## wpiea2019296-print-pdf — Introduction

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---

### Trends and motivation for publishing Autonomous Factor Forecasts (AFF)
- Central banks have become more independent and transparent over the past three decades (Dincer and Eichengreen 2014).
- Transparency aims to increase accountability and reinforce smooth policy implementation by fostering understanding of central bank objectives and building credibility (Ötker-Robe and others 2007; Laurens and others 2015).
- Transparency increased in macroeconomic forecasting and inflation targeting, but not equally in monetary policy implementation (Bindseil 2016).
- Sample and publication incidence:
  - Sample: 36 economies (17 advanced and 19 emerging markets), including nine EU non-euro and five EU candidates.
  - Of the 36 economies, 16 publish some sort of forecast (either AFF or a liquidity forecast based on projected autonomous factors).
  - Publication formats vary: most publish the sum of AFF without details; Denmark and Russia provide forecasts for individual autonomous factors.
- Rationale for AFF publication:
  - Current and future autonomous factors are pivotal for market participants to anticipate liquidity conditions and guide participation in central bank OMOs (Carpenter and Demiralp 2006; Vogel 2016).
  - Publication can create a level playing field by disclosing expected liquidity developments and help stabilize short-term rates close to the targeted policy rate.
- Association with operational frameworks:
  - A monetary policy framework with an interest rate target appears to motivate publication; many publishers operate an interest rate corridor under neutral liquidity allotment.
  - Economies operating corridor systems (22 in sample) more often publish forecasts than floor systems (10) or other systems (4).
  - Most sample central banks use calibrated allotment for OMOs (28); six use fixed rate and full allotment.

### Perceived costs and central bank reluctance
- Reluctance to publish AFF often stems from concerns about forecast quality and potential impact on central bank credibility when forecasts exhibit noticeable errors.
- No inherent reservations against publishing balance sheet items per se; reluctance is tied specifically to forecast errors and forecast quality.

### Objectives and structure of the analysis
- Objectives:
  - Analyze approaches of 36 economies to understand motivations to publish (or not) AFF.
  - Propose a framework for evaluating AFF and develop a forecast quality control paradigm to mitigate reservations.
  - Use the Eurosystem as a case study to implement the framework and analyze variations in forecast errors over time and correlates of forecast quality.
- Paper layout summary:
  - Section II: Policy of autonomous factors publication in the Eurosystem and other central banks; rationale; international best practices; Eurosystem publication history.
  - Section III: Evaluation of Eurosystem AFF in terms of accuracy and reliability; analysis of forecast errors and correlates.
  - Section IV: Conclusion.

### Evaluation framework: accuracy and reliability
- Two key dimensions:
  - Accuracy: Size of forecast errors; one-sided errors (bias) can lead to unwarranted market actions.
  - Reliability: Even unbiased forecasts can impose a liquidity premium if the likelihood of large forecast errors is high (i.e., low reliability).
- Three operational tests:
  - Root mean square error (RMSE) to test forecast accuracy (quadratic loss function).
  - Tests for conditional and unconditional forecasting bias (unbiasedness tests via regression).
  - Tests of reliability by examining volatility of forecast errors over time (e.g., moving-window RMSE).

### Data coverage and basic forecast-error statistics (Eurosystem)
- Data coverage: all published AFF from June 26, 2000, to August 19, 2019; realized autonomous liquidity factors and detailed OMO information published daily since January 1, 1999.
- Forecast error definition: AFF − AFR (autonomous factor forecast minus autonomous factor realized).
- Descriptive statistics:
  - Average absolute forecast error: EUR 2.2 billion for the first forecast.
  - Average absolute forecast error: EUR 1.7 billion for the second forecast.
  - Twice the standard error of the first forecast error: EUR 25 billion.
  - First forecast errors exceeded EUR 25 billion in 4 percent of the periods.
  - Second forecast errors exceeded EUR 25 billion in 2.4 percent of the periods.
- Moving-window and efficiency testing:
  - RMSE computed on a 90-forecast-period moving window (about 90 weeks).
  - Usefulness (efficiency) tested by checking whether forecast errors are uncorrelated with information known at forecast time.

### Best-practice implications for liquidity managers
- Good practice: analyze forecast errors as frequently as every maintenance period; incorporate accountability into transparency.
- Evaluation should include both accuracy (size) and reliability (frequency/volatility of large errors).
- High-quality AFF publication requires:
  - Use of the most contemporaneous information.
  - Awareness of market structure dynamics (e.g., money market segmentation) that can impair forecast quality.

---

### Box 1 — Autonomous Factors and the Eurosystem Information Advantage

- Composition: six autonomous-factor items in Eurosystem balance sheet:
  - (1) government deposits;
  - (2) net foreign assets;
  - (3) items in course of settlement;
  - (4) net assets denominated in euro (NADIE);
  - (5) banknotes in circulation; and
  - (6) other autonomous factors (OAF).
- Largest items: banknotes in circulation, government deposits, NADIE and OAF.
- Net Foreign Assets: play no role in the euro area under free-floating exchange rates (reduces need for official FX intervention).
- Predictability and information advantages:
  - Banknotes in circulation: predictable with statistical models capturing trends and seasonality; short-term signals from cash handlers.
  - Government deposits: main driver of AFF errors; central banks can use historical monthly/seasonal patterns and often have information-sharing with treasuries.
  - NADIE and OAF: NCBs may act as financial agent and can reinvest balances; client agreements to report large changes aid forecasting.
- Market mechanics under fixed rate and full allotment:
  - Two counterparty types: L1 (excess reserves) and L2 (refinancing needs).
  - If L2 banks are certain of S (supply of reserves), they can bid BL2 − S at MRO; coordination failure or market segmentation can prevent S from being fully available and produce volatile short-term rates or precautionary excess reserve demand.
- Historical episodes: after fixed rate and full allotment began in October 2008, there were periods (examples: 2009–2011 and 2014) where excess liquidity stock was insufficient to absorb banks’ needs, contributing to money market strains.

---

### International publication practices and timing (selected)
- Publication types observed across sample: AFF, liquidity forecasts, liquidity histories, liquidity targets, allotment targets.
- Timing and frequency examples:
  - Nine economies provide a forecast or target every day; one publishes intra-daily updates.
  - Eurosystem: weekly AFF in stocks (not flows); publication cadence commonly runs Monday to the Tuesday of the next week covering the seven-day MRO maturity (Wednesday to Tuesday) plus two extra days.
  - Japan: Daily projection for next business day plus monthly projection on first business day of month.
  - Canada: daily liquidity target for LVTS balance (tomorrow horizon), OMO match: No.
  - United States: FRBNY publishes factors affecting reserve balances weekly (one week horizon; timing Thursday 4.30 pm).
- Publication incidence patterns:
  - Publication practice similar across advanced and emerging economies, with a slightly greater tendency in emerging economies to not publish.
  - More central banks publish AFF under flexible exchange rate regimes than under fixed regimes.
  - Publication usually aligned with the maturity of main OMOs, but formats and timing conventions differ (Market open / Market close / OMO announcement / OMO allotment / Mondays-Tuesdays).

---

### Eurosystem publication history and procedures (selected)
- Regular publication of average AFF began June 2000 at MRO announcement.
- March 2004 changes:
  - Reserve maintenance timing aligned with MRO settlement; MRO maturity reduced from two weeks to one.
  - Publication of a benchmark allotment amount for MRO in addition to AFF; benchmark includes an excess liquidity objective (null or low under neutral allotment 2000–08; stable but not enforced under fixed rate and full allotment 2008–14).
  - Eurosystem publishes different AFF horizons: a nine-day forecast at MRO announcement and a seven-day forecast after MRO allotment.
  - From March 2004, an update on allotment day (Tuesday) substitutes the forecast of the first Monday with realized AFR for that day (cannot be used to bid at that MRO but helps interpret allotment deviations).
- Internal forecasting: NCBs and ECB jointly prepare AFF for all days of full maintenance period, updating to a minimum of 11 days; internal forecasts are not published.

---

### Forecast performance dynamics: fixed rate and full allotment (post-October 2008)
- RMSE and accuracy:
  - RMSE was close to one from October 2003 to December 2007, indicating high forecast accuracy during that period (post-March 2004 revision).
  - Introduction of the “new system” (fixed rate and full allotment, October 2008) associated with changes: despite a drop in 2009, RMSE remained above best pre-2008 performance as relatively larger forecast errors became more frequent.
  - Revised forecasts (“2nd forecasts”) generally more accurate than initial (“1st forecasts”) due to incorporation of more up-to-date information and inclusion of one day of AFR.
- Bias testing framework:
  - Regression: ∆log(AFRt) = c + β * ∆log(AFFt) + et
  - Unbiased forecast: β = 1 and c = 0.
  - Joint Wald test on rolling window of 90 forecasting periods (~90 weeks) from 2000 to 2019.
  - Test outcomes:
    - For the 1st forecast: the test rejects the null for 37 periods of 90 days out of 953 periods (4 percent) from 2000 to 2019.
    - For the 2nd forecast: the test rejects the null for 119 periods (12.5 percent).
  - Estimated conditional-bias coefficient β:
    - Significant for all periods and remained below one for each period.
    - Converged toward 1 from 2004 to 2008.
    - After 2008, β fluctuated between 0.9 and 0.5, indicating persistent overestimation bias.
- Error distribution and reliability:
  - Forecast-error distribution (Jul 2000–Aug 2019) is leptokurtic and positively skewed:
    - Forecast 1 (Jul 2000–Aug 2019): Kurtosis: 6.9; Skewness: 2.7
    - Forecast 2 (Jul 2000–Aug 2019): Kurtosis: 9.0; Skewness: 2.7
    - Forecast 2 (Mar 2004–Oct 2008): Kurtosis: 13.4; Skewness: 3.7
    - Forecast 2 (Jul 2000–Feb 2004 and Nov 2008–Aug 2019): Kurtosis: 3.7; Skewness: 2.1
  - Distributional asymmetry: right tail long (higher likelihood of overestimating AFR), but the fat tail of largest outliers lies on the left (largest errors underestimate AFR).
  - 2nd forecast errors are more concentrated around smaller values than 1st forecast; 1st forecast experienced larger and more frequent underestimation outliers.

---

### Explanatory regressions — factors correlated with forecast errors
- 1st forecast error specification:
  - e1,t = c + α1 * dL + α2 * dp + α3 * e1,t-1 + γ Xt + δ Zt + μt
  - Key variables:
    - dL: length of forecast in days (usually nine; reduced to seven for first operation of maintenance period).
    - dp: dummy for periods (March 2004–October 2008 reference).
    - Xt: market-segmentation indicators (sovereign spread, excess reserves as percent of reserve requirements, EONIA overnight volumes).
    - Zt: EONIA (controls for low interest rate environment).
- 2nd forecast error specification:
  - e2,t = c + α1 * dL + α2 * dp + α3 * e1,t + α4 * e2,t-1 + γ Xt + δ Zt + μt
  - Includes e1,t to test information use between forecasts (error-correction role).
- Main regression findings:
  - Both 1st and 2nd errors significantly correlated with explanatory variables (forecasts are not “strong” in efficiency; public information helps explain errors).
  - 2nd forecast yields smaller errors and less bias but is less “efficient” (higher R-square) because the 1st forecast error is a main explanatory variable.
  - Significant correlates for 1st forecast (full specification): sovereign spreads, excess reserves, and the March 2004–October 2008 dummy (lower errors in benchmark).
  - Significant correlates for 2nd forecast (full specification): excess reserves, EONIA volumes, the 1st forecast errors, and the March 2004–October 2008 dummy.
  - Persistence: 1st forecast errors correlated with previous-period 1st forecast errors; this persistence not corroborated for 2nd forecast errors.
  - Low interest-rate environment: 2nd forecast errors negatively correlated with EONIA levels; not corroborated for 1st forecast errors.
- Representative R-squared values (selected reported examples):
  - 1st forecast: 0.333, 0.334, 0.063, 0.197, 0.280, 0.246, 0.008, 0.161, 0.084
  - 2nd forecast: 0.463, 0.470, 0.026, 0.125, 0.203, 0.191, 0.000, 0.437, 0.088, 0.140

---

### Policy implications and recommendations
- Central banks could expand evaluation methods for AFF; the proposed forecast-bias test is simple to implement and would provide important information affecting forecast credibility.
- The forecast-bias test could be conducted separately for different types of autonomous factors to enhance diagnostics.
- Explaining forecast errors with public correlates offers hindsight on external factors influencing forecast quality; finer data granularity could improve diagnostics.
- Market conditions materially affect forecast quality: correlation between forecast errors and market-segmentation and low interest rate indicators corroborates market-environment influence.
  - Benchmark period 2004–2008 had high accuracy and reliability; forecast quality declined after the global financial crisis.
- Publication considerations:
  - Publication of AFF may become more salient as excess reserves decline; accurate forecasts are necessary to guide counterparty bidding under fixed rate and full allotment when high reserves no longer absorb coordination failures.
  - Improvements in market functioning and higher policy rates may improve forecast quality without central bank action.
  - Recommendation: central banks could run a dry-run evaluation period using the proposed methods before publication and publish forecasts once confident in their quality to protect credibility.
  - The evaluation method can inform the appropriate maturity of regular OMOs by indicating the horizon of high-quality forecasts.

*Source: wpiea2019296-print-pdf — Introduction (IMF staff summary of Box 1 and related sections).*

### Introduction ...........................................................................................................

### Introduction

### Trends and motivation for publishing Autonomous Factor Forecasts (AFF)
- Central banks have become more independent and transparent over the past three decades (Dincer and Eichengreen 2014).
- Transparency aims to increase accountability and reinforce smooth policy implementation by fostering understanding of central bank objectives and building credibility (Ötker-Robe and others 2007; Laurens and others 2015).
- Transparency has increased in macroeconomic forecasting and inflation targeting, but not equally in the implementation of monetary policy (Bindseil 2016).
- Only a limited number of central banks publish Autonomous Factor Forecasts (AFF) and readily accessible data on realized autonomous factors (AFR).
- Current and future autonomous factors are pivotal for money market participants to anticipate current and future liquidity conditions and to guide participation in central bank monetary policy operations (Carpenter and Demiralp 2006; Vogel 2016).
- Publication of AFF and AFR can create a level playing field by disclosing expected liquidity developments and help stabilize short-term rates close to the targeted policy rate.

### Perceived costs and central bank reluctance
- Reluctance to publish AFF often stems from concerns about forecast quality and potential impact on central bank credibility when forecasts exhibit noticeable errors.
- There are no inherent reservations against publishing balance sheet items that comprise autonomous factors; reluctance is tied to forecast errors and forecast quality.

### Objectives of the analysis in this content unit
- Analyze approaches of 36 economies to understand motivations to publish (or not) AFF.
- Propose a framework for evaluating AFF and develop a forecast quality control paradigm to mitigate reservations about forecast quality.
- Use the Eurosystem as a case study to implement the framework and analyze variations in forecast errors over time to identify factors influencing forecast quality.

### Key observations from international comparisons and the Eurosystem case
- About half of central banks publish AFF on a regular basis.
- Frequency, forecast horizon, and level of detail of AFF publications vary significantly across central banks.
- A monetary policy framework with an interest rate target appears to motivate publication; many publishers maintain an interest rate corridor system under neutral liquidity allotment (where the central bank calibrates its OMOs to provide the amount of reserve that banks require).
- The Eurosystem has published granular data on AFF and AFR since 2000, providing a time series long enough to cover shifts in liquidity conditions and operational frameworks.
- Using the most contemporaneous information supports high-quality forecasts.
- Money market segmentation reduces forecast quality.

### Structure of proposed evaluation and use of the Eurosystem dataset
- The evaluation framework emphasizes two dimensions of forecast quality:
  - Accuracy: Size of forecast errors; one-sided errors (bias) can lead to unwarranted market actions.
  - Reliability: Even unbiased forecasts can impose a liquidity premium if the likelihood of large forecast errors is high (i.e., low reliability).
- Three sets of tests operationalize these dimensions:
  - Root mean square error (RMSE) to test forecast accuracy (commonly used by liquidity managers).
  - Tests for conditional and unconditional forecasting bias to supplement accuracy checks.
  - Tests of reliability by examining the volatility of forecast errors over time.
- The Eurosystem case study is employed to run these tests and to identify correlates of forecast errors driven by structural changes in liquidity conditions and operational frameworks.

### Publication of Autonomous Factor Forecasts — Rationales and forecasting context

### The role of autonomous factors in banks' reserve demand and OMOs
- Banks’ demand for reserves is motivated by three factors:
  1. the reserve requirement;
  2. autonomous factors (which changes have an exogenous impact on banks’ reserves);
  3. a possible demand for excess reserves.
- Central banks need to forecast these three factors to calibrate their open market operations (OMOs) until the end of the maintenance period and to keep excess reserves low at the end of the maintenance period (Kraenzlin and Schlegel 2012).
- Proper forecasting anchors short-term rates close to the policy rate and prevents rates from drifting lower (if reserves are in excess) or higher (if reserves are insufficient) (Hilton and Hrung 2010).

### Predictability of components
- Reserve requirement: set by the central bank and known before the maintenance period, so no uncertainty over average reserves to be maintained.
- Demand for excess reserves: expected to be small, stable, and predictable in well-functioning money markets; may become large, volatile, and unpredictable if risk perception increases and money market functioning deteriorates (leading to market segmentation, increased volatility, and uneven market access).
- Forecast exercise focuses on autonomous factors that exhibit volatility over maintenance periods but that central banks can forecast with some accuracy.
- In the Eurosystem, besides currency in circulation, holdings at central banks by non-financial institutional clients (e.g., governments) are a main driver of autonomous factors.

### Best-practice implications for central bank liquidity managers
- Good practice suggests liquidity managers should analyze forecast errors as frequently as every maintenance period; such evaluations form part of accountability that accompanies transparency.
- Evaluation should go beyond accuracy (size of errors) and include reliability (frequency and volatility of large errors).
- High-quality AFF publication requires:
  - Use of the most contemporaneous information.
  - Awareness of market structure dynamics (e.g., money market segmentation) that can impair forecast quality.

### Paper layout (as presented)
- Section II: Policy of autonomous factors publication in the Eurosystem and other central banks; rationale; international best practices; history of publication in the Eurosystem.
- Section III: Evaluation of Eurosystem AFF in terms of accuracy and reliability; analysis of forecast errors and identification of supporting factors and impediments to forecast quality.
- Section IV: Conclusion.

*Source: wpiea2019296-print-pdf — Introduction*

### Box 1. Autonomous Factors and the Eurosystem Information Advantage

### Box 1. Autonomous Factors and the Eurosystem Information Advantage

### Definition and Composition of Autonomous Factors
- Six items qualify as autonomous factors in the Eurosystem balance sheet:
  - (1) government deposits;
  - (2) net foreign assets;
  - (3) items in course of settlement;
  - (4) net assets denominated in euro (NADIE);
  - (5) banknotes in circulation; and
  - (6) other autonomous factors (OAF).
- Largest and most important items: banknotes in circulation, government deposits, NADIE and OAF.
- Net Foreign Assets play no role in the euro area under free-floating exchange rates because such arrangements reduce the need for official FX intervention and thus stabilize the stock of these assets.

### Behavior and Forecasting of Key Autonomous Factors
- Banknotes in circulation:
  - Fluctuate with public demand for means of payment.
  - Long-term drivers: macroeconomic variables (for example, GDP growth) and financial innovation in payment systems.
  - Short-term drivers: seasonal patterns (higher use during holiday periods and often at year’s end).
  - Predictable in normal times with statistical models that capture long-term trends and seasonal tendencies; central banks can liaise with major cash handlers for near-term signals.
- Government deposits:
  - Influenced by tax collection, government payments (such as pensions or civil servant salaries), government debt issuance and redemption, and sovereign treasury cash management.
  - Size of AFF errors traditionally driven mainly by government deposits; error magnitude depends on how actively the treasury manages cash flows.
  - Central banks can derive monthly and seasonal patterns (especially tax collections) from historical data and often have information-sharing mechanisms with national treasuries, giving them an informational advantage over counterparties.
- NADIE and OAF:
  - Important due to reserve management services provided by several NCBs and by some clients that are neither Eurosystem banks nor governments (including non-Eurosystem central banks, supra-national, European, and international institutions).
  - NCBs sometimes act as financial agent for such institutional clients and can reinvest balances to neutralize liquidity impacts; in other cases clients manage accounts themselves.
  - Agreements to provide information about changes above a certain size help NCBs anticipate large changes.

### Market Implications and the Eurosystem Information Advantage
- Publication of AFF provides market participants information on expected supply of reserves (S), influencing banks’ decisions to seek market funding or central bank refinancing.
- Under fixed rate and full allotment:
  - Two counterparty types assumed: (1) banks with significant excess reserves and no refinancing needs (L1); (2) banks with refinancing needs (L2).
  - L2 banks may obtain unlimited refinancing for seven days at predetermined rate Rc (subject to collateral) or borrow in the overnight market at rate R (not determined ex ante).
  - If L2 banks are certain of S, they can bid exactly BL2 − S at MRO and collectively produce enough excess in L1 to drive short-term rates to the deposit facility rate.
  - Failure to collectively bid (coordination failure) or market segmentation (restrictive credit lines, country risk limits, collateral concentration limits) can make only part of S available in the market and lead to volatile short-term rates or precautionary excess reserve demand.
- Historical episodes:
  - Since introduction of fixed rate and full allotment in October 2008, periods occurred where excess liquidity stock was insufficient to absorb all banks’ needs, contributing to money market strains and high short-term rates (examples cited: 2009–2011 and 2014).

### International Publication Practices (Sample of 36 Economies)
- Sample composition:
  - 36 European Union (EU) and non-euro economies: 17 advanced and 19 emerging markets.
  - Includes nine EU non-euro countries (Bulgaria, Croatia, Czech Republic, Denmark, Hungary, Poland, Romania, Sweden, and United Kingdom) and five EU candidates (Albania, Montenegro, North Macedonia, Serbia, and Turkey).
  - Complemented by other advanced economies and OECD members (listed in source).
- Publication incidence and formats:
  - Of the 36 economies, 16 publish some sort of forecast (either autonomous factors forecast or a liquidity forecast based on projected autonomous factors).
  - Most central banks publish the sum of AFF without details; Denmark and Russia provide forecasts for individual autonomous factors.
  - Six economies provide a public target either for OMO allotment (allotment target) or for balance of banks’ accounts at the central bank (liquidity forecast).
  - Fourteen monetary authorities do not publish a forecast but publish some liquidity history, balance sheets, or broad monetary aggregates.
  - The Federal Reserve publishes a survey asking banks the minimum level of reserves they would be comfortable holding — the only initiative in the sample to publish an estimate of counterparties’ demand for reserves.
- Distributional findings:
  - Publication practice similar across advanced and emerging economies, with a slightly greater tendency in emerging economies to not publish.
  - More central banks publish AFF under flexible exchange rate regimes than under fixed regimes.
  - Economies operating corridor systems (22 in sample) more often publish forecasts than floor systems (10) or other systems (4).
  - Most sample central banks use calibrated allotment for OMOs (28); six stand out as fixed rate and full allotment; three had no applicable information.
- Timing and frequency:
  - Publication usually covers maturity of main OMOs, but some publish independently from OMOs.
  - Nine economies provide a forecast or target every day; one publishes intra-daily updates.
  - Publication formats vary: Eurosystem publishes AFF in stocks (not in flows), offering advantages in reconciling with balance sheet developments and comparing AFF and AFR at two points in time.

### Eurosystem Publication History and Procedures
- Eurosystem began regularly publishing average AFF in June 2000 in context of MRO announcement.
- March 2004 changes:
  - Timing of reserve maintenance period aligned to settlement of any MRO; MRO maturity reduced from two weeks to one.
  - Decided to publish a benchmark allotment amount for MRO in addition to AFF; benchmark is ECB estimate of liquidity to inject to fulfill banks’ liquidity needs (ECB not bound by benchmark).
  - Benchmark calculation includes an excess liquidity objective: null or low under neutral liquidity allotment (2000–08) or a stable (but not enforced) level of excess reserves under fixed rate and full allotment (2008–14).
- Forecast horizons and publication cadence:
  - Eurosystem publishes different horizons for AFF: a nine-day forecast published at MRO announcement and a seven-day forecast published after MRO allotment.
  - For published AFF, liquidity publication normally runs from Monday to the Tuesday of the next week, covering the seven-day MRO maturity (Wednesday to Tuesday) plus two extra days (first Monday and Tuesday).
  - For the first week of the maintenance period, estimates are reduced to seven days (Wednesday to Tuesday).
  - About 70 percent of estimates commenced on a Monday and 22 percent on a Wednesday (remainder due to holidays).
  - In March 2004 Eurosystem also began publishing an update of the autonomous factor estimate on the allotment day (Tuesday), substituting the forecast of the first Monday with the realized AFR for that day; this update cannot be used to bid at that MRO but helps interpret allotment deviations.
- Internal forecasting process:
  - At start of each maintenance period, NCBs and ECB jointly prepare AFF for all days of full maintenance period, updating forecasts for the rest of the period up to a minimum of 11 days; these internal forecasts are not published.

### Evaluating Forecast Quality: Accuracy and Reliability
- Data coverage for evaluation:
  - Study covers all published AFF from June 26, 2000, to August 19, 2019.
  - Realized autonomous liquidity factors and detailed information on OMOs and related operations have been published daily since January 1, 1999.
- Forecast errors and descriptive statistics:
  - Forecast errors defined as AFF − AFR (autonomous factor forecast minus autonomous factor realized).
  - Average absolute forecast error:
    - EUR 2.2 billion for the first forecast.
    - EUR 1.7 billion for the second forecast.
  - Twice the standard error of the first forecast error amounted to EUR 25 billion.
  - First forecast errors exceeded EUR 25 billion in 4 percent of the periods; second forecast errors exceeded EUR 25 billion in 2.4 percent of the periods — indicating notable improvement from first to second forecast.
- Evaluation metrics and methodology:
  - Accuracy assessed using RMSE (quadratic loss function) and unbiasedness tests; a 90-forecast-period moving window used to compute RMSE over time.
  - Reliability assessed as consistency of forecast performance (low volatility of forecast errors over time); sudden large deviations can create structural demand for excess reserves and money market premiums.
  - Usefulness (efficiency) evaluated by testing whether forecast errors are uncorrelated with information known at forecast time; a forecast is efficient if its error cannot be explained by information available when the forecast was made.
- Observed accuracy pattern:
  - RMSE was close to one from October 2003 to December 2007, indicating high forecast accuracy during that period; this broadly corresponds to the period after the March 2004 revision of the Eurosystem’s liquidity management framework.

*Source: IMF staff summary of "Box 1. Autonomous Factors and the Eurosystem Information Advantage" from wpiea2019296-print-pdf.*

### introduction of the fixed rate and full allotment in October 2008 (hereafter, the “new

### introduction of the fixed rate and full allotment in October 2008 (hereafter, the “new system”)

### Forecast accuracy and RMSE
- The introduction of the “new system” is associated with changes in forecast performance; despite a drop in 2009, the RMSE remained above its best performances after 2008 as relatively larger forecast errors became more frequent.
- The revised forecasts (“2nd forecasts”) tend to have a higher accuracy than the initial forecasts (“1st forecasts”), reflecting incorporation of more up-to-date information and inclusion of one day of AFR in the forecast average.
- Forecast accuracy reached its highest level during the new system period and errors were minimal.
- The Student statistic test for the constant c in the forecast-bias regression never exceeds a critical value of 1.5.

### Forecast bias testing and regression framework
- Forecasting bias assessed via OLS regression of first differences:
  - ∆log(AFRt) = c + β * ∆log(AFFt) + et
  - ∆AFRt: log-difference of realized autonomous factor for the MRO week (t)
  - ∆AFFt: log-difference of autonomous factor forecast for the MRO week (t)
  - et: residual = estimated forecast errors
- Unbiased forecast implications:
  - β = 1 (perfect elasticity of realized value to estimate)
  - c = 0 (no unconditional drift)
- Joint Wald test of β = 1 and c = 0 performed on a rolling window of 90 forecasting periods (about 90 weeks) from 2000 to 2019.
- Test outcomes:
  - For the 1st forecast: the test rejects the null for 37 periods of 90 days out of 953 periods (4 percent) from 2000 to 2019.
  - For the 2nd forecast: the test rejects the null for 119 periods (12.5 percent).
  - It is generally more difficult to reject bias in the 1st forecast than in the 2nd forecast.
- Estimated conditional-bias coefficient β:
  - Estimated coefficient is significant for all periods and remains below one for each period.
  - Converged toward 1 from 2004 to 2008.
  - After 2008, β fluctuated between 0.9 and 0.5, indicating persistent overestimation bias (forecaster expected larger change in autonomous factor than realized).

### Forecast reliability and error distribution
- Reliability defined as persistence of accurate forecasts (low probability of significant “surprises”).
- Distributional properties of forecast errors (July 2000 to August 2019):
  - Leptokurtic: distribution peak higher around mean and fatter tails than normal distribution; outlier errors more frequent and extreme.
  - Positively skewed: right tail long (higher likelihood of overestimating AFR), but the fat tail of the largest outliers is on the left (largest forecast errors underestimate AFR).
- Comparison of 1st vs 2nd forecast errors:
  - Forecast errors concentrated around smaller values for the 2nd forecast than for the 1st forecast.
  - 1st forecast experienced larger and more frequent underestimation outliers than the 2nd forecast.
- Benchmark period for high forecast quality: March 2004 to October 2008 (248 forecasts).
  - Second-forecast errors more concentrated around smaller values during the benchmark period than in the rest of the sample (804 forecasts).
  - Benchmark distribution more leptokurtic: reported kurtosis and skewness figures:
    - Forecast 1 (Jul 2000–Aug 2019): Kurtosis: 6.9; Skewness: 2.7
    - Forecast 2 (Jul 2000–Aug 2019): Kurtosis: 9.0; Skewness: 2.7
    - Forecast 2, Mar 2004–Oct 2008: Kurtosis: 13.4; Skewness: 3.7
    - Forecast 2, Jul 2000–Feb 2004 and Nov 2008–Aug 2019: Kurtosis: 3.7; Skewness: 2.1

### Factors influencing forecast errors (explanatory regressions)
- 1st forecast error specification (equation 3):
  - e1,t = c + α1 * dL + α2 * dp + α3 * e1,t-1 + γ Xt + δ Zt + μt
  - e1,t: absolute value of forecast errors (AFR − 1st forecast)
  - dL: length of the forecast in days (usually nine days; reduced to seven for first operation of maintenance period)
  - dp: dummy for periods (March 2004–October 2008 used as reference)
  - Xt: vector of market-segmentation indicators (sovereign spread, excess reserves as percent of reserve requirements, EONIA overnight volumes)
  - Zt: EONIA (controls for low interest rate environment)
- 2nd forecast error specification (equation 4):
  - e2,t = c + α1 * dL + α2 * dp + α3 * e1,t + α4 * e2,t-1 + γ Xt + δ Zt + μt
  - e2,t: absolute value of forecast errors (AFR − 2nd forecast)
  - e1,t included to test use of information between 1st and 2nd forecasts (error-correction role)
- Key regression findings:
  - Both 1st and 2nd forecast errors significantly correlated with the set of explanatory variables, implying forecasts are not “strong” in efficiency (public information helps explain errors).
  - The 2nd forecast yields smaller errors and less bias, but is less “efficient” than the 1st forecast in the sense of higher R-square for the full specification; main contributor to 2nd forecast R-square is the 1st forecast error.
  - For the 1st forecast (full specification): significant correlates include sovereign spreads and excess reserves (market segmentation indicators), and the March 2004–October 2008 dummy (lower errors during benchmark).
  - For the 2nd forecast (full specification): significant correlates include excess reserves, EONIA volumes, the 1st forecast errors, and the March 2004–October 2008 dummy.
  - Differences between 1st and 2nd errors:
    - 1st forecast errors correlated with previous-period 1st forecast errors (suggesting some persistence and potential inefficiency); this is not corroborated for 2nd forecast errors.
    - 2nd forecast errors negatively correlated with EONIA levels (low interest rate environment contribution); not corroborated for 1st forecast errors.
- Representative R-squared values from table specifications:
  - 1st forecast: example R-squared values reported include 0.333, 0.334, 0.063, 0.197, 0.280, 0.246, 0.008, 0.161, 0.084
  - 2nd forecast: example R-squared values reported include 0.463, 0.470, 0.026, 0.125, 0.203, 0.191, 0.000, 0.437, 0.088, 0.140

### Policy implications and recommendations (Conclusion)
- Central banks could expand evaluation methods for autonomous factors forecasts (AFF); the proposed forecast-bias test is simple to implement and would provide important information affecting forecast credibility.
- The forecast-bias test could be conducted separately for different types of autonomous factors to enhance analysis.
- Explaining forecast errors with public correlates offers hindsight on external factors influencing forecast quality; finer granularity (more detailed data) could improve diagnostics.
- Market conditions materially affect forecast quality: correlation between forecast errors and market-segmentation and low interest rate indicators corroborates market environment influence.
  - Period 2004–2008 had high accuracy and reliability; forecast quality declined after the global financial crisis.
- Publication of AFF may become more salient as excess reserves decline; accurate forecasts are necessary to guide counterparty bidding under fixed rate and full allotment when high reserves no longer absorb coordination-failure consequences.
- Improvements in market functioning and higher policy rates (driving money market rates away from zero and enabling NCB clients to actively manage reserves) may improve forecast quality without central bank action.
- The paper does not advocate publication of autonomous factors per se, but aims to ease central bank concerns by offering expanded forecast-evaluation methods:
  - Central banks could run a dry-run evaluation period using the proposed methods before publication.
  - Publish forecasts once confident in their quality to protect central bank credibility.
  - The evaluation method can inform the appropriate maturity of regular OMOs by indicating the horizon of high-quality forecasts.

*Source: European Central Bank, authors’ calculations (content from wpiea2019296-print-pdf).*

### REFERENCES

### REFERENCES

### Bibliographic references
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- Bank of England. 2015. “Evaluating Forecast Performance.” Independent Evaluation Office, London.
- Beirne, J. 2012. “The EONIA Spread Before and During the Crisis of 2007–2009: The Role of Liquidity and Credit Risk.” Journal of International Money and Finance 31 (3): 534–51.
- Bindseil, U. 2001. “Central Bank Forecast of Liquidity Factors: Quality, Publication, and the Control of the Overnight Rate.” ECB Working Paper 70, European Central Bank, Frankfurt.
- Bindseil, U. 2016. “Evaluating Monetary Policy Operational Frameworks.” Jackson Hole Economic Policy Symposium, Federal Reserve Bank of Kansas City.
- Cabrero, A., G. Camba-Mendez, A. Hirsch, and F. Nieto. 2002. “Modelling the Daily Banknotes in Circulation in the Context of the Liquidity Management of the European Central Bank.” ECB Working Paper 142, European Central Bank, Frankfurt.
- Carpenter, S., and S. Demiralp. 2006. “Anticipation of Monetary Policy and Open Market Operations.” International Journal of Central Banking 2 (2): 25–63.
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- Dincer, N., and B. Eichengreen. 2014. “Central Bank Transparency and Independence: Updates and New Measures.” International Journal of Central Banking 10 (1): 189-253.
- Ejerskov, S., C. M. Moss, and L. Stracca. 2008. “How Does the ECB Implement Monetary Policy?” Journal of International Money and Finance 27 (8): 1199–1214.
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- Frankel, J., and K. Froot. 1989. “Forward Discount Bias: Is It an Exchange Risk Premium?” The Quarterly Journal of Economics 104 (1): 139-61.
- Froot, K. 1989. “New Hope for the Expectations Hypothesis of the Term Structure of Interest Rates.” Journal of Finance 44 (2): 283-305.
- Gray, S. 2008. “Liquidity Forecasting.” Handbook No. 27, Center for Central Banking Studies, Bank of England, London.
- Hilton, S., and W. B. Hrung. 2010. “The Impact of Banks’ Cumulative Reserve Position on Federal Funds Rate Behavior.” International Journal of Central Banking 6 (3): 101-18.
- International Monetary Fund. 2016. Annual Report on Exchange Rate Arrangements and Exchange Restrictions. Washington, DC: International Monetary Fund.
- Kraenzlin, S., and M. Schlegel. 2012. “Bidding Behavior in the SNB’s Repo Auctions.” Journal of International Money and Finance 31 (2): 170-88.
- Laurens, B. J., K. Eckhold, D. King, N. Maehle, A. Naseer, and A. Durré. 2015. “The Journey to Inflation Targeting: Easier Said than Done: The Case for Transitional Arrangements Along the Road.” IMF Working Paper15/136, International Monetary Fund, Washington, DC.
- Ötker-Robe, I., D. Vávra, and others. 2007. Moving to Greater Exchange Rate Flexibility Operational Aspects Based on Lessons from Detailed Country Experiences. IMF Occasional Paper 256. Washington, DC: International Monetary Fund.
- Patton, A. J., and A. Timmermann. 2012. “Forecast Rationality Tests Based on Multi-Horizon Bounds.” Journal of Business & Economic Statistics 30 (1): 1-17.
- Ranaldo, A., and M. Rupprecht. 2019. “The Forward Premium in Short-term Rates.” Working Paper on Finance 2016/19, University of St. Gallen, Switzerland.
- Vogel, E. 2016. “Forward Looking Behavior in ECB Liquidity Auctions: Evidence from the Pre-crisis Period.” Journal of International Money and Finance 61 (March): 120–42.

*Source: REFERENCES section of the content unit.*

### Appendix I. Sample for international comparison — key classifications (selected entries)
- Albania: Group 1: EU candidate; Group 2*: EMDE; Exchange Rate Regime: Floating; Monetary Policy Framework: Inflation targeting; Interest Rate Regime: Corridor system; Allotment Mechanism: Calibrated allotment.
- Australia: Group 1: Advanced economies; Group 2*: AE; Exchange Rate Regime: Free floating; Monetary Policy Framework: Inflation targeting; Interest Rate Regime: Floor system; Allotment Mechanism: Calibrated allotment.
- Brazil: Group 1: OECD partnership; Group 2*: EMDE; Exchange Rate Regime: Floating; Monetary Policy Framework: Inflation targeting; Interest Rate Regime: Floor system; Allotment Mechanism: Calibrated allotment.
- Bulgaria: Group 1: EU non-euro; Group 2*: EMDE; Exchange Rate Regime: Currency board; Monetary Policy Framework: Exchange rate anchor; Interest Rate Regime: Other; Allotment Mechanism: N/A.
- Euro area: Group 1: Euro area; Group 2*: AE; Exchange Rate Regime: Free floating; Monetary Policy Framework: Other; Interest Rate Regime: Corridor system; Allotment Mechanism: Fixed-rate full allotment.
- India: Group 1: OECD partnership; Group 2*: EMDE; Exchange Rate Regime: Floating; Monetary Policy Framework: Inflation targeting; Interest Rate Regime: Floor system; Allotment Mechanism: Fixed-rate full allotment.
- Japan: Group 1: Advanced economies; Group 2*: AE; Exchange Rate Regime: Free floating; Monetary Policy Framework: Inflation targeting; Interest Rate Regime: Floor system; Allotment Mechanism: Calibrated allotment.
- Norway: Group 1: Advanced economies; Group 2*: AE; Exchange Rate Regime: Free floating; Monetary Policy Framework: Inflation targeting; Interest Rate Regime: Floor system; Allotment Mechanism: Fixed-rate full allotment.
- United States: Group 1: Advanced economies; Group 2*: AE; Exchange Rate Regime: Free floating; Monetary Policy Framework: Other; Interest Rate Regime: Floor system; Allotment Mechanism: Calibrated allotment.

- Note: AE = advanced economy, EMDE = emerging market and developing economy.
- Footnotes appearing in the table:
  - 1/ 2019 classification.
  - 2/ refers to the framework prior 2009.

*Source: APPENDIX I — sample for international comparison.*

### Appendix II. International comparison of publication practices — selected practices and timing
- Albania
  - Content: Liquidity forecast
  - Details: The Bank of Albania publishes weekly liquidity forecast.
  - Frequency: Weekly
  - Horizon / Tenor: 1-week
  - OMO match: Yes
  - Timing: OMO announcement
  - Source: https://www.bankofalbania.org/Markets/Operations_of_the_Bank_of_Albania/Interventions_in_the_money_market/
- Australia
  - Content: Liquidity forecast
  - Details: Publication of estimated cash positions with announcement for OMOs.
  - Frequency: OMO (intra-day)
  - Horizon / Tenor: Today
  - OMO match: Yes
  - Timing: OMO announcement
  - Source: http://www.rba.gov.au/mkt-operations/resources/tech-notes/open-market-operations.html
- Brazil
  - Content: Liquidity history
  - Details: Remaining in a structural liquidity surplus, BCB absorbs liquidity via security-selling auctions and overnight borrowing. Publication of results.
  - Frequency: OMO History only
  - Horizon / Tenor: N/A
  - OMO match: N/A
  - Timing: OMO allotment
  - Source: https://www.bcb.gov.br/acessoinformacao/legado?url=https:%2F%2Fwww.bcb.gov.br%2Fhtms%2Finfecon%2Fdema b%2Fma201909%2Findex.asp
- Canada
  - Content: Liquidity target
  - Details: Publication of a target for balance of the CAD settlements system (LVTS), which is also based on the internal projection of changes in autonomous factors.
  - Frequency: Daily
  - Horizon / Tenor: Tomorrow
  - OMO match: No
  - Timing: Market close
  - Source: http://www.bankofcanada.ca/markets/market-operations-liquidity-provision/framework-market-operations-liquidity-provision/
- Euro area
  - Content: AFF
  - Details: Publication of forecast of autonomous factors at the time of announcement and allotment of main refinancing operation as well as benchmark allotment, implying a liquidity target.
  - Frequency: Weekly
  - Horizon / Tenor: 1-week
  - OMO match: Yes
  - Timing: Mondays / Tuesdays
  - Source: http://www.ecb.europa.eu/mopo/liq/html/index.en.html
- Japan
  - Content: AFF
  - Details: Publication of projection of “Sources of Changes in Current Account Balances at the Bank of Japan and Market Operations,” distinguishing “Banknotes” and “Treasury Funds and Others,” along with preliminary and final results. (1) Daily projection for the next business day and preliminary results of the current business day in the evening; (2) Monthly projection on the first business day of the month.
  - Frequency: Daily / Monthly
  - Horizon / Tenor: Today / 1-month
  - OMO match: No
  - Timing: Market close / Month-start
  - Source: http://www.boj.or.jp/en/statistics/boj/fm/juq/index.htm/
- Mexico
  - Content: Liquidity forecast
  - Details: Mexico targets a zero overnight reserve balance, requiring frequent open-market operations. Correspondingly, daily publication of domestic current account balances of banks at opening at Banco de Mexico, expected change in liquidity, programmed daily intervention in the money market settled SD.
  - Frequency: Daily
  - Horizon / Tenor: Today
  - OMO match: Yes
  - Timing: Market open
  - Source: https://www.banxico.org.mx/politica-monetaria/operaciones-objetivos-mecanis.html
- Norway
  - Content: Liquidity forecast
  - Details: Publication of a structural liquidity forecast on the NB website, with updates every Monday and Thursday.
  - Frequency: Weekly twice
  - Horizon / Tenor: 2-months
  - OMO match: No
  - Timing: Mondays / Thursdays
  - Source: http://www.norges-bank.no/en/Liquidity-and-markets/The-liquidity-management-system/Liquidity-forecast/
- Sweden
  - Content: Allotment target
  - Details: Offered emission volume of Riksbank certificates “are calculated with the help of a forecast of the banking system’s liquidity surplus (or previously deficit) for the coming week.” While the projection is not published explicitly, the intended amount is.
  - Frequency: Weekly
  - Horizon / Tenor: 1-week
  - OMO match: Yes
  - Timing: OMO announcement
  - Source: Sveriges Riksbank (2014), The Riksbank’s operational framework for the implementation of monetary policy – a review, Riksbank Studies, March 2014.
- United Kingdom
  - Content: Liquidity forecast
  - Details: Publication of the week’s short-term OMO, being the forecast weekly liquidity position adjusted for errors in the previous week’s forecast. After 2009, OMOs were discontinued as well as the OMO liquidity publication.
  - Frequency: Weekly
  - Horizon / Tenor: 1-week
  - OMO match: Yes
  - Timing: OMO announcement
  - Source: https://www.bankofengland.co.uk/markets
- United States
  - Content: Liquidity history
  - Details: The FRBNY publishes the factors affecting reserve balances.
  - Frequency: Weekly
  - Horizon / Tenor: One week
  - OMO match: No
  - Timing: Thursday 4.30 pm
  - Source: https://www.federalreserve.gov/releases/h41/

- Additional notes from Appendix II:
  - Many central banks publish a mix of liquidity forecasts, liquidity histories, liquidity targets, AFF publications, or allotment targets.
  - Timing conventions include Market open, Market close, OMO announcement, OMO allotment, Mondays / Tuesdays, Market close / Month-start, Thursday 4.30 pm, among others.
  - Source: Central Banks.

*Source: APPENDIX II — international comparison of publication practices.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019296-print-pdf.pdf_