALIBER.SOLVE(s=, =s,o=n) CALIBER.MAKEGROU(a) FREEZE(CALIBRATED) CALIGR 35

36 Calibration Calibration Results for the Core Moel of an Open Economy obs OMEGA SIGMA BETAD BETAM CES CET GAMMAD GAMMAE HI RHO Source: Author s calculations 36

37 Valiation A series of tests to ensure that the calibrate moel behaves accoring to the unerlying structure Check calibration Single equation solution (no interaction) to isolate possibly offening equation. Simultaneous solution to check coherence (make sure moel reprouce baseline). 37

38 Valiation Within the Walrasian Framework: Check Walras law: roppe equation must be satisfie by solution (if using ummy to exclue equation, solve ummy must equal zero or be very close to zero). Homogeneity test: the assumptions of optimization an interaction within competitive markets imply that the moel is homogenous of egree zero. Multiplying the numéraire price by a constant k prouces a solution where real values remain unchange but all nominal values are multiplie by k. 38

39 Valiation Homogeneity test: Multiply numéraire price by 2. Omega Sigma EXR D E M X Walras YHH XD XE XM XQ Source: Author s calculations 39

40 Implications of Dutch Disease Dutch Disease Refers to ecline of the Netherlans export competitiveness in the 1970s following iscovery an exploitation of the Groningen natural gas fiels (Benjamin, Devarajan an Weiner 1989). In general, the averse effect that real exchange appreciation has on some traable sectors of the economy as a result of an increase in foreign capital inflow. Use above moel to simulate implications of an increase of the balance of trae from 0 to

41 Dutch Disease Structural an Welfare Implications Omega Sigma EXR D X RD RX XD XE XM XQ Source: Author s calculations 41

42 Dutch Disease Contraction of traable sector relative to non-traable inuce by an increase in omestic prices relative to worl prices (real appreciation of the exchange rate, Devarajan et al. 1990). On the eman sie: The foreign transfer goes entirely to the consumer (by assumption) hence consumption an welfare (XQ) increase (see above table). 42

43 Dutch Disease Deman sie In the limit, increase in welfare equals the amount of the transfer. There is an increase in the consumption of both omestic goo (XD) an imports (XM) leaing to an increase in the price of the omestic goo (D) relative to price of traable. Hence real appreciation (EXR/D ranges from 0.38 to 1). 43

44 Dutch Disease Supply sie Real appreciation shifts incentives in favor of the omestic sector against exports. Resources move accoringly. More of the omestic goo is prouce. Export sector eclines. Role of structural parameters The higher the elasticity of transformation, the closer the increase in welfare equal the amount of the transfer. 44

45 Dutch Disease Role of structural parameters The magnitue of the elasticity of substitution unerpins the extent of real appreciation (Devarajan et al. 1990): (1) If zero, imports an omestic goos are perfect complements. More of both goos are consume, an an increase in price of the omestic goo leas to real appreciation. (2) If infinity, both goos are perfect substitutes. The eman for the omestic goo will not change an therefore there will be no real appreciation an no Dutch isease. 45

46 Dutch Disease Shoul it be a matter of policy concern? If unerlying real appreciation is suen or reversible, then policymakers may wish to mitigate its impact on traable sectors (Coren 2002). If fixe exchange rate with inepenent monetary policy (or in the regime of manage float) the government may try to sterilize the effects of foreign capital inflows on the money supply. Fiscal contraction can also help. 46

47 Dutch Disease Case of Cameroon uring the oil boom of the 1970s: (Benjamin, Devarajan an Weiner 1989): Fixe exchange rate an no inepenent monetary policy. Save a large share of oil revenue abroa an use part of winfall to increase proucer price of cash crop thus counteracting the averse incentive effects inuce by real appreciation. 47

48 A Deterioration of the Terms of Trae Structural an Welfare Implications Omega Sigma EXR D X RD RX XD XE XM XQ Source: Author s calculations 48

49 A Deterioration of the Terms of Trae A 10% increase in the worl price of imports There is a ecrease in welfare associate with this eterioration of the terms of Trae (XQ is uniformly lower than its base value). As expecte, structural impact hinges on chosen elasticities. Two cases: Sigma less than one Sigma greater than one 49

50 A Deterioration of the Terms of Trae Case 1: Domestic goos an imports are complements Less consumption of both omestic goo an imports. A fall in the price of omestic goos leas to a real epreciation of the exchange rate which attracts resources in the export sector. Increase in the prouction of exports to pay for more expensive imports. 50

51 A Deterioration of the Terms of Trae Case 2: Domestic goos an imports are substitutes There is an increase in the consumption of the home goo with less consumption of imports. There is an appreciation of the real exchange rate as the price of the omestic goo increases relative to that of foreign goos. Real appreciation shifts resources away from export sector to home goos. 51

52 A Deterioration of the Terms of Trae What rives the outcome? Income an substitution effects associate with the increase in the worl price of imports. When sigma less than one (case 1), income effect ominates the substitution effect. There is real epreciation inuce by fall in omestic price. Incentive configuration favors the export sector. When sigma is greater than one, substitution effect ominates income effect. Real appreciation leas to the expansion of the omestic sector an a contraction of the export sector. 52

53 References Benjamin N. C., Devarajan, S. an Weiner R. J The "Dutch" Disease in a Developing Country : Oil Reserves in Cameroon. Journal of Development Economics. Vol. 30: Coren W. Max Too Sensational: On the Choice of Exchange Rate Regimes. Cambrige (Massachusetts): The MIT ress. De Melo Jaime an Robinson Sherman rouct Differentiation an the Treatment of Foreign Trae in Computable General Equilibrium Moels of Small Economies. Journal of International Economics, Vol. 27: Devarajan, S., J. D. Lewis, an S. Robinson olicy Lessons from Two-Sector Moels. Journal of olicy Moeling 12 (4):

54 References Dinwiy, C.L. an F.J. Teal The Two-Sector General Equilibrium Moel: A new Approach. Oxfor: hilip Allan. Dixit, A. K Optimization in Economic Theory. Oxfor: Oxfor University ress. Linblom, C. E The Market System: What Is It, How It Works an What to Make of It. New Haven, CT: Yale University ress. Varian, H. R Microeconomic Analysis. New York: Norton & Company. 54

55 The En. 55