new_* function interactions

Introduction

The Recca package provides several new_* functions that allow the user to estimate a new version of an energy conversion chain (ECC) based on localized changed to one portion of the ECC. The functions can have some interesting interactions, particularly if they are called sequentially. This vignette show how to understand and deal with those interactions. The functions new_k_ps() and new_Y() are used for this purpose.

Setup

To investigate the interactions, we first make the simplest possible ECC that retains the features to be tested, a minimum working example (MWE). This example has two resource industries (R1 and R2), one intermediate industry (I), and two final demand sectors (Y1 and Y2). The R1 industry makes product R1p.
The R2 industry makes product R2p. Industry I makes product Ip. Product Ip is consumed by final demand sectors Y1 and Y2.

The resources (\(\mathbf{R}\)), use (\(\mathbf{U}\)), make (\(\mathbf{V}\)), final demand (\(\mathbf{Y}\)), and unit summation (\(\mathbf{S}_{units}\)) matrices are given below.

library(magrittr)
library(matsbyname)
library(Recca)
U <- matrix(c(0, 0, 10,
              0, 0, 10,
              0, 0,  0),
            byrow = TRUE, nrow = 3, ncol = 3,
            dimnames = list(c("R1p", "R2p", "Ip"), c("R1", "R2", "I"))) %>% 
  setrowtype("Products") %>% setcoltype("Industries")

# There is no EIOU, so U_feed and U are the same.
U_feed <- U

R_plus_V <- matrix(c(10,  0, 0,
                     0, 10, 0, 
                     0,  0, 4), 
                   byrow = TRUE, nrow = 3, ncol = 3, 
                   dimnames = list(c("R1", "R2", "I"), 
                                   c("R1p", "R2p", "Ip"))) %>% 
  setrowtype("Industries") %>% setcoltype("Products")

RV_mats <- separate_RV(U = U, R_plus_V = R_plus_V)
R <- RV_mats$R
V <- RV_mats$V

Y <- matrix(c(0, 0,
              0, 0, 
              2, 2),
            byrow = TRUE, nrow = 3, ncol = 2,
            dimnames = list(c("R1p", "R2p", "Ip"), c("Y1", "Y2"))) %>% 
  setrowtype("Products") %>% setcoltype("Industries")

S_units <- matrix(c(1, 
                    1, 
                    1), 
                  byrow = TRUE, nrow = 3, ncol = 1,
                  dimnames = list(c("R1p", "R2p", "Ip"), c("quad"))) %>% 
  setrowtype("Products") %>% setcoltype("Units")

We’ll use Sankey diagrams to visualize several ECCs. The make_sankey() function creates the diagrams. A Sankey diagram that shows the base energy conversion chain is shown below. make_sankey() returns a list with a named item “Sankey” that we must extract to insert the diagram into this vignette.

make_sankey(R = R, U = U, V = V, Y = Y) %>% 
  extract2("Sankey")

Adjust inputs to industry I

We can change the proportion of inputs to industry I using new_k_ps(). To do so, we must first calculate the input-output structure of the ECC using the calc_io_mats() function. Then, we call the new_k_ps() function with a new k vector that indicates industry I now uses 20 quads of R1 instead of a 50/50 split between R1 and R2.

library(Recca)
iomats <- calc_io_mats(R = R, U = U, U_feed = U_feed, V = V, Y = Y, S_units = S_units)
k_prime <- matrix(c(1,
                    0), 
                  byrow = TRUE, nrow = 2, ncol = 1,
                  dimnames = list(c("R1p", "R2p"), c("I"))) %>% 
  setrowtype("Products") %>% setcoltype("Industries")
change_input_proportions <- new_k_ps(c(iomats, 
                                       list(R = R, U = U, V = V, Y = Y,
                                            S_units = S_units, 
                                            k_prime = k_prime)))
# There is no EIOU, so U and U_feed are same.
change_input_proportions[["U_feed_prime"]] <- change_input_proportions[["U_prime"]]
make_sankey(R = change_input_proportions$R_prime, 
            U = change_input_proportions$U_prime, 
            V = change_input_proportions$V_prime, 
            Y = Y) %>% 
  extract2("Sankey")

Change final demand

We can calculate the ECC that would be required to meet a new level of final demand with the new_Y() function. The new_k_ps() and new_Y() functions interact in ways that might be surprising to the user, depending on whether the input-output structure of the ECC is re-calculated between sequential function calls.

Without recalculating the structure of the ECC

Now let’s change final demand, saying that consumption by Y1 doubles. But we’ll call new_Y() without recalculating the structure of the ECC with the calc_io_mats() function.

Y_prime <- matrix(c(0, 0,
                    0, 0, 
                    4, 2),
                  byrow = TRUE, nrow = 3, ncol = 2,
                  dimnames = list(c("R1p", "R2p", "Ip"), c("Y1", "Y2"))) %>% 
  setrowtype("Products") %>% setcoltype("Industries")
change_final_demand <- new_Y(c(iomats, list(Y_prime = Y_prime)))
make_sankey(R = change_final_demand$R_prime, 
            U = change_final_demand$U_prime, 
            V = change_final_demand$V_prime, 
            Y = change_final_demand$Y_prime) %>% 
  extract2("Sankey")

Industry I is back to using both R1p and R2p in a 50/50 split to make its output. Both R1p and R2p now supply 15 quads to I to account for increased final demand.

The new_Y() function is performing exactly as expected, given that iomats was supplied to new_Y(). iomats contains information about an ECC in which industry I’s inputs are split 50/50 between R1p and R2p. So when new_Y() calculates a new ECC, it assumes that industry I’s needs are a 50/50 split between R1p and R2p.

In fact, it would be a mistake to think that new_Y() would give anything but a 50/50 split between R1p and R2p when using the iomats description of the ECC.

After recalculating the structure of the ECC

If you want new_Y() to start from the Sankey in which all energy supplied to industry I comes from R1p, you need to first recalculate the input-output structure of the ECC based on the ECC in which industry I uses only R1p. I.e., you need to re-calculate an iomats object after calling new_k_ps() and before calling new_Y(). Then, you must submit that updated description of the input-output structure of the ECC to new_Y(). The following code demonstrates the approach.

iomats2 <- calc_io_mats(R = change_input_proportions$R_prime, 
                        U = change_input_proportions$U_prime, 
                        U_feed = change_input_proportions$U_feed_prime,
                        V = change_input_proportions$V_prime, 
                        Y = Y, S_units = S_units)
change_final_demand2 <- new_Y(c(iomats2, list(Y_prime = Y_prime)))
make_sankey(R = change_final_demand2$R_prime, 
            U = change_final_demand2$U_prime, 
            V = change_final_demand2$V_prime, 
            Y = change_final_demand2$Y_prime) %>% 
  extract2("Sankey")

The Sankey diagram above shows that we have successfully increased the demand from Y1 while ensuring that all inputs to industry I come from R1p. The “trick” is to recalculate the input-output structure of the ECC between the two steps.

Conclusion

The new_* function of the Recca package can be called sequentially. But the interactions among the new_* functions can be surprising if their behavior is not fully understood. This vignette provides a detailed example using the new_k_ps() and new_Y() functions. If they are called sequentially without first recalculating the input-output structure of the ECC, the call to new_Y() will be based on the original input-output structure of the ECC (from before new_k_ps() was called). If calc_io_mats() is called between the sequential calls to new_k_ps() and new_Y() and the results are fed to new_Y(), the input-output structure of the ECC after calling new_k_ps() will be used for the calculations by new_Y().

Matthew Kuperus Heun