Dynamic modeling of systemic risk and firm value: A case of Pakistan

Figures & data

Table 10. Variable formulation and empirical evidence

Variable	Measurements & Source	Empirical Evidence
Bank Level Determinants
Size	$Logarithm$ $ofTotalAssets$ State Bank of Pakistan	Kleinow and Nell (2015), Strobl (2016), Kleinow et al. (2017)
Leverage	$\frac{Debt}{TotalAssets}$ State Bank of Pakistan	Strobl (2016), Black et al. (2016), Andries and Mutu (2016)
Profitability	Return on Equity State Bank of Pakistan	Black et al. (2016), de Mendonça and Da Silva (2017)
Liquidity	$\frac{\mathrm{c}\mathrm{a}\mathrm{s}\mathrm{h}\mathrm{f}\mathrm{l}\mathrm{o}\mathrm{w}\mathrm{f}\mathrm{r}\mathrm{o}\mathrm{m}\mathrm{o}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}}{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{i}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{e}\mathrm{s}}$ State bank of Pakistan	Lin et al. (2016), de Mendonça and Da Silva (2017), Soedarmono and Sitorus (2017), Black et al. (2016)
Non- Interest Income	$\frac{Non-Interestincome}{TotalinterstIncome}$ State Bank of Pakistan	Kleinow et al. (2017),Strobl (2016)
Deposit Ratio	$\frac{Deposit}{TotalAssets}$ State Bank of Pakistan	Zedda and Cannas (2017), de Mendonça and Da Silva (2017)
Idiosyncratic Risk	$R_{it}={\alpha }_{it}+\beta R_{M,t}$+${\epsilon }_{it}$ $R_{M,t}$ denotes KSE 100 index return. Standard deviation of ${\epsilon }_{it}$ explains the idiosyncratic volatility	Strobl (2016).
Firm Value	$tobinQ=\frac{MarketValueofequity+BookValueofDebt}{TotalAssets}$	Soedarmono and Sitorus (2017), Strobl, 2016)
Sector Level
Munificence	1. Regressing time against the Revenues of banking sector over the period of study and 2. Taking the ratio of the regression slope coefficient to the mean value of revenues over the same period. (Computed by Authors)	Boyd (1995), Kayo and Kimura (2011)
Dynamism	Standard error of munificent slope coefficient divided by the mean value of revenues over the same period. (Computed by Authors)	Boyd (1995), Kayo and Kimura (2011)
Concentration	HHI is the sum of the squares of the market shares (assets) of each bank in the financial system. (Computed by Authors)	Anginer et al. (2014)
Country level
Political Stability	Index of instability of Democracy extracted from Worldwide Governance Indicators.	Kleinow &Nell(2015), Kleinow et al. (2017)
Bank Claim	Banks’ claims on central government as a percentage of GDP include loans to central government institutions net of deposits.(WDI)	Kleinow &Nell (2015), Kleinow et al. (2017)
Monetary Policy	Monetary policy Interest Rate	de Mendonça and Da Silva (2017), Gang and Qian (2015)

Note: The table provides definition and data sources of Firm, Sector and Country level variables.

Table 1. Descriptive statistics

Variable	Obs	Mean	Std. Dev.	Min	Max
Term Spread	911	1.4624	1.2417	−3.2191	4.3208
Change in T-bill	911	0.0032	0.3207	−3.7503	2.6294
Market Return	911	0.3590	3.0743	−18.2103	11.5575
Rolling SD	911	0.6306	0.9811	0.0104	5.1289
Inflation	911	2.0464	0.9930	0.3212	4.7307
Change Spread	911	−5.0045	2.1590	− 8.6500	0.3200

Note: The table shows weekly statistics of state variables incorporated for the measurement of $\mathrm{\Delta }Co\hat{V}a{R}_{99t}^{System}$.

Table 2. Quantile regression with stock return (Losses) and system return (Losses) as dependent variable

	Quantile 0.01		Quantile 0.50
	$R_t^i$	$R_t^{System}$	$R_t^i$	$R_t^{System}$
Market Return	0.6109*** (3.60)	0.3956*** (8.26)	0.8769***(62.46)	0.6524***(7.13)
Term Spread	0.1361 (0.39)	−0.0408 (0.77)	0.0479* (1.66)	0.0736***(4.20)
Change in t-bill	−2.5736 (−1.43)	−1.9162*** (−9.73)	−0.3514*** (−2.95)	−0.2915***(−5.19)
Rolling SD	−1.5238***(−5.54)	−1.6170*** (−6.74)	−0.0164 (−0.71)	0.0936***(4.90)
Inflation	−0.9142***(−2.64)	−0.8377*** (−7.82)	0.0344 (1.27)	−0.0552** (−2.35)
Change Spread	−1.1861 (−0.91)	−0.4062 ***(−5.85)	0.0346* (1.93)	0.0023 (0.28)
$R_t^i$	____	0.4122*** (3,71)	____	0.2417***(4.54)
Constant	−8.7142***(−7.14)	−2.7848*** (−3.28)	−0.4871***(−4.59)	−0.1469***(−2.63)
Number of obs	14,728	14,728	14,728	14,728
Pseudo R2	0.4541	0.6118	0.3519	0.4011

Note: Table reports the results of 1 and 50% quantile regression results with return of individual financial institution as dependent variable. (*), (**) and (***) shows significance at 1, 5, and 10%, respectively. T-values are shown in parenthesis. Quantile regression shows pseudo R2 instead of adjusted R2.

Table 3. Descriptive statistics of weekly results (in %)

Variable	Obs	Mean	Std. Dev.	Min	Max
$Va{R}_{95,t}^i$	14,728	−8.059	7.105	−51.457	−2.257
$Va{R}_{99,t}^i$	14,728	−12.51	13.214	−84.890	−3.631
$\mathrm{\Delta }CoVa{R}_{99,t}^i$	14,728	−1.326	1.562	−6.910	−0.183
$\mathrm{\Delta }CoVa{R}_{95,t}^i$	14,728	−0.805	0.595	−4.031	−0.086
$Va{R}_{99,t}^{System}$	907	−5.175	3.499	−32.726	−2.185

Note: The table shows weekly statistics of risk measures along with respective mean and standard deviation. All the values are shown in weekly percentage points.

Figure 1. Average CoVaR.

Table 4. Systemic importance of financial institutions with respect to $\mathrm{\Delta }CoVa{R}_{99}^i$. The ranking of systemically important financial institutions using∆ CoVaR

Rank	Institution	Average Weekly ∆CoVaR
1	Muslim Commercial Bank (MCBL)	−0.0355
2	United Bank Limited(UBL)	−0.0312
3	Habib Bank Limited (HBL)	−0.0299
4	National Bank Limited (NBPL)	−0.0246
5	Allied Bank Limited (ABL)	−0.0235
6	Meezan Bank Limited	−0.0187
7	Bank Al-Habib Limited	−0.0151
8	Bank ALfalah Limited	−0.0146
9	Bank of Punjab Limited	−0.0117
10	Habib Metro Bank Limited	−0.0098
11	Faysal Bank Limited	−0.0089
12	Standard Chartered Bank Limited	−0.0084
13	Askari Bank Limited	−0.0072
14	Bank of Khyber Limited	−0.0050
15	Soneri Bank Limited	−0.0048
16	BankIslami Pakistan Limited	−0.0044
17	Silk Bank Limited	−0.0042
18	Samba Bank Limited	−0.0039
19	JS Bank Limited	−0.0036
20	Summit Bank Limited	−0.0027

Table 5. Descriptive statistics

Variable	Mean	Std. Dev.	Min	Max
Firm
Idiosyncratic	2.1710	1.0446	1.0791	6.0126
Size	8.1349	5.4611	6.5417	9.4082
Non-Interest	0.1981	0.1025	0.0074	0.3762
Liquidity	0.0671	0.0906	−0.3158	0.2722
Leverage	0.7952	0.9546	0.6339	0.8698
Deposit Ratio	0.7539	0.8612	0.4411	0.8954
Sector
Munificence	0.1014	0.0911	−0.0131	0.2267
Concentration	971.3164	103.1475	852.5903	1525.91
Dynamism	0.0296	0.0133	0.0008	0.0614
Country
Political	−2.3914	0.3491	−2.8100	−1.5831
Claims	0.2161	0.7008	0.1141	0.3166
Monetary Interest	0.0925	0.0263	0.0575	0.1447

Note: The table presents descriptive statistics for bank, sector and country specific financial data used in the panel regressions. Bank-specific data are taken from the databases of State Bank of Pakistan. Sector level variables are computed by authors. Political stability and Bank claims are provided by World Wide Governance and development indicators.

Table 6. Correlation matrix

Systemic	IDIO	Size	LEV	Non-Int	LIQ	Deposit	MUN	CONC	DYNA	Political Claims	Monetary
Systemic	1.0000
Idiosyncratic	0.1087	1.0000
Size	0.3282	−0.2430	1.0000
LEV	0.1514	0.2949	0.2597	1.0000
Non-Int	0.0905	0.0568	0.0257	0.1970	1.0000
LIQ	− 0.0622	−0.0983	0.3921	−0.1182	−0.0783	1.0000
Deposit	−0.0066	−0.1871	0.3871	0.6179	0.1781	0.1116	1.0000
MUN	−0.2107	−0.4988	0.4905	0.4576	−0.1907	−0.0359	0.1359	1.0000
CONC	−0.0296	−0.1376	0.4406	0.0171	0.2107	−0.1164	0.0853	0.0802	1.0000
DYNA	−0.1207	0.5508	−0.0812	−0.0469	0.0834	−0.1476	−0.0463 -	0.5132	−0.5438	1.0000
Political	−0.1807	−0.3510	0.1052	0.0214	−0.0261	−0.1442	0.0390	0.2436	0.1507	−0.1152	1.0000
Claims	0.0513	−0.3184	0.1435	0.0766	−0.0499	0.0029	0.0219	0.0794	−0.3911	0.1813	−0.4256	1.0000
Monetary	0.1318	0.2333	−0.2241	−0.0396	−0.0280	−0.0294	0.1558	−0.5124	0.2072	0.3210	0.1944	−0.1076	1.000

Table 7. Systemic risk granger-cause idiosyncratic risk

W-bar	=	7.2179
Z-bar	=	16.8365 (p = (0.0000)
Z-bar tilde	=	6.3753 (p = 0.0000)

Note: The table reports the statistics Dumitrescu and Hurlin (2012) Granger non-causality test results.

The null hypothesis is ∆CoVaR does not Granger cause idiosyncratic risk.

Table 8. Idiosyncratic risk granger-cause systemic risk

W-bar	=	2.4219
Z-bar	=	1.1961 (p = .2410)
Z-bar tilde	=	−0.1512 (p = .8941)

Table 9. Estimation of firm value

tobinQ	R.E	SGMM1	SGMM2
$tobin{Q}_{t-1}$		0.993 (0.777)	0.225** (0.661)
Systemic Risk	0.174* (0.099)	0.308 (0.218)	0.270* (0.149)
IDIO	−1.451* (0.799)	−0.201** (0.093)	−0.183* (0.102)
Size	0.431*** (0.079)	0.282** (0.134)	0.141* (0.077)
Leverage	−0.310***(0.059)	−0.016* (0.007)	−0.017** (0.006)
Profitability	0.040 (0.063)	0.030** (0.012)	0.022 (0.284)
Non-Interest	−0.103 (0.079)	−0.346 (0.443)	−0.483** (0.235)
Liquidity	0.023 (0.029)	0.146** (0.053)	0.087* (0.044)
Deposit Ratio	0.188 (0.230)	0.091 (0.125)	0.142 (0.117)
Concentration	0.001 (0.002)	0. 0002 (0.0002)	0.004 (0.039)
Constant	1.645***(0.311)	1.138* (0.568)	0.655** (0.300)
Num of obs	309	289	289
$Adj.R{ }^2$	0.4120
F-stat(P-value)	65.72(0.00)	89.99(0.000)	116.43 (0.00)
N.Ins/N.Groups		(0.80)	(0.80)
J-stat(p-value)			12.63(0.404)
Sargan(p-value)		7.53(0.247)	14.14(0.285)
AR(1)p-value		−1.71(0.086)	−2.04(0.045)
AR(2)p-value		0.63(0.547)	0.94 (0.386)

Note: (*), (**) and (***) shows significance at 1, 5, and 10%, respectively. Standard errors are shown in parenthesis. Heteroskedasticity-robust Huber-White standard errors are used AR (1) and AR (2) present results of first and second order correlation in first differenced results. Sargan and J-stat show if instruments are exogenous. J-stat is reported by stata in one-step, resultantly only Sargan stat is reported.

Table 11. Selection of preferred model (Artificial nested testing procedure)

ATNP	Firm	Firm & Sector	Firm & Country	Sector & Country
Systemic risk	F = 22.40	F = 20.35	F = 3.453	F = 74.81
	p = 0.0000	p = 0.0000	p = 0.0173	p = 0.0173

Note: Table A.5 shows F-value and probability of artificial nested testing procedure results. All the restricted combinations are compared with unrestricted model. The null hypothesis is that restricted model is statistically better than unrestricted model. The probability of F-test is 0.000 in all the cases that rejects the null hypothesis that restricted model is better than unrestricted model.

Table 12. Diagnostics and post estimation of fixed effect regression

Test/ Diagnostic	Systemic Risk	Firm Value
Hausman Specification	chi2 = 88.35	chi2 = 7.18
	p = 0.0000	p = 0.6118
Wooldridge test for autocorrelation in panel data	F = 1.914	F = 1.0490
	p = 0.1164	p = 0.3219
Pesaran’s test of cross sectional dependence	Stat = 1.2791
	p = 0.2166
Breusch and Pagan test for Random Effects		Chi-squared = 295.0
		p = 0.000
t-test for significance of sector level variables	F = 3.46
	p = 0.0169

Note: The table provides tests for fixed/random effect regression. Hausman Specification shows application of fixed effect and Wooldridge test rejects the presence of serial correlation. Pesaran Test also rejects cross sectional dependence. Heteroskedasticity-robust Huber-White standard errors are used. T-test shows the significance of sector level variables and validate the inclusion of sector level variables in the model.

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