Currency reform, currency biases and Ghana’s forex market fluctuations: Beyond the macroeconomic fundamentals

Figures & data

Table 1. Estimated bias from nominal exchange rate

Years	Actual Observation(1)	Subjective Value(2)	BIAS Error (B1)
2006	−0.087
2007	−0.067	−0.086	0.019
2008	0.056	−0.077	0.133
2009	0.343	−0.052	0.395
2010	0.358	−0.027	0.385
2011	0.413	−0.000	0.413
2012	0.585	0.034	0.551
2013	0.670	0.074	0.596
2014	1.065	0.134	0.931
2015	1.300	0.205	1.095
2016	1.363	0.276	1.087
2017	1.470	0.349	1.121
2018	1.523	0.420	1.103

Note: The table presents a forecasted bias based on the subjective values obtained from the subjective model and the actual data observations of the study variable (NER). The deviation between the two columns; the actual observations and the subjective values produce the expected bias values (last column). The data starts from 2007 because that is the year of redenomination policy adaptation. The bias for Nominal Exchange Rate is B₁.

Table 2. Estimated bias from Gross domestic product

Years	Actual Observation	Subjective Value	BIAS Error (B2)
2006	23.652
2007	23.865	23.652	0.213
2008	24.130	23.665	0.465
2009	24.323	23.693	0.630
2010	24.553	23.732	0.821
2011	24.815	23.782	1.033
2012	24.045	23.798	0.247
2013	25.541	23.904	1.637
2014	25.769	24.017	1.752
2015	25.918	24.133	1.785
2016	26.094	24.253	1.841
2017	26.271	24.375	1.896
2018	26.429	24.501	1.928

Note: The table presents a forecasted bias based on the subjective values obtained from the subjective model and the actual data observations of the study variable (GDP). The deviation between the two columns; the actual observations and the subjective values produce the expected bias values (last column). The data starts from 2007 because that is the year of redenomination policy adaptation. The bias for Gross Domestic Product is B₂.

Table 3. Estimated bias from fiscal deficit

Years	Actual Observation	Subjective Value	BIAS Error (B3)
2006	−4.710
2007	−5.590	−4.748	0.842
2008	−8.490	−4.800	3.690
2009	−5.820	−5.073	0.747
2010	−6.520	−5.161	1.359
2011	−4.010	−5.091	1.081
2012	−11.60	−5.487	6.113
2013	−7.650	−5.619	2.031
2014	−6.840	−5.693	1.147
2015	−4.860	−5.643	0.783
2016	−6.880	−5.549	1.331
2017	−5.540	−5.548	0.008
2018	−3.410	−5.418	2.008

Note: The table presents a forecasted bias based on the subjective values obtained from the subjective model and the actual data observations of the study variable (FD). The deviation between the two columns; the actual observations and the subjective values produce the expected bias values (last column). The data starts from 2007 because that is the year of redenomination policy adaptation. The bias for Fiscal Deficit is B₃.

Table 4. Stationarity test

Variables	Level		First difference		OI
	C	CT	C	CT
Elliott-Rothenberg-Stock DF-GLS test
LGDP	0.1960	−1.6595	−2.2714**	−3.4461**	I(1)
LER	−0.4772	−1.9489	−3.3067***	−4.0635***	I(1)
LREER	−0.9355	−1.9255	−5.0280***	−1.9417*	I(1)
LINF	−3.1530***	−5.4856***			I(0)
LTOT	−4.1770***	−4.8126***			I(0)
RIR	−3.7610***	−5.8295***			I(0)
FDEF	−4.1770***	−4.8126***			I(0)
B1	0.4412*	0.8972	−4.1714***	−4.9891	I(1)
B2	0.7304	−0.9191***			I(0)
B3	−3.8975***	−5.0778***			I(0)
Phillips-Peron test
LGDP	2.7734	−3.4109*	−3.4559**	−3.4935*	I(1)
LNER	−5.6094***	−2.0681			I(0)
LREER	−1.5295	−1.8621	−6.2827***	−6.8304***	I(1)
LINF	−3.5223**	−5.4417***			I(0)
LTOT	−1.8832	−3.0571	−6.8353***	−7.5745***	I(1)
RIR	−4.0807***	−5.7193***			I(0)
FDEF	−4.1856***	−4.7320***	−17.300***		I(0)
B1	0.5470	−1.1358	−3.6574***	−1.6275	I(1)
B2	−4.0633***	−4.1875**			I(0)
B3	−3.3044**	−2.8620			I(0)
Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test
LGDP	0.7448	0.2115	0.5284	0.1335***	I(1)
LNER	0.7304	0.2086	0.4913	0.0777***	I(1)
LREER	0.5769	0.1627	0.1276***	0.1030***	I(1)
LINF	0.7537	0.0844***			I(0)
LTOT	0.3103***	0.1852			I(0)
RIR	0.6051	0.0965***			I(0)
FDEF	0.4999	0.1414***			I(0)
B1	0.5678	0.2089	0.3532***	0.1781	I(1)
B2	0.4742	0.0963***			I(0)
B3	0.7642	0.1817	0.5489	0.0916***	I(1)
ADF Test
LGDP	0.8527	−2.8375	−3.5777**	−3.7525**	I(1)
LNER	−3.5470**	−1.7876			I(0)
LREER	−1.6566	−2.5239	−6.2827***	−6.4816***	I(1)
LINF	−3.6380***	−5.3548***			I(0)
LTOT	−0.4445	−3.0066	−6.0254***	−6.2737***	I(1)
RIR	−4.1421***	−5.6735***			I(0)
FDEF	−4.1856***	−4.7696***			I(0)
B1	−0.0248	0.7397	1.5939*	3.4574	I(1)
B2	−4.0174***	−4.1875**			I(0)
B3	−2.7609*	−2.8290	−6.3077***	−7.1293***	I(1)

Note: LNER = Nominal Exchange Rate; LREER = Real Effective Exchange Rate; RIR = Real Interest Rate; LGDP = Gross Domestic Product; FD = Fiscal Deficit; LTOT=Terms of Trade; LINF = Inflation. ***,** and * represents rejection at 1%, 5% and 10% level of significance for ADF, DF-GLS and PP estimates while it represents no rejection for KPSS estimate.

Source: Computed from study data by Researcher.

Table 5. Results of REER estimates

Variables	Sequential Sum of Squares	Degrees of Freedom	F-Statistic	P-Value
$B_1$ LGDP LINF RIR LTOT FD Model Residual R-Squared Adjusted R-Squared Observations	5.9774 15.7209 0.4953 5.8718 1.7648 0.1054 29.9357 4.3935 0.8720 0.8480 39	1 1 1 1 1 1 6 32	43.54 114.50 3.61 42.77 12.85 0.77 36.34	0.0000*** 0.0000*** 0.0666* 0.0000*** 0.0011*** 0.3874 0.0000***
$B_2$ LGDP LINF RIR LTOT FD Model Residual R-Squared Adjusted R-Squared Observations	6.2061 15.7293 0.4268 5.9225 1.5909 0.1538 30.0293 4.2999 0.8747 0.8513 39	1 1 1 1 1 1 6 32	46.19 117.06 3.18 44.08 11.84 1.14 37.25	0.0000*** 0.0000*** 0.0842* 0.0000*** 0.0016*** 0.2927 0.0000***
$B_3$ LGDP LINF RIR LTOT FD Model Residual R-Squared Adjusted R-Squared Observations	2.9586 16.5308 1.5929 4.9885 3.2781 0.1273 29.4763 4.8529 0.8586 0.8321 39	1 1 1 1 1 1 6 32	19.51 109.00 10.50 32.89 21.62 0.84 32.39	0.0001*** 0.0000*** 0.0028*** 0.0000*** 0.0001*** 0.3664 0.0000***

Note: ***, ** and * represent 1%, 5% and 10% respectively.

Source: Computed from study data by Researcher.

The table presents an ANCOVA results where REER is the dependent variable and the rest of the variables presented in table are independent variables including the bias estimates. The effect of each bias is estimated independently and all 3 biases are statistically significant at 1% after controlling for some major macroeconomic fundamentals that are known in the literature to be drivers of exchange rate.

Table 6. Results of NER estimates

Variables	Sequential Sum of Squares	Degrees of Freedom	F-Statistic	P-Value
${\mathit{B}}_1$ LGDP LINF RIR LTOT FD Model Residual R-Squared Adjusted R-Squared Observations	98.4966 173.2797 0.2033 9.5749 10.7334 0.6694 292.9573 12.7045 0.9584 0.9506 39	1 1 1 1 1 1 6 32	248.09 436.46 0.51 24.12 27.04 1.69 122.98	0.0000*** 0.0000*** 0.4794 0.0000*** 0.0000*** 0.2034 0.0000***
${\mathit{B}}_2$ LGDP LINF RIR LTOT FD Model Residual R-Squared Adjusted R-Squared Observations	103.8556 168.1965 0.1252 9.7544 9.9970 1.0126 292.9413 12.7206 0.9584 0.9506 39	1 1 1 1 1 1 6 32	261.26 423.12 0.32 24.54 25.15 2.55 122.82	0.0000*** 0.0000*** 0.5785 0.0000*** 0.0000*** 0.1203 0.0000***
${\mathit{B}}_3$ LGDP LINF RIR LTOT FD Model Residual R-Squared Adjusted R-Squared Observations	52.1344 202.3458 3.8672 6.6929 21.7524 0.2583 287.0510 18.6108 0.9391 0.9277 39	1 1 1 1 1 1 6 32	89.64 347.92 6.65 11.51 37.40 0.44 82.26	0.0000*** 0.0000*** 0.0147** 0.0019*** 0.0000*** 0.5099 0.0000***

Note: ***, ** and * represent 1%, 5% and 10% respectively.

Source: Computed from study data by Researcher

The table present an ANCOVA results where NER is the dependent variable and the rest of the variables presented in table are independent variables including the bias estimates. The dependent variable is changed in this second model because there is the need to check the nominal inertia of money illusion. The effect of each bias is estimated independently and all 3 biases are statistically significant at 1% after controlling for some major macroeconomic fundamentals that are known in the literature to be drivers of exchange rate.

Table A1. Proportion of tourism figures in GDP Terms

YEAR	GDP (Billions Dollars)	Tourism (Dollars)	% of GDP
1997	6.891308594	35000000	0.5079
1998	7.480968858	304000000	4.0636
1999	7.719354839	325000000	4.2102
2000	4.983024408	357000000	7.1643
2001	5.314909954	374000000	7.0368
2002	6.166330136	383000000	6.2112
2003	7.632406553	441000000	5.7780
2004	8.881368538	495000000	5.5735
2005	10.74467521	867000000	8.0691
2006	20.44089302	910000000	4.4519
2007	24.82784495	990000000	3.9875
2008	28.67870189	970000000	3.3823
2009	26.04810819	849000000	3.2594
2010	32.19727280	706000000	2.1927
2011	39.33731481	797000000	2.0261
2012	41.27095474	1154000000	2.7962
2013	62.82304370	1010000000	1.6077
2014	51.71748262	1027000000	1.9858
2015	47.49890669	911000000	1.9179
2016	54.49945183	952000000	1.7468
2017	58.84521200	919000000	1.5617
2018	65.31595512	996000000	1.5249

Note: The table reports Ghana’s annual GDP and tourism figures in dollars term. The percentage terms, which show the proportion of tourism amount that is represented in the total GDP, are also presented in the last column of the table. The trend of interest is the year 2007 upwards.

Table A2. Result of break Test

Variables	L vs L + 1	F. Statistics	Critical Values**
NER	0 Vs 1* 1 Vs 2* 2 Vs 3* 3 Vs 4* 4 Vs 5*	73.74 98.15 50.95 42.45 14.59	8.58 10.13 11.14 11.83 12.25
TOT	0 Vs 1* 1 Vs 2* 2 Vs 3* 3 Vs 4* 4 Vs 5*	80.68 13.38 15.90 13.05 15.32	8.58 10.13 11.14 11.83 12.25
NFA	0 Vs 1* 1 Vs 2* 2 Vs 3* 3 Vs 4	50.83 72.57 56.11 2.24	8.58 10.13 11.14 11.83
REER	0 Vs 1* 1 Vs 2	10.85 9.94	8.58 10.13
CAB	0 Vs 1* 1 Vs 2	15.56 2.15	8.58 10.13
RIR	0 Vs 1* 1 Vs 2* 2 Vs 3* 3 Vs 4	8.78 12.97 25.49 5.41	8.58 10.13 11.14 11.83
GDP	0 Vs 1* 1 Vs 2* 2 Vs 3* 3 Vs 4* 4 Vs 5*	100.15 63.80 48.15 43.51 23.06	8.58 10.13 11.14 11.83 12.25
FD	0 Vs 1* 1 Vs 2	15.55 1.94	8.58 10.13
GD	0 Vs 1* 1 Vs 2* 2 Vs 3* 3 Vs 4* 4 Vs 5	109.49 28.58 12.74 31.74 11.92	8.58 10.13 11.14 11.83 12.25
MS	0 Vs 1* 1 Vs 2* 2 Vs 3	94.31 61.89 8.28	8.58 10.13 11.14

Source: Computed from study data by Researcher.

Table A3. Result of break Dates

Variables	Sequential	Repartition
NER	1994 2000 2012 1985 2007	1985 1993 2000 2007 2014
TOT	2008 1985 2002 1990 1995	1985 1990 1995 2002 2009
NFA	2014 2000 2004	2004 2009 2014
REER	1985	1985
CAB	1992	1992
RIR	1985 2000 2012	1985 2000 2012
GDP	1998 2007 2013 1988 1993	1986 1993 2000 2006 2013
FD	2007	2007
GD	1986 1993 2004 2013	1986 1994 2005 2013
MS	1997 1992	1992 2000

Note: This table reports the date (year) within which a particular break occurred in each of the partitions under each of the study variables using Bai and Perron Sequential Selection. Ghana's currency redenomination took place in 2007 so this table identifies which of the variables have 2007 as one of the break years. From the table, 3 variables (NER, GDP, FD) are found to have break in line with the policy adapted year.

Source: Computed from study data by Researcher.

Table A4. Estimation of Ghana’s average growth rate

Year	Actual Observation	Forecast Averages	Absolute Deviation	Square of Deviation
1997	4.196
1998	4.700
1999	4.400
2000	3.700	4.432	0.732	0.536
2001	4.000	4.267	0.267	0.071
2002	4.500	4.033	0.467	0.218
2003	5.200	4.067	1.133	1.284
2004	5.600	4.567	1.033	1.067
2005	5.900	5.100	0.800	0.640
2006	6.400	5.567	0.833	0.694
2007		5.967

MAD = 0.752 MSE = 0.644

Note: In estimating$\alpha$for the subjective valuation (equation 3.1), the three month moving is employed. The table reports the estimated average (5.967) from the actual growth values with absolute and square deviations of 0.752 and 0.644 respectively.

Table A5. Descriptive Statistics of study Variables

Variables	LGDP	FD	LNER	LREER	RIR
Skewness Kurtosis Jarque-Bera Probability	−0.1427 2.8622 2.1212 0.3462	−0.273 3.276 5.303 0.171	−0.4237 2.8610 4.3608 0.1730	0.8710 3.6733 32.6059 0.1210	−0.8461 3.7183 87.310 0.1110
Variable	LINF	B1	B2	B3	TOT
Skewness Kurtosis Jarque-Bera Probability	0.8253 3.3593 4.3985 0.1109	1.7048 4.3371 21.7974 0.0000	1.5551 3.7306 16.5872 0.0003	3.1208 13.5211 243.1855 0.0000	0.163 1.762 2.665 0.264

Note: LNER = Nominal Exchange Rate; LREER = Real Effective Exchange Rate; RIR = Real Interest Rate; LGDP=Gross Domestic Product; FD = Fiscal Deficit.

TOT = Terms of Trade; LINF = Inflation; B₁ = First Bias; B₂ = Second Bias and B₃ = Third Bias

The essence of this table is to report the statistical (descriptive) properties of the variables that are being used for the empirical analysis in this study. There are 10 variables in all.

Table A6. Correlation Matrix

	B1	B2	B3	LTOT	LINF	RIR	LGDP
B1	1.0000
B2	0.6621	1.0000
B3	0.4245	0.3736	1.0000
LTOT	0.6294	0.6414	0.4868	1.0000
LINF	−0.3875	−0.3912	−0.4342	−0.1090	1.0000
RIR	0.3481	0.3534	0.2704	−0.1087	−0.6533	1.0000
LGDP	0.8018	0.6146	0.5620	0.4960	−0.6423	0.5646	1.0000

Note: The result represents correction between any two independent variables as used in the ANCOVA model. It is being used to check multicollinearity issues.

Table A7. Box test for autocorrelation (REER)

	AC	PAC	Q-Stat	Prob.
1	0.022	0.022	0.0208	0.885
2	0.113	0.113	0.5637	0.754
3	−0.292	−0.300	4.2554	0.235
4	−0.108	−0.111	4.7795	0.311
5	−0.099	−0.026	5.2352	0.388
6	−0.040	−0.109	5.3124	0.504
7	0.002	−0.050	5.3126	0.622
8	0.053	0.024	5.4566	0.708
9	0.020	−0.038	5.4780	0.791
10	0.028	−0.014	5.5198	0.854
11	−0.121	−0.129	6.3481	0.849
12	−0.059	−0.074	6.5484	0.886
13	−0.038	−0.008	6.6369	0.920
14	0.055	−0.003	6.8304	0.941
15	0.048	−0.013	6.9843	0.958
16	0.132	0.100	8.1798	0.943

Note: This is autocorrelation test result on dependent variable (REER) which is a time series data in the ANCOVA model. The result suggests there is no autocorrelation within the lags.

Table A8. Box test for autocorrelation (NER)

	AC	PAC	Q-Stat	Prob.
1	0.463	0.463	8.8084	0.103
2	0.025	−0.241	8.8344	0.112
3	0.111	0.282	9.3690	0.125
4	0.079	−0.165	9.6488	0.147
5	0.013	0.117	9.6564	0.156
6	0.037	−0.044	9.7207	0.177
7	0.018	0.013	9.7375	0.204
8	−0.008	−0.012	9.7406	0.284
9	0.069	0.108	9.9929	0.351
10	0.085	−0.025	10.390	0.407
11	0.026	0.028	10.427	0.492
12	0.004	−0.035	10.428	0.578
13	0.047	0.076	10.562	0.647
14	0.031	−0.057	10.623	0.715
15	−0.040	−0.022	10.729	0.772
16	0.101	0.204	11.437	0.782

Note: This is autocorrelation test result on dependent variable (NER) which is a time series data in the ANCOVA model. The result suggests there is no autocorrelation within the lags

Table A9. Levene’s test NER and B₁

B1	Mean	Std. dev.	Freq
0	−3.1012775	2.6201999	27
0.0188	−.06694371	0	1
0.0212	.05624642	0	1
0.2914	.34273827	0	1
0.3313	.35839096	0	1
0.4129	.41333407	0	1
0.5495	.58545989	0	1
0.5959	.66990411	0	1
0.9306	1.0646331	0	1
1.0871	1.3634862	0	1
1.0946	1.2996534	0	1
1.1029	1.5231862	0	1
1.1214	1.4703463	0	1

Note: W0 = 1.3564906 df(12, 26) Pr > F = 0.2480187

This is homogeneity test result for the dependent variable NER (continuous) and the independent variable B₁ (categorical) in the ANCOVA model. The result suggests there is equality of variance.

Table A10. Levene’s test NER and B₂

B2	Mean	Std. dev.	Freq
0	−3.1012775	2.6201999	27
0.2130	−.06694371	0	1
0.2474	.58545989	0	1
0.4650	.05624642	0	1
0.6297	.34273827	0	1
0.8214	.35839096	0	1
1.0334	.41333407	0	1
1.6372	.66990411	0	1
1.7516	1.0646331	0	1
1.7849	1.2996534	0	1
1.8415	1.3634862	0	1
1.8956	1.4703463	0	1
1.9285	1.5231862	0	1

Note: W0 = 1.3564906 df(12, 26) Pr > F = 0.2480187

This is homogeneity test result for the dependent variable NER (continuous) and the independent variable B₂ (categorical) in the ANCOVA model. The result suggests there is equality of variance.

Table A11. Levene’s test NER and B₃

B3	Mean	Std. dev.	Freq
0	−3.1012775	2.6201999	27
0.0084	1.4703463	0	1
0.7472	.34273827	0	1
0.7826	1.2996534	0	1
0.8418	−.06694371	0	1
1.0808	.41333407	0	1
1.1467	1.0646331	0	1
1.3311	1.3634862	0	1
1.3591	.35839096	0	1
2.0082	1.5231862	0	1
2.0311	.66990411	0	1
3.6905	.05624642	0	1
6.1128	.58545989	0	1

Note: W0 = 1.3564906 df(12, 26) Pr > F = 0.2480187

This is homogeneity test result for the dependent variable NER (continuous) and the independent variable B₃ (categorical) in the ANCOVA model. The result suggests there is equality of variance.

Table A12. Levene’s test REER and B₁

B1	Mean	Std. dev.	Freq
0	5.3594735	1.0172047	27
0.0188	4.6924009	0	1
0.0212	4.6426759	0	1
0.2914	4.5521436	0	1
0.3313	4.6051702	0	1
0.4129	4.5561223	0	1
0.5495	4.4597659	0	1
0.5959	4.4572368	0	1
0.9306	4.1953349	0	1
1.0871	4.3070745	0	1
1.0946	4.169261	0	1
1.1029	4.3020364	0	1
1.1214	4.2989697	0	1

Note: W0 = 0.92887265 df(12, 26) Pr > F = 0.53412492

This is homogeneity test result for the dependent variable REER (continuous) and the independent variable B₁ (categorical) in the ANCOVA model. The result suggests there is equality of variance.

Table A13. Levene’s test REER and B₂

B2	Mean	Std. dev.	Freq
0	5.3594735	1.0172047	27
0.2130	4.6924009	0	1
0.2474	4.4597659	0	1
0.4650	4.6426759	0	1
0.6297	4.5521436	0	1
0.8214	4.6051702	0	1
1.0334	4.5561223	0	1
1.6372	4.4572368	0	1
1.7516	4.1953349	0	1
1.7849	4.169261	0	1
1.8415	4.3070745	0	1
1.8956	4.2989697	0	1
1.9285	4.3010364	0	1

Note: W0 = 0.92887265 df(12, 26) Pr > F = 0.53412492

This is homogeneity test result for the dependent variable REER (continuous) and the independent variable B₂ (categorical) in the ANCOVA model. The result suggests there is equality of variance.

Table A14. Levene’s test REER and B3

B3	Mean	Std. dev.	Freq
0	5.3594735	1.0172047	27
0.0084	4.2989697	0	1
0.7472	4.5521436	0	1
0.7826	4.169261	0	1
0.8418	4.6924009	0	1
1.0808	4.5561223	0	1
1.1467	4.1953349	0	1
1.3311	4.3070745	0	1
1.3591	4.6051702	0	1
2.0082	4.3010364	0	1
2.0311	4.4572368	0	1
3.6905	4.6426759	0	1
6.1128	4.4597659	0	1

Note: W0 = 0.92887265 df(12, 26) Pr > F = 0.53412492

This is homogeneity test result for the dependent variable REER (continuous) and the independent variable B3 (categorical) in the ANCOVA model. The result suggests there is equality of variance.