Panel Data

Question 1

Assumptions OLS

Answer 1

1. Linear in parameters
2. Strict Exogeneity
3. No Multicolliniearity
4. Spherical Error Variance
5. Simple random Sample

Question 2

Assumptions Random Effects

Answer 2

1. Random Effect
2. Strict Exogeneity
3. Constant Variance
4. No Seriell Correlation
5. RE is homoskedastic

Additional Linearity, Ramdom Sapmling and Modified Rank condition

Question 3

Assumptions Fixed Effects

Answer 3

2. Stickt Exogeneity

And Linearity, Random Sampling and Modified Rank condition

Question 4

First Difference vs. Fixed Effects

Answer 4

Homoskedastic errors and no seriell correlation - FE
if the errors follow a Random walk - FD

in policy evaluations FD is mostly needed

Question 5

Hausman-Type tests

Answer 5

Two estimators. The assumptions of one are a subset of the other. Test checks the difference in the variance of the two estiamtors.

Uses to decide between RE and FD but it is only one tool and not the only basis for the decission.

Question 6

Fixed Effects Instrumental Variable Approach

Answer 6

Same as FE just with the instrument instead of x_it
additional
validity assumptions E(z,e) = 0
relevance assumptions E(z,x) neq 0

Question 7

Random Effects Instrumental Variable Approach

Answer 7

same as RE just z instead of x and validity and relevance condition

Question 8

Mundlak Approach

Answer 8

Assumes a functional form for E(v|X) i.e.
v = psi + x’delta + a_i
where a_i is the new error term and then we can use a Pooled OLS to estimate the model.
Test whether delta = to check fro RE assumption.

Question 9

Hausman-Taylor Approach

Answer 9

Assuming, that there is a set of independent and a set of not independent covarities.
We want to estimate time-invariant effects thus we cant use a FE estimation.
Use those independent as instrument for the dependent ones and estimate the model

Question 10

Anderson -Hsiao Estimator

Answer 10

Dynamic model.
FD and then instument the laged difference with one further level
requires 3 periods.
Can be estimated with 2SLS or a GMM estimator

Question 11

Arellano-Bond GMM

Answer 11

Not only uses this first moment restriction rather all that are possible.

Problem: Weak instruments can cause a poor estimate.
high correaltion rho -1 will cause weak instruments

Question 12

Blundell-Bover-Bond GMM

Answer 12

Additionall to Arellano-Bond GMM assumes initial condition.

Initial values are drawn from a steady state.

Question 13

Binary Choice: RE-Probit

Answer 13

can integrate the Random effect out.

Question 14

Fixed Effects Logit

Answer 14

Classical logit model. Under certain assumptions we are able to eliminate the fixed effect i.e. cornflakes purchases, think in conditional probabilities

Question 15

Chemberlain Probit Model

Answer 15

Simillar to Mundlak Approach. Assuming an explicit functional form for v_i and plugging that in and assuming, that the remaining error is exogenous and homoskedastic.

Question 16

Censoring

Answer 16

survival time T is unobserved

either left or right censoring

Question 17

Truncation

Answer 17

probability of appearing in the sample depends on the survival time

Question 18

in-flow sample

Answer 18

survey new entrens to a state, follow them for a fixed period (“observational window”)

Question 19

out-flow sample

Answer 19

Survery those leaving a state record start date.

Question 20

Stock Sample

Answer 20

Survery those in state (record start date)

Question 21

Stock sample with follow up

Answer 21

Survey those in state (record start date) and follow them for a given time

Question 22

Population Sample/Random sample

Answer 22

Survaey whole polulation/Survey a representive group of people.

Question 23

Likelihood: Random Sample no censorin nor truncation

Answer 23

product of the individual failure rates

Question 24

Likelihood: Random Sample right censoring

Answer 24

Product of indicvidual failures rates for those where failure was observed time the product of the survival rates for those surviving the study time or getting censored.

Question 25

Likelihood: Left-gruncated spell data possible right censoring

Answer 25

condition on survival until the beginning of the survay

Question 26

Likelihood: Stock Sample with no follow up

Answer 26

very difficult. No information for conditioning

Question 27

Likelihood: Right truncated spell data (outflow sample)

Answer 27

condtioning on cummmulative failure rate

Question 28

Median duration

Answer 28

S(m) = 0.5 or F(m) = 0.5

Question 29

Mean Duration

Answer 29

E(T) integrating over the t*f(t) dt

Question 30

Proportional Hazard

Answer 30

Hazard can be seperated into a baseline hazard and a time invariant effect of covarieties. Better to see in the log-hazard representation of the model

Question 31

Accelerated failure time

Answer 31

model in the survival time that fulfill | lnT = Xß + z

Question 32

Gometz Hazard Function

Answer 32

``` lambda exp(\gamma t) continious time PH model no AFT model ```

Question 33

Log-Logistic Model

Answer 33

psi^1/\gamma .... | continious time

Question 34

Log-Logistic Model

Answer 34

psi^1/\gamma .... continious time no PH model AFT model

Question 35

Log-Normal Model

Answer 35

pdf(lnt-\mu/sigma)/1+cdf(lnt-\mu/sigma) continious time no PH model AFT model

Question 36

Weibull Model

Answer 36

alpha t ^[alpha-1) \lambda continious time PH and AFT

Question 37

Piecewise constant Exponential (PCE) hazard

Answer 37

piecewise defined hazrad function with \lambda defined over intervals, where the effect of the covarities is assumed to be constant

Question 38

C-Log-Log (Complementory log-log model

Answer 38

1-exp(-exp(Xß+\gamma)) \gamma = ln(H_0(aj)-H_0(aj-1)) discreat time model Benifits: Comparable results independent of the intervals, since the model is assuming an continious underlying process. Thus different observation periods do not change the results.

Question 39

Cox's Model

Answer 39

baseline hazard times lambda Continious time model PH and AFT Baseline hazard has no specific form. Thus we are estimating a semi parametric model.

Question 40

Generalized Gamma

Answer 40

Depending on the parameters k = 1 - Weibull k = 1 sigma = 1 - Exponential k = 0 log-normal model

Question 41

Cloglog vs. Logit/Probit

Answer 41

linear function Xß + specific baseline hazard \gamma | for the estiamtion we assume a specific functional form for \gamma.

Question 42

Cloglog vs. Logit/Probit

Answer 42

linear function Xß + specific baseline hazard \gamma | for the estiamtion we assume a specific functional form for \gamma.

Question 43

Kaplan-Meier Estimator

Answer 43

Exit rate = #failures/#risk of failing survival rate = 1- exit rate = h S = product over h

Question 44

Time varrying covariities

Answer 44

similar to the PCE we can use intervals to ensure PH within the interval

Question 45

Independent Competing Risks (ICR)

Answer 45

The individual likelihoods are multiplied and are set up by experienceing one but surving the other.

Question 46

Multiple Spells

Answer 46

if the processes effecting the fifert spells are equal/simillar we can just built a product

Question 47

Unobserved heterogeneity

Answer 47

caused by omitted variables, measurment errors | might be able to integrate the effect out.