Topic Summaries Flashcards
Maximium Likelihood Estimation
Identifying assumptions come into distributional assumption (eg. mu = 0 , sigma = 1) –> Without these, we cannot identify the parameters.
Interpret MEs not coefficients –> OLS has linear MEs, nonlinear allows effect to vary. Careful computing categorical vs continuous approx. MEs.
- ME largest at 0 where normal reaches max, easily relaxed by other estimators eg. “Scobit”
- Sample average of ME vs ME at average
Estimator Properties
- Consistency
- Asympototic normality -
- Efficiency: minimised asympototic variance - “Cramer-Rao lower bound”
- Invariance: 1:1 continuously differentiable functions
Binary Choice Models
Underpinned by basic choice-theoretic foundational model.
Logit
- Paramter estimates = effect on log odds ratio
- Fatter tails
Probit
LPM
- Heteroskedasticity –> Use White’s HC robust or WLS –> more efficient (req. predicted probabilities to lie on 0,1)
- Unbounded
- Constant ME = Parameter estimates
Discrete Choice Models
Underpinned either by optimal stopping (ordered choice) or random utility models (unordered choice)
Ordered Probit - “index shift”
Generalised Ordered Probit - index and cutoff shifting
OLS is now near impossible to justify as numerical assignments have no meaning or interpretation!
Censoring and Truncation
Truncation: info lost on both dependent variable and regressors eg. Only sampling low income households
Censoring: info lost on only dependent variable eg. £100,000+ annual salaries reported due to confidentiality
Truncation loses more info than censoring.
Censoring is an issue as it will effect groups of the sample differently eg. Degree - impact 50% of £100k+, while GCSE only - impact 5%. –> Need to correct for top-coding
Heckman Selection
Participation Equation
Outcome Equation
Exclusion restriction
Two Step Procedure:
1. Run a Probit on the participation equation to estimate the IMR
- Run an OLS on the outcome equation including the IMR as an additional regressor
