<p>Your equation can be re-written (through the properties of logs) as:</p>

<p><span class="math-container">$$
\ln(y_{it} / y_{it-1}) = \beta\ln(x_{it} / x_{it-1})
$$</span></p>

<p>So it becomes a log-log regression equation.  In this form, it means that if we change the ratio of <span class="math-container">$x_{it}$</span> to <span class="math-container">$x_{it-1}$</span> by one percent, the ratio of <span class="math-container">$y_{it}$</span> to <span class="math-container">$y_{it-1}$</span> will change by <span class="math-container">$\beta$</span> percent, on average.  In other words, if <span class="math-container">$x_{i}$</span> grows by one percent between two periods, <span class="math-container">$y_{i}$</span> is expected to grow by <span class="math-container">$\beta$</span> percent in that same time span. </p>

CC BY-SA 4.0
2019-04-14T20:53:31.993Z
2019-04-14T22:42:50.977Z
2019-04-14T22:42:50.977Z
AlexK
<p>Imagine we have a DGP such that</p>

<p><span class="math-container">$$
\Delta \ln y_{it}=\beta\times\Delta\ln x_{it}
$$</span></p>

<p>How do you interpret the <span class="math-container">$\beta$</span> coefficient, since it is expressed in an approximation of a growth rate?</p>

<p>Thanks for your help</p>

<econometrics>
Interpreting coefficients with Delta ln as independant and dependent variables
Mr. Fafa
# Interpreting coefficients with Delta ln as independant and dependent variables

(Asked by: username_0 on 2019-04-14)

Imagine we have a DGP such that

$$
\Delta \ln y\_{it}=\beta\times\Delta\ln x\_{it}
$$

How do you interpret the $\beta$ coefficient, since it is expressed in an approximation of a growth rate?

Thanks for your help

**Tags:** econometrics

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## 1 answers

### Answer by username_1 on 2019-04-14. Score: 2

Your equation can be re-written (through the properties of logs) as:

$$
\ln(y\_{it} / y\_{it-1}) = \beta\ln(x\_{it} / x\_{it-1})
$$

So it becomes a log-log regression equation. In this form, it means that if we change the ratio of $x\_{it}$ to $x\_{it-1}$ by one percent, the ratio of $y\_{it}$ to $y\_{it-1}$ will change by $\beta$ percent, on average. In other words, if $x\_{i}$ grows by one percent between two periods, $y\_{i}$ is expected to grow by $\beta$ percent in that same time span.


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