EconGeo (version 2.0)

mort: Compute an index of knowledge complexity of industries using the method of reflection

Description

This function computes an index of knowledge complexity of industries using the method of reflection from regions - industries (incidence) matrices. The index has been developed by Hidalgo and Hausmann (2009) for country - product matrices and adapted by Balland and Rigby (2016) to city - technology matrices.

Usage

mort(mat, rca = FALSE, steps = 19)

Value

If `steps` is set to 0, the function returns a numeric vector representing the ubiquity (number of regions that have a relative comparative advantage) of industries. Otherwise, it returns a numeric vector representing the index of knowledge complexity of industries based on the specified number of iteration steps.

Arguments

mat

An incidence matrix with regions in rows and industries in columns

rca

Logical; should the index of relative comparative advantage (RCA - also refered to as location quotient) first be computed? Defaults to FALSE (a binary matrix - 0/1 - is expected as an input), but can be set to TRUE if the index of relative comparative advantage first needs to be computed

steps

Number of iteration steps. Defaults to 19, but can be set to 0 to give ubiquity (number of regions that have a RCA in a industry), to 1 to give the average diversity of the regions that have a RCA in this industry, to 2 to give the average ubiquity of technologies developed in the same regions, or to any other number of steps < or = to 21. Note that above steps = 2 the index will be rescaled from 0 (minimum relative complexity) to 100 (maximum relative complexity).

Author

Pierre-Alexandre Balland

References

Hidalgo, C. and Hausmann, R. (2009) The building blocks of economic complexity, Proceedings of the National Academy of Sciences 106: 10570 - 10575.

Balland, P.A. and Rigby, D. (2017) The Geography of Complex Knowledge, Economic Geography 93 (1): 1-23.

See Also

location_quotient, ubiquity, diversity, kci, tci, morc

Examples

## generate a region - industry matrix with full count
set.seed(31)
mat <- matrix(sample(0:10, 20, replace = TRUE), ncol = 4)
rownames(mat) <- c("R1", "R2", "R3", "R4", "R5")
colnames(mat) <- c("I1", "I2", "I3", "I4")

## run the function
mort(mat, rca = TRUE)
mort(mat, rca = TRUE, steps = 0)
mort(mat, rca = TRUE, steps = 1)
mort(mat, rca = TRUE, steps = 2)

## generate a region - industry matrix in which cells represent the presence/absence of a rca
set.seed(32)
mat <- matrix(sample(0:1, 20, replace = TRUE), ncol = 4)
rownames(mat) <- c("R1", "R2", "R3", "R4", "R5")
colnames(mat) <- c("I1", "I2", "I3", "I4")

## run the function
mort(mat)
mort(mat, steps = 0)
mort(mat, steps = 1)
mort(mat, steps = 2)

## generate the simple network of Hidalgo and Hausmann (2009) presented p.11 (Fig. S4)
countries <- c("C1", "C1", "C1", "C1", "C2", "C3", "C3", "C4")
products <- c("P1", "P2", "P3", "P4", "P2", "P3", "P4", "P4")
my_data <- data.frame(countries, products)
my_data$freq <- 1
mat <- get_matrix(my_data)

## run the function
mort(mat)
mort(mat, steps = 0)
mort(mat, steps = 1)
mort(mat, steps = 2)