The asymmetric impacts of oil price and shocks on inflation in BRICS: a multiple threshold nonlinear ARDL model

Figures & data

Table 1. Descriptive statistics

Variable	Mean	Std.Dev	Median	Min	Max	Skewness	Kurtosis
Oil price	63.5863	29.5449	59.6150	18.3800	132.7200	0.4519	2.1580
Components
Supply shock	0.0023	0.8278	−0.0117	−7.8955	1.7397	−3.6577	37.0383
Demand shock	−0.0165	5.9325	0.0631	−25.6707	22.2441	0.1636	5.3566
Risk shock	−0.1457	19.9171	−3.1410	−47.2767	78.7026	0.8356	4.4659
CPI
Brazil	78.5306	27.3541	72.3713	37.1333	131.6604	0.2987	1.8478
Russia	69.7960	33.2664	66.5565	19.0190	128.8338	0.1928	1.7105
India	73.8008	30.5315	68.2818	35.6541	132.1010	0.3520	1.6915
China	88.8562	13.8024	87.0982	68.9724	113.7000	0.0846	1.6283
South Africa	81.3322	25.5154	77.2277	44.4324	129.7121	0.3441	1.7948

Source: Authors’ calculation.

Table 2. Unit root tests without structural break

Variables		Level (I(0))			Difference (I(1))
		Intercept	Intercept and trend		Intercept	Intercept and trend
Oil price	ADF	−2.5391	−2.5535		−10.6497***	−10.6399***
	PP	−2.0582	−1.9939		−10.1015***	−10.0743***
	KPSS	0.6175	0.3743***		0.1205	0.0434
Components
Supply shock	ADF	−14.4329***	−14.4043***		−11.6881***	−11.6663***
	PP	−14.5995***	−14.5592***		−110.3428***	−110.5583***
	KPSS	0.0717	0.0719		0.1462	0.1071
Demand shock	ADF	−18.5331***	−18.7043***		−11.9359***	−11.9542***
	PP	−18.4297***	−18.6092***		−172.8561***	−271.5955***
	KPSS	0.3514	0.0532		0.0474	0.0274
Risk shock	ADF	−15.6886***	−15.6848***		−11.8143***	−11.7885***
	PP	−15.7182***	−15.7190***		−148.5100***	−152.2843***
	KPSS	0.1451	0.0842		0.3090	0.2296***
CPI
Brazil	ADF	2.1209	−0.7631		−7.6949***	−8.0741***
	PP	2.4334	−0.8239		−7.7812***	−8.1659***
	KPSS	2.0260***	0.4511***		0.6336	0.0787
Russia	ADF	0.7146	−2.6180		−2.8472*	−3.0015
	PP	1.2397	−1.9172		−6.9416***	−7.0162***
	KPSS	2.0480***	0.3516***		0.2996***	0.0821
India	ADF	4.1306	−2.6761		−1.8773	−9.3768***
	PP	2.6378	−2.1129		−12.2186***	−12.4892***
	KPSS	2.0244***	0.4299***		0.9819***	0.1216
China	ADF	−0.1906	−4.0491***		−2.9722**	−2.9368
	PP	0.7937***	−3.9125**		−12.3313***	−12.3107***
	KPSS	2.0466***	0.2006		0.2203	0.0888
South Africa	ADF	2.3599	−1.3139		−10.5940***	−11.0273***
	PP	2.6551	−1.1745		−10.5940***	−10.8601***
	KPSS	2.0282***	0.4600***		0.8327***	0.0900

Note: Significant at 10% (*), 5% (**), and 1% (***). The null hypothesis of KPSS is that data are stationary, which is contrary to the ADF and PP tests. Source: Authors’ calculation.

Table 3. Unit root with breaks

Variables	Level (I(0))			Difference (I(1))
	Intercept	Intercept and trend		Intercept	Intercept and trend
Oil price	−3.3018	−5.2278**		−11.3957***	−11.3465***
Components
Supply shock	−17.1906***	−17.2129***		−24.4765***	−24.4268***
Demand shock	−20.0741***	−20.7977***		−32.5353***	−32.4703***
Risk shock	−16.3727***	−16.4664***		−26.1850***	−26.1348***
CPI
Brazil	−0.3711	−3.1684		−8.7651***	−8.9103***
Russia	−0.8908	−6.4240***		−7.8509***	−8.0861***
India	−0.9031	−3.3477		−12.2954***	−12.6819***
China	−2.1155	−5.0600**		−12.7361***	−12.7516***
South Africa	−0.2229	−4.7290*		−11.0724***	−11.3869***

Note: Significant at 10% (*), 5% (**), and 1% (***). Source: Authors’ calculation.

Table 4. BDS test of independence

Embedding dimension	2	3	4	5	6
Oil price	50.4773***	53.5486***	57.1238***	62.1830***	69.0054***
Components
Supply shock	5.0153***	4.9001***	5.0495***	4.9486***	5.0402***
Demand shock	1.4228	1.5582	1.8458*	1.8857*	1.4575
Risk shock	2.5066**	3.0468***	2.3061**	2.1962**	1.5846
CPI
Brazil	70.4608***	75.4636***	81.9963***	91.5449***	104.7080***
Russia	75.6292***	81.0374***	88.0043***	98.1753***	112.1739***
India	71.9160***	77.1056***	83.8066***	93.6208***	107.1656***
China	78.8418***	84.7229***	92.2101***	103.1357***	118.0989***
South Africa	71.1610***	76.2641***	82.8877***	92.5961***	105.9217***

Note: Significant at 10% (*), 5% (**), and 1% (***). Source: Authors’ calculation.

Table 5. Toda-Yamamoto causality results

	Null hypothesis	k+ dmax	Statistic	Causality
Brazil	CPI$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$Oil Oil$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$CPI	3	0.13269 2.8715	No causality
	S$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$CPI	3	2.2908	No causality
	CPI$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$S		0.17841
	D$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$CPI	3	2.2117	No causality
	CPI$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$D		2.9484
	R$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$CPI	5	16.682***	R$\Rightarrow$CPI
	CPI$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$R		3.7507
Russia	CPI$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$Oil Oil$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$CPI	3	4.736* 10.866***	$\mathrm{O}\mathrm{i}\mathrm{l}\Rightarrow$CPI
	S$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$CPI	4	7.8734**	S$\Rightarrow$CPI
	CPI$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$S		5.669
	D$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$CPI	3	4.048	No causality
	CPI$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$D		0.93781
	R$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$CPI	4	3.6847	No causality
	CPI$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$R		1.1888
India	CPI$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$Oil Oil$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$CPI	3	0.10522 4.5286	No causality
	S$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$CPI	3	6.5642**	S$\Rightarrow$CPI
	CPI$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$S		0.81678
	D$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$CPI	3	3.5462	No causality
	CPI$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$D		1.5154
	R$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$CPI	3	0.91795	No causality
	CPI$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$R		3.9105
China	CPI$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$Oil Oil$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$CPI	3	0.00919 3.2438	No causality
	S$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$CPI	4	6.2912	No causality
	CPI$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$S		5.7289
	D$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$CPI	5	6.6159	No causality
	CPI$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$D		6.805
	R$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$CPI	3	5.5425	No causality
	CPI$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$R		2.4516
South Africa	CPI$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$Oil Oil$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$CPI	5	3.4019 45.029	$\mathrm{O}\mathrm{i}\mathrm{l}\Rightarrow$CPI
	S$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$CPI	4	46.678***	S$\Rightarrow$CPI
	CPI$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$S		5.2852
	D$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$CPI	5	15.121***	D$\Rightarrow$CPI CPI$\Rightarrow$D
	CPI$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$D		12.521**
	R$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$CPI	3	2.0645	No causality
	CPI$\text{setbox}0=\Rightarrow \text{t}o\text{wd}0\text{hss}/\text{hss}\text{box}0$R		1.0924

Note: Significant at 10% (*), 5% (**), and 1% (***). Source: Authors’ calculation.

Table 6. ARDL results

	Regressors	Regressand Δ(CPI)
		Brazil	Russia	India	China	South Africa
Panel A: Oil price
Short run	Δ(CPI(−1))	0.580***	0.684***	0.191***	0.211***	0.295***
	Δ(Oil)	0.00328	−0.00570*	0.00640	0.0121*	0.00434
	Δ(Oil(−1))	0.00238	−0.00927***	0.000103	0.00295	0.0159***
Long run	CPI(−1)	0.00193***	0.000901*	0.00174*	0.000396	0.00212***
	Oil(−1)	3.01e-05	0.00103*	0.00294***	0.00146	0.000977
	R^2	0.748	0.772	0.358	0.158	0.612
	F statistic	20.92***	13.96***	27.78***	7.59***	38.22***
Panel B: Supply shock
Short run	Δ(CPI(−1))	0.589***	0.685***	0.205***	0.229***	0.301***
	Δ(S)	2.67e-05	−0.00590***	0.00264	0.00203	0.00446**
	Δ(S(−1))	0.000692	0.00113	−0.00756**	0.00396	−0.00304
Long run	CPI(−1)	0.00191***	0.00170***	0.00396***	0.00143***	0.00284***
	S(−1)	0.00173	−0.0111***	0.0150**	0.000151	0.0160***
	R^2	0.747	0.769	0.356	0.143	0.606
	F statistic	20.28***	17.48***	27.40***	6.71***	42.81***
Panel C: Demand shock
Short run	Δ(CPI(−1))	0.582***	0.706***	0.227***	0.229***	0.348***
	Δ(D)	0.00193	0.00232	0.00416	0.00846	−0.00510
	Δ(D(−1))	−0.00129	0.00549*	0.00286	−0.00501	−0.00805**
Long run	CPI(−1)	0.00196***	0.00158***	0.00382***	0.0015***	0.00266***
	D(−1)	0.00760	−0.00266	−0.00805	0.0194*	0.00883
	R^2	0.748	0.756	0.346	0.148	0.576
	F statistic	21.48***	11.22***	23.71***	8.34***	32.51***
Panel D: Risk shock
Short run	Δ(CPI(−1))	0.588***	0.704***	0.224***	0.226***	0.351***
	Δ(R)	−0.000338	0.000523	−0.00280	0.00265	−3.76e-05
	Δ(R(−1))	−0.000371	−0.000961	0.00112	0.00237	0.00150
Long run	CPI(−1)	0.00191***	0.00162***	0.00384***	0.0014***	0.00263***
	R(−1)	−0.00167	0.00272*	−0.00234	−0.00301	−0.00160
	R^2	0.750	0.756	0.347	0.165	0.564
	F statistic	20.64***	12.59***	23.76***	7.58***	30.63***

Note: Significant at 10% (*), 5% (**), and 1% (***). The F-statistic is calculated by the Wald test (with H₀: ${\theta }_1={\theta }_2=0$) and compared with the upper bound critical value. Source: Authors’ calculation.

Table 7. NARDL results

	Regressors	Regressand Δ(CPI)
		Brazil	Russia	India	China	South Africa
Panel A: Oil price
Short run	Δ(CPI(−1))	0.579***	0.643***	0.188***	0.208***	0.296***
	Δ(Oil^−)	0.00332	−0.00779	0.0254**	0.0305***	0.00597
	Δ(Oil^−(−1))	−0.000667	−0.0156***	−0.0164	−0.00242	0.0130**
	Δ(Oil^+)	0.00342	−0.00175	−0.0162	−0.0146	0.00336
	Δ(Oil^+(−1))	0.00773	0.00146	0.0185	0.00347	0.0199***
Long run	CPI(−1)	0.00203**	0.00325**	0.00130	0.00163	0.00214**
	Oil^−(−1)	−0.000259	0.000618	0.00360**	0.00192	0.000958
	Oil^+(−1)	−0.000308	5.60e-05	0.00394***	0.00191	0.00101
	R^2	0.749	0.777	0.374	0.176	0.612
	F statistic	6.86***	3.42**	9.37***	4.60***	11.97***
	Wald_short	0.35	1.50	1.76	2.14*	1.26
	Wald_long	0.06	2.11	0.33	0.00	0.05
Panel B: Supply shock
Short run	Δ(CPI(−1))	0.577***	0.641***	0.211***	0.199***	0.297***
	Δ(S^−)	0.00244	−0.00843***	−0.00650	0.0181***	0.00538
	Δ(S^−(−1))	−0.000365	0.00173	−0.00431	0.00230	0.00224
	Δ(S^+)	−0.00211	−0.00524**	0.00277	−0.00716	0.00428
	Δ(S^+(−1))	0.00236	0.00179	−0.00528	0.00753	−0.00475*
Long run	CPI(−1)	0.00288*	−0.00401	0.000685	0.00198	0.00808***
	S^−(−1)	0.000258	−0.0132***	0.00623	−0.00182	0.0154***
	S^+(−1)	0.000154	−0.0127***	0.00669	−0.00178	0.0150***
	R^2	0.748	0.779	0.352	0.177	0.604
	F statistic	8.07***	11.58***	9.10***	5.38***	20.54***
	Wald_short	0.67	4.19***	0.57	3.50**	2.43*
	Wald_long	0.42	2.30	1.02	0.09	5.69**
Panel C: Demand shock
Short run	Δ(CPI(−1))	0.575***	0.671***	0.228***	0.203***	0.333***
	Δ(D^−)	0.00388	−0.00370	0.00175	0.0173**	−4.82e-05
	Δ(D^−(−1))	−0.00183	0.00432	−3.56e-06	0.00186	−0.00327
	Δ(D^+)	0.000721	0.0123***	0.0148*	0.00231	−0.00803
	Δ(D^+(−1))	−0.000946	0.000600	−0.00572	−0.0122	−0.0142***
Long run	CPI(−1)	0.000269	−0.000960	−0.00383	−0.00115	0.00116
	D^−(−1)	0.00842*	0.00487	0.00600	0.0229**	0.0111*
	D^+(−1)	0.00860*	0.00516	0.00718	0.0232**	0.0113*
	R^2	0.750	0.764	0.353	0.168	0.588
	F statistic	10.21***	3.41**	8.50***	6.97***	19.98***
	Wald_short	0.51	2.07	1.09	2.85**	2.24*
	Wald_long	0.42	0.25	2.80*	1.43	0.57
Panel D: Risk shock
Short run	Δ(CPI(−1))	0.586***	0.656***	0.225***	0.221***	0.342***
	Δ(R^−)	0.000720	−0.00208	−0.00640**	0.00187	0.000483
	Δ(R^−(−1))	−0.00181	−0.00123	0.00624**	0.00373	0.00240
	Δ(R^+)	−0.00125	0.00252*	0.000298	0.00344	−0.000528
	Δ(R^+(−1))	0.00128	0.000467	−0.00498	0.000731	−9.09e-05
Long run	CPI(−1)	0.00241**	0.00291	0.00522*	0.00156	0.00364***
	R^−(−1)	−0.00162	0.00135	−0.00223	−0.00285	−0.00104
	R^+(−1)	−0.00166	0.00124	−0.00227	−0.00284	−0.00107
	R^2	0.753	0.764	0.363	0.166	0.566
	F statistic	6.80***	1.31	8.37***	2.36*	12.20***
	Wald_short	0.96	2.20*	2.83**	0.19	0.81
	Wald_long	0.60	1.02	0.08	0.03	0.33

Note: Significant at 10% (*), 5% (**), and 1% (***). The F-statistic is calculated by the Wald test (with H₀: ${\theta }_1={\theta }_2={\theta }_3=0$) and compared with the upper bound critical value. Wald_short and Wald_long, respectively, represent the F-statistics used by the Wald test to assess asymmetry in the short run (with H₀: ${\phi }_{2\mathrm{i}}={\phi }_{3\mathrm{i}}$) and long run (with H₀: ${\theta }_2={\theta }_3$). Source: Authors’ calculation.

Table 8. MTNARDL (two thresholds) results

	Regressors	Regressand Δ(CPI)
		Brazil	Russia	India	China	South Africa
Panel A: Oil price
Short run	Δ(CPI(−1))	0.569***	0.643***	0.186***	0.189***	0.270***
	Δ(Oil($\mathrm{\Phi }1$))	0.00267	−0.00836	0.0261**	0.0267***	0.00487
	Δ(Oil($\mathrm{\Phi }1$) (−1))	0.00130	−0.0156***	−0.0156	−0.00351	0.0149**
	Δ(Oil($\mathrm{\Phi }2$))	0.00878	0.0198	−0.0240	0.0731*	0.00570
	Δ(Oil($\mathrm{\Phi }2$) (−1))	−0.0164	−0.000724	−0.00192	0.0321	−0.00191
	Δ(Oil($\mathrm{\Phi }3$))	0.00351	−0.00256	−0.0166	−0.0137	0.00463
	Δ(Oil($\mathrm{\Phi }3$) (−1))	0.00710	0.00189	0.0173	0.00315	0.0209***
Long run	CPI(−1)	0.00410**	0.00229	0.00137	−0.00102	0.00523***
	Oil($\mathrm{\Phi }1$) (−1)	−0.000286	0.000603	0.00361**	0.00279**	0.000822
	Oil($\mathrm{\Phi }2$) (−1)	−0.00401	0.00101	0.00470	0.00884*	−0.00586*
	Oil($\mathrm{\Phi }3$) (−1)	−0.000183	9.59e-05	0.00383***	0.00209	0.00133*
	R^2	0.752	0.778	0.376	0.194	0.621
	F statistic	5.72***	2.04*	7.03***	2.70**	9.76***
	Wald_short	0.52	1.12	1.18	2.28**	1.07
	Wald_long	0.82	0.94	0.09	0.85	2.26
Panel B: Supply shock
Short run	Δ(CPI(−1))	0.575***	0.646***	0.216***	0.197***	0.293***
	Δ(S($\mathrm{\Phi }1$))	0.00173	−0.00839***	−0.00600	0.0176***	0.00483
	Δ(S($\mathrm{\Phi }1$) (−1))	0.000312	0.00157	−0.00295	0.00283	0.00113
	Δ(S($\mathrm{\Phi }2$))	0.00218	0.00504	0.0164	0.00530	0.00532
	Δ(S($\mathrm{\Phi }2$) (−1))	−0.00574	0.00586	−0.00228	0.0240	−0.00802
	Δ(S($\mathrm{\Phi }3$))	−0.00161	−0.00591***	0.00126	−0.00739*	0.00459*
	Δ(S($\mathrm{\Phi }3$) (−1))	0.00207	0.00176	−0.00513	0.00710	−0.00415
Long run	CPI(−1)	0.00308*	−0.00320	−0.000707	0.00116	0.00831***
	S($\mathrm{\Phi }1$) (−1)	0.000689	−0.0132***	0.00447	−0.00369	0.0161***
	S($\mathrm{\Phi }2$) (−1)	−0.000436	−0.0135***	0.0101	0.00208	0.0124***
	S($\mathrm{\Phi }3$) (−1)	0.000447	−0.0127***	0.00567	−0.00303	0.0153***
	R^2	0.749	0.781	0.358	0.189	0.606
	F statistic	6.72***	9.56	8.20***	4.83***	16.27***
	Wald_short	0.51	2.96**	0.51	2.63**	1.47
	Wald_long	0.29	0.94	1.15	0.64	3.04**
Panel C: Demand shock
Short run	Δ(CPI(−1))	0.559***	0.677***	0.238***	0.206***	0.329***
	Δ(D($\mathrm{\Phi }1$))	0.00301	−0.00399	−0.000426	0.0170**	−0.00231
	Δ(D($\mathrm{\Phi }1$) (−1))	−0.00142	0.00438	0.000499	0.00151	−0.00306
	Δ(D($\mathrm{\Phi }2$))	−0.000983	0.0237	0.0348	−0.00553	0.00803
	Δ(D($\mathrm{\Phi }2$) (−1))	−0.00255	−0.00910	0.00115	0.00819	−0.0195
	Δ(D($\mathrm{\Phi }3$))	0.00237	0.0107***	0.0148*	0.00358	−0.00623
	Δ(D($\mathrm{\Phi }3$) (−1))	−0.00281	0.000783	−0.00808	−0.0117	−0.0162***
Long run	CPI(−1)	0.000335	−0.000404	−0.00419	−0.00133	0.000714
	D($\mathrm{\Phi }1$) (−1)	0.0102**	0.00405	0.00591	0.0227**	0.0127**
	D($\mathrm{\Phi }2$) (−1)	0.000904	0.00799	0.00194	0.0200	0.00453
	D($\mathrm{\Phi }3$) (−1)	0.0106**	0.00421	0.00741	0.0231**	0.0132**
	R^2	0.753	0.765	0.358	0.170	0.593
	F statistic	9.00	3.09**	6.93***	5.30***	16.14***
	Wald_short	0.42	1.59	0.91	1.73	1.67
	Wald_long	1.75	0.29	1.49	0.76	1.12
Panel D: Risk shock
Short run	Δ(CPI(−1))	0.586***	0.657***	0.228***	0.221***	0.330***
	Δ(R($\mathrm{\Phi }1$))	0.000284	−0.00220	−0.00703**	0.00231	0.000275
	Δ(R($\mathrm{\Phi }1$) (−1))	−0.00127	−0.000856	0.00694***	0.00277	0.00251*
	Δ(R($\mathrm{\Phi }2$))	0.00290	0.00418	0.00189	−0.00388	−0.00510
	Δ(R($\mathrm{\Phi }2$) (−1))	−0.000561	0.00171	−0.00363	0.0184***	−0.000881
	Δ(R($\mathrm{\Phi }3$))	−0.00104	0.00225*	7.63e-05	0.00315	−9.34e-05
	Δ(R($\mathrm{\Phi }3$) (−1))	0.000640	1.35e-05	−0.00511*	0.000451	8.73e-05
Long run	CPI(−1)	0.00234*	0.00228	0.00392	6.06e-05	0.00360***
	R($\mathrm{\Phi }1$) (−1)	−0.00154	0.00122	−0.00277	−0.00316	−0.00129
	R($\mathrm{\Phi }2$) (−1)	−0.00147	0.00179	−0.00158	−0.000932	−0.00137
	R($\mathrm{\Phi }3$) (−1)	−0.00157	0.00112	−0.00279	−0.00315	−0.00132
	R^2	0.753	0.767	0.376	0.208	0.569
	F statistic	6.44	2.03*	8.21***	2.73**	11.31***
	Wald_short	0.54	1.64	2.60**	1.84	0.85
	Wald_long	0.32	1.33	0.47	1.22	0.15

Note: Significant at 10% (*), 5% (**), and 1% (***). The F-statistic is calculated by the Wald test (with H₀: ${\theta }_1={\theta }_2={\theta }_3={\theta }_4=0$) and is compared with the upper bound critical value. Wald_short and Wald_long, respectively, represent the F-statistics used by the Wald test to assess asymmetry in the short run (with H₀: ${\phi }_{2\mathrm{i}}={\phi }_{3\mathrm{i}}={\phi }_{4\mathrm{i}}$) and long run (with H₀: ${\theta }_2={\theta }_3={\theta }_4$). Source: Authors’ calculation.

Table 9. MTNARDL (four thresholds) results

	Regressors	Regressand Δ(CPI)
		Brazil	Russia	India	China	South Africa
Panel A: Oil price
Short run	Δ(CPI(−1))	0.540***	0.626***	0.198***	0.182***	0.268***
	Δ(Oil($\mathrm{\Phi }1$))	−0.000714	−0.00842	0.0299**	0.0259**	0.00463
	Δ(Oil($\mathrm{\Phi }1$) (−1))	−0.00182	−0.0177***	−0.0215*	−0.00553	0.0136**
	Δ(Oil($\mathrm{\Phi }2$))	−0.0729***	−0.00954	0.0854	0.0479	0.0174
	Δ(Oil($\mathrm{\Phi }2$) (−1))	−0.00580	−0.0373	−0.131**	0.0249	0.00612
	Δ(Oil($\mathrm{\Phi }3$))	0.0475	0.0188	−0.214**	0.204**	−0.0162
	Δ(Oil($\mathrm{\Phi }3$) (−1))	0.0342	0.0618	0.0918	0.0960	0.0658
	Δ(Oil($\mathrm{\Phi }4$))	0.0363**	−0.00317	−0.0204	0.0256	0.0128
	Δ(Oil($\mathrm{\Phi }4$) (−1))	0.00680	0.00719	0.0487	0.0216	0.0134
	Δ(Oil($\mathrm{\Phi }5$))	0.0119*	−0.000922	−0.0299*	−0.0181	0.00469
	Δ(Oil($\mathrm{\Phi }5$) (−1))	0.0123*	0.00745	0.0293*	0.00301	0.0280***
Long run	CPI(−1)	0.000973	−6.01e-05	0.00174	−0.00187	0.00379*
	Oil($\mathrm{\Phi }1$) (−1)	−0.000651	0.000315	0.00348**	0.00334**	0.000847
	Oil($\mathrm{\Phi }2$) (−1)	−0.0111*	−0.00914	0.00769	0.00744	−0.0149*
	Oil($\mathrm{\Phi }3$) (−1)	−0.0159	−0.0146	0.00341	0.0142	−0.0257**
	Oil($\mathrm{\Phi }4$) (−1)	−0.00206	0.00295	0.00664	0.00733	−0.00183
	Oil($\mathrm{\Phi }5$) (−1)	−0.000320	−0.000754	0.00348*	0.00184	0.00132
	R^2	0.765	0.781	0.397	0.222	0.631
	F statistic	2.16**	0.88	3.15***	1.62	4.85***
	Wald_short	1.52	0.72	1.60	2.12**	0.91
	Wald_long	1.34	0.77	0.09	0.74	2.20*
Panel B: Supply shock
Short run	Δ(CPI(−1))	0.575***	0.633***	0.179***	0.179***	0.259***
	Δ(S($\mathrm{\Phi }1$))	0.00331	−0.00968***	−0.00708	0.0185***	0.00677*
	Δ(S($\mathrm{\Phi }1$) (−1))	0.000405	0.00189	0.000268	−0.00328	0.000390
	Δ(S($\mathrm{\Phi }2$))	−0.00406	0.000390	−0.00425	0.0148	0.0113
	Δ(S($\mathrm{\Phi }2$) (−1))	0.00381	0.00569	−0.0139	0.0156	−0.000225
	Δ(S($\mathrm{\Phi }3$))	0.00473	−0.0164	−0.0174	0.00700	0.00710
	Δ(S($\mathrm{\Phi }3$) (−1))	−0.000807	0.0378*	0.0484	−0.0742*	−0.0607***
	Δ(S($\mathrm{\Phi }4$))	−0.00686	0.000459	0.0238	0.0155	0.0121
	Δ(S($\mathrm{\Phi }4$) (−1))	−0.00621	−0.00134	−0.0313	0.0421**	−0.00298
	Δ(S($\mathrm{\Phi }5$))	−0.00163	−0.00567**	0.00554	−0.00650	0.00451*
	Δ(S($\mathrm{\Phi }5$) (−1))	0.00165	0.00120	−0.0104**	0.00811*	−0.00480*
Long run	CPI(−1)	0.00295	−0.00511	−0.00200	−0.00180	0.00471**
	S($\mathrm{\Phi }1$) (−1)	0.000661	−0.0124***	0.0125*	−0.00193	0.0180***
	S($\mathrm{\Phi }2$) (−1)	0.00137	−0.0135***	0.0176**	−0.00287	0.0200***
	S($\mathrm{\Phi }3$) (−1)	0.00316	−0.0129*	0.0283**	0.0195*	0.0242***
	S($\mathrm{\Phi }4$) (−1)	0.00134	−0.0104***	0.0205**	−0.000112	0.0234***
	S($\mathrm{\Phi }5$) (−1)	0.000745	−0.0127***	0.0139**	−0.00110	0.0173***
	R^2	0.753	0.787	0.392	0.231	0.631
	F statistic	3.15***	5.66***	4.90***	1.64	8.66***
	Wald_short	0.57	1.81*	1.03	2.55***	2.12**
	Wald_long	0.36	1.03	2.62**	1.43	3.27**
Panel C: Demand shock
Short run	Δ(CPI(−1))	0.569***	0.664***	0.248***	0.221***	0.302***
	Δ(D($\mathrm{\Phi }1$))	0.00180	−0.00449	0.00209	0.0185**	−0.00415
	Δ(D($\mathrm{\Phi }1$) (−1))	−0.00106	0.00426	−0.00534	−0.00305	−0.00271
	Δ(D($\mathrm{\Phi }2$))	0.00369	0.00218	0.0232	0.0100	0.0266*
	Δ(D($\mathrm{\Phi }2$) (−1))	−0.00675	−0.0111	−0.00625	0.000145	0.00251
	Δ(D($\mathrm{\Phi }3$))	0.0726*	0.0283	−0.141	0.0212	0.0667
	Δ(D($\mathrm{\Phi }3$) (−1))	−0.0160	0.00817	0.250***	−0.0368	0.0247
	Δ(D($\mathrm{\Phi }4$))	−0.00245	0.0153	0.0313	−0.0307	−0.0106
	Δ(D($\mathrm{\Phi }4$) (−1))	0.00414	−0.00533	0.0316	0.0295	−0.00306
	Δ(D($\mathrm{\Phi }5$))	0.000387	0.0122***	0.00771	0.00264	−0.0112**
	Δ(D($\mathrm{\Phi }5$) (−1))	−0.00145	0.00228	−0.00198	−0.0128	−0.0161***
Long run	CPI(−1)	−0.000369	−0.00233	−0.00467	−0.000873	0.000587
	D($\mathrm{\Phi }1$) (−1)	0.00600	0.00488	0.00164	0.0238**	0.00573
	D($\mathrm{\Phi }2$) (−1)	0.00678	0.00803	0.00210	0.0214*	0.0112*
	D($\mathrm{\Phi }3$) (−1)	0.00729	0.00873	0.0153	0.0226	0.0159
	D($\mathrm{\Phi }4$) (−1)	0.00474	0.00891	0.00233	0.0246**	0.00643
	D($\mathrm{\Phi }5$) (−1)	0.00711	0.00512	0.00302	0.0230**	0.00769
	R^2	0.756	0.768	0.390	0.198	0.607
	F statistic	3.32***	1.38	2.74**	1.91*	7.58***
	Wald_short	0.58	1.09	1.62	1.76*	1.75*
	Wald_long	0.55	0.53	0.83	0.44	0.78
Panel D: Risk shock
Short run	Δ(CPI(−1))	0.589***	0.649***	0.188***	0.221***	0.329***
	Δ(R($\mathrm{\Phi }1$))	0.00115	−0.00207	−0.00586*	0.000992	0.00103
	Δ(R($\mathrm{\Phi }1$) (−1))	−0.00211*	−0.00151	0.00500*	0.00238	0.00205
	Δ(R($\mathrm{\Phi }2$))	−0.000165	−0.00657	−0.00144	−0.0119	0.00529
	Δ(R($\mathrm{\Phi }2$) (−1))	−0.00413	−0.00102	−0.00294	0.0127*	−0.00346
	Δ(R($\mathrm{\Phi }3$))	0.00780	0.00732	0.0104	−0.000301	0.00249
	Δ(R($\mathrm{\Phi }3$) (−1))	−0.0152*	0.00315	0.0204	0.0178	0.00269
	Δ(R($\mathrm{\Phi }4$))	−0.00380	0.00298	−0.00472	0.00578	−0.00262
	Δ(R($\mathrm{\Phi }4$) (−1))	0.00414	0.000400	−0.00308	0.00596	0.000714
	Δ(R($\mathrm{\Phi }5$))	−0.000908	0.00281*	−0.00110	0.00460*	−0.000938
	Δ(R($\mathrm{\Phi }5$) (−1))	0.00131	0.000470	−0.00317	0.000223	0.000580
Long run	CPI(−1)	0.00179	0.000202	−0.000626	−0.00272	0.00546*
	R($\mathrm{\Phi }1$) (−1)	−0.00135	0.00148	−0.00247	−0.00339	−0.000536
	R($\mathrm{\Phi }2$) (−1)	−0.00140	0.00109	−0.00370	−0.00395	−0.000768
	R($\mathrm{\Phi }3$) (−1)	−0.000231	0.000589	−0.00322	0.00615	−0.00625
	R($\mathrm{\Phi }4$) (−1)	−0.00183	0.00179	−0.000581	−0.00333	−0.000431
	R($\mathrm{\Phi }5$) (−1)	−0.00121	0.00125	−0.00341	−0.00366	−0.000690
	R^2	0.762	0.767	0.394	0.215	0.577
	F statistic	2.24**	0.68	4.51***	1.16	4.49***
	Wald_short	1.18	0.91	1.17	1.10	0.57
	Wald_long	0.27	0.50	2.26*	0.97	0.69

Note: Significant at 10% (*), 5% (**), and 1% (***). The F-statistic is calculated by the Wald test (with H₀: ${\theta }_1={\theta }_2={\theta }_3={\theta }_4={\theta }_5={\theta }_6=0$) and is compared with the upper bound critical value. Wald_short and Wald_long, respectively, represent the F-statistics used by the Wald test to assess asymmetry in the short run (with H₀:${\phi }_{2\mathrm{i}}={\phi }_{3\mathrm{i}}={\phi }_{4\mathrm{i}}={\phi }_{5\mathrm{i}}={\phi }_{6\mathrm{i}}$) and long run (with H₀: ${\theta }_2={\theta }_3={\theta }_4={\theta }_5={\theta }_6$). Source: Authors’ calculation.

Table 10. Test statistic to ascertain the strength of the cointegrated relationship

Country	ARDL	NARDL	MTNARDL 2 thresholds	MTNARDL 4 thresholds	Strength of relationship
Panel A: Oil price
Brazil	20.92***	6.86***	5.72***	2.16**	Very strong
Russia	13.96***	3.42**	2.04*	0.88	Weak
India	27.78***	9.37***	7.03***	3.15***	Very strong
China	7.59***	4.60***	2.70**	1.62	Strong
South Africa	38.22***	11.97***	9.76***	4.85***	Very strong
Panel B: Supply shock
Brazil	20.28***	8.07***	6.72***	3.15***	Very strong
Russia	17.48***	11.58***	9.56	5.66***	Strong
India	27.40***	9.10***	8.20***	4.90***	Very strong
China	6.71***	5.38***	4.83***	1.64	Strong
South Africa	42.81***	20.54***	16.27***	8.66***	Very strong
Panel C: Demand shock
Brazil	21.48***	10.21***	9	3.32***	Strong
Russia	11.22***	3.41**	3.09**	1.38	Strong
India	23.71***	8.50***	6.93***	2.74**	Very strong
China	8.34***	6.97***	5.30***	1.91*	Strong
South Africa	32.51***	19.98***	16.14***	7.58***	Very strong
Panel D: Risk shock
Brazil	20.64***	6.80***	6.44	2.24**	Strong
Russia	12.59***	1.31	2.03*	0.68	Weak
India	23.76***	8.37***	8.21***	4.51***	Very strong
China	7.58***	2.36*	2.73**	1.16	Weak
South Africa	30.63***	12.20***	11.31***	4.49***	Very strong

Note: Significant at 10% (*), 5% (**), and 1% (***). Source: Authors’ calculation.

Table 11. Test statistic to ascertain the asymmetry strength in the short and long run

Country	NARDL	MTNARDL 2 thresholds	MTNARDL 4 thresholds	Strength of asymmetry		NARDL	MTNARDL 2 thresholds	MTNARDL 4 thresholds	Strength of asymmetry
	Short run					Long run
Panel A: Oil price
Brazil	0.35	0.52	1.52	Nil		0.06	0.82	1.34	Nil
Russia	1.50	1.12	0.72	Nil		2.11	0.94	0.77	Nil
India	1.76	1.18	1.6	Nil		0.33	0.09	0.09	Nil
China	2.14*	2.28**	2.12**	Strong		0.00	0.85	0.74	Nil
South Africa	1.26	1.07	0.91	Nil		0.05	2.26	2.20*	Nil
Panel B: Supply shock
Brazil	0.67	0.51	0.57	Nil		0.42	0.29	0.36	Nil
Russia	4.19***	2.96**	1.81*	Strong		2.3	0.94	1.03	Nil
India	0.57	0.51	1.03	Nil		1.02	1.15	2.62**	Weak
China	3.50**	2.63**	2.55***	Strong		0.09	0.64	1.43	Nil
South Africa	2.43*	1.47	2.12**	Weak		5.69**	3.04**	3.27**	Strong
Panel C: Demand shock
Brazil	0.51	0.42	0.58	Nil		0.42	1.75	0.55	Nil
Russia	2.07	1.59	1.09	Nil		0.25	0.29	0.53	Nil
India	1.09	0.91	1.62	Nil		2.80*	1.49	0.83	Nil
China	2.85**	1.73	1.76*	Weak		1.43	0.76	0.44	Nil
South Africa	2.24*	1.67	1.75*	Weak		0.57	1.12	0.78	Nil
Panel D: Risk shock
Brazil	0.96	0.54	1.18	Nil		0.6	0.32	0.27	Nil
Russia	2.20*	1.64	0.91	Nil		1.02	1.33	0.5	Nil
India	2.83**	2.60**	1.17	Weak		0.08	0.47	2.26*	Nil
China	0.19	1.84	1.1	Nil		0.03	1.22	0.97	Nil
South Africa	0.81	0.85	0.57	Nil		0.33	0.15	0.69	Nil

Note: Significant at 10% (*), 5% (**), and 1% (***). Source: Authors’ calculation.