bsvarPost

bsvarPost provides post-estimation methods for posterior objects from bsvars and bsvarSIGNs. It computes cumulative effects, tabular posterior summaries, comparisons across model specifications, posterior probabilities, representative draws, event-specific historical decompositions, and diagnostics for sign-restricted models.

The package is intended for analyses after model estimation. Use the parent packages to specify and estimate a BSVAR, and bsvarPost to summarise and evaluate the resulting posterior distribution.

What question are you trying to answer?

Research question	Function(s)
How can posterior impulse responses be represented in tabular form?	tidy_irf()
What is the cumulative response through a chosen horizon?	cdm()
Are posterior conclusions robust across model specifications?	compare_irf() or compare_cdm()
What is the posterior probability of an economically meaningful hypothesis?	hypothesis_irf() or hypothesis_cdm()
Does a hypothesis hold jointly, or over an entire response path?	joint_hypothesis_irf() or simultaneous_irf()
Which posterior draw provides a coherent representative response?	median_target_irf()
When does an impulse response peak, persist, or decay?	peak_response() and the timing summaries
Which structural shocks account for a particular historical episode?	tidy_hd_event() and shock_ranking()
How well do posterior draws satisfy identifying restrictions?	restriction_audit() and acceptance_diagnostics()

The examples use one question throughout: how does a government-spending shock affect cumulative US GDP?

Installation

Install the two modelling packages first, then install bsvarPost from GitHub:

install.packages(c("bsvars", "bsvarSIGNs", "remotes"))
remotes::install_github("DavidZenz/bsvarPost", build_vignettes = TRUE)

Basic posterior analysis

1. Obtain a posterior distribution

If a posterior distribution from bsvars or bsvarSIGNs is already available, assign it to post and skip this step. The following minimal estimation only provides the posterior object used below; model specification and estimation are documented by bsvars.

library(bsvars)
library(bsvarPost)

data(us_fiscal_lsuw)
set.seed(123)
spec <- specify_bsvar$new(us_fiscal_lsuw, p = 1)
post <- estimate(spec, S = 1e3, thin = 1, show_progress = FALSE)

2. Summarise an impulse response

tidy_irf() computes posterior summaries and credible intervals for each model, response variable, structural shock, and horizon, and returns them in tabular form.

irf_tbl <- tidy_irf(post, horizon = 20, probability = 0.90)
subset(irf_tbl, variable == "gdp" & shock == "gs" &
                  horizon %in% c(0, 4, 8, 20))

The corresponding tidy_*() functions provide the same tabular representation for cumulative dynamic multipliers, forecast error variance decompositions, historical decompositions, forecasts, and structural shocks. Set draws = TRUE when posterior draw-level output is required.

3. Compute cumulative dynamic multipliers

cdm() computes cumulative dynamic multipliers from the posterior distributions produced by the parent packages. It returns posterior draws, so cumulative uncertainty is evaluated draw by draw rather than by summing marginal posterior quantiles.

multiplier <- cdm(post, horizon = 20)
multiplier_tbl <- tidy_cdm(multiplier)
gdp_multiplier <- subset(multiplier_tbl, variable == "gdp" & shock == "gs")
ggplot2::autoplot(gdp_multiplier)

For cumulative responses normalised by the sample standard deviation of the corresponding observed variable, use scale_by = "shock_sd". The default retains the shock scale of the estimated model.

Posterior inference and model comparison

Is the conclusion robust to specification choices?

Given a second estimated posterior distribution, named arguments identify the model specifications in the combined posterior summary:

comparison <- compare_cdm(baseline = post, alternative = post_alt,
                          horizon = 20)
ggplot2::autoplot(comparison)

Related functions compare impulse responses, forecast error variance decompositions, forecasts, historical episodes, response timing, and identifying restrictions. The Inference and Comparison article describes how to select a comparison that corresponds to the research hypothesis.

How strong is the posterior evidence?

Posterior probabilities evaluate hypotheses directly and should not be inferred from whether pointwise credible intervals overlap:

hypothesis_cdm(post, variables = "gdp", shocks = "gs", horizon = 8,
               relation = ">", value = 0)

joint_hypothesis_cdm(post, variable = "gdp", shock = "gs", horizon = 0:8,
                     relation = ">", value = 0)

magnitude_audit() evaluates economically relevant thresholds. simultaneous_irf() and simultaneous_cdm() compute credible bands with simultaneous coverage over a selected response path. See Inference and Comparison for pointwise and joint hypotheses, magnitude thresholds, and simultaneous credible bands.

Which single draw should represent the posterior?

Quantiles computed separately at each horizon need not correspond to a single admissible posterior draw. median_target_irf() and median_target_cdm() select a representative draw whose response path is coherent across horizons. peak_response(), duration_response(), half_life_response(), and time_to_threshold() summarise the magnitude and timing of the resulting responses.

What drove a historical episode?

tidy_hd_event() summarises structural-shock contributions over a selected period. shock_ranking() ranks shocks by their contributions, and compare_hd_event() compares the same period across model specifications. The Historical-Decomposition Analysis article develops these analyses without repeating the construction of a historical decomposition.

What changes for sign-restricted models?

For a PosteriorBSVARSIGN, most_likely_admissible_irf() and most_likely_admissible_cdm() select representative draws among those that satisfy the identifying restrictions. restriction_audit() evaluates those restrictions, while acceptance_diagnostics() reports the retained posterior sample and the support for admissible draws. See Analysis of Sign-Restricted Models.

From results to a figure or table

Tabular posterior summaries can be visualised directly with ggplot2::autoplot(). report_bundle() returns a plot, compact table, and caption based on the same posterior results:

result <- compare_cdm(baseline = post, alternative = post_alt, horizon = 20)
publication <- report_bundle(result,
  caption = "Cumulative output response to a government-spending shock",
  preset = "compact", digits = 3)

publication$plot
publication$table

Use publish_bsvar_plot() to apply the package's graphical style to a plot. Additional output formats and integrations are documented in the function reference.

Where next?

• Post-estimation Analysis with bsvarPost develops the fiscal example from posterior estimation to an interpretable cumulative response.
• Inference and Comparison considers sensitivity across model specifications and posterior hypotheses.
• Historical-Decomposition Analysis examines structural-shock contributions during selected historical episodes.
• Analysis of Sign-Restricted Models presents representative admissible draws, restriction evaluation, and acceptance diagnostics.
• Function reference documents all functions and optional integrations.

License

bsvarPost is licensed under GPL (>= 3).