## 1. We estimate a DFM with only the two global factors. If a common global factor structure

## Source details

**Canonical URL:** [1. We estimate a DFM with only the two global factors. If a common global factor structure](https://www.imf.org/-/media/files/publications/wp/2026/english/wpiea2026048-source-pdf.pdf)

## Other formats

- [Markdown version](/-/media/files/publications/wp/2026/english/wpiea2026048-source-pdf.pdf.md)
- [Structured JSON version](/-/media/files/publications/wp/2026/english/wpiea2026048-source-pdf.pdf.json)

---

### Methodology: testing for regional factors beyond two global factors
- A dynamic factor model (DFM) with only the two global factors is estimated.
- Diagnostic logic:
  - If a common global factor structure describes the data well, residuals for regional variable blocks should be no more correlated with one another than with residuals outside that region.
  - Higher within-region correlation indicates missing regional factors.
- Procedure (following Moench et al. 2013):
  - Principal components (PCs) of the dataset are regressed on the global factors from the DFM.
  - Residuals from that regression represent variation the PCs regard as common but not captured by the DFM.
  - Those residuals are then regressed on the regional factors; explanatory power of regional factors for these residuals supports the presence of regional variation identified by PCs.

### Empirical evidence for regional structure (residual correlations and PC residual regressions)
- Residual correlation evidence (Table 2: Average Within Group / Average Outside Group)
  - USA 0.15 0.11
  - China 0.20 0.14
  - Asia 0.18 0.14
  - Europe 0.18 0.13
- Interpretation:
  - Residuals for variables within regional blocks are generally better correlated with each other than with variables outside those blocks, suggesting missing regional factors not captured by the two-global-factor DFM.
- PC residual regressions (Table 3: Sum of R2s for regressions of PC residuals on regional factors)
  - US 0.31
  - Asia 0.16
  - Europe 0.17
  - China 0.11
- Interpretation:
  - The US factor explains 31% of variation in residuals of the first and second principal components relative to the DFM global factor; Asia, Europe, China explain 16%, 17%, 11% respectively, indicating some common variation from PCs aligns with regional factors, particularly the US.

### Estimation sample and factor interpretation
- Estimation sample: data over 2005-19 (Covid omitted from estimation sample).
- Roles of factors:
  - Global factor 1: best correlated with surveys and PMI indicators; picks up broad underlying trend (e.g., Global Financial Crisis fall; slowdown in 2018-19).
  - Global factor 2: better correlated with hard data; reflects month-to-month variation in hard data.
  - US regional factor: uncorrelated or negatively correlated with other factors; suggests it picks up idiosyncratic US news and possibly US/global financial conditions not captured elsewhere.
- Regional factors capture fluctuations around the global trend.

### Correlations and explanatory power (Tables 4 and 5)
- Correlation matrix between factors (Table 4: entries preserved)
  - Global1: 1.00, 0.32, -0.01, 0.41, 0.48, -0.10  (Global1 with Global2, US, Asia, Europe, China)
  - Global2: 0.32, 1.00, 0.04, 0.54, 0.54, -0.21
  - US: -0.01, 0.04, 1.00, -0.11, -0.19, 0.19
  - Asia: 0.41, 0.54, -0.11, 1.00, 0.77, -0.10
  - Europe: 0.48, 0.54, -0.19, 0.77, 1.00, -0.27
  - China: -0.10, -0.21, 0.19, -0.10, -0.27, 1.00
- Explanatory power: top ten variables by R2 for each factor (Table 5: top entries preserved)
  - Global1 R2 (top entries):
    - Global PMI new export orders 0.72
    - Global PMI manufacturing 0.68
    - Euro-area manufacturing PMI 0.68
    - Advanced economies industrial production 0.66
    - EU incl UK manufacturing PMI 0.66
    - Euro-area PMI new export orders 0.64
    - World trade 0.62
    - World industrial production 0.61
    - Germany manufacturing PMI 0.60
    - Germany PMI new export orders 0.60
  - Global2 R2 (top entries):
    - France industrial production 0.53
    - Advanced economies industrial production 0.52
    - Euro-area industrial production (ex IRL) 0.52
    - UK industrial production 0.52
    - Italy exports 0.49
    - Germany exports 0.46
    - Euro-area industrial production 0.45
    - EM Asia ex China industrial production 0.43
    - Euro-area manufacturing exports 0.43
    - ChinaR2 entries and others preserved below
  - US R2 (top entries):
    - US high-yield spread 0.56
    - MSCI World Index 0.36
    - Brent oil price 0.30
    - US nominal effective exchange rate 0.29
    - US PMI new export orders 0.09
    - US retail sales 0.08
    - Global PMI stocks of purchases 0.07
    - US manufacturing PMI 0.05
    - US goods consumption 0.04
    - US exports 0.04
  - Asia R2 (top entries):
    - Advanced economies industrial production 0.48
    - EM Asia ex China industrial production 0.38
    - China industrial production 0.23
    - World industrial production 0.22
    - China retail sales 0.19
    - China NBS PMI manufacturing 0.16
    - World trade 0.16
    - ASEAN PMI new export orders 0.12
    - Emerging Asia ex China exports 0.12
    - Malaysia exports 0.10
  - Europe R2 (top entries):
    - Euro-area industrial production (ex IRL) 0.56
    - UK industrial production 0.55
    - France industrial production 0.52
    - Global container throughput index 0.16
    - Germany exports 0.50
    - World trade 0.15
    - Italy exports 0.49
    - Euro-area manufacturing exports 0.47
    - Euro-area exports 0.46
    - Germany industrial production 0.44
  - China R2 (top entries):
    - China exports 0.33
    - China imports 0.19
    - China industrial production 0.10
    - China retail sales 0.03
    - China international aviation cargo and mail 0.05
    - US high-yield spread 0.04
    - Global PMI stocks of purchases 0.03
    - Additional entries preserved as listed in the source.

### Spillovers: methodology and findings
- Methodology:
  - Use generalized forecast error variance decomposition (GFEVD) and generalized impulse responses (Pesaran and Shin 1998; Diebold and Yilmaz 2012).
  - VAR(1) factor dynamics: f_t = A1 f_{t−1} + u_t, moving average representation f_t = sum_{j=0}^{∞} Ψ_j u_{t−j}, with u ~ N(0,Q).
  - Variance shares for H-step ahead errors: θ^g_{ij}(H) formula preserved as in source.
  - Normalize rows because row sums are not equal to one: ˜θ^g_{ij}(H) = θ^g_{ij}(H) / sum_{j=1}^N θ^g_{ij}(H).
  - Define directional spillovers received and transmitted:
    - S^g_{i←}(H) = (sum_{j=1, j≠i}^N ˜θ^g_{ij}(H) / N) 100
    - S^g_{i→}(H) = (sum_{j=1, j≠i}^N ˜θ^g_{ji}(H) / N) 100
- Key empirical findings:
  - In the short run, most forecast error variance in each region is due to news in its own factor; over time, the first global factor drives more of the variation.
  - The Asian factor has the largest and most persistent spillovers to other factors, particularly to Europe, and is the largest contributor to news in the global factor.
  - The first global factor and the Asian factor are the two largest contributors to forecast error variance in other factors.
  - The US factor is a relatively small generator of forecast error variance but a significant recipient, consistent with it picking up short-term idiosyncratic US variation.
  - Total spillover index is 73% (reported as 73 in the table): majority of forecast error variance is driven by innovations to other factors rather than own-innovations.

### Volatility spillover table (Table 6) — three months ahead contributions
- Interpretation: Row entries show contribution to forecast error variance of factor i from innovations in factor j; diagonal entries are own-factor shares. Directional totals and Total spillover index preserved.
- Table 6 (rows: contributor; columns: recipient; final columns: Directional FROM others; Directional TO others; Total spillover index reported)
  - Global1 row: 57.0 13.1 5.6 11.8 8.1 4.5 43.0
  - Global2 row: 36.6 23.4 4.6 19.3 8.9 7.3 76.6
  - US row: 51.6 12.4 11.1 12.6 7.1 5.2 88.9
  - Asia row: 43.1 6.8 7.6 24.4 8.5 9.5 75.6
  - Europe row: 23.5 13.3 10.1 28.6 20.6 3.8 79.4
  - China row: 48.4 6.2 7.2 11.7 4.0 22.4 77.6
  - Directional TO others totals (column sums reported): 203.2 51.9 35.1 84.0 36.6 30.3
  - Directional including own (row sums): 260.2 75.2 46.2 108.4 57.2 52.8 Total spillover index: 73.5
- Interpretation:
  - The first global and Asian factors are dominant contributors; the US primarily receives spillovers.
  - The table indicates high interconnectedness in trade-related factors.

### Forecast accuracy: pseudo out-of-sample nowcasting evaluation
- Model design:
  - Monthly model focused on nowcasting underlying trend of quarterly trade growth; quarterly growth approximated from monthly forecasts using Mariano and Murasawa 2003 formula:
    - y^{3m/3m}_t = (y^{m/m}_t + 2 y^{m/m}_{t−1} + 3 y^{m/m}_{t−2} + 2 y^{m/m}_{t−3} + y^{m/m}_{t−4}) / 3
  - Pseudo real-time re-estimation: model re-estimated each month using the unbalanced dataset with standard publication lags up to end of 2019; after that, parameters are fixed using 2005-19 estimation.
- Benchmarks:
  - AR(1), random walk, and single-factor DFM (one factor loading on all variables).
- Evaluation samples:
  - 2017-19: slowdown in global trade (heightened trade tensions, reduced policy support, auto sector slowdown).
  - 2020-22: Covid peak with sharp drop and divergence in regional trade trends (China and Asia recovered more strongly).
- Main accuracy results:
  - The DFM outperforms benchmarks, including single-factor DFM, at most horizons.
  - Figure 6 (RMSFE across horizons) shows improvements especially before the start of the nowcasted quarter (weeks -20 to -12).
  - Table 7: Relative RMSFE and MAE (ratio of DFM error to benchmark error; values < 1 indicate DFM is more accurate). Selected table values preserved exactly:
    - Relative RMSFE vs Single-factor DFM (Pre-Covid weeks): 0.60 40 0.59 10 0.60 70 0.67 20 0.82 00
    - Relative RMSFE vs Single-factor DFM (Covid weeks): 0.82 70 0.61 80 0.60 90 0.71 30 0.76 50
    - Relative RMSFE vs AR(1) (Pre-Covid weeks): 0.83 80 0.89 10 0.83 10 0.86 40 0.98 20
    - Relative RMSFE vs AR(1) (Covid weeks): 1.32 20 0.92 20 0.71 30 0.72 90 0.61 30
    - Relative RMSFE vs Random walk (Pre-Covid weeks): 0.18 50 0.23 50 0.24 90 0.25 90 0.43 60
    - Relative RMSFE vs Random walk (Covid weeks): 1.15 50 0.52 40 0.28 40 0.68 30 0.54 90
    - Relative MAE vs Single-factor DFM (Pre-Covid weeks): 0.58 60 0.56 90 0.65 20 0.73 30 0.93 30
    - Relative MAE vs Single-factor DFM (Covid weeks): 0.87 00 0.76 70 0.63 50 0.65 40 0.75 00
    - Diebold-Mariano p-values vs Single-factor DFM (Pre-Covid weeks): 0.062* 0.045* 0.067* 0.095* 0.174
    - Diebold-Mariano p-values vs Single-factor DFM (Covid weeks): 0.16 0.14 0.147 0.142 0.142 0.088*
- Interpretation:
  - Improvement in forecast performance is greatest before the start of the nowcasted quarter (e.g., Week -12).
  - Example: RMSFE of the DFM is 40% lower than that of a single-factor model in week -12 of pre-Covid sample and 20% lower than an AR(1) in that week.
  - Diebold-Mariano tests indicate DFM out-performance relative to the single-factor model is statistically significant at most horizons in the pre-Covid period (Harvey et al. 1997 adjustment used for small samples).
  - Relative performance narrows as the end of the quarter approaches because more monthly data become available and the final month carries a smaller weight in quarterly growth (final month weight 11%).

### Robustness and caveats
- Alternative specifications (different factor structures, lag orders, estimation windows) yield qualitatively similar out-of-sample performance.
- The baseline multi-factor model does not outperform single-global-factor specifications during periods dominated by a global trade cycle (example: 2014–2016).
- Sample sizes for pseudo out-of-sample evaluation are relatively small (twelve quarters in each sub-period), though statistical tests are reported.

### Case studies (Section 4.4)
- Overview:
  - Purpose: Illustrate that a multi-factor framework is best suited to episodes with strong regional dynamics affecting global trade rather than a single common global driver.
  - Focus: world trade over a year in three episodes: 2020, 2023 and 2008.
  - Data handling: models forecast annual trade growth for a given year using data restricted to end-previous-year and then update the forecast incrementally as one additional month of data is added through the year.
- Case study I: 2020 and the Covid shock
  - Dataset restricted to end-2019 to forecast 2020, then forecasts recalculated monthly through end-2020 (Level: 2019 = 100).
  - Findings:
    - Cumulative world trade data surprises are smaller in the multi-factor model than the single-factor DFM, indicating better month-by-month prediction conditional on other data.
    - The multi-factor DFM detected a sharp contraction in world trade in 2020 earlier than the single-factor model.
    - China’s trade contracted sharply in the first three months of 2020, while trade elsewhere was relatively resilient; the multi-factor model places greater weight on this concentrated China shock.
    - The multi-factor model captured the unexpectedly rapid recovery in world trade in the second half of 2020 by identifying China’s trade recovery beginning by spring 2020; the single-factor model overweighted European data and missed this early reversal.
  - Mechanism: Regional contributions to cumulative forecast revisions illustrate how regional data surprises drive revisions.
  - Implication: Multi-factor structure can distinguish concentrated regional shocks (e.g., China) from global noise and update global trade forecasts more accurately during uneven regional episodes.
- Case study II: 2023 and post-Covid trade divergence
  - Context: By late 2022 global trade showed signs of recovery but recovery was uneven into 2023.
  - Findings:
    - In 2023, trade recovered strongly in China while remaining weak across most Advanced Economies.
    - By the start of 2023 the multi-factor model revised up its forecast for world trade growth in 2023 by 3 percentage points due to China’s outperformance.
    - The single-factor model continued to forecast a contraction in global trade until August 2023, whereas world trade growth was overall positive in 2023.
  - Implication: Multi-region factor structure accommodates divergent regional recoveries and produces timelier upward revisions when a major region (China) outperforms.
- Case study III: 2008 and a global trade slowdown
  - Context: Synchronized global downturn (Global Financial Crisis).
  - Findings:
    - Both multi-factor and single-factor models overpredicted the strength of global trade at the start of 2008.
    - As the crisis unfolded both models downgraded forecasts for world trade growth in 2008 by around 4 percentage points.
    - The single-factor model picked up the deterioration slightly earlier than the multi-factor model.
    - Drivers of revisions were weaker-than-expected global data and worse data in the US.
  - Implication: When the slowdown is synchronous and global in nature, a multi-factor structure that models regional variation adds little additional forecasting power relative to a single-factor model.

### Synthesis and policy-relevant insights
- Model performance depends on the nature of shocks:
  - Synchronized global events (e.g., 2008 financial crisis) — single-factor models perform well.
  - Episodes of regional heterogeneity (e.g., Covid in 2020; post-Covid divergence in 2023) — multi-factor models provide superior near-term forecasts.
- Regional factors matter:
  - Regional factors, particularly for Asia, are significant sources of spillovers to other regions and to the global outlook, consistent with Asia’s integration into global value chains.
- Practical advantage:
  - Identifying geographic origins of shocks to global trade in real-time improves economic surveillance and offers a timelier, richer narrative of ongoing trade dynamics than relying solely on a global aggregate.

*Source: 4.4 Case studies, Nowcasting World Trade With a Multi-Region Factor Model (Working Paper No. WP/2026/049).*

### 1.  We estimate a DFM with only the two global factors.  If a common global factor structure

### 1.  We estimate a DFM with only the two global factors.  If a common global factor structure

### Methodology: testing for regional factors beyond two global factors
- A dynamic factor model (DFM) with only the two global factors is estimated.
- If a common global factor structure describes the data well, residuals for regional variable blocks should be no more correlated with one another than with residuals outside that region; higher within-region correlation would indicate missing regional factors.
- Following Moench et al. 2013:
  - Principal components (PCs) of the dataset are regressed on the global factors from the DFM.
  - Residuals from that regression represent variation the PCs regard as common but not captured by the DFM.
  - Those residuals are then regressed on the regional factors; explanatory power of regional factors for these residuals supports the presence of regional variation identified by PCs.

### Empirical evidence for regional structure (residual correlations and PC residual regressions)
- Table 2: Correlation of residuals within and outside of regional group (Average Within Group / Average Outside Group)
  - USA 0.15 0.11
  - China 0.20 0.14
  - Asia 0.18 0.14
  - Europe 0.18 0.13
- Interpretation: Residuals for variables within regional blocks are generally better correlated with each other than with variables outside those blocks, suggesting missing regional factors not captured by the two-global-factor DFM.
- Table 3: Sum of R2s for regressions of PC residuals on regional factors (Principal Component PC1, PC2)
  - US 0.31
  - Asia 0.16
  - Europe 0.17
  - China 0.11
- Interpretation: The US factor explains 31% of variation in residuals of the first and second principal components relative to the DFM global factor; Asia, Europe, China explain 16%, 17%, 11% respectively, indicating that some common variation from PCs aligns with regional factors, particularly the US.

### Estimation sample and factor interpretation
- Estimation sample: data over 2005-19 (Covid omitted from estimation sample).
- The first global factor is well correlated with global trade growth and captures the broad underlying trend (e.g., Global Financial Crisis fall; slowdown in 2018-19).
- The regional factors capture fluctuations around the global trend.
- Factor roles:
  - Global factor 1: best correlated with surveys and PMI indicators; picks up broad underlying trend.
  - Global factor 2: better correlated with hard data; reflects month-to-month variation in hard data.
  - US regional factor: uncorrelated or negatively correlated with other factors; suggests it picks up idiosyncratic US news and possibly US/global financial conditions not captured elsewhere.

### Correlations and explanatory power (Tables 4 and 5)
- Table 4: Correlation between factors (matrix entries preserved as presented)
  - Global1: 1.00, 0.32, -0.01, 0.41, 0.48, -0.10  (Global1 with Global2, US, Asia, Europe, China)
  - Global2: 0.32, 1.00, 0.04, 0.54, 0.54, -0.21
  - US: -0.01, 0.04, 1.00, -0.11, -0.19, 0.19
  - Asia: 0.41, 0.54, -0.11, 1.00, 0.77, -0.10
  - Europe: 0.48, 0.54, -0.19, 0.77, 1.00, -0.27
  - China: -0.10, -0.21, 0.19, -0.10, -0.27, 1.00
- Table 5: Explanatory power of factors (top ten variables by R2 for each factor)
  - Global1 R2 (top entries):
    - Global PMI new export orders 0.72
    - Global PMI manufacturing 0.68
    - Euro-area manufacturing PMI 0.68
    - Advanced economies industrial production 0.66
    - EU incl UK manufacturing PMI 0.66
    - Euro-area PMI new export orders 0.64
    - World trade 0.62
    - World industrial production 0.61
    - Germany manufacturing PMI 0.60
    - Germany PMI new export orders 0.60
  - Global2 R2 (top entries):
    - France industrial production 0.53
    - Advanced economies industrial production 0.52
    - Euro-area industrial production (ex IRL) 0.52
    - UK industrial production 0.52
    - Italy exports 0.49
    - Germany exports 0.46
    - Euro-area industrial production 0.45
    - EM Asia ex China industrial production 0.43
    - Euro-area manufacturing exports 0.43
    - ChinaR2 entries and others preserved below
  - US R2 (top entries):
    - US high-yield spread 0.56
    - MSCI World Index 0.36
    - Brent oil price 0.30
    - US nominal effective exchange rate 0.29
    - US PMI new export orders 0.09
    - US retail sales 0.08
    - Global PMI stocks of purchases 0.07
    - US manufacturing PMI 0.05
    - US goods consumption 0.04
    - US exports 0.04
  - Asia R2 (top entries):
    - Advanced economies industrial production 0.48
    - EM Asia ex China industrial production 0.38
    - China industrial production 0.23
    - World industrial production 0.22
    - China retail sales 0.19
    - China NBS PMI manufacturing 0.16
    - World trade 0.16
    - ASEAN PMI new export orders 0.12
    - Emerging Asia ex China exports 0.12
    - Malaysia exports 0.10
  - Europe R2 (top entries):
    - Euro-area industrial production (ex IRL) 0.56
    - UK industrial production 0.55
    - France industrial production 0.52
    - Global container throughput index 0.16
    - Germany exports 0.50
    - World trade 0.15
    - Italy exports 0.49
    - Euro-area manufacturing exports 0.47
    - Euro-area exports 0.46
    - Germany industrial production 0.44
  - China R2 (top entries):
    - China exports 0.33
    - China imports 0.19
    - China industrial production 0.10
    - China retail sales 0.03
    - China international aviation cargo and mail 0.05
    - US high-yield spread 0.04
    - Global PMI stocks of purchases 0.03
    - Additional entries preserved as listed in the source.

### Spillovers: methodology and findings
- Methodology:
  - Use generalized forecast error variance decomposition (GFEVD) and generalized impulse responses (Pesaran and Shin 1998; Diebold and Yilmaz 2012).
  - VAR(1) factor dynamics: f_t = A1 f_{t−1} + u_t, moving average representation f_t = sum_{j=0}^{∞} Ψ_j u_{t−j}, with u ~ N(0,Q).
  - Variance shares for H-step ahead errors: θ^g_{ij}(H) formula preserved as in source.
  - Normalize rows because row sums are not equal to one: ˜θ^g_{ij}(H) = θ^g_{ij}(H) / sum_{j=1}^N θ^g_{ij}(H).
  - Define directional spillovers received and transmitted:
    - S^g_{i←}(H) = (sum_{j=1, j≠i}^N ˜θ^g_{ij}(H) / N) 100
    - S^g_{i→}(H) = (sum_{j=1, j≠i}^N ˜θ^g_{ji}(H) / N) 100
- Key empirical findings:
  - In the short run, most forecast error variance in each region is due to news in its own factor; over time, the first global factor drives more of the variation.
  - The Asian factor has the largest and most persistent spillovers to other factors, particularly to Europe, and is the largest contributor to news in the global factor.
  - The first global factor and the Asian factor are the two largest contributors to forecast error variance in other factors.
  - The US factor is a relatively small generator of forecast error variance but a significant recipient, consistent with it picking up short-term idiosyncratic US variation.
  - Total spillover index is 73% (reported as 73 in the table): majority of forecast error variance is driven by innovations to other factors rather than own-innovations.

### Volatility spillover table (Table 6) — three months ahead contributions (preserved matrix entries)
- Row entries show contribution to forecast error variance of factor i from innovations in factor j; diagonal entries are own-factor shares.
- Table 6 (rows: contributor; columns: recipient; final columns: Directional FROM others; Directional TO others; Total spillover index reported)
  - Global1 row: 57.0 13.1 5.6 11.8 8.1 4.5 43.0
  - Global2 row: 36.6 23.4 4.6 19.3 8.9 7.3 76.6
  - US row: 51.6 12.4 11.1 12.6 7.1 5.2 88.9
  - Asia row: 43.1 6.8 7.6 24.4 8.5 9.5 75.6
  - Europe row: 23.5 13.3 10.1 28.6 20.6 3.8 79.4
  - China row: 48.4 6.2 7.2 11.7 4.0 22.4 77.6
  - Directional TO others totals (column sums reported): 203.2 51.9 35.1 84.0 36.6 30.3
  - Directional including own (row sums): 260.2 75.2 46.2 108.4 57.2 52.8 Total spillover index: 73.5 (presented as 73.5 in the table)
- Interpretation: first global and Asian factors are dominant contributors; US primarily receives spillovers; high interconnectedness in trade factors.

### Forecast accuracy: pseudo out-of-sample nowcasting evaluation
- Model design: monthly model focused on nowcasting underlying trend of quarterly trade growth; quarterly growth approximated from monthly forecasts using Mariano and Murasawa 2003 formula:
  - y^{3m/3m}_t = (y^{m/m}_t + 2 y^{m/m}_{t−1} + 3 y^{m/m}_{t−2} + 2 y^{m/m}_{t−3} + y^{m/m}_{t−4}) / 3
- Pseudo real-time re-estimation: model re-estimated each month using the unbalanced dataset with standard publication lags up to end of 2019; after that, parameters are fixed using 2005-19 estimation.
- Benchmarks: AR(1), random walk, and single-factor DFM (one factor loading on all variables).
- Evaluation samples:
  - 2017-19: slowdown in global trade (heightened trade tensions, reduced policy support, auto sector slowdown).
  - 2020-22: Covid peak with sharp drop and divergence in regional trade trends (China and Asia recovered more strongly).
- Main accuracy results:
  - The DFM outperforms benchmarks, including single-factor DFM, at most horizons.
  - Figure 6 (RMSFE across horizons) shows improvements especially before the start of the nowcasted quarter (weeks -20 to -12).
  - Table 7: Relative RMSFE and MAE (ratio of DFM error to benchmark error; values < 1 indicate DFM is more accurate). Selected table values preserved exactly:
    - Relative RMSFE vs Single-factor DFM (Pre-Covid weeks): 0.60 40 0.59 10 0.60 70 0.67 20 0.82 00
    - Relative RMSFE vs Single-factor DFM (Covid weeks): 0.82 70 0.61 80 0.60 90 0.71 30 0.76 50
    - Relative RMSFE vs AR(1) (Pre-Covid weeks): 0.83 80 0.89 10 0.83 10 0.86 40 0.98 20
    - Relative RMSFE vs AR(1) (Covid weeks): 1.32 20 0.92 20 0.71 30 0.72 90 0.61 30
    - Relative RMSFE vs Random walk (Pre-Covid weeks): 0.18 50 0.23 50 0.24 90 0.25 90 0.43 60
    - Relative RMSFE vs Random walk (Covid weeks): 1.15 50 0.52 40 0.28 40 0.68 30 0.54 90
    - Relative MAE vs Single-factor DFM (Pre-Covid weeks): 0.58 60 0.56 90 0.65 20 0.73 30 0.93 30
    - Relative MAE vs Single-factor DFM (Covid weeks): 0.87 00 0.76 70 0.63 50 0.65 40 0.75 00
    - Diebold-Mariano p-values vs Single-factor DFM (Pre-Covid weeks): 0.062* 0.045* 0.067* 0.095* 0.174
    - Diebold-Mariano p-values vs Single-factor DFM (Covid weeks): 0.16 0.14 0.147 0.142 0.142 0.088*
  - Interpretation:
    - Improvement in forecast performance is greatest before the start of the nowcasted quarter (e.g., Week -12).
    - Example: RMSFE of the DFM is 40% lower than that of a single-factor model in week -12 of pre-Covid sample and 20% lower than an AR(1) in that week.
    - Diebold-Mariano tests indicate DFM out-performance relative to the single-factor model is statistically significant at most horizons in the pre-Covid period (Harvey et al. 1997 adjustment used for small samples).
    - Relative performance narrows as the end of the quarter approaches because more monthly data become available and the final month carries a smaller weight in quarterly growth (final month weight 11%).

### Robustness and caveats
- Alternative specifications (different factor structures, lag orders, estimation windows) yield qualitatively similar out-of-sample performance.
- The baseline multi-factor model does not outperform single-global-factor specifications during periods dominated by a global trade cycle (example: 2014–2016).
- Sample sizes for pseudo out-of-sample evaluation are relatively small (twelve quarters in each sub-period), though statistical tests are reported.

*Source: wpiea2026048-source-pdf - 1.  We estimate a DFM with only the two global factors.  If a common global factor structure*

### 4.4  Case studies

### 4.4 Case studies

### Overview
- Purpose: Illustrate that a multi-factor framework is best suited to episodes with strong regional dynamics affecting global trade rather than a single common global driver.
- Focus: world trade over a year in three episodes: 2020, 2023 and 2008.
- Data handling: models forecast annual trade growth for a given year using data restricted to end-previous-year and then update the forecast incrementally as one additional month of data is added through the year.
- Visual references in source: Figure 7 (evolution of world and regional trade growth in the three episodes) and Figure 8 (world trade growth forecasts and regional contributions to forecast revisions).

### Case study I: 2020 and the Covid shock
- Context:
  - Dataset restricted to end-2019 to forecast 2020, then forecasts recalculated monthly through end-2020.
  - Level chart reference: (Level: 2019 = 100) shown in Figure 8a.
- Key comparative findings (multi-factor DFM vs single-factor DFM):
  - Cumulative world trade data surprises are smaller in the multi-factor model than the single-factor DFM, indicating better month-by-month prediction conditional on other data.
  - The multi-factor DFM detected a sharp contraction in world trade in 2020 earlier than the single-factor model.
  - China’s trade contracted sharply in the first three months of 2020, while trade elsewhere was relatively resilient; the multi-factor model places greater weight on this concentrated China shock.
  - The multi-factor model captured the unexpectedly rapid recovery in world trade in the second half of 2020 by identifying China’s trade recovery beginning by spring 2020; the single-factor model overweighted European data and missed this early reversal.
- Mechanisms highlighted:
  - Regional contributions to cumulative forecast revisions (shown in second and third charts of Figure 8a) illustrate how regional data surprises (including world trade data bars that capture monthly surprises and their impact on projected rest-of-year trade) drive revisions.
- Implication: Multi-factor structure can distinguish concentrated regional shocks (e.g., China) from global noise and update global trade forecasts more accurately during uneven regional episodes.

### Case study II: 2023 and post-Covid trade divergence
- Context:
  - By late 2022 global trade showed signs of recovery from the pandemic and severe supply shocks, but recovery was uneven into 2023.
  - Figure 7b shows year-on-year percent dynamics; Figure 8b displays forecasts and regional contributions.
- Key findings:
  - In 2023, trade recovered strongly in China while remaining weak across most Advanced Economies.
  - By the start of 2023 the multi-factor model revised up its forecast for world trade growth in 2023 by 3 percentage points due to China’s outperformance (Figure 8b).
  - Global and Advanced Economy indicators continued to underperform; the single-factor model therefore expected weak trade growth and only picked up the recovery much later.
  - The single-factor model continued to forecast a contraction in global trade until August 2023, whereas world trade growth was overall positive in 2023.
- Implication: Multi-region factor structure accommodates divergent regional recoveries and produces timelier upward revisions when a major region (China) outperforms.

### Case study III: 2008 and a global trade slowdown
- Context:
  - Episode of a synchronized global downturn (Global Financial Crisis); year-on-year percent dynamics shown in Figure 7c and forecasts in Figure 8c.
- Key findings:
  - Both multi-factor and single-factor models overpredicted the strength of global trade at the start of 2008.
  - As the crisis unfolded both models downgraded forecasts for world trade growth in 2008 by around 4 percentage points.
  - The single-factor model picked up the deterioration slightly earlier than the multi-factor model.
  - Drivers of revisions were weaker-than-expected global data and worse data in the US (Figure 8c).
- Implication: When the slowdown is synchronous and global in nature, a multi-factor structure that models regional variation adds little additional forecasting power relative to a single-factor model.

### Synthesis and policy-relevant insights
- Model performance depends on the nature of shocks:
  - Synchronized global events (e.g., 2008 financial crisis) — single-factor models perform well.
  - Episodes of regional heterogeneity (e.g., Covid in 2020; post-Covid divergence in 2023) — multi-factor models provide superior near-term forecasts.
- Regional factors matter:
  - Regional factors, particularly for Asia, are significant sources of spillovers to other regions and to the global outlook, consistent with Asia’s integration into global value chains.
- Practical advantage:
  - Identifying geographic origins of shocks to global trade in real-time improves economic surveillance and offers a timelier, richer narrative of ongoing trade dynamics than relying solely on a global aggregate.

*Source: 4.4 Case studies, Nowcasting World Trade With a Multi-Region Factor Model (Working Paper No. WP/2026/049).*

---


_Source: https://www.imf.org/-/media/files/publications/wp/2026/english/wpiea2026048-source-pdf.pdf_