13.16 Standard errors

• Standard errors can be messed up in may ways because assumptions are violated
• We can account for this, though
• correlated errors change the sampling distribution: mean is swingier, larger standard deviation

13.16.1 Assumptions

1. error term $\epsilon$ is normally distributed –> OLS is mostly okay with this
2. error term is independent and identically distributed (iid)

• autocorrelation: temporal/spatial
• heteroskedasticity
• we have to figure out how this assumption fails

13.16.2 Fixes (mostly sandwich estimators)

• heteroskedasticity: Huber-White
• auto-correlation: HAC, e.g. Newey-West
• geographic correlation: Conley spatial standard errors
• hierarchical structure: clustered standard errors, e.g. Liang-Zenger
• right level of clustering: treatment level/domain knowledge
• only works for large number of clusters, $ >50$; fix: wild cluster bootstrap standard errors
• bootstrapped standard errors

13.16.3 Bootstrapping

1. start with data set with $N$ observations
2. randomly sample $N$ observations (with replacement)
3. estimate statistic
4. repeat many times (a couple of 1,000)
5. look at distribution of estimates

• can be used for any statistic
• need large samples
• don’t perform well with extreme value distributions
• doesn’t do well with autocorrelation