Panel Data Flashcards
Assumptions OLS
- Linear in parameters
- Strict Exogeneity
- No Multicolliniearity
- Spherical Error Variance
- Simple random Sample
Assumptions Random Effects
- Random Effect
- Strict Exogeneity
- Constant Variance
- No Seriell Correlation
- RE is homoskedastic
Additional Linearity, Ramdom Sapmling and Modified Rank condition
Assumptions Fixed Effects
- Stickt Exogeneity
And Linearity, Random Sampling and Modified Rank condition
First Difference vs. Fixed Effects
Homoskedastic errors and no seriell correlation - FE
if the errors follow a Random walk - FD
in policy evaluations FD is mostly needed
Hausman-Type tests
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.
Fixed Effects Instrumental Variable Approach
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
Random Effects Instrumental Variable Approach
same as RE just z instead of x and validity and relevance condition
Mundlak Approach
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.
Hausman-Taylor Approach
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
Anderson -Hsiao Estimator
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
Arellano-Bond GMM
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
Blundell-Bover-Bond GMM
Additionall to Arellano-Bond GMM assumes initial condition.
Initial values are drawn from a steady state.
Binary Choice: RE-Probit
can integrate the Random effect out.
Fixed Effects Logit
Classical logit model. Under certain assumptions we are able to eliminate the fixed effect i.e. cornflakes purchases, think in conditional probabilities
Chemberlain Probit Model
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.
Censoring
survival time T is unobserved
either left or right censoring
Truncation
probability of appearing in the sample depends on the survival time
in-flow sample
survey new entrens to a state, follow them for a fixed period (“observational window”)
out-flow sample
Survery those leaving a state record start date.
Stock Sample
Survery those in state (record start date)
Stock sample with follow up
Survey those in state (record start date) and follow them for a given time
Population Sample/Random sample
Survaey whole polulation/Survey a representive group of people.
Likelihood: Random Sample no censorin nor truncation
product of the individual failure rates
Likelihood: Random Sample right censoring
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.
Likelihood: Left-gruncated spell data possible right censoring
condition on survival until the beginning of the survay
Likelihood: Stock Sample with no follow up
very difficult. No information for conditioning
Likelihood: Right truncated spell data (outflow sample)
condtioning on cummmulative failure rate
Median duration
S(m) = 0.5 or F(m) = 0.5
Mean Duration
E(T) integrating over the t*f(t) dt
Proportional Hazard
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
Accelerated failure time
model in the survival time that fulfill
lnT = Xß + z
Gometz Hazard Function
lambda exp(\gamma t) continious time PH model no AFT model
Log-Logistic Model
psi^1/\gamma ….
continious time
Log-Logistic Model
psi^1/\gamma ….
continious time
no PH model
AFT model
Log-Normal Model
pdf(lnt-\mu/sigma)/1+cdf(lnt-\mu/sigma)
continious time
no PH model
AFT model
Weibull Model
alpha t ^[alpha-1) \lambda
continious time
PH and AFT
Piecewise constant Exponential (PCE) hazard
piecewise defined hazrad function with \lambda defined over intervals, where the effect of the covarities is assumed to be constant
C-Log-Log (Complementory log-log model
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.
Cox’s Model
baseline hazard times lambda
Continious time model
PH
and AFT
Baseline hazard has no specific form. Thus we are estimating a semi parametric model.
Generalized Gamma
Depending on the parameters
k = 1 - Weibull
k = 1 sigma = 1 - Exponential
k = 0 log-normal model
Cloglog vs. Logit/Probit
linear function Xß + specific baseline hazard \gamma
for the estiamtion we assume a specific functional form for \gamma.
Cloglog vs. Logit/Probit
linear function Xß + specific baseline hazard \gamma
for the estiamtion we assume a specific functional form for \gamma.
Kaplan-Meier Estimator
Exit rate = #failures/#risk of failing
survival rate = 1- exit rate = h
S = product over h
Time varrying covariities
similar to the PCE we can use intervals to ensure PH within the interval
Independent Competing Risks (ICR)
The individual likelihoods are multiplied and are set up by experienceing one but surving the other.
Multiple Spells
if the processes effecting the fifert spells are equal/simillar we can just built a product
Unobserved heterogeneity
caused by omitted variables, measurment errors
might be able to integrate the effect out.
