derive an M matrix for IEF models

[bl-young]

When an M matrix is present an N matrix will also be constructed during the regular course of model build.

[bl-young]

Leaving this as draft for now as it may require further discussion.

[bl-young]

A few notes about this approach:

• Sectors for which have no final demand (e.g. "211") will have coefficients of 0 in the M matrix, even if values exist in M_m and M_d
• I had assumed that for all sectors, the M value for any flow and sector would be somewhere in between the value for M_m and M_d, but this is not the case, perhaps this relates to the first point

Example:
M_d:

M_m:

derived M:

[bl-young]

• I had assumed that for all sectors, the M value for any flow and sector would be somewhere in between the value for M_m and M_d, but this is not the case, perhaps this relates to the first point

And this is especially clear for the flows not available in the IEFs which are identical for M_m and M_d e.g. HFCs

[bl-young]

@WesIngwersen see the commit above which is using ratios from the domestic production demand vector relative to the import consumption demand vector, which I'm not sure is quite right still

[WesIngwersen]

Yes i reviewed the approach and its still problematic, perhaps due to differences in the demand vectors as well as the negatives present which mess up ratios.

I propose more of a weighted average approach, using commodity output, q and the total imports m

$$dr = q/(q+m)$$

$$mr = 1 - dr$$

$$M = M_d \hat{dr} + M_m \hat{mr}$$

[WesIngwersen]

Have you made any scripts for testing this with different models?

[bl-young]

Have you made any scripts for testing this with different models?

The automated model builds include USEEIOv2.3-GHG and USEEIOv2.3-s-GHG, as well as a two region model (GA) with IEFs GAEEIOv1.1-GHG-19-IF. So all those models are able to build the M.

But no I haven't done an external script to do that explicitly - are there certain validations that we want to test after building the M this way?

[WesIngwersen]

Make sure each value is in between the respective value in M_m and M_d. To do this might need to get max and min matrices

[bl-young]

the detail model is failing for S00900 Rest of World Adjustment.
total imports for that sector are negative, so the ratios are dr > 1, and mr <0 for that sector, causing the error. Would it make sense to force that ratio to all domestic for that sector (dr = 1)

[WesIngwersen]

the detail model is failing for S00900 Rest of World Adjustment. total imports for that sector are negative, so the ratios are dr > 1, and mr <0 for that sector, causing the error. Would it make sense to force that ratio to all domestic for that sector (dr = 1)

That's OK, that should not be an issue - we always have exceptions with RoW adjustment since its an accounting correction row and meaningless for use in the model.

thanks I assume this check passes for some state models and the summary model?

[bl-young]

That's OK, that should not be an issue - we always have exceptions with RoW adjustment since its an accounting correction row and meaningless for use in the model.

ok I'll change this from a stop to a print statement or something like that as a form of validation, not a requirement

thanks I assume this check passes for some state models and the summary model?

I need to check - the other models may not have run on the action when the detail model failed, but yes I tested this with those models as well and it should work.

[bl-young]

Confirmed that the validation passes for summary model and 2R GA model, and prints the failures for the detail model:

[WesIngwersen]

OK I think we can proceed with updating N and related vars using this new M

[bl-young]

by building $M$ in this way, which is to say, right after $M_m$ and $M_d$, means that $N$ is produced automatically

useeior/R/BuildModel.R

Lines 72 to 83 in e232ca1

	# Calculate total impacts per dollar (N), impact category x sector
	if(!is.null(model$M)) {
	logging::loginfo("Calculating N matrix (total environmental impacts per dollar)...")
	model$N <- model$C %*% model$M
	}
	if(!is.null(model$M_m)) {
	logging::loginfo("Calculating N_m matrix (total environmental impacts per dollar from imported activity)...")
	model$N_m <- model$C %*% model$M_m
	}
	logging::loginfo("Calculating N_d matrix (total environmental impacts per dollar from domestic activity)...")
	model$N_d <- model$C %*% model$M_d
	}

[bl-young]

We will need to decide if this is going to be integrated with v1.6.1 (CBEI model release) or wait until v1.7

[bl-young]

Bring this in w/ v1.6.1 as it will be described in the CBEI report.