Table 2.
Panel data estimation results for changes on stock market VIX.
| Dependent Variable |
VIX changes |
||||||||
|---|---|---|---|---|---|---|---|---|---|
| Independent Variables | Exp. Sign | Pooled with PCSE | Fixed Effects with PCSE | Random Effects with PCSE | Pooled OLS with PCSE and AR(1) | Fixed Effects with PCSE and AR(1) | |||
| Model |
(1) |
(2) |
(1) |
(2) |
(1) |
(2) |
(2) |
(2) |
|
| C | +/− | 0.0067 | 0.0083 | 0.0108 | 0.0112 | 0.0096 | 0.0103 | 0.0078 | 0.0077 |
| (0.04)** | (0.01)** | (0.00)*** | (0.00)*** | (0.21) | (0,00)*** | (0.00)*** | (0.00)*** | ||
| GTR changes(t) | + | 0.1206 | 0.1352 | 0.0926 | 0.0993 | 0.1028 | 0.1105 | 0.1398 | 0.1405 |
| (0.00)*** | (0.00)*** | (0.00)*** | (0.00)*** | (0.00)*** | (0.00)*** | (0.00)*** | (0.00)*** | ||
| GTR changes(t-1) | + | 0.0338 | −0.0093 | 0.0034 | |||||
| (0.12) | (0.71) | (0.91) | |||||||
| Stock changes(t) | – | −1.9618 | −2.0118 | −1.5027 | −1.5058 | −1.6523 | −1.6656 | −2.1183 | −2.1220 |
| (0.00)*** | (0.00)*** | (0.00)*** | (0.00)*** | (0.00)*** | (0.00)*** | (0.00)*** | (0.00)*** | ||
| Stock changes(t) x GTR changes(t) | – | −3.4598 | −0.8889 | −1.5054 | |||||
| (0.11) | (0.66) | (0.33) | |||||||
| Stock changes(t) x GTR changes(t-1) | – | −3.2075 | −4.3030 | −3.7950 | −3.6266 | −3.6301 | −3.7408 | −4.1490 | −4.2142 |
| (0.04)** | (0.00)*** | (0.00)*** | (0.00)*** | (0.00)*** | (0.00)*** | (0.00)*** | (0.00)*** | ||
| ρ [AR(1) coeff.] | +/− | −0.1654 | −0.1675 | ||||||
| (0.00)*** |
(0.00)*** |
||||||||
| Country Effects | no | no | yes | no | yes | no | no | yes | |
| Time Effects | no | no | yes | yes | yes | yes | no | no | |
| R2 | 35.71% | 35.33% | 55.77% | 56.53% | 34.90% | 34.55% | 34.27% | 36.09% | |
| F Test | 86.09*** | 140.53*** | 13.87*** | 17.33*** | 38.52*** | 63.72*** | 113.21*** | 28.04*** | |
| Durbin-Watson stat. | 2.35 | 2.33 | 2.76 | 2.75 | 2.65 | 2.28 | 2.03 | 2.03 | |
| N =(ixT) |
767 |
767 |
767 |
767 |
767 |
767 |
754 |
754 |
|
| Specification tests | |||||||||
| Cross section F-test (pooled OLS vs. FEM) p-value | (0.99) | (0.99) | |||||||
| Period F-test (pooled OLS vs. FEM) p-value | (0.00)*** | (0.00)*** | |||||||
| Hausman test (FEM vs REM) - Period Random | (0.08)* | ||||||||
| Test of cross-sectional independence by Frees | (0.00)*** | ||||||||
| Modified Wald test for group wise heteroskedasticity | (0.00)*** | ||||||||
Notes: This table presents the estimation results for VIX changes regressed on stock market changes, google trends indicator (GTR) contemporaneously (t) and with a lag (t-1), and on cross terms of stock changes with GTR measurement each time. The pooled, fixed and random effects models with panel corrected standard errors (PCSE) are estimated regarding Equation (1) for the period from 02 January 2020 to 09 April 2020. P-values are in parentheses. *,** and ***indicate statistical significance at the 10%, 5%, and 1% level respectively. The column Exp. Sign refers to expected signs of the coefficient of the relevant explanatory variable. Coefficient ρ is estimated assuming a common across countries autoregressive model [(AR(1)] for the residuals. Next panel of the table reports the adjusted R2 coefficient, the F-test, the Durbin–Watson value and the number of observations [market units (i) x time observations (t)]. The lower part of the table presents specification tests for the models estimated. Initially pooled versus fixed effects are tested, and then a Hausman test is applied between fixed versus random effects models for cases where previously fixed effects models are selected versus pooled models. Finally, p-values of tests for cross sectional independence and group wise heteroscedasticity are reported.