13 Solving the model

13.1 Overview

ems_solve() solves the constrained optimization problem according to a range of runtime configuration options. In order to solve, a teems Docker image must be prebuilt. Singularity, accuracy, and error checks are carried out following a successful run. By default, solver outputs are automatically parsed into structured R objects via ems_compose().

13.2 Arguments

Argument	Default	Description
`cmf_path`	`NULL`	Path to the CMF file generated by `ems_deploy()`
`n_tasks`	`1L`	Number of tasks to run in parallel. Must be `1L` if `matrix_method` is `"LU"`
`n_subintervals`	`1L`	Number of subintervals for the applied shock. More subintervals may alleviate accuracy issues stemming from large shock magnitudes
`matrix_method`	`"LU"`	Matrix solution method (see below)
`solution_method`	`"Johansen"`	Solution method (see below)
`steps`	`c(2L, 4L, 8L)`	Vector of steps for the modified midpoint method. Must be all odd or all even, length 3
`laA`	`300L`	Memory parameter (%) for `"LU"` and `"SBBD"` methods
`laD`	`200L`	Memory parameter (%) for `"DBBD"` and `"NDBBD"` methods
`laDi`	`500L`	Memory parameter (%) for `"NDBBD"` method
`terminal_run`	`FALSE`	When `TRUE`, exits without running the solver, allowing the user to close R and run from the terminal
`suppress_outputs`	`FALSE`	When `TRUE`, solver outputs are not automatically parsed with `ems_compose()`

13.3 Basic usage

outputs <- ems_solve(
  cmf_path = cmf_path,
  matrix_method = "LU",
  solution_method = "Johansen"
)

13.4 Matrix methods

Method	Description
`"LU"`	Standard LU decomposition. The most robust and potentially slowest for large models. `n_tasks` must be `1L`. Works with both static and dynamic models
`"DBBD"`	Doubly bordered block diagonal. Parallel solution method for static models. Potentially faster than `"LU"` although less robust
`"SBBD"`	Singly bordered block diagonal. Parallel solution method for intertemporal models. Potentially faster than `"LU"` although less robust
`"NDBBD"`	Nested doubly bordered block diagonal. Parallel solution method for large intertemporal models with many timesteps

13.5 Solution methods

Method	Description
`"Johansen"`	Fast one-step approximation. Should only be used as a rough approximation due to handling of nonlinear equations. See COPS manual
`"mod_midpoint"`	Modified midpoint method that performs multiple passes for improved accuracy. The `steps` parameter controls the number of passes. See COPS manual

13.6 Memory parameters

If the solver returns “Error return from MA48B/BD because LA is …”, increase the relevant memory parameter gradually:

laA applies to "LU" and "SBBD" methods
laD applies to "DBBD" and "NDBBD" methods
laDi applies to the "NDBBD" method only

outputs <- ems_solve(
  cmf_path = cmf_path,
  matrix_method = "LU",
  solution_method = "Johansen",
  laA = 500L
)

13.7 Parallel solving

For models that support parallel matrix methods, increase n_tasks:

outputs <- ems_solve(
  cmf_path = cmf_path,
  n_tasks = 4L,
  matrix_method = "SBBD",
  solution_method = "Johansen"
)

13.8 Multi-step solution

For greater accuracy, use the modified midpoint method with subintervals:

outputs <- ems_solve(
  cmf_path = cmf_path,
  n_subintervals = 3L,
  matrix_method = "LU",
  solution_method = "mod_midpoint",
  steps = c(2L, 4L, 8L)
)

13.9 Terminal mode

For long-running models, terminal_run allows the user to close any R IDE prior to running from the terminal:

ems_solve(
  cmf_path = cmf_path,
  matrix_method = "LU",
  solution_method = "Johansen",
  terminal_run = TRUE
)