<p>Constant returns to scale are mostly mathematical convenience. Empirically they can occur but there is no guarantee that they will. Although you should note that Solow model can be tweaked to accommodate both increasing and decreasing returns to scale. See <a href="https://www.sciencedirect.com/science/article/pii/S0378437119311999?casa_token=mWpoRMQfKckAAAAA:wir9DE0ianAtS7xl7GI-W-Morxj6dPU6a42yFvLSWElI2X7LrQhTacLDkLB_77KCy7B0F0xK8_c" rel="nofollow noreferrer">Neto, Claeyssen, &amp; Júnior (2019</a>) paper as an example of people doing that, so this assumption is mainly there to make the model easier for students.</p>
<p>For example, <a href="https://www.journals.uchicago.edu/doi/abs/10.1086/262073" rel="nofollow noreferrer">Basu &amp; Fernald (1997)</a> found in their study that <em>on average</em> US firms in their sample had slightly decreasing returns to scale (although they are quite close to be being constant). However, this is by no means something that has to hold it is just empirical observation. Empirically you can have constant, increasing or decreasing returns to scale  and it depends on the time and place.</p>
<p>If you want to read more studies than just the ones I listed above you can simply use google scholar using the keyword returns to scale and then country and period you are looking for (if you would want to know it on more micro level you can add industry).  The literature on this subject is too wide to provide any exhaustive overview.</p>

CC BY-SA 4.0
2020-11-23T17:36:25.130Z
That individual firms have decreasing returns to scale does not mean that the aggregate production technology has decreasing returns to scale.
Michael Greinecker
CC BY-SA 4.0
2020-11-23T17:38:16.957Z
@MichaelGreinecker of course, that is why in my answer I was talking also then about broader studies, my point was to highlight that there is large heterogeneity in returns to scale. In the end overall production function is just aggregation of all production functions
1muflon1
CC BY-SA 4.0
2020-11-23T17:43:26.543Z
The question is what "aggregation" means. If one firm can transform one discrete unit of input into one unit of output, but the number of firms is unlimited, each firm has extreme decreasing returns to scale, but the aggregate technology has constant returns to scale.
Michael Greinecker
CC BY-SA 4.0
2020-11-23T17:52:14.360Z
@MichaelGreinecker well I am not disputing that but I just thought its worth while to point out that there is quite large heterogeneity between different industries and firms as well. Anyway I deleted the paragraph that talked about industry level analysis if you consider it problematic given the question
1muflon1
CC BY-SA 4.0
2020-11-23T17:55:19.013Z
My point is simply that is very hard to judge the assumption in terms of individual firm level data.
Michael Greinecker
CC BY-SA 4.0
2020-11-23T18:04:23.107Z
@MichaelGreinecker well that is a good point but as far as I can see most authors agree that panel data on firm level are preferable for analysis of returns to scale as with aggregate time series data you run into problems of having structural breaks and other issues.
1muflon1
CC BY-SA 4.0
2020-11-23T17:23:02.873Z
2020-11-23T17:51:35.780Z
2020-11-23T17:51:35.780Z
1muflon1
<p>I am currently learning the Solow model of growth, where a constant returns to scale production function for the economy is assumed. I realise that the assumption makes further analysis much simpler, by allowing us to write output per unit productive labour simply as a function of capital per unit productive labour.</p>
<p>Apart from the mathematical convenience, is there any empirical reason for evoking the CRS assumption? Where can I read studies that have tested this claim?</p>

<macroeconomics><reference-request><economic-growth><empirical-evidence>
Empirical justification for a constant-returns-to-scale production function in the Solow model
Ishan Kashyap Hazarika
# Empirical justification for a constant-returns-to-scale production function in the Solow model

(Asked by: username_0 on 2020-11-23)

I am currently learning the Solow model of growth, where a constant returns to scale production function for the economy is assumed. I realise that the assumption makes further analysis much simpler, by allowing us to write output per unit productive labour simply as a function of capital per unit productive labour.

Apart from the mathematical convenience, is there any empirical reason for evoking the CRS assumption? Where can I read studies that have tested this claim?

**Tags:** macroeconomics, reference-request, economic-growth, empirical-evidence


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## 1 answers

### Answer by username_1 on 2020-11-23. Score: 2 | Accepted answer

Constant returns to scale are mostly mathematical convenience. Empirically they can occur but there is no guarantee that they will. Although you should note that Solow model can be tweaked to accommodate both increasing and decreasing returns to scale. See [Neto, Claeyssen, & Júnior (2019](https://www.sciencedirect.com/science/article/pii/S0378437119311999?casa_token=mWpoRMQfKckAAAAA:wir9DE0ianAtS7xl7GI-W-Morxj6dPU6a42yFvLSWElI2X7LrQhTacLDkLB_77KCy7B0F0xK8_c)) paper as an example of people doing that, so this assumption is mainly there to make the model easier for students.

For example, [Basu & Fernald (1997)](https://www.journals.uchicago.edu/doi/abs/10.1086/262073) found in their study that *on average* US firms in their sample had slightly decreasing returns to scale (although they are quite close to be being constant). However, this is by no means something that has to hold it is just empirical observation. Empirically you can have constant, increasing or decreasing returns to scale and it depends on the time and place.

If you want to read more studies than just the ones I listed above you can simply use google scholar using the keyword returns to scale and then country and period you are looking for (if you would want to know it on more micro level you can add industry). The literature on this subject is too wide to provide any exhaustive overview.

> **Comments:**
> **username_2**: That individual firms have decreasing returns to scale does not mean that the aggregate production technology has decreasing returns to scale.  
> **username_1**: @username_2 of course, that is why in my answer I was talking also then about broader studies, my point was to highlight that there is large heterogeneity in returns to scale. In the end overall production function is just aggregation of all production functions  
> **username_2**: The question is what "aggregation" means. If one firm can transform one discrete unit of input into one unit of output, but the number of firms is unlimited, each firm has extreme decreasing returns to scale, but the aggregate technology has constant returns to scale.  
> **username_1**: @username_2 well I am not disputing that but I just thought its worth while to point out that there is quite large heterogeneity between different industries and firms as well. Anyway I deleted the paragraph that talked about industry level analysis if you consider it problematic given the question  
> **username_2**: My point is simply that is very hard to judge the assumption in terms of individual firm level data.  
> **username_1**: @username_2 well that is a good point but as far as I can see most authors agree that panel data on firm level are preferable for analysis of returns to scale as with aggregate time series data you run into problems of having structural breaks and other issues.  

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