<blockquote>
<p>For the first fact: Can I use GDP per capita as &quot;output per worker&quot;? Or should I use &quot;gross national income&quot;?</p>
</blockquote>
<p>No, you shouldn't use per capita measure because not everyone is worker.</p>
<p>Also wikipedia is wrong, Kaldor in his paper did not talked necessarily about output per worker but about labor productivity (see Kaldor 1961 pp 178). Output per worker is a good measure of productivity, but its hardly the only measure of labor productivity.</p>
<p>Hence you can use in principle any productivity measure and in fact a good research would typically try to see if results are robust to different ways of measurement.</p>
<p>If you only wan't output per worker you can use GDP divided by some measure of labor force. You could also use GNI but then you need to also make sure that the numerator (labor force) is only based on residents, which might be difficult and time consuming to do for little benefit (outside having a slightly different measure for more robustness checks).</p>
<hr />
<blockquote>
<p>How exactly can I measure &quot;capital&quot;? Where can I find such data in an open data source?</p>
</blockquote>
<p>This is a Nobel Prize winning question. Famously, Hicks (1981 Wealth and Welfare) once remarked:</p>
<blockquote>
<p>The measurement of capital is one of the nastiest jobs that economists
have set to statisticians.</p>
</blockquote>
<p>Even today there is no generally agreed good way to measure capital. There are various proxies but most people agree they are problematic.</p>
<p>This being said, this does not mean that people did not develop a lot of measures, for example, World Bank has its measure of capital,  IMF has its own. Different sources may measure it differently.</p>
<p>In the previous section using robustness checks was more of an suggestion, here due to lack of agreement on how to measure capital stock you should collect various different measurement and see how results differ.</p>
<hr />
<blockquote>
<p>What is the difference between &quot;rate of return on capital&quot; and &quot;rate of return on investment&quot;? Again, where can I find such data?</p>
</blockquote>
<p>In economics capital is typically defined only as an asset used for production. That is in economics we do not use capital for things like money in bank or various financial instruments like in finance. Rate of return to capital is the explicit or implied interest rate (via profit) that capital commands.</p>
<p>Investment in economics is broader term which encompasses all non-consumed production. Hence, it would also include investment in bonds or financial papers but also simply holding inventory. Average rate of return on investment is just an average interest rate.</p>
<p>You can calculate these from data that is published by organization such as Wharton Research Data Services or Bloomberg.</p>
<hr />
<blockquote>
<p>The sixth fact states that &quot;income share of capital <span class="math-container">$\frac{rK}{Y}$</span> and labor <span class="math-container">$\frac{wL}{Y}$</span> is constant overtime&quot;. Again, how can I measure <span class="math-container">$r$</span> and <span class="math-container">$w$</span>? Where can I find the data?</p>
</blockquote>
<p>This is actually 5th stylized fact not sixth (see Kaldor 1961).</p>
<p>The <span class="math-container">$r$</span> is the return on capital. Hence see the previous point.</p>
<p>The <span class="math-container">$w$</span> is wage. You can use data on average wages, you can get data like that from virtually any statistical office or places like OECD or World Bank.</p>

CC BY-SA 4.0
2024-03-18T21:12:17.337Z
Thank you so much for answering. Can I use this (https://fred.stlouisfed.org/series/DFF) as the data for "return on capital"?
Ludwig Gershwin
CC BY-SA 4.0
2024-03-18T22:32:46.973Z
@LudwigGershwin definitely not, return to capital is orthogonal on Feds policy rate, again as my answer explains in economics capital is not equal to money like in finance, capital is the actual machines, buildings etc used in production process. Return to capital is determined by the marginal product of capital which is not determined by the funds rate but by real economic factors.
1muflon1
CC BY-SA 4.0
2024-03-18T23:22:56.923Z
But how to find the marginal product of capital? What are the variables that I need to collect?
Ludwig Gershwin
CC BY-SA 4.0
2024-03-18T23:33:08.050Z
@LudwigGershwin you can calculate it from the rate of profit and rate of return on borrowed capital from firm level data. You can find firm level data at WRDS or Bloomberg. If you come from finance you can use WACC which is probably closest to the economics measure of return to capital although they are not completely the same
1muflon1
CC BY-SA 4.0
2024-03-18T23:38:44.753Z
what about open sources? seems like I cannot access WRDS or Bloomberg.
Ludwig Gershwin
CC BY-SA 4.0
2024-03-18T23:42:14.423Z
@LudwigGershwin open sources don't have micro data. Then you can just use google scholar and look at someone else's estimates. Usually in paper people will make graph or table you can try to read off data points from there, or send an email to authors. Google key words like trends in WACC or rate of return on capital
1muflon1
CC BY-SA 4.0
2024-03-18T20:48:09.947Z
2024-03-18T20:48:09.947Z
1muflon1
<p>I have just started to do economic research and I was asked to replicate the <a href="https://en.wikipedia.org/wiki/Kaldor%27s_facts" rel="nofollow noreferrer">Kaldor stylized facts</a>. But I've encountered some problems; specifically, I don't know how I can find such data:</p>
<ol>
<li>For the first fact: Can I use GDP per capita as &quot;output per worker&quot;? Or should I use &quot;gross national income&quot;?</li>
<li>How exactly can I measure &quot;capital&quot;? Where can I find such data in an open data source?</li>
<li>What is the difference between &quot;rate of return on capital&quot; and &quot;rate of return on investment&quot;? Again, where can I find such data?</li>
<li>The sixth fact states that &quot;income share of capital <span class="math-container">$\frac{rK}{Y}$</span> and labor <span class="math-container">$\frac{wL}{Y}$</span> is constant overtime&quot;. Again, how can I measure <span class="math-container">$r$</span> and <span class="math-container">$w$</span>? Where can I find the data?</li>
</ol>
<p>These questions may sound silly. We've always talked about capital in class but I've never actually thought about what capital is exactly and how to measure it.</p>

<economic-growth>
How can I replicate the Kaldor facts?
Ludwig Gershwin
# How can I replicate the Kaldor facts?

(Asked by: username_0 on 2024-03-18)

I have just started to do economic research and I was asked to replicate the [Kaldor stylized facts](https://en.wikipedia.org/wiki/Kaldor%27s_facts). But I've encountered some problems; specifically, I don't know how I can find such data:

1. For the first fact: Can I use GDP per capita as "output per worker"? Or should I use "gross national income"?
2. How exactly can I measure "capital"? Where can I find such data in an open data source?
3. What is the difference between "rate of return on capital" and "rate of return on investment"? Again, where can I find such data?
4. The sixth fact states that "income share of capital $\frac{rK}{Y}$ and labor $\frac{wL}{Y}$ is constant overtime". Again, how can I measure $r$ and $w$? Where can I find the data?

These questions may sound silly. We've always talked about capital in class but I've never actually thought about what capital is exactly and how to measure it.

**Tags:** economic-growth


---

## 1 answers

### Answer by username_1 on 2024-03-18. Score: 1

> For the first fact: Can I use GDP per capita as "output per worker"? Or should I use "gross national income"?

No, you shouldn't use per capita measure because not everyone is worker.

Also wikipedia is wrong, Kaldor in his paper did not talked necessarily about output per worker but about labor productivity (see Kaldor 1961 pp 178). Output per worker is a good measure of productivity, but its hardly the only measure of labor productivity.

Hence you can use in principle any productivity measure and in fact a good research would typically try to see if results are robust to different ways of measurement.

If you only wan't output per worker you can use GDP divided by some measure of labor force. You could also use GNI but then you need to also make sure that the numerator (labor force) is only based on residents, which might be difficult and time consuming to do for little benefit (outside having a slightly different measure for more robustness checks).

---

> How exactly can I measure "capital"? Where can I find such data in an open data source?

This is a Nobel Prize winning question. Famously, Hicks (1981 Wealth and Welfare) once remarked:

> The measurement of capital is one of the nastiest jobs that economists
> have set to statisticians.

Even today there is no generally agreed good way to measure capital. There are various proxies but most people agree they are problematic.

This being said, this does not mean that people did not develop a lot of measures, for example, World Bank has its measure of capital, IMF has its own. Different sources may measure it differently.

In the previous section using robustness checks was more of an suggestion, here due to lack of agreement on how to measure capital stock you should collect various different measurement and see how results differ.

---

> What is the difference between "rate of return on capital" and "rate of return on investment"? Again, where can I find such data?

In economics capital is typically defined only as an asset used for production. That is in economics we do not use capital for things like money in bank or various financial instruments like in finance. Rate of return to capital is the explicit or implied interest rate (via profit) that capital commands.

Investment in economics is broader term which encompasses all non-consumed production. Hence, it would also include investment in bonds or financial papers but also simply holding inventory. Average rate of return on investment is just an average interest rate.

You can calculate these from data that is published by organization such as Wharton Research Data Services or Bloomberg.

---

> The sixth fact states that "income share of capital $\frac{rK}{Y}$ and labor $\frac{wL}{Y}$ is constant overtime". Again, how can I measure $r$ and $w$? Where can I find the data?

This is actually 5th stylized fact not sixth (see Kaldor 1961).

The $r$ is the return on capital. Hence see the previous point.

The $w$ is wage. You can use data on average wages, you can get data like that from virtually any statistical office or places like OECD or World Bank.

> **Comments:**
> **username_0**: Thank you so much for answering. Can I use this (https://fred.stlouisfed.org/series/DFF) as the data for "return on capital"?  
> **username_1**: @username_0 definitely not, return to capital is orthogonal on Feds policy rate, again as my answer explains in economics capital is not equal to money like in finance, capital is the actual machines, buildings etc used in production process. Return to capital is determined by the marginal product of capital which is not determined by the funds rate but by real economic factors.  
> **username_0**: But how to find the marginal product of capital? What are the variables that I need to collect?  
> **username_1**: @username_0 you can calculate it from the rate of profit and rate of return on borrowed capital from firm level data. You can find firm level data at WRDS or Bloomberg. If you come from finance you can use WACC which is probably closest to the economics measure of return to capital although they are not completely the same  
> **username_0**: what about open sources? seems like I cannot access WRDS or Bloomberg.  
> **username_1**: @username_0 open sources don't have micro data. Then you can just use google scholar and look at someone else's estimates. Usually in paper people will make graph or table you can try to read off data points from there, or send an email to authors. Google key words like trends in WACC or rate of return on capital  

---

