## Introduction (IMF Working Paper wpiea2021043-print-pdf)

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### Motivation and scope
- Research question: Examine the role that changes in credit and fiscal positions play in explaining current account fluctuations.
- Sample: 38 advanced and emerging economies.
- Period covered in empirical analysis: 1986-2017.
- Methodological approach: Combine empirical evidence with a two-country international real business cycle model with financial frictions and fiscal policy; estimate the model using annual U.S. and “rest of the world” aggregate data with a Generalized Method of Moments approach.
- Credit-gap measurement: BIS methodology using a one-sided Hodrick-Prescott filter with a penalty parameter (lambda) of 25,000 for annual data.

### Key empirical relationships documented
- Credit and current account:
  - Contemporaneous correlation between the credit gap and the current account: −0.41 (full sample mean).
  - Advanced economies mean: −0.38; Emerging market and developing economies mean: −0.45.
  - Median correlations (k = 0): full sample −0.56; Advanced economies −0.56; EMDEs −0.51.
  - Negative contemporaneous correlation in 31 out of 38 countries.
  - Strong country examples: Spain −0.86; United States −0.64; France −0.81 to −0.77 across lags; Germany −0.55 to −0.59 across lags.
  - Robustness: 1-year cumulative credit-to-GDP change average correlation −0.34; 3-year cumulative change correlation −0.39 (entire sample).
- Fiscal balance and current account:
  - Fiscal balance positively comoves with the current account (confirmation of “twin deficits”).

### Model purpose and specification
- Two-country international RBC model with financial frictions (in the spirit of Heathcote and Perri (2002) and Jones, Midrigan and Philippon (2020)).
- Flexible credit-channel parameter α estimated endogenously.
- Structural analysis distinguishes drivers: credit booms from relaxed lending standards versus productivity-driven credit increases; procyclical versus countercyclical fiscal responses.

### Main quantitative findings and counterfactuals
- Estimated contributions to U.S. current account fluctuations:
  - Domestic credit shocks: about 30 percent.
  - Foreign credit shocks: about one-third.
  - Fiscal shocks: about 14 percent.
- Historical counterfactual: Without U.S. credit and fiscal shocks, U.S. current account deficit would have been much smaller and less volatile, notably during 1995-2006 when the deficit rose from less than 2 percent of GDP to almost 6 percent of GDP.

### Policy implications (overview)
- Macroprudential rules reacting to domestic credit conditions or house prices would have reduced and smoothed the U.S. current account deficit by taming the domestic financial cycle; these rules are calibrated to maximize domestic welfare, with current account effects incidental.
- Countercyclical fiscal policy targeting domestic output growth would reduce the level and volatility of the U.S. current account.
- Global implication: Countercyclical macroprudential and fiscal policies in the U.S. would have helped reduce global imbalances because large U.S. deficits are mirrored by surpluses elsewhere.

*Source: IMF Working Paper — Introduction section (wpiea2021043-print-pdf).*

---

### Empirical evidence on fiscal balance and current account (Section 2.2)

### “Twin deficits” empirical findings
- For 38 countries, fiscal balance–current account correlation at annual frequency is positive in 31 out of 38 countries (fiscal deficits tend to coincide with current account deficits).
- Correlation stronger in advanced economies than in EMDEs:
  - AEs, Mean correlation: 0.37 (for k = −3) … 0.03 (for k = 3).
  - EMDEs, Mean correlation: 0.09 (for k = −3) … −0.06 (for k = 3).
  - Full sample, Mean: 0.26 (for k = −3) … −0.01 (for k = 3).
  - Full sample, Median: 0.31 (for k = −3) … −0.04 (for k = 3).
- Representative country correlations (fiscal balance at t+k vs current account at t):
  - Sweden: 0.90 (k = −3), 0.93 (k = −2), 0.90 (k = −1), 0.84 (k = 0), 0.76 (k = 1), 0.67 (k = 2), 0.59 (k = 3).
  - United States: 0.75 (k = −3), 0.60 (k = −2), 0.42 (k = −1), 0.29 (k = 0), 0.15 (k = 1), 0.03 (k = 2), −0.09 (k = 3).
  - Germany: 0.49 (k = −3), 0.53 (k = −2), 0.58 (k = −1), 0.61 (k = 0), 0.54 (k = 1), 0.45 (k = 2), 0.37 (k = 3).
  - France: 0.35 (k = −3), 0.49 (k = −2), 0.44 (k = −1), 0.40 (k = 0), 0.37 (k = 1), 0.29 (k = 2), 0.17 (k = 3).
  - Italy: 0.23 (k = −3), 0.32 (k = −2), 0.38 (k = −1), 0.39 (k = 0), 0.30 (k = 1), 0.16 (k = 2), −0.04 (k = 3).
  - Japan: −0.32 (k = −3), −0.14 (k = −2), 0.20 (k = −1), 0.33 (k = 0), 0.26 (k = 1), 0.06 (k = 2), −0.20 (k = 3).
  - Spain: 0.48 (k = −3), 0.41 (k = −2), 0.28 (k = −1), 0.01 (k = 0), −0.28 (k = 1), −0.46 (k = 2), −0.61 (k = 3).
  - Australia: 0.21 (k = −3), −0.13 (k = −2), −0.28 (k = −1), −0.33 (k = 0), −0.47 (k = 1), −0.44 (k = 2), −0.38 (k = 3).
- Positive contemporaneous correlations reported for selected EMDEs: Brazil 0.26 (k = 0); China 0.45 (k = 0); Colombia 0.28 (k = 0); Peru 0.38 (k = 0).

### Interpretation and caveats
- Positive comovement supports “twin deficits” in most sampled countries but varies across countries and leads/lags (k = −3 to k = 3).
- Relationship generally stronger in AEs than EMDEs; median contemporaneous correlations similar (AEs median 0.29 vs EMDEs median 0.25 as reported in text).
- Correlations are bilateral, annual-frequency, descriptive moments motivating a structural model to identify mechanisms.

*Source: wpiea2021043-print-pdf (Section 2.2).*

---

### Model and estimation (Sections 3–4 and 4.2)

### Model key mechanisms
- Two-country international RBC model with trade in intermediate goods, credit frictions (Jones, Midrigan and Philippon (2020) approach), and fiscal policy.
- Credit frictions:
  - Households face idiosyncratic preference shocks v_it drawn from Pareto Pr(v_it ≤ v) = 1 − v^(−α).
  - Borrowing constraint tied to housing value: q_t b_{t+1} ≤ m_t e_t h_{t+1}, with log m_t following an AR process (credit shocks).
  - Dispersion parameter α governs fraction constrained: lower α ⇒ larger fraction constrained ⇒ stronger credit-channel effects.
- Fiscal policy:
  - Taxes follow debt-stabilizing rule: t_t / y_t = t^y + φ_b (b^g_{t+1}/(P_t y_t) − b^g/(P y)).
  - Government spending: g_t = g^y y_t + ξ_{g,t}, with log ξ_{g,t} = ρ_g log ξ_{g,t−1} + σ_g ε_{g,t}.
  - Government budget constraint: 1/R_t b^g_{t+1} − b^g_t = P_t g_t − P_t t_t.

### Estimation: data, sample, observables
- Estimation approach: Generalized Method of Moments (GMM) on first-order approximation to equilibrium.
- Country mapping: United States = Home; aggregate of other advanced economies = ROW (Australia, Canada, France, Germany, Italy, Japan, Spain, Sweden, United Kingdom).
- Sample period for estimation: 1980-2017 at annual frequency.
- Observables matched (U.S.): current account/GDP; fiscal balance/GDP; annual change in private credit/GDP; real GDP growth.
- Observables matched (ROW): fiscal balance/GDP; annual change in private credit/GDP; real GDP growth.
- ROW current account not used as observable.

### Calibrated parameters (selected)
- κ, κ∗: Share of domestic goods in domestic production = 0.8
- h̄: Housing stock = 1
- r = 1/q − 1: Real interest rate = 0.02
- m̄: Steady-state credit shock (Average LTV) = 0.29
- ν: Inverse Frisch elasticity labor supply = 2
- ω: Capital share of output = 1/3
- δ: Depreciation rate = 0.1
- g/Y, g∗/Y∗: Government spending to GDP ratio, U.S. and ROW = 0.2
- b_g/Y, b_g∗/Y∗: Debt to GDP ratio, U.S. and ROW = 0.6
- Aggregate housing to income ratio set to 2.5; housing supply normalized to one.
- Current account and net international investment position assumed balanced in steady state.

### GMM estimated parameters (point estimates and standard deviations)
- α Dispersion of Taste Shocks: Point Estimate 2.38; Standard Dev 0.03
- σ Elasticity of Substitution H/F Goods: Point Estimate 2.50; Standard Dev 0.64
- φb U.S. Tax Response to Debt: Point Estimate 0.16; Standard Dev 0.06
- φb∗ ROW Tax Response to Debt: Point Estimate 0.06; Standard Dev 0.01
- φk Investment Adjustment Costs: Point Estimate 6.57; Standard Dev 1.88
- ρz U.S. TFP AR(1) Parameter: Point Estimate 0.98; Standard Dev 0.01
- ρz∗ ROW TFP AR(1) Parameter: Point Estimate 0.46; Standard Dev 0.26
- ρm U.S. Credit Shock AR(1) Parameter: Point Estimate 0.997; Standard Dev 0.002
- ρm∗ ROW Credit Shock AR(1) Parameter: Point Estimate 0.80; Standard Dev 0.14
- ρg U.S. Fiscal Shock AR(1) Parameter: Point Estimate 0.42; Standard Dev 0.08
- ρg∗ ROW Fiscal Shock AR(1) Parameter: Point Estimate 0.60; Standard Dev 0.17
- σz U.S. TFP Innovation Std. Dev.: Point Estimate 1.33; Standard Dev 0.07
- σz∗ ROW TFP Innovation Std. Dev.: Point Estimate 0.83; Standard Dev 0.30
- σm U.S. Credit Shock Innovation Std. Dev.: Point Estimate 4.26; Standard Dev 0.33
- σm∗ ROW Credit Shock Innovation Std. Dev.: Point Estimate 8.55; Standard Dev 0.45
- σg U.S. Fiscal Shock Innovation Std. Dev.: Point Estimate 4.35; Standard Dev 0.26
- σg∗ ROW Fiscal Shock Innovation Std. Dev.: Point Estimate 2.41; Standard Dev 0.19
- σ∗Δy Measurement Error, ROW Output Growth: Point Estimate 1.00; Standard Dev 0.34
- Note: standard deviations of shocks are expressed in percentage points.

### Model fit and variance decomposition (selected results)
- Model matches many standard deviations, especially U.S. variables; underestimates ROW credit-to-GDP change volatility.
- Selected model vs data moments:
  - Current Account/GDP, U.S.: Data Std. Dev. 1.51; Data Autocorr 0.86; Model Std. Dev. 1.51; Model Autocorr 0.63
  - Credit/GDP, Change, U.S.: Data Std. Dev. 3.04; Data Autocorr 0.62; Model Std. Dev. 3.59; Model Autocorr −0.03
  - Fiscal Balance/GDP, U.S.: Data Std. Dev. 3.01; Data Autocorr 0.81; Model Std. Dev. 2.43; Model Autocorr 0.38
  - Credit/GDP, Change, ROW: Data Std. Dev. 10.13; Data Autocorr 0.27; Model Std. Dev. 7.25; Model Autocorr −0.12
- Variance decomposition for U.S. observables (percent contributions):
  - Current Account to GDP: Productivity U.S. 18.6; Productivity ROW 0.4; Credit U.S. 28.9; Credit ROW 33.2; Gov Spending U.S. 13.9; Gov Spending ROW 4.9
  - U.S. Credit to GDP: Productivity U.S. 0.5; Productivity ROW 0.09; Credit U.S. 90.2; Credit ROW 0.4; Gov Spending U.S. 8.8; Gov Spending ROW 0.1
  - U.S. GDP Growth: Productivity U.S. 89.6; Productivity ROW 0.0; Credit U.S. 0.3; Credit ROW 0.5; Gov Spending U.S. 9.5; Gov Spending ROW 0.1
  - U.S. Fiscal Balance to GDP: Productivity U.S. 1.0; Productivity ROW 0.0; Credit U.S. 0.0; Credit ROW 0.0; Gov Spending U.S. 98.9; Gov Spending ROW 0.0
- Interpretation:
  - U.S. current account fluctuations driven mainly by U.S. and ROW credit shocks (each about 30 percent); domestic productivity explains 18.6 percent; fiscal shocks 13.9 percent.
  - U.S. credit-to-GDP changes largely driven by U.S. credit shocks; U.S. GDP growth driven by productivity shocks; U.S. fiscal balance driven by government spending shocks.

### Impulse response highlights
- U.S. credit shock (increase in borrowing ability):
  - Private credit-to-output ratio increases to about 3 percent of GDP.
  - Consumption and investment increase; output shows hump-shaped response due to initial hours decline then recovery.
  - House prices increase; current account moves into deficit and converges monotonically to zero.
  - Fiscal balance moves to slight deficit: −0.03 percent of GDP.
- U.S. government spending shock:
  - Produces “twin deficits”: fiscal and current account deficits as percent of GDP.
  - Private credit-to-GDP ratio contracts.
  - Impact multiplier of fiscal balance on current account ≈ 0.25.
  - Fiscal multiplier on intermediate-goods output ≈ 0.15 on impact; multiplier on final goods production ≈ 0.35.
- U.S. productivity shock:
  - Current account deficit on impact then quickly moves to surplus as exports rise with production.
  - Private credit increases but private credit-to-GDP ratio declines because of large output expansion.
  - Fiscal balance moves to deficit due to fiscal rule-triggered lump-sum tax cut.

### Role of α (dispersion of idiosyncratic shocks)
- Correlation between Current Account and ∆ Credit across α:
  - U.S. Data: −0.44
  - α = 2.3: −0.29
  - α = 4: −0.07
  - α = 8: 0.06
- Mechanism: Lower α (more idiosyncratic uncertainty) increases intra-period liquidity demand; reductions in credit availability force households to cut consumption/imports → negative comovement between current account and credit changes as observed in data.

*Source: wpiea2021043-print-pdf - Sections 3–4 and 4.2 (GMM estimation and parameter estimates).*

---

### Fiscal policy experiments and counterfactuals (Section 5.3)

### Fiscal rule studied
- Alternative fiscal rule: government spending responds to lagged output growth:
  - g_t = g_Y Y_{t−φ_g} log(y_{t−1} / y_{t−2}) + ξ_{g,t} (equation (36)).
  - φ_g parameterizes the extent government spending leans against output growth.
- Optimal policy value reported in Appendix: φ_g = 2.1.
- Welfare-based result reported elsewhere in Appendix: welfare maximized around φ_g = −0.7 (Figure C.2).

### Effects on current account, debt, and GDP (φ_g = 2.1)
- Current account:
  - Under the rule parameterized at φ_g = 2.1, the current account deficit would contract over most of the sample period.
- Debt:
  - Path of debt-to-income is little changed under the rule.
- GDP and recessions:
  - The rule withdraws domestic demand in expanding periods, lowering the U.S. current account deficit in normal times.
  - Main exception: Great Recession (2009) — fiscal support that would have occurred under actual policy helped GDP; under the countercyclical rule the current account deficit would have been somewhat larger during that deep recession.
- Fiscal balance counterfactuals:
  - During recessions the rule would have led to larger fiscal deficits.
  - During 2009 to 2010, the U.S. fiscal deficit would have been more negative by 4 to 5 percentage points.
  - The rule would have called for faster fiscal consolidation in boom years 1996-2000 and towards end of sample 2016-2017.

### Policy interpretation and link to broader findings
- A more countercyclical fiscal policy (higher φ_g) can reduce the level and volatility of the U.S. current account deficit in normal times by contracting domestic demand in booms.
- In deep recessions, such a rule may increase current account deficits because fiscal support that stabilizes output would be reduced.
- Complements broader conclusions that credit market shocks are major drivers of the U.S. current account (about 30 percent domestic and about one-third foreign), while U.S. fiscal shocks explain about 13.9 percent of current account volatility; macroprudential and fiscal rules can both help lower level and volatility of the U.S. current account.

*Source: wpiea2021043-print-pdf - Section 5.3 (Fiscal Policy).*

*Source: IMF Working Paper — wpiea2021043-print-pdf.*

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

### 1. Introduction

### Motivation and scope
- Research question: Examine the role that changes in credit and fiscal positions play in explaining current account fluctuations.
- Sample: 38 advanced and emerging economies.
- Period covered in empirical analysis: 1986-2017.
- Methodological approach: Combine empirical evidence with a two-country international real business cycle model with financial frictions and fiscal policy; estimate the model using annual U.S. and “rest of the world” aggregate data with a Generalized Method of Moments approach.
- Credit-gap measurement: BIS methodology using a one-sided Hodrick-Prescott filter with a penalty parameter (lambda) of 25,000 for annual data.

### Key empirical relationships documented
- Credit and current account:
  - Contemporaneous correlation between the credit gap and the current account: −0.41 (full sample mean).
  - Advanced economies mean: −0.38; Emerging market and developing economies mean: −0.45.
  - Median correlations (k = 0): full sample −0.56; Advanced economies −0.56; EMDEs −0.51.
  - For a large majority of countries, the contemporaneous correlation is negative (31 out of 38 countries).
  - Strong negative correlations for selected countries (examples from Table 1 and Figure 1): Spain (−0.86), United States (−0.64), France (−0.81 to −0.77 across lags), Germany (−0.55 to −0.59 across lags).
  - Robustness: Negative correlation persists when using cumulative annual changes in credit-to-GDP over 1- to 3-year windows; 1-year change average correlation −0.34 and 3-year cumulative change correlation −0.39 for the entire sample.
- Fiscal balance and current account:
  - The fiscal balance positively comoves with the current account (the “twin deficits” result is confirmed).

### Model purpose and specification
- Two-country international RBC model in the spirit of Heathcote and Perri (2002) with financial frictions as in Jones, Midrigan and Philippon (2020).
- Flexible specification allowing the strength of the credit channel (α) to be determined in estimation.
- Uses structural analysis to distinguish drivers: e.g., credit boom from relaxed lending standards versus credit increase driven by improved productivity; procyclical versus countercyclical fiscal responses.

### Main quantitative findings from estimation and counterfactuals
- Estimated contribution to U.S. current account fluctuations:
  - Domestic credit shocks: about 30 percent.
  - Foreign credit shocks: about one-third.
  - Fiscal shocks: about 14 percent.
- Historical counterfactual: Absent U.S. credit and fiscal shocks, the U.S. current account deficit would have been much smaller and less volatile, especially during the 1995-2006 period when the deficit grew from less than 2 percent of GDP to almost 6 percent of GDP.

### Policy analysis and implications
- Macroprudential policy rules:
  - Rules that react to domestic credit conditions or to domestic house prices would have led to a smaller and less volatile U.S. current account deficit by taming the domestic financial cycle.
  - Macroprudential rules studied target domestic indicators (credit or house prices) and are calibrated to maximize domestic welfare; effects on the current account are a byproduct.
- Fiscal policy rules:
  - A countercyclical fiscal policy rule aimed at stabilizing domestic output growth would help to reduce the level and volatility of the U.S. current account.
- Global implication:
  - Because large U.S. current account deficits must be mirrored by surpluses elsewhere, countercyclical macroprudential and fiscal policies in the U.S. would have helped reduce global imbalances over the last three decades.
  - The paper emphasizes that these rules target domestic objectives rather than the current account directly, yet have meaningful external effects.

### Paper organization (overview)
- Section 2: Empirical evidence on comovement between credit, fiscal balance, and the current account.
- Section 3: Two-country model with financial frictions and fiscal policy.
- Section 4: Estimation procedure and implications of the estimated model.
- Section 5: Counterfactuals and effects of macroprudential and fiscal policy rules.
- Section 6: Conclusion.

*Source: IMF Working Paper — Introduction section (wpiea2021043-print-pdf).*

### 2.2  The Relationship between the Fiscal Balance and the Current

### 2.2  The Relationship between the Fiscal Balance and the Current Account

### Empirical findings on comovement ("twin deficits")
- For the sample of 38 countries, the correlation between the fiscal balance and the current account at annual frequency is positive for 31 out of 38 countries (fiscal deficits tend to coincide with current account deficits), a phenomenon labelled “twin deficits.”
- Correlation is stronger in advanced economies (AEs) than in emerging markets and developing economies (EMDEs):
  - AEs, Mean correlation: 0.37 (for k = −3) … 0.03 (for k = 3) as reported in Table 2 (row "AEs, Mean").
  - EMDEs, Mean correlation: 0.09 (for k = −3) … −0.06 (for k = 3) as reported in Table 2 (row "EMDEs, Mean").
  - Full sample, Mean: 0.26 (for k = −3) … −0.01 (for k = 3).
  - Full sample, Median: 0.31 (for k = −3) … −0.04 (for k = 3).
- Representative country correlations (from Table 2, correlation between the fiscal balance at t+k and the current account at t):
  - Sweden: 0.90 (k = −3), 0.93 (k = −2), 0.90 (k = −1), 0.84 (k = 0), 0.76 (k = 1), 0.67 (k = 2), 0.59 (k = 3).
  - United States: 0.75 (k = −3), 0.60 (k = −2), 0.42 (k = −1), 0.29 (k = 0), 0.15 (k = 1), 0.03 (k = 2), −0.09 (k = 3).
  - Germany: 0.49 (k = −3), 0.53 (k = −2), 0.58 (k = −1), 0.61 (k = 0), 0.54 (k = 1), 0.45 (k = 2), 0.37 (k = 3).
  - France: 0.35 (k = −3), 0.49 (k = −2), 0.44 (k = −1), 0.40 (k = 0), 0.37 (k = 1), 0.29 (k = 2), 0.17 (k = 3).
  - Italy: 0.23 (k = −3), 0.32 (k = −2), 0.38 (k = −1), 0.39 (k = 0), 0.30 (k = 1), 0.16 (k = 2), −0.04 (k = 3).
  - Japan: −0.32 (k = −3), −0.14 (k = −2), 0.20 (k = −1), 0.33 (k = 0), 0.26 (k = 1), 0.06 (k = 2), −0.20 (k = 3).
  - Spain: 0.48 (k = −3), 0.41 (k = −2), 0.28 (k = −1), 0.01 (k = 0), −0.28 (k = 1), −0.46 (k = 2), −0.61 (k = 3).
  - Australia: 0.21 (k = −3), −0.13 (k = −2), −0.28 (k = −1), −0.33 (k = 0), −0.47 (k = 1), −0.44 (k = 2), −0.38 (k = 3).
- The correlation is positive in selected EMDEs: Brazil (0.26 at k = 0), China (0.45 at k = 0), Colombia (0.28 at k = 0), Peru (0.38 at k = 0).
- Figure 2 (scatterplots) confirms mostly positive contemporaneous correlations (k = 0) between fiscal balance (% of GDP) and current account (% of GDP) for the selected advanced economies, with notable exceptions (e.g., Spain and Australia).

### Interpretation and caveats in the empirical evidence
- The positive comovement supports the “twin deficits” view in most sampled countries, but strength varies substantially across countries and over leads/lags (k = −3 to k = 3).
- The relationship is generally stronger in advanced economies than in EMDEs; median correlations are more similar (AEs median 0.29 vs EMDEs median 0.25 for the contemporaneous correlation reported in text).
- The reported correlations are bilateral, annual-frequency correlations and are descriptive; they motivate building a structural model to understand driving mechanisms.

### Model: objective and key mechanisms
- Objective: To understand factors driving current account dynamics and the comovement of credit, fiscal balance, and the current account using an open-economy DSGE model with credit frictions and fiscal policy.
- Model class: Two-country international real business cycle model with trade in intermediate goods and credit frictions; Home and Foreign countries; final goods used for consumption and investment in country-specific capital; model is annual and abstracts from nominal frictions.
- Credit frictions (Jones, Midrigan and Philippon (2020) approach):
  - Households are continua of members with idiosyncratic preference shocks v_it drawn from a Pareto distribution Pr(v_it ≤ v) = 1 − v^(−α).
  - Distinction between liquid and illiquid assets; households allocate wealth between assets prior to realization of v_it; consumption of each member limited by a liquidity constraint.
  - Borrowing constraint tied to housing value: q_t b_{t+1} ≤ m_t e_t h_{t+1}, where log m_t follows an AR process with shocks (credit shocks) (equation (16)).
  - Credit shocks are shocks to the demand for borrowing tied to housing value; in equilibrium, households borrow up to the limit to alleviate liquidity constraints.
  - The dispersion parameter α governs how binding liquidity constraints are: lower α (more dispersion) ⇒ larger fraction constrained ⇒ stronger role for credit shocks in cutting consumption.
- Fiscal policy:
  - Government spending g_t is added and financed by lump-sum taxes t_t and government debt b^g_t (government borrowing only domestically).
  - Taxes follow a debt-stabilizing rule: t_t / y_t = t^y + φ_b (b^g_{t+1}/(P_t y_t) − b^g/(P y)) (equation (18)).
  - Government spending rule: g_t = g^y y_t + ξ_{g,t}, with log ξ_{g,t} = ρ_g log ξ_{g,t−1} + σ_g ε_{g,t} (equations (19)–(20)).
  - Government budget constraint: 1/R_t b^g_{t+1} − b^g_t = P_t g_t − P_t t_t (equation (21)).
- Households’ decision rules and wedges:
  - First-order conditions generate wedges between private borrowing costs (1/q_t) and government debt interest rates (R_t) because of liquidity and borrowing constraints (see equations (22)–(24)).
  - Consumption profile per individual: c_t(v) = min[v/(β q_t P_t E_t μ_{t+1}), x_t] (equation (26)); aggregate relationships relate average consumption to minimum consumption via α (equation (28)).
  - Capital and labor optimality conditions given by equations (29) and (30).

### Estimation: data, sample, and observables
- Estimation approach: Generalized Method of Moments (GMM); match selected moments from model to data.
- Country mapping for estimation: United States = Home; aggregate of other advanced economies = Foreign (ROW).
- ROW aggregate includes: Australia, Canada, France, Germany, Italy, Japan, Spain, Sweden, and the United Kingdom.
- Sample period: 1980-2017 at annual frequency.
- Observables used in estimation:
  - For the U.S. (Home): current account to GDP ratio; fiscal balance to GDP ratio; annual change in private credit to GDP ratio; real GDP growth.
  - For ROW (Foreign): fiscal balance to GDP ratio; annual change in private credit to GDP ratio; real GDP growth.
  - Note: ROW current account is not used as an observable because the ROW aggregate does not include all U.S. trading partners, and in the model ROW current account would mirror the U.S. current account.
- Aggregation details:
  - Fiscal and credit-to-GDP ratios for ROW computed as weighted averages using nominal GDP in USD as weights for each year.
  - Real GDP growth aggregated using real GDP in USD as weights for each year.
- Use of the annual change in the credit-to-GDP ratio: chosen to compute theoretical correlation with the current account in the model and to facilitate GMM matching with selected moments.

*Source: wpiea2021043-print-pdf (Section 2.2, and model and estimation discussion in Sections 3–4, as provided).*

### 4.2  GMM Estimation and Parameter Estimates

### 4.2  GMM Estimation and Parameter Estimates

### Estimation methodology
- First-order approximation to equilibrium conditions and GMM to match key moments (following Andreasen, Fernandez-Villaverde and Rubio-Ramirez (2018)).
- Match standard deviation of variables, contemporaneous second moments and persistence.
- Moment vector:
  - Mt ≡ [ vech(zt z′t) ; diag(zt z′t) ; diag(zt z′t−1) ] with size 35×1.
- GMM estimator:
  - Θ̂GMM = arg min (1/T ∑t=1^T Mt − E[M(Θ)])′ W (1/T ∑t=1^T Mt − E[M(Θ)]).
- Two-step weighting:
  - Step 1: W = inverse of long-run variance of sample moments centered at sample mean to obtain Θ̂0.
  - Step 2: W = inverse of variance-covariance of (1/T ∑t=1^T Mt − E[M(Θ̂0)]) obtained with Newey-West estimator with 3 lags to obtain Θ̂1.
- Seven macroeconomic variables used for estimation; model has six shocks. To avoid singularity when extracting shocks for counterfactuals, an observation error shock is included in ROW output growth equation.

### Calibrated parameters (Table 3)
- κ, κ∗ Share of domestic goods in domestic production: 0.8
- h̄ Housing stock: 1
- r = 1/q − 1 Real interest rate: 0.02
- m̄ Steady-state credit shock (Average LTV): 0.29
- ν Inverse Frisch elasticity labor supply: 2
- ω Capital share of output: 1/3
- δ Depreciation rate: 0.1
- g/Y, g∗/Y∗ Government spending to GDP ratio, U.S. and ROW: 0.2
- b_g/Y, b_g∗/Y∗ Debt to GDP ratio, U.S. and ROW: 0.6
- Notes/implications:
  - Share of imports to GDP set to 0.2 (corresponds to κ of 0.8).
  - Capital share and depreciation set to standard RBC values (1/3 and 10% annual).
  - Real interest rate set to 2 percent annual.
  - Aggregate housing to income ratio set to 2.5 (as in Jones, Midrigan and Philippon (2020)); housing supply normalized to one.
  - Given these values and estimate for α, discount factor β and housing weight ηH pinned down endogenously.
  - Steady-state government spending to GDP ratio assumed 20 percent of GDP; target debt-to-GDP in fiscal rule assumed 60 percent.
  - Current account and net international investment position assumed balanced in steady state.

### GMM estimated parameters and standard deviations (Table 4)
- α Dispersion of Taste Shocks: Point Estimate 2.38; Standard Dev 0.03
- σ Elasticity of Substitution H/F Goods: Point Estimate 2.50; Standard Dev 0.64
- φb U.S. Tax Response to Debt: Point Estimate 0.16; Standard Dev 0.06
- φb∗ ROW Tax Response to Debt: Point Estimate 0.06; Standard Dev 0.01
- φk Investment Adjustment Costs: Point Estimate 6.57; Standard Dev 1.88
- ρz U.S. TFP AR(1) Parameter: Point Estimate 0.98; Standard Dev 0.01
- ρz∗ ROW TFP AR(1) Parameter: Point Estimate 0.46; Standard Dev 0.26
- ρm U.S. Credit Shock AR(1) Parameter: Point Estimate 0.997; Standard Dev 0.002
- ρm∗ ROW Credit Shock AR(1) Parameter: Point Estimate 0.80; Standard Dev 0.14
- ρg U.S. Fiscal Shock AR(1) Parameter: Point Estimate 0.42; Standard Dev 0.08
- ρg∗ ROW Fiscal Shock AR(1) Parameter: Point Estimate 0.60; Standard Dev 0.17
- σz U.S. TFP Innovation Std. Dev.: Point Estimate 1.33; Standard Dev 0.07
- σz∗ ROW TFP Innovation Std. Dev.: Point Estimate 0.83; Standard Dev 0.30
- σm U.S. Credit Shock Innovation Std. Dev.: Point Estimate 4.26; Standard Dev 0.33
- σm∗ ROW Credit Shock Innovation Std. Dev.: Point Estimate 8.55; Standard Dev 0.45
- σg U.S. Fiscal Shock Innovation Std. Dev.: Point Estimate 4.35; Standard Dev 0.26
- σg∗ ROW Fiscal Shock Innovation Std. Dev.: Point Estimate 2.41; Standard Dev 0.19
- σ∗Δy Measurement Error, ROW Output Growth: Point Estimate 1.00; Standard Dev 0.34
- Note: all the estimates for standard deviation of the shocks are expressed in percentage points.
- Interpretations:
  - Estimated α = 2.38 implies discount factor of 0.945 and spread between interest rate and rate of time preference of about 3.6 percent; indicates relatively strong preference for liquidity enhancing endogenous correlation between credit and real variables.
  - σ = 2.5 is relatively high compared to standard international BC calibrations but closer to estimates using disaggregated data.
  - U.S. tax response to debt (φb = 0.16) stronger than ROW counterpart (φb∗ = 0.06).
  - Investment adjustment cost parameter φk = 6.57.

### Notes on estimation outputs
- Asymptotic standard errors computed using asymptotic expression for variance-covariance of parameters under GMM with optimal weighting matrix.
- Estimated shock processes themselves are not highly informative in isolation; model fit discussed next.

### Model fit (summary of Section 4.3.1; Tables 5–7)
- Model fit to selected second moments:
  - Model fits most standard deviations well, especially U.S. variables.
  - Model underestimates volatility of change in credit-to-GDP ratio in ROW but matches ROW real GDP growth volatility.
  - Model close to matching persistence of U.S. current account and ROW fiscal balances.
  - Model poorly matches persistence of credit-to-GDP change and real GDP growth in both U.S. and ROW.
- Specific model vs data moments (selected entries from Table 5):
  - Current Account/GDP, U.S.: Data Std. Dev. 1.51; Data Autocorr 0.86; Model Std. Dev. 1.51; Model Autocorr 0.63
  - Credit/GDP, Change, U.S.: Data Std. Dev. 3.04; Data Autocorr 0.62; Model Std. Dev. 3.59; Model Autocorr −0.03
  - Fiscal Balance/GDP, U.S.: Data Std. Dev. 3.01; Data Autocorr 0.81; Model Std. Dev. 2.43; Model Autocorr 0.38
  - Real GDP Growth, U.S.: Data Std. Dev. 1.8; Data Autocorr 0.34; Model Std. Dev. 1.5; Model Autocorr 0.03
  - Credit/GDP, Change, ROW: Data Std. Dev. 10.13; Data Autocorr 0.27; Model Std. Dev. 7.25; Model Autocorr −0.12
  - Fiscal Balance/GDP, ROW: Data Std. Dev. 1.19; Data Autocorr 0.75; Model Std. Dev. 2.14; Model Autocorr 0.77
  - Real GDP Growth, ROW: Data Std. Dev. 1.51; Data Autocorr 0.36; Model Std. Dev. 1.52; Model Autocorr −0.13
- Correlations (selected from Table 6) — Data vs Model:
  - (CA, CRE): Data −0.44; Model −0.29
  - (CA, CRE*): Data −0.19; Model 0.44
  - (CA, GDP): Data −0.09; Model −0.12
  - (CA, FB): Data 0.46; Model 0.36
  - (CRE, FB*): Data 0.62; Model 0.01
  - (GDP, GDP*): Data 0.65; Model 0.02
- Variance decomposition for U.S. observables (Table 7; percent contributions):
  - Current Account to GDP: Productivity U.S. 18.6; Productivity ROW 0.4; Credit U.S. 28.9; Credit ROW 33.2; Gov Spending U.S. 13.9; Gov Spending ROW 4.9
  - U.S. Credit to GDP: Productivity U.S. 0.5; Productivity ROW 0.09; Credit U.S. 90.2; Credit ROW 0.4; Gov Spending U.S. 8.8; Gov Spending ROW 0.1
  - U.S. GDP Growth: Productivity U.S. 89.6; Productivity ROW 0.0; Credit U.S. 0.3; Credit ROW 0.5; Gov Spending U.S. 9.5; Gov Spending ROW 0.1
  - U.S. Fiscal Balance to GDP: Productivity U.S. 1.0; Productivity ROW 0.0; Credit U.S. 0.0; Credit ROW 0.0; Gov Spending U.S. 98.9; Gov Spending ROW 0.0
- Key interpretation:
  - U.S. current account fluctuations driven mainly by U.S. and ROW credit shocks (each about 30 percent), with domestic productivity explaining 18.6 percent and fiscal shocks 13.9 percent.
  - U.S. credit-to-GDP changes largely driven by U.S. credit shocks; U.S. GDP growth driven by productivity shocks; U.S. fiscal balance driven by government spending shocks.

### Impulse responses (summary of Section 4.3.2)
- U.S. credit shock (increase in borrowing ability):
  - Private credit-to-output ratio increases to about 3 percent of GDP with highly persistent impact.
  - Domestic consumption and investment increase; output (intermediate goods production) exhibits hump-shaped response due to initial decline in hours worked, then recovery as employment and capital accumulate.
  - House prices increase, relaxing borrowing constraints.
  - Current account moves into deficit and converges back to zero monotonically.
  - Fiscal balance moves to slight deficit: −0.03 percent of GDP (negligible in quantitative terms) due to fiscal rule.
- U.S. government spending shock (increase):
  - Replicates "twin deficits": both fiscal and current account balances turn into deficits as percent of GDP.
  - Fiscal impulse expansionary; short-lived increase in output.
  - Private credit-to-GDP ratio contracts (crowding out from government borrowing not fully offset via international borrowing).
  - Impact multiplier of fiscal balance on current account ≈ 0.25 (close to single-equation model estimates).
  - Fiscal multiplier on output (intermediate goods production) ≈ 0.15 on impact; multiplier on final goods production ≈ 0.35.
  - Multipliers smaller than many estimates in literature due to absence of features like hand-to-mouth consumers, nominal rigidities, weak monetary policy response to inflation, and labor market frictions.
- U.S. productivity shock (increase):
  - Current account moves to deficit on impact then quickly to surplus as increased production increases exports relative to imports.
  - Private credit increases but private credit-to-GDP ratio declines because of large output expansion.
  - Fiscal balance moves to deficit due to fiscal rule: higher output reduces government debt-GDP ratio, triggering lump-sum tax cut that temporarily lowers government revenue.

### Role of α (Section 4.4)
- α is degree of idiosyncratic uncertainty (dispersion of taste shocks) key to how credit shocks affect real variables.
- Table 8: Correlation between Current Account and ∆ Credit across α values:
  - U.S. Data: −0.44
  - α = 2.3: −0.29
  - α = 4: −0.07
  - α = 8: 0.06
- Mechanism and interpretation:
  - Lower α (higher idiosyncratic uncertainty) increases preference for liquid savings within household to smooth marginal utilities across members within period; reductions in credit availability lead household to maintain liquid assets and cut consumption and imports → generates negative comovement between current account and changes in credit as in data.
  - Higher α (lower idiosyncratic uncertainty) reduces effect of credit changes because household smooths intertemporally using liquid savings → model cannot match negative comovement between current account and household credit.

*Italic: Source: wpiea2021043-print-pdf - 4.2  GMM Estimation and Parameter Estimates*

### 5.3  Fiscal Policy

### 5.3 Fiscal Policy

### Fiscal rule specification
- Government spending in the baseline adjusts in line with changes in output, subject to an autoregressive innovation.
- Alternative fiscal rule studied (government spending responds to lagged output growth):
  - g_t = g_Y Y_{t−φ_g} log(y_{t−1} / y_{t−2}) + ξ_{g,t}  (equation (36) in source)
  - φ_g parameterizes the extent to which government spending leans against output growth.
- Optimal policy value reported in the Appendix: φ_g = 2.1.
- Welfare-based result reported elsewhere in the Appendix: welfare is maximized around a coefficient of φ_g = −0.7 (Figure C.2).

### Effects on current account, debt, and GDP
- Under the fiscal rule (36) parameterized at φ_g = 2.1:
  - The current account deficit would contract over most of the sample period.
  - The path of debt-to-income is little changed.
- General interpretation:
  - A more countercyclical fiscal policy (higher φ_g) would have withdrawn domestic demand in periods where the economy was growing, thereby lowering the U.S. current account deficit for most of the time period considered.
  - Main exception: during the Great Recession (2009), fiscal policy offsetting the large negative growth rate would have benefited GDP, and in that period the current account deficit would have been somewhat larger.

### Fiscal balance implications (counterfactual)
- Figure 10 counterfactual fiscal balance under the rule responding to lagged output growth shows:
  - During recessions the fiscal rule would have led to larger fiscal deficits.
  - During 2009 to 2010, the U.S. fiscal deficit would have been more negative by 4 to 5 percentage points.
  - The rule would have called for faster fiscal consolidation in the boom years of 1996-2000.
  - The rule would have called for faster fiscal consolidation towards the end of the sample period considered (2016-2017).

### Policy interpretation and linkage to broader findings
- Countercyclical fiscal policy that leans against output growth can reduce the level and volatility of the U.S. current account deficit in normal times by contracting domestic demand in booms.
- In deep recessions (e.g., Great Recession) such a rule may exacerbate current account deficits because stabilizing output through fiscal support would increase the deficit.
- The analysis complements the paper’s broader conclusions linking credit cycles, fiscal policies, and global imbalances, including that:
  - Credit market shocks are major drivers of the U.S. current account (about roughly 30 percent from domestic credit market shocks and another one-third from foreign credit market shocks).
  - U.S. fiscal shocks explain about 13.9 percent of the U.S. current account volatility.
  - Macroprudential rules stabilizing the domestic credit cycle and fiscal rules stabilizing the business cycle can help lower the level and volatility of the U.S. current account.

*Source: wpiea2021043-print-pdf - 5.3  Fiscal Policy*

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_Source: https://www.imf.org/-/media/files/publications/wp/2021/english/wpiea2021043-print-pdf.pdf_