Clustering One Way Slides

Clustering One Way Slides - Bootstrap-Based Improvements...

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Bootstrap-Based Improvements for Inference with Clustered Errors Colin Cameron, Jonah Gelbach, Doug Miller U.C. - Davis, U. Maryland, U.C. - Davis May, 2008 Colin Cameron, Jonah Gelbach, Doug Miller Cluster Bootstrap May, 2008 1 / 41
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1. Introduction OLS regression with individual-level data ( i ) with cluster or grouping ( g ) y ig = x 0 ig β + u ig , i = 1 , ..., N g , g = 1 , ..., G . E.g. y ig is (log) wage of ith individual who lives in state g and x ig includes regressor correlated within state g and u ig is error correlated within state g . Colin Cameron, Jonah Gelbach, Doug Miller Cluster Bootstrap May, 2008 2 / 41
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Default OLS standard errors based on s 2 ( X 0 X ) & 1 that ignore clustering can greatly understate true standard errors. See Moulton (1986, 1990). Colin Cameron, Jonah Gelbach, Doug Miller Cluster Bootstrap May, 2008 3 / 41
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Default OLS standard errors based on s 2 ( X 0 X ) & 1 that ignore clustering can greatly understate true standard errors. See Moulton (1986, 1990). Standard solution is to get cluster-robust (CR) standard errors. This is the cluster option in Stata. Colin Cameron, Jonah Gelbach, Doug Miller Cluster Bootstrap May, 2008 3 / 41
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Default OLS standard errors based on s 2 ( X 0 X ) & 1 that ignore clustering can greatly understate true standard errors. See Moulton (1986, 1990). Standard solution is to get cluster-robust (CR) standard errors. This is the cluster option in Stata. If the number of clusters G is small then: 1. CR standard errors are downwards biased (too small) 2. t statistic is not standard normal distributed 3. t-tests using standard normal critical values over-reject. Colin Cameron, Jonah Gelbach, Doug Miller Cluster Bootstrap May, 2008 3 / 41
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Default OLS standard errors based on s 2 ( X 0 X ) & 1 that ignore clustering can greatly understate true standard errors. See Moulton (1986, 1990). Standard solution is to get cluster-robust (CR) standard errors. This is the cluster option in Stata. If the number of clusters G is small then: 1. CR standard errors are downwards biased (too small) 2. t statistic is not standard normal distributed 3. t-tests using standard normal critical values over-reject. This paper is concerned with better inference when there are few clusters . Colin Cameron, Jonah Gelbach, Doug Miller Cluster Bootstrap May, 2008 3 / 41
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Wrong standard errors and critical values: 5% Colin Cameron, Jonah Gelbach, Doug Miller Cluster Bootstrap May, 2008 4 / 41
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Outline of Talk 1 Introduction 2 Cluster-Robust Inference 3 Cluster Bootstrap (without and with re&nement) 4 Monte Carlo Simulations 5 Bertrand, Du±o and Mullainathan (2004) Simulations 6 Gruber and Poterba (1994) Application 7 Conclusion Colin Cameron, Jonah Gelbach, Doug Miller Cluster Bootstrap May, 2008 5 / 41
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2.1 OLS with Cluster Errors Model for G clusters with N g individuals per cluster: y ig = x 0 ig β + u ig , i = 1 , ..., N g , g = 1 , ..., G , y g = X g β + u g , g = 1 , ..., G , y = X β + u , OLS estimator b β = ( G g = 1 N g i = 1 x ig x 0 ig ) & 1 ( G g = 1 N g i = 1 x ig y ig ) = ( G g = 1 X 0 g X g ) & 1 ( G g = 1 X g y g ) = ( X 0 X ) & 1 X 0 y .
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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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Clustering One Way Slides - Bootstrap-Based Improvements...

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