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The goal of the sfcr package is to provide an intuitive
and tidy way to estimate stock-flow consistent (SFC) models
with R.
sfcr is on CRAN and can be installed with:
install.packages("sfcr")For the development version available on GitHub, use the devtools
package for installation:
# install.packages("devtools")
devtools::install_github("joaomacalos/sfcr")This is a basic example which shows how to simulate the “SIM” model from Godley and Lavoie (2007ch. 3), as well as how to add scenarios to this baseline model.
The sfcr_set() function is used to create define the
equations and external variables of the model.
These sets are used to simulate the baseline scenario of the model
with the sfcr_baseline() function:
library(sfcr)
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
)
sim <- sfcr_baseline(
equations = eqs,
external = external,
periods = 60,
)
sim
#> # A tibble: 60 x 17
#> period TXs YD Cd Hh Ns Nd Cs
#> * <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 1.00e-15 1.00e-15 1.00e-15 1.00e-15 1.00e-15 1.00e-15 1.00e-15
#> 2 2 7.69e+ 0 3.08e+ 1 1.85e+ 1 1.23e+ 1 3.85e+ 1 3.85e+ 1 1.85e+ 1
#> 3 3 9.59e+ 0 3.83e+ 1 2.79e+ 1 2.27e+ 1 4.79e+ 1 4.79e+ 1 2.79e+ 1
#> 4 4 1.12e+ 1 4.48e+ 1 3.59e+ 1 3.15e+ 1 5.59e+ 1 5.59e+ 1 3.59e+ 1
#> 5 5 1.25e+ 1 5.02e+ 1 4.27e+ 1 3.90e+ 1 6.27e+ 1 6.27e+ 1 4.27e+ 1
#> 6 6 1.37e+ 1 5.48e+ 1 4.85e+ 1 4.53e+ 1 6.85e+ 1 6.85e+ 1 4.85e+ 1
#> 7 7 1.47e+ 1 5.86e+ 1 5.33e+ 1 5.06e+ 1 7.33e+ 1 7.33e+ 1 5.33e+ 1
#> 8 8 1.55e+ 1 6.19e+ 1 5.74e+ 1 5.52e+ 1 7.74e+ 1 7.74e+ 1 5.74e+ 1
#> 9 9 1.62e+ 1 6.47e+ 1 6.09e+ 1 5.90e+ 1 8.09e+ 1 8.09e+ 1 6.09e+ 1
#> 10 10 1.68e+ 1 6.71e+ 1 6.38e+ 1 6.22e+ 1 8.38e+ 1 8.38e+ 1 6.38e+ 1
#> # ... with 50 more rows, and 9 more variables: Gs <dbl>, Y <dbl>, TXd <dbl>,
#> # Hs <dbl>, Gd <dbl>, W <dbl>, alpha1 <dbl>, alpha2 <dbl>, theta <dbl>With the steady state values at hand, we can use the
sfcr_scenario() function to see what happens if we increase
government expenditures Gd from 20 to 30:
shock <- sfcr_shock(
variables = sfcr_set(
Gd ~ 30
),
start = 5,
end = 60
)
sim2 <- sfcr_scenario(
baseline = sim,
scenario = shock,
periods = 60
)
sim2
#> # A tibble: 60 x 17
#> period TXs YD Cd Hh Ns Nd Cs Gs Y TXd Hs
#> * <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 20.0 80.0 80.0 80.0 100. 100. 80.0 20 100. 20.0 80.0
#> 2 2 20.0 80.0 80.0 80.0 100. 100. 80.0 20 100. 20.0 80.0
#> 3 3 20.0 80.0 80.0 80.0 100. 100. 80.0 20 100. 20.0 80.0
#> 4 4 20.0 80.0 80.0 80.0 100. 100. 80.0 20 100. 20.0 80.0
#> 5 5 23.8 95.4 89.2 86.2 119. 119. 89.2 30 119. 23.8 86.2
#> 6 6 24.8 99.2 94.0 91.4 124. 124. 94.0 30 124. 24.8 91.4
#> 7 7 25.6 102. 98.0 95.8 128. 128. 98.0 30 128. 25.6 95.8
#> 8 8 26.3 105. 101. 99.5 131. 131. 101. 30 131. 26.3 99.5
#> 9 9 26.8 107. 104. 103. 134. 134. 104. 30 134. 26.8 103.
#> 10 10 27.3 109. 107. 105. 137. 137. 107. 30 137. 27.3 105.
#> # ... with 50 more rows, and 5 more variables: Gd <dbl>, W <dbl>, alpha1 <dbl>,
#> # alpha2 <dbl>, theta <dbl>With sfcr, the models are written entirely within R and
use the standard R syntax. Furthermore, their output is a
tibble, meaning that it can be easily manipulated with
dplyr and other tidyverse tools and plotted
with ggplot2.
Check the notebooks that replicate the models in Godley and Lavoie (2007) for more detailed examples on the usage of the package.
Q: Can you add exogenous series to a sfcr
model?
A: Since version 0.2, the sfcr package recommends the
utilization of exogenous variables only in the
sfcr_scenario() function. This functionality is going to be
excluded from sfcr_baseline() function in the future
because it led to unexpected behavior when calculating scenarios on the
top of those baseline models.
The exogenous series can be added to the model with the help of
sfcr_shock() and sfcr_set() functions. It is
further required that the length of the exogenous time series being
supplied be either 1 or exactly equal to length of the shock.
For example, the code supplied above can be modified to make
Gd increase from 30 to 40 between periods 1 and 60 of the
scenario:
library(dplyr) # for select() and everything() functions
shock <- sfcr_shock(
variables = sfcr_set(
Gd ~ seq(30, 40, length.out=60)
),
start = 1,
end = 60
)
sim2 <- sfcr_scenario(
baseline = sim,
scenario = shock,
periods = 60
)
#> Warning: Passing exogenous series with a shock can lead to unexpected behavior if the length of the series is smaller than the periods to the end of the scenario. Be cautious when using this functionality.
#> This warning is displayed once per session.
select(sim2, period, Gd, everything())
#> # A tibble: 60 x 17
#> period Gd TXs YD Cd Hh Ns Nd Cs Gs Y TXd
#> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 30 20.0 80.0 80.0 80.0 100. 100. 80.0 20 100. 20.0
#> 2 2 30.2 23.9 95.6 89.4 86.3 120. 120. 89.4 30.2 120. 23.9
#> 3 3 30.3 24.9 99.8 94.4 91.7 125. 125. 94.4 30.3 125. 24.9
#> 4 4 30.5 25.8 103. 98.7 96.3 129. 129. 98.7 30.5 129. 25.8
#> 5 5 30.7 26.6 106. 102. 100. 133. 133. 102. 30.7 133. 26.6
#> 6 6 30.8 27.3 109. 106. 104. 137. 137. 106. 30.8 137. 27.3
#> 7 7 31.0 27.9 112. 109. 107. 140. 140. 109. 31.0 140. 27.9
#> 8 8 31.2 28.5 114. 111. 110. 142. 142. 111. 31.2 142. 28.5
#> 9 9 31.4 28.9 116. 113. 112. 145. 145. 113. 31.4 145. 28.9
#> 10 10 31.5 29.4 118. 115. 114. 147. 147. 115. 31.5 147. 29.4
#> # ... with 50 more rows, and 5 more variables: Hs <dbl>, W <dbl>, alpha1 <dbl>,
#> # alpha2 <dbl>, theta <dbl>Q: How to add random variation to endogenous variables?
A: The recommended way to add random variation to endogenous
variables is with the sfcr_random() function. This function
can only be used inside sfcr_set(), be it when you’re
creating a set of exogenous variables or when defining the variables
inside a sfcr_shock(). The advantage of utilizing this
function is that it smartly guesses the length of the models, avoiding
any unwanted mistake.
The sfcr_random() function can accept three arguments as
its first .f argument: "rnorm",
"rbinom", and "runif". These arguments
implement wrappers around the built-in functions rnorm(),
rbinom(), and runif() – random series
generator function – but guessing the correct length of the
sfcr_baseline(), sfcr_scenario(), or
sfcr_shock() from where they are called. The
sfcr_random() function also accepts any extra argument that
can be passed to these functions.
Snippet:
sfcr_set(
Ra ~ sfcr_random("rnorm", sd=0.05)
)
#> [[1]]
#> Ra ~ sfcr_random("rnorm", sd = 0.05)
#>
#> attr(,"class")
#> [1] "sfcr_set" "list"An utilization of this functionality in practice is provided in the article replicating the Portfolio Choice model from Godley and Lavoie (2007ch. 4).
Alternatively, the direct utilization of the random generator
functions from stats are still allowed to ensure the
compatibility with the v0.1.1 of the package. Nonetheless, the user must
be careful when using this functionality at the
sfcr_baseline() level since this expression is going to be
evaluated again at the sfcr_scenario() level. The safest
way to use these functions is by passing periods instead of
an integer as their first argument.
Snippet:
# Not recommended but work:
sfcr_set(
Ra ~ rnorm(periods, sd=0.05)
)
#> [[1]]
#> Ra ~ rnorm(periods, sd = 0.05)
#>
#> attr(,"class")
#> [1] "sfcr_set" "list"
# NOT RECOMMENDED!
sfcr_set(
Ra ~ rnorm(60, sd=0.05)
)
#> [[1]]
#> Ra ~ rnorm(60, sd = 0.05)
#>
#> attr(,"class")
#> [1] "sfcr_set" "list"Q: Can you add endogenous variables with more than one lag?
A: Yes, you can, but you need to use auxiliary variables.
For example, say that you want to modify model SIM to have
Consumption Cd in period t defined as function
of the moving average of disposable income. In this situation, you would
have to code the variables as:
eqs <- sfcr_set(
TXs ~ TXd,
YD ~ W * Ns - TXs,
YDlag1 ~ YD[-1],
YDlag2 ~ YDlag1[-1],
YDlag3 ~ YDlag2[-1],
YDmav ~ (YD + YDlag1 + YDlag2 + YDlag3) / 4,
Cd ~ alpha1 * YDmav + 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]
)Everyone is invited to submit your published SFC models developed
with the sfcr package to the package repository to be
displayed together with the models of Godley and Lavoie (2007).
To do so, please submit a pull request or send me an email.
I’m grateful to Severin Reissl for his very useful comments and for always pointing me in the right direction, to Marc Lavoie for answering all my questions about SFC modeling, and to Italo Pedrosa for our discussions about the state of the SFC field.
I’d also like to acknowledge all the developers and academics that
share their code and make the SFC field alive. In particular, many
thanks to Antoine Godin for answering all my queries about the
PKSFC package,
from which I draw much inspiration, specially in the DAGs section of the
package, to Gabriel Petrini da Silveira and Kenn Takara for their
pysolve3 package, from which I
found the references to implement the Broyden solver in R, and to
Gennaro Zezza for his invaluable macros to
simulate the models in Godley and Lavoie (2007).
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.