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Webinar Series in Applied Quantitative Analysis - Updated

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

������ �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

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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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1. In your meeting/webinar controls, click Interpretation .
2. 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

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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.

Dynamic Panel Data Estimation I - Theory

Ashu Handa

Institute Fellow – AIR

Kenan Eminent Professor of Public Policy – UNC-CH

August 22, 2024

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Why this topic?

• Large number of panel data sets slowly becoming available in Africa

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• Panel data supports more sophisticated statistical methods to address endogeneity (e.g. fixed effects, fixed effects with IV—FEIV)

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• The Arellano-Bond (1991) and Blundell-Bond (1998) methods provide a solution to a specific problem where there is an endogenous lagged dependent variable

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Panel data sets you should have on your computer!

• World Bank Integrated Surveys on Agriculture (LSMS-ISA)
• Eight countries, national panel data, multiple waves
• https://www.worldbank.org/en/programs/lsms/initiatives/lsms-ISA

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• Ghana Socioeconomic Panel Survey
• Three waves, national
• https://dataportal.isser.edu.gh/index.php/catalog/4

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• Transfer Project cash transfer evaluation data sets (panels)
• Kenya, Lesotho, Ghana; Malawi and Zambia coming soon
• https://transfer.cpc.unc.edu/datasets/

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• Kagera (TZ), NIDS (RSA), Young Lives in Ethiopia, etc
• https://www.younglives.org.uk/

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Why would we have a lagged dependent variable?

• Almost all human behavior is conditioned on past choices – what we did in the past influences what we do in the present
• Panel data lets us build statistical models that include past choices

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• More importantly, many outcomes of interest are highly dependent on their past value

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• Y_it = f(Y_it-1, X) where i is the individual/household and t is time

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Why would we have a lagged dependent variable?

• Education: child does poorly this year, more likely to do poorly next year
• Nutrition: child is low weight or small this period, more likely to be low weight or small next period
• Physical health: adult has high BMI this year, likely to have high BMI next year
• Mental health, chronic disease, many other examples
• State dependency: the extent to which an outcome or variable depends on its past value

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Use the case of child nutrition (height or stunting - H) to illustrate the problem

H_it = β₀ + β₁(H_it-1) + β₂(X_it) + β₃(X_ht) + (ε_it + µ_i)

Current period (t) height depends on lagged height (t-1)

Truly random error: not correlated

with Xs nor H_it-1

Health endowment of child: fixed over

time and correlated with H_i in each period

National Educational Longitudinal Survey - NELS

We have an endogeneity problem: H_it-1 is correlated with the error term!

H_it = β₀ + β₁(H_it-1) + β₂(X_it) + β₃(X_ht) + (ε_it + µ_i)

We can solve this using IV. Instruments must satisfy two criteria (remember?)

1. Must be highly correlated with H_it-1;
2. Must not directly affect H_it;

POLL

Now let us look at the Arellano-Bond (1991) strategy

H_it = β₀ + β₁(H_it-1) + β₂(X_it) + β₃(X_ht) + (ε_it + µ_i) (1)

H_it-1 = β₀ + β₁(H_it-2) + β₂(X_it-1) + β₃(X_ht-1) + (ε_it-1 + µ_i) (2)

ΔH_it = β₁(ΔH_it-1) + β₂(ΔX_it) + β₃(ΔX_ht) + (Δε_it) (3)

Take the difference in these two equations (t) – (t-1)

µ_i has been removed in (3) – good

But there is still a problem

Now let us look at the Arellano-Bond (1991) strategy

ΔH_it = β₁(ΔH_it-1) + β₂(ΔX_it) + β₃(ΔX_ht) + (Δε_it) (3)

H_it-1 – H_it-2

H_it-1 is obviously correlated with ε_it-1

ε_it – ε_it-1

Arellano-Bond propose H_it-2 as an instrument for (H_it-1 – H_it-2)

Is this a valid instrument?

H_it-2 depends on µ_i of course, but u_i is not in (3)!!

Tthe Arellano-Bond (1991) strategy when facing an endogenous lagged dependent variable

ΔH_it = β₁(ΔH_it-1) + β₂(ΔX_it) + β₃(ΔX_ht) + (Δε_it) (3)

H_it-1 – H_it-2

H_it-1 is correlated with ε_it-1

ε_it – ε_it-1

Use H_it-2 as an instrument for (H_it-1 – H_it-2)

“Use the two-period value of the dependent variable in levels as an instrument in the differenced equation”

Blundell-Bond 1998 (building on Arellano-Bover 1995)

• When N is large and T is small
• These are exactly the data sets I listed at the beginning, large, national data sets (N in the thousands) but just a few waves (T around 3, 4 or 5)

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• In these data, Y_it-2 tends to be a very weak instrument for (Y_it-1) – (Y_it-2)

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• Their solution is a ‘system estimator’
• XTDPDSYS or XTDPD in STATA (will use it next week)

What is the Blundell-Bond (1998) solution?

H_it = β₀ + β₁(H_it-1) + β₂(X_it) + β₃(X_ht) + (ε_it + µ_i) (1)

Use (H_it-1 – H_it-2) as an instrument for H_it-1

But isn’t (H_it-1 – H_it-2) correlated with µ_i?

H_it-1 and H_it-2 are both dependent on µ_i

But when you subtract the two, µ_i cancels out!!

Estimate the levels equation (1) using the lagged difference in Y as the instrument together with the Arellano-Bond (1991) estimator” as a

system “system estimator”

Recap of the Blundell-Bond (1998) system estimator

H_it = β₀ + β₁(H_it-1) + β₂(X_it) + β₃(X_ht) + (ε_it + µ_i) (1)

Use (H_it-1 – H_it-2) as an instrument for H_it-1

Use H_it-2 as the instrument for (H_it-1 – H_it-2)

ΔH_it = β₁(ΔH_it-1) + β₂(ΔX_it) + β₃(ΔX_ht) + (Δε_it) (3)

Levels equation with a lagged

differenced instrument

Differenced equation with a lagged

levels instrument

Weak instrument problem identified by Blundell-Bond

Differenced equation with

two period lagged instrument in levels

System estimator

Levels equation with lagged instrument

in differences