Nonstandard Standard Error Issues
We have normality. I repeat, we have normality.
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Today, software packages routinely compute asymptotic standard errors derived under weak assumptions about the sampling process or underlying model. For example, you get regression standard errors based on formula (3.1.7) using the Stata option robust. Robust standard errors improve on old-fashioned standard errors because the resulting inferences are asymptotically valid when the regression residuals are heteroskedastic, as they almost certainly are when regression approximates a nonlinear conditional expectation function (CEF). In contrast, old-fashioned standard errors are derived assuming homoskedasticity. The hangup here is that estimates of robust standard errors can be misleading when the asymptotic approximation that justifies these estimates is not very good. The first part of this chapter looks at the failure of asymptotic inference with robust standard error estimates and some simple palliatives.
A pillar of traditional cross section inference—and the discussion in section 3.1.3—is the assumption that the data are independent. Each observation is treated as a random draw from the same population, uncorrelated with the observation before or after. We understand today that this sampling model is unrealistic and potentially even foolhardy. Much as in the time series studies common in macroeconomics, cross section analysts must worry about correlation between observations. The most important form of dependence arises