Title:	Simulate Stock-Flow Consistent Models
Version:	0.2.1
Description:	Routines to write, simulate, and validate stock-flow consistent (SFC) models. The accounting structure of SFC models are described in Godley and Lavoie (2007, ISBN:978-1-137-08599-3). The algorithms implemented to solve the models (Gauss-Seidel and Broyden) are described in Kinsella and O'Shea (2010) <doi:10.2139/ssrn.1729205> and Peressini and Sullivan (1988, ISBN:0-387-96614-5).
License:	MIT + file LICENSE
Encoding:	UTF-8
RoxygenNote:	7.1.1
URL:	https://github.com/joaomacalos/sfcr
BugReports:	https://github.com/joaomacalos/sfcr/issues
Imports:	dplyr (≥ 1.0.2), expm (≥ 0.999.5), forcats (≥ 0.5.0), igraph (≥ 1.2.6), kableExtra (≥ 1.3.1), magrittr (≥ 1.5), purrr (≥ 0.3.4), Rdpack (≥ 2.1), rootSolve (≥ 1.8.2.1), rlang (≥ 0.4.7), tibble (≥ 3.0.3), tidyr (≥ 1.1.2), tidyselect (≥ 1.1.0), stringr (≥ 1.4.0), utils, vctrs (≥ 0.3.5), Rcpp (≥ 1.0.5)
Suggests:	ggraph, ggplot2, grDevices, knitr, pkgdown, rmarkdown, RColorBrewer, testthat (≥ 2.3.2), tidygraph, tidyverse, networkD3
VignetteBuilder:	knitr
RdMacros:	Rdpack
LinkingTo:	Rcpp, RcppArmadillo
NeedsCompilation:	yes
Packaged:	2021-10-11 07:46:08 UTC; JouJo
Author:	Joao Macalos [aut, cre]
Maintainer:	Joao Macalos <joaomacalos@gmail.com>
Repository:	CRAN
Date/Publication:	2021-10-11 08:00:02 UTC

Pipe operator

Description

See magrittr::%>% for details.

Usage

lhs %>% rhs

Abort if duplicated variables

Description

Abort if duplicated variables

Usage

.abort_if_dup(dups)

Arguments

Author(s)

João Macalós

Abort if typo on the codes of columns

Description

Abort if typo on the codes of columns

Usage

.abort_typo_code(nms)

Arguments

Author(s)

João Macalós

Abort if column validation is not fulfilled

Description

Abort if column validation is not fulfilled

Usage

.abort_water_leakc(c2names, which)

Arguments

Author(s)

João Macalós

Abort if row validation is not fulfilled

Description

Abort if row validation is not fulfilled

Usage

.abort_water_leakr(r2names, which)

Arguments

Author(s)

João Macalós

Find dependencies and order the equations

Description

Find dependencies and order the equations

Usage

.add_time2(x)

Arguments

Author(s)

João Macalós

Find dependencies and order the equations

Description

Find dependencies and order the equations

Usage

.add_time_stamps(eq_as_tb)

Arguments

Author(s)

João Macalós

Check if all values in x are equal

Description

Check if all values in x are equal

Usage

.all_equal(x, tol)

Arguments

Author(s)

João Macalós

Take arguments and make them a row of a tibble

Description

Take arguments and make them a row of a tibble

Usage

.args_to_row(arg, tb)

Arguments

Author(s)

João Macalós

Broyden solver algorithm

Description

Broyden solver algorithm

Usage

.broyden_solver(.x0, .fn, max_ite, tol)

Arguments

Note

Check https://www.math.usm.edu/lambers/mat419/lecture11.pdf for a quick reference on the algorithm.

Author(s)

João Macalós

Check shocks for length consistency and warn about risks of using exogenous series

Description

This function makes two checks:

Usage

.check_external_consistency(external, periods = periods)

Arguments

Details

1. The exogenous variable is a constant that is repeated over time;

2. The exogenous variable has exactly the same length as the shock.

Furthermore, it throws a warning that using exogenous series in a shock can lead to unexpected behavior if the length of the shock is not the same as the periods in the scenario.

Author(s)

João Macalós

Check shocks for length consistency and warn about risks of using exogenous series

Description

This function executes two checks and issues one warning.

Usage

.check_shock_consistency(shock, periods = periods)

Arguments

Details

First, it checks that the start of the shock is not negative and that the end of the shock is not bigger than the number of periods in the scenario.

Secondly, it checks for consistency on the length of the shocks added to the scenario. Only two types of exogenous variables are allowed:

1. The exogenous variable is a constant that is repeated over time;

2. The exogenous variable has exactly the same length as the shock.

Furthermore, it throws a warning that using exogenous series in a shock can lead to unexpected behavior if the length of the shock is not the same as the periods in the scenario.

Author(s)

João Macalós

Check that symmetry condition is valid and fulfill missing entries

Description

Check that symmetry condition is valid and fulfill missing entries

Usage

.check_symmetry(m)

Arguments

Author(s)

João Macalós

Split the formulae into a tibble with the left-hand side and right-hand side as columns

Description

Split the formulae into a tibble with the left-hand side and right-hand side as columns

Usage

.eq_as_tb(equations)

Arguments

Author(s)

João Macalós

Extend a baseline matrix

Description

This function is called if a scenario is to be created that just continues with the baseline specification. It is useful to create a benchmark model to compare new scenarios.

Usage

.extend_baseline_matrix(baseline, periods)

Arguments

Author(s)

João Macalós

Fill all possible rows and columns and validate

Description

Fill all possible rows and columns and validate

Usage

.fill_rows_and_cols(m)

Arguments

Author(s)

João Macalós

Find blocks of independent equations (wrapper around igraph functions)

Description

Find blocks of independent equations (wrapper around igraph functions)

Usage

.find_blocks(adj)

Arguments

Author(s)

João Macalós

Find names for display matrix

Description

Clean cells to display in latex format

Usage

.find_names(matrix)

Arguments

Author(s)

João Macalós

Get numeric matrix for evaluation from balance-sheet or transactions-flow matrices

Description

Get numeric matrix for evaluation from balance-sheet or transactions-flow matrices

Usage

.get_matrix(mtrx, bl1, bl2)

Arguments

Author(s)

João Macalós

Check if two values are equal

Description

Check if two values are equal

Usage

.is_equal(x, y, tol)

Arguments

Author(s)

João Macalós

Make the underlying matrix that will be modified in place by the solvers

Description

Make the underlying matrix that will be modified in place by the solvers

Usage

.make_matrix(equations, external, periods, initial = NULL)

Arguments

Author(s)

João Macalós

Prep equations for Broyden and Newton solvers

Description

Prep equations for Broyden and Newton solvers

Usage

.prep_broyden(.block)

Arguments

Author(s)

João Macalós

Re-wrote the equations with the correct matrix syntax that will be used to evaluate the expressions inside the Gauss Seidel algorithm

Description

Re-wrote the equations with the correct matrix syntax that will be used to evaluate the expressions inside the Gauss Seidel algorithm

Usage

.prep_equations(ordered_eqs, external)

Arguments

Author(s)

João Macalós

Pattern replacement var

Description

Pattern replacement var

Usage

.pvar(x)

Arguments

Author(s)

João Macalós

Pattern replacement lag

Description

Pattern replacement lag

Usage

.pvarlag(x)

Arguments

Author(s)

João Macalós

Find cyclical nodes

Description

Find cyclical nodes

Usage

.return_loops(m)

Arguments

Note

See Networks: an introduction from M.E.J. Newman, 2010, p. 136-139 for a reference on this algorithm.

Scan columns to fill whenever there's only one value missing.

Description

Scan columns to fill whenever there's only one value missing.

Usage

.scan_cols(m)

Arguments

Author(s)

João Macalós

Scan rows to fill whenever there's only one value missing.

Description

Scan rows to fill whenever there's only one value missing.

Usage

.scan_rows(m)

Arguments

Author(s)

João Macalós

Broyden solver wrapper

Description

Broyden solver wrapper

Usage

.sfcr_broyden(m, equations, periods, max_ite, tol)

Arguments

Details

This function implements the Broyden method to solve the cyclical blocks of equations.

Author(s)

João Macalós

Check for missing endogenous variables

Description

Check for missing endogenous variables

Usage

.sfcr_eqs_check(m, equations)

Arguments

Author(s)

João Macalós

Find adjacency matrix for a system of equations

Description

Find adjacency matrix for a system of equations

Usage

.sfcr_find_adjacency(equations)

Arguments

Author(s)

João Macalós

Place the equations in the correct order for estimation

Description

Place the equations in the correct order for estimation

Usage

.sfcr_find_order(equations)

Arguments

Details

Create an adjacency matrix and apply .find_blocks() function to identify the blocks of independent equations.

Author(s)

João Macalós

Gauss Seidel algorithm

Description

Gauss Seidel algorithm

Usage

.sfcr_gauss_seidel(m, equations, periods, max_ite, tol)

Arguments

Details

This algorithm simulates the model by recursion by using nested for loops. At each round of iteration, the values calculated are compared to the previous values. If the difference is below a tolerance value set by the user, the round of calculations have converged and the algorithm jump to the next block of equations.

The algorithm modifies a matrix in place to optimize its performance.

Author(s)

João Macalós

Make matrix for scenario calculations

Description

Make matrix for scenario calculations

Usage

.sfcr_make_scenario_matrix(baseline, scenario, periods)

Arguments

Details

This function generates the base matrix that is going to be modified in place by the different solvers.

Author(s)

João Macalós

Newton-Raphson solver implemented with rootSolve::multiroot()

Description

Newton-Raphson solver implemented with rootSolve::multiroot()

Usage

.sfcr_newton(m, equations, periods, max_ite, tol, ...)

Arguments

Details

This function implements the Newton-Raphson method to solve the cyclical blocks of equations. It relies on the multiroot() function from rootSolve.

Author(s)

João Macalós

Transform entries into latex style

Description

Transform entries into latex style

Usage

.to_latex_style(matrix, nms)

Arguments

Author(s)

João Macalós

Validate a balance-sheet or transactions-flow matrix on the simulated data

Description

Validate a balance-sheet or transactions-flow matrix on the simulated data

Usage

.validate_matrix(mtrx, m, which = "tfm", tol, rtol = FALSE)

Arguments

Author(s)

João Macalós

Check that the portfolio matrix respect the horizontal and vertical adding-up constraints

Description

Check that the portfolio matrix respect the horizontal and vertical adding-up constraints

Usage

.validate_scan(m, which)

Arguments

Author(s)

João Macalós

Abort if not

Description

Abort if not

Usage

abortifnot(cnd, message = NULL)

Arguments

Author(s)

João Macalós

sfcr_mlt constructor

Description

sfcr_mlt constructor

Usage

new_sfcr_mlt(multis, fixed)

Arguments

Author(s)

João Macalós

sfcr_mlt_set constructor

Description

sfcr_mlt_set constructor

Usage

new_sfcr_mlt_set(x, original)

Arguments

Author(s)

João Macalós

sfcr_mlt_shock constructor

Description

sfcr_mlt_shock constructor

Usage

new_sfcr_mlt_shock(x, original)

Arguments

Author(s)

João Macalós

sfcr_set constructor

Description

sfcr_set constructor

Usage

new_sfcr_set(list)

Arguments

Author(s)

João Macalós

new_sfcr_tbl constructor

Description

new_sfcr_tbl constructor

Usage

new_sfcr_tbl(tbl, matrix, calls, external)

Arguments

Author(s)

João Macalós

Simulate the baseline scenario of a stock-flow consistent model

Description

The sfcr_baseline() function is used to simulate a SFC model.

Usage

sfcr_baseline(
  equations,
  external,
  periods,
  initial = NULL,
  hidden = NULL,
  max_iter = 350,
  .hidden_tol = 0.1,
  tol = 1e-08,
  method = "Broyden",
  rhtol = FALSE,
  ...
)

Arguments

Details

The output of a sfcr_baseline() is a sfcr_tbl. The only difference between a sfcr_tbl and a standard tbl_df is that the former has two extra attributes: matrix and call. The matrix attribute, for example, can be accessed by calling attributes(sfcr_sim_object)$matrix. It is possible to see, in the matrix, the number of iterations required to calculate each block of equations in the model. The call attribute shows the blocks of equations and preserve the call that are used internally.

The equations, exogenous, and parameters arguments must be written with the R formula syntax, i.e., the left-hand side of each item is separated to the right-hand side by a twiddle. Variables that represent lags of endogenous or exogenous variables must be followed by [-1]. See examples for details on the syntax.

Before solving the system of equations, two consecutive depth-first searches identify and order the blocks of independent equations in the system. The system is then solved sequentially, i.e., the variables that depend only on lagged or exogenous values are evaluated first, and then the variables that depends on these variables, etc. The solving algorithms are only applied to the blocks of mutually dependent equations. The great igraph package is used to implement the two consecutive depth-first searches.

• Methods:

The sfcr package provides three algorithms to solve the blocks of cyclical equations: the Gauss-Seidel algorithm, the Broyden algorithm, and the Newton-Raphson algorithm. The default method is "Broyden" as it tends to be fastest one.

See (Kinsella and OShea 2010) for details on the Gauss-Seidel algorithm and (Peressini et al. 1988) for details on the Broyden and Newton-Raphson algorithms.

The "Broyden" algorithm uses the rootSolve::jacobian.full() function to get the initial Jacobian matrix, and compiled code from RcppArmadillo to invert the jacobians. See also https://www.math.usm.edu/lambers/mat419/lecture11.pdf.

The Gauss Seidel algorithm is implemented as described by (Kinsella and OShea 2010). Finally, the "Newton" method uses the rootSolve::multiroot() function to solve the system.

• Hidden equation:

One of the defining aspects of a SFC model is its water tight accounting. One way to check whether the model was correctly defined is to see if the hidden (redundant) equation is satisfied after the model is simulated. In stationary models, an absolute comparison should suffice as the model converges to a stationary state. However, growth models converge to a stable growth rate where stocks are perpetually increasing. It is inadequate to use a absolute comparison in such models. In these cases, the rhtol argument ("relative hidden tolerance") must be set to TRUE in order to perform a relative comparison. The relative comparison evaluates the numerical discrepancy in the hidden equation as a ratio of one of its elements. For example, if hidden = c("Bbs" = "Bbd"), the hidden equation will be evaluated according to the following steps:

1. d = (Bbs - Bbd)

2. isTRUE(d/Bbs < .hidden_tol)

In general, the .hidden_tol argument should be set to a small number (e.g. 1e-6). The function will check that this proportion remains the same for all simulated periods.

Value

A sfcr_tbl.

Author(s)

João Macalós, joaomacalos@gmail.com

References

Kinsella S, OShea T (2010). “Solution and Simulation of Large Stock Flow Consistent Monetary Production Models via the Gauss Seidel Algorithm.” SSRN Electronic Journal. doi: 10.2139/ssrn.1729205, https://doi.org/10.2139/ssrn.1729205. Peressini AL, Sullivan FE, Uhl JJ (1988). The Mathematics of Nonlinear Programming. Springer-Verlag, Berlin, Heidelberg. ISBN 0387966145.

Examples

eqs <- sfcr_set(
  TXs ~ TXd,
  YD ~ W * Ns - TXs,
  Cd ~ alpha1 * YD + alpha2 * Hh[-1],
  Hh ~ YD - Cd + Hh[-1],
  Ns ~ Nd,
  Nd ~ Y / W,
  Cs ~ Cd,
  Gs ~ Gd,
  Y ~ Cs + Gs,
  TXd ~ theta * W * Ns,
  Hs ~ Gd - TXd + Hs[-1]
)

external <- sfcr_set(Gd ~ 20, W ~ 1, alpha1 ~ 0.6, alpha2 ~ 0.4, theta ~ 0.2)

# Periods is set to 10 to run faster. A usual model should run at
# least 50 periods to find a steady state
sfcr_baseline(equations = eqs, external = external, periods = 10)

Create a tbl_graph object blocks and cycles information

Description

Create a tbl_graph object blocks and cycles information

Usage

sfcr_dag_blocks(equations)

Arguments

Details

This function creates a tbl_graph with information about the blocks and cycles attached to it. This object can then be used to plot the DAG of the model.

Value

A tbl_graph

Author(s)

João Macalós, joaomacalos@gmail.com

Plot the DAG with blocks and cycles information

Description

Plot the DAG with blocks and cycles information

Usage

sfcr_dag_blocks_plot(equations, title = NULL, size = 10)

Arguments

Details

This function creates a tbl_graph with information about the cycles attached to it. This object can then be used to plot the DAG of the model.

Value

A tbl_graph

Author(s)

João Macalós, joaomacalos@gmail.com

Create a tbl_graph object with cycles information

Description

Create a tbl_graph object with cycles information

Usage

sfcr_dag_cycles(equations)

Arguments

Details

This function creates a tbl_graph with information about the cycles attached to it. This object can then be used to plot the DAG of the model.

Value

A tbl_graph

Author(s)

João Macalós, joaomacalos@gmail.com

Plot the DAG with cycles information

Description

Plot the DAG with cycles information

Usage

sfcr_dag_cycles_plot(equations, title = NULL, size = 10)

Arguments

Author(s)

João Macalós

Expand variables to implement sensitivity analysis

Description

The sfcr_expand() function is a s3 generic that takes a list of external objects and returns a expanded set of these lists. It has methods for sfcr_set objects and for sfcr_shock objects.

Usage

sfcr_expand(x, variable, values)

Arguments

Details

There are two available methods for the sfcr_expand() function:

• sfcr_set: Takes a sfcr_set object with external variables and creates a list of sets that inherits all the aspects of the x set supplied but set the values of the variable to the each element of value. The output is a sfcr_mlt_set object.

• sfcr_shock: Takes a sfcr_shock object and creates a list of shocks that inherits all the aspects of the x shock but set the values of the variable to each element of value. The output of this method is a sfcr_mlt_shock object.

Author(s)

João Macalós

Examples

# 1. Expand a external set:
external <- sfcr_set(G_d ~ 20, W ~ 1, alpha1 ~ 0.6, alpha2 ~ 0.4, theta ~ 0.2)
sfcr_expand(external, alpha2, c(0.1, 0.2))

# 2. Expand a shock:
shock <- sfcr_shock(variables = sfcr_set(alpha1 ~ 0.8), start = 5, end = 50)
sfcr_expand(shock, alpha1, c(0.7, 0.8, 0.9))

Get block structure of a sfcr_tbl object

Description

Get block structure of a sfcr_tbl object

Usage

sfcr_get_blocks(sfcr_tbl)

Arguments

Author(s)

João Macalós

Get Matrix form of sfcr_tbl object

Description

Get Matrix form of sfcr_tbl object

Usage

sfcr_get_matrix(sfcr_tbl)

Arguments

Author(s)

João Macalós

Create balance-sheet or transactions-flow matrices

Description

Create balance-sheet or transactions-flow matrices

Usage

sfcr_matrix(columns, codes, ...)

Arguments

Note

This function can be used to generate a transactions- flow matrix as well as a balance-sheet matrix. If the user wishes to validate these matrices with the simulated data, please pay attention to the following details:

• Transactions-flow Matrix: In the transactions-flow matrix, the sum column is going to be generated automatically by the validation function. Please do not add it by hand.

• Balance-sheet Matrix: In the balance-sheet matrix, it might be the case that some rows do not sum to zero. Therefore, the user must supply by hand the non-zero values of the sum column. This column should always be the last column of the matrix and should always be named as "Sum". If there's no column named as "Sum", it will be generated automatically by the validation function with all entries equal to zero.

Author(s)

João Macalós, joaomacalos@gmail.com

Examples

# Balance-sheet matrix

bs_pc <- sfcr_matrix(
  columns = c("Households", "Firms", "Government", "Central bank", "sum"),
  codes = c("h", "f", "g", "cb", "s"),
  r1 = c("Money", h = "+Hh", cb = "-Hs"),
  r2 = c("Bills", h = "+Bh", g = "-Bs", cb = "+Bcb"),
  r3 = c("Balance", h = "-V", g = "+V")
)


# Transactions-flow matrix
tfm_pc <- sfcr_matrix(
  columns = c("Households", "Firms", "Government", "CB current", "CB capital"),
  codes = c("h", "f", "g", "cbc", "cbk"),
  c("Consumption", h = "-C", f = "+C"),
  c("Govt. Expenditures", f = "+G", g = "-G"),
  c("Income", h = "+Y", f = "-Y"),
  c("Int. payments", h = "+r[-1] * Bh[-1]", g = "-r[-1] * Bs[-1]", cbc = "+r[-1] * Bcb[-1]"),
  c("CB profits", g = "+r[-1] * Bcb[-1]", cbc = "-r[-1] * Bcb[-1]"),
  c("Taxes", h = "-TX", g = "+TX"),
  c("Ch. Money", h = "-(Hh - Hh[-1])", cbk = "+(Hs - Hs[-1])"),
  c("Ch. Bills", h = "-(Bh - Bh[-1])", g = "+(Bs - Bs[-1])", cbk = "-(Bcb - Bcb[-1])")
)

Print matrix to screen

Description

Print matrix to screen

Usage

sfcr_matrix_display(matrix, which = "tfm")

Arguments

Details

This function takes a matrix as input and generate a kableExtra table with math symbols displayed in latex style.

Note

This function converts the math expressions used to build the sfcr_matrix into a latex format, but cannot add modifications to it. The user is invited to explore the source code and the kableExtra package in order to personalize his/her own matrices.

Author(s)

João Macalós

Examples

# Balance-sheet matrix

bs_insout <- sfcr_matrix(
  columns = c("Households", "Firms", "Government", "Central bank", "Banks", "Sum"),
  codes = c("h", "f", "g", "cb", "b", "s"),
  r1 = c("Inventories", f = "+INV", s = "+INV"),
  r2 = c("HPM", h = "+Hhd", cb = "-Hs", b = "+Hbd"),
  r3 = c("Advances", cb = "+As", b = "-Ad"),
  r4 = c("Checking deposits", h = "+M1h", b = "-M1s"),
  r5 = c("Time deposits", h = "+M2h", b = "-M2s"),
  r6 = c("Bills", h = "+Bhh", g = "-Bs", cb = "+Bcb", b = "+Bbd"),
  r7 = c("Bonds", h = "+BLh * pbl", g = "-BLs * pbl"),
  r8 = c("Loans", f = "-Ld", b = "+Ls"),
  r9 = c("Balance", h = "-V", f = 0, g = "+GD", cb = 0, b = 0, s = "-INV")
)

sfcr_matrix_display(bs_insout, "bs")

Simulate multiple SFC models at the same time

Description

The sfcr_multis() function is used to simulate multiple models at the same time, returning a list of sfcr_tbls.

Usage

sfcr_multis(expanded, fixed, periods, ...)

Arguments

Details

The sfcr_multis() function takes an expanded object and a fixed to simulate multiple models that will share the content of fixed but vary on the expanded.

This function is a generic, which means that its implementation depends on the class of the expanded argument.

The available methods for the sfcr_multis() function depends on the expanded argument. There are three possible methods:

• sfcr_mlt_set: When the sfcr_multis() takes an sfcr_mlt_set class as the input of expanded, it must take a list of equations of the sfcr_set class as the fixed input. This method simulates many baseline models that accept the same set of equations and vary on the external variables supplied with the expanded argument.

• sfcr_mlt_shock: When the sfcr_multis() takes an sfcr_mlt_shock class as the input of expanded, it must also take an object of sfcr_tbl class as the input of fixed. It will simulate multiple scenario models that takes the same baseline model and diverge on the content of the multiple shocks provided with the expanded argument that are applied to it.

• sfcr_mlt: When the sfcr_multis() function takes a sfcr_mlt class object as the input of the expanded argument, a sfcr_shock object must be supplied with the fixed argument. This method simulates multiple scenario models that applies the same shock to a varying number of baseline models.

Author(s)

João Macalós

Examples

eqs <- sfcr_set(
  TX_s ~ TX_d,
  YD ~ W * N_s - TX_s,
  C_d ~ alpha1 * YD + alpha2 * H_h[-1],
  H_h ~ YD - C_d + H_h[-1],
  N_s ~ N_d,
  N_d ~ Y / W,
  C_s ~ C_d,
  G_s ~ G_d,
  Y ~ C_s + G_s,
  TX_d ~ theta * W * N_s,
  H_s ~ G_d - TX_d + H_s[-1]
)

external <- sfcr_set(G_d ~ 20, W ~ 1, alpha1 ~ 0.6, alpha2 ~ 0.4, theta ~ 0.2)

shock <- sfcr_shock(
  variables = sfcr_set(
    alpha2 ~ 0.3
  ),
  start = 1,
  end = 3
)

baseline <- sfcr_baseline(eqs, external, periods = 5)

# Example 1: Many external sets, 1 set of equations:
expanded1 <- sfcr_expand(external, alpha1, c(0.7, 0.8))
multis1 <- sfcr_multis(expanded = expanded1, fixed = eqs, periods = 5)

# Example 2: Many shocks, 1 baseline model:
expanded2 <- sfcr_expand(shock, alpha2, c(0.1, 0.2))
multis2 <- sfcr_multis(expanded = expanded2, fixed = baseline, periods = 5)

# Example 3: Many baseline models, 1 shock:
multis3 <- sfcr_multis(expanded = multis1, fixed = shock, periods = 5)

Find a valid matrix of portfolio parameters

Description

The sfcr_portfolio() function calculates a valid matrix of portfolio parameters by applying the symmetry condition and then filling the missing rows accordingly to the vertical and horizontal adding-up constraints.

Usage

sfcr_portfolio(m, known)

Arguments

Details

This function calculates only the values of the rates of return matrix, i.e., the internal matrix. The adding-up constraint number 1, that calculates the share of assets in the net wealth and the impact of regular income to wealth ratio must be calculated separately.

If supplied with insufficient parameters, the function will return a matrix with NA values.

This function requires at least (n^2 - n)/2 known parameters to find a valid portfolio matrix, where n is the number of rows/columns. This is achieved by setting known parameters outside the diagonal and not on symmetrical entries, i.e., not lambda12 and lambda21, for example.

Author(s)

João Macalós

Examples

j1 <- matrix(paste0("lambda", c(11:14, 21:24, 31:34, 41:44)), ncol = 4, nrow = 4, byrow = TRUE)
j2 <- c(lambda12 = 0, lambda13 = 0, lambda14 = 0, lambda23 = -15, lambda24 = -15, lambda34 = -15)

sfcr_portfolio(j1, j2)

Generate random sequences inside sfcr_set()

Description

This function can only be used inside sfcr_set() when generating variables. It smartly guesses the length of the sfcr_baseline() model or of the sfcr_shock() that it is inserted.

Usage

sfcr_random(.f, ...)

Arguments

Author(s)

João Macalós

Examples

# Create a random normal series to pass along an endogenous series
# Example taken from model PC EXT 2.
sfcr_set(
    Ra ~ sfcr_random("rnorm", mean=0, sd=0.05)
)

Plot Sankey's diagram representation of transactions-flow matrix

Description

Plot Sankey's diagram representation of transactions-flow matrix

Usage

sfcr_sankey(tfm, baseline, when = "start")

Arguments

Author(s)

João Macalós

Add scenarios to a sfcr model.

Description

Add scenarios to a sfcr model.

Usage

sfcr_scenario(
  baseline,
  scenario,
  periods,
  max_iter = 350,
  tol = 1e-10,
  method = "Broyden",
  ...
)

Arguments

Details

Add scenario(s) to a model generated with sfcr_baseline() functions.

This function inherits the block structure from the steady state model. See sfcr_baseline for further details on the algorithms.

Author(s)

João Macalós, joaomacalos@gmail.com

See Also

sfcr_baseline

Examples

eqs <- sfcr_set(
  TX_s ~ TX_d,
  YD ~ W * N_s - TX_s,
  C_d ~ alpha1 * YD + alpha2 * H_h[-1],
  H_h ~ YD - C_d + H_h[-1],
  N_s ~ N_d,
  N_d ~ Y / W,
  C_s ~ C_d,
  G_s ~ G_d,
  Y ~ C_s + G_s,
  TX_d ~ theta * W * N_s,
  H_s ~ G_d - TX_d + H_s[-1]
)

external <- sfcr_set(G_d ~ 20, W ~ 1, alpha1 ~ 0.6, alpha2 ~ 0.4, theta ~ 0.2)

# t is set to 10 to run faster. A usual model should run at least 50 periods to find a steady state
steady_state <- sfcr_baseline(eqs, external, periods = 10)

# Increase G_d from 20 to 30 between periods 5 and 10
shock1 <- sfcr_shock(sfcr_set(G_d ~ 30), 5, 10)

sfcr_scenario(steady_state, scenario = list(shock1), 10)

# Increase W to 2, alpha2 to 0.5, and decrease theta to 0.15
shock2 <- sfcr_shock(
  variables = sfcr_set(
  W ~ 2,
  alpha2 ~ 0.5,
  theta ~ 0.15
  ),
  start = 5,
  end = 10)

sfcr_scenario(steady_state, list(shock2), 10)

Define the formulas of the model

Description

The sfcr_set() function is used to create the lists of equations, external variables, initial values, and also to modify the variables inside the sfcr_shock() function.

Usage

sfcr_set(..., exclude = NULL)

Arguments

Details

This function is a S3 generic that applicable to only two inputs: formula and sfcr_set. It is used to create a new set of equations or to modify an existing one.

Therefore, the equations must be written using the R formula syntax, i.e., the left-hand side of each equation is separated from the right-hand side with a ~ ("twiddle") instead of a =.

Furthermore, the sfcr_set() function recognizes two symbols that are not native to R language: [-1], and d().

• If a variable defined with sfcr_set() is followed by [-1], it will be recognized as a lagged variable.

• If a variable is defined inside d(), the sfcr engines will transform them into a first difference equation. For example, d(Hh) is internally transformed into (Hh - Hh[-1]).

Random variables can be created using the sfcr_random() function. See sfcr_random for further details.

Author(s)

João Macalós

Examples

# Endogenous set
equations <- sfcr_set(
  TXs ~ TXd,
  YD ~ W * Ns - TXs,
  Cd ~ alpha1 * YD + alpha2 * Hh[-1],
  Hh ~ YD - Cd + Hh[-1],
  Ns ~ Nd,
  Nd ~ Y / W,
  Cs ~ Cd,
  Gs ~ Gd,
  Y ~ Cs + Gs,
  TXd ~ theta * W * Ns,
  Hs ~ Gd - TXd + Hs[-1]
  )

# Exogenous set
exogenous <- sfcr_set(alpha1 ~ 0.8, alpha2 ~ 0.15)

# Modify an existing set
equations2 <- sfcr_set(equations, Hh ~ Hh[-1] + d(Hs), exclude = 4)

# Add normal random variable
sfcr_set(Ra ~ sfcr_random("rnorm", mean=10, sd=2))

Get names of endogenous vars and their index

Description

The sfcr_set_index() function takes a list of equations as its input and returns a tibble containing the name of the variable on the left-hand side of the equations and their position in the equations list.

Usage

sfcr_set_index(eqs)

Arguments

Details

This function aims to facilitate locating a specific equation in the list in order to modify the list of equations.

To add random variation to endogenous variables, use sfcr_random().

Author(s)

João Macalós

Create shock(s) to add to a sfcr_scenario().

Description

Create shock(s) to add to a sfcr_scenario().

Usage

sfcr_shock(variables, start, end)

Arguments

Author(s)

João Macalós, joaomacalos@gmail.com

Examples

sfcr_shock(
 variables = sfcr_set(G_d ~ 30, W ~ 1.5),
 start = 5,
 end = 66)

sfcr_shock(
 variables = sfcr_set(G_d ~ seq(30, 40, length.out=62)),
 start = 5,
 end = 66)

Validate a transactions-flow or balance-sheet matrix

Description

This function validates a transactions-flow or balance-sheet matrix with the simulated data obtained with sfcr_baseline() function

Usage

sfcr_validate(matrix, baseline, which, tol = 1, rtol = FALSE)

Arguments

Details

The relative discrepancy is calculated differently if we are dealing with a transactions-flow matrix or with a balance-sheet matrix. If which is set to tfm, the sum of the row/column is evaluated against the sum of the positive entries of that row/column.

For example, in a transactions-flow matrix with three entries in the "change in the stock of bills" row (-Delta (Bhd), + Delta (Bs), and + Delta (Bbd)), the discrepancy d = Delta Bs - Delta Bhd - Delta Bbd is evaluated against Delta Bs, i.e., the row is validated if d/Delta Bs < tol.

In a balance-sheet matrix, all the rows/columns that sum to zero are validated exactly as in a transactions-flow matrix. The exception to this rule is when there is a expected value. In this case, the discrepancy is evaluated as a proportion of the expected. value

To prevent unnecessary calculations, a absolute check with tolerance defined as 1e-3 is executed prior to this evaluation.

The absolute discrepancy set with tol should be enough to validate a stationary SFC Model.

Author(s)

João Macalós