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 6 Quantile cointegration estimates for S&P 500 model

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

Panel A. 10 years
\({\varvec{\tau}}\)	0.05	0.1	0.15	0.2	0.25	0.3	0.35	0.4	0.45
\({\beta }_{d}\)	0.91	0.84	0.82	0.73	0.71	0.75	0.72	0.72	0.64
p-value	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
\({\beta }_{EPS}\)	0.41	0.43	0.42	0.49	0.46	0.43	0.41	0.43	0.43
p-value	0.02	0.02	0.03	0.01	0.01	0.43	0.03	0.04	0.04
\({\beta }_{FED}\)	− 0.02	− 0.01	− 0.02	0.00	0.01	0.01	0.02	0.02	0.03
p-value	0.62	0.89	0.63	0.93	0.77	0.87	0.60	0.70	0.44
\({\beta }_{Lev}\)	1.26	1.21	1.04	1.35	1.34	1.47	1.45	1.48	1.47
p-value	0.00	0.01	0.03	0.00	0.00	0.01	0.00	0.01	0.01
\({\beta }_{ETF FOF}\)	0.05	0.07	0.07	0.07	0.08	0.09	0.10	0.10	0.12
p-value	0.36	0.23	0.16	0.26	0.13	0.08	0.08	0.13	0.07
\({\beta }_{Y10}\)	0.02	0.00	0.01	− 0.02	− 0.04	− 0.04	− 0.06	− 0.05	− 0.08
p-value	0.81	1.00	0.79	0.77	0.50	0.52	0.30	0.42	0.27

\({\varvec{\tau}}\)	0.5	0.55	0.60	0.65	0.70	0.80	0.85	0.90	0.95
\({\beta }_{d}\)	0.64	0.47	0.56	0.55	0.56	0.48	0.56	0.48	0.58
p-value	0.00	0.03	0.00	0.00	0.00	0.01	0.00	0.02	0.02
\({\beta }_{EPS}\)	0.42	0.47	0.47	0.49	0.46	0.48	0.44	0.43	0.37
p-value	0.05	0.05	0.04	0.03	0.03	0.03	0.03	0.06	0.15
\({\beta }_{FED}\)	0.05	0.05	0.05	0.05	0.06	0.07	0.06	0.07	0.09
p-value	0.26	0.19	0.15	0.08	0.12	0.04	0.06	0.08	0.08
\({\beta }_{Lev}\)	1.40	1.24	1.29	1.30	1.17	1.04	0.94	0.82	0.73
p-value	0.02	0.04	0.04	0.03	0.03	0.12	0.16	0.26	0.36
\({\beta }_{ETF FOF}\)	0.12	0.15	0.14	0.10	0.11	0.13	0.13	0.12	0.12
p-value	0.06	0.01	0.02	0.05	0.04	0.03	0.03	0.03	0.12
\({\beta }_{Y10}\)	− 0.09	− 0.10	− 0.06	− 0.06	− 0.05	− 0.06	− 0.03	− 0.06	− 0.04
p-value	0.27	0.21	0.38	0.35	0.49	0.35	0.62	0.49	0.65

Panel B. Spread BAA/AAA
\({\varvec{\tau}}\)	0.05	0.1	0.15	0.2	0.25	0.3	0.35	0.4	0.45
\({\beta }_{d}\)	0.91	0.87	0.75	0.78	0.80	0.83	0.83	0.80	0.77
p-value	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
\({\beta }_{EPS}\)	0.38	0.39	0.36	0.33	0.36	0.42	0.42	0.45	0.42
p-value	0.00	0.00	0.00	0.01	0.01	0.42	0.00	0.00	0.02
\({\beta }_{FED}\)	− 0.06	− 0.04	− 0.01	0.00	0.01	0.00	0.00	− 0.01	− 0.01
p-value	0.01	0.03	0.62	1.00	0.70	0.88	0.91	0.49	0.48
\({\beta }_{Lev}\)	1.44	1.26	0.59	0.56	0.77	0.97	1.21	1.38	1.33
p-value	0.00	0.00	0.15	0.23	0.10	0.03	0.01	0.01	0.02
\({\beta }_{ETF FOF}\)	0.04	0.04	0.08	0.09	0.10	0.06	0.05	0.06	0.09
p-value	0.59	0.46	0.10	0.04	0.03	0.28	0.46	0.32	0.15
\({\beta }_{\mathrm{Spread BAA}/{\text{AAA}}}\)	0.00	0.06	0.22	0.12	0.07	0.04	0.09	0.02	0.02
p-value	0.99	0.70	0.28	0.49	0.68	0.84	0.61	0.91	0.91

\({\varvec{\tau}}\)	0.5	0.55	0.60	0.65	0.70	0.80	0.85	0.90	0.95
\({\beta }_{d}\)	0.68	0.55	0.61	0.58	0.51	0.48	0.46	0.42	0.37
p-value	0.00	0.00	0.00	0.00	0.01	0.02	0.04	0.08	0.11
\({\beta }_{EPS}\)	0.52	0.51	0.49	0.47	0.51	0.54	0.55	0.56	0.61
p-value	0.01	0.01	0.02	0.02	0.01	0.01	0.01	0.02	0.01
\({\beta }_{FED}\)	− 0.01	0.03	0.04	0.04	0.04	0.05	0.06	0.06	0.06
p-value	0.79	0.10	0.02	0.01	0.01	0.00	0.00	0.00	0.00
\({\beta }_{Lev}\)	1.44	0.97	1.06	0.94	0.88	0.81	0.77	0.69	0.61
p-value	0.01	0.04	0.03	0.07	0.09	0.09	0.10	0.11	0.15
\({\beta }_{ETF FOF}\)	0.11	0.15	0.14	0.13	0.13	0.13	0.12	0.13	0.13
p-value	0.06	0.02	0.04	0.05	0.04	0.01	0.06	0.09	0.08
\({\beta }_{\mathrm{Spread BAA}/{\text{AAA}}}\)	0.13	0.17	0.09	0.09	0.12	0.18	0.20	0.24	0.40
p-value	0.54	0.43	0.71	0.70	0.59	0.36	0.31	0.26	0.06

Panel C Net equity share
\({\varvec{\tau}}\)	0.05	0.1	0.15	0.2	0.25	0.3	0.35	0.4	0.45
\({\beta }_{d}\)	0.85	0.72	0.87	0.69	0.87	0.82	0.79	0.77	0.78
p-value	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
\({\beta }_{EPS}\)	0.37	0.47	0.31	0.45	0.37	0.43	0.48	0.44	0.44
p-value	0.02	0.00	0.04	0.00	0.00	0.43	0.00	0.00	0.01
\({\beta }_{FED}\)	− 0.01	− 0.01	− 0.02	0.00	0.01	0.00	0.00	− 0.02	− 0.01
p-value	0.85	0.78	0.30	0.99	0.59	0.89	0.77	0.23	0.55
\({\beta }_{Lev}\)	0.68	0.60	0.87	0.77	0.92	1.04	1.28	1.44	1.41
p-value	0.23	0.25	0.05	0.08	0.01	0.00	0.00	0.00	0.00
\({\beta }_{ETF FOF}\)	0.11	0.09	0.10	0.13	0.09	0.07	0.07	0.10	0.10
p-value	0.10	0.15	0.20	0.10	0.21	0.28	0.28	0.07	0.06
\({\beta }_{Net equity share}\)	− 0.16	− 0.26	− 0.02	− 0.15	0.01	− 0.05	− 0.06	− 0.01	0.03
p-value	0.71	0.50	0.97	0.73	0.98	0.87	0.86	0.98	0.92

\({\varvec{\tau}}\)	0.5	0.55	0.60	0.65	0.70	0.80	0.85	0.90	0.95
\({\beta }_{d}\)	0.74	0.66	0.65	0.55	0.50	0.47	0.45	0.50	0.44
p-value	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.01	0.01
\({\beta }_{EPS}\)	0.49	0.56	0.54	0.62	0.61	0.64	0.62	0.62	0.60
p-value	0.01	0.01	0.01	0.01	0.03	0.01	0.01	0.03	0.05
\({\beta }_{FED}\)	-0.01	0.02	0.03	0.03	0.04	0.05	0.05	0.06	0.07
p-value	0.73	0.41	0.22	0.11	0.03	0.00	0.00	0.00	0.00
\({\beta }_{Lev}\)	1.47	1.37	1.28	1.34	1.16	1.25	1.15	1.33	0.95
p-value	0.01	0.01	0.02	0.02	0.06	0.06	0.08	0.03	0.19
\({\beta }_{ETF FOF}\)	0.09	0.10	0.11	0.13	0.13	0.15	0.16	0.18	0.16
p-value	0.02	0.02	0.02	0.05	0.00	0.00	0.00	0.00	0.02
\({\beta }_{Net equity share}\)	− 0.01	− 0.12	− 0.12	− 0.21	− 0.16	− 0.20	− 0.20	− 0.24	− 0.34
p-value	0.98	0.74	0.76	0.61	0.67	0.56	0.58	0.55	0.40

Expanding the set of state variables
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 S&P500 price data, variables related to index fundamentals and fund flows to ETFs. The model estimated is \({Q}_{{p}_{t}\left(\tau |{\mathcal{F}}_{t}\right)}=\mathrm{\alpha }\left(\tau \right)+{\beta }_{d}\left(\tau \right){d}_{t}+{\beta }_{EPS}\left(\tau \right){EPS}_{t}+{\beta }_{FED}\left(\tau \right){FED}_{t}+{\beta }_{Leverage}\left(\tau \right){Leverage}_{t}+{\beta }_{ETF FOF}\left(\tau \right){ETF FOF}_{t}+{\beta }_{Y10}\left(\tau \right){Y10}_{t}+\sum_{j=-K}^{K}{\pi }_{d,j}\left(\tau \right)\Delta {d}_{t-j}+\sum_{j=-K}^{K}{\pi }_{EPS,jt}\Delta {EPS}_{t-j}+\sum_{j=-K}^{K}{\pi }_{FED,j}\left(\tau \right)\Delta {FED}_{t-j}+\sum_{j=-K}^{K}{\pi }_{Leverage,j}\left(\tau \right)\Delta {Leverage}_{t-j}+\sum_{j=-K}^{K}{\pi }_{ETF FOF,j}\left(\tau \right)\Delta {ETF FOF}_{t-j}++\sum_{j=-K}^{K}{\pi }_{Y10,j}\left(\tau \right)\Delta {Y10}_{t-j}+{F}_{\varepsilon }^{-1}\left(\tau \right)\), 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, ETF FOF is the ratio of net FoF to equity ETFs to nominal GDP and Y10 is the long-term interest rate. Quarterly data for the period 1994–2020 is used. Most data is retrieved from Bloomberg.
Panel B 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 S&P500 price data, variables related to index fundamentals and fund flows to ETFs. The model estimated is \({Q}_{{p}_{t}\left(\tau |{\mathcal{F}}_{t}\right)}=\mathrm{\alpha }\left(\tau \right)+{\beta }_{d}\left(\tau \right){d}_{t}+{\beta }_{EPS}\left(\tau \right){EPS}_{t}+{\beta }_{FED}\left(\tau \right){FED}_{t}+{\beta }_{Leverage}\left(\tau \right){Leverage}_{t}+{\beta }_{ETF FOF}\left(\tau \right){ETF FOF}_{t}+{\beta }_{ \mathrm{Spread BAA}/{\text{AAA}}}\left(\tau \right){Spread BAA/AA}_{t}+\sum_{j=-K}^{K}{\pi }_{d,j}\left(\tau \right)\Delta {d}_{t-j}+\sum_{j=-K}^{K}{\pi }_{EPS,jt}\Delta {EPS}_{t-j}+\sum_{j=-K}^{K}{\pi }_{FED,j}\left(\tau \right)\Delta {FED}_{t-j}+\sum_{j=-K}^{K}{\pi }_{Leverage,j}\left(\tau \right)\Delta {Leverage}_{t-j}+\sum_{j=-K}^{K}{\pi }_{ETF FOF,j}\left(\tau \right)\Delta {ETF FOF}_{t-j}++\sum_{j=-K}^{K}{\pi }_{\mathrm{Spread BAA}/{\text{AAA}},j}\left(\tau \right)\Delta {Spread BAA/AAA}_{t-j}+{F}_{\varepsilon }^{-1}\left(\tau \right)\), 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, ETF FOF is the ratio of net FoF to equity ETFs to nominal GDP and the spread BAA/AAA. Quarterly data for the period 1994–2020 is used. Most data is retrieved from Bloomberg.
Panel C 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 S&P500 data, variables related to index fundamentals and fund flows to ETFs. The model estimated is \({Q}_{{p}_{t}\left(\tau |{\mathcal{F}}_{t}\right)}=\mathrm{\alpha }\left(\tau \right)+{\beta }_{d}\left(\tau \right){d}_{t}+{\beta }_{EPS}\left(\tau \right){EPS}_{t}+{\beta }_{FED}\left(\tau \right){FED}_{t}+{\beta }_{Leverage}\left(\tau \right){Leverage}_{t}+{\beta }_{ETF FOF}\left(\tau \right){ETF FOF}_{t}+{\beta }_{Net equity share}\left(\tau \right)Net equity share+\sum_{j=-K}^{K}{\pi }_{d,j}\left(\tau \right)\Delta {d}_{t-j}+\sum_{j=-K}^{K}{\pi }_{EPS,jt}\Delta {EPS}_{t-j}+\sum_{j=-K}^{K}{\pi }_{FED,j}\left(\tau \right)\Delta {FED}_{t-j}+\sum_{j=-K}^{K}{\pi }_{Leverage,j}\left(\tau \right)\Delta {Leverage}_{t-j}+\sum_{j=-K}^{K}{\pi }_{ETF FOF,j}\left(\tau \right)\Delta {ETF FOF}_{t-j}++\sum_{j=-K}^{K}{\pi }_{Net equity share,j}\left(\tau \right)\Delta {Net equity share}_{t-j}+{F}_{\varepsilon }^{-1}\left(\tau \right)\), 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, ETF FOF is the ratio of net FoF to equity ETFs to nominal GDP and New equity share is the share of equity issues in total new equity and debt issues Quarterly data for the period 1994–2020 is used. Most data is retrieved from Bloomberg.

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