Overview

This vignette walks through the full replication pipeline that backs the paper “Two-Stage Detection and Attribution of Cross-Border Financial Contagion Channels”. The package contagionchannels exposes a deliberately small set of verbs that map one-to-one onto the empirical sections of the manuscript: a Stage 1 detection step that estimates a directed Wavelet-Quantile Transfer Entropy (WQTE) network, and a Stage 2 attribution step that decomposes the detected linkages into five economically interpretable channels (Trade, Financial, Geopolitical, Behavioral, Monetary_Policy) using a battery of identification strategies.

The headline numbers reproduced below are the ones reported in the published tables. Every code chunk is annotated so that a careful reader can follow how each row of Tables 1, 2, and 6 is built, and how Figures 1-7 are assembled. We intentionally make the most expensive Stage 1 estimation eval = FALSE so the vignette compiles in seconds; all illustrative chunks use a single sub-period to keep run-time below CRAN’s check threshold.

1. Setup

library(contagionchannels)
library(xts)
library(dplyr)
library(tidyr)
library(ggplot2)
library(igraph)
#> 
#> Attaching package: 'igraph'
#> The following object is masked from 'package:tidyr':
#> 
#>     crossing
#> The following objects are masked from 'package:dplyr':
#> 
#>     as_data_frame, groups, union
#> The following objects are masked from 'package:stats':
#> 
#>     decompose, spectrum
#> The following object is masked from 'package:base':
#> 
#>     union

The package leans on a handful of well-established CRAN dependencies: waveslim for the maximal-overlap discrete wavelet transform, quantreg for the conditional quantile machinery used inside WQTE, RTransferEntropy for shuffled bias correction, AER for IV/2SLS, hdm for Belloni-Chernozhukov- Hansen LASSO IV, lpirfs for local projections, and igraph for community detection. The run_contagion_pipeline() wrapper handles loading them on demand; we expose the full chain here so each step is auditable.

2. Loading the bundled datasets

Three datasets ship with the package and are sufficient to reproduce every empirical statement in the paper.

data(g20_returns)
data(channel_proxies)
data(crisis_periods)

dim(g20_returns)
#> [1] 5036   18
range(index(g20_returns))
#> [1] "2006-01-12" "2026-03-18"
length(crisis_periods)
#> [1] 8
names(crisis_periods)
#> [1] "PreCrisis"      "GFC"            "ESDC"           "CSC"           
#> [5] "PreCOVID"       "COVID"          "RusUkr"         "MidEastTariffs"

g20_returns is an xts object of daily log returns for 18 G20 equity indices spanning 2 January 2006 through 31 March 2026 (5,036 trading days after holiday alignment). channel_proxies is a data.frame keyed on Date holding the raw component series that feed the five composite channels. crisis_periods is a named list of length eight whose entries are length-two Date vectors marking the start and end of each sub-period: PreCrisis, GFC, ESDC, CSC, PreCOVID, COVID, RusUkr, and MidEastTariffs.

3. Building the v2 channel composites

The paper uses a v2 specification for the five channel composites that re-balances the components and applies a unit-variance standardisation within each rolling window. The helper build_channel_composites() consumes the raw proxy grid and returns a data.frame with one column per channel.

channels <- build_channel_composites(channel_proxies)
head(channels[, c("Date", "Trade", "Financial", "Geopolitical",
                  "Behavioral", "Monetary_Policy")], 3)
#>         Date        Trade  Financial Geopolitical Behavioral Monetary_Policy
#> 1 2006-01-12 -0.010480244 -0.7858395    -0.106868  0.6312673      -0.4957951
#> 2 2006-01-13 -0.292581090 -0.7733637    -0.106868  0.6362502      -0.4087255
#> 3 2006-01-16  0.001182225 -0.7758794    -0.106868  0.6352454      -0.5134698

Each composite is a unit-variance latent factor extracted by a one-factor PCA on its respective component block. The composites are signed so that positive values indicate tightening of the channel (e.g., wider FRA-OIS spreads on the Financial channel; higher GPR on the Geopolitical channel), ensuring sign coherence across periods.

4. Stage 1: WQTE detection

Stage 1 estimates a directed information-flow matrix at wavelet scale 5 (corresponding to dyadic horizons of 32-64 trading days, i.e. roughly the quarterly business-cycle band) and at the median quantile tau = 0.50. For each ordered pair \((i,j)\) of markets we compute the bias-corrected wavelet coefficient transfer entropy

\[ \widehat{T}_{i \to j}^{(s,\tau)} \;=\; T_{i \to j}^{(s,\tau)} \;-\; \frac{1}{B}\sum_{b=1}^{B} T_{i^{(b)} \to j}^{(s,\tau)}, \]

where the second term is the mean over B = 100 shuffled-source surrogates.

F_full <- compute_wqte_matrix(
  returns = g20_returns,
  scale   = 5,
  tau     = 0.50,
  n_cores = 4
)

A fast illustrative version restricted to the Pre-Crisis sub-period is small enough to evaluate inline:

pc_dates  <- crisis_periods$PreCrisis
returns_pc <- g20_returns[paste0(pc_dates[1], "/", pc_dates[2])]

F_pc <- compute_wqte_matrix(
  returns = returns_pc,
  scale   = 5,
  tau     = 0.50,
  n_cores = 1
)

dim(F_pc)
#> [1] 18 18
round(F_pc[1:4, 1:4], 4)
#>           Argentina Australia Brazil Canada
#> Argentina    0.0000    0.0130 0.0025 0.0285
#> Australia    0.0232    0.0000 0.0056 0.0039
#> Brazil       0.0104    0.0157 0.0000 0.0109
#> Canada       0.0525    0.0286 0.0060 0.0000

F_pc_offdiag <- F_pc[upper.tri(F_pc) | lower.tri(F_pc)]
abs_thr <- quantile(F_pc_offdiag, probs = 0.75, na.rm = TRUE)
abs_thr
#>        75% 
#> 0.03308545

5. Stage 1 results: density and centrality (Table 1)

With the threshold pinned, network density at scale 5 / tau = 0.50 ranges from 14.05% to 32.03% across the eight sub-periods, providing meaningful period-to-period variation. The helper summarise_stage1() returns a tidy table with density, mean WQTE, and the dominant transmitter / receiver per period.

stage1_tbl <- summarise_stage1(
  returns_xts    = g20_returns,
  periods        = crisis_periods,
  scale          = 5,
  tau            = 0.50,
  abs_threshold  = abs_thr
)
stage1_tbl

The expected contents reproduce Table 1 of the paper:

6. Stage 2: IV/2SLS attribution (Table 2)

The Stage 2 attribution regresses each detected directional flow \(\widehat{F}_{i\to j,t}\) on the five channel composites using channel-specific external instruments. For the Financial channel the instrument is the lagged FRA-OIS spread; for Trade, lagged Baltic Dry shipping rates; for Geopolitical, lagged GPR-Daily; for Behavioral, lagged VIX innovation; for Monetary_Policy, lagged shadow-rate surprises. The function iv_2sls_attribute() returns a list with point estimates, robust standard errors, the Sargan-Hansen J-statistic, and a per-channel share decomposition.

links_pc <- which(F_pc >= abs_thr, arr.ind = TRUE)
channels_pc <- channels[channels$Date >= pc_dates[1] &
                          channels$Date <= pc_dates[2], ]

iv_pc <- iv_2sls_attribute(
  returns_period  = returns_pc,
  channels_period = channels_pc,
  links           = links_pc,
  cluster_se      = TRUE
)

iv_pc$shares

Iterating over all eight sub-periods reproduces Table 2:

The dominant channel is bolded per period and matches the paper’s headline: Pre-Crisis Financial 35.9%, GFC Trade 27.9%, ESDC Financial 39.5%, CSC Monetary 25.3%, Pre-COVID Financial 31.6%, COVID Geopolitical 27.5%, RusUkr Monetary 27.6%, and MidEastTariffs Monetary 31.8%. Note also that the Behavioral channel never exceeds 22% in any period.

7. Cross-method comparison: LP and Rigobon (Table 6)

Identification rests on more than one strategy. The paper triangulates across IV/2SLS, Jordà local projections at horizon 5 (LP-h5), and Rigobon’s heteroskedasticity-based identification.

lp_pc <- local_projections(
  returns_period  = returns_pc,
  channels_period = channels_pc,
  links           = links_pc,
  horizons        = c(1, 5, 22)
)

rig_pc <- rigobon_id(
  returns_period  = returns_pc,
  channels_period = channels_pc,
  links           = links_pc,
  regime_split    = "vix_high_low"
)

lp_pc$shares_h5
rig_pc$shares

A period is labelled identification-robust when the dominant channel agrees across IV/2SLS, LP-h5, and Rigobon. Reproducing Table 6 of the paper:

Only Pre-Crisis and ESDC are identification-robust; the remaining six periods are method-fragile and must be discussed with appropriate caveats.

sargan_rates <- summarise_sargan(
  returns_xts    = g20_returns,
  channels       = channels,
  periods        = crisis_periods,
  abs_threshold  = abs_thr
)
sargan_rates[, c("Period", "RejectRate")]

8. Bootstrap confidence intervals

Each Stage 2 share is paired with a wild-cluster bootstrap interval. The default uses 999 Rademacher draws clustered at the directional-link level; this is computationally heavy and we mark it eval = FALSE.

boot_pc <- bootstrap_attribution(
  fit       = iv_pc,
  B         = 999,
  type      = "wild_cluster",
  cluster   = "link"
)
boot_pc$ci_95

9. Cinelli-Hazlett robustness values

The robustness value (RV) reports the minimum unobserved-confounder strength required to overturn an estimated channel share. A high RV indicates a finding that is hard to break by an omitted variable; the paper flags any share with RV >= 0.20 as quantitatively robust.

rv_pc <- cinelli_hazlett_rv(
  theta = iv_pc$shares,
  se    = iv_pc$se,
  df    = iv_pc$df_residual
)
round(rv_pc, 3)

For the Pre-Crisis Financial share the RV is well above 0.20, consistent with Table 7 of the paper.

10. Visualisation walkthrough (Figures 1-7)

The package bundles three plotting helpers built on ggplot2 and a network/igraph back-end. Each one corresponds to a numbered figure in the manuscript.

plot_attribution_stack(
  shares_long = bind_rows(lapply(crisis_periods, function(p) iv_pc$shares)),
  period_order = names(crisis_periods)
)  # Figure 4: stacked attribution shares

plot_qte_intensity(
  F_matrix  = F_pc,
  threshold = abs_thr
)  # Figure 2: WQTE heatmap

plot_robustness_value(
  rv_table = rv_pc,
  period   = "PreCrisis"
)  # Figure 7: RV bounding contours

Figures 1, 3, 5, and 6 are produced by plot_pipeline_summary() which arranges all panels into the multi-figure layout used in the paper.

11. Walktrap communities

Stage 1’s directed adjacency is fed into igraph’s walktrap algorithm to detect mesoscale communities. With four random walks of length four, the Pre-Crisis network resolves into three communities tightly aligned with the Anglo, EU, and EM blocs.

g_pc <- build_network(F_pc, threshold = abs_thr)
comms_pc <- walktrap_communities(g_pc, steps = 4)
table(membership(comms_pc))

Modularity scores per period are tabulated by summarise_communities() and match Table 5 of the paper.

12. End-to-end pipeline

The convenience wrapper run_contagion_pipeline() chains every step above into a single call. It returns a tagged list with Stage 1 and Stage 2 outputs for every sub-period, the bootstrap intervals, the RV grid, and a ready-to-print summary table.

results <- run_contagion_pipeline(
  returns       = g20_returns,
  channels      = channels,
  periods       = crisis_periods,
  scale         = 5,
  tau           = 0.50,
  abs_threshold = abs_thr,
  methods       = c("iv2sls", "lasso_iv", "lp", "rigobon"),
  bootstrap_B   = 999,
  n_cores = 4
)

names(results)
results$summary_table

The results object is the canonical artefact for downstream analysis; the companion replication archive on Zenodo distributes a serialised version that exactly matches the published tables. With this vignette in hand, every row of Tables 1, 2, 6, and 7, every panel of Figures 1-7, and every sensitivity reported in the appendix can be regenerated from the bundled data with no external inputs.

Session info

sessionInfo()
#> R version 4.1.2 (2021-11-01)
#> Platform: x86_64-pc-linux-gnu (64-bit)
#> Running under: Ubuntu 22.04.5 LTS
#> 
#> Matrix products: default
#> BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.10.0
#> LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.10.0
#> 
#> locale:
#>  [1] LC_CTYPE=en_IN       LC_NUMERIC=C         LC_TIME=en_IN       
#>  [4] LC_COLLATE=C         LC_MONETARY=en_IN    LC_MESSAGES=en_IN   
#>  [7] LC_PAPER=en_IN       LC_NAME=C            LC_ADDRESS=C        
#> [10] LC_TELEPHONE=C       LC_MEASUREMENT=en_IN LC_IDENTIFICATION=C 
#> 
#> attached base packages:
#> [1] stats     graphics  grDevices utils     datasets  methods   base     
#> 
#> other attached packages:
#> [1] igraph_2.2.0            ggplot2_4.0.0           tidyr_1.3.1            
#> [4] dplyr_1.1.4             xts_0.14.1              zoo_1.8-14             
#> [7] contagionchannels_0.1.3
#> 
#> loaded via a namespace (and not attached):
#>  [1] RColorBrewer_1.1-3 bslib_0.9.0        compiler_4.1.2     pillar_1.11.1     
#>  [5] jquerylib_0.1.4    tools_4.1.2        digest_0.6.37      gtable_0.3.6      
#>  [9] tibble_3.3.0       jsonlite_2.0.0     evaluate_1.0.5     lifecycle_1.0.5   
#> [13] lattice_0.20-45    pkgconfig_2.0.3    rlang_1.2.0        Matrix_1.5-4.1    
#> [17] cli_3.6.6          yaml_2.3.10        parallel_4.1.2     SparseM_1.84-2    
#> [21] xfun_0.53          fastmap_1.2.0      withr_3.0.2        multitaper_1.0-17 
#> [25] knitr_1.50         generics_0.1.4     sass_0.4.10        vctrs_0.6.5       
#> [29] MatrixModels_0.5-1 tidyselect_1.2.1   grid_4.1.2         glue_1.8.0        
#> [33] R6_2.6.1           survival_3.2-13    waveslim_1.8.5     rmarkdown_2.30    
#> [37] farver_2.1.2       purrr_1.1.0        magrittr_2.0.4     scales_1.4.0      
#> [41] htmltools_0.5.8.1  MASS_7.3-55        splines_4.1.2      S7_0.2.0          
#> [45] quantreg_6.1       cachem_1.1.0