Mathematical statement of the BMW computable general equilibrium model of the Indian economy (with glossary of variables)

DISCUSSION PAPER Report No.: UDD-38 MATHEMATICAL STATEMENT OF THE BMW COMPUTABLE GENERAL EQUILIBRIUM MODEL OF THE INDIAN ECONOMY (with Glossary of Variables) by Charles M. Becker Edwin S. Mills Jeffrey G. Williamson January, 1983 Water Supply and Urban Development Department Operations Policy Staff The World Bank The views presented here are those of the authors, and they should not be nterpreted as reflecting those of the World Bank. The authors are consultants with Water Supply and Urban Development Department. Charles M. Becker is Assistant Professor of Economics at Vanderbilt University, Edwin S. Mills, Professor of Economics at Princeton University and Jeffrey G. Williamson, Professor of Economics at Harvard Univ2rsity. RPO 672-64 Indian Urban Development Research Project Related PaDer: Report No.: UDD-22 5,- 1 bA ABSTRACT This paper presents mathematical equations which are used in the BMW (Becker-Mills-Williamson) model of computable general equilibrium (CGE) which is beeing prepared to estimate urban development in India. It is a mathematical appendix to Discussion Paper No. UDD 22, "Public Policy, Urbanization and Development: An Introduction to a Computable General Equilibrium Model of the Indian Economy" by the same authors. Sr ~f~f[IVA L CONTENTS page MATHEMATICAL STATEMENT 1. Production . . . . . . . . . . . . . . . . . . . . . . 1 2. Value added/Gross Price Relationships . . . . . ... . 1 3. Composite Commodities . . . . . . . . . . . . . . . . 2 4. Primary Factor Markets . . . . . . . . . . . . . . . 2 a. Labor Markets . . . . . . . . . . . . . . . . . . . 2 b. Labor Migration . . . . . . . . . . . . . . . . . . 2 c. Capital Markets . . . . . . . . . . . . . . . . . . 3 d. Private Firms and Public Enterprise Investment Allocation . . . . . . . . . . . . . . . . . . . . 3 e. Intermediate Inputs Markets . . . . . . . . . . . . 5 f. Land Markets . . . . . . . . . . . . . . . . . . . 5 g. Factor Employment . . . . . . . . . . . . . . . . . 8 5. Foreign Trade Sector and the World/Domestic Price Relationship . . . . . . . . . . . . . . . . . . .. . . 9 6. Government Sector . . . . . . . . .. . . . . . . .. . . . 9 a. Government Taxes . . . . . . . . . . . . . . . . . . 9 b. Government Spending and Saving . . . . . . . . . . . 10 7. Household Demand, Saving and Income . . . . . . . . . . 10 8. Remittances . . . . . . . . . . . . . . . . . . . . . . 13 9. Private Consumption Demand . . . . . . . . . . . . . . 13 10. Investment and Savings . . . . . . . . . . . . . . . . 14 a. Housing Investment . . . . . . . . . . . . . . . . . 14 b. Aggregate and Sectoral Savings for Non-Housing Investment . . . . . . . . . . . .. . . . . . . . . . 15 11. Market Clearing . . . . . . . . . . . . . . . . . . . . 17 12. Dynamic Equations . . . . . . . . . . . . . . . . . . . 18 a. Accumulation of Capital and Residential Structures . 18 b. Land Growth and Technological Progress . . . . . . . 18 c. Training and Skills Investment . . . . . . . . . . . 18 d. Labor Force Growth . . . . . . . . . . . . . . . . . 19 GLOSSARY................ ..... . . . . . . 20 A. Subscripts...................... 20 i. Sector Subscripts (production) . . . . ...... 20 ii. Factor Subscripts (production) . . ......21 iii. Location Subscripts........'............21 iv. Commodity Subscripts (demand).......... 21 v. Household Subscripts (demand).......... 22 B. Parameters...................... 22 C. Exogenous Variables . . ................ 27 D. Endogenous Variables.............. . . . . 28 .l .r 21 1. Production (1) Q. = A i,F Z a i,z i ,1j i i i,F i . i,3 (Cyi 1) cy i(ai-) /ci CYi (i i,F i i + (1- i)[z.L.] } (c.-1 /a! (a! -1)/cya a. (a -1 { [x iKi] + (l-q)[yiS.] } ij + a i,F + ai,z ' i = M, KS, US, PSU, PSR, RS j = A*, M*, KS, k, # i k =PSU when i = M, KS, US k PSR = RS t (2) Q = AA [XAKAa A,K , [ASA AA,S , AA A,L • AaA,R , AaA,R , . A aA,j = 1, also define AF A,K + A,S + A,L i' = M*, KS, PSR j = K, S, L, R, Z, M*, KS, PSR (3) QAa . A_ . • H , • k,H,j H,j H,j i U,j k,H,j i=,,(k, H) ' j et R,RS = 0 (that is, no land term is present in rural housing) i = KS, US, RS k = PSU when j = KS, US PSR = RS 2. Value Added/Gross Price Relationships tax i,j _ ZZ (1+TIMP,Z ij Q. Q. ~ i,F J i i i = M, A, KS, PSU, PSR, US, RS j = A*, M*, KS, k> i k = PSU when i = M, KS, US PSR =RS, A 2 (5)Pta = P. for all (i,j) except (i = A or RS, j = M*) ,3 J where P ax Ptax p w , =PRS,M* M*(+TA,M 3. Composite Commodities i,COM i,COM~1 i,COM (6) Q = { Q i,COM + (1-) i1,COM i,COM i~* i'II,ir 2. 2Qi,EXP i= A, M 4. Primary Factor Markets A. Labor Markets Q Q l/a W (7) W , p 1 Q - [ ) [L for i = M, KS, PSU, US, PSR, RS. Q, Q 1/r. i /a! W (8) w. = P!U(-ED) , , i,S i i,F i i si Yi for i = M, KS, PSU, US, PSR, RS QA W. A,j p A A,j b-j bA for j,J = L, S and b {z for j=L y j=S B. Labor Migration (10) wA,j RS,j PSR,j j L, S (11) (l-TY,FS (l-T S) • W = (l-Y )WPSU,S Y,US US,S YF S, (l- Y,Ps AVllB 3 (12) WM,L "KS,L = WPSU,L WUS,L W WM - (C *P A,L M,L M,L KS' (13) CCL-, given COL COLL COLL L U US R U W (1-t ) W *(1-'r) - (C *P ) AS Y,A WM,S Y,FS M,SOKS (14) CL CL , given COL = COLs SSU US C. Capital Markets t ,iF __i__ (15) r. = P.* ]i_ ] S 1 i,F 1 1 1 i = M, KS, PSU, PSR, US, RS Q rA 1l6) rA =~ P " =-- A A A,K xAKA xA D. Private Firm and Public Enterprise Investment Allocation (17) MINIMIZE {Return Differentials = r* * (1-T ) - r* (1-c )} {I i,,FSIM 7T,M KS Tr,KS i,M,FS such that desired investment in the urban formal sector is completely allocated: I = 1I. M,FS i,M,FS; i =M, KS and where 3r. rt = {r + [1(-1) 6I - 6.K.} - 6.PM* i 3 K. i,M,FS i i i Ki i = M, KS (18) MINIMIZE {Return Differentials = r* - r*} {I. RS A i,M,R BEST COIAALABLE 4 such that desired investment in rural production is completely allocated: IMI ' i = RS, A I,R i,M,R' i and where Dr. = {r. + 1 (-1) * I - 6. * K.]} - 6.P i 1 K. i,M,R 1 i i M* K. i = RS, A Funds available for capital accumulation in the urban informal sector can go only to one "industry," US. Investment in the US sector must thereby equal capital made available for investment by informal sector savers, after allowing for housing investment: (19) PM* M,US = sLU * L US US E,US,US US M*KUS + sSU * SUS KS H,KS,US Sector-wide discount rates are weighted averages of expected returns on private investment: S(1-T ) K. rt (20) i FS FSK J M* K, j = M, KS K. r? (21) iA = P M* . K PM*. j j = RS, A r (22) i IF 6 IS P US M* P I~ 5 Total private and public enterprise investment, TM, equals (23) IM M,US +.M,R +IM,FS' E. Intermediate Inputs Markets P.a. Q (24) 7 i a,zQi ZZ. i = RS, PSR, US, PSU, KS, A, M P.a. .Q. (25) Ptax ii,jQi i,j Qi, 1,]j where j = KS, M*, A*, k i = A, M, PSU, PSR, RS, US, KS j k PSU when j = KS, US, M PSR = A, RS (26) P = H,jak,H,jQH,j k,H,j Q j = KS, US, RS PSU for j = US, KS PSR = RS where P Pk for j = KS, RS k,H,j PSU (1 + T PSUIH,US) for j = US * F. Land Markets Let r* . and d* . be the structure and land rents perceived by consumers. H,j U3 Let r . and d Uj be the ("net") structure and land rents received by H,j U asset owners, Note that H,KS is the only non-zero property tax rate. Define P = nominal unit rental cost of housing of type j, INCLUDING property taxes and public services' user charges; BEST COPY 'AMILABLE 6 S P = nominal net unit rental cost of housing of type j, AFTER Hj property taxes and public services' user charges; VH,j = taxable value of urban residential property per hoLlsing service unit, j = US, KS, RS. Then for KS housing S . PSU,H,KSQPSU,H,KS (27) P = i * V =P - T V - H,KS FS H,KS H,KS H,KS H,KS QKS FS (i S -. HKS OPSU,H,KS) H,KS (28) P = (1 a )P H,j k,H,j H,j for j = US, RS k =PSU for j = US PSR j = RS T6 relate structure and land rents to the price of owner-occupied housing, it is first necessary to relate "gross" and "net" rents. Euler's theorem ensures product exhaustion: r* *K d* R P (29a) P = 'S',S + dU,KS U,KS PSU,H,KS PSU,H,KS H,KS QH,KS + H,KS QH,KS Net factor payments must also add up: S PH,KS * HKS dU,KS * RU,KS + PSU,H,KSQPSU,H,KS (2b) PH,KS Q -+ Q + CH,KS VH, KS +Q* H,KS H,KS H,KS Substitute VHKS from (27) into (29b): BEST C A 」 8 P S a Q (33) d Hjj R,j H,j UIj R U'j . (1-a PSU,H,J) j = KS, US For land in agricultural use (34) d P aA IRQA A R A Finally, urban land rental market equilibrium requires: (35) du'M = d U'Us GRADIENT1 As noted, Euler's theorem applies to the housing services production equations. That is, total user rent equals site rep-AL plus structure rent plus property taxes plus public service charges. The gross price relationships corresponding to (4) are thus (36) P r H,j 0 H i + P k,H,j . Qk.,H,j + d U'j . RU'j H,j QH,j j = US, RS = SU for US k P SR j RS and dU'j = R U'j = 0 for j RS, while, substituting (26) into (27) and rearranging to solve for V H,KS' and substituting into (29b) and rearranging gives (37) P (i FS + 'r H,KS) - I r H,KSHKS + PPSUQPSU,H,KS + dURU,KS H,KS UFS + a PSU,H,KS T H,KS) QH,KS_ G. Factor Employment (38) TJRB i us + (i KS + i M + PSU) J = L, S j us + i U BEST COPY AVAILABLE 9 (39) JR iPSR +JRS + JA J = L, S (40) j = URB + JR J = L, S (41) N. = C. + S. + L. j U, R J1 J J J and C R 0 (42) N Nu + NR (43) R = (Ru,us + RU,KS) + RA = RU + RA 5. Foreign Trade Sector and World/Domestic Price Relationships i i,EXP (1 + Ti,EX + F - Qi,IMP Z Z = 0 i = A, M j = PSU, PSR, KS, US, A, M, RS. p i • (1 + T iE) (45) Qi,EXP = i,EXP L -W i = A, M. P. (46) P = P (1 - ){] iCOM i = A, M i (47) (1+ T )aP> = P ]/M. i,IMP 6. Government Sector A. Government Taxes (48) T = TMMM HKSVHKSHKS + TA,M M*(QA,M + QRS,M) + T ** S + T Y** S + T [Y** s + Y**c] Y,A R,S R Y,US US,S US Y,FS FS,S u + i T ir åM*I + L{T3 Q P. T. Q. p T ¯r - M P + {T j,EXP j,EXP + j,IMP j,TMP i i = M, KS j = A, M BEST COPY AVALABLE 10 (49) GOVREV = T + F + K.(r. - 6.PM), i = PSU, PSR. 1 B. Government Spending and Saving (50) G. = . + Y.N (-l) i = PSU, PSR 1 1 1 h U for i = PSU fR i = PSR (51) G =a G + B G GOVREV; G< GOVREV (52) GRESID MAX {0, GS - GPSU - G PSR (53) GOVO =GOVREV - GSU - GPSR - GRESID (54) G. = g. * GRESID i = M, KS, 1 1 where gKS 1 - gM. 7. Household Demand, Saving and Income (55) v = P . *y + . * Y- - (P * yk.), i,k = A*, M*, T, S, H 3k k,j k, (56) c. = v. (57) s. Yt , J 1 j P. .v. (58) COL. = 1 'J 121 i j = LR, covering households supplying LA, LRS, LPSR = S covering households supplying SA3 SRS' SPSR = LU, covering households supplying LM, LKS, LPSU = L us, covering households supplying Lus = Su, covering households supplying SM, SKS' SPSU = SuS' covering households supplying Sus = C, covering indolent capitalists and landlords. BEST COP AVAILABLE 11 (59) Households face the following prices: P = P* for all j A*,j A PM*j PM(l+rM) for all j PT,j KS for all j PS,j RS for all j = LR, SR P = P for j = Lu, Su, L u, S us C H,j PH,KS for j = Sus, Su, C P Hj= P for j = LUSS LU PH-j = 1H,RS for j = LR, SR Household gross incomes, Yt**, are: i (60) Yt** = W. + J1 [P Q + dRR + KSHR . K.(r - .PM*)] j j H,RS H,RS,j 3 A R,jSHR where i = A, RS j = LR, SR with J = number of households of type j and W = W A W = W A,L' SR A,S (61) Yt** = W.+J1 [PH 1Q +KSHZKU(r 6PM)+ KSHM i(1- )K (r -6 iPt)]+REB., HJ J ,zH,k,j ~usSusM7r ,,i. i =-M, KS j= LUS, Su, Sus k US for j = LU, Lus KS j u= Su, Sus h = j for j = LU, SU and KSHh = 0 otherwise; = j for j = Lus, Sus and KSH2 = 0 otherwise; and W = W = W WS=W = W = W L LU M,L S M,S S wUS,S 12 SU,H,US pPSUQPSU,H,USQH,US,j for J Lus (62) REB. = SUUS,US J 0 otherwise KS'k, C •[(rA~'APM* )KA + (rRS~'RSPM*YKKS ] + dA RCRA + KSH,C [YM (T ),M (rMPM KM* + YKS ) (1Tjr 3) (rKS-6 KS M*)K KS (63) YcH,KS H,KS,CC (63) Y*** c ~sHs Four household groups, J = SR' SU' Sus and C, face income taxes. Taxable income for these groups is given by Yt*: SJ ~H,kj. k c (64) Y** = Y*** - ,R' S US, C k RS for j S R . KS =SU' S us, C. Disposable incomes: (65) Y = Y**- T J** + TRF., j= L R' SR Lu, Lus' Suý Sus, C. j j Y,k jj A for i = SR FS j = Su, C k= US j = sus L j = LR, LU, LUS and T 0 Y,L (66) R =1, i = LR' SR' C. J (67) KSHR = 1 i = LR' SR, C. i (KSHRi .= K. .()/l K.(0); i = A, RS). BEST COP MMALABLE 긔 14 lo. Investment and Savings A. Housing Investment (73) 1* = MIN {[s L +s s ]p -1 1 N + 8 H HýRS L R R s R R RS H,RS HýRS RS i = MAX {0. I* H,RS H,RS E: H i H,RS 0 H,RS [r H,RS (74) 1* = MIN {s iP-1 3' 1 N + 6 H H.ýhsj i h H,h,j H,h h5j} i = MAX {0, I* H,h,j H,h,j N E: H i H,h,j 0 H,h [r H,h,j j,J Lus> LUY s us h US for j,J L us, L u KS j J S us (75) 1* = MIN Us s + s C]P- i i N + 8 (H H H,KS,FSC s u u c KS H,KS,FSC HKS KS KS,S us = MAX {0, I* H,KS,FSC H,KS,FSC i N E) H -il H,KS,FSC H,KSIr H,KS,FSC s,l (76) 1 H,KSj I i H,KS,FSC i, I, J SU, c s (77) 1 H,KS = i H,KS,FSC + i H,KS,S us (78) 1 H,US = i H,US,L + i H,US.-L u ý us r H,RS 6 H,RS p RS (79) r H , RS i Å 0 p RS B E l I A B I E 15 r -, 6 * Ph (80) r H,h,j i k h j= FSC, Sus, LUS' LU h KS for j = FSC, Sus fUS j = Lus, LU FS for i = FSC, LU IFS j = L us"S us S (H,US H,US H,US (81) rHU S( SH H,US HUS(I-aPSU,H,USj S aE,KSQH,KSP,KS (82) r = , where r is a net of property tax rate of H,KS HKS (1-PSU,H,KS H,j return. a H,RSQH,RSP H,RS (83) r =,SHR E,RS HRS (84) HOUSING = PRS H,RS US H,US KS H,KS B. Aggregate and Sectoral Savings for Non-Housing Investment (85) PRIVATE SAVINGS = (1-.) (1-T r i) (r.-6.P )K i+ 6 P K +1 s.J, . 7,i 2. 1 M*i 9. M* 2 1 1j i = M, KS k = M, KS, US, RS, A j = Lus, Lu, LR' SUS' SU' SR' C Private savings is divided into informal sector investment, IM,US' given in eqn. (48), formal sector investment, TM,FS' and rural private investment, I,R' BEST COPY AVAR LABLE 16 (86) 1, = P~• [p (1-Y.)(1-T .)(r.-6.P )K.+f 6 P K .+ s.J M,FS m* . i 7r, i i i M- i . iM4 . - , h,j h + URBCAP (s c - I HKS,P )], i = M, KS US forj Lu J,j = Su, Lu KS for j = u iri (87) URBCAP = [C • Y*]_1 '[ (1-T )KSHM • Y .(1-T .)(r .6 .PM*)K,. c Y,FS ,C .r ,i i iM i + p KS HKSC}., i =M, KS. (88) IM,R pM i PM*K + ZSi J - PRS H,RS + (1-URBCAP)(sCC-I H,KSC KS i = A, RS j,J = SR' LR Total investment: (89) TIM,i = M,i i = R, US (90) TIM. = i. i = A, RS -1 (91) TIi = iMFS + G XPM. i = M, KS. (92) TIM,FS TIM i = M, KS (93) TI Gi M* +6 .K. i = PSU, PSR. These definitions imply the following identities: Private investment in value terrms is (94) Pm*I = PRIVATE SAVINGS - HOUSING, and total investment in value terms is BEST COPY AVAILABLE 17 (95) P*TIM = PRIVATE SAVINGS - HOUSING + Gs + 6 PM*K =IM TIZ, i = PSU, PSR = R, US, FS, PSU, PSR. 11. Market Clearing (96) QM* =M* + TIM + QiM*i = A, PSU, PSR, KS, RS, US. (97) QA* = DA* + Q i,A*, i = PSU, PSR, KS, RS, US, M. P (1-W*) a. (46a) Qi = Q[] i,COM + Q i = A, M. (98) QPsu= Qi,Psu i = KS, M, US, (H,US) (99) Q PSR = Q i,PSR i = A, RS, (H,RS) (100) Qu =DK + GOV 1+ iKS + iKQ i = PSR, PSR, A, M, US, KS (0)~=KS +OKS ~KS + ,K i,KS (101) Q. = D. + I . i = US, RS i i H,i (102) Q = D. i = (H, US), (H, RS), (H, KS) H1,1 i A final identity: (103) GDP = jPQ + P QH, + ,MM*D HKSVH,KSQH,KS + TA,M(QA,M + QRS,M) i J + Z,EXP ,EXP + T ,PQZIMP}; i = M, KS, PSU, PSR, US, RS, A j = US, KS, RS £ = A, M BEST CPY AAILABLE 18 12. Dyn-mic Equations A. Accumulation of Capital and Residential Structures (104) K. = (1-6.)K.(-l) + TIM , i = M, KS, A, RS, US, PSU, PSR 1 1 1Mi (105) H. (1-6 j) H.(-1) + I (-1) j = US, RS, KS B. Land Growth and Technological Progress (106) x. = x.(-l) * e i i = A, RS, M, KS, US, PSU, PSR 1 1 (107) yi = i(-1) * e Si i = A, RS, M, KS, US, PSU, PSR (108) z. = z.(-l) * e Li i = A, RS, M, KS, US, PSU, PSR 11 (109) Ai = Ai(-l) e i = A, RS, M, KS, US, PSU, PSR, (H,KS) , (H,US),, (H,RS). (110) R = (1+p) * R(-1) C. Training and Skills Investment Training and skills investment are exogenous in the preliminary version of BMW. Define J(0) as the number of households of type j prior to intra-period equilibrium adjustments and J(-l) as the number of house- holds of type j at the end of the preceding period. Then, (111) S. (0) = (1 + BR.)S. (-1) + TR. * L.(-1). j = R, US, U R for j = R i= U j = U, us BESTA ppVAILABLE 느 20 MATHEMATICAL STATEMENT OF BMW: GLOSSARY A. Subscripts i. Sector Subscripts (production)_ A: Agriculture H,KS: urban "luxury" (pucca) housing; housing stock originally constructed in KS sector. H,US; urban non-luxury housing (katcha housing, squatter settle- ments); housing stock originally constructed in US sector. H,RS: rural housing; housing stock originally constructed in RS sector. KS: capital intensive services (defense, education, administra- tion, finance, commerce, construction of H,KS housing); urban based. PSU: urban public services (electricity, gas, water, transporta- tion and communications). PSR: rural public services (public roads, irrigation projects, rural transport, rural government). M: manuf acturirig (urban manuf acturing and mining) . US: urban labor-intensive services (domestics, personal services, construction of H,US housing, small-scale commercial and repair services, small-scale transport). RS: rural labor-intensive services (d omestics, personal services, rural housing construction, other rural construction, small- scale rural commerce, manufacturing and -repair services). 017 21 ii. Factor Subscripts (production) K: capital L: unskilled labor R: land S: "skilled" labor Z: imported raw materials, including fuel but not manufacturers. M*: composite manufacturing good, containing both imports and domestic production A*: composite agricultural good, containing both imports and domestic production. iii. Location Subscripts FS: formal sector (urban): KS, PSU, M sector IFS: informal sector (urban): US sector FSC: formal sector 'plus capitalists and landlords (urban resi- dents other than informal sector workers). R:., rural U: urban iv. Commodity Subscripts (demand) A*: food, a composite of domestic A sector production and imports. M*: clothing and durables, a composite of domestic M sector producticn and imports T: transportation and communications (KS sector) S: labor intensive personal services (RS or US sector) H: rent (H,KS; H,US; or H,RS sectors) EST COPY VILABL F 22 v. Household Subscripts (demand) C: capitalists and landlords LR: rural unskilled SR: rural "skilled" LU : "formal sector" unskilled workers (in M, KS, PSU sectors) LUS: "informal sector" unskilled (in US sector) SU: "formal sector" skilled workers (in M, KS, PSU sectors) S :"informal sector" skilled workers (in US sector) us B. Parameters (numbers in parentheses gives the equation the parameter first appears in) "aAj: output elasticity (and cost share) of the jth (primary or intermediate) input in the A sector; j = K,S,L,R,Z,M*,KS,PSR. (2). "G: intercept in the government saving function. (51). "F : output elasticity (and cost share) of composite of primary inputs in ith sector (a value-added share in gross output); i = M,KS,PSU,US,RS,PSR. (1). " .j output elasticity (and cost share) of housing stock input into housing services production of type i; i = KS,US,RS. (3). a intercept in expenditure function for government services of type i; i = PSU,PSR. (50). output elasticity (and cost share) of Z in the ith sector, i = M,KS,PSU,US,RS,PSR. (1). 23 .th itreit output elasticity (and cost share) of j intermediate input in the ith sector for i = M,KS,PSU,US,PSR,RS; and j = A*,M*,KS,k#i, where k = PSU for i = M,KS,US; k = PSU for i = RS, k = 0 otherwise. (1) a .: output elasticity (and cost share) of public services of type k in housing production of type j; j = KS,US,RS; k = PSU for j = KS,US; k = PSU for j = RS. (3). . R,j: output elasticity (and cost share) of urban land in urban housing production, j = US,KS. (3). G: marginal propensity to save out of government revenue (taxes, foreign inflows and aid, and earnings on public service in- vestment). (51). th B.j. marC:.-;nal propensity to consume the i commodity out of supernumary income; by the jth household type; i = A*,M*,T,S,H; j = LR,SR,LU,LUS,SU,SUS,C. (55). marginal propensity by the government to spend on public services of type i; i = PSU,PSR. (50). yj or y,subsistence bundle, ith (or k th) commodity, jth household type; i or k = A*,M*,T,S,H; j = LR,SR,LU,LUS,SU,SUS,C. (55). depreciation rate on residential (housing) structures, j = US,RS,KS. (73). depreciation rate for physical ("productive") capital in sector i; i = A,RS,PSR,PSU,US,KS,M. (17) C H elasticity parameter in the net housing investment functions. (73). 6H,j: multiplicative parameter in the net housing investment function, j = US,KS,RS. (73). BEST COPY AVAILABLE 24 rate of total-factor productivity growth in the ith sector attributable to neutral, disembodied, sector-specific technological change, i = A,RS,PSR,PSU,US,KS,M,(H,US), (E,RS) , (H,KS). (109). Tl: price elasticity of export demand faced by Indian producers in sector i; i = A,M. (45). r sector-specific rate of augmentation of physical capital through technological change, i = A,RS,PSR,PSU,US,KS,M. (106). X . : sector-specific rate of skilled labor augmentation through technological change, i = A,RS,PSR,PSU,US,KS,M. (107). X Li: sector-specific rate of unskilled labor augmentation through technological change, i = A,RS,PSR,PSU,US,KS,M. (108). distribution parameter in the ith sector value-added CES production function (Q i,), i = M,KS,PSU,US,RS,PSR. (1). th distribution parameter in the i sector composite capital 1-. function (4 ), i = M,KS,PSU,US,RS,PSR. (1). p: rate of augmentation of land stock through technological change. (110). a.: elasticity of substitution between "composite capital," 1 p, and the unskilled labor in the ith sector value-added production function (Q ), i = M,KS,PSU,US,RS,PSR. (1). i,F a. elasticity of substitution between capital and skilled labor 1 in the i th sector composite capital function (cp) i = M,KS,PSU,US,PSR,RS. (1). . :'O elasticity of substitution between domestic and imported th components of the i composite good; i = A,M. (6). . T CI Y AAR ABLE 25 TA,M: tax (or subsidy) rate on agricultural intermediate inputs purchased from manufacturing. (5). T H,KS property tax rate on the value of urban capital-intensive housing. (29b). ,EX : export tax/subsidy rate on goods exported from sector i; i r A,M. (44). TiI. : import tariff rate on imported goods of type i; i = A,M. (47). T IMPZ: tax rate on imported Z goods. (4) T PSU,H,US: "shadow" tax rate for use of public services paid by consumers of US housing. (62) TY,FS: income tax rate on personal income (excluding rental income from owner-occupied housing) for skilled workers in the formal sector, and for capitalists. (11) TY,US: income tax rate on personal income (excluding rental income from owner-occupied housing) for skilled informal sector workers. (11) T Y,A: income tax rate for personal income (excluding rental income from owner-occupied housing) for "skilled" peasants and workers in rural areas. (14) 7T)j d: proportional "corporate" profit tax rate in sector j; j = M,KS. (17) TM: sales tax rate on consumption of M sector goods. (48) F: share of urban workers' incomes transferred to rural households. (70) BEST CO Fy 26 ce: share of capitalists and landlords in the total population. (113) after tax, "corporate" pay-out rate, i = MIKS. (61) .th distribution parameter in the i composite good function, i = A,M. (6) GRADIENT1: fixed ratio of land rental rate applicable at H,KS sites to the rate on H,US sites, reflecting the fact that KS housing is built on more valuable urban land. (35). g.: proportion of the government physical capital investment fund spent on i sector projects, i = M,KS. (54) R. proportion of rural land owned by households of type j, j = LR,SR,C. (60) KSHR,j: proportion of rural private capital stock (from RS,A sectors) owned by households of type j; j = LR,SR,C. (60) KSHz or KSH.: share of urban informal sector private sector stock owned by households of type t (or j); Z = Lus,S US (61) KSHM or KSHM,h: share of urban formal sector private capital stock owned by households of type j (or h); j = LU,SU,C. (61) BR.: net "birth" rate (births 2 labor force entrants less :1 retirees, excluding transfers) in sector i; i = R for TR = TRR; i = U for TR = TRUS,RU. (111) TR.: rate of transfer of workers from unskilled to skilled category in sector j; j = R (rural), US (urban informal) sector), U (urban formal sector). (111) BEST CWY AMLABLE 27 C. Exogenous Variables A H,j: intercept in the jth housing production function; j = KS,US,RS. (3) th A.: intercept in the i sector's production function; 1 i = M,KS,PSU,US,A,PSR,RS. (1) C: number of capitalists and landlords. (55-8) F: nominal value of foreign aid and private capital inflow. (49) K. (0): initial capital stock in production sector i; 1 i = A,RS,M,KS,US. (67) K. . (0): initial capital stock in sector i owned by household type 1,J j; j = LR, SR,C for i = A,RS; j = LU,SU,C for i = M,KS; j = Lus,Sus for i = US. (67) L: total unskilled labor stock. (40) N: total population in the labor force. (42) P. : c.i.f. price ("world price") of imports of type i; 1 i = A,M. (44) P Z: price per unit of imported raw materials. (3) 0 Q ,EXP multiplicative parameter in export demand function faced by Indian producers in sector i; i = A,M. (45) R: total land stock. (43) RA: rural land stock. (2) R U: urban land stock. (43) S: total skilled labor force stock. (40) x.: augmentation level of physical capital through technological change in sector i; i = M,KS,PSU,US,A,RS,PSR. (1) BEST AVAILABLE 28 y augmentation level of skilled labor through technological change in sector i; i = M,KS,PSU,US,A,RS,PSR. (1) z.: augmentation level of unskilled labor through technological 1 change in sector i; i = M,KS,PSU,US,A,RS,PSR. (1) C M,L: cost of moving from rural to urban areas for unskilled workers. (13) Ir C MS: cost of moving from rural to urban areas for skilled workers. (14) D. Endogenous Variables th C.: nominal consumption by j type of household; j = LR,SR,LU,SUILUS,SUS,C. (56) COL.: cost of living index for the j th household; j = LR,SR,LU,SU,LUS,SUS. (13) C: growth in number of capitalists and landlords. (113) C: number of capitalists and landlords. (48) dA: nominal rent per hectare of farmland. (34) d ui: nominal net rent (the amount received by land owners) per hectare of urban land containing H,i type structures; i=US,KS. (29b) d* gross nominal rent per hectare of urban land containing U,KS KS type structures. (29a) GDP: gross domestic product. (103) D. total private consumption demand for goods of type i, i = M*,A*,KS,RS,US,(H,US),(H,RS),(H,KS). (48); See also (71) D h,j private consumption demand for good h by class j; h = (H,US),(H,KS); j = Lus,LU for h = (H,US); j = Sus,SU,C for h = (H,KS). (72) EST COPY AVALA LE 29 GOVREV: "total government revenue" from taxes, foreign aid, and remitted profits from public services, plus other capital transfers from abroad. (49) G. nominal government net investment in sector i; i = PSU,PSR,KS,M. (50) GS: total government savings. (51) G R government savings not invested in urban or rural public RESID' services. (52) GOVKS: nominal government expenditures on KS services. (53) th H. J t type housing stock; j =KS,US,RS. (3) Hh,j h type housing stock owned by workers in sector j; j = LU3LUS,SUS; h = US for j = LU,LUS; h KS for j = SU (74) HOUSING: total gross investment in housing. (84) i discount rate applicable in rural areas. (21) iFS: discount rate applicable in the urban formal sector and in government evaluation of housing stock. (20) ilFS: discount rate applicable in the urban informal sector. (22) I. :F investment of physical capital in sector i; i = M,KS. (17) IM,FS: non-housing total private urban formal sector physical capital investment. (17) li,M,R private rural physical capital investment in sector i; i = RS,A. (18) IM,R: total private non-housing rural physical capital invest- ment. (18) BET COPY AVA LABLE 30 I : private physical capital investment in the urban US M ,US sector. (19) IM: total private non-housing physical capital investment demand. (23) IRN "intended" net housing investment in rural areas. (73) H,RS IH,S "intended" gross rural housing investment, given savings constraints. (73) IH,j total investment housing demand, for housing produced by sector j; j = RS,KS,US. (73) N I . intended net housing investment for housing produced in E,h,j sector h by consumers of type j; j = us,LU,SUS,SU,C,SC; h = US for j = Lus,LU; h = KS for j = SUS,SU,C,FSC. (74) IH,h,j: investment housing demand for housing of type h by con- sumers of type j; j = Lus,LU,SUS,SSUC,FSC; h = US for j = Lus,LU; h = KS for j = SUS,SUSC,FSC. (74) I*hj .:"intended" gross demand for housing investment of type h H,h,j by consumers of type j, given their savings constraints; j = Lus,LUISUS,SU,C,FSC; h = US for j = LULus; h = KS for j = Sus,SU,CFSC. (74) K physical (productive) capital in the ith sector, i = M,KS,PSU,US,A,RS,PSR. (1) unskilled labor in the ith sector; i = M,KS,PSU,US,A,RS,PSR. (1) L: total unskilled labor. (40) LR: unskilled labor in rural areas. (39) LURB: unskilled labor in the urban "formal" sectors (KS,M, and PSU). (38) PIEST CerP111,ILABLE 31 L U unskilled labor in urban employment. (38) L: net increase in total unskilled labor force. (115) N: total population growth. (113) N.: total labor force in location j; j = U,R, including capitalists and landlords. (41) N: total labor force, including capitalists and landlords. (42) PH: nominal rental cost of jth type of housing; j = KS,US,RS. (26) P k,H,j price per unit of public service inputs into housing of type j paid by consumers of type k; j = US,RS,KS; k = PSU for j = US,KS; k = PSR for j = RS. (26) tax P .user cost per unit of good j paid by sector i; i = A,M,KS,PSU,PSR,US,RS; j = A*,M*,KS,k and j#i; k = PSU for i = M,KS,US; k = PSR for i = RS,A. (4) P. per unit value added price of output of sector i; 1 i = A,M,KS,PSU,PSR,US,RS. (4) P.: per unit price of sector i output; i A,M,KS,PSU,PSR,US,RS. (4) P per unit price of composite good j; j = A,M. (5) s th P .: nominal net unit rental cost of j type of housing, after property taxes and public services' user changes; j = KS,US,RS. (27) th th P .:j price of j commodity paid by i household; i = A*,M*,T,S,H; j = LR,SR,LU,SU,LUS,SUS,C. (59) PRIVATE SAVINGS: Total gross savings by households, private firms and public enterprises in the M and KS sector. (85) BEST COPY AVAILABLE 32 4)1:composite capital" in the 1 hsector; i = M,KS,PSU, US,RS,PSR. (1) i'h Qioutput of the i hsector; i = MA,KS,PSU,US,A,RS,PSR. (1) Q .t: output of the i t composite good; = A,M. (6) r th "rental units" produced by the jth type housing stock; j = KS,US,RS. (3). Quantity imported of good i; i = A,M. (6) Qi,EXP : Exported quantity of good i; i = A,M. (6) "rental units" of type k housing stock consumed by house- hold of type j; j = LR,LU3SR,SU,LUS,SUS,C; k = KS for j = SuUSC; k = US for j = LU,Lus; k = RS for j = SR,LR' (60) composite of primary inputs in the ith sector; i = M,KS, PSU,US,RS,PSR. (1) intermediate input of the jth good into the ith sector; for i = M,KS,PSU,US, j = M*,KS,PSU,A* # i; for i = A,RS,PSR, j = A*,M*,KS,PSR # i. (1) Qk,H,j: public services inputs of type k as an intermediate good into housing of type j; j = KS,US,RS; k = PSU for j = KS,US; k = PSR for j = RS. (3) REB.: "shadow rebate" returning income to LU, Lus households paying a shadow tax on public services inputs into their housing (thus providing marginal price effects but no nominal income loss). (61) r pre-tax returns to physical capital in sector i; i = M,KS,PSU,PSR,US,RS,A. (15) ~dVA IW4L ALE 33 pre-tax quasi-rents expected after accounting for depre- ciation on investment per unit of physical capital in sec- to i; i = M,KS,RS,A. (17) r. ipre-tax returns to efficiency capital in sector i; i = M,KS,PSU,PSR,,US,RS,A. (15) r :RS profitability index of the RS type of housing. (73) th r ,h,j relative profitability index of the h type of housing for households of type j; j = L,LU3S,SUSFSC; h = KS for j = FSC,Sus; h = US for j = Lus,LU. (74) SH,: net of tax rate of return to structures of type j (structure rents on type j housing); j = KS,RS,US. (29b) r* :gross of tax rate of return to KS structures (structure H,KS rents on KS housing). (29a) R U. urban land stock used in production of housing services of type (H,j); j = KS,US. (3) s.: nominal saving by households of type j; j = LR,SR,LU,SU' Lus,SUS,C. (19) S.: skilled labor in sector i; i = M,KS,PSU,US,A,RS,PSR. (1) S: total skilled labor force. (4) SURB: skilled labor force in urban areas. (38) S : skilled labor in urban "formal" sectors. (38) u SR: "skilled" rural labor force. (39) S: net increase in total skilled labor force. (114) T: government tax revenue. (48) TI M,FS total non-housing investment in physical capital in the urban formal sector, excluding public services. (92) BEST COPY AVAILABLE 34 TI M.: total non-housing investment in physical capital in sector i; i = R,US,A,RS,M,KS. (89) TI PSR: total investment in rural public services. (93) TI PSU: total investment in urban public services. (93) TIM: total non-housing investment in physical capital. (95) TRF.: remittances sent (for urban households) or received (for rural households) per household; j = LR,SR,LU,SU,Lus,Sus. (65) URBCAP: proportion of income of capitalists and landlords from urban sources. (86) VA: unit value of farmland (per hectare). (18) taxable value of residential property per housing service unit; j = US,KS,RS. (27) nominal expenditures by jth households on ith commodity; i = A,M,T,S,H: j = LR,SR,LU,SU,LUS,SUS,C. (55) W efficiency wage; unskilled labor in ith sector; i = M,KS,PSU,US,PSR,RS,A. (7) WijL annual earnings; unskilled labor in ith sector; i = M,KS,PSU,US,RS,PSR,A. (7) th W efficiency wage; skilled labor in i sector; i = M,KS,PSU,US,PSR,RS,A. (8) Wi's annual earnings; skilled labor in ith sector; i = M,KS,PSU,US,PSR,RS,A. (8) Yt**: gross non-transfer incomes of a household of type j, including imputed rents to owner-occupied housing; j = LR,SR,LU,SU,LUS,SUS,C. (60) Yt*: taxable income of a household of type j; j = SR,SU,SUS (48) AE A OLE