## ch2annex

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---

### UIP Premium: Definition and Construction
- The UIP premium captures a currency’s excess return due to interest rate differentials and expected exchange rate adjustments that do not offset each other.
- It is derived by calculating individual UIP deviations against the US dollar for each of the 7 advanced economy currencies included in the US dollar index and constructing a weighted average of these deviations using the US dollar index weights.
- Example (GBP against USD): the GBP excess return over the US dollar is defined as the sum of two components: the interest rate differential between GBP and US dollar yields on a comparable asset and the expected US dollar depreciation against the GBP.
- The UIP Premium in Online Annex Figure 2.3.1 is based on a weighted average of UIP premia using 12-month deposit rates and consensus forecast exchange rate forecasts for the US against the 7 advanced economies in the Fed USD AE Index (Australia, Canada, the Euro Area, Japan, Sweden, Switzerland, and the UK).
- The correlation between the global dollar cycle and the UIP premium is 0.69. Using a 3-month horizon the correlation is 0.58.

### Decomposition of the UIP Premium
- Decomposition (following Kalemli-Özcan (2019)):
  - IR differential: AE deposit rate minus US deposit rate.
  - ER adjustment: the expected US dollar depreciation.
- The bulk of the variation in the UIP premium is related to the expected exchange rate adjustment rather than interest rate differentials, as interest rate differentials have been rather low and less volatile for advanced economies over the last 20 years (Online Annex Figure 2.3.2).
- Kalemli-Özcan (2019) and Kalemli-Özcan and Varela (2023) link the comovement of the UIP Premium with the exchange rate adjustment term to global risk via significant correlations of UIP premia with the VIX for advanced economies.

### Correlations of Individual Country UIP Premia with the US dollar
- Correlations of λ_{i,t} (UIP deviation as defined in the text) with LC/USD and USD index for select economies (table entries preserved):
  - Australia: 0.73, 0.63, 0.81
  - Canada: 0.66, 0.65, 0.79
  - Euro Area: 0.73, 0.67, 0.87
  - Japan: 0.39, 0.08, 0.31
  - Sweden: 0.86, 0.96, 0.79
  - Switzerland: -0.32, 0.27, 0.16
  - United Kingdom: 0.24, 0.44, 0.70
  - AE Index Average: 0.81, 1.00
- Average weights for AEs in the index: AUD 2.7%, CAD 30.4%, JPY 14.3%, SWK 1.3%, CHF 4.5%, GBP 10.6%, EUR 36%.
- An appreciation of the US dollar is associated with an increase in advanced economies’ excess returns against the US dollar as measured by the UIP premium—except for Switzerland where the correlation is negative. The correlation is positive but small for Japan and the UK.

### Current Account Breakdown
- Regression results for the current account breakdown (goods, services, income) conditional on being an emerging or advanced economy:
  - Emerging markets: The increase in the trade balance for goods drives the increase in the current account after the initial quarters, in particular due to a larger contraction in imports than exports.
  - Advanced economies: The increase in the trade balance in services accounts for the increase in the current account in the initial quarters, driven by a larger increase in exports than imports.
- Impulse responses show a 10 percent appreciation in the nominal US dollar Index with 90 percent confidence intervals.

### Sample Detail for State-Dependent Local Projections
- Features are defined such that 1 represents the category with a more negative GDP response. The table is constructed for 2017Q1 except for high US dollar liability, which is time-varying. For presentational purposes, in this table high US dollar liability is 1 if the country spent more than 12 quarters in the top quartile.
- The following features are not time-varying: emerging market/advanced economy status, commodity exporter/importer, below median anchoring, high US dollar export invoicing.
- Selected sample entries (rows preserved):
  - TUR: 1 1 1 0 1 0 1
  - ZAF: 1 0 1 0   0 0
  - ARG: 1   1 1 1 1 1
  - BRA: 1 1 1 0 1 1 1
  - CHL: 1 1 1 1 0 1 1
  - ... (table continues with country-level binary feature indicators as in source)

### Exchange Rate Regime Results
- Conditional impulse responses for freely floating versus other exchange rate regimes for the emerging market sample only:
  - Output recovers faster for countries with freely floating exchange rate regimes.
  - The REER depreciates on impact and remains depreciated until the rebound in growth after the ninth quarter.
  - Countries with freely floating exchange rate regimes are highly negatively correlated with countries that have a high share of exports indexed in US dollars (a correlation of -0.8 for the emerging market sample).
- Impulse responses show a 10 percent appreciation in the nominal US dollar Index with 90 percent confidence intervals. Coarse classification from Ilzetzki, Reinhart and Rogoff (2019) where freely floating is 4 and other is 1, 2, or 3. An increase in the REER is a depreciation.

### Policies and Structural Features: Categorization
- Measures and thresholds used to categorize countries:
  - Exchange rate regime: coarse classification from Ilzetzki, Reinhart, and Rogoff (2019). Freely floating: 4; other regime: 1, 2, or 3.
  - Monetary policy credibility: country average of the measure in Bems and others (2021); threshold: Median.
  - US dollar liability exposure: share of foreign liabilities in US dollars from Bénétrix and others (2019); threshold: 75th percentile.
  - US dollar export invoicing: country average share of exports invoiced in US dollars from Boz and others (2022); threshold: 75 percent of exports.
  - Trade openness: (Exports + Imports)/GDP from IMF Balance of Payments Statistics; threshold: Median.
  - Commodity exporter/importer: country median trade balance in all commodities from UN Comtrade; threshold: 5 percent of GDP.
- Notes on classification:
  - Classification into freely floating and other exchange rate regimes is extended through 2021 using the IMF's Annual Report on Exchange Arrangements and Exchange Restrictions.
  - The country average for monetary policy credibility and the share of exports invoiced in US dollars is used for the whole sample period.
  - The US dollar liability exposure classification is kept constant after 2017.

### Robustness: First Stage and Local Projections
- First-stage regression robustness (equation (1)) — established factors explain a limited share of variation in the US dollar index against advanced economies:
  - Substituting the policy rate differential with 3-month, 12-month, and 10-year government bond differentials yields adjusted R2 values of 0.22, 0.22, and 0.27, respectively.
  - Substituting ANFCI with the excess bond premium (Gilchrist and Zakrajšek 2012) yields adjusted R2 of 0.24. Substituting with the VIX, or adding the VIX, does not increase explained variation.
  - Expanding the growth factor to include the US and major advanced economies yields adjusted R2 of 0.22.
  - Excluding the lagged US GDP regressor yields adjusted R2 of 0.187.
  - Controlling, one at a time, for several monetary policy shocks produces a highest adjusted R2 of 0.34 with the two Jarocinski & Karadi (2020) shocks.
  - Controlling for oil supply shocks (Baumeister and Hamilton 2019) yields adjusted R2 of 0.23.
  - Including quadratic terms for all regressors yields adjusted R2 of 0.28; adding quadratic terms except for the lagged USD Index yields adjusted R2 of 0.32.
  - Re-estimating the global dollar cycle by explaining bilateral exchange rates and aggregating residuals yields a global dollar cycle similar to baseline with correlation 0.81.
- Local projections robustness (equation (3)):
  - Removing global controls increases the magnitude of the decline in output for both advanced and emerging economies; advanced economies still experience a shallower and shorter-lived contraction (Online Annex Figure 2.4.3).
  - Removing all advanced economies included in the US dollar trade-weighted index does not have a major impact on point estimates, though error bands increase (Online Annex Figure 2.4.4).
  - Replacing the US dollar index with the UIP premium yields broadly similar results (Online Annex Figure 2.4.5):
    - An increase in the UIP wedge results in negative spillovers to both advanced and emerging countries, with a more adverse impact on emerging market economies.
    - Advanced economies exhibit a larger decline in output relative to the baseline but still recover around the seventh quarter.
    - Output decline in emerging markets peaks sooner than in the baseline.
    - For current accounts: advanced economies see a more persistent positive current account than in the baseline owing to investment which remains negative and does not rebound as in the baseline; in emerging markets investment declines but reverts to zero, driving the current account toward zero whereas in the baseline it remains negative.
  - Controlling for Bu, Rogers and Wu (2021) monetary policy shock and associated orthogonal information effect shock and for oil supply shocks yields similar results for emerging markets as the baseline: output declines more in emerging markets than advanced economies, and the current account increases after a temporary initial decline. For advanced economies, output is stable and the current account is positive but marginally significant.

### Additional FSGM Details
- All country/regional blocks in the FSGM are structurally identical but may have different steady-state ratios of key macro aggregates and behavioral parameters.
- Real GDP in the model:
  - Long run: determined by data-driven calibration of the level of potential output based on Cobb-Douglas production technology with trend total factor productivity, the steady-state labor force, the natural rate of unemployment, and the capital stock.
  - Short run: determined by the sum of its demand components.

### 1. Real GDP — Impulse-response robustness: US dollar appreciation
- Variable labels: "1. Real GDP (Percent change)" and "2. Current Account (Percent of GDP)".
- Horizons labeled "Quarter" with tick markers "0 4 8 12".
- Impulse responses show a "10 percent appreciation in the nominal US dollar Index with 90 percent confidence intervals."
- Samples: "Advanced economies" and "Emerging markets".
- Note on sample exclusion: "Advanced economies exclude countries with weights in the US dollar index that are larger than 4 percent in 2020: Canada, France, Germany, Ireland, Italy, Japan, Switzerland, and the United Kingdom."
- Visual axis ranges as presented:
  - Real GDP vertical axis annotation includes "-6 -4 -2 0 2 4".
  - Emerging markets Real GDP axis annotation includes "-2 -1 0 1 2 3".
  - Current Account vertical axis annotations appear in the figure context (percent of GDP).

### 1. Real GDP — Impulse-response robustness: UIP deviation
- Variable labels: "1. Real GDP (Percent change)" and "2. Current Account (Percent of GDP)".
- Horizons labeled "Quarter" with tick markers "0 4 8 12".
- Impulse responses show a "10 standard deviation increase in the UIP deviation with 90 percent confidence intervals."
- Samples: "Advanced economies" and "Emerging markets".
- Note on sample exclusion: "Advanced economies exclude countries with weights in the US dollar index that are larger than 4 percent in 2020: Canada, France, Germany, Ireland, Italy, Japan, Switzerland, and the United Kingdom."
- Visual axis ranges as presented:
  - Real GDP vertical axis annotation includes "-8 -6 -4 -2 0 2 4 6 8".
  - Emerging markets Real GDP panel shows "-4 -2 0 2 4 6".
  - Current Account vertical axis annotations appear in the figure context (percent of GDP).

### Model structure: FSGM features (selected)
- Consumption block: "micro founded and uses an overlapping generations (OLG) model with a fraction of liquidity constrained households that consume all their income each period, amplifying the non-Ricardian properties of the basic OLG framework."
- Private business investment: "micro founded, featuring forward-looking profit maximizing firms and limits to the pace of investment that slow down the transition after a shock."
- Government absorption: consists of spending on consumption and investment goods. The government's overall deficit is determined by a fiscal rule.
- For further model details: "For further details on FSGM are provided in Andrle and other (2015)."

*Source: ch2annex - Annex Figure 2.3.1), Online Annex Figures and Tables, External Sector Report Chapter 2 (IMF staff calculations; sources listed in the annex).*

### Annex Figure 2.3.1), offering a way to interpret the

### Annex Figure 2.3.1)

### UIP Premium: Definition and Construction
- The UIP premium captures a currency’s excess return due to interest rate differentials and expected exchange rate adjustments that do not offset each other.
- The UIP premium is derived by calculating individual UIP deviations against the US dollar for each of the 7 advanced economy currencies included in the US dollar index and constructing a weighted average of these deviations using the US dollar index weights.
- Example definition (GBP against USD): the GBP excess return over the US dollar is defined as the sum of two components: the interest rate differential between GBP and US dollar yields on a comparable asset and the expected US dollar depreciation against the GBP.
- The UIP Premium in Online Annex Figure 2.3.1 is based on a weighted average of UIP premia using 12-month deposit rates and consensus forecast exchange rate forecasts for the US against the 7 advanced economies in the Fed USD AE Index (Australia, Canada, the Euro Area, Japan, Sweden, Switzerland, and the UK).
- The correlation between the global dollar cycle and the UIP premium is 0.69. Using a 3-month horizon the correlation is 0.58.

### Decomposition of the UIP Premium
- Following Kalemli-Özcan (2019), the UIP Premium is decomposed into:
  - IR differential: AE deposit rate minus US deposit rate.
  - ER adjustment: the expected US dollar depreciation.
- The bulk of the variation in the UIP premium is related to the expected exchange rate adjustment rather than interest rate differentials, as interest rate differentials have been rather low and less volatile for advanced economies over the last 20 years (Online Annex Figure 2.3.2).
- Kalemli-Özcan (2019) and Kalemli-Özcan and Varela (2023) link the comovement of the UIP Premium with the exchange rate adjustment term to global risk via significant correlations of UIP premia with the VIX for advanced economies.

### Correlations of Individual Country UIP Premia with the US dollar (Online Annex Table 2.3.1)
- Correlations of λ_{i,t} (UIP deviation as defined in the text) with LC/USD and USD index for select economies (table entries preserved as in source):
  - Australia: 0.73, 0.63, 0.81
  - Canada: 0.66, 0.65, 0.79
  - Euro Area: 0.73, 0.67, 0.87
  - Japan: 0.39, 0.08, 0.31
  - Sweden: 0.86, 0.96, 0.79
  - Switzerland: -0.32, 0.27, 0.16
  - United Kingdom: 0.24, 0.44, 0.70
  - AE Index Average: 0.81, 1.00
- The average weights for AEs in the index are: AUD 2.7%, CAD 30.4%, JPY 14.3%, SWK 1.3%, CHF 4.5%, GBP 10.6%, EUR 36%.
- An appreciation of the US dollar is associated with an increase in advanced economies’ excess returns against the US dollar as measured by the UIP premium—except for Switzerland where the correlation is negative. The correlation is positive but small for Japan and the UK.

### Current Account Breakdown (Online Annex Figure 2.4.1)
- Regression results for the current account breakdown (goods, services, income) conditional on being an emerging or advanced economy show:
  - Emerging markets: The increase in the trade balance for goods drives the increase in the current account after the initial quarters, in particular due to a larger contraction in imports than exports.
  - Advanced economies: The increase in the trade balance in services accounts for the increase in the current account in the initial quarters, driven by a larger increase in exports than imports.
- Impulse responses show a 10 percent appreciation in the nominal US dollar Index with 90 percent confidence intervals.

### Sample Detail for State-Dependent Local Projections (Online Annex Table 2.4.1)
- Features are defined such that 1 represents the category with a more negative GDP response. The table is constructed for 2017Q1 except for high US dollar liability, which is time-varying. For presentational purposes, in this table high US dollar liability is 1 if the country spent more than 12 quarters in the top quartile.
- The following features are not time-varying: emerging market/advanced economy status, commodity exporter/importer, below median anchoring, high US dollar export invoicing.
- Selected sample entries (rows preserved as in source):
  - TUR: 1 1 1 0 1 0 1
  - ZAF: 1 0 1 0   0 0
  - ARG: 1   1 1 1 1 1
  - BRA: 1 1 1 0 1 1 1
  - CHL: 1 1 1 1 0 1 1
  - ... (table continues with country-level binary feature indicators as in source)

### Exchange Rate Regime Results (Online Annex Figure 2.4.2)
- Conditional impulse responses for freely floating versus other exchange rate regimes for the emerging market sample only:
  - Output recovers faster for countries with freely floating exchange rate regimes.
  - The REER depreciates on impact and remains depreciated until the rebound in growth after the ninth quarter.
  - Countries with freely floating exchange rate regimes are highly negatively correlated with countries that have a high share of exports indexed in US dollars (a correlation of -0.8 for the emerging market sample).
- Impulse responses show a 10 percent appreciation in the nominal US dollar Index with 90 percent confidence intervals. Coarse classification from Ilzetzki, Reinhart and Rogoff (2019) where freely floating is 4 and other is 1, 2, or 3. An increase in the REER is a depreciation.

### Policies and Structural Features: Categorization (Online Annex Table 2.4.2)
- Measures and thresholds used to categorize countries:
  - Exchange rate regime: coarse classification from Ilzetzki, Reinhart, and Rogoff (2019). Freely floating: 4; other regime: 1, 2, or 3.
  - Monetary policy credibility: country average of the measure in Bems and others (2021); threshold: Median.
  - US dollar liability exposure: share of foreign liabilities in US dollars from Bénétrix and others (2019); threshold: 75th percentile.
  - US dollar export invoicing: country average share of exports invoiced in US dollars from Boz and others (2022); threshold: 75 percent of exports.
  - Trade openness: (Exports + Imports)/GDP from IMF Balance of Payments Statistics; threshold: Median.
  - Commodity exporter/importer: country median trade balance in all commodities from UN Comtrade; threshold: 5 percent of GDP.
- Notes on classification:
  - Classification into freely floating and other exchange rate regimes is extended through 2021 using the IMF's Annual Report on Exchange Arrangements and Exchange Restrictions.
  - The country average for monetary policy credibility and the share of exports invoiced in US dollars is used for the whole sample period.
  - The US dollar liability exposure classification is kept constant after 2017.

### Robustness: First Stage and Local Projections
- Robustness checks for the first-stage regression (equation (1)) showing established factors explain a limited share of variation in the US dollar index against advanced economies:
  - Substituting the policy rate differential with 3-month, 12-month, and 10-year government bond differentials yields adjusted R2 values of 0.22, 0.22, and 0.27, respectively.
  - Substituting ANFCI with the excess bond premium (Gilchrist and Zakrajšek 2012) yields adjusted R2 of 0.24. Substituting with the VIX, or adding the VIX, does not increase explained variation.
  - Expanding the growth factor to include the US and major advanced economies yields adjusted R2 of 0.22.
  - Excluding the lagged US GDP regressor yields adjusted R2 of 0.187.
  - Controlling, one at a time, for several monetary policy shocks produces a highest adjusted R2 of 0.34 with the two Jarocinski & Karadi (2020) shocks.
  - Controlling for oil supply shocks (Baumeister and Hamilton 2019) yields adjusted R2 of 0.23.
  - Including quadratic terms for all regressors yields adjusted R2 of 0.28; adding quadratic terms except for the lagged USD Index yields adjusted R2 of 0.32.
  - Re-estimating the global dollar cycle by explaining bilateral exchange rates and aggregating residuals yields a global dollar cycle similar to baseline with correlation 0.81.
- Robustness checks for local projections (equation (3)):
  - Removing global controls increases the magnitude of the decline in output for both advanced and emerging economies; advanced economies still experience a shallower and shorter-lived contraction (Online Annex Figure 2.4.3).
  - Removing all advanced economies included in the US dollar trade-weighted index does not have a major impact on point estimates, though error bands increase (Online Annex Figure 2.4.4).
  - Replacing the US dollar index with the UIP premium yields broadly similar results (Online Annex Figure 2.4.5):
    - An increase in the UIP wedge results in negative spillovers to both advanced and emerging countries, with a more adverse impact on emerging market economies.
    - Advanced economies exhibit a larger decline in output relative to the baseline but still recover around the seventh quarter.
    - Output decline in emerging markets peaks sooner than in the baseline.
    - For current accounts: advanced economies see a more persistent positive current account than in the baseline owing to investment which remains negative and does not rebound as in the baseline; in emerging markets investment declines but reverts to zero, driving the current account toward zero whereas in the baseline it remains negative.
  - Controlling for Bu, Rogers and Wu (2021) monetary policy shock and associated orthogonal information effect shock and for oil supply shocks yields similar results for emerging markets as the baseline: output declines more in emerging markets than advanced economies, and the current account increases after a temporary initial decline. For advanced economies, output is stable and the current account is positive but marginally significant.

### Additional FSGM Details (Online Annex 2.5)
- All country/regional blocks in the FSGM are structurally identical but may have different steady-state ratios of key macro aggregates and behavioral parameters.
- Real GDP in the model:
  - Long run: determined by data-driven calibration of the level of potential output based on Cobb-Douglas production technology with trend total factor productivity, the steady-state labor force, the natural rate of unemployment, and the capital stock.
  - Short run: determined by the sum of its demand components.

*Source: ch2annex - Annex Figure 2.3.1), Online Annex Figures and Tables, External Sector Report Chapter 2 (IMF staff calculations; sources listed in the annex).*

### 1. Real GDP

### ch2annex - 1. Real GDP

### Impulse-response robustness: US dollar appreciation (Online Annex Figure 2.4.6)
- Variable labels shown: "1. Real GDP (Percent change)" and "2. Current Account (Percent of GDP)".
- Impulse responses shown for horizons labeled "Quarter" with tick markers "0 4 8 12".
- Impulse responses show a "10 percent appreciation in the nominal US dollar Index with 90 percent confidence intervals."
- Samples: "Advanced economies" and "Emerging markets".
- Note on sample exclusion: "Advanced economies exclude countries with weights in the US dollar index that are larger than 4 percent in 2020: Canada, France, Germany, Ireland, Italy, Japan, Switzerland, and the United Kingdom."
- Visual axis ranges as presented:
  - For Real GDP: vertical axis annotation includes "-6 -4 -2 0 2 4".
  - For Emerging markets panel shown similarly with axis annotations "-2 -1 0 1 2 3".
  - For Current Account: vertical axis annotations appear in the figure context (percent of GDP).

### Impulse-response robustness: UIP deviation (Online Annex Figure 2.4.5)
- Variable labels shown: "1. Real GDP (Percent change)" and "2. Current Account (Percent of GDP)".
- Impulse responses shown for horizons labeled "Quarter" with tick markers "0 4 8 12".
- Impulse responses show a "10 standard deviation increase in the UIP deviation with 90 percent confidence intervals."
- Samples: "Advanced economies" and "Emerging markets".
- Note on sample exclusion: "Advanced economies exclude countries with weights in the US dollar index that are larger than 4 percent in 2020: Canada, France, Germany, Ireland, Italy, Japan, Switzerland, and the United Kingdom."
- Visual axis ranges as presented:
  - For Real GDP: vertical axis annotation includes "-8 -6 -4 -2 0 2 4 6 8".
  - For Emerging markets Real GDP panel shows "-4 -2 0 2 4 6".
  - For Current Account: vertical axis annotations appear in the figure context (percent of GDP).

### Model structure: Flexible System of Global Models (FSGM) features (text summary)
- "The consumption block is micro founded and uses an overlapping generations (OLG) model with a fraction of liquidity constrained households that consume all their income each period, amplifying the non-Ricardian properties of the basic OLG framework."
- "Private business investment is also micro founded, featuring forward-looking profit maximizing firms and limits to the pace of investment that slow down the transition after a shock."
- "Government absorption consists of spending on consumption and investment goods. The government's overall deficit is determined by a fiscal rule."
- For further details: "For further details on FSGM are provided in Andrle and other (2015)."

### Key references cited in this annex (selection of cited works as presented)
- Acosta, Miguel. 2023. "The Perceived Causes of Monetary Policy Surprises." Published Manuscript URL https://www.acostamiguel.com/papers/acosta_mp.pdf.
- Andrle, Michal, Patrick Blagrave, Pedro Espaillat, Keiko Honjo, Benjamin Hunt, Mika Kortelainen, René Lalonde, and others. 2015. “The Flexible System of Global Models–FSGM.” IMF Working Paper 15/64, International Monetary Fund, Washington, DC.
- Baumeister, Christiane, and James D. Hamilton. 2019. "Structural Interpretation of Vector Autoregressions with Incomplete Identification: Revisiting the Role of Oil Supply and Demand Shocks." American Economic Review, 109: 1873–1910.
- Bu, Chunya, John Rogers, and Wenbin Wu. 2021. "A Unified Measure of Fed Monetary Policy Shocks." Journal of Monetary Economics, 118: 331–49.
- Jarociński, Marek, and Peter Karadi. 2020. "Deconstructing Monetary Policy Surprises—the Role of Information Shocks." American Economic Journal: Macroeconomics 12: 1–43.
- Jordà, Òscar. 2005. "Estimation and Inference of Impulse Responses by Local Projections." American Economic Review 95 (1): 161–82.
- Kalemli-Özcan, Şebnem. 2019. “US Monetary Policy and International Risk Spillovers.” Paper presented at Jackson Hole Economic Policy Symposium “Challenges for Monetary Policy,” Jackson Hole, Wyoming, August 23.
- Other cited works include studies on exchange arrangements, global dollar cycle, zero lower bound modeling, and invoicing currency in global trade as listed in the annex.

*Source: ch2annex - 1. Real GDP (PDF chapter).*

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_Source: https://www.imf.org/-/media/files/publications/esr/2023/english/ch2annex.pdf_