Cluster Sampling Slides

Cluster Sampling Slides - Whats New in Econometrics?...

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What’s New in Econometrics? Lecture 8 Cluster and Stratified Sampling Jeff Wooldridge NBER Summer Institute, 2007 1. The Linear Model with Cluster Effects 2. Estimation with a Small Number of Groups and Large Group Sizes 3. What if G and M g are Both “Large”? 4. Nonlinear Models 1
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1 . The Linear Model with Cluster Effects . For each group or cluster g ,let  y gm , x g , z gm : m 1,. .., M g be the observable data, where M g is the number of units in cluster g , y gm is a scalar response, x g is a 1 K vector containing explanatory variables that vary only at the group level, and z gm is a 1 L vector of covariates that vary within (as well as across) groups. The linear model with an additive error is y gm x g z gm v gm (1) for m 1,. .., M g , g 1,. .., G . Key questions: Are we primarily interested in or ? Does v gm contain a common group effect, as in 2
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v gm c g u gm , m 1,. .., M g , (2) where c g is an unobserved cluster effect and u gm is the idiosyncratic error? Are the regressors x g , z gm appropriately exogenous? How big are the group sizes ( M g and number of groups G ? Two kinds of sampling schemes. First, from a large population of relatively small clusters, we draw a large number of clusters ( G ), where cluster g has M g members. For example, sampling a large number of families, classrooms, or firms from a large population. This is like the panel data setup we have covered. In the panel data setting, G is the number of cross-sectional units and M g is the number of time periods for unit g . A different sampling scheme results in data sets that also can be arranged by group, but is better 3
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interpreted in the context of sampling from different populations or different strata within a population. We stratify the population into into G 2 nonoverlapping groups. Then, we obtain a random sample of size M g from each group. Ideally, the group sizes are large in the population, hopefully resulting in large M g . Large Group Asymptotics The theory with G and the group sizes, M g , fixed is well developed. How should one use these methods? If E v gm | x g , z gm 0 (3) then pooled OLS estimator of y gm on 1, x g , z gm , m 1,. .., M g ; g 1,. .., G , is consistent for , , (as G with M g fixed) and G -asymptotically normal. In panel data case, (3) 4
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does allow for non-strictly exogenous covariates, but only if there is no unobserved effect. Robust variance matrix is needed to account for correlation within clusters or heteroskedasticity in Var v gm | x g , z gm , or both. Write W g as the M g 1 K L matrix of all regressors for group g . Then the 1 K L 1 K L variance matrix estimator is Avar ̂ POLS g 1 G W g W g 1 g 1 G W g v ̂ g v ̂ g
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This note was uploaded on 12/26/2011 for the course ECON 245a taught by Professor Staff during the Fall '08 term at UCSB.

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Cluster Sampling Slides - Whats New in Econometrics?...

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