<p>If you want to model exports and imports you need  interregional (or multiregional) Leontief input–output model instead of standard one.</p>
<p>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 <a href="https://www.sciencedirect.com/science/article/pii/S1574008000800115" rel="nofollow noreferrer">Hewings, G. J., &amp; Jensen, R. C., 1987</a>):</p>
<p><a href="https://i.sstatic.net/Hf99L.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Hf99L.png" alt="enter image description here" /></a></p>
<p>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, &amp; Jensen (1987) which has all the details on how input-output analysis is different for open economy.</p>

CC BY-SA 4.0
2020-11-17T08:37:02.590Z
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"?
thecpaptain
CC BY-SA 4.0
2020-11-17T08:52:15.533Z
@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
CC BY-SA 4.0
2020-11-17T09:27:39.547Z
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".
thecpaptain
CC BY-SA 4.0
2020-11-17T09:30:10.803Z
@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
CC BY-SA 4.0
2020-11-17T09:34:28.657Z
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)?
thecpaptain
CC BY-SA 4.0
2020-11-17T09:38:01.000Z
@thecpaptain that is simply generally not valid assumption because it will make the economy look bigger than it is - rather I would say if this is just for fun then you can make that assumption on account that yea I already achieved something by estimating such model it would be too time consuming to move further. If this is for serious research then neither the assumption 1 or 2 would fly and you should use appropriate model.
1muflon1
CC BY-SA 4.0
2020-11-17T09:41:07.683Z
Ok, thanks for your thorough input =). It has been helpful.
thecpaptain
CC BY-SA 4.0
2020-11-16T20:03:20.957Z
2020-11-16T20:08:49.557Z
2020-11-16T20:08:49.557Z
1muflon1
<p>I'm trying to estimate what the &quot;necessary&quot; economic output of a society is using Leontief input-output impact analysis. The data I have available is OECD input-output tables (see <a href="https://stats.oecd.org/Index.aspx?DataSetCode=IOTSI4_2018" rel="nofollow noreferrer">link</a>). I'm not a trained economist, so please correct any mistakes you see in my thinking.</p>
<p>My idea for how to make this estimation is the following: proceed with a standard impact analysis and get the Leontief matrix <code>L</code>. Then check how much economic output <code>x_need</code> that remains  if we let the consumers spend only a &quot;living-wage budget&quot; 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 <code>x_need</code> by <code>f_need</code>, where <code>f_need</code> is the new final demand vector that has been altered by letting private consumers <em>only</em> spend their living-wage-budget. Then we can compare <code>x_old</code> and <code>x_need</code> to see the differences in economic output.</p>
<p>I hope that this so far is not controversial.</p>
<p><strong>Now here's the question:</strong> how do I handle imports (and exports) in the construction of <code>f_need</code>?</p>
<p>I want <code>f_need</code> 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 <strong>general strategies</strong> for how to do so:</p>
<ol>
<li><strong>Ignore imports</strong>. 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 <code>f_need</code>). This gives us <code>f_need</code>, which we can use to create <code>x_need</code> for comparison with the original economic output <code>x_old</code>.</li>
<li><strong>Assume that all imports are domestically produced</strong>. Create and compare <code>x_need</code> to the economic output <code>x_own_produce</code> the country would have if all imports were produced domestically. Get <code>x_own_produce</code> from a final demand vector <code>f_own_produce</code> that we get by assuming that all imports are domestically produced. Get <code>f_need</code> by removing exports and assuming that domestic consumers only spend according to their living-wage-budget. We can then get <code>x_need</code> from <code>f_need</code>, and finally compare <code>x_need</code> with <code>x_own_produce</code>.</li>
</ol>
<p>I hope that the above is understandable. Let me know what I need to clarify otherwise.</p>
<p><strong>Detailed questions:</strong>
Which of the two general strategies gives a better estimation? Are there better strategies that I can use to make my estimation?</p>
<p>Any (constructive) feedback is appreciated.</p>

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

(Asked by: username_0 on 2020-11-16)

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](https://stats.oecd.org/Index.aspx?DataSetCode=IOTSI4_2018)). 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.

**Tags:** macroeconomics

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## 1 answers

### Answer by username_1 on 2020-11-16. Score: 1 | Accepted answer

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](https://www.sciencedirect.com/science/article/pii/S1574008000800115)):

[![enter image description here](https://i.sstatic.net/Hf99L.png)](https://i.sstatic.net/Hf99L.png)

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.

> **Comments:**
> **username_0**: 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"?  
> **username_1**: @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.  
> **username_0**: 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".  
> **username_1**: @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.  
> **username_0**: 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)?  
> **username_1**: @thecpaptain that is simply generally not valid assumption because it will make the economy look bigger than it is - rather I would say if this is just for fun then you can make that assumption on account that yea I already achieved something by estimating such model it would be too time consuming to move further. If this is for serious research then neither the assumption 1 or 2 would fly and you should use appropriate model.  
> **username_0**: Ok, thanks for your thorough input =). It has been helpful.  

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