Simulate Stock-Flow Consistent Models.

sfcr

The goal of the sfcr package is to provide an intuitive and tidy way to estimate stock-flow consistent (SFC) models with R.

Installation

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")

Example

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.

Frequently Asked Questions

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]
)

Submitting your code to the package repository

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.

Acknowledgments

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 PKSFCpackage, from which I draw much inspiration, specially in the DAGs section of the package, to Gabriel Petrini da Silveira and Kenn Takara for their pysolve3package, 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).

References