<p>This is not a structural paper. The authors are not "<em>deriving</em>" a log-linear relationship from a model, which they then proceed to estimate. They rather start by postulat the relationship: </p>

<blockquote>
  <p>Let $C^J_{it}$ be the number of citations made by the patent
  applications Japanese firm i filed in year t to the cumulated stock of
  bindigenousQ U.S.-invented patents granted as of year $t$. I can then
  write the log of $C^J_{it}$ as a simple log-linear function of several
  other observables</p>
  
  <p>$$ c^J_{it} = \beta_0 + \beta_1 p_{it} + \beta_2 FDI_{it} + \gamma_i +
&gt; \alpha_t + \epsilon_{it}$$</p>
</blockquote>

<p>which is their equation (1).</p>

CC BY-SA 3.0
2015-09-11T19:05:08.067Z
Thanks @Foobar but: 
(1) how is postulating different from estimating a model and;
(2) under what circumstances would each be more suitable. 
I ask because I believe both requires making assumptions and testing those assumptions with an equation. Thanks.
od320
CC BY-SA 3.0
2015-09-11T15:54:44.060Z
2015-09-11T15:54:44.060Z
FooBar
<p>Can <strong>beta</strong> be an exponent within a function prior to taking the log of that function to arrive at a simple, log-linear estimation equation?</p>

<p>I am curious because I found an equation that had beta as an exponent on <strong>page 7</strong> of this article by Lee Branstetter(2004): <a href="http://bit.ly/1OGSFx9" rel="nofollow">http://bit.ly/1OGSFx9</a> titled: <em>Is Foreign Direct Investment a Channel of Knowledge Spillovers? Evidence from Japan’s FDI in the United States</em></p>

<p>I believe there this is not out-of-order. I am however, seeking an explanation to the equation. </p>

<p>I have tried to check different sources and the closest explanation is that the function is a linear-log function.</p>

<econometrics>
Beta as an exponent?
od320
# Beta as an exponent?

(Asked by: username_0 on 2015-09-11)

Can **beta** be an exponent within a function prior to taking the log of that function to arrive at a simple, log-linear estimation equation?

I am curious because I found an equation that had beta as an exponent on **page 7** of this article by Lee Branstetter(2004): <http://bit.ly/1OGSFx9> titled: *Is Foreign Direct Investment a Channel of Knowledge Spillovers? Evidence from Japan’s FDI in the United States*

I believe there this is not out-of-order. I am however, seeking an explanation to the equation.

I have tried to check different sources and the closest explanation is that the function is a linear-log function.

**Tags:** econometrics

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## 1 answers

### Answer by username_1 on 2015-09-11. Score: 2 | Accepted answer

This is not a structural paper. The authors are not "*deriving*" a log-linear relationship from a model, which they then proceed to estimate. They rather start by postulat the relationship:

> Let $C^J\_{it}$ be the number of citations made by the patent
> applications Japanese firm i filed in year t to the cumulated stock of
> bindigenousQ U.S.-invented patents granted as of year $t$. I can then
> write the log of $C^J\_{it}$ as a simple log-linear function of several
> other observables
>
> $$ c^J\_{it} = \beta\_0 + \beta\_1 p\_{it} + \beta\_2 FDI\_{it} + \gamma\_i +
> > \alpha\_t + \epsilon\_{it}$$

which is their equation (1).

> **Comments:**
> **username_0**: Thanks @Foobar but:  (1) how is postulating different from estimating a model and; (2) under what circumstances would each be more suitable.  I ask because I believe both requires making assumptions and testing those assumptions with an equation. Thanks.  

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