Below are misc. documents for applied econometrics research, that I update regularly. (Originally personal notes, then used as foundation for teaching PhD students, now put online in case they can be useful to others.)
Applied statistics

Probability distributions in regression modeling
The essential statistics definitions & theorems (esp. LLN & CLT) that make the statistics below work. 
Microeconometrics within Inferential Statistics
Basic inferential statistics most commonly used in applied microeconometrics. Models as probability distributions; inference workflow …  Causal inference in observational studies, Theory & Methods
Using regression to uncover the causal effect of a treatment on a population. Underlying theoretical framework: potential outcomes
 Applied methods (RDD, IV…); equivalence of the regression slope estimate in terms of potential outcomes
 Improving inferences (matching & controls, falsification tests, randomization inference…)
 Assumptions of the classical linear regression model (and what to do when they fail)
 Typical assumptions
 What do they provide? (Estimator properties)
 What to do when they are violated?