Information overflow between monetary policy transparency and inflation expectations using multivariate stochastic volatility models

Figures & data

Figure 1. Dynamic changing trend of China’s monetary policy transparency.

Table 1. Estimated parameter results and effects of 9 models under normal distribution based on national inflation rates.

Estimated parameter	Model 1	Model 2	Model 3	Model 4a	Model 4b	Model 5a	Model 5b	Model 6	Model 7
${\alpha }_{\text{c}}$	1.307;	1.36;	1.331;	1.255;	1.42;	1.319;	1.5;	1.381;	1.429;
	0.4822;	0.7852;	0.7435;	0.5812;	0.8692;	0.6196;	0.9491;	0.7436;	0.7444;
	0.6768	0.9299	0.8922	0.7203	1.027	0.7777	1.086	0.8836	0.9056
${\alpha }_{\text{e}}$	0.673;	0.7042;	0.6599;	0.6623;	0.6438;	0.7489;	0.7161;	0.7021;	0.7511;
	0.0734;	0.3025;	0.2624;	0.3007;	0.1283;	0.3725;	0.2249;	0.297;	0.3752;
	0.2408	0.3924	0.3564	0.382	0.2526	0.4536	0.3356	0.377	0.4569
${\beta }_{\text{cc}}$	0.9312;	0.9278;	0.9274;	0.7898;	0.8987;	0.8141;	0.9054;	0.8086;	0.795;
	0.8292;	0.804;	0.8034;	0.5527;	0.6949;	0.5834;	0.7134;	0.5593;	0.5478;
	0.8631	0.8498	0.8488	0.6178	0.7669	0.6463	0.785	0.6317	0.6185
${\beta }_{\text{ee}}$	0.8893;	0.8546;	0.8575;	0.8587;	0.7939;	0.8538;	0.7941;	0.8389;	0.8322;
	0.7192;	0.6447;	0.6486;	0.6629;	0.5414;	0.6434;	0.5506;	0.6036;	0.5949;
	0.7762	0.7089	0.7129	0.7225	0.6156	0.7078	0.6182	0.6736	0.6655
${\beta }_{\text{ce}}$				1.069;		0.8379;		0.7088;	0.8138;
				0.2402;		−		−	0.0314;
				0.395		0.7308;		0.6648;	0.1456
						−0.2434		−0.107
${\beta }_{\text{ec}}$					0.2218;		0.1963;	−0.007;	−0.0183;
					−0.7716;		−0.4734;	−0.2728;	−0.317;
					−0.2012		−0.1095	−0.161	−0.1362
$\chi$			0.8585;			0.855;	0.8586;		0.8517;
			0.6515;			0.6415;	0.6516;		0.6371;
			0.7154			0.7071	0.7139		0.7017
$\rho$		0.7855;	0.7833;	0.7678;	0.7699;	0.7983;	0.7892;	0.7708;	0.7875;
		0.6915;	0.6668;	0.6605;	0.6689;	0.6641;	0.6641;	0.6668;	0.6686;
		0.7162	0.6997	0.6894	0.6962	0.7052	0.7015	0.6942	0.7036
DIC	459.885	414.115	413.18	408.411	415.415	410.302	414.138	411.353	410.265

Table 2. Estimated parameter results and effects of 9 models under t distribution based on national inflation rates.

Estimated parameter	Model 1	Model 2	Model 3	Model 4a	Model 4b	Model 5a	Model 5b	Model 6	Model 7
${\alpha }_{\text{c}}$	1.202;	1.181;	1.256;	1.105;	1.312;	1.13;	1.307;	1.416;	1.313;
	0.417;	0.6027;	0.7148;	0.3835;	0.8432;	0.3863;	0.8156;	0.5611;	0.6506;
	0.6133	0.7572	0.8493	0.5535	0.9393	0.5594	0.9429	0.7584	0.8122
${\alpha }_{\text{e}}$	0.5296;	0.4703;	0.5526;	0.4569;	0.5347;	0.4778;	0.5317;	0.6362;	0.5614;
	−0.0005;	0.0583;	0.1406;	0.0042;	0.0074;	0.0967;	0.0146;	0.136;	0.0862;
	0.1252	0.1539	0.2331	0.1229	0.1214	0.1813	0.1246	0.2416	0.1968
${\beta }_{\text{cc}}$	0.9265;	0.9149;	0.9156;	0.7922;	0.8752;	0.7994;	0.8906;	0.8104;	0.8168;
	0.8077;	0.7572;	0.7686;	0.5333;	0.6471;	0.5445;	0.6769;	0.5588;	0.5781;
	0.8503	0.8166	0.8219	0.6116	0.722	0.6129	0.7506	0.6287	0.6428
${\beta }_{\text{ee}}$	0.8872;	0.8602;	0.8511;	0.8779;	0.7959;	0.8608;	0.7936;	0.8475;	0.8406;
	0.7079;	0.6516;	0.6326;	0.6854;	0.5492;	0.6577;	0.5495;	0.6241;	0.6038;
	0.7671	0.7161	0.6995	0.7471	0.6181	0.7203	0.6146	0.6908	0.6757
${\beta }_{\text{ce}}$				0.9066;		0.9426;		0.6216;	0.6427;
				0.0236;		−0.6785;		−0.0825;	−0.296;
				0.2676		0.1856		0.1064	0.0157
${\beta }_{\text{ec}}$					0.1274;		0.2543;	0.0051;	−0.0739;
					−1.212;		−0.4232;	−0.2317;	−0.6149;
					−0.5507		−0.1632	−0.0796	−0.3731
$\chi$			0.8644;			0.8565;	0.8619;		0.8595;
			0.6592;			0.643;	0.6504;		0.6487;
			0.722			0.7097	0.7153		0.7135
$\rho$		0.7815;	0.8031;	0.773;	0.7782;	0.7748;	0.7775;	0.7819;	0.7871;
		0.6831;	0.6929;	0.6645;	0.6731;	0.6407;	0.6404;	0.6755;	0.6544;
		0.7094	0.7252	0.6936	0.7012	0.68	0.6767	0.705	0.6931
$\tau$		9.595;	9.831;	10.18;	9.801;	10.22;	9.724;	10.29;	10.29;
		4.744;	4.852;	5.016;	4.794;	5.116;	4.828;	5.135;	4.987;
		5.45	5.593	5.785	5.528	5.88	5.532	5.907	5.757
DIC	466.576	348.145	351.357	340.131	351.305	345.438	348.337	345.472	350.021

Figure 2. Changing trends of β ce at double chains.

Figure 3. Changing trends of β ce at double chains.

Figure 4. Probabilities of β ce values.

Figure 5. The Gelman-Rubin test of β ce.

Figure 6. Probabilities of β ce values in model 4a.

Figure 7. Probabilities of β ce values in model 5a.

Figure 8. Probabilities of β ce values in model 6.

Figure 9. Probabilities of β ce values in model 7.

Table 3. Estimated parameter results and effects of 9 models under normal distribution based on urban inflation rates.

Estimated parameter	Model 1	Model 2	Model 3	Model 4a	Model 4b	Model 5a	Model 5b	Model 6	Model 7
${\alpha }_{\text{c}}$	1.246;	1.323;	1.38;	1.273;	1.409;	1.303;	1.397;	1.355;	1.41;
	0.3467;	0.7011;	0.7967;	0.551;	0.87;	0.5935;	0.8139;	0.6824;	0.7013;
	0.5548	0.8506	0.9389	0.6908	1.011	0.7393	0.9637	0.8324	0.8584
${\alpha }_{\text{e}}$	0.575;	0.6292;	0.6762;	0.6005;	0.6091;	0.6387;	0.6187;	0.6327;	0.6652;
	−0.018;	0.2124;	0.2909;	0.2563;	0.1184;	0.2935;	0.0637;	0.2534;	0.2442;
	0.1434	0.3127	0.3734	0.3268	0.2278	0.3745	0.1882	0.3335	0.3241
${\beta }_{\text{cc}}$	0.9367;	0.9329;	0.926;	0.7821;	0.9055;	0.787;	0.9196;	0.8111;	0.8043;
	0.8427;	0.8185;	0.7972;	0.5409;	0.7111;	0.5409;	0.7589;	0.5781;	0.5587;
	0.8732	0.8609	0.8449	0.6108	0.7828	0.6107	0.8215	0.6391	0.6207
${\beta }_{\text{ee}}$	0.8916;	0.8565;	0.8517;	0.8659;	0.7913;	0.8619;	0.7985;	0.8512;	0.8488
	0.7213;	0.6509;	0.6421;	0.6666;	0.5414;	0.6687;	0.5612;	0.6291;	0.6307;
	0.7785	0.7146	0.7054	0.729	0.6123	0.7272	0.6291	0.6973	0.696
${\beta }_{\text{ce}}$				1.194;		0.9796;		0.6396;	0.646;
				0.3298;		−1.066;		−0.696;	−0.7568;
				0.467		−0.4644		−0.3592	−0.3341
${\beta }_{\text{ec}}$					0.1668;		0.2034;	0.0009;	−0.0288;
					−0.8006;		−0.2263;	−0.2053;	−0.3393;
					−0.1654		−0.0289	−0.1234	−0.1995
$\chi$			0.8555;			0.8531;	0.8532;		0.8545;
			0.6444;			0.6449;	0.6403;		0.6444;
			0.7089			0.7075	0.7035		0.7081
$\rho$		0.7935;	0.8104;	0.7693;	0.778;	0.7832;	0.7785;	0.779;	0.7916;
		0.6998;	0.7012;	0.6638;	0.6784;	0.6501;	0.6539;	0.6742;	0.661;
		0.7248	0.7303	0.6919	0.7052	0.6902	0.688	0.7023	0.6949
DIC	448.612	402.801	403.529	395.686	404.095	396.77	403.195	398.66	399.767

Figure 10. Probabilities of β ce values in model 4a.

Figure 11. Probabilities of β ce values in model 5a.

Figure 12. Probabilities of β ce values in model 6.

Figure 13. Probabilities of β ce values in model 7.

Table 4. Estimated parameter results and effects of 9 models under t distribution based on urban inflation rates.

Estimated parameter	Model 1	Model 2	Model 3	Model 4a	Model 4b	Model 5a	Model 5b	Model 6	Model 7
${\alpha }_{\text{c}}$	1.147;	1.21;	1.194;	1.152;	1.309;	1.213;	1.32;	1.359;	1.365;
	0.261;	0.6121;	0.607;	0.4362;	0.7817;	0.4632;	0.7615;	0.6045;	0.6;
	0.4742	0.7621	0.7494	0.5978	0.9016	0.644	0.8968	0.752	0.7657
${\alpha }_{\text{e}}$	0.4492;	0.4547;	0.4465;	0.4092;	0.4924;	0.4821;	0.4956;	0.5102;	0.5394;
	−0.072;	0.0157;	0.0183;	0.0246;	−0.0455;	0.0227;	−0.0498;	0.0916;	0.0754;
	0.0535	0.1219	0.1105	0.092	0.0695	0.1386	0.0641	0.1763	0.1737
${\beta }_{\text{cc}}$	0.9348;	0.918;	0.923;	0.7989;	0.901;	0.8092;	0.9096;	0.8038;	0.8072;
	0.834;	0.7709;	0.789;	0.5713;	0.6951;	0.5711;	0.7294;	0.5552;	0.5511;
	0.8683	0.8254	0.8389	0.6267	0.7696	0.6363	0.7958	0.6254	0.6261
${\beta }_{\text{ee}}$	0.8878;	0.857;	0.8526;	0.8702;	0.7966;	0.8762;	0.794;	0.8439;	0.8462;
	0.7068	0.6503;	0.6399;	0.6603;	0.5478;	0.6849;	0.5481;	0.612;	0.62;
	;0.7662	0.7122	0.7047	0.7273	0.6161	0.7442	0.6183	0.6824	0.6887
${\beta }_{\text{ce}}$				0.9573;		0.9097;		0.7921;	0.7114;
				−1.029;		−0.2766;		0.002;	0.0861;
				0.2112		0.26		0.1446	0.1602
${\beta }_{\text{ec}}$					0.0836;		0.204;	0.0475;	0.0278;
					−0.9794;		−0.2583;	−0.0717;	−0.1868;
					−0.346		−0.0848	−0.0431	−0.0711
$\chi$			0.8564;			0.854;	0.8589;		0.854;
			0.6462;			0.6419;	0.6507;		0.6424;
			0.7106			0.7068	0.714		0.7065
$\rho$		0.7962;	0.8;	0.7736;				0.7813;	0.7849;
		0.6989;	0.68;	0.6677;				0.6772;	0.6531;
		0.7253	0.7135	0.6954				0.7054	0.6908
$\tau$	10.9;	10.02;	9.998;	10.39;	10.11;	10.54;	9.924;	10.3;	10.23;
	5.515;	4.852;	4.929;	5.224;	4.962;	5.31;	4.822;	5.184;	5.105;
	6.328	5.641	5.668	6.005	5.744	6.11	5.58	5.957	5.877
DIC	455.982	334.353	340.518	330.884	339.796	330.072	338.346	331.996	330.537

Figure 14. Probabilities of β ce values in model 4a.

Figure 15. Probabilities of β ce values in model 5a.

Figure 16. Probabilities of β ce values in model 6.

Figure 17. Probabilities of β ce values in model 7.

Table 5. Granger causality test results of inflation volatility, inflation expectations volatility, and transparency.

Hypothesis H0	F-statistic and p-value
Inflation expectations volatility is not Granger’ s cause of transparency	0.2173 (0.8839)
Transparency is not Granger’ s cause of inflation expectations volatility	2.8374 (0.0473)
Inflation volatility is not Granger’ s cause of transparency	0.8319 (0.4827)
Transparency is not Granger’ s cause of inflation volatility	1.1861 (0.3245)
Inflation volatility is not Granger’ s cause of inflation expectations volatility	0.0595 (0.9807)
Inflation expectations volatility is not Granger’ s cause of inflation volatility	49.9918 (4* 10^− 15)

Figure 18. Structural impulse responses of inflation volatility, inflation expectations volatility and transparency.

Figure 19 . Structural variance decomposition of inflation volatility, inflation expectations volatility and transparency.

Table 6. Granger causality testing results of inflation volatility, inflation expectations volatility, and transparency.

Hypothesis H0	F-statistic and p-value
Inflation expectations volatility is not Granger’ s cause of transparency	0.3662 (0.6951)
Transparency is not Granger’ s cause of inflation expectations volatility	5.2142 (0.0086)
Inflation volatility is not Granger’ s cause of transparency	0.50219 (0.6081)
Transparency is not Granger’ s cause of inflation volatility	0.72762 (0.4878)
Inflation volatility is not Granger’ s cause of inflation expectations volatility	0.26724 (0.7665)
Inflation expectations volatility is not Granger’ s cause of inflation volatility	35.5515 (2* 10^− 10)

Figure 20. Impulse responses of inflation volatility, inflation expectations volatility and transparency.

Figure 21. Variance decomposition of inflation volatility, inflation expectations volatility and transparency.

Table 7. Granger causality results of inflation, inflation expectations, and transparency.

Hypothesis H0	F-statistic and p-value
Inflation expectations are not Granger’ s cause of transparency	0.8587 (0.4957)
Transparency is not Granger’ s cause of inflation expectations	3.9876 (0.007)
Inflation is not Granger’ s cause of transparency	1.8025 (0.1442)
Transparency is not Granger’ s cause of inflation	4.4842 (0.0038)
Inflation is not Granger’ s cause of inflation expectations	11.6808 (1* 10^− 06)
Inflation expectations are not Granger’ s cause of inflation	2.3931 (0.0638)

Figure 22. Impulse responses of inflation, inflation expectations and transparency.

Figure 23. Variance decomposition of inflation, inflation expectations and transparency.

Table 8. Granger causality results of inflation, inflation expectations, and transparency.

Hypothesis H0	F-statistic and p value
Inflation expectations are not Granger’ s cause of transparency	0.86249 (0.4934)
Transparency is not Granger’ s cause of inflation expectations	3.79489 (0.0094)
Inflation is not Granger’ s cause of transparency	1.85947 (0.1333)
Transparency is not Granger’ s cause of inflation	4.27216 (0.0050)
Inflation is not Granger’ s cause of inflation expectations	10.7135 (3* 10^− 06)
Inflation expectations are not Granger’ s cause of inflation	2.51951 (0.0536)

Figure 24. Impulse responses of inflation, inflation expectations and transparency.

Figure 25. Variance decomposition of inflation, inflation expectations and transparency.

Data availability statement

The data supporting the conclusions of this article are available from the authors, without undue reservation.