# How to estimate "necessary" economic output using Leontief input-output impact analysis? In particular: how to handle imports

I'm trying to estimate what the "necessary" economic output of a society is using Leontief input-output impact analysis. The data I have available is OECD input-output tables (see link). I'm not a trained economist, so please correct any mistakes you see in my thinking.

My idea for how to make this estimation is the following: proceed with a standard impact analysis and get the Leontief matrix L. Then check how much economic output x_need that remains if we let the consumers spend only a "living-wage budget" proportionally to the different sectors of the economy (so if 50% of spending in the original demand goes to say food, then 50% of the living-wage final demand should also go to food). So basically: calculate x_need by f_need, where f_need is the new final demand vector that has been altered by letting private consumers only spend their living-wage-budget. Then we can compare x_old and x_need to see the differences in economic output.

I hope that this so far is not controversial.

Now here's the question: how do I handle imports (and exports) in the construction of f_need?

I want f_need to represent the final demand of the domestic private consumers when spend precisely their living-wage-budget. Exports can probably simply be removed since they don't provide goods and services to the domestic population. But what about imports? How do I best deal with them in my estimation? I see two general strategies for how to do so:

1. Ignore imports. Alter private domestic consumer according to their living-wage-budget, remove exports, and ignore imports (i.e. don't make any changes in how imports affect final demand f_need). This gives us f_need, which we can use to create x_need for comparison with the original economic output x_old.
2. Assume that all imports are domestically produced. Create and compare x_need to the economic output x_own_produce the country would have if all imports were produced domestically. Get x_own_produce from a final demand vector f_own_produce that we get by assuming that all imports are domestically produced. Get f_need by removing exports and assuming that domestic consumers only spend according to their living-wage-budget. We can then get x_need from f_need, and finally compare x_need with x_own_produce.

I hope that the above is understandable. Let me know what I need to clarify otherwise.

Detailed questions: Which of the two general strategies gives a better estimation? Are there better strategies that I can use to make my estimation?

Any (constructive) feedback is appreciated.

If you want to model exports and imports you need interregional (or multiregional) Leontief input–output model instead of standard one.

The way how these models work is that you will have separate foreign sector in your input output model, along what you can see in the table below (taken from Hewings, G. J., & Jensen, R. C., 1987): This is in spirit similar to assuming that foreign are just some other production sector - but the issue is that spending and productivity might not necessary be the same as at home. There is also more nuance to it. I would recommend going over the above mentioned Hewings, & Jensen (1987) which has all the details on how input-output analysis is different for open economy.

• Thank you for the feedback! I will look into your suggestion. My main purpose is not to model imports and exports per say: it is to estimate the "necessary" part of the economy. I'm in fact ok with assuming that all goods were produced domestically with the productivity inside the country (it's even preferable). Would my second strategy (2) be an ok estimate if I rephrased the question as: assuming that all necessities were produced domestically, what portion of the economy is "necessary"? Nov 17 '20 at 8:37
• @thecpaptain the problem is that when you have imports and exports and you do not model them appropriately you can easily find yourself in situation where the system looks like it is unproductive due to imports>exports even if it isn't. Generally you would run into situations where consumption/inputs are not equal output with foreign sector. Also, if this is just for fun then I guess you can just use either 1 or 2 to save time you would get some results. Already the other assumptions of the model are unusual but I did not commented on the as I assumed it is built upon some niche literature.
– 1muflon1
Nov 17 '20 at 8:52
• Ok, so I interpret what you say the following way: if one does not model imports properly then the Leontief matrix (that represents the domestic economic machinery) might show strange results if the imports are simply assumed to be produced domestically since the domestic economy may not say have the productive capacity to produce those domestic goods. Have I understood you correctly? Is there a way to test when the assumption of imports being produced domestically would be valid? For example if sum(exports) > sum(imports) then the approximation is "good". Nov 17 '20 at 9:27
• @thecpaptain you understood correctly. Also I would not say it is more valid if sum(exports)> sum(imports) because then you will find that your economy is under consuming and wasting resources producing something that seemingly nobody wants - but that is just mirage because actually those exports are exchanged for imports that people want. It would just show different sort of problem.
– 1muflon1
Nov 17 '20 at 9:30
• Ok. Do you know of any criteria that could be used to determine the validity of the second assumption (of all imports being produced domestically)? Nov 17 '20 at 9:34