Table 1.

Efficiency Gains of the Two-Step FGLS procedure

Procedure		A		B		C		D
		N=50, T=6, AR(1), ρ=0.8		N=50, T=12 AR(1), ρ=0.8		N=50, T=12, AR(2) ρ1=0.6, ρ2=0.3		N=50, T=6 AR(0)
		Mean	SD	Mean	SD	Mean	SD	Mean	SD
I. Facility fixed effect	β	1.090	0.761	0.964	0.532	0.960	0.508	1.033	0.682
w/ clustered SE	SE of β	0.772	0.147	0.533	0.0803	0.485	0.0770	0.767	0.124
II. Two-step DD	β	1.088	0.597	0.945	0.458	0.913	0.427	1.050	0.548
w/ clustered SE	SE of β	0.699	0.102	0.484	0.0577	0.431	0.0546	0.693	0.0858
III. Two-step FGLS	β	1.055	0.423	0.994	0.306	0.925	0.336	1.039	0.535
w/ clustered SE	SE of β	0.473	0.0626	0.294	0.0328	0.341	0.0385	0.629	0.0798
IV. Two-step FGLS	β	1.055	0.423	0.993	0.306	0.925	0.336	1.039	0.535
w/ jackknife SE	SE of β	0.475	0.0408	0.205	0.0161	0.249	0.0222	0.591	0.0495
Efficiency Gain		39%		45%		30%		18%

Notes: Simulations are for 50 states, with 0–100 facilities per state, over 6 or 12 time periods. We set the true β equal to one and carry out the exercise 100 times implementing (I) DD estimation with standard errors clustered at the state level, (II) Two-step DD with standard errors clustered by states, (III) Two-step FGLS with standard errors clustered by states, and (IV) Two-step FGLS with standard errors jack-knifed at the state level. The underlying AR process for the first two columns is AR(1), the third AR(2), and the last AR(0). Efficiency gain calculates percentage reduction in the standard error of β from implementing procedure III relative to procedure I. SD and SE denote standard deviation and standard error, respectively.