<p>I am currently getting ready for Econometrics 1 exam and I have some problems deriving the FD estimator sometimes.</p>
<p>Lets say we have a data set with the following observations:</p>
<p><span class="math-container">$FoodAS_{it}$</span> = food assumption pr day for person i in year t,</p>
<p><span class="math-container">$Weight_{it}$</span> = weight for person i in year t</p>
<p>and a dummy variable: <span class="math-container">$Bicity_{it}$</span> = a dummy for big cities</p>
<p>We have the following model</p>
<p><span class="math-container">$Weight_{it} = \beta_1FoodAS_{it} + \beta_2 Bigcity_{it}, t = \{2010,2015\} $</span></p>
<p>When calculating the estimator, I would say we get</p>
<p><span class="math-container">$$
\Delta Weight_{it} = Weight_{i2} - Weight_{i1} = \beta_1(FoodAS_{i2} - FoodAS_{i2}) + \beta_2(Bigcity_{i2} - Bigcity_{i1})
$$</span>
But for some reason, the result states that the correct answer is
<span class="math-container">$$
\Delta Weight_{it} = Weight_{i2} - Weight_{i1} = \beta_1(FoodAS_{i2} - FoodAS_{i2})
$$</span>
I have noticed this multiple times. Almost always, the dummy variables are removed. Why is this?</p>
<p>Kind regards</p>

CC BY-SA 4.0
2021-11-04T08:15:14.833Z
First-differencing in the within/time-series dimension is going to remove any variable that is time-invariant---e.g. fixed effect. Here, there may be an implicit assumption that the "Bigcity" dummy is time-invariant. Someone in the dataset either lives or not lives in a big city for both periods.
Michael
CC BY-SA 4.0
2021-11-04T08:41:12.120Z
That makes sense. Thank you very much
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<econometrics><first-difference>
Dummy variables are removed when estimating first-differences
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# Dummy variables are removed when estimating first-differences

(Asked by: username_0 on 2021-11-04)

I am currently getting ready for Econometrics 1 exam and I have some problems deriving the FD estimator sometimes.

Lets say we have a data set with the following observations:

$FoodAS\_{it}$ = food assumption pr day for person i in year t,

$Weight\_{it}$ = weight for person i in year t

and a dummy variable: $Bicity\_{it}$ = a dummy for big cities

We have the following model

$Weight\_{it} = \beta\_1FoodAS\_{it} + \beta\_2 Bigcity\_{it}, t = \{2010,2015\} $

When calculating the estimator, I would say we get

$$
\Delta Weight\_{it} = Weight\_{i2} - Weight\_{i1} = \beta\_1(FoodAS\_{i2} - FoodAS\_{i2}) + \beta\_2(Bigcity\_{i2} - Bigcity\_{i1})
$$
But for some reason, the result states that the correct answer is
$$
\Delta Weight\_{it} = Weight\_{i2} - Weight\_{i1} = \beta\_1(FoodAS\_{i2} - FoodAS\_{i2})
$$
I have noticed this multiple times. Almost always, the dummy variables are removed. Why is this?

Kind regards

**Tags:** econometrics, first-difference

> **Comments:**
> **username_1**: First-differencing in the within/time-series dimension is going to remove any variable that is time-invariant---e.g. fixed effect. Here, there may be an implicit assumption that the "Bigcity" dummy is time-invariant. Someone in the dataset either lives or not lives in a big city for both periods.  
> **username_0**: That makes sense. Thank you very much  

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## 0 answers

