The linkage between oil price, stock market indices, and exchange rate before, during, and after COVID-19: Empirical insights of Pakistan

Figures & data

Table 1. Unit root tests

Variables	At Level		First Differencing		Integration Order
	Intercept	Intercept+Trend	Intercept	Intercept+Trend
Augmented Dicky-Fuller (ADF) Test
Oil prices	−1.993	−1.969	−36.260^a	−36.250^a	I(1)
Stock index	−2.064	−2.100	−31.275^a	−31.265^a	I(1)
Exchange rate	−0.621	−1.192	−40.202^a	−40.188^a	I(1)
Phillips-Perron (PP) Test
Oil prices	−2.125	−2.106	−36.344^a	−36.332^a	I(1)
Stock index	−2.137	−2.170	−31.496^a	−31.486^a	I(1)
Exchange rate	−0.641	−1.275	−40.198^a	−40.185^a	I(1)
KPSS Test
Oil prices	0.699^b	0.664^a	0.096	0.078	I(1)
Stock index	0.477^b	0.375^a	0.108	0.101	I(1)
Exchange rate	4.136^a	0.520^a	0.238	0.239^a	I(1)

^aand ^b indicate 1% and 5% level of significance.

Source: Author’s own with data extraction from Bloomberg.

Table 2. Descriptive statistics

	Pre-COVID period			COVID period				Overall period
	OP	SI	ER	OP		SI	ER	OP	SI	^ER
Mean	58.90	40,368.91	120.39	48.19		40,093.95	160.24	56.19	40,299.39	130.46
Median	59.51	40,521.26	110.59	45.17		40,798.43	160.00	56.12	40,571.48	123.75
Maximum	86.29	52,876.46	163.50	69.63		46,933.63	168.10	86.29	52,876.46	168.10
Minimum	27.88	28,764.63	104.11	19.33		27,228.80	151.72	19.33	27,228.80	104.11
Std. Dev.	11.57	5230.97	19.37	12.38		4696.16	4.77	12.66	5100.72	24.21
Skewness	−0.16	0.04	0.85	−0.09		−0.63	0.00	−0.23	−0.09	0.18
Kurtosis	2.64	2.45	2.17	2.25		2.51	1.84	2.66	2.50	1.31
Jarque–Bera	9.95	12.88	148.27	8.38		25.60	18.73	18.14	15.44	165.16
Probability	9.95	0.00	0.00	0.02		0.00	0.00	0.00	0.00	0.00
Observations	990			335				1,325

Figure 1. VAR Granger Causality Test. Source: Author’s own.

Table 3. Wald Joint Sig. Test

	Dependent Variables			Lag Length
	Δ OP	Δ SI	Δ ER
	Chi-Sq Stat.	Chi-Sq Stat.	Chi-Sq Stat.
Pre-COVID Period
Δ OP	NA	4.5701	3.4320	3
Δ SI	1.4571	NA	11.6757a	3
Δ ER	2.8086	2.0073	NA	3
COVID Period
Δ OP	NA	17.9653a	11.5659	6
Δ SI	5.7750	NA	21.3660a	6
Δ ER	9.4924	4.8954	NA	6
Overall Period
Δ OP	NA	7.6255	2.2633	3
Δ SI	2.1844	NA	21.5135a	3
Δ ER	4.5610	4.7512	NA	3

^aindicates statistical significance at 1%. Δ is a difference operator.

Source: Author’s estimation with data extraction from Bloomberg

Table 4. Unrestricted VAR

	Pre-COVID Period			Overall Period
	Δ OP	Δ SI	Δ ER	Δ OP	Δ SI	Δ ER
Δ OP−1	−0.068 (0.034)b	23.854 (0.038)b	0.031 (0.116)	0.001 (0.967)	25.106 (0.012)b	0.016 (0.308)
Δ OP−2	−0.007 (0.835)	−4.323 (0.708)	−0.013 (0.519)	0.002 (0.947)	−10.956 (0.271)	−0.010 (0.516)
Δ OP−3	0.007 (0.822)	0.125 (0.991)	−0.013 (0.509)	0.016 (0.577)	0.870 (0.930)	−0.014 (0.367)
Δ SI−1	−0.000 (0.507)c	0.179 (0.000)a	−0.000 (0.789)	−0.000 (0.830)	0.147 (0.000)a	−0.000 (0.037)b
Δ SI−2	0.000 (0.281)	−0.040 (0.220)	−0.000 (0.001)a	0.000 (0.143)	−0.016 (0.560)	−0.000 (0.000)a
Δ SI−3	−0.000 (0.659)	−0.011 (0.723)	0.000 (0.947)	−0.000 (0.703)	0.018 (0.522)	0.000 (0.729)
Δ ER−1	−0.017 (0.748)	22.399 (0.237)	−0.088 (0.006)a	0.014 (0.764)	31.357 (0.067)c	−0.110 (0.000)a
Δ ER−2	−0.082 (0.119)	6.144 (0.745)	−0.047 (0.143)	−0.097 (0.043)	2.137 (0.901)	0.023 (0.406)
Δ ER−3	−0.039 (0.463)	15.568 (0.408)	0.103 (0.001)a	−0.032 (0.509)	19.420 (0.255)	0.078 (0.005)a
C	0.042 (0.261)	4.237 (0.752)	0.053 (0.018)b	0.029 (0.406)	5.064 (0.680)	0.039 (0.048)c

Table 5. Unrestricted VAR

	COVID Period
	Δ OP	Δ SI	Δ ER
Δ OP−1	0.148 (0.012)b	34.704 (0.093)c	−0.003 (0.928)
Δ OP−2	−0.032 (0.590)	−34.189 (0.102)	−0.016 (0.590)
Δ OP−3	0.028 (0.638)	−11.976 (0.564)	−0.018 (0.536)
Δ OP−4	0.022 (0.711)	24.119 (0.245)	0.085 (0.003)a
Δ OP−5	0.010 (0.861)	65.828 (0.002)a	−0.050 (0.085)c
Δ OP−6	0.068 (0.262)	13.040 (0.540)	0.023 (0.437)
Δ SI−1	−0.000 (0.548)	0.056 (0.341)	−0.000 (0.004)a
Δ SI−2	0.000 (0.199)	0.052 (0.371)	−0.000 (0.097)c
Δ SI−3	−0.000 (0.583)	0.094 (0.108)	0.000 (0.262)
Δ SI−4	0.000 (0.113)	−0.022 (0.704)	−0.000 (0.080)c
Δ SI−5	−0.000 (0.209)	0.057 (0.344)	−0.000 (0.097)c
Δ SI−6	0.000 (0.566)	0.008 (0.899)	0.000 (0.266)
Δ ER−1	0.086 (0.452)	46.645 (0.247)	−0.110 (0.050)c
Δ ER−2	−0.114 (0.320)	12.629 (0.755)	0.249 (0.000)a
Δ ER−3	0.003 (0.977)	42.375 (0.299)	−0.023 (0.685)
Δ ER−4	0.082 (0.476)	−26.388 (0.519)	−0.173 (0.002)a
Δ ER−5	0.031 (0.782)	−28.240 (0.481)	0.021 (0.713)
Δ ER−6	0.261 (0.019)b	35.304 (0.367)	0.088 (0.108)
C	0.002 (0.975)	7.791 (0.780)	0.002 (0.952)

P-values in bracket. ^a p < 1%, ^b p < 5%, and ^c p < 10%. −1 to −6 indicate number of lags.

Source: Author’s estimation with data extraction from Bloomberg.

Figure 2. Impulse-Response-Function pre-COVID period. Source: Author’s own.

Figure 3. Impulse-Response-Function during COVID period. Source: Author’s own.

Figure 4. Impulse-Response-Function in overall period. Source: Author’s own.

Table 6. Variance Decompositions (VDCs)—pre-COVID period

Period	S.E.	ER	SI	OP
VDCs of ER
1	0.7011	100.00	0.00	0.00
2	0.7046	99.74	0.00	0.25
5	0.7135	98.43	1.16	0.41
10	0.7136	98.42	1.17	0.41
VDCs of SI
1	416.1378	0.18	99.82	0.00
2	423.9896	0.28	99.30	0.43
5	424.2676	0.34	99.23	0.43
10	424.2699	0.34	99.23	0.43
VDCs of OP
1	1.1608	0.12	0.11	99.77
2	1.1639	0.14	0.17	99.70
5	1.1662	0.41	0.28	99.32
10	1.1662	0.41	0.28	99.31

Table 7. Variance Decompositions (VDCs)—during COVID period

Period	S.E.	ER	SI	OP
VDCs of ER
1	0.7081	100.00	0.00	0.00
2	0.7230	97.09	2.91	0.00
5	0.7665	93.05	4.13	2.82
10	0.7808	89.75	6.03	4.22
VDCs of SI
1	508.8268	0.00	100.00	0.00
2	514.2182	0.51	98.64	0.85
5	520.2627	0.96	97.07	1.96
10	535.4033	1.23	93.16	5.60
VDCs of OP
1	1.4410	0.49	9.15	90.36
2	1.4572	0.75	8.96	90.29
5	1.4705	1.14	10.04	88.81
10	1.4915	3.14	10.18	86.68

Table

Lag Length Criteria
Lag	LogL	LR	FPE	AIC	SC	HQ
Pre-COVID Period
0	−17,486.18	NA	5.91E+11	35.62	35.63	35.63
1	−9918.05	15,074.62	121,843.50	20.22	20.28*	20.25
2	−9892.16	51.41	117,724.10	20.19	20.29	20.23*
3	−9882.56	19.00*	117,581.10*	20.19*	20.34	20.25
4	−9876.95	11.07	118,395.60	20.20	20.39	20.27
5	−9871.45	10.82	119,243.50	20.20	20.44	20.29
6	−9867.98	6.81	120,594.00	20.21	20.50	20.32
7	−9862.15	11.39	121,376.90	20.22	20.55	20.35
8	−9858.94	6.26	122,817.30	20.23	20.61	20.37
COVID Period
0	−5335.60	NA	1.39E+10	31.87	31.91	31.89
1	−3519.83	3588.18	288,352.40	21.09	21.22*	21.14*
2	−3507.27	24.59	282,293.70	21.06	21.30	21.16
3	−3495.75	22.36	278,081.90	21.05	21.39	21.19
4	−3493.22	4.85	289,060.60	21.09	21.53	21.26
5	−3479.27	26.57	280,671.70	21.06	21.60	21.28
6	−3468.01	21.25	276,944.30*	21.04*	21.69	21.30
7	−3460.45	14.13	279,393.00	21.05	21.80	21.35
8	−3450.51	18.40*	277,900.00	21.05	21.90	21.39
Overall Period
0	−24,229.05	NA	1.92E+12	36.80	36.81	36.80
1	−13,488.98	21,414.91	160,972.50	20.50	20.55*	20.52
2	−13,458.23	61.16	155,744.40	20.47	20.55	20.50*
3	−13,446.92	22.45	155,198.80*	20.47*	20.58	20.51
4	−13,441.61	10.51	156,071.70	20.47	20.63	20.53
5	−13,432.03	18.94	155,932.60	20.47	20.66	20.54
6	−13,420.20	23.30*	155,266.10	20.47	20.69	20.55
7	−13,414.59	11.05	156,066.20	20.47	20.73	20.57
8	−13,406.69	15.50	156,328.20	20.47	20.77	20.58

* indicates lag order selected by the criterion

LR: sequential modified LR test statistic (each test at 5% level)

FPE: Final prediction error

AIC, SC, and HQ represent Akaike, Schwarz, and Hannan–Quinn information criteria, respectively

Table

VAR Residual Serial Correlation LM Tests
Null hypothesis: No serial correlation at lag h
	Pre-COVID Period		COVID Period		Overall Period
Samples:	04/01/2016–31/12/2019		01/01/2020–30/04/2021		04/01/2016–30/04/2021
Observations:	986		335		1,321
Lags	LRE* Stat.	Prob.	LRE* Stat.	Prob.	LRE* Stat.	Prob.
1	9.708	0.375	14.663	0.101	16.734	0.053
2	7.129	0.624	15.047	0.090	12.745	0.175
3	12.287	0.198	16.771	0.052	17.978	0.035
4	10.086	0.344	25.715	0.002	18.253	0.032
5	4.732	0.857	10.650	0.300	19.668	0.020
6	10.283	0.328	12.080	0.209	10.180	0.336

*Edgeworth expansion corrected likelihood ratio statistic.

Source: Author’s own.