Dynamic Stochastic General Equilibrium (DSGE): gEcon + Rmarkdown
DKWC
2021-06-25
gEcon packages of R
gEcon is the package of R to model both Dynamic Stochastic General Equilibrium (DSGE) and Static General Equilibrium. Static General Equilibrium is also called Computable General Equilibrium(CGE). The computational solvers of traditional econometric modeling software packages such as GAMS, GEMPACK and Dynare are based on the first order conditions (FOCs) and linearization equations. Different from them, the computational solver of gEcon is an algorithm for automatic derivation of FOCS with symbolic computations library. gEcon can handle large-scale (100+ variables) models.
Demontration:
Sample scripts of Epstein-Zin Model
# ############################################################################
# (c) Chancellery of the Prime Minister 2012-2015 #
# #
# Authors: Grzegorz Klima, Karol Podemski, Kaja Retkiewicz-Wijtiwiak #
# ############################################################################
# Stochastic growth model with Epstein-Zin preferences
# ############################################################################
options
{
output logfile = TRUE;
output LaTeX = TRUE;
};
tryreduce
{
pi[], L_s[], K_d[], L_d[];
};
block CONSUMER
{
definitions
{
u[] = (C[]^(1 - eta) - 1) / (1 - eta);
};
controls
{
K_s[], C[], I[];
};
objective
{
U[] = u[] + beta * E[][U[1]^(1 - theta_EZ)]^(1 / (1 - theta_EZ));
};
constraints
{
I[] + C[] = pi[] + r[] * K_s[-1] + W[] * L_s[];
K_s[] = (1 - delta) * K_s[-1] + I[];
};
identities
{
L_s[] = 1;
};
calibration
{
delta = 0.025;
beta = 0.99;
eta = 2;
theta_EZ = 0.05;
};
};
block FIRM
{
controls
{
K_d[], L_d[], Y[];
};
objective
{
pi[] = Y[] - L_d[] * W[] - r[] * K_d[];
};
constraints
{
Y[] = Z[] * K_d[]^alpha * L_d[]^(1 - alpha);
};
calibration
{
r[ss] * K_s[ss] = 0.36 * Y[ss] -> alpha;
};
};
block EQUILIBRIUM
{
identities
{
K_d[] = K_s[-1];
L_d[] = L_s[];
};
};
block EXOG
{
identities
{
Z[] = exp(phi * log(Z[-1]) + epsilon_Z[]);
};
shocks
{
epsilon_Z[];
};
calibration
{
phi = 0.95;
};
};run Epstein-Zin Model with gEcon
library(gEcon)
ez = make_model("epstein_zin.gcn")## model parsed in 0.05s
## model loaded in 0.06sez = initval_calibr_par(ez, c(alpha = 0.4))
ez = steady_state(ez)## Steady state has been FOUNDget_ss_values(ez)## Steady-state values:
##
## Steady-state value
## q__CONSUMER_1 51.7476
## r 0.0351
## C 2.7543
## I 0.9497
## K_s 37.9893
## U 63.6935
## W 2.3706
## Y 3.7041
## Z 1.0000get_par_values(ez)## Model parameters:
##
## Value
## alpha 0.360
## beta 0.990
## delta 0.025
## eta 2.000
## phi 0.950
## theta_EZ 0.050ez = initval_calibr_par(ez, c(alpha = 0.4))
ez = steady_state(ez, calibration = FALSE)## Steady state has been FOUNDget_ss_values(ez, to_tex = TRUE)## Steady-state values:
##
## Steady-state value
## q__CONSUMER_1 58.4346
## r 0.0351
## C 3.6213
## I 1.4427
## K_s 57.7077
## U 72.3856
## W 3.0384
## Y 5.0640
## Z 1.0000
##
##
## results written to: 'C:/Users/Heatfront/Desktop/blibtexfolder/dynarefolder/dynareA001/epstein_zin.results.tex'get_par_values(ez, to_tex = TRUE)## Model parameters:
##
## Value
## alpha 0.400
## beta 0.990
## delta 0.025
## eta 2.000
## phi 0.950
## theta_EZ 0.050
##
##
## results written to: 'C:/Users/Heatfront/Desktop/blibtexfolder/dynarefolder/dynareA001/epstein_zin.results.tex'ez = solve_pert(ez, loglin = TRUE)## Model has been SOLVEDget_pert_solution(ez, to_tex = TRUE)##
## Matrix P:
##
## K_s[-1] Z[-1]
## K_s[] 0.9781 0.0578
## Z[] 0.0000 0.9500
##
##
## Matrix Q:
##
## epsilon_Z
## K_s 0.0608
## Z 1.0000
##
##
## Matrix R:
##
## K_s[-1] Z[-1]
## q__CONSUMER_1[] 0.0424 0.0542
## r[] -0.4897 0.7270
## C[] 0.3793 0.2084
## I[] 0.1223 2.3122
## U[] 0.0456 0.0572
## W[] 0.3265 0.8616
## Y[] 0.3061 0.8077
##
##
## Matrix S:
##
## epsilon_Z
## q__CONSUMER_1 0.0570
## r 0.7652
## C 0.2193
## I 2.4339
## U 0.0602
## W 0.9069
## Y 0.8503
##
##
## results written to: 'C:/Users/Heatfront/Desktop/blibtexfolder/dynarefolder/dynareA001/epstein_zin.results.tex'ez = set_shock_cov_mat(ez, matrix(c(1), 1, 1), shock_order = "epsilon_Z")
ez = compute_model_stats(ez, ref_var="Y")
get_model_stats(model = ez, variables = c("C", "K_s", "W", "I", "r", "Y"),
var_dec = FALSE, to_tex = TRUE)## Basic statistics:
##
## Steady-state value Std. dev. Variance Loglin
## C 3.6213 0.2991 0.0895 Y
## K_s 57.7077 0.2842 0.0807 Y
## W 3.0384 1.1799 1.3922 Y
## I 1.4427 3.1705 10.0520 Y
## r 0.0351 1.0158 1.0318 Y
## Y 5.0640 1.1062 1.2236 Y
##
## Correlation matrix:
##
## r C I K_s W Y
## r 1 0.875 0.989 0.082 0.977 0.977
## C 1 0.937 0.554 0.958 0.958
## I 1 0.228 0.998 0.998
## K_s 1 0.293 0.293
## W 1 1.000
## Y 1.000
##
## Cross correlations with the reference variable (Y):
##
## Std. dev. rel. to Y Y[-5] Y[-4] Y[-3] Y[-2] Y[-1] Y[] Y[1] Y[2]
## r[] 0.918 0.102 0.222 0.368 0.542 0.745 0.977 0.641 0.366
## C[] 0.270 -0.154 -0.028 0.142 0.359 0.630 0.958 0.769 0.594
## I[] 2.866 0.026 0.152 0.309 0.501 0.730 0.998 0.697 0.445
## K_s[] 0.257 -0.493 -0.439 -0.341 -0.193 0.015 0.293 0.480 0.593
## W[] 1.067 -0.008 0.119 0.280 0.479 0.718 1.000 0.718 0.479
## Y[] 1.000 -0.008 0.119 0.280 0.479 0.718 1.000 0.718 0.479
## Y[3] Y[4] Y[5]
## r[] 0.147 -0.022 -0.147
## C[] 0.436 0.297 0.177
## I[] 0.239 0.075 -0.052
## K_s[] 0.645 0.649 0.619
## W[] 0.280 0.119 -0.008
## Y[] 0.280 0.119 -0.008
##
## Autocorrelations:
##
## Lag 1 Lag 2 Lag 3 Lag 4 Lag 5
## r 0.713 0.470 0.270 0.109 -0.017
## C 0.759 0.544 0.356 0.196 0.063
## I 0.714 0.472 0.272 0.111 -0.016
## K_s 0.960 0.864 0.731 0.577 0.415
## W 0.718 0.479 0.280 0.119 -0.008
## Y 0.718 0.479 0.280 0.119 -0.008
##
##
## results written to: 'C:/Users/Heatfront/Desktop/blibtexfolder/dynarefolder/dynareA001/epstein_zin.results.tex'plotirf = compute_irf(ez, variables = c("C", "K_s", "W", "I", "r", "Y"))
print(plotirf)## Impulse response functions
## Simulation horizon: 40
## Variables (6):
## C, K_s, W, I, r, Y
## Shocks (1):
## epsilon_Zsummary(ez)##
## Steady state:
##
## q__CONSUMER_1 58.434570
## r 0.035101
## C 3.621306
## I 1.442693
## K_s 57.707726
## U 72.385650
## W 3.038399
## Y 5.063999
## Z 1.000000
##
## ----------------------------------------------------------
##
## Parameter values:
##
## alpha 0.400
## beta 0.990
## delta 0.025
## eta 2.000
## phi 0.950
## theta_EZ 0.050
##
## ----------------------------------------------------------
##
## Linearisation:
## x_t = P x_{t-1} + Q epsilon_t
## y_t = R x_{t-1} + S epsilon_t
##
## P:
## K_s[-1] Z[-1]
## K_s[] 0.978058 0.057806
## Z[] 0.000000 0.950000
##
## Q:
## epsilon_Z
## K_s 0.060848
## Z 1.000000
##
## R:
## K_s[-1] Z[-1]
## q__CONSUMER_1[] 0.042383 0.054157
## r[] -0.489749 0.726970
## C[] 0.379305 0.208369
## I[] 0.122324 2.312240
## U[] 0.045615 0.057232
## W[] 0.326499 0.861595
## Y[] 0.306093 0.807745
##
## S:
## epsilon_Z
## q__CONSUMER_1 0.057008
## r 0.765232
## C 0.219335
## I 2.433937
## U 0.060245
## W 0.906942
## Y 0.850258
##
## ----------------------------------------------------------
##
## Shock covariance matrix:
##
## epsilon_Z
## epsilon_Z 1
##
## Basic statistics:
##
## Steady-state value Std. dev. Variance Loglin
## q__CONSUMER_1 58.4346 0.0745 0.0056 Y
## r 0.0351 1.0158 1.0318 Y
## C 3.6213 0.2991 0.0895 Y
## I 1.4427 3.1705 10.052 Y
## K_s 57.7077 0.2842 0.0807 Y
## U 72.3856 0.0788 0.0062 Y
## W 3.0384 1.1799 1.3922 Y
## Y 5.064 1.1062 1.2236 Y
## Z 1 1.3034 1.699 Y
##
## Correlation matrix:
##
## q__CONSUMER_1 r C I K_s U W Y Z
## q__CONSUMER_1 1 0.956 0.979 0.989 0.372 1 0.997 0.997 0.987
## r 1 0.875 0.989 0.082 0.955 0.977 0.977 0.991
## C 1 0.937 0.554 0.979 0.958 0.958 0.933
## I 1 0.228 0.988 0.998 0.998 1
## K_s 1 0.375 0.293 0.293 0.217
## U 1 0.996 0.996 0.986
## W 1 1 0.997
## Y 1 0.997
## Z 1
##
## Autocorrelations:
##
## Lag 1 Lag 2 Lag 3 Lag 4 Lag 5
## q__CONSUMER_1 0.726 0.491 0.295 0.134 0.006
## r 0.713 0.470 0.270 0.109 -0.017
## C 0.759 0.544 0.356 0.196 0.063
## I 0.714 0.472 0.272 0.111 -0.016
## K_s 0.960 0.864 0.731 0.577 0.415
## U 0.726 0.492 0.296 0.135 0.007
## W 0.718 0.479 0.280 0.119 -0.008
## Y 0.718 0.479 0.280 0.119 -0.008
## Z 0.713 0.471 0.271 0.110 -0.016
##
## Cross correlations with reference variable (Y):
##
## Y[-5] Y[-4] Y[-3] Y[-2] Y[-1] Y[] Y[1] Y[2] Y[3]
## q__CONSUMER_1[] -0.051 0.077 0.242 0.448 0.698 0.997 0.739 0.516 0.328
## r[] 0.102 0.222 0.368 0.542 0.745 0.977 0.641 0.366 0.147
## C[] -0.154 -0.028 0.142 0.359 0.630 0.958 0.769 0.594 0.436
## I[] 0.026 0.152 0.309 0.501 0.730 0.998 0.697 0.445 0.239
## K_s[] -0.493 -0.439 -0.341 -0.193 0.015 0.293 0.480 0.593 0.645
## U[] -0.053 0.075 0.240 0.447 0.698 0.996 0.740 0.518 0.329
## W[] -0.008 0.119 0.280 0.479 0.718 1.000 0.718 0.479 0.280
## Y[] -0.008 0.119 0.280 0.479 0.718 1.000 0.718 0.479 0.280
## Z[] 0.032 0.157 0.314 0.504 0.732 0.997 0.694 0.440 0.233
## Y[4] Y[5]
## q__CONSUMER_1[] 0.172 0.046
## r[] -0.022 -0.147
## C[] 0.297 0.177
## I[] 0.075 -0.052
## K_s[] 0.649 0.619
## U[] 0.174 0.048
## W[] 0.119 -0.008
## Y[] 0.119 -0.008
## Z[] 0.068 -0.059
##
## Variance decomposition:
##
## epsilon_Z
## q__CONSUMER_1 1
## r 1
## C 1
## I 1
## K_s 1
## U 1
## W 1
## Y 1
## Z 1
