## _wp16120

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---

### I. Introduction and objective
- Modern central banks aim to smooth overnight interbank rates at or close to the policy rate to influence and stabilize longer-term rates and prices.
- Purpose of the paper:
  - Analyze transmission of changes in the policy rate to the interbank interest rate.
  - Assess how volatility in overnight interbank rates affects volatility in other maturities in Kenya relative to a sample of seven IT countries (Ghana, Hungary, Poland, South Africa, Sweden, Thailand, and Uganda).
- Empirical approach:
  - Estimate exponential generalized autoregressive conditional heteroskedasticity (E-GARCH) models to examine daily volatility of interbank rates for Kenya and the seven IT countries.
  - Assess, for each country, effects of fitted variances of interbank rates on variances of longer-term interest rates.

### II. High-level findings
- Differences between countries in transition (including Kenya) and more advanced IT countries:
  - Volatility transmission, and its persistence and autocorrelation, are more likely in countries in transition to a more forward-looking monetary policy framework.
  - Central banks can influence short-term yields and their volatility through more pro-active smoothing of interbank interest rates around the policy rate.
  - Reserve requirements and direct targeting of interbank rates help mitigate volatility along the yield curve (literature evidence).

### III. Evolution of Kenya’s monetary policy framework
- Since the late 1990s Kenya pursued an inflation objective in the context of a managed float, with reserve money as the operational target.
- Since 2011 CBK embarked on modernizing its framework to make monetary policy more forward looking by shifting the operational target away from reserve money.
- Key operational changes since October 2011:
  - Central Bank Rate (CBR) gradually centered as operational anchor, acting as a ceiling for repo (7-day) and a floor for reverse repo (overnight).
  - Money market rates broadly converged to the CBR by end-2012.
  - July 2012: introduction of term auction deposits (TAD) with 14-, 21-, and 28-day maturities; CBR acts as ceiling in fixed volume auctions.
  - May 2015: CBK raised the spread for TAD actions to 250 basis points above the CBR.
  - June 2015: CBK introduced 3-day repos.
- Mandate and accountability:
  - Principal objective: formulate and implement monetary policy to achieve and maintain price stability and foster and maintain a stable financial system (2010 Central Bank Act).
  - Without prejudice to these, CBK directed to support growth and employment.
  - Central Bank Act: National Treasury in consultation with CBK sets the inflation target at the beginning of every fiscal year.
  - Inflation target range: 5±2.5 percent since July 2012. (Text fragment shows "2012. In case of deviations..." implying the range and procedures.)

### IV. CBK operational context, inflation and money market outcomes
- CBK publishes a Monetary Policy Statement every six months since 1997; Monetary Policy Committee (MPC) normally meets every other month.
- Exchange rate and reserves:
  - Flexible exchange rate since mid-2000s with CBK interventions to mitigate excessive volatility and to build international reserves consistent with the East African Monetary Union convergence criterion of 4.5 months of import cover.
- Fiscal and reserve arrangements:
  - National Treasury may access overdraft facility at CBK up to 5 percent of most recent audited revenues of central government (about 1 percent of GDP).
  - Reserve requirement ratio: 5.25 percent of total commercial bank domestic and foreign currency liabilities; maintenance period 30 days; commercial bank reserves required not to fall below 3 percent of total liabilities on a daily basis.
- Inflation performance:
  - Official inflation target range: 5±2.5 percent.
  - Headline inflation stayed above the official target in 28 of the last 37 months and has not been below the mid-point of the target range since June 2013.
  - Average non-food non-oil inflation during the same period was slightly above 5 percent.
- Interbank rate deviations and volatility:
  - Large and persistent deviations of the overnight interbank rate from the policy rate: mostly fluctuated within a +/-250 basis points range, but at times deviations have exceeded 1,500 basis points.
  - Median absolute deviation of the overnight rate from the policy rate is about 185 basis points since October 2011, 210 basis points for the first nine months of 2015.

### V. Macro-financial frictions affecting money markets
- Main contributors to persistent deviations of the overnight interbank rate from the policy rate:
  - Large and unpredictable fiscal flows.
  - Narrow room for short-term financing to the government as use of the overdraft facility is frequently at the ceiling.
  - Weak coordination between fiscal and monetary authorities in their interaction with financial markets.
  - Ad-hoc central bank measures in response to exchange rate pressures (e.g., suspension of reverse-repo liquidity injections and restrictions to banks’ access to the overnight discount window).
- Net government deposits at the CBK are volatile (figure referenced in source).

### VI. Data, analytical capacity and data limitations
- Monthly inflation rates released by Kenya National Bureau of Statistics at month-end.
- CBK conducts end-year inflation expectations survey every other month (not published).
- 2013: CBK created a Monetary Policy Analysis Unit within Research Department using an in-house forecasting and policy analysis system (FPAS), re-designed into an inflation modeling and forecasting unit in March 2015.
- Data coverage and limitations:
  - For SSA countries (Kenya, Ghana, South Africa, Uganda), lack of daily secondary market T-bill data restricts analysis to weekly/bi-weekly auction yields.
  - Weekly auction yields for 3- and 6-month T-bill auction yields available in Kenya since 2012; 12-month T-bills auctioned once a month until March 2013 and weekly thereafter.
- Countries in the sample and data sources: Kenya, Ghana, Hungary, Poland, South Africa, Sweden, Thailand, and Uganda (annex lists specific series and frequencies).

### VII. Econometric approach
- E-GARCH(1,1) specification to model overnight interbank rate volatility and transmission to 3-, 6-, and 12-month yields; allows for asymmetric positive and negative deviations.
- Two-stage estimation:
  - Stage 1: model interbank volatility with AR(m) mean equation including an error-correction term (lagged interbank-policy rate spread) and control variables X (e.g., VIX, maintenance-period dummies).
  - Stage 2: model volatilities of 3-, 6-, 12-month rates with same approach but include estimated conditional variance of interbank rate (log) in the variance equation to measure volatility transmission.
- Differenced yields used (unit root tests indicate integration of maximum order 1). Student’s t-distribution used due to leptokurtosis in residuals.
- E-GARCH parameter notation (Annex III):
  - ∑ࢼ: sum of autoregressive coefficients.
  - ∑ߛ: sum of policy rate change coefficients.
  - ࢻ૚: coefficient of spread (interbank less policy rate).
  - ࣐: coefficient of the ARCH effect.
  - ࣓: coefficient on the GARCH effect.
  - ߜ: asymmetric volatility effect.
  - Ω: coefficient of ln conditional volatility of interbank rate (positive and significant → volatility transmission).

### VIII. Main empirical findings — transmission in means and errors
- Kenya (January 2012–June 2015 interbank dynamics):
  - A change in the official rate has an insignificant impact on Kenya’s overnight rate in the mean model.
  - Error-correction (rate at which difference between official and overnight rates narrows) equals 0.004 percent per period, indicating very slow mean reversion.
  - Policy rate had a weak impact on interbank rates during 2012-2015 in Kenya.
- Cross-country mean-adjustment examples (reported in source):
  - Uganda: a 100 percentage point official rate change impacts the 7-day interbank rate by 21 percentage points, with a decay rate of 28 percent per period; 80 percent of adjustment complete after about 4 days.
  - Hungary and Thailand: 80 percent of adjustment complete in 2 days and 7 days, respectively; Poland: 23 days for 80 percent.
  - Ghana: interbank rate does not respond significantly to policy rate changes; error-correcting term insignificant (behaves like a “random walk” around the policy rate).

### IX. Main empirical findings — volatility, asymmetry and transmission to T-bills
- Variance and asymmetry:
  - For Kenya and other SSA countries, variance equations show highly significant first-order ARCH and GARCH effects (autocorrelation and persistence in conditional volatility).
  - No evidence of asymmetric effects in conditional variance equations for Kenya, Ghana, Poland, and South Africa.
  - Asymmetric effects present in Uganda (6- and 12-month), Hungary (6-month), Sweden, and Thailand (all maturities).
- Volatility transmission to T-bills:
  - Evidence of volatility transmission from interbank rate to 3-, 6-, and 12-month T-bill yields in Kenya, Ghana, Hungary, Thailand, and Uganda.
  - Kenya immediate impact of volatility transmission:
    - 17 to 19 percent for 3- and 6-month maturities.
    - 16 percent for the 12-month maturity (not statistically significant).
  - Uganda: immediate volatility transmission ranges from 7 to 38 percent from the 7-day interbank rate.
  - Ghana: significant volatility transmission from overnight to 6-month maturity of 11 percent.
  - No volatility transmission found in South Africa, Poland, and Sweden.
  - Negligible transmission in Thailand (3-5 percent) and Hungary (only 6-month).
- Volatility along the yield curve:
  - Interbank conditional volatilities (overnight or 7-day) generally larger than for other maturities, except for Hungary and Uganda.
  - Uganda, Kenya, Hungary, and Ghana show the largest estimated conditional volatilities among the eight IT countries in the sample.

### X. Selected numerical results and reported parameter values (Kenya and comparisons)
- Kenya model summary (selected Table 1 / Annex III entries; values as in source):
  - Mean equation coefficients (Kenya):
    - α0 (overnight) = -0.009.
    - ∑β = 0.718 (3-month), ∑β = 0.633 (6-month), ∑β = 0.528 (12-month), ∑β = 0.402 (other autoregressive sum as printed).
    - Error correction α1 (overnight) = -0.004.
  - Variance equation coefficients (Kenya):
    - α2 (overnight) = -1.303.
    - ω (overnight) = 0.730.
    - δ (overnight) = 0.018.
    - φ (overnight) = 0.882.
    - Mean GARCH (overnight) = 0.103.
  - Variance-equation Ω (volatility transmission coefficients reported):
    - Ω = 0.171 (3-month), Ω = 0.189 (6-month), Ω = 0.164 (12-month).
  - Sample periods and observations:
    - Sample: 2012-15 for overnight and 3-, 6-, 12-month series.
    - N: 884 (overnight), 180 (3-month), 185 (6-month), 123 (12-month).
- Kenya descriptive statistics (Table A2.1 selected):
  - Mean: 0.012 (Overnight), 2.290 (|Spread|), -0.039 (3-month), -0.034 (6-month), 0.009 (12-month).
  - Median: 0.027 (Overnight), 1.738 (|Spread|), -0.016 (3-month), 0.000 (6-month), 0.000 (12-month).
  - Maximum: 0.998 (Overnight), 9.296 (|Spread|), 1.414 (3-month), 2.987 (6-month), 1.395 (12-month).
  - Minimum: -1.189 (Overnight), 0.001 (|Spread|), -1.298 (3-month), -1.848 (6-month), -1.045 (12-month).
  - Std. Dev.: 0.412 (Overnight, resized series), 1.855 (|Spread|), 0.456 (3-month, resized series), 0.488 (6-month), 0.302 (12-month).
  - Observations: 887 (Overnight), 887 (|Spread|), 189 (3-month), 189 (6-month), 126 (12-month).
  - Footnote: For differenced overnight and 3-month rates, top 5% most extreme values resized to equal 95th percentile. For overnight, std. dev. of original data is 0.564 and in resized data it is 0.412. For 3-month, std. dev. of original data is 0.545 and in resized data it is 0.456.
- Cross-country standing facility corridor widths (Jan. 2012–Jun. 2015 averages):
  - Kenya (informal): +/-250 bps.
  - Ghana: +/-190 bps.
  - South Africa: +/-100 bps.
  - Uganda: +/-200 bps.
  - Hungary: +/-100 bps.
  - Poland: +/-140 bps.
  - Sweden: +/-75 bps.
  - Thailand: +/-50 bps.

### XI. Policy implications and recommendations
- For countries transitioning toward IT (including Kenya), greater attention to smoothing interbank rates around the policy rate can:
  - improve transmission of policy rate changes to longer-term maturities,
  - reduce volatility transmitted along the yield curve,
  - help stabilize funding costs for longer-term financing.
- Tools and operational changes to mitigate yield-curve volatility:
  - Proactive day-to-day liquidity operations centered on the policy rate (narrower corridor).
  - Use of reserve requirements and direct targeting of interbank rates.
  - Introduction and tuning of short- and medium-term instruments (e.g., TAD, 3-day repos) to facilitate fine-tuning.
- Complementary policies to support a narrower corridor and smoother interbank rates:
  - Enhance coordination between fiscal and monetary operations.
  - Improve market infrastructure.
  - Reduce unpredictability of fiscal flows and expand short-term government financing room (overdraft frequently at ceiling).
- Central bank stance during exchange rate episodes:
  - Rapid smoothing of overnight rates around the policy rate can contain volatility transmission and make monetary policy more effective.

### XII. Areas suggested for further research (as noted in source)
- Whether slow overnight rate response in Kenya is endogenous to significant deviations of overnight rates from the policy rate.
- Whether faster response requires a larger central bank presence in markets in transition economies.

*Source: _wp16120 — IMF Working Paper content extracted from the supplied PDF.*

### 1. Policy Rate, Exchange Rate, and Inflation ______________________________________4

### 1. Policy Rate, Exchange Rate, and Inflation ______________________________________4

### I. Introduction: role of policy and interbank rates
- Modern central banks aim to smooth overnight interbank rates at or close to the policy rate to influence and stabilize longer-term rates and prices.
- Increased volatility of the overnight interbank interest rate can undermine the transmission of policy rate changes to longer-term funding costs.
- Transition away from conventional monetary targeting in many developing countries (including Kenya) reflected:
  - decreases in inflation rates to single digits,
  - rapid financial innovation,
  - greater integration with the global economy,
  - deregulation of financial markets and unstable money demand.
- Operational challenges in consistently hitting an interbank-rate operational target raise questions about readiness to adopt full-fledged inflation targeting (IT) frameworks.

### II. Objective and approach of the paper
- Purpose:
  - Analyze transmission of changes in the policy rate to the interbank interest rate.
  - Assess how volatility in overnight interbank rates affects volatility in other maturities in Kenya relative to a sample of seven IT countries.
- Sample of seven IT countries examined: Ghana, Hungary, Poland, South Africa, Sweden, Thailand, and Uganda.
- Empirical approach:
  - Estimate exponential generalized autoregressive conditional heteroskedasticity (E-GARCH) models to examine daily volatility of interbank rates for Kenya and the seven IT countries.
  - Assess, for each country, effects of fitted variances of interbank rates on variances of longer-term interest rates.

### III. Key findings (high-level)
- Results indicate important differences between countries in transition (including Kenya) and more advanced IT countries.
- Volatility transmission, and its persistence and autocorrelation, are more likely in countries in transition to a more forward-looking monetary policy framework.
- Central banks can influence short-term yields and their volatility through more pro-active smoothing of interbank interest rates around the policy rate.
- Evidence from the literature suggests reserve requirements and direct targeting of interbank rates help mitigate volatility along the yield curve.

### IV. Evolution of monetary policy framework in Kenya
- Since the late 1990s Kenya pursued an inflation objective in the context of a managed float, with reserve money as the operational target.
- Following frequent misses of monetary targets and a disconnect between money-target deviations and inflation performance, since 2011 the Central Bank of Kenya (CBK) embarked on modernizing its framework to make monetary policy more forward looking by shifting the operational target away from reserve money.
- Since October 2011, CBK steps toward a more forward-looking framework moving gradually towards an IT regime:
  - Central Bank Rate (CBR) was gradually centered as the operational anchor, acting as a ceiling for repo (7-day maturity) and a floor for reverse repo (overnight) operations.
  - Money market rates broadly converged to the CBR by end-2012.
  - To facilitate fine-tuning monetary operations, longer maturity instruments were introduced in July 2012: term auction deposits (TAD) with 14-, 21-, and 28-day maturities, with the CBR acting as a ceiling in fixed volume auctions.
  - CBK raised the spread for TAD actions to 250 basis points above the CBR in May 2015.
  - CBK introduced 3-day repos in June 2015.
- Mandate and accountability:
  - Principal objective of the CBK is formulating and implementing monetary policy to achieve and maintain price stability as well as fostering and maintaining a stable financial system (2010 Central Bank Act).
  - Without prejudice to these two objectives, CBK is also directed to support growth and employment.
  - The Central Bank Act stipulates that the National Treasury in consultation with the CBK sets the inflation target at the beginning of every fiscal year.
  - The inflation target range has been 5±2.5 percent since July

### V. Policy implications (drawn from findings)
- For countries transitioning toward IT (including Kenya), greater attention to smoothing interbank rates around the policy rate can:
  - improve transmission of policy rate changes to longer-term maturities,
  - reduce volatility transmitted along the yield curve,
  - help stabilize funding costs for longer-term financing.
- Tools to consider for mitigating yield-curve volatility include:
  - proactive day-to-day liquidity operations centered on the policy rate,
  - use of reserve requirements and direct targeting of interbank rates,
  - introduction and tuning of short- and medium-term instruments (e.g., TAD, 3-day repos) to facilitate fine-tuning.

*Source: _wp16120 - 1. Policy Rate, Exchange Rate, and Inflation ______________________________________4*

### 2012. In case of deviations from the target range for three consecutive months, the CBK is

### _wp16120 - 2012. In case of deviations from the target range for three consecutive months, the CBK is

### CBK framework and operational context
- The CBK has published a Monetary Policy Statement every six months since 1997.
- The Monetary Policy Committee (MPC) normally meets every other month and signals stance through the policy rate.
- Since mid-2000s Kenya has maintained a flexible exchange rate regime with CBK interventions to mitigate excessive volatility and to build international reserves consistent with the East African Monetary Union convergence criterion of 4.5 months of import cover.
- The Central Bank Act allows the National Treasury to access an overdraft facility at the CBK up to a ceiling of 5 percent of the most recent audited revenues of the central government (about 1 percent of GDP).
- Reserve requirement ratio is currently 5.25 percent of total commercial bank domestic and foreign currency liabilities; maintenance period is 30 days; commercial bank reserves are required not to fall below 3 percent of total liabilities on a daily basis.

### Inflation and monetary outcomes
- The official inflation target range is 5±2.5 percent.
- Headline inflation stayed above the official target in 28 of the last 37 months and has not been below the mid-point of the target range since June 2013.
- Average non-food non-oil inflation during the same period was slightly above 5 percent.
- Kenya has experienced large and persistent deviations of the overnight interbank rate from the policy rate; the interbank rate mostly fluctuated within a +/-250 basis points range, but at times deviations have exceeded 1,500 basis points.
- The median absolute deviation of the overnight rate from the policy rate is about 185 basis points since October 2011, 210 basis points for the first nine months of 2015.

### Macro-financial frictions affecting money markets
- Main contributors to persistent deviations of the overnight interbank rate from the policy rate:
  - Large and unpredictable fiscal flows.
  - Narrow room for short-term financing to the government as use of the overdraft facility is frequently at the ceiling.
  - Weak coordination between fiscal and monetary authorities in their interaction with financial markets.
  - Ad-hoc central bank measures in response to exchange rate pressures (for example, suspension of reverse-repo liquidity injections and restrictions to banks’ access to the overnight discount window).
- Net government deposits at the CBK are volatile (Figure 5 referenced).

### Data and analytical capacity
- Monthly inflation rates are released by Kenya National Bureau of Statistics at month-end.
- CBK conducts end-year inflation expectations survey every other month (not published).
- In 2013 CBK created a Monetary Policy Analysis Unit within Research Department using an in-house forecasting and policy analysis system (FPAS), re-designed into an inflation modeling and forecasting unit in March 2015.
- Data compiled for Kenya and seven IT countries: Ghana, Hungary, Poland, South Africa, Sweden, Thailand, and Uganda. For SSA countries (Kenya, Ghana, South Africa, Uganda), lack of daily secondary market T-bill data restricts analysis to weekly/bi-weekly auction yields.
- Weekly auction yields for 3- and 6-month T-bill auction yields are available in Kenya since 2012; 12-month T-bills auctioned once a month until March 2013 and weekly thereafter.

### Econometric approach
- E-GARCH(1,1) specification used to model overnight interbank rate volatility and transmission to 3-, 6-, and 12-month yields; allows for asymmetric positive and negative deviations.
- Two-stage estimation:
  - Stage 1: model interbank volatility with AR(m) mean equation including an error-correction term (lagged interbank-policy rate spread) and control variables X (e.g., VIX, maintenance-period dummies).
  - Stage 2: model volatilities of 3-, 6-, 12-month rates with same approach but include estimated conditional variance of interbank rate (log) in the variance equation to measure volatility transmission.
- Differenced yields used (unit root tests indicate integration of maximum order 1). Student’s t-distribution used due to leptokurtosis in residuals.

### Main empirical findings
- Interbank market dynamics (Kenya, January 2012–June 2015):
  - A change in the official rate has an insignificant impact on Kenya’s overnight rate in the mean model.
  - The error-correction (rate at which difference between official and overnight rates narrows) equals 0.004 percent per period, indicating very slow mean reversion.
  - The policy rate had a weak impact on interbank rates during 2012-2015 in Kenya.
- Cross-country comparison:
  - Uganda: a 100 percentage point official rate change impacts the 7-day interbank rate by 21 percentage points, with a decay rate of 28 percent per period; 80 percent of adjustment complete after about 4 days.
  - Hungary and Thailand: 80 percent of adjustment complete in 2 days and 7 days, respectively; Poland slower at 23 days.
  - Ghana: interbank rate does not respond significantly to policy rate changes and error-correcting term is insignificant (behaves like a “random walk” around the policy rate).
- Variance and asymmetry:
  - For Kenya and other SSA countries, variance equations show highly significant first-order ARCH and GARCH effects (autocorrelation and persistence in conditional volatility).
  - No evidence of asymmetric effects in conditional variance equations for Kenya, Ghana, Poland, and South Africa.
  - Asymmetric effects present in Uganda (6- and 12-month), Hungary (6-month), Sweden, and Thailand (all maturities).
- Volatility transmission to T-bills (Kenya and others):
  - Evidence of volatility transmission from interbank rate to 3-, 6-, and 12-month T-bill yields in Kenya, Ghana, Hungary, Thailand, and Uganda.
  - In Kenya the immediate impact of volatility transmission is:
    - 17 to 19 percent for 3- and 6-month maturities.
    - 16 percent for the 12-month maturity (not statistically significant).
  - Uganda: immediate volatility transmission ranges from 7 to 38 percent from the 7-day interbank rate.
  - Ghana: significant volatility transmission from overnight to 6-month maturity of 11 percent.
  - No volatility transmission found in South Africa, Poland, and Sweden; negligible transmission in Thailand (3-5 percent) and Hungary (only 6-month).
- Volatility along the yield curve:
  - Interbank conditional volatilities (overnight or 7-day) are generally larger than for other maturities, except for Hungary and Uganda.
  - Uganda, Kenya, Hungary, and Ghana show the largest estimated conditional volatilities among the eight IT countries in the sample.
- Summary numerical details from Kenya model (Table 1; values reported as in source):
  - Mean equation coefficients (Kenya): α0 = -0.009 (overnight), ∑β = 0.718 (3-month), ∑β = 0.633 (6-month), ∑β = 0.528 (12-month), ∑β = 0.402 (note: table formatting shows autoregressive sums by maturity).
  - Error correction α1 = -0.004 (overnight).
  - Variance equation coefficients (Kenya): α2 = -1.303 (overnight), ω = 0.730 (overnight), δ = 0.018 (overnight), φ = 0.882 (overnight), Mean GARCH = 0.103 (overnight).
  - Sample periods in table: overnight and 3-, 6-month: 2012-15; 12-month: 2013-15.
  - Number of observations N reported in Table 1: 884 (overnight), 180 (3-month), 185 (6-month), 123 (12-month).
- Standing facility corridor widths (Jan. 2012–Jun. 2015 averages):
  - Kenya (informal): +/-250 bps.
  - Ghana: +/-190 bps.
  - South Africa: +/-100 bps.
  - Uganda: +/-200 bps.
  - Hungary: +/-100 bps.
  - Poland: +/-140 bps.
  - Sweden: +/-75 bps.
  - Thailand: +/-50 bps.

### Policy implications and recommendations
- Strengthen commitment to the interbank rate as the operational target:
  - Creating a narrower corridor would force a faster rate of convergence in overnight rates, reduce persistence in volatility, and mitigate absolute volatility along the yield curve.
- Support narrowing corridor with complementary policies:
  - Enhance coordination between fiscal and monetary operations.
  - Improve market infrastructure.
  - Reduce unpredictability of fiscal flows and expand short-term government financing room (overdraft frequently at ceiling).
- Central bank stance during exchange rate episodes:
  - Rapid smoothing of overnight rates around the policy rate can contain volatility transmission and make monetary policy more effective.
- Areas for further research (hypotheses noted in source):
  - Whether slow overnight rate response in Kenya is endogenous to significant deviations of overnight rates from the policy rate.
  - Whether faster response requires a larger central bank presence in markets in transition economies.

*Source: IMF working paper content provided in the supplied PDF excerpt.*

### References

### _wp16120 - References

### References
- Ayuso, j., A. G. Haldane, and F. Restoy, 1997, “Volatility Transmission along the Money Market Yield Curve,” Weltwirtschaftliches Archiv, Vol. 133, No. 1, pp. 56-75.
- Carpenter S. B. and S. Demiralp, 2011, "Volatility, money market rates, and the transmission of monetary policy," Finance and Economics Discussion Series 2011-22, Board of Governors of the Federal Reserve System.
- Cohen, B., 1999, "Monetary Policy Procedures and Volatility Transmission along the Yield Curve," CGFS Papers chapters, in: Bank for International Settlements (ed.), Market Liquidity: Research Findings and Selected Policy Implications, volume 11, pages 1-22 Bank for International Settlements.
- Hammond, G., 2012, “State of the Art of Inflation Targeting,” Handbook No. 29, Centre for Central Banking Studies, Bank of England.
- IMF, 2014, Regional Economic Outlook: Sub-Saharan Africa (Washington, April).
- IMF, 2015a, “Evolving Monetary Policy Frameworks in Low-Income and Other Developing Countries,” Staff Report.
- IMF, 2015b, “Evolving Monetary Policy Frameworks in Low-Income and Other Developing Countries—Background Paper: Country Experiences,” Staff Report.
- Jacome, L., M. Matamorors-Indorf, M. Sharma, and S. Townsend, 2012, “Central Bank Credit to the Government: What Can we Learn from International Practices?” IMF Working Paper, WP/12/16.
- Maehle, N., 2015, “Monetary Policy Implementation: Operational Issues for Countries with Evolving Monetary Policy Regimes”, unpublished manuscript.
- Saxegaard, M., 2006, “Excess Liquidity and the Effectiveness of Monetary Policy: Evidence from Sub-Saharan Africa,” IMF Working Paper, WP/06/115.

### Annex I. Data and Sources — Data description (Table A1.1)
- Countries and data sources:
  - Kenya: Central bank website. Policy rate: Central Bank Rate; daily; Central Bank of Kenya (CBK). Interbank rate: Overnight interbank weighted average; daily; CBK. 3-, 6-, 12-month rates: CBK Treasury bill bid rates; weekly; CBK. Date IT adopted: Transitioning since 2011.
  - Ghana: Central bank website and Bloomberg. Policy rate: Monetary Policy Rate, daily, Bank of Ghana (BOG). Interbank rate: Overnight interbank weighted average; daily; BOG. 3-, 6-, 12-month rates: 91-, 182-day discount rates, 1-year fixed rate note; weekly; Bloomberg. Date IT adopted: Informally in 2002, formally from May 2007.
  - Hungary: Central bank website and DataStream. Policy rate: Central Bank Base Rate; daily; National Bank of Hungary. Interbank rate: HUFONIA; daily; National Bank of Hungary. 3-, 6-, 12-month rates: Treasury bill rates; daily; DataStream. Date IT adopted: June 2001.
  - Poland: Central bank website and DataStream. Policy rate: Reference Rate; daily; National Bank of Poland. Interbank rate: POLONIA; daily; National Bank of Poland. 3-, 6-, 12-month rates: WIBOR; daily; DataStream. Date IT adopted: 1998.
  - South Africa: Central bank website and Bloomberg. Policy rate: Repo rate; daily; South African Reserve Bank. Interbank rate: SABOR; daily; South African Reserve Bank. 3-, 6-, 12-month rates: Treasury bill bid rates; weekly; Bloomberg. Date IT adopted: February 2000.
  - Sweden: Central bank website. Policy rate: Repo Rate; daily; Sveriges Riksbank. Interbank rate: Sweden interbank tomorrow/next; daily; Sveriges Riksbank. 3-, 6-, 12-month rates: STIBOR, daily, Sveriges Riksbank. Date IT adopted: Announced in January 1993 and applied as of 1995.
  - Thailand: Central bank website. Policy rate: Bank of Thailand 1-day repo rate; daily; Bank of Thailand. Interbank rate: Weighted average interbank overnight; daily; Bank of Thailand. 3-, 6-, 12-month rates: BIBOR; daily; Bank of Thailand. Date IT adopted: May 2000.
  - Uganda: Central bank website and Bloomberg. Policy rate: Central Bank Rate; daily; Bank of Uganda. Interbank rate: 7-day interbank weighted average; daily; Bank of Uganda. 3-, 6-, 12-month rates: Treasury bill bid rates; biweekly; Bloomberg. Date IT adopted: Informally in July 2011, formally from June 2014.
- Note: See Hammond (2012) referenced for Date IT adopted footnote.

### Annex I — Figures (descriptive)
- Fig. A1.1: Policy and interbank rates in Kenya and IT economies in SSA, 2006-2015 (country-specific scales in vertical axes).
- Figure A1.2: Policy and interbank rates in selected IT economies, 2006-2015 (country-specific scales in vertical axes).
  - Plots referenced include Kenya (2012-2015), Ghana (2006-2015), South Africa (2007-2015), Uganda (2012-2015), Hungary (2006-2015), Poland (2006-2015), Sweden (2006-2015), Thailand (2011-2015). Axes tick values shown (examples): 0, 5, 10, 15, 20, 25, 30; and country-specific smaller scales (e.g., 0–14 for Ghana; -2–7 for Sweden; 0–4 for Thailand).

### Annex II. Descriptive statistics — Sub-Saharan Africa and remaining IT countries (Annex II tables)
- General notes on differenced rates:
  - For differenced overnight and 3-month rates, the top 5% most extreme values are resized to equal the 95th percentile in several country tables; the text reports original and resized standard deviations where applicable.
- Kenya (Table A2.1): Summary statistics of (differenced) rates (table headings include Overnight, |Spread|, 3-month, 6-month, 12-month). Selected reported values:
  - Mean: 0.012, 2.290, -0.039, -0.034, 0.009.
  - Median: 0.027, 1.738, -0.016, 0.000, 0.000.
  - Maximum: 0.998, 9.296, 1.414, 2.987, 1.395.
  - Minimum: -1.189, 0.001, -1.298, -1.848, -1.045.
  - Std. Dev.: 0.412, 1.855, 0.456, 0.488, 0.302.
  - Skewness: -0.395, 1.257, -0.036, 0.457, 0.499.
  - Kurtosis: 54613  9 (as printed).
  - Observations: 887, 887, 189, 189, 126.
  - Footnote: For differenced overnight and 3-month rates, top 5% most extreme values resized to equal 95th percentile. For overnight, std. dev. of original data is 0.564 and in resized data it is 0.412. For 3-month, std. dev. of original data is 0.545 and in resized data it is 0.456.
- Ghana (Table A2.2): Selected reported values:
  - Mean: 0.019, 2.242, 0.082, 0.084, -.
  - Median: 0.000, 1.850, 0.013, 0.007, -.
  - Maximum: 0.250, 6.750, 1.999, 3.532, -.
  - Minimum: -0.250, 0.000, -1.637, -0.914, -.
  - Std. Dev.: 0.082, 1.625, 0.361, 0.445, -.
  - Skewness: 0.162, 1.022, 2.037, 4.657, -.
  - Kurtosis: 631633- (as printed).
  - Observations: 847, 847, 176, 176, -.
  - Footnote: For the differenced overnight rates, the top 5% most extreme values are resized to equal the 95th percentile. The standard deviation of the original data is 0.159 and in the resized data it is 0.082.
- South Africa (Table A2.3): Selected reported values:
  - Mean: -0.002, 0.202, -0.009, -0.008, -0.001.
  - Median: 0.000, 0.210, 0.000, 0.000, 0.000.
  - Maximum: 0.420, 0.660, 1.060, 0.730, 1.030.
  - Minimum: -0.930, 0.000, -0.790, -0.690, -0.580.
  - Std. Dev.: 0.051, 0.082, 0.121, 0.117, 0.126.
  - Skewness: -9.133, 0.119, -0.312, -0.647, 1.880.
  - Kurtosis: 1734281621 (as printed).
  - Observations: 2174, 2174, 413, 410, 363.
- Uganda (Table A2.4): (table headings and summary statistics present; specific numeric entries not fully reproduced in source extract).
- Hungary (Table A2.5): Summary statistics (selected):
  - 7-day interbank |Spread| 3-month 6-month 12-month:
  - Mean: -0.022, 0.902, 0.001, 0.001, 0.005.
  - Median: 0.000, 0.310, 0.050, 0.060, 0.083.
  - Maximum: 4.836, 12.110, 4.005, 4.003, 4.642.
  - Minimum: -4.836, 0.000, -3.929, -5.609, -5.571.
  - Std. Dev.: 0.962, 1.572, 1.052, 1.068, 1.168.
  - Skewness: -0.209, 3.522, -0.953, -0.725, -0.210.
  - Kurtosis: 91881211 (as printed).
  - Observations: 749, 749, 103, 103, 103.
- Poland (Table A2.6): Selected reported values:
  - Mean: -0.003, 0.524, -0.003, -0.003, -0.003.
  - Median: -0.007, 0.348, 0.000, 0.000, 0.000.
  - Maximum: 2.280, 2.160, 0.200, 0.770, 0.920.
  - Minimum: -1.730, 0.000, -0.200, -0.680, -0.710.
  - Std. Dev.: 0.234, 0.451, 0.055, 0.077, 0.088.
  - Skewness: 0.469, 1.113, 0.079, 0.825, 1.228.
  - Kurtosis: 14472828 (as printed).
  - Observations: 2746, 2746, 2746, 2746, 2746.
  - Footnote: For the differenced 3-month rates, the top 5% most extreme values are resized to equal the 95th percentile. The standard deviation of the original data is 0.074 and in the resized data it is 0.055.
- Sweden (Table A2.7): Selected reported values:
  - Mean: -0.003, 0.161, -0.003, -0.003, -0.003.
  - Median: 0.000, 0.080, 0.000, 0.000, 0.000.
  - Maximum: 1.430, 1.380, 0.400, 0.610, 0.300.
  - Minimum: -1.190, 0.000, -0.350, -0.520, -0.300.
  - Std. Dev.: 0.193, 0.206, 0.101, 0.128, 0.119.
  - Skewness: 1.646, 2.515, 0.028, 0.067, -0.022.
  - Kurtosis: 1711564 (as printed).
  - Observations: 1006, 1006, 1006, 1006, 1006.
  - Footnote: For the differenced 12-month rates, the top 5% most extreme values are resized to equal the 95th percentile. The standard deviation of the original data is 0.133 and in the resized data it is 0.119.
- Thailand (Table A2.8): Selected reported values:
  - Overnight |Spread| 3-month 6-month 24-month:
  - Mean: -0.001, 0.116, -0.001, -0.001, -0.001.
  - Median: 0.000, 0.100, 0.000, 0.000, -0.001.
  - Maximum: 0.780, 1.725, 0.248, 0.290, 1.340.
  - Minimum: -1.751, 0.000, -0.639, -0.465, -0.248.
  - Std. Dev.: 0.071, 0.131, 0.037, 0.037, 0.051.
  - Skewness: -7.621, 5.634, -3.432, -1.529, 8.015.
  - Kurtosis: 213 555529218 (as printed).
  - Observations: 2322, 2322, 2322, 2322, 2322.
- Additional table entries report similar descriptive statistics for remaining maturities and difference adjustments; footnotes specify resizing of top 5% extreme values and corresponding original vs. resized standard deviations where applicable.

### Annex III. Estimation results — Model symbols and interpretation
- Definitions of symbols used in E-GARCH tables:
  - ∑ࢼ: the sum of coefficients of autoregressive lagged interest rates. Significance corresponds to most significant lag.
  - ∑ߛ: the sum of coefficients of current and possible lags of policy rate changes. Significance corresponds to most significant lag.
  - ࢻ૚: the coefficient of spread, defined as the interbank less the policy rate.
  - ࣓: the coefficient on the GARCH effect.
  - ߜ: the asymmetric volatility effect arising from idiosyncratic disturbances.
  - ࣐: the coefficient of the ARCH effect.
  - Ω: Coefficient of the natural logarithm of the conditional volatility of the relevant interbank rate. A positive and significant value implies volatility transmission from interbank rate to longer maturity instrument.

### Annex III — E-GARCH estimation results (selected tables and key reported values)
- Kenya (Table A3.1: E-GARCH model Estimation Results, 2012-15, daily/weekly). Mean Equation and Variance Equation selected entries:
  - Mean Equation ON (d), 3-month T-Bills (w), 6-month T-Bills (w), 12-month T-Bills (w):
    - α0: -0.009, -0.005, 0.000, -0.003.
    - ∑β: 0.718, 0.633, 0.528, 0.402.
    - ∑γ: -0.081, -0.018, 0.050, 0.203.
    - α1: -0.004 (ON only).
  - Variance Equation:
    - α2: -1.303, -0.392, 0.299, -0.830.
    - ω: 0.730, 1.057, 0.999, 1.634.
    - δ: 0.018, -0.116, -0.261, 0.234.
    - φ: 0.882, 0.821, 0.899, 0.727.
    - Ω: -, 0.171, 0.189, 0.164.
    - Mean GARCH: 0.103, 0.271, 0.628, 0.241.
    - Sample: 2012-15 for all maturities.
    - Error Dist.: Stu. t-dist. for all series.
    - N: 884, 180, 185, 123.
  - Note: Bold values indicate significance at 10 percent. Other control variables in mean and variance equations (not reported) may include VIX, garch-in-mean term, and dummy variables to account for maintenance period.
- Ghana (Table A3.2): Table present but detailed numeric entries not reproduced in source extract beyond notes. Note: Ghana's 1-year note yields have been constant during March 21, 2014 - October 30, 2015 at 22.5 percent. This rules out estimation at this maturity.
- South Africa (Table A3.3: E-GARCH model Estimation Results, 2007-15, daily/weekly). Selected entries:
  - Mean Equation ON (d), 3-month T-Bills (w), 6-month T-Bills (w), 12-month T-Bills (w):
    - α0: -0.001, 0.000, 0.001, 0.021.
    - ∑β: -0.237, 0.088, 0.223, 0.146.
    - ∑γ: 0.208, 0.497, 0.307, -0.168.
    - α1: -0.017 (ON only).
  - Variance Equation:
    - α2: -1.453, -0.890, -0.306, -1.967.
    - ω: 0.342, 0.423, 0.852, 0.856.
    - δ: 0.050, -0.020, -0.157, -.
    - φ: 0.801, 0.957, 0.777, 0.795.
    - Ω: -, -0.051, 0.192, -0.047.
    - Mean GARCH: 0.003, 0.028, 0.034, 0.033.
    - Sample periods: 2007-15 (ON), 2008-15 (3-month), 2008-15 (6-month), 2009-15 (12-month).
    - Error Dist.: Stu. t-dist. for all series.
    - N: 2156 (ON), 412 (3-month), 2389 (6-month), 352 (12-month) as printed.
- Uganda (Table A3.4): E-GARCH results referenced for 2012-15, daily/bi-weekly; specific numeric entries in source extract are limited.
- Hungary (Table A3.5: E-GARCH model Estimation Results, 2009-15, daily). Selected entries:
  - Mean Equation 7-day (d), 3-month T-Bills (bi-m), 6-month T-Bills (bi-m), 12-month T-Bills (bi-m):
    - α0: -0.020, -0.404, -0.411, -0.238.
    - ∑β: -0.363, 0.306, 0.400, 0.371.
    - ∑γ: 0.212, 0.230, 0.235, 0.298.
    - α1: -0.281 (7-day only).
  - Variance Equation:
    - α2: -0.228, 0.455, 0.003, -0.986.
    - ω: 0.353, 0.238, -0.480, -1.593.
    - δ: 0.047, 1.024, -0.281, -0.887.
    - φ: 0.989, -0.046, 0.839, 0.247.
    - Ω: -, 0.181, 0.073, 0.377.
    - Sample and Error Dist.: Sample entries include 2012-15 and 2013-15; Error Dist.: Stu. t-dist. for applicable series.
    - N: 746, 919, 164, 164 (as printed).
- Poland (Table A3.6): E-GARCH results (2012-15, daily). Selected entries:
  - Mean Equation ON (d), 3-month T-Bills (d), 6-month T-Bills (d), 12-month T-Bills (d):
    - α0: 0.013, -0.001, 0.000, -0.003.
    - ∑β: 0.097, 0.009, -0.036, 0.004.
    - ∑γ: 0.767, 0.022, 0.075, 0.081.
    - α1: -0.115 (ON only).
  - Variance Equation:
    - α2: -0.414, -0.447, -0.432, -0.773.
    - ω: 0.126, 3.417, 2.828, 1.000.
    - δ: 0.519, 0.875, -0.134, -0.074.
    - φ: 0.917, 0.950, 0.954, 0.925.
    - Ω: -0.014, 0.077, -0.008, -.
    - Sample: 2009-15 and 2009-15 entries indicated; Error Dist.: Stu. t-dist; N: 1658, 1658, 1495, 1495 as printed.
- Sweden (Table A3.7: E-GARCH model Estimation Results, 2006-15, daily). Selected entries:
  - Mean Equation ON (d), 3-month STIBOR (d), 6-month STIBOR (d), 2-year STIBOR (d):
    - α0: 2.213, 0.000, 1.713, 0.006.
    - ∑β: 0.048, -0.004, -0.167, -0.006.
    - ∑γ: 0.001, 0.015, -0.001, 0.018.
    - α1: -0.019 (ON only).
  - Variance Equation:
    - α2: -5.344, -0.027, -1.050, -0.535.
    - ω: 0.186, 0.672, 0.559, 0.157.
    - δ: 0.131, 0.128, -0.071, -0.045.
    - φ: 0.298, 0.998, 0.860, 0.937.
    - Ω: -0.011, 0.042, 0.007, -.
    - Sample: 2006-15 for all series; Error Dist.: G.E.D., Stu. t-dist., Stu. t-dist., G.E.D. as printed.
    - N: 2322, 2323, 2223, 2322, 2322 (as printed).
- Thailand (Table A3.8: E-GARCH model Estimation Results, 2011-15, daily). Selected entries:
  - Mean Equation ON (d), 3-month BIBOR (d), 6-month BIBOR (d), 12-month BIBOR (d):
    - α0: -0.008, 0.000, 0.000, 0.000.
    - ∑β: -0.488, 0.233, 0.316, 0.269.
    - ∑γ: 0.414, 0.058, 0.176, 0.033.
    - α1: -0.137 (ON only).
  - Variance Equation:
    - α2: -0.206, -0.096, -0.003, -.
    - ω: -0.330, 0.271, 0.905, -.
    - δ: -0.222, 0.116, 0.491, -.
    - φ: -0.988, 0.959, 0.964, -.
    - Ω: -0.057, 0.051, 0.031, -.
    - Sample: 2011-15 for all series; Error Dist.: Stu. t-dist. for reported series.
    - N: 1127, 1127, 1121, 1127 as printed.
- General note: In all tables, "Notes: Bold values indicate significance at 10 percent. Other control variables in mean and variance equations (not reported in the table) may include VIX, garch-in-mean term, and dummy variables to account for maintanence period."

*IMF Working Paper _wp16120 — References and Annexes (extracted content).*

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