F12 Panel data II (dynamic models) Flashcards

1
Q

What is a dynamic panel data model? Wawro (2022)

A

A dynamic model refers to persistence in the outcome. Theres is serial correlation in outcome across time.

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2
Q

What is the difference between a panel data model and a dynamic panel data model?

A

In dynamic models there is a degree of autocorrelation in the dependent variable. The value in t-1 affect the value in t. A degree of persistency.

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3
Q

What happens if you incorrectly apply OLS to a dynamic panel data format?

A

OLS becomes biased and inconsistent because we assume E(ε|x)=E(ε) and no autocorrelation.

The lagged term (one of our predictor variables) is correlated with the error term and unit-specific fixed effects.

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4
Q

What are the two approaches to deal with dynamic panel data models according to Wawro (2022)?

A

Anderson Hsiao-estimator (first-difference estimator) or GMM (generalized methods of moments)

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5
Q

Explain the Anderson Hsiao-estimator

A

The estimator eliminates unit-specific FE by using a first-difference transformation (eliminate time-invariant factors).

The lagged term (t-1) is still correlated with the error term. This is fix by using another lagged term (t-2) as an instrument.

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6
Q

What does it mean to first-difference transform data?

A

We simply difference the variables We subtract the value from the previous period. A change variable capital Delta.

As time invariant factors does not vary over time their influence is ruled out.

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7
Q

Why is y_i,t-2 a valid instrument in dynamic panel data models?

A

y_i,t-2 only affect y_i,t through y_i,t-1, so it meets the conditions for a valid instrument (exclusion criterion).

Relies on the assumption of only one significant time period. If there are several significant lagged periods use GMM.

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8
Q

What are two other problems with the Anderson Hsiao-estimator

A

(1) If the effect of the lagged term is close to one it’s a sign of an extremely high degree of autocorrelation. Only marginal changes over time e.g. institutional settings are sticky over time (GINI). Especially a problem with binary measures (democracy or not).

(2) Small sample size. Difficult to estimate the correct value of lags.

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9
Q

What is GMM and when is it used?

A

GMM stands for generalized methods of moments and is used when there are more than one significant lagged period.

It’s possible to include further lags and additional instruments.

Improves efficiency of the estimator.

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10
Q

What is important for GMM?

A

All instruments must meet the exclusion criterion

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11
Q

How can you test whether all instruments meet the exclusion criterion in GMM?

A

Via the Sargan test. Tests whether the dependent instrument only affects the dependent variable through the autocorrelated term.

Stars/significance is bad.

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12
Q

What package is used in R?

A

PLM. Can among other things introduce multiple lags and see how many is significant.

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13
Q

What is level and change variables? Relevance from Plümper et al. (2005)

A

Variables that measure levels (e.g., GDP per capita) and variables that measure changes (e.g. GDP growth)

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14
Q

What are four key insights from Plümper et al. (2005)?

A
  1. If your theory predicts an influence of a level-measure X on a change-measure Y, you must not include fixed effects
  2. If you include a lagged measure of your dependent variable or period dummies, you may absorb time trends in the dependent variable
  3. The magnitude of the effect of lagged DVs may differ between units (→ it may be problematic to assume uniform lags). The degree of autocorrelation may not be the same for all.
  4. For longer observation periods, slopes of key variables and error term variances may change over time (time dependence of coefficients)
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15
Q

How does Wawro (2022) argue for use of dynamic panel data models?

A

Two traditional ways.

(1) In typical time-series analysis, lags of the dependent variable are included as regressors to model persistence/serial correlation (ignoring panel aspect)

(2) Assume there are individual specific effects are not persistent (ignoring dynamic aspect)

Dynamic panel models include both – they allow modeling of dynamics while accounting for individual-level heterogeneity (FE).

Whether past behavior directly affects current behavior or whether individuals are predisposed to behave on way or another.

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16
Q

What does the bias/variance trade-off mean regarding GMM according to Wawro (2022)?

A

The more periods in panel data the more instruments available. Instruments from earlier periods are weaker the further we go into the panel – using all instruments might be efficient but cause severe downward bias aka. overfitting the model.