dinam.gms : DINAMICO A Dynamic Multi-Sectoral Multi-Skill Model
Dinamico is multi-sector, multi-skill model of the Mexican economy. for
complete description of data and model consult the reference.
Reference:
- Manne, A S, Dinamico, A Multi-Sector, Multi-skill Model. In Goreaux, L M, and Manne, A S, Eds, Multi-level Planning: Case Studies in Mexico. North-Holland, Amsterdam, 1973.
Large Model of Type: LP
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$Title Dinamico, Dynamic Multi-Sector, Multi-skill Model (DINAM,SEQ=35)
$Stitle Introduction
$Ontext
Dinamico is multi-sector, multi-skill model of the Mexican economy. for
complete description of data and model consult the reference.
Manne, A S, Dinamico, A Multi-Sector, Multi-skill Model. In Goreaux,
L M, and Manne, A S, Eds, Multi-level Planning: Case Studies in Mexico.
North-Holland, Amsterdam, 1973.
$Offtext
Set tm labels appearing in the transaction matrices and reports /
agri-ka agriculture - capital-labor substitution
agri agriculture
agri-total total annual investment in agriculture
mine mining
petrol petroleum
food food
text textiles
wood wood
chem chemicals
n-met non-metallics
b-met basic metals
mach machinery
const construction
elec electricity
comm commerce
trans transportation
serv services
imp imports
hc household consumption
gc government consumption
tc tourist consumption
exp exports
fi fixed investment
ii investment inventories
err errors and ommisions
va value added (gross)
gvp gross value of production
g-d-p gross domestic production
consumed aggregate consumption
savings aggregate domestic savings
r-gap resource gap
investment aggregate annual investment
gdp-gr annual growth rate of gdp
con-gr annual growth rate of consumption
sav-gr annual growth rate of savings
inv-gr annual growth rate of investment
inc-k-o incremental-capital-output ratio
mps marginal propensity to save (%)
aps average propensity to save (%)
imports
ea+zt export earnings and tourism
rgap-fexch resource gap: imports - export earnings and tourism
fcl foreign concessional capital inflows
fdpl foreign direct capital inflows
infcl interest payments on concessional capital
infdpl interest payments on direct foreign capital
rgap-fgap resource gap: algebraic sum of capital inflows and outflows
for-exch dual variable ft: 1960 pesos worth of maximand per 1000 1960 pesos worth
trad-manu tradeable manufactures
ratio efficiency price of foreign exchange relative to price of tradeable manufactures
eff-sl1 efficiency wages
dual dual variables for labor constraints
fc-infc concessional capital inflows less interest
res-gap resource gap
fexch-m efficiency price of foreign exchange
fgap-m efficiency price of foreign aid
relative efficiency price of foreign exchange relative to price of tradeable manufactures
export-e merchandize exports
high-cost exports of high-cost manufactures at producers prices
earnings foreign exchange earnings at market prices
gap resource gap: imports less merchandize exports and tourism
zm4 exports of high-cost manufactures
za4 merchandize exports
zt4 tourism
eff-wages efficiency wages annual average centered on 1980
con4 aggregate consumption in 1980
income labor income: employment x efficiency wages
aggregate
income-t /
$Stitle set definitions
Set te plan horizon / 1968, 1971, 1974, 1977, 1980, 1983, 1986, 1989 /
t(te) optimization horizon/ 1971, 1974, 1977, 1980, 1983, 1986 /
jd(tm) sectors-of-destination used in data estimation /
agri, mine, petrol, food, text, wood, chem, n-met, b-met, mach, const, elec, comm, trans,
serv, hc, gc, tc, exp, fi, ii /
j(jd) input-output sectors of destination /
agri, mine, petrol, food, text, wood, chem, n-met, b-met, mach, const, elec, comm, trans, serv /
id(tm) sectors-of-origin used in data estimation /
agri, mine, petrol, food, text, wood, chem, n-met, b-met, mach, const, elec, comm, trans, serv, imp /
i(id) input-output sectors of origin /
agri, mine, petrol, food, text, wood, chem, n-met, b-met, mach, const, elec, comm, trans, serv /
im(i) merchandize commodities / agri, mine, petrol, food, text, wood, chem, n-met, b-met, mach /
inc(id) foreign commodities - non-competitive / imp /
s labor skill categories / eng engineers and scientists
tech other professional and technical workers
admin administrative and clerical workers
man manual and sales workers outside agriculture
unskill unskilled agriculture workers /
sun(s) unskilled agricultural workers / unskill /
l lag structure for human capital formation / 0*2 /
eit education input types / change, input /
sst(te,s) skill substitutions allowed during time periods / (1971,1974).(eng,tech,admin),
(1971,1974,1977,1980,1983,1986,1989).man /
Alias(te,tep),(t,tp),(s,sp);
$Stitle transactions matrix manipulations from 1960 data
Set ic1(tm) row labels for transactions matrix /
agri, mine, petrol, food, text, wood, chem, n-met, b-met, mach, const, elec, comm, trans,
serv, imp, err, va, gvp /
jdp(jd) jd sectors from 1 thru 21 but not 19
Scalar interval time interval between optimization years / 3 /;
jdp(jd) = yes; jdp("exp") = no; display jdp;
Table tm1960(tm,tm) transactions matrix for 1960 (billions of 1960 pesos)
agri mine petrol food text wood chem n-met b-met mach const elec comm trans serv
agri 2.028 .014 .001 8.049 1.091 .521 .55 .001 .002 .028 .003 .004 .018
mine .001 1.007 .128 .025 .004 .008 .093 .109 .455 .143 .216 .005 .01 .007 .006
petrol .621 .154 2.944 .445 .185 .097 .126 .218 .275 .173 .124 .216 .163 1.022 .094
food 1.66 .012 .011 4.697 .054 .033 .13 .005 .021 .026 .041 .002 .056 .028 .109
text .522 .012 .015 .094 2.565 .038 .094 .012 .025 .081 .038 .005 .09 .012 .084
wood .123 .035 .074 .438 .1 1.038 .246 .092 .043 .182 .613 .013 .428 .048 .357
chem .741 .099 .054 .134 .661 .134 1.018 .049 .043 .43 .191 .011 .078 .304 .318
n-met .003 .012 .007 .252 .008 .013 .056 .18 .063 .051 1.428 .001 .02 .002 .017
b-met .048 .068 .025 .144 .058 .039 .066 .033 .873 1.249 1.166 .013 .132 .027 .149
mach .224 .05 .048 .317 .114 .051 .095 .043 .057 .904 .867 .052 .206 .097 .463
const .14 .024 .026 .045 .038 .016 .02 .025 .022 .011 .06 .043 .083 .072 .367
elec .073 .106 .003 .165 .122 .062 .075 .075 .062 .063 .049 .08 .25 .03 .156
comm 1.199 .165 .197 2.632 1.527 .483 .869 .249 .314 .544 1.66 .093 .351 .619 1.28
trans .001 .009 .012 .057 .032 .021 .03 .008 .007 .046 .02 .012 2.943 .024 .13
serv .159 .152 .227 .681 .337 .241 .347 .078 .239 .312 .348 .043 1.61 .243 5.439
imp .548 .061 .704 .567 .599 .44 1.664 .156 .366 1.934 .921 .107 .119 .482 .429
err .105 .025 .023 .093 .028 .021 0.057 .013 .046 .047 .088 .007 .116 .027 .344
va 23.97 2.306 5.128 10.62 5.434 2.347 3.245 1.182 1.786 4.278 6.105 1.502 46.88 4.996 30.732
+ hc gc tc exp fi ii
$Maxcol 72
agri 14.846 .013 .073 2.88 .943 1.101 the submatrix consisting of the 15 input-output
mine .002 .001 2.007 .024 .06 sectors (and import on the row) represents the
petrol 2.257 .116 .173 .002 .222 interindustry flows. from this we obtain the
food 19.711 .042 .083 2.3 .04 .394 interindustry input-output coefficients.
text 7.835 .023 .19 .651 .027 .544 the column vectors "hc" (household consumption)
wood 1.242 .117 .035 .13 .05 .199 "gc" (government consumption), "tc" (tourists
chem 3.635 .217 .221 .073 .379 consumption), "exp" (exports), "fi" (fixed
n-met .099 .117 .072 .026 .101 investment), "ii" (inventory investment) are
b-met .024 .092 .222 .262 final demand vectors - of these sectors for
mach 3.28 .281 .094 .114 2.529 .616 goods from the 16 row sectors.
const .028 12.787 .131
elec .54 .179 .115
comm 35.835 .222 .336 1.125 3.625 .214
trans 4.309 .18 .111 .001 .087
serv 20.58 7.501 1.166 .217 .572
imp 1.313 .231 .055 3.84 .479
err -.036 -1.009 .01
Table t1968(tm,tm) independently estimated data for 1968 (billions of 1960 pesos)
exp gvp the "exp" column represents the
agri 3.860 44.775 export column vector in the trans-
mine 2.360 5.074 actions matrix in 1968.
petrol .450 17.001
food 2.880 48.689 the "gvp" column is the gross value
text .580 22.671 of production for 1968 - the row and
wood .310 9.827 column totals for the inter-industry
chem .660 17.913 transactions matrix in 1968.
n-met .120 5.351
b-met .230 10.768
mach .560 27.231
const 26.774
elec 5.669
comm 1.560 89.838
trans 12.598
serv .300 72.242
hc 191.1
gc 17.7
tc 4.22
exp 13.870
imp 21.0
fi 49.5
ii 5.5
va 13.870
$Maxcol 120
Parameter xj60(jd) gross production in sector j in 1960 (column totals - billions of 1960 pesos)
ax60(id,jd) transaction flows in 1960 (billions of 1960 pesos)
aij60(id,jd) i-o coefficient matrix for transactions in 1960
xj68(jd) gross output in sector j in 1968 (column totals - billions of 1960 pesos)
yi68(id) row totals for 1968 (billions of 1960 pesos)
ax19(id) export vector for 1968 (billions of 1960 pesos)
aij68(tm,tm) i-o coefficient matrix for transactions in 1968
ax68 transaction flows in 1968 (billions of 1960 pesos)
rho(id) annual technological rate of change between 1960 and 1968 (%);
** initialize 1960 parameters
xj60(jd) = sum(ic1, tm1960(ic1,jd));
ax60(id,jd) = tm1960(id,jd);
aij60(id,jd)$xj60(jd) = tm1960(id,jd)/xj60(jd);
* initialize the column and row totals and the export column in the transactions matrix for 1968
* from the known data in table t1968
xj68(jdp) = t1968(jdp,"gvp");
yi68(id) = t1968(id,"gvp");
ax19(id) = t1968(id,"exp");
$Maxcol 72
* obtain the technological rate of change. the only available information are the detailed
matrix for 1960 and the aggregate demand and
Parameter temp1(id) row totals; production for 1968. therefore assume there
temp1(id) = sum(jdp, aij60(id,jdp)*xj68(jdp)); exists an annual rate of technological change
rho(id)$temp1(id) = ((yi68(id) - ax19(id))/temp1(id))**(1/8) - 1; in the coefficients for row i, rho(i). this
is applied in the row correction procedure
Display xj60,ax60,aij60,xj68,yi68,ax19,temp1,rho; (in place of ras) to project the detailed
transactions matrix for 1968.
aij68(id,jdp) = ((1 + rho(id))**8)*aij60(id,jdp);
ax68(id,jdp) = aij68(id,jdp)*xj68(jdp);
ax68(id,"exp") = ax19(id);
Display aij68,ax68;
Parameter rho2(id) corrected rho - after subjective corrections to computed rho
rhotp rho for plan horizon;
rho2(id) = rho(id); to project beyond 1968, the values of rho(i)
rho2("mach") = .03; obtained above are adjusted subjectively in
rho2("elec") = .03; certain cases. it is assumed the historical
rho2("mine") = -.03; rates cannot possibly be maintained in the
rho2("imp") = -.03; future.
rhotp(id,te) = (1 + rho2(id))**(interval*(ord(te)-1));
Display rho,rho2,rhotp;
$Maxcol 120
$Stitle i-o and consumption coefficients
Parameter x0(j) base (1968) year output of sector j (billions of 1960 pesos)
a0(id,j) i-o matrix for base year of optimization period (1968)
a(id,tm,te) i-o matrix for optimization horizon
apc0(id) average propensity to consume in base year (1968) - household & government
apc(id,te) average propensity to consume in year t - household and government
apz0(id) average propensity to consume item i by tourists in base year (1968)
apz(id,te) average propensity to consume item i by tourists in year t
muc(te) column correction factor for apc
muz(te) column correction factor for apz;
** i-o matrices and output levels **
x0(j) = t1968(j,"gvp");
a0(id,j) = aij68(id,j);
a(id,j,te) = rhotp(id,te)*a0(id,j);
a(id,id,te)$t(te) = a(id,id,te) - 1;
Display x0,a0,a;
** consumption coefficients **
Scalar total gross consumption by households and government in base year (1968);
$Maxcol 72
total = sum(id, ax68(id,"hc") + ax68(id,"gc")); the consumption expenditure coefficient for
good i by domestic consumers (government &
apc0(id) = (ax68(id,"gc") + ax68(id,"hc"))/total; household) is the gross 1968 expenditure
muc(te) = 1 / sum(id, (apc0(id) * rhotp(id,te))) ; divided by total consumption outlay in 1968.
apc(id,te) = apc0(id) * rhotp(id,te) * muc(te) ; to project these coefficients into the future
we multiply by rho(i) (above) and mu(t) - mu(t)
apz0(id) = aij68(id,"tc") ; ensures that the coefficients sum to 1.
muz(te) = 1 / sum(id, (apz0(id) * rhotp(id,te))) ;
apz(id,te) = apz0(id) * rhotp(id,te) * muz(te) ; similarly for tourists.
Display apc0,muc,apc,apz0,muz,apz,total;
$Stitle capital-output coefficients
$Maxcol 120
Table b0(id,j) capital-output ratios for base year (1968) in billions of 1960 pesos
agri mine petrol food text wood chem n-met b-met mach const elec comm trans serv
agri .934
mine .124
petrol .004
food .048
text .047
wood .154
chem .102
n-met .088
b-met .352
mach .207 .261 .395 .197 .155 .3 .203 .319 .263 .176 .085 .886 .189 1.634 .273
const .588 .331 .615 .299 .145 .296 .232 .447 .275 .235 .015 2.109 .169 5.173 2.328
elec .462
comm .224 .204 .378 .193 .194 .307 .294 .279 .348 .234 .070 .707 .126 1.363 .199
trans .159
serv .039 .196 .154
imp .262 .100 .339 .183 .264 .316 .455 .202 .497 .336 .042 .369 .011 .835 .055
Parameter b(id,j,te) ratio of capital originating in sector i per unit of gross output in sector j
k(j,te) capital coefficients of sector j
bk(id,j,te) sector of origin ratios;
b(id,j,te) = rhotp(id,te) * b0(id,j) ;
k(j,te) = sum(id, b(id,j,te)) ;
bk(id,j,te) = b(id,j,te) / k(j,te) ;
Display b,k,bk;
$Stitle labor data
Parameter lreq0(s,j) input requirement for labor skill s per unit output in sector j
lreq(s,j,te) input requirement for labor skill s per unit output in sector j year t
sigt(s,j,te) time trend factor for reduction of labor input s in sector j year t
alr(te) agricultural labor released per unit of cumulative capital
pvv producers price value
Scalar wage1960 wage of unskilled agri labor in 1960 - assumed to be marginal productivity / 2400 /
mpc annual marginal productivity of capital in agriculture - assume constant (%)/ 16 /
mrs marginal rate of substitution - pesos of capital per man-year
Parameter csm(id) commerce and service margins / comm .1125
serv .0217 /;
pvv = 1 - sum(id, csm(id));
Display pvv;
Table labor(j,s) 1968 employment in millions
eng tech admin man unskill
agri .00541 .02705 .06222 7.02400
mine .00376 .00376 .00730 .09249
petrol .00437 .00611 .01746 .05937
food .00238 .00510 .03742 .29528
text .00189 .00631 .02650 .59632
wood .00143 .01061 .02122 .25344
chem .00585 .00704 .03629 .07020
n-met .00105 .00210 .00876 .10484
b-met .00152 .00228 .00718 .07347
mach .01857 .02837 .07831 .49140
const .00916 .02185 .07332 .60063
elec .00394 .00258 .02523 .04402
comm .00220 .03002 .29730 1.13501
trans .00182 .00684 .10212 .34511
serv .01365 .48598 .58137 1.28942
Table ls(te,s) labor supply projection by year and skill (thousands of persons)
eng tech admin man unskill
1968 .077 .646 1.382 5.451 7.024
1971 .097 .791 1.623 6.125 7.389
1974 .117 .936 1.864 6.906 7.841
1977 .137 1.081 2.105 7.827 8.321
1980 .157 1.226 2.346 8.966 8.830
1983 .177 1.371 2.587 10.291 9.370
1986 .197 1.516 2.828 11.746 9.943
1989 .217 1.661 3.069 13.416 10.552
Table sigma(j,s) labor productivity changes (% per year)
eng tech admin man unskill
agri 1.0 1.0 1.5 2.0 2.0
mine 1.0 1.0 1.5 1.5 1.5
petrol 1.0 1.0 1.5 3.5 3.5
food 1.0 1.0 1.5 3.5 3.5
text 1.0 1.0 1.5 3.5 3.5
wood 1.0 1.0 1.5 3.5 3.5
chem 1.0 1.0 1.5 3.5 3.5
n-met 1.0 1.0 1.5 3.5 3.5
b-met 1.0 1.0 1.5 3.5 3.5
mach 1.0 1.0 1.5 3.5 3.5
const 1.0 1.0 1.5 1.5 1.5
elec 1.0 1.0 1.5 3.5 3.5
comm 1.0 1.0 1.5 3.5 3.5
trans 1.0 1.0 1.5 1.5 1.5
serv 1.0 1.0 1.5 1.5 1.5
Table sf(eit,s,l,s) coefficients for human capital formation activities
$Maxcol 80
2.eng 1.eng 0.eng 1.tech 0.tech 1.admin 0.admin view the columns as processes. for
example, the engineering education
change.eng 1.0 process two years before an engineer
change.tech .3 1.0 is "produced" would require certain
change.admin -2.0 .6 .1 -1.9 .9 1.0 inputs. there are 2 types of inputs -
change.man -2.0 1.0 "input" which are short-term - only in
input.eng -.17 -.14 -.02 that period as support - and "change"
input.tech -.09 -.18 -.16 which is transformed permenantly into
input.admin -.04 into a new kind of labor or reverts
to its old classification. in the
model these permenant changes ("flows")
are then summed up (a "stock").
$Maxcol 72
Table ldg(s,s) labor downgrading coefficients
the labor downgrading and upgrading mechanisms
eng tech admin man are only for short-term (annual) adjustments.
eng -1.0 labor downgrading can occur throughout the
tech 1.0 -1.0 model horizon and is a one-to-one replacement.
admin 1.0 -1.0
man 1.0 -1.0 labor upgrading on the other hand is costly to
unskill 1.0 the economy (eg. to replace 1 engineer requires
1 technician, .5 administrators and 4 manuals)
and is applicable in the first 2 periods only
Table lug(s,s) labor upgrading coefficients (after when the endogenous educational activi-
ties come on stream). the exception is the
eng tech admin man movement of unskilled rural labor into the
urban labor force which can occur through the
eng 1.0 entire model horizon. the cost to the economy
tech -1.0 1.0 is reflected in the requirement of inputs by
admin -0.5 -1.0 1.0 the service sector (parameter ssr and material
man -4.0 -2.0 -3.0 1.0 balance constraint). the time nature of labor
unskill -1.0 upgrading is set in the parameter lugt below.
$Maxcol 120
Parameter lugt(s,sp,te) time allowed labor upgrading coefficients ;
lugt(s,sp,te) = lug(s,sp)$sst(te,sp);
lreq0(s,j)$t1968(j,"gvp") = labor(j,s) / t1968(j,"gvp") ;
sigt(s,j,te) = (1/(1 + sigma(j,s)/100))**(interval*(ord(te)-1)) ;
lreq(s,j,te) = sigt(s,j,te) * lreq0(s,j) ;
mrs = wage1960/(mpc/100);
alr(te) = 1 / ((mrs/1000) * (1 + sigma("agri","unskill")/100)**(8+(interval*(ord(te)-1))));
Display lugt,lreq0,lreq,sigt,mrs,alr;
Parameter length; length(s) = max(0, smax((sp,l)$sf("change",sp,l,s), ord(l)));
Display length;
$Stitle trade and capital data
Set rsfdp(te) reset limits on capital inflows in case 7 for following periods /
1974, 1977, 1980, 1983 /
Parameter pfc(te) foreign concessional capital inflows (billions of 1960 pesos) /
1968 2.1, 1971 4.3, 1974 4.7, 1977 4.3, 1980 3.1, 1983 1.5, 1986 -.5 /
infc(te) interest on fc (billions of 1960 pesos) /
1968 -1.4, 1971 -1.9, 1974 -2.7, 1977 -3.4, 1980 -4.0, 1983 -4.4, 1986 -4.2 /
es(i) export share of subsidized high-cost export manufactures in 1986 /
food .409, text .064, wood .044, chem .183, n-met .022, b-met .064, mach .214 /
fdpup(t) upper bound on direct foreign capital inflows during each period /
1971 5, 1974 5.5, 1977 5.5, 1980 5.5, 1983 5.5, 1986 5.0 /
zmi(te,tep) linear decreasing factor for nominal implicit protection rate
Scalar dpc cost level of high cost manufacture relative to foreign exch earnings (1) / 1.3 /
rcd rate of change of cost differential from 30% to 0 (% points each interval)
cfdp upper bound on cumulative foreign direct inflows / 30 /;
rcd = (dpc - 1)/card(t);
zmi(t,tp) = dpc - rcd*(ord(t) - ord(tp));
Display rcd,zmi;
Table begr(*,*) bounds on export growth rates
lower upper
agri 2.0 6.0
mine 4.0
petrol 1.5
food 6.0
text 4.5
wood 6.0
chem 10.0
n-met 7.5
b-met 10.0
mach 12.0
tourism 8.0 13.0
Parameter e0(i) base year (1968) export levels (billions of 1960 pesos)
elo(i,te) lower bound on export levels (billions of 1960 pesos)
eup(i,te) upper bound on export levels (billions of 1960 pesos)
z0 base year (1968) earnings from tourism (billions of 1960 pesos)
zlo(te) lower bound on earnings from tourism (billions of 1960 pesos)
zup(te) upper bound on earnings from tourism (billions of 1960 pesos);
e0(i) = ax68(i,"exp");
elo(i,te) = e0(i) * (1 + begr(i,"lower")/100)**(interval*(ord(te)-1)) ;
eup(i,te) = e0(i) * (1 + begr(i,"upper")/100)**(interval*(ord(te)-1)) ;
z0 = sum(i, ax68(i,"tc"));
zlo(te) = z0 * (1 + begr("tourism","lower")/100)**(interval*(ord(te)-1)) ;
zup(te) = z0 * (1 + begr("tourism","upper")/100)**(interval*(ord(te)-1)) ;
Display e0, elo,eup,z0,zlo,zup;
$Stitle "special" initial and terminal conditions
Parameter deltae post-terminal year increment in exports (billions of 1960 pesos)
deltaz post-terminal year increment in tourist expenditures(billions of 1960 pesos)
Scalar con68 aggregate consumption in 1968 / 208.8 /
inv68 aggregate investment in 1968 / 55 /
sav68 aggregate savings in 1968 / 52.1 /
gdp68 gross domestic product in 1968 / 260.9 /
infdpt interest & profit remitaances on capital borrowed prior to plan / 4.9 /
rgap68 resource gap in 1968 / 2.9 /
eazt68 foreign exchange earned from exports and tourism in 1968 / -18.1 /
fc68 concessional capital inflow in 1968 / 2.1 /
fdp68 direct foreign capital inflow in 1968 / 6.0 /
infdp68 interest & profit remittances in 1968 on foreign direct capital / -3.8 /;
deltae(im) = eup(im,"1989") - eup(im,"1986");
deltae("total") = sum(im, deltae(im));
deltae(i)$csm(i) = csm(i)*deltae("total");
deltaz(id) = zlo("1989")*apz(id,"1989") - zlo("1986")*apz(id,"1986");
Display deltae,deltaz;
$Stitle model parameterizations
Scalar mps marginal propensity to save / .3 /
g growth rate - annual / .07 /
r discount rate / .15 /
beta present value
betatr present value for year 7 in discounted maximand
gamma growth factor - three year period
gv3 growth rate - three year period for incremental capacity variable
acc annual cost of capital - for private foreign capital (%) / .15 /
pci income payments for capital inflows within the horizon
initial initial period in model / 1 /
last last period of optimization horizon / 7 /
Parameter ts(te,tep) time summation matrix
ts2(te,tep) time summation matrix - for tau from t equal 1 to t-1
ssr(i,s) service sector requirements to convert rural to urban labor
betat(te) present value
w1(te) weight for objective function 1
w2a(te) weight for first component of objective function 2
w2b(te) weight for second component of objective function 2
w3(te) weight for objective function 3;
gamma = (1 + g)**interval;
gv3 = gamma - 1;
pci = (1 + acc)**interval - 1;
beta = (1 + r)**(-interval);
betat(te) = (1 + r)**(-(interval*(ord(te)-1)));
betatr = betat("1989")/(1 - beta*gamma);
ssr("serv","man") = 2.4;
ts(te,tep) = 1$(ord(te) ge ord(tep));
ts2(te,tep) = 1$(ord(te) gt ord(tep));
w1(te) = 0; w1("1971") = 1;
w2a(te) = 0; w2a(t) = betat(t); w2b(te) = 0; w2b("1989") = betatr;
w3(te) = 0; w3("1989") = 1;
Display ts,ts2,mps,g,r,beta,betat,betatr,gamma,gv3,acc,pci,ssr,w1,w2a,w2b,w3;
$Stitle model definition
Equations
mb(i,te) material balance constraint (10e9 pesos)
cap(j,te) capacity constraint (10e9 pesos)
tic(i,te) terminal year investment constraint (10e9 pesos)
ldsc(s,te) labor demand and supply constraint (10e6 man y)
drql(s,te) definition of labor requirements (10e6 man y)
trql(s,te) terminal year labor requirements (10e6 man y)
exdef(te) exports definition (10e9 pesos)
fexch(te) foreign exchange constraint (10e9 pesos)
fgap(te) resource gap definition (10e9 pesos)
ffdp bound on cumulative direct private capital inflows (10e9 pesos)
ginv(te) aggregate investment definition (10e9 pesos)
gsav(te) gross savings definition (10e9 pesos)
ggdp(te) gross domestic product definition (10e9 pesos)
h(te) gradualist consumption path (10e9 pesos)
tcc(te) terminal conditions on consumption - in place of h (10e9 pesos)
dsc(te) domestic savings constraint (10e9 pesos)
obj1 objective function: base case - maximize initial consumption (10e9 pesos)
obj2 objective function: case 3 - maximize discounted consumption (10e9 pesos)
obj3 objective function: case 4 - maximize terminal consumption (10e9 pesos)
Variables
rgap(te) resource gap in year t (10e9 pesos)
max1 maximand: maximization of initial consumption (10e9 pesos)
max2 maximand: maximization of discounted consumption (10e9 pesos)
max3 maximand: maximization of terminal consumption (10e9 pesos)
Positive Variables
x(jd,te) gross output of sector j in year t (10e9 pesos)
v(jd,te) one-year increase in cap of sector - investment resources expended(10e9 pesos)
ld(s,te) labor downgraded from category s in year t (10e6 man y)
ul(s,te) labor upgraded into category s in year t (10e6 man y)
ka(te) capital added to agriculture in substitution for unskilled labor (10e9 pesos)
ed(s,te) education processes for human capital - skill s first available (10e6 man y)
rql(s,te) requirements for labor skill s in year t (10e6 man y)
e(i,te) exports of item i in year t (10e9 pesos)
em(te) exports of high-cost manufactures - first exported in year t (10e9 pesos)
ea(te) aggregate merchandize exports in year t (10e9 pesos)
zt(te) earning from tourism in year t (10e9 pesos)
fdp(te) foreign direct private capital inflows net of amortization (10e9 pesos)
inv(te) gross domestic investment in year t (10e9 pesos)
sav(te) gross domestic savings in year t (10e9 pesos)
con(te) aggregate consumption expenditures - household & government (10e9 pesos)
gdp(te) gross domestic product in year t (10e9 pesos)
infdp interest & profit remittances on foreign direct capital- prior (10e9 pesos)
fc(te) concessional foreign capital inflows - net of amortization (10e9 pesos) ;
$Eject
$Double
mb(i,t).. sum(j, a(i,j,t)*x(j,t) + b(i,j,t)*v(j,t)) + bk(i,"agri",t)*ka(t) + apc(i,t)*con(t) + apz(i,t)*zt(t)
+ es(i)*sum(tep$ts(t,tep), zmi(t,tep)*em(tep)) + e(i,t)$im(i) + csm(i)*ea(t) + sum(s, ssr(i,s)*ul(s,t)) =l= 0;
cap(j,t).. x(j,t) =l= x0(j) + interval*sum(te$ts2(t,te), v(j,te));
tic(i,te)$(ord(te) gt last)..
apc(i,te-1)*(con(te) - con(te-1)) + gv3*sum(j, b(i,j,te-1)*v(j,te-1)) + deltae(i) + deltaz(i)
=l= interval*sum(j, -a(i,j,te-1)*v(j,te-1));
drql(s,t).. sum(j, lreq(s,j,t)*x(j,t)) - alr(t)*(ka(t) + interval*sum(te$ts2(t,te), ka(te)))$sun(s) =e= rql(s,t);
trql(s,te)$(ord(te) gt last)..
sum(j, lreq(s,j,te)*(x(j,te-1) + interval*v(j,te-1))) - interval*alr(te)*sum(tep$ts2(te,tep), ka(tep))$sun(s)
=e= rql(s,te);
$Maxcol 73
$Single
ldsc(s,te)$(ord(te) gt initial)..
rql(s,te) =l= requirement of s is less than or equal to
ls(te,s) supply of s
+ sum(sp, ldg(s,sp)*ld(sp,te) + lugt(s,sp,te)*ul(sp,te)) plus labor downgraded out of s
plus labor upgraded out of s
+ sum((tep,sp,l)$(((ord(tep)+(ord(l)-1)) gt length(sp))$ts(te,tep)), plus the sum of the net change in s due to
sf("change",s,l,sp)*ed(sp,tep+(ord(l)-1))) education over the sets tep(years), sp
(other labor groups) and l (lag) such
that these activities are possible in t
+ sum((sp,l)$((ord(te)+(ord(l)-1)) gt length(sp)), plus the sum of the inputs of s required for
sf("input",s,l,sp)*ed(sp,te+(ord(l)-1))); education over the sets sp (other labor)
and l such that these actvities are
possible in year t.
$Double
$Maxcol 120
exdef(t).. pvv*ea(t) =e= sum(im, e(im,t)) + sum(tp$ts(t,tp), em(tp));
fexch(t).. sum(inc, apc(inc,t)*con(t) + bk(inc,"agri",t)*ka(t)
+ sum(j, a(inc,j,t)*x(j,t) + b(inc,j,t)*v(j,t)) ) =e= ea(t) + zt(t) + rgap(t);
fgap(t).. rgap(t) - fc(t) - fdp(t) + infdp + pci*sum(tp$ts2(t,tp), fdp(tp)) =e= infc(t);
ffdp.. sum(t, fdp(t)) =l= cfdp;
ginv(te)$(ord(te) le last).. sum(j, k(j,te)*v(j,te)) + ka(te) =e= inv(te);
gsav(t).. inv(t) =e= sav(t) + rgap(t);
ggdp(t).. con(t) + sav(t) =e= gdp(t);
dsc(te)$t(te).. sav(te) - sav(te-1) =l= mps*(gdp(te) - gdp(te-1));
h(te)$t(te).. con(te+1) - con(te) =e= gamma * (con(te) - con(te-1));
tcc(te)$(ord(te) gt last).. con(te) =e= gamma*con(te-1);
obj1.. max1 =e= sum(te, w1(te)*con(te));
obj2.. max2 =e= sum(te, (w2a(te) + w2b(te))*con(te));
obj3.. max3 =e= sum(te, w3(te)*con(te));
$Single
$Stitle model definitions and bounds
*initial conditions:
con.fx("1968") = con68;
inv.fx("1968") = inv68;
sav.fx("1968") = sav68;
gdp.fx("1968") = gdp68;
fdp.up(t) = fdpup(t);
infdp.fx = infdpt;
fc.fx(t) = pfc(t);
e.lo(im,t) = elo(im,t);
e.up(im,t) = eup(im,t);
zt.lo(t) = zlo(t);
zt.up(t) = zup(t);
Model din0 dinamico base case modeland manne cases 6 and 8 /
mb, cap, tic, ldsc, drql, trql, exdef, fexch, fgap, ffdp, ginv, gsav, ggdp, dsc, h, obj1, obj2, obj3 /
din1 dinamico model for manne cases 3 and 4 /
mb, cap, tic, ldsc, drql, trql, exdef, fexch, fgap, ffdp, ginv, gsav, ggdp, dsc, tcc, obj1, obj2, obj3 /
din2 dinamico model for manne case 7 /
mb, cap, tic, exdef, fexch, fgap, ffdp, ginv, gsav, ggdp, dsc, h, obj1, obj2, obj3 /
$Stitle d i n a m i c o - report for macro model of mexico: declarations
Set t1(te) / 1968, 1971, 1974, 1977, 1980, 1983, 1986 /
ji / agri-ka, agri-total, agri, mine , petrol, food, text , wood, chem,
n-met , b-met , mach, const, elec , comm, trans, serv /
sm1 / g-d-p, consumed, savings, r-gap, investment, gdp-gr, con-gr, sav-gr, inv-gr /
sm2 / g-d-p, consumed, savings, r-gap, investment /
sm3 / gdp-gr, con-gr, sav-gr, inv-gr /
sf1 / imports, ea+zt, rgap-fexch,fcl,fdpl,infcl,infdpl,rgap-fgap /
sf2 / imports, ea+zt, fcl, fdpl, infcl, infdpl /
mm(sm2,sm3) / g-d-p.gdp-gr, consumed.con-gr, savings.sav-gr, investment.inv-gr /
tb / 1968-71, 1971-74, 1974-77, 1977-80, 1980-83, 1983-86 /
mtb(tb,t1) / 1968-71.1971, 1971-74.1974, 1974-77.1977, 1977-80.1980, 1980-83.1983, 1983-86.1986 /
sl1 / employed, eff-sl1, dual, ori-74-80 /
runset / gradualist, discounted, terminal, alternate6, alternate7, alternate8 /
run(runset)
y74(te) / 1974 /
y80(te) / 1980 /
y7480(te) / 1974, 1980 /
mac11 / g-d-p, consumed, savings, investment /
Parameter macroecon1 macroeconomic results (billions of 1960 pesos) - (table 6 pg 134)
macroecon2 growth rates of macroeconomic variables - (table 6 pg 134)
forexch foreign exchange (billions of 1960 pesos) - (table 7 pg 136)
production levels (billions of 1960 pesos) - (table 8 pg 138)
investment percentage composition of net investment by sector of destination - (pg 139)
effprices efficiency prices of foreign exchange and tradeable manufactures - pg 141
laborc efficiency wages & dual variables for labor constraint ldsc - (pg 143)
macrorun macroeconomic results (billions of 1960 pesos) - pg 153
resource resource gap - financial flows (billions of 1960 pesos) - pg 155
epfe efficiency prices of foreign exchange and foreign aid - pg 158
fep80 foreign exchange projections for 1980 (billions of 1960 pesos) - pg 157
gpl80 gross production levels in 1980 (billions of 1960 pesos) - pg 159
efw80 employment and income - pg 160;
$Stitle solution scenario and report definition: number 1
run(runset) = no; run("gradualist") = yes;
Solve din0 maximizing max1 using lp;
** detailed scenario report **
macroecon1("g-d-p",t1) = gdp.l(t1);
macroecon1("consumed",t1) = con.l(t1);
macroecon1("savings",t1) = sav.l(t1);
macroecon1("r-gap",t1) = rgap.l(t1);
macroecon1("investment",t1) = inv.l(t1);
macroecon1("r-gap","1968") = rgap68;
macroecon1("aps",t1) = round(100*sav.l(t1)/gdp.l(t1),1);
macroecon1(sm2,t1) = round( macroecon1(sm2,t1),1);
macroecon2(sm3,tb) = sum((sm2,t1)$(mtb(tb,t1)*mm(sm2,sm3)),
100*((macroecon1(sm2,t1)/macroecon1(sm2,t1-1))**(1/3) - 1) );
macroecon2(sm3,"1968-86") = sum(sm2$mm(sm2,sm3), 100*((macroecon1(sm2,"1986")/macroecon1(sm2,"1968"))**(1/18) -1) );
macroecon2(sm3,tb) = round( macroecon2(sm3,tb),1);
macroecon2("inc-k-o",tb) = round( 100*sum(t1$mtb(tb,t1), (inv.l(t1)-inv.l(t1-1))/sum(j,x.l(j,t1)-x.l(j,t1-1))), 1);
macroecon2("mps",tb) = round( 100*sum(t1$mtb(tb,t1), (sav.l(t1)-sav.l(t1-1))/(gdp.l(t1)-gdp.l(t1-1))), 1);
forexch("imports",t1) = sum(inc, apc(inc,t1)*con.l(t1) + sum(j, a(inc,j,t1)*x.l(j,t1) + b(inc,j,t1)
*v.l(j,t1)) + bk(inc,"agri",t1)*ka.l(t1));
forexch("ea+zt",t1) = -ea.l(t1) - zt.l(t1);
forexch("imports","1968") = t1968("imp","gvp");
forexch("ea+zt","1968") = eazt68;
forexch("rgap-fexch",t1) = forexch("imports",t1) + forexch("ea+zt",t1);
forexch("fcl",t1) = fc.l(t1);
forexch("fdpl",t1) = fdp.l(t1);
forexch("infcl",t1) = infc(t1);
forexch("infdpl",t1) = -(infdp.l + pci*sum(tep$ts2(t1,tep), fdp.l(tep)));
forexch("fcl","1968") = fc68;
forexch("fdpl","1968") = fdp68;
forexch("infcl","1968") = infc("1968");
forexch("infdpl","1968") = infdp68;
forexch("rgap-fgap",t1) = forexch("fcl",t1) + forexch("fdpl",t1) + forexch("infcl",t1) + forexch("infdpl",t1);
forexch(sf1,t1) = round(forexch(sf1,t1),1);
production(j,t1) = round( x.l(j,t1), 1);
production(j,"1968") = t1968(j,"gvp");
production(j,"1960-68") = round( 100*((t1968(j,"gvp")/xj60(j))**(1/8)-1),1);
production(j,"1968-80") = round( 100*((production(j,"1980")/production(j,"1968"))**(1/12)-1),1);
investment("agri-ka",t1) = 100*ka.l(t1)/inv.l(t1);
investment(j,t1) = 100*(k(j,t1)*v.l(j,t1))/inv.l(t1);
investment("agri-total",t1) = investment("agri-ka",t1) + investment("agri",t1);
investment("**total**",t1) = sum(j, investment(j,t1)) + investment("agri-ka",t1);
investment(ji,t1) = round(investment(ji,t1),1);
effprices("for-exch",t) = - round(fexch.m(t)*1000,2);
effprices("trad-manu",t) = - round(sum(i, 1000*mb.m(i,t)*es(i)),2);
effprices("ratio",t) = round(effprices("for-exch",t)/effprices("trad-manu",t),2);
effprices("for-exch","ori-74-80") = round(100*((effprices("for-exch","1974")/effprices("for-exch","1980"))**(1/6)
- 1),1);
effprices("trad-manu","ori-74-80") = round(100*((effprices("trad-manu","1974")/effprices("trad-manu","1980"))**(1/6)
- 1),1);
laborc(s,t,"eff-sl1") = - round(ldsc.m(s,t),3);
laborc(s,t,"dual") = round(ldsc.m(s,t)/(sum(i, apc(i,t)*mb.m(i,t)) + apc("imp",t)*fexch.m(t)),1);
laborc(s,"ori-74-80","eff-sl1") = round(100*((laborc(s,"1974","eff-sl1")/laborc(s,"1980","eff-sl1"))**(1/6) - 1));
** comparative report **
macrorun(run,y7480,mac11) = macroecon1(mac11,y7480);
macrorun(run,"1968-80","mps") = round(100*(sav.l("1980")-sav.l("1968"))/(gdp.l("1980")-gdp.l("1968")),1);
macrorun(run,"1968-80","gdp-gr") = round(100*((gdp.l("1980")/gdp.l("1968"))**(1/12) - 1),1);
resource(run,t,"fdpl") = fdp.l(t);
resource(run,t,"infdpl") = forexch("infdpl",t);
resource(run,t,"fc-infc") = fc.l(t) + infc(t);
resource(run,t,"res-gap") = forexch("rgap-fgap",t);
epfe(run,y7480,"fexch-m") = -round(1000*fexch.m(y7480),2);
epfe(run,y7480,"fgap-m") = -round(1000*fgap.m(y7480),2);
epfe(run,y7480,"relative") = effprices("ratio",y7480);
fep80(run,"imports","imports") = round(forexch("imports","1980"),2);
fep80(run,im,"export-e") = round(e.l(im,"1980"),2);
fep80(run,"zm4","high-cost") = round( em.l("1971") + em.l("1974") + em.l("1977") + em.l("1980"), 2);
fep80(run,"za4","earnings") = ea.l("1980");
fep80(run,"zt4","earnings") = zt.l("1980");
fep80(run,"resource","gap") = forexch("rgap-fexch","1980");
fep80("lower-bd",im,"export-e") = e.lo(im,"1980");
fep80("upper-bd",im,"export-e") = e.up(im,"1980");
fep80("lower-bd","zt4","earnings") = zt.lo("1980");
fep80("upper-bd","zt4","earnings") = zt.up("1980");
gpl80(run,j) = round(x.l(j,"1980"),1);
efw80(run,s,"employed") = rql.l(s,"1980");
efw80(run,"total-1-4","employed") = sum(s$(not sun(s)), rql.l(s,"1980"));
efw80(run,"total-1-5","employed") = sum(s, rql.l(s,"1980"));
efw80(run,s,"eff-wages") = round((ldsc.m(s,"1977")+ldsc.m(s,"1980")+ldsc.m(s,"1983"))/
(3*(sum(i, apc(i,"1980")*mb.m(i,"1980"))
+ apc("imp","1980")*fexch.m("1980"))),1);
efw80(run,s,"income") = round(rql.l(s,"1980")*efw80(run,s,"eff-wages"),1);
efw80(run,"total-1-5","income") = sum(s, efw80(run,s,"income"));
efw80(run,"con4","aggregate") = con.l("1980");
efw80(run,"con4","income-t") = round(100*efw80(run,"total-1-5","income")/efw80(run,"con4","aggregate"));
Display macroecon1,macroecon2,forexch,production,investment,effprices,laborc,macrorun,resource,epfe,fep80,gpl80,efw80;
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