Table 3

State-year panel data with differences-in-differences estimation Impacts of Clustering and Estimation Choices on Estimated Coefficients, Standard Errors, and p-values

Model: Estimation Method:	Standard Errors			p-values
Model: Estimation Method:	1 OLS-FE	2 OLS-no FE	3 FGLS AR(1)	1 OLS-FE	2 OLS-no FE	3 FGLS AR(1)
Slope coefficient	0.0156	0.0040	−0.0042
Standard errors
Default standard errors, T(N − k) for critical value	0.0037	0.0062	0.0062	0.000	0.521	0.494
White Robust, T(N − k) for critical value	0.0037	0.0055	na	0.000	0.470	na
Cluster on state, T(G − 1) for critical value	0.0119	0.0226	0.0084	0.195	0.861	0.617
Cluster on state, CR2 bias correction, T(G − 1) for critical value	0.0118	0.0226	na	0.195	0.861	na
Cluster on state, CR2 bias correction, T(IK degrees of freedom)	0.0118	0.0226	na	0.195	0.861	na
Pairs cluster bootstrap for standard error, T(G − 1) for critical value	0.0118	0.0221	0.0086	0.191	0.857	0.624
Bootstrap percentile-T methods
Pairs cluster bootstrap	na	na		0.162	0.878
Wild cluster bootstrap, Rademacher two-point distribution	na	na		0.742	0.968
Wild cluster bootstrap, Webb six-point distribution	na	na		0.722	0.942
Imbens-Kolesar effective DOF	50	50
CSS effective number of clusters	51	51
Number of observations	1,836	1,836	1,836
Number clusters (states)	51	51	51

Notes: March 1997–2012 CPS data, from IPUMS download. Models 1 and 3 include state and year fixed effects and a “fake policy” dummy variable that turns on in 1995 for a random subset of half of the states. Model 2 includes year fixed effects but not state fixed effects. The bootstraps use 999 replications. Model 3 uses FGLS, assuming an AR(1) error within each state. “IK effective DOF” from Imbens and Kolesar (2013), and “CSS effective number of clusters” from Carter, Schnepel, and Steigerwald (2013), see Section VID.