<p>It's hard to say. Presumably you think you have some fixed (unobservable) omitted variables, which is why you ran fixed effects (FE) / first differences. So I see one of two things going on here:</p>

<ol>
<li><p>The fixed omitted variables caused significance in the first regression, which means you do not have a significant effect. Do you have fixed omitted variables? If not, go with the first regression instead.</p></li>
<li><p>A quadratic model fits the data much better and hence you have significance in the first model, but not the second. In that case, you probably do have a significant effect. Is that true though? Why did you choose a quadratic specification? Does theory or the scatter plot suggest that is a good idea? If not go with the second regression. </p></li>
</ol>

<p>My suggestion would be to try fixed effects/first differences  with the qudratic terms if you have good reason for both. Otherwise use the specification you think has the most merit.</p>

<p>Unfortunately, I am not familiar with R and cannot comment on the code.</p>

CC BY-SA 4.0
2017-09-12T23:57:13.747Z
2019-04-11T06:59:01.310Z
2019-04-11T06:59:01.310Z
BB King
<p>Im doing some research with  some <a href="https://en.wikipedia.org/wiki/Panel_data" rel="nofollow noreferrer">panel data</a> I have on firm output and investment.</p>

<p>I ran two equations.</p>

<ol>
<li>$$y=\beta_0+\beta_1x+\beta_2x^2+\mu$$</li>
<li>$$\Delta y=\alpha_0+\Delta\alpha_1x+\epsilon$$</li>
</ol>

<p>in R these equations were prodouced using these commands</p>

<pre><code>   1) lm(output~investment+I(investment^2))
   2) lm(diff(output)~diff(investment))
</code></pre>

<p>The first equation had statistical significance on the 1% level, however with the first differenced data statistical significance was lost, and I ended up with rather high p-values as if there is no relationship between the two variables.</p>

<p>What is the interpretation of such results (i.e is there a relationship between investment and output in this data set) and which regression should I use in my research?</p>

CC BY-SA 3.0
2017-09-13T06:13:29.970Z
Have you tested for cointegration? The first relation might be spurious if there is no cointegration. Also, where is the investment squared in the second equation?
luchonacho
CC BY-SA 3.0
2017-09-13T15:50:25.013Z
@luchonacho I didn't add a quadratic term in the second equation because I saw that there was no relationship with the differenced investment variable. I did not test for co-integration.
EconJohn
CC BY-SA 3.0
2017-09-13T18:37:45.947Z
Including an intercept in the second equation corresponds to including a linear time trend in the first equation. Now you have one but not the other.
Richard Hardy
CC BY-SA 3.0
2017-09-13T20:51:08.460Z
This seems very similar to your previous question here https://economics.stackexchange.com/questions/17695/interpretation-of-a-differenced-regression?rq=1.
Adam Bailey
CC BY-SA 3.0
2017-09-13T20:58:53.007Z
@AdamBailey that one is not using panel data.
EconJohn
<applied-econometrics><self-study><r>
When first differences contradict a regular regression regarding Investment vs Output relationship
EconJohn
# When first differences contradict a regular regression regarding Investment vs Output relationship

(Asked by: username_0 on 2017-09-12)

Im doing some research with  some panel data I have on firm output and investment.
I ran two equations.

$$y=\beta_0+\beta_1x+\beta_2x^2+\mu$$
$$\Delta y=\alpha_0+\Delta\alpha_1x+\epsilon$$

in R these equations were prodouced using these commands
   1) lm(output~investment+I(investment^2))
   2) lm(diff(output)~diff(investment))

The first equation had statistical significance on the 1% level, however with the first differenced data statistical significance was lost, and I ended up with rather high p-values as if there is no relationship between the two variables.
What is the interpretation of such results (i.e is there a relationship between investment and output in this data set) and which regression should I use in my research?

**Tags:** applied-econometrics, self-study, r
> **Comments:**
> **username_1**: Have you tested for cointegration? The first relation might be spurious if there is no cointegration. Also, where is the investment squared in the second equation?  
> **username_0**: @luchonacho I didn't add a quadratic term in the second equation because I saw that there was no relationship with the differenced investment variable. I did not test for co-integration.  
> **username_2**: Including an intercept in the second equation corresponds to including a linear time trend in the first equation. Now you have one but not the other.  
> **username_3**: This seems very similar to your previous question here https://economics.stackexchange.com/questions/17695/interpretation-of-a-differenced-regression?rq=1.  
> **username_0**: @AdamBailey that one is not using panel data.  

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## 1 answers

### Answer by username_4 on 2017-09-12. Score: 1 | Accepted answer

It's hard to say. Presumably you think you have some fixed (unobservable) omitted variables, which is why you ran fixed effects (FE) / first differences. So I see one of two things going on here:

1. The fixed omitted variables caused significance in the first regression, which means you do not have a significant effect. Do you have fixed omitted variables? If not, go with the first regression instead.
2. A quadratic model fits the data much better and hence you have significance in the first model, but not the second. In that case, you probably do have a significant effect. Is that true though? Why did you choose a quadratic specification? Does theory or the scatter plot suggest that is a good idea? If not go with the second regression.

My suggestion would be to try fixed effects/first differences with the qudratic terms if you have good reason for both. Otherwise use the specification you think has the most merit.

Unfortunately, I am not familiar with R and cannot comment on the code.


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