Asymmetric cointegration between exchange rate and trade balance in Nigeria

Figures & data

Figure 1. Official US dollar - Nigerian naira exchange rates, January 1999–December, 2013.

Figure 2. Trade balance in domestic currency, January 1999–December, 2013.

Figure 3. Crude oil price in US dollars, January 1999–December, 2013.

Table 1. ADF unit root tests for trade balance and exchange rates

Variables		LTBt	∆LTBt	LEXt	∆LEXt
		−2.65(3)	−12.40^***(2)	−2.41(1)	−7.88^***(1)
Critical values	1%	−3.47	−3.47	−3.47	−3.47
	5%	−2.88	−2.88	−2.88	−2.88
	10%	−2.58	−2.58	−2.58	−2.58

Notes: To allow for representation of alternative hypotheses, we include both a constant term and linear time trends in levels of the variables, while at their first difference, only a constant term is included. Numbers in parentheses are lag lengths used in the ADF test (as determined by HQC) to remove serial correlation in the residuals.

^*** Rejection of the null hypothesis at the 1% significant level.

Source: Own results.

Table 2. Estimated Eagle–Granger, TAR and MTAR cointegration tests

	(1)ADF	(2)TAR	(3)MTAR	(4)TAR-consistent	(5)MTAR-consistent
ρ0^a	−2.61^***(−2.58)	–	–	–	–
ρ1^a	–	−.275 (−2.021)	−.369 (−2.770)	−.246 (−2.013)	−.274 (−2.543)
ρ2^a	–	−.420 (−3.63)	−.359 (−3.01)	−.487 (−3.89)	−.566 (−3.94)
λ1	–	−.490 (−4.74)	−.501 (−4.81)	−.467 (−4.48)	−.429 (−3.94)
λ2	–	−.133 (−1.61)	−.135 (−1.64)	−.130 (−1.59)	−.118 (−1.43)
Φμ	–	7.213^**	6.272^**	8.118^**	8.621^**
ρ1 = ρ2^s	–	.895	.004	2.555	3.476^**
τ	–	0	0	.164	−.205

Notes: Entries of Φ_μ represent the F-statistics that follows a non-standard distribution of the sample values for the null hypothesis ρ₁ = ρ₂ = 0. S Entries represent the sample F-statistics for the null hypothesis of symmetric adjustment ρ₁ = ρ₂ and, τ denotes threshold values.

^a Entries in parentheses are the t-statistics for the null hypothesis of the ρ_i values.

^** Level of significance level at 5%.

^*** Level of significance at 1%.

Source: Own results.

Table 3. Estimated asymmetric error correction models

	ΔLTBt	ΔLEXt
λ^+ coefficient	−.417^*** (−4.476)	−.010 (−1.206)
λ^− coefficient	−1.117^***(−4.146)	−.012 (−.439)
ϖi = 0	18.56ⱳ1 [.000]	22.85 [.000]
γi = 0	12.46ⱳ1 [0.00]	.45 [.501]
R^2	.50	.145
DW- statistic	2.13	1.88
Serial correlation LM test	5.00Sc [.082]	4.61 [.100]
Hetroskedasticity test	.420H [.517]	27.06 [.000]
F-statistics	36.93 [.000]	6.265 [.000]

Notes: ⱳ1, Sc and H denote Wald, Breusch–Godfrey Chi-square values for serial correlation (set to a maximum of 2 lags as determined by HQC) and autoregressive conditional hetroskedasticity test values respectively. Figures in parentheses are t-statistics and numbers in curly brackets are probability values.

^*** Rejection of the null hypothesis at the 1% significance level.

Source: Own results.

Table 4. Estimated asymmetric error correction models

(a) Exchange rates and the trade balance dynamics (1999M01-2010M12)
$\mathrm{\Delta }LT{B}_t=\underset{(.557)}{.007}\underset{(-5.526)}{-.502{\mathit{\lambda }}^{+a}}\underset{(-2.834)}{-.881{\mathit{\lambda }}^{-a}}\underset{(-2.290)}{-.187\mathrm{\Delta }LT{B}_{t-1}^b}\underset{(-2.290)}{-.379\mathrm{\Delta }LE{X}_{t-1}^a}$
R^2 = 42	LM = 1.193(.167)
F-statistics = 25.37(.000)	ARCH = .527(.468)
(b) Exchange rates and the trade balance dynamics (1999M01-2013M12)
$\mathrm{\Delta }LT{B}_t=\underset{(.279)}{.013}\underset{(-3.837)}{-.320{\mathit{\lambda }}^{+a}}\underset{(-2.405)}{-.733{\mathit{\lambda }}^{-b}}\underset{(-5.327)}{-.495\mathrm{\Delta }LT{B}_{t-1}^a}\underset{(-2.791)}{-.257\mathrm{\Delta }LT{B}_{t-2}^a}\underset{(-2.713)}{-.189\mathrm{\Delta }LT{B}_{t-3}^a}\underset{(-3.340)}{-2.390\mathrm{\Delta }LE{X}_{t-1}^a}$
R^2= 49	LM = .004(.947)
F-statistics = 26.85(.000)	ARCH = .373(.541)
(c) Exchange rates, oil prices and the trade balance dynamics (1999M01-2013M12)
$\mathrm{\Delta }LT{B}_t=\underset{(.813)}{.009}\underset{(-3.672)}{-.314{\mathit{\lambda }}^{+a}}\underset{(-3.201)}{-1.010{\mathit{\lambda }}^{-a}}\underset{(-5.158)}{-.484\mathrm{\Delta }LT{B}_{t-1}^a}\underset{(-2.992)}{-.268\mathrm{\Delta }LT{B}_{t-2}^a}\underset{(-2.869)}{-.198\mathrm{\Delta }LT{B}_{t-3}^a}\underset{(-2.821)}{-1.99\mathrm{\Delta }LE{X}_{t-1}^a}\underset{(-1.840)}{+.226\mathrm{\Delta }Lo{p}_{t-1}^c}$
R^2 = 50	LM = .659(.417)
F-statistics = 24.35(.000)	ARCH = .197(.657)

Notes: ^{a, b} and ^c denote rejection of the null hypothesis at the 1, 5 and 10% significance levels. Figures in parentheses are p-values. LM and ARCH denote Breusch–Godfrey Chi-square values for serial correlation and autoregressive conditional hetroskedasticity test values respectively. Figures in parentheses are t-statistics and numbers in curly brackets are probability values.

Source: Own results.

Table

Variables		LTBt	∆LTBt	LEXt	∆LEXt
		−3.13	−10.94***	−2.71	−7.84***
Critical values	1%	−4.02	−4.02	−4.02	−4.02
	5%	−3.44	−3.44	−3.44	−3.44
	10%	−3.15	−3.15	−3.15	−3.15

Table

Variables		LTBt	∆LTBt	LEXt	∆LEXt	LOP	∆LOP
		−3.20	−13.05^***	−2.99	−8.90^***	−2.88	−11.27^***
Critical values	1%	−4.01	−4.01	−4.01	−4.01	−4.01	−4.01
	5%	−3.43	−3.43	−3.43	−3.43	−3.43	−3.43
	10%	−3.14	−3.14	−3.14	−3.14	−3.14	−3.14

Table

	(1) ADF	(2) TAR	(3) MTAR	(4) TAR-consistent	(5) MTAR-consistent
ρ0^a	−2.61*** (−2.58)	–	–	–	–
ρ1^a	–	−.202 (−1.49)	−.307 (−2.45)	−.210 (−1.92)	−.251 (−2.36)
ρ2^a	–	−.441 (−3.54)	−.351 (−2.85)	−.661 (−4.89)	−.661 (−4.54)
λ1	–	−.454 (−4.01)	−.481 (−4.20)	−.289 (−2.88)	−.289 (−2.79)
λ2	–	−.326 (−3.18)	−.149 (−1.68)	−.197 (−2.47)	−.204 (−2.54)
Φμ	–	6.55**	5.49*	12.47**	11.44**
ρ1 = ρ2^s	–	2.02	.071	8.22**	6.37**
τ	–	0	0	−.185	−.172

Table

	(1) ADF	(2) TAR	(3) MTAR	(4) TAR-consistent	(5) MTAR-consistent
ρ0^a	−3.31** (−2.88)	–	–	–	–
ρ1^a	–	−.260 (−2.21)	−.375 (−3.22)	−.234 (−2.40)	−.959 (−3.64)
ρ2^a	–	−.431 (−4.35)	−.355 (−3.46)	−.572 (−4.86)	−.344 (−4.18)
λ1	–	−.446 (−4.97)	−.466 (−5.10)	−.385 (−4.13)	−.419 (−4.68)
λ2	–	−.107 (−1.46)	−.112 (−1.53)	−.089 (−1.23)	−.072 (−.977)
Φμ	–	10.42**	9.58**	12.40**	12.71**
ρ1 = ρ2^s	–	1.53	.020	6.05**	5.66**
τ	–	0	0	−.214	.162

Table

	(1) ADF	(2) TAR	(3) MTAR	(4) TAR-consistent	(5) MTAR-consistent
ρ0^a	−3.28 (−2.88)	–	–	–	–
ρ1^a	–	−.254 (−2.14)	−.367 (−3.03)	−.247 (−2.42)	−.997 (−3.39)
ρ2^a	–	−.467 (−4.54)	−.387 (−3.73)	−.564 (−4.84)	−.375 (−4.43)
λ1	–	−.443 (−4.87)	−.464 (−5.06)	−.404 (−4.34)	−.409 (−4.41)
λ2	–	−.116 (−1.59)	−.121 (−1.66)	−.104 (−1.44)	−.083 (−1.12)
Φμ	–	11.07**	9.79**	12.74**	12.45**
ρ1 = ρ2^s	–	2.32	.021	5.32**	4.12**
τ	–	0	0	−.193	.167

Table

	Mean	Minimum	Maximum	Standard deviation	Observation
LTB	12.48	8.75	14.59	1.03	172
LEX	4.86	4.45	5.07	.152	172
LOP*	3.56	2.32	4.93	.622	172