Rwanda: Selected Issues and Statistical Appendix

International Monetary Fund

doi:10.5089/9781451833331.002.A003

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Rwanda: Selected Issues and Statistical Appendix

Author: International Monetary Fund

Publication Date:: 03 Dec 2004

eISBN:: 9781451833331

ISBN:: 9781451833331

Language:: English

Keywords:: ISCR; CR; export; Rwanda; price; bank; GDP deflator; time deposit ratio; reserve ratio; component ratio; excess reserves; Monetary base; Currencies; Exchange rates; Money markets

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This Selected Issues paper for Rwanda reports the growth strategy described in the Poverty Reduction Strategy Paper (PRSP). The PRSP constitutes a critical effort aimed at generating poverty-reducing economic growth. Sustained growth in the primary sector serves as an engine of growth in the rural nontradable sector. The consequent rural employment generation provides income to the poorest among the rural poor. In generating an annual rural nonfarm growth rate of 6.7 percent, the PRSP assumes an elasticity of rural nonfarm activities with respect to farm growth.

Abstract

III. Modeling Rwanda’s Money Multipliers and Money Demand⁵²

A. Introduction and Summary

81. This paper investigates the potential usefulness of econometric analysis of the money multipliers and money demand for informing monetary policy in Rwanda. We examine the reliability of the results generated by simplified versions of econometric models for the behavior of the money multipliers and of money demand commonly used by central banks in more advanced countries.

82. The findings are generally encouraging for the use of econometric models for monetary analysis in Rwanda. Despite serious data limitations, common models yield results that are sufficiently reliable to usefully inform policymaking. Nevertheless, the judgment of policymakers will always remain the pivotal point of monetary policy implementation.

83. On the supply side, the multipliers can be forecast with reasonable reliability. For all multipliers and component ratios, it is possible to construct simple time series models that reduce the residuals to white noise. The aggregate approach to forecasting the multiplier yields somewhat better results than the components approach. Examining the component ratios from the structural side, we can establish the relationships found in studies on industrial economies for the reserve ratio that reflects the behavior of the banks, but not for the ratios reflecting the behavior of the non-bank public.

84. On the demand side, the long-term money demand relationship can be characterized by a cointegrating vector, and for the short-term relationship, a Vector Error Correction Model (VECM) can be fitted well to the actual series (in levels). The long-term relationship includes the price level, real output, and the exchange rate as a proxy of the opportunity cost of holding nominal balances of domestic currency. However, some variables frequently used in long-term money demand models cannot be included due to data problems. The periods of excess money demand or supply resulting from this cointegrating equation can be shown to be intimately associated with discernable shocks. The short-term specification, in addition to the variables in the long-run specification, also includes structural and seasonal dummies.

B. Data

85. Monetary statistics in Rwanda are broadly adequate for econometric analysis. The National Bank of Rwanda (NBR) publishes its balance sheet and data on its money and foreign exchange market operations, including exchange rates and interest rates, on a weekly, and the banking sector balance sheet on a monthly basis. Format and detail of the information provided conform mostly to generally accepted standards.

86. Nevertheless, some serious data limitations must be born in mind in the economic interpretation of the statistical results subsequently presented: (a) Most series have several breaks, most importantly due to the war and genocide in 1994. (b) Some series important for our analysis (for example, borrowed reserves) are only available after 1995. (c) Interest rate and exchange rate controls during some periods limited not only the variance of some variables, but also their economic interpretation.⁵³ (d) With regard to national accounts, only annual GDP statistics are available and those only for the production side.⁵⁴ (e) For prices, the GDP deflator shares the problems just mentioned, while the consumer price index (CPI) is constrained by its technical implementation and uneven regional coverage.

87. while we will deal with more specific data issues in the money multiplier and money demand sections, respectively, we upfront define the monetary aggregates as: The monetary base is currency in circulation outside banks plus bank reserves (including cash in banks) plus non-bank deposits in the NBR, as defined for the IMF program.⁵⁵ The adjusted monetary base is the monetary base excluding borrowed reserves. M1 is currency in circulation plus demand deposits with commercial banks. M2 is M1 plus time and savings deposits with commercial banks. M1 in real terms is M1 in nominal terms deflated by a measure of the price level (either the CPI or the GDP deflator). Currency outside banks in real terms is measured in a similar way.

88. Limitations on control over the monetary base by the central bank limit not only the effectiveness of monetary policy, but also the usefulness of monetary control models. In principle, the central bank can control three sources of the monetary base: net foreign assets, net credit to government, and credit to the private sector. The fourth source, other items net, contains assets and liabilities that are mostly outside the direct control of the central bank, such as the counterpart to valuation changes in its net foreign assets. However, net foreign assets are also largely outside the control of the central bank when foreign exchange inflows are uncertain, as in the case of substantial grant flows. The same applies to net credit to government in the case of fiscal dominance, particularly when coordination between the treasury and the central bank is lacking.

89. The NBR has obtained increasing, albeit still limited, control over the monetary base in recent years. Table III-1 shows the annual growth rates of the monetary base from 1995 to 2003, and the respective contributions of the four sources of the base. On the back of higher grant inflows, 2000–2002 permitted a lessening of fiscal dominance, although the year 2003 marked a backslash here. While net credit to the private sector was a minor contributing factor to the growth in the monetary base up to the year 2000, it has gained considerably in importance during recent years.

Table III-1.

Sources of the Monetary Base

(Percentage change relative to the beginning-of-period monetary base)

Sources: National Bank of Rwanda; authors’ calculations.Notes: B…Monetary Base, NFA…Net Foreign Assets, NCG…Net Credit to Government (credit minus deposits, includes all public entities except for public enterprises), CPS…Credit to Private Sector (includes commercial banks, other financial institutions, and private and public enterprises), OIN…Other Items Net.

Table III-1.

Sources of the Monetary Base

(Percentage change relative to the beginning-of-period monetary base)

Period	B	NFA	NCG	CPS	OIN
1995	39.4	89.1	−68.5	6.8	12.0
1996	23.7	19.8	11.8	−4.5	−3.4
1997	6.1	43.5	19.9	−7.6	−49.8
1998	−8.3	−26.6	−8.2	9.7	16.8
1999	15.8	−3.0	18.8	0.2	−0.2
2000	−9.0	27.3	−27.9	3.8	−12.1
2001	4.6	39.8	−11.2	−23.6	−0.5
2002	13.0	58.3	−56.8	16.9	−5.4
2003	15.2	−17.0	44.0	2.1	−13.8

Table III-1.

Sources of the Monetary Base

(Percentage change relative to the beginning-of-period monetary base)

Period	B	NFA	NCG	CPS	OIN
1995	39.4	89.1	−68.5	6.8	12.0
1996	23.7	19.8	11.8	−4.5	−3.4
1997	6.1	43.5	19.9	−7.6	−49.8
1998	−8.3	−26.6	−8.2	9.7	16.8
1999	15.8	−3.0	18.8	0.2	−0.2
2000	−9.0	27.3	−27.9	3.8	−12.1
2001	4.6	39.8	−11.2	−23.6	−0.5
2002	13.0	58.3	−56.8	16.9	−5.4
2003	15.2	−17.0	44.0	2.1	−13.8

C. Modeling the Money Multipliers

90. In this section, we examine the scope for modeling Rwanda’s money multiplier and its components. First, we introduce the money multipliers and component ratios, including descriptive statistics. Second, we examine whether ARIMA models can forecast the money multipliers with reasonable reliability. Third, we look at whether the component ratios obey the same well-established structural relationships in Rwanda as in many other countries.⁵⁶

91. While the money multiplier approach has come out of fashion in industrial countries, more interest has recently been devoted to it for developing countries. According to classic monetarist theory (for example, Brunner, 1997), the multiplier reflects the behavior of the public and of the banks, while the monetary base reflects actions of the central bank. However, most well known studies of the multipliers in industrial countries date back to the 1970s and 1980s,⁵⁷ as central banks in industrial and middle-income countries have increasingly shifted from controlling the money stock through reserve aggregates to targeting credit market conditions through interest rates. But in low-income countries, where the estimated interest rate elasticity of money demand is more uncertain, targeting reserve aggregates remains prevalent,⁵⁸ and several papers have been devoted to the money multiplier in developing countries more recently, for example, Darbha (2002), Hasan (2001), and Zaki (1995).

Introducing the money multipliers and component ratios

92. We use the following concepts: ⁵⁹ The monetary base (B) is currency held by non-banks (C) plus bank reserves (R). The adjusted monetary base (Ba) excludes borrowed reserves. Narrow money (M1) is currency held by nonbanks and demand deposits (D). Broad money (M2) is M1 plus time and savings deposits (T). Four multipliers relate the (adjusted) monetary base to narrow and broad money: m1, m1_a, m2, and m2_a. The components of the multipliers are the currency ratio (c = C/D), the deposit ratio (t = T/D), and the (adjusted) reserve ratio (r = R/[D+T] or r_a = R_a/[D+T]). The multipliers and their components are related as follows (replace r by r_a, m1 by m1_a, and m2 by m2_a for the multipliers based on adjusted bank reserves):

\begin{matrix} M 1 = \frac{1 + c}{c + r (1 + t)} B = m 1 * B & (1) \end{matrix}

\begin{matrix} M 2 = \frac{1 + c + t}{c + r (1 + t)} B = m 2 * B & (2) \end{matrix}

93. We do not adjust the monetary base for changes in the reserve requirement ratio. This allows all the effect of changes in the reserve requirement to appear in the r-ratio and, hence, as fluctuations in the multipliers. The multipliers rise when the reserve requirement ratio is lowered and fall when the reserve requirement ratio is raised.⁶⁰

94. We use monthly observations from 1/1995 to 12/2003. Descriptive statistics of multipliers and components are in shown in Table III-2. During this period, the M2 multiplier rose by 83.7 percent, an increase entirely due to a 222.9 percent increase in the time deposit ratio. At the same time, the currency ratio declined by 9.3 percent and the reserve ratio declined by 65.4 percent. Obviously, adjusted multipliers that exclude borrowed reserves are more volatile than the unadjusted multipliers.

Table III-2.

Descriptive Statistics of the Multipliers and Components

Source: Authors’ calculations.

Table III-2.

Descriptive Statistics of the Multipliers and Components

	M1	M1_a	m2	m2_a	c	t	r	r_a
Mean	1.58	1.62	2.74	2.82	0.66	1.19	0.19	0.18
Median	1.57	1.61	2.71	2.71	0.63	1.12	0.19	0.19
Maximum	1.90	2.17	3.66	4.24	0.99	1.83	0.34	0.34
Minimum	1.19	1.19	1.89	1.89	0.49	0.38	0.10	0.04
Std. Dev.	0.13	0.17	0.49	0.59	0.10	0.32	0.05	0.06

Source: Authors’ calculations.

Table III-2.

Descriptive Statistics of the Multipliers and Components

	M1	M1_a	m2	m2_a	c	t	r	r_a
Mean	1.58	1.62	2.74	2.82	0.66	1.19	0.19	0.18
Median	1.57	1.61	2.71	2.71	0.63	1.12	0.19	0.19
Maximum	1.90	2.17	3.66	4.24	0.99	1.83	0.34	0.34
Minimum	1.19	1.19	1.89	1.89	0.49	0.38	0.10	0.04
Std. Dev.	0.13	0.17	0.49	0.59	0.10	0.32	0.05	0.06

Source: Authors’ calculations.

95. Plots of the multipliers and their components are shown in Figure III-1. Both m1 and m2 have been trending upwards for most of the sample period (Figures III-1a and III-1b).⁶¹ The residuals of m1 and m2 after detrending and seasonal adjustment (with Census X-12) were smaller in 1999 to 2003 than in 1995 to 1998. The currency ratio has remained relatively stable since 2001, after a precipituous decline from 1995 to 2000 (Figure III-1c). The time deposit ratio trended upward during most of the sample period, but has stabilized somewhat since end-2001 (Figure III-1d). The reserve ratio and the adjusted reserve ratio have trended downward over the sample period, due to the decline in the excess reserve ratio that arguably reflects both the development of better investment opportunities for the commercial banks (government and central bank bills) and the deteriorating solvency of the banking system during the sample period (Figures III-1e and III-1f).

96. Regressing the multipliers on their components (Table III-3) suggests that the reserve ratio causes most of the volatility in the multipliers. This crude measure (serial correlation in the residuals is ignored) also shows that volatility in the deposit ratio t accounts for some of the volatility in the m1 multiplier, but is insignificant for the m2 multiplier. All significant coefficients have the expected signs.

Table III-3.

Sources of Volatility in the Multipliers

Source: Authors’ calculations.Note: Absolute values of t-statistics are in parentheses.

Table III-3.

Sources of Volatility in the Multipliers

	Δm1	ΔM1_a	Δm2	Δm2_a
Δc	−0.35 [R²=0.03]	−0.22 [R²=0.00]	0.06 [R²=0.01]	0.32 [R²=0.00]
	(1.79)	(0.74)	(0.17)	(0.59)
Δt	−0.33 [R²=0.15]	−0.36 [R²=0.08]	0.21 [R²=0.01]	0.20 [R²=0.00]
	(4.40)	(2.98)	(1.53)	(0.88)
Δr	−2.83 [R²=0.66]	−3.80 [R²=0.53]	−5.11 [R²=0.77]	−6.90 [R²=0.54]
	(14.43)	(10.78)	(18.74)	(6.07)
Δr_a	−2.18 [R²=0.61]	−3.66 [R²=0.75]	−3.93 [R²=0.70]	−6.74 [R²=0.79]
	(12.87)	(17.95)	(15.86)	(19.93)

Source: Authors’ calculations.Note: Absolute values of t-statistics are in parentheses.

Table III-3.

Sources of Volatility in the Multipliers

	Δm1	ΔM1_a	Δm2	Δm2_a
Δc	−0.35 [R²=0.03]	−0.22 [R²=0.00]	0.06 [R²=0.01]	0.32 [R²=0.00]
	(1.79)	(0.74)	(0.17)	(0.59)
Δt	−0.33 [R²=0.15]	−0.36 [R²=0.08]	0.21 [R²=0.01]	0.20 [R²=0.00]
	(4.40)	(2.98)	(1.53)	(0.88)
Δr	−2.83 [R²=0.66]	−3.80 [R²=0.53]	−5.11 [R²=0.77]	−6.90 [R²=0.54]
	(14.43)	(10.78)	(18.74)	(6.07)
Δr_a	−2.18 [R²=0.61]	−3.66 [R²=0.75]	−3.93 [R²=0.70]	−6.74 [R²=0.79]
	(12.87)	(17.95)	(15.86)	(19.93)

Source: Authors’ calculations.Note: Absolute values of t-statistics are in parentheses.

97. The high contribution of (excess) bank reserves to the volatility of the multiplier has important policy implications. As excess reserves (required reserves are proportional to total deposits and thus rather stable) are at least partly determined by the central bank’s policy stance through open market operations, the multipliers cannot be regarded as exogenous with respect to the NBR’s policy stance. Thus, policymakers must also predict the effect of their actions on the multiplier when pursuing the multiplier approach to money stock control.⁶² Against this background, the central bank should (a) aim to predict the effects of their policy actions on excess reserves and thus on the multiplier, and (b) promote structural measures to reduce the volatility in excess reserves.⁶³

ARIMA forecasts of the money multipliers

98. We asses the forecast power of ARIMA models of the multipliers and the component ratios based on the aggregrate (forecast the multipliers directly) vs. the components approach (calculate the multipliers from the forecasts of the components). All the series we examine in this section are integrated of order I(1). As Rasche and Johannes (1984), we do not seasonally adjust the series in order to avoid the introduction of spurious autocorrelation from the standard seasonal adjustment techniques. As yearly seasonal patters in the multipliers can be observed, we followed Box and Jenkins (1976) by including 12-month seasonal autoregressive (AR) and moving average (MA) terms in all models; results, however, were inferior to those of other models.

Table III-4.

Preferred Models for Multipliers and Components

Source: Authors’ calculations.Notes: Standard errors of coefficients in parentheses. Q(24) is the Ljung-Box statistic at lag 24. S.E. is the standard error of the regression.

Table III-4.

Preferred Models for Multipliers and Components

y	p, d, q		Q(24)	S.E.
m1	9,1,1	$y_{t} = \underset{(0.1041)}{0.2849 y_{t - 9}} - \underset{(0.0864)}{0.5313 ɛ_{t - 1}} + ɛ_{t}$	23.7	0.0814
m1a	9,1,1	$y_{t} = \underset{(0.1017)}{0.4345 y_{t - 9}} - \underset{(0.0834)}{0.5839 ɛ_{t - 1}} + ɛ_{t}$	25.3	0.1126
m2	0,1,1	$\begin{matrix} y_{t} = \underset{(0.0884)}{- 0.4263 ɛ_{t - 1}} & + ɛ_{t} \end{matrix}$	22.9	0.1469
m2_a	9,1,1	$y_{t} = \underset{(0.1003)}{0.4817 y_{t - 9}} - \underset{(0.0834)}{0.5801 ε_{t - 1} + ε_{t}}$	18.4	0.2068
c	0,1,2	$\begin{matrix} y_{t} = \underset{(0.0906)}{- 0.3611 ɛ_{t - 2}} & + ɛ_{t} \end{matrix}$	20.4	0.0434
t	0,1,2	$\begin{matrix} y_{t} = \underset{(0.0903)}{- 0.3782 ɛ_{t - 2}} & + ɛ_{t} \end{matrix}$	20.3	0.1056
r	0,1,1	$\begin{matrix} y_{t} = \underset{(0.0903)}{- 0.3932 ɛ_{t - 1}} & + ɛ_{t} \end{matrix}$	21.6	0.0255
r_a	0,1,1	$\begin{matrix} y_{t} = \underset{(0.0829)}{- 0.5001 ɛ_{t - 1}} & + ɛ_{t} \end{matrix}$	21.9	0.0305

Source: Authors’ calculations.Notes: Standard errors of coefficients in parentheses. Q(24) is the Ljung-Box statistic at lag 24. S.E. is the standard error of the regression.

Table III-4.

Preferred Models for Multipliers and Components

y	p, d, q		Q(24)	S.E.
m1	9,1,1	$y_{t} = \underset{(0.1041)}{0.2849 y_{t - 9}} - \underset{(0.0864)}{0.5313 ɛ_{t - 1}} + ɛ_{t}$	23.7	0.0814
m1a	9,1,1	$y_{t} = \underset{(0.1017)}{0.4345 y_{t - 9}} - \underset{(0.0834)}{0.5839 ɛ_{t - 1}} + ɛ_{t}$	25.3	0.1126
m2	0,1,1	$\begin{matrix} y_{t} = \underset{(0.0884)}{- 0.4263 ɛ_{t - 1}} & + ɛ_{t} \end{matrix}$	22.9	0.1469
m2_a	9,1,1	$y_{t} = \underset{(0.1003)}{0.4817 y_{t - 9}} - \underset{(0.0834)}{0.5801 ε_{t - 1} + ε_{t}}$	18.4	0.2068
c	0,1,2	$\begin{matrix} y_{t} = \underset{(0.0906)}{- 0.3611 ɛ_{t - 2}} & + ɛ_{t} \end{matrix}$	20.4	0.0434
t	0,1,2	$\begin{matrix} y_{t} = \underset{(0.0903)}{- 0.3782 ɛ_{t - 2}} & + ɛ_{t} \end{matrix}$	20.3	0.1056
r	0,1,1	$\begin{matrix} y_{t} = \underset{(0.0903)}{- 0.3932 ɛ_{t - 1}} & + ɛ_{t} \end{matrix}$	21.6	0.0255
r_a	0,1,1	$\begin{matrix} y_{t} = \underset{(0.0829)}{- 0.5001 ɛ_{t - 1}} & + ɛ_{t} \end{matrix}$	21.9	0.0305

Source: Authors’ calculations.Notes: Standard errors of coefficients in parentheses. Q(24) is the Ljung-Box statistic at lag 24. S.E. is the standard error of the regression.

99. For all the multipliers and components, it is possible to construct a simple ARIMA model that reduces the residuals to white noise. ⁶⁴ The preferred models are shown in III-Table 4. The models for m1, m1a and m2a, in addition to the error, each consist of an AR(9) and an MA(1) term. The models for m2, r and r_a, each consist of only an MA(1) term. The models for c and t each consist of only an MA(2) term.

100. The aggregate approach yields somewhat better results than the components approach. ⁶⁵ Comparing their forecasting power in a static (one-step-ahead) forecasting framework,⁶⁶ all diagnostic indicators (III-Table 5) consistently support this finding for all four multipliers defined here. The only two indicators that are better for the components approach are the variance proportion of m1 and the bias proportion of m2.

Table III-5.

Multipliers Forecast Diagnostics

Source: Authors’ calculations.Notes: RMSE is the root mean squared error. MAE is the mean absolute error. MAPE is the mean absolute percent error. TIC is the Theil inequality coefficient. BP, VP and CP are the bias, variance and covariance proportions, respectively. Better forecasts have higher values.

Table III-5.

Multipliers Forecast Diagnostics

	RMSE	MAE	MAPE	TIC	BP	VP	CP
Aggregate approach
m1	0.0805	0.0672	4.2869	0.0254	0.0013	0.0305	0.9683
m1_a	0.1114	0.0885	5.4191	0.0341	0.0007	0.0299	0.9694
m2	0.1462	0.1121	4.0798	0.0264	0.0320	0.0034	0.9646
m2_a	0.2047	0.1556	5.3406	0.0348	0.0030	0.0110	0.9860
Components approach
c	0.0431	0.0322	4.9412	0.0324	0.0014	0.0037	0.9949
t	0.1051	0.0821	7.0173	0.0428	0.0237	0.0012	0.9751
r	0.0254	0.0199	11.0202	0.0652	0.0112	0.0064	0.9824
r_a	0.0304	0.0234	16.6710	0.0806	0.0120	0.0123	0.9757
m1	0.0895	0.0729	4.6090	0.0282	0.0035	0.0176	0.9893
m1_a	0.1263	0.0924	5.5351	0.0387	0.0059	0.0389	0.9656
m2	0.1507	0.1160	4.1138	0.0266	0.0233	0.0083	0.9786
m2_a	0.3175	0.1974	6.2477	0.0551	0.1238	0.1075	0.7778

Table III-5.

Multipliers Forecast Diagnostics

	RMSE	MAE	MAPE	TIC	BP	VP	CP
Aggregate approach
m1	0.0805	0.0672	4.2869	0.0254	0.0013	0.0305	0.9683
m1_a	0.1114	0.0885	5.4191	0.0341	0.0007	0.0299	0.9694
m2	0.1462	0.1121	4.0798	0.0264	0.0320	0.0034	0.9646
m2_a	0.2047	0.1556	5.3406	0.0348	0.0030	0.0110	0.9860
Components approach
c	0.0431	0.0322	4.9412	0.0324	0.0014	0.0037	0.9949
t	0.1051	0.0821	7.0173	0.0428	0.0237	0.0012	0.9751
r	0.0254	0.0199	11.0202	0.0652	0.0112	0.0064	0.9824
r_a	0.0304	0.0234	16.6710	0.0806	0.0120	0.0123	0.9757
m1	0.0895	0.0729	4.6090	0.0282	0.0035	0.0176	0.9893
m1_a	0.1263	0.0924	5.5351	0.0387	0.0059	0.0389	0.9656
m2	0.1507	0.1160	4.1138	0.0266	0.0233	0.0083	0.9786
m2_a	0.3175	0.1974	6.2477	0.0551	0.1238	0.1075	0.7778

101. In sum, the aggregate approach permits to forecast the multipliers with considerable reliability, particularly for a relatively unsophisticated monetary system. The diagnostic indicators for the aggregate approach (arguably with the exception of the variance proportion in the m1 and the bias proportion in the m2 forecasts⁶⁷) are all at acceptable levels. However, the diagnostic indicators for the components approach are more mixed. Not surprisingly, the t ratio (which contains also the foreign-currency deposits) and the r and r_a ratios prove to be most difficult to forecast. The forecasts of the adjusted multipliers are consistently less robust than those of the unadjusted multipliers. This is not surprising, given the intrinsicly higher volatility of the adjusted multipliers (which exclude borrowed reserves).

102. Two additional factors make us relatively comfortable with our results. First, the differences in the forecast diagnostics between the two approaches are small. This shows that the multipliers in Rwanda’s case are no “black boxes” that could potentially hide large unexplainable variations in the multiplier components when analyzed with the aggregate approach. Second, the robustness of the forecasts for Rwanda compares favorably to those found in similar studies of the cases of other other low-income countries (for example, Zaki 1995).⁶⁸

103. The forecast diagnostics of their respective multipliers are ambiguous on the question whether Ml or M2 can be controlled with greater precision. While the mean absolute percent error points to M2, the other scale-invariable indicator, the Theil inequality coefficient, is about the same for M1 and M2. The covariance proportion is slightly lower for M1, where M1 suffers from a higher variation proportion and M2 from a higher bias proportion. However, as a higher bias proportion is arguably more problematic than a higher variance proportion, M1 would be preferred over M2 for monetary targeting.

Explaining the M2 component ratios by structural models

104. In this section, we broadly apply Beenstock’s (1989) framework for the United Kingdom to the structural analysis of the M2 component ratios in Rwanda. However, we are somewhat restricted by data availability. There is, for instance, no reliable measure of velocity to include as an independent variable, as we do not have quarterly, but only annual, observations for GDP.

105. The currency ratio and the time deposit ratio do not seem to behave in line with relationships well-established in other (more advanced) economies. Usually, the currency ratio (time deposit ratio) can be shown to be decreasing (increasing) in income and in the deposit rate. However, for Rwanda we cannot establish this relationship in regressions of the currency ratio and the time deposit ratio on GDP and the 3-month deposit rate, which reflects the opportunity cost of holding currency vs. time deposit balances (demand deposits are typically unremunerated in Rwanda), and between demand deposits and time deposits, respectively. That is, economic agents seem to choose between currency vs. demand deposits and demand deposits vs. time deposits independently of income and of the opportunity cost of holding currency and (usually unremunerated) demand deposits vs. time deposits.

106. The reserve ratio behaves well in line with the results generally found for advanced economies. The demand for excess reserves (only they are genuinely determined by the banks) is likely to increase with the mean and the variance of the frequency distribution of withdrawals. It is thus expected to vary inversely with the t-ratio, that is, with the share of time deposits in total deposits, because withdrawals from time deposits require advance notification (unless a penalty is paid), and the variance of time deposits is therefore usually lower. The tightness of the NBR’s money market policy is likely to affect the demand for reserves. If the central bank assisted the market through its “front window”, that is, at market rather than penalty rates, the banks’ demand for reserves would tend to fall.⁶⁹ To capture this effect, we use Howard’s (1982) variable PEN, defined by

P E N = discount rate • \frac{outstaning discount window borrowing from the NBR}{cash reserves of the banking system} . (3)

However, as Howard, we do not find PEN to be significant. As an alternative (and arguably more parsimonious) indicator for the NBR’s money market policy stance, we include the discount rate in the model and find it to be highly significant. Since r is naturally constrained between zero and unity, we estimate the model:

\begin{array}{l} \ln {(r / (1 - r))}_{t} = \underset{(- 2.26)}{- 0.90} + \underset{(2.40)}{0.32 \ln} {(r / (1 - r))}_{t - 1} + \underset{(2.29)}{0.22 \ln} {(r / (1 - r))}_{t - 2} - \underset{(- 3.40)}{0.72 t_{t}} + \underset{\begin{matrix} (2.29) & R^{2} = 0.70 \end{matrix}}{0.05 R_{d i s, t,}} & (\begin{matrix} 4 \end{matrix}) \end{array}

where t is the deposit ratio and R_dis is the discount rate; t-statistics are in parentheses. The reserve ratio behaves well in line with the results generally found for advanced economies. As expected, a higher t-ratio reduces demand for reserves, while a higher discount rate increases demand for reserves. All coefficients are significant at the 1 or 5 percent level.

107. In sum, structural models can characterize only the reserve ratio with reasonable reliability. Forecasting the multiplier by structural equations is unlikely to yield reliable results given the apparent independence of the currency ratio and the time deposit ratio of variables suggested by theory and empirical studies on many other countries. However, there is a statistically sound basis for forecasting the reserve ratio r by a structural model such as the one suggested by equation (4), combined with the model for t in Table III-4.

D. Modeling Money Demand

108. In this section, we examine the scope for modeling Rwanda’s money demand both for the long and short terms. For the long-run, we identify a money market equilibrium condition by a cointegrating vector of real money balances, output and the exchange rate. For the short run, money demand is estimated by a vector error correction model (VECM). We use quarterly data for the years 1980 to 2003. We limit the analysis in this section to M1, since M2 (a) is composed of assets reacting differently to changes in the interest rate, and (b) includes dollar-denominated deposits depending highly on foreign investment projects.

Theoretical framework and cointegration analysis

109. We assume a standard functional form for real money demand. Thus, real money demand is assumed to be a function of output, y (as a proxy for expenditure), a vector including variables that proxy the opportunity cost of holding money balances, ψ, and a vector that includes other variables that influence the demand for real balances, ζ. In the long-run, the money market equilibrium condition can be expressed as

\begin{matrix} M 1 / P = f (y, ψ; ζ) & (5) \end{matrix}

The sign of output is expected to be positive and the sign of the opportunity cost of holding money is expected to be negative.

110. We specify the following variables: Real money balances are the difference between the logs of M1 in nominal terms, lm1, and either the GDP deflator (lgdpdef), or the CPI (lcpi), while expenditures are proxied by the log of real GDP (lgdpr). The vector ψ, which will be part of the more general VECM, is proxied by the inflation rate, measured either as the log first difference of the GDP deflator (dlgdpdef) or the CPI (dlipc) and the depreciation of the exchange rate (dlerya). In addition, we include structural dummies, one for the period of war and genocide (1993:4–1995:1), dumg, and another to reflect changes in the exchange rate peg or in the exchange rate system, dumer (1990:4–1991:1 and 1995:1–1995:3⁷⁰). Dummy variables will also be included to account for seasonal factors (dumq², dumq³, dumq⁴).

Table III-6.

Variable Specifications

Table III-6.

Variable Specifications

Variable	Definition	Source
erya	Quarterly average of the official exchange rate	Rwandese authorities and IFS-IMF
erye	end-of period (quarterly) official exchange rate	Rwandese authorities and IFS-IMF
eryem	end-of period (quarterly) official exchange rate	Rwandese authorities and IFS-IMF
gdpr	quarterly real GDP, resulting from smoothing the annual series using a quadratic approximation	Rwandese authorities and Fund staff calculations
gdpn	quarterly nominal GDP, resulting from smoothing the annual series using a quadratic approximation	Rwandese authorities and Fund staff calculations
		Rwandese authorities and Fund staff
gdpdef	implicit quarterly deflator from gdpr and gdpn	calculations
ipc	end-of period (quarterly) consumer price index	Rwandese authorities and IFS-IMF
irate	three-month deposit rate in RF	Rwandese authorities and IFS-IMF
ml	M1 in nominal terms	Rwandese authorities and IFS-IMF
mlp	M1 in real terms deflated by the CPI	Rwandese authorities and IFS-IMF
cil	Currency outside banks in nominal terms	Rwandese authorities and IFS-IMF
cilp	Currency outside banks in real terms deflated by the CPI	Rwandese authorities and IFS-IMF

Table III-6.

Variable Specifications

Variable	Definition	Source
erya	Quarterly average of the official exchange rate	Rwandese authorities and IFS-IMF
erye	end-of period (quarterly) official exchange rate	Rwandese authorities and IFS-IMF
eryem	end-of period (quarterly) official exchange rate	Rwandese authorities and IFS-IMF
gdpr	quarterly real GDP, resulting from smoothing the annual series using a quadratic approximation	Rwandese authorities and Fund staff calculations
gdpn	quarterly nominal GDP, resulting from smoothing the annual series using a quadratic approximation	Rwandese authorities and Fund staff calculations
		Rwandese authorities and Fund staff
gdpdef	implicit quarterly deflator from gdpr and gdpn	calculations
ipc	end-of period (quarterly) consumer price index	Rwandese authorities and IFS-IMF
irate	three-month deposit rate in RF	Rwandese authorities and IFS-IMF
ml	M1 in nominal terms	Rwandese authorities and IFS-IMF
mlp	M1 in real terms deflated by the CPI	Rwandese authorities and IFS-IMF
cil	Currency outside banks in nominal terms	Rwandese authorities and IFS-IMF
cilp	Currency outside banks in real terms deflated by the CPI	Rwandese authorities and IFS-IMF

111. Figure III-2 shows the evolution (in natural logs) of the variables used in the estimation. The discrete changes in output and exchange rates are apparent for the moments of political conflict or when there are changes in the policies implemented. Regarding nominal money balances, note how limited the response was during moments of political turmoil: This seems to hint that the adjustment to desired real money balances occurred through the functioning of other adjustment mechanisms, most possibly the inflation rate and exchange rate depreciations, the latter in particular during the second half of the sample.⁷¹

112. As we cannot use some variables common for long-run money demand, we estimate the disequilibrium in the market for real money balances in period t by

E_{t} = lm 1 - β_{2} lcpi - β_{3} lgdpr + β_{4} lerya, (6)

where the coefficient on lm1, β_1, is normalized to unity. Some papers on money demand (Celasun and Goswami, 2002, among others), include the inflation rate and/or the depreciation of the exchange rate and the interest rate in their formulation of the long-run equilibrium. In the case of Rwanda, this is not possible as these variables are all in levels. This holds even considering different subsamples.⁷² Furthermore, since the only interest rate (irate) available for most of the period studied, the three-month deposit rate, was under the control of the monetary authorities during an extended period of time, it cannot be used as a genuine measure of the opportunity cost of holding money.

113. Through the Johansen trace statistic, we find one cointegrating relationship of long-term money demand at the 1 percent significance level and with the expected signs,

\begin{matrix} l m 1 - 1.13 l c p i = 6.06 + 1.27 l g d p r - 0.38 l e r y a .^{73} & (7) \end{matrix}

The coefficient of the price level is not significantly different from unity, nor is the coefficient on output at usual confidence levels; this is consistent with a constant velocity in the long run. Note that there is a negative association in the long run between real money balances and the level of the exchange rate. There could be two mutually related reasons for this: (a) CPI seems to be a good proxy for the prices of non-tradable goods and the price of food staples; (b) the prices of some goods are fully dollarized, regardless whether they are quoted in domestic currency. As a consequence, it seems that the presence of the exchange rate in the cointegrating equation behaves like a shadow price index for tradable goods.

114. The disequilibrium in the market for nominal money balances, E_t (Figure III-3) shows excess demand for most of the 1980s and a monetary overhang related to the genocide. From (6) it is clear that if E_t<0, there is an excess demand for real money balances. Equilibrium could be restored either through the adjustment of endogenous variables (the price level, the exchange rate level or the level of real income), or through increases in the money supply. (Conversely, if E_t >0, there is an excess supply of real money balances.) Under deteriorating political and economic conditions, the market turned to excess supply during 1994–95 and returned to equilibrium only at the end of the 1990s, since when it has fluctuated around equilibrium. However, the figure shows some monetary overhang at the end of 2003, consistent with what the IMF program review noted at that time.

Short-term demand and VECM

115. There are different approaches to model and estimate the demand for real money balances in the short term. One of these is to integrate the long-run equilibrium condition obtained from the Johansen methodology as one of the terms into a short-term demand in first differences. A more comprehensive approach is to recognize the mutual interaction of the variables included in the money demand specification, and integrate the short-term demand into a more general macroeconometric model such as

\begin{matrix} Δ X_{t} = Π_{0} + Π X_{t - 1} + Π_{1} Δ X_{t - 1} + Π_{2} Δ X_{t - 2} + ....... + Π_{p} Δ X_{t - p} + Γ Z_{t} + ɛ_{t} . & (8) \end{matrix}

Here, ΔX_t is a 4x1 vector of log first differences of the endogenous variables, Π₀ is a 4x1 vector of constants, Π is a 4x4 matrix including the coefficients (betas) and adjustment coefficient (alphas) of the cointegrating relation, X_t-1 is a 4x1 vector of the endogenous variables in levels for the period t-1, while the rest is composed by lags of ΔX_t and their respective matrices of coefficients. Finally, Z_t is a vector of exogenous variables and ε_t is a 4x1 vector of disturbances that are such that ε_it may be correlated with ε_jt.

116. We model a VECM in the first differences of the variables considered in the estimation of the cointegration equation, plus structural and seasonal dummies. Based on the Akaike information criterion and Cholesky decomposition, we proceed to estimate a model with lerya, lgdpr, lcpi, lml and four lags (reducing the sample to 91 observations from 1981:2 to 2003:4).⁷⁴ We use the log first difference of real GDP as the second equation in the VECM because it is often affected by weather-related shocks to the agricultural sector.

117. The coefficients of the lagged portion of the short-term money demand are generally in line with economic theory (Table III-7). Output is positively associated with money demand. Price increases precipitate an initial increase of the demand of nominal balances, but a subsequent decrease associated with the need to economize money balances to avoid the inflation tax. In addition, money demand is negatively associated with exchange rate depreciation, which also is the reflection of a higher opportunity cost of holding money.

Table III-7.

Lagged Coefficients of Estimated (Short-Term) Money Demand

Source: Authors’ calculations.

Table III-7.

Lagged Coefficients of Estimated (Short-Term) Money Demand

Lag		1	2	3	4
d (lerya)		−0.15	0.07	0.32	−0.14
	std	−0.14	−0.15	−0.14	−0.12
	t	−1.03	0.49	2.30	−1.14
d (lgdpr)		0.39	0.52	−0.46	−0.20
	std	−0.16	−0.17	−0.17	−0.17
	t	2.41	3.05	−2.76	−1.17
d (lipc)		0.60	−0.29	−0.60	0.25
	std	−0.35	−0.38	−0.38	−0.32
	t	1.71	−0.76	−1.57	0.80
d (lm1)		−0.30	−0.12	0.03	0.29
	std	−0.12	−0.12	−0.12	−0.12
	t	−2.47	−1.02	0.28	2.47

Source: Authors’ calculations.

Table III-7.

Lagged Coefficients of Estimated (Short-Term) Money Demand

Lag		1	2	3	4
d (lerya)		−0.15	0.07	0.32	−0.14
	std	−0.14	−0.15	−0.14	−0.12
	t	−1.03	0.49	2.30	−1.14
d (lgdpr)		0.39	0.52	−0.46	−0.20
	std	−0.16	−0.17	−0.17	−0.17
	t	2.41	3.05	−2.76	−1.17
d (lipc)		0.60	−0.29	−0.60	0.25
	std	−0.35	−0.38	−0.38	−0.32
	t	1.71	−0.76	−1.57	0.80
d (lm1)		−0.30	−0.12	0.03	0.29
	std	−0.12	−0.12	−0.12	−0.12
	t	−2.47	−1.02	0.28	2.47

Source: Authors’ calculations.

118. The size and signs found for the seasonal and structural dummies (Table III-8) seem to adequately reflect Rwanda’s seasonality and economic circumstances. Money demand is stronger in the second quarter than in the third and fourth quarters (associated with the agricultural crop cycle), and decreases in the first quarter compared with the fourth. The structural dummies for episodes of rapid depreciation (DUMER) and the genocide period (DUMG) are both positive, reflecting discrete reductions in the demand for nominal money in response to these shocks.

Table III-8.

Structural Coefficients of Estimated (Short-Term) Money Demand

Source: Author’s calculations.

Table III-8.

Structural Coefficients of Estimated (Short-Term) Money Demand

	DUMER	DUMG	DUMQ2	DUMQ3	DUMQ4
Coefficient	0.02	0.08	0.11	0.05	0.05
std	−0.04	−0.06	−0.03	−0.02	−0.03
t	−0.60	1.38	4.19	2.91	1.90

Source: Author’s calculations.

Table III-8.

Structural Coefficients of Estimated (Short-Term) Money Demand

	DUMER	DUMG	DUMQ2	DUMQ3	DUMQ4
Coefficient	0.02	0.08	0.11	0.05	0.05
std	−0.04	−0.06	−0.03	−0.02	−0.03
t	−0.60	1.38	4.19	2.91	1.90

Source: Author’s calculations.

119. Regarding the long-term equilibrium condition, the associated adjustment coefficients (alphas, Table III-9) have signs consistent with economic intuition. If E_t > 0, nominal money decreases, while the price level, the exchange rate and real GDP increase to restore equilibrium in the market for real money balances. The alpha for the equation concerning the log first difference of nominal money (the first equation of the VECM) implies that the demand for nominal money balances in the short run will be partially explained by the adjustment towards equilibrium, provided there was disequilibrium in the previous period. Obviously, the magnitude of this disequilibrium changes period to period in response to new innovations. Although this adjustment seems small, it was already hinted by observing the evolution of nominal money balances in Figure III-4.⁷⁵ The alpha for consumer prices implies that approximately 2 percent per year of the disequilibrium in the market for money is translated into changes in the price level, that is, into positive inflation rates provided there is excess supply in the market for real money balances. The alpha for the exchange rate implies that part of a depreciation occurring in a given year will be partially explained by the adjustment in the market for money (approximately 1 percent of the market’s disequilibrium). Real output adjusts more to disequilibria in the money market is, with approximately 8 percent of the disequilibrium per year being transmitted to this variable.⁷⁶

Table III-9.

Long-Term Equilibrium Condition for Money

Source: Author’s calculations.

Table III-9.

Long-Term Equilibrium Condition for Money

	d (lerya)	d (lgdpr)	d (lipc)	d (lm1)
Coefficient	0.003	0.018	0.004	−0.002
std	−0.004	−0.004	−0.002	−0.006
t	−0.721	5.045	2.295	−0.289

Source: Author’s calculations.

Table III-9.

Long-Term Equilibrium Condition for Money

	d (lerya)	d (lgdpr)	d (lipc)	d (lm1)
Coefficient	0.003	0.018	0.004	−0.002
std	−0.004	−0.004	−0.002	−0.006
t	−0.721	5.045	2.295	−0.289

Source: Author’s calculations.

120. It is possible to construct a VECM of money demand in levels that fits the actual series well (Figure III-4). Table III-10 shows the nominal money demand in levels resulting from the reduced form of the VECM in levels, blending both short- and long-term estimated portions. The resulting series fits the actual series remarkably well, in particular up to 1997. The larger residuals for the later part of the sample could be, among others, due to a combination of (i) more frequent shocks; (ii) more alternatives to money offered by the banks.

Table III-10.

VECM of Money Demand

Source: Authors’ calculations.

Table III-10.

VECM of Money Demand

Lag		1	2	3	4	5
Constant	−0.11
DUMER	0.03
DUMG	0.08
DUMQ2	0.11
DUMQ3	0.05
DUMQ4	0.05
lerya		−0.15	0.22	0.25	−0.46	0.14
lgdpr		0.41	0.13	−0.98	0.26	0.20
lipc		0.61	−0.89	−0.31	0.85	−0.25
lm1		0.69	0.18	0.15	0.26	−0.29

Source: Authors’ calculations.

Table III-10.

VECM of Money Demand

Lag		1	2	3	4	5
Constant	−0.11
DUMER	0.03
DUMG	0.08
DUMQ2	0.11
DUMQ3	0.05
DUMQ4	0.05
lerya		−0.15	0.22	0.25	−0.46	0.14
lgdpr		0.41	0.13	−0.98	0.26	0.20
lipc		0.61	−0.89	−0.31	0.85	−0.25
lm1		0.69	0.18	0.15	0.26	−0.29

Source: Authors’ calculations.

121. A number of potential extensions could complement and improve the analysis of money demand presented here, in particular:

to distinguish between monetary and non-monetary GDP and to pursue further the effects of weather-related shocks to the agricultural sector;⁷⁷
to consider a “core CPI” in measuring real money balances, also because core inflation could be a unit root process;⁷⁸
to compile a series for exchange rate premia in parallel markets for the entire observation period, as black market premia have in the past often been significant;
to use a structural VECM imposing theory-motivated identification conditions instead of the relatively simple Cholesky approach for the identification of the VECM.

E. Policy Recommendations

122. Amongst others, our findings suggest the following implications for the NBR’s monetary control framework: First, as excess reserves are the main source of volatility in the money multplier, the NBR should favor measures that could stabilize excess reserves. Such measures could include closing the commercial bank accounts at the central bank later in the day and promoting the interbank market by reducing credit risk through more transparency (for example, an automated book-entry system).

123. Second, The NBR’s monetary programming could benefit from paying more attention to the specification of money demand. The analysis presented here shows that, despite political and economic turmoil, and extensive controls, money demand, both in the short and long terms, reacts in a way consistent with economic fundamentals. Taking this into account when devising its program of interventions in the money market could help the NBR to avoid unwanted monetary overhangs, undesired exchange rate volatility, or bursts in core inflation.

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Prepared by D. Hauner and G. Di Bella, drawing on a draft Working Paper by the authors.

Unfortunately, collection of parallel exchange market data has started only recently.

Agricultural production is estimated per season (approximately every six months) and the estimates published by the minister of agriculture. However, this series also present voids and some inconsistencies in the methodology used for its compilation.

While non-bank deposits in the central bank do not, strictly speaking, constitute high-powered money, a large part of “non-bank deposits” are deposits by (money-creating) other non-bank financial institutions, most importantly the Union des Banques Populaires Rwandaises (UBPR).

We limit our analysis in this section to the period after the genocide, i.e., 1995 to 2003, for three reasons: First, we would have to omit the year 1994 due to the lack of data and the exceptional circumstances in this period. Second, many data series are available only for the time after the genocide. Third, substantial interest rate controls limit the usefulness of interest rate data for the time before 1995.

For example, Beenstock (1989), Frost (1977), Rasche and Johannes (1987), Garfinkel and Thornton (1991). Baghestani and Mott (1997) and Freeman and Kydland (2000) are more recent examples.

Rasche and Johannes (1987) show that the expected utility loss from deviations of actual money around its targeted level in an interest rate regime versus a reserve aggregate regime mostly depends on the uncertainty of the estimated interest rate elasticity versus the variance of the multiplier forecasts.

For the definitions of the monetary aggregates see the data section.

An alternative approach would have been to use the reserve adjustment magnitude (RAM) developed by Brunner and Meltzer (see, for example, in Burger and Rasche, 1977, and Frost, 1977). We regard RAM as overly sophisticated for the present context, because the NBR only very rarely changed the reserve requirement in past years, and our concern here is mostly the short-run predictability of the multipliers. Ex post, the ARIMA results below support this decision, as the longest lag in the preferred model for the r-ratio is only an MA(1) term.

The downward spike at the beginning of 1997 reflects an extremely abrupt expansion in the monetary base (through NCG and NFA at a time) during that period.

See Garfinkel and Thornton (1991).

Potential measures include closing the commercial bank accounts at the central bank later in the day, and promoting the interbank market by reducing credit risk through more transparency (for example, an automated book-entry system).

We try several models and keep those (i) whose coefficients are all significant at the 1 percent level, and (ii) for which the LM and Ljung-Box tests do not reject the null hypothesis of no serial correlation in the residuals. Among the short-listed models, we use the Akaike and Schwarz criterions to guide us in the selection of the most parsimonous model.

For the United States, Hafer and Hein (1984) came to the same conclusion.

See Hafer and Hein (1984) and Rasche and Johannes (1987) for more elaborate discussions of this approach.

The variance proportion tells us how far the variation of the forecast is from the variation of the actual series, while the bias proportion tells us how far the mean of the forecast is from the mean of the actual series.

Obviously, the robustness of money multiplier forecasts for a low-income country cannot favorably compare to those for industrial countries (for example, Rasche and Johannes, 1987).

For a more detailed exposition of the preceding argument, see Beenstock (1989).

These are the only periods in which the quarterly depreciation rate (on average) was higher than 10 percent.

This also seems to indicate difficulties to convert domestic currency into foreign currency as a form to adjust to excesses in money supply; in these cases, the adjustment seemed to have been through exchange rate movements or capital controls.

The null that the first log difference of the GDP deflator (dlgdpdef) has a unit root cannot be rejected at usual significance levels. Building on that, several models using dlgdpdef as a measure of opportunity cost in the cointegrating relationship were tested, some of them with positive results with regard to the economic significance of the coefficients found. However, the goodness of fit was less impressive, in particular for the period after 1998.

Unit-root tests indicate that all the variables considered are I(1). Alternative models combined some of the variables included in (7) with various other variables, including end-of-period instead of quarterly average exchange rates, interest rates, a dummy to account for differences in interest rates regimes, and the consideration of the real money demand as a unique variable forcing the coefficient on the price level to unity.

Structural innovations in lerya are assumed to simultaneously affect the innovations in the other variables, while structural innovations in hnl, do not. This ordering seems reasonable as the exchange rate remained fixed during a significant part of the sample period, and, even after exchange rate liberalization, the central bank continued intervening in the market.

In the particular case of Rwanda, the failure of nominal money balances to adjust to disequilibrium in the market for real balances could also be the consequence the existence of dormant accounts in the wake of the genocide.

It is possible that the alphas of the CPI, the exchange rate and M1 are underestimated, as the one of GDP may be overestimated for two reasons. First, a significant part of the variance observed in the GDP series is related to weather-related shocks affecting the agricultural GDP that are, initially, non-monetary in nature; second, the strong recovery in both real money balances and GDP after 1994 may have biased the results.

Positive shocks could increase the share of the monetized sector (more households achieve a level of production beyond subsistence), and real money demand pressures could arise.

Particularly through food, a significant part of the variance in the CPI is weather-related. Therefore, the cyclical variations observed in the index are mostly the consequence of cyclical changes in food prices generated by a stationary “weather process.”

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Rwanda: Selected Issues and Statistical Appendix

Author: International Monetary Fund

Volume/Issue:: Volume 2004: Issue 383

Publisher:: International Monetary Fund

ISBN:: 9781451833331

ISSN:: 1934-7685

Pages:: 110

DOI:: https://doi.org/10.5089/9781451833331.002

Keywords
III. Modeling Rwanda’s Money Multipliers and Money Demand52

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The Multipliers and their Components

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The Multipliers and their Components

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The Main Variables of the Money Demand Function

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The Disequilibrium in the Market for Nominal Money Balances

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Actual and Fitted Money Demand

Foresee

Table III-10.

VECM of Money Demand

Lag		1	2	3	4	5
Constant	−0.11
DUMER	0.03
DUMG	0.08
DUMQ2	0.11
DUMQ3	0.05
DUMQ4	0.05
lerya		−0.15	0.22	0.25	−0.46	0.14
lgdpr		0.41	0.13	−0.98	0.26	0.20
lipc		0.61	−0.89	−0.31	0.85	−0.25
lm1		0.69	0.18	0.15	0.26	−0.29

Source: Authors’ calculations.

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Abstract

III. Modeling Rwanda’s Money Multipliers and Money Demand52

A. Introduction and Summary

B. Data

C. Modeling the Money Multipliers

Introducing the money multipliers and component ratios

ARIMA forecasts of the money multipliers

Explaining the M2 component ratios by structural models

D. Modeling Money Demand

Theoretical framework and cointegration analysis

Short-term demand and VECM

E. Policy Recommendations

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Asian Development Bank

Food and Agriculture Organization

Inter-American Development Bank

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III. Modeling Rwanda’s Money Multipliers and Money Demand⁵²