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Post-Estimation Workflows in bsvarPost

Source: vignettes/post-estimation-workflows.Rmd
post-estimation-workflows.Rmd

This vignette picks up where “Getting Started” left off. After extracting impulse responses and CDMs, deeper analytical questions remain: Which draw best represents the posterior as a whole? When exactly does a spending shock peak, and how long does it last? Which structural shocks drove observed fiscal dynamics? This vignette works through those questions using the same us_fiscal_lsuw dataset — quarterly US data on tax revenue (ttr), government spending (gs), and output (gdp) — comparing a one-lag baseline against a three-lag alternative specification.

Representative-model summaries

Pointwise posterior medians may not correspond to any one coherent structural draw. median_target_irf() finds the stored draw whose IRF matrix is closest (in L2 distance) to the posterior median. The result is a single self-consistent model that typifies the posterior center.

rep_irf <- median_target_irf(post, horizon = 20)
summary(rep_irf)
#> # A tibble: 189 × 13
#>    model  object_type variable shock horizon   mean median    sd  lower  upper
#>    <chr>  <chr>       <chr>    <chr>   <dbl>  <dbl>  <dbl> <dbl>  <dbl>  <dbl>
#>  1 model1 irf         ttr      ttr         0 0.0296 0.0296    NA 0.0296 0.0296
#>  2 model1 irf         ttr      ttr         1 0.0277 0.0277    NA 0.0277 0.0277
#>  3 model1 irf         ttr      ttr         2 0.0260 0.0260    NA 0.0260 0.0260
#>  4 model1 irf         ttr      ttr         3 0.0243 0.0243    NA 0.0243 0.0243
#>  5 model1 irf         ttr      ttr         4 0.0227 0.0227    NA 0.0227 0.0227
#>  6 model1 irf         ttr      ttr         5 0.0212 0.0212    NA 0.0212 0.0212
#>  7 model1 irf         ttr      ttr         6 0.0198 0.0198    NA 0.0198 0.0198
#>  8 model1 irf         ttr      ttr         7 0.0185 0.0185    NA 0.0185 0.0185
#>  9 model1 irf         ttr      ttr         8 0.0173 0.0173    NA 0.0173 0.0173
#> 10 model1 irf         ttr      ttr         9 0.0161 0.0161    NA 0.0161 0.0161
#> # ℹ 179 more rows
#> # ℹ 3 more variables: draw_index <int>, method <chr>, score <dbl>

The draw_index slot records which posterior draw was selected. This can be used to extract other quantities (CDMs, FEVD) from the same draw for a fully coherent representative model.

A pre-rendered figure from the same posterior at the full S = 200 resolution:

The representative IRF for the gs spending shock shows the typical fiscal transmission shape: an immediate positive effect on government spending itself, with the gdp response peaking a few quarters later.

Response timing summaries

Researchers often need to report precisely when effects arrive and how long they persist. bsvarPost provides four timing summaries, each with full posterior uncertainty.

Peak response — at what horizon does the fiscal spending shock produce the largest gdp effect?

peak_response(post, type = "irf", horizon = 20, variables = 3, shocks = 2)
#> # A tibble: 1 × 14
#>   model  object_type variable shock mean_value median_value sd_value lower_value
#>   <chr>  <chr>       <chr>    <chr>      <dbl>        <dbl>    <dbl>       <dbl>
#> 1 model1 peak_irf    gdp      gs        0.0379   -0.0000250    0.537    -0.00114
#> # ℹ 6 more variables: upper_value <dbl>, mean_horizon <dbl>,
#> #   median_horizon <dbl>, sd_horizon <dbl>, lower_horizon <dbl>,
#> #   upper_horizon <dbl>

Duration response — how many quarters does the cumulative multiplier remain positive?

duration_response(
  post,
  type     = "cdm",
  horizon  = 20,
  variables = 3,
  shocks   = 2,
  relation = ">",
  value    = 0,
  mode     = "total"
)
#> # A tibble: 1 × 12
#>   model  object_type  variable shock relation threshold mode  mean_duration
#>   <chr>  <chr>        <chr>    <chr> <chr>        <dbl> <chr>         <dbl>
#> 1 model1 duration_cdm gdp      gs    >                0 total          4.10
#> # ℹ 4 more variables: median_duration <dbl>, sd_duration <dbl>,
#> #   lower_duration <dbl>, upper_duration <dbl>

Half-life — how quickly does the impulse response decay from its peak?

half_life_response(
  post,
  type     = "irf",
  horizon  = 20,
  variables = 3,
  shocks   = 2,
  baseline = "peak"
)
#> # A tibble: 1 × 12
#>   model  object_type   variable shock fraction baseline mean_half_life
#>   <chr>  <chr>         <chr>    <chr>    <dbl> <chr>             <dbl>
#> 1 model1 half_life_irf gdp      gs         0.5 peak               5.67
#> # ℹ 5 more variables: median_half_life <dbl>, sd_half_life <dbl>,
#> #   lower_half_life <dbl>, upper_half_life <dbl>, reached_prob <dbl>

Time to threshold — when does the cumulative multiplier first exceed zero?

time_to_threshold(
  post,
  type     = "cdm",
  horizon  = 20,
  variables = 3,
  shocks   = 2,
  relation = ">",
  value    = 0
)
#> # A tibble: 1 × 12
#>   model  object_type           variable shock relation threshold mean_horizon
#>   <chr>  <chr>                 <chr>    <chr> <chr>        <dbl>        <dbl>
#> 1 model1 time_to_threshold_cdm gdp      gs    >                0        0.351
#> # ℹ 5 more variables: median_horizon <dbl>, sd_horizon <dbl>,
#> #   lower_horizon <dbl>, upper_horizon <dbl>, reached_prob <dbl>

These four summaries characterise when the fiscal spending effect arrives, how large it becomes, and how quickly it dissipates — the standard set of timing statistics for fiscal multiplier papers.

Comparing response summaries

Does the estimated timing change under a three-lag specification? The compare_* helpers place both posteriors side by side.

cmp_peak <- compare_peak_response(
  baseline    = post,
  alternative = post_alt,
  type        = "irf",
  horizon     = 20,
  variables   = 3,
  shocks      = 2
)
cmp_peak
#> # A tibble: 2 × 14
#>   model  object_type variable shock mean_value median_value sd_value lower_value
#>   <chr>  <chr>       <chr>    <chr>      <dbl>        <dbl>    <dbl>       <dbl>
#> 1 basel… peak_irf    gdp      gs        0.0379   -0.0000250  5.37e-1   -0.00114 
#> 2 alter… peak_irf    gdp      gs    66131.        0.000115   9.35e+5   -0.000904
#> # ℹ 6 more variables: upper_value <dbl>, mean_horizon <dbl>,
#> #   median_horizon <dbl>, sd_horizon <dbl>, lower_horizon <dbl>,
#> #   upper_horizon <dbl>
compare_duration_response(
  baseline    = post,
  alternative = post_alt,
  type        = "cdm",
  horizon     = 20,
  variables   = 3,
  shocks      = 2,
  relation    = ">",
  value       = 0
)
#> # A tibble: 2 × 12
#>   model       object_type  variable shock relation threshold mode  mean_duration
#>   <chr>       <chr>        <chr>    <chr> <chr>        <dbl> <chr>         <dbl>
#> 1 baseline    duration_cdm gdp      gs    >                0 cons…          3.95
#> 2 alternative duration_cdm gdp      gs    >                0 cons…          4.16
#> # ℹ 4 more variables: median_duration <dbl>, sd_duration <dbl>,
#> #   lower_duration <dbl>, upper_duration <dbl>

as_kable() formats any bsvar_post_tbl as a compact knitr::kable table ready for Rmd reports.

as_kable(cmp_peak, preset = "compact")
Model Variable Shock Mean value Median value Lower value Upper value Mean horizon Median horizon Lower horizon Upper horizon
baseline gdp gs 3.791410e-02 -0.0000250 -0.0011445 0.0009886 1.105 0 0 10.5
alternative gdp gs 6.613149e+04 0.0001149 -0.0009040 0.0033801 4.740 1 0 20.0

The three-lag alternative typically shows a later peak with wider credible bands, reflecting the richer lag dynamics.

Historical decomposition workflows

Historical decompositions (HD) answer two complementary questions: how do structural shock contributions evolve over the full sample, and how do those same contributions aggregate over a selected event window?

Start with the full-sample HD object. tidy_hd() returns the contribution of each structural shock to each variable at each point in time, which then feeds the dedicated plotting helpers.

hd_full <- tidy_hd(post)
plot_hd_overlay(post, variables = "gdp", top_n = 3)
plot_hd_stacked(post, variables = "gdp", top_n = 3)
plot_hd_total(post, variables = "gdp", shocks = c("gs", "ttr"))
plot_hd_lines(post, variables = "gdp", top_n = 3)

Use plot_hd_overlay() first when you want to compare how the main shock contributions move over time within one variable. This is the best first-look diagnostic because it keeps the contribution paths in a common panel without mixing in the raw observed level.

A pre-rendered full-sample HD overlay plot from the same S = 200 posterior:

plot_hd_stacked() then gives the composition view over time. By default it shows the stacked structural shock contributions; add include_baseline = TRUE when you want the explicit non-shock reconstruction term as well.

plot_hd_total() plays a different role: it compares the observed series to the reconstructed decomposition total, so it is the natural validation view once the main shock drivers are clear.

When overlay and stacked views become too compressed, plot_hd_lines() gives the detailed inspection view by separating the component paths rather than forcing them into one panel.

After the full-sample HD plots have identified a period of interest, move to the event-window summaries. tidy_hd_event() aggregates those contributions over a chosen window.

The us_fiscal_lsuw sample begins in 1948. To examine which shocks drove fiscal dynamics in the first year (four quarters: 1948.25 through 1948.75):

hd_event <- tidy_hd_event(post, start = "1948.25", end = "1948.75")
head(hd_event)
#> # A tibble: 6 × 11
#>   model  object_type variable shock event_start event_end     mean    median
#>   <chr>  <chr>       <chr>    <chr> <chr>       <chr>        <dbl>     <dbl>
#> 1 model1 hd_event    gdp      gdp   1948.25     1948.75    3.28     3.32    
#> 2 model1 hd_event    gs       gdp   1948.25     1948.75    0.0116   0.000610
#> 3 model1 hd_event    ttr      gdp   1948.25     1948.75   -0.282   -0.289   
#> 4 model1 hd_event    gdp      gs    1948.25     1948.75   -0.0295  -0.0188  
#> 5 model1 hd_event    gs       gs    1948.25     1948.75   -0.906   -0.880   
#> 6 model1 hd_event    ttr      gs    1948.25     1948.75    0.00140  0.00680 
#> # ℹ 3 more variables: sd <dbl>, lower <dbl>, upper <dbl>

plot_hd_event() keeps the window summary in contribution units, while plot_hd_event_share() converts the same event into within-window shares. plot_hd_event_cumulative() shows how those contributions accumulate inside the window, and plot_hd_event_distribution() focuses on posterior uncertainty for each shock.

shock_ranking() is the event-summary ranking tool: it orders the structural shocks by their absolute contribution to a target variable over the selected window. Which shock moved gdp the most?

shock_ranking(post, start = "1948.25", end = "1948.75", ranking = "absolute")
#> # A tibble: 9 × 14
#>   model  object_type variable shock event_start event_end     mean    median
#>   <chr>  <chr>       <chr>    <chr> <chr>       <chr>        <dbl>     <dbl>
#> 1 model1 hd_event    gdp      gdp   1948.25     1948.75    3.28     3.32    
#> 2 model1 hd_event    gdp      ttr   1948.25     1948.75    0.520    0.458   
#> 3 model1 hd_event    gdp      gs    1948.25     1948.75   -0.0295  -0.0188  
#> 4 model1 hd_event    gs       gs    1948.25     1948.75   -0.906   -0.880   
#> 5 model1 hd_event    gs       ttr   1948.25     1948.75    0.0646   0.00766 
#> 6 model1 hd_event    gs       gdp   1948.25     1948.75    0.0116   0.000610
#> 7 model1 hd_event    ttr      ttr   1948.25     1948.75   -7.94    -8.01    
#> 8 model1 hd_event    ttr      gdp   1948.25     1948.75   -0.282   -0.289   
#> 9 model1 hd_event    ttr      gs    1948.25     1948.75    0.00140  0.00680 
#> # ℹ 6 more variables: sd <dbl>, lower <dbl>, upper <dbl>, ranking <chr>,
#> #   rank_score <dbl>, rank <int>

For a composition-oriented event view, plot_hd_event_share() rescales the same event-window contributions into shares:

plot_hd_event(post, start = "1948.25", end = "1948.75")
plot_hd_event_share(post, start = "1948.25", end = "1948.75", top_n = 3)
plot_hd_event_cumulative(post, start = "1948.25", end = "1948.75", top_n = 3)
plot_hd_event_distribution(post, start = "1948.25", end = "1948.75", top_n = 3)

And a pre-rendered event-share composition plot:

A pre-rendered HD event figure from a richer S = 200 run:

Publication-ready reporting

All bsvarPost outputs are bsvar_post_tbl data frames and accept the same family of reporting helpers.

knitr table (always available):

as_kable(summary(rep_irf), preset = "compact", digits = 3)
Model Variable Shock Horizon Mean Median Lower Upper
model1 ttr ttr 0 0.030 0.030 0.030 0.030
model1 ttr ttr 1 0.028 0.028 0.028 0.028
model1 ttr ttr 2 0.026 0.026 0.026 0.026
model1 ttr ttr 3 0.024 0.024 0.024 0.024
model1 ttr ttr 4 0.023 0.023 0.023 0.023
model1 ttr ttr 5 0.021 0.021 0.021 0.021
model1 ttr ttr 6 0.020 0.020 0.020 0.020
model1 ttr ttr 7 0.019 0.019 0.019 0.019
model1 ttr ttr 8 0.017 0.017 0.017 0.017
model1 ttr ttr 9 0.016 0.016 0.016 0.016
model1 ttr ttr 10 0.015 0.015 0.015 0.015
model1 ttr ttr 11 0.014 0.014 0.014 0.014
model1 ttr ttr 12 0.013 0.013 0.013 0.013
model1 ttr ttr 13 0.012 0.012 0.012 0.012
model1 ttr ttr 14 0.011 0.011 0.011 0.011
model1 ttr ttr 15 0.010 0.010 0.010 0.010
model1 ttr ttr 16 0.009 0.009 0.009 0.009
model1 ttr ttr 17 0.009 0.009 0.009 0.009
model1 ttr ttr 18 0.008 0.008 0.008 0.008
model1 ttr ttr 19 0.007 0.007 0.007 0.007
model1 ttr ttr 20 0.007 0.007 0.007 0.007
model1 ttr gs 0 0.000 0.000 0.000 0.000
model1 ttr gs 1 0.000 0.000 0.000 0.000
model1 ttr gs 2 0.000 0.000 0.000 0.000
model1 ttr gs 3 -0.001 -0.001 -0.001 -0.001
model1 ttr gs 4 -0.001 -0.001 -0.001 -0.001
model1 ttr gs 5 -0.001 -0.001 -0.001 -0.001
model1 ttr gs 6 -0.001 -0.001 -0.001 -0.001
model1 ttr gs 7 -0.001 -0.001 -0.001 -0.001
model1 ttr gs 8 -0.001 -0.001 -0.001 -0.001
model1 ttr gs 9 -0.001 -0.001 -0.001 -0.001
model1 ttr gs 10 -0.002 -0.002 -0.002 -0.002
model1 ttr gs 11 -0.002 -0.002 -0.002 -0.002
model1 ttr gs 12 -0.002 -0.002 -0.002 -0.002
model1 ttr gs 13 -0.002 -0.002 -0.002 -0.002
model1 ttr gs 14 -0.002 -0.002 -0.002 -0.002
model1 ttr gs 15 -0.002 -0.002 -0.002 -0.002
model1 ttr gs 16 -0.002 -0.002 -0.002 -0.002
model1 ttr gs 17 -0.002 -0.002 -0.002 -0.002
model1 ttr gs 18 -0.002 -0.002 -0.002 -0.002
model1 ttr gs 19 -0.002 -0.002 -0.002 -0.002
model1 ttr gs 20 -0.002 -0.002 -0.002 -0.002
model1 ttr gdp 0 0.000 0.000 0.000 0.000
model1 ttr gdp 1 0.001 0.001 0.001 0.001
model1 ttr gdp 2 0.002 0.002 0.002 0.002
model1 ttr gdp 3 0.003 0.003 0.003 0.003
model1 ttr gdp 4 0.003 0.003 0.003 0.003
model1 ttr gdp 5 0.004 0.004 0.004 0.004
model1 ttr gdp 6 0.005 0.005 0.005 0.005
model1 ttr gdp 7 0.005 0.005 0.005 0.005
model1 ttr gdp 8 0.006 0.006 0.006 0.006
model1 ttr gdp 9 0.007 0.007 0.007 0.007
model1 ttr gdp 10 0.007 0.007 0.007 0.007
model1 ttr gdp 11 0.008 0.008 0.008 0.008
model1 ttr gdp 12 0.008 0.008 0.008 0.008
model1 ttr gdp 13 0.008 0.008 0.008 0.008
model1 ttr gdp 14 0.009 0.009 0.009 0.009
model1 ttr gdp 15 0.009 0.009 0.009 0.009
model1 ttr gdp 16 0.010 0.010 0.010 0.010
model1 ttr gdp 17 0.010 0.010 0.010 0.010
model1 ttr gdp 18 0.010 0.010 0.010 0.010
model1 ttr gdp 19 0.011 0.011 0.011 0.011
model1 ttr gdp 20 0.011 0.011 0.011 0.011
model1 gs ttr 0 0.000 0.000 0.000 0.000
model1 gs ttr 1 -0.001 -0.001 -0.001 -0.001
model1 gs ttr 2 -0.001 -0.001 -0.001 -0.001
model1 gs ttr 3 -0.002 -0.002 -0.002 -0.002
model1 gs ttr 4 -0.002 -0.002 -0.002 -0.002
model1 gs ttr 5 -0.002 -0.002 -0.002 -0.002
model1 gs ttr 6 -0.003 -0.003 -0.003 -0.003
model1 gs ttr 7 -0.003 -0.003 -0.003 -0.003
model1 gs ttr 8 -0.003 -0.003 -0.003 -0.003
model1 gs ttr 9 -0.004 -0.004 -0.004 -0.004
model1 gs ttr 10 -0.004 -0.004 -0.004 -0.004
model1 gs ttr 11 -0.004 -0.004 -0.004 -0.004
model1 gs ttr 12 -0.004 -0.004 -0.004 -0.004
model1 gs ttr 13 -0.004 -0.004 -0.004 -0.004
model1 gs ttr 14 -0.004 -0.004 -0.004 -0.004
model1 gs ttr 15 -0.004 -0.004 -0.004 -0.004
model1 gs ttr 16 -0.004 -0.004 -0.004 -0.004
model1 gs ttr 17 -0.004 -0.004 -0.004 -0.004
model1 gs ttr 18 -0.004 -0.004 -0.004 -0.004
model1 gs ttr 19 -0.004 -0.004 -0.004 -0.004
model1 gs ttr 20 -0.004 -0.004 -0.004 -0.004
model1 gs gs 0 0.025 0.025 0.025 0.025
model1 gs gs 1 0.024 0.024 0.024 0.024
model1 gs gs 2 0.023 0.023 0.023 0.023
model1 gs gs 3 0.021 0.021 0.021 0.021
model1 gs gs 4 0.020 0.020 0.020 0.020
model1 gs gs 5 0.019 0.019 0.019 0.019
model1 gs gs 6 0.018 0.018 0.018 0.018
model1 gs gs 7 0.017 0.017 0.017 0.017
model1 gs gs 8 0.016 0.016 0.016 0.016
model1 gs gs 9 0.015 0.015 0.015 0.015
model1 gs gs 10 0.014 0.014 0.014 0.014
model1 gs gs 11 0.014 0.014 0.014 0.014
model1 gs gs 12 0.013 0.013 0.013 0.013
model1 gs gs 13 0.012 0.012 0.012 0.012
model1 gs gs 14 0.012 0.012 0.012 0.012
model1 gs gs 15 0.011 0.011 0.011 0.011
model1 gs gs 16 0.010 0.010 0.010 0.010
model1 gs gs 17 0.010 0.010 0.010 0.010
model1 gs gs 18 0.009 0.009 0.009 0.009
model1 gs gs 19 0.009 0.009 0.009 0.009
model1 gs gs 20 0.008 0.008 0.008 0.008
model1 gs gdp 0 0.000 0.000 0.000 0.000
model1 gs gdp 1 0.000 0.000 0.000 0.000
model1 gs gdp 2 0.001 0.001 0.001 0.001
model1 gs gdp 3 0.001 0.001 0.001 0.001
model1 gs gdp 4 0.001 0.001 0.001 0.001
model1 gs gdp 5 0.002 0.002 0.002 0.002
model1 gs gdp 6 0.002 0.002 0.002 0.002
model1 gs gdp 7 0.002 0.002 0.002 0.002
model1 gs gdp 8 0.002 0.002 0.002 0.002
model1 gs gdp 9 0.002 0.002 0.002 0.002
model1 gs gdp 10 0.003 0.003 0.003 0.003
model1 gs gdp 11 0.003 0.003 0.003 0.003
model1 gs gdp 12 0.003 0.003 0.003 0.003
model1 gs gdp 13 0.003 0.003 0.003 0.003
model1 gs gdp 14 0.003 0.003 0.003 0.003
model1 gs gdp 15 0.003 0.003 0.003 0.003
model1 gs gdp 16 0.003 0.003 0.003 0.003
model1 gs gdp 17 0.003 0.003 0.003 0.003
model1 gs gdp 18 0.003 0.003 0.003 0.003
model1 gs gdp 19 0.003 0.003 0.003 0.003
model1 gs gdp 20 0.003 0.003 0.003 0.003
model1 gdp ttr 0 0.003 0.003 0.003 0.003
model1 gdp ttr 1 0.003 0.003 0.003 0.003
model1 gdp ttr 2 0.003 0.003 0.003 0.003
model1 gdp ttr 3 0.002 0.002 0.002 0.002
model1 gdp ttr 4 0.002 0.002 0.002 0.002
model1 gdp ttr 5 0.002 0.002 0.002 0.002
model1 gdp ttr 6 0.001 0.001 0.001 0.001
model1 gdp ttr 7 0.001 0.001 0.001 0.001
model1 gdp ttr 8 0.001 0.001 0.001 0.001
model1 gdp ttr 9 0.001 0.001 0.001 0.001
model1 gdp ttr 10 0.000 0.000 0.000 0.000
model1 gdp ttr 11 0.000 0.000 0.000 0.000
model1 gdp ttr 12 0.000 0.000 0.000 0.000
model1 gdp ttr 13 0.000 0.000 0.000 0.000
model1 gdp ttr 14 0.000 0.000 0.000 0.000
model1 gdp ttr 15 -0.001 -0.001 -0.001 -0.001
model1 gdp ttr 16 -0.001 -0.001 -0.001 -0.001
model1 gdp ttr 17 -0.001 -0.001 -0.001 -0.001
model1 gdp ttr 18 -0.001 -0.001 -0.001 -0.001
model1 gdp ttr 19 -0.001 -0.001 -0.001 -0.001
model1 gdp ttr 20 -0.001 -0.001 -0.001 -0.001
model1 gdp gs 0 -0.001 -0.001 -0.001 -0.001
model1 gdp gs 1 -0.001 -0.001 -0.001 -0.001
model1 gdp gs 2 -0.001 -0.001 -0.001 -0.001
model1 gdp gs 3 -0.001 -0.001 -0.001 -0.001
model1 gdp gs 4 -0.001 -0.001 -0.001 -0.001
model1 gdp gs 5 -0.001 -0.001 -0.001 -0.001
model1 gdp gs 6 -0.001 -0.001 -0.001 -0.001
model1 gdp gs 7 -0.001 -0.001 -0.001 -0.001
model1 gdp gs 8 -0.001 -0.001 -0.001 -0.001
model1 gdp gs 9 -0.001 -0.001 -0.001 -0.001
model1 gdp gs 10 -0.001 -0.001 -0.001 -0.001
model1 gdp gs 11 -0.001 -0.001 -0.001 -0.001
model1 gdp gs 12 -0.001 -0.001 -0.001 -0.001
model1 gdp gs 13 -0.001 -0.001 -0.001 -0.001
model1 gdp gs 14 -0.001 -0.001 -0.001 -0.001
model1 gdp gs 15 -0.001 -0.001 -0.001 -0.001
model1 gdp gs 16 -0.001 -0.001 -0.001 -0.001
model1 gdp gs 17 -0.001 -0.001 -0.001 -0.001
model1 gdp gs 18 -0.001 -0.001 -0.001 -0.001
model1 gdp gs 19 -0.001 -0.001 -0.001 -0.001
model1 gdp gs 20 -0.001 -0.001 -0.001 -0.001
model1 gdp gdp 0 0.010 0.010 0.010 0.010
model1 gdp gdp 1 0.010 0.010 0.010 0.010
model1 gdp gdp 2 0.010 0.010 0.010 0.010
model1 gdp gdp 3 0.010 0.010 0.010 0.010
model1 gdp gdp 4 0.010 0.010 0.010 0.010
model1 gdp gdp 5 0.010 0.010 0.010 0.010
model1 gdp gdp 6 0.011 0.011 0.011 0.011
model1 gdp gdp 7 0.011 0.011 0.011 0.011
model1 gdp gdp 8 0.011 0.011 0.011 0.011
model1 gdp gdp 9 0.011 0.011 0.011 0.011
model1 gdp gdp 10 0.011 0.011 0.011 0.011
model1 gdp gdp 11 0.011 0.011 0.011 0.011
model1 gdp gdp 12 0.011 0.011 0.011 0.011
model1 gdp gdp 13 0.011 0.011 0.011 0.011
model1 gdp gdp 14 0.011 0.011 0.011 0.011
model1 gdp gdp 15 0.011 0.011 0.011 0.011
model1 gdp gdp 16 0.011 0.011 0.011 0.011
model1 gdp gdp 17 0.011 0.011 0.011 0.011
model1 gdp gdp 18 0.011 0.011 0.011 0.011
model1 gdp gdp 19 0.011 0.011 0.011 0.011
model1 gdp gdp 20 0.011 0.011 0.011 0.011

gt table (when the gt package is installed):

as_gt(cmp_peak, caption = "Peak response: 1-lag vs 3-lag", digits = 3,
      preset = "compact")
Peak response: 1-lag vs 3-lag
Model Variable Shock Mean value Median value Lower value Upper value Mean horizon Median horizon Lower horizon Upper horizon
baseline gdp gs 0.038 0 -0.001 0.001 1.105 0 0 10.5
alternative gdp gs 66131.493 0 -0.001 0.003 4.740 1 0 20.0

flextable (when the flextable package is installed):

as_flextable(cmp_peak, caption = "Peak response: 1-lag vs 3-lag", digits = 3,
             preset = "compact")
Peak response: 1-lag vs 3-lag

Model

Variable

Shock

Mean value

Median value

Lower value

Upper value

Mean horizon

Median horizon

Lower horizon

Upper horizon

baseline

gdp

gs

0.038

0

-0.001

0.001

1.105

0

0

10.5

alternative

gdp

gs

66,131.493

0

-0.001

0.003

4.740

1

0

20.0

Publication plot — publish_bsvar_plot() applies a paper-ready theme and returns the plot object for further adjustment or direct saving.

publish_bsvar_plot(rep_irf, preset = "paper")

A pre-rendered diagnostics figure demonstrating the publication styling layer:

This diagnostics plot is not an economic-effects plot. It summarizes the health of the stored admissible-draw sample for the sign-restricted model. Start with effective_sample_size and kernel_zero_share: they tell you whether the accepted draws contain enough effective information and whether a large share of the admissible support is effectively degenerate. The restriction counts and other kernel summaries then provide context for how demanding the identification problem is.

Next steps

The Hypothesis Testing vignette covers formal posterior probability statements — hypothesis_irf(), joint_hypothesis_irf(), and simultaneous_irf() — for testing sign and magnitude restrictions on the fiscal transmission mechanism.