M16 - Panel data regression

Question 1

Panel data regression

• def
• basic idea
• sources of variation
• e.g.

Answer 1

several time points
several observations
several items

• its a combination of cross-sectional data and time series
• 1. between units, 2. within each unit
• Annual data from firms before/after IPO

Question 2

Sources of variation in Panel data regression

Answer 2

• between units: as with cross-sectional; examine differences between the observed units
• within each unit: variation between different points in time

Question 3

Adv Panel data

Answer 3

+ high internal & external validity
+ allows to control the impact of latent heterogeneity
+ more df –> higher efficacy in estimating
+ testing of more complex hypothesis possible

• Data collection takes time
• costly
• Panel mortality
• time series problem: the standard quality measures of regression (R², F, etc.) only tell us how well the model fits the OBSERVED values

Question 4

Disadv Panel data

Answer 4

+ high internal & external validity
+ allows to control the impact of latent heterogeneity
+ more df –> higher efficacy in estimating
+ testing of more complex hypothesis possible

• Data collection takes time
• costly
• Panel mortality
• time series problem: the standard quality measures of regression (R², F, etc.) only tell us how well the model fits the OBSERVED values

Question 5

Ways to analyze Panel data

• methods
• what about alpha
• what if Xk captures all relevent aspects of Y?

Answer 5

fixed effects
random effecty
pooled OLS

• alpha captures unobserved effects for unit i
• if Xk captures all variables, than we can drop alpha and use pooled OLS because we have no unobserved variables

Question 6

fixed effects?

• def
• aim

Answer 6

• every unit of observation has a different constant

–> measure the effect of the explanatory variable, even if individual, time-constant heterogeneity is correlated with the explanatory variable
If we assume fixed effects, we impose time independent effects for each entity that are possibly correlated with the regressors.

• erase individual heterogeneity by transformation
• individual heterogeneity is fix for each entity over time

Question 7

How to deal with fixed effects alpha i?

Answer 7

• -> introduce dummy variable Aj to make it comparable to x
• -> analysing first differences between successive error terms –> eliminating alphaAj

OR –>within-groups fixed effects:
eliminating alphai by subtracting from each
variable for each unit its mean value (over time)

Question 8

Interpretation of fixed effects

• df
• slopes?
• constant?

Answer 8

–> we lose n degress of freedom for the estimation of betak
(we either lose n observations or estaimate n additional parameters (dummy v))

• -> slopes are the same for all units, but const differ
• -> constant captures the combined effects f several unknown variales that are different between units, but stable over time

Question 9

Pooled OLS

Answer 9

take every observations of every time period as totally indpendent point

–> only possible to use, if you have no unobserved variables

Question 10

Random effects

• def
• why cant we use OLS here?
• adv over FE

Answer 10

random effects works under the assumption that alphai are totally uncorrelated with Xj, purely random

• uij is typically subject to autocorrelation
• -> OLS is inefficient and the standard errors are estimated wrong
• -> Use GLS (generalized least squares)
• we do not lose n degress of freedom –> more efficient

Question 11

Hausman Test

• def
• tests if …
• whats H0?

Answer 11

to assess whether to use fixed or random effects estimation
–> tests if the unobserved effects alphai are independent of the explanatory variables xj

• H0: alphai is distributed independently of Xj
• -> if rejected: RER will be subject to unobserved heterogeneity–> use FER (not randomly /dep of Xj)
• -> if not rejected: FER and RER are consistent, but FER will be inefficient –> use RER (randomly /indep of Xj)

Question 12

which types of models can be used for Panel data?

Answer 12

OLS
Logit
Probit, Tobit
autoregressive models
other time series models

Question 13

Panel regression is not so much an … method, but a type of … or …

Answer 13

Panel regression is not so much an ANALYSIS method, but a type of DATA SET
or DATA STRUCTURE