The data in CENSUS2000 is a random sample of individuals from the United States. Here we are interested in estimating a simple regression model relating the log of weekly income, lweekinc, to schooling, educ. There are 29,501 observations. Associated with each individual is a state identifier (state) for the 50 states plus the District of Columbia. A less coarse geographic identifier is puma, which takes on 610 different values indicating geographic regions smaller than a state.

Running the simple regression of lweekinc on educ gives a slope coefficient equal to .1083 (to four decimal places). The heteroskedasticity-robust standard error is about .0024. The standard error clustered at the puma level is about .0027, and the standard error clustered at the state level is about .0033. For computing a confidence interval, which of these standard errors is the most reliable? Explain.