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**Unformatted text preview: **1. Economics 245A: Cluster Sampling & Matching (This document was created using the AMS Proceedings Article shell document.) Cluster sampling arises in a number of contexts. For example, con- sider a study of retirement saving. It is likely the case that retirement saving for employees within a &rm will be correlated, because of com- mon features of the &rm (such as type of retirement plan) or because of common (often unobserved) characteristics of employees within a &rm. Each &rm represents a group, or cluster, and we may sample several workers from each of a large number of &rms. Other examples might be a study of teenage peer e/ects, in which we have a few teenagers from each of a large number of neighborhoods (the neighborhoods are the cluster) or high schools, or a study of sib- lings in a large sample of families (families are the cluster). The key is that we sample a large number of clusters and each cluster consists of a relatively small number of observations compared with the overall sample size. We allow the units within the cluster to be correlated, but we assume independence across clusters. 2. Matched Pairs Let us begin with a study of siblings in a large sample of families. The idea is to use siblings to control for unobserved family backgrounds. Our thought experiment is to have two identical individuals, for whom we vary one exogenous e/ect. We attempt to capture our two identi- cal individuals by studying siblings. For each family i there are two siblings y i 1 = x i 1 & + f i + u i 1 y i 2 = x i 2 & + f i + u i 2 where the equations are for siblings 1 and 2 and f i is an unobserved family e/ect. The strict exogeneity assumption now implies that the error u is in each sibling¡s equation is uncorrelated with the explanatory variables in both equations. For example, let y be log(wage) and let x contain years of schooling. Then we must assume that sibling¡s schooling has no e/ect on wages once we control for own schooling, the family e/ect and other observed covariates. If f i is assumed to be uncorrelated with x i 1 and x i 2 , then random e/ects analysis can be used. 1 2 More commonly, f i is assumed to be correlated with x i 1 and x i 2 , in which case di/erencing across siblings to remove f i is the appropri- ate strategy. Under this strategy, x cannot contain common observ- able family background variables, as these are indistinguisable from f i . Standard IV estimators can be applied directly to the di/erence equation y i 1 & y i 2 = ( x i 1 & x i 2 ) & + ( u i 1 & u i 2 ) : 3. General Cluster Samples Matched pairs are a special case of a cluster sample.Matched pairs are a special case of a cluster sample....

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