fim: Fiscal Impact Measure

#this script creates an mpc function out of inputs that are defined in the mpc sheet in data/forecast.xlsx

# The mpcs variable contains how much of the impulse is spent x quarters after
# disbursement of the funds. For example, an mpcs = c(0.3, 0.2, 0.1) means that 
# if $100 is disbursed in 2020 Q1, then $30 is spent in 2020 Q1, an additional 
# $20 is spent in 2020 Q2, and an additional $10 is spent in 2020 Q3, for a total
# of $60 spent within the first 3 quarters of the fiscal injection.

# The x variable indicates how much money was injected in each period. I'm not sure
# what period is the starting period. But let's say the first element of the vector
# represents 2020 Q1. If x = c(100, 0, 0, 0, 100), that means that $100 was 
# injected in 2020 Q1, and then nothing was injected for the next 3 quarters. Then,
# an additional $100 was injected in 2021 Q1.

# The roll_sum calculates a rolling dot product. Let's use the example above, with
# mpcs = c(0.3, 0.2, 0.1) and 
# x = c(100, 0, 0, 0, 100)
# Here's a visualization of what happens
#   NA   NA    100    0     0    0    100   NA   NA
#  [0.1  0.2   0.3]
#       [0.1  0.2   0.3]
#             [0.1  0.2   0.3]
#                   [0.1  0.2   0.3]
#                         [0.1  0.2   0.3]
#                               [0.1  0.2   0.3]
#                                     [0.1  0.2   0.3]
# 2020 Q1 fiscal impulse is the following dot product:
# <NA, NA, 100> * <0.1, 0.2, 0.3> where NAs are treated as 0s
# = $30
# 2020 Q2 fiscal impulse:
# <NA, 100, 0> * <0.1, 0.2, 0.3> = $20
# And skipping to the end... 2021 Q3 fiscal impulse is...
# <100, NA, NA> * <0.1, 0.2, 0.3> = $10
# You get the idea. Implicitly by assigning the MPCs vector a length of 3, we assume
# that the impulse on the economy goes to 0 after 3 quarters. In our code, our
# MPCs vectors are longer to represent a more gradual spending pattern of the recipients
# of the transfer.



create_vectors_from_rows <- function(df) {
  for (i in 1:nrow(df)) {
    variable_name <- as.character(df[i, "variable"])
    variable_name <- paste0("mpc_", variable_name)
    values <- as.numeric(df[i, c("1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12")])
    assign(variable_name, values, envir = .GlobalEnv)
  }
}


apply_mpc<-function (x, mpc_vector) {
  1 * roll::roll_sum(x, 
                     width = length(mpcs), 
                     weights = rev(mpcs), 
                     online = FALSE, 
                     min_obs = 1)
}