Can ETFs affect U.S. financial stability? A quantile cointegration analysis

Laborda, Juan; Laborda, Ricardo; de la Cruz, Javier

doi:10.1186/s40854-023-00591-2

Financial Innovation

Table 5 Quantile cointegration estimates for Small and Value Caps models

From: Can ETFs affect U.S. financial stability? A quantile cointegration analysis

Panel A. Quantile cointegration estimates for Small caps model
\({\varvec{\tau}}\)	0.05	0.1	0.15	0.2	0.25	0.3	0.35	0.4	0.45
\({\beta }_{d}\)	0.05	0.04	0.04	0.04	0.05	0.05	0.05	0.05	0.05
p-value	0.00	0.00	0.00	0.01	0.00	0.00	0.00	0.00	0.00
\({\beta }_{EPS}\)	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.01
p-value	0.05	0.00	0.00	0.00	0.00	0.02	0.00	0.03	0.05
\({\beta }_{FED}\)	− 0.03	− 0.04	− 0.03	− 0.04	− 0.03	− 0.03	− 0.03	− 0.03	− 0.03
p-value	0.05	0.00	0.00	0.00	0.00	0.01	0.00	0.01	0.01
\({\beta }_{Lev}\)	0.10	− 0.03	− 0.02	0.04	0.15	0.10	0.15	0.13	0.17
p-value	0.81	0.93	0.95	0.89	0.53	0.67	0.50	0.53	0.31
\({\beta }_{ETF FOF}\)	0.19	0.20	0.21	0.19	0.19	0.23	0.22	0.21	0.20
p-value	0.05	0.05	0.04	0.07	0.03	0.00	0.00	0.00	0.00

\({\varvec{\tau}}\)	0.5	0.55	0.60	0.65	0.70	0.80	0.85	0.90	0.95
\({\beta }_{d}\)	0.05	0.05	0.05	0.05	0.04	0.04	0.05	0.05	0.05
p-value	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
\({\beta }_{EPS}\)	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.01
p-value	0.08	0.13	0.10	0.06	0.05	0.10	0.17	0.19	0.21
\({\beta }_{FED}\)	− 0.03	− 0.02	− 0.02	− 0.03	− 0.03	− 0.03	− 0.01	− 0.01	− 0.01
p-value	0.01	0.05	0.12	0.08	0.05	0.14	0.39	0.49	0.45
\({\beta }_{Lev}\)	0.13	0.13	0.15	0.19	0.34	0.24	− 0.05	− 0.13	− 0.08
p-value	0.47	0.43	0.48	0.48	0.26	0.44	0.89	0.75	0.84
\({\beta }_{ETF FOF}\)	0.23	0.23	0.25	0.26	0.27	0.31	0.22	0.20	0.19
p-value	0.00	0.00	0.00	0.00	0.00	0.00	0.01	0.01	0.00

Panel B. Quantile cointegration estimates for Value caps model
\({\varvec{\tau}}\)	0.05	0.1	0.15	0.2	0.25	0.3	0.35	0.4	0.45
\({\beta }_{d}\)	0.02	0.02	0.01	0.02	0.02	0.02	0.02	0.02	0.03
p-value	0.24	0.25	0.54	0.29	0.11	0.07	0.11	0.05	0.01
\({\beta }_{EPS}\)	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.01
p-value	0.20	0.23	0.08	0.15	0.08	0.01	0.06	0.15	0.27
\({\beta }_{FED}\)	0.04	0.04	0.04	0.04	0.03	0.03	0.02	0.03	0.01
p-value	0.40	0.38	0.41	0.35	0.40	0.41	0.61	0.19	0.67
\({\beta }_{Lev}\)	− 0.29	− 0.29	− 0.18	− 0.24	− 0.23	− 0.30	− 0.21	− 0.40	− 0.21
p-value	0.66	0.62	0.77	0.64	0.65	0.55	0.66	0.34	0.57
\({\beta }_{ETF FOF}\)	0.24	0.24	0.25	0.21	0.18	0.18	0.16	0.18	0.14
p-value	0.01	0.01	0.01	0.01	0.02	0.01	0.02	0.00	0.03

\({\varvec{\tau}}\)	0.5	0.55	0.60	0.65	0.70	0.80	0.85	0.90	0.95
\({\beta }_{d}\)	0.03	0.02	0.02	0.02	0.02	0.02	0.03	0.03	0.03
p-value	0.01	0.01	0.00	0.00	0.00	0.00	0.00	0.00	0.00
\({\beta }_{EPS}\)	0.01	0.01	0.01	0.01	0.01	0.01	0.00	0.01	0.01
p-value	0.19	0.12	0.09	0.06	0.11	0.13	0.47	0.23	0.23
\({\beta }_{FED}\)	0.01	0.01	0.00	0.00	0.00	0.00	− 0.01	− 0.01	− 0.01
p-value	0.63	0.77	0.94	1.00	0.94	0.83	0.69	0.55	0.57
\({\beta }_{Lev}\)	− 0.19	− 0.02	0.17	0.17	0.12	0.12	0.11	0.26	0.26
p-value	0.63	0.96	0.66	0.71	0.77	0.72	0.75	0.49	0.49
\({\beta }_{ETF FOF}\)	0.14	0.16	0.14	0.15	0.15	0.13	0.12	0.10	0.10
p-value	0.01	0.00	0.00	0.00	0.00	0.00	0.01	0.02	0.04

Panel A The table shows the quantile regression estimates of the cointegrating coefficients and the respective p-values using a lag of order 2 (K = 2) applied to the Russell 2000 price data, variables related to index fundamentals and fund flows to ETFs. The model estimated is \({Q}_{{p}_{t}\left(\tau |{\mathcal{F}}_{t}\right)}=\mathrm{\alpha }\left(\tau \right)+{\beta }_{d}\left(\tau \right){d}_{t}+{\beta }_{EPS}\left(\tau \right){EPS}_{t}+{\beta }_{FED}\left(\tau \right){FED}_{t}+{\beta }_{Leverage}\left(\tau \right){Leverage}_{t}+{\beta }_{ETF FOF}\left(\tau \right){ETF FOF}_{t}+\sum_{j=-K}^{K}{\pi }_{d,j}\left(\tau \right)\Delta {d}_{t-j}+\sum_{j=-K}^{K}{\pi }_{EPS,jt}\Delta {EPS}_{t-j}+\sum_{j=-K}^{K}{\pi }_{FED,j}\left(\tau \right)\Delta {FED}_{t-j}+\sum_{j=-K}^{K}{\pi }_{Leverage,j}\left(\tau \right)\Delta {Leverage}_{t-j}+\sum_{j=-K}^{K}{\pi }_{ETF FOF,j}\left(\tau \right)\Delta {ETF FOF}_{t-j}+{F}_{\varepsilon }^{-1}\left(\tau \right)\), where \({\text{d}}\), is the logarithm over the last twelve months in dividend per share, EPS is the logarithm over the last twelve months in earning per share, FED is the U.S. Federal Funds Effective Rate, Lev, is the natural logarithm of the debt-to-equity ratio of the S&P 500, and ETF FOF is the ratio of net FoF to equity ETFs to nominal GDP. Quarterly data for the period 1995-2020 is used. Most data is retrieved from Bloomberg.
Panel B The table shows the OLS and quantile regression estimates of the cointegrating coefficients and the respective p-values using a lag of order 2 (K = 2) applied to the Value caps price data (SVX Index from Bloomberg), variables related to index fundamentals and fund flows to ETFs. The model estimated is \({Q}_{{p}_{t}\left(\tau |{\mathcal{F}}_{t}\right)}=\mathrm{\alpha }\left(\tau \right)+{\beta }_{d}\left(\tau \right){d}_{t}+{\beta }_{EPS}\left(\tau \right){EPS}_{t}+{\beta }_{FED}\left(\tau \right){FED}_{t}+{\beta }_{Leverage}\left(\tau \right){Leverage}_{t}+{\beta }_{ETF FOF}\left(\tau \right){ETF FOF}_{t}+\sum_{j=-K}^{K}{\pi }_{d,j}\left(\tau \right)\Delta {d}_{t-j}+\sum_{j=-K}^{K}{\pi }_{EPS,jt}\Delta {EPS}_{t-j}+\sum_{j=-K}^{K}{\pi }_{FED,j}\left(\tau \right)\Delta {FED}_{t-j}+\sum_{j=-K}^{K}{\pi }_{Leverage,j}\left(\tau \right)\Delta {Leverage}_{t-j}+\sum_{j=-K}^{K}{\pi }_{ETF FOF,j}\left(\tau \right)\Delta {ETF FOF}_{t-j}+{F}_{\varepsilon }^{-1}\left(\tau \right)\), where \({\text{d}}\), is the logarithm over the last twelve months in dividend per share, EPS is the logarithm over the last twelve months in earning per share, FED is the U.S. Federal Funds Effective Rate, Lev, is the natural logarithm of the debt-to-equity ratio of the S&P 500, and ETF FOF is the ratio of net FoF to equity ETFs to nominal GDP. Quarterly data for the period 2004-2020 is used. Most data is retrieved from Bloomberg.

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