<blockquote>
  <p><em>This is how I'd approach the problem. Please point out any issues on this method as it is based on my own approach (I have no textbook to reference this to).</em></p>
</blockquote>

<p>Based on the information you have, you would run a regression of log output on log-labor, log-capital and log-human capital. This would give you a model like this.</p>

<p>$$\ln(Y)=\beta_0+\beta_1\ln(L)+\beta_2\ln(K)+\beta_3\ln(H)+\mu$$</p>

<p>in terms of a more "economic looking" equation, we take the expectation of this equation and take $e$ and raise it to the power of both sides giving us our production function.</p>

<p>$$\mathbb{E}[\ln(Y)]=\mathbb{E[}\beta_0+\beta_1\ln(L)+\beta_2\ln(K)+\beta_3\ln(H)+\mu]$$</p>

<p>$$\ln(Y)=\beta_0+\beta_1\ln(L)+\beta_2\ln(K)+\beta_3\ln(H)$$</p>

<p><em>Recall that we view $\beta_0$s the co-efficient on omitted variable $\ln(A)$ as the rate of technological change<sup>1,2</sup></em>
$$\exp\{\ln(Y)\}=\exp\{\beta_0+\beta_1\ln(L)+\beta_2\ln(K)+\beta_3\ln(H)\}$$</p>

<p>$$Y=A^{\beta_0}L^{\beta_1}K^{\beta_2}H^{\beta_3}$$</p>

<p>Using this form you can more comfortably  calculate elasticity of subsitution between $L$ and $K$. If your elasticity of substitution is greater than or equal to 1 you have a labor saving process, however if elasticity of substitution is less than 1, we either have a process which is either a Human capital augmented process of TFP augmented process <sup>3</sup>.</p>

<p>Hope this helps</p>

<hr>

<p><sub>1. <a href="https://en.wikipedia.org/wiki/Solow_residual#Regression_analysis_and_the_Solow_residual" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Solow_residual#Regression_analysis_and_the_Solow_residual</a></sub></p>

<p><sub>2. the actual "quantity" of $A$ can be calculated by
$$A=\left(\frac{Y}{L^{\beta_1}K^{\beta_2}H^{\beta_3}}\right)^{\frac{1}{\beta_0}}$$</sub></p>

<p><sub>3. this is of course assuming that either  $\beta_3&gt;0$ and/or $\beta_0&gt;0$.</sub></p>

CC BY-SA 3.0
2017-12-31T12:41:43.610Z
Thanks @EconJohn, not sure if a Cobb-Douglass type function can be used to differentiate between forms of technical change. This is because technical change is assumed to be Hicks neutral in C-B type functions. CES functions may be approriate for this empirical exercise, but I may hve to deal with non-linearities in the parameters.
london
CC BY-SA 3.0
2017-12-31T19:07:18.897Z
@london, can you send me the source for your view on hicks neutrality of the cobb-douglas function?
EconJohn
CC BY-SA 3.0
2018-01-01T09:20:03.123Z
@EconJon, note that your model is based on the Hicks neutrality assumption of $A$. Also, isn't the substitution elasticity between $K$ and $L$ is $1$ in Cobb-Douglass?
london
CC BY-SA 3.0
2018-01-01T18:25:01.117Z
@london Ah I see. I don't think that case universally though I am open to being wrong.
EconJohn
CC BY-SA 4.0
2019-01-01T12:45:26.923Z
Elasticity of substitution is 1 in cobb-douglas. You need to estimate a CES or translog.
chatGPT
CC BY-SA 4.0
2019-01-02T21:18:11.420Z
@user928172 I know, but using a "generalized" cobb douglas can get you similar results.
EconJohn
CC BY-SA 3.0
2017-12-31T02:53:38.990Z
2017-12-31T15:50:18.693Z
2017-12-31T15:50:18.693Z
EconJohn
<p>I've read a number of posts on the above topic but none refers to published empirical papers. Google searches have been hopeless. Does anyone know of any paper on empirical derivation of technical change indices? </p>

<p>A lot of papers use these terms interchangibly, there is a clear difference between them (labour-saving technical change stems from bias in technical chnage). Using some historical data, I am trying to establish if technical change has been labour-saving or labour-augmenting. However, I've yet to read an empirical paper on the topic.</p>

CC BY-SA 3.0
2017-12-27T21:57:12.230Z
On an outset, they seem like the same thing. Seems like it would be impossible to identify a difference.
EconJohn
CC BY-SA 3.0
2017-12-28T10:44:14.437Z
@EconJohn Yes, but they appear to have different defining properties and I want to identify the difference empirically. Responses to this earlier post shed some light on the difference: https://economics.stackexchange.com/questions/18079/labour-saving-vs-labour-augmenting-what-is-the-difference
london
CC BY-SA 3.0
2017-12-28T15:22:20.190Z
I think a more fundamental question what data is necessary to estimate elasticity of substitution. do you have such data?
EconJohn
CC BY-SA 3.0
2017-12-28T16:43:11.573Z
Yes, I do have aggregate data on factors of produciton and output. what can be done using these to identify the difference?
london
CC BY-SA 3.0
2017-12-29T19:02:56.337Z
I think you would need data on human capital to properly Identify labor saving and labor augmenting. This is because we have to separate the specific impacts of labor and capital on the production process.
EconJohn
CC BY-SA 3.0
2017-12-30T14:13:02.430Z
I think, I have data on human capital, how would I proceed from there onwards? Are you aware of any empirical strategy to identify the  differences using these variables? Thanks.
london
CC BY-SA 3.0
2017-12-31T04:18:54.820Z
What do you think?
EconJohn
CC BY-SA 3.0
2018-04-06T17:24:23.740Z
1) Productivity is a residual (poor prospects for useful literature). 2) The answer is both labour-saving and also labour augmenting. If the same amount can be produced with less hours of labour, additional labour may be available for other activities, including new ones. (creative destruction). 3) Human capital data is generally in the form of years of education, or thresholds of education (e.g., high school completion, college completion, MA completion) or years of industry experience, and does not include things like specific training taken to be able to effectively use new technologies.
nathanwww
<reference-request><economic-growth><directed-technical-change><technological-progress>
Labour-saving vs. Labour-augmenting technical change
london
# Labour-saving vs. Labour-augmenting technical change

(Asked by: username_0 on 2017-12-14)

I've read a number of posts on the above topic but none refers to published empirical papers. Google searches have been hopeless. Does anyone know of any paper on empirical derivation of technical change indices?

A lot of papers use these terms interchangibly, there is a clear difference between them (labour-saving technical change stems from bias in technical chnage). Using some historical data, I am trying to establish if technical change has been labour-saving or labour-augmenting. However, I've yet to read an empirical paper on the topic.

**Tags:** reference-request, economic-growth, directed-technical-change, technological-progress
> **Comments:**
> **username_1**: On an outset, they seem like the same thing. Seems like it would be impossible to identify a difference.  
> **username_0**: @EconJohn Yes, but they appear to have different defining properties and I want to identify the difference empirically. Responses to this earlier post shed some light on the difference: https://economics.stackexchange.com/questions/18079/labour-saving-vs-labour-augmenting-what-is-the-difference  
> **username_1**: I think a more fundamental question what data is necessary to estimate elasticity of substitution. do you have such data?  
> **username_0**: Yes, I do have aggregate data on factors of produciton and output. what can be done using these to identify the difference?  
> **username_1**: I think you would need data on human capital to properly Identify labor saving and labor augmenting. This is because we have to separate the specific impacts of labor and capital on the production process.  
> **username_0**: I think, I have data on human capital, how would I proceed from there onwards? Are you aware of any empirical strategy to identify the  differences using these variables? Thanks.  
> **username_1**: What do you think?  
> **username_2**: 1) Productivity is a residual (poor prospects for useful literature). 2) The answer is both labour-saving and also labour augmenting. If the same amount can be produced with less hours of labour, additional labour may be available for other activities, including new ones. (creative destruction). 3) Human capital data is generally in the form of years of education, or thresholds of education (e.g., high school completion, college completion, MA completion) or years of industry experience, and does not include things like specific training taken to be able to effectively use new technologies.  

---

## 1 answers

### Answer by username_1 on 2017-12-31. Score: 1

> *This is how I'd approach the problem. Please point out any issues on this method as it is based on my own approach (I have no textbook to reference this to).*

Based on the information you have, you would run a regression of log output on log-labor, log-capital and log-human capital. This would give you a model like this.

$$\ln(Y)=\beta\_0+\beta\_1\ln(L)+\beta\_2\ln(K)+\beta\_3\ln(H)+\mu$$

in terms of a more "economic looking" equation, we take the expectation of this equation and take $e$ and raise it to the power of both sides giving us our production function.

$$\mathbb{E}[\ln(Y)]=\mathbb{E[}\beta\_0+\beta\_1\ln(L)+\beta\_2\ln(K)+\beta\_3\ln(H)+\mu]$$

$$\ln(Y)=\beta\_0+\beta\_1\ln(L)+\beta\_2\ln(K)+\beta\_3\ln(H)$$

*Recall that we view $\beta\_0$s the co-efficient on omitted variable $\ln(A)$ as the rate of technological change1,2*
$$\exp\{\ln(Y)\}=\exp\{\beta\_0+\beta\_1\ln(L)+\beta\_2\ln(K)+\beta\_3\ln(H)\}$$

$$Y=A^{\beta\_0}L^{\beta\_1}K^{\beta\_2}H^{\beta\_3}$$

Using this form you can more comfortably calculate elasticity of subsitution between $L$ and $K$. If your elasticity of substitution is greater than or equal to 1 you have a labor saving process, however if elasticity of substitution is less than 1, we either have a process which is either a Human capital augmented process of TFP augmented process 3.

Hope this helps

---

1. <https://en.wikipedia.org/wiki/Solow_residual#Regression_analysis_and_the_Solow_residual>

2. the actual "quantity" of $A$ can be calculated by
$$A=\left(\frac{Y}{L^{\beta\_1}K^{\beta\_2}H^{\beta\_3}}\right)^{\frac{1}{\beta\_0}}$$

3. this is of course assuming that either $\beta\_3>0$ and/or $\beta\_0>0$.

> **Comments:**
> **username_0**: Thanks @EconJohn, not sure if a Cobb-Douglass type function can be used to differentiate between forms of technical change. This is because technical change is assumed to be Hicks neutral in C-B type functions. CES functions may be approriate for this empirical exercise, but I may hve to deal with non-linearities in the parameters.  
> **username_1**: @london, can you send me the source for your view on hicks neutrality of the cobb-douglas function?  
> **username_0**: @EconJon, note that your model is based on the Hicks neutrality assumption of $A$. Also, isn't the substitution elasticity between $K$ and $L$ is $1$ in Cobb-Douglass?  
> **username_1**: @london Ah I see. I don't think that case universally though I am open to being wrong.  
> **username_3**: Elasticity of substitution is 1 in cobb-douglas. You need to estimate a CES or translog.  
> **username_1**: @user928172 I know, but using a "generalized" cobb douglas can get you similar results.  

---

