Difference in Difference Meets Generalized Least Squares: Higher Order Properties of Hypotheses Tests∗

We investigate estimation and inference in difference in difference econometric models used in the analysis of treatment effects. When the innovations in such models display serial correlation, commonly used ordinary least squares (OLS) procedures are inefficient and may lead to tests with incorrect size. Implementation of feasible generalized least squares (FGLS) procedures is often hindered by too few observations in the cross section to allow for unrestricted estimation of the weight matrix without leading to tests with similar size distortions as conventional OLS based procedures. We analyze the small sample properties of FGLS based tests with a higher order Edgeworth expansion that allows us to construct a size corrected version of the test. We also address the question of optimal temporal aggregation as a method to reduce the dimension of the weight matrix. We apply our procedure to data on regulation of mobile telephone service prices. We find that a size corrected FGLS based test outperforms tests based on OLS. ∗We thank Matthew Harding, Alan Grant, Anne Hall and Jie Yang for excellent research assistance. Whitney Newey engaged in helpful conversations. †MIT, Department of Economics, 50 Memorial Drive, Cambridge, MA 02142; email: [email protected]. ‡Boston University, Department of Economics, 270 Bay State Road, Boston, MA 02215, email: [email protected]. Financial support from NSF Grant SES 0095132 is gratefully acknowledged.