On the stability of the money multiplier in Nigeria: Co-integration analyses with regime shifts in banking system liquidity

Figures & data

Figure 1. Plots of base money (mb) and broad money (m2).

Table 1. The Perron and Yabu (2009) test for structural break

Series	Model	WRQF	Break
LMB	Intercept	3.313	2012M06
	Slope	1.011	2010M09
	Both	7.909	2011M09
LM2	Intercept	23.152	2007M02
	Slope	2.030	2009M10
	Both	38.030	2008M01

Table 2. Unit root with a structural break in both the intercept and trend

Panel A: Zivot–Andrews
Variables	t-statistics^*	Break point
Log-levels
M2	−2.37211	2008M03
MB	−3.22113	2013M07
Log-differences
M2	−10.52881	2006M03
MB	−9.945609	2013M07
Panel B: Harvey–Leybourne–Taylor (2013)
Variables	MDF statistics	Break point
Log-levels
M2	−2.371567	2009M08
MB	−3.280699	2008M12
Log-differences
M2	−8.178207	2008M12
MB	−6.915647	2009M01

* The critical values for Zivot–Andrews test are −5.57, −5.08, and 4.82 at 1%, 5%, and 10% levels of significance, respectively, while the critical values for Harvey–Leybourne–Taylor are −4.02, −3.49, and −3.20 at 1%, 5%, and 10% levels of significance, respectively.

Figure 2. Plots of estimated timing of structural breaks.

Table 3. Gregory-Hansen co-integration test results

Model specification	Testing procedure	Test statistic	5% critical value^*	Break point
Level and regime shifts
	ADF^*	−7.95^**	−6.00	2009M11
	Zt^*	−7.96^**	−6.00	2009M11
	Zα^*	−89.43^**	−68.94	2009M11

* Critical values were obtained from Gregory and Hansen (1996).

** Statistical significance at the 5% level.

Table 4. Arai–Kurozumi co-integration test results for level and regime shifts

Break date	2009M04
Break fraction	0.421
L4	0.134^*
L12	0.069
La	2.985^**
P(L4)	0.058
P(L12)	0.045
P(La)	2.613^**

Note: P(z) refers to prewhitened statistics.

* Level of significance at 5%.

** Level of significance at 1%.

Table 5. Estimated conditional and marginal models

Panel A: Conditional model
Variable	Coefficient	Prob.^*
C	0.767967	0.0520
LM2(−1)	−0.046761	0.1241
LMB(−1)	−0.063456	0.0792
Trend	0.001734	0.0879
DLM2(−1)	−0.167762	0.0442
DLM2(−8)	−0.165705	0.0369
DLMB(−5)	−0.109864	0.0259
Panel B: Marginal model
Variable^*	Coefficient	Prob.
C	0.015223	0.0000
AR(1)	−0.418922	0.0000
AR(2)	−0.314910	0.0006
AR(3)	−0.294307	0.0015
AR(4)	−0.174160	0.0739
AR(5)	−0.028819	0.7293
AR(6)	−0.065572	0.4418
AR(7)	0.060159	0.5093
SIGMASQ	0.006833	0.0000

^* Optimal DW statistic is 1.9989.

Figure 3. Recursive estimate of the MB parameter in the conditional model.

Figure 4. Recursive residual estimate of the conditional model.

Table 6. Multiple breakpoint test (Bai & Perron, 2003) of the conditional model

Sequential F-statistic determined breaks: 2
Break test	F-statistic	Scaled F-statistic	Critical value^**
0 vs. 1^*	12.30849	86.15945	21.87
1 vs. 2^*	3.636783	25.45748	24.17
2 vs. 3	1.096975	7.678826	25.13
Break dates	Sequential	Repartition
1	2006M04	2006M03
2	2008M01	2008M01

^* Significant at the 0.05 level.

^** Bai-Perron (Econometric Journal, 2003) critical values.

Table 7. Quandt–Andrews unknown breakpoint test for the marginal model

Statistic	Value	Prob.
Maximum LR F-statistic (2009M06)	1.921757	0.4049
Maximum Wald F-statistic (2005M02)	46.15305	0.0000
Exp LR F-statistic	0.404148	0.8855
Exp Wald F-statistic	18.59905	0.0000
Ave LR F-statistic	0.784216	0.7352
Ave Wald F-statistic	17.56240	0.0083

Perron, P., & Yabu, T., (2009). Testing for shifts in trend with an integrated or stationary noise component. Journal of Business and Economic Statistics, 27, 369–396.

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Gregory, A. W., & Hansen, B. E. (1996). Residual-based tests for cointegration in models with regime shifts. Journal of Econometrics, 70, 99–126.10.1016/0304-4076(69)41685-7

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Bai, J., & Perron, P. (2003). Computation and analysis of multiple structural change models. Journal of Applied Econometrics, 18(1), 1–22

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