NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH

NBER Publications by A. Colin Cameron

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Working Papers and Chapters

September 2007Bootstrap-Based Improvements for Inference with Clustered Errors
with Jonah B. Gelbach, Douglas L. Miller: t0344
Researchers have increasingly realized the need to account for within-group dependence in estimating standard errors of regression parameter estimates. The usual solution is to calculate cluster-robust standard errors that permit heteroskedasticity and within-cluster error correlation, but presume that the number of clusters is large. Standard asymptotic tests can over-reject, however, with few (5-30) clusters. We investigate inference using cluster bootstrap-t procedures that provide asymptotic refinement. These procedures are evaluated using Monte Carlos, including the example of Bertrand, Duflo and Mullainathan (2004). Rejection rates of ten percent using standard methods can be reduced to the nominal size of five percent using our methods.
September 2006Robust Inference with Multi-way Clustering
with Jonah B. Gelbach, Douglas L. Miller: t0327
In this paper we propose a new variance estimator for OLS as well as for nonlinear estimators such as logit, probit and GMM, that provcides cluster-robust inference when there is two-way or multi-way clustering that is non-nested. The variance estimator extends the standard cluster-robust variance estimator or sandwich estimator for one-way clustering (e.g. Liang and Zeger (1986), Arellano (1987)) and relies on similar relatively weak distributional assumptions. Our method is easily implemented in statistical packages, such as Stata and SAS, that already offer cluster-robust standard errors when there is one-way clustering. The method is demonstrated by a Monte Carlo analysis for a two-way random effects model; a Monte Carlo analysis of a placebo law that extends the state-year effects e...
August 1992Do Gasoline Prices Respond Asymmetrically to Crude Oil Price Changes?
with Severin Borenstein: w4138
Our empirical investigation confirms the common belief that retail gasoline prices react more quickly to increases in crude oil prices than to decreases. Nearly all of the response to a crude oil price increase shows up in the pump price within 4 weeks, while decreases are passed along gradually over 8 weeks. The asymmetry could indicate market power of some producers or distributors, or it could result from inventory adjustment costs. By analyzing price transmission at different points in the distribution chain we investigate these theories. We find that some asymmetry occurs at the level of the competitive spot market for gasoline, perhaps reflecting inventory costs. Wholesale gasoline prices, however, exhibit no asymmetry in responding to crude oil price changes, indicating that refiner...

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