<p>The difference between first and second expressions is that the first expression is measured in dollars using prices.</p>
<p>Value added is nothing else just the prices times quantity of gross output <span class="math-container">$=p_QQ$</span>. That is why the first expression has <span class="math-container">$p_K K$</span> and <span class="math-container">$p_L L$</span> in the numerator.</p>
<p>You would use the first expression when you work with values (e.g. when you have data on value of output, value of capital, value of labor). Working with values is often necessary because firm-level data do not record how many units of capital they have in their firm, and also often they do not record the quantities of labor just the total value of the wage bill etc.</p>

CC BY-SA 4.0
2021-12-07T11:58:32.010Z
2021-12-07T11:58:32.010Z
1muflon1
<p>In some papers the authors use value-added over capital and labor as TFP measure, what is the intuition behind this?
For example, in one paper I just read the authors use</p>
<p><span class="math-container">$ \frac{VA}{(p_{K}K + p_{L}L)} $</span>, where VA = value added.</p>
<p>I'm a bit confused, since we normally use a standard Cobb-Douglas production function. Transforming the equation by this following simple step leads to a similar but still different measure of the TFP &quot;A&quot;, i.e. here I have gross output in the nominator and in the denominator there is a multiplication and not an addition?</p>
<p><span class="math-container">$ Q=AK^{α}L^{1-α} $</span></p>
<p><span class="math-container">$ \frac{Q}{(K^{α}L^{1-α})}=A $</span></p>

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2022-01-06T15:20:21.170Z
Do you have any reference for your first "TFP measure"? I never saw this. If the profit is zero, then your TFP measure is 1 (and conversely). So your measure looks more like a kind of profit rate than a measure for TFP.
Bertrand
<production-function><productivity><value>
Intuition behind value added as TFP measure
futur3boy
# Intuition behind value added as TFP measure

(Asked by: username_0 on 2021-12-06)

In some papers the authors use value-added over capital and labor as TFP measure, what is the intuition behind this?
For example, in one paper I just read the authors use

$ \frac{VA}{(p\_{K}K + p\_{L}L)} $, where VA = value added.

I'm a bit confused, since we normally use a standard Cobb-Douglas production function. Transforming the equation by this following simple step leads to a similar but still different measure of the TFP "A", i.e. here I have gross output in the nominator and in the denominator there is a multiplication and not an addition?

$ Q=AK^{α}L^{1-α} $

$ \frac{Q}{(K^{α}L^{1-α})}=A $

**Tags:** production-function, productivity, value
> **Comments:**
> **username_1**: Do you have any reference for your first "TFP measure"? I never saw this. If the profit is zero, then your TFP measure is 1 (and conversely). So your measure looks more like a kind of profit rate than a measure for TFP.  

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## 1 answers

### Answer by username_2 on 2021-12-07. Score: 1

The difference between first and second expressions is that the first expression is measured in dollars using prices.

Value added is nothing else just the prices times quantity of gross output $=p\_QQ$. That is why the first expression has $p\_K K$ and $p\_L L$ in the numerator.

You would use the first expression when you work with values (e.g. when you have data on value of output, value of capital, value of labor). Working with values is often necessary because firm-level data do not record how many units of capital they have in their firm, and also often they do not record the quantities of labor just the total value of the wage bill etc.


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