## _wp11273 - 2007.  Domestic  capital  markets  have  also  started  to  develop,  although  still  remaining  nascent,

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---

### Objective and background
- Objective: analyze the stability of the demand for money in Ghana.
- Motivation and context:
  - Domestic capital markets started to develop, offering stocks, treasury bills and bonds.
  - New payment instruments (credit and debit cards), modern payment technology, and electronic banking are making inroads and are expected to reduce cash demand and expand banking services to rural communities.
  - Financial deepening may affect money velocity and the stability of the monetary transmission mechanism, with potential implications for monetary policy frameworks (e.g., move to inflation targeting).
- Data:
  - Study period: 1990Q1—2009Q4 (80 data points).
  - Rebased national accounts increased Ghana’s per capita incomes on average by about 65 percent.
  - Quarterly frequency for most variables; nominal GDP converted to quarterly series by direct and smooth decomposition of annual data.

### Literature review (selected findings)
- General empirical findings on money demand:
  - Estimated average income elasticity usually close to one, sensitive to monetary aggregate choice and inclusion of additional explanatory factors.
  - Interest rate inclusion yields negative estimated elasticity for money demand.
- Mixed evidence on financial liberalization:
  - Some studies find instability in money demand when deregulation and innovation occur; other studies find stability when accounting for alternative financial assets.
- African and Ghana-specific evidence:
  - Bahmani-Oskooee and Gelan (2009): in most African countries, including Ghana, a stable cointegrating money demand relation can be established between broad money, income, inflation, and nominal exchange rate.
  - South Africa: Nell (2003), Todani (2007) find relatively stable money demand but weak linkage between money and inflation.
  - Ghana prior studies:
    - Ghartey (1998): stable demand for nominal narrow money (1970Q4–1992Q4).
    - Bawumia and Abradu-Otoo (2003): stable long-run relationship between inflation and broad money (1983–1999).
    - Amoah and Mumuni (2008): structural reforms led to parameter instability in demand for broad money (1980Q1–2007Q1).

### Empirical approach and data characteristics
- Unit-root testing:
  - Augmented Dickey-Fuller tests with lag length by Schwarz information criterion; tests include constant and with/without trend.
  - Cannot reject unit root in level variables; most variables stationary in first difference except broad money (both nominal and real).
  - Cannot reject unit root in first difference of nominal broad money (M2+) and tests suggest a linear time trend in real broad money.
- Modeling framework:
  - Bounds testing (Pesaran et al., 2001) used to assess existence of stable money demand; accommodates I(0) and I(1) variables.
  - ARDL specification estimated; model selection guided by Akaike’s and Schwarz’s criteria and serial correlation tests (LM(1), LM(4)).
  - Financial variables (various interest rates) produced statistically insignificant estimates; nominal effective exchange rate (NEER) performed better than GH¢/USD.
  - Monetary aggregate: M2+ (broad money including foreign currency deposits) provided better empirical fit.

### Key estimation results
- Lag selection and bounds tests:
  - Information criteria and serial correlation tests suggested including four lags to minimize residual serial correlation.
  - Bounds F-tests reject null of no long-run money demand equation at 1 percent significance for models with four or five lags.
  - No deterministic trend preferred for t-test on real money.
- Parsimonious long-run ARDL: ARDL(6, 8, 4) for (real money, income, NEER).
- Long-run coefficients (ARDL(6, 8, 4):
  - Income elasticity (long-run): 1.75.
  - NEER coefficient (long-run): -2.6.
    - Interpretation: currency depreciation increases demand for broad money due to valuation and substitution into foreign-currency deposits.
- Short-run dynamics (error-correction model):
  - Mean-reversion (error-correction) coefficient: -0.47 (suggests substantial correction within one-year time frame).
  - Short-run income elasticity: close to one.
  - Short-run parameters sum to 0.39 (indicating initial overshooting of money demand from changes in real income).
  - Initial short-run exchange rate effect: -0.14.
  - Compounded exchange rate effect over five quarters: -0.76.
- ARDL short-run coefficients (selected reported estimates):
  - Log(M2+/P): coefficient -0.14, Errort 0.04, t-Stat. -3.17, Prob. 0.00.
  - Log(y): coefficient 0.25, Errort 0.08, t-Stat. 3.17, Prob. 0.00.
  - D_Log(NEER): coefficient -0.37, Errort 0.18, t-Stat. -2.04, Prob. 0.05.
  - Constant: -0.64, Errort 0.20, t-Stat. -3.13, Prob. 0.00.
- Model diagnostics (error-correction form):
  - R-squared: 0.91.
  - Adjusted R-squared: 0.87.
  - S.E. of regression: 0.03.
  - Sum squared resid: 0.04.
  - Akaike info criterion: -3.88.
  - Schwarz criterion: -3.14.
  - Hannan-Quinn criter.: -3.58.
  - F-statistic: 21.68.
  - Prob(F-statistic): 0.00.
  - Durbin-Watson stat: 1.87.
- Stability tests:
  - Recursive CUSUM and CUSUM squares tests applied to residuals of the error-correction model.
  - Test statistics remain within 5 percent critical values, confirming stability of the estimated money demand equation over the sample.

### Conclusions and policy-relevant implications
- Main conclusion: despite considerable volatility and financial reforms during 1990Q1—2009Q4, a stable money demand function for Ghana is found using the Pesaran et al. (2001) bounds testing approach.
- Determinants and parameter findings:
  - Key determinants of money demand: real income and exchange rate.
  - Other financial variables (interest rates) were statistically insignificant.
  - Exchange rate importance suggests currency substitution and valuation effects are relevant in Ghana.
  - Insignificance of interest rates may indicate financial markets are yet to play an important role in the public’s financial decisions—an area for further research.
- Monetary policy implications:
  - Ghana implements monetary policy within an inflation-targeting arrangement where the operating target is a short-term money market interest rate; effectiveness of policy thus does not rest on stability of money velocity.
  - Money and credit aggregates are reviewed by the monetary policy committee alongside other information to assess policy stance.
  - Having a stable money demand relation does not by itself imply that broad money should play a more prominent role in policy; the information content of money for forecasting prices remains an open question for Ghana and is left for future research.
- Observational remark: in recent times, rapid money growth has been observed amid falling inflation in Ghana.

### Appendix — selected summary statistics (1990Q1–2009Q4, Observations: 79)
- Means:
  - D(LOG M2): 0.07
  - D(LOG M2+): 0.08
  - VELOCITY: 6.44
  - LOG(1+DEP_INT): 0.05
  - LOG(1+TB_INT): 0.06
  - LOG(RGDP): 3.71
  - INFL: 0.05
- Medians:
  - D(LOG M2): 0.05
  - D(LOG M2+): 0.06
  - VELOCITY: 6.19
  - LOG(1+DEP_INT): 0.05
  - LOG(1+TB_INT): 0.06
  - LOG(RGDP): 3.60
  - INFL: 0.04
- Maximums:
  - D(LOG M2): 0.30
  - D(LOG M2+): 0.25
  - VELOCITY: 11.98
  - LOG(1+DEP_INT): 0.09
  - LOG(1+TB_INT): 0.11
  - LOG(RGDP): 4.42
  - INFL: 0.18
- Minimums:
  - D(LOG M2): -0.04
  - D(LOG M2+): -0.02
  - VELOCITY: 3.60
  - LOG(1+DEP_INT): 0.02
  - LOG(1+TB_INT): 0.02
  - LOG(RGDP): 3.15
  - INFL: -0.02
- Standard deviations:
  - D(LOG M2): 0.08
  - D(LOG M2+): 0.06
  - VELOCITY: 1.99
  - LOG(1+DEP_INT): 0.02
  - LOG(1+TB_INT): 0.02
  - LOG(RGDP): 0.36
  - INFL: 0.04
- Selected distribution statistics:
  - Skewness (VELOCITY): 0.99; Kurtosis (VELOCITY): 3.40; Jarque-Bera (VELOCITY): 3.55; Probability: 0.0
  - D(LOG M2) Jarque-Bera: 14.91; Probability: 0.0
  - D(LOG M2+) Jarque-Bera: 10.91; Probability: 0.0

*Source: authors' estimates and analysis provided in the content unit.*

### 2007.  Domestic  capital  markets  have  also  started  to  develop,  although  still  remaining  nascent,

### _wp11273 - 2007.  Domestic  capital  markets  have  also  started  to  develop,  although  still  remaining  nascent,

### Objective and background
- Objective: analyze the stability of the demand for money in Ghana.
- Motivation:
  - Domestic capital markets started to develop, offering stocks, treasury bills and bonds.
  - New payment instruments (credit and debit cards), modern payment technology, and electronic banking are making inroads and are expected to reduce cash demand and expand banking services to rural communities.
  - Financial deepening may affect money velocity and the stability of the monetary transmission mechanism, with potential implications for monetary policy frameworks (e.g., move to inflation targeting).
- Data context:
  - Study period: 1990Q1—2009Q4 (80 data points).
  - Rebased national accounts increased Ghana’s per capita incomes on average by about 65 percent.
  - Quarterly frequency for most variables; nominal GDP converted to quarterly series by direct and smooth decomposition of annual data.

### Literature review (selected findings)
- General empirical findings on money demand:
  - Estimated average income elasticity usually close to one, sensitive to monetary aggregate choice and inclusion of additional explanatory factors.
  - Interest rate inclusion yields negative estimated elasticity for money demand.
- Mixed evidence on effects of financial liberalization:
  - Some studies find instability in money demand when deregulation and innovation occur; other studies find stability when accounting for alternative financial assets.
- African evidence:
  - Bahmani-Oskooee and Gelan (2009) report that in most African countries, including Ghana, a stable cointegrating money demand relation can be established between broad money, income, inflation, and nominal exchange rate.
  - South Africa studies (Nell (2003), Todani (2007)) find relatively stable money demand but weak linkage between money and inflation.
- Ghana-specific prior studies:
  - Ghartey (1998): stable demand function for nominal narrow money (1970Q4–1992Q4).
  - Bawumia and Abradu-Otoo (2003): stable long-run relationship between inflation and broad money (1983–1999).
  - Amoah and Mumuni (2008): structural reforms led to parameter instability in demand for broad money (1980Q1–2007Q1).

### Empirical approach and data characteristics
- Unit-root testing (Augmented Dickey-Fuller):
  - Lag length chosen by Schwarz information criterion; tests include constant and with/without trend.
  - Conclusion: cannot reject unit root in level variables; most variables stationary in first difference except broad money (both nominal and real).
  - Cannot reject unit root in first difference of nominal broad money (M2+) and tests suggest a linear time trend in real broad money.
- Modeling framework:
  - Bounds testing (Pesaran et al., 2001) employed to assess existence of a stable money demand function; allows variables that are I(0) or I(1).
  - ARDL specification used; model selection guided by Akaike’s and Schwarz’s criteria and serial correlation tests (LM(1), LM(4)).
  - Financial variables (various interest rates) produced statistically insignificant estimates; nominal effective exchange rate (NEER) performed better than Ghana cedi/USD exchange rate.
  - Monetary aggregate: broad money inclusive of foreign currency deposits (M2+ inclusive of foreign currency deposits) provided better empirical fit.

### Key estimation results
- Lag selection and bounds tests:
  - Information criteria and serial correlation tests suggested including four lags to minimize residual serial correlation.
  - Bounds F-tests reject null of no long-run money demand equation at 1 percent significance for models with four or five lags (no deterministic trend preferred for t-test on real money).
- Parsimonious long-run ARDL chosen: ARDL(6, 8, 4) for (real money, income, NEER) respectively.
- Long-run coefficients (from ARDL(6, 8, 4)):
  - Income elasticity (long-run): 1.75.
  - Nominal effective exchange rate coefficient (long-run): -2.6.
    - Interpretation: currency depreciation increases demand for broad money due to valuation and substitution into foreign-currency deposits.
- Short-run dynamics (error-correction model):
  - Mean-reversion (error-correction) coefficient: -0.47 (suggests substantial correction within one-year time frame).
  - Short-run income elasticity: close to one.
  - Short-run parameters sum to 0.39 (indicating initial overshooting of money demand from changes in real income).
  - Initial short-run exchange rate effect: -0.14.
  - Compounded exchange rate effect over five quarters: -0.76.
- ARDL short-run coefficients (selected exact reported estimates):
  - Parameter for Log(M2+/P): coefficient -0.14, Errort 0.04, t-Stat. -3.17, Prob. 0.00.
  - Parameter for Log(y): coefficient 0.25, Errort 0.08, t-Stat. 3.17, Prob. 0.00.
  - Parameter for D_Log(NEER): coefficient -0.37, Errort 0.18, t-Stat. -2.04, Prob. 0.05.
  - Constant: -0.64, Errort 0.20, t-Stat. -3.13, Prob. 0.00.
- Model diagnostics (error-correction form reported):
  - R-squared: 0.91; Adjusted R-squared: 0.87.
  - S.E. of regression: 0.03; Sum squared resid: 0.04.
  - Akaike info criterion: -3.88; Schwarz criterion: -3.14; Hannan-Quinn criter.: -3.58.
  - F-statistic: 21.68; Prob(F-statistic): 0.00.
  - Durbin-Watson stat: 1.87.
- Stability tests:
  - Recursive CUSUM and CUSUM squares tests applied to residuals of the error-correction model.
  - Test statistics remain within 5 percent critical values, confirming stability of the estimated money demand equation over the sample.

### Conclusions and policy-relevant implications
- Main conclusion: despite considerable volatility and financial reforms during 1990Q1—2009Q4, a stable money demand function for Ghana is found using the Pesaran et al. (2001) bounds testing approach.
- Key determinants of money demand: real income and exchange rate. Other financial variables (interest rates) were statistically insignificant.
- Exchange rate importance suggests currency substitution and valuation effects are relevant in Ghana.
- Insignificance of interest rates may indicate that financial markets are yet to play an important role in the public’s financial decisions—an area for further research.
- Implications for monetary policy:
  - Ghana implements monetary policy within an inflation-targeting arrangement where the operating target is a short-term money market interest rate; effectiveness of policy thus does not rest on stability of money velocity.
  - Money and credit aggregates are reviewed by the monetary policy committee alongside other information to assess policy stance.
  - Having a stable money demand relation does not by itself imply that broad money should play a more prominent role in policy; the information content of money for forecasting prices remains an open question for Ghana and is left for future research.
- Noted observational remark: in recent times, rapid money growth has been observed amid falling inflation in Ghana.

*Source: authors' estimates and analysis provided in the content unit.*

### REFERENCES

### _wp11273 - REFERENCES

### References
- Addison, Ernest,2008, “Lessons from Inflation-Targeting Developing Countries: The Case of Ghana,” International Symposium on Monetary Policy and Price Stability in the West African Economic and Monetary Union Zone, Dakar, Senegal.
- Akinlo, A Enisan, 2005, “The Stability of Money Demand in Nigeria: An Autoregressive Distributed Lag Approach,” Journal of Policy Modeling, 28, pp. 445-452.
- Amoah, Benjamin and Zakari Mumuni, 2008, “Choice of Monetary Policy Regime in Ghana,” Working Paper, Monetary Policy Analysis and Financial Stability Department, WP/BOG-2008/07, Bank of Ghana.
- Baharumshah, Ahmad Zubaidi, Siti Hamizah Mohd, and A. Mansur M. Masih, 2009, “The Stability of Money Demand in China: Evidence from the ARDL Model,” Economic Systems, 33, pp. 231-244.
- Bahmani-Oskooee, Mohsen and Abera Gelan, 2009, “How Stable is the Demand for Money in African Countries,” Journal of Economic Studies, 36(3), pp. 216-235.
- Bahmani-Oskooee, Mohsen and Hafez Rehman, 2005, “Stability of the Money Demand Function in Asian Developing Countries,” Applied Economics, 37, pp. 773-792.
- Bawumia, Mahamadu and Philip Abradu-Otoo, 2003, “Monetary Growth, Exchange Rate and Inflation in Ghana: An Error-Correction Analysis,” Working Paper, Monetary Policy Analysis and Financial Stability Department, WP/BOG-2003/05, Bank of Ghana.
- Buch, Claudia M., 2001, “Money Demand in Hungary and Poland,” Applied Economics, 33, pp. 989-999.
- Ghartey, Edward E., 1998, “Monetary Dynamics in Ghana: Evidence from Cointegration, Error Correction Modeling, and Exogeneity,” Journal of Development Economics, 57, pp. 473-486.
- Gil-Alana, 2004, “Modeling U.S. Interest Rates In Terms of I(d) Statistical Models,” The Quarterly Review of Economics and Finance,“ 44, pp. 475-86.
- Knell, Markus and Helmut Stix, 2006, “Three Decades of Money Demand Studies: Differences and Similarities,” Applied Economics, 38, pp. 805-818.
- Lee, Chien-Chiang and Mei-Se Chien, 2008, “Stability of Money Demand Function Revisited in China,” Applied Economics, 40, pp. 3185-3197.
- Mishkin, Frederic S., 1999, “International Experiences With Different Monetary Policy Regimes,” Journal of Monetary Economics, 43, pp. 579-605.
- Nell, Kevin S., 2003, “The Stability of M3 Money Demand and Monetary Growth Targets: The Case of South Africa,” The Journal of Development Studies, 39(3), pp. 151-180.
- Pesaran, M. Hashem, Yongcheol Shin, and Richard J. Smith, 2001, “Bounds Testing Approaches to the Analysis of Level Relationships, “Journal of Applied Econometrics, 16(3), pp. 289-326.
- Pradhan, Basanta K. and Arvind Subramanian, 2003, “On the Stability of Demand for Money in A Developing Economy: Some Empirical Issues,” Journal of Development Economics, 72, pp. 335-351.
- Rose, Andrew K., 1988, “Is the Real Interest Rate Stable?,” Journal of Finance, 43, pp. 1095–1112.
- Sriram, Subramanian S., 2001, “A Survey of Recent Empirical Money Demand Studies,” Staff Papers, International Monetary Fund, 47(3), pp. 334-365.
- Todani, K.R., 2007, “Long-Run M3 Demand in South Africa: A Cointegration VAR Model,” South African Journal of Economics, 75(4), pp. 681-692.
- Wu, Ge, 2009, “Broad Money Demand and Asset Substitution in China,” IMF Working Papers, 09/131 (Washington: International Monetary Fund).

### Figures
- Figure 1. Selected Data, 1990Q1–2009Q4
  - Series plotted (labels shown): LOG(M2+), LOG(CPI), LOG(RGDP), LOG(NEER), LOG(1+DEP_INT), LOG(1+US_TB_INT)
  - Time axis labels shown: 90 92 94 96 98 00 02 04 06 08 (interpreted as years 1990–2008 quarters within 1990Q1–2009Q4)
- Figure 2. CUSUM Test
  - Plot includes a 5% significance line labeled "CUSUM5% Significance"
  - Time axis labels shown: 98 99 00 01 02 03 04 05 06 07 08 09
- Figure 3. CUSUM of Squares Test
  - Plot includes a 5% significance line labeled "CUSUM of Squares5% Significance"
  - Time axis labels shown: 98 99 00 01 02 03 04 05 06 07 08 09

### Appendix Table 1. Summary Statistics, 1990Q1–2009Q4
- Variables (as labeled in table header): D(LOG M2), D(LOG M2+), VELOCITY, LOG(1+DEP_INT), LOG(1+TB_INT), LOG(RGDP), INFL
- Mean
  - D(LOG M2): 0.07
  - D(LOG M2+): 0.08
  - VELOCITY: 6.44
  - LOG(1+DEP_INT): 0.05
  - LOG(1+TB_INT): 0.06
  - LOG(RGDP): 3.71
  - INFL: 0.05
- Median
  - D(LOG M2): 0.05
  - D(LOG M2+): 0.06
  - VELOCITY: 6.19
  - LOG(1+DEP_INT): 0.05
  - LOG(1+TB_INT): 0.06
  - LOG(RGDP): 3.60
  - INFL: 0.04
- Maximum
  - D(LOG M2): 0.30
  - D(LOG M2+): 0.25
  - VELOCITY: 11.98
  - LOG(1+DEP_INT): 0.09
  - LOG(1+TB_INT): 0.11
  - LOG(RGDP): 4.42
  - INFL: 0.18
- Minimum
  - D(LOG M2): -0.04
  - D(LOG M2+): -0.02
  - VELOCITY: 3.60
  - LOG(1+DEP_INT): 0.02
  - LOG(1+TB_INT): 0.02
  - LOG(RGDP): 3.15
  - INFL: -0.02
- Std. Dev.
  - D(LOG M2): 0.08
  - D(LOG M2+): 0.06
  - VELOCITY: 1.99
  - LOG(1+DEP_INT): 0.02
  - LOG(1+TB_INT): 0.02
  - LOG(RGDP): 0.36
  - INFL: 0.04
- Skewness
  - D(LOG M2): 1.03
  - D(LOG M2+): 0.91
  - VELOCITY: 0.99
  - LOG(1+DEP_INT): 0.24
  - LOG(1+TB_INT): -0.02
  - LOG(RGDP): 0.50
  - INFL: 0.68
- Kurtosis
  - D(LOG M2): 3.52
  - D(LOG M2+): 3.16
  - VELOCITY: 3.40
  - LOG(1+DEP_INT): 1.84
  - LOG(1+TB_INT): 2.09
  - LOG(RGDP): 2.04
  - INFL: 3.42
- Jarque-Bera
  - D(LOG M2): 14.91
  - D(LOG M2+): 10.91
  - VELOCITY: 3.55
  - LOG(1+DEP_INT): 5.22
  - LOG(1+TB_INT): 2.86
  - LOG(RGDP): 6.46
  - INFL: 7.0
- Probability
  - D(LOG M2): 0.0
  - D(LOG M2+): 0.0
  - VELOCITY: 0.0
  - LOG(1+DEP_INT): 0.10
  - LOG(1+TB_INT): 0.30
  - LOG(RGDP): 0.00
  - INFL: 0.0
- Sum
  - D(LOG M2): 5.8
  - D(LOG M2+): 6.15
  - VELOCITY: 509.1
  - LOG(1+DEP_INT): 4.0
  - LOG(1+TB_INT): 5.1
  - LOG(RGDP): 293.3
  - INFL: 3.8
- Sum Sq. Dev.
  - D(LOG M2): 0.4
  - D(LOG M2+): 0.33
  - VELOCITY: 7.80
  - LOG(1+DEP_INT): 0.00
  - LOG(1+TB_INT): 0.40
  - LOG(RGDP): 0.1
- Observations: 79 for all variables
- Sources: Ghanaian authorities and authors' calculations.

### Appendix Table 2. Data Definitions
- M2: Broad money, excluding foreign currency deposits (in millions of cedis)
- M2+: Broad money, including foreign currency deposits (in millions of cedis)
- P: Consumer price index (100 = 2000)
- Y: Real GDP (in millions of cedis)
- NEER: Nominal effective exchange rate index (100 = 2000)
- Deposit rate: Average deposit interest rate offered by banks (annual percentage)
- TB rate: Three-month treasury bill interest rate (annual percentage)
- US TB rate: Three-month treasury bill interest rate (annual percentage)
- USD Libor: Three-month U.S. Libor interest rate (annual percentage)
- GH¢/USD: The exchange rate of Ghanaian cedi against the U.S. dollar.
- Velocity: Ratio Y/M2+

*Sources: Ghanaian authorities and authors’ estimates.*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2011/_wp11273.pdf_