## wpiea2023158-print-pdf

## Source details

**Canonical URL:** [wpiea2023158-print-pdf](https://www.imf.org/-/media/files/publications/wp/2023/english/wpiea2023158-print-pdf.pdf)

## Other formats

- [Markdown version](/-/media/files/publications/wp/2023/english/wpiea2023158-print-pdf.pdf.md)
- [Structured JSON version](/-/media/files/publications/wp/2023/english/wpiea2023158-print-pdf.pdf.json)

---

### 1. Introduction — problem, solution, data, and methods
- Problem statement: limited availability and timeliness of quarterly GDP data
  - More than 60 countries do not publish official quarterly GDP statistics.
  - These include:
    - about 20 countries in sub-Saharan Africa (SSA),
    - more than half of low-income developing countries (LIDCs),
    - more than two-thirds of fragile and conflict-affected states (FCS).
  - For about 20 countries, the time lag in releasing quarterly GDP exceeds one quarter.
- Proposed solution: panel nowcasting framework
  - Objective: nowcast quarterly GDP growth for countries that do not publish quarterly GDP statistics by estimating conditional expectation E[y_i,t | X_i,t].
  - Key assumption: a common statistical function f(X_i,t) applies across countries and periods:
    - y_i,t = f(X_i,t) + ε_i,t, with nowcast ŷ_i,t ≝ f(X_i,t).
  - Estimation methods used:
    - Light gradient boosting regression (LGB) with default hyperparameters.
    - Ordinary least squares (OLS).
  - Ensemble approach to mitigate missing input variables and deliver nowcasts for all country-period pairs.
- Data coverage and input variables
  - Collected 117 quarterly indicators related to economic activity.
    - Among them, 76 indicators are from nontraditional data sources.
    - Coverage: as many as 200 economies since 2008Q1.
  - Variables available for all economies for all sample periods:
    - six global commodity prices,
    - two global financial indexes (U.S. 2-year bond yields, U.S. stock market volatility index),
    - 14 world-wide search volume indexes (out of 28 in the sample).
  - Minimum common variable set: these 22 variables (plus quarter and country group dummies).
  - Note: relying only on the minimum set may be insufficient to capture growth dynamics.
- Ensemble nowcasts and specification variants
  - Construct an ensemble of nowcasts by averaging over all specifications based on data available for each country-period pair.
  - Three ensemble models:
    - "average" — baseline: average across all usable specifications for the country-period.
    - "maximum" — the specification with the largest number of input variables available for that country-period.
    - "minimum" — the specification with the smallest number of input variables (the model with the 22 common variables).
  - Subsample estimation:
    - In addition to the full (Global) sample, nowcasts are generated by subsamples (e.g., SSA, fuel exporters, tourism-oriented) to leverage similarity within country groups.
    - Baseline remains the full sample to maximize coverage.
- Interpretation and attribution of inputs: SHAP and contributions
  - For LGB, use SHAP (SHapley Additive exPlanations) to estimate contributions {ŝ_k,i,t} of input variables {x_k,i,t}:
    - ŷ_i,t = Ê(y_i,t) + Σ_k ŝ_k,i,t, where Ê(y_i,t) denotes the sample mean.
  - For OLS, SHAP value simplifies to ŝ_k,i,t = β̂_k x_k,i,t.
  - To assess contributors to quarter-to-quarter changes include differences in SHAP values and the previous-quarter residual −ε̂_i,t−1 in decompositions; ensemble SHAP values require an additional residual term when specifications change over time.
- Relation to existing work and organization
  - Complements IMF and literature efforts on high-frequency indicators and nontraditional data (e.g., nighttime lights, Google Trends, Google Places API).
  - Paper organization outlined for Sections 2–5 (framework, evaluation, SSA demonstration, conclusion).

### 3. Evaluation of Panel Nowcast Performance — approach and principal results
- Evaluation approach and tradeoffs
  - Theoretical tradeoff: panel nowcasts may reduce overfitting and improve out-of-sample fit relative to country-specific models, at the cost of lower in-sample fit.
  - Two out-of-sample evaluation directions:
    - Country-wise evaluation: exclude a country from estimation sample and compute RMSEs using its observations.
    - Period-wise evaluation: exclude recent periods (e.g., up to 2021Q3) to assess how historical relationships predict recent quarters.
  - Neither evaluation can directly evaluate errors for countries without quarterly data because observed quarterly growth is required for error calculation.
- Country-wise versus period-wise performance (selected 15 SSA countries)
  - General result:
    - Out-of-sample fit is generally good when evaluated country-wise but poor period-wise.
    - Country-wise baseline panel nowcast ("average" LGB, Global sample) compares relatively well to a naïve random walk (one-quarter lag).
  - Theil U index (ratio of RMSEs to RMSE of random walk):
    - Theil U is less than 75 percent for 9 out of 15 countries.
    - Theil U is less than 50 percent for 5 countries.
    - Theil U exceeds 500 percent for Tanzania; panel nowcast out-of-sample RMSE = 5.27 percent in that case.
  - Period-wise results:
    - Period-wise out-of-sample RMSEs are larger than the random walk nowcast.
    - Poor period-wise performance partly reflects difficulty capturing volatile growth since the onset of the pandemic.
  - Directional accuracy:
    - Panel nowcasts have directional accuracy > 70 percent for 9 out of 15 cases.
    - In some cases (Ghana, Mauritius) directional accuracy ≈ ½.
  - Estimation methods:
    - LGB-based nowcasts tend to perform better than OLS-based nowcasts.
- Subsample estimation and potential improvements
  - Estimating LGB only for 25 SSA countries with quarterly growth data improves period-wise out-of-sample performance (Theil U < 1) and tends to improve country-wise performance to some extent.
  - Improvements are less obvious for other subsamples; exploring methods to identify optimal subsamples is recommended.
- Direct evaluation for countries without quarterly growth data (annual growth nowcasts derived from quarterly nowcasts)
  - Method: annual growth nowcasts derived from quarterly growth nowcasts via growth of the four-quarter sum of implied levels, with parsimonious no-seasonality base assumption (Y_{2008,q} = 1).
  - For latest estimation year with partial quarters, compute year-on-year growth of the average of available quarterly nowcasts (e.g., first three quarters).
  - LGB model key results (selected):
    - Out-of-sample RMSEs show reductions from naïve random walk though magnitudes remain large.
    - The Theil U index shows about 30 percent reduction in RMSE across specifications.
    - Out-of-sample RMSEs exceed 6 percent for all but one case.
    - In-sample RMSE for baseline model = 1.71 percent.
    - In-sample RMSEs for other LGB-based average-ensemble subsample models range from 0.90-1.91 percent.
    - Uniform positive out-of-sample bias above 1 percent across specifications; in-sample bias is -0.03 for baseline and ranges from -0.04-0.10 percent for other LGB-based subsample models.
  - Selected Table 3 entries for LGB average (2010-2022 sample sizes preserved exactly):
    - LGB, Global, average (1,017): Out-of-sample bias = 1.06; Out-of-sample RMSE = 6.64; Theil U = 0.67
    - LGB, EMDEs, average (926): Out-of-sample bias = 1.07; Out-of-sample RMSE = 6.75; Theil U = 0.68
    - LGB, SSA, average (293): Out-of-sample bias = 1.08; Out-of-sample RMSE = 6.10; Theil U = 0.75
    - LGB, Comm. exp., average (480): Out-of-sample bias = 1.78; Out-of-sample RMSE = 8.56; Theil U = 0.70
    - LGB, Fuel exp., average (164): Out-of-sample bias = 2.60; Out-of-sample RMSE = 11.72; Theil U = 0.67
    - LGB, Tourism, average (207): Out-of-sample bias = 1.22; Out-of-sample RMSE = 4.37; Theil U = 0.52
- Remaining challenges and research directions
  - Panel nowcasts still tend to produce larger out-of-sample RMSEs than the best country-specific nowcasts in some studies.
  - Out-of-sample bias remains large.
  - Opportunities: explore better estimation methods and hyperparameter calibration; identify subsamples/groupings that improve out-of-sample fit.

### 4. Quarterly GDP Nowcasts for SSA Countries — demonstration, diagnostics, and limitations
- Coverage and intent
  - Out of 45 SSA countries, 20 do not publish quarterly GDP; panel nowcasts are produced for these countries using the common estimation structure.
- Country examples and diagnostics
  - Uganda (quarterly GDP published)
    - Baseline quarterly nowcast (LGB-based average-ensemble, Global sample) largely follows actual quarterly real GDP growth.
    - Baseline captures pandemic trough and peak; actual quarterly growth lies within estimation-uncertainty areas in most periods except e.g., 2019Q4, 2021Q3.
    - SHAP decomposition: growth nowcast for 2022Q3 picks up from 4.8 percent to 5.3 percent, mostly reflecting better external conditions (trading partners’ growth and worldwide attention to Uganda).
    - Annual comparison: 2022 shown as "2022 5.1%".
    - In-sample annual growth RMSE = 1.15 percent.
  - Sierra Leone (quarterly GDP unavailable)
    - Quarterly nowcasts broadly follow annual real GDP growth (annual growth repeated quarterly to show dynamics).
    - Baseline nowcasts depict pandemic recession, recovery, and 2022Q1 shock related to spillovers from the war in Ukraine.
    - SHAP decomposition: growth nowcast for 2022Q3 picks up from 2.8 percent to 4.2 percent, due to easing supply constraints (seaborne import estimates) and price developments (CPI and exchange rate), while domestic financial conditions show downside.
    - Annual comparison: 2022 shown as "2022 2.7%".
    - Out-of-sample annual RMSE = 8.57 percent.
- Nowcast construction and uncertainty visuals
  - Baseline quarterly GDP nowcast = average over available specifications estimated by LGB (red line in figures).
  - Shaded area = variation across specifications (methodologies LGB and OLS; country group specifications Global, EMDE, SSA, commodity exporters, fuel exporters, tourism-oriented economies; ensemble options minimum, average, maximum). Each 1/8th percentile illustrated with a different gray shade.
- SHAP decompositions and interpretation
  - SHAP values identify top contributing factors to quarter-to-quarter changes; examples: WSVI, Trade Partners, i_LIDC, US VIX, Deposits, Uncertainty Index, Passenger Capacity, Broad Money, Domestic SVI, Sea Imports, FX rate, CPI, Sea Exports, Private Credit, US 2yr Rate.
  - Example numeric decompositions for 2022Q3 preserved exactly:
    - Uganda: E[y(t-1)|X(t-1)] = 4.8; E[y(t)|X(t)] = 5.3.
    - Sierra Leone: E[y(t-1)|X(t-1)] = 2.8; E[y(t)|X(t)] = 4.2.
  - SHAP contributions are descriptive and should not be interpreted as causal effects due to possible reverse causality.
- Limitations and country idiosyncrasies
  - Sierra Leone’s weak fit (RMSE 8.57 percent) driven by extreme historical annual growth deviations:
    - 2012: 14 percent
    - 2013: 19 percent
    - 2015: -23 percent
    - These reflect country-specific events (iron ore production start 2012–2013; Ebola outbreak and iron ore price collapse 2014–2015).
  - Mining production, epidemic impacts, and timing lags may not align with international indicators used in the panel.
  - Operational implication: large deviations between nowcasts and observed growth can flag exceptional circumstances for country teams to apply judgemental adjustments.
- Suggested improvements and future directions
  - Pool selection: choose panel pool optimally depending on out-of-sample fits.
  - Pre-estimation preparation: structured data preparation to handle measurement issues and idiosyncrasies.
  - Hybrid adjustment: combine country-specific indicators parsimoniously with panel nowcasts (e.g., regression of observed growth on country indicators and panel nowcasts).
  - Mixed-frequency estimation: produce annual growth estimates directly in a mixed-frequency setup to reconcile annual and quarterly data and address sampling noise.
- Conclusion summary points
  - Panel nowcasting framework provides quarterly GDP estimates for countries lacking published quarterly GDP by learning from other countries’ quarterly data.
  - SHAP decomposition helps form evidence-based narratives to support policy discussions and recalibration of macro frameworks.
  - Panel approach has limitations during large idiosyncratic shocks or structural changes but signals when judgemental interventions are warranted.
  - Scope for improvement through optimal pooling, structured data preparation, parsimonious combination with country-specific indicators, and mixed-frequency estimation.

### Annex: Data, transformations, estimation, missing-data treatment, coverage, and performance tables
- Data collection and key datasets
  - Conventional sources: International Financial Statistics (IMF 2022b); World Economic Outlook (IMF 2022c); Haver Analytics (Haver 2022); data.IMF.org.
  - Unconventional sources emphasized: Google Trends; nighttime lights; maritime/seaborne trade indicators; Passenger Flight Capacity; World Uncertainty Index.
  - Total variables collected: 117 quarterly indicators, with 76 nontraditional indicators.
- Variable transformation and sample period
  - All variables transformed into quarterly growth from a year ago, with exceptions where levels and lagged levels are used for variables with many missing observations or zeros.
  - Passenger capacity index available only since 2019 and zero-padded before 2019.
  - Sample period set from 2008Q1 to latest available (example given: 2022Q3); start quarter 2008Q1 chosen so 2009Q1 is first period with year-ago quarterly growth available.
- Estimation methods and software
  - LGB: Light GBM (Ke and others 2017) with default hyperparameters (python package lightgbm).
  - OLS: scikit-learn (Pedregosa and others 2011).
  - Stata 17 used for dataset management and to run Python packages on Stata 17.
- Constructing annual nowcasts from quarterly nowcasts (formulas preserved exactly)
  - Quarterly year‑ago growth: y_{τ,q} ≝ ln(Y_{τ,q}) − ln(Y_{τ−1,q})
  - Annual level: Y_{τ} ≝ ∏_{q=1}^{4} Y_{τ,q}
  - Annual growth: y_{τ} ≝ ln(Y_{τ}) − ln(Y_{τ−1})
  - Cumulative level: ln(Y_{τ,q}) = ln(Y_{2008,q}) + ∑_{u=2008}^{τ} y_{u,q}, with parsimonious initial condition Y_{2008,q} = 1 for all q.
  - For current year with three quarters available: ŷ_{τ} ≝ ln(Ŷ_{τ}) − ln(Ŷ_{τ−1}), where Ŷ_{τ} ≝ ∏_{q=1}^{3} Y_{τ,q}. Conservative alternative ŷ_{τ}^{c} defined in source.
  - Alternative approaches noted: mixed-frequency annual estimation; supplement quarterly nowcasts with forecasts for remaining quarters; annualize inputs for annual-frequency estimation.
- Handling missing observations and ensemble strategy
  - Baseline ensemble averaging: ŷ_{i,t}^{avg} ≝ (1 / n_{i,t}) ∑_{m ∈ M_{i,t}} ŷ_{m,i,t}; also compute ŷ_{i,t}^{min} and ŷ_{i,t}^{max}.
  - Two alternatives trialed:
    1. Use gradient boosting trees’ built-in handling of missing observations — computational savings but weak out-of-sample performance in trials.
    2. Impute all input variables (e.g., missingpy) — computationally expensive with weak out-of-sample performance in trials.
  - Practical rule: remove observations partially observed at monthly frequency (treat as missing).
- SHAP methodology and implementation
  - Use python package shap to estimate additive contributions s_{m,k,i,t} such that ŷ_{m,i,t} = ∑_{k ∈ K_{m}} s_{m,k,i,t}.
  - Time-difference decompositions defined for minimum, maximum, and average specifications; residual terms S̃_{i,t}^{max} and S̃_{i,t}^{avg} capture specification-change effects (formulas preserved in source).
- Country coverage (Annex Table 1 summary)
  - Total sample: 200 economies.
  - Quarterly growth included in sample: 127 economies; not included: 73 economies.
  - Breakdown preserved exactly where provided:
    - LIDCs (59): 23 with quarterly growth included; 36 without.
    - EMDEs (97): 67 included; 30 without.
    - Advanced economies (40): 37 included; 3 without.
    - Other economies (4): 0 included; 4 without.
  - Subsamples:
    - SSA (45): 25 with quarterly growth data included; 20 without.
    - Tourism-oriented economies (29): 14 with quarterly growth data included; 15 without.
- Annex variable list (Annex Table 2) and selected series codes
  - Full variable list preserved in source; examples include:
    - Agriculture Material Prices, Index (GAS) — PAGRIW — WEO (GAS)
    - Broad Money, Domestic Currency — FMB_XDC — IFS
    - Consumer Prices — PCPI_IX — IFS
    - Nighttime lights — NL — Authors
    - Passenger Flight Capacity — PASSENGERCAPACITY — IMF STA Estimates
    - Trading Partners’ Real GDP Growth — NGDP_R_WX001 — WEO (GEE)
    - U.S. Treasury Y2 Yield, p.a., NSA — FTA2YK — HAVER
    - U.S. VIX, p.a., NSA — SPVIX — HAVER
    - Worldwide Google Trends: All — WSVI_ALL — Narita and Yin (2018) and Google Trends
  - Note on nighttime lights: sourced from VIIRS Day/Night Band (DNB) data produced by the Earth Observation Group, NOAA/NCEI.
- Performance tables (Annex Tables 3–9) — selected preserved numeric examples
  - Annex Table 3 (LGB, EMDE subsample, Panel B period-wise evaluation):
    - Test sample period 2020Q1-2022Q3 (sample size) (1716): In-sample bias = -0.05; In-sample bias on test sample = 0.05; Out-of-sample bias = 1.92; In-sample direction = 0.83; In-sample direction on test sample = 0.89; Out-of-sample direction = 0.67; In-sample RMSE = 1.92; In-sample RMSE on test sample = 2.52; Out-of-sample RMSE = 9.28; Theil U = 1.01
    - Test sample period 2020Q4-2022Q3 (sample size) (1248): In-sample bias = -0.05; In-sample bias on test sample = -0.06; Out-of-sample bias = -4.80; In-sample direction = 0.83; In-sample direction on test sample = 0.87; Out-of-sample direction = 0.59; In-sample RMSE = 1.92; In-sample RMSE on test sample = 2.23; Out-of-sample RMSE = 8.83; Theil U = 1.10
  - Annex Table 4 (LGB, commodity exporter subsample, Panel B period-wise evaluation):
    - Test sample period 2020Q1-2022Q3 (sample size) (693): In-sample bias = 0.01; In-sample bias on test sample = 0.01; Out-of-sample bias = 2.08; In-sample direction = 0.90; In-sample direction on test sample = 0.93; Out-of-sample direction = 0.57; In-sample RMSE = 1.52; In-sample RMSE on test sample = 1.80; Out-of-sample RMSE = 7.32; Theil U = 1.04
  - Annex Table 5 (LGB, fuel exporter subsample, Panel B period-wise evaluation):
    - Test sample period 2020Q1-2022Q3 (sample size) (286): In-sample bias = -0.01; In-sample bias on test sample = 0.02; Out-of-sample bias = 2.39; In-sample direction = 0.93; In-sample direction on test sample = 0.96; Out-of-sample direction = 0.54; In-sample RMSE = 0.64; In-sample RMSE on test sample = 0.83; Out-of-sample RMSE = 5.99; Theil U = 1.41
  - Annex Table 6 (LGB, tourism-oriented subsample, Panel B period-wise evaluation):
    - Test sample period 2020Q1-2022Q3 (sample size) (319): In-sample bias = -0.01; In-sample bias on test sample = 0.29; Out-of-sample bias = 2.62; In-sample direction = 0.88; In-sample direction on test sample = 0.92; Out-of-sample direction = 0.62; In-sample RMSE = 2.56; In-sample RMSE on test sample = 5.70; Out-of-sample RMSE = 17.76; Theil U = 1.11
  - Annex Table 7 (OLS, global sample, Panel B period-wise evaluation):
    - Test sample period 2020Q1-2022Q3 (sample size) (495): In-sample bias = -0.07; In-sample bias on test sample = 0.04; Out-of-sample bias = 4.55; In-sample direction = 0.59; In-sample direction on test sample = 0.79; Out-of-sample direction = 0.59; In-sample RMSE = 4.54; In-sample RMSE on test sample = 7.07; Out-of-sample RMSE = 11.47; Theil U = 1.25
  - Annex Table 8 (OLS, SSA subsample, Panel B period-wise evaluation):
    - Test sample period 2020Q1-2022Q3 (sample size) (495): In-sample bias = -0.03; In-sample bias on test sample = -0.00; Out-of-sample bias = 6.62; In-sample direction = 0.62; In-sample direction on test sample = 0.75; Out-of-sample direction = 0.51; In-sample RMSE = 3.76; In-sample RMSE on test sample = 3.48; Out-of-sample RMSE = 17.52; Theil U = 2.08
  - Annex Table 9 (OLS performance for countries without quarterly growth data, 2010-2022):
    - OLS, Global, average (1,017): Out-of-sample bias = 1.27; Out-of-sample RMSE = 6.90; Theil U = 0.69; Out-of-sample direction = 0.62
    - OLS, EMDEs, average (926): Out-of-sample bias = 1.26; Out-of-sample RMSE = 6.99; Theil U = 0.70; Out-of-sample direction = 0.63
    - OLS, SSA, average (293): Out-of-sample bias = 1.62; Out-of-sample RMSE = 6.09; Theil U = 0.75; Out-of-sample direction = 0.64
    - OLS, Comm. exp., average (480): Out-of-sample bias = 2.10; Out-of-sample RMSE = 8.55; Theil U = 0.70; Out-of-sample direction = 0.62
    - OLS, Fuel exp., average (164): Out-of-sample bias = 2.81; Out-of-sample RMSE = 12.08; Theil U = 0.69; Out-of-sample direction = 0.65
    - OLS, Tourism, average (207): Out-of-sample bias = 1.01; Out-of-sample RMSE = 4.75; Theil U = 0.56; Out-of-sample direction = 0.66

*Source: https://www.imf.org/-/media/files/publications/wp/2023/english/wpiea2023158-print-pdf.pdf*

### 1. Introduction ........................................................................................................

### 1. Introduction

### Problem statement: limited availability and timeliness of quarterly GDP data
- More than 60 countries do not publish official quarterly GDP statistics.
- These include:
  - about 20 countries in sub-Saharan Africa (SSA),
  - more than half of low-income developing countries (LIDCs),
  - more than two-thirds of fragile and conflict-affected states (FCS).
- For about 20 countries, the time lag in releasing quarterly GDP exceeds one quarter.
- This limited availability and timeliness hinder policymakers’ ability to respond rapidly to sudden shifts in economic conditions.

### Proposed solution: panel nowcasting framework
- Objective: nowcast quarterly GDP growth for countries that do not publish quarterly GDP statistics by estimating conditional expectation E[y_i,t | X_i,t].
- Key assumption: a common statistical function f(X_i,t) applies across countries and periods:
  - y_i,t = f(X_i,t) + ε_i,t, with nowcast ŷ_i,t ≝ f(X_i,t).
- Estimation methods used:
  - Light gradient boosting regression (LGB) with default hyperparameters.
  - Ordinary least squares (OLS).
- Ensemble approach to mitigate missing input variables and deliver nowcasts for all country-period pairs.

### Data coverage and input variables
- Collected 117 quarterly indicators related to economic activity.
  - Among them, 76 indicators are from nontraditional data sources.
  - Coverage: as many as 200 economies since 2008Q1.
- Variables available for all economies for all sample periods:
  - six global commodity prices,
  - two global financial indexes (U.S. 2-year bond yields, U.S. stock market volatility index),
  - 14 world-wide search volume indexes (out of 28 in the sample).
- Minimum common variable set: these 22 variables (plus quarter and country group dummies).
- Note: relying only on the minimum set may be insufficient to capture growth dynamics.

### Ensemble nowcasts and specification variants
- Construct an ensemble of nowcasts by averaging over all specifications based on data available for each country-period pair.
- Three ensemble models:
  - "average" — baseline: average across all usable specifications for the country-period.
  - "maximum" — the specification with the largest number of input variables available for that country-period.
  - "minimum" — the specification with the smallest number of input variables (the model with the 22 common variables).
- Subsample estimation:
  - In addition to the full (Global) sample, nowcasts are generated by subsamples (e.g., SSA, fuel exporters, tourism-oriented) to leverage similarity within country groups.
  - Baseline remains the full sample to maximize coverage.

### Interpretation and attribution of inputs: SHAP and contributions
- For LGB, use SHAP (SHapley Additive exPlanations) to estimate contributions {ŝ_k,i,t} of input variables {x_k,i,t}:
  - ŷ_i,t = Ê(y_i,t) + Σ_k ŝ_k,i,t, where Ê(y_i,t) denotes the sample mean.
- For OLS, SHAP value simplifies to ŝ_k,i,t = β̂_k x_k,i,t.
- To assess what contributed to growth in the quarter of interest relative to the previous quarter, compute differences in SHAP values over time and include the previous-quarter residual ε̂_i,t−1 as a contributing factor:
  - ŷ_i,t − y_i,t−1 = (y_i,t − ŷ_i,t−1) + (ŷ_i,t−1 − y_i,t−1) = Σ_k (ŝ_k,i,t − ŝ_k,i,t−1) + (−ε̂_i,t−1),
  - assuming no change in the set of input variables between t−1 and t.
- Note: ensemble SHAP values require an additional residual term when specifications change over time.

### Relation to existing work and organization
- Complements IMF and literature efforts on high-frequency indicators and nontraditional data for economic activity (e.g., nighttime lights, Google Trends, Google Places API).
- Paper organization:
  - Section 2: overview of panel nowcasting framework (details in Annex I).
  - Section 3: evaluation of panel nowcast performance.
  - Section 4: demonstration for selected SSA countries.
  - Section 5: conclusion with caveats and room for improvement.

*Source: https://www.imf.org/-/media/files/publications/wp/2023/english/wpiea2023158-print-pdf.pdf — 1. Introduction.*

### 3. Evaluation of Panel Nowcast Performance

### 3. Evaluation of Panel Nowcast Performance

### Theory and evaluation approach
- Theoretical tradeoff:
  - Panel nowcasts may lead to lower in-sample fit than country-specific nowcasts but potentially better out-of-sample fit by suffering less from overfitting.
  - Keeping model complexity constant, in-sample fit may be better if estimated specific to a country; panel estimation imposes a common structure across countries that can reduce overfitting.
- Two directions of out-of-sample evaluation (when quarterly growth data are available):
  - Country-wise evaluation: estimation sample excludes a country whose observations are used only to calculate RMSEs; assesses how nowcasts perform for countries without quarterly growth data and how other countries’ data help nowcast a country of interest.
  - Period-wise evaluation: estimation sample excludes recent periods (e.g., up to 2021Q3); assesses how historical statistical relationships help estimate nowcasts.
  - Neither evaluation can directly evaluate panel nowcasts for countries without quarterly growth data because nowcast errors require observed quarterly growth data.

### Country-wise versus period-wise performance (selected 15 SSA countries)
- General result:
  - Out-of-sample fit is generally good when evaluated country-wise but poor period-wise.
  - Country-wise evaluation for the baseline panel nowcast (the “average” ensemble nowcast based on the LGB estimated using the full “global” sample) compares relatively well to a naïve random walk nowcast (one-quarter lag).
- Theil U index (ratio of RMSEs to RMSE of random walk):
  - Theil U is less than 75 percent for 9 out of 15 countries.
  - Theil U is less than 50 percent for 5 countries, implying nowcast error reductions by more than a half.
  - Theil U is very off exceeding 500 percent for Tanzania; this is due to the random walk nowcast performing very well in that case, while the panel nowcast’s out-of-sample RMSE is 5.27 percent.
- Period-wise results:
  - Period-wise out-of-sample RMSEs show larger RMSEs than the random walk nowcast.
  - Poor period-wise performance partly stems from difficulty capturing volatile growth since the onset of the pandemic and suggests it may not be easy to learn about the present from the past.
- Directional accuracy:
  - Panel nowcasts tend to be correct in their directions (positive vs negative growth) with probability of more than 70 percent for 9 out of 15 cases.
  - In some cases (Ghana, Mauritius) directional predictions are correct with probability ½.
- Estimation methods:
  - LGB-based nowcasts tend to perform better than OLS-based nowcasts (Annex Tables 7, 8), implying scope to explore estimation methods and hyperparameter calibration.

### Subsample estimation and potential improvements
- Tailoring estimation samples:
  - Estimating the LGB model only for 25 SSA countries with quarterly growth data improves period-wise out-of-sample performance (Theil U index of less than one) and tends to improve country-wise performance to some extent (Table 2).
  - Improvements are not as obvious for other subsample estimations (Annex Tables 3, 4, 5, 6).
  - It may be worth exploring methods to identify subsamples that lead to better out-of-sample fit (as suggested by Bolhuis and Rayner (2020)).

### Direct evaluation for countries without quarterly growth data (annual growth nowcasts derived from quarterly nowcasts)
- Method:
  - Annual growth nowcasts are derived from quarterly growth nowcasts by calculating growth of the four-quarter sum of implied levels of quarterly real GDP, parsimoniously assuming no seasonality in levels of real GDP across quarters in the initial year (2008 in the sample).
  - For the latest estimation year when nowcasts do not cover some quarters, annual growth nowcast is calculated as year-on-year growth of the average of quarterly nowcasts available to date (e.g., first three quarters).
- Key results (LGB models; Table 3):
  - Out-of-sample RMSEs show reductions from the naïve random walk nowcast, although RMSE magnitudes remain large.
  - The Theil U index shows about 30 percent reduction in RMSE across specifications.
  - Out-of-sample RMSEs exceed 6 percent for all but one case.
  - In-sample RMSE for the baseline model is 1.71 percent (evaluated on the sample where quarterly growth data are available).
  - In-sample RMSEs for other LGB-based average-ensemble models on subsamples range from 0.90-1.91 percent.
  - There is a uniform positive out-of-sample bias of above 1 percent across specifications (including OLS-based models); in-sample bias is -0.03 for the baseline model and ranges from -0.04-0.10 percent for other LGB-based average-ensemble subsample models. This out-of-sample positive bias may reflect sampling bias regarding availability of quarterly growth data.

- Table 3 selected entries (LGB models for countries without quarterly growth data):
  - LGB, Global, average (1,017): Out-of-sample bias = 1.06; Out-of-sample RMSE = 6.64; Theil U = 0.67
  - LGB, EMDEs, average (926): Out-of-sample bias = 1.07; Out-of-sample RMSE = 6.75; Theil U = 0.68
  - LGB, SSA, average (293): Out-of-sample bias = 1.08; Out-of-sample RMSE = 6.10; Theil U = 0.75
  - LGB, Comm. exp., average (480): Out-of-sample bias = 1.78; Out-of-sample RMSE = 8.56; Theil U = 0.70
  - LGB, Fuel exp., average (164): Out-of-sample bias = 2.60; Out-of-sample RMSE = 11.72; Theil U = 0.67
  - LGB, Tourism, average (207): Out-of-sample bias = 1.22; Out-of-sample RMSE = 4.37; Theil U = 0.52

### Remaining challenges and research directions
- Even when Theil U is small, panel nowcasts tend to produce larger out-of-sample RMSEs than country-specific nowcasts (example: Barhoumi and others 2022 show about 2 percent RMSEs for selected best models).
- Out-of-sample bias remains large.
- Opportunities for improvement:
  - Explore better estimation methods and hyperparameter calibration (LGB outperforms OLS in current tests).
  - Identify subsamples or grouping strategies that improve out-of-sample fit for target countries with limited data.

*Source: Authors (chapter 3, "Evaluation of Panel Nowcast Performance")*

### 4. Quarterly GDP Nowcasts for SSA Countries

### 4. Quarterly GDP Nowcasts for SSA Countries

### Overview
- Out of the 45 countries in SSA, there are 20 countries that do not publish quarterly GDP, but panel nowcasts are available for these countries.
- The panel nowcast framework imposes a common estimation structure across countries to produce quarterly GDP estimates for countries without observed quarterly GDP, learning from observed quarterly GDP in other countries.

### Examples: Uganda (quarterly GDP published) and Sierra Leone (quarterly GDP unavailable)
- Uganda
  - Baseline quarterly nowcast (LGB-based average-ensemble estimated using the full global sample) largely follows actual quarterly real GDP growth.
  - The baseline nowcast captures the bottom and peak of the growth path during the COVID-19 pandemic; actual quarterly growth lies within the shaded estimation-uncertainty areas in most periods, except a few (e.g., 2019Q4, 2021Q3).
  - SHAP decomposition: growth nowcast for 2022Q3 picks up from 4.8 percent to 5.3 percent, mostly reflecting better external conditions (trading partners’ growth and worldwide attention to Uganda, measured by Google Trends indicators).
  - Annual comparison: chart indicates 2022 annual values shown as "2022 5.1%".
  - In-sample annual growth RMSE: 1.15 percent.
- Sierra Leone
  - Quarterly nowcasts broadly follow actual annual real GDP growth; annual growth data are repeated four times to show quarterly dynamics.
  - Baseline quarterly nowcasts depict within-year dynamics, including a recession at the onset of the pandemic, subsequent recovery, and another shock in 2022Q1 related to spillovers from the war in Ukraine.
  - SHAP decomposition: growth nowcast for 2022Q3 picks up from 2.8 percent to 4.2 percent, seemingly due to easing supply-side constraints (increase in seaborne import estimates) and price developments (CPI and exchange rate), while domestic financial conditions show downside effects (private credit, broad money, deposits).
  - Annual comparison: chart indicates 2022 annual values shown as "2022 2.7%".
  - Out-of-sample annual RMSE: 8.57 percent, reflecting large deviations driven by country idiosyncrasies.

### Nowcast performance, diagnostics, and interpretation
- Nowcast construction and uncertainty
  - The baseline quarterly GDP nowcast is averaged over available specifications estimated by the LGB using the full global sample (red line in figures).
  - Shaded area represents variation across specifications (estimation methodologies LGB and OLS; country group specifications Global, EMDE, SSA, commodity exporters, fuel exporters, tourism-oriented economies; ensemble options minimum, average, maximum). Each 1/8th percentile is illustrated with a different gray shade.
- Annual nowcasts derived from quarterly nowcasts
  - The red line in annual charts shows annualized growth rates approximately derived from the baseline quarterly nowcast; blue dashed line shows annualized growth rates derived from quarterly data if available.
  - For 2022, panel nowcasts indicate slightly higher growth than the October 2022 World Economic Outlook (WEO) vintage (IMF 2022c).
- SHAP values for decomposition and narrative
  - SHAP values identify top contributing factors to quarter-to-quarter changes in nowcasts; examples include Worldwide SVI, Trade Partners, i_LIDC, US VIX, Deposits, Uncertainty Index, Passenger Capacity, Broad Money, Domestic SVI, Sea Imports, FX rate, CPI, Sea Exports, Private Credit, US 2yr Rate.
  - Example numeric decompositions for 2022Q3:
    - Uganda: E[y(t-1)|X(t-1)] = 4.8; E[y(t)|X(t)] = 5.3.
    - Sierra Leone: E[y(t-1)|X(t-1)] = 2.8; E[y(t)|X(t)] = 4.2.
  - SHAP contributions should not be interpreted as causal effects due to potential reverse causality between growth and individual indicators.

### Limitations and country idiosyncrasies
- Sierra Leone’s weak out-of-sample fit (RMSE 8.57 percent) is driven by extreme historical deviations in annual growth:
  - 2012: 14 percent
  - 2013: 19 percent
  - 2015: -23 percent
  - These deviations reflect country-specific developments (start of new iron ore production in 2012–2013; Ebola outbreak and collapse in iron ore prices in 2014–2015).
- Reasons for misfit
  - Mining production capacity developments and halts do not necessarily align with international commodity prices or may follow with time lags not captured by the panel.
  - Some epidemic impacts may be partly captured by Google Trends (e.g., health category), but coverage is imperfect.
- Operational implication
  - Large deviations between nowcasts and observed growth can flag exceptional circumstances for country teams, prompting judgemental adjustments when economies are not in "relatively normal" situations.

### Suggested improvements and future directions
- Pool selection: choose the pool of countries in the panel optimally depending on out-of-sample fits (Bolhuis and Rayner 2020).
- Pre-estimation preparation: implement a more structured pre-estimation data preparation to better handle measurement issues and country idiosyncrasies.
- Hybrid adjustment: combine an indicator for substantial country-specific developments with the panel nowcast in a parsimonious way (for example, run an additional regression of observed GDP growth on country-specific indicators and panel nowcasts).
- Mixed-frequency estimation: produce annual growth estimates directly in a mixed-frequency setup to reconcile annual and quarterly data and address sampling noise in unconventional data (example reference to Eichenauer and others 2022).
- Further research: explore these options and refinements in future work.

### Conclusion (summary points)
- The panel nowcasting framework provides quarterly GDP estimates for countries lacking published quarterly GDP by learning from other countries’ quarterly data.
- Decomposition via SHAP helps form evidence-based narratives to support policy discussions and recalibration of macro frameworks.
- The panel approach has limitations when countries experience large idiosyncratic shocks or structural changes; however, it offers operational advantages by signaling when judgemental interventions are warranted.
- There is scope to improve the framework through optimal pooling, structured data preparation, parsimonious combination with country-specific indicators, and mixed-frequency estimation.

*Source: IMF Working Paper — "Panel Nowcasting for Countries Whose Quarterly GDPs are Unavailable", Section 4 (Quarterly GDP Nowcasts for SSA Countries).*

### Annex Table 2 for a full list of collected indicators and statistics.

### wpiea2023158-print-pdf - Annex Table 2 for a full list of collected indicators and statistics.

### Data collection and sources
- Conventional data are downloaded automatically using IMF Datatools (IMF internal only).
- Primary conventional sources mentioned:
  - International Financial Statistics (IMF 2022b)
  - World Economic Outlook (IMF 2022c)
  - Haver Analytics (Haver 2022)
  - data.IMF.org website
- Key conventional variables for panel nowcasts:
  - Global variables (e.g., commodity prices)
  - Country-specific: commodity terms of trade (Gruss and Kebhaj 2019); CPI and its 12 components; nominal and real exchange rates; monetary aggregates; balance of payments data
- Fiscal data gathering is noted as challenging and left for future work.
- Unconventional data emphasized to capture country-specific developments where conventional data are sparse:
  - Google Trends (Narita and Yin 2018)
  - Remote sensing: nighttime lights (Debbich 2019; Hu and Yao 2022; Beyer, Hu, and Yao 2022)
  - Maritime/seaborne trade indicators (Cerdeiro and others 2020)
  - Passenger capacity index (IMF STA using FlightRadar24; O’Hanlon and Sozzi, forthcoming)
  - World Uncertainty Index (Ahir, Bloom, and Furceri 2022)

### Variable transformation and sample period
- All variables are transformed into quarterly growth from a year ago, with some exceptions.
- For variables with many missing observations or zero values (e.g., passenger capacity index, world uncertainty index), both the level and its four-quarter lag level are included instead of year‑ago growth.
- Passenger capacity index availability:
  - Available only since 2019; included with zero padding for periods before 2019.
- Sample period:
  - Set from 2008Q1 to the latest available (example given: 2022Q3 at the time of writing).
  - Google Trends data cover all 200 economies in the sample since 2004 up to the latest previous month (except for several search categories), but are noisier pre-2010.
  - Start quarter chosen: 2008Q1, with 2009Q1 being the first period for nowcasts of quarterly growth since a year ago to be available.

### Estimation methods and implementation
- Two estimation methods used:
  - LGB: Light GBM (decision-tree based, Ke and others 2017, Python package lightgbm) with default hyperparameters
  - OLS using Python package scikit-learn (Pedregosa and others 2011)
- Software environment:
  - Stata 17 for dataset management and to run the Python packages on Stata 17

### Constructing annual nowcasts from quarterly nowcasts
- Definitions and procedures used (notation preserved from source):
  - Quarterly year‑ago growth: y_{τ,q} ≝ ln(Y_{τ,q}) − ln(Y_{τ−1,q})
  - Annual level: Y_{τ} ≝ ∏_{q=1}^{4} Y_{τ,q}
  - Annual growth: y_{τ} ≝ ln(Y_{τ}) − ln(Y_{τ−1})
- Cumulative calculation of ln(Y_{τ,q}) from an assumed base:
  - ln(Y_{τ,q}) = ln(Y_{τ−1,q}) + y_{τ,q} = ⋯ = ln(Y_{2008,q}) + ∑_{u=2008}^{τ} y_{u,q}
- Parsimonious initial condition:
  - Assume Y_{2008,q} = 1 for all q = 1,2,3,4 (i.e., ln(Y_{2008,q}) = 0). Note: this implies quarterly seasonality on the level of real GDP is not reflected.
- For the current year, annual nowcast when only the first three quarters are available:
  - ŷ_{τ} ≝ ln(Ŷ_{τ}) − ln(Ŷ_{τ−1}), where Ŷ_{τ} ≝ ∏_{q=1}^{3} Y_{τ,q}
  - A conservative alternative ŷ_{τ}^{c} assumes zero growth in the rest of the year:
    - ŷ_{τ}^{c} ≝ ln(Ŷ_{τ}^{c}) − ln(Ŷ_{τ−1}^{c}), with Ŷ_{τ}^{c} ≝ ∏_{q=1}^{3} Y_{τ,q} + Y_{τ,3}
- Alternative approaches for annual nowcasts noted:
  1. Directly estimating annual nowcasts in a mixed frequency model
  2. Supplementing quarterly nowcasts with quarterly forecasts for the rest of the year
  3. Annualizing input variables to estimate a model at the annual frequency

### Handling missing observations—approach, alternatives, and trade-offs
- Baseline ensemble approach:
  - For each specification m available for economy i in period t, predicted value ŷ_{m,i,t}
  - Average ensemble: ŷ_{i,t}^{avg} ≝ (1 / n_{i,t}) ∑_{m ∈ M_{i,t}} ŷ_{m,i,t}, where M_{i,t} is the set of specifications available and n_{i,t} its cardinality
  - Also compute minimum specification ŷ_{i,t}^{min} ≝ ŷ_{0,i,t} (model available for every economy in every period) and maximum specification ŷ_{i,t}^{max} ≝ ŷ_{m*_{i,t},i,t} (specification with maximum number of input variables)
- Two alternative missing-data strategies considered:
  1. Use gradient boosting trees’ built-in handling of missing observations (assign missing to leaf that maximizes objective gain)
     - Benefit: estimate a single, most general specification (computational savings relative to estimating many specifications; current setup has 78 specifications)
     - Caveat: works best if missingness is informative (not missing at random); trials indicated weak out-of-sample performance in this application
  2. Impute all input variables (e.g., using missingpy which sequentially imputes until convergence)
     - Drawback: computationally time-consuming (number of estimations increases at least by the number of input variables); trials indicated weak out-of-sample performance, potentially due to misspecification error between observed and imputed relationships
- Bias-variance trade-off in imputation:
  - Increasing observations reduces variance but can add attenuation bias from measurement error
  - Trials indicate added noise may outweigh variance reduction benefits
- Practical rule applied:
  - Remove observations that are only partially observed at monthly frequency (e.g., if nighttime lights observed for April and May but not June, treat the corresponding 2nd quarter data point as missing)

### Estimated contributions of input variables (SHAP methodology)
- Use python package shap to estimate locally additive contributions of input variables to nowcasts
- SHAP approach:
  - For each specification m for economy i in period t, SHAP values {s_{m,k,i,t}} for each input x_{k} in set K_{m} add up to the predicted value:
    - ŷ_{m,i,t} = ∑_{k ∈ K_{m}} s_{m,k,i,t}
- To analyze changes over time, differences in SHAP values are computed with distinct formulas for:
  - Minimum specification: simple time difference of SHAP values
  - Maximum specification: formula accounts for change in specification from m*_{i,t−1} to m*_{i,t}, decomposing into contributions from:
    - Common variables across specifications (K̃_{1})
    - Newly included variables (K̃_{2})
    - Dropped variables (K̃_{3})
    - A residual term S̃_{i,t}^{max} capturing residual contribution from specification changes
  - Average specification: formula additionally accounts for change in the number of input variables n_{i,t−1} to n_{i,t}; adjusted SHAP values s'_{m,k,i,t}^{avg} are defined with s_{m,k,i,t}' = 0 for k' ∉ K_{m} to enable averaging; residual term S̃_{i,t}^{avg} captures change in specifications
- Implementation detail:
  - Residual contributions computed as:
    - S̃_{i,t}^{max} = ŷ_{i,t}^{max} − ŷ_{i,t−1}^{max} − ∑_{k1 ∈ K̃_{1}} ( s_{m*_{i,t},k1,i,t} − s_{m*_{i,t−1},k1,i,t−1} )
    - S̃_{i,t}^{avg} = ŷ_{i,t}^{avg} − ŷ_{i,t−1}^{avg} − ∑_{k4 ∈ K̃_{4}} ( s_{k4,i,t}^{avg} − s_{k4,i,t−1}^{avg} )

### Country coverage (Annex Table 1 summary)
- Total sample: 200 economies
- Panel A: List of 200 economies by availability of quarterly real GDP growth data
  - Quarterly growth data are included in the sample: 127 economies
  - Quarterly growth data are not included in the sample: 73 economies
  - Breakdown by group with counts preserved where provided:
    - Low-income developing countries (LIDCs; 59): 23 with quarterly growth included; 36 without
    - Emerging market and middle-income economies (97): 67 with quarterly growth included; 30 without
    - Advanced economies (40): 37 with quarterly growth included; 3 without
    - Other economies (4): 0 with quarterly growth included; 4 without
- Panel B: Selected subsamples
  - Sub-Saharan African countries (45): 25 with quarterly growth data included; 20 without
  - Tourism-oriented economies (29): 14 with quarterly growth data included; 15 without
- Note: The terms “country” and “economy” are used interchangeably in the source text.

*Source: Annex Table 2 and accompanying text from wpiea2023158-print-pdf.*

### Annex Table 2. Full variable list with data sources

### Annex Table 2. Full variable list with data sources

### Variable list and source databases
- Agriculture Material Prices, Index (GAS) — Series code: PAGRIW — Database: WEO (GAS)
- Broad Money, Domestic Currency — Series code: FMB_XDC — Database: IFS
- Consumer Prices — Series code: PCPI_IX — Database: IFS
- Consumer Prices, Alcoholic Beverages, Tobacco, and Narcotics — Series code: PCPIFBT_IX — Database: IFS
- Consumer Prices, Clothing and Footwear — Series code: PCPIA_IX — Database: IFS
- Consumer Prices, Communication — Series code: PCPIEC_IX — Database: IFS
- Consumer Prices, Education — Series code: PCPIED_IX — Database: IFS
- Consumer Prices, Food and Non-alcoholic Beverages — Series code: PCPIF_IX — Database: IFS
- Consumer Prices, Furnishings, Household Equipment and Routine Household Maintenance — Series code: PCPIHO_IX — Database: IFS
- Consumer Prices, Health — Series code: PCPIM_IX — Database: IFS
- Consumer Prices, Housing, Water, Electricity, Gas and Other Fuels — Series code: PCPIH_IX — Database: IFS
- Consumer Prices, Recreation and Culture — Series code: PCPIR_IX — Database: IFS
- Consumer Prices, Restaurants and Hotels — Series code: PCPIRE_IX — Database: IFS
- Consumer Prices, Transport — Series code: PCPIT_IX — Database: IFS
- Climate Data: Precipitation — Series code: PRE — Database: Authors
- Climate Data: Temperature — Series code: TEMP — Database: Authors
- CPI-Based Real Effect Exchange Rate — Series code: EREER_IX — Database: IFS
- Domestic Google Trends: All — Series code: DSVI_ALL — Database: Narita and Yin (2018) and Google Trends
- Domestic Google Trends: Arts and Entertainment — Series code: DSVI_ENT — Database: Narita and Yin (2018) and Google Trends
- Domestic Google Trends: Autos and Vehicles — Series code: DSVI_VEH — Database: Narita and Yin (2018) and Google Trends
- Domestic Google Trends: Beauty and Fitness — Series code: DSVI_FIT — Database: Narita and Yin (2018) and Google Trends
- Domestic Google Trends: Books and Literature — Series code: DSVI_LIT — Database: Narita and Yin (2018) and Google Trends
- Domestic Google Trends: Business — Series code: DSVI_BUS — Database: Narita and Yin (2018) and Google Trends
- Domestic Google Trends: Computers and Electronics — Series code: DSVI_CMP — Database: Narita and Yin (2018) and Google Trends
- Domestic Google Trends: Finance — Series code: DSVI_FIN — Database: Narita and Yin (2018) and Google Trends
- Domestic Google Trends: Food and Drink — Series code: DSVI_FOD — Database: Narita and Yin (2018) and Google Trends
- Domestic Google Trends: Games — Series code: DSVI_GAM — Database: Narita and Yin (2018) and Google Trends
- Domestic Google Trends: Health — Series code: DSVI_HTH — Database: Narita and Yin (2018) and Google Trends
- Domestic Google Trends: Hobbies and Leisure — Series code: DSVI_LEI — Database: Narita and Yin (2018) and Google Trends
- Domestic Google Trends: Home and Garden — Series code: DSVI_HOM — Database: Narita and Yin (2018) and Google Trends
- Domestic Google Trends: Internet and Telecom — Series code: DSVI_TEL — Database: Narita and Yin (2018) and Google Trends
- Domestic Google Trends: Jobs — Series code: DSVI_JOB — Database: Narita and Yin (2018) and Google Trends
- Domestic Google Trends: Jobs and Education — Series code: DSVI_JED — Database: Narita and Yin (2018) and Google Trends
- Domestic Google Trends: Law and Government — Series code: DSVI_LAW — Database: Narita and Yin (2018) and Google Trends
- Domestic Google Trends: Military — Series code: DSVI_ARM — Database: Narita and Yin (2018) and Google Trends
- Domestic Google Trends: News — Series code: DSVI_NEW — Database: Narita and Yin (2018) and Google Trends
- Domestic Google Trends: Online Communities — Series code: DSVI_OCM — Database: Narita and Yin (2018) and Google Trends
- Domestic Google Trends: Pets and Animals — Series code: DSVI_PET — Database: Narita and Yin (2018) and Google Trends
- Domestic Google Trends: Real Estate — Series code: DSVI_RES — Database: Narita and Yin (2018) and Google Trends
- Domestic Google Trends: Reference — Series code: DSVI_REF — Database: Narita and Yin (2018) and Google Trends
- Domestic Google Trends: Science — Series code: DSVI_SCI — Database: Narita and Yin (2018) and Google Trends
- Domestic Google Trends: Shopping — Series code: DSVI_SHP — Database: Narita and Yin (2018) and Google Trends
- Domestic Google Trends: Sports — Series code: DSVI_SPT — Database: Narita and Yin (2018) and Google Trends
- Domestic Google Trends: Travel — Series code: DSVI_TVL — Database: Narita and Yin (2018) and Google Trends
- Domestic Google Trends: Weather — Series code: DSVI_WTH — Database: Narita and Yin (2018) and Google Trends
- Export Commodity Prices — Series code: X_GDP — Database: Gruss and Kebhaj (2019)
- Export of Goods and Services, USD — Series code: BXGS_BP6_USD — Database: IFS
- Export of Goods, USD — Series code: BXG_BP6_USD — Database: IFS
- Export of Services, USD — Series code: BXS_BP6_USD — Database: IFS
- Export Prices (export-value weighted average of real GDP growth in export destination countries) — Series code: TM_D_WX001 — Database: WEO (GEE)
- Food Prices, Index (GAS) — Series code: PFOODW — Database: WEO (GAS)
- Fuel Prices, Index (GAS) — Series code: PNRGW — Database: WEO (GAS)
- Import Commodity Prices — Series code: M_GDP — Database: Gruss and Kebhaj (2019)
- Import of Goods and Services, USD — Series code: BMGS_BP6_USD — Database: IFS
- Import of Goods, USD — Series code: BMGS_BP6_USD — Database: IFS
- Import of Services, USD — Series code: BMGS_BP6_USD — Database: IFS
- Import Prices (export-value weighted average of real GDP growth in export destination countries) — Series code: TX_D_WX001 — Database: WEO (GEE)
- Metal Prices, Index (GAS) — Series code: PMETAW — Database: WEO (GAS)
- Nighttime lights — Series code: NL — Database: Authors
- NO2 Emissions — Series code: NO2_MEAN — Database: Authors
- Non-fuel Prices, Index (GAS) — Series code: PNFUELW — Database: WEO (GAS)
- Oil Prices, U.S. Dollar (GAS) — Series code: POILAPSP — Database: WEO (GAS)
- Other Depository Corporations Survey: All Deposits Included in Broad Money, Domestic Currency — Series code: FOS_XDC — Database: IFS
- Other Depository Corporations Survey: Claims on Private Sector, Domestic Currency — Series code: FOSAOP_XDC — Database: IFS
- Passenger Flight Capacity — Series code: PASSENGERCAPACITY — Database: IMF STA Estimates
- Primary Income: Credit, USD — Series code: BXIP_BP6_USD — Database: IFS
- Primary Income: Debit, USD — Series code: BMIP_BP6_USD — Database: IFS
- Real GDP, level — Series code: NGDP_R — Database: WEO
- Seaborne Export Volumes: Bulk — Series code: EXP_BULK — Database: Cerdeiro and others (2020)
- Seaborne Export Volumes: Container — Series code: EXP_CONTAINER — Database: Cerdeiro and others (2020)
- Seaborne Export Volumes: Foodstuff — Series code: EXP_FOODSTUFF — Database: Cerdeiro and others (2020)
- Seaborne Export Volumes: LPG/LNG — Series code: EXP_LPG_LNG — Database: Cerdeiro and others (2020)
- Seaborne Export Volumes: Oil and Chemicals — Series code: EXP_ OIL_CHEMICALS — Database: Cerdeiro and others (2020)
- Seaborne Export Volumes: Vehicles — Series code: EXP_VEHICLES — Database: Cerdeiro and others (2020)
- Seaborne Export Volumes: Total — Series code: EXP_TOTAL — Database: Cerdeiro and others (2020)
- Seaborne Import Volumes: Bulk — Series code: IMP_BULK — Database: Cerdeiro and others (2020)
- Seaborne Import Volumes: Container — Series code: IMP_CONTAINER — Database: Cerdeiro and others (2020)
- Seaborne Import Volumes: Foodstuff — Series code: IMP_ FOODSTUFF — Database: Cerdeiro and others (2020)
- Seaborne Import Volumes: LPG/LNG — Series code: IMP_ LPG_LNG — Database: Cerdeiro and others (2020)
- Seaborne Import Volumes: Oil and Chemicals — Series code: IMP_ OIL_CHEMICALS — Database: Cerdeiro and others (2020)
- Seaborne Import Volumes: Vehicles — Series code: IMP_ VEHICLES — Database: Cerdeiro and others (2020)
- Seaborne Import Volumes: Total — Series code: IMP_ TOTAL — Database: Cerdeiro and others (2020)
- Secondary Income: Credit, USD — Series code: BXISXF_BP6_USD — Database: IFS
- Secondary Income: Debit, USD — Series code: BMIS_BP6_USD — Database: IFS
- Trading Partners’ Real GDP Growth (export-value weighted average of real GDP growth in export destination countries) — Series code: NGDP_R_WX001 — Database: WEO (GEE)
- Total Reserves minus Gold — Series code: RAXG_USD — Database: IFS
- ULC-Based Real Effect Exchange Rate — Series code: EREER_ULC_IX — Database: IFS
- U.S. Treasury Y2 Yield, p.a., NSA — Series code: FTA2YK — Database: HAVER
- USD Rate, Period Average — Series code: ENDA_XDC_USD_RATE — Database: IFS
- U.S. VIX, p.a., NSA — Series code: SPVIX — Database: HAVER
- World Uncertainty Index — Series code: WUI — Database: Ahir, Bloom, and Furceri (2022)
- Worldwide Google Trends: All — Series code: WSVI_ALL — Database: Narita and Yin (2018) and Google Trends
- Worldwide Google Trends: Arts and Entertainment — Series code: WSVI_ENT — Database: Narita and Yin (2018) and Google Trends
- Worldwide Google Trends: Autos and Vehicles — Series code: WSVI_VEH — Database: Narita and Yin (2018) and Google Trends
- Worldwide Google Trends: Beauty and Fitness — Series code: WSVI_FIT — Database: Narita and Yin (2018) and Google Trends
- Worldwide Google Trends: Books and Literature — Series code: WSVI_LIT — Database: Narita and Yin (2018) and Google Trends
- Worldwide Google Trends: Business — Series code: WSVI_BUS — Database: Narita and Yin (2018) and Google Trends
- Worldwide Google Trends: Computers and Electronics — Series code: WSVI_CMP — Database: Narita and Yin (2018) and Google Trends
- Worldwide Google Trends: Finance — Series code: WSVI_FIN — Database: Narita and Yin (2018) and Google Trends
- Worldwide Google Trends: Food and Drink — Series code: WSVI_FOD — Database: Narita and Yin (2018) and Google Trends
- Worldwide Google Trends: Games — Series code: WSVI_GAM — Database: Narita and Yin (2018) and Google Trends
- Worldwide Google Trends: Health — Series code: WSVI_HTH — Database: Narita and Yin (2018) and Google Trends
- Worldwide Google Trends: Hobbies and Leisure — Series code: WSVI_LEI — Database: Narita and Yin (2018) and Google Trends
- Worldwide Google Trends: Home and Garden — Series code: WSVI_HOM — Database: Narita and Yin (2018) and Google Trends
- Worldwide Google Trends: Internet and Telecom — Series code: WSVI_TEL — Database: Narita and Yin (2018) and Google Trends
- Worldwide Google Trends: Jobs — Series code: WSVI_JOB — Database: Narita and Yin (2018) and Google Trends
- Worldwide Google Trends: Jobs and Education — Series code: WSVI_JED — Database: Narita and Yin (2018) and Google Trends
- Worldwide Google Trends: Law and Government — Series code: WSVI_LAW — Database: Narita and Yin (2018) and Google Trends
- Worldwide Google Trends: Military — Series code: WSVI_ARM — Database: Narita and Yin (2018) and Google Trends
- Worldwide Google Trends: News — Series code: WSVI_NEW — Database: Narita and Yin (2018) and Google Trends
- Worldwide Google Trends: Online Communities — Series code: WSVI_OCM — Database: Narita and Yin (2018) and Google Trends
- Worldwide Google Trends: Pets and Animals — Series code: WSVI_PET — Database: Narita and Yin (2018) and Google Trends
- Worldwide Google Trends: Real Estate — Series code: WSVI_RES — Database: Narita and Yin (2018) and Google Trends
- Worldwide Google Trends: Reference — Series code: WSVI_REF — Database: Narita and Yin (2018) and Google Trends
- Worldwide Google Trends: Science — Series code: WSVI_SCI — Database: Narita and Yin (2018) and Google Trends
- Worldwide Google Trends: Shopping — Series code: WSVI_SHP — Database: Narita and Yin (2018) and Google Trends
- Worldwide Google Trends: Sports — Series code: WSVI_SPT — Database: Narita and Yin (2018) and Google Trends
- Worldwide Google Trends: Travel — Series code: WSVI_TVL — Database: Narita and Yin (2018) and Google Trends
- Worldwide Google Trends: Weather — Series code: WSVI_WTH — Database: Narita and Yin (2018) and Google Trends

Sources and notes included in the original table:
- Sources: Ahir, Bloom, and Furceri (2022); Cerdeiro and others (2020); Google Trends; Gruss and Kebhaj (2019); Haver Analytics (2022); International Financial Statistics (IFS, IMF, 2022b); Narita and Yin (2018); World Economic Outlook (WEO, IMF, 2022c); and authors.
- Note on nighttime lights data: sourced from Visible Infrared Imaging Radiometer Suite (VIIRS) Day/Night Band (DNB) data produced by the Earth Observation Group, NOAA/NCEI.

### Performance tables referenced (Annex Tables 3–8): sample coverage and notes
- Annex Table 3 (LGB, EMDE subsample): estimation sample includes 4,475 observations for 90 EMDEs from 2009Q1 to 2022Q3.
- Annex Table 4 (LGB, commodity exporter subsample): estimation sample includes 1,335 observations for 28 commodity exporting economies from 2009Q1 to 2022Q3.
- Annex Table 5 (LGB, fuel exporter subsample): estimation sample includes 673 observations for 14 fuel exporting economies from 2009Q1 to 2022Q3.
- Annex Table 6 (LGB, tourism-oriented country subsample): estimation sample includes 704 observations for 14 tourism-oriented economies from 2009Q1 to 2022Q3.
- Annex Table 7 (OLS, global sample): estimation sample includes 1,134 observations for 25 SSA countries from 2009Q1 to 2022Q3.
- Annex Table 8 (OLS, SSA subsample): estimation sample includes 1,134 observations for 25 SSA countries from 2009Q1 to 2022Q3.

### Selected performance metrics reported (examples preserved exactly as in tables)
- From Annex Table 3 (LGB, EMDE subsample, Panel B period-wise evaluation):
  - Test sample period 2020Q1-2022Q3 (sample size) (1716): In-sample bias = -0.05; In-sample bias on test sample = 0.05; Out-of-sample bias = 1.92; In-sample direction = 0.83; In-sample direction on test sample = 0.89; Out-of-sample direction = 0.67; In-sample RMSE = 1.92; In-sample RMSE on test sample = 2.52; Out-of-sample RMSE = 9.28; Theil U = 1.01
  - Test sample period 2020Q4-2022Q3 (sample size) (1248): In-sample bias = -0.05; In-sample bias on test sample = -0.06; Out-of-sample bias = -4.80; In-sample direction = 0.83; In-sample direction on test sample = 0.87; Out-of-sample direction = 0.59; In-sample RMSE = 1.92; In-sample RMSE on test sample = 2.23; Out-of-sample RMSE = 8.83; Theil U = 1.10
- From Annex Table 4 (LGB, commodity exporter subsample, Panel B period-wise evaluation):
  - Test sample period 2020Q1-2022Q3 (sample size) (693): In-sample bias = 0.01; In-sample bias on test sample = 0.01; Out-of-sample bias = 2.08; In-sample direction = 0.90; In-sample direction on test sample = 0.93; Out-of-sample direction = 0.57; In-sample RMSE = 1.52; In-sample RMSE on test sample = 1.80; Out-of-sample RMSE = 7.32; Theil U = 1.04
- From Annex Table 5 (LGB, fuel exporter subsample, Panel B period-wise evaluation):
  - Test sample period 2020Q1-2022Q3 (sample size) (286): In-sample bias = -0.01; In-sample bias on test sample = 0.02; Out-of-sample bias = 2.39; In-sample direction = 0.93; In-sample direction on test sample = 0.96; Out-of-sample direction = 0.54; In-sample RMSE = 0.64; In-sample RMSE on test sample = 0.83; Out-of-sample RMSE = 5.99; Theil U = 1.41
- From Annex Table 6 (LGB, tourism-oriented subsample, Panel B period-wise evaluation):
  - Test sample period 2020Q1-2022Q3 (sample size) (319): In-sample bias = -0.01; In-sample bias on test sample = 0.29; Out-of-sample bias = 2.62; In-sample direction = 0.88; In-sample direction on test sample = 0.92; Out-of-sample direction = 0.62; In-sample RMSE = 2.56; In-sample RMSE on test sample = 5.70; Out-of-sample RMSE = 17.76; Theil U = 1.11
- From Annex Table 7 (OLS, global sample, Panel B period-wise evaluation):
  - Test sample period 2020Q1-2022Q3 (sample size) (495): In-sample bias = -0.07; In-sample bias on test sample = 0.04; Out-of-sample bias = 4.55; In-sample direction = 0.59; In-sample direction on test sample = 0.79; Out-of-sample direction = 0.59; In-sample RMSE = 4.54; In-sample RMSE on test sample = 7.07; Out-of-sample RMSE = 11.47; Theil U = 1.25
- From Annex Table 8 (OLS, SSA subsample, Panel B period-wise evaluation):
  - Test sample period 2020Q1-2022Q3 (sample size) (495): In-sample bias = -0.03; In-sample bias on test sample = -0.00; Out-of-sample bias = 6.62; In-sample direction = 0.62; In-sample direction on test sample = 0.75; Out-of-sample direction = 0.51; In-sample RMSE = 3.76; In-sample RMSE on test sample = 3.48; Out-of-sample RMSE = 17.52; Theil U = 2.08

- Additional country-wise and period-wise metrics are reported in Annex Tables 3–8 for multiple countries and subsamples (figures reproduced exactly in the original tables).

*Italic: Sources: Authors estimations and original table sources as listed in the PDF annex.*

### Annex Table 9. Performance of panel nowcasts for countries without quarterly growth data: OLS

### Annex Table 9. Performance of panel nowcasts for countries without quarterly growth data: OLS

### Table summary by model (2010-2022 sample)
- Columns (in table order): Model | 2010-2022 (sample size) | In-sample bias | In-sample bias on test sample | Out-of-sample bias | In-sample direction | In-sample direction on test sample | Out-of-sample direction | In-sample RMSE | In-sample RMSE on test sample | Out-of-sample RMSE | Theil U

- OLS, Global, average
  - 2010-2022 (sample size): (1,017)
  - In-sample bias: -
  - In-sample bias on test sample: -
  - Out-of-sample bias: 1.27
  - In-sample direction: -
  - In-sample direction on test sample: -
  - Out-of-sample direction: 0.62
  - In-sample RMSE: -
  - In-sample RMSE on test sample: -
  - Out-of-sample RMSE: 6.90
  - Theil U: 0.69

- OLS, EMDEs, average
  - 2010-2022 (sample size): (926)
  - In-sample bias: -
  - In-sample bias on test sample: -
  - Out-of-sample bias: 1.26
  - In-sample direction: -
  - In-sample direction on test sample: -
  - Out-of-sample direction: 0.63
  - In-sample RMSE: -
  - In-sample RMSE on test sample: -
  - Out-of-sample RMSE: 6.99
  - Theil U: 0.70

- OLS, SSA, average
  - 2010-2022 (sample size): (293)
  - In-sample bias: -
  - In-sample bias on test sample: -
  - Out-of-sample bias: 1.62
  - In-sample direction: -
  - In-sample direction on test sample: -
  - Out-of-sample direction: 0.64
  - In-sample RMSE: -
  - In-sample RMSE on test sample: -
  - Out-of-sample RMSE: 6.09
  - Theil U: 0.75

- OLS, Comm. exp., average
  - 2010-2022 (sample size): (480)
  - In-sample bias: -
  - In-sample bias on test sample: -
  - Out-of-sample bias: 2.10
  - In-sample direction: -
  - In-sample direction on test sample: -
  - Out-of-sample direction: 0.62
  - In-sample RMSE: -
  - In-sample RMSE on test sample: -
  - Out-of-sample RMSE: 8.55
  - Theil U: 0.70

- OLS, Fuel exp., average
  - 2010-2022 (sample size): (164)
  - In-sample bias: -
  - In-sample bias on test sample: -
  - Out-of-sample bias: 2.81
  - In-sample direction: -
  - In-sample direction on test sample: -
  - Out-of-sample direction: 0.65
  - In-sample RMSE: -
  - In-sample RMSE on test sample: -
  - Out-of-sample RMSE: 12.08
  - Theil U: 0.69

- OLS, Tourism, average
  - 2010-2022 (sample size): (207)
  - In-sample bias: -
  - In-sample bias on test sample: -
  - Out-of-sample bias: 1.01
  - In-sample direction: -
  - In-sample direction on test sample: -
  - Out-of-sample direction: 0.66
  - In-sample RMSE: -
  - In-sample RMSE on test sample: -
  - Out-of-sample RMSE: 4.75
  - Theil U: 0.56

### Key findings implied by the table entries
- Out-of-sample bias values (preserved exactly as in the table) vary across samples:
  - Global: 1.27
  - EMDEs: 1.26
  - SSA: 1.62
  - Comm. exp.: 2.10
  - Fuel exp.: 2.81
  - Tourism: 1.01
- Out-of-sample direction metrics (preserved exactly) range from 0.62 to 0.66 across groups:
  - Global: 0.62
  - EMDEs: 0.63
  - SSA: 0.64
  - Comm. exp.: 0.62
  - Fuel exp.: 0.65
  - Tourism: 0.66
- Out-of-sample RMSE (preserved exactly) indicates differing forecast accuracy across groups:
  - Global: 6.90
  - EMDEs: 6.99
  - SSA: 6.09
  - Comm. exp.: 8.55
  - Fuel exp.: 12.08
  - Tourism: 4.75
- Theil U statistics (preserved exactly) reported for each group:
  - Global: 0.69
  - EMDEs: 0.70
  - SSA: 0.75
  - Comm. exp.: 0.70
  - Fuel exp.: 0.69
  - Tourism: 0.56

### Data and methodological notes
- Sources: Authors estimations (see Annex Table 2 for data sources).
- Notes: The estimation sample period is from 2009Q1 to 2022Q3 (see Annex I for details).
- Abbreviations preserved exactly as in source:
  - Comm. exp.=commodity exporting economies
  - Fuel exp.=fuel exporting economies
  - EMDEs=emerging market and developing economies
  - OLS=ordinary least squares
  - SSA=sub-Saharan Africa
  - Tourism=tourism-oriented economies

*Source: Annex Table 9, wpiea2023158-print-pdf*

---


_Source: https://www.imf.org/-/media/files/publications/wp/2023/english/wpiea2023158-print-pdf.pdf_