吕炜等:供给侧结构性改革加剧价格波动吗 2017 年第 8 期
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一、 稳态求解思路
在动态随机一般均衡模型的构建过程中,模型的稳态求解往往是比较困难的部分,尤其
对多部门的大模型而言,较多的方程数量使得手动计算难以实现。但如果直接应用 Matlab
中的函数去求解稳态,往往难以直接收敛至稳态水平。因此,在计算稳态的过程中需要手动
计算对模型进行化简。在本文所构建的动态随机一般均衡模型中,150 余个方程最后可以化
简成以下方程组。
1
1
1
1
1
1
1
1
(1 )
(1 )
(1 )
1
11 1
s
f
Y
N
N
θ
βδ
ρ
ρθ θ ρ
θρ θ
−
−
−
=
−
−
+−
−− −
(1)
2
2
1
1
2
2
1
1
(1 )
(1 )
(1 )
1
11 1
s
f
Y
N
N
θ
βδ
ρ
ρθ θ ρ
θρ θ
−
−
−
=
−
−
+−
−− −
(2)
3
3
1
1
3
3
1
1
(1 )
(1 )
(1 )
1
11 1
s
f
Y
N
N
θ
βδ
ρ
ρθ θ ρ
θρ θ
−
−
−
=
−
−
+−
−− −
(3)
4
4
1
1
4
4
1
1
(1 )
(1 )
(1 )
1
11 1
s
f
Y
N
N
θ
βδ
ρ
ρθ θ ρ
θρ θ
−
−
−
=
−
−
+−
−− −
(4)
5
5
1
1
5
5
1
1
(1 )
(1 )
(1 )
1
11 1
s
f
Y
N
N
θ
βδ
ρ
ρθ θ ρ
θρ θ
−
−
−
=
−
−
+−
−− −
(5)
6
6
1
1
6
6
1
1
(1 )
(1 )
(1 )
1
11 1
s
f
Y
N
N
θ
βδ
ρ
ρθ θ ρ
θρ θ
−
−
−
=
−
−
+−
−− −
(6)
7
7
1
1
7
7
1
1
(1 )
(1 )
(1 )
1
11 1
s
f
Y
N
N
θ
βδ
ρ
ρθ θ ρ
θρ θ
−
−
−
=
−
−
+−
−− −
(7)
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吕炜等:供给侧结构性改革加剧价格波动吗 2017 年第 8 期
8
8
1
1
8
8
1
1
(1 )
(1 )
(1 )
1
11 1
s
f
Y
N
N
θ
βδ
ρ
ρθ θ ρ
θρ θ
−
−
−
=
−
−
+−
−− −
(8)
1
1 11s
Y NY
θ
θ
−
=
(9)
1
2 22s
Y NY
θ
θ
−
=
(10)
1
3 33
s
Y NY
θ
θ
−
=
(11)
1
4 44
s
Y NY
θ
θ
−
=
(12)
1
5 55s
Y NY
θ
θ
−
=
(13)
1
6 66s
Y NY
θ
θ
−
=
(14)
1
7 77s
Y NY
θ
θ
−
=
(15)
1
8 88s
Y NY
θ
θ
−
=
(16)
1 11
a PY
=
(17)
2 22
a PY=
(18)
3 33
a PY=
(19)
4 44
a PY=
(20)
5 55
a PY
=
(21)
6 66
a PY=
(22)
7 77
a PY=
(23)
8 88
a PY=
(24)
1
1
1 1 11
1
11
1
WL PY
N
θ
θρ
γ
θρ
−
−−
=
−
(25)
1
1
2 2 22
2
11
1
WL PY
N
θ
θρ
γ
θρ
−
−−
=
−
(26)
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吕炜等:供给侧结构性改革加剧价格波动吗 2017 年第 8 期
1
1
3 3 33
3
11
1
WL PY
N
θ
θρ
γ
θρ
−
−−
=
−
(27)
1
1
4 4 44
4
11
1
WL PY
N
θ
θρ
γ
θρ
−
−−
=
−
(28)
1
1
5 5 55
5
11
1
WL PY
N
θ
θρ
γ
θρ
−
−−
=
−
(29)
1
1
6 6 66
6
11
1
WL PY
N
θ
θρ
γ
θρ
−
−−
=
−
(30)
1
1
7 7 77
7
11
1
WL PY
N
θ
θρ
γ
θρ
−
−−
=
−
(31)
1
1
8 8 88
8
11
1
WL PY
N
θ
θρ
γ
θρ
−
−−
=
−
(32)
1
1 11
G
Gs
K L NY
α
γ
=
(33)
2
2 22
G
Gs
K L NY
α
γ
=
(34)
3
3 33
G
Gs
K L NY
αγ
=
(35)
4
4 44
G
Gs
K L NY
α
γ
=
(36)
5
5 55
G
Gs
K L NY
αγ
=
(37)
6
6 66
G
Gs
K L NY
αγ
=
(38)
7
7 77
G
Gs
K L NY
αγ
=
(39)
8
8 88
G
Gs
K L NY
αγ
=
(40)
7
1
GG
PK
δ
=
(41)
12345678
0.33LLLLLLLL+++++++=
(42)
方程个数的大幅减少,能够有助于更好的求解稳态。但是由于方程大多是非线性的,而
且,尽管做了相应的简化,但是在求解的过程中还是会存在一定的求解误差。
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吕炜等:供给侧结构性改革加剧价格波动吗 2017 年第 8 期
二、投入产出网络模型程序
模型稳态求解完毕后,可以将模型代入到 Dynare 软件中进行模拟。Dynare 编程包括内
生变量、外生变量、参数、模型等几个部分。
var P_1 P_2 P_3 P_4 P_5 P_6 P_7 P_8 m T A_1 A_2 A_3 A_4 A_5 A_6 A_7 A_8 M_34s
MC_1s MC_2s MC_3s MC_4s MC_5s MC_6s MC_7s MC_8s V_1 V_2 L_2s M_78s
V_3 V_4 V_5 V_6 V_7 V_8 D_1 D_2 D_3 D_4 D_5 D_6 D_7 D_8 L_1s L_3s
L_4s L_5s L_6s L_7s L_8s M_11s M_12s M_13s M_14s M_15s M_16s M_17s M_18s
M_21s M_22s M_23s M_24s M_25s Y_4 M_26s M_27s M_28s M_31s M_32s M_33s
M_35s M_36s M_37s M_38s M_41s M_42s M_43s M_44s M_45s Y_1 Y_1s Y_2s Y_3s
Y_8s N_1 N_2 N_3 Y_5 N_4 N_5 N_6 N_7 N_8 W K_G P_1s P_2s P_3s P_4s P_5s
P_6s P_7s Y_8 P_8s M_46s M_47s M_48s Y_2 Y_4s Y_6s Y_7s M_64s M_77s
M_51s M_52s M_53s Y_3 M_54s M_55s M_56s M_57s M_58s M_61s M_62s M_63s
M_65s M_66s Y_7 M_67s M_68s M_71s M_72s Y_5s M_73s Y_6 M_74s M_75s M_76s
M_81s M_82s M_83s M_84s M_85s M_86s M_87s M_88s P C C_1 C_2 C_3 C_4 C_5
C_6 C_7 C_8 L G g G_s;
varexo e_m e_G e_A;
parameters beta delta a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 c_5 c_7
fai gbar mbar Tbar rho_m rho_A rho_G rho_f beta_11
beta_12 beta_13 beta_14 beta_15 beta_16 beta_17 beta_18
beta_21 beta_22 beta_23 beta_24 beta_25 beta_26 beta_27
beta_28 beta_31 beta_32 beta_33 beta_34 beta_35 beta_36
beta_37 beta_38 beta_41 beta_42 beta_43 beta_44 beta_45
beta_46 beta_47 beta_48 beta_51 beta_52 beta_53 beta_54
beta_55 beta_56 beta_57 beta_58 beta_61 beta_62 beta_63
beta_64 beta_65 beta_66 beta_67 beta_68 beta_71 beta_72
beta_73 beta_74 beta_75 beta_76 beta_77 beta_78 beta_81
beta_82 beta_83 beta_84 beta_85 beta_86 beta_87 beta_88
garma_1 garma_2 garma_3 garma_4 garma_5 garma_6 garma_7
garma_8 delta_G alpha_G rho theta f_1 f_2 f_3 f_4 f_5 f_6
f_7 f_8 P_1bar P_2bar P_3bar P_4bar P_5bar P_6bar P_7bar M_87sbar
P_8bar Y_1bar Y_2bar Y_3bar Y_4bar Y_5bar Y_6bar Y_7bar M_52sbar
Y_8bar Y_1sbar Y_2sbar Y_3sbar Y_4sbar Y_5sbar Y_6sbar Y_7sbar
Y_8sbar N_1bar N_2bar N_3bar N_4bar N_5bar N_6bar N_7bar N_8bar
Wbar K_Gbar P_1sbar P_2sbar P_3sbar P_4sbar P_5sbar P_6sbar
P_7sbar P_8sbar MC_1sbar MC_2sbar MC_3sbar MC_4sbar MC_5sbar
MC_6sbar MC_7sbar MC_8sbar V_1bar V_2bar V_3bar V_4bar V_5bar
V_6bar V_7bar V_8bar D_1bar D_2bar D_3bar D_4bar D_5bar D_6bar
D_7bar D_8bar L_1sbar L_2sbar L_3sbar L_4sbar L_5sbar L_6sbar
L_7sbar L_8sbar M_11sbar M_12sbar M_13sbar M_14sbar M_15sbar
M_16sbar M_17sbar M_18sbar M_21sbar M_22sbar M_23sbar M_24sbar
M_25sbar M_26sbar M_27sbar M_28sbar M_31sbar M_32sbar M_33sbar
M_34sbar M_35sbar M_36sbar M_37sbar M_38sbar M_41sbar M_42sbar
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吕炜等:供给侧结构性改革加剧价格波动吗 2017 年第 8 期
M_43sbar M_44sbar M_45sbar M_46sbar M_47sbar M_48sbar M_51sbar
M_53sbar M_54sbar M_55sbar M_56sbar M_57sbar M_58sbar M_61sbar
M_62sbar M_63sbar M_64sbar M_65sbar M_66sbar M_67sbar M_68sbar
M_71sbar M_72sbar M_73sbar M_74sbar M_75sbar M_76sbar M_77sbar
M_78sbar M_81sbar M_82sbar M_83sbar M_84sbar M_85sbar M_86sbar
M_88sbar Pbar Cbar C_1bar C_2bar C_3bar C_4bar C_5bar C_6bar
C_7bar C_8bar Lbar Gbar b_1 b_2 b_3 b_4 b_5 b_7;
beta=0.985; delta=0.03;a_1=0.293539193;a_2=0.000822986;a_3=0.036749519;
a_4=0.071128153;a_5=0.076334423;a_6=0.104230183;a_7=0.032610202;a_8=0.384585342;
delta_G=0.09;alpha_G=0.3;rho=0.7;theta=11;mbar=1;Tbar=1;fai=1.025049338790992;
beta=0.985;delta=0.03;beta_11=0.705648968;beta_12=0.0021739;beta_13=0.031316787;
beta_14=0.013038255;beta_15=0.012942062;beta_16=0.001202286;beta_17=0.093703195;
beta_18=0.139974547;beta_21=0.009479973;beta_22=0.262403218;beta_23=0.171199798;
beta_24=0.025163809;beta_25=0.15413197;beta_26=0.00499693;beta_27=0.147076949;
beta_28=0.225547353;beta_31=0.005932282;beta_32=0.495769922;beta_33=0.30888396;
beta_34=0.00239199;beta_35=0.059144686;beta_36=0.003829124;beta_37=0.02150254;
beta_38=0.102545497;beta_41=0.138376517;beta_42=0.006069774;beta_43=0.024810761;
beta_44=0.523253789;beta_45=0.02428689;beta_46=0.002484871;beta_47=0.147856438;
beta_48=0.13286096;beta_51=0.004977205;beta_52=0.003445641;beta_53=0.024693695;
beta_54=0.018753331;beta_55=0.503323765;beta_56=0.002742396;beta_57=0.289761092;
beta_58=0.152302873;beta_61=0.014299504;beta_62=0.007253786;beta_63=0.03584337;
beta_64=0.040801514;beta_65=0.115900069;beta_66=0.054290499;beta_67=0.489729827;
beta_68=0.24188143;beta_71=0.036294382;beta_72=0.146213045;beta_73=0.123997582;
beta_74=0.019604037;beta_75=0.038777056;beta_76=0.001948343;beta_77=0.506576506;
beta_78=0.126589047;beta_81=0.081407392;beta_82=0.001151815;beta_83=0.09203892;
beta_84=0.066037746;beta_85=0.13281179;beta_86=0.063502712;beta_87=0.072692078;
beta_88=0.490357546;garma_1=0.362930049;garma_2=0.276700571;garma_3=0.072934289;
garma_4=0.118355064;garma_5=0.098955223;garma_6=0.189945304;garma_7=0.079634241;
garma_8=0.34854348;delta_G=0.09;alpha_G=0.3;rho=0.7;theta=11;f_1=0.1896628;f_2=0.37895
76;f_3=0.416816;f_4=0.0586065;f_5=0.1278277;f_6=0.3;f_7=0.1869456;f_8=0.5512625;
P_1bar =65.730235403789678;P_2bar =36.117543978105680;P_3bar =50.537417362323872;
P_4bar =43.565262200486842;P_5bar =59.477778777446311;P_6bar =35.893259642201635;
P_7bar =81.095661593910691;P_8bar =62.495850302434249;Y_1bar =0.008054097728811;
Y_2bar =0.003084529059221;Y_3bar =0.002829534055363;Y_4bar =0.003532857710946;
Y_5bar =0.003428624295292;Y_6bar =0.002385903670946;Y_7bar =0.004087976596247;
Y_8bar =0.004765341527202;Y_1sbar =0.031313917657887;Y_2sbar =0.047457069864968;
Y_3sbar =0.051061170149597;Y_4sbar =0.013332335816801;Y_5sbar =0.021667653776102;
Y_6sbar =0.039299737226330;Y_7sbar =0.028670057838809;Y_8sbar =0.065429452163388;
N_1bar =0.248539713255006;N_2bar =0.120620320553864;N_3bar =0.116417505841004;
N_4bar =0.319327276938569;N_5bar =0.221746207427320;N_6bar =0.132317257127295;
N_7bar =0.191188090198786;N_8bar =0.108712825611691;Wbar =1.040659227198977;
K_Gbar =0.109873783569172;P_1sbar =0.786235289357806;P_2sbar =0.723911070679170;
P_3sbar =0.721116897463318;P_4sbar =0.811191158500232;P_5sbar =0.775574468258787;
P_6sbar =0.731298956509843;P_7sbar =0.762250957515847;P_8sbar =0.715776868102587;
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