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Financial Innovation

Table 7 The causality test in threshold model

From: Are life insurance futures a safe haven during COVID-19?

Insurance company

Regime

Threshold model

\({\varvec{H}}_{{\varvec{0}}} {\varvec{:dm}}\xrightarrow{{\varvec{ \times }}}{\varvec{dp}}\) \(\left( {\sum\nolimits_{{{\varvec{i = 1}}}}^{{\varvec{L}}} {{\varvec{\alpha }}_{{{\varvec{2i}}}}^{{\varvec{k}}} } } \right)\)

\({\varvec{H}}_{{\varvec{0}}} {\varvec{:dc}}\xrightarrow{{\varvec{ \times }}}{\varvec{dp}}\) \(\left( {\sum\nolimits_{{{\varvec{i = 1}}}}^{{\varvec{L}}} {{\varvec{\alpha }}_{{{\varvec{3i}}}}^{{\varvec{k}}} } } \right)\)

\({\varvec{H}}_{{\varvec{0}}} {\varvec{:dp}}\xrightarrow{{\varvec{ \times }}}{\varvec{dm}}\) \(\left( {\sum\nolimits_{{{\varvec{i = 1}}}}^{{\varvec{L}}} {{\varvec{\beta }}_{{{\varvec{1i}}}}^{{\varvec{k}}} } } \right)\)

\({\varvec{H}}_{{\varvec{0}}} {\varvec{:dc}}\xrightarrow{{\varvec{ \times }}}{\varvec{dm}}\) \(\left( {\sum\nolimits_{{{\varvec{i = 1}}}}^{{\varvec{L}}} {{\varvec{\beta }}_{{{\varvec{3i}}}}^{{\varvec{k}}} } } \right)\)

HDFC

 

TVECM (L = 8, d = 6)

    

Regime 1

\(dc_{t - 6} >\) 8.161721% s

94.280***

49.715***

29.819***

27.169***

  

(0.932)

(1.290)

(0.101)

(0.032)

Regime 2

\(dc_{t - 6} \le\) 8.161721%

19.664***

9.102

38.933***

56.838***

  

(− 0.208)

(0.247)

(− 0.165)

(− 0.069)

ICICI

 

TVAR (L = 8, d = 6)

    

Regime 1

\(dc_{t - 6} >\) 0.13131321%

30.971***

30.703***

28.015***

34.459***

  

(0.403)

(0.166)

(0.012)

(− 0.010)

Regime 2

\(dc_{t - 6} \le\) \(0.131321\)%

11.573

16.316**

20.688***

40.976***

  

(− 0.377)

(− 1.990)

(5.051)

(4.079)

SBIL

 

TVAR (L = 5, d = 5)

    

Regime 1

\(dc_{t - 5} >\) 0.243924%

3.481

15.162***

5.580

5.756

  

(0.176)

(0.296)

(0.025)

(0.001)

Regime 2

\(dc_{t - 5} \le\) \(0.243924\)%

10.919**

16.662***

1.646

2.755

  

(0.403)

(0.370)

(0.871)

(1.290)

TWN

 

TVAR (L = 5, d = 1)

    

Regime 1

\(dc_{t - 1} >\) 0.086630%

10.631*

16.518***

12.304**

7.445

  

(− 0.064)

(0.421)

(0.039)

(0.030)

Regime 2

\(dc_{t - 1} \le\) \(0.086630\)%

5.644

12.349**

8.949

12.313**

  

(0.531)

(0.095)

(− 13.47)

(− 11.24)

  1. We use Akaike information criterion (AIC) statistic to select the optimal Lag periods (L) and the Wald chi-square statistic to test the causality between variables. When the null hypothesis is rejected, there is a significant causal relationship between the variables. The notation "***", "**" and "*" represent 1%, 5% and 10% significance levels, respectively; L represents the Lag periods, d is delay periods. TVECM threshold vector error correction model, TVAR threshold vector autoregression model
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