<p>To add to @keepAlive's answer, even when natural resources are added typically stocks are used, at least in theoretical work. The flow of the used up resource is converted to a stock variable by assuming a fixed percentage of depletion each year (see for example Nordhaus Lethal model of 1992 <a href="https://www.brookings.edu/wp-content/uploads/1992/06/1992b_bpea_nordhaus_stavins_weitzman.pdf" rel="nofollow noreferrer">here</a>)</p>

CC BY-SA 4.0
2017-02-21T10:16:47.357Z
2021-09-08T12:54:56.527Z
2021-09-08T12:54:56.527Z
Maarten Punt
<p>There are a few apparent misconceptions in this question that need addressing.</p>

<ol>
<li>In the actual exercise of national accounting, nothing is "measured" except for currency flows.  The degree of sophistication of accounting comes down to the degree of nuance with which said flows are categorized.  For your purposes, this is a good thing, because it means the confusing issue about "two companies, one unit capital" is irrelevant.</li>
<li>Most common macro growth models represent both capital and labor as stocks, <em>from which</em> value-added (read: goods and services, or "GDP") flows. Within the context of a given model, "investment" is essentially the mechanism through which this value-added is transformed into more capital, while the stock of labor is typically assumed to grow via natural processes or netted-out by normalizing the model on a per-worker basis.  In either case, this growth is not a flow, any more than punching multiple taps into a keg is a flow.  At the abstract level of most models, labor and capital are fundamentally stocks.</li>
</ol>

<p>With that out of the way, you ask:</p>

<blockquote>
  <p>are capital and labour measured in terms of the flow of services that these factors produce, or in terms of the stock of factors available in an economy over time</p>
</blockquote>

<p>It may be more accurate to say that capital and labor are <em>priced</em> according to the flow of services they produce.  They are typically "measured" according to their share of GDP, which isn't quite the same as a count of tractors or a number of employed persons because the point of growth models isn't to capture nominal values at all.  It's to understand the aggregate, dynamic behavior of the system.  Scale invariance (homogeneity of degree one) is usually assumed as a matter of convenience, and so "counting" as such is often irrelevant.</p>

<p>That's probably not a very satisfactory answer, but as some others have touched upon, this high degree of abstraction allows avoiding almost philosophical arguments about what a "unit of labor" is, or how "sectors" are defined, that are actually quite complicated and difficult to resolve in a clear and universal way.</p>

CC BY-SA 4.0
2019-12-17T21:57:35.030Z
2019-12-17T21:57:35.030Z
heh
<p>I realize this question might be too old to reply to, but it was just bumped to the homepage. But anyway:</p>

<p>I think other answers might be missing the forest for the trees a bit. Most basic economic models could be defined with either "stocks" or "flows" as you've defined them. Ultimately, it's about measuring productivity in a generalized production function. You can define the inputs however you'd like- labor could be defined in "full time employee equivalents," or "hours worked," or a vareity of other things. Capital, as many other answers have noted, is incredibly hard to pin down in some cases. That said, it can often be defined and measured through depreciation, investment, "hours of machine X used," "number of tractors used," etc.. </p>

<p>More generally, both are pinned down by their relative factor income shares: an early estimation of which led to the creation of the Cobb-Douglas Production Function, which is an instructive example. For that, you define labor as the number of person hours worked (so if you worked for two companies, four hours each, it would count as 8 total "units" of labor), and capital as the total value of all machinery, buildings, equipment, etc.. You then look at how productive resources are allocated between the two, and back out income shares. For this, you never needed to really touch the "stock vs flow" issue, you just had to make sure your definitions were consistent.</p>

CC BY-SA 4.0
2018-05-26T02:18:22.480Z
2018-05-26T02:18:22.480Z
AndrewC
<p><strong>Determinants of Growth are based on both stocks and flows, depending on the nature of the individual factors.</strong></p>
<p>As pointed out in previous answers, in simpler theoretical models with only <em>aggregate</em> production, labor is often considered a stock, because labor = labor supply on aggregate, and because intermediate consumption is often ignored in these simpler models. Once we look closer, workers produce labor services (a flow) from their own human capital (stock).</p>
<p>However it's a little bit more intricate, once we disentangle intermediate consumption and production and allow for more detail. Using your example and the definition of stock and flow variables:</p>
<ul>
<li>For the tractor rental firm, tractors are capital (stock) which produce tractor rental services (flow). Depreciation of the tractors is &quot;negative&quot; production (flow) and the expansion of the fleet, or it's maintenance require repair services (flow) or investment (flow).</li>
<li>Farmers use land (stock), labor services (flow), and tractor rental services (flow), and potentially other inputs to produce output (flow).</li>
<li>Workers use their human capital (stock) and other inputs (such as consumption, a flow) to produce labor services, which are consumed by farmers and Uber. For the Uber ride services workers also use their own car (stock) to produce transport services. Statements such as &quot;Households provide labor services to firms&quot; are frequently used in more disaggregate DSGE models (see, for example <a href="https://www.newyorkfed.org/medialibrary/media/research/staff_reports/sr647.pdf" rel="nofollow noreferrer">here</a></li>
<li>Uber uses labor services (flow) and their proprietary system (stock) to produce intermediation services (connecting riders to drivers) (flow).</li>
</ul>

CC BY-SA 4.0
2021-09-08T11:06:33.643Z
2021-09-08T15:07:46.693Z
2021-09-08T15:07:46.693Z
BrsG
<p>In Nicholas Stern (1991)'s <a href="http://www.jstor.org/stable/2233847?origin=JSTOR-pdf" rel="nofollow noreferrer">The Determinants of Growth</a> first equation (I a), without preconceived ideas, one reads</p>

<p>$\frac{\dot{K}}{K} 
= \frac{d K}{d t} \frac{1}{K}$</p>

<p>Which means explicitly (in discret values)</p>

<p>$= \frac{K_{t+dt}-K_{t}}{dt} \frac{1}{K_{t}}$</p>

<p>If $t$ is in years, and that we are interested in the variation of $K$ over $1$ year (<i>i.e.</i> $dt=1$), one obtains</p>

<p>$= -1 +\frac{K_{t+1}}{K_{t}}$</p>

<p>Even if the above equality could represent either the variation of a stock or the variation of a flow, the story behind this is about stocks. To summarize</p>

<ul>
<li><p>$K_{t}$ is the stock of capital in the economy at year $t$</p></li>
<li><p>$dK = K_{t+dt}-K_{t}$ is a flow of capital occuring at year $t$, differently put an <b>investment</b> in capital.</p></li>
<li><p>$\dot{K}=\frac{d K}{d t}$ is the <b>absolute dynamic</b> of investments in capital in economy $\forall t$</p></li>
<li><p>$\frac{\dot{K}}{K}$ is the <b>relative dynamic</b> of investments in capital in economy $\forall t$</p></li>
</ul>

<p>Depending on the object you are looking at, it can be both measured in flow or in stock. To know with what you are dealing with, you must understand the story behind equations.</p>

<p>To the practice side of the issue, you cannot make realistic analogy between Solow's capital and, say, tractors. The <b>least abusive</b> perception of $K$ would be cumulated flows of investment in terms of money since, for example in micro-based CGE modelling, it is conceived as representative of the shareholding structure of the economy, and is thus linked to income formation via dividends (see the zero profit condition). In this non-realistic framework, although non-abusively linked to the everyday-life object, $L$ is very similar to $K$, is a self owned stock, and gives right to wages, that are flow objects, as dividends are. Still on the practice side of the issue, the difference between $L$ and labor force is the fact that the former is effectively employed, while the latter is not. Put differently, the link between the two is the labor market, $L$ is a demand, while labor force is a supply, and both form jointly a labor market whose equilibrium is reached via deflation/inflation of wages.</p>

<p>Finally, to my knowledge, the fact that <i> the same factor of production (stock) is employed in more than one activity over a given period (flow).</i> is not really a neoclassic native notion, I would say, once again when one refers to CGE modelling, because of the capital market clearing condition. It is more a monetary-macro-financial object, and is, <i>e.g.</i> all what debt is about when dealing with capital. However I do not see any analogy with $L$ in this case.</p>

CC BY-SA 3.0
2017-02-18T17:46:38.320Z
Thanks, but I don't think this answer the question (where is the discussion on labour?). The accumulation and depreciation of capital suggests $K_t$ is better understood as a stock. No doubt about that. However, in terms of production, what seems to matter more is the flow definition of factors of production. That is the point of the two examples I give. The question relates not to theory but to the practice side of the issue.
luchonacho
CC BY-SA 3.0
2017-02-18T14:31:38.313Z
2017-02-19T08:57:57.137Z
2017-02-19T08:57:57.137Z
keepAlive
<p>Consider the following cases:</p>

<ul>
<li><p>One machine (capital) is used by multiple producers within one year. For instance, farmers renting tractors from the same company. In this case, in terms of GDP, there is one unit of capital which was used to produce value added by many producers.</p></li>
<li><p>One worker (labour) which have two jobs. For instance, in a factory during the day, and as a Uber driver during the night. In this case, in terms of GDP, there is one unit of labour, used to produce value added in different goods/services.</p></li>
</ul>

<p>The common feature is that the same factor of production (<strong>stock</strong>) is employed in more than one activity over a given period (<strong>flow</strong>).</p>

<p><strong>Is the measurement of capital and labour used in the standard "determinants of growth" studies based on the stock or flow approach?</strong></p>

<p>In other words, are capital and labour measured in terms of the <strong>flow of services</strong> that these factors produce, or in terms of the <strong>stock of factors</strong> available in an economy over time? It is clear to me that the latter approach is plagued with problems, and the former is clearly more accurate.</p>

<p>My experience is that the use of stock is more common.</p>

CC BY-SA 3.0
2017-02-18T16:06:33.190Z
To me capital is always a stock while labor is always a flow. The corresponding stock to labor would be labor force, but it is quite clear that the size of the labor force is not a "factor of production". The flows of capital would be investment, depreciation, obsolescence and destruction. In studies of the determinants of growth based on the Solow model, the data for the stock of capital are quite often measured by adding up the series of investment and depreciation of the previous years.
user11629
<reference-request><labor-economics><economic-growth><capital>
In GDP growth studies, are factors of production measured as stock or flows?
luchonacho
# In GDP growth studies, are factors of production measured as stock or flows?

(Asked by: username_0 on 2017-02-16)

Consider the following cases:

* One machine (capital) is used by multiple producers within one year. For instance, farmers renting tractors from the same company. In this case, in terms of GDP, there is one unit of capital which was used to produce value added by many producers.
* One worker (labour) which have two jobs. For instance, in a factory during the day, and as a Uber driver during the night. In this case, in terms of GDP, there is one unit of labour, used to produce value added in different goods/services.

The common feature is that the same factor of production (**stock**) is employed in more than one activity over a given period (**flow**).

**Is the measurement of capital and labour used in the standard "determinants of growth" studies based on the stock or flow approach?**

In other words, are capital and labour measured in terms of the **flow of services** that these factors produce, or in terms of the **stock of factors** available in an economy over time? It is clear to me that the latter approach is plagued with problems, and the former is clearly more accurate.

My experience is that the use of stock is more common.

**Tags:** reference-request, labor-economics, economic-growth, capital
> **Comments:**
> **username_1**: To me capital is always a stock while labor is always a flow. The corresponding stock to labor would be labor force, but it is quite clear that the size of the labor force is not a "factor of production". The flows of capital would be investment, depreciation, obsolescence and destruction. In studies of the determinants of growth based on the Solow model, the data for the stock of capital are quite often measured by adding up the series of investment and depreciation of the previous years.  

---

## 5 answers

### Answer by username_2 on 2017-02-21. Score: 2

To add to @keepAlive's answer, even when natural resources are added typically stocks are used, at least in theoretical work. The flow of the used up resource is converted to a stock variable by assuming a fixed percentage of depletion each year (see for example Nordhaus Lethal model of 1992 [here](https://www.brookings.edu/wp-content/uploads/1992/06/1992b_bpea_nordhaus_stavins_weitzman.pdf))


---

### Answer by username_3 on 2019-12-17. Score: 0

There are a few apparent misconceptions in this question that need addressing.

1. In the actual exercise of national accounting, nothing is "measured" except for currency flows. The degree of sophistication of accounting comes down to the degree of nuance with which said flows are categorized. For your purposes, this is a good thing, because it means the confusing issue about "two companies, one unit capital" is irrelevant.
2. Most common macro growth models represent both capital and labor as stocks, *from which* value-added (read: goods and services, or "GDP") flows. Within the context of a given model, "investment" is essentially the mechanism through which this value-added is transformed into more capital, while the stock of labor is typically assumed to grow via natural processes or netted-out by normalizing the model on a per-worker basis. In either case, this growth is not a flow, any more than punching multiple taps into a keg is a flow. At the abstract level of most models, labor and capital are fundamentally stocks.

With that out of the way, you ask:

> are capital and labour measured in terms of the flow of services that these factors produce, or in terms of the stock of factors available in an economy over time

It may be more accurate to say that capital and labor are *priced* according to the flow of services they produce. They are typically "measured" according to their share of GDP, which isn't quite the same as a count of tractors or a number of employed persons because the point of growth models isn't to capture nominal values at all. It's to understand the aggregate, dynamic behavior of the system. Scale invariance (homogeneity of degree one) is usually assumed as a matter of convenience, and so "counting" as such is often irrelevant.

That's probably not a very satisfactory answer, but as some others have touched upon, this high degree of abstraction allows avoiding almost philosophical arguments about what a "unit of labor" is, or how "sectors" are defined, that are actually quite complicated and difficult to resolve in a clear and universal way.


---

### Answer by username_4 on 2018-05-26. Score: 0

I realize this question might be too old to reply to, but it was just bumped to the homepage. But anyway:

I think other answers might be missing the forest for the trees a bit. Most basic economic models could be defined with either "stocks" or "flows" as you've defined them. Ultimately, it's about measuring productivity in a generalized production function. You can define the inputs however you'd like- labor could be defined in "full time employee equivalents," or "hours worked," or a vareity of other things. Capital, as many other answers have noted, is incredibly hard to pin down in some cases. That said, it can often be defined and measured through depreciation, investment, "hours of machine X used," "number of tractors used," etc..

More generally, both are pinned down by their relative factor income shares: an early estimation of which led to the creation of the Cobb-Douglas Production Function, which is an instructive example. For that, you define labor as the number of person hours worked (so if you worked for two companies, four hours each, it would count as 8 total "units" of labor), and capital as the total value of all machinery, buildings, equipment, etc.. You then look at how productive resources are allocated between the two, and back out income shares. For this, you never needed to really touch the "stock vs flow" issue, you just had to make sure your definitions were consistent.


---

### Answer by username_5 on 2021-09-08. Score: -1

**Determinants of Growth are based on both stocks and flows, depending on the nature of the individual factors.**

As pointed out in previous answers, in simpler theoretical models with only *aggregate* production, labor is often considered a stock, because labor = labor supply on aggregate, and because intermediate consumption is often ignored in these simpler models. Once we look closer, workers produce labor services (a flow) from their own human capital (stock).

However it's a little bit more intricate, once we disentangle intermediate consumption and production and allow for more detail. Using your example and the definition of stock and flow variables:

* For the tractor rental firm, tractors are capital (stock) which produce tractor rental services (flow). Depreciation of the tractors is "negative" production (flow) and the expansion of the fleet, or it's maintenance require repair services (flow) or investment (flow).
* Farmers use land (stock), labor services (flow), and tractor rental services (flow), and potentially other inputs to produce output (flow).
* Workers use their human capital (stock) and other inputs (such as consumption, a flow) to produce labor services, which are consumed by farmers and Uber. For the Uber ride services workers also use their own car (stock) to produce transport services. Statements such as "Households provide labor services to firms" are frequently used in more disaggregate DSGE models (see, for example [here](https://www.newyorkfed.org/medialibrary/media/research/staff_reports/sr647.pdf)
* Uber uses labor services (flow) and their proprietary system (stock) to produce intermediation services (connecting riders to drivers) (flow).


---

### Answer by username_6 on 2017-02-18. Score: -1

In Nicholas Stern (1991)'s [The Determinants of Growth](http://www.jstor.org/stable/2233847?origin=JSTOR-pdf) first equation (I a), without preconceived ideas, one reads

$\frac{\dot{K}}{K}
= \frac{d K}{d t} \frac{1}{K}$

Which means explicitly (in discret values)

$= \frac{K\_{t+dt}-K\_{t}}{dt} \frac{1}{K\_{t}}$

If $t$ is in years, and that we are interested in the variation of $K$ over $1$ year (*i.e.* $dt=1$), one obtains

$= -1 +\frac{K\_{t+1}}{K\_{t}}$

Even if the above equality could represent either the variation of a stock or the variation of a flow, the story behind this is about stocks. To summarize

* $K\_{t}$ is the stock of capital in the economy at year $t$
* $dK = K\_{t+dt}-K\_{t}$ is a flow of capital occuring at year $t$, differently put an **investment** in capital.
* $\dot{K}=\frac{d K}{d t}$ is the **absolute dynamic** of investments in capital in economy $\forall t$
* $\frac{\dot{K}}{K}$ is the **relative dynamic** of investments in capital in economy $\forall t$

Depending on the object you are looking at, it can be both measured in flow or in stock. To know with what you are dealing with, you must understand the story behind equations.

To the practice side of the issue, you cannot make realistic analogy between Solow's capital and, say, tractors. The **least abusive** perception of $K$ would be cumulated flows of investment in terms of money since, for example in micro-based CGE modelling, it is conceived as representative of the shareholding structure of the economy, and is thus linked to income formation via dividends (see the zero profit condition). In this non-realistic framework, although non-abusively linked to the everyday-life object, $L$ is very similar to $K$, is a self owned stock, and gives right to wages, that are flow objects, as dividends are. Still on the practice side of the issue, the difference between $L$ and labor force is the fact that the former is effectively employed, while the latter is not. Put differently, the link between the two is the labor market, $L$ is a demand, while labor force is a supply, and both form jointly a labor market whose equilibrium is reached via deflation/inflation of wages.

Finally, to my knowledge, the fact that  *the same factor of production (stock) is employed in more than one activity over a given period (flow).* is not really a neoclassic native notion, I would say, once again when one refers to CGE modelling, because of the capital market clearing condition. It is more a monetary-macro-financial object, and is, *e.g.* all what debt is about when dealing with capital. However I do not see any analogy with $L$ in this case.

> **Comments:**
> **username_0**: Thanks, but I don't think this answer the question (where is the discussion on labour?). The accumulation and depreciation of capital suggests $K_t$ is better understood as a stock. No doubt about that. However, in terms of production, what seems to matter more is the flow definition of factors of production. That is the point of the two examples I give. The question relates not to theory but to the practice side of the issue.  

---

