## wp1846 — "13. Peripheral Lenders: Interaction with Global Banks’ Retrenchment"

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### Introduction and purpose
- Documents structural change after the GFC: total cross-border banking lending shrunk while lender–borrower connections within the same region—especially in the periphery—expanded (regionalization).
- Objective:
  - Analyze drivers of regionalization for direct cross-border lending (CB) and foreign affiliates’ local lending (S).
  - Account for multidimensional drivers (geography, culture, institutions, regulation, retrenchment), extensive vs intensive margins, and bank heterogeneity (productivity, size, profitability).
- Data:
  - BIS Consolidated Banking Statistics (CBS) at ultimate risk basis covering 28 BIS reporting countries and over 160 non-reporting countries from 2005Q1 to 2016Q2.
  - Flows: Flow_X_ijt = max(X_ijt − X_ij(t−4), 0).
  - Local affiliate claims adjusted to exclude local deposit funding following Cerutti (2015).

### Theoretical framework and empirical strategy
- Gravity-style model combining Helpman–Melitz–Rubinstein (2008)-style extensive/intensive margins with latent bank heterogeneity and a Heckman-style selection term.
- Modes of internationalization: direct cross-border lending (CB) and foreign affiliates’ local lending (S: subsidiaries/branches).
- Key model elements:
  - Bank-specific inverse efficiency parameter a ~ Pareto (shape k, k>max{εCB, εS}).
  - Fixed and monitoring costs are country-pair and bank-specific; τ captures multiplicative variable cost; distance enters multiplicatively.
- Two-stage estimation:
  - First stage: Probit for extensive margin (T_x_ij) → predict inverse Mills ratio and latent ẑ_x*_ij.
  - Second stage: non-linear MLE for intensive margin (log flow) including log{exp[δ(ˆz_x*+ˆη_x*)]−1} and Heckman correction term β·ˆη.

### Baseline empirical findings
- Traditional gravity determinants:
  - Borrower GDP and trade (FTA) positively associated with connection probability and flow size.
  - Common legal system and colonial ties positively associated with both margins.
  - Geographical distance strong negative effect:
    - elasticity of direct cross-border flows w.r.t. geographical distance ≈ -1 (examples: Log Distance −0.984***, −0.966***, −0.964***, −0.940*** in Table A9).
    - elasticity of local affiliate flows w.r.t. geographical distance ≈ -1.4 (examples in Table A10: −1.363***).
- Bank heterogeneity and selection:
  - δ (non-linear adjustment) highly significant for both CB and S.
  - β (inverse Mills / selection term) significant → selection into lending matters.
- Regionalization pattern:
  - Regionalization exists beyond gravity variables and is stronger at the extensive margin.
  - Particularly pronounced among peripheral lenders in EMs and non-core systems (examples: Australia, Canada, Hong Kong, Singapore).
  - Regionalization increased for peripheral lenders since the GFC and decreased among core lenders during/after the GFC.
  - Much of the regional effect manifests at the extensive margin; intensive-margin effects are weaker.

### Distinguishing regional effect from gravity interactions
- Regional dummy captures more than geography; interaction analysis shows:
  - Region × Log Distance positive in first stage (regional proximity reduces distance barrier at extensive margin).
  - Region × Legal positive at intensive margin (shared legal origin matters more within region).
  - Peripheral lenders drive post-crisis regionalization (Region * Peripheral * Post-crisis positive and significant in multiple specifications, e.g., 0.171*** in Table A1; 0.690*** in Table A5).

### Additional drivers tested
- Regulation (Barth, Caprio, Jr, and Levine (2013) bank activity restriction indices):
  - First stage: Region × borrower regulation index significantly positive; Region × lender–borrower regulatory distance significantly negative.
  - Second stage: region × borrower-regulation interaction positive and significant for CB and affiliates → within-region connections/flows associated with changes in regulatory restrictiveness.
  - Post-crisis evidence consistent with banks expanding within-region into countries with stricter regulations (regional banks adapting to tighter global policy environment rather than regulatory arbitrage to lighter regulation).
- Trade linkages (lender’s export to borrower as share of borrower’s total imports):
  - Small contributions; first-stage interactions of region with export share small and sometimes negative; intensive-margin interactions weak/close to zero.
- Global banks’ retrenchment (peripheral lenders filling gaps):
  - Retrenchment proxies: ∆Share of exposure of core / European lenders experiencing systemic banking crises to a borrower (4-quarter differences); ∆Bank presence: change in number of banks in borrower country owned by stressed advanced lenders (t−1 minus t−2).
  - First-stage: strong evidence peripheral lenders expanded within-region local affiliate connections where advanced stressed global banks reduced presence (region × retrenchment × post-crisis significant).
  - Interpretation: peripheral lenders increased local affiliate presence to substitute for retrenching core/European lenders, clearest for local affiliates; weaker evidence for direct cross-border substitution.
  - Second-stage: peripheral lenders’ intensive-margin expansions have not fully matched funding levels of former global banks (insignificant second-stage coefficients in some specs).

### Policy-relevant implications and considerations
- Persistence and drivers:
  - Regionalization since the GFC is persistent, driven by structural reallocation after European retrenchment and synergies with gravity factors (distance, legal origin).
- Potential benefits:
  - Easier regional coordination and supervisory collaboration where regional banks dominate (example: Vienna Initiative experience).
  - Regional banks may reduce the export of large credit booms by global banks if they operate at smaller scales.
- Potential risks:
  - Increased regional fragmentation could reduce risk-sharing and raise vulnerability to regional shocks.
  - New regional lenders may lack cross-border monitoring experience; EM regional banks’ funding structures may be limited and more sensitive to regional shocks.
  - Post-crisis regulatory framework changes (e.g., regional banks expanding into stricter-regulation neighbors) may not foster a diverse global banking environment.
- Conclusion: increase in regionalization—driven by peripheral lenders and associated with European retrenchment and regulatory changes—warrants further research on financial stability and growth implications.

### Robustness and alternative estimation methods (selected exact estimates and diagnostics)
- Alternative regional classifications (World Bank and IMF) largely confirm baseline findings: peripheral lenders as key regional players evolved since the crisis.
- Select first-stage Probit (WB grouping, Table A1):
  - Region: 0.0333***, 0.106***, −0.0329**, 0.0588***.
  - Region * Crisis: −0.0708***, −0.0794***.
  - Region * Post-crisis: −0.0866***, −0.115***.
  - Region * Peripheral: 0.192***, 0.0714***.
  - Region * Peripheral * Crisis: 0.0650***.
  - Region * Peripheral * Post-crisis: 0.171***.
  - N: 139216; Pseudo R-sq: 0.2240, 0.2260, 0.2280, 0.231.
- First-stage (WB grouping) local affiliates (Table A2):
  - Region: 0.0480***, 0.0602***, 0.0433**, 0.0597***.
  - Region * Post-crisis: −0.0161*, −0.0236***.
  - Region * Peripheral * Post-crisis: 0.0542**.
  - N: 91996; Pseudo R-sq: 0.2620–0.263.
- Second-stage (WB grouping) direct cross-border (Table A5):
  - Region: 0.479***, 0.451***, 0.1140, 0.208.
  - Region * Peripheral: 0.839***, 0.506***.
  - Region * Peripheral * Post-crisis: 0.690***.
  - N: 37625; Lender + Borrower FE: YES; Quarter FE: YES.
- Non-linear least squares / MLE (Tables A9–A10):
  - Direct cross-border: Region * Peripheral: 0.806***, 0.606***.
  - Local affiliate: Region * Peripheral * Post-Crisis: 1.367**.
  - Gravity examples (Table A9):
    - Language: 0.157, 0.152, 0.190*, 0.188*.
    - Colonizer: 0.464***, 0.453***, 0.392**, 0.387**.
    - Legal: 0.153**, 0.150**, 0.150**, 0.148**.
    - Log Distance: −0.984***, −0.966***, −0.964***, −0.940***.
    - Lender Log GDP: 0.809**, 0.809**, 0.790**, 0.758**.
    - Borrower Log GDP: 0.693***, 0.674***, 0.683***, 0.653***.
  - R-squared: ~0.678–0.680 (direct CB); ~0.546–0.548 (local affiliates).
- Semiparametric (polynomials of z, Table A11):
  - Direct cross-border: Region * Peripheral: 0.815**, 0.504***.
  - Polynomial z terms significant (examples): z: −77.87***; z^2: 137.3***; z^3: −115.5***; z^4: 46.32***; z^5: −7.163***.
  - R-sq: 0.680–0.682 (CB); 0.548–0.550 (S).
- PPML (Table A12):
  - Direct cross-border: Region * Peripheral: 1.301***, 0.523**; Region * Peripheral * Post-Crisis: 1.448***, 0.756.
  - Region * Crisis / Region * Post-crisis often negative and significant for CB (e.g., Region * Crisis: −0.545***, −0.538***; Region * Post-crisis: −0.783***, −0.917***).
  - Log Distance examples: −0.372***, −0.361***, −0.405***, −0.397*** (CB); −0.794*** … −0.811*** (S).
  - Borrower Log GDP positive (examples: 1.175***, 1.008***, 1.175***, 0.894*** for CB).
  - PPML preserves zero flows but lacks latent productivity model; aligns with baseline for CB, weaker for S.
- OLS second-stage (Table A13) and OLS on log differences (Table A16):
  - OLS example coefficients (CB): Log Distance −0.975***, −0.976***, −0.959***, −0.957***; Lender Log GDP: 0.939***, 0.948***, 0.957***, 0.773***; Borrower Log GDP: 0.601***, 0.576***, 0.612***, 0.494***.
  - OLS on year-over-year growth yields poor fit: R-sq 0.038–0.039 (CB); 0.064–0.066 (S); Log Distance often insignificant.

### Key empirical takeaways (preserving reported estimates)
- Common region indicator and interactions:
  - Positive and significant triple-interaction estimates (examples): Region * Peripheral * Post-crisis: 0.171*** (Table A1 first-stage); 0.690*** (Table A5 second-stage).
  - Large Region * Peripheral second-stage coefficients: 0.806*** (Table A9), 0.839*** (Table A5), 1.301*** (Table A12 PPML).
- Distance deterrent examples:
  - Log Distance −0.984*** (Table A9), −1.363*** (Table A10), −0.975*** (Table A13).
- Gravity variables positive and consistent:
  - Legal 0.153**, Colonial Relation 0.840*** (examples), Language 0.157 (Table A9).
- Selection and non-linearity matter:
  - δ and β examples (Table A9): δ: 0.148, 0.157, 0.149, 0.211; β: 0.803*, 0.717, 0.819*, 0.763*.
  - Ignoring selection/non-linearities biases estimates, especially for local affiliate flows.

*Source: IMF Working Paper — "13. Peripheral Lenders: Interaction with Global Banks’ Retrenchment", wp1846 (chapter/section and appendix material supplied).*

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

### References

### Appendix
- A.Additional Estimation Results    .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .44
- A.1. Alternative Regional Groupings  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .44
- A.2. Alternative Methods   .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .49
- A.3. Gravity Factor Interactions, Alternative Definition of Flow  .  .55

### List of Tables
- 1.Summary Statistics   .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .19
- 2.List of CBS Reporting Countries, Regional Classification and Grouping   .  .21
- 3.Baseline Regional Grouping: First Stage – Direct Cross-Border  .  .  .23
- 4.Baseline Regression: First Stage – Local Affiliate   .  .  .  .  .  .  .  .24
- 5.Baseline Estimation: Second Stage – Direct Cross-Border  .  .  .  .  .  .25
- 6.Baseline Estimation: Second Stage – Local Affiliates   .  .  .  .  .  . 26
- 7.Region as an Interaction Term – First Stage    .  .  .  .  .  .  .  .  .  .28
- 8.Region as an Interaction Term – Second Stage  .  .  .  .  .  .  .  .  .  .29
- 9.Variable Definitions: Interaction Variables   .  .  .  .  .  .  .  .  .  .32
- 10.    Summary Statistics: Additional Interaction Variables    .  .  .33
- 11.    Interaction with Bank Activity Restrictions .  .  .  .  .  .  .  .34
- 12.    Interaction with Trade Linkages    .  .  .  .  .  .  .  .  .  .  .35

*Source: wp1846 - References (wp1846.pdf).*

### 13.    Peripheral Lenders: Interaction with Global Banks’ Retrenchment    .  .  .  .  .  .  .  .  .36

### 13.    Peripheral Lenders: Interaction with Global Banks’ Retrenchment

### Introduction and purpose
- Documents a structural change in the global banking network after the global financial crisis (GFC): total cross-border banking lending shrunk, driven by sharp reduction in cross-border lending by most European banking systems, while lender–borrower connections within the same region—especially in the periphery—expanded (regionalization).
- Objective: move beyond documentation to analyze the nature and drivers of regionalization for both direct cross-border lending and foreign affiliates’ local lending, accounting for:
  - multidimensional drivers (geography, culture, institutions, regulation, retrenchment);
  - extensive margin (lending / no-lending decisions) and intensive margin (quantity of flows);
  - bank heterogeneity (productivity, size, profitability).
- Data: BIS Consolidated Banking Statistics (CBS) at ultimate risk basis covering 28 BIS reporting countries and over 160 non-reporting countries from 2005Q1 to 2016Q2 (with sample restrictions in parts of the estimation).

### Theoretical framework and empirical strategy
- Model: gravity-style model of bank internationalization combining Helpman, Melitz, and Rubinstein (2008)-style treatment of extensive and intensive margins with latent bank heterogeneity and a Heckman-style selection term.
- Modes of internationalization distinguished:
  - direct cross-border lending (CB);
  - foreign affiliates’ local lending (S: subsidiaries/branches).
- Key assumptions and structure:
  - bank-specific inverse efficiency parameter a drawn from a Pareto distribution (shape parameter k, k>max{εCB, εS});
  - fixed costs and monitoring costs are country-pair and bank-specific;
  - τ captures multiplicative variable cost; distance enters multiplicatively.
- Two-stage estimation:
  - First stage: Probit for the extensive margin (connection indicator T_x_ij); predict inverse Mills ratio and a predicted latent z_x*_ij.
  - Second stage: non-linear (estimated by maximum likelihood) equation for the intensive margin (log flow) including log{exp[δ(ˆz_x*+ˆη_x*)]−1} and the Heckman correction term β·ˆη.
- Data adjustments: local affiliate claims adjusted to exclude local deposit funding following Cerutti (2015); flows defined as positive 4-quarter differences: Flow_X_ijt = max(X_ijt − X_ij(t−4), 0).

### Baseline empirical findings (summarized)
- Traditional gravity determinants work as expected:
  - Borrower GDP and trade (FTA) positively associated with both the probability of a connection and the level of flows.
  - Common legal system and colonial ties positively associated with both margins.
  - Geographical distance has a strong negative effect:
    - elasticity of direct cross-border flows with respect to geographical distance is close to -1.
    - elasticity of local affiliate flows with respect to geographical distance is around -1.4.
- Role of bank heterogeneity and selection:
  - δ (non-linear adjustment parameter) is highly significant for both direct cross-border and local affiliate flows, indicating important unobserved bank-level heterogeneity.
  - β (inverse Mills / selection term) is significant, indicating selection into lending matters for consistent estimation.
- Regionalization pattern:
  - Regionalization is present beyond traditional gravity variables and is more prevalent at the extensive margin.
  - It is particularly pronounced among peripheral lenders in EMs and non-core banking systems (explicit examples: Australia, Canada, Hong Kong, Singapore).
  - Regionalization was present before the GFC but increased for peripheral lenders since the GFC and decreased among core lenders during and after the GFC.
  - Much of the regional effect is manifested at the extensive margin (connections), with second-stage intensive-margin effects weaker (some regional effects already absorbed in extensive margin).

### Distinguishing regional effect from interactions with gravity factors
- The regional dummy captures more than plain geography and overlaps with other gravity characteristics; interaction analysis shows:
  - Regional proximity dampens the barrier imposed by geographical distance at the extensive margin (Region * Log Distance interaction positive in first stage).
  - Regional proximity increases the role of shared legal origin at the intensive margin (positive interaction of Region and Legal at intensive margin).
  - After accounting for interactions, peripheral lenders have a markedly different regional effect than the baseline regional dummy—i.e., peripheral lenders act as the drivers of post-crisis regionalization.

### Additional drivers tested: regulation, trade linkages, and global banks’ retrenchment
- Regulatory environment
  - Used Barth, Caprio, Jr, and Levine (2013) bank activity restriction indices assigned to pre-crisis, crisis, and post-crisis periods.
  - Findings:
    - First-stage: interaction of common region with borrower regulation index is significantly positive; interaction of common region with lender–borrower regulatory distance is significantly negative.
    - Second-stage: positive and significant coefficient for the region × borrower-regulation interaction (direct CB and local affiliate), implying within-region connections and flows are associated with changes in regulatory restrictiveness measures.
    - Post-crisis: evidence consistent with banks expanding within-region into countries with stricter regulations (i.e., regional banks adapting to tighter global policy environment rather than pursuing regulatory arbitrage toward lighter regulation).
- Trade linkages
  - Measured as lender’s export to borrower as share of borrower’s total imports.
  - Findings:
    - Small contributions. First-stage interactions of region with export share are small (some negative marginal effects) and significant but overall trade linkages are not a strong driver of the regionalization trend once gravity controls are included.
    - Intensive-margin interactions are weak and close to zero.
- Global banks’ retrenchment (peripheral lenders filling gaps)
  - Restricted sample to peripheral lenders; constructed retrenchment proxies:
    - ∆Share of exposure of core / European lenders experiencing systemic banking crises to a borrower (4-quarter differences for exposure).
    - ∆Bank presence: change in number of banks in borrower country owned by stressed advanced lenders (transformed as year t−1 minus t−2).
  - Findings:
    - First-stage (extensive margin): strong evidence that peripheral lenders expanded within-region local affiliate connections where advanced stressed global banks reduced presence (post-crisis triple interaction region × retrenchment × post-crisis significant and negative margin coefficients reflect substitution).
    - Interpretation: peripheral lenders increased local affiliate presence (branches/subsidiaries and claims) to take advantage of retrenchment by core/European lenders, especially after the crisis. This is clearest for local affiliate connections; evidence for direct cross-border substitution is weaker.
    - Second-stage: peripheral lenders’ intensive-margin expansions have not fully matched the funding levels of the former global banks (insignificant second-stage coefficients in some specifications).

### Policy-relevant implications and considerations
- The regionalization trend since the GFC appears persistent and driven by both structural factors (reallocation after European retrenchment) and synergies with traditional gravity factors (distance, legal origin).
- Potential benefits:
  - Easier regional coordination and supervisory collaboration may be achievable where regional banks dominate (example: Vienna Initiative experience).
  - Regional banks may reduce chances of large global banks exporting credit booms to local markets if they operate at smaller scales.
- Potential risks:
  - Increased regional fragmentation could reduce risk-sharing and raise vulnerability to regional shocks.
  - New regional lenders may lack experience monitoring cross-border activities; EM regional banks’ funding structures may be more limited and more sensitive to regional shocks.
  - Changes in post-crisis regulatory frameworks (e.g., regional banks expanding into tighter-regulation neighbors) may not foster a diverse or inclusive global banking environment.
- Conclusion: the increase in regionalization, especially driven by peripheral lenders and partly associated with retrenchment of European lenders and regulatory changes, merits further research on its financial stability and growth implications.

*Source: IMF Working Paper — "13.    Peripheral Lenders: Interaction with Global Banks’ Retrenchment", wp1846 (chapter/section text supplied).*

### REFERENCES

### wp1846 - REFERENCES (Appendix material summary)

### Robustness of regional grouping results
- Alternative regional classifications (World Bank and IMF) largely confirm baseline findings that "the role of peripheral lenders as key regional players in the global banking network has evolved and developed significantly since the crisis."
- Select first-stage Probit coefficients (WB regional grouping, Table A1):
  - Region: 0.0333***, 0.106***, -0.0329**, 0.0588***
  - Region * Crisis: -0.0708***, -0.0794***
  - Region * Post-crisis: -0.0866***, -0.115***
  - Region * Peripheral: 0.192***, 0.0714***
  - Region * Peripheral * Crisis: 0.0650***
  - Region * Peripheral * Post-crisis: 0.171***
  - N: 139216; Pseudo R-sq: 0.2240, 0.2260, 0.2280, 0.231
- First-stage (WB grouping) for local affiliates (Table A2):
  - Region: 0.0480***, 0.0602***, 0.0433**, 0.0597***
  - Region * Post-crisis: -0.0161*, -0.0236***
  - Region * Peripheral * Crisis: -0.0295*
  - Region * Peripheral * Post-crisis: 0.0542**
  - N: 91996; Pseudo R-sq: 0.2620–0.263
- IMF regional grouping, first-stage direct cross-border (Table A3):
  - Region: 0.0462***, 0.0986***, -0.00328, 0.0748***
  - Region * Crisis: -0.0474***, -0.0588***
  - Region * Post-crisis: -0.0633***, -0.0980***
  - Region * Peripheral: 0.159***, 0.0537***
  - Region * Peripheral * Post-crisis: 0.152***
  - N: 139216; Pseudo R-sq: 0.2250–0.230
- Second-stage (WB grouping) direct cross-border (Table A5):
  - Region: 0.479***, 0.451***, 0.1140, 0.208
  - Region * Peripheral: 0.839***, 0.506***
  - Region * Peripheral * Crisis: 0.246*
  - Region * Peripheral * Post-crisis: 0.690***
  - N: 37625 (multiple columns); Lender + Borrower FE: YES; Quarter FE: YES

### Alternative estimation methods and their main outcomes
- Non-linear least squares / MLE (second stage, Tables A9–A10):
  - Direct cross-border (Table A9): Region * Peripheral: 0.806***, 0.606***; Region: -0.0591, -0.0479, -0.405***, -0.318*** (columns vary).
  - Local affiliate (Table A10): Region * Peripheral * Post-Crisis: 1.367** (column 4).
  - Notable gravity and control coefficients (Table A9, column examples):
    - Language: 0.157, 0.152, 0.190*, 0.188*.
    - Colonizer: 0.464***, 0.453***, 0.392**, 0.387**.
    - Legal: 0.153**, 0.150**, 0.150**, 0.148**.
    - Log Distance: -0.984***, -0.966***, -0.964***, -0.940***.
    - Lender Log GDP: 0.809**, 0.809**, 0.790**, 0.758**.
    - Borrower Log GDP: 0.693***, 0.674***, 0.683***, 0.653***.
  - R-squared around 0.678–0.680 for direct cross-border; R-squared around 0.546–0.548 for local affiliates (Tables A9–A10).
- Semiparametric approach (polynomials of z from first-stage Probit, Table A11):
  - Direct cross-border: Region * Peripheral: 0.815**, 0.504*** (columns vary).
  - Polynomial terms (z powers) appear significant for cross-border: z: -77.87***, -77.49***, -73.69***, -70.08***; z^2: 137.3***, 135.4***, 132.8***, 124.2***; z^3: -115.5***, -112.5***, -113.1***, -103.7***; z^4: 46.32***, 44.48***, 45.90***, 41.11***; z^5: -7.163***, -6.770***, -7.163***, -6.270***.
  - R-sq for cross-border: 0.680–0.682; for local affiliate: 0.548–0.550.
- Poisson pseudo-maximum likelihood (PPML, Table A12):
  - Direct cross-border: Region * Peripheral: 1.301***, 0.523** (columns differ); Region * Peripheral * Post-Crisis: 1.448***, 0.756.
  - Region * Crisis and Region * Post-crisis coefficients often negative and significant for direct cross-border (e.g., Region * Crisis: -0.545***, -0.538***; Region * Post-crisis: -0.783***, -0.917***).
  - Log Distance negative and significant for cross-border and local affiliate (e.g., -0.372***, -0.361***, -0.405***, -0.397*** for cross-border; -0.794*** … -0.811*** for local affiliates).
  - Borrower Log GDP positive and significant across methods (e.g., PPML direct: 1.175***, 1.008***, 1.175***, 0.894***).
  - Notes: PPML preserves zero flows but lacks a model-based account for latent productivity causing zeros; PPML results align with baseline for direct cross-border but are weaker for local affiliates.
- OLS (log-linear counterpart, Table A13; OLS on log differences reported in Table A16):
  - OLS second-stage (Table A13) yields similar patterns for many gravity factors but lacks non-linear and Heckman adjustments; example coefficients:
    - Log Distance: -0.975***, -0.976***, -0.959***, -0.957*** (direct cross-border).
    - Lender Log GDP: 0.939***, 0.948***, 0.957***, 0.773*** (direct cross-border).
    - Borrower Log GDP: 0.601***, 0.576***, 0.612***, 0.494*** (direct cross-border).
  - OLS on log differences (Table A16) — using year-over-year growth as the flow variable — yields poor model fit (R-sq: 0.038–0.039 for cross-border; 0.064–0.066 for local affiliate) and sometimes counterintuitive signs (e.g., Log Distance often insignificant); authors caution growth-rate flows may be incompatible with time-invariant gravity factors.

### Gravity factor interactions and sample-period sensitivity
- Region interacted with static gravity factors (first- and second-stage on 2006Q1–2009Q2 sample, Tables A14–A15) finds:
  - First-stage (Table A14) signs and marginal effects:
    - Region: -0.316***, -0.312*** (direct cross-border); -0.0915, -0.0892 (local affiliate).
    - Region * Peripheral: 0.120***, 0.108** (direct cross-border).
    - Log Distance * Region: 0.0881***, 0.0742*** (direct cross-border), indicating distance effects differ inside vs outside region pre-/during-crisis.
    - N: 558545–585432 for direct cross-border; Pseudo R-sq: ~0.308–0.321.
  - Second-stage (Table A15) highlights regional peripheral effects pre-crisis:
    - Region * Peripheral: 1.303***, 1.039 (direct cross-border).
    - Log Distance: -1.090***, -0.984*** (direct cross-border).
    - δ and β estimates reported (e.g., δ: 0.212***, 0.282*; β: 1.409***, 1.471*** for direct cross-border).
    - σ estimates: 1.428***, 1.422*** (direct cross-border); σ: 2.047***, 2.044*** (local affiliate).
- Alternative flow definition (year-over-year growth, Table A16) produces:
  - Region: 0.0310**, 0.0990***, 0.0289*, 0.162*** (direct cross-border columns 1–4).
  - Region * Peripheral * Post-Crisis: 0.281*** (direct cross-border), 0.539*** (local affiliate).
  - Lender Log GDP and Borrower Log GDP retain some positive significance in OLS growth regressions, but Log Distance is generally insignificant, and overall R-squared is low (0.038–0.039 cross-border; 0.064–0.066 local affiliate).

### Key empirical takeaways (preserving reported estimates)
- The common region indicator and its interaction with peripheral lender status and post-crisis period often produce:
  - Positive and significant triple-interaction estimates in first-stage (e.g., Region * Peripheral * Post-crisis: 0.171*** in Table A1) and second-stage estimations (e.g., Region * Peripheral * Post-crisis: 0.690*** in Table A5).
  - Large positive Region * Peripheral coefficients in several second-stage specifications (e.g., 0.806*** in Table A9; 0.839*** in Table A5; 1.301*** in Table A12 PPML).
- Distance remains a strong deterrent to cross-border and affiliate flows across methods:
  - Examples: Log Distance -0.984*** (Table A9), -1.363*** (Table A10), -0.975*** (Table A13 OLS).
- Legal system, colonial ties, shared language, and FTA indicators consistently enter with positive coefficients in many specifications (examples: Legal 0.153**, Colonial Relation 0.840***, Language 0.157 in Table A9).
- Selection and non-linearity matter:
  - Non-linear adjustment term δ and Heckman inverse-Mills term β are estimated in non-linear specifications (e.g., δ: 0.148, 0.157, 0.149, 0.211 and β: 0.803*, 0.717, 0.819*, 0.763* in Table A9; Table A10 reports δ and β values for local affiliates).
  - Ignoring selection and non-linearities (plain OLS) can bias estimates, especially for local affiliate flows.

*Source: wp1846 - REFERENCES (appendix tables and notes, as provided).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2018/wp1846.pdf_