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Model Equations Complement to the Article submitted to the Journal of Policy Modeling Titled The Euro-Mediterranean Free Trade Agreement An Inquiry into the Cost of Adjustment to Tariff Liberalization for the Egyptian Economy An Intertemporal General Equilibrium Analysis Abeer Elshennawy Assistant Professor The American University in Cairo AUC Avenue, P.O. Box74. New Cairo 11835 Egypt e-mail [email protected] [email protected] 0 Model Equations The model draws upon the contributions to intertemporal General Equilibrium models by Mercenier and Sampaio de Souza (1993), Mercenier (1995), Go (1991) , Diao and Somwaru (1996), Diao and Somwaru (1997), Diao and Somwaru (1999) and is composed of two parts: a dynamic part - in which both households and firms decision to consume and invest is a result of dynamic optimization- and a standard within period static CGE model. A detailed description of the dynamic part can be found in Elshennawy, 2011 The consumer problem: The representative household chooses the path of consumption that maximizes the discrete intertemporal utility function : Uo t (1/1)t ln(TCt ) A1 The intertemporal budget constraint is t=1Rt PtctTCt t=1Rt ( wl p,t LSUP p,t + wl NP,t LSUP NP,t +THGt )+ A2 TCt s CDSa,(ts ) A3 Rt = =0 1 1+r A4 Variables and Parameters = Aggregate consumption TCt CD( S ,t ) = private consumption of good s Rt Ptct = discount factor from time t to time zero wl( P ,t ) wl( NP ,t ) LSUP( P ,t ) = wage rate of production labor = the price of total consumption = wage rate of nonproduction labor = labor supply of production labor 1 LSUP( NP ,t ) = labor supply of nonproduction labor THGt rt = transfer of government revenue to household = instantaneous interest rate = value of the household initial financial wealth SAVt = wl p,t LSUPp,t +wlNP,t LSUPNP,t + s DIVs +THGt - rt Dt 1 - PtctTCt A5 First order (Euler conditions) imply TCt 1 Ptct (1 ) (1 rt ) TCt Ptct 1 A6 The Firm Problem Asset market equilibrium condition r where DIVs Vs Vs Vs r is the world interest rate, A7 DIV is dividends, V is the value of the firm. In addition, the following terminal condition is imposed to rule out Ponzi schemes limt RV t S ,t 0 A8 solving the above difference equation yields VS ,1 t 1 Rt DIVS ,t A9 The market value of the firm is defined as the sum of discounted stream of future dividends. Dividends are defined as 2 PVA f[(L ,K ] - wl P, t LSUP P, t - wl NP, t LSUP NP, t - ADC - PI I S,t S,t S,t S,t S ,t S ,t ADCS ,t I S2,t S PVAS ,t K S ,t A11 A10 and ADC is the adjustment cost of investment while PVA is value added price Capital accumulation constraint K S ,t 1 (1 S ) K S ,t I S ,t A12 Differentiating with respect to the control variable qS ,t PI S ,t 2PVAS ,tS I yields I S ,t KS ,t A13 which determines the shadow price of capital (Tobin q). Differentiating with respect to the state variable K yields the no arbitrage condition wkS ,t PVAS ,tS ( I S ,t 2 ) (1 S )qS ,t (1 r )qS ,t 1 0 K S ,t which is the same as the asset equilibrium condition since V=q K. Variables and Parameters wk( S ,t ) =capital rental rate PVA( S ,t ) =value added price 3 A14 K ( S ,t ) S =capital stock =depreciation rate I S ,t AK S S INVDS S ,S,S A15 is a composite good produced from all final goods - with fixed share - using a constant returns technology, It Variables and Parameters =shift parameter in the investment function AK S INVD( S ,S ) =investment demand by sector of origin I ( S ,t ) PI ( S ,t ) =new physical capital good =price of new capital good Current Account Dynamics In open economy, investment is not constrained by the availability of domestic savings and any discrepancy is financed through foreign borrowing. Current account equilibrium is described by Dt Dt 1 rt Dt 1 TBt A16 The above equation shows that the increase in foreign debt deficit TBt Dt is composed of the trade and the interest payment on foreign debt . Within period equations (the time subscript is omitted to simplify notation) Price block Domestic price of imports PM S ,R [1 mS ,R ]PWIM S ,R A17 4 Domestic price of exports PES ,R [1 eS ,R ]PWES ,R A18 Composite import price m 1 1 m 1+ m 1 m PMM S = [ m1+ m PM S1+,W m + (1 )m1+ m PM S1+,EU ] m ACM A19 Composite export price E E E 1 1 1 - 1-1 E 1 E 1 PEES = [ E E PES ,W +(1- E )- E 1PES,W ] E ATE A20 Domestic supply price PCS PDS DS MM S PMM S CS CS A21 Domestic output price PX S PDS DS EES PEES XS XS A22 Value added price PVAS [1 iS ]PX S S IOS ,S PCS A23 Price of investment (unit cost function for producing investment good) 5 PI S S PCS S ,S AK S . S A24 S ,S S ,S Variables and Paramters: Variables = domestic good price (sold domestically) PDS PM ( S , R ) = domestic price of imports from region R PMM S = composite price of imports PE( S , R ) = domestic price of exports to region R PEES PCS PX S PVAS DS = composite price of exports M ( S ,R ) = quantity of imports from region R = domestic supply price = domestic output price = value added price = quantity of domestic output sold domestically = composite quantity of imports MM S = quantity of exports to region R E( S ,R ) = composite quantity of exports EES CS = quantity of good supplied domestically X S = quantity of domestic output Parameters mS eS iS = import tariff rate = export subsidy rate = input output coefficient PWIM S , R PWES ,R = world price of imports from region R ( S ,S ) = share of good s’ in sector s investment AK S = shift parameter in the investment production function = world price of exports from region R 6 Output supply and demand block AX S [KS SK LSSL ] A25 Labor is a Cobb Douglas aggregation of two skill categories; production and nonproduction labor LS LS S LS S P P A26 NP NP Profit maximization by producers lead to the following factor demand equations Factor demand LDS P LDS NP PVAS X S S S L wlP P PVAS X S S S L wlNP A27 NP A28 The rental rate of capital is determined from the following equation KS PVAS K X S wkS A29 Intermediate demand INTDS S IO( S ,S ) X S A30 7 Intermediate demand is determined according to leontif technology and is therefore equal to the sum of fixed input output coefficients IO( S ,S ) multiplied by domestic output X S Armington Functions CS ACS [S MM SCS (1 S )DSCS ]1/ CS MM S ACm[ m M S,Wm 1 m (1 m )M S ,EU ] m A31 A32 Import demand MM S DS [ PDS S ]1/(1CS ) PMM S .(1 S ) M ( S ,W ) = M (S,EU) [ A33 PM (S,EU) m 1 ] 1+ m PM (S,W) (1- m ) A34 CET Functions X S ATS [ S EESTS (1 S )DSTS ]1/ TS A35 1 EES = ATE[ E ES,EW +(1- E )ES,EEU ] E 8 A36 Export Supply EES DS [ PEES 1 S ) 1/( S 1) ] PDS S E(S,W) = E(S,EU) [ A37 PE(S,W) E 1 ] ( E -1) PE(S,EU) (1- E ) A38 Since there are no imports in the case of nontradables, supply consists only of output sold domestically. Variables and Parameters: wlP = production labor wage rate wlNP = non production labor wage rate wkS = capital wage rate KS = capital stock in sector s LD( P,S ) =demand for production labor by sector s LD( NP,S ) = demand for non production labor by sector s INTDS =intermediate demand of good S AX S = production function shift parameter ( K ,S ) = share of capital in value added of sector s ( L,S ) = share of labor in value added of sector s ( P,S ) =share of production labor in total labor input ( NP,S ) =share of non production labor in total labor input ACS = shift parameter in Armington ACM S = shift parameter in Regional Armington elasticity S = share parameter in Armington 9 (m,S ) = share parameter in Regional Armington CS = Armington exponent (m,S ) = Regional Armington exponent ATS = shift parameter in CET ATES = shift parameter in Regional CET S = share parameter in CET E = share parameter in Regional CET T = CET exponent S E = Regional CET exponent CS = elasticity of substitution between domestic goods and imports X S = elasticity of substitution between domestic use and exports Factor and institution block Household flow income YHt wl( P,t ) LSUP( P,t ) wl( NP,t ) LSUP( NP,t ) S DIV(S ,t ) THGt rt Dt 1 A39 Household demand PCS CDS aS (YH SAV ) Demand for each good is a fixed share A40 a of total expenditure on goods Sectoral investment demand (by sector of origin) PCS INVD( S ,S ) ( S ,S ) PI S .I S A41 Variables and Parameters YH = household income D = foreign debt 10 SAV = household saving CDS =HH demand for good S INVD( S ,S ) = sector S investment demand for good S’ (investment demand by sector of origin) I S = new investment aS = spending share for HH on good S AKS = shift parameter in investment equation ( S ,S ) = share of good s’ in sector s investment Government transfers iS PX S X S + R s mS,R PWIM S,R M S,R - R s eS ,R PWES,R ES,R A42 Government transfers to household THG is a transfer of net government revenue which consists of government income that is revenue from indirect taxes and tariffs less subsidies. Government consumption and government deficit is ignored. Consequently, household savings is equal to national savings. Equilibrium conditions Factor market equilibrium Labor S S S L S S S L p PVAS X S LSUPp wLp NP A43 PVAS X S LSUPNP wlNP A44 Demand for labor of each skill category equal its supply. Capital 11 S S .PVAS .X S K S .wkS A45 k Commodity market equilibrium CS =CDS +INVDS +INTDS Supply of output for good S, A46 C must equal consumption demand, investment demand and intermediated demand. Current account SPWIM S M S - SPWES ES =TB A47 current account equilibrium requires imports less exports must equal foreign savings Variables and Parameters KS =capital supply (capital stock) TB = Foreign savings LSUPP = supply of production labor LSUPNP = supply of non production labor d = direct tax rate Terminal condition (last period is SS) KS S = ISS A48 The first condition indicates that in the steady state investment is equal to depreciated capital. rSS = A49 The second condition follows form the Euler equation evaluated in the steady state and states that the interest rate must be equal to the rate of time preference. Assuming that the world economy is in a steady state and therefore (r )is constant implies in turn that the rate of time preference is also constant. 12 rSS DSS +TBSS =0 A50 Debt is constant in the steady state. If D is positive then foreign savings (the trade deficit) must be negative. That is the country must run a trade surplus in order to pay the interest rate on debt. If the above equation holds then domestic savings must be equal to investment. rSSVSS = DIVSS A51 Since the condition for asset market equilibrium and the no arbitrage condition are equivalent, the above equation must hold in the steady state implying that the average return to capital is constant. Variables and Parameters: TBt = foreign savings ( trade deficit) r = interest rate Welfare evaluation (Equivalent Variation index) t 1 t 0 1 ln TC 1 t 0 1 1 t ln TCt A52 Where TC is base year consumption. This implies that the welfare gain arising for a policy change is equivalent form the point of view of the representative household to increasing the reference consumption profile by REFERENCES Diao, X., and A. Somwaru .(1996) “Dynamic Gains and Losses from Trade Reform: An Intertemporal General Equilibrium Model of the United States and MERCOUSR.” 13 Diao, X., and A. Somwaru .(1997) “Trade Creation and Trade Diversion under MERCORSUR: A Global Intertemporal General Equilibrium Analysis”, Department of Applied Economics. University of Minnesota. Diao, X., and A. Somwaru .(1999) “MERCOUSR and the U.S.: An Intertemporal General Equilibrium Evaluation of the Regional Integration”, International Economic Journal. Vol 13, No1, pp.27-43. Go, Delfin. (1991) “External Shocks, Adjustment Policies, and Investment. Illustration from a Forward-Looking CGE Model of the Philippines”, World Bank Working Papers No. 737. Elshennawy, Abeer. (2011) “The Tranistional Costs to Trade Liberalization. An Intertemporal General Equilibrium Model for Egypt”, Econmodels.com. Elsevier. Go, Delfin.. (1991) External Shocks, Adjustment Policies, and Investment. Illustration from a Forward-Looking CGE Model of the Philippines”, Journal of Development Economics, Vol 44. pp. 229-261. Mercenier, J., and M. da C.S de Souza.. (1993) “Structural Adjustment and Growth in a Highly Indebted Market Economy: Brazil”, In J. Mercenier and T. Srinivasan eds. Applied General Analysis and Economic Development, Ann Arbor. Univesity of Michigan Press. Mercenier.J. (1995) “ Can 1992 reduce unemployment in Europe? On Welfare and Employment Effects of Europe’s Move to a single Market”, Journal of Policy Modeling Vol. 17 No.1.. pp.137 14 15