Estimation of Dynamic Panel Data Models with Stochastic Volatility Using Particle Filters
Abstract
:1. Introduction
2. The Models and State Space Representation
3. Estimation by Particle Filters
4. Monte Carlo Studies
5. Conclusions
Acknowledgments
Conflicts of Interest
Appendix A. Deriving the Equations (7)–(10)
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- 1.See Creal [21] for a survey of particle filters for economic applications.
- 2.We assume , so .
- 3.It is an ad-hoc choice for stability of the algorithm, see Shephard [27].
- 4.If there is more than one point having the smallest distance from ω, the point with lowest index g will be chosen.
- 5.τ, which measures the degree of cross-section to time-series variation, can influence the finite sample properties of GMM-type estimators.
FDML | GMM | SGMM | PF | FDML | GMM | SGMM | PF | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
50 | 0 | 0 | 0.000 | 0.000 | 0.001 | 0.003 | 50 | 0 | 0 | −0.000 | 0.000 | 0.002 | 0.003 |
(0.000) | (0.001) | (0.002) | (0.003) | (0.000) | (0.000) | (0.002) | (0.003) | ||||||
−0.000 | 0.000 | 0.000 | 0.003 | 0.000 | 0.000 | 0.000 | 0.003 | ||||||
(0.000) | (0.000) | (0.001) | (0.003) | (0.000) | (0.000) | (0.001) | (0.003) | ||||||
0.99 | 0.5 | −0.003 | −0.002 | 0.000 | 0.002 | 0.99 | 0.5 | −0.001 | −0.002 | −0.000 | 0.003 | ||
(0.009) | (0.012) | (0.012) | (0.007) | (0.005) | (0.009) | (0.010) | (0.005) | ||||||
0.001 | 0.001 | 0.001 | 0.004 | 0.001 | 0.001 | 0.001 | 0.004 | ||||||
(0.017) | (0.017) | (0.016) | (0.013) | (0.009) | (0.013) | (0.013) | (0.011) | ||||||
0.99 | 1 | −0.011 | −0.007 | −0.002 | 0.000 | 0.99 | 1 | −0.006 | −0.006 | −0.002 | 0.002 | ||
(0.022) | (0.035) | (0.023) | (0.037) | (0.015) | (0.023) | (0.023) | (0.029) | ||||||
0.078 | 0.002 | −0.037 | −0.008 | −0.010 | −0.042 | −0.062 | −0.001 | ||||||
(1.444) | (0.983) | (1.909) | (0.106) | (1.664) | (1.800) | (2.418) | (0.082) | ||||||
100 | 0 | 0 | 0.016 | 0.000 | 0.001 | 0.003 | 100 | 0 | 0 | −0.000 | 0.000 | 0.001 | 0.003 |
(0.028) | (0.000) | (0.001) | (0.003) | (0.000) | (0.000) | (0.001) | (0.003) | ||||||
−0.007 | 0.000 | −0.000 | 0.003 | 0.000 | −0.000 | −0.000 | 0.003 | ||||||
(0.012) | (0.000) | (0.001) | (0.003) | (0.000) | (0.000) | (0.000) | (0.003) | ||||||
0.99 | 0.5 | 0.016 | −0.001 | −0.000 | 0.002 | 0.99 | 0.5 | −0.001 | −0.001 | 0.000 | 0.003 | ||
(0.033) | (0.008) | (0.008) | (0.016) | (0.004) | (0.006) | (0.006) | (0.004) | ||||||
−0.007 | 0.001 | 0.001 | 0.003 | 0.001 | 0.000 | 0.000 | 0.003 | ||||||
(0.018) | (0.017) | (0.017) | (0.027) | (0.017) | (0.010) | (0.008) | (0.018) | ||||||
0.99 | 1 | 0.009 | −0.004 | −0.002 | −0.002 | 0.99 | 1 | −0.007 | −0.003 | −0.001 | 0.003 | ||
(0.039) | (0.024) | (0.019) | (0.048) | (0.013) | (0.019) | (0.017) | (0.037) | ||||||
0.050 | −0.054 | −0.057 | −0.007 | 0.004 | 0.007 | −0.005 | −0.008 | ||||||
(1.134) | (2.978) | (3.046) | (0.103) | (0.942) | (1.510) | (1.591) | (0.103) |
50 | 0 | 0 | 0.968 | 0.242 | 0.077 | 50 | 0 | 0 | 0.969 | 0.160 | 0.019 |
(0.968) | (0.275) | (0.172) | (0.969) | (0.167) | (0.055) | ||||||
0.99 | 0.5 | −0.052 | 0.082 | 0.254 | 0.99 | 0.5 | −0.029 | 0.063 | 0.233 | ||
(0.080) | (0.184) | (0.383) | (0.038) | (0.149) | (0.366) | ||||||
0.99 | 1 | −0.058 | −0.091 | 0.447 | 0.99 | 1 | −0.040 | −0.086 | 0.454 | ||
(0.091) | (0.186) | (0.571) | (0.062) | (0.185) | (0.576) | ||||||
100 | 0 | 0 | 0.968 | 0.317 | 0.155 | 100 | 0 | 0 | 0.968 | 0.182 | 0.054 |
(0.969) | (0.357) | (0.266) | (0.968) | (0.204) | (0.149) | ||||||
0.99 | 0.5 | −0.051 | 0.112 | 0.324 | 0.99 | 0.5 | −0.031 | 0.076 | 0.261 | ||
(0.081) | (0.208) | (0.441) | (0.042) | (0.164) | (0.381) | ||||||
0.99 | 1 | −0.060 | −0.096 | 0.476 | 0.99 | 1 | −0.046 | −0.089 | 0.505 | ||
(0.091) | (0.191) | (0.588) | (0.066) | (0.181) | (0.609) |
FDML | GMM | SGMM | PF | FDML | GMM | SGMM | PF | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
50 | 0 | 0 | −0.002 | −0.090 | 0.183 | −0.035 | 50 | 0 | 0 | 0.000 | −0.038 | 0.181 | −0.011 |
(0.015) | (0.123) | (0.184) | (0.042) | (0.009) | (0.053) | (0.182) | (0.014) | ||||||
0.99 | 0.5 | 0.020 | −0.057 | 0.085 | −0.028 | 0.99 | 0.5 | 0.026 | −0.032 | 0.076 | −0.008 | ||
(0.059) | (0.110) | (0.121) | (0.042) | (0.066) | (0.066) | (0.111) | (0.022) | ||||||
0.99 | 1 | 0.030 | −0.068 | 0.065 | −0.009 | 0.99 | 1 | 0.035 | −0.034 | 0.048 | 0.004 | ||
(0.090) | (0.280) | (0.115) | (0.060) | (0.089) | (0.084) | (0.099) | (0.054) | ||||||
100 | 0 | 0 | −0.001 | −0.058 | 0.178 | −0.033 | 100 | 0 | 0 | 0.000 | −0.021 | 0.173 | −0.009 |
(0.010) | (0.083) | (0.179) | (0.041) | (0.007) | (0.032) | (0.174) | (0.016) | ||||||
0.99 | 0.5 | 0.025 | −0.038 | 0.079 | −0.021 | 0.99 | 0.5 | 0.033 | −0.021 | 0.076 | −0.003 | ||
(0.063) | (0.083) | (0.112) | (0.040) | (0.074) | (0.053) | (0.109) | (0.030) | ||||||
0.99 | 1 | 0.036 | −0.037 | 0.061 | −0.001 | 0.99 | 1 | 0.045 | −0.028 | 0.053 | 0.009 | ||
(0.093) | (0.096) | (0.107) | (0.073) | (0.097) | (0.081) | (0.098) | (0.059) |
50 | 0 | 0 | 0.955 | 0.292 | 0.022 | 50 | 0 | 0 | 0.968 | 0.176 | 0.014 |
(0.956) | (0.367) | (0.034) | (0.968) | (0.197) | (0.022) | ||||||
0.99 | 0.5 | −0.109 | 0.227 | 0.167 | 0.99 | 0.5 | −0.073 | 0.211 | 0.151 | ||
(0.136) | (0.303) | (0.309) | (0.089) | (0.280) | (0.278) | ||||||
0.99 | 1 | −0.092 | −0.012 | 0.321 | 0.99 | 1 | −0.067 | 0.007 | 0.353 | ||
(0.123) | (0.101) | (0.488) | (0.086) | (0.082) | (0.512) | ||||||
100 | 0 | 0 | 0.935 | 0.431 | 0.033 | 100 | 0 | 0 | 0.960 | 0.231 | 0.021 |
(0.936) | (0.530) | (0.047) | (0.960) | (0.303) | (0.032) | ||||||
0.99 | 0.5 | −0.128 | 0.251 | 0.151 | 0.99 | 0.5 | −0.084 | 0.273 | 0.149 | ||
(0.165) | (0.316) | (0.279) | (0.104) | (0.328) | (0.272) | ||||||
0.99 | 1 | −0.104 | −0.022 | 0.313 | 0.99 | 1 | −0.075 | 0.001 | 0.330 | ||
(0.137) | (0.109) | (0.476) | (0.098) | (0.090) | (0.497) |
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Xu, W. Estimation of Dynamic Panel Data Models with Stochastic Volatility Using Particle Filters. Econometrics 2016, 4, 39. https://doi.org/10.3390/econometrics4040039
Xu W. Estimation of Dynamic Panel Data Models with Stochastic Volatility Using Particle Filters. Econometrics. 2016; 4(4):39. https://doi.org/10.3390/econometrics4040039
Chicago/Turabian StyleXu, Wen. 2016. "Estimation of Dynamic Panel Data Models with Stochastic Volatility Using Particle Filters" Econometrics 4, no. 4: 39. https://doi.org/10.3390/econometrics4040039