<p>The index is just that, a dimensionless series of numbers (constructed in a <a href="https://en.wikipedia.org/wiki/T%C3%B6rnqvist_index" rel="nofollow noreferrer">particular form</a>). I'm not sure how deep that can go. For instance, if I have a series of prices, say \$1.5 in year 1 and \$3 in year 2, you can turn that into an index like 100 and 200 respectively. The index has no units. It just maps the growth rates of the underlying series into a fixed base (in the example above, 100 in year 1). If you happen to know the original series, you can recover the units of the series.</p>

<p>However, the natural question that follows is, what are the units of $A$?
In an aggregate production function $Y=F(A,K,L)$, the units and the dimension of $A$ depends on the unit and dimension of the other factors. For example, if $Y$ is units of output per year, $K$ is units of capital per year, and $L$ is number of hours worked per year, then the unit of $A$ is a function of units of output over units of capital and hours. However, if you change $L$ from hours to workers using some transformation (e.g. average working hours), the units of $A$ change too. </p>

<p>Now, since it seems you want to compute $Y$, and because you have both (i) obtained an index for $A$ (ii) that is probably not related to the series of $K$ and $L$ you will use to compute $Y$, the units of $Y$ will not have direct meaning. This is, you cannot deduce that the resulting quantity of $Y$ corresponds to, say, millions of Euros per year. </p>

<p>Is this bad? Not really, if you are interested in computing the <strong>growth rate</strong> of $Y$. </p>

<p>Finally, is this a logical method to compute $Y$? Absolutely not. Lee Sin's comment is entirely pertinent. <strong>You are given $Y$ in national statistics</strong>. Why to compute it? Instead, what you want is to study the determinants of growth, which goes into estimating $A$ using methods like <a href="https://en.wikipedia.org/wiki/Growth_accounting" rel="nofollow noreferrer">Growth accounting</a>. That is a field as old as the <a href="http://www2.econ.iastate.edu/classes/econ521/Orazem/Papers/cobb-douglas.pdf" rel="nofollow noreferrer">Cobb and Douglas production function</a> itself (probably older).</p>

CC BY-SA 3.0
2017-08-24T15:37:41.200Z
I really appreciate your advice. But let's say that I want to use historical GDP data to determine whether GDP growth was mainly driven by a.Technology or b. Capital & labor (ie. China & Cambodia). So I have **Y** as GDP PPP, **L** as labor force and **K** as gross capital formation, I'll use this to compute **A**. Is this a proper way in your opinion?
Hoang Trieu Duong Kim
CC BY-SA 3.0
2017-08-25T08:24:05.770Z
@HoangTrieuDuongKim Precisely. That is the exact proceedure. Actually, the series of $A$ that you say you got from somewhere could only be estimated using a procedure like growth accounting or related.
luchonacho
CC BY-SA 3.0
2017-08-23T19:49:26.740Z
2017-08-23T19:49:26.740Z
luchonacho
<p>I've seen the Tornqvist used as many measures of total factor productivity but have not seen it in conjunction with the Solow growth model. My understanding of how the Solow growth models measures TFP is by having values for economic output, labout and capital, and assigning the disparity to TFP.</p>

CC BY-SA 3.0
2017-08-23T17:56:23.427Z
I intend to do the reverse: input labor, capital and TFP to calculate economic output, to see whether the growth is driven by technological advance or heavy capital investment. But thanks for your comment anyway XD
Hoang Trieu Duong Kim
CC BY-SA 3.0
2017-08-23T18:01:05.497Z
This doesn't actually tell you anything valuable about drivers though. If you're calculated field if economic output, then all you're measuring is economic output (assuming you're correct). If you want to calculate drivers you need to start with output and work backwards.
Lee Sin
CC BY-SA 3.0
2017-08-23T17:47:46.540Z
2017-08-23T17:47:46.540Z
Lee Sin
<p>In the Solow growth model, to compute economic output $Y$, you need variable $A$ being total factor productivity. I found some data about my country's TFP but it's estimated as a Tornqvist Index. What does it mean? Can I simply use that number in the equation to calculate $Y$?</p>

<econometrics><macroeconomics>
What is a number estimated as a Tornqvist Index?
Hoang Trieu Duong Kim
# What is a number estimated as a Tornqvist Index?

(Asked by: username_0 on 2017-08-22)

In the Solow growth model, to compute economic output $Y$, you need variable $A$ being total factor productivity. I found some data about my country's TFP but it's estimated as a Tornqvist Index. What does it mean? Can I simply use that number in the equation to calculate $Y$?

**Tags:** econometrics, macroeconomics

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## 2 answers

### Answer by username_1 on 2017-08-23. Score: 0 | Accepted answer

The index is just that, a dimensionless series of numbers (constructed in a [particular form](https://en.wikipedia.org/wiki/T%C3%B6rnqvist_index)). I'm not sure how deep that can go. For instance, if I have a series of prices, say \$1.5 in year 1 and \$3 in year 2, you can turn that into an index like 100 and 200 respectively. The index has no units. It just maps the growth rates of the underlying series into a fixed base (in the example above, 100 in year 1). If you happen to know the original series, you can recover the units of the series.

However, the natural question that follows is, what are the units of $A$?
In an aggregate production function $Y=F(A,K,L)$, the units and the dimension of $A$ depends on the unit and dimension of the other factors. For example, if $Y$ is units of output per year, $K$ is units of capital per year, and $L$ is number of hours worked per year, then the unit of $A$ is a function of units of output over units of capital and hours. However, if you change $L$ from hours to workers using some transformation (e.g. average working hours), the units of $A$ change too.

Now, since it seems you want to compute $Y$, and because you have both (i) obtained an index for $A$ (ii) that is probably not related to the series of $K$ and $L$ you will use to compute $Y$, the units of $Y$ will not have direct meaning. This is, you cannot deduce that the resulting quantity of $Y$ corresponds to, say, millions of Euros per year.

Is this bad? Not really, if you are interested in computing the **growth rate** of $Y$.

Finally, is this a logical method to compute $Y$? Absolutely not. Lee Sin's comment is entirely pertinent. **You are given $Y$ in national statistics**. Why to compute it? Instead, what you want is to study the determinants of growth, which goes into estimating $A$ using methods like [Growth accounting](https://en.wikipedia.org/wiki/Growth_accounting). That is a field as old as the [Cobb and Douglas production function](http://www2.econ.iastate.edu/classes/econ521/Orazem/Papers/cobb-douglas.pdf) itself (probably older).

> **Comments:**
> **username_0**: I really appreciate your advice. But let's say that I want to use historical GDP data to determine whether GDP growth was mainly driven by a.Technology or b. Capital & labor (ie. China & Cambodia). So I have **Y** as GDP PPP, **L** as labor force and **K** as gross capital formation, I'll use this to compute **A**. Is this a proper way in your opinion?  
> **username_1**: @HoangTrieuDuongKim Precisely. That is the exact proceedure. Actually, the series of $A$ that you say you got from somewhere could only be estimated using a procedure like growth accounting or related.  

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### Answer by username_2 on 2017-08-23. Score: 0

I've seen the Tornqvist used as many measures of total factor productivity but have not seen it in conjunction with the Solow growth model. My understanding of how the Solow growth models measures TFP is by having values for economic output, labout and capital, and assigning the disparity to TFP.

> **Comments:**
> **username_0**: I intend to do the reverse: input labor, capital and TFP to calculate economic output, to see whether the growth is driven by technological advance or heavy capital investment. But thanks for your comment anyway XD  
> **username_2**: This doesn't actually tell you anything valuable about drivers though. If you're calculated field if economic output, then all you're measuring is economic output (assuming you're correct). If you want to calculate drivers you need to start with output and work backwards.  

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