## _wp05178

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---

### Introduction and scope
- Uncertainty about money demand and the money multiplier is identified as one of the main challenges to monetary policy design and implementation in most low-income countries.
- The paper revisits the scope for econometric analysis in low-income countries using a case study for Rwanda.
- Rwanda chosen because of:
  - a floating exchange rate;
  - reliance on indirect monetary policy instruments;
  - somewhat typical data and institutional shortcomings.
- Analysis jointly examines demand and supply sides of money (money demand and the money multiplier) using simplified versions of common econometric models.

### Constraints on econometric analysis and data limitations
- Key data limitations and institutional constraints:
  - most series have several breaks, most importantly due to the war and genocide in 1994;
  - some series (e.g., borrowed reserves) available only after 1995;
  - interest rate and exchange rate controls during some periods limited variance and economic interpretation of these series;
  - only annual GDP statistics available and those only for the production side;
  - CPI constrained by technical implementation and uneven regional coverage.
- Control over the monetary base is limited by:
  - other items net and uncertain grant-related foreign exchange inflows;
  - fiscal dominance and lack of treasury–central bank coordination.
- Table 1 (annual percentage-change contributions relative to beginning-of-period monetary base) — selected entries:
  - 1995: B 39.4, NFA 89.1, NCG -68.5, CPS 6.8, OIN 12.0
  - 1996: B 23.7, NFA 19.8, NCG 11.8, CPS -4.5, OIN -3.4
  - 1997: B 6.1, NFA 43.5, NCG 19.9, CPS -7.6, OIN -49.8
  - 1998: B -8.3, NFA -26.6, NCG -8.2, CPS 9.7, OIN 16.8
  - 1999: B 15.8, NFA -3.0, NCG 18.8, CPS 0.2, OIN -0.2
  - 2000: B -9.0, NFA 27.3, NCG -27.9, CPS 3.8, OIN -12.1
  - 2001: B 4.6, NFA 39.8, NCG -11.2, CPS -23.6, OIN -0.5
  - 2002: B 13.0, NFA 58.3, NCG -56.8, CPS 16.9, OIN -5.4
  - 2003: B 15.2, NFA -17.0, NCG 44.0, CPS 2.1, OIN -13.8
- NBR has obtained increasing, albeit still limited, control over the monetary base in recent years; net credit to private sector gained importance after 2000.

### Supply side — Multipliers: concepts and descriptive facts
- Definitions and component ratios:
  - Monetary base (B) = currency held by non-banks (C) + bank reserves (R).
  - Adjusted monetary base (Ba) excludes borrowed reserves.
  - M1 = currency (C) + demand deposits (D). M2 = M1 + time and savings deposits (T).
  - Component ratios: c = C/D; t = T/D; r = R/[D+T]; ra = Ra/[D+T].
  - Multipliers: m1, m1a, m2, m2a relate (adjusted) monetary base to narrow and broad money via standard algebraic relations.
- Sample: monthly observations 1/1995–12/2003.
- Descriptive changes over the sample:
  - M2 multiplier rose by 83.7 percent (entirely due to time deposit ratio increase of 222.9 percent).
  - Currency ratio declined by 9.3 percent.
  - Reserve ratio declined by 65.4 percent.
  - Adjusted multipliers (excluding borrowed reserves) are more volatile than unadjusted multipliers.
- Graphical trends:
  - m1 and m2 trended upwards for most of sample.
  - currency ratio relatively stable since 2001 after sharp decline 1995–2000.
  - time deposit ratio trended upward until stabilizing since end-2001.
  - reserve and adjusted reserve ratios trended downward over sample due to decline in excess reserve ratio.

### Supply side — Sources of multiplier volatility and structural findings
- Regression evidence (Table 2) highlights reserve ratio importance:
  - For m1: c coefficient -0.35 [R2=0.03] (t=1.79); t coefficient -0.33 [R2=0.15] (t=4.40); r coefficient -2.83 [R2=0.66] (t=14.43); ra coefficient -2.18 [R2=0.61] (t=12.87).
  - For m2: r and ra show the largest R2 contributions (e.g., r -5.11 [R2=0.77] (t=18.74)).
- Interpretation:
  - Reserve (especially excess reserves) causes most volatility in multipliers.
  - Excess reserves are partly determined by central bank policy (open market operations), so multipliers are not exogenous relative to NBR stance.
- Structural modeling results:
  - Currency ratio (c) and time deposit ratio (t) do not exhibit the expected relationships with income and deposit rate in Rwanda data.
  - Reserve ratio (r) follows expected relationships; preferred structural model (in log-odds form) estimated:
    - ln[r/(1-r)]t = – 0.90 + 0.32 ln[r/(1-r)]t-1 + 0.22 ln[r/(1-r)]t-2 – 0.72 tt + 0.05 Rdis,t.
    - t-statistics reported: (-2.26) (2.40) (2.29) (-3.40) (2.29). R2 = 0.70.
  - Higher t reduces demand for reserves; higher discount rate increases demand for reserves.
- Conclusion: structural models can reliably characterize the reserve ratio r; structural forecasting of the full multiplier unlikely to be reliable because c and t appear independent of usual explanatory variables in this context.

### Supply side — Time-series forecasting (ARIMA) and forecast diagnostics
- All series I(1); seasonal AR/MA(12) terms tested but performed worse than chosen models.
- Preferred ARIMA specifications and diagnostics (Table 3):
  - m1: (9,1,1). Model: yt = 0.2849 yt-9 – 0.5313 εt-1 + εt (std. errors: (0.1041) (0.0864)); Q(24)=23.7; S.E.=0.0814.
  - m1a: (9,1,1). yt = 0.4345 yt-9 – 0.5839 εt-1 + εt (std. errors: (0.1017) (0.0834)); Q(24)=25.3; S.E.=0.1126.
  - m2: (0,1,1). yt = –0.4263 εt-1 + εt (std. error: (0.0884)); Q(24)=22.9; S.E.=0.1469.
  - m2a: (9,1,1). yt = 0.4817 yt-9 – 0.5801 εt-1 + εt (std. errors: (0.1003) (0.0834)); Q(24)=18.4; S.E.=0.2068.
  - c: (0,1,2). yt = –0.3611 εt-2 + εt (std. error: (0.0906)); Q(24)=20.4; S.E.=0.0434.
  - t: (0,1,2). yt = –0.3782 εt-2 + εt (std. error: (0.0903)); Q(24)=20.3; S.E.=0.1056.
  - r: (0,1,1). yt = –0.3932 εt-1 + εt (std. error: (0.0903)); Q(24)=21.6; S.E.=0.0255.
  - ra: (0,1,1). yt = –0.5001 εt-1 + εt (std. error: (0.0829)); Q(24)=21.9; S.E.=0.0305.
- Forecasting approaches compared: aggregate (forecast multipliers directly), components (forecast components and recompute multipliers), combinations (unweighted mean; restricted regression weights summing to unity; unrestricted regression weights).
- Multiplier forecast diagnostics (aggregate approach results, Table 4):
  - m1: RMSE 0.0805, MAE 0.0672, MAPE 4.2869, TIC 0.0254, BP 0.0013, VP 0.0305, CP 0.9683.
  - m1a: RMSE 0.1114, MAE 0.0885, MAPE 5.4191, TIC 0.0341, BP 0.0007, VP 0.0299, CP 0.9694.
  - m2: RMSE 0.1462, MAE 0.1121, MAPE 4.0798, TIC 0.0264, BP 0.0320, VP 0.0034, CP 0.9646.
  - m2a: RMSE 0.2047, MAE 0.1556, MAPE 5.3406, TIC 0.0348, BP 0.0030, VP 0.0110, CP 0.9860.
- Key forecasting findings:
  - Aggregate approach yields better results than components approach for all four multipliers.
  - Combining aggregate and components adds value only for m1 (and only with unrestricted regression weighting).
  - Adjusted multipliers forecasts (excluding borrowed reserves) are consistently less robust than unadjusted multipliers.
  - Theil inequality coefficients around 0.3 considered acceptable given volatility; most forecasting error explained by covariance proportion.
  - Chow tests: M2 multiplier preferred (null of no structural break not rejected at 5 percent at any interval); results for M1 more ambiguous.

### Demand side — Long-run cointegration and disequilibrium
- Focus on M1 using quarterly data 1980–2003.
- Long-run money market equilibrium: M1 / P = f(y, ψ, ζ).
- Variables and dummies used:
  - lm1 less lcpi or lgdpdef; lgdpr as real GDP; ψ proxied by inflation (dlgdpdef or dlipc) and exchange rate depreciation (dlerya).
  - Structural dummies dumg (4/1993–1/1995) and dumer (4/1990–1/1991; 1/1995–3/1995); seasonal dummies dumq2, dumq3, dumq4.
- Johansen trace test suggests one cointegrating relationship at 1 percent with expected signs. Estimated cointegrating relation (normalized on lm1):
  - lm1 – 1.13 lcpi = 6.06 + 1.27 lgdpr – 0.38 lerya.
- Interpretation:
  - Coefficient on price level not significantly different from unity; coefficient on output not significantly different from unity at usual levels — consistent with constant velocity in the long run.
  - Negative long-run association between real money balances and exchange rate level (lerya).
- Disequilibrium series Εt = lm1 – β2 lcpi – β3 lgdpr + β4 lerya shows:
  - Excess demand for most of 1980s;
  - Monetary overhang following the civil war (1994–95 excess supply);
  - Return to equilibrium end-1990s;
  - Some monetary overhang at end-2003.
- Periods of excess money demand or supply identified from the cointegrating equation are closely associated with discernible shocks.

### Demand side — Short-run VECM and dynamics
- VECM estimated in first differences for vector (lerya, lgdpr, lcpi, lm1) with four lags; sample 2/1981–4/2003 (91 observations); structural and seasonal dummies included.
- Short-run lag coefficients (selected, Table 5):
  - d(lerya) lags 1–4 coefficients: -0.15 (t -1.03), 0.07 (0.49), 0.32 (2.30), -0.14 (-1.14).
  - d(lgdpr) lags 1–4 coefficients: 0.39 (t 2.41), 0.52 (3.05), -0.46 (-2.76), -0.20 (-1.17).
  - d(lipc) lags 1–4 coefficients: 0.60 (t 1.71), -0.29 (-0.76), -0.60 (-1.57), 0.25 (0.80).
  - d(lm1) lags 1–4 coefficients: -0.30 (t -2.47), -0.12 (-1.02), 0.03 (0.28), 0.29 (2.47).
- Structural and seasonal dummies (Table 6):
  - DUMER coefficient 0.02 (t -0.60).
  - DUMG coefficient 0.08 (t 1.38).
  - DUMQ2 coefficient 0.11 (t 4.19).
  - DUMQ3 coefficient 0.05 (t 2.91).
  - DUMQ4 coefficient 0.05 (t 1.90).
  - Interpretation: seasonality consistent with agricultural cycle; DUMER and DUMG positive reflecting discrete reductions in nominal money demand responding to shocks.
- Long-run adjustment coefficients (alphas) from VECM (Table 7):
  - d(lerya) alpha = 0.003 (t -0.721).
  - D(lgdpr) alpha = 0.018 (t 5.045).
  - d(lipc) alpha = 0.004 (t 2.295).
  - d(lm1) alpha = -0.002 (t -0.289).
- Interpretation of adjustment:
  - Adjustment of nominal money partly driven by disequilibrium; about 2 percent per year of disequilibrium transmitted to the price level; about 8 percent per year transmitted to real output (text notes "approximately 8 percent of the disequilibrium per year being transmitted to this variable" for GDP when annualized).
- Model fit:
  - VECM in levels fits actual series well up to 1997; larger residuals later in sample possibly due to more frequent shocks and more alternatives to money offered by banks.
  - Reduced-form VECM in levels produces fitted nominal money demand series (Figure 4 and Table A3 provide fitted values and lag structure).

### Conclusions and policy recommendations
- Overall assessment:
  - Econometric monetary analysis for Rwanda yields statistically and economically reasonable results useful for policymaking, but experienced policy judgment must supersede models.
  - Statistical properties weaker than for advanced economies.
  - For multipliers: non-theoretical (time series) models outperform structural models given data limitations.
  - For money demand: short-run VECM performs better than relying on long-run cointegration alone because of frequent shocks.
- Main policy implications and recommendations:
  - Public sector operations should be coordinated more closely to reduce volatility in the multipliers.
    - Most volatility in multipliers comes from reserve ratio (monetary policy operations of NBR) rather than currency ratio.
    - Need to coordinate public sector operations given their effect on liquidity and analyze use of different monetary policy instruments.
  - NBR should promote measures to stabilize excess reserves.
    - Examples: closing commercial bank accounts at the central bank later in the day; promoting interbank market by reducing credit risk through more transparency (for example, an automated book-entry system).
  - NBR’s monetary programming should attribute higher weight to specification of money demand.
    - Despite volatility and controls, money demand in short and long run reacts consistent with fundamentals.
    - Incorporating money demand when planning FX and money market interventions (discount rate changes and open market operations) could help avoid monetary overhangs, exchange rate volatility, or bursts in core inflation.

### Suggested extensions and further empirical work
- Distinguish between monetary and non-monetary GDP in the analysis.
- Include a measure of “core” CPI.
- Include a measure of exchange rate premium in parallel markets.
- Consider alternative methods to identify the structural VAR associated with the money demand VECM (structural identification rather than Cholesky ordering).
- Investigate weather-related shocks and their effect on monetized sector and real money demand.

*Source: _wp05178 (IMF Working Paper content; authors’ calculations; National Bank of Rwanda data) as provided in the supplied PDF excerpt.*

### References..............................................................................................................

### _wp05178 - References

### Introduction
- Uncertainty about money demand and the money multiplier is identified as one of the main challenges to monetary policy design and implementation in most low-income countries.
- Improved analytical frameworks for monetary policy implementation are widely recognized as beneficial. (Footnote indicators in source: "2" and "3".)
- Common impediments to econometric usefulness cited:
  - shortcomings in the availability, frequency, and accuracy of data;
  - fiscal dominance limiting central bank control over the monetary base;
  - erratic movements associated with (usually quarterly) IMF test dates under conditionality that affect statistical conclusiveness.

### Scope and case study approach
- The paper revisits the scope for econometric analysis in low-income countries using a case study for Rwanda.
- The analysis jointly examines demand and supply sides of money (money demand and the money multiplier), using simplified versions of common econometric models.
- Rwanda is highlighted as a pertinent case because of:
  - a floating exchange rate;
  - reliance on indirect monetary policy instruments;
  - somewhat typical data and institutional shortcomings.

### Key findings — Supply side (multipliers)
- Multipliers and component ratios can be forecast with reasonable reliability.
- For all multipliers and component ratios, simple time series models can be constructed that reduce residuals to white noise.
- The aggregate approach to forecasting the multiplier performs somewhat better than the components approach.
- Structural analysis of component ratios:
  - For the reserve ratio (reflecting bank behavior), relationships usually found in such studies can be established.
  - For ratios reflecting behavior of the non-bank public, the usual structural relationships could not be established.

### Key findings — Demand side (money demand)
- Long-term money demand relationship:
  - Can be characterized by a cointegrating vector.
  - Includes the price level, real output, and the exchange rate (used as a proxy for the opportunity cost of holding nominal balances of domestic currency).
  - Some commonly used variables in long-term money demand models cannot be included due to data problems.
- Short-term money demand relationship:
  - A Vector Error Correction Model (VECM) can be fitted well to the actual series (in levels).
  - The short-term specification includes the long-run variables plus structural and seasonal dummies.
- Periods of excess money demand or supply identified from the cointegrating equation are closely associated with discernible shocks.

### Practical assessment and policy relevance
- Despite serious data limitations, common econometric models yield results sufficiently reliable to usefully inform policymaking in Rwanda.
- Nonetheless, policymakers’ judgment remains pivotal in monetary policy implementation.

### Suggested extensions and further work
- Distinguish between monetary and non-monetary GDP in the analysis.
- Include a measure of “core” CPI.
- Include a measure of exchange rate premium in parallel markets.
- Consider alternative methods to identify the structural VAR associated with the money demand VECM.
- Additional sections in the source document (tables and figures listed) indicate detailed empirical material, including:
  - Tables 1–7 on sources of the monetary base, volatility, preferred models, forecast diagnostics, and estimated coefficients;
  - Figures 1–4 on multipliers, money demand variables, disequilibrium in nominal money balances, and actual vs fitted money demand;
  - Appendix Tables 1–3 with descriptive statistics, variable specifications, and a VECM of money demand.

*Source: _wp05178 - References*

### Section IV models of money demand. Section V concludes with a number of policy

### _wp05178 - Section IV models of money demand. Section V concludes with a number of policy

### Constraints on econometric analysis
- Monetary statistics: NBR publishes weekly balance sheet and money/FX market operations; banking sector balance sheet monthly; format mostly conforms to standards.
- Important data limitations:
  - most series have several breaks, most importantly due to the war and genocide in 1994;
  - some series (e.g., borrowed reserves) available only after 1995;
  - interest rate and exchange rate controls during some periods limited variance and economic interpretation of these series;
  - only annual GDP statistics available and those only for the production side;
  - GDP deflator shares the problems above; CPI is constrained by technical implementation and uneven regional coverage.
- Control over monetary base limited: central bank can in principle control net foreign assets, net credit to government, and credit to private sector; other items net and uncertain grant-related foreign exchange inflows limit effective control. Fiscal dominance and lack of treasury–central bank coordination further limit control.
- Table 1 (sources of monetary base): annual percentage-change contributions (relative to beginning-of-period monetary base)
  - 1995: B 39.4, NFA 89.1, NCG -68.5, CPS 6.8, OIN 12.0
  - 1996: B 23.7, NFA 19.8, NCG 11.8, CPS -4.5, OIN -3.4
  - 1997: B 6.1, NFA 43.5, NCG 19.9, CPS -7.6, OIN -49.8
  - 1998: B -8.3, NFA -26.6, NCG -8.2, CPS 9.7, OIN 16.8
  - 1999: B 15.8, NFA -3.0, NCG 18.8, CPS 0.2, OIN -0.2
  - 2000: B -9.0, NFA 27.3, NCG -27.9, CPS 3.8, OIN -12.1
  - 2001: B 4.6, NFA 39.8, NCG -11.2, CPS -23.6, OIN -0.5
  - 2002: B 13.0, NFA 58.3, NCG -56.8, CPS 16.9, OIN -5.4
  - 2003: B 15.2, NFA -17.0, NCG 44.0, CPS 2.1, OIN -13.8
- NBR has obtained increasing, albeit still limited, control over the monetary base in recent years; net credit to private sector gained importance after 2000.

### Modeling the money multipliers
A. Concepts, descriptive statistics, and behavior
- Definitions and component ratios:
  - Monetary base (B) = currency held by non-banks (C) + bank reserves (R).
  - Adjusted monetary base (Ba) excludes borrowed reserves.
  - M1 = currency (C) + demand deposits (D). M2 = M1 + time and savings deposits (T).
  - Components: currency ratio c = C/D; deposit ratio t = T/D; reserve ratio r = R/[D+T]; adjusted reserve ratio ra = Ra/[D+T].
  - Multipliers: m1, m1a, m2, m2a relate (adjusted) monetary base to narrow and broad money with standard algebraic relations (equations (1) and (2) in source).
- Sample: monthly observations 1/1995–12/2003.
- Key descriptive changes over sample:
  - M2 multiplier rose by 83.7 percent (entirely due to time deposit ratio increase of 222.9 percent).
  - Currency ratio declined by 9.3 percent.
  - Reserve ratio declined by 65.4 percent.
  - Adjusted multipliers (excluding borrowed reserves) are more volatile than unadjusted multipliers.
- Graphical trends (Figure 1 summary):
  - m1 and m2 trended upwards for most of sample.
  - currency ratio relatively stable since 2001 after sharp decline 1995–2000.
  - time deposit ratio trended upward until stabilizing since end-2001.
  - reserve and adjusted reserve ratios trended downward over sample due to decline in excess reserve ratio.

B. Sources of multiplier volatility (regressions of multipliers on components)
- Table 2 (coefficients with R2 and absolute t-statistics in brackets) highlights reserve ratio importance:
  - For m1: c coefficient -0.35 [R2=0.03] (t=1.79); t coefficient -0.33 [R2=0.15] (t=4.40); r coefficient -2.83 [R2=0.66] (t=14.43); ra coefficient -2.18 [R2=0.61] (t=12.87).
  - For m2: r and ra show the largest R2 contributions (e.g., r -5.11 [R2=0.77] (t=18.74)).
- Interpretation:
  - Reserve (especially excess reserves) causes most volatility in multipliers.
  - Excess reserves partly determined by central bank policy (open market operations), so multipliers are not exogenous relative to NBR stance.
- Policy implication (from analysis): central bank should (a) aim to predict effects of its policy actions on excess reserves and thus on the multiplier, and (b) promote structural measures to reduce volatility in excess reserves.

C. ARIMA forecasts of multipliers and components
- All series I(1); seasonal AR/MA(12) terms were tested but performed worse than chosen models.
- Preferred ARIMA models (Table 3; standard errors in parentheses; Q(24) and S.E. reported):
  - m1: (p,d,q) = 9,1,1. Model: yt = 0.2849 yt-9 – 0.5313 εt-1 + εt (std. errors: (0.1041) (0.0864)); Q(24)=23.7; S.E.=0.0814.
  - m1a: 9,1,1. yt = 0.4345 yt-9 – 0.5839 εt-1 + εt (std. errors: (0.1017) (0.0834)); Q(24)=25.3; S.E.=0.1126.
  - m2: 0,1,1. yt = –0.4263 εt-1 + εt (std. error: (0.0884)); Q(24)=22.9; S.E.=0.1469.
  - m2a: 9,1,1. yt = 0.4817 yt-9 – 0.5801 εt-1 + εt (std. errors: (0.1003) (0.0834)); Q(24)=18.4; S.E.=0.2068.
  - c: 0,1,2. yt = –0.3611 εt-2 + εt (std. error: (0.0906)); Q(24)=20.4; S.E.=0.0434.
  - t: 0,1,2. yt = –0.3782 εt-2 + εt (std. error: (0.0903)); Q(24)=20.3; S.E.=0.1056.
  - r: 0,1,1. yt = –0.3932 εt-1 + εt (std. error: (0.0903)); Q(24)=21.6; S.E.=0.0255.
  - ra: 0,1,1. yt = –0.5001 εt-1 + εt (std. error: (0.0829)); Q(24)=21.9; S.E.=0.0305.
- Forecasting approaches compared:
  - Aggregate (forecast multipliers directly) vs. components (forecast components and recompute multipliers) vs. combinations (unweighted mean; restricted regression weights summing to unity; unrestricted regression weights).
- Multiplier forecast diagnostics (selected aggregate approach results from Table 4):
  - m1: RMSE 0.0805, MAE 0.0672, MAPE 4.2869, TIC 0.0254, BP 0.0013, VP 0.0305, CP 0.9683.
  - m1a: RMSE 0.1114, MAE 0.0885, MAPE 5.4191, TIC 0.0341, BP 0.0007, VP 0.0299, CP 0.9694.
  - m2: RMSE 0.1462, MAE 0.1121, MAPE 4.0798, TIC 0.0264, BP 0.0320, VP 0.0034, CP 0.9646.
  - m2a: RMSE 0.2047, MAE 0.1556, MAPE 5.3406, TIC 0.0348, BP 0.0030, VP 0.0110, CP 0.9860.
- Key findings on forecasting:
  - Aggregate approach yields better results than components approach for all four multipliers.
  - Combining aggregate and components adds value only for m1 (and only with unrestricted regression weighting).
  - Adjusted multipliers forecasts (excluding borrowed reserves) are consistently less robust than unadjusted multipliers.
  - Theil inequality coefficients around 0.3 considered acceptable given volatility; most forecasting error explained by covariance proportion.
  - Chow tests for structural breaks give preference to M2 multipliers: for M2 multiplier, null of no structural break not rejected at 5 percent at any interval; results for M1 are more ambiguous.

D. Structural models for M2 component ratios
- Currency ratio (c) and time deposit ratio (t) do not exhibit expected relationships with income and deposit rate (in Rwanda data: regressions on GDP and three-month deposit rate fail to establish typical decreasing/increasing relationships).
  - Interpretation: consumers appear to choose between currency vs. demand deposits and demand vs. time deposits independently of income and opportunity cost variables measured.
- Reserve ratio (r) follows expected relationships:
  - Demand for excess reserves expected to vary inversely with t (share of time deposits) and to be affected by central bank money market stance.
  - Howard’s PEN variable tested but not significant; discount rate performs better as indicator of NBR stance.
  - Preferred structural model for reserve ratio (equation (4), estimated):
    - ln[r/(1-r)]t = – 0.90 + 0.32 ln[r/(1-r)]t-1 + 0.22 ln[r/(1-r)]t-2 – 0.72 tt + 0.05 Rdis,t.
    - t-statistics (in parentheses in source): (-2.26) (2.40) (2.29) (-3.40) (2.29). R2 = 0.70.
  - Coefficients: higher t reduces demand for reserves; higher discount rate increases demand for reserves.
- Conclusion: structural models can reliably characterize the reserve ratio r; structural forecasting of full multiplier unlikely to be reliable because c and t appear independent of usual explanatory variables in this context.

### Modeling money demand
A. Cointegration analysis (long-run)
- Focus: M1 (quarterly data 1980–2003) because M2 includes assets reacting differently to interest and dollar-denominated deposits tied to foreign investment.
- Long-run money market equilibrium specified as: M1 / P = f(y, ψ, ζ).
- Variables: lm1 minus lcpi or lgdpdef; lgdpr as real GDP; ψ proxied by inflation (dlgdpdef or dlipc) and exchange rate depreciation (dlerya); structural dummies dumg (4/1993–1/1995) and dumer (4/1990–1/1991; 1/1995–3/1995); seasonal dummies dumq2, dumq3, dumq4.
- Johansen trace test suggests one cointegrating relationship at 1 percent with expected signs. Estimated cointegrating relation (normalized on lm1):
  - lm1 – 1.13 lcpi = 6.06 + 1.27 lgdpr – 0.38 lerya.
  - Interpretation: coefficient on price level not significantly different from unity; coefficient on output not significantly different from unity at usual levels—consistent with constant velocity in long run; negative long-run association between real money balances and exchange rate level (lerya).
- Disequilibrium series Εt = lm1 – β2 lcpi – β3 lgdpr + β4 lerya shows:
  - Excess demand for most of 1980s; monetary overhang following the civil war (1994–95 excess supply); return to equilibrium end-1990s; some monetary overhang at end-2003.

B. Short-run VECM
- VECM estimated in first differences for vector (lerya, lgdpr, lcpi, lm1) with four lags; sample 2/1981–4/2003 (91 observations); structural and seasonal dummies included.
- Lagged short-run dynamics (Table 5, coefficients and t-statistics summarized):
  - d(lerya): lags 1–4 coefficients: -0.15 (t -1.03), 0.07 (0.49), 0.32 (2.30), -0.14 (-1.14).
  - d(lgdpr): lags 1–4 coefficients: 0.39 (t 2.41), 0.52 (3.05), -0.46 (-2.76), -0.20 (-1.17).
  - d(lipc): lags 1–4 coefficients: 0.60 (t 1.71), -0.29 (-0.76), -0.60 (-1.57), 0.25 (0.80).
  - d(lm1): lags 1–4 coefficients: -0.30 (t -2.47), -0.12 (-1.02), 0.03 (0.28), 0.29 (2.47).
- Structural and seasonal dummies (Table 6):
  - DUMER coefficient 0.02 (t -0.60).
  - DUMG coefficient 0.08 (t 1.38).
  - DUMQ2 coefficient 0.11 (t 4.19).
  - DUMQ3 coefficient 0.05 (t 2.91).
  - DUMQ4 coefficient 0.05 (t 1.90).
  - Interpretation: seasonality consistent with agricultural cycle; DUMER and DUMG positive reflecting discrete reductions in nominal money demand responding to shocks.
- Long-run adjustment coefficients (alphas) from VECM (Table 7; coefficients and t-statistics):
  - d(lerya) alpha = 0.003 (t -0.721).
  - D(lgdpr) alpha = 0.018 (t 5.045).
  - d(lipc) alpha = 0.004 (t 2.295).
  - d(lm1) alpha = -0.002 (t -0.289).
  - Interpretation: adjustment of nominal money partly driven by disequilibrium; about 2 percent per year of disequilibrium transmitted to price level; about 8 percent per year transmitted to real output (as noted in text, GDP alpha approx 0.08/year when annualized interpretation—source text states "approximately 8 percent of the disequilibrium per year being transmitted to this variable").
- Model fit:
  - VECM in levels fits actual series well up to 1997; larger residuals later in sample possibly due to more frequent shocks and more alternatives to money offered by banks.
  - Reduced-form VECM in levels produces fitted nominal money demand series (Figure 4 and Table A3 provide fitted values and lag structure).

C. Possible extensions (identified in source)
- Distinguish between monetary and non-monetary GDP (agricultural barter/nonmarket activity).
- Investigate weather-related shocks: positive shocks expand monetized sector raising real money demand; negative shocks shrink monetized sector causing excess supply of real balances.
- Use a “core CPI” to separate weather-related food volatility from core inflation; core inflation may be I(1).
- Compile parallel market exchange rate premia series to better reflect relative price of foreign exchange (official market may not reflect black market premia).
- Consider structural identification in VECM (structural VECM with theory-motivated identification conditions rather than Cholesky ordering).

### Conclusions and policy recommendations
- Overall assessment:
  - Econometric monetary analysis for Rwanda yields statistically and economically reasonable results useful for policymaking, but experienced policy judgment must supersede models.
  - Statistical properties weaker than for advanced economies.
  - For multipliers: non-theoretical (time series) models outperform structural models given data limitations.
  - For money demand: short-run VECM better than long-run cointegration due to frequent shocks.
- Main policy implications (as stated in source):
  - Public sector operations should be coordinated more closely to reduce volatility in the multipliers.
    - Most volatility in multipliers comes from reserve ratio (monetary policy operations of NBR) rather than currency ratio.
    - Need to coordinate public sector operations given their effect on liquidity and analyze use of different monetary policy instruments.
  - NBR should promote measures to stabilize excess reserves.
    - Examples of measures: closing commercial bank accounts at the central bank later in the day; promoting interbank market by reducing credit risk through more transparency (for example, an automated book-entry system).
  - NBR’s monetary programming should attribute higher weight to specification of money demand.
    - Despite volatility and controls, money demand in short and long run reacts consistent with fundamentals.
    - Incorporating money demand when planning FX and money market interventions (discount rate changes and open market operations) could help avoid monetary overhangs, exchange rate volatility, or bursts in core inflation.

*Source: IMF Working Paper content (authors’ calculations; National Bank of Rwanda data) as provided in the supplied PDF excerpt.*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2005/_wp05178.pdf_