Estimate the Simultaneous Equations Model (SEM)

Estimate a system of simultaneous equations model (SEM) using a Bayesian approach. This function incorporates Gibbs sampling and allows for both density and point forecasts.

Usage

estimate(
  ts_data,
  sys_eq,
  dates,
  ...,
  options = list(gibbs = list(), fill = list(method = "mean")),
  estimates = NULL
)

# S3 method for class 'list'
estimate(
  ts_data,
  sys_eq,
  dates,
  ...,
  options = list(gibbs = list(), fill = list(method = "mean")),
  estimates = NULL
)

Arguments

ts_data

Time-series data set for the estimation.

sys_eq

A koma_seq object (system_of_equations) containing details about the system of equations used in the model.

dates

Key-value list for date ranges in various model operations.

...

Additional parameters.

options

Optional settings for estimation. Use list(gibbs = list(), fill = list(method = "mean")). Elements:

gibbs: Gibbs sampler settings (see Gibbs Sampler Specifications).
fill$method: "mean" or "median" used to fill ragged edges during estimation.

See Gibbs Sampler Specifications.

estimates

Ignored. Re-estimating only some equations of a previously estimated model is currently disabled; passing a koma_estimate object gives a warning and all equations are estimated.

Value

An object of class koma_estimate.

An object of class koma_estimateis a list containing the following elements:

estimates: The estimated parameters and other relevant information obtained from the model.
sys_eq: A koma_seq object containing details about the system of equations used in the model.
ts_data: The time-series data used for the estimation, with any NA values removed and lagged variables created.
y_matrix: The Y matrix constructed from the balanced data, used in the estimation process.
x_matrix: The X matrix constructed from the balanced data, used in the estimation process.
gibbs_specifications: The specifications used for the Gibbs sampling.
dates: The date ranges used during estimation.
plain_ts_names: Character vector of series names that were supplied as plain ts (not koma_ts) in ts_data. These are assumed to already be in rates and tagged accordingly; see the "Plain ts input" section below.

Details

After estimation, use summary for a full table of posterior summaries (with optional credible intervals and texreg output) and print for a concise console-friendly overview of the estimated system.

Parallel

This function provides the option for parallel computing through the future::plan() function. For a detailed example on executing estimate in parallel, see the vignette: vignette("parallel"). For more details, see the future package documentation.

Plain ts input

If any element of ts_data is a plain ts rather than a koma_ts (see ets), it is assumed to already be in rates, the form the model estimates on, and is converted to koma_ts with series_type = "rate", method = "none": the values are used as-is, no rate/level transformation is applied. A warning lists the affected series, and the same list is stored in the returned object as plain_ts_names (also surfaced when the koma_estimate is printed). If a series actually needs to be converted from levels (e.g. via a percentage or diff_log growth rate), convert it first with ets or as_ets; see vignette("koma-extended-timeseries").

koma_ts objects may carry custom attributes beyond series_type/ method (e.g. a project-specific value_type). Since all series in ts_data must share the same attribute names (see as_mets), any such extra attributes found on sibling koma_ts series are set to NA on the converted series.

Gibbs Sampler Specifications

ndraws: Integer specifying the number of Gibbs sampler draws. Default is 2000.
burnin_ratio: Numeric specifying the ratio for the burn-in period. Default is 0.5.
nstore: Integer specifying the frequency of stored draws. Every nstore-th draw after the burn-in is kept. Default is 1.
tau: Numeric tuning parameter for enforcing an acceptance rate. Default is 1.1.

Examples

data("simulated_sem")
set.seed(11)

fit <- estimate(
  ts_data = simulated_sem$ts_data,
  sys_eq = simulated_sem$sys_eq,
  dates = simulated_sem$dates,
  options = list(gibbs = list(ndraws = 10))
)
#> 
#> ── Gibbs Sampler Settings ──────────────────────────────────────────────────────
#> 
#> ── System Wide Settings ──
#> • Number of draws (`ndraws`): 10
#> • Burn-in ratio (`burnin_ratio`): 0.5
#> • Burn-in (`burnin`): 5
#> • Store frequency (`nstore`): 1
#> • Number of saved draws (`nsave`): 5
#> • Tau (`tau`): 1.1
#> 
#> 
#> ── Estimation ──────────────────────────────────────────────────────────────────
print(fit)
#> 
#> ── Estimates ───────────────────────────────────────────────────────────────────
#>     consumption ~  1.23 - 0.33 * gdp  +  0.49 * consumption.L(1)  +  0.22 * consumption.L(2)
#>      investment ~  2.47 - 1.32 * gdp  +  0.41 * investment.L(1)  +  0.35 * real_interest_rate
#> current_account ~  1.53 - 0.51 * current_account.L(1)  +  0.5 * world_gdp
#>   manufacturing ~  0.59  +  0.05 * manufacturing.L(1)  +  0.34 * world_gdp
#>         service ~  0.04  +  0.12 * service.L(1)  +  0.08 * population - 0.74 * gdp
#>             gdp == 0.4 * manufacturing  +  0.6 * service