| Title: | Simulate Stock-Flow Consistent Models |
|---|---|
| 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). |
| Authors: | Joao Macalos [aut, cre] |
| Maintainer: | Joao Macalos <[email protected]> |
| License: | MIT + file LICENSE |
| Version: | 0.2.1.9 |
| Built: | 2024-11-06 04:43:09 UTC |
| Source: | https://github.com/joaomacalos/sfcr |
The sfcr_baseline() function is used to simulate a SFC model.
sfcr_baseline( equations, external, periods, initial = NULL, hidden = NULL, max_iter = 350, .hidden_tol = 0.1, tol = 1e-08, method = "Broyden", rhtol = FALSE, ... )sfcr_baseline( equations, external, periods, initial = NULL, hidden = NULL, max_iter = 350, .hidden_tol = 0.1, tol = 1e-08, method = "Broyden", rhtol = FALSE, ... )
equations |
A |
external, initial
|
A |
periods |
A number specifying the total number of periods of the model to be simulated. |
|
Named object that identify the two variables that make the hidden equality
in the SFC model, e.g., |
|
max_iter |
Maximum iterations allowed per period. |
|
Error tolerance to accept the equality of the hidden equation. Defaults to 1.
In growth models, computational errors might buildup in the hidden equation, which renders any absolute
comparison inadequate. For such models, please turn |
|
tol |
Tolerance accepted to determine convergence. |
method |
The method to use to find a solution. Defaults to "Broyden". |
rhtol |
A logical argument that defines whether the a relative measure is used to evaluate
the hidden equation or not. Defaults to |
... |
Extra arguments to pass to |
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:
d = (Bbs - Bbd)
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.
A sfcr_tbl.
João Macalós, [email protected]
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. Peressini AL, Sullivan FE, Uhl JJ (1988). The Mathematics of Nonlinear Programming. Springer-Verlag, Berlin, Heidelberg. ISBN 0387966145.
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)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)
tbl_graph object blocks and cycles informationCreate a tbl_graph object blocks and cycles information
sfcr_dag_blocks(equations)sfcr_dag_blocks(equations)
equations |
A |
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.
A tbl_graph
João Macalós, [email protected]
Plot the DAG with blocks and cycles information
sfcr_dag_blocks_plot(equations, title = NULL, size = 10)sfcr_dag_blocks_plot(equations, title = NULL, size = 10)
equations |
A |
title |
Title of the plot. |
size |
Size of the points. |
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.
A tbl_graph
João Macalós, [email protected]
tbl_graph object with cycles informationCreate a tbl_graph object with cycles information
sfcr_dag_cycles(equations)sfcr_dag_cycles(equations)
equations |
A |
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.
A tbl_graph
João Macalós, [email protected]
Plot the DAG with cycles information
sfcr_dag_cycles_plot(equations, title = NULL, size = 10)sfcr_dag_cycles_plot(equations, title = NULL, size = 10)
equations |
A |
title |
Title of the plot. |
size |
Size of the points. |
João Macalós
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.
sfcr_expand(x, variable, values)sfcr_expand(x, variable, values)
x |
A external set created with |
variable |
the name of variable to be expanded. |
values |
a vector containing the new values of the external or shock variable. |
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.
João Macalós
# 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))# 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))
sfcr_tbl objectGet block structure of a sfcr_tbl object
sfcr_get_blocks(sfcr_tbl)sfcr_get_blocks(sfcr_tbl)
sfcr_tbl |
A |
João Macalós
sfcr_tbl objectGet Matrix form of sfcr_tbl object
sfcr_get_matrix(sfcr_tbl)sfcr_get_matrix(sfcr_tbl)
sfcr_tbl |
A |
João Macalós
Create balance-sheet or transactions-flow matrices
sfcr_matrix(columns, codes, ...)sfcr_matrix(columns, codes, ...)
columns |
Vector containing the name of the columns in the matrix. |
codes |
A vector containing the abbreviation of the
column names that is going to be used as a reference to
build the rows. They must be provided in the same order
as the |
... |
Vectors that fill the rows of the matrix.
The first element of each vector must be the name of the
row in the respective matrix. The remaining elements of the vector
must be name-value pairs that exactly matches the |
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.
João Macalós, [email protected]
# 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])") )# 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
sfcr_matrix_display(matrix, which = "tfm")sfcr_matrix_display(matrix, which = "tfm")
matrix |
A balance sheet or transactions-flow matrix |
which |
A character string for the matrix. Is it a balance-sheet or
a transactions-flow matrix? here are two options:
|
This function takes a matrix as input and generate a kableExtra
table with math symbols displayed in latex style.
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.
João Macalós
# 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")# 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")
The sfcr_multis() function is used to simulate multiple models
at the same time, returning a list of sfcr_tbls.
sfcr_multis(expanded, fixed, periods, ...)sfcr_multis(expanded, fixed, periods, ...)
expanded |
A |
fixed |
A |
periods |
A number specifying the total number of periods of the model to be simulated. |
... |
Additional arguments to pass to the underlying implementation of the
|
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.
João Macalós
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)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)
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.
sfcr_portfolio(m, known)sfcr_portfolio(m, known)
m |
A matrix of parameter names |
known |
A named vector of known parameters. One entry for each symmetry condition is enough to find a valid matrix. |
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.
João Macalós
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)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)
sfcr_set()
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.
sfcr_random(.f, ...)sfcr_random(.f, ...)
.f |
This argument accepts three options: "rnorm", "rbinom", and "runif",
and implement the respective functions from the built-in |
... |
Extra arguments to be passed to the |
João Macalós
# 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) )# 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
sfcr_sankey(tfm, baseline, when = "start")sfcr_sankey(tfm, baseline, when = "start")
tfm |
A transactions-flow matrix |
baseline |
A baseline model |
when |
When the Sankey's diagram should be evaluated?
|
João Macalós
sfcr model.Add scenarios to a sfcr model.
sfcr_scenario( baseline, scenario, periods, max_iter = 350, tol = 1e-10, method = "Broyden", ... )sfcr_scenario( baseline, scenario, periods, max_iter = 350, tol = 1e-10, method = "Broyden", ... )
baseline |
A model generated with the |
scenario |
Either a shock created with |
periods |
A number specifying the total number of periods of the model to be simulated. |
max_iter |
Maximum iterations allowed per period. |
tol |
Tolerance accepted to determine convergence. |
method |
The method to use to find a solution. Defaults to "Broyden". |
... |
Extra arguments to pass to |
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.
João Macalós, [email protected]
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)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)
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.
sfcr_set(..., exclude = NULL)sfcr_set(..., exclude = NULL)
... |
The formulas used to define the equations and external values of the system |
exclude |
One or more indices of equations to be excluded. The
correct indices can be found with |
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.
João Macalós
# 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))# 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))
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.
sfcr_set_index(eqs)sfcr_set_index(eqs)
eqs |
A list of equations created with |
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().
João Macalós
sfcr_scenario().Create shock(s) to add to a sfcr_scenario().
sfcr_shock(variables, start, end)sfcr_shock(variables, start, end)
variables |
A It is possible to add exogenous series a shock instead of constant variables. However, the length of such series must be exactly the same as the period of the shock (i.e., the difference between start and end). |
start |
An integer indicating the period when the shock takes place. |
end |
An integer indicating the period when the shock ends. |
João Macalós, [email protected]
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)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)
This function validates a transactions-flow or balance-sheet
matrix with the simulated data obtained with sfcr_baseline()
function
sfcr_validate(matrix, baseline, which, tol = 1, rtol = FALSE)sfcr_validate(matrix, baseline, which, tol = 1, rtol = FALSE)
matrix |
A transactions-flow or balance sheet matrix |
baseline |
A baseline model. |
which |
Either "bs" (balance-sheet matrix) or "tfm" (transactions-flow matrix). |
tol |
A numerical value indicating the absolute accepted discrepancy accepted to validate whether the rows and columns are equal to their expected values. |
rtol |
A logical value indicating whether relative discrepancies should be
evaluated. It defaults to |
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.
João Macalós