\$TITLE htsim: HALL-TAYLOR SIMULATION \$EOLCOM # \$OFFSYMXREF OFFSYMLIST * Developed by Ruben Mercado * Modified by Alan Mehlenbacher OPTION SYSOUT = OFF; OPTION LIMROW = 7; OPTION LIMCOL = 0; OPTION SOLPRINT = OFF; option NLP=MINOS; *********************************************************************** * SECTION 1 : DEFINITION OF PARAMETER VALUES FOR THE ORIGINAL * NONLINEAR HALL-TAYLOR MODEL *********************************************************************** SCALARS a minimum consumption / 220 / b marg prop to consume / 0.7754 / d interest elast of invest. / 2000 / ee maximum investment / 1000 / f coeff. on excess aggr dem. / 0.8 / gg maximum net exports / 600 / h interest elast of mon dem. / 1000 / k income elast of money dem. / 0.1583 / mm income elast of net exp / 0.1 / n real ex rate elast of net exp / 100 / q constant / 0.75 / tax tax rate / 0.1875 / v constant / 5 / alpha coeff. on 1 lagged inflation / 0.4 / beta coeff. on 2 lagged inflation / 0.2 / mu elast. of empl. wrt GDP / 0.33 / ; *********************************************************************** * SECTION 2: DEFINITION OF TEMPORAL HORIZON FOR SIMILATION *********************************************************************** * If you change the extension of the horizon, make the necessary * adjustments in the section of shocks' definition (Section 3) SETS T EXTENDED HORIZON / 0*15 / T0(T) PERIOD ZERO T1(T) PERIOD ONE ; T0(T) = YES\$(ORD(T) EQ 1); T1(T) = YES\$(ORD(T) EQ 2); DISPLAY T0, T1; display T; *********************************************************************** * SECTION 3 : DEFINITION OF CHANGES IN POLICY AND EXOGENOUS VARIABLES *********************************************************************** PARAMETERS * Definition of policy shocks in percentage (0 to 1) changes Mper(T) money supply shock (in % change) Gper(T) Gov. expenditure shock (in % change) Ynper(T) potential GDP shock (in % change) Pwper(T) foreign prices shock (in % change); * Default values for policy shocks Mper(T) = 0.0 ; Gper(T) = 0.0 ; Ynper(T) = 0.0 ; Pwper(T) = 0.0 ; PARAMETERS * Definition of exogenous variables (in levels) M(T) money stock (in levels) G(T) Gov. expenditure (in levels) Yn(T) potential GDP (in levels) Pw(T) foreign prices (in levels); SCALARS * Base values for exogenous variables Mbase base value for money supply /900/ Gbase base value for government expenditures /1200/ Ynbase base value for potential GDP /6000/ Pwbase base value for foreign price level /1/; M(T) = Mbase; G(T) = Gbase; Yn(T) = Ynbase; Pw(T) = Pwbase; ****************************** * SET THE SHOCKS ****************************** * DIFFERENT TIME PERIODS FOR SHOCKS (all, single, few: change as required) *Note that these time periods are set up this way just as possible examples SETS TS1(T) all periods / 4*15 / TS2(T) single period / 8 / TS3(T) few periods / 4*7 / TS4(T) few periods / 8*11 / TS5(T) few periods / 12*15 / ; * SHOCK IN MONEY SUPPLY Mper(TS1) = 0.10 ; * SHOCK IN GOVERNMENT EXPENDITURE Gper(TS1) = 0.00; * SHOCK IN POTENTIAL GNP (notice that the natural rate of * unemployment remains the same) Ynper(TS1) = 0.0; * SHOCK IN FOREIGN PRICES Pwper(TS1) = 0.0; * APPLY SHOCKS TO LEVEL VARIABLES * Application of shocks over different time periods (EXAMPLE ONLY) M(TS1) = Mbase * (1 + Mper(TS1)) ; G(TS2) = Gbase * (1 + Gper(TS2)) ; Yn(TS3) = Ynbase * (1 + Ynper(TS3)) ; Pw(TS4) = Pwbase * (1 + Pwper(TS4)) ; * reporting policy and exogenous variables values PARAMETER REPORTEX POLICY AND EXOGENOUS VARIABLES VALUES; REPORTEX(T,"Money") = M(T); REPORTEX(T,"Gov. Exp.") = G(T); REPORTEX(T,"Pot. GDP") = Yn(T); REPORTEX(T,"Fgn Price") = Pw(T); *********************************************************************** * SECTION 4: VARIABLES and EQUATIONS *********************************************************************** PARAMETERS Un(T) natural rate of unemployment ; Un(T) = 0.05 ; VARIABLES Y(T) gdp Yd(T) disposable income C(T) consumption I(T) investment R(T) interest rate P(T) price level pi(T) inflation rate piex(T) expected inflation rate E(T) nominal exchange rate X(T) net exports Gd(T) government deficit U(T) unemployment rate J dummy objective function * Equation numbering agrees with book EQUATIONS eq1(T) gdp identity eq2(T) disposable income eq3(T) consumption eq4(T) investment eq5(T) money demand eq6(T) expected inflation eq7(T) inflation rate eq8(T) price level eq9(T) real exchange rate eq10(T) net exports eq11(T) government deficit eq12(T) unemployment rate JD dummy objective equation; JD.. J =E= 0 ; *AD-IS equations eq1(t+2).. Y(t+2) =E= C(t+2) + I(t+2) + G(t+2) + X(t+2) ; eq2(t+2).. Yd(t+2) =E= (1 - tax) * Y(t+2) ; eq3(t+2).. C(t+2) =E= a + b * Yd(t+2) ; eq4(t+2).. I(t+2) =E= ee - d * R(t+2) ; eq9(t+2).. E(t+2) * P(t+2) / Pw(t+2) =E= q + v * R(t+2) ; eq10(t+2).. X(t+2) =E= gg - mm*Y(t+2) - n*(E(t+2)*P(t+2)/Pw(t+2)); *AD-LM equation eq5(t+2).. M(t+2) / P(t+2) =E= k * Y(t+2) - h * R(t+2) ; *AS equations (Expectations Augmented Phillips Curve) eq6(t+2).. piex(t+2)=E= alpha * pi(t+1) + beta * pi(t) ; eq7(t+2).. pi(t+2) =E= piex(t+2) + f*(Y(t+1)-Yn(t+2))/Yn(t+2) ; eq8(t+2).. P(t+2) =E= P(t+1) * (1 + pi(t+2)) ; *Equations of interest for deficit and unemployment eq11(t+2).. Gd(t+2) =E= G(t+2) - tax * Y(t+2) ; eq12(t+2).. U(t+2) =E= Un(t+2) - mu*(Y(t+2)-Yn(t+2))/Yn(t+2) ; *********************************************************************** * In what follows, we assign initial variables' values and lower bounds * WARNING: The order of declaration of assignments is very important * Successive assignments to a same variable undo the previous ones *********************************************************************** * Guess of initial values for the solution algorithm. * Without them, the problem may be declared "infeasible" * That is, the algorithm will converge to a solution from some initial * positions but not from others * This is common in nonlinear problems R.L(T+2) = 0.09 ; Y.L(T+2) = 6500 ; E.L(T+2) = 1.2; C.L(T+2) = 4500 ; I.L(T+2) = 900 ; X.L(T+2) = -100 ; Gd.L(T+2) = 75 ; U.L(T+2) = 0.07 ; Yd.L(T+2)= 4875 ; pi.L(T+2) = 0.1 ; piex.L(T+2)=0.2 ; P.L(T+2) = 1.1 ; * lower bound for p, to avoid division by zero P.LO(T+2) = 0.0001 ; * fixing initial steady-state values for lagged endogenous variables P.FX(T0) = 1 ; P.FX(T1) = 1 ; pi.FX(T0) = 0 ; pi.FX(T1) = 0 ; Y.FX(T0) = Ynbase ; Y.FX(T1) = Ynbase ; MODEL NONLDYN /eq1, eq2, eq3, eq4, eq5, eq6, eq7, eq8, eq9, eq10, eq11, eq12, JD / ; SOLVE NONLDYN MINIMIZING J USING NLP; * Reporting solution values PARAMETER REPORTS SOLUTION VALUES IN LEVELS; REPORTS(T,"GDP") = Y.L(T); REPORTS(T,"Inflation") = pi.L(T); REPORTS(T,"Int.Rate") = R.L(T); REPORTS(T,"Exch.Rate") = E.L(T); REPORTS(T,"Gov.Def") = Gd.L(T); REPORTS(T,"Unemploy") = U.L(T); * Showing final results DISPLAY REPORTEX; DISPLAY REPORTS; * Write to File * Define the file: change this name for different experiments file htsimfile /htsimfile01.txt/; * Make the current file put htsimfile; * Write periods to file put 't '; loop(t, put ',', put t.tl); put /; * Write variables to file put 'Y '; loop(t, put ',', put Y.l(t)); put /; put 'pi '; loop(t, put ',', put pi.l(t)); put /; put 'R '; loop(t, put ',', put R.l(t)); put /; put 'E '; loop(t, put ',', put E.l(t)); put /; put 'Gd '; loop(t, put ',', put Gd.l(t)); put /; put 'U '; loop(t, put ',', put U.l(t)); put /; put 'P '; loop(t, put ',', put P.l(t)); put /; put 'I '; loop(t, put ',', put I.l(t)); put /; put 'X '; loop(t, put ',', put X.l(t)); put /; put 'C '; loop(t, put ',', put C.l(t)); put /; * Close the file putclose htsimfile;