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Webinar Series in Applied Quantitative Analysis - Updated

https://www.airp3-africa.org/applied-quantitative-analysis-webinar-series

Date	Topic
�February 29�March 7	Session One�Potential Outcomes and Omitted Variable Bias I (Theory) �Potential Outcomes and Omitted Variable Bias II (Application)
�March 21�March 28	Session Two�Difference-in-differences I (Theory)�Difference-in-differences II (Application)
�April 25�May 2	Session Three�Power analysis, clustering and sample size calculations I (Theory)�Power analysis, clustering and sample size calculations II (Application)
May 23�May 30	Session Four�Propensity score matching (Theory)�Propensity score matching (Application)
�June 20�June 27	Session Five�Fixed-effects I (Theory)�Fixed-effects II (Application)
�July 25�August 1	Session Six�Instrumental variables I (Theory)�Instrumental Variables II (Application)
August 22 August 29	Session Seven�Lagged dependent variables and the Arellano-Bond Estimator I (Theory)�Lagged dependent variables and the Arellano-Bond Estimator II (Application)

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�� Écoute de l'interprétation d'une langue �Windows | macOS�

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�1. Dans les contrôles de votre réunion/webinaire, cliquez sur Interprétation .

2. Cliquez sur la langue que vous souhaitez entendre. (Nous aurons le français) Pas besoin de choisir l'anglais, c'est la langue de la salle Zoom principale

3. (Facultatif) Pour entendre uniquement la langue interprétée, cliquez sur Couper le son original.

Remarques:

Vous devez rejoindre l’audio de la réunion via l’audio/VoIP de votre ordinateur. Vous ne pouvez pas écouter l’interprétation linguistique si vous utilisez les fonctions audio de connexion ou d’appel téléphonique.
En tant que participant rejoignant une chaîne linguistique, vous pouvez retransmettre sur le canal audio principal canal si vous réactivez votre audio et parlez.

.

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Listening to language interpretation� Windows | macOS

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In your meeting/webinar controls, click Interpretation .
Click the language that you would like to hear. (We will have French) No need to choose English, that is the language in the main Zoom room

3. (Optional) To hear the interpreted language only, click Mute Original Audio.

Notes:

You must join the meeting audio through your computer audio/VoIP. You cannot listen to language interpretation if you use the dial-in or call me phone audio features.
As a participant joining a language channel, you can broadcast back into the main audio

channel if you unmute your audio and speak.

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Fixed Effects Theory

Professor Jeremy Moulton

Department of Public Policy

University of North Carolina at Chapel Hill

June 20, 2024

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Panel Data

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id	time
1	1	2	0
1	2	2	0
1	3	5	1
2	1	2	0
2	2	4	1
2	3	4	1
3	1	5	1
3	2	5	1
3	3	5	1

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6

Y

X

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Pooled OLS (simple OLS regression)

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Y

X

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Between Estimator

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Y

X

Y

X

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Within Estimator (Fixed Effects)

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Y

X

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The Set Up

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First Difference (T = 2)

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What are you doing?

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First Differences Model

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First Difference (T > 2)

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The First Difference Data

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id	time
1	1	2	0
1	2	2	0	0	0
1	3	5	1	3	1
2	1	2	0
2	2	4	1	2	1
2	3	4	1	0	0
3	1	5	1
3	2	5	1	0	0
3	3	5	1	0	0

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Fixed Effects Model

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Between Effects Model

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Fixed Effect: De-Meaned version

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Let’s go back to an earlier class

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Positive slope

If most of the observations are in quadrants I and III, then the slope is positive

Quadrant I: X and Y are above their mean
Quadrant III: X and Y are below their mean

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I

II

IV

III

X_i

Y_i

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Negative slope

If most of the observations are in quadrants II and IV, then the slope is negative

Quadrant II: X is below and Y above their mean
Quadrant IV: X is above and Y below their mean

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I

II

IV

III

X_i

Y_i

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OK, now go back to the future

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Do that again, but with Fixed Effects

Fixed Effects changes the reference point from the overall mean to the individual mean.

How do you in one time period compare to your average – instead of how do you in one time period compare to everyone’s average?

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I

II

IV

III

X_i

Y_i

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Fixed Effects: De-Meaned version

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id	time
1	1	2	0	3	0.33
1	2	2	0	3	0.33
1	3	5	1	3	0.33
2	1	2	0	3.33	0.67
2	2	4	1	3.33	0.67
2	3	4	1	3.33	0.67
3	1	5	1	5	1
3	2	5	1	5	1
3	3	5	1	5	1

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Fixed Effects: De-Meaned version

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id	time
1	1	2	0	3	0.33	-1	-.33
1	2	2	0	3	0.33	-1	-.33
1	3	5	1	3	0.33	2	.67
2	1	2	0	3.33	0.67	-1.33	-.67
2	2	4	1	3.33	0.67	.67	.33
2	3	4	1	3.33	0.67	.67	.33
3	1	5	1	5	1	0	0
3	2	5	1	5	1	0	0
3	3	5	1	5	1	0	0

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Ok, but how do I actually do it?

First Difference:

reg D.(y x)

Fixed Effects:
You could create a fixed effect for every individual:

tab id, gen(idFE)
reg y x idFE*

You could include a temporarily created fixed effect for ever individual:

reg y x i.id

You could use the xt version:

xtset id year
xtreg y x, fe

Or other options:

areg y x, absorb(id)
reghdfe y x, absorb(id)

You need to install this ado file, but it is very helpful when using a large number of fixed effects

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But, what about time-varying unobservables?

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Time Varying Unobservables

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Time Varying Unobservables

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Fixed Effects or First Differences will not “fix” all of our problems

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Time invariant independent variables

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Fixed Effects vs. Pooled OLS

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Fixed Effects

Pooled OLS

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How do I know if OLS or FE is better?

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Test difference in coefficients

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