@madredalchemist Right, he says there's a correlation but it's not as strong as that of labour.
@thardin He says "almost as well", I don't know what that means exactly as he didn't give a figure for it. I don't think it contradicts LTV as software's universality is necessarily mediated by human labor.
@madredalchemist True. No computer ultimately does anything without a human setting it in motion. This is more a philosophical point that I don't think belongs in this thread however.
@thardin Agreed.
I'll start another thread on this once I find the work Cockshott alluded to in the presentation.
So if the goal is to weigh centrality by downstream labor intensity and against sector labor intensity then I think I need to take the adjancency matrix and weigh the entries aij by Lj/Li and then compute eigenvector centrality.
So far what I have is
(L^-1)AL
Where A is the adjacency matrix of the input-output table
L = diag(l), l is the labor content vector where li is the labor content of sector i
the eigendecomposition of (L^-1)AL should render an eigenvector centrality weighted against the labor content in sector i and by the labor content downstream of sector i
@madredalchemist occurs to me what youd would want to do is figure out which goods are the most common inputs, and identify bottlenecks. Accordingly, case study research combined with a more simple input-output analysis might be better if the question is where to coordinate industrial action.
which goods are the most common inputs, and identify bottlenecks
The purpose of the centrality analysis is to identify which industries are furthest up the supply chain; these industries are the most critical and are therefore the bottleneck industries. The weighting is to identify which sectors will result in the largest losses with respect to the ease of interrupting its production. My goal is to create a theoretical model which I can then constrain to specific conditions.
@madredalchemist shouldn't this be apparent simply by looking at which industry provides the largest share of inputs to other industries?
@casperadmin I guess the difference would be if you're in a country that is expanding its oil production to meet the demands of a growing population whilst oil is provided as an input to many different industries an interruptions in the production of drilling equipment which only provides inputs to say oil and mining percolates to oil production and every other sector dependent on it.
another example would be silicon, silicon itself provides inputs to glass, semiconductors, other chemical products etc. but those three downstream industries provide inputs to a lot more than three industries themselves.
The best analogy I can come up with is that a tree might have only a few limbs but those limbs might have many branches
I concede my expertise is in math and engineering so it's entirely possible I'm overlooking some economic nuances, but this is based on my understanding of the work I linked earlier in the thread.
(very) rough sketch of the model in Python.
I definitely need to confirm if I did the modeling properly and then incorporate real economic data but it's a start.
N = 10 # number of sectors lmax = 10 # max labor intensity l = np.random.randint(lmax, size=N)+1 # labor vector L1 = np.diag(1/l,0) # weight against sector labor L2 = np.diag(l,0) # weight by downstream labor A = np.random.randint(2, size=(N, N)) # I/O adjacency matrix B = np.matmul(np.matmul(L1,A),L2) # weighted matrix eigval, eigvec = LA.eig(B) # eigenvalues and eigenvectors C = abs(eigvec[1,:]/eigval[1]) # eigencentrality print(C)