Understanding the structure - PowerPoint Presentation

1. Understanding the structureAnd equations of MINIMAL model1

2. Equilibrium = > Supply = DemandLet’s start with demand2

3. DEMANDX(“shoes”, “domestic”, “household”)X(“shoes”, “import”, “household”)X(“wheat”, “import”, “noodle”)c  COM # Commodities # (AgricMining, Manufacture, Utilities, Construction, TradeTranspt, FinanProprty, Services); s  SRC # Source of commodities # (dom,imp);U  USER # All users # (AgricMining, Manufacture, Utilities, Construction, TradeTranspt, FinanProprty, Services, Investment, Households, Government, Exports) ;3

4. TOTAL DEMAND4

5. SOURCINGDomestic and imported goods are competing goodsWhen price of a domestic good rise, and the price of the imported one stays the same, the demand for the domestically produced good will decline, and vice-versa. How to model this mechanism? ARMINGTON equation5

6. Define composite goods!6

7. Composite goodsElasticity of substitutionCES AggregationDomestikImporDomestikImporDomestikImpor7

8. The model of consumer’s behaviour in choosing the optimum combination of domestic and imported commoditiesFor every unit of X_S,Each user (u), for each commodity (c),minimizes:Subject to:8

9. X_SX(‘dom’)X(‘imp’)P(‘dom’)/P(‘imp’)MinimizeSubject toThe solution or First Order Conditions9

10. How is the quantity of the composite good determined??In MINMAL, each user has its own behaviourUser (u) consists of:Industry, Household, Gov’t, Investment10

11. Industry demand X_S as raw materialOUTPUTCONSTANTLEONTIEFPARAMETERDemand for composite-goods as raw material only depend on the amount of output of the industry11

12. HOUSEHOLD?MaximizeSubject to:Solution:12

13. Other users?13

14. RECAP:14

15. 15

16. EKSPOR Demand16Exports of each good c are a declining function of price in foreign currency, P(c,"dom")/PHI relative to the world price PWORLD(c).EXP_ELAST(c) = the +ve elasticity of export demand. Suppose = 5, 1% increase in price would cause a 5% fall in foreign demand.Shift variable F4Q could be used to simulate exogenous shifts in foreign demands.

17. SUPPLY17

18. Production Function OUTPUT = F(INPUT)18

19. LEONTIEF Production FunctionX1X27.52.5Y = 10Cost minimizing input demand:19

20. Production Function in MINIMALatau20

21. Cost minimization: bottom levelSolusi:21

22. Cost minimization: bottom levelX1LAB(i)X1CAP(i)X1PRIM(i)P1LAB/P1CAP(i)22

23. Cost minimization: Top LevelSolusi (optimum condition):23

24. Supplies meets Demands:MARKET CLEARING FOR Domestic COMMODITIES24

25. Prices are determined25

26. Import price are “exogenous”, determined by the world price.26

27. Input Market in MINIMALLABORExogenous27

28. Input Market in MINIMALCAPITALCapitalLaborabK1K2X1X2X3Specific factor model;Capital cannot move to other sector;Price of capital is determined within each of the industries.28

29. OTHERSOther equations are aggregation or definition of various index of quantity and prices. 29

30. Understanding tablo file of Minimal30

31. See the handout for linearization of minimal equations31

32. 32Excerpt 1a: Sets for usersUSERFINALUSERINDInvestmentHouseholdsGovernmentExportsAgricMiningManufactureUtilitiesConstructionTradeTransptFinanProprtyServicesIMPUSER

33. 33Excerpt 1a: Sets for usersSet ! User categories: IO table columns ! IND # Industries # read elements from file BASEDATA header "IND"; FINALUSER # Final demanders # (Investment, Households, Government, Exports); USER # All users #= IND union FINALUSER; NIMPUSER # Non-import user # (Exports);Subset NIMPUSER is subset of FINALUSER;Set IMPUSER # Non-export demanders: users of imports # = USER - NIMPUSER;Subset IND is subset of IMPUSER;

34. 34Excerpt 1b: Other sets; Flows DataSet ! Input categories: IO table rows ! COM # Commodities # = IND; SRC # Source of commodities # (dom,imp); FAC # Primary factors # (Labour, Capital); Coefficient (all,c,COM)(all,s,SRC)(all,u,USER) USE(c,s,u) # USE matrix #; (all,f,FAC)(all,i,IND)FACTOR(f,i) # Wages and profits #; (all,i,IND) V1PTX(i) # Production tax revenue #; (all,c,COM) V0MTX(c) # import tax revenue #;Read USE from file BASEDATA header "USED"; FACTOR from file BASEDATA header "1FAC"; V0MTX from file BASEDATA header "0TAR"; V1PTX from file BASEDATA header "1PTX";

35. 35Excerpt 2: Useful aggregates of the dataCoefficient (all,c,COM)(all,u,USER) USE_S(c,u) # USE matrix, dom+imp together#; (all,u,USER) USE_CS(u) # Total user expenditure on goods #; (all,c,COM)(all,s,SRC) SALES(c,s) # Total value of sales #; (all,i,IND) V1PRIM(i) # Wages plus profits #; (all,i,IND) V1TOT(i) # Industry Costs #; (all,c,COM) V0CIF(c) # Aggregate imports at border prices #;Formula (all,c,COM)(all,u,USER) USE_S(c,u) = sum{s,SRC,USE(c,s,u)}; (all,u,USER) USE_CS(u) = sum{c,COM,USE_S(c,u)}; (all,c,COM)(all,s,SRC) SALES(c,s) = sum{u,USER,USE(c,s,u)}; (all,i,IND) V1PRIM(i) = sum{f,FAC,FACTOR(f,i)}; (all,i,IND) V1TOT(i) = V1PRIM(i) + sum{c,COM,USE_S(c,i)}; (all,c,COM) V0CIF(c) = SALES(c,"imp") - V0MTX(c);

36. 36Excerpt 3: Total Demands for commoditiesVariable (all,c,COM)(all,s,SRC)(all,u,USER) x(c,s,u) # Demand by user u for good c, source s #; (all,c,COM)(all,s,SRC) x0(c,s) # Total demand for good c, source s #;Equation E_x0 (all,c,COM)(all,s,SRC) SALES(c,s)*x0(c,s)= sum{u,USER,USE(c,s,u)*x(c,s,u)};In the levels: X0(c,s) = S X(c,s,u)Percent change: X0(c,s)*x0(c,s) = S X(c,s,u)*x(c,s,u)X common price: P(c,s)*X0(c,s)*x0(c,s) = S P(c,s)*X(c,s,u)*x(c,s,u)Finally: SALES(c,s)*x0(c,s) = S USE(c,s,u)*x(c,s,u)

37. 37Variable (all,c,COM)(all,s,SRC) p(c,s) # User price of good c, source s #; (all,c,COM)(all,u,IMPUSER) p_s(c,u) # User price of composite good c #; (all,c,COM)(all,u,IMPUSER) x_s(c,u) # Use of composite good c #;Coefficient (parameter) (all,c,COM) SIGMA(c) # elasticity of substitution: domestic/imported #; (all,c,COM)(all,s,SRC)(all,u,IMPUSER) SRCSHR(c,s,u) # imp/dom shares #;Read SIGMA from file BASEDATA header "ARM";Formula (all,c,COM)(all,s,SRC)(all,u,IMPUSER) SRCSHR(c,s,u) = USE(c,s,u)/USE_S(c,u);Equation E_x (all,c,COM)(all,s,SRC)(all,u,IMPUSER) x(c,s,u) = x_s(c,u) - SIGMA(c)*[p(c,s) - p_s(c,u)];Equation E_p_s (all,c,COM)(all,u,IMPUSER) p_s(c,u) = sum{s,SRC, SRCSHR(c,s,u)*p(c,s)};Excerpt 4: CES Imported/domestic Substitution

38. 38Demands for primary factorsChoose inputs of labour and capital, X1LAB(i) and X1CAP(i), to minimize primary factor cost, P1LAB*X1LAB(i) + P1CAP(i)*X1CAP(i) where X1PRIM(i) = CES[ X1LAB(i), X1CAP(i) ], regarding as fixed: P1LAB and P1CAP(i) and X1PRIM(i).Answer: (all,i,IND) x1lab(i) = x1prim(i) - SIGMA1PRIM(i)*[p1lab-p1prim(i)]; x1cap(i) = x1prim(i) - SIGMA1PRIM(i)*[p1cap(i)-p1prim(i)]; V1PRIM(i)*p1prim(i) = FACTOR("Labour",i)*p1lab + FACTOR("Capital",i)*p1cap(i);Could write p1prim(i) = S1LAB(i)*p1lab + S1CAP(i)*p1cap(i), x1prim(i) = S1LAB(i)*x1lab(i) + S1CAP(i)*x1cap(i)S1LAB and S1CAP are shares of labour and capital in primary factor cost.

39. 39Excerpt 5: Demands for capital and labourVariable (all,i,IND) x1prim(i) # Industry demand for primary-factor composite #; (all,i,IND) p1prim(i) # Price of primary factor composite #; (all,i,IND) x1lab(i) # Employment by industry #; p1lab # Economy-wide wage rate #; (all,i,IND) x1cap(i) # Current capital stock #; (all,i,IND) p1cap(i) # Rental price of capital #;Coefficient (parameter) (all,i,IND) SIGMA1PRIM(i) # CES substitution, primary factors #;Read SIGMA1PRIM from file BASEDATA header "P028";Equation E_x1lab (all,i,IND) x1lab(i) = x1prim(i) - SIGMA1PRIM(i)*[p1lab-p1prim(i)];Equation E_x1cap (all,i,IND) x1cap(i) = x1prim(i) - SIGMA1PRIM(i)*[p1cap(i)-p1prim(i)];Equation E_p1prim (all,i,IND) V1PRIM(i)*p1prim(i) = FACTOR("Labour",i)*p1lab + FACTOR("Capital",i)*p1cap(i);

40. 40Excerpt 6: Top level industry demands X_S(c,i) = A_S(c,i).X1TOT(i), iIND, cCOM X1PRIM(i) = A1PRIM(i).X1TOT(i), iINDVariable (all,i,IND) x1tot(i) # Industry output #; (all,i,IND) a1prim(i) # All primary-factor augmenting technical change #; (all,i,IND) p1tot(i) # Unit cost of production #;Equation E_x1 # demand for commodity composites # (all,c,COM)(all,i,IND) x_s(c,i)= x1tot(i);Equation E_x1prim # demand for primary-factor composites # (all,i,IND) x1prim(i) = a1prim(i) + x1tot(i);Materials and primary factors used in proportion to X1TOT(i). A_S(c,i) = amount of composite good c used per unit of output (constant).A1PRIM(i) = amount of primary-factor needed to make unit of output.1% decrease in A1PRIM(i) implies a 1% increase in factor productivity

41. 41Excerpt 6: Cost of productionLevels: V1TOT(i) = sum{c,COM, sum{s,SRC, USE(c,s,i)}} + FACTOR("Labour",i) + FACTOR("Capital",i);Equation E_p1tot # cost of production = cost of all inputs # (all,i,IND) V1TOT(i)*[p1tot(i)+ x1tot(i)] = sum{c,COM,sum{s,SRC, USE(c,s,i)*[p(c,s) + x(c,s,i)]}} + FACTOR("Labour",i)*[p1lab + x1lab(i)] + FACTOR("Capital",i)*[p1cap(i)+ x1cap(i)];Right hand terms = 100 times the change in expenditure on some input.Left hand side = 100 times the change in total costs.Change in the value of output, V1TOT(i) = sum of the changes in expenditure on materials and primary factors.

42. 42Excerpt 7 Household demandsVariable p3tot # Consumer price index #; x3tot # Real household consumption #; w3tot # Nominal total household consumption #;Equation E_x3 (all,c,COM) x_s(c,"Households") + p_s(c,"Households") = w3tot;Equation E_x3tot USE_CS("Households")*x3tot = sum{c,COM, USE_S(c,"Households")*x_s(c,"Households")};Equation E_p3tot USE_CS("Households")*p3tot = sum{c,COM, USE_S(c,"Households")*p_s(c,"Households")};

43. 43Excerpt 8: Export demandsLevels X(c,"dom","Exports") = F4Q(c)[ ]-EXP_ELAST(c)Exports of each good c are a declining function of:price in foreign currency, P(c,"dom")/PHIrelative to the world price PWORLD(c).EXP_ELAST(c) = the +ve elasticity of export demand Suppose = 5,1% increase in price would cause a 5% fall in foreign demand.Shift variable F4Q could be used to simulate exogenous shifts in foreign demands.Variable (all,c,COM) pworld(c) # World prices, measured in foreign currency #; (all,c,COM) f4q(c) # Quantity shift in foreign demand #; phi # Exchange rate, (local $)/(foreign $) #;Coefficient (parameter)(all,c,COM) EXP_ELAST(c) # Export demand elasticities #;Read EXP_ELAST from file BASEDATA header "P018";Equation E_x4a (all,c,COM) x(c,"dom","Exports") = f4q(c) - ABS[EXP_ELAST(c)]*[{p(c,"dom")-phi}- pworld(c)];Equation E_x4b (all,c,COM) x(c,"imp","Exports") = 0;

44. 44Excerpt 9: Domestic market clearing and pricesEquation E_x1tot (all,c,COM) x1tot(c) = x0(c,"dom");Variable (change)(all,c,COM) Delptxrate(c) # Ordinary change in rate of domestic tax #;Equation E_pA (all,c,COM) p(c,"dom") = p1tot(c) + 100*[V1TOT(c)/(V1TOT(c)+V1PTX(c))]*Delptxrate(c);E_x1tot says: Output of each industry, X1TOT(i) = total demand for the domestically produced commodity, X0(c,"dom").User price = production cost + tax P(c,"dom") = P1TOT(c)*[1 + PTXRATE(c)]Rule: %Change A = 100.DA/A So: %Change [1+A] = 100.DA/[1+A]1/[1 + PTXRATE(c)] = share of production cost in user price = V1TOT(c)/[V1TOT(c)+V1PTX(c)]

45. 45Excerpt 10: Prices of importsLevels: P(c,"imp") = PHI*PWORLD(c)*[1 + MTXRATE(c)]Variable (change)(all,c,COM) Delmtxrate(c) # Ordinary change in rate of import tax #;Equation E_pB(all,c,COM) p(c,"imp") = pworld(c)+phi + 100*[V0CIF(c)/SALES(c,"imp")]*Delmtxrate(c);share of border cost in user price

46. 46Excerpt 11a GDP from income sideVariable w0gdpinc # Nominal GDP from income side #;Variable w0gdpinc # Nominal GDP from income side #;Coefficient V0GDPINC # GDP from income side #;Formula V0GDPINC = sum{i,IND, sum{f,FAC, FACTOR(f,i)}} + sum{c,COM, V1PTX(c) + V0MTX(c)};Equation E_w0gdpincV0GDPINC*w0gdpinc = sum{i,IND, FACTOR( "Labour",i)*[p1lab + x1lab(i)]} +sum{i,IND, FACTOR("Capital",i)*[p1cap(i) + x1cap(i)]} +sum{c,COM, 100*V1TOT(c)*Delptxrate(c) + V1PTX(c)*[x1tot(c)+ p1tot(c)]} +sum{c,COM, 100*V0CIF(c)*Delmtxrate(c) + V0MTX(c)*[x0(c,"imp")+pworld(c)+phi]};Each term = 100 times ordinary change100  change in tax rate  the original tax baseoriginal tax revenue  percent change in tax base

47. 47Excerpt 11b GDP from expenditure sideGDP = C+I+G+X-MVariable w0gdpexp # Nominal GDP from expenditure side #; p0gdpexp # GDP price index, expenditure side #; x0gdpexp # Real GDP from expenditure side #;Coefficient V0GDPEXP # GDP from expenditure side #;Formula V0GDPEXP = sum{c,COM, sum{s,SRC,sum{u,FINALUSER, USE(c,s,u)}} - V0CIF(c)};Equation E_w0gdpexp V0GDPEXP*w0gdpexp = sum{c,COM, sum{s,SRC,sum{u,FINALUSER, USE(c,s,u)*[p(c,s)+x(c,s,u)]}} - V0CIF(c)*[x0(c,"imp")+ pworld(c)+phi]};Equation E_p0gdpexp V0GDPEXP*p0gdpexp = sum{c,COM, sum{s,SRC,sum{u,FINALUSER, USE(c,s,u)*p(c,s)}} - V0CIF(c)*[pworld(c)+phi]};Equation E_x0gdpexp x0gdpexp = w0gdpexp - p0gdpexp;

48. 48Excerpt 13a More macro variablesVariable x4tot # Export volume index #; p4tot # Export price index #; p2tot # Investment price index #; x0cif_c # Import volume index, CIF prices #;(change) delB # (Balance of trade)/GDP #;Equation E_x4tot sum{c,COM, USE(c,"dom","Exports")*[x4tot - x(c,"dom","Exports")]} = 0;Equation E_p4tot sum{c,COM, USE(c,"dom","Exports")*[p4tot - p(c,"dom")]} = 0;Equation E_p2tot sum{c,COM, sum{s,SRC, USE(c,s,"Investment")*[p2tot - p(c,s)]}} = 0;Equation E_x0cif_c sum{c,COM, V0CIF(c)*[x0cif_c - x0(c,"imp")]}=0;Equation E_x4tot might have been written: sum{c,COM,USE(c,"dom","Exports")}*x4tot =sum{c,COM,USE(c,"dom","Exports")*x(c,"dom","Exports")};

49. 49Excerpt 13b Balance of Trade/GDPEquation E_delB 100*V0GDPEXP*delB= sum{c,COM, USE(c,"dom","Exports")*[p(c,"dom")+x(c,"dom","Exports")-w0gdpexp] - V0CIF(c)*[x0(c,"imp")+ pworld(c)+phi-w0gdpexp]};B = [X-M]/GDPB*GDP = [X-M]GDP*DB + B*DGDP = D[X-M]100*GDP*DB + 100*B*DGDP = 100*D[X-M]100*GDP*DB + B*GDP*gdp = Xx - Mm100*GDP*DB + [X-M]*gdp = Xx - Mm100*GDP*DB = X[x-gdp] - M[m-gdp]

50. 50Excerpt 14: Factor market variablesVariable realwage # Wage rate deflated by CPI #; employ # Aggregate employment #; (all,i,IND) gret(i) # Gross rate of return #;Equation E_realwage realwage = p1lab - p3tot;Equation E_employ sum{i,IND, FACTOR("Labour",i)*[employ - x1lab(i)]}=0;Equation E_gret (all,i,IND) gret(i) = p1cap(i) - p2tot;REALWAGE = P1LAB/P3TOT constant in sticky labour markets.employ = % index of aggregate employment, with wage-bill weightsGRET(i) = P1CAP(i)/P2TOT P1CAP = annual revenue from unit of capitalP2TOT = cost of creating new unit of capitalGRET = gross rate of return on a unit of new capital: stable in long run

51. 51Excerpt 15: Updating the flows dataUpdates tell GEMPACK how to make post-simulation or updated database.Product updates:Formula: USE(c,s,u) = P(c,s)*X(c,s,u) cCOM, sSRC, uUSERUpdate: USE(c,s,u)  USE(c,s,u)*[1+0.01*p(c,s)+0.01*x(c,s,u)]Update (all,c,COM)(all,s,SRC)(all,u,USER) USE(c,s,u) = p(c,s)*x(c,s,u); (all,i,IND) FACTOR("Labour",i) = p1lab*x1lab(i); (all,i,IND) FACTOR("Capital",i) = p1cap(i)*x1cap(i);Change updates: explicit formulae for ordinary change (change)(all,c,COM) V0MTX(c) = V0CIF(c)*Delmtxrate(c) + 0.01*V0MTX(c)*[x0(c,"imp")+ pworld(c)+phi]; (change)(all,c,COM) V1PTX(c) = V1TOT(c)*Delptxrate(c) + 0.01*V1PTX(c)*[x1tot(c)+ p1tot(c)];change in tax rate the original tax baseoriginal tax revenue  proportional change (=%/100) in tax base

52. 52Excerpt 16: Creating a data summary filecheck that the input data adds up properly: assist in explaining results.File (new) SUMMARY # output file for summary data #Coefficient (all,c,COM) CHECK(c) # (costs + tax) - sales : should = 0 #;Formula (all,c,COM) CHECK(c) =V1TOT(c) +V1PTX(c) -SALES(c,"dom");Set COSTCAT # cost categories # = SRC union FAC;Coefficient(all,c,COSTCAT)(all,i,IND) COSTMAT(c,i) # Summary of industry costs #;Formula(all,i,IND)(all,s,SRC) COSTMAT(s,i) = sum{c,COM,USE(c,s,i)};(all,i,IND)(all,f,FAC) COSTMAT(f,i) = FACTOR(f,i);Coefficient (all,i,IND) CAPSHR(i) # Share capital in primary factor costs #;Formula (all,i,IND) CAPSHR(i) = FACTOR("capital",i)/V1PRIM(i);Coefficient (all,c,COM) IMPSHR(c) # Share imports in local purchases #;Formula (all,c,COM) IMPSHR(c) = sum{u,IMPUSER,USE(c,"imp",u)}/sum{u,IMPUSER,USE_S(c,u)};

53. 53Closing the modelEach equation explains a variable.More variables than equations.Endogenous variables: explained by modelExogenous variables: set by userClosure: choice of exogenous variablesMany possible closuresNumber of endogenous variables = Number of equationsOne way to construct a closure:(a) Find the variable that each equation explains; it is endogenous.(b) Other variables, not explained by equations, are exogenous.MINIMAL equations are named after the variable they SEEM to explain.

54. 54The ORANI short-run closureIndustry capital stocks, real wages and absorption fixed"Shortrun" might be 2 years

55. 55A possible long-run closure· Capital stocks adjust in such a way to maintain fixed rates of return (gret). · Aggregate employment is fixed and the real wage adjusts.· DelB fixed instead of x3tot (real household consumption)