## _wp0923

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---

### I. Introduction — key themes and vulnerabilities
- Financial integration in advanced and emerging economies of Europe has increased cross-border ownership of assets, offering income smoothing through cross-border asset diversification but introducing new risks.
- Benefits:
  - Dispersion of claims to broader portfolios improves risk spreading.
  - Potential to smooth incomes through cross-border diversification and stabilize income against asymmetric shocks.
- Risks and vulnerabilities:
  - Cross-border ownership exposes financial institutions to macroeconomic, financial, and asset price fluctuations in countries where they hold positions.
  - Complex cross-border linkages make shock transmission and ultimate risk locations more opaque.
  - Reliance on foreign funding channeled primarily through the banking sector increased in many countries through end-2007.
- Empirical indicators:
  - Loan-to-deposit ratios rose through end-2007 in most countries in the region, roughly doubling since the early 2000s in the Baltic countries.
  - In Ukraine, Hungary, and Russia, loan-to-deposit ratios ranged from 120 to 150 percent in 2007.
  - Except for Moldova; Serbia; Macedonia, FYR; and Bosnia and Herzegovina, changes in the ratio of bank credit to GDP significantly exceeded those in the ratio of bank deposits to GDP by end-2007.
- Concentration of cross-border exposures:
  - Emerging European economies are heavily exposed to—and dependent on—western European banks.
  - Most countries in the region have concentrated exposures to banks in Austria, Italy, and Germany; the Baltic countries have large exposures to Sweden.
  - Some countries (e.g., the Czech Republic and Poland) are more diversified; several depend on funding from very few countries.
- Transmission horizons:
  - Asset prices are the main short-run international transmission channel for financial shocks.
  - Cost and quantity of credit become important channels over longer horizons.

### II. The GVAR model (1999-2008) — structure and dataset
- Purpose:
  - To shed light on international spillovers and feedback between real and financial sectors via time-profile of cross-country transmission while accounting for regional interdependencies.
- Model scope and data:
  - GVAR model estimated for 26 European countries, grouped into 5 regions plus the United States.
  - Monthly data on real GDP growth, real interest rates, real growth in credit to the corporate sector, and equity prices, from June 1999 to April 2008.
  - Later text indicates the full dataset includes 27 countries; the GVAR covers 27 developed and emerging economies.
- Variable definitions:
  - gequ_it = ln(EQU_it / EQU_i,t−12) × 100 − ln(CPI_it / CPI_i,t−12) × 100
  - gcc_it = ln(CC_it / CC_i,t−12) × 100 − ln(CPI_it / CPI_i,t−12) × 100
  - ggdp_it = ln(GDP_it / GDP_i,t−12) × 100 − ln(CPI_it / CPI_i,t−12) × 100
  - ibk_it = IBK_it − ln(CPI_it / CPI_i,t−12) × 100
  - Where EQU_it is nominal equity prices index, CC_it is nominal credit to corporations, CPI_it is consumer price index, GDP_it is nominal GDP, IBK_it is nominal interbank rate, for country i at time t.
- Construction of foreign-specific variables:
  - x*_it = sum_{j=1}^N w_ij x_jt, with w_ii = 0 and sum_{j=1}^N w_ij = 1.
  - Weights w_ij are fixed and computed using average annual bank lending exposures over the period 1999-2007 (financial weights are an original contribution).
- Model dimensions and lags:
  - Each country model contains 4 domestic variables and 4 foreign-specific counterparts (k_i = k*_i = 4).
  - Lag orders of both domestic and foreign variables set to one.
  - GVAR includes in total 108 (27 × 4) endogenous variables.
  - Country models treated as VARX*(1,1) and estimated individually with x*_it treated as weakly exogenous I(1).
- Regional aggregation:
  - Regional impulse responses and forecast error variances obtained as weighted averages of country-level counterparts.
  - Aggregation weights based on averages of Purchasing Power Parity GDPs for 1999-2008.

### II.A. Structure of the model — formal representation (selected equations and assumptions)
- Country VARX*(1,1) representation:
  - x_it = a_i0 + a_i1 t + Φ_i x_{i,t−1} + Λ_i0 x*_it + Λ_i1 x*_{i,t−1} + u_it
  - z_it = (x'_it, x*'_it)' and z_it = W_i x_t, with W_i constructed from financial weights.
- Global stacking and reduced form:
  - Stacked form: G x_t = a_0 + a_1 t + H x_{t−1} + u_t
  - Reduced form (if G nonsingular): x_t = b_0 + b_1 t + F x_{t−1} + v_t, with F = G^{-1} H.
- Assumptions on shocks and exogeneity:
  - u_it ∼ i.i.d.(0, Σ_ii) with allowed contemporaneous cross-country covariance Σ_ij for i ≠ j.
  - Weak exogeneity of foreign variables implies each non-US country is considered small open economy in long-run.

### II.B. Data properties and pretesting
- Sample and frequency:
  - Monthly sample spans June 1999 to April 2008; 27 countries included.
- Integration properties:
  - ADF tests (lag order by AIC, max lag 6) indicate hypothesis of unit root cannot be rejected for most variables in most countries.
  - Weighted Symmetric DF (WS) tests per Park and Fuller (1995) also indicate majority of series is I(1).
- Seasonal adjustment and interpolation:
  - Quarterly GDP growth exponentially interpolated to monthly frequency; series seasonally adjusted using Census X12 where necessary.
- Data sources:
  - Monthly credit growth in corporate sector: national central banks.
  - Equity prices: Bloomberg.
  - 3-month interbank interest rates and consumer price indices: IMF International Financial Statistics.

### III. Estimation — methodology and validation
- Estimation strategy:
  - Country-by-country estimation of country-VARX* models treating foreign variables as weakly exogenous; weights are computed (not estimated).
  - Cointegration and VECM framework applied where appropriate via Johansen reduced-rank procedure.
  - Lag orders set to one; cointegration rank determined by trace and maximum eigenvalue statistics using MacKinnon et al. (1999) critical values.
  - When cointegration found, estimate country-VARX* in VECMX* form; if rank zero, estimate in differences.
  - White’s heteroskedasticity-corrected standard errors used for hypothesis testing.

### III.A. Conditions for the GVAR estimation — sufficiency checks and results
- PSW (2004a) sufficient conditions applied:
  1. Dynamic stability: eigenvalues of F must lie on or inside the unit circle.
     - All 108 eigenvalues of F are on or within the unit circle; number of eigenvalues on the unit circle (unitary roots) is 78.
  2. Weights must be relatively small: sum_{j=1}^N w_{ij}^2 → 0 as N → ∞ for each i.
     - Financial weights reported in a 27×27 matrix; most weights are granular and not too close to one.
     - Largest individual weights: Sweden → Estonia 0.76; Sweden → Latvia 0.691; Sweden → Lithuania 0.672.
  3. Cross-dependence of idiosyncratic shocks must be sufficiently small: sum_{j=1}^N σ_{ij,ls} / N → 0 as N → ∞ for all i, l, s.
     - VARX residuals (including foreign variables) are generally weakly correlated and in some cases uncorrelated, supporting simulation of mainly country-specific shocks.
- Conclusion: All three requirements are met in this GVAR implementation.

### III.C. Testing for weak exogeneity — summary findings
- The weak exogeneity assumption is not rejected for most of the foreign variables, despite some exceptions.
- Variables rejected at the 5% significance level:
  - the foreign rate of change of real equity prices in Switzerland;
  - the foreign rate of change of real credit to corporations in Belgium and France;
  - the foreign rate of real GDP in Belgium, France, Hungary and Sweden;
  - the foreign real interbank rate in Estonia.
- For countries with no cointegrating relations — Austria, Croatia, Ireland, Netherland and Poland — weak exogeneity of foreign variables is automatically assured.
- Overall: only 8 out of 108 foreign variables fail to satisfy the weak exogeneity assumption; these outcomes are considered acceptable and justify the estimation procedure of each country model in the GVAR.

### Impact elasticities — estimation and interpretation
- Estimated as coefficients of contemporaneous foreign variables in differences; measure contemporaneous variation of a domestic variable due to a one percent change in its corresponding foreign-specific counterpart.
- Standard errors / t-ratios calculated using White’s heteroscedasticity-consistent variance estimator.
- Key findings:
  - gequ (growth rate of real equity prices):
    - Impact elasticities statistically significant for most countries.
    - All values are positive, either greater or lower than one.
    - Impact elasticities > 1 indicate domestic overreaction; < 1 indicate underreaction.
    - Implication: strong co-movements in equity prices across countries and synchronization of GIRFs associated with changes in real equity prices.
  - gcc (real credit to corporations):
    - Almost all coefficient estimates not statistically significant.
    - Implication: no evidence of strong international linkages across countries in national dynamics of real credit to corporations.
  - ggdp and ibk:
    - Estimated impact elasticities seldom statistically significant.
    - Implication: no striking evidence of linkages across countries for these variables.

### Dynamic analysis — methodology
- Method: Generalized Impulse Response Functions (GIRFs) as in Koop, Pesaran and Potter (1996) and Pesaran and Shin (1998).
- GIRF properties:
  - Does not orthogonalize residuals; accounts for historical correlations via the estimated variance-covariance matrix.
  - Invariant to variable ordering; does not require a priori restrictions.
  - Since shocks are not identified, GIRFs do not provide causal inference but are advantageous in multi-country frameworks.
- Simulation exercise:
  - A negative one standard error shock to the US growth rate of real equity prices is simulated.
  - Time horizon: 2 years.
  - Confidence intervals at the 68 percent significance level calculated using the sieve bootstrap technique with 1000 replications.

### GIRF empirical results — regional responses to a one standard error negative US equity shock
- General note: with few exceptions, responses are statistically not significant using custom confidence intervals, reflecting estimator inefficiency given only 95 monthly observations. Analysis focuses on synchronization of dynamics across regions rather than statistical significance of individual signs.
- Real equity prices (selected outcomes):
  - US response:
    - instantaneous fall of 2.86 percent;
    - increases over time until it reaches a peak after four months (equal to a 2.37 percent decrease);
    - reaches 3.17 percent below the baseline after two years.
  - Other regions:
    - Generally display synchronized dynamics with the US, indicating strong interrelation of equity markets, particularly for countries with mature financial systems.
    - Southeastern European countries: mainly self-driven GIRF dynamics, implying a low degree of financial integration with the rest of the world.
- Real credit to corporations:
  - US response:
    - on impact, a 0.15 percent decline;
    - minimum of 0.32 percent below the pre-shock level after four months;
    - after two years, the effect averages a 0.27 percent decrease with respect to the baseline.
  - Other developed European countries:
    - start on impact from the zero line, rapidly falling 0.2 percent below it, stabilizing around that level.
  - Baltic and Central-eastern European countries:
    - decrease in the short run, return over time to initial levels.
  - Euro Area:
    - credit growth hardly increases above its pre-shock level.
  - Southeastern European countries:
    - fluctuate considerably; increase during initial months, peak after four months (0.14 percent increase), complete reabsorption after two years.
  - Implication: credit growth responses are mainly region-specific.
- Real GDP growth rates:
  - General decrease in GIRFs across all regions; dynamic behaviors moderately correlated.
  - US:
    - GIRF monotonically decreases over time and stabilizes after two years to 0.13 percent below the pre-shock level.
  - Euro area and other developed European countries:
    - GIRFs mildly decrease over time, both reaching levels which average 0.05 percent below the zero line.
  - Other regions:
    - Behave differently in the first months but stabilize below baseline after two years.
  - Implication: considerable international co-movement of real growth among regions.
- Real interbank rates:
  - Majority of GIRFs decrease over time.
  - US real interbank rate:
    - decreases on impact by 8 basis points;
    - averages 14 basis points below baseline after two years.
  - Other developed European countries:
    - overreact; minimum after four months (28 basis points decrease), stabilizing around a 27 basis points loss.
  - Southeastern European countries:
    - diverge from other regions; increase, reaching a 7 basis points increase after three months, returning to the zero line after 15 months.

### GFEVD — key allocations and dynamics (selected figures from Table 10)
- Historical shock: initial observed shock magnitude: 7.12 percent for the real equity prices growth.
- On impact (k = 0) contributions to the variance of the historical shock (US variables):
  - gequ: 42.43
  - gcc: 7.24
  - ggdp: 0.05
  - ibk: 6.11
  - US Vars (aggregate): 55.83
- After one year (k = 12) contributions (US variables):
  - gequ: 9.66
  - gcc: 15.82
  - ggdp: 12.67
  - ibk: 7.38
  - US Vars (aggregate): 45.53
- After two years (k = 24) contributions (US variables):
  - gequ: 7.12
  - gcc: 15.21
  - ggdp: 17.38
  - ibk: 7.17
  - US Vars (aggregate): 46.88
- Selected non-US regional aggregate contributions (k = 0, 1, 2, 4, 8, 12, 24):
  - Euro Area (EA Vars): 9.47, 9.66, 10.21, 10.84, 11.40, 12.13, 13.62
  - Other Developed European countries (OTH Vars): 11.26, 15.03, 17.07, 18.73, 18.25, 17.14, 15.72
  - Baltic countries (BALT Vars): 10.23, 10.93, 11.43, 12.28, 12.47, 11.38, 9.23
  - South-Eastern Europe (SEE Vars): 3.34, 2.89, 2.66, 2.34, 1.96, 1.84, 1.75
  - Central-Eastern Europe (CEE Vars): 9.86, 9.82, 10.15, 10.76, 11.47, 11.98, 12.81
  - Non-US Vars (aggregate): 44.17, 48.33, 51.52, 54.94, 55.55, 54.47, 53.12
- Short-run vs. long-run pattern:
  - On impact, the US domestic innovations explain 55.83 percent of the variance of the shock.
  - On impact, the largest foreign regional contributors are:
    - Other Developed European countries: 11.26 percent
    - Baltic countries: 10.23 percent
  - After two years, the forecast error variance of the historical shock is mainly explained by foreign variables: 53.12 percent.
  - After two years, regional contributions change: Other Developed European countries 15.72 percent; Euro area 13.62 percent.
- Note: percentages reported for k-step ahead forecast error variance; totals rescaled for readability.

### Substantive findings on transmission channels and dynamics
- Financial shocks are transmitted relatively quickly and often get amplified traveling from the US to the euro area.
- Equity markets are more synchronous internationally compared to banking systems.
- Short-run transmission channel: asset prices are the main channel through which financial shocks are transmitted internationally.
- Longer-horizon transmission channels: real credit growth, real interbank rate, and real GDP growth gain increasing relevance.
- Interregional linkages matter: the relative contribution of each region to forecast error variance highlights geographic transmission patterns and vulnerabilities.
- Novelty: Country-specific foreign variables constructed using cross-country financial flows from international banking statistics (annual bank lending exposures over 1999-2007).

### Policy-relevant observations and implications
- Greater financial integration and increased cross-border ownership of assets:
  - Are associated with better growth opportunities, with the link stronger where integration is faster.
  - Can amplify business cycle fluctuations and the impact of asset price movements on real activity by strengthening cross-border financial spillovers.
- European vulnerabilities:
  - Sizable cross-border financial linkages across Europe highlight vulnerabilities from reliance on concentrated foreign funding.
  - International banking statistics suggest most emerging European economies are heavily exposed to—and dependent on—western banks.
- GVAR framework utility:
  - Presents a manageable spatio-temporal structure for analyzing international transmission of financial shocks and second-round effects.
  - Can be modified and extended according to policy interests.

*Source: _wp0923 - 3. The weak exogeneity assumption and related sections (PDF chapter/section).*

### References .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .

### _wp0923 - References .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .

### I. Introduction — key themes and vulnerabilities
- Financial integration in advanced and emerging economies of Europe has increased cross-border ownership of assets, offering income smoothing through cross-border asset diversification but introducing new risks.
- Benefits highlighted:
  - Dispersion of claims to broader portfolios improves risk spreading.
  - Potential to smooth incomes through cross-border diversification and stabilize income against asymmetric shocks.
- Risks and vulnerabilities identified:
  - Cross-border ownership exposes financial institutions to macroeconomic, financial, and asset price fluctuations in countries where they hold positions.
  - Complex cross-border linkages make shock transmission and ultimate risk locations more opaque.
  - Reliance on foreign funding channeled primarily through the banking sector increased in many countries through end-2007.
- Empirical indicators:
  - Loan-to-deposit ratios rose through end-2007 in most countries in the region, roughly doubling since the early 2000s in the Baltic countries.
  - In Ukraine, Hungary, and Russia, loan-to-deposit ratios ranged from 120 to 150 percent in 2007.
  - Except for Moldova; Serbia; Macedonia, FYR; and Bosnia and Herzegovina, changes in the ratio of bank credit to GDP significantly exceeded those in the ratio of bank deposits to GDP by end-2007.
- Concentration of cross-border exposures:
  - Emerging European economies are heavily exposed to—and dependent on—western European banks.
  - Most countries in the region have concentrated exposures to banks in Austria, Italy, and Germany; the Baltic countries have large exposures to Sweden.
  - Some countries (e.g., the Czech Republic and Poland) are more diversified; several depend on funding from very few countries.
- Short- and long-run transmission:
  - Asset prices are the main short-run international transmission channel for financial shocks.
  - Cost and quantity of credit become important channels over longer horizons.

### II. The GVAR model (1999-2008) — structure and dataset
- Purpose:
  - To shed light on international spillovers and feedback between real and financial sectors via time-profile of cross-country transmission while accounting for regional interdependencies.
- Model scope and data:
  - GVAR model estimated for 26 European countries, grouped into 5 regions plus the United States.
  - Monthly data on real GDP growth, real interest rates, real growth in credit to the corporate sector, and equity prices, from June 1999 to April 2008.
  - Later text indicates the full dataset includes 27 countries; the GVAR covers 27 developed and emerging economies.
- Variable definitions (constructed exactly as in source):
  - gequ_it = ln(EQU_it / EQU_i,t−12) × 100 − ln(CPI_it / CPI_i,t−12) × 100
  - gcc_it = ln(CC_it / CC_i,t−12) × 100 − ln(CPI_it / CPI_i,t−12) × 100
  - ggdp_it = ln(GDP_it / GDP_i,t−12) × 100 − ln(CPI_it / CPI_i,t−12) × 100
  - ibk_it = IBK_it − ln(CPI_it / CPI_i,t−12) × 100
  - Where EQU_it is nominal equity prices index, CC_it is nominal credit to corporations, CPI_it is consumer price index, GDP_it is nominal GDP, IBK_it is nominal interbank rate, for country i at time t.
- Construction of foreign-specific variables:
  - Foreign variables x*_it are weighted averages of other countries’ corresponding variables: x*_it = sum_{j=1}^N w_ij x_jt, with w_ii = 0 and sum_{j=1}^N w_ij = 1.
  - Weights w_ij are fixed and computed using average annual bank lending exposures over the period 1999-2007 (financial weights are an original contribution).
- Model dimensions and lags:
  - Each country model contains 4 domestic variables and 4 foreign-specific counterparts (k_i = k*_i = 4).
  - Lag orders of both domestic and foreign variables set to one due to data limitations.
  - GVAR includes in total 108 (27 × 4) endogenous variables.
  - Country models treated as VARX*(1,1) and estimated individually with x*_it treated as weakly exogenous I(1).
- Regional aggregation:
  - Regional impulse responses and forecast error variances obtained as weighted averages of country-level counterparts.
  - Aggregation weights based on averages of Purchasing Power Parity GDPs for 1999-2008.

### II.A. Structure of the model — formal representation (selected equations and assumptions)
- Country VARX*(1,1) representation:
  - x_it = a_i0 + a_i1 t + Φ_i x_{i,t−1} + Λ_i0 x*_it + Λ_i1 x*_{i,t−1} + u_it
  - z_it = (x'_it, x*'_it)' and z_it = W_i x_t, with W_i constructed from financial weights.
- Global stacking and reduced form:
  - Stacked form: G x_t = a_0 + a_1 t + H x_{t−1} + u_t
  - Reduced form (if G nonsingular): x_t = b_0 + b_1 t + F x_{t−1} + v_t, with F = G^{-1} H.
- Assumptions on shocks and exogeneity:
  - u_it ∼ i.i.d.(0, Σ_ii) with allowed contemporaneous cross-country covariance Σ_ij for i ≠ j.
  - Weak exogeneity of foreign variables implies each non-US country is considered small open economy in long-run.

### II.B. Data properties and pretesting
- Sample and frequency:
  - Monthly sample spans June 1999 to April 2008; 27 countries included.
- Unit root and integration:
  - ADF tests (lag order by AIC, max lag 6) indicate hypothesis of unit root cannot be rejected for most variables in most countries (results reported in Table5).
  - Weighted Symmetric DF (WS) tests per Park and Fuller (1995) also indicate majority of series is I(1) (results in Table6).
- Seasonal adjustment and interpolation:
  - Quarterly GDP growth exponentially interpolated to monthly frequency; series seasonally adjusted using Census X12 where necessary.
- Data sources:
  - Monthly credit growth in corporate sector: national central banks.
  - Equity prices: Bloomberg.
  - 3-month interbank interest rates and consumer price indices: IMF International Financial Statistics.

### III. Estimation — methodology and validation
- Estimation strategy:
  - Country-by-country estimation of country-VARX* models treating foreign variables as weakly exogenous; weights are computed (not estimated).
  - Cointegration and VECM framework applied where appropriate via Johansen reduced-rank procedure.
  - Lag orders set to one; cointegration rank determined by trace and maximum eigenvalue statistics using MacKinnon et al. (1999) critical values; results reported in Table9 and ranks in Table2.
  - When cointegration found, estimate country-VARX* in VECMX* form; if rank zero, estimate in differences.
  - White’s heteroskedasticity-corrected standard errors used for hypothesis testing.

### III.A. Conditions for the GVAR estimation — sufficiency checks and results
- PSW (2004a) sufficient conditions applied:
  1. Dynamic stability: eigenvalues of F must lie on or inside the unit circle.
     - All 108 eigenvalues of F are on or within the unit circle; number of eigenvalues on the unit circle (unitary roots) is 78.
  2. Weights must be relatively small: sum_{j=1}^N w_{ij}^2 → 0 as N → ∞ for each i.
     - Financial weights reported in a 27×27 matrix (Table7); most weights are granular and not too close to one.
     - Largest individual weights: Sweden → Estonia 0.76; Sweden → Latvia 0.691; Sweden → Lithuania 0.672.
  3. Cross-dependence of idiosyncratic shocks must be sufficiently small: sum_{j=1}^N σ_{ij,ls} / N → 0 as N → ∞ for all i, l, s.
     - Pair-wise cross-section correlations computed for variables in levels and differences and for VAR and VARX residuals (Table8).
     - VARX residuals (including foreign variables) are generally weakly correlated and in some cases uncorrelated, supporting simulation of mainly country-specific shocks.
- Conclusion: All three requirements are met in this GVAR implementation.

### III.B. Estimation of the country-specific models
- Cointegration testing:
  - Johansen reduced-rank procedure with trace and max-eigenvalue tests used; trend coefficients restricted into cointegrating space and intercepts unrestricted.
  - Rank test outcomes in Table9; cointegrating ranks per country in Table2.
- Treatment by cointegration rank:
  - Countries with cointegration estimated in VECMX* form; rank-zero countries estimated in differences.

### III.C. Testing for weak exogeneity
- Weak exogeneity tests:
  - Joint significance of estimated error-correcting terms in marginal models for foreign variables tested per Johansen (1992) and Harbo et al. (1998).
  - Regression for each element l of x*_it in country i:
    - Δx*_{it,l} = μ_{il} + sum_{j=1}^{r_i} γ_{ij,l} ECM_{j i,t−1} + φ_{i,l} Δx_{i,t−1} + θ_{i,l} Δx*_{i,t−1} + ε_{it,l}
  - An F-test conducted for joint hypothesis γ_{ij,l} = 0 for j = 1, …, r_i.
- Results:
  - Weak exogeneity test outcomes reported in Table (text indicates outcomes reported in Table — presumably subsequent table not included in supplied excerpt).

### IV. Dynamic analysis and key empirical findings (summary as anticipated in text)
- Dynamic analysis reveals:
  - Considerable comovements of equity prices across countries characterized by mature financial markets.
  - Effects on credit growth are generally country-specific.
  - Asset prices serve as main short-run international transmission channel for financial shocks.
  - Cost and quantity of credit play an important role over longer horizons.

*Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp0923.pdf*

### 3. The weak exogeneity assumption

### _wp0923 - 3. The weak exogeneity assumption

### Weak exogeneity testing — summary findings
- The weak exogeneity assumption is not rejected for most of the foreign variables, despite some exceptions.
- Variables for which the assumption is rejected at the 5% significance level:
  - the foreign rate of change of real equity prices in Switzerland;
  - the foreign rate of change of real credit to corporations in Belgium and France;
  - the foreign rate of real GDP in Belgium, France, Hungary and Sweden;
  - the foreign real interbank rate in Estonia.
- For countries with no cointegrating relations (and thus no error-correcting terms) — namely Austria, Croatia, Ireland, Netherland and Poland — the weak exogeneity of foreign variables is automatically assured.
- Overall assessment: only 8 out of 108 foreign variables fail to satisfy the weak exogeneity assumption; these outcomes are considered acceptable and justify the estimation procedure of each country model in the GVAR.

### Impact elasticities (estimation and interpretation)
- Impact elasticities are estimated from each country-VECMX* model as coefficients of contemporaneous foreign variables in differences; they measure the contemporaneous variation of a domestic variable due to a one percent change in its corresponding foreign-specific counterpart.
- Standard errors / t-ratios are calculated using White’s heteroscedasticity-consistent variance estimator.
- Key empirical findings:
  - Growth rate of real equity prices (gequ):
    - Impact elasticities are statistically significant for most countries.
    - All values are positive, either greater or lower than one.
    - Interpretation: impact elasticities greater than one indicate domestic overreaction to a variation in real equity prices of financial partners; elasticities lower than one indicate underreaction.
    - Implication: strong co-movements in equity prices’ dynamics across countries and anticipated strong synchronization of GIRFs associated with changes in real equity prices across regions.
  - Rate of growth of real credit to corporations (gcc):
    - Almost all coefficient estimates are not statistically significant.
    - Implication: no evidence of strong international linkages across countries concerning national dynamics of real credit to corporations.
  - Rate of growth of real GDP (ggdp) and real interbank rate (ibk):
    - Estimated impact elasticities are seldom statistically significant.
    - Implication: no striking evidence of linkages across countries for these variables.

### Dynamic analysis — methodology
- Method: Generalized Impulse Response Functions (GIRFs) as proposed by Koop, Pesaran and Potter (1996) and developed in Pesaran and Shin (1998) for vector error-correcting models.
- GIRF characteristics:
  - Does not orthogonalize residuals; accounts for historical correlations via the estimated variance-covariance matrix.
  - Does not require a priori economic-based restrictions and is invariant to variable ordering.
  - Since shocks are not identified, GIRFs do not provide information about causal relationships — limiting for policy simulation — but advantageous in multi-country frameworks like the GVAR.
- Simulation exercise:
  - A negative one standard error shock to the US growth rate of real equity prices is simulated to assess interregional financial spillovers (one standard error is set following common empirical practice).
  - Dynamic responses analyzed over a time horizon of 2 years (short-run macroeconomic inference).
  - Confidence intervals at the 68 percent significance level are calculated using the sieve bootstrap technique with 1000 replications.

### GIRF empirical results — regional responses to a one standard error negative US equity shock
- General note: with few exceptions, responses are statistically not significant using custom confidence intervals, reflecting estimator inefficiency given only 95 monthly observations. Analysis focuses on synchronization of dynamics across regions rather than statistical significance of individual signs.

- Real equity prices (Figure 3):
  - US response:
    - instantaneous fall of 2.86 percent;
    - increases over time until it reaches a peak after four months (equal to a 2.37 percent decrease);
    - reaches 3.17 percent below the baseline after two years.
  - Other regions:
    - Generally display synchronized dynamics with the US, indicating strong interrelation of equity markets, particularly for countries with mature financial systems.
    - Southeastern European countries: mainly self-driven GIRF dynamics, implying a low degree of financial integration with the rest of the world.

- Real credit to corporations (Figure 4):
  - US response:
    - on impact, a 0.15 percent decline;
    - minimum of 0.32 percent below the pre-shock level after four months;
    - after two years, the effect averages a 0.27 percent decrease with respect to the baseline.
  - Other developed European countries:
    - start on impact from the zero line, rapidly falling 0.2 percent below it, stabilizing around that level.
  - Baltic and Central-eastern European countries:
    - decrease in the short run, return over time to initial levels.
  - Euro Area:
    - credit growth hardly increases above its pre-shock level.
  - Southeastern European countries:
    - fluctuate considerably; increase during initial months, peak after four months (0.14 percent increase), complete reabsorption after two years.
  - Implication: credit growth responses are mainly region-specific, denoting that national credit developments do not follow common international dynamics.

- Real GDP growth rates (Figure 5):
  - General decrease in GIRFs across all regions; dynamic behaviors moderately correlated.
  - US:
    - GIRF monotonically decreases over time and stabilizes after two years to 0.13 percent below the pre-shock level.
  - Euro area and other developed European countries:
    - GIRFs mildly decrease over time, both reaching levels which average 0.05 percent below the zero line.
  - Other regions:
    - Behave differently in the first months but stabilize below baseline after two years.
  - Implication: considerable international co-movement of real growth among regions.

- Real interbank rates (Figure 6):
  - Majority of GIRFs decrease over time.
  - US real interbank rate:
    - decreases on impact by 8 basis points;
    - averages 14 basis points below baseline after two years.
  - Other developed European countries:
    - overreact; minimum after four months (28 basis points decrease), stabilizing around a 27 basis points loss.
  - Southeastern European countries:
    - diverge from other regions; increase, reaching a 7 basis points increase after three months, returning to the zero line after 15 months.

### Generalized Forecast Error Variance Decompositions (GFEVD) — key allocations
- Results reported in Table 10 (summary from the text):
  - Following the historical shock to the US growth rate of real equity prices, among the US variables:
    - On impact contributions to the variance of the historical shock:
      - real equity prices: 42.43 percent;
      - real credit to corporations: 7.24 percent;
      - real interbank rate: 6.11 percent;
      - real GDP: 0.05 percent.
    - After one year contributions:
      - real equity prices: 9.66 percent;
      - real credit: 15.82 percent;
      - real GDP: 12.67 percent;
      - real interbank rate: 7.38 percent.
    - After two years relative contributions (in decreasing order):
      - 17.38 percent for the real GDP growth;
      - 15.21 percent for the real credit growth;
      - 7.17 percent for the real interbank rate;
      - and

*Source: _wp0923 - 3. The weak exogeneity assumption*

### 7.12 percent for the real equity prices growth. Hence, as a first result, we observe that among

### _wp0923 - 7.12 percent for the real equity prices growth. Hence, as a first result, we observe that among

### Short-run vs. long-run transmission of the historical US equity-price shock
- Initial observed shock magnitude: 7.12 percent for the real equity prices growth.
- Short run:
  - Among US variables, the variable which explains most of the variance of the shock on impact is the real equity prices growth.
  - On impact, the US (domestic innovations) explains most of the variance of the shock in the short run: 55.83 percent.
  - Across other regions on impact, the largest foreign regional contributors to the variance are:
    - Other developed European countries: 11.26 percent
    - Baltic countries: 10.23 percent
- After two years (longer horizon):
  - The relative importance of real equity price growth decreases over time; other domestic variables gain increasing relevance.
  - After two years, real credit growth, real GDP growth, and real interbank rate explain most of the variance of the shock; the order of importance of these three variables is generally region-specific.
  - Regional contributions change over time; after two years:
    - Other developed European countries explain 15.72 percent of the shock.
    - Euro area explains 13.62 percent.
  - In the longer term, the forecast error variance of the historical shock is mainly explained by foreign variables: 53.12 percent.

### Key numerical variance-decomposition profile (Table 10)
- Table 10 header months: 0 1 2 4 8 12 24
- US Variables (percentage of k-step ahead forecast error variance attributable to each US domestic variable)
  - gequ: 42.43, 35.64, 29.65, 20.98, 12.74, 9.66, 7.12
  - gcc: 7.24, 9.28, 11.18, 13.85, 15.66, 15.82, 15.21
  - ggdp: 0.05, 0.07, 0.45, 2.50, 8.39, 12.67, 17.38
  - ibk: 6.11, 6.67, 7.20, 7.73, 7.65, 7.38, 7.17
  - US Vars (aggregate): 55.83, 51.67, 48.48, 45.06, 44.45, 45.53, 46.88
- Selected Non-US regional aggregates (aggregate contribution to shock variance at same horizons)
  - Euro Area (EA Vars): 9.47, 9.66, 10.21, 10.84, 11.40, 12.13, 13.62
  - Other Developed European countries (OTH Vars): 11.26, 15.03, 17.07, 18.73, 18.25, 17.14, 15.72
  - Baltic countries (BALT Vars): 10.23, 10.93, 11.43, 12.28, 12.47, 11.38, 9.23
  - South-Eastern Europe (SEE Vars): 3.34, 2.89, 2.66, 2.34, 1.96, 1.84, 1.75
  - Central-Eastern Europe (CEE Vars): 9.86, 9.82, 10.15, 10.76, 11.47, 11.98, 12.81
  - Non-US Vars (aggregate): 44.17, 48.33, 51.52, 54.94, 55.55, 54.47, 53.12
- Total (rescaled for readability): 100.00 at each reported horizon (note: percentages do not sum to 100 due to non-zero covariance between shocks; rescaled as in source).

### Methodology and data linkages
- Modeling framework: Global Vector Autoregression (GVAR) model that:
  - Generates forecasts for a core set of macroeconomic and financial factors for a set of regions and countries.
  - Explicitly allows for interdependencies between national and international factors via systematic inclusion of country-specific foreign variables in individual country models.
- Novel linkage in this study: Each country is linked to the rest of the world economy using cross-country financial flows from international banking statistics — specifically, annual bank lending exposures over the period 1999-2007.
- Financial weights source: Bank of International Settlements; Quarterly Review, December 2007 (weights used to construct country-specific foreign variables and connections).

### Substantive findings on transmission channels and dynamics
- Financial shocks are transmitted relatively quickly and often get amplified traveling from the US to the euro area.
- Equity markets are more synchronous internationally compared to banking systems.
- Short-run transmission channel: asset prices are the main channel through which financial shocks are transmitted internationally.
- Longer-horizon transmission channels: cost and quantity of credit (real credit growth and interbank rates) and real GDP growth start playing a significant role.
- Interregional linkages matter: the relative contribution of each region to forecast error variance highlights geographic transmission patterns and vulnerabilities.

### Policy-relevant observations and implications
- Greater financial integration and increased cross-border ownership of assets:
  - Are associated with better growth opportunities, with the link stronger where integration is faster.
  - Can amplify business cycle fluctuations and the impact of asset price movements on real activity by strengthening cross-border financial spillovers.
- European vulnerabilities:
  - Sizable cross-border financial linkages across Europe highlight vulnerabilities from reliance on concentrated foreign funding.
  - International banking statistics suggest most emerging European economies are heavily exposed to—and dependent on—western banks (either directly or through local borrowing systems).
- GVAR framework utility:
  - Presents a manageable spatio-temporal structure for analyzing international transmission of financial shocks and second-round effects.
  - Can be modified and extended according to policy interests.

*Source: _wp0923 - 7.12 percent for the real equity prices growth. Hence, as a first result, we observe that among (PDF chapter/section).*

### REFERENCES

### _wp0923 - REFERENCES

### References

- Bickel, P. J. & Buhlmann, P. (1999), ‘A New Mixing Notion and Functional Central Limit Theorems for a Sieve Bootstrap in Time Series’,Bernoulli5(3), 413–446.
- Buhlmann, P. (1997), ‘Sieve bootstrap for time series’,Bernoulli3(2), 123–148.
- De Nicol`o, G. & Ivaschenko, I. (2008), Financial integration and risk-adjusted growth opportunities, IMF Working Paper 08/126, International Monetary Fund.
- D ́ees, S., di Mauro, F., Pesaran, M. H. & Smith, L. V. (2007), ‘Exploring the international linkages of the euro area: a global VAR analysis’,Journal of Applied Econometrics 22(1), 1–38.
- Garratt, A., Lee, K., Pesaran, M. H. & Shin, Y. (2003), ‘A Long run structural macroeconometric model of the UK’,Economic Journal113(487), 412–455.
- Harbo, I., Johansen, S., Nielsen, B. & Rahbek, A. (1998), ‘Asymptotic Inference on Cointegrating Rank in Partial Systems’,Journal of Business & Economic Statistics 16(4), 388–399.
- Hiebert, P. & Vansteenkiste, I. (2007), International trade, technological shocks and spillovers in the labour market; a GVAR analysis of the US manufacturing sector, Working Paper Series 731, European Central Bank.
- IMF (2008),Regional Economic Outlook: Europe, International Monetary Fund, Washington.
- Johansen, S. (1992), ‘Cointegration in partial systems and the efficiency of single-equation analysis’,Journal of Econometrics52(3), 389–402.
- Johansen, S. (1995),Likelihood-Based Inference in Cointegrated Vector Autoregressive Models, Oxford University Press, Oxford.
- Koop, G., Pesaran, M. H. & Potter, S. M. (1996), ‘Impulse response analysis in nonlinear multivariate models’,Journal of Econometrics74(1), 119–147.
- Kreiss, J. P. (1989), Bootstrap procedures for AR(∞)-processes.,inK. H. Jockel, G. Rothe & W. E. Sendler, eds, ‘Bootstrapping and Related Techniques. Lecture Notes in Economics and Mathematical Systems’, Vol. 376, Springer-Verlag, Heidelberg, pp. 107–113.
- MacKinnon, J. G., Haug, A. A. & Michelis, L. (1999), ‘Numerical Distribution Fuctions of Likelihood Ratio Tests for Cointegration’,Journal of Applied Econometrics 14(5), 563–577.
- McGuire, P. & Wooldridge, P. (2005), ‘The bis consolidated banking statistics: Structure, uses and improvements’,BIS Quarterly Review.
- Park, H. J. & Fuller, W. A. (1995), ‘Alternative Estimatiors and Unit Root Tests for the Autoregressive Process’,Journal of Time Series Analysis16(4), 415–429.
- Pesaran, M. H., Schuermann, T. & Weiner, S. M. (2004a), ‘Modelling Regional Interdependencies using a Global Error-Correcting macro-econometric model’,Journal of Business and Economic Statistics22(2), 129–162.
- 32
- Pesaran, M. H., Schuermann, T. & Weiner, S. M. (2004b), ‘Rejoinder to Comments on Modelling Regional Interdependencies using a Global Error-Correcting macro-econometric model’,Journal of Business and Economic Statistics22(2), 175–181.
- Pesaran, M. H. & Shin, Y. (1998), ‘Generalized impulse response analysis in linear multivariate models’,Economics Letters58(1), 17–29.
- Pesaran, M. H., Shin, Y. & Smith, R. J. (2000), ‘Structural analysis of vector error correction models with exogenous I(1) variables’,Journal of Econometrics97(2), 293–343.
- Sims, C. A. (1980), ‘Macroeconomics and Reality’,Econometrica48(1), 1–48.
- Vansteenkiste, I. (2007), Regional housing market spillovers in the US - lessons from regional divergences in a common monetary policy setting, Working Paper Series 708, European Central Bank.
- Wang, P. J. (2002),Financial Econometrics: Methods and Models., Routledge, London.

*Source: _wp0923 - REFERENCES*

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